text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
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Waxworms are the caterpillar larvae of wax moths, which belong to the family Pyralidae (snout moths). Two closely related species are commercially bred – the lesser wax moth (Achroia grisella) and the greater wax moth (Galleria mellonella). They belong to the tribe Galleriini in the snout moth subfamily Galleriinae. Another species whose larvae share that name is the Indian mealmoth (Plodia interpunctella), though this species is not available commercially.
The adult moths are sometimes called "bee moths", but, particularly in apiculture, this can also refer to Aphomia sociella, another Galleriinae moth which also produces waxworms, but is not commercially bred.
Waxworms are medium-white caterpillars with black-tipped feet and small, black or brown heads.
In the wild, they live as nest parasites in bee colonies and eat cocoons, pollen, and shed skins of bees, and chew through beeswax, thus the name. Beekeepers consider waxworms to be pests. Galleria mellonella (the greater wax moths) will not attack the bees directly, but feed on the wax used by the bees to build their honeycomb. Their full development to adults requires access to used brood comb or brood cell cleanings—these contain protein essential for the larvae's development, in the form of brood cocoons. The destruction of the comb will spill or contaminate stored honey and may kill bee larvae or be the cause of the spreading of honey bee diseases.
When kept in captivity, they can go a long time without eating, particularly if kept at a cool temperature. Captive waxworms are generally raised on a mixture of cereal grain, bran, and honey.
Waxworms as a food source
Waxworms are a commonly used food for many insectivorous animals and plants in captivity.
These larvae are grown extensively for use as food for humans, as well as live food for terrarium pets and some pet birds, mostly due to their high fat content, their ease of breeding, and their ability to survive for weeks at low temperatures. They are recommended for use as a treat rather than a staple food, due to their relative lack of nutrients when compared to crickets and mealworms. Their high fat and calorie density can also contribute to obesity in captive animals if they are fed waxworms too often, especially in animals with a low metabolism, such as reptiles.
Most commonly, they are used to feed reptiles such as bearded dragons (species in the genus Pogona), the neon tree dragon (Japalura splendida), geckos, brown anole (Anolis sagrei), turtles such as the three-toed box turtle (Terrapene carolina triunguis), and chameleons. They can also be fed to amphibians such as Ceratophrys frogs, newts such as the Strauch's spotted newt (Neurergus strauchii), and salamanders such as axolotls. Small mammals such as the domesticated hedgehog can also be fed with waxworms, while birds such as the greater honeyguide can also appreciate the food. They can also be used as food for captive predatory insects reared in terrarium, such as assassin bugs in the genus Platymeris, and are also occasionally used to feed certain kinds of fish in the wild, such as bluegills (Lepomis macrochirus).
Waxworms as bait
Waxworms may be store-bought or raised by anglers. Anglers and fishing bait shops often refer to the larvae as "waxies". They are used for catching some varieties of panfish, members of the sunfish family (Centrarchidae), Green sunfish (Lepomis cyanellus) and can be used for shallow water fishing with the use of a lighter weight. They are also used for fishing some members of the family Salmonidae, Masu salmon (Oncorhynchus masou), white-spotted char (Salvelinus leucomaenis), and rainbow trout (Oncorhynchus mykiss).
Uses
Fishing
Anglers use wax-worms usually provided by commercial suppliers to catch trout fish.
Wax-worms are popular bait for anglers in Japan. Anglers throw handfuls into the "swim" they are targeting, attracting the trout fish to the area. The angler then use the largest or most attractive wax-worms on the hook, hoping to be irresistible to the trout fish.
Waxworms as an alternative to mammals in animal research
Waxworms can replace mammals in certain types of scientific experiments with animal testing, especially in studies examining the virulence mechanisms of bacterial and fungal pathogens. Waxworms prove valuable in such studies because the innate immune system of insects is strikingly similar to that of mammals. Waxworms survive well at human body temperature and are large enough in size to allow straightforward handling and accurate dosing. Additionally, the considerable cost savings when using waxworms instead of small mammals (usually mice, hamsters, or guinea pigs) allows testing throughput that is otherwise impossible. Using waxworms, it is now possible to screen large numbers of bacterial and fungal strains to identify genes involved in pathogenesis or large chemical libraries with the hope of identifying promising therapeutic compounds. The later studies have proved especially useful in identifying chemical compounds with favorable bioavailability.
Biodegradation of plastic
Two species of waxworm, Galleria mellonella and Plodia interpunctella have both been observed eating and digesting polyethylene plastic. The waxworms metabolize polyethylene plastic films into ethylene glycol, a compound which biodegrades rapidly. This unusual ability to digest matter classically thought of as non-edible may originate with the waxworm's ability to digest beeswax as a result of gut microbes that are essential in the biodegradation process. Two strains of bacteria, Enterobacter asburiae and Bacillus sp, isolated from the guts of Plodia interpunctella waxworms, have been shown to decompose polyethylene in laboratory testing. In a test with a 28-day incubation period of these two strains of bacteria on polyethylene films, the films' hydrophobicity decreased. In addition, damage to the films' surface with pits and cavities (0.3-0.4 μm in depth) was observed using scanning electron microscopy and atomic-force microscopy.
Placed in a polyethylene shopping bag, approximately 100 Galleria mellonella waxworms consumed almost 0.1 gram (0.0032 ounces) of the plastic over the course of 12 hours in laboratory conditions.
Studies carried out in 2020 by Bastian Barton at the Fraunhofer Institute for Structural Durability and System Reliability (LBF) (https://www.lbf.fraunhofer.de/en.html) in Darmstadt, Germany, disproved the ability of Galleria melonella caterpillars to digest and biologically degrade polyethylene. Even though the waxworms would eat holes into polyethylene bags, they ingested only a small proportion, excreted the polyethylene unaltered and showed significant loss of body weight.
See also
Pyralidae
Mealworm
Pyralis regalis
Hypsopygia mauritialis
References
Agricultural pest insects
Fishing equipment
Galleriinae
Insect rearing
Pet foods
Western honey bee pests
Insects in culture
Insect common names
Beekeeping | {
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Q: Is there a known reason why I'm getting different LUFS values for loudnorm vs ebur128? I'm using FFMpeg to try to get the LUFS of a video file. When running it against the ebur128 filter I get a fairly different value than the loudnorm filter.
ffmpeg.exe -i "C:\Users\Name\Documents\sample.mpg" -nostats -filter_complex ebur128 -f null - 2>&1
ffmpeg.exe -i "C:\Users\Name\Documents\sample.mpg" -nostats -filter_complex loudnorm=print_format=json -f null - 2>&1
For most media files, I'm getting a difference of +/- 0.2 LUFS between the two which I understand to be a difference in rounding of datatypes and/or sampling rates.
However for one file I have a difference of +0.95, with EBUR128 reporting -26.4 LUFS and LoudNorm reporting it as -25.45. Is this still just within the realm of rounding and sampling differences or are there functional differences between the two filters?
| {
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} | 5,234 |
Q: Why can't I step into a C++ cout standard library function in GDB? I wrote a simple test.cc as follows:
#include <iostream>
using namespace std;
int main()
{
cout << "Hello world" << endl;
return 0;
}
And I compiled with:
g++ -g test.cc -o test.o
I ran gdb and put a breakpoint at the "Hello world" line:
$ gdb test.o
(gdb) b 7
(gdb) c
Then gdb stops at the "Hello world" line, but when I run
(gdb) s
It fails to step into the cout function. So my question is, how can I step into the cout function?
A: If it wasn't linked against a version of the standard library with debugging information, it doesn't know how to step into the library; it can only step over it (that is, run until control returns to the code with the debugging information).
Consult the documentation for your system to find out how to install the debug version of the standard C and C++ libraries.
A: Without the debugging information it's still possible to debug it, just a whole lot more painful. See here.
If like me, you just want to break on other calls to the same function without digging any deeper, it's not too difficult to set a breakpoint on the function address obtained from the disassembly with disas.
| {
"redpajama_set_name": "RedPajamaStackExchange"
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var LIB = Script.require("./musVisLib.js?" + Date.now());
var MIC_SYNC_SCRIPT = Script.resolvePath("adjuster_scripts/micSync.js?" + Date.now());
var AUDIO_SYNC_SCRIPT = Script.resolvePath("adjuster_scripts/audioFileSync.js?" + Date.now());
var TRAIL_LEFT_SCRIPT = Script.resolvePath("adjuster_scripts/effectTrailerLeft.js?" + Date.now());
var TRAIL_RIGHT_SCRIPT = Script.resolvePath("adjuster_scripts/effectTrailerRight.js?" + Date.now());
var CLEAR_SELECTION_TEXT = "Clear selection";
(function() {
var APP_NAME = "MUS VIS";
var APP_URL = "https://hifi-content.s3.amazonaws.com/elisalj/music_visualizer/musicVisualizerUI.html?" + Date.now();
var APP_ICON = "https://hifi-content.s3.amazonaws.com/elisalj/music_visualizer/icons/particles-i-01.svg";
var APP_ICON_ACTIVE = "https://hifi-content.s3.amazonaws.com/elisalj/music_visualizer/icons/particles-a-01.svg";
var tablet = Tablet.getTablet("com.highfidelity.interface.tablet.system");
var WANT_DEBUG = false;
var audioFile = "";
var existingParticles = [];
var button = tablet.addButton({
icon: APP_ICON,
activeIcon: APP_ICON_ACTIVE,
text: APP_NAME
});
// Activates tablet UI when selected from menu
function onClicked() {
if (!shown) {
tablet.gotoWebScreen(APP_URL);
} else {
tablet.gotoHomeScreen();
}
}
button.clicked.connect(onClicked);
var shown = false;
// Changes active status of tablet button
function onScreenChanged(type, url) {
if (type === 'Web' && url === APP_URL) {
button.editProperties({ isActive: true });
if (!shown) {
tablet.webEventReceived.connect(onWebEventReceived);
}
shown = true;
} else {
button.editProperties({ isActive: false });
if (shown) {
tablet.webEventReceived.disconnect(onWebEventReceived);
}
shown = false;
}
}
tablet.screenChanged.connect(onScreenChanged);
// Gives position right in front of user's avatar
function getPositionToCreateEntity() {
var direction = Quat.getFront(MyAvatar.orientation);
var distance = 0.3;
var position = Vec3.sum(MyAvatar.position, Vec3.multiply(direction, distance));
position.y += 0.5;
return position;
}
// adds the particle to world
function createParticle(effectName, micSync, behavior, file) {
if (WANT_DEBUG) {
print(effectName + " particle is being added");
}
var position = getPositionToCreateEntity();
var effectJSON = LIB.getEffect(effectName, LIB.effectLib);
effectJSON.position = position;
// mic sync and audio file are mutually exclusive
if (micSync) {
effectJSON.script = MIC_SYNC_SCRIPT;
if (WANT_DEBUG) {
print("attached script: " + effectJSON.script);
}
} else if (audioFile) {
if (WANT_DEBUG) {
print("the audio file is:" + audioFile + ".");
}
effectJSON.userData = JSON.stringify({
grabbableKey: {
grabbable: true,
ignoreIK: false
},
audio: audioFile
});
effectJSON.script = AUDIO_SYNC_SCRIPT;
if (WANT_DEBUG) {
print("attached script: " + effectJSON.script);
}
}
// creates invisible sphere as parent to effect
if (behavior === "dynamic") {
var invisible = LIB.getEffect("invisible", LIB.effectLib);
invisible.position = position;
var invisSphere = Entities.addEntity(invisible);
effectJSON.parentID = invisSphere;
var behaviorParticle = Entities.addEntity(effectJSON);
existingParticles.push(behaviorParticle);
}
// creates trail effect
if (behavior === "finger") {
effectJSON.isEmitting = false;
effectJSON.lifespan = 2;
effectJSON.userData = JSON.stringify({
grabbableKey: {
grabbable: true,
ignoreIK: false
},
equipHotspots: [{
position: {x: 0.11031082272529602, y: 0.19449540972709656, z: 0.0405043363571167},
radius: 0.25,
joints: {
RightHand: [
{x: 0.11031082272529602, y: 0.19449540972709656, z: 0.0405043363571167},
{x: 0.2807741165161133, y: 0.6332069635391235, z: 0.2997693121433258, w: -0.6557632088661194}
],
LeftHand: [
{x: -0.10801754891872406, y: 0.15447449684143066, z: 0.030637264251708984},
{x: -0.32700979709625244, y: 0.623619794845581, z: 0.28943854570388794, w: 0.6483823657035828}
]
},
modelURL: 'http://hifi-content.s3.amazonaws.com/alan/dev/equip-Fresnel-3.fbx',
modelScale: {
x: 1,
y: 1,
z: 1
}
}]
});
var effectLeft = Entities.addEntity(effectJSON);
var effectRight = Entities.addEntity(effectJSON);
// an overlay that only the user sees to know when they have equipped finger trails
var equipLeft = Overlays.addOverlay("sphere", {
localPosition: {x:0, y:0, z:0},
parentID: effectLeft,
parentJointIndex: MyAvatar.getJointIndex("LeftHand"),
size: 0.05,
color: { red: 200, green: 200, blue: 200 },
alpha: 0.5,
solid: true,
visible: false
});
var equipRight = Overlays.addOverlay("sphere", {
localPosition: {x:0, y:0, z:0},
parentID: effectRight,
parentJointIndex: MyAvatar.getJointIndex("RightHand"),
size: 0.05,
color: { red: 200, green: 200, blue: 200 },
alpha: 0.5,
solid: true,
visible: false
});
existingParticles.push(effectLeft);
existingParticles.push(effectRight);
existingParticles.push(equipLeft);
existingParticles.push(equipRight);
// allow time for equip
Script.setTimeout(function() {
Messages.sendLocalMessage('Hifi-Hand-Grab', JSON.stringify({
hand: "left",
entityID: effectLeft
}));
Messages.sendLocalMessage('Hifi-Hand-Grab', JSON.stringify({
hand: "right",
entityID: effectRight
}));
var effectLeftProps = Entities.getEntityProperties(effectLeft, "script");
var effectRightProps = Entities.getEntityProperties(effectRight, "script");
effectLeftProps.script = TRAIL_LEFT_SCRIPT;
effectRightProps.script = TRAIL_RIGHT_SCRIPT;
Entities.editEntity(effectLeft, effectLeftProps);
Entities.editEntity(effectRight, effectRightProps);
var equipLeftProps = Entities.getEntityProperties(equipLeft, "visible");
var equipRightProps = Entities.getEntityProperties(equipRight, "visible");
equipLeftProps.visible = true;
equipRightProps.visible = true;
Overlays.editOverlay(equipLeft, equipLeftProps);
Overlays.editOverlay(equipRight, equipRightProps);
}, 700);
// once particles are equipped tablet must be auto closed
button.editProperties({ isActive: false });
tablet.webEventReceived.disconnect(onWebEventReceived);
tablet.gotoHomeScreen();
Messages.sendLocalMessage("home", HMD.homeButtonID);
shown = false;
}
if (behavior === "nobehavior") {
var noBehaviorParticle = Entities.addEntity(effectJSON);
existingParticles.push(noBehaviorParticle);
}
// clears audio file selection
updateSelection("");
}
// to modify HTML page's listed filename
function updateSelection(filename) {
if (filename === "") {
audioFile = "";
}
tablet.emitScriptEvent(JSON.stringify({
"file": filename
}));
}
function onWebEventReceived(event) {
var htmlEvent = JSON.parse(event);
if (WANT_DEBUG) {
print("Event: " + JSON.stringify(htmlEvent));
}
// Handles particle button clicks to retrieve the effect JSON from musVisLib
if (htmlEvent.type === "click") {
var effectName = htmlEvent.data;
var micSync = htmlEvent.sync;
var file = audioFile;
var behavior = htmlEvent.behavior;
if (WANT_DEBUG) {
print("Audio file: " + file);
}
createParticle(effectName, micSync, behavior, file);
// Handles audio file browsing event
} else if (htmlEvent.type === "chooseAudioFile") {
if (htmlEvent.value !== CLEAR_SELECTION_TEXT) {
audioFile = Window.browse("Choose a .wav audio file", "", "*.wav");
if (audioFile !== null) {
var filenameArr = audioFile.split("/");
var filename = filenameArr[filenameArr.length - 1];
updateSelection(filename);
} else {
updateSelection("");
}
} else {
updateSelection("");
}
// Resets saved audio file when contradiction present
} else if (htmlEvent.type === "contradiction") {
updateSelection("");
} else if (htmlEvent.type === "cleanUpParticles") {
cleanUpParticles();
}
}
function cleanUpParticles() {
if (WANT_DEBUG) {
print("Cleaning up particles");
}
while (existingParticles.length > 0) {
Entities.deleteEntity(existingParticles.pop());
}
}
// When tablet UI is closed and app is removed from menu
function cleanup() {
tablet.removeButton(button);
if (shown) {
tablet.webEventReceived.disconnect(onWebEventReceived);
}
cleanUpParticles();
}
Script.scriptEnding.connect(cleanup);
}());
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,595 |
Strzępy honoru – powieść amerykańskiej pisarki Lois McMaster Bujold, rozpoczynająca Sagę Vorkosiganów.
Powieść opowiada o początku znajomości między Cordelią Naismith, oficerem betańskiego zwiadu naukowego, a Aralem Vorkosiganem, admirałem wojsk barrayarskich, których los skazał na wędrówkę po bezdrożach dziewiczej planety. Początkowa niechęć, po kilku wspólnie spędzonych dniach, przeradza się w powoli rosnące uczucie. Nie jest w stanie go zmienić nawet konflikt międzyplanetarny, który plącze ścieżki głównych bohaterów. Pod warstwą przygodowej space opery kryje się pełna głębi psychologicznej opowieść o ludzkich charakterach.
Epilogiem powieści jest opowiadanie Po walce o dwuosobowej załodze przeszukującej przestrzeń kosmiczną w poszukiwaniu zwłok żołnierzy po, opisywanej w powieści, kosmicznej wojnie.
Przypisy
Saga Vorkosiganów
Powieści fantastycznonaukowe z 1986 roku | {
"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"https:\/\/math.stackexchange.com\/questions\/1717453\/non-geometric-proof-of-pythagorean-theorem?noredirect=1","text":"# Non-geometric Proof of Pythagorean Theorem [closed]\n\nIs there a purely algebraic proof for the Pythagorean theorem that doesn't rely on a geometric representation? Just algebra\/calculus. I want to TRULY understand the WHY of how it is true. I know it works and I know the geometric proofs.\n\n## closed as unclear what you're asking by Brandon Carter, John Gowers, Macavity, Michael Albanese, Daniel W. FarlowMar 28 '16 at 20:21\n\nPlease clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it\u2019s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.\n\n\u2022 Well...what does the theorem even say without a geometric representation? \u2013\u00a0lulu Mar 28 '16 at 17:50\n\u2022 Did you check the 116 proofs proposed on this site? \u2013\u00a0J.-E. Pin Mar 28 '16 at 17:51\n\u2022 When you've stripped out the geometry, it is not so clear that the algebraic fact, which follows straightforwardly from the definition of an inner product, a norm induced by an inner product, and orthogonality, has any geometric significance. Indeed this proof just goes as follows: assume $x,y$ are orthogonal vectors, then $\\| x+y \\|^2=\\langle x+y,x+y \\rangle = \\langle x,x \\rangle + \\langle y,y \\rangle + \\langle x,y \\rangle + \\langle y,x \\rangle = \\| x \\|^2 + \\| y \\|^2 + 0 + 0$ $= \\| x \\|^2 + \\| y \\|^2$ if $x,y$ are orthogonal. \u2013\u00a0Ian Mar 28 '16 at 17:53\n\u2022 Possible duplicate of Proof of Pythagorean theorem without using geometry for a high school student? \u2013\u00a0John Gowers Mar 28 '16 at 17:57\n\u2022 My question to you is why would a purely algebraic proof be more satisfying or convincing than a geometric proof? Generally, geometric proofs are a bit more intuitive, and for most of the history of mathematics, considered to be more rigorous. \u2013\u00a0Doug M Mar 28 '16 at 17:59\n\nThe \"modern\" approach is this : first we define the field $\\mathbb{R}$ (for instance, it's the only totally ordered field with the supremum property).\n\nThen we define what a $\\mathbb{R}$-vector space is : it's an abelian group with an external action of $\\mathbb{R}$ satifying some axioms.\n\nThen there is a notion of dimension : we can define a vector space of dimension $2$.\n\nThe notion of Euclidean distance is obtained by defining what an inner product is : it's a symmetric bilinear form such that $\\langle x,x\\rangle>0$ if $x\\neq 0$. The distance is then $||x-y||$ with $||x||=\\sqrt{\\langle x,x\\rangle}$. We also have the notion of orthogonality from this inner product.\n\nWell, once you did that, then the Pythagorean theorem is a triviality : $||x-y||^2 = \\langle x-y,x-y \\rangle = \\langle x,x \\rangle - 2\\langle x,y \\rangle + \\langle y,y \\rangle = ||x||^2 + ||y||^2$ (assuming of course that $\\langle x,y\\rangle=0$, the orthogonality hypothesis).\n\nOf course all the work went into the definitions, which is contrary to the basic approach of geometry which deduces properties of distance from a set of axioms (generally ill-defined, but it can be made precise with a little work).\n\nThe interesting thing about this modern approach is that algebraic structures come before geometric content. This is powerful because algebraic structures have enough rigidity. For instance, if you start with a set of points and lines satisfying some incidence axioms, it's very hard to define what it means that it has a certain dimension. But if you have a vector space structure, then it's easy.\n\nOf course it can be a little disappointing beacause it feels like we \"cheated\" : we made the theorem obvious by somewhat putting it in the definitions. But on the other hand, it's very clear and precise : can you properly define what distance or an angle is using \"high school geometry\" ? Not so easy. Even in Euclide's Elements, this is kind of put under the rug as \"primitive notions\". This approach makes everyting perfectly well-defined and easy to work with.\n\n\u2022 How do you derive the inner product definition? It appears only to be a postulate. \u2013\u00a0Carpenter Oct 1 '16 at 5:32\n\u2022 Were you treating $x$ and $y$ like points in $\\mathbb{R}^2$ and defining that for any points in $\\mathbb{R}^2$, $x$ and $y$, $\\langle x, y \\rangle$ means the dot product of $x$ and $y$? If so, I think I actually understand your proof. I independently thought of that proof long before I understood what you were saying in this one and wrote my form of it in the comments under the body of the question. From reading the comment to this answer, it seems that the OP, Carpenter doesn't find the answer good enough and to them, it was proven that that definition satisfies certain assumptions but wasn't \u2013\u00a0Timothy Jan 22 at 4:14\n\u2022 proven that anything satisfying those assumptions must be that function. I think most people go the other way and assume those assumptions and deduce the distance formula but don't check that that function actually satisfies them. \u2013\u00a0Timothy Jan 22 at 4:16\n\nA \"proof\" of the Pythagorean Theorem depends on some kind of definitions of:\n\n\u2022 right angle\n\u2022 length\/area\n\u2022 stright line\n\nThe axioms of Euclid are not completely formalized but we have other formal axiomatic systems that mimic euclidean axioms and definitions of these notions (for example the Hilbert's axioms) so that we can derive Pythagorean theorem there. A formal proof with these axiomatic systems wouldn't require any reference to pictures in principle.\n\nProving Pytagorean Theorem in completely different context such as analytic geometry (or\"calculus\") could be possibly trivial or meaningless depending on what definition of \"right angle\" we are going to consider. For example it would be trivial if you define a right angle with the scalar product and the distance with $\\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$, but you could try with different ones and the proof of the theorem could get more and more complicated depending on which definition you want to take (you could want to define areas with Peano Jordan's measure for example).","date":"2019-06-25 03:43:59","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\": 0.8288241028785706, \"perplexity\": 325.0912849527272}, \"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-2019-26\/segments\/1560627999787.0\/warc\/CC-MAIN-20190625031825-20190625053825-00372.warc.gz\"}"} | null | null |
Los Angeles, CA – December 28, 2012 The Federal Reserve's policy of maintaining historically low interest rates has resulted in increased pricing for long-term care insurance reports a leading industry expert.
While cost remains a factor among those considering long term care insurance, Slome notes that many consumers can start with coverage costing about $100 a month. "One can still buy a considerable amount of protection if you take advantage of discounts and work with someone who takes into account you other retirement savings and assets," Slome concludes.
The organization predicts sales will continue to grow in 2013. Established in 1998 as a non-profit trade group, the Westlake Village, California-based American Association for Long Term Care Insurance advocates for the importance of planning for long term care and supports insurance and financial professionals who market LTC insurance. To learn more about long term care insurance costs call the organization's offices at (818) 597-3227 or visit the Association's website.
This entry was posted on Friday, December 28th, 2012. Trackback from your own site. | {
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https://www.nhregister.com/news/article/Blumenthal-announces-millions-for-coastal-13309433.php
Blumenthal announces millions for coastal resiliency project in West Haven
By Mark Zaretsky
Updated 9:34 am EDT, Tuesday, October 16, 2018
U.S. Sen. Richard Blumenthal, second from right, speaks about the recently authorized Water Resources Development Act, at a press conference behind the Savin Rock Conference Center in West Haven Monday.
Photo: Arnold Gold / Hearst Connecticut Media
WEST HAVEN — The U.S. government is prepared to spend millions to create and restore dunes and berms to help protect the shoreline from the Savin Rock Conference Center to Beach Street, U.S. Sen. Richard Blumenthal announced Monday.
"The dunes and berms of West Haven are a perfect example of how both the beauty and protective value of our shoreline needs to be rebuilt and preserved..." Blumenthal, D-Conn., said at a rainy day press conference overlooking Long Island Sound on the gazebo behind the conference center. "Resiliency is the common theme here..."
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"Resiliency is as important in Georgia and the Carolinas as it is in Connecticut, and we are leading the way — showing by example and leading by examples," said Blumenthal, who was flanked by Mayor Nancy Rossi and state Reps. Dorinda Borer, D-West Haven, and Charles Ferraro, R-West Haven.
As climate change continues, hurricanes and other severe storms "are becoming the new normal," Blumenthal said. "We need to be prepared."
Dunes are "not only beautiful ... but they offer protection," he said.
Protecting the West Haven shore — which was authorized in the recently passed, bipartisan Water Resources Development Act — would safeguard properties of thousands of people, many of whom are at risk for flooding as sea level rises, officials have said.
Members of the state's Congressional delegation also are looking to do projects along Congress Street in Bridgeport, as well as in the Hartford area and eastern Connecticut, Blumenthal said.
The exact cost of the work "is as yet undetermined," Blumenthal said. "There are various estimates from $3 million to $7 million.
"But whatever is needed, this project will begin," he said. "Whatever the amount of money, the commitment has been made at the federal level that this project should be prioritized — and, trust me, we are going to be pounding the United States Army Corps of Engineers to get it done."
Blumenthal said he hopes to see the work done next year.
Rossi called the announcement "good news for West Haven.
"Long Island Sound restoration and stewardship is important to West Haven because we are one of many shoreline municipalities that directly impact the water quality of Long Island Sound," she said.
According to a letter earlier this year from city grant writer Eileen Krugel to Blumenthal and U.S. Sen. Chris Murphy, D-Conn., the project the city aims to do would create and/or restore dunes from the West Haven Conference Center at Rock Street to Beach Street near Morse Avenue, a distance of about one mile.
"There are some duned areas, but this request would provide uniformed dunes that would include protective grasses, fencing and dune crossovers preventing degradation by pedestrians," Krugel wrote. "These dunes would provide a protective measure in West Haven's resiliency efforts."
Among properties most at-risk from some future storm surge or the effects of rising sea level are the West Walk Condominiums, which are built at ground level, located just north of the shorefront walkway between Altschuler Plaza and where Beach Street curves around into Washington Avenue, officials said.
Ferraro said it was "very special" for him to have Blumenthal talk about resiliency along the beaches east of Savin Rock "because I grew up on that beach, right there," he said, pointing to the area just east of where officials were standing.
Borer said it was "nice to see a project happen so quickly." She said at West Walk, "we are just one superstorm away" from a potential disaster.
She also talked about the planned raising of Beach Street, which was previously approved but has stalled because of soil issues that greatly raised the price of it. She said she hopes "to have good news " on that project soon.
Ruby Melton, president of the West Walk Condominium Association, thanked Blumenthal and other officials for keeping protection of the area on their radar.
She said that during Tropical Storm Irene and Superstorm Sandy, West Walk experienced flooding that was worse than it ever had seen before, and the association has been pushing for great protection through beefed-up dunes or a berm "for a long time."
mark.zaretsky@hearstmediact.com
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\section{Introduction}
It is widely accepted that magnetic activity of the late-type stars
is due to the large-scale hydromagnetic dynamo which results from
actions of differential rotation and cyclonic turbulent motions in
their convective envelopes \citep{park,KR80}. Solar and stellar observations
show that the surface magnetic activity forms a complicated multi-scale
structure \citep{2009ARAA_donat,2013AARv2166S}. The large-scale organization
of the surface magnetic activity on the Sun and other late-type stars
could be related to starspots \citep{2005LRSP2.8B}. Currently, there
is no consistent theory simultaneously explaining the large-scale
magnetic activity of the Sun and emergence of sunspots at the solar
photosphere. However, each of these two phenomena can be modeled separately.
Moreover, there is no consensus about details of the origin mechanisms
of the large-scale magnetic activity of the Sun and solar-type stars.
The models of the flux-transport dynamos and the concurrent paradigm
of the distributed turbulent dynamos are outlined in reviews of \citet{chrev05},
\citet{brsu05} and \citet{pi13r}. The origin and formations of sun/star
spots are extensively studied as well, (see, e.g., \citealt{2010ApJ720.233C,2010ApJ719.307K,2012ApJ753L13S,2013ApJ777L.37W}).
Results of direct numerical simulations of solar-type stars and M-dwarfs
\citep{2008ApJ676.1262B,brown2011,2015ApJ813L31Y,2016ApJ819.104G,2018AA609A..51W}
show that magnetic field and turbulent convective flows are highly
aligned at the near surface layers. Generally, it is found that in
the regions occupied by the magnetic field the cross-helicity density
$\left\langle \gamma\right\rangle =\left\langle \mathbf{u}\cdot\mathbf{b}\right\rangle $
is not zero. Here, $\mathbf{u}$ and $\mathbf{b}$ are the convective
velocity and fluctuating magnetic field. Alignment of the velocity
and magnetic field is found inside sunspots \citep{2011JPhCS.271a2001B}.
Analysis of the full-disk solar magnetograms show that similar to
the current helicity \citep{zetal10}, the cross-helicity can have
the hemispheric rule \citep{2011SoPh..tmp...39Z}. In other words,
the signs of $\left\langle \gamma\right\rangle $ in the North and
South hemispheres can be opposite. The spottiness (or spot filling
factor) and magnetic filling factors of the fast rotating solar analogs
are estimated to be much larger than for the Sun \citep{2005LRSP2.8B}.
The same is true for the fully convective stars. However physical
properties of starspots may change with a decrease of the stellar
mass (see the above-cited review). Results of the stellar magnetic
cartography (the so-called ZDI methods) showed that the fast rotating
M-dwarfs demonstrate the strong large-scale dipole (or multi-pole)
poloidal magnetic field of strength $>1$kG \citep{2008MNRAS390.567M}.
Using the solar analogy we could imagine that such a field can be
accompanied by the cross-helicity density magnitude which is observed
in sunspots. This leads to a question about how the cross-helicity
can affect the large-scale dynamo on these objects.
After \citet{KR80} there was understood that the alignment of the
turbulent convective velocity and the magnetic field is typical for
saturation stage of the turbulent generation due to the mean electromotive
force (EMF), $\boldsymbol{\mathcal{E}}=\left\langle \mathbf{u}\times\mathbf{b}\right\rangle $.
This consideration does not account effects of cross-helicity that
take place in the strongly stratified subsurface layers of the stellar
convective envelope. The direct numerical simulations show the directional
alignment of the velocity and magnetic field fluctuations in the presence
of gradients of either pressure or kinetic energy \citep{2008PhRvL.100h5003M}.
The dynamo scenarios based on the cross-helicity were suggested earlier
in a number of papers \citep{1993ApJ407.540Y,2000ApJ...537.1039Y,2013GApFD107.114Y}
In the current framework of dynamo studies, the effects of non-uniform
large-scale flows are taken into account only through the differential
rotation or so-called $\Omega$-effect {[}$\nabla\times({\bf {U}}\times{\bf {B}})${]}.
In marked contrast to this differential rotation effect, the non-uniform
flow effect has not been considered in the turbulence effects on the
mean-field induction represented by the turbulent electromotive force
$\boldsymbol{\mathcal{E}}=\left\langle \mathbf{u}\times\mathbf{b}\right\rangle $
. However, if we see the velocity and magnetic-field fluctuation equations
in the presence of the inhomogeneous mean velocity, the turbulent
cross helicity, defined by the correlation between the velocity and
magnetic-field fluctuations ($\left\langle \mathbf{u}\cdot\mathbf{b}\right\rangle $),
should naturally enter the expression of the turbulent EMF as the
coupling coefficient for the mean absolute vorticity (rotation and
the mean relative vorticity) \citep{2016ApJ824.67Y}. This suggests
that, in the presence of a non-uniform large-scale flow, the turbulent
dynamo mechanism arising from the cross helicity should be taken into
account as well as the counterparts of the turbulent magnetic diffusivity
and turbulent helicity or the so-called $\alpha$-effect.
\begin{figure}
\includegraphics[width=0.99\columnwidth]{fig_crh}
\caption{a) Generation of the mean electromotive force from cross-helicity
(see explanation in the text); b) the $\alpha$-effect from the axial-aligned
magnetic field.}
\end{figure}
{The cross-helicity may have a particular interest for consideration
of the dynamo mechanisms operating in the fully-convective stars.
For convenience, we briefly remind the physical mechanism behind the
cross-helicity generation effect. Illustration of this mechanism is
shown in Figure 1a. We consider the aligned turbulent velocity and
magnetic field in the plane that is perpendicular to the rotation
axis. The Coriolis force acting on the turbulent motion results in
the mean electromotive force along the rotation axis, $\boldsymbol{\mathcal{E}}^{\gamma}=\left\langle \delta\mathbf{u}\times\mathbf{b}\right\rangle $
(see, Fig1a). This electromotive force can generate the large-scale
toroidal magnetic field due to the $\boldsymbol{\nabla}\times\boldsymbol{\mathcal{E}}^{\gamma}$-term
in the induction equation. The alternative mechanism is given by the
$\alpha$-effect, (see Figure 1b). In this case, the mean electromotive
force results from the large-scale axial magnetic field and the cyclonic
motions in the plane perpendicular to the rotation axis. Note that
for a regime of the fast rotation the energy of the turbulent vortexes
across rotation axis is suppressed. Therefore the axisymmetric $\alpha^{2}$-dynamo
cannot use the axial magnetic field for the dynamo generation \citep{kit-rud:1993b}.
Our consideration gives an idea that the cross-helicity effect can
generate the axisymmetric magnetic field even in the case of the quasi
2D turbulence that is expected for the fast-rotating M-dwarfs. The
differential rotation of the fast rotating M-dwarfs is rather small
\citep{D2-2008MNRAS,2008MNRAS390.567M}. The direct numerical simulations
of \citet{2008ApJ676.1262B} show absence of the differential rotation
in the magnetic case. Therefore we can expect that the axisymmetric
magnetic field is likely generated by means of the turbulent mechanisms
with no regards for the large-scale shear flow. As was mentioned above
the $\alpha$-effect is unlikely to support the axisymmetric dynamo
for the case of the fast-rotating M-dwarfs.}
In this paper, the cross-helicity effects are studied for in the full-sphere
non-axisymmetric dynamo. We identify the different dynamo scenarios
and study the magnetic properties of the fully convective stars using
the nonlinear dynamo models.
\section{Basic equations}
The mean-field convective dynamo is governed by the induction equation
of the large-scale magnetic field $\mathbf{B}$,
\begin{equation}
\frac{\partial\mathbf{B}}{\partial t}=\nabla\times\left(\mathbf{\mathcal{E}}+\overline{\boldsymbol{U}}\times\left\langle \mathbf{B}\right\rangle \right),\label{eq:dyn}
\end{equation}
where $\mathbf{\mathcal{E}}=\left\langle \mathbf{u}\times\mathbf{b}\right\rangle $
is the mean electromotive force of the turbulent convective flows,
$\mathbf{u}$, and, the turbulent magnetic field, $\mathbf{b}$. The
mean-electromotive force includes the generation effects due to the
helical turbulent flows and magnetic field, the generation effect
due to the cross-helicity. {Also, it includes the turbulent
pumping, and the anisotropic (because of rotation) eddy-diffusivity
etc.. For convenience, we divide the expression of the mean-electromotive
force into two parts:
\begin{eqnarray}
\boldsymbol{\boldsymbol{\mathcal{E}}} & = & \boldsymbol{\boldsymbol{\mathcal{E}}}^{\alpha,\eta,V}+\boldsymbol{\boldsymbol{\mathcal{E}}}^{\gamma},\label{eq:emf}
\end{eqnarray}
where $\boldsymbol{\boldsymbol{\mathcal{E}}}^{\gamma}$ results from
the cross-helicity effect (\citealp{2013GApFD107.114Y}, hereafter
Y13):
\begin{equation}
\boldsymbol{\boldsymbol{\mathcal{E}}}^{\gamma}=C_{\gamma}\frac{\boldsymbol{\Omega}}{\Omega}\left\langle \gamma\right\rangle f_{\gamma}\left(\Omega^{*}\right)\psi_{\gamma}\left(\beta\right),
\end{equation}
where, $\left\langle \gamma\right\rangle =\left\langle \mathbf{u}\cdot\mathbf{b}\right\rangle $,
$\Omega^{*}=4\pi\tau_{c}/P^{*}$ is the Coriolis number, where $\tau_{c}$
is the convective turnover time and the $P^{*}$ is the period of
rotation of a star. Analytical calculations of Y13 do not include
the nonlinear feedback due to the Coriolis force and the large-scale
magnetic field. In our study, these effects will be treated in a simplified
way via quenching functions $f_{\gamma}\left(\Omega^{*}\right)$,
and $\psi_{\gamma}\left(\beta\right)$. The function $f_{\gamma}\left(\Omega^{*}\right)$
takes into account the nonlinear effect of the Coriolis force in the
fast rotation regime. The function $\psi_{\gamma}\left(\beta\right)$,
where $\mathrm{\beta=\left\langle \left|\mathbf{B}\right|\right\rangle /\sqrt{4\pi\overline{\rho}u'^{2}}}$,
$\mathrm{u'}$ is the RMS of the convective velocity, describes the
magnetic quenching of the cross-helicity dynamo effect. Those quenching
functions will be specified later.}
{The part $\boldsymbol{\boldsymbol{\mathcal{E}}}^{\alpha,\eta,V}$
includes the others common contributions of the mean-electromotive
force. It is written as follows:}
\begin{eqnarray}
\boldsymbol{\boldsymbol{\mathcal{E}}}^{\alpha,\eta,V} & = & \hat{\alpha}\circ\left\langle \mathbf{B}\right\rangle +\mathbf{V}^{\left(p\right)}\times\mathbf{\left\langle B\right\rangle }\\
& - & \left(\eta_{T}+2\eta_{T}^{(\parallel)}\right)\boldsymbol{\nabla}\times\mathbf{\left\langle B\right\rangle }-2\eta_{T}^{(\parallel)}\frac{\boldsymbol{\Omega}}{\Omega^{2}}\mathbf{\boldsymbol{\Omega}\cdot\left(\boldsymbol{\nabla}\times\mathbf{\left\langle B\right\rangle }\right)},\nonumber
\end{eqnarray}
It is convenient to divide the large-scale magnetic field induction
vector for axisymmetric and non-axisymmetric parts as follows:
\begin{eqnarray}
\left\langle \mathbf{B}\right\rangle & = & \overline{\mathbf{B}}+\tilde{\mathbf{B}}\label{eq:b0}\\
\mathbf{\overline{B}} & = & \hat{\boldsymbol{\phi}}\mathrm{B}+\nabla\times\left(\frac{\mathrm{A}\hat{\boldsymbol{\phi}}}{r\sin\theta}\right)\label{eq:b1}\\
\tilde{\mathbf{B}} & = & \mathrm{\boldsymbol{\nabla}\times\left(\hat{\mathbf{r}}T\right)+\boldsymbol{\nabla}\times\boldsymbol{\nabla}\times\left(\hat{\mathbf{r}}S\right),}\label{eq:b2}
\end{eqnarray}
where $\overline{\mathbf{B}}$ is the axisymmetric, and $\tilde{\mathbf{B}}$
is non-axisymmetric part of the large-scale magnetic field; $\mathrm{A}$,
$\mathrm{B}$, $\mathrm{T}$ and $\mathrm{S}$ are scalar functions;
$\hat{\boldsymbol{\phi}}$ is the unit vector in the azimuthal direction
and $\hat{\mathbf{r}}$ is the radius vector; $r$ is the radial distance
and $\theta$ is the polar angle. The cross-helicity pseudo-scalar
is decomposed to the axisymmetric and non-axisymmetric parts, as well,
\begin{equation}
\left\langle \gamma\right\rangle =\overline{\gamma}+\tilde{\gamma}.\label{eq:gam}
\end{equation}
For the non-axisymmetric part of the problem we employ the spherical
harmonics decomposition, i.e., the scalar functions $\mathrm{T}$,
$\mathrm{S}$ and $\tilde{\gamma}$ are represented as follows:
\begin{eqnarray}
\mathrm{T\left(r,\mu,\phi,t\right)} & \mathrm{=} & \mathrm{\sum\hat{T}_{l,m}\left(r,t\right)\bar{P}_{l}^{\left|m\right|}\exp\left(im\phi\right),}\label{eq:tdec}\\
\mathrm{S\left(r,\mu,\phi,t\right)} & \mathrm{=} & \mathrm{\sum\hat{S}_{l,m}\left(r,t\right)\bar{P}_{l}^{\left|m\right|}\exp\left(im\phi\right),}\label{eq:sdec}\\
\tilde{\gamma}\left(r,\mu,\phi,t\right) & = & \sum\hat{\gamma}_{l,m}\left(r,t\right)\bar{P}_{l}^{\left|m\right|}\exp\left(im\phi\right)
\end{eqnarray}
where $\mathrm{\bar{P}_{l}^{m}}$ is the normalized associated Legendre
function of degree $\mathrm{l\ge1}$ and order $\mathrm{m\ge1}$.
Note that $\mathrm{\hat{S}_{l,-m}=\hat{S}_{l,m}^{*}}$ and the same
for $\hat{T}_{l,m}$ and $\hat{\gamma}_{l,m}$.
The equations governing evolution of the axisymmetric part of the
magnetic field are as follows:
\begin{eqnarray}
\frac{\partial B}{\partial t} & = & \frac{1}{r}\left(\frac{\partial r\boldsymbol{\mathcal{E}}_{\theta}^{\alpha,\eta,V}}{\partial r}+\sin\theta\frac{\partial\boldsymbol{\mathcal{E}}_{r}^{\alpha,\eta,V}}{\partial\mu}\right)-\frac{\sin\theta}{r}\frac{\partial\left(\Omega,A\right)}{\partial\left(r,\mu\right)}\label{eq:B}\\
& - & \frac{1}{r}\left(\frac{\partial r\overline{U}_{r}B}{\partial r}-\sin\theta\frac{\partial\overline{U}_{\theta}B}{\partial\mu}\right)\nonumber \\
& - & \frac{C_{\gamma}\sin\theta}{r}\left(\frac{\partial}{\partial r}\left(r\left\langle \gamma\psi_{\gamma}\left(\beta\right)\right\rangle f_{\gamma}\left(\Omega^{*}\right)\right)-\frac{\partial}{\partial\mu}\left(\mu\left\langle \gamma\psi_{\gamma}\left(\beta\right)\right\rangle f_{\gamma}\left(\Omega^{*}\right)\right)\right),\nonumber \\
\frac{\partial A}{\partial t} & = & r\sin\theta\boldsymbol{\mathcal{E}}_{\phi}^{\alpha,\eta,V}-\left(\boldsymbol{\overline{U}}\cdot\boldsymbol{\nabla}\right)A,\label{eq:A}
\end{eqnarray}
where all the parts of the $\boldsymbol{\mathcal{E}}$ except the
cross-helicity effect are written in the symbolic form (see, e.g.,
\citealt{2016ApJ824.67Y}). The Eq(\ref{eq:A}) does not have a contribution
from the cross-helicity. This results in a difference in the cross-helicity
dynamo for the axisymmetric and non-axisymmetric magnetic fields.
Another important observation is that the cross-helicity dynamo can
contribute to generation of the axisymmetric toroidal magnetic field
even when the axisymmetric cross-helicity is zero. It results from
condition $\overline{\tilde{\gamma}\psi_{\gamma}\left(\beta\right)}\ne0$
for the nonlinear case in presence of the axisymmetric and non axisymmetric
magnetic field.
To get the equation for the functions $\mathrm{S}$ and $\mathrm{T}$
we follow the procedure, which is described in detail by \citet{KR80}.
For example, to get the equation for the $\mathrm{S}$ we take the
scalar product of the Eq(\ref{eq:dyn}) with the $\hat{\mathrm{\boldsymbol{r}}}$
and for the equation governing the $\mathrm{T}$ we do the same after
taking the curl of the Eq(\ref{eq:dyn}). Therefore we will have,
\begin{eqnarray}
-\frac{\partial\Delta_{\Omega}S}{\partial t} & = & \boldsymbol{\hat{\mathrm{r}}}\cdot\nabla\times\left(\mathbf{\boldsymbol{\mathcal{E}}}+\overline{\boldsymbol{U}}\times\left\langle \mathbf{B}\right\rangle \right),\label{eq:S}\\
-\frac{\partial\Delta_{\Omega}T}{\partial t} & = & \boldsymbol{\hat{\mathrm{r}}}\cdot\nabla\times\nabla\times\left(\boldsymbol{\mathbf{\mathcal{E}}}+\overline{\boldsymbol{U}}\times\left\langle \mathbf{B}\right\rangle \right),\label{eq:T}
\end{eqnarray}
where $1/r^{2}\Delta_{\Omega}$ is the Laplace operator on the surface
$r=\mathrm{const}$.
With the contributions of the cross-helicity the Eqs(\ref{eq:S},\ref{eq:T})
are re-written as follows
\begin{eqnarray}
-\frac{\partial\Delta_{\Omega}S}{\partial t} & = & \boldsymbol{\hat{\mathrm{r}}}\cdot\nabla\times\left(\mathbf{\boldsymbol{\boldsymbol{\mathcal{E}}}^{\alpha,\eta,V}}+\overline{\boldsymbol{U}}\times\left\langle \mathbf{B}\right\rangle \right)+C_{\gamma}f_{\gamma}\left(\Omega^{*}\right)\frac{\partial}{\partial\phi}\left(\tilde{\gamma}\psi_{\gamma}\left(\beta\right)\right),\label{eq:S-1}\\
-\frac{\partial\Delta_{\Omega}T}{\partial t} & = & \boldsymbol{\hat{\mathrm{r}}}\cdot\nabla\times\nabla\times\left(\boldsymbol{\boldsymbol{\mathcal{E}}}^{\alpha,\eta,V}+\overline{\boldsymbol{U}}\times\left\langle \mathbf{B}\right\rangle \right)\label{eq:T-1}\\
& - & \frac{C_{\gamma}f_{\gamma}\left(\Omega^{*}\right)}{r}\Delta_{\Omega}\left(\mu\tilde{\gamma}\psi_{\gamma}\left(\beta\right)\right)+\frac{C_{\gamma}}{r}\frac{\partial}{\partial\mu}\left(\sin^{2}\theta\frac{\partial}{\partial r}r\tilde{\gamma}f_{\gamma}\left(\Omega^{*}\right)\psi_{\gamma}\left(\beta\right)\right).\nonumber
\end{eqnarray}
We put some details about derivation of Eqs(\ref{eq:S-1}, \ref{eq:T-1})
in Appendix. From these equations, we see that the nonaxisymmetric
part of the cross-helicity is coupled with the evolution of the non
axisymmetric magnetic field. This can provide the dynamo instability
of the large-scale non axisymmetric magnetic field. In particular,
the nonaxisymmetric magnetic field could be generated solely due to
the cross-helicity dynamo effect.
In general case, all coefficients in the Eq(\ref{eq:emf}) depends
on the Coriolis number $\Omega^{*}=4\pi\tau_{c}/P^{*}$, where $\tau_{c}$
is the convective turnover time and the $P^{*}$is the period of rotation
of a star. Also, the magnetic feedback on the generation and transport
effects in the $\boldsymbol{\boldsymbol{\mathcal{E}}}$ should be
taken into account. For the case of $\Omega^{*}\gg1$, the $\alpha$-effect
tensor can be represented as follows \citep{kit-rud:1993b,pi08Gafd}:
\begin{eqnarray}
\mathrm{\alpha_{ij}} & \mathrm{\approx} & \mathrm{c_{\alpha}u'\ell\left|\mathbf{\boldsymbol{\Lambda}}^{(\rho)}\right|\cos\theta\psi_{\alpha}(\beta)f_{5}^{(a)}\left(\Omega^{*}\right)\left\{ \delta_{ij}-\frac{\Omega_{i}\Omega_{j}}{\Omega^{2}}\right\} }\label{alp2d}
\end{eqnarray}
where, $\mathrm{\mathbf{\boldsymbol{\Lambda}}^{(\rho)}=\boldsymbol{\nabla}\log\overline{\rho}}$
is the gradient of the mean density. Although, $f_{5}^{(a)}\left(\Omega^{*}\right)\rightarrow\pi/2$,
when $\Omega^{*}\gg1$, we will keep the dependence on the Coriolis
number for the nonlinear solution. For the case $\Omega^{*}\gg1$,
the magnitude of the kinetic part $\alpha$ effect is given by
\begin{equation}
\alpha_{0}={\displaystyle \frac{\pi}{2}c_{\alpha}u'\ell\left|\mathbf{\boldsymbol{\Lambda}}^{(\rho)}\right|}.\label{eq:alpha0}
\end{equation}
The magnetic quenching function of the kinetic part of $\alpha$-effect
is defined by
\begin{equation}
\psi_{\alpha}=\frac{5}{128\beta^{4}}\left(16\beta^{2}-3-3\left(4\beta^{2}-1\right)\frac{\arctan\left(2\beta\right)}{2\beta}\right),
\end{equation}
where $\mathrm{\beta=\left\langle \left|\mathbf{B}\right|\right\rangle /\sqrt{4\pi\overline{\rho}u'^{2}}}$.
For the cross-helicity dynamo effect we assume that $\psi_{\gamma}=\psi_{\alpha}$.
For the sake of simplicity, we skip the magnetic quenching due to
the magnetic helicity conservation, (cf, \citealt{pip13M}).
The turbulent pumping of the mean-field contains the sum of the contributions
due to the mean density gradient (see,\citealp{pi08Gafd}, hereafter
P08) and the mean-filed magnetic buoyancy \citep{kp93},
\begin{eqnarray}
\mathbf{V}^{\left(p\right)}\times\mathbf{\left\langle B\right\rangle } & \mathrm{=} & 3\eta_{0}f_{1}^{(a)}\left(\Omega^{*}\right)\left(\frac{\left(\Omega\cdot\boldsymbol{\Lambda}^{(\rho)}\right)}{\Omega^{2}}\boldsymbol{\Omega}\times\mathbf{\left\langle B\right\rangle }-\left(\boldsymbol{\Omega}\cdot\mathbf{\left\langle B\right\rangle }\right)\left(\boldsymbol{\Omega}\times\boldsymbol{\Lambda}^{(\rho)}\right)\right)\label{eq:pumpr}\\
& + & \frac{\alpha_{MLT}u'}{\Gamma_{1}}\beta^{2}K\left(\beta\right)\mathrm{\mathbf{g}}\times\mathbf{\left\langle B\right\rangle }\nonumber
\end{eqnarray}
where the $\mathrm{\alpha_{MLT}}$ is the parameter of the mixing
length theory, $\Gamma_{1}$ is the adiabatic exponent and the function
$\mathrm{K\left(\beta\right)}$ is defined in \citep{kp93} and $\mathbf{g}$
is the unit vector in the radial direction. When $\Omega^{*}\gg1$,
we have $f_{1}^{(a)}\left(\Omega^{*}\right)\rightarrow\pi/(8\Omega^{\ast})$.
The function of the Coriolis number $f_{1}^{(a)}\left(\Omega^{*}\right)$
is given in P08. Dependence of the eddy-diffusivity coefficients on
the Coriolis number is as follows
\begin{eqnarray*}
\eta_{T} & = & \frac{\eta_{0}}{\Omega^{*2}}\left(1-\frac{\arctan\Omega^{*}}{\Omega^{*}}\right)\\
\eta_{T}^{\|} & = & \frac{3\eta_{0}}{4\Omega^{*2}}\left(\left(\Omega^{*2}+3\right)\frac{\arctan\Omega^{*}}{\Omega^{*}}-3\right),
\end{eqnarray*}
where the eddy-diffusivity coefficient is defined ${\displaystyle \eta_{0}=\mathrm{\nu_{0}/Pm_{T}}}$
where $\nu_{0}=\mathrm{u}'\ell/3$ is the eddy viscosity.
The quenching of the cross-helicity dynamo for the fast rotating case
was not studied before. We will assume that the cross-helicity effect
is quenched in the same way as the turbulent diffusivity coefficients,
i.e., we put
\begin{equation}
f_{\gamma}\left(\Omega^{*}\right)=\frac{1}{\pi}\frac{\arctan\Omega^{*}}{1+\Omega^{*}}\label{eq:gamq}
\end{equation}
The Eq(\ref{eq:gamq}) affect the amplitude of the cross-helicity
effect in the large-scale dynamo.
The evolution of the cross-helicity is govern by the conservation
law
\begin{equation}
\frac{\partial\left\langle \gamma\right\rangle }{\partial t}=\frac{1}{3\overline{\rho}}\left(\left\langle \mathbf{B}\right\rangle \cdot\nabla\right)\overline{\rho}\left\langle \mathbf{u}^{2}\right\rangle -2\boldsymbol{\boldsymbol{\mathcal{E}}}\cdot\boldsymbol{\Omega}+\eta_{0}\Delta\left\langle \gamma\right\rangle \label{eq:crhg}
\end{equation}
In the stellar conditions, the typical spatial scale of the density
stratification is much less than the spatial scale of the mean magnetic
field. Thus, the first term in the Eq(\ref{eq:crhg}) dominates the
second one. Either rotation-induced anisotropy of the $\alpha$-effect,
the eddy diffusivity, and the pumping do not contribute to the cross-helicity
generation. Substituting the general expression of the mean-electromotive
force into Eq(\ref{eq:crhg}) we get,
\begin{equation}
\frac{\partial\left\langle \gamma\right\rangle }{\partial t}=\frac{\eta_{0}}{\tau_{c}}\left(\left\langle \mathbf{B}\right\rangle \cdot\boldsymbol{\Lambda}^{(\rho)}\right)+2\eta_{T}\boldsymbol{\Omega}\cdot\left(\boldsymbol{\nabla}\times\mathbf{\left\langle B\right\rangle }\right)-\frac{\Omega\alpha_{MLT}u'}{\Gamma_{1}}\beta^{2}K\left(\beta\right)\sin\theta\left\langle B_{\phi}\right\rangle +\eta_{0}\Delta\gamma,\label{eq:crh}
\end{equation}
For the numerical solution, we reduce the equations to the dimensionless
form. The radial distance is measured in the units of the solar radius,
as usual for the stellar astrophysics. Thus, we will have the following
set of parameters, the $\Omega_{\star}$ is the rotation rate of the
star, the $\nu_{0}$ is the magnitude of the eddy viscosity, the parameter
$\mathrm{Pm_{T}}$.
{The boundary conditions are as follows. The cross-helicity
and magnetic field are put to zero at the inner boundary which is
close to the center of the star. For the top, we use the vacuum boundary
conditions for the magnetic field. The boundary condition for the
cross-helicity at the top is unknown, we put the radial derivative
to zero at the top.}
\subsection{The possible dynamo scenarios}
{The possible dynamo scenarios depend upon the magnetic field
generation mechanisms, such as the $\alpha$-effect, the so-called
$\Omega$-effect (associating with the differential rotation) and
the cross-helicity dynamo effect (denoted as the $\gamma$-effect).
Following conventions of the dynamo theory \citep{KR80}, we can identify
the following scenarios: $\alpha^{2}$, $\alpha^{2}\Omega$, $\gamma^{2}$,
$\gamma^{2}\Omega$, $\alpha^{2}\gamma^{2}$, and $\alpha^{2}\gamma^{2}\Omega$.
More scenarios can be found in \citet{KR80}. From the point of view
of this study, the scenarios of $\gamma^{2}$ , $\alpha^{2}\gamma^{2}$,
and $\alpha^{2}\gamma^{2}\Omega$ present particular interest. All
of them depend on the cross-helicity generation governed by the Eq(\ref{eq:crh}).}
{The conceivable scenarios of the cross-helicity dynamos depend
on the cross-helicity generation effect.} The simplest scenario realized
when the cross-helicity is generated from the axial current, e.g.,
the term $2\eta_{T}\boldsymbol{\Omega}\cdot\left(\boldsymbol{\nabla}\times\mathbf{\left\langle B\right\rangle }\right)$
in the RHS of the Eq(\ref{eq:crh}). If we consider the axisymmetric
magnetic field, $\gamma^{2}$ dynamo can give generation of the toroidal
magnetic field from the cross-helicity effect. The poloidal field
is decoupled from the system of the dynamo equation and it can have
only a decaying solution. This scenario was discussed previously by
\citet{1993ApJ407.540Y} and \citet{2013GApFD107.114Y} for the dynamo
in accretion disks.
{In stellar convection zone, the cross-helicity generation
due to the density stratification is one of the most important mechanism.
This is supported by the direct numerical simulations of \citet{2008PhRvL.100h5003M}.
This effect is accounted by the first term in the cross-helicity evolution
equation. With regards to the density stratification, all the dynamo
equations are coupled and there is a possibility for $\gamma^{2}$
dynamo.} In this case, only the non-axisymmetric modes can be unstable
in linear solution because the mean electromotive force $\boldsymbol{\boldsymbol{\mathcal{E}}}=\dots+C_{\gamma}\left\langle \gamma\right\rangle \tau_{c}\boldsymbol{\Omega}+\dots$
has no contribution in the equation for the axisymmetric poloidal
magnetic field (associated with the potential A). In what follows
we discuss $\gamma^{2}$ , $\alpha^{2}\gamma^{2}$, and $\alpha^{2}\gamma^{2}\Omega$
scenarios based on the cross-helicity generation effect which comes
from the first term of the Eq(\ref{eq:crh}).
\section{Results}
\subsection{The eigenvalue problem}
For the linear eigenvalue problem we consider the simplified set of
the equations. We assume that the eddy diffusivity, $\eta_{0}=\nu_{0}/\mathrm{Pm_{T}}$
with $\nu_{0}=5\cdot10^{10}\mathrm{cm^{2}}$/s is constant over radial
distance. This corresponds to set of parameters in our model for the
$0.3\mathrm{M}_{\odot}$ star rotating with the period of 10 days.
The density gradient scale has sharp variation in the upper part of
the star and it is nearly constant in depth. It was found that it
is important to keep the spatial variations of the $\mathbf{\boldsymbol{\Lambda}}_{r}^{(\rho)}$
for the for the cross-helicity evolution equation. For the eigenvalue
problem we introduce a new variable, $\xi=R_{\odot}\mathbf{\boldsymbol{\Lambda}}_{r}^{(\rho)}$,
and employ the adiabatic profile of the density variation scale,
\begin{equation}
\xi\left(r\right)=\frac{1}{2}R_{\star}R_{\odot}/\left(r\left(R_{\star}-r\right)\right).\label{eq:xi}
\end{equation}
Parameter $\xi$ is nearly uniform in the bulk of the star, having
$\xi\approx-10$ and it rapidly falls to $\xi\approx-500$ toward
the surface. For the sake of simplicity, we put the constant $\xi=-50$
in the pumping terms. The amplitude of the $\alpha$-effect will be
determined by parameter $C_{\alpha}={\displaystyle \alpha_{0}R_{\odot}/\nu_{0}}$.
Additional parameter is the ratio $C_{\tau}={\displaystyle R_{\odot}^{2}/\left(\nu_{0}\tau_{c}\right)}$.
It determines the generation of the cross-helicity. Therefore, in
the linear problem, the reduced expression of the mean-electromotive
force is
\begin{eqnarray}
\hat{\mathcal{E}}_{i} & = & \mathrm{C_{\alpha}\mathrm{Pm_{T}^{-1}}\left\{ \left\langle B_{i}\right\rangle -\frac{\Omega_{i}\left(\boldsymbol{\Omega}\cdot\left\langle \mathbf{B}\right\rangle \right)}{\Omega^{2}}\right\} }+C_{h}\hat{\gamma}\label{eq:emf-l}\\
& & +\mathrm{Pm_{T}^{-1}}\left(\frac{\left(\Omega\cdot\boldsymbol{\xi}\right)}{\Omega^{2}}\boldsymbol{\Omega}\times\mathbf{\left\langle B\right\rangle }-\left(\boldsymbol{\Omega}\cdot\mathbf{\left\langle B\right\rangle }\right)\left(\boldsymbol{\Omega}\times\boldsymbol{\xi}\right)\right),\nonumber \\
& - & \mathrm{Pm_{T}^{-1}}\left(\left(1+2a\right)\boldsymbol{\nabla}\times\mathbf{\left\langle B\right\rangle }+2a\frac{\boldsymbol{\Omega}}{\Omega^{2}}\mathbf{\boldsymbol{\Omega}\cdot\left(\boldsymbol{\nabla}\times\mathbf{\left\langle B\right\rangle }\right)}\right),\nonumber
\end{eqnarray}
where $a=\eta_{T}^{\|}/\eta_{T}$. In what follows we assume that
$a=1$. Also, in the linear problem the parameter $C_{h}=C_{\gamma}\Omega_{\star}\tau_{c}$
in the Eq(\ref{eq:emf-l}) absorbs the Coriolis number dependence.
The hat sign in Eq(\ref{eq:emf-l}) means that the mean electromotive
force was scaled about $\nu_{0}$. The cross-helicity is governed
by equation
\begin{equation}
\frac{\partial\hat{\gamma}}{\partial t}=C_{\tau}\mathrm{Pm_{T}^{-1}}\left(\left\langle \mathbf{B}\right\rangle \cdot\boldsymbol{\xi}\right)+\mathrm{Pm_{T}^{-1}}\Delta\hat{\gamma},\label{eq:crh-l}
\end{equation}
Our purpose to investigate the eigenvalue solution of the Eqs(\ref{eq:dyn},\ref{eq:emf-l},\ref{eq:crh-l})
for the set of parameters like $\mathrm{Pm_{T}}$ $C_{\alpha}$, $C_{\gamma}$,
and $C_{\tau}$. The effect of the differential rotation can be controlled
by the angular velocity of the star and the distribution of the differential
rotation. We put $C_{\tau}=100$ because the typical diffusive time
scale is order of 100 years and the $\tau_{c}\approx1$ year for this
star. For the external layers of the star, the $C_{\tau}$ is much
larger. We consider the profile of the differential rotation from
our previous paper \citep{2017MNRAS.466.3007P}. It is illustrated
in Figure \ref{fig:basic}.
\begin{figure*}
\includegraphics[width=1\textwidth]{Fi000} \caption{\label{fig:basic}a) The Coriolis number $\Omega^{*}=2\tau_{c}\Omega_{\star}$
(dash-dot line), where $\tau_{c}$ is the turn-over time of convection,
the turbulent diffusivity parameter, solid line, both the $\tau_{c}$
and the diffusivity are estimated from the MESA code; the dashed line
shows the isotropic eddy viscosity from the heat transport model;
b) angular velocity profiles with contour levels which cover the range
of values which are depicted on the grey scale bar; c) geometry of
the meridional circulation, in the Northern hemisphere.}
\end{figure*}
{In linear solution, all the partial dynamo modes are decoupled.
We restrict discussion to a few partial modes of the large-scale magnetic
field, including the axisymmetric modes S0 and A0 and the non-axisymmetric
modes S1 and A1. We follow convention suggested by \citet{KR80}:
the letter ``S'' means the mode symmetrical about equator and the
letter ``A'' is for the antisymmetric mode. }
With no regards for the cross-helicity dynamo effect, e.g., in case
of $C_{\tau}=0$ or $C_{h}=0$ , the large-scale dynamo instability
is provided by the $\alpha^{2}$ or $\alpha^{2}\Omega$ scenarios.
For the $\alpha^{2}$ scenario, the critical $C_{\alpha}$ does not
depend on $\mathrm{Pm_{T}}$. Also, in this scenario, the non-axisymmetric
modes are preferable having thresholds at $C_{\alpha}^{(cr)}\approx37$
for the A1 mode and at $C_{\alpha}^{(cr)}\approx42$ for the S1 mode
and for $a=0$. The thresholds are about factor one-half higher for
$a=1$ than for $a=0$.{ This means that the additional diffusive
mixing of the large-scale magnetic field quenches efficiency of the
dynamo mechanisms. In $\alpha^{2}\Omega$ dynamo the instability depends
largely on parameter Pm, because this parameter controls the efficiency
of the large-scale magnetic field stretching by the differential rotation.}
For the $\mathrm{Pm_{T}}$=20, the axisymmetric modes are unstable
first, having thresholds around $C_{\alpha}^{(cr)}\approx10$.
The cross-helicity generation effect adds the new parameters for the
study. Results are shown in Figures \ref{fig:Ch}a and b. We restrict
the study by fixing the $C_{\alpha}$ parameter below the dynamo thresholds
of $\alpha^{2}$ and $\alpha^{2}\Omega$ dynamo regimes. {We
put the $C_{\alpha}=10$ and the anisotropy parameter $a=0$, and
study the dynamo instability against the parameter $C_{h}$ for the
variable magnetic Prandtl number $\mathrm{Pm_{T}}$ . Figures \ref{fig:Ch}a
shows results for the pure turbulent dynamo scenarios, i.e., the differential
rotation is disregarded. It is found that the mode A1 keeps the least
dynamo threshold. Also, we found the $\gamma^{2}$ scenario has the
smaller dynamo instability thresholds for modes A1 and S1 than the
$\alpha^{2}\gamma^{2}$ scenario. Therefore we can conclude that the
magnetic field generation by the concurrent cross-helicity and $\alpha^{2}$
dynamos reduce the efficiency of both dynamo mechanisms. The results
of the linear analysis tells us that without the differential rotation
the nonaxisymmetric dynamo solution is preferable. We can conclude
that during the linear stage of the dynamo process the $\gamma^{2}$
scenario does not give any preference for the axisymmetric magnetic
field generation. Moreover, as it was anticipated from the dynamo
equations the $\gamma^{2}$ scenario provide the additional mechanisms
for the non-axisymmetric magnetic field generation.}
\begin{figure}
\includegraphics[width=1\columnwidth]{fig2}\caption{\label{fig:Ch}a) Excitation thresholds for $\alpha^{2}\gamma^{2}$
scenario (red lines for the A-modes and blue lines for the S-modes)
and $\gamma^{2}$-scenario (black lines, the dashed line is for the
A1 mode and the solid line is for S1-mode) dynamos; b) the same as
(a) for the $\alpha^{2}\Omega\gamma^{2}$ dynamos. The $\alpha$-effect
parameter $C_{\alpha}=10$.}
\end{figure}
{Figure 2b shows that with an account of the differential rotation
effect, i.e., in considering the $\alpha^{2}\Omega\gamma^{2}$ dynamo
scenario, we get the instability thresholds for all the modes close
to each other with an increase of $\mathrm{Pm_{T}}$. Also, the efficiency
of the axisymmetric dynamo instability increases with the increase
of $\mathrm{Pm_{T}}$. Within the studied parameter range of $\mathrm{Pm_{T}}$
the nonaxisymmetric mode A1 keeps to be the most unstable. We also
studied instability for the spatially nonuniform density stratification
parameter $\xi$. In this case the dynamo instability thresholds are
about a factor of magnitude larger than in the case of the constant
$\xi$. However, the order of the instability thresholds among the
different partial dynamo modes remains the same as it is shown in
Figures \ref{fig:Ch}a and b.}
\subsection{The nonlinear solution}
For the nonlinear solution, we employ the model which keeps the spatial
dependence of the turbulent parameters provided by the {\footnotesize{}{}MESA}
code and solution of the heat transport problem (see Pipin 2017).
Using the results of the eigenvalue problem we bear in mind that the
parameters $C_{h}$ and $C_{\tau}$ in the Eqs(\ref{eq:emf-l}) and
(\ref{eq:crh-l}) absorb the dependence upon the parameter $\tau_{c}$.
{It is found that the Coriolis number parameter $\Omega^{*}=4\pi\tau_{c}/P^{*}$,
where $P^{*}=10$ days, varies from about 1 near the surface to 200
in the depth of the star.} This means that the critical threshold
of the $C_{\gamma}=2C_{h}/\Omega^{*}\ll1\sim0.01$ for $\alpha^{2}\Omega\gamma^{2}$
dynamo if $\mathrm{Pm_{T}}=3$. We use this $\mathrm{Pm_{T}}$ in
all models below. Three different models will be considered. Parameters
of the models are listed in Table 1. The model M1 represent the $\gamma^{2}$
scenario, the model M2 represents the $\alpha^{2}\gamma^{2}$ scenario
and M3 stands for $\alpha^{2}\tilde{\gamma}^{2}$. In the latter case,
we disregard the contribution of the axisymmetric cross-helicity in
the mean-electromotive force. This imitates the situation when the
mean cross-helicity has no hemispheric sign rule. The nonlinear combination
of the nonaxisymmetric magnetic field and cross helicity can produce
the axisymmetric magnetic field. The model M3 was introduced to study
this situation. In this paper, we consider models with the solid body
rotation.
\begin{table}
\caption{}
\centering{}%
\begin{tabular}{|cccc|}
\hline
\multicolumn{1}{|c|}{Model} & \multicolumn{1}{c|}{Scenario} & \multicolumn{1}{c}{$C_{\gamma}$} & $C_{\alpha}$\tabularnewline
\hline
M1 & $\gamma^{2}$ & 0.01 & \tabularnewline
\hline
M2 & $\alpha^{2}\gamma^{2}$ & 0.01 & 0.03\tabularnewline
\hline
M3 & $\alpha^{2}\tilde{\gamma}^{2}$ & 0.01 & 0.03\tabularnewline
\hline
\end{tabular}
\end{table}
Regime $\gamma^{2}$ provides the simplest scenario of the cross-helicity
dynamo. Contrary to the $\alpha^{2}$ dynamo, the $\gamma^{2}$ works
only in the nonaxisymmetric regime. In this scenario evolution of
the axisymmetric components of the toroidal and poloidal magnetic
fields are decoupled. Figures \ref{M1a} and \ref{M1b} show evolution
of the partial modes in the model M1 as well as snapshots of the magnetic
field and the cross-helicity distributions at the stationary stage
of evolution. It is seen that the axisymmetric mode of the toroidal
magnetic field evolves non-monotonically showing growth at the beginning
and it decays afterwhile. In nonlinear case, the cross-helicity that
is produced by the non-axisymmetric magnetic field may contribute
to generation of the axisymmetric toroidal magnetic field, because
in general $\left\langle \gamma\psi_{\gamma}\left(\beta\right)\right\rangle \ne0$
(see, eq.\ref{eq:B}). Therefore, the nonaxisymmetric cross-helicity
affects generation of the axisymmetric toroidal magnetic field. However,
evolution of the axisymmetric poloidal magnetic field is decoupled
of the toroidal magnetic field and the axisymmetric cross-helicity.
Therefore, there is no true axisymmetric dynamo in this case. The
axisymmetric field starts to decay when parts of the product $\left\langle \gamma\psi_{\gamma}\left(\beta\right)\right\rangle $
get synchronized. Both the non-axisymmetric cross-helicity density
$\gamma$ and magnetic field can be represented by the equatorial
dipole which changes orientation rotating around the axis of stellar
rotation. This phenomenon is known as the nonaxisymmetric dynamo waves.
\begin{figure}
\includegraphics[width=1\columnwidth]{fig3}
\caption{\label{M1a}The model M1 ( $\gamma^{2}$ dynamo), a) shows evolution
of the partial modes of the toroidal magnetic field at at the $\mathrm{r=\frac{3}{4}R_{\star}}$;
b) the time-latitude diagram of the toroidal magnetic field shown
by the color image and contours (range of $\pm$1kG). }
\end{figure}
\begin{figure}
\includegraphics[width=1\columnwidth]{fig4}\caption{\label{M1b}The model M1, snapshots of the cross-helicity and magnetic
field distributions in the stationary phase of dynamo evolution, a)
the cross-helicity distributions is shown by color and the radial
magnetic field (iso-lines $\pm1$kG); b) strength of the toroidal
magnetic field at the $\mathrm{r=\frac{3}{4}R_{\star}}$ for axisymmetric
and non-axisymmetric magnetic field and the ratio between energy of
the axisymmetric magnetic field and total magnetic energy; b) the
time-latitude diagram for axisymmetric toroidal magnetic field at
the $\mathrm{r=\frac{3}{4}R_{\star}}$and the color image shows shows
the axisymmetric radial magnetic field at the surface. }
\end{figure}
The scenario of the $\alpha^{2}\gamma^{2}$ dynamo has a possibility
for the axisymmetric magnetic field generation. Figures \ref{M2}
and \ref{M2b} show evolution of the partial modes in the model M2
as well as snapshots of the magnetic field and the cross-helicity
distributions at the stationary stage of evolution. We use the output
of the model M1 as an initial condition for the model M2. The Figs.\ref{M2}(a)
and (b) show that the axisymmetric toroidal magnetic field started
to grow at the beginning phase showing some oscillations. The dynamo
solution reaches the stage with the constant dipole-like distribution
at the end of simulation. The similar behavior is demonstrated by
the cross-helicity evolution. The cross-helicity has the opposite
signs in the northern and southern hemispheres. The polar magnetic
field in model M2 reaches a magnitude of the 2kG. At the end of simulation,
the model keeps a substantial nonaxisymmetric magnetic field. It has
more than one order of magnitude less strength than the axisymmetric
magnetic field. Snapshots of the magnetic field and cross-helicity
distributions show that these nonaxisymmetric components concentrate
in the near equatorial regions. The field lines of the magnetic field
distribution show that the overall configuration of the magnetic field
is dipole-like both inside and outside the star.
\begin{figure}
\includegraphics[width=1\columnwidth]{fig5}
\caption{\label{M2}The model M2 ($\alpha^{2}\gamma^{2}$ dynamo) a) shows
evolution of the partial modes of the toroidal magnetic field at at
the $\mathrm{r=\frac{3}{4}R_{\star}}$; b) time-latitude diagram of
the radial magnetic field at the surface shown by the color image
and contours show the toroidal magnetic field at at the $\mathrm{r=\frac{3}{4}R_{\star}}$
(range of $\pm$3kG); c) shows the time-latitude evolution for the
cross-helicity}
\end{figure}
Using the output of the model M2 we made additional run neglecting
the cross-helicity generation effects. This return the dynamo model
to the $\alpha^{2}$ scenario. Similar to \citet{2017MNRAS.466.3007P}
we get the non-axisymmetric magnetic field at the end of the run.
Also, we made additional runs with the decreased $C_{\gamma}$. For
the given parameter $C_{\alpha}$ it was found that the model keeps
axisymmetric magnetic even in the case when $C_{\gamma}$ is by a
factor 2 less than in the model M2.
\begin{figure}
\includegraphics[width=1\columnwidth]{fig6}\caption{\label{M2b}The same as Fig.\ref{M1b} for the model M2.}
\end{figure}
The interesting question is if the axisymmetric dynamo can be sustained
by the cross-helicity generation effect when the spatially averaged
cross-helicity is zero. {The model M3 illustrates this scenario.
In this model, we disregard the contribution of the axisymmetric cross-helicity
in the mean-electromotive force by neglecting contributions of the
axisymmetric magnetic field in the equation of the cross-helicity
evolution.} Results are shown in Figures \ref{M3} and \ref{M3b}.
Results show that contrary to the pure $\gamma^{2}$ scenario the
axisymmetric magnetic field is generated. This means that the azimuthally
averaged cross-helicity dynamo effect is not zero, $\left\langle \gamma\psi_{\gamma}\left(\beta\right)\right\rangle \ne0$,
because the terms of the product $\left\langle \gamma\psi_{\gamma}\left(\beta\right)\right\rangle $
are not synchronized in the azimuthal direction. It is caused by the
nonlinear generation of the non axisymmetric magnetic field both by
the $\gamma^{2}$ and the $\alpha^{2}$ mechanisms. We see that the
strength of the axisymmetric and nonaxisymmetric toroidal magnetic
field is same by the order of magnitude. The axisymmetric magnetic
field shows the solar-like time-latitude evolution of the toroidal
magnetic field inside the star. The radial magnetic field at the surface
shows the dominant nonaxisymmetric magnetic field and the nonaxisymmetric
distribution of the cross-helicity. During the nonlinear evolution
the pattern of the magnetic field distribution shown in Fig. \ref{M3b}b
moves about the axis of rotation, representing the azimuthal dynamo
wave. Also, it weakly oscillates around the perpendicular axis which
corresponds to the axis of the equatorial dipole. By this reason,
the model can show the nearly axisymmetric configuration of the polar
magnetic field during the minims and maxims of the axisymmetric magnetic
field cycle. The frequency of the non-axisymmetric m=1 mode is twice
of the axisymmetric one.
\section{Discussion and conclusions}
The physical origin of this cross-helicity effect lies in the combination
of the local angular-momentum conservation in a rotational motion
and the presence of the velocity-magnetic-field correlation \citep{2013GApFD107.114Y}.
Unlike the $\Omega$ effect, the cross-helicity effect does not depend
on the particular configuration of the differential rotation. Provided
that a finite turbulent cross helicity exists, the cross-helicity
effect should work in the presence of the absolute vorticity (rotation
and relative vorticity). This means that we can expect the cross-helicity
dynamo mechanism to work even in the case that the differential rotation
is negligibly small. How and how much cross helicity exists in turbulence
is another problem. In our models, the turbulent cross helicity is
generated by means of the large-scale magnetic field and density stratification.
This generation mechanism was analytically found in a number of papers
\citep{1999PhFl...11.2307Y,2011ApJ...743..160P,2011SoPh..269....3R,2013GApFD107.114Y}
using the mean-field magnetohydrodynamics framework. Our results show
that this turbulent cross-helicity generation effect results in a
number of the new dynamo scenarios.
\begin{figure}
\includegraphics[width=1\columnwidth]{fig8}
\caption{\label{M3}The $\alpha^{2}\tilde{\gamma}^{2}$ dynamo, a) shows evolution
of the partial modes of the toroidal magnetic field at at the $\mathrm{r=\frac{3}{4}R_{\star}}$;
b) time-latitude diagram of the radial magnetic field at the surface
shown by the color image and contours show the toroidal magnetic field
at at the $\mathrm{r=\frac{3}{4}R_{\star}}$ (range of $\pm$3kG).}
\end{figure}
\begin{figure}
\includegraphics[width=1\columnwidth]{fig7}\caption{\label{M3b}The same as Fig.\ref{M1b} for the model M3.}
\end{figure}
{It was shown that for the solid body rotation regime there
are three possible dynamo scenarios: the $\gamma^{2}$-dynamo (pure
cross-helicity dynamo), the $\alpha^{2}\gamma^{2}$-dynamo and its
modification - the $\alpha^{2}\tilde{\gamma}^{2}$ dynamo. The latter
is operating from the purely nonaxisymmetric cross-helicity distribution.
In nonlinear case, both the $\gamma^{2}$ and the $\alpha^{2}$ dynamo
scenarios sustain only the nonaxisymmetric magnetic field.} For the
$\gamma^{2}$ scenario the evolution axisymmetric components of the
magnetic field are decoupled. Therefore this regime cannot sustain
the axisymmetric magnetic field against decay.
{An interesting new effect was considered. It is found that,
in general, it is possible to generate some axisymmetric magnetic
field in nonlinear regime if the spatial variations of the non-axisymmetric
distributions of the cross-helicity and magnetic energy are not synchronized
in the azimuthal direction.} This gives generation of the axisymmetric
toroidal magnetic field due to the cross-helicity dynamo effect because
for the axisymmetric part of $\left\langle \gamma\psi_{\gamma}\left(\beta\right)\right\rangle $
we have
\begin{equation}
\left\langle \gamma\psi_{\gamma}\left(\beta\right)\right\rangle =\overline{\gamma}\overline{\psi_{\gamma}\left(\beta\right)}+\overline{\tilde{\gamma}\tilde{\psi_{\gamma}\left(\beta\right)}}\ne0,\label{eq:gg}
\end{equation}
where the first term of RHS is zero in $\gamma^{2}$ regime. The second
term of the RHS of this equation is not necessarily zero. Results
of the model M1 show that in the $\gamma^{2}$ scenario the $\tilde{\gamma}$
and $\tilde{\psi_{\gamma}\left(\beta\right)}$ get synchronized. This
prevents the axisymmetric toroidal magnetic field generation. On the
other hand, if there is an additional mechanism of the nonaxisymmetric
magnetic field generation, e.g. by the $\alpha^{2}$ dynamo, then
the axisymmetric dynamo can be excited even if the axisymmetric part
of the cross-helicity is zero. This was demonstrated by model M3 using
the $\alpha^{2}\tilde{\gamma}^{2}$ scenario. There, the effect of
the axisymmetric cross-helicity generation was disregarded. The given
mechanism shows a mixture of the non-axisymmetric and axisymmetric
modes with a dominance of the equatorial dipole-like mode.
One of the most important findings of our work is that the axisymmetric
magnetic field can be generated by means of the cross-helicity generation
and $\alpha^{2}$ in this case we employ the standard formulation
of the mean-electromotive force suggested by \citet{2000ApJ...537.1039Y}.
The dynamo mechanism operates with regards to the axisymmetric and
non-axisymmetric cross-helicity generation. In this case, the strong
axisymmetric dipole-like magnetic field is generated. Unlike the nonlinear
$\alpha^{2}\Omega$ regimes (cf. \citealp{2017MNRAS.466.3007P}),
this scenario produces the constant in time magnetic field configuration
with antisymmetric about equator cross-helicity, toroidal and radial
magnetic field distributions. Our scenario was demonstrated for the
solid body regime. This means that it can be realized on the fast
rotating M-dwarfs with a period of rotation about 1day, which often
show only a small amount of the differential rotation \citep{D2-2008MNRAS}.
Moreover the direct numerical simulation e.g., \citet{2008ApJ676.1262B},
and mean-field models, e.g., \citet{2017MNRAS.466.3007P} show suppression
of the differential rotation in nonlinear regimes. For the solid body
rotation, $\alpha^{2}$ dynamo produce the nonaxisymmetric magnetic
field \citep{2006AA446.1027C,elst07}. This because the $\alpha$-effect
cannot use the component of the large-scale magnetic field along rotation
for generation the axial electromotive force and this results from
the anisotropic $\alpha$-effect in the case of the high Coriolis
number (see, Eq\ref{alp2d} and \citealp{kit-rud:1993b}). The cross-helicity
can generate the poloidal electromotive force in this case \citep{2013GApFD107.114Y}.
This provides generation of the axisymmetric magnetic field by the
$\alpha^{2}\gamma^{2}$-dynamo. The magnetic field configuration produced
in our model of $\alpha^{2}\gamma^{2}$-dynamo is very similar to
those which was found on the fast rotating M-dwarfs, e.g., V374 Peg
and YZ CMi \citep{2008ASPC..384..156D,D2-2008MNRAS,2009ARAA_donat}.
In our paper we employ rather simplified approach to model the cross-helicity
generation effects for the fast rotating regimes. For the further
application the analytical results for the cross-helicity generation
effect in case of the fast rotation and strong magnetic field have
to be developed. We hope that future work could shed more light about
usability of the cross-helicity generation effects in stellar dynamos.
\textbf{Acknowledgments} We thank support RFBR under grant 16-52-50077.
Valery Pipin thank the grant of Visiting Scholar Program supported
by the Research Coordination Committee, National Astronomical Observatory
of Japan (NAOJ) and the project II.16.3.1 of ISTP SB RAS.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,318 |
require 'nmea_plus/message/ais/vdm_payload/payload'
require 'nmea_plus/message/ais/vdm_payload/mmsi_info'
module NMEAPlus
module Message
module AIS
module VDMPayload
# The base class for the {NMEAPlus::Message::AIS::VDM#ais AIS payload}, which uses its own encoding for its own subtypes
class VDMMsg < NMEAPlus::Message::AIS::VDMPayload::Payload
payload_reader :message_type, 0, 6, :_u
payload_reader :repeat_indicator, 6, 2, :_u
payload_reader :source_mmsi, 8, 30, :_u
# Detailed information produced from the MMSI
# @!parse attr_reader :source_mmsi_info
# @return [MMSIInfo] MMSI information structure
def source_mmsi_info
MMSIInfo.new(source_mmsi)
end
# The ship cargo type description lookup table
# @param code [Integer] The cargo type id
# @return [String] Cargo type description
def get_ship_cargo_type_description(code)
case code
when 0 then nil
when 1...19 then "(future use)"
when 20 then "WIG (any)"
when 21 then "WIG Hazardous category A"
when 22 then "WIG Hazardous category B"
when 23 then "WIG Hazardous category C"
when 24 then "WIG Hazardous category D"
when 25...29 then "WIG (future use)"
when 30 then "Fishing"
when 31 then "Towing"
when 32 then "Towing (large)"
when 33 then "Dredging/underwater ops"
when 34 then "Diving ops"
when 35 then "Military ops"
when 36 then "Sailing"
when 37 then "Pleasure craft"
when 38, 39 then "Reserved"
when 40 then "High Speed Craft"
when 41 then "HSC Hazardous category A"
when 42 then "HSC Hazardous category B"
when 43 then "HSC Hazardous category C"
when 44 then "HSC Hazardous category D"
when 45...48 then "HSC (reserved)"
when 49 then "HSC (no additional information)"
when 50 then "Pilot Vessel"
when 51 then "Search and Rescue Vessel"
when 52 then "Tug"
when 53 then "Port Tender"
when 54 then "Anti-pollution equipment"
when 55 then "Law Enforcement"
when 56, 57 then "Spare - Local Vessel"
when 58 then "Medical Transport"
when 59 then "Noncombatant ship according to RR Resolution No. 18"
when 60 then "Passenger"
when 61 then "Passenger, Hazardous category A"
when 62 then "Passenger, Hazardous category B"
when 63 then "Passenger, Hazardous category C"
when 64 then "Passenger, Hazardous category D"
when 65..68 then "Passenger, Reserved for future use"
when 69 then "Passenger, No additional information"
when 70 then "Cargo"
when 71 then "Cargo, Hazardous category A"
when 72 then "Cargo, Hazardous category B"
when 73 then "Cargo, Hazardous category C"
when 74 then "Cargo, Hazardous category D"
when 75..78 then "Cargo, Reserved for future use"
when 79 then "Cargo, No additional information"
when 80 then "Tanker"
when 81 then "Tanker, Hazardous category A"
when 82 then "Tanker, Hazardous category B"
when 83 then "Tanker, Hazardous category C"
when 84 then "Tanker, Hazardous category D"
when 85.88 then "Tanker, Reserved for future use"
when 89 then "Tanker, No additional information"
when 90 then "Other Type"
when 91 then "Other Type, Hazardous category A"
when 92 then "Other Type, Hazardous category B"
when 93 then "Other Type, Hazardous category C"
when 94 then "Other Type, Hazardous category D"
when 95..98 then "Other Type, Reserved for future use"
when 99 then "Other Type, no additional information"
end
end
# An MMSI is associated with an auxiliary craft when it is of the form 98XXXYYYY
def auxiliary_craft?
source_mmsi_info.category == :auxiliary_craft
end
# @param code [Integer] The navigational status id
# @return [String] Navigational status description
def get_navigational_status_description(code)
return nil if code.nil?
case code
when 0 then "Under way using engine"
when 1 then "At anchor"
when 2 then "Not under command"
when 3 then "Restricted manoeuverability"
when 4 then "Constrained by her draught"
when 5 then "Moored"
when 6 then "Aground"
when 7 then "Engaged in Fishing"
when 8 then "Under way sailing"
when 9...13 then "Reserved for future use"
when 14 then "AIS-SART active"
else
"Not defined"
end
end
end
# We haven't defined all the {NMEAPlus::Message::AIS::VDM#ais AIS payload} types, so this is a catch-all
class VDMMsgUndefined < VDMMsg; end
end
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,534 |
Racine police say driver in hit-and-run involving pregnant woman & young daughter IDENTIFIED
Racine police seek driver who hit pregnant woman, young daughter
RACINE (WITI) -- Racine police say a driver hit a pregnant woman and her toddler on Tuesday night, November 4th. Surveillance video shows the driver stopped initially, but then fled the scene. Police said late Wednesday they have been able to identify the driver with the public's help, but that driver hasn't yet been taken into custody.
The incident occurred around 6:00 p.m. at the intersection of Goold and N. Main Street in Racine.
Genie Webb
Police say 31-year-old Genie Webb, who was 38 weeks pregnant, and her three-year-old daughter were struck by the vehicle while they were walking in a crosswalk.
Following the crash, police say the driver made a left turn onto N. Main St. from Goold, stopped briefly and then fled the scene.
Webb was seriously injured. She was taken to the hospital, where an emergency C-section was performed to deliver the baby, who was listed in serious condition.
The three-year-old girl was thrown several feet and suffered minor injuries.
The boyfriend of the pregnant woman says he's been told both mom and baby are expected to survive.
"I`ve never in my life met someone as genuinely nice as she is, and it`s just sad something like this would happen to her," the woman's boyfriend, Daniel Mitchell said.
Mitchell says he feels somewhat responsible for what happened to his girlfriend.
"I talked her into voting yesterday, so I kinda take the blame in part because she didn`t plan on voting, actually," Mitchell said.
Mitchell says he was getting gas near Main and Goold. Webb had voted across the street, and was coming over to the gas station to meet him when she and her daughter were hit by the car.
Wisconsin bail reform proposal allows judges to tie cash to danger | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,587 |
La Ruta Nacional 32, oficialmente Carretera Braulio Carrillo en su trayecto de 64 kilómetros hasta la ciudad de Guápiles, es una ruta primaria intermontana de 127,2 kilómetros de extensión. Está ubicada entre San José (capital de Costa Rica) y Limón, principal ciudad y puerto comercial del país en el Mar Caribe. La Ruta 32 inició su construcción en 1978 y fue inaugurada el 28 de marzo de 1987.
Buena parte del recorrido inicial atraviesa el parque nacional Braulio Carrillo, por lo que cuenta con un gran atractivo escénico.
El tramo entre Guápiles y Limón de esta ruta, junto con la totalidad de la Ruta 4, conforman el Corredor Noratlántico, que comunica la costa caribeña con el cantón de La Cruz en la provincia de Guanacaste, recorriendo la zona norte del país.
Descripción
En la provincia de San José, la ruta atraviesa el cantón de Goicoechea (los distritos de San Francisco, Calle Blancos), el cantón de Vázquez de Coronado (el distrito de Dulce Nombre de Jesús), el cantón de Tibás (los distritos de San Juan, Anselmo Llorente), el cantón de Moravia (el distrito de San Jerónimo).
En la provincia de Heredia, la ruta atraviesa el cantón de Santo Domingo (los distritos de San Miguel, Pará), el cantón de San Isidro (el distrito de San José).
En la provincia de Limón, la ruta atraviesa el cantón de Limón (los distritos de Limón, Río Blanco), el cantón de Pococí (los distritos de Guápiles, Jiménez), el cantón de Siquirres (los distritos de Siquirres, Pacuarito, Germania, Cairo), el cantón de Matina (los distritos de Matina, Batán, Carrandi), el cantón de Guácimo (los distritos de Guácimo, Mercedes, Pocora).
Historia
El 28 de marzo de 1987 se inauguró oficialmente la Autopista Braulio Carrillo, que une San José con Limón, principal puerto caribeño de Costa Rica, desde donde entran y salen la mayoría de mercaderías al país. Fue la culminación de un viejo sueño acariciado desde los tiempos del Presidente Braulio Carrillo Colina quien en el siglo XIX ya había tratado de lograr una ruta hacia el Caribe cruzando la Cordillera Volcánica Central por el llamado Paso de La Palma, una zona selvática e inhóspita por donde entran los vientos nortes que refrescan el país en diciembre.
Esta ruta se denominó "Camino Carrillo" y salía de San José con un trazo paralelo a la actual autopista, por vados y montañas atravesando parte de los actuales cantones Goicoechea, Moravia y Vázquez de Coronado. Llegó a desarrollarse toda una población de hasta 600 personas en el Alto de La Palma y en el Bajo de la Hondura, lugar punta de lanza desde donde se construía la trocha. El esfuerzo sin embargo se vio truncado por miles de dificultades y falta de atractivo económico y la población disminuyó notablemente al no lograrse continuar la ruta. Hoy aun quedan algunas casas y lecherías en el Bajo de la Hondura, así como la antiquísima ermita del Alto de La Palma, ambas ubicadas a unos 20 y 17 kilómetros al norte de San José respectivamente.
El viejo sueño fue quedando guardado y con la construcción del Ferrocarril al Atlántico en 1890 y posteriormente las carreteras que iban a Limón atravesando Sarapiquí y Turrialba (que le dan un extenso giro a la Cordillera) fueron engavetando y restándole prioridad al viejo sueño de Carrillo. Seguía latente sin embargo la idea en el siglo XX, se especulaba que se podría construir aprovechando la ruta que atraviesa Vázquez de Coronado pasando por la ciudad San Isidro, Cascajal y Las Nubes, pero el terreno sumamente accidentado hizo desistir de tal trazado.
Ante la urgente necesidad de una ruta de acceso más rápida con la zona del Caribe, en el Gobierno de José Joaquin Trejos Fernández se inicia la carretera rústica a Limón, obra que se concluye en el Gobierno de Orlich, siendo Ministro de Obras Públicas y Transportes el Ingeniero Mario Quirós Sasso. A finales de la década de 1970 en el gobierno de Rodrigo Carazo se inició la construcción de la Carretera Braulio Carrillo, nombrada así en honor a su impulsor. Esta sale de Tournón, Goicoechea, a unos dos kilómetros del centro de San José, justo donde hoy se encuentra la sede del Diario La República. Desde este punto hasta el puente sobre el Río Virilla que marca límite entre las provincias San José y Heredia, tiene 4 carriles y zona central de drenaje.
A partir de dicho lugar, la vía tiene dos carriles en zonas planas y tres en áreas de ascenso, lo cual mantiene hasta llegar al cruce de la carretera a Sarapiquí en el punto llamado Río Frío.
En total la construcción de la también llamada Ruta 32, se dio entre 1979 y 1987 con un total de 42 kilómetros atravesando planicies y la Cordillera Volcánica Central por el actual Parque Nacional Braulio Carrillo. Disminuyó en 100 kilómetros el viaje hacia Puerto Limón descongestionando las sinuosas rutas de Sarapiquí y Turrialba, que en gran medida no son aptas para vehículos articulados.
Uno de los aspectos que más se le ha criticado es que se provocó mucha inestabilidad de taludes al cortar en 90 grados las elevaciones, lo cual combinado con el clima altamente lluvioso convirtió el área en zona de frecuentes derrumbes, así como el hecho de haber partido la selva en dos partes y crear conflicto con las especies nativas. Tiene un alto costo de mantenimiento y por ser de tan alto tránsito frecuentemente debe ser repintada, recarpeteada y equipada con ojos de gato para la espesa neblina imperante.
La Autopista Braulio Carrillo es una obra notable en sí misma por el gran esfuerzo que supuso realizarla. Hay sin embargo, algunas obras de la vía que destacan enormemente y que fueron en su momento parte de los grandes obstáculos que debieron enfrentar quienes se dieron a la titánica labor de construcción.
Características
Geografía
La carretera inicia su recorrido al noreste de la ciudad de San José, a una altitud promedio de 1,160 msnm, zona con una temperatura que oscila entre 15º y 28º C, hasta llegar a Siquirres a 62 msnm y un clima cálido y húmedo con una temperatura promedio de 25º C. La altitud máxima que recorre es de poco más de 1,600 msnm a la altura del cerro Hondura.
Las ciudades más importantes que cruza la ruta 32 son Guápiles y Siquirres. Esta última ciudad fue muy importante para el desarrollo del Ferrocarril al Atlántico durante el siglo XIX, época en la que no existían vías de comunicación de otro tipo; por ese motivo, resultaba de vital importancia construir una carretera. Otras poblaciones adyacentes con la vía son Pocora, Guácimo y Jiménez.
Un aspecto importante de esta vía es el que atraviesa el parque nacional Braulio Carrillo en al menos 40 km, uno de los parques más grandes de Costa Rica, con una extensión superior a las 44,099 hectáreas y que alberga siete hábitats diferentes. Cuenta con un clima muy húmedo, lo que caracteriza un bosque siempre verde. Esto hace del lugar un sitio especial para la observación y estudio de especies vegetales y animales.
En 1977 dio inicio la construcción de esta obra automovilística y un año después, para evitar la destrucción de una zona de configuración abrupta, de altas montañas, denso bosque, innumerables ríos y una admirable fauna, se creó este Parque Nacional, bajo decreto ejecutivo, gracias al esfuerzo de grupos conservacionistas.
En sus cercanías se aprecian algunas estribaciones del macizo del Volcán Barva: los cerros Cacho Negro y Zurquí, entre otros, también de origen volcánico. El cerro Hondura es atravesado por un túnel excavado.
En el trayecto por el parque nacional, la carretera encuentra diversos cursos de agua: el sector Quebrada González, que está ubicado a 2 km al este del puente sobre el río Sucio, con una altitud de 500 El del río Sucio es el último puente de importancia que se debió construir; arrastra en sus aguas minerales de origen volcánico, originando su característico color.
Condiciones técnicas
La carretera consta esencialmente de dos vías de 3,65 m de ancho cada una, de pavimento bituminoso mezclado en caliente en planta y espaldones de 1,5 a 2,2 m de ancho a cada lado, de tratamiento superficial bituminoso. En ciertos trayectos montañosos se construyó una tercera vía de ascenso de 3,05 m de ancho.
El proyecto se dividió en 6 secciones o etapas constructivas, para un total de 127,2 km:
Sección 1- Siquirres- Guácimo de 23,4 km
Sección 2- Guácimo- Río Patria 30,6 km
Sección 3. Río Patria-Mata de Café, 31,6 km
Sección 4, Mata de Café-Ruta 102, 12,7 km
Sección 5- Río Sucio-Puerto Viejo 28,9 km
Sección 6- Seis puentes mayores
Financiamiento de la obra
La carretera Braulio Carrillo se inició con un préstamo de $39 millones de dólares proveniente del Banco Mundial, e inicialmente se adjudicó a la compañía ecuatoriana Monolítica, la cual no logró cumplir con los objetivos firmados por razones económicas. Luego de varios años de labores y con buena parte del trayecto realizado, Monolítica se declaró en quiebra.
Esta situación representó un atraso de varios años en la finalización del proyecto vial, luego del finiquito y los consiguientes litigios judiciales. A pesar de estos inconvenientes, el Ministerio de Obras Públicas y Transportes (MOPT), siguió adelante con la carretera y las secciones que faltaban de construir fueron adjudicadas a compañías constructoras nacionales, las que culminaron el proyecto casi 9 años después de que se iniciara.
La obra total tuvo un costo final de ¢2541 millones de colones, incluyendo los ¢125 900 millones de colones asignados en la ley de presupuesto de 1987.
Obras notables
Puente sobre el río Virilla. También conocido a menudo como el "Puente del Saprissa" por su cercanía con el Estadio Ricardo Saprissa Aymá, en San Juan de Tibás. Es una estructura de puente viga de concreto con 4 pilotes. Tiene una longitud de 269 metros y una altura de más de 100 metros. El cañón marca el límite entre las provincias de San José y Heredia, específicamente entre los cantones de Tibás y Santo Domingo. Fue el primer obstáculo a vencer y a principios de la década de 1980 ya estaba concluido. En 2019, se empezó la construcción de un segundo puente sobre el río Virilla a tres carriles que serviría para descongestionar el tránsito en la zona. El puente nuevo circula en dirección Limón - San José, mientras que el puente ya existente lo hará en dirección San José - Limón. El 2 de septiembre de 2020 el segundo puente fue puesto en servicio.
Túnel Zurquí. Es un túnel de concreto a dos carriles, excavado para atravesar el Cerro Hondura, y fue construido por la empresa Kier Internacional Limited. Está ubicado en el cantón de Vázquez de Coronado, en el extremo norte de la provincia josefina. Es una de las obras de ingeniería costarricense más espectaculares: tiene 600 m de longitud, 12 de ancho y 10 metros de alto. Es el único túnel automovilístico del país.
Otras estructuras importantes son el puente sobre el río Sucio de 187 m de longitud, el puente sobre el río Chirripó de 430 metros y el puente sobre el río Toro Amarillo de 180 metros.
Véase también
Carreteras de Costa Rica
Anexo:Red Vial Nacional de Costa Rica
Referencias
Costa Rica. MOPT. "Proyecto San José-Guapiles-Siquirres". Revista Caminos, N° 4, Mar. 1987.
Costa Rica. MOPT. "La carretera San José-Siquirres: esbozo histórico". Revista Caminos, N° 7, jul-ago. 1987.
Costa Rica. MOPT. "Foto San José-Siquirres-Puerto Viejo". Mensaje, ene-feb., 1985.
Enlaces externos
crhoy.com: Noticias de la Ruta 32
Carretera es motor y prioridad para la economía costarricense
La Ruta 32, Carretera Nacional Braulio Carrillo
Estado de las rutas Policía de Tránsito
Ruta 32 en Wikimapia
Transporte de Costa Rica
Carreteras de Costa Rica | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,748 |
Oncocnemis viriditincta är en fjärilsart som beskrevs av Smith 1894. Oncocnemis viriditincta ingår i släktet Oncocnemis och familjen nattflyn. Inga underarter finns listade i Catalogue of Life.
Källor
Nattflyn
viriditincta | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 794 |
REC TOPPER: Forecasting the animal world
There is a lot of folklore and old wives' tales associated with animal and insect winter predictors. Maybe the most famous on a yearly basis is Punxsutawney Phil, the world-renowned groundhog prognosticator from north-central Pennsylvania.
AccuWeather.com meteorologists have weighed in with their forecast for this coming winter, but what about the forecasters from the animal world?
Here, courtesy of AccuWeather, is a closer look:
March of the insects
Some of the folklore surrounding a bad winter include ants and hornets building their nests higher than normal, an early migration of the Monarch butterfly, an increase of spiders weaving larger webs and going into homes in greater numbers and honeybees going into their hives sooner than usual.
Not so, said John R. Wallace, a biology professor at Millersville University of Pennsylvania and a member of the Pennsylvania Entomological Society.
"I think the upshot here is that there is plenty of lore and a paucity of data to assign any fragment of truth on these prognosticating 'wanna-bees,' pun intended," Wallace said.
Getting squirrelly
Squirrels have been associated with winter weather lore for their nut-gathering abilities ahead of wintry weather. The bushiness of squirrels' tails has also been believed to be a harbinger of a bad winter.
"I have not heard a story where squirrel tail bushiness or nest location is used to predict winter weather," said Carolyn Mahan, a biology professor at Penn State Altoona.
Rings of truth
Of all the animal and insect folklore, there is one species that stands out for having grains of truth. That is the woolly bear caterpillar.
According to Michael J. Raupp, an entomology professor at the University of Maryland, C.H. Curran, an entomologist from the American Museum in New York, collected data from 1948 through 1956 and compared those observations to the actual winter weather experienced. Other researchers have done similar projects, and predictions with up to 80 percent accuracy are reported, Raupp said.
The prognosticating prowess comes from the width of the caterpillar's band.
"A broad orange band equals a mild winter. A narrow band equals a harsh winter," Raupp said.
People can be mistaken into thinking there will be a harsh winter because they looked at the wrong caterpillar.
"There is a pure black woolly bear relative that is often confused with the banded woolly bear," Raupp said.
Related Topics: WEATHERWILDLIFE | {
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Żalinowo is a village in the administrative district of Gmina Inowrocław, within Inowrocław County, Kuyavian-Pomeranian Voivodeship, in north-central Poland. It lies approximately south-west of Inowrocław, south-west of Toruń, and south of Bydgoszcz.
References
Villages in Inowrocław County | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,438 |
{"url":"https:\/\/questioncove.com\/updates\/508c0379e4b077c2ef2ea2be","text":"OpenStudy (anonymous):\n\nIt is given that at the point $[x_0,y_0,z_0]$ the normal vector to the plane is $n= [p,r,s]$. You can deduce from this that the equation of the plane is $p(x-x_0)+r(y-y_0)+s(z-z_0) =0$ How?\n\n5 years ago\nOpenStudy (turingtest):\n\nI would walk you through this personally, but my connection sucks right now, so... http:\/\/tutorial.math.lamar.edu\/Classes\/CalcIII\/EqnsOfPlanes.aspx\n\n5 years ago\nOpenStudy (anonymous):\n\nthink of it as a dot product...\n\n5 years ago\nOpenStudy (anonymous):\n\n(x -xo), (y-yo) etc are the components of any vector in the plane....\n\n5 years ago\nOpenStudy (anonymous):\n\nif <p,r,s > dot < any vector in the plane>=0, then <p,r,s> is normal to the plane and defines the surface..\n\n5 years ago\nOpenStudy (anonymous):\n\nor the orientation of the surface, rather\n\n5 years ago\nOpenStudy (anonymous):\n\nYes, POMN says similarly. I think I've got the intuition, thanks both.\n\n5 years ago\nOpenStudy (anonymous):\n\nwhat's POMN?\n\n5 years ago\nOpenStudy (anonymous):\n\noh, Paul's online math notes... never mind:)\n\n5 years ago","date":"2017-11-22 19:55:40","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\": 0.7430737018585205, \"perplexity\": 6353.864435557998}, \"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-2017-47\/segments\/1510934806660.82\/warc\/CC-MAIN-20171122194844-20171122214844-00719.warc.gz\"}"} | null | null |
\section{#1}}
\def\ssa #1 {\ifhmode{\par}\fi\refstepcounter{subsection}
\noindent {\bf\thesubsection}. {\em #1}.\quad
\addcontentsline{toc}{subsection}{\protect\numberline{\thesubsection} #1}%
}
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\noindent {\bf\thesubsection.} {\em #1.}\quad
\addcontentsline{toc}{subsection}{\protect\numberline{\thesubsection} #1}%
}
\def\ifhmode{\par}\fi\refstepcounter{proposition {\ifhmode{\par}\fi\refstepcounter{proposition}
\noindent {\bf Proposition \thesection.\arabic{proposition}}. \quad}
\def\ifhmode{\par}\fi\refstepcounter{theorem {\ifhmode{\par}\fi\refstepcounter{theorem}
\noindent {\bf Theorem \thesection.\arabic{theorem}}. \quad}
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\noindent {\bf Lemma \thesection.\arabic{lemma}}. \quad}
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\noindent {\bf Definition \thesection.\arabic{definition}}. \quad}
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\noindent {\bf Remark \thesection.\arabic{remark}}. \quad}
\begin{document}
\hfill{\sl November 2006, Preprint UTM-706} \\
\par
\LARGE
\noindent
{\bf Some recent results in linear scalar quantum field
theory in globally hyperbolic asymptotically
flat spacetimes} \\
\par
\normalsize
\noindent
{\bf Valter Moretti} \\
\par
\small
\noindent Dipartimento di Matematica, Universit\`a di Trento,
and Istituto Nazionale di Alta Matematica ``F.Severi'' unit\`a locale di Trento,
and Istituto Nazionale di Fisica Nucleare Gruppo Collegato di Trento,\\ via Sommarive 14
I-38050 Povo (TN), Italy. \\
E-mail: moretti@science.unitn.it\\
\normalsize
\small
\noindent {\bf Abstract}. {
\noindent The content of this paper is that of an invited plenary talk at the
{\em XVII SIGRAV Conference held in Torino, September 4-7, 2006}.\\
Some recent results obtained by the author and
collaborators about QFT in asymptotically flat spacetimes at null infinity are reviewed.
In particular it is shown that bosonic QFT can be defined on the null boundary $\scri$ of any asymptotically
flat spacetime $M$. This theory admits a state $\lambda$ which is uniquely determined from invariance under
BMS group and a BMS-energy positivity requirement. There is a nice interplay with bosonic
(massless, conformally coupled)
QFT defined in the bulk spacetime. In particular, under suitable further requirements, the universal state $\lambda$ induces
in the bulk spacetime $M$ a state,
$\lambda_M$, which enjoys the following remarkable properties.
It reduces to standard Minkowski vacuum whenever $M$ is Minkowski spacetime and
in the general case, it is invariant under the group of isometries
of the spacetime $M$, it is a ground state (i.e. it satisfies the positive energy condition) with respect to any timelike Killing time of $M$
without zero-modes, finally $\lambda_M$ enjoys the global Hadamard property so that it is suitable for locally covariant
perturbative renormalization procedures.\\}
\section{Asymptotically Flat Spacetimes and $BMS$ group}
Asymptotically flat spacetimes -- by definition -- have a certain {\em asymptotic structure}.
The main motivation of the works in the references \cite{DMP,CMP5,last} has been investigating if that asymptotic structure
{\em determines canonically preferred states in every asymptotically flat spacetime} for (linear)
scalar quantum field theory. The properties of those states have been also focused.
Let us remind the main definition \cite{As80} (See \cite{Wald1} for further discussions and references).\\
\noindent {\bf Definition 1.} \label{sefasympt} ({\bf Asymptotically flat vacuum spacetime at future null infinity})
{\em A four dimensional spacetime $(M,g)$ is called {\bf asymptotically flat vacuum spacetime at future null infinity} if:\\
{\bf (a)} $(M,g)$ can be seen as an embedded submanifold of a larger spacetime $(\tilde{M},\tilde{g})$
with $\tilde{g}\spa\rest_M= \Omega^2 g$, $\Omega$ being a smooth function on $\tilde{M}$, strictly positive on $M$. \\
{\bf (b)} $\scri:= \partial M$, called {\bf future null infinity} of $M$, is a $3$-dim $\tilde {M}$-submanifold satisfying
(i) $\Omega\spa\rest_{\scri} =0$ but $d\Omega\spa\rest_{\scri} \neq 0$,
(ii) $\scri \cap \tilde{J}^-(M) = \emptyset$,
(iii) $\scri$ diffeomorphic to $\bS^2\times \bR$, and it is
union of the {\bf null} curves tangent to $n := \nabla \Omega$.
These curves are {\bf complete null geodesics} for a certain choice of $\Omega$.\\
{\bf (c)} About $\scri$, $(M,g)$ is strongly causal and satisfies $Ric(g) =0$.}\\
\noindent In fact $\scri$ is a $3$-dim. null submanifold of $\tilde{M}$
with {\em degenerate metric} $\tilde{h}$ induced by $\tilde{g}$.
$\scri$ is the {\em conic surface} indicated by $\:\mbox{I}^+\:$ in the figure.
The tip is {\em not} a point of $\tilde{M}$.
\begin{figure}[th]
\begin{center}
\includegraphics[scale=.7]{scri}
\end{center}
\caption{Asimptotically flat spacetime.}
\end{figure}
\noindent There are {\em gauge transformations} permitted by the definition: $\Omega \to \omega \Omega$ with
$\omega>0$ in a neighborhood of $\scri$,
$$
\scri \to \scri \:,\:\:\:\:\: \tilde{h} \to \omega^2 \tilde{h} \:,\:\:\:\:\: n \to \omega^{-1} n \:.
$$
For a fixed a.f. spacetime $(M,g)$, $C_{(M,g)}$ is the class of all triples $\{(\scri,\tilde{h}, n)\}$
connected by gauge transformations. $C_{(M,g)}$ encodes the whole geometric extent
of $\scri$.\\
It is important to stress that there is no physically preferred element of $C_{(M,g)}$ therefore
it is mathematical convenient to pass from
$\Omega$ to $\Omega_B = \omega_B \Omega$ such that $(\scri,\tilde{h}_B,n_B)$ reads
\begin{center}$\displaystyle \scri = \bR \times \bS^2\:, \quad \tilde{h}_B = d\theta \otimes d\theta +\sin^2\theta d\varphi \otimes d\varphi\:, \quad n_B = \frac{\partial \:\:}{\partial u}$\end{center}
in coordinates $u\in \bR$ (futuredirected), $(\theta,\varphi) \in \bS^2$. $(u,\theta,\varphi)$ is a
{\bf Bondi frame} on $\scri$.\\
Notice that if $(M_1,g_1) \neq (M_2,g_2)$, for a suitable choice of $(\scri_1,\tilde{h}_1, n_1)\in C_{(M_1,g_1)}$
and $(\scri_2,\tilde{h}_2, n_2)\in C_{(M_2,g_2)}$,
$\exists$ diffeomorphism $\gamma: \scri_1 \to \scri_2$ with
\begin{center}$\gamma(\scri_1) = \scri_2 \:,\:\:\:\:\: \gamma^* \tilde{h}_1=\tilde{h}_2 \:,\:\:\:\:\:\gamma^*
n_1=n_2$ \end{center}
In this sense the class $C=C_{(M,g)}$ is {\bf universal} for all a.f. spacetimes.\\
We have the following subsequent definition \cite{BMS70-80}:\\
\noindent{\bf Definition 2.} ({\bf Bondi-Metzner-Sachs (BMS) group}.)
{\em $G_{BMS}$ is the group of diffeomorphisms $\chi : \scri \to \scri$ preserving the universal structure of $\scri$, i.e. {\bf $\chi$ are isometries up to gauge transformations}:
$$\chi (\scri) = \scri\:, \quad \chi^*\tilde{h} = \omega^2_\chi \tilde{h}\:,\quad \chi^*n = \omega^{-1}_\chi n
\qquad \mbox{for some $\omega_\chi >0$.}$$}
\noindent Let us examine the structure of $G_{BMS}$. Fix a {\em Bondi frame} $(u,\varphi,\theta)$ on $\scri$
and pass to complex coordinates on the sphere $\bS^2$
$(u,\varphi,\theta) \leftrightarrow (u,\zeta,\overline{\zeta})$, with
$\zeta := e^{i\varphi}\cot(\theta/2) \in \bC \cup \{+\infty\}\:,$ the usual Riemann sphere.
In this framework $G_{BMS}$ has the structure of a semi-direct product,
$G_{BMS} = SO(3,1)\sp\uparrow \times C^\infty(\bS^2)$, where the group composition law is defined in this way:
\begin{eqnarray}
G_{BMS} &\ni& (\Lambda, f) : (u,\zeta,\overline{\zeta}) \mapsto (u',\zeta',\overline{\zeta}')\:, \nonumber \\
u' &:=& K_\Lambda(\zeta,\overline{\zeta})(u + f(\zeta,\overline{\zeta}))\:,\quad
\zeta' \:\::= \:\: \frac{a_\Lambda\zeta + b_\Lambda}{c_\Lambda\zeta +d_\Lambda}\:,\nonumber \\
K_\Lambda(\zeta,\overline{\zeta}) &:=& \frac{(1+\zeta\overline{\zeta})}{|a_\Lambda\zeta + b_\Lambda|^2 +|c_\Lambda\zeta +d_\Lambda|^2}
\label{K}\:\: \: \mbox{and}\:\:\:\:
\Pi \left[
\begin{array}{cc}
a_\Lambda & b_\Lambda\\
c_\Lambda & d_\Lambda
\end{array}
\right] = \Lambda \:.\nonumber
\end{eqnarray}
Above $SO(3,1)\sp\uparrow$ is the special orthochronous Poincar\'e group and $\Pi : SL(2,\bC) \to SO(3,1)\sp\uparrow$ is the standard covering homomorphism.\\
It is worth stressing that pairs of Bondi frames are connected by transformations of a subgroup of $G_{BMS}$.
Moreover notice that the decomposition $G_{BMS} = SO(3,1)\sp\uparrow \times C^\infty(\bS^2)$ depends on the used frame,
however the subgroup:
$$T^4 := \mbox{{real span of the first} {\bf $4$} {\bf spheric harmonics}} \subset C^\infty(\bS^2)$$
is a {\bf normal} $G_{BMS}$-subgroup. It is called the subgroup of {\bf $4$-translations}.
Thus $T^4$ is $BMS$-{\bf invariant}, i.e. {\bf independent} from used reference (Bondi) frames, and so it may
have physical interest. Another important fact is that there is a {\em Minkowskian decomposition}
$T^4 \ni \alpha = \displaystyle \sum_{\mu=0}^3 \alpha^\mu Y_\mu$
where $\{Y_\mu\}$ is a certain real basis of $T^4$. In this framework, if $\alpha,\alpha' \in T^4$
the {\em Minkowskian scalar product} $(\alpha,\alpha') := \sum_{\mu,\nu}\eta_{\mu\nu} \alpha^\mu {\alpha'}^\nu$ turns out to
be
$BMS$-{\bf invariant},
i.e. invariant under $\alpha \mapsto := g\circ \alpha \circ g^{-1}$, $g\in
G_{BMS}$ and $\alpha \in C^\infty(\bS^2)$. ($\eta = diag (-1,1,1,1)$.)\\
We conclude that there is a $BMS$-{\bf invariant} decomposition of $T^4$ and thus we have {\em spacelike, (fut./past. directed) timelike,
(fut./past. directed) null} $4$-translations. Time orientation is induced by that of $(M,g)$ (see \cite{last} for details.)\\
\noindent {\bf Remarks}.\\
{\bf (1)} A timelike future-directed {\bf direction} $\{\lambda \alpha\}_{\lambda\in \bR}$ in $T^4$
individuates a Bondi frame $(u,\zeta,\overline{\zeta})$ uniquely: that where the action of $\{\lambda \alpha\}_{\lambda\in \bR}$
is $u\mapsto u+\lambda$.\\
{\bf (2)} The orthochronous proper Poincar\'e group ${\cal P} :=SO(3,1)\sp\uparrow \times T^4$ is {\it not}
a normal subgroup of $G_{BMS}$, hence there is {\bf no} physical way
to pick out a preferred Poincar\'e subgroup of $G_{BMS}$. \\
{\bf (3)} It is known that $G_{BMS}$ {\em encodes the bulk symmetries of each fixed asymptotically
flat vacuum at null infinity spacetime $(M,g)$} as well as all the
{\em asymptotic symmetries} of all bulk spacetimes. Indeed
the following result holds true \cite{GerochAshtekarXanthopoulos80}.\\
\noindent {\bf Theorem 1.}
{\it Let $(M,g)$ be asymptotically flat vacuum at null infinity spacetime. The following holds.\\
{\bf (a)} If $\xi$ is a Killing vector field of the bulk $M$, then $\xi$
smoothly extends to a vector field $\tilde{\xi}$, different from the zero vector field and
tangent to $\scri$,
which generates a one-parameter subgroup of $G_{BMS}$.\\
{\bf (b)} In that way, the isometry group of $M$ is mapped {\bf into} a subgroup $G_M\subset G_{BMS}$ with:\\
\indent (i) $G_M$ is isomorphic to a subgroup of a certain Poincar\'e group
${\cal P}\subset G_{BMS}$ where ${\cal P}$ generally
{\em depends} on the particular spacetime $M$,\\
\indent (ii) only proper $4$-translations are admitted in $G_M \cap C^\infty(\bS^2)$.\\
{\bf (c)} $\tilde{\xi}$ generates an one-parameter subgroup of $G_{BMS}$, if and only if it smoothly extends back to a
field $\xi$ in $M$ with $\Omega^2 \pounds_\xi g \to 0$ smoothly approaching $\scri$.}\\
\noindent
The item (c) states, in fact, that $G_{BMS}$ contains the so called so-called {\bf asymptotic symmetries} of the physical
spacetime $M$ \cite{Wald1}.
The BMS group is the group of invariance of any physical theory defined on $\scri$: mathematical objects
defined on $\scri$ may have physical sense only if they are invariant under $G_{BMS}$.
\section{Weyl quantization on $\scri$ and interplay with QFT in the bulk: the state $\lambda_M$.}
In \cite{DMP} it has been established that it is possible to define a bosonic QFT for a field defined on $\scri$.
The approach is that algebraic based on Weyl quantization \cite{Wald}. The ingredients are the following ones.
A {\em real symplectic space}: $({\mathsf S}(\scri),\sigma)$, where $\sigma$ nondegenerate {\em symplectic form},
whereas the real vector space ${\ca S}(\scri)$ is defined as (for a fixed Bondi frame):
\begin{eqnarray} {\mathsf S}(\scri) := \left\{ \left.\psi \in C^\infty(\scri)\: \:\right|\:\: \psi\:, \partial_u
\psi \in L^2(\bR\times \bS^2, du \wedge \epsilon_{\bS^2}(\zeta,\overline{\zeta})) \right\}, \label{S}\end{eqnarray}
whereas the explicit form of $\sigma$ is the following:
\begin{eqnarray} \displaystyle \sigma(\psi_1,\psi_2) := \int_{\bR\times \bS^2}
\left(\psi_2 \frac{\partial\psi_1}{\partial u} -
\psi_1 \frac{\partial\psi_2}{\partial u}\right)
du \wedge \epsilon_{\bS^2}(\zeta,\overline{\zeta})\:, \label{sigma} \end{eqnarray}
where $\epsilon_{\bS^2}$ is the standard measure on a unit $2$-sphere.
There is a {\bf weighted representation of $G_{BMS}$}, $A_g : C^\infty(\scri) \to C^\infty(\scri)$,
$g\in G_{BMS}$, acting on the considered symplectic space:
\begin{eqnarray} (A_g\psi)(u,\zeta,\overline{\zeta}):=(K_\Lambda^{-1}\cdot \psi)(g^{-1}(u,\zeta,\overline{\zeta}))\:\:\: \mbox{(notice the weight
$K_\Lambda^{-1}$, $g= (\Lambda,f))$}\:. \label{A}\end{eqnarray}
Notice that $A_g\spa\rest_{{\mathsf S}(\scri)} \subset {\mathsf S}(\scri)$, moreover,
due to the weight $K_\Lambda^{-1}$, the $G_{BMS}$ representation $A$ {\em preserves} the symplectic form of $\sigma$,
so that, in particular, the mentioned structure does not depend on the used Bondi frame.
With those ingredients one defines the (unique)
{\bf Weyl $C^*$-algebra} ${\ca W}({\mathsf S}(\scri),\sigma)$ with generators $W(\psi)\neq 0$, $\psi \in {\mathsf S}(\scri)$, satisfying
Weyl relations (also known as {\bf CCR}):
$$ W(-\psi)= W(\psi)^*\:,\quad\quad W(\psi)W(\psi') = e^{i\sigma(\psi,\psi')/2} W(\psi+\psi')\:.
$$
Moreover the representation $A$ induces a {\em $*$-automorphism $G_{BMS}$-representation}
\begin{eqnarray} \alpha : {\ca W}({\mathsf S}(\scri),\sigma) \to {\ca W}({\mathsf S}(\scri),\sigma)\label{alpha} \end{eqnarray}
uniquely individuated by the requirement
$\alpha_g(W(\psi)):= W(A_{g^{-1}}\psi)$.\\
In order to find a possible physical meaning of the theory constructed above,
a natural question arises: Spacetime physics is BMS-invariant so,
{\em are there BMS-invariant (quasifree) algebraic states on ${\ca W}({\mathsf S}(\scri),\sigma)$?}\\
An answer has been found in \cite{DMP}. There it has demonstrated that, in fact, there is a (quasifree pure)
$BMS$-invariant state. Let us summarize this result.
Consider the quasifree pure state $\lambda$ on ${\ca W}({\mathsf S}(\scri),\sigma)$ uniquely induced by linearity and continuity from:
\begin{eqnarray} \lambda(W(\psi)) = e^{-\mu_\lambda(\psi,\psi)/2}\:,\quad \mu_\lambda(\psi_1,\psi_2):= -i \sigma(\overline{\psi_{1+}},\psi_{2+})\:,
\quad\psi \in {\mathsf S}(\scri)\:, \label{lambda} \end{eqnarray}
where $\psi_+$ is the {\em positive $u$-frequency part} of $\psi$, with respect to any (arbitrarily fixed) Bondi frame
defined on $\scri$. The positive frequency part is obtained performing the usual Fourier transform with respect to the
variable $u$ considered as a ``time'' coordinate (see \cite{DMP} for details).
Then we pass to focus on the GNS representation $(\gH_\lambda, \Pi_\lambda, \Upsilon_\lambda)$. It turns out that the Hilbert
space
$\gH_\lambda$ is a bosonic Fock space ${\ca F}_+({\ca H})$ with $1$-particle Hilbert space
${\ca H} \equiv L^2(\bR^+\times \bS^2; dE \otimes \epsilon_{\bS^2})\quad$ (containing $u$-Fourier transforms $\widehat{\psi}_+ $),
the GNS Cyclic vector is the Fock vacuum $\Upsilon_\lambda$.
Since the GNS representation is a Fock representation, $\lambda$ is a regular state and
{\em symplectically-smeared} field operators $\Psi(\psi)$ with
$\Pi_\lambda(W(\psi)) = e^{-i\overline{\Psi(\psi)}}$ can be defined using Stone theorem directly (see e.g. \cite{Wald} for the
general theory).\\
In this context we have the following theorem established in \cite{DMP}.\\
\noindent {\bf Theorem 2.}
{\it Referring to the Weyl algebra ${\ca W}({\mathsf S}(\scri),\sigma)$,
its GNS representation $(\gH_\lambda, \Pi_\lambda, \Upsilon_\lambda)$, the BMS representation $\alpha$ (\ref{alpha}),
and the state $\lambda$ (\ref{lambda}), the following facts are valid.\\
{\bf (\bf a)} $\lambda$ is {\bf $G_{BMS}$-invariant}: $\lambda(\alpha_g(a)) = \lambda(a)$ if
$g\in G_{BMS}$ and $a\in {\ca W}({\mathsf S}(\scri),\sigma)$.\\
{\bf (\bf b)} The unique unitary representation of $G_{BMS}$
leaving $\Upsilon_{\lambda}$ invariant (that is $U_g \Upsilon_\lambda = \Upsilon_\lambda$) and implementing $\alpha$
(i.e. $U_g \Pi_\lambda(a) U^*_g = \Pi_\lambda(\alpha_g(a))$) is that induced by:
\begin{eqnarray} \left(U_{(\Lambda,f)}\widehat{\psi}_+\right)(E,\zeta,\overline{\zeta}) =
\frac{e^{iE K_{\Lambda}(\Lambda^{-1}(\zeta,\overline{\zeta}))f(\Lambda^{-1}(\zeta,\overline{\zeta}))}}{
\sqrt{K_{\Lambda}(\Lambda^{-1}(\zeta,\overline{\zeta}))}}
\widehat{\psi}_+\left(E K_{\Lambda}\left(\Lambda^{-1}(\zeta,\overline{\zeta})\right),\Lambda^{-1}(\zeta,\overline{\zeta})\right) \:.
\label{U}\end{eqnarray}
$\widehat{\psi}_+$ being the positive-frequency part of $\psi\in {\mathsf S}(\scri)$ in Fourier representation ($E$ being
the conjugate variable with $u$).\\
{\bf (\bf c)} Making $G_{BMS}$ topological
equipping $C^\infty(\bS^{2}) \subset G_{BMS}$ with test-function Fr\'echet topology, consider the representation
$G_{BMS} \ni g \mapsto U_g$, then one has:
(i) it is {\em irreducible and strongly continuous},
(ii) it is a {\em Wigner-Mackey-like representation} associated with a scalar representation of the
little group, $\Delta \subset SL(2,\bC)$, the double covering of the $2D$
Euclidean group,
(iii) it is defined on an orbit in space of characters $\chi$ with $m^2_{BMS}(\chi) = 0$. }\\
\noindent To make a comment to (c) we stress that
the Abelian $G_{BMS}$-subgroup $C^\infty(\bS^2)$ is {\it infinite dimensional and non-locally-compact},
but
Mackey machinery {\it works anyway} as proved in \cite{McCarthyPRSL}.
Moreover, concerning (iii) notice that the characters, $\chi_\beta$,
are labeled by distributions (here ${\ca D}'(\bS^2)$ is the dual space of $C_0^\infty(\bS^2)$)
$\beta \in {\ca D}'(\bS^2)$, $\chi_\beta(\alpha) = e^{i\beta(\alpha)}$,
$\forall \alpha \in C^\infty(\bS^2)$. Therefore, in the space of characters can be defined a {\em BMS-invariant mass}:
$m^2_{BMS}(\beta) := -\eta^{\mu\nu}\beta(Y_\mu)\beta(Y_\nu)$ which turns out to be invariant with respect to
the dual action $(g(\beta))(\alpha) := \beta(g(\alpha))$, $\forall g\in G_{BMS}$. This is a notion of mass
which is {\em a priori} independent from that invariant under the action of Poincar\'e group.
Now a question arises naturally: {\em Is there any relation with massless particles propagating
in the bulk spacetime?}
The answer is positive as established in \cite{DMP}: the fields $\psi$ on $\scri$ are ``extensions''
of linear, massless, conformally coupled fields
in the bulk spacetime and the action of symmetries on the fields in the bulk is
equivalent to the action of $G_{BMS}$ on the
associated fields on $\scri$.\\
\noindent {\bf Theorem 3.}
{\it Let $(M,g)$ be an asymptotically flat vacuum at future null infinity spacetime with associated unphysical spacetime
$(\tilde{M},\tilde{g}= \Omega^2 g)$. Assume that both $M,\tilde{M}$ are {\em globally hyperbolic}. Consider Weyl QFT in $(M,g)$
based on the symplectic space $({\ca S}(M),\sigma_M)$. ${\ca S}(M)$ is the space of real
smooth, compactly supported on Cauchy surfaces, solutions $\phi$ of massless, conformally-coupled, K-G equation\\
$$\displaystyle \Box \phi - \frac{1}{6} R \phi =0\quad \mbox{in $M$.}$$
with isometry-invariant symplectic form:\\
$$\sigma_M(\phi_1,\phi_2) := \int_\Sigma \left(\phi_2 \nabla_N \phi_1 - \phi_1 \nabla_N \phi_2\right)\:
d\mu^{(S)}_g\:,$$ $\Sigma$ being any
Cauchy surface of $M$. Then:\\
{\bf (a)} $\phi$ vanishes approaching $\scri$ but $\Omega_B^{-1}\phi$ extends to a smooth field $\psi := \Gamma\phi$
on $\scri$ uniquely, $\Gamma$ being linear.\\
{\bf (b)} If $\{g_t\}$ is a $1$-parameter group of $M$-isometries and $\{g'_t\}$ the associated $G_{BMS}$-subgroup:
the action of $\{g_t\}$ on $\phi$ ($\phi \mapsto \alpha_{g_t}(\phi) := \phi \circ g_{-t}$) is equivalent to the action of
$A_{g'_t}$ on $\psi = \Gamma\phi$,
\begin{center} $\displaystyle A_{g'_t}(\psi) = \Gamma(\alpha_{g_t}(\phi))
\quad \mbox{if $\quad\psi = \Gamma\phi$}$\:.\end{center}}
\noindent {\bf Remark}. The more usual point of view in considering QFT in globally hyperbolic spacetimes $(M,g)$
is that based on field operators $\Phi(f)$ smeared with smooth compactly supported functions $f\in C_0^\infty(M)$, instead of
with solutions of Klein-Gordon equation of ${\ca S}(M)$. Actually the two points of view, for linear theories, are {\em completely equivalent},
see \cite{Wald} for instance. If $\phi \in {\mathsf S}(M)$, the Weyl generators $W(\phi)$ are to be formally understood
as $W(\phi):= e^{-i\sigma_M(\Phi,\phi)}$, where $\sigma_M(\Phi,\psi)$ is the {\bf field operator symplectically smeared} with elements of $ {\mathsf S}(M)$.
In this context, it turns out that $\Phi(f):= \sigma_M(\Phi,Ef)$ where $E = A-R : C^\infty_0(M) \to {\ca S}(M)$ is the
{\bf causal propagator} (or ``advanced-minus retarded'' fundamental solution) of Klein-Gordon operator \cite{Wald}.\\
\noindent To go on, assume that furthermore $\Gamma : {\mathsf S}(M) \to {\mathsf S}(\scri)$ is an {\em injective
symplectomorphism} i.e.
(H1) $Range [\Gamma] \subset {\mathsf S}(\scri)\qquad$
(H2) $\sigma_\scri(\Gamma
\phi_1,\Gamma \phi_2) = \sigma_M (\phi_1,\phi_2)$.\\
In this case one finds that {\it the field observables of the bulk $M$
can be identified with observables of the boundary $\scri$}.
More precisely \cite{DMP}: $\exists !$ a (isometric) $*$-homomorphism from the Weyl algebra ${\ca W}({\mathsf S}(M), \sigma_M)$
of field observables of the bulk, to the Weyl-algebra ${\ca W}({\mathsf S}(\scri), \sigma)$:
$$\imath_\Gamma: {\ca W}({\mathsf S}(M),\sigma_M) \to {\ca W}({\mathsf S}(\scri),\sigma)$$ determined by the requirement on Weyl generators:
$$\imath_\Gamma(W_M(\phi)) = W_{\scri}(\Gamma \phi)\:.$$
As a consequence of the existence of the $*$-homomorphism $\imath_\Gamma$, one may induce a preferred state
$\lambda_M$ on the observables in the bulk $M$ form the natural state $\lambda$ defined on the observables
on the boundary $\scri$. In other words,
{\it the boundary state $\lambda$ can be pulled back to a quasifree state $\lambda_M$
acting on observables for the field $\phi$ propagating in the bulk spacetime $M$}:
\begin{equation}\lambda_M(a):= \lambda(\imath_\Gamma(a))\quad \mbox{for all $a\in {\ca W}({\mathsf S}(M), \sigma_M)$} \label{lambdaM}
\end{equation}
In \cite{DMP} it has been shown that
If $(M,g)$ is Minkowski spacetime (so that $(\tilde{M},\tilde{g})$ is Einstein closed universe), hypotheses
{\bf H1} and {\bf H2} are fulfilled so that $\imath_M$ {\em exists} and {\em $\lambda_M$ coincides with Minkowski vacuum}.
This is not the only case. To illustrate it we recall an important notion.
Let $(M,g)$ be an asymptotically flat vacuum at future null infinity spacetime. One says that it
admits {\bf future time infinity} $i^+$ if $\exists i^+ \in \tilde{M} \cap I^+(M)\:\:\:$ ($i^+ \not \in \scri$)
such that the geometric extent of $\scri \cup \{i^+\}$ about $i^+$ ``is the same as
that in a region about the tip $i^+$ of a light cone in a (curved) spacetime''. The rigorous definition has been given by
Friedrich \cite{Friedrich}.
\begin{figure}[th]
\begin{center}
\includegraphics[scale=.7]{scri-i}
\end{center}
\caption{Asimptotically flat spacetime with future time infinity $i^+$.}
\end{figure}
We stress that there are lots of Einstein eq.s solutions admitting $i^+$ as established by Friedrich
(actually he considered the past time infinity $i^-$, but the extend is completely symmetric).
With this notion we may state the following result \cite{CMP5} whose proof
is based on fine estimations of the behaviour about $i^+$ of $\Gamma \phi$.
The difficult point is to show that $Range [\Gamma] \subset {\mathsf S}(\scri)$.
Then, barring technicalities, $\sigma(\Gamma \phi_1,\Gamma \phi_2) = \sigma_M (\phi_1,\phi_2)$
is a consequence of divergence theorem.\\
\noindent{\bf Theorem 4.} {\it If $(M,g)$ is asymptotically flat at future null infinity, $(M,g)$ and $(\tilde{M},\tilde{g})$
are both globally hyperbolic and $(M,g)$
admits future time infinity $i^+$, then hypotheses {\bf H1} and {\bf H2} are fulfilled
so that $\imath_M$ {\bf exists} and
$\lambda_M$ {\bf can be induced in the bulk form the $BMS$-invariant state on $\scri$},
$\lambda$.}
\section{Uniqueness of $\lambda$ and remarkable properties of $\lambda_M$.}
The state $\lambda$ is {\em universal}: it does not depend on the particular bulk
spacetime $M$, but it induces a preferred state $\lambda_M$ on the observables in the bulk
in any considered asymptotically flat spacetime
(provided that relevant hypotheses on asymptotic flatness and existence of $i^+$ be fulfilled).
Let us investigate some properties of $\lambda$ and $\lambda_M$ \cite{CMP5,last}.\\
\noindent {\bf Theorem 5}.
{\it Assume that hypotheses (H1) and (H2) hold for the globally hyperbolic a.f. spacetime $(M,g)$
(with $(\tilde{M},\tilde{g})$ globally hyperbolic as well)
so that
the state $\lambda_M$ exists.\\
{\bf (a)} $\lambda_M$ is {\bf invariant under} under the (unit component Lie) group of isometries of $M$, $\{g_t\}$.\\
{\bf (b)} If the Killing generator $\xi$ of $\{g_t\}$ is {\bf timelike and future directed}, then the associated
unitary $1$-parameter group in the $GNS$ representation of $\lambda_M$ {\bf admits positive self-adjoint generator}
and in the one-particle space there are no zero modes for that generator.}\\
\noindent {\bf Comments on the proofs.}\\
(a) Let $\{ \beta_{g_t}\}$ and $\{\beta_{g'_t}\}$ be, respectively,
the groups of $*$-automorphisms induced by $\{g_t\}$ and $\{g'_t\}\subset G_{BMS}$, acting on bulk
and boundary observables $a \in {\ca W}(M,\sigma_M)$, $b \in {\ca W}(\scri,\sigma)$
respectively. The action of $\{\beta_{g_t}\}$ on $\lambda_M$ is equivalent to
the action of $\{\beta_{g'_t}\}$ on $\lambda$ and $\lambda$ is $G_{BMS}$-invariant. Therefore:
$\lambda_M(\beta_{g_t}(a)) = \lambda(\beta_{g'_t}(\Gamma(a))) =
\lambda(\Gamma(a)) = \lambda_M(a)$.\\
(b) If the Killing generator of $\{g_t\}$ is {\it timelike and future directed} then $\{g'_t\} \subset G_{BMS}$
is generated by a single {\it causal, future directed} $4$-translation of $T^4$. Then
passing to GNS Hilbert spaces, using $\{U_{(\Lambda,\alpha)}\}$,
one sees, by direct inspection, that $\{U_{\beta_{g'_t}}\}$ has {\it positive self-adjoint generator}.
The analog holds in the GNS representation of $\lambda_M$.\\
Positivity of self-adjoint generators of timelike future-directed $4$-translation of $T^4$
holds true also for $\lambda$.
It is a remnant of {\bf energy positivity condition} in the bulk.
Positivity condition on energy is a stability requirement: it guarantees that, under small (external) perturbations, the system
does not collapse to lower and lower energy states.
Actually positive energy condition determines uniquely $\lambda$.
In fact the subsequent result is valid \cite{CMP5,last}.\\
\noindent {\bf Theorem 6}.
{\em In the hypotheses of theorem 5, fix a timelike future-directed
$4$-translation in $T^4$ and let $\{g_t\}$ be the generated $1$-parameter $G_{BMS}$-subgroup. Under those hypotheses
the following facts are true.\\
{\bf (a)} If $\omega$ is a pure quasifree algebraic state on ${\ca W}({\mathsf S}(\scri), \sigma)$ satisfying both:\\
\indent (i) it is invariant under $\{g_t\}$,\\
\indent (ii)$\{g_t\}$ admits positive self-adjoint generator in the GNS representation of $\omega$,\\
then $\omega$ must be {\bf invariant} under the {\bf whole} BMS group and $\omega$ must {\bf coincide} with $\lambda$.\\
{\bf (b)} If $\omega$ is a pure (not necessarily quasifree) algebraic state on ${\ca W}({\mathsf S}(\scri), \sigma)$ and it is
invariant under $\{g_t\}$, the folium of $\omega$ cannot contain other
$\{g_t\}$-invariant states.}\\
\noindent {\bf Comments on the proofs.}\\
(a) consequence of {\em cluster property}:
$\lim_{t\to +\infty} \omega(a\beta_{g_t}(b)) \to \omega(a)\omega(b)$, $\forall a,b \in {\ca W}({\mathsf S}(\scri), \sigma)$
valid for a $\{g_t\}$-invariant pure state, and a uniqueness results by B.S.Kay
\cite{KayJMP79}. \\
(b) consequence of
of {\em weak asymptotic commutativity} valid for a $\{\beta_{g_t}\}$-invariant pure state $\omega$:\\
$\mbox{w-}\lim_{t\to +\infty} \left[U(g_t)AU(g_t)^*, B \right] =0$,
$\forall A\in \Pi_\omega({\ca W}({\mathsf S}(\scri), \sigma))$,
$B\in \gB(\gH_\omega)$.
\section{The Hadamard property.} Does $\lambda_M$ satisfy the {\em Hadamard property}?
if the answer is positive, $\lambda_M$ is a good starting point for generally covariant and local renormalization procedure,
in particular it determines a well-behaved renormalized stress-energy tensor
\cite{KW,hadamard}. Let $\omega$ be a regular state on ${\ca W}(M,\sigma_M)$. Let us denote by
$\omega(x,y)$ the integral kernel of the two-point function of the state $\omega$:
\begin{center} $\omega(\Phi(f)\Phi(g)) = \omega(Ef,Eg)$ \end{center}
where $\Phi(f)$ is the standard {\em field-operator} smeared with a test function $f\in C^\infty_0(M) $,
$E = A-R : C^\infty_0(M) \to {\ca S}(M)$ being the
{\em causal propagator} (or ``advanced-minus retarded'' fundamental solution) of Klein-Gordon operator \cite{Wald}.
The {\bf global Hadamard property} states that in normal geodesically convex
neighborhoods of every point of the spacetime:
\begin{center} $\omega(x,y) = \Delta(x,y)\sigma(x,y)^{-1} + v(x,y) \ln \sigma(x,y) + \mbox{regular function}$ \end{center}
where $\sigma(x,y)$ is the squared geodesic distance and $\Delta$, $v$ depend on the local geometry only.
The {\bf global Hadamard property}
is similar, but it involves the (complicated) behaviour of the two-point function in a neighborhood of a Cauchy surface of $M$
\cite{KW}. This is a condition {\em very} difficult to check directly for $\omega = \lambda_M$!\\
Radzikowski found out a micro-local characterization of the (global) Hadamard condition \cite{Rad}:
{\em If} $\omega \in {\ca D}'(M\times M)$, that is if $\omega$ is a distribution on $M\times M$ thus satisfying continuity
with respect to the relevant seminorm topologies,
the global Hadamard property is {\bf equivalent} to a specific shape of {\em wave front set} of $\omega$, $WF(\omega)$.
More precisely $WF(\omega)$ is made of the elements
$(x,{\bf p}_x,y,-{\bf p}_y) \in T^*(M\times M) \setminus 0$
such that:\\
(1) ${\bf p}_x$ is future directed and \\
(2) there is a null geodesic from $x$ to $y$ having there cotangent vectors
${\bf p}_x$ and $-{\bf p}_y$ respectively.)\\
Using Radzikowski framework as far as the item (b) has been concerned, the following final result has been recently obtained \cite{last}.\\
\noindent {\bf Theorem}. {\em Assume the hypotheses of theorem 5. The following facts are true.\\
{\bf (a)} $\lambda_M \in {\ca D}'(M\times M)$ also if there are
bad compositions of distributions (${\mathsf S}(\scri)$ nonstandard space of test functions).\\
{\bf (b)} $\lambda_M$ is globally Hadamard on $M$.} \\
\noindent {\bf Comments on the proof.}\\
The proof of (b) has been performed establishing first the validity of the local Hadamard condition. Then
the global Hadamard property has be reached using a ``local-to-global'' argument
introduced by Radzikowski in the second paper in \cite{Rad}.
\section{Final comments.}
The unique, positive energy, $BMS$-invariant, quasifree, pure state $\lambda$
is completely defined using the universal structure of the class of asymptotically flat
vacuum spacetimes at null infinity, no reference to any particular spacetime is necessary.
In this sense $\lambda$ is {\bf universal}.
On the other hand $\lambda$ induces a well-behaved quasifree state $\lambda_M$ in each asymptotically flat spacetime
$M$ admitting $i^+$.
$\lambda_M$ is quite natural: it coincides with Minkowski vacuum when $M$ is Minkowski spacetime, $\lambda_M$ it is invariant under
every isometry of $M$ and fulfills the requirement of energy positivity with respect to every
timelike Killing field in $M$.
$\lambda_M$ may have the natural interpretation of {\bf outgoing scattering vacuum}.
Finally $\lambda_M$ has been showed to verify the Hadamard condition and therefore
it may be used as background
for perturbative procedures (renormalization in particular), and it provides a natural notion of massless
particle also in absence of Poincar\'e symmetry but in the presence of asymptotic flatness.
Indeed all the construction works for {\em massless} fields (with conformal coupling).
What about {\em massive} fields?\\
How to connect bulk massive fields to $BMS$-massive fields on $\scri$
and to known unitary representations of $G_{BMS}$ with $m_{BMS} >0$? \cite{AD}.
This is an open issue which deserves future investigation
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,199 |
Q: Ansible: Task structure of roles I have 4 playbooks. 2 of them are deploying services on my target machines and 2 of them are removing them again.
Now I want to put them in roles. But I'm not sure what the best-practice is.
The 2 deploy playbooks are doing the exact same thing only with different variables and templates. Same applies to the remove playbooks.
Atm my structure looks like this:
ansible.cfg
ssh_key
inventoryfile
group_vars
....
roles
deployservicegroupA
vars
...
templates
...
tasks
main.yml (this file simply includes the two tasks right below)
copy-service-templates.yml
start-services.yml
deployservicegroupB
vars
...
templates
...
tasks
main.yml (this file simply includes the two tasks right below)
copy-service-templates.yml
start-services.yml
removeservicegroupA
vars
...
templates
...
tasks
main.yml (this file simply includes the two tasks right below)
remove-services.yml
cleanup.yml
removeservicegroupB
vars
...
templates
...
tasks
main.yml (this file simply includes the two tasks right below)
remove-services.yml
cleanup.yml
Is this they way it was intended to be done by users?
I'm especially wondering about my tasks that do the exact same thing, but can be found in different roles. And also if I should include my tasks in the main.yml task file.
A: As per your comment you are using a group for each service, you can use group_vars to specify the variables you want to use.
You can then merge the roles together, the only thing you will have to do is load specific templates based on the group you are running your play on.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,767 |
Jennifer Nettles Releases 'Hey Heartbreak' Video
(Radio.com) Country singer Jennifer Nettles has released a new music video for the song "Hey Heartbreak". The track comes from her sophomore album Playing with Fire.
The sunny video finds Nettles "breaking up with heartbreak" because she's ready to start living her life again. Shot along the California coast, Nettles enjoys the beautiful weather by strolling along the beach, lounging in a sun-filled hotel room and going out to eat by herself.
Directed by Shane Drake, the video plays on all the motifs typically associated with couples and romance, and instead finds Nettles enjoys those moments solo. "The whole idea here is that she is letting go of a heartbreak," Drake stated in a press release. "She's letting go of all the things that make you feel down -- make you feel constricted. We decided to take positive approach towards ourselves, where Jennifer can have Santa Barbara to recharge and re-energize." Watch the video here.
Jennifer Nettles Music, DVDs, Books and more
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More Jennifer Nettles News
� Jennifer Nettles Releases 'Hey Heartbreak' Video
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� Jennifer Nettles Announces Second Album 'Playing with Fire'
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Jennifer Nettles Music | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,122 |
\section{Introduction}
After the discovery of the Higgs boson by the ATLAS and CMS
collaborations~\cite{ATLAS,CMS}, much attention has been given to the
measurement of the properties of this particle. In principle,
accurate measurements of the Higgs properties can tell us
whether the corresponding Higgs field is the sole source of mass
for quarks, leptons, and gauge bosons, and whether there
are new particles that also receive mass from this field. The
report \cite{Higgsworking} for the 2013 Snowmass Community
Summer Study reviews the
current status of measurements of the Higgs boson couplings
and projections of the capabilities of future collider programs.
However accurately the couplings of the Higgs boson are
measured, though, these measurements are useful only if
combined with comparably accurate predictions from the
Standard Model (SM). New physics associated with the
Higgs boson appears as deviations from the SM
predictions. The report \cite{Higgsworking} gives
many examples of new physics effects that alter the
Higgs boson couplings at the few-percent level. The
discovery of these effects will require both the measurements and
theory of these couplings
to have uncertainties below the percent level. If deviations cannot be discerned because of
intrinsic uncertainty in the the theoretical predictions, the goal of
the program of precision measurements on the Higgs
boson will be frustrated.
In particular, the proposed experiments at the
International Linear Collider have demonstrated the
capability of measuring individual Higgs boson couplings
in a model-independent way
to the level of parts per mil~\cite{ILCHiggs,myILCHiggs}.
This seems to us an important goal, but it is
only important if the
SM predictions for Higgs boson couplings can be
given with similar accuracy.
Currently, the partial widths of the Higgs boson within
the SM are generally agreed to be predicted to accuracies of a few percent.
This situation is summarized in the work of the
LHC Higgs Cross Section Working Group~\cite{HiggsBRs,HiggsBRstoo}
and in a recent paper by Almeida, Lee, Pokorski, and
Wells~\cite{WellsHiggsBRs}. This latter paper
presents a significant challenge:
\begin{quote}
``... the SM uncertainty in computing $B(H\to b\bar b)$ is
presently 3.1\% (sum of absolute values of all errors) and expected to
not get better than 2.2\%, with most of that coming from the
uncertainty of the bottom Yukawa coupling determination ... Thus,
without a higher-order calculation to substantially reduce this error,
any new physics contribution to the $b\bar b$ branching fraction
that is not at least a factor of two or three
larger than 2\% cannot be discerned. Thus, a deviation of
at least 5\% is required of detectable new physics.''~\cite{WellsHiggsBRs}
\end{quote}
We agree with the general conclusions of
\cite{HiggsBRs,HiggsBRstoo,WellsHiggsBRs}
as far as the current situation is concerned, and
we will often refer to these useful papers in our
analysis below. However, we believe that the quote in the
previous paragraph, which applies the current uncertainties
to experiments that will be done a decade from now and
draws pessimistic conclusions, is seriously misleading.
Most importantly,
it underestimates the power of lattice QCD to
give us precision knowledge of the $b$ quark mass and
of its renormalization to the Higgs boson mass scale.
We will argue here that the SM predictions for the
Higgs boson partial width to $b\bar b$, and for the
other dominant decay modes, will be improved to the
parts-per-mil level on a time scale that matches the
needs of the High-Luminosity LHC and ILC experimental
programs.
This paper is organized as follows: In Section 2, we
develop basic notation for our study of Higgs partial
width uncertainties. In Section 3, we review perturbative
computations of the partial widths to the dominant SM
decay modes and the uncertainties that they imply. Our conclusion
is that it is within the current state of the art to reduce the
uncertainties from missing terms in perturbation theory to the
parts-per-mil level. For many of the Higgs boson partial widths, this
is already achieved.
In Section 4, we discuss the determination
of the most important
input parameters --- $\alpha_s$
and the $b$ and $c$ quark masses ---
from lattice gauge theory. Data from lattice QCD simulations can be used to
determine the QCD parameters in several different ways. The most
straightforward method to describe is to compute the spectrum of
heavy-quark mesons, adjust the parameters of the lattice action to
fit the measurements, and then convert these parameters to
a continuum definition (for example, \MSbar\ subtraction). This
method is typically limited by the accuracy of existing lattice QCD
perturbation theory calculations. An alternative and more promising
method is to use lattice simulations to predict continuum quantities
such as QCD sum rules that can be readily interpreted
using
continuum QCD calculations. It is worth noting that
almost all of the
highest-precision determinations of $\alpha_s$ and many of the
highest-precision determinations of $b$ and $c$ mass reported by the
Particle Data Group~\cite{PDG} use this strategy.
In Section 4, we illustrate this
approach with the lattice calculation of the moments of $b$ and $c$
quark pseudoscalar current correlation functions. These correlation
functions were used in \cite{McN} to provide measurements
of $\alpha_s$, $m_b$ and $m_c$ with accuracy at the current state
of the art. Using toy Monte
Carlo calculations, we estimate how much the uncertainties computed
in \cite{McN} could be decreased
over the next decade using the increased computer resources
that should become available over this time.
Section 5 gives our conclusions.
\section{Structure of Higgs boson partial widths}
In this paper, we will quote uncertainties using the
Higgs boson partial widths. Our common coin will be
the relative theoretical uncertainty $\delta_A$ on the extracted coupling of
the Higgs boson to $A\bar A$, which
we will take uniformly to be $\frac{1}{2}$ of the uncertainty on the
the corresponding partial width.
\begin{equation}
\delta_A = \frac{1}{2} {\Delta \Gamma(h\to A\bar A)\over \Gamma(h\to
A\bar A)} .
\eeq{defDelta}
For definiteness,
we set the Higgs boson mass to $m_h = 126.0$~GeV
throughout this paper.
More generally in this paper, we will use the symbol $\Delta$ to denote an absolute
uncertainty on a measurable quantity, and $\delta$ to denote the
relative uncertainty,
\begin{equation}
\delta X = {\Delta X\over X} \ .
\eeq{defsmdelta}
In this notation, $\delta_A = \frac{1}{2} \delta \Gamma(h\to A\bar A)$.
There are two contributions to the $\delta_A$. The first
is
the {\it theoretical error} due to the fact that the perturbation
theory
is computed only up to a certain order. As we will see, theoretical
errors for the $\delta_A$ are, in almost all cases, already at the
few parts-per-mil level. The second is the {\it parametric error}
due to the uncertainties of needed input parameters. These
parametric errors will have most of our attention in the paper.
In
\cite{HiggsBRs} and \cite{WellsHiggsBRs},
uncertainties are quoted for the prediction of Higgs branching
ratios. We prefer to work with partial widths, because these
are more primitive objects. Branching ratios are composites
that depend on all of the partial widths, through
\begin{equation}
BR(h\to A\bar A) = {\Gamma(h\to A\bar A)\over \sum_C \Gamma(h\to
C\bar C)} \ ,
\eeq{BRcomp}
where the sum over $C$ runs over all decay modes.
This can potentially lead to some confusion.
For example, in Table IV of \cite{HiggsBRs}, the
authors quote an uncertainty of 2\% in the branching ratios
$BR(h\to \tau^+\tau^-)$ and $BR(h \to WW^*)$ for a 120 GeV Higgs
boson due to parametric
dependence on the $b$ quark mass. This comes entirely from the
dependence on $\Gamma(h\to b\bar b)$ in the denominator of
\leqn{BRcomp} and has nothing to do with the Higgs couplings to
$\tau^+\tau^-$ or $WW$. This impression is rectified in the
presentation in Table 1 of \cite{HiggsBRstoo}.
We note that the complete program
of Higgs boson measurements planned for the ILC allows the
absolutely normalized partial widths to be extracted in a
model-independent
way~\cite{ILCHiggs}.
A Higgs boson partial width typically has the structure
\begin{equation}
\Gamma(h\to A\bar A) = {G_F\over \sqrt{2}} {m_h m_A^2 \over
4\pi} \cdot {\cal F}
\eeq{GHstruct}
where ${\cal F}$ is a scalar function of coupling constants and mass ratios.
The
factor $m_A^2$ arises from the fact that the Higgs coupling to
$A\bar A$ is proportional to $m_A$. It is often the case that the dominant
contribution to the parametric uncertainty in $\Gamma(H\to A\bar A)$
comes from this term.
The contributions to $\delta_A$
from the first two terms of the prefactor are
\begin{Eqnarray}
\delta_A &=& \frac{1}{2} \delta G_F \oplus \frac{1}{2} \delta m_h
\nonumber \\
& = & (3\times 10^{-7}) \oplus (1.2\times 10^{-4}) \ ,
\eeqa{DeltaApref}
where the first term uses the current uncertainty~\cite{PDG} and
the second term assumes a Higgs boson mass measurement with an
uncertainty of 30~MeV, as expected at the ILC~\cite{ILCHiggs}. The
dependence
on the Higgs mass is larger in the $h\to gg, \gamma\gamma, \gamma Z$
partial widths, which are proportional to $m_h^3$. However, it is
only
non-negligible for the partial
widths to $WW^*$ and $ZZ^*$, which depend strongly on the available
phase space. The uncertainty in \leqn{DeltaApref}
coming from $m_A$ depends on the particle species in question. For
$\tau$, $W$, and $Z$, there are well-defined on-shell values
which
are known quite accurately~\cite{PDG}:
\begin{equation}
\delta m_\tau = 9\times 10^{-5} \qquad
\delta m_W = 1.9\times10^{-4} \qquad \delta m_Z =
2.3\times 10^{-5} \ .
\eeq{Deltams}
These estimates give the impression, which is also correct in the
complete
theory, that the uncertainties in Higgs couplings due to the
uncertainties in
these input parameters are negligible.
For quark and gluon final states, the situation is quite different.
Well-defined on-shell states are not theoretically accessible, and so
we must rely on QCD perturbation theory, which potentially
brings in sizable parametric uncertainties.
QCD perturbation theory
is best behaved if one
evaluates
Higgs partial widths using the
\MSbar\ mass evaluated at the Higgs boson mass scale.
However, the masses of the quarks are usually
quoted at a much lower scale, either as the perturbative pole masses or
as the \MSbar\ masses at
scale near the quark threshold. The conversion of these mass values
to \MSbar\ masses at $m_h$ is often a dominant uncertainty in
the prediction of the Higgs boson couplings.
QCD sum rules measure off-shell quark masses at momenta of the order
of $2m_Q$. The Higgs boson couplings are obtained most accurately
by directly extrapolating these values to $m_h$. We will use the
\MSbar\ masses $m_b$(10.0 GeV) and $m_c$(3.0 GeV) as our
basic inputs. The conversion of a
mass value at $2m_Q$ to a pole mass brings in a substantial
QCD uncertainty,
and there is an additional uncertainty in converting the pole mass
back
to an \MSbar\ value at $m_h$. The papers
\cite{HiggsBRs,HiggsBRstoo,WellsHiggsBRs} use the pole masses as
inputs.
This leads to a stronger dependence on the input mass and $\alpha_s$
values than what we quote below and, consequently, an overestimate
of the uncertainty.
The QCD theory of the evolution of
mass parameters is nicely reviewed by Che\-tyr\-kin, K\"uhn, and
Steinhauser in \cite{RunDec}, with a computer code {\tt RunDec}
implementing
their prescriptions with terms up to NNNLO also provided.
The uncertainty
in the conversion from low scale masses to $m_Q(m_h)$ due to the
truncation of perturbation theory is small: for example,
the NNNLO terms
in the series give a relative correction of $0.8\times 10^{-4}$. In
the following, and in our later discussion of QCD effects,
\begin{equation}
a(\mu) = {\alpha_s^{\overbar{MS}}(\mu)\over \pi}
\eeq{adefin}
Using the notation of \cite{RunDec},
the parametric uncertainties in $m_b(m_h)$ are proportional to the
derivatives
\begin{Eqnarray}
{m_b(10) \over m_b(m_h)} { d m_b(m_h)\over d m_b(10)} &=& 1 \nonumber \\
{\alpha_s(m_Z)\over m_b(m_h)} { d m_b(m_h)\over d \alpha_s(m_Z)} &=&
a(m_Z)\cdot {\gamma_m(a(m_h)) -
\gamma_m(a(10))\over
\beta(a(m_Z))} = -0.38 \ .
\eeqa{mbconvert}
The numerical values are computed using 5-flavor running and the
current PDG value $\alpha_s(m_Z) = 0.1185$. Note that the derivative in the first line is
reduced by taking a fixed renormalization point of 10.0~GeV for $m_b$ rather than
one that depends on $m_b$. If we took $m_b(m_b)$ as a reference,
this coefficient would be 1.19; for the pole mass, this coefficient is
1.28.
We will also need the conversion factor
\begin{equation}
{\alpha_s(m_Z)\over \alpha_s(m_h)}{ d \alpha_s(m_h)\over d
\alpha_s(m_Z)} = {\alpha_s(m_Z)\over \alpha_s(m_h)} {\beta(a(m_h))\over
\beta(a(m_Z))} = 0.95 \ .
\eeq{alphaconvert}
For the input variable $m_c$(3), we need to take into account
4-flavor running between $m_b$ and the reference point. The bulk
of the effect is accounted in
\begin{Eqnarray}
{\alpha_s(m_Z)\over m_c(m_h)} { d m_c(m_h)\over d \alpha_s(m_Z)} & =&
\nonumber \\
& & \hskip -1.3in a(m_Z)\cdot {\gamma_m(a(m_h)) -
\gamma_m(a(m_b)) + \gamma^{(4)}_m(a^{(4)}(m_b)) -
\gamma^{(4)}_m(a^{(4)}(3))\over
\beta(a(m_Z))} = -0.91 \ .
\eeqa{mcconvert}
There is also a small dependence of
$m_c(m_h)$ on the position of the matching point $m_b$, given
approximately by
\begin{equation}
{m_b(m_b)\over m_c(m_h)} {d m_c(m_h)\over d m_b(m_b)} =
2 (\gamma_m(a(m_b)) - \gamma^{(4)}_m(a^{(4)}(m_b))) = 0.004 \ .
\eeq{mcgap}
Finally, there are tiny discontinuities between the 5-flavor
and 4-flavor formulae that sightly change the dependences given in
these two equations. We quote the final result in \leqn{mbmcsumm}.
In all, we find that the term $m_Q^2$ in \leqn{GHstruct}, for the
cases of $Q = b$ or $c$, gives a
contribution to the uncertainty from the parametric dependence
on quark masses and on $\alpha_s$. This dependence is
given by
\begin{Eqnarray}
\delta m_b(m_h) &=& 1.0 \cdot \delta m_b(10)
\oplus (-0.38) \cdot \delta \alpha_s(m_Z) \nonumber \\
\delta m_c(m_h) &=& 1.0 \cdot \delta m_c(3) \oplus(- 0.90)
\cdot \delta \alpha_s(m_Z)
\oplus ( 0.006)\cdot \delta m_b(10) \ .
\eeqa{mbmcsumm}
The coefficients in this expression are of order 1, so it is already
clear that very accurate
values
of the parameters on the right-hand side are needed to predict Higgs
partial widths to part-per-mil accuracy.
\section{Perturbation theory for Higgs boson partial widths}
With the orientation given in the previous section, we now review the
status of perturbative computations of the partial width for the major
decay modes of the SM Higgs boson. A detailed overview of SM Higgs
decay modes is given in Djouadi's review paper~\cite{Djouadi}.
That discussion has been updated
in \cite{HiggsBRstoo,WellsHiggsBRs}. In particular, Table~3 of
\cite{WellsHiggsBRs} gives the parametric dependence of the
predictions
for the full set of input parameters. However, since we are using a
different scheme of inputs,we must revisit the
dependence on the most important parameters $m_b$, $m_c$, and
$\alpha_s$.
\subsection{$h\to b\bar b$}
The corrections to the partial width $\Gamma(h\to b\bar b)$ can be
grouped as (i) QCD corrections to the correlation function of scalar
currents $b\bar b$, (ii) additional QCD corrections involving flavor
singlet intermediate states, (iii) electroweak corrections and mixed
QCD/electroweak corrections. All terms are proportional to
$m_b^2(m_h)$. The dominant corrections are of the type (i).
The corrections of type (i) are known to ${\cal O}(\alpha_s^4)$
through
a very impressive calculation of Baikov, Chetyrkin, and
K\"uhn~\cite{BCK}. They evaluate to
\begin{Eqnarray}
\tilde R &=& 1 + 5.667 a + 29.15 a^2 + 41.76 a^3 -
825.7 a^4 \nonumber \\
&=& 1 + 0.2037 + 0.0377 + 0.0019 -0.0013 \ ,
\eeqa{BCKresult}
so that the series seems to be converging, with a residual error at the
part-per-mil level in $\delta_b$~\cite{Wang}. The parametric dependence of
\leqn{BCKresult} on $\alpha_s$ is obtained as
\begin{equation}
\frac{\alpha_s(m_h)}{\tilde R}
{d\over d\alpha_s(m_h)} \tilde R = 0.22
\eeq{BCKparam}
This must be combined with the dependence of the prefactor given
in \leqn{mbmcsumm}.
The
corrections (ii) begin in ${\cal O}(a^2)$, are known to ${\cal
O}(a^3)$,
and are less than 1\%
corrections to $\delta\Gamma_b$~\cite{Kwiat,ChStein}.
For the corrections of type (iii),
the complete ${\cal O}(\alpha)$ result is
known~\cite{Bardin,Kniehlbb,Dabelstein}, but at the 2-loop level
only the leading terms of ${\cal O}( \alpha a
m_t^2/m_h^2)$~\cite{Kwiattb,KniehlSpira}
and ${\cal O}( \alpha^2
m_t^4/m_h^4)$~\cite{Buttenschorn} have been computed.
Numerically, these three terms are, respectively,
\begin{equation}
{\delta\Gamma} = 0.3\% - 0.02\% + 0.05\%
\eeq{numbb}
Thus, the theoretical understanding of this decay is already
close to the part-per-mil level in $\delta_b$. The parametric
dependence on the most important parameters is
\begin{equation}
\delta_b = 1. \cdot \delta m_b(10) \oplus (- 0.28) \cdot \delta
\alpha_s(m_Z) \ .
\eeq{finalforb}
In~\cite{myILCHiggs}, it was estimated that the $hb\bar b$ coupling
would be measured to 0.3\% at the ILC in its late stages.
\subsection{$h\to c\bar c$}
The theoretical calculation of the partial width
$\Gamma(h\to c\bar c)$ is essentially
the same as that for $h \to b\bar b$. In
particular,
the qualitative picture that the theory is close to part-per-mil
accuracy continues to hold. The parametric uncertainty, combining
\leqn{mbmcsumm} and \leqn{BCKparam}, is
\begin{equation}
\delta_c = 1. \cdot \delta m_c(3) \oplus( - 0.80) \cdot \delta
\alpha_s(m_Z) \ .
\eeq{finalforc}
In~\cite{myILCHiggs}, it was estimated that the $hc\bar c$ coupling
would be measured to 0.7\% at the ILC in its late stages.
\subsection{$h\to\tau^+\tau^-$}
The theoretical calculation of the partial width
$\Gamma(h\to\tau^+\tau^-)$ is very similar to
that for $h \to b\bar b$, except that there are no
QCD corrections except for universal ones. We see no
issue here in obtaining a precise SM prediction.
In~\cite{myILCHiggs}, it was estimated that the $h\tau^+\tau^-$
coupling
would be measured to 0.7\% at the ILC in its late stages.
\subsection{$h\to gg$}
The theoretical prediction for the partial width $\Gamma(h\to gg)$
begins in ${\cal O}(a^2)$. The series of QCD corrections has been
computed to ${\cal O}(a^4)$ by Schreck and Steinhauser~\cite{SStein},
with each term given as a series in $\tau = m_h^2/4m_t^2$. Baikov and
Chetyrkin~\cite{BC} and Moch and Vogt~\cite{MV} have also obtained
the leading term at ${\cal O}(a^5)$. If $\Gamma_0$ is the
leading-order
result for $m_t \gg m_h$, the series evaluates to
\begin{Eqnarray}
{\Gamma\over \Gamma_0} &=& 1.0671 + 19.306 a + 172.76 a^2 + 467.68 a^3\nonumber \\
&=& 1.0671 + 0.6942 + 0.2234 + 0.0217
\eeqa{ggseries}
The parametric dependence of
\leqn{ggseries} on $\alpha_s$ is obtained as
\begin{equation}
{ \alpha_s(m_h)\over \Gamma } {d\over d\alpha_s(m_h)} \Gamma = 2.6
\eeq{SSparam}
There is also an electroweak correction of $+5\%$, known only to the
leading order (which is already ${\cal O}(\alpha a^2)$), computed by
Actis, Passarino, Sturm, and Uccirati~\cite{Actis}. At the 1\%
level, some final states produced by the $hgg$ coupling contain
$b\bar b$ due to gluon splitting. It should be clarified through
simulation
to what extent these final states will be classified by the
experiments
as $h\to b\bar b$ rather
than
$h\to gg$ decays.
We find that the uncertainty from theory in the prediction of the $hgg$ coupling is
now at the 1\% level. This situation is improvable, although computing
additional orders of perturbation theory will be challenging.
The important parametric dependence of the SM prediction is
\begin{equation}
\delta_g = 1.2 \cdot \delta \alpha_s(m_Z) \ .
\eeq{finalforg}
In~\cite{myILCHiggs}, it was estimated that the $hgg$
coupling
would be measured to 0.6\% at the ILC in its late stages.
\subsection{$h\to \gamma\gamma$}
For $\Gamma(h\to \gamma\gamma)$, the leading term
is ${\cal O}(\alpha^2)$. The electroweak correction
of order ${\cal O}(\alpha^2)$. has been computed by
Passarino, Sturm, and Uccirati~\cite{Pass}, and the QCD
corrections of ${\cal O}(\alpha\alpha_s^2)$ and
${\cal O}(\alpha\alpha_s^3)$ have
been computed by Maierh\"ofer and Marquard~\cite{MandM}.
The relative sizes of the corrections are, respectively,
\begin{equation}
- 1.6\% + 1.8\% + 0.08\% \ .
\eeq{finalforgamma}
The uncertainty in the prediction of the $h\gamma\gamma$
coupling is, then, at the parts-per-mil level, and there is no
significant parametric uncertainty.
In~\cite{myILCHiggs}, it was estimated that the $h\gamma\gamma$
coupling
would eventually
be measured to 0.8\% using a combination of LHC and ILC
results.
\subsection{$h\to WW^*$, $h\to ZZ^*$}
The situation for the decays $h\to WW^*$ and $h\to ZZ^*$ is somewhat
more complicated, and beyond the scope of this paper to explain in
full. The decay involves color-singlet particles in leading order,
so the radiative corrections are at the percent level. The complete
${\cal O}(\alpha_s)$ and ${\cal O}(\alpha)$ corrections have been
computed by Bredenstein, Denner, Dittmaier, and Weber~\cite{Breden}.
These authors find corrections of, for example, 1\% for $h\to
e^+e^- \mu^+\mu^-$, 3\% for $h \to \nu_e e^+ \mu^-\bar\nu_\mu$,
7\% for $h \to \nu_e e^+ q\bar q$, and 10\% for $h\to q\bar q q \bar
q$. Quite consistently, the difference between the full radiative
corrections
and those of the Improved Born Approximation (IBA), in which the two
off-shell vector bosons are treated separately, is 1\%. Additional
corrections to the IBA are known, including corrections of
${\cal O}(\alpha a m_t^2/m_h^2)$, ${\cal O}(\alpha a^2 m_t^2/m_h^2)$,
and ${\cal O}(\alpha^2 m_t^4/m_h^4)$. These corrections are reviewed
in \cite{Veretin}; they bring the calculation of this approximation to
the part-per-mil level. A full 2-loop analysis without the IBA
approximation
will be more
difficult.
These partial widths have no important parametric uncertainty due to
$\alpha_s$ or $m_b$, but they do depend strongly on the mass of the
Higgs boson. From \cite{WellsHiggsBRs} (based on \cite{Breden}),
\begin{equation}
\delta_W = 6.9 \cdot \delta m_h\ , \quad
\delta_Z = 7.7\cdot \delta m_h \ .
\eeq{WZparam}
That is, a
measurement of the Higgs boson mass to 30~MeV precision would lead
to a 0.2\% theoretical uncertainty in these partial widths.
In~\cite{myILCHiggs}, it was estimated that the $hWW$ and $hZZ$
couplings would each be measured to 0.2\% at the ILC in its late
stages.
It seems within the state of the art for theory to match this level
of accuracy, though it will be a challenge.
\section{Improved parameters from lattice QCD}
One of the implications of the previous section is that the SM
predictions
for several of the Higgs boson partial widths depend strongly
on $\alpha_s$, $m_b$, $m_c$, and $\alpha_s$. The current values of
these parameters are
\begin{Eqnarray}
\alpha_s(m_Z) &=& 0.1185 \pm 0.0006 \qquad\quad\ (\pm 0.5\%)\nonumber \\
m_b(10) &=& 3.617 \pm 0.025~\mbox{GeV} \qquad \quad (\pm 0.7\%) \nonumber \\
m_c(3) & = & 0.986 \pm 0.006~\mbox{GeV} \qquad (\pm 0.6\%)
\eeqa{currentparams}
The first of line of \leqn{currentparams} is the current Particle Data Group
value~\cite{PDG}. The second and third lines are lattice gauge
theory determinations, from \cite{McN}. These are consistent with
the PDG averages, with a slightly larger error for $m_b$ and a
somewhat smaller error for $m_c$. Using the values in
\leqn{currentparams},
assuming that the errors are uncorrelated and that it is
correct to combine errors in quadrature, we find the parametric components of the
uncertainty in Higgs coupling predictions to be
\begin{equation}
\delta_b = 0.7\% \ , \quad \delta_c = 0.7\% \ , \quad \delta_g = 0.6\% \ .
\eeq{currentdelta}
This is already quite impressive accuracy, but the future program of
precision Higgs measurements will require that we do better.
In the rest of this section we will describe how one uses lattice QCD (LQCD) to
extract the $\overline{\mathrm{MS}}$~coupling and masses. We will
illustrate these ideas with a simple example, and use that example
to explore what improvements will be possible over the next decade.
Finally we will briefly survey other approaches from LQCD that
are likely to contribute over that period.
\subsection{Lattice QCD}
In LQCD, continuous
space and time are replaced by a discrete mesh
of lattice sites with a lattice spacing~$a$ that is typically of
order 0.15\,fm or less. The path integral
describing QCD becomes an ordinary multidimensional integral
in this approximation, with the lattice functioning as
the ultraviolet regulator. Lattice simulations integrate the
path integral numerically, using Monte Carlo methods, to
obtain Monte Carlo estimates for vacuum expectation values
of a wide variety of operators from which physics is extracted.
Having chosen a value for the bare coupling, the first step
in an LQCD simulation is to tune the bare quark masses and the
lattice spacing to values that reproduce physical results from
the real world.
The masses are typically adjusted to reproduce
experimental results for particular, well-measured hadron masses:
for example, $m_\pi$, $m_K$, $m_{\eta_c}$, and $m_{\eta_b}$. The
lattice spacing is set using some other well-measured
quantity, such as the pion decay constant~$f_\pi$. Once one
has tuned
these parameters, renormalized matrix elements
from a LQCD simulation will
agree with the corresponding matrix elements from
continuum QCD up to errors
of $\mathcal{O}(a^2)$. Simulations are generally performed at
multiple values of~$a^2$ and results extrapolated to~$a=0$.
The quark masses and the QCD coupling constant are specified quite accurately
by the tuning process, but they are defined for the lattice
regulator, not the \MSbar\ regulator typically used in
continuum calculations. In principle, bare
lattice masses and couplings can be converted
into~$\overline{\mathrm{MS}}$ quantities using perturbation
theory\---\,see, for example, \cite{Lee:2013mla}
and~\cite{Davies:2008sw}. In practice, however,
the precision of this approach has been limited by the
difficulty involved in calculating the conversion formulae,
which require high-order perturbative calculations using
the (very complicated) lattice regulator.
A different approach that has proven quite successful is to use
lattice simulations to generate nonperturbative values for
renormalized short-distance quantities, such as matrix
elements of current-current correlators at short distances.
Renormalized quantities are regulator independent, and
therefore values obtained from LQCD simulations can be
analyzed using ordinary continuum~\MSbar\
perturbation theory once they have been extrapolated
to zero lattice spacing. Such analyses can be used
to extract values for the~\MSbar\
coupling and masses in the same way that values are
extracted from experimental data.
\subsection{An example}
One quantity that can be used to compute
all three of our important input parameters $m_b$, $m_c$ and~$\alpha_s$
is the current-current correlator
\begin{equation}
G(t) \equiv a^3 \sum_{\mathbf{x}} m_{0Q}^2
\langle 0 | j_{5Q}(\mathbf{x},t)\,j_{5Q}(0,0) | 0 \rangle
\eeq{Gdefin}
where $j_{5Q} \equiv \overline{\psi}_Q\gamma_5\psi_Q$
is the pseudoscalar density for a heavy quark~$Q$
(either~$c$
or~$b$)~\cite{McN}.
This correlator is a close relative of the vector current-current correlators, which may be
obtained from $e^+e^-$ heavy-quark production. The data for
these
vector correlators, analyzed with continuum perturbation theory,
currently provide the most precise determinations of the heavy
quark masses~\cite{Chetyrkin:2009fv}.
We consider only the connected correlator, where both
currents are on the same quark line, since this simplifies both
the lattice simulation and the continuum analysis. The factors
of the LQCD bare quark mass~$m_{0Q}$ in \leqn{Gdefin} make $G(t)$ ultraviolet
finite. Then the lattice and continuum versions are
equal up to finite-lattice spacing corrections:
\begin{equation}
G_\mathrm{cont}(t) = G_\mathrm{lat}(t) + \mathcal{O}(a^2).
\eeq{close}
Low-$n$ moments of $G(t)$,
\begin{equation}
G_{2n} \equiv a\sum_t t^{2n} G(t)
= (-1)^n \frac{\partial^{2n}}{\partial E^{2n}}G(E=0),
\eeq{moments}
are perturbative,
since the energy $E=0$ at which they are evaluated is far below
the threshold $E\approx2m_Q$
for heavy quarks.
Moments with $2n\ge4$ are ultraviolet finite. Consequently,
in perturbation theory, we obtain
\begin{equation}
G_{2n} =
\frac{g_{2n}(\alpha_{\overline{\mathrm{MS}}}(\mu))}{m_Q(\mu)^{2n-4}}
\eeq{Gtwon}
where $\mu$ is the renormalization scale and
$g_{2n}(\alpha_{\overline{\mathrm{MS}}})$
is a perturbation series known through third order for $2n = 4$, 6, 8,
and 10~\cite{Chetyrkin:2006xg,Boughezal:2006px,Maier:2008he,Maier:2009fz,Kiyo:2009gb}. The scale $\mu$ should
be taken close to $2m_Q$ to avoid large logarithms. One then adjusts the
values of the
\MSbar\ coupling and quark masses so that the
(continuum) perturbative expressions agree
with the nonperturbative values for the moments $G_{2n}$ generated by LQCD.
A detailed LQCD analysis of correlator moments is given in~\cite{McN}.
It replaces the moments $G_{2n}$ by reduced moments~$R_{2n}$ in order
to suppress systematic errors caused by the simulation; statistical
errors
from the Monte Carlo are insignificant. The values obtained for
$m_c(3\,\mathrm{GeV})$ and $\alpha_{\overline{\mathrm{MS}}}(M_Z)$ are
accurate to 0.6\%, while $m_b(10\,\mathrm{GeV})$ is accurate to 0.7\%.
The dominant source of uncertainty in the first two quantities is the
lack
of $4^\mathrm{th}$-order perturbation theory. The dominant error in
$m_b(10\,\mathrm{GeV})$ comes from the finite lattice spacing, which
matters more for the $b$~quark because of its larger mass.
An LQCD simulation offers several advantages over experiment as
a source for nonperturbative results, beyond the obvious fact
that it is easier to instrument a simulation than an experiment.
For example, we can produce results not only for $m_Q=m_c$ and
$m_Q=m_b$, but also for several quark masses in between~$m_c$
and~$m_b$. This allows us to vary the value of
$\alpha_{\overline{\mathrm{MS}}}(\mu)$, since $\mu \sim 2m_Q$,
and therefore to use the simulation data to estimate and bound
perturbative corrections beyond third order. The result is a much
more reliable estimate of the perturbative errors than comes from the
standard procedure of replacing $\mu$ by~$\mu/2$ and~$2\mu$.
Varying the quark mass also allows us to probe and fit the
leading nonperturbative behavior, from the gluon condensate.
The Operator Product Expansion implies that
\begin{equation}
G_{2n} = G_{2n}^\mathrm{short-distance}
\left\{
1 + d_{2n}(\alpha_{\overline{\mathrm{MS}}})
\frac{\langle \alpha_s G^2/\pi\rangle}{(2m_Q)^4} + \cdots
\right\}
\end{equation}
In practice the condensate correction turns out
to be negligible compared to other
uncertainties, because it is suppressed by $1/(2m_Q)^4$.
LQCD simulations also allow us for the first time to determine
ratios of quark masses nonperturbatively~\cite{McN,Davies:2009ih}.
These ratios, which can be determined quite accurately,
provide a highly non-trivial check on values obtained from
perturbative methods, and can be used to leverage a precise
determination of one mass into precise determinations of other
masses.
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{cluster-cost}
\caption{ \label{Fig:cpucost}
Measured cost per megaflop of lattice QCD computing on the
USQCD cluster facilities at Fermilab and Jefferson Lab, plotted versus year.
The exponentially improving price/performance of conventional cluster
hardware (blue crosses) that was observed through
2011 has fallen off somewhat in the last few years.
This has been mitigated by the introduction, where possible, of GPU-accelerated clusters
(magenta circles) for lattice calculations.}
\end{figure}
\subsection{Projections}
The LQCD analysis described above has yielded the heavy quark
masses and the QCD coupling constant with precisions that are already
below 1\%.
A detailed study of those results shows that the most important
limiting factors are the lack of higher-order perturbation
theory ($4^\mathrm{th}$-order) and the finite lattice
spacing~\cite{McN}.
Both sources of error can potentially be reduced. It seems
feasible, given time, to compute the next term in perturbation theory
for the correlator moment, bringing these to $4^\mathrm{th}$~order in
$\alpha_s$.
The extent to which
the lattice spacing can be reduced depends upon further
reductions in the cost of computing. Figure~\ref{Fig:cpucost}
shows that computing costs have fallen by roughly a factor of~100
since~2005 at the USQCD facilities at Fermilab and Jefferson Lab. Similar reductions
are expected over the next 10--15~years. Simulation costs
scale
roughly as $1/a^6$, and so we expect
that the smallest lattice space used for this simulation could be
reduced by about a factor of two, from 0.045\,fm used in \cite{McN} to
0.023\,fm.
There are more issues to face, beyond securing adequate
hardware, if one wishes to achieve per-mil accuracy in LQCD simulations.
Some, like the inclusion of isospin violation and electromagnetic corrections,
we expect will be straightforward.
It is possible that some may prove greater challenges.
For example,
topological structure in the
gauge field develops more slowly in simulations at smaller
lattice spacing, which may pose problems at very small
lattice spacing.
Such issues might require new ideas, but
the tremendous advances in LQCD over the past decade make us
optimistic that any new obstacles
will be overcome during the next 10--15~years.
The existing lattice analysis can be used to predict the impact
of these improvements in the order of perturbation
theory and the size of the lattice spacing
on the precision with which we can determine
the coupling constant and masses from the correlator
moments. The current analysis compares results from
multiple lattice spacings in order
to determine the dependence of LQCD results on
the lattice spacing. This allows us to
extrapolate existing results to smaller lattice spacings.
By adding realistic noise to these extrapolations,
we create synthetic data for smaller lattice
spacings that can be combined with
existing LQCD data in a new analysis of the
masses and coupling. The results tell us
the extent to which smaller lattice spacings
reduce errors on the masses and coupling. The impact
of higher-order perturbation theory is also
easily evaluated by adding fake $4^\mathrm{th}$-order
terms to the perturbation theory.
We have gone through this exercise starting from the
analysis in~\cite{McN}. Our results are presented in
Table~\ref{projected}. This table shows the percent errors we
expect in the masses and coupling from the correlator analysis
under various scenarios for improvements: PT denotes the
effect of computing QCD perturbation theory through
$4^\mathrm{th}$~order. LS denotes the effect of decreasing
the lattice spacing to 0.03\,fm. LS$^2$ denotes the effect
of using lattices with 0.03\,fm and 0.023\,fm lattice spacing.
We recall that the stage LS$^2$ corresponds to
an increase in computing power by about a factor of 100.
ST denotes the effect of improving the statistics by a factor
of 100. We also
show percent errors for the Higgs couplings to
$b\bar b$, $c\bar c$, and~$gg$, accounting
for correlations among the errors in the determination
of the parameters. The last line of the table gives, for
comparison,
the experimental uncertainties in the Higgs boson
couplings expected after the ILC
measurements~\cite{myILCHiggs}.
\begin{table*}
\begin{tabular}{r|ccc|ccc}
& $\delta m_b(10) $
& $\delta \alpha_s(m_Z)$
& $\delta m_c(3)$ &
$\delta_{b}$
& $\delta_{c}$ & $\delta_{g}$ \\ \hline\hline
current errors \cite{McN}
& 0.70 & 0.63 & 0.61 & 0.77 & 0.89 & 0.78
\\ & & & & & & \\
+ PT
& 0.69 & 0.40 & 0.34 & 0.74 & 0.57 & 0.49
\\
+ LS
& 0.30 & 0.53 & 0.53 & 0.38 & 0.74 & 0.65
\\
+ LS$^2$
& 0.14 & 0.35 & 0.53 & 0.20 & 0.65 & 0.43
\\ & & & & & & \\
+ PT + LS
& 0.28 & 0.17 & 0.21 & 0.30 & 0.27 & 0.21
\\
+ PT + LS$^2$
& 0.12 & 0.14 & 0.20 & 0.13 & 0.24 & 0.17
\\
+ PT + LS$^2$ + ST
& 0.09 & 0.08 & 0.20 & 0.10 & 0.22 & 0.09
\\ & & & & & & \\
ILC goal
& & & & 0.30 & 0.70 & 0.60
\end{tabular}
\caption{\label{projected}Projected fractional errors, in percent, for the
$\overline{\mathrm{MS}}$~QCD coupling and heavy quark masses under different
scenarios for improved analyses. The improvements considered are:
PT - addition of $4^\mathrm{th}$~order QCD perturbation theory, LS, LS$^2$ -
reduction of the lattice spacing to 0.03\,fm and to 0.023\,fm; ST -
increasing the statistics of the simulation by a factor of 100. The last three
columns
convert the errors in input parameters into errors on Higgs couplings,
taking account of correlations. The bottom line gives the
target
values of these errors suggested by the projections for the ILC
measurement
accuracies.}
\end{table*}
We find that reducing the lattice spacing to 0.023\,fm
is sufficient to bring parametric errors for
the Higgs couplings below the errors expected from
the full ILC. Adding $4^\mathrm{th}$-order perturbation
theory reduces the parametric errors
further, to about half of the expected ILC~errors. Adding
statistics gives a relatively small further reduction in the errors.
These error
estimates are likely conservative because they assume that
there will be no further innovation in LQCD simulation methods.
There already are many alternative lattice methods for
extracting the QCD coupling from LQCD simulations: see, for
example,~\cite{Davies:2008sw,Shintani:2010ph,Bazavov:2012ka,Jansen:2011vv,Fritzsch:2012wq}.
None of these methods involve
heavy quark masses directly and so none have correlations between
$\alpha_s$ and heavy quark masses. Small lattice spacings are
important for an accurate $b$~mass because of $(am_b)^2$~errors;
these can be avoided completely by using effective field theories
such as NRQCD~\cite{Lee:2013mla}
or the Fermilab formalism~\cite{ElKhadra:1996mp} for $b$-quark dynamics
in correlators, rather than (highly corrected) relativistic
actions. Other renormalized
lattice matrix elements, such
as off-shell expectation values of $m_Q \overline{\psi}\gamma_5\psi$,
can be used to compute masses~\cite{Martinelli:1994ty}.
There are many ideas that are likely
to come into play over the next decade or so.
\section{Conclusions}
In this paper, we have surveyed the current status of the
uncertainties in the Standard Model calculations of the Higgs boson
partial widths. We have shown that the current theory of these
partial widths is already accurate to better than 1\%. We have also
seen that both the perturbation theory and the parametric inputs
to this theory can be improved, to yield predictions at an accuracy
beyond even the high level expected for the experiments at the ILC.
Lattice gauge theory has a crucial role to play in improving the
determination of the most important input parameters.
There is much work to be done in the next decade to realize
the program we have outlined. But the result will be that these
calculations, combined with the results of precision experiments,
will offer a powerful probe into the mysteries of the Higgs boson.
\Acknowledgements
The general idea for a connection between Higgs physics and lattice
gauge
theory calculation arose in discussions for the Snowmass 2013 Energy
Frontier reports. We are especially grateful to Sally Dawson, Heather Logan,
Laura Reina,
Chris Tully, and Doreen Wackeroth for providing the impetus for this
study.
MEP thanks Ayres Freitas for an introduction to the literature on
precision
Higgs calculations and Sven Heinemeyer, Michael Spira, and James Wells for
illuminating discussions.
We thank Don Holmgren for the data and plot in Fig.~\ref{Fig:cpucost}.
The work of GPL was supported by the National Science Foundation.
GPL would also like to thank
the Department of Applied Mathematics and Theoretical Physics
at Cambridge University for their hospitality while this work
was in progress.
The work of PBM was supported by the US Department of Energy,
Contract No. DE-AC02-07CH11359.
The work of MEP was supported by
the U.S. Department
of Energy under contract DE--AC02--76SF00515.
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\section{Introduction -- states and observables}
In part~I of this series of papers we have discussed how time
asymmetry arose in quantum mechanics. Here we explain the meaning of
the time \mbox{$t=0$} of preparation of a quantum state. In the present paper
we describe an experiment which verifies our concept. It is based on
the idea of quantum jumps for a single ion.
In essentially all discussions of the foundation of quantum theory,
one distinguishes between {\em states} and {\em observables}. States,
described by a state vector $\phi^+$ (or a density operator $W$)
fulfill the Schr\"odinger equation
\begin{equation}
\label{se}
i\hbar\frac{d}{d t}\phi^+(t) = H \phi^+(t)\,.
\end{equation}
The state represents the preparation apparatus of an experiment.
Observables, described by operators $A = A^\dagger$ or projection
operators $\L$ ($\L = \L^2$) or, in the simplest case, by
one-dimensional projections $\L=|\psi^-\>\<\psi^-|$, or vectors (up
to a phase factor) $\psi^-$, fulfill the Heisenberg equation
\begin{subequations}
\label{he}
\begin{equation}
\label{hea}
i\hbar\frac{d}{d t}\psi^-(t) = -H\psi^-(t)\,
\end{equation}
\begin{equation}
\label{heb}
i\hbar\frac{d\Lambda(t)}{dt} = -[H,\Lambda(t)]\,,
\end{equation}
\end{subequations}
where \eqref{heb} for an operator $\Lambda(t)$, is the more familiar
form of this dynamical equation. The observable represents the
registration apparatus (detector) of an experiment.
The experimental quantities are the probabilities $\P_W(\L(t))$ of the
observable $\L(t)$ in the state $W$. Theoretically, $\P_W(\L)$ are
calculated as the Born probabilities
\begin{align}
\label{bp1}
{\P}_W(\L(t)) = \text{Tr}(\L(t)W) = \text{Tr}(\L W(t))
\end{align}
which for the special case of an observable $|\psi^-\>\<\psi^-| =
\Lambda$ in a pure state $|\phi^+\>\<\phi^+|=W$ is given by
\begin{align}
\label{bp2} {\P}_{\phi^+}(\psi^-(t)) = \begin{array}[t]{c}
|\<\psi^-(t)|\phi^+\>|^2\\ \text{Heisenberg picture}\end{array} =
\begin{array}[t]{c} |\<\psi^-|\phi^+(t)\>|^2\\ \text{Schrodinger
picture}\end{array}\,.
\end{align}
Experimentally the probabilities $\P_W(\L)$ are measured as ratios of
large detector counts, e.g.,
\begin{equation}
\P_W(\L(t)) = \frac{N(t)}{N}\,,
\end{equation}
where $N(t)$ is the number of detector count at time $t$, and $N$ is
the total number of counts.
The solutions of the dynamical differential equations like \eqref{se}
and \eqref{he} have to be found under {\em boundary conditions}. For
standard quantum mechanics, the boundary condition is given by the
Hilbert space axiom:
The solutions of \eqref{se} {\em and} of \eqref{he} are elements of
the (norm-complete) Hilbert space $\H$.
\begin{equation}
\label{sa}
\text{set of states} \{\phi^+(t)\} = \H = \text{set of
observables}\{\psi^-(t)\}\,.
\end{equation}
(This means the energy wavefunctions $\psi^-(E) = \<^-E|\psi^-\>$,
$\phi^+(E) = \<^+E|\phi^+\>$, must be {\em Lebesgues} square
integrable.)
In paper I \cite{paper1}, it was argued that under the standard axiom
\eqref{sa} one could not have a consistent theory of resonance and
decay phenomena: If one wants to include states for which the
approximate lifetime-width relation of the Weisskopf-Wigner methods,
$(2.9)$ of \cite{paper1}, becomes an exact equality, $\tau =
\hbar/\Gamma$, in particular if one wants to have Gamow vectors
$\phi^G(t)$ with exponential time evolution, then one cannot sustain
the standard axiom \eqref{sa}. Therefore, we chose a new boundary
condition for the old dynamical equations \eqref{se}, \eqref{he}, the
{\em Hardy space axiom}:
\begin{equation}
\label{hsa}
\begin{split}
&\text{Set of prepared (in-) states} & \{\phi^+\} =
\Phi_-\subset\H\subset\Phi_-^\times \\
&\text{Set of detected (out-) observables} & \{\psi^-\} =
\Phi_+\subset\H\subset\Phi_+^\times
\end{split}
\end{equation}
where $\Phi_\mp$ are the two different Hardy spaces of the same
Hilbert space $\H$, corresponding to the complex energy semiplanes
$\mathbb{C}_\mp$. This means the energy wavefunctions $\psi^-(E) =
\<^-E|\psi^-\>$ of out-observables must be smooth functions that can
be analytically continued into the upper complex energy plane ${\mathbb{C}}_+$,
and the wavefunctions $\phi^+(E) = \<^+E|\phi^+\>$ of the in-state
must be smooth functions that can be analytically continued into the
lower complex energy plane ${\mathbb{C}}_-$.
Since the in-states are defined by the preparation apparatus (e.g.,
accelerator) and the out-observables are defined by the registration
apparatus (e.g., detector) of an experiment on micro-systems, there is
no need to identify $\{\phi^+(E)\} = \{\psi^-(E)\}$ and use the
standard axiom \eqref{sa} which in the mathematical description
identifies states and observables with the Hilbert space.
\section{Time asymmetry}
A consequence of the new Hardy space axiom is the time asymmetry $t\ge
t_0 = 0$ of the dynamical evolution given by the semigroup solutions
$(4.6)$ and $(4.7)$ of \cite{paper1}. In particular the Gamow state
$\phi^G$ fulfilling $H^\times\phi^G = (E_R-i\Gamma/2)\phi^G$, evolves
in time according to $(4.6)$ of \cite{paper1} as
\begin{equation}
\label{gs}
\phi^G(t) = e^{-iH^\times t}\phi^G = e^{-iE_Rt}e^{-(\Gamma/2)
t}\phi^G\,,\quad t\ge 0\,.
\end{equation}
and exists only for $t\ge t_0 = 0$.
Since from the Hilbert space solution of the dynamical equations
\eqref{se}, \eqref{he}, we are used to time symmetric solutions,
$-\infty < t < +\infty$, such a time asymmetry may appear surprising.
But, from other areas of physics, we are quite familiar with
time-asymmetric solutions of time symmetric dynamical equations due to
time-asymmetric boundary conditions, e.g., the retarded and the
advanced solutions of electrodynamics. The Maxwell equations, like
the equations \eqref{se} and \eqref{he}, are symmetrical in time. The
additional axiom which chooses the retarded potential over the
advanced potential is called the ``radiation arrow of time''; it is
formulated as a boundary condition for the Maxwell equations, which
excludes the strictly incoming field in every space-time region
(Sommerfeld radiation condition). All fields possess advanced sources:
Radiation must be emitted first by a source before it can be detected
by a receiver.
A similar ``arrow of time'' exist for quantum physics: A state must be
prepared first by a preparation apparatus at $t_0=0$ before at a later
time $t > t_0$ an observable can be measured or registered by a
registration apparatus. In order to formulate this quantum mechanical
arrow of time we speak of states and observables, and we make a
distinction between the states $\{\phi^+\}$ and the observables
$\{\psi^-\}$. In quantum mechanics in general one always {\em speaks}
of states and observables, but then using the standard axiom
\eqref{sa} one identifies them in the mathematical description.
However, as discussed in \cite{paper1}, if we want to derive for the
pole term of the $S$-matrix element $(\psi^-,\phi^+)$ in $(3.8)$ of
\cite{paper1}, the relation $\Gamma = \hbar/\tau$ between the
Lorentzian width $\Gamma$ and the exponential lifetime $\tau$, then we
are forced to distinguish also mathematically between states and
observables and use the new axiom \eqref{hsa}. This in turn leads to
the semigroup evolution which introduces a ``beginning of time'', the
semigroup time $t_0 = 0$.
\section{Demonstrating the quantal beginning of time}
The question in quantum physics then is: What is the meaning of a
``beginning of time $t_0$'' ? How does one observe it and why have we
not been more aware of its existence ?
Most experiments in quantum physics deal with large ensembles of
quantum systems (elementary particles, or atoms, or ions) which are
prepared at a variety of times. That means individual atoms of an
ensemble are prepared at many different times and there is no way to
distinguish which has been prepared at a time, say $t_0^{(1)}$ and
which at a time $t_0^{(2)}$ (by the clocks in the lab). If, however,
one could work with {\em single quantum systems and identify the
preparation time of a single quantum system}, then one could
consider the quantum mechanical state, say $\phi^G$, whose ensemble is
the collections of the single quantum systems prepared at the
``ensemble of times'' $t_0^{(1)}$, $t_0^{(2)}$, $t_0^{(3)}$, $\cdots$
Such experiments on the excited states of an individual quantum system
have been performed in experiments with single laser cooled $Ba^+$
ions \cite{nagourney, sauter}, $Hg^+$ ions \cite{bergquist} and $In^+$
ions \cite{peik} using Dehmelt's idea of shelving the single ion on a
metastable level \cite{dehmelt}. Experiments of this kind require an
atom with two excited states both of which are radiatively coupled to
the same ground state but have vastly different transition rates. We
will discuss here in detail the experiment in \cite{peik} with an
$In^+$ ion.
For the $In^+$ these two levels are the $\,^3P_1$ and $\,^3P_0$
levels, Fig.(\ref{fig1}) \cite{peik}.
\begin{figure}
\begin{center}
\begin{picture}(300,200)(0,0)
\put(10,0){\line(1,0){60}}
\put(40,0){\line(0,1){80}}
\put(40,180){\line(0,-1){80}}
\put(10,180){\line(1,0){60}}
\put(80,140){\line(1,0){50}}
\put(130,115){\line(1,0){50}}
\put(180,90){\line(1,0){50}}
\put(155,115){\vector(-1,-1){114}}
\put(155,115){\vector(2,-1){50}}
\put(205,90){\vector(-3,-2){135}}
\put(10,5){\makebox(0,0)[b]{$5s^2\ ^1S_0$}}
\put(10,185){\makebox(0,0)[b]{$5s\,5p\ ^1P_1$}}
\put(190,110){\makebox(0,0){$A_2$}}
\put(85,65){\makebox(0,0){$A_1$}}
\put(155,40){\makebox(0,0){$A_0$}}
\put(160,125){\makebox(0,0)[c]{$\,^3P_1$}}
\put(210,100){\makebox(0,0)[c]{$\,^3P_0$}}
\put(100,85){\makebox(0,0)[b]{$231\,nm$}}
\put(190,60){\makebox(0,0)[b]{$237\,nm$}}
\put(80,150){\makebox(0,0){$5s\,5p\ ^3P_2$}}
\put(40,90){\makebox(0,0){$159\,nm$}}
\put(70,120){\makebox(0,0){$218\,nm$}}
\end{picture}
\end{center}
\caption{Simplified energy-level scheme of the $In^+$ ion. \cite{peik}}
\label{fig1}
\end{figure}
We denote the transitions involved by $A_1$, by $A_2$ and $A_0$.
One has the following resonance scattering and decay processes
\begin{equation}
\label{dp}
\begin{array}{cccccc}
\gamma +\ ^1S_0 & \begin{array}{l}
\underleftarrow{ \begin{array}{l}\text{fluorescence} \\
\text{transition $A_1$\phantom{ition}}\end{array} } \\
\overrightarrow{ \begin{array}{l}\text{laser driven} \\ \text{fast
transition $A_1$\ }\end{array} }
\end{array} & \,^3P_1 & \begin{array}[t]{c}
\xrightarrow[\quad\qquad\quad]{}\\ A_2\end{array} &
\text{\begin{picture}(0,0)(0,-5)
\put(0,0){\makebox(0,0)[cl]{$\gamma^\prime +\, ^3P_0$}}
\put(35,-5){\line(0,-1){20}}
\put(35,-25){\vector(1,0){20}}
\put(55,-25){\makebox(0,0)[cl]{$\,^1S_0 + \gamma^{\prime\prime}$}}
\put(35,-33){\makebox(0,0){$A_0$ slow}}
\end{picture}} &
\end{array}
\end{equation}
We focus our attention on the excited (metastable) level $\,^3P_0$
which is the state we describe by the Gamow vector $\phi^G =
|z_R,J^\pi,\cdots\> = |''3P_0''\>$.
The Gamow vector is an eigenket of the total, interaction
incorporating Hamiltonian $H$ with complex energy eigenvalue $z_R =
E_R-i\Gamma_R/2$ where $\Gamma_R = \frac{\hbar}{\tau}$, and $\tau =
\tau(\,^3P_0)\approx 0.14\,s$. We use here the standard spectroscopic
notation, e.g., $\,^3P_0 =\, ^{2s+1}(L)_J$, with $s=1$ and $J=0$ for
the excited energy levels, but $H$ is the exact Hamiltonian which
includes spin orbit {\em and} hyperfine interaction, and $\phi^G$ is
an eigenstate of $H$ and of total angular momentum-parity, $J^\pi$.
Due to the hyperfine interaction, the state of the $\,^3P_0$ level
includes also a superposition with a very small $J=1$
contribution\footnote{due to the magnetic dipole component of the
hyperfine interaction \cite{garstang}} which in turn is a
superposition of a small amount
of triplet and singlet states: \\
($|''\,^3P_0''\> = |\,^3P_0\> + \alpha|\,^3P_1\> + \beta|\,^1P_1\>$).
Due to this $J=1$ component there is a ``slow'' transition $A_0$.
The transition $\gamma +\, ^1S_0\rightarrow\, ^3P_1$ is laser driven
and the intensity of the fluorescence transition $A_1$:
$\,^3P_1\rightarrow\,^1S_0 + \gamma$ (with a lifetime
$\tau(\,^3P_1)\approx 4\times 10^{-7}\,s$) is monitored. Occasionally
$\,^3P_1$ makes the magnetic dipole transition into $\,^3P_0$ with a
branching ratio $10^{-8}$ (there can also be a laser induced
transition from $\,^1S_0$ to $\,^3P_0$). This is the metastable state
$|''\,^3P_0''\>\equiv \phi^G$ in which the ion will be shelved for a
long time ($\tau(\,^3P_0) \approx 0.14\,s$).
The experiment is done on a {\em single} $In^+$ and while it is
shelved it can not participate in the back and forth transitions
\begin{equation}
\label{mt}
\,^1S_0 + \gamma \overleftarrow{\overrightarrow}\,^3P_1
\end{equation}
so the shelve time is observed as a dark period of the fluorescence
transition $A_1$: $\,^3P_1\rightarrow\,^1S_0 + \gamma$.
The state of $In^+$ could be either the metastable state
$|''\,^3P_0''\> = |\phi^G(t)\>$ evolving in time by \eqref{gs}, or it
could go through many $(10^6)$ back-and-forth transitions \eqref{mt}
or it could evolve through superpositions of these three states.
\begin{figure}[h]
\centering
\includegraphics[width=\textwidth]{fig4b}
\caption{Two examples of observed quantum jumps resulting in dark
periods~\cite{peik}. The sudden drop in fluorescence defines the
beginning of time in $i$-th individual quantum state
$''^{3}P_{0}''$. The duration of the dark period $\Delta t^{(i)}$ is
the individual lifetime of this $''^{3}P_{0}''$. The average lifetime
$\tau$ is the weighted average of these $\Delta t^{(i)}$.}
\label{fig2}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=\textwidth]{fig5b}
\caption{The fit of the number of dark periods shorter than $t$ to
the experimental law~(\ref{tau}) provides an estimate of the
average lifetime of the $^{3}P_{0}$ level.}
\label{fig3}
\end{figure}
What one observes (Fig.~\ref{fig2}, \cite{peik}) is a sudden onset of
periods of no fluorescence at a time $t_0^{(1)}$ and a sudden return
of the original fluorescence intensity at a later time $t^{(1)}$.
These onsets of dark periods followed by the return of the
fluorescence repeat themselves (about $150$ times in the experiment
\cite{peik}): at $t_0^{(1)},t_0^{(2)},\cdots,t_0^{(150)}$ one sees
sudden jumps of the fluorescence intensity to $0$, followed by a
sudden return of the fluorescence radiation at the later times
$t^{(1)},t^{(2)},\cdots,t^{(150)}$.
The only reasonable interpretation of this is that during the dark
periods the single $In^+$ ion is shelved on the level $''\,^3P_0''$.
While $In^+$ is ``shelved'' on the metastable level $\,^3P_0$, it
cannot participate in the fluorescence transitions
$\,^3P_1\overrightarrow{\overleftarrow}\, ^1S_0 + \gamma$ and one
obtains dark periods (``shelf level dwell period'') of various
durations
\begin{equation}
\label{vd}
\Delta t^{(i)} = t^{(i)} - t_0^{(i)}\,,\quad \Delta t^{(i)} >
0\,,\quad t^{(i)} > t_0^{(i)}\,.
\end{equation}
Two of these dark periods for the fluorescence transition are shown in
Fig.~\ref{fig2}. A dark period means that the system is on
the metastable level $\,^3P_0$, which is described by $\phi^G =
|''\,^3P_0''\>$; this means that at every of the times $t_0^{(i)}$ an
individual $\,^3P_0$ is prepared, it ``lives'' for the duration
$\Delta t^{(i)}$ and decays at the time $t^{(i)}$.
The state vector $\phi^G(t)$ for the meta-stable $''\,^3P_0''$-state
therefore represents an ensemble of individual $\,^3P_0$-levels of
$In^+$; the $i$-th member of this ensemble is created (or prepared) at
a definite time $t_0^{(i)}$ which is the time $t=0$ in the life of
this $i$-th member. This is also the time $t=0$ of the state
$\phi^G(t)$.
A quantum mechanical state vector $\phi^+$, or $\phi^G$, or state
operator $W$, represents an ensemble (a large number) of individual
micro-systems. Usually one thinks of an ensemble of microsystems as of
collections of many particles that are present at one particular point
of time (in our live, or by the laboratory clocks); in this experiment
one has one single ion in the $\,^3P_0$ level at a collection of many
preparation times $\{t_0^{(i)}\}$. The preparation time for this
ensemble of single shelved $In^+$ is the ensemble of times
$\{t_0^{(i)}\}$. This ensemble of times $\{t_0^{(i)}\}$ is the
preparation time $t_0 = 0$ of the state operator
$|\phi^G(t)\>\<\phi^G(t)|$. The state vector $\phi^G(t)$ which
represents the ensemble of $In^+$ in the $\,^3P_0$ level has thus a
time evolution $0\le t<\infty$, and the semigroup time $t=0$ is the
ensemble of times $\{t_0^{(i)}\}$ where the times $t_0^{(i)}$ are the
onset times of dark periods, i.e., the times at which the $\,^3P_1$
level stops participating in the fluorescence transitions \eqref{mt}
and prepares the state $\phi^G = |''\,^3P_0''\>$.
Since the lifetime $\,^3P_1$ is $10^{-6}\,s$, and the lifetime of
$''\,^3P_0''$ is $10^{-1}\,s$, the onset time of the dark periods
$t_0^{(i)}$ are determined with very high accuracy. The same applies
to the time $t^{(i)}$, since one observes a {\em sudden} return of
fluorescence. This is the time at which the $i$-th
$''\,^3P_0''$-level has decayed into $\,^1S_0 + \gamma$, and the
processes \eqref{mt} can resume. The duration of a dark period
$\Delta t^{(i)} = t^{(i)}-t_0^{(i)}$ is thus the individual lifetime
of the $i$-th $\,^3P_0$ level, and it is defined to very high
accuracy. Two of these individual lifetimes $\Delta t^{(i)}$ of the
$\,^3P_0$ levels are shown by the duration of the dark periods in
Fig.~\ref{fig3}, \cite{peik}.
Summarizing, the interpretation of our observation is the following:
Since the single $In^+$ can either make the fluorescence monitored
transitions \eqref{mt} or be in the quasistable state $|''\,^3P_0''\>$
the time interval $\Delta t^{(i)} = t^{(i)}-t_0^{(i)}$ is the time
which the $i$-th single $In^+$ at the $''\,^3P_0''$ level of $In^+$
has ``lived'', from its preparation at $t_0^{(i)}$ to its decay into
$\,^1S_0 + \gamma$ at $t^{(i)}$.
\section{The exponential of the average lifetime}
The ensemble of the $''\,^3P_0''$ levels is described by the state
vector $\phi^G(t)$. The preparation time $t_0$ of the state
$\phi^G(t)$ is the ensemble of times $\{t_0^{(i)}\}$,
\begin{equation}
\label{new1.12}
\,\quad\qquad \quad t_0 \Leftrightarrow \{t_0^{(i)}\}\,.
\end{equation}
This time $t_0 > -\infty$ is the time zero in the existence of each
individual $''\,^3P_0''$-$In^+$-ion state. We choose it thus as the
time $t = 0$ of the time evolution semigroups
\begin{equation}
\label{new1.13-}
U_-^\times(t) = \{ e^{-iH^\times t}\,|\,0\le t < \infty \}
\end{equation}
for the Gamow state vector $\phi^G(t)$ of \eqref{gs}. And similarly
one defines the semigroup for any state $\phi^+\in\Phi_-$ in $(4.6)$
of \cite{paper1}.
Therewith we have identified the experimental definition of the
semigroup time $t_0 = 0$, of the state $\phi^G(t)$: it is the ensemble
of onset times of the dark periods $\{t_0^{(i)}\}$ when the $In^+$ is
shelved on the $\,^3P_0$ level, and where it remains for an ensemble
of individual lifetimes $\Delta t^{(i)}$.
The quantities predicted by quantum theory are the Born probabilities
and averages (expectation values) not the properties of individual
quantum systems like the $\Delta t^{(i)}$. The Born probability for
the Gamow state \eqref{gs} (survival probability) is given by the
exponential law
\begin{equation}
\label{new1.14m}
\P(\,^3P_0(t)) \equiv \P_D(t) = e^{-\Gamma t/\hbar} =
e^{-t/\tau}\,,\qquad t > 0\,.
\end{equation}
These probabilities are measured by the counting ratios:\footnote{the
sign $\simeq$ in \eqref{new1.14} and below indicates that this is an
equality between theoretical quantities on the left hand side and
experimental quantities on the right hand side (which would become
an exact equality in the unrealistic case of continuously infinite
events).}
\begin{equation}
\label{new1.14}
e^{-t/\tau} = \P_D(t) \simeq \frac{N_D(t:\Delta t^{(i)} > t)}{N_D} =
\text{counting ratio}
\end{equation}
where
\begin{equation*}
N_D(t:\Delta t^{(i)} > t) = \text{number of dark periods of
duration}\quad \Delta t^{(i)} > t\,,
\end{equation*}
and $N_D$ is the total number of dark period events that are included.
We call
\begin{equation*}
N(t:\Delta t^{(i)} < t ) = \text{number of dark periods of
duration}\quad \Delta t^{(i)} \le t\,.
\end{equation*}
Intuitively, $N_D(t:\Delta t^{(i)} > t)$ is the number of $\,^3P_0$
levels that live longer than $\Delta t^{(i)}$, and $N(t:\Delta t^{(i)}
< t )$ is the number of $\,^3P_0$ levels that have already decayed
into $\,^1S_0 + \gamma$.
It is clear that for every time $t\ge 0$
\begin{equation}
\label{new1.15}
N(t:\Delta t^{(i)}\le t) + N_D(t:\Delta t^{(i)}>t ) = N_D
\end{equation}
where $N_D(\approx 150)$ is the total number of dark periods that have
been observed. To check the exponential law \eqref{new1.14} and to
obtain an estimate of the average lifetime $\tau = \Gamma/\hbar$, the
number of dark periods with duration shorter than $t$, $N(t:\Delta
t^{(i)}\le t)\equiv d(t)$ is considered. Only dark periods of duration
larger than $t_s = 70\,ms$ could be identified in the experiment
\cite{peik}. Since from \eqref{new1.15} with \eqref{new1.14} follows
\begin{multline}
N_D(t:\Delta t^{(i)} > t) = N_D e^{-t_s/\tau}e^{-(t-t_s)/\tau} = N_D
- N(t:\Delta t^{(i)} < t ) \\
= a' e^{-(t-t_s)/\tau} = a - d(t)\,,
\end{multline}
the quantities $a-d(t)$ are plotted versus time in a logarithmic plot,
Fig.~\ref{fig3}. The straight line confirms the exponential decay law
and from the slope of the straight line one obtains the lifetime of
the $\,^3P_0$-level as $\tau(\,^3P_0) \approx 0.14\,s$.
Since the counting ratios in \eqref{new1.14} are according to
Fig.~\ref{fig3} in agreement with the exponential law, the average of
the lifetime is given by $\tau$:
\begin{equation}
\label{tau}
\int_0^\infty dt\, \P_D(t) = \int_0^\infty dt\,e^{-t/\tau} = \tau\,.
\end{equation}
Since according to \eqref{new1.14} $\P_D(t)$ is observed as the
counting ratio\\
$N_D(t:\Delta t^{(i)}>0)/N_D$, the lifetime is measured as the
weighted average of the dark periods $\Delta t^{(i)}$:
\begin{equation}
\label{sld}
\tau \simeq \sum_i \Delta t^{(i)}\frac{N_D(t:\Delta t^{(i)} > t)}{N_D}\,.
\end{equation}
The ensemble of quasistable quantum objects in the state $\phi^G$ is
an ensemble of individual $''\,^3P_0''$s each of which is prepared at
the collection of times $t_0^{(i)}$ and decays at the collections of
times $t^{(i)}$ and lives for a duration of time $\Delta t^{(i)} =
t^{(i)} - t_0^{(i)}$. Not the values $\Delta t^{(i)}$ are
characteristic quantities of the Gamow state but the weighted average
\eqref{sld} which corresponds to the theoretical lifetime $\tau$ of
the Gamow state in \eqref{gs} with $\tau = \Gamma/\hbar$.
The lifetime $\tau$ is one of the characteristics of the Gamow state
$(3.12)$ of \cite{paper1}. It is defined by the exponential law
\eqref{new1.14m} which follows from \eqref{gs}. It is given by the
$S$-matrix pole position $z_R = E_R-i\Gamma/2$ which defines a complex
energy eigenvector $(3.14)$ of \cite{paper1} which describes a
resonance state of Breit-Wigner width $\Gamma$. And the lifetime of
the decaying state is related to the width of the resonance by the
exact lifetime-width relation $\tau = \frac{\hbar}{\Gamma}$.
\section{Conclusion}
The time asymmetry of quantum theory which was shown in \cite{paper1}
to be a byproduct of a unified theory of resonance scattering and
decay phenomena, distinguishes a particular time $t_0$, the time $t =
0$ of a semigroup time evolution. This is the time at which the state
(e.g., decaying state) has been prepared and the registration of the
observable (e.g., decay products) can begin.
This semigroup $t=0$ is measured as the collection of times
$\{t_0^{(i)}\}$ at which the individual $\,^3P_0$-levels of a single
$In^+$ were prepared. These times of preparation of $\,^3P_0$ levels
are documented by the sudden onset times $t_0^{(i)}$ of the dark
periods for the single $In^+$ ion. Each dark period also has its
individual end $t^{(i)}$ (documented by the end of the dark period).
Thus each dark period has its individual lifetime $\Delta t^{(i)} =
t^{(i)}-t_0^{(i)}$. The quantum mechanical state $\phi^G$ describes
the ensemble of individual microsystems created under the same
condition at an ensemble of different times $\{t_0^{(i)}\}$. This
ensemble of preparation times is the preparation time $t_0=0$ of the
state $\phi^G$: $t_0 \leftrightarrow \{t_0^{(i)}\}$.
In traditional quantum mechanics the state would be asymptotically
prepared for $t\rightarrow -\infty$ as a state of the
$(\,^1S_0,\gamma)$-system and evolve in time through a superpositions
of vectors representing $(\,^1S_0,\gamma)$, $\,^3P_1$,
$(\gamma',\,^3P_0)$, $(\,^1S_0,\gamma'')$,$\cdots$. Using the Hilbert
space axiom \eqref{sa}, the probability for $\,^3P_0$ would be
different from zero -- at least infinitesimally -- at any time $t$
between $-\infty < t < \infty$. It could be significantly different
from zero at a particular time $t_0$, but there could not be sudden
jumps as used for the interpretation of the sudden onset of dark
periods at $t_0^{(i)}$.
On the other hand the existence of these quantum jumps is an
experimental confirmation of the semigroup time evolution. The new
Hardy space hypothesis \eqref{hsa} which was conjectured in order to
obtain a consistent theory that unifies Breit-Wigner resonances and
exponentially decaying Gamow states also led to a semigroup evolution
\cite{paper1} and therewith the semigroup time $t_0 = 0$. This time
$t_0$ represents the ensemble of preparation times $\{t_0^{(i)}\}$ for
the metastable level $\,^3P_0$ which is described by the Gamow state
vector $\phi^G = |''\,^3P_0''\>$.
Quantum theory describes ensembles of (large) numbers of quantum
systems. In the usual experiments this means or at least includes a
large number of micro-systems at any given time. In the experiments
with single ions, it involves only one single ion state which is
prepared at a large number of different times $t_0^{(i)}$ under
identical conditions. This exposes the time of preparations for the
state of the single quantum system. What is remarkable about these
marvelous experiments \cite{sauter,bergquist,peik} is that they can
measure quantities that the theory cannot predict, like the individual
lifetimes of a single excited ion level.
\section*{Acknowledgment}
This work is part of a collaboration sponsored by the US National
Science Foundation Award No. OISE-0421936.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,963 |
\section{Introduction}
\subsection{The Abell 85 Galaxy Cluster}
Abell 85 is a galaxy cluster that is in the process of merging with two
subclusters \citep{ichinohe2015}. As a bright X-ray cluster with a complex structure,
Abell~85 has been intensively studied with all modern X-ray observatories: Chandra,
XMM-Newton and Suzaku \citep[e.g.][]{kempner2002, durret2003, schenck2014}.
The galaxy population of Abell 85 was recently analyzed at optical wavelengths by \citet{agulli2016}
who determined the spectroscopic luminosity function with 460 confirmed cluster members.
\citet{owen1997} and \citet{schenck2014} made clear detections of radio emission emanating from
the Abell 85 cluster and its BCG. Radio relics located $\sim$320 kpc from the core of Abell 85
were discovered by \citet{slee2001} -- see also \citet{schenck2014} and \citet{bagchi1998}.
These relics are likely the result from shocks of past cluster mergers.
\subsection{A fanciful trio of black holes}
In the optical and X-rays, SDSS J004150.75-091824.3 is a bright ($g$=14.03 mag), point-like
source located $\sim14\arcsec$ away from the nucleus of the Abell 85 BCG -- see
Fig.~\ref{geminichandra}. SDSS J004150.75-091824.3 is also the closest X-ray point source
to the nucleus of the BCG. The core of the BCG shows a diffuse X-ray emission while
SDSS~J004150.75-091824.3 is bright and point-like.
\begin{figure*}
\centering
\begin{tabular}{cc}
\includegraphics[scale=0.45]{geminiabell85v0-eps-converted-to.pdf} & \includegraphics[scale=0.45]{chandraabell85v0-eps-converted-to.pdf}\\
\end{tabular}
\caption{Central region of Abell 85 as viewed by Gemini (left) and Chandra (right). The center of the Abell 85 BCG
is depicted with a red solid circle. The location of SDSS J004150.75-091824.3 is shown with a blue dotted circle.
These circles have diameters of 4 arcseconds. The optical image was originally presented in \citet{madrid2016}
while the X-ray data was presented in \citet{ichinohe2015}. North is up and east is left. X-ray data kindly provided
by Y. Ichinohe.\label{geminichandra}}
\end{figure*}
SDSS J004150.75-091824.3 was included in the photometric selection of quasars from the SDSS
by \citet{richards2004,richards2009}. SDSS J004150.75-091824.3 was found to have a photometric
redshift of $z$= 0.925 in \citet{richards2004}. This value was later revised to $z$=0.675
in \citet{richards2009}.
SDSS J004150.75-091824.3 was identified as a possible AGN in the detailed X-ray study carried out by
\citet{durret2005}. These authors identify SDSS J004150.75-091824.3 as an X-ray point source on their
Chandra data and also identify an optical counterpart on a SDSS image (see their Fig.\ 2).
SDSS J004150.75-091824.3 is located within an X-ray cavity \citep{durret2005, ichinohe2015}.
Given the projected proximity of SDSS J004150.75-091824.3 to the center of the Abell 85 BCG,
\citet{lopez2014} surmised that stellar light could have biased the redshift and classification
given by \citet{richards2009}. \citet{lopez2014} speculated that \textsc{SDSS J004150.75-091824.3}
could be ``a third" supermassive black hole associated with the Abell 85 brightest cluster galaxy.
The other two black holes of Abell 85 would have been a hypothetical binary pair in the
core of the BCG. \citet{lopez2014} claimed the presence of a substantial light deficit on the nuclear
region of the Abell 85 BCG. \citet{lopez2014} interpreted this light deficit as evidence
for the presence of an ``ultramassive" SMBH.
When galaxies merge, their central black holes are thought to consolidate into one entity.
During the process of black hole coalescence, supermassive black hole binaries are thus created
\citep{begelman1980}. Stars that come in close proximity to a binary supermassive black hole
(SMBH) can be slingshot away through gravitational interactions \citep{begelman1980, ebisuzaki1991, milo2001}.
Over time, as this process repeats itself, a SMBH creates a deficit of stars in its vicinity.
The presence of a binary SMBH can then be inferred by the detection of stellar light deficits on
the optical surface brightness profiles of, for instance, elliptical galaxies
\citep[e.g.][]{graham2004,dullo2019}. When light deficits are present in surface brightness
profiles, the steep slope of the profile in the outer parts of the galaxy becomes flatter,
sometimes even close to constant, with decreasing radii \citep[e.g.][]{graham2004}.
Given the small spatial scales involved, the accurate characterization of the properties
of stellar cores and, among them, their light deficits, require Hubble Space Telescope data
\citep{ferrarese2006}. Light deficits associated with SMBH occur in spatial scales of a few
hundred parsecs in galaxies located megaparsecs away. For instance, cores in galaxies belonging
to the Virgo cluster have spatial scales of 1 to 4 arcseconds \citep{ferrarese1994}.
With few exceptions \citep[e.g., 3C~75;][]{owen1985}, unequivocal detections of close pairs
of binary AGN remain rare. Binary black holes are elusive, even when dedicated observing
campaigns are carried out \citep{tingay2011}.
In the following sections a new radio map of the Abell 85 BCG with the highest resolution
ever achieved is introduced. This radio map is used to search for the presence of a binary AGN.
A new optical spectrum of SDSS J004150.75-091824.3 is also presented. This spectrum is used
to make a precise determination of the redshift for this source. A new Gemini spectrum of
the Abell 85 BCG is also shown. High-resolution imaging obtained with Gemini and Chandra
are used as ancillary data to place the new observations in a wider context. Finally, by
presenting optical data obtained under different atmospheric conditions we illustrate the
effect of seeing on optical surface brightness profiles.
At the distance of Abell 85 ($D=233.9$ Mpc) 1$\arcsec$ corresponds to 1.075 kpc.
\section{Observations and data reduction}
\subsection{X-ray Imaging}
The Chandra data shown in Fig.~\ref{geminichandra} was analyzed and presented by \citet{ichinohe2015}.
Details of the observations and data reduction for this dataset are given in that reference.
\citet{ichinohe2015} created a Chandra image that is a factor of $\sim$5 deeper than the initial Chandra
image of $\sim$37 ks analyzed by \citet{kempner2002}. \citet{ichinohe2015} also included XMM–-Newton and
Suzaku data out to the virial radius of the cluster. \citet{ichinohe2015} found evidence that the
Abell 85 cluster is undergoing two mergers and has gas sloshing out to a radius of $r\sim600$ kpc from
its center.
\subsection{Optical Imaging}
Figure \ref{geminichandra} also shows a Gemini image of the Abell 85 BCG. The Gemini $r$-band
image was obtained with the Gemini Multi-Object Spectrograph (GMOS). This dataset was presented
and discussed in depth in \citet{madrid2016}. A new Gemini image obtained under poor seeing conditions
is also presented in section 4 (Gemini program GS-2016B-Q-87). The data reduction for this new
image is identical to the one described in \citet{madrid2016}.
\begin{figure}
\epsscale{1.3}
\plotone{vla_abell85v12.pdf}
\caption{VLA synthesized image of the Abell 85 BCG. This image shows two bipolar jets emanating from the core
of Abell 85. Contours are shown at 0.02, 0.06, and 0.1 mJy. The scale bar on the lower right is 1$\arcsec$ in length.
North is up and east is left.
\label{vlamap}}
\end{figure}
\begin{figure*}
\epsscale{0.85}
\plotone{abell85plotspectrumv1.pdf}
\caption{\textit{Top:} Gemini spectrum of the Abell 85 BCG. \textit{Bottom:} GTC spectrum of SDSS J004150.75-091824.3.
Both spectra are shown on their observed wavelength without correcting for radial velocities. The letter \textsc{T}
denotes a telluric absorption line.
\label{spectra}}
\end{figure*}
\subsection{Optical Spectroscopy}
The Gemini spectrum of the Abell 85 BCG was obtained with GMOS-South on spectroscopic mode.
Five exposures of 900 seconds were obtained on 2016 September 14. The grating used was R400 which
has its blaze wavelength at 764 nanometers. The slit width was 1.$\arcsec$5.
The first task of the data reduction process is to apply {\sc gprepare} to the raw science data
obtained through the Gemini archive. {\sc gprepare} applies a flatfield and performs overscan
subtraction. The spectrum is extracted from the fits file by using the task {\sc gsextract}.
This tasks extracts the intensity values along the spectral dimension of the CCD chip.
Calibration is carried out with the task {\sc gswavelength}. The details of the reduction procedure
used here were described in \citet{madrid2013}.\\
The spectroscopic data for SDSS J004150.75-091824.3 was obtained with the Optical System for Imaging and
low Intermediate Resolution Integrated Spectroscopy (OSIRIS) on the Gran Telescopio Canarias. OSIRIS
is an optical imager and spectrograph. A $2\times2$ binning was used for the CCD resulting in a spatial
scale of 0.$\arcsec$26 per pixel. Likewise, the resulting spectral resolution is 2.12~\AA/pixel.
The slit had a width of 1$\arcsec$ and the grating in use was R1000B.
The spectrum of SDSS J004150.75-091824.3 presented here was obtained on 2017 August 17. Raw science data,
bias, flats and arcs were retrieved from the Grantecan public archive.
Both science data extraction and sky subtraction were done using the \textsc{pyraf} task \textsc{apall}.
In the same way, arcs, bias and flats are processed with \textsc{apall}. The science spectra had the bias
removed and were normalized by the flat. The HgAr and Ne calibration arcs were used for wavelength
calibration. The emission lines given on the reference arcs provided by the observatory were used
as part of the wavelength calibration. The spectra were extracted using a spatial width of 7 pixels,
or 1.$\arcsec$8. The spectrophotometric standard star {\sc Feige 110} is used to flux calibrate the spectra
using the tasks \textsc{standard, sensfunction} and \textsc{calibrate}.
\subsection{Radio Data}
Karl G. Jansky Very Large Array (VLA) data was obtained from the National Radio Astronomy
Observatory public archive. Abell 85 was observed with the VLA in its A configuration on
2018 March 25. The total observation time was 4 hours, resulting in 2.8 hours on-source
after overheads. The observations used the X-band receiver with 4 GHz of correlated
bandwidth centered at 10 GHz.
The VLA data were processed with a series of tasks found within the Common Astronomy
Software Applications (CASA). Standard interferometric data reduction procedures were
followed to calibrate the delay, bandpass, phase, amplitude and flux. One round of
phase-only self-calibration was also included. During imaging, a Briggs robust
weighting of $+0.5$ was used to suppress Point Spread Function (PSF) sidelobes and
achieve a resolution of $0.\arcsec29 \times 0.\arcsec19$ at a position angle
of 32 degrees. The final image had a measured sensitivity of 3 $\mu$Jy/beam.
\section{The Abell 85 AGN}
The high-resolution and sensitivity of the radio data allows the detection of the central AGN
and bipolar diffuse emission. Compact radio sources are ubiquitous in the core of early type
elliptical galaxies \citep{ekers1973}, and the Abell 85 BCG is no exception. The VLA image
also shows two bipolar jets emanating from the compact core. Both jets are less than $\sim$2 kpc
in length (projected). The image shown in Fig.~\ref{vlamap} is the first radio image
to clearly identify the jets emanating from the Abell 85 BCG.
Interestingly, the southern jet is well aligned with the location of the X-ray cavity
described by \citet{durret2005} and \citet{ichinohe2015}; see Fig.~\ref{geminichandra}.
This X-ray cavity is, however, at about 20 kpc south of the core whereas the southern
radio jet does not show radio emission beyond 2 kpc from the center of the BCG.
The VLA image of the Abell 85 BCG shows a single core and no evidence of double nuclei.
Similarly, the X-ray image only shows diffuse X-ray emission in the core of the galaxy.
Binary black holes, when present, appear as two distinct point sources in X-ray images
\citep{komossa2003, fabbiano2011}.
The null detection of binary black holes in the X-ray and very high resolution radio data
implies that the central massive object in the Abell 85 BCG is likely a single
entity. Should a binary AGN exist in the Abell 85 BCG, its detection would require very
long baseline interferometry (VLBI) given that the pair would be separated by less than
$\sim$400 pc. Using data obtained with the Very Long Baseline Array (VLBA), \citet{rodriguez2006}
discovered a supermassive binary black hole in the radio galaxy IVS 0402$+$379
(B1950)\footnote{IVS stands for International VLBI Service. The VLBA Calibrator Survey
gives the (J2000.0) name for this source: J0405+3803 \citep{beasley2002}.},
the projected separation between the two black holes is only 7.3 pc.\\
\section{SDSS J004150.75-091824.3 is a distant quasar}
Three star-like sources are present in the optical image within 14$\arcsec$ (or 15.05 kpc)
of the nucleus of the BCG. One of these sources is SDSS J004150.75-091824.3, see
Fig.~\ref{geminichandra}. On the other hand, in the X-ray image, SDSS J004150.75-091824.3
is the only point-like source within one arcminute of the center of Abell 85. With the
Gemini image we can derive an accurate position for SDSS J004150.75-091824.3 at R.A.=0:41:50.764
and dec=$-$9:18:24.4.
The core of Abell 85 has a diffuse and extended X-ray emission that envelops SDSS~J004150.75-091824.3.
The presence of this extended X-ray emission was misinterpreted by \citet{lopez2014} as an
indication that SDSS J004150.75-091824.3 was a low redshift AGN.
In Fig.~\ref{spectra}, the spectrum of SDSS J004150.75-091824.3 show four prominent emission
lines: C\,{\sc iv}, He\,{\sc ii}, C\,{\sc iii}], and Mg\,{\sc ii}. These emission lines are
characteristic of quasar spectra, e.g.,\citet{wilkes1986, vandenberk2001}. With the Grantecan
spectrum the redshift of SDSS J004150.75-091824.3 is determined to be $z=1.5603\pm 0.003$.
The spectrum of the Abell 85 BCG, also shown in Fig.~\ref{spectra}, has a prominent
H$\alpha~+$ [N\,{\sc ii}] 6584 emission line. The H$\alpha$ line has a [N\,{\sc ii}]
emission line on either side. The forbidden [S\,{\sc ii}] 6717/6730 doublet is also
clearly visible. The Franhofer absorption lines for magnesium and sodium are easily seen.
The above emission and absorption lines are used to confirm the redshift of the BCG to
be $z=0.05538 \pm 0.0004$. This value is in agreement with several earlier determinations
of the redshift of the Abell 85 BCG \citep[][among others]{nesci1990}.
It should be noted that the spectrum of the BCG is similar to the archival spectrum of this
galaxy available through the SDSS archive. The spectrum of the Abell 85 BCG is presented
here as a comparison with the spectrum of SDSS J004150.75-091824.3 but also as a baseline
spectrum for studies of this galaxy, e.g.,~\citet{edwards2016}.
\section{Mirage Supermassive Black Holes}
\subsection{The Effect of Seeing on Optical Surface Brightness Profiles}
The presence of a binary black hole in the Abell 85 BCG was postulated based on the
analysis of its surface brightness profile \citep{lopez2014}. However, the obvious effect
of poor seeing has been ignored in recent studies that attempt to use ground-based data
without sufficient resolution to study the surface brightness profile of the Abell 85 BCG.
This section highlights the risks of inferring the presence of a light deficit, or any
other nuclear property of a distant galaxy, using ground-based data.
The BCG of Abell 85 has been reported during recent years as having both a
light deficit and a light excess in its core \citep{lopez2014, bonfini2015, madrid2016, mehrgan2019}.
These apparently contradicting results are a clear example of the effects of data quality
on optical surface brightness profiles.
\begin{figure}
\centering
\begin{tabular}{c}
\includegraphics[scale=0.4]{goodseeingv100.pdf}\\
\includegraphics[scale=0.4]{badseeingv100.pdf} \\
\end{tabular}
\caption{Surface brightness profile of a model galaxy observed with optimal seeing (\textit{top panel})
or with bad seeing (\textit{bottom panel}). The seeing is represented by a PSF that has been normalized.
Units are arbitrary.
\label{seeingconvolve}
}
\end{figure}
The effect of seeing on surface brightness profiles can be easily modeled, as we do
in this section. Atmospheric turbulence blurs and smears images obtained with ground
based telescopes. Poor seeing degrades and erases the innermost structure of surface brightness
profiles. This effect is not only intuitive but was well defined over four decades ago
by \citet{schweizer1979}, among others. More recently, \citet{cote2006} showed
that data with poor seeing miss the presence of structures in galactic nuclei.
Let's consider a galaxy whose light profile can be described by two main components:
a nuclear point spread function and an outer spheroid. The nuclear component can be
accurately modeled as a Gaussian and the main component can be represented by a
S\'ersic function \citep{sersic1968}.
The surface brightness profile of the above galaxy observed with a ground based
telescope can be evaluated by convolving its profile with the seeing. Here, seeing is
considered as the distorting effects of both atmospheric turbulence and telescope optics.
\begin{figure*}
\epsscale{0.7}
\plotone{abell85sbnologv100.pdf}
\caption{Surface brightness profile of the Abell 85 BCG obtained with Gemini and the KPNO 0.9-m.
Two epochs of observations with Gemini are plotted. One epoch with excellent seeing (0.$\arcsec$56)
and a second epoch of observations obtained under poor weather conditions with a seeing of (1.$\arcsec$60).
\label{abell85sb}}
\end{figure*}
Fig.~\ref{seeingconvolve} shows the effect of seeing on the innermost regions of a surface
brightness profile. Observing a galaxy light profile with excellent seeing recovers
the actual profile with no distortions, as shown in the top panel of Fig.~\ref{seeingconvolve}.
Both the nuclear and spheroidal components are detected when the light profile is obtained
under ideal seeing conditions.
On the other hand, when the same light profile is observed with poor seeing, its central
part is entirely misrepresented, as shown in the bottom panel of Fig.~\ref{seeingconvolve}.
The central nuclear component is fully blurred by seeing effects. Under bad seeing conditions,
instead of detecting a central Gaussian component the slope of the profile becomes
flat toward the nucleus of the galaxy.
A surface brightness profile observed with bad seeing could give the illusion of a light deficit.
Poor seeing also alters the light profile creating a break on its slope. The above can mislead
observers to believe on the detection of a depleted core and its associated SMBH when galaxies
are observed with poor seeing conditions.
\subsection{Optical observations of Abell 85}
\citet{lopez2014} used data obtained with the Kitt Peak National Observatory (KPNO) 0.9-meter
telescope to analyze the central surface brightness profile of the Abell 85 BCG. The seeing
for the KPNO 0.9-m data is reported to be 1.$\arcsec$67. \citet{bonfini2015} published
a detailed analysis of the surface brightness profile of Abell 85 using data obtained with
the Canada-France-Hawaii telescope (CFHT). The CFHT data analyzed by \citet{bonfini2015} has
subarcsecond resolution: 0.$\arcsec$74. \citet{bonfini2015} found that the light deficit
claimed by \citet{lopez2014} did not exist. Moreover, contrary to a light deficit, \citet{bonfini2015}
find a modest light excess in the core of the Abell 85 BCG.
\citet{madrid2016} obtained Gemini data of the Abell 85 BCG with a seeing of 0.$\arcsec$56.
\citet{madrid2016} confirmed the presence of a light excess in the core of this galaxy initially
found by \citet{bonfini2015}. The superior seeing of the Gemini data allow \citet{madrid2016}
to detect an additional nuclear component within the inner 2 kpc of the center of the Abell 85 BCG.
This nuclear component is well resolved, with a FWHM of 0.$\arcsec$85. At the distance of Abell 85
this nuclear component has a size of $\sim$0.9 kpc \citep{madrid2016}.
The empirical effect of seeing on the central surface brightness profile of the Abell 85 BCG is shown
in Fig.~\ref{abell85sb}. This figure shows the light profile derived with Gemini data obtained
during two different epochs with different seeing conditions. Fig.~\ref{abell85sb} also shows
the KPNO 0.9-m data used by \citet{lopez2014}. Note that the true inner structure is lost to both
Gemini and KPNO 0.9-m under poor seeing conditions.
The Gemini data presented in Fig.~\ref{abell85sb} allow us to quantify the impact of seeing.
The surface brightness profile with excellent seeing and the Gemini profile with poor seeing
have a small, but measurable, difference of 0.01 mag/arcsec at $r=4.5$ kpc. This difference
increases to 0.02 mag/arcsec at $r=2.0$ kpc, and to 0.04 mag/arcsec at $r=1.0$ kpc. As shown in
Fig.~\ref{abell85sb}, the two Gemini profiles begin to diverge at about $\sim$1.5 kpc
from the nucleus of the galaxy.
The fact that the profile obtained with bad seeing fails to accurately record the true
profile of the galaxy at such large radii is crucial. \citet{lopez2014} claims that the
Abell 85 BCG has a cusp radius of $r_{\gamma}=4.57 \pm 0.06$ kpc. This value is within the
range where the surface brightness profile is affected by seeing effects. It is precisely
this cusp radius that is used to infer the presence of a supermassive black hole.
\section{Final remarks}
A new VLA map shows bipolar AGN jets aligned along the north-south direction in the Abell 85 BCG.
X-ray and radio images show no evidence of a binary black hole in the core of this galaxy.
The optical spectra shown here demonstrate that the Abell 85 BCG and SDSS J004150.75-091824.3 are
two entirely different objects with no relation whatsoever, other than their close projected
proximity in the sky.
Studies searching for light deficits associated with SMBHs in the inner regions
of surface brightness profiles must use high resolution data. Poor seeing distorts the central
region of any surface brightness profile creating the mirage hallmarks of a SMBH. When possible,
the ideal surface brightness profile should be created by combining HST data in the core
and ground based data on the outskirts of any given galaxy.
\acknowledgments
We thank Yuto Ichinohe of the Japanese Space Agency (JAXA) for providing the
exquisite X-ray data. We thank the referee for providing a prompt and constructive report.
This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France.
Based on data from the GTC Public Archive at CAB (INTA-CSIC).
Based on observations obtained at the Gemini Observatory which is
operated by AURA under a cooperative agreement with the NSF on
behalf of the Gemini partnership.
The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under cooperative agreement by Associated
Universities, Inc.
\software: Astropy \citep{astropy2013}, Matplotlib \citep{hunter2007}, Numpy \citep{vanderwalt2011}.
Common Astronomy Software Applications (CASA) \citep{mcmullin2016}.
\facilities Gemini, Chandra, VLA, Grantecan.
\bigskip
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,505 |
/*
* To change this license header, choose License Headers in Project Properties.
* To change this template file, choose Tools | Templates
* and open the template in the editor.
*/
package Behavioral.Iterator.Iter;
/**
*
* @author argshub
*/
public interface Iterator<T> {
public T next();
public boolean hasNext();
}
| {
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{"url":"https:\/\/old.xwiki.org\/xwiki\/bin\/view\/Documentation\/DevGuide\/Architecture\/URL%20Architecture\/Standard%20URL%20Format\/?viewer=changes&rev1=23.1&rev2=24.1","text":"# Changes for page Standard URL Format\n\n<\nFrom version\nedited by Thomas Mortagne\non 2008\/12\/10\nTo version\nedited by Thomas Mortagne\non 2008\/12\/10\n>\nChange comment: There is no comment for this version\n\n## Details\n\nPage properties\nContent\n ... ... @@ -62,6 +62,7 @@ 62 62 1.1 Attachment 63 63 This part indicate the attachment you want to download from a particular page. 64 64 65 +See [platform:Features.Attachments] for more details about attachments. 65 65 1.1 Query string 66 66 Actions can use URL parameters to modify there action depending of there value. 67 67","date":"2023-04-01 20:51:10","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\": 0.8311544060707092, \"perplexity\": 11684.317196272434}, \"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\/1679296950247.65\/warc\/CC-MAIN-20230401191131-20230401221131-00775.warc.gz\"}"} | null | null |
{"url":"https:\/\/tex.stackexchange.com\/questions\/227876\/i-am-having-problems-with-typeset","text":"# I am having problems with typeset?\n\nMy document is called introduction.tex. I have the following code:\n\n\\documentclass{article}\n\\begin{document}\n\\title{Identification of potential therapeutic targets in human breast cancer}\n\\author{myName}\n\\date{August 2015}\n\\end{document}\n\n\nThis is what I get when I \"click\" the typeset button on the TexShop interface:\n\nThis is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014)\nrestricted \\write18 enabled.\nentering extended mode\n(.\/introduction.tex\nLaTeX2e <2014\/05\/01>\nBabel <3.9k> and hyphenation patterns for 78 languages loaded.\n(\/usr\/local\/texlive\/2014\/texmf-dist\/tex\/latex\/base\/article.cls\nDocument Class: article 2007\/10\/19 v1.4h Standard LaTeX document\nclass\n(\/usr\/local\/texlive\/2014\/texmf-dist\/tex\/latex\/base\/size10.clo))\n(.\/introduction.aux) (.\/introduction.aux) )\nNo pages of output.\nTranscript written on introduction.log.\n\n\nI would greatly appreciate the community's feedback. Thank you! :)\n\n\u2022 Add \\maketitle after your \\date command. You might also want to type some text after that ... perhaps something like \"Hello World! I'm using \\LaTeX{}.\" \u2013\u00a0jon Feb 13 '15 at 2:36\n\nYou have not given the compiler anything to publish. Just put Hi right before the \\end to verify this. And you need to move some content around and add a command for the titlepage as follows\n\n\\documentclass{article}\n\\title{Identification of potential therapeutic targets in human breast cancer}\n\\author{myName}\n\\date{August 2015}\n\\begin{document}\n\\maketitle\nhi\n\n\\end{document}\n\n\u2022 Strictly speaking, you don't need to have the \"metadata\" before \\begin{document} (for some classes, at least). \u2013\u00a0jon Feb 13 '15 at 3:00","date":"2019-11-18 21:24:05","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\": 0.9198135137557983, \"perplexity\": 8746.227153751182}, \"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-2019-47\/segments\/1573496669847.1\/warc\/CC-MAIN-20191118205402-20191118233402-00026.warc.gz\"}"} | null | null |
The Wolverhampton Civic Hall is a music venue in Wolverhampton, West Midlands, England. It has been one of the most notable live music venues in the county for several decades. It is part of a complex also including Wulfrun Hall and the Slade Rooms (previously known as The Little Civic). The complex is owned by City of Wolverhampton Council, operated by AEG Presents and is a Grade II listed building.
Construction and development
The hall, which was designed by Lyons and Israel in the Classical style was completed in May 1938. The smaller Wulfrun Hall had been inspired by the architecture of the Stockholm Concert Hall. It was officially opened by the Earl of Dartmouth on 12 May 1938. Jack Hylton and his orchestra provided the entertainment for the occasion. Queen Elizabeth II visited the Civic Hall and had lunch with civic leaders during a visit to the West Midlands on 24 May 1962.
It was renovated and extended to a design by Penoyre & Prasad in 2001.
The venue was reconfigured to create the new Slade Rooms in March 2010.
City of Wolverhampton Council announced plans for a revamp of the Civic Halls with a budget of £10.4 million in March 2015. The halls closed in December 2015 at which time the cost projection had increased to £14.4 million. In March 2019 it was announced that the halls would not reopen until autumn 2021 and that the cost was projected at £38.1 million.
In November 2021 it was announced that the Civic Halls were now due to reopen in Autumn 2022, which in October 2022 was officially revised to June 2023. The City Council also announced that they had signed a 25-year deal with AEG Presents to manage and promote the venues, which have been expanded to 3,404 in the Civic Hall and 1,289 in the Wulfrun Hall.
The reopening of the place will officially take place in June 2023, with a series of concerts including Siouxsie's.
Organ
A Compton Organ was specially designed for the Civic Hall. The organ was made up of over 5,500 pipes and contained an early electronic division known as a Melotone. G. D. Cunningham, then Birmingham City Organist, had the distinction of being the first musician to play there to invited guests. The Organ was re-built and enlarged in 2001, and was capable of being played as a concert organ or theatre organ.
In September 2016 it was announced that the organ would be removed and would not return to the Civic Hall. In February 2019 it was revealed that the pipes had been scrapped, despite several offers to restore them, free of charge.
Events
The first concert was performed on the evening of 16 May 1938, by the Old Royals Association, with Anne Ziegler, Webster Booth and several other soloists.
Comedians, such as Ken Dodd, Peter Kay and Jim Davidson, have appeared at the hall.
It has also staged some sports events. Throughout much of the 1970s and 1980s professional wrestling was broadcast live from the venue on Saturday afternoons. On 16 March 2006 the venue was first utilized by the Professional Darts Corporation as it hosted Week 4 of the 2006 Premier League Darts. From 2007 the venue has staged the Grand Slam of Darts. However the tournament in 2018 was moved to Aldersley Leisure Village due to on going refurbishments at the Civic Hall. Gary Anderson, having competed every year in tournament since its conception, says he prefers the Civic Hall over the new venue. "The Civic Hall - that was the Grand Slam of Darts."
There have also been some memorable concerts. Morrissey played his first solo performance at the Civic Hall on 22 December 1988. Nirvana performed "All Apologies" for the first time before a live audience at the Wulfrun Hall on 6 November 1991 and Louise Redknapp performed there on the final date of her Soft and Gentle Tour on 18 December 1997.
In 2009, The Specials played a concert at the Civic Hall as part of their 30th anniversary reunion tour; the performance was later released on DVD. More recently, the Welsh rock band, the Manic Street Preachers, gave a concert in June 2015.
It was announced in February 2023, Siouxsie would play her first UK gig after a ten year absence at the Civic Hall in June 2023.
References
External links
Official Website
Music venues in the West Midlands (county)
Buildings and structures in Wolverhampton
Darts venues
Tourist attractions in Wolverhampton
Grade II listed buildings in the West Midlands (county) | {
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Watch Live: Biden Delivers Remarks On Border Security As Admin Expands Title 42
Thursday, Jan 05, 2023 - 04:21 PM
President Joe Biden on Thursday will read remarks regarding border security, as his administration has now flip-flopped, and is working to expand Title 42, the Trump-era policy which allows the US Government to expel immigrants while they wait for asylum hearings, as opposed to allowing them to walk free in the United States.
Watch Live:
As the Wall Street Journal notes, "The Biden administration is expanding its use of a pandemic-era border measure known as Title 42 to begin rapidly expelling migrants from Cuba, Haiti, Nicaragua and Venezuela, while opening a new legal path for up to 30,000 migrants from those countries to enter the U.S. a month."
The new policy represents the broadest effort yet that the Biden administration has undertaken to deter migrants seeking asylum from crossing the border illegally. It also relies on an expanded use of Title 42 as a border-control measure, even while the administration is arguing in court that the measure is no longer justified on public-health grounds and must end. The Supreme Court is set to hear oral arguments on Title 42 in February.
The new program will require migrants hoping to seek asylum in the U.S. to be paired with financial sponsors and would give applicants two years of humanitarian protections, under which they can work legally and apply for asylum. -WSJ
Meanwhile, Biden indicated on Wednesday that he will visit the US-Mexico border for the first time since he took office nearly two years ago.
As the Epoch Times' Jack Phillips notes;
President Joe Biden indicated Wednesday that he will visit the U.S.–Mexico border for the first time since he took office nearly two years ago.
While in Kentucky, the president was asked if he will be going to the border in connection to a meeting next week in Mexico City with other world leaders. "That's my intention, we're working out the details now," Biden said.
Biden is slated to attend the North American Leaders' Summit in Mexico City on Jan. 9 and Jan. 10, where he is expected to meet with Mexican President Andrés Manuel López Obrador and Canadian Prime Minister Justin Trudeau.
Republicans and some Democrats who represent districts along the U.S.–Mexico border have repeatedly called on Biden to visit the border amid surging numbers of illegal immigrants crossing the border. They've also accused the administration of pursuing an "open borders" agenda by rescinding numerous Trump-era immigration rules.
In December, Biden was chided as he flew to Arizona to deliver a speech at a computer chip factory and highlighted jobs but did not visit the border. At the time, the president said that he could not visit "because there are more important things going on … they are going to invest billions of dollars in a new enterprise in the state."
Data released by U.S. Customs and Border Protection (CBP) show that nearly 2.4 million people were arrested for illegally crossing the border in the 2022 fiscal year, which ended Sept. 30. That's up from 1.7 million during the previous fiscal year.
White House press secretary Karine Jean-Pierre addressed Title 42, a border rule established under the Trump administration that allowed the federal government to quickly expel people at the border, after the Supreme Court last week ruled that the policy should remain while it considers arguments. A lower court had ruled to end the policy, which would have ended in December.
"To truly fix our broken immigration system though, we need Congress to act," Jean-Pierre told reporters Tuesday. "We saw the president on his first day in office put forth a comprehensive immigration policy, and he did that to show how important this was, how much of a priority this was for him."
And when she was asked about a possible Biden visit to the border, Jean-Pierre said in late December that "the president's focus right now is to come up with solutions" and "his focus on making sure that we have the resources to manage the challenges that we're seeing at the border."
After the midterms, top House Republicans have indicated that investigating the administration's border policies will be a priority. Last month, House Republican Leader Kevin McCarthy (R.-Calif.) told reporters that he had invited Biden to visit the border with him when Biden met with McCarthy and other GOP leaders following the Nov. 8 midterms.
People cross the Rio Grande towards the U.S.–Mexico border in Ciudad Juarez, Mexico, on Dec. 20, 2022. (Christian Chavez/AP Photo)
"The control of our border is lost right now. That is why I asked [the] homeland security secretary to resign. And come January, we'll have an investigation of why the border has become the situation it is and not allow them to continue along the same path," said McCarthy, who is currently vying to become the next House speaker amid opposition among members of his own party.
Some GOP lawmakers have said that Homeland Security Secretary Alejandro Mayorkas, who oversees the CBP and U.S. Immigration and Customs Enforcement, could face impeachment.
Mayorkas on Wednesday again acknowledged that the number of illegal immigrant encounters at the border is causing strain on the system.
"We're operating within a system that is fundamentally broken. No one disagrees with that. We just can't seem to agree upon the solution and a solution is long overdue. Within the broken immigration system that we are operating, we are managing the number of encounters and we are prepared to address the end of Title 42," he told the Washington Post.
Rep. Henry Cuellar (D-Texas), whose district sits along the border, said in late December that Biden should visit to see what he described as an escalating crisis.
"I don't know why they keep avoiding the border and saying there's other things, more important things, than visiting the border. If there is a crisis, show up. Just show up," he told CNN in December, coming days before the Supreme Court allowed Title 42 to remain for the time being.
Biden "showing up at the border would send a strong signal to the communities that he's there, he cares about the border communities," Cuellar said. "Just show up! It doesn't take much to just show up at the border."
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{"url":"http:\/\/www.tomshardware.com\/forum\/100578-45-index-cleared","text":"Sign in with\nSign up | Sign in\n\n# index.dat - can it be cleared?\n\nTags:\nLast response: in Windows XP\nShare\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nIs there an easy way to clear the content of Index.dat in Windows XP?\nAre there downloadable programs to do this for XP?\n--\nRemove the \"Delany\" to reply.\n\nMore about : index dat cleared\n\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nYou may find third party applications that clear index.dat (or claim to).\nBut the truth is: There is no need to clear the indexes. This is one of the\nmost enduring myths on the Internet.\n\nTed Zieglar\n\n\"Babel17delany\" <Babel17delany@optonline.net> wrote in message\nnews:vm4xd.3236$v22.173@fe11.lga... > Is there an easy way to clear the content of Index.dat in Windows XP? > Are there downloadable programs to do this for XP? > -- > Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) But what if I want to remove information about how I used a computer from a machine that others may have access to? Ted Zieglar wrote: > You may find third party applications that clear index.dat (or claim > to). But the truth is: There is no need to clear the indexes. This is > one of the most enduring myths on the Internet. > > Ted Zieglar > > \"Babel17delany\" <Babel17delany@optonline.net> wrote in message > news:vm4xd.3236$v22.173@fe11.lga...\n>\n>> Is there an easy way to clear the content of Index.dat in Windows XP?\n>> Are there downloadable programs to do this for XP?\n>> --\n>> Remove the \"Delany\" to reply.\n>\n>\n\n--\nRemove the \"Delany\" to reply.\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nOthers users can't see your indexes.\n\nTed Zieglar\n\n\"Babel17delany\" <Babel17delany@optonline.net> wrote in message\nnews\u00a0r5xd.3250$Et2.200@fe11.lga... > But what if I want to remove information about how I used a computer from > a machine that others may have access to? > > Ted Zieglar wrote: >> You may find third party applications that clear index.dat (or claim to). >> But the truth is: There is no need to clear the indexes. This is one of >> the most enduring myths on the Internet. >> >> Ted Zieglar >> >> \"Babel17delany\" <Babel17delany@optonline.net> wrote in message >> news:vm4xd.3236$v22.173@fe11.lga...\n>>\n>>> Is there an easy way to clear the content of Index.dat in Windows XP?\n>>> Are there downloadable programs to do this for XP?\n>>> --\n>>> Remove the \"Delany\" to reply.\n>>\n>>\n>\n> --\n> Remove the \"Delany\" to reply.\nRelated ressources\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nYes use Cleancache from www.buttuglysoftware.com (it is free) You can see my\nreview of the product either by clicking on the review link on the buttugly\nsoftware website or visiting my web site at:\n\nhttp:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n\nclick on the Review button on my web site and then click the CleanCache\noption.\n\nI use this application every day and find it very useful.\n\n--\nJohn Barnett MVP\nAssociate Expert\nhttp:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n\n\"Babel17delany\" <Babel17delany@optonline.net> wrote in message\nnews:vm4xd.3236$v22.173@fe11.lga... > Is there an easy way to clear the content of Index.dat in Windows XP? > Are there downloadable programs to do this for XP? > -- > Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) Thank you very much for your reply. If you don't mind, might I ask two more related questions: 1. This may sound silly, but is the program truly SAFE to use with XP? I ask this because I once used with XP two cleaning programs that I used without difficulty in Windows 98. I ended up with a system crash (\"NTLDR Is Missing\" ) that was very difficult to recover from (and required much phone time with manufacturer's technical support). Is this program truly made for XP? 2. I'm not sure I understand the need for \".NET Framework\". If I remember correctly, \".Net\" is a Microsoft program that has something to do with \"Passport\" and is used to enter passwords and such. Please correct me if I am wrong about this. If this is what \".Net\" refers to, I elected to not install it. Why is \".Net\" required for CleanCache to work? Is \".Net\" a safe program to install? Thank you very much for your time and expertise. John Barnett MVP wrote: > Yes use Cleancache from www.buttuglysoftware.com (it is free) You can see my > review of the product either by clicking on the review link on the buttugly > software website or visiting my web site at: > > http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm > > click on the Review button on my web site and then click the CleanCache > option. > > I use this application every day and find it very useful. > -- Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) Thank you very much for your reply. If you don't mind, might I ask two more related questions: 1. This may sound silly, but is the program truly SAFE to use with XP? I ask this because I once used with XP two cleaning programs that I used without difficulty in Windows 98. I ended up with a system crash (\"NTLDR Is Missing\" ) that was very difficult to recover from (and required much phone time with manufacturer's technical support). Is this program truly made for XP? 2. I'm not sure I understand the need for \".NET Framework\". If I remember correctly, \".Net\" is a Microsoft program that has something to do with \"Passport\" and is used to enter passwords and such. Please correct me if I am wrong about this. If this is what \".Net\" refers to, I elected to not install it. Why is \".Net\" required for CleanCache to work? Is \".Net\" a safe program to install? Thank you very much for your time and expertise. John Barnett MVP wrote: > Yes use Cleancache from www.buttuglysoftware.com (it is free) You can see my review of the product either by clicking on the review link on the buttugly software website or visiting my web site at: > > http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm > > click on the Review button on my web site and then click the CleanCache option. > > I use this application every day and find it very useful. > -- Remove the \"Delany\" to reply. John Barnett MVP wrote: > Yes use Cleancache from www.buttuglysoftware.com (it is free) You can see my > review of the product either by clicking on the review link on the buttugly > software website or visiting my web site at: > > http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm > > click on the Review button on my web site and then click the CleanCache > option. > > I use this application every day and find it very useful. > -- Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) \"Babel17delany\" <Babel17delany@optonline.net> wrote in message news:Zo5xd.3249$dD2.929@fe11.lga\n>\n> 2. I'm not sure I understand the need for \".NET Framework\". If I\n> remember correctly, \".Net\" is a Microsoft program that has something\n> to do with \"Passport\" and is used to enter passwords and such. Please\n> correct me if I am wrong about this. If this is what \".Net\" refers\n> to, I elected to not install it. Why is \".Net\" required for\n> CleanCache to work? Is \".Net\" a safe program to install?\n>\n> Thank you very much for your time and expertise.\n\n..NET Framework is needed to run programs written with the .NET tools like\nDBXpress (www.oehelp.com).\n\n--\nFrank Saunders, MS-MVP, IE\/OE\nPlease respond in Newsgroup only. Do not send email\nhttp:\/\/www.fjsmjs.com\nProtect your PC\nhttp:\/\/www.microsoft.com\/security\/protect\/\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\n..Net sounds harmless enough. I may have mistaken is for something else,\nlike \"Passport\".\n\nFrank Saunders, MS-MVP wrote:\n> \"Babel17delany\" <Babel17delany@optonline.net> wrote in message\n> news:Zo5xd.3249$dD2.929@fe11.lga > >> >> 2. I'm not sure I understand the need for \".NET Framework\". If I >> remember correctly, \".Net\" is a Microsoft program that has something >> to do with \"Passport\" and is used to enter passwords and such. Please >> correct me if I am wrong about this. If this is what \".Net\" refers >> to, I elected to not install it. Why is \".Net\" required for >> CleanCache to work? Is \".Net\" a safe program to install? >> >> Thank you very much for your time and expertise. > > > .NET Framework is needed to run programs written with the .NET tools > like DBXpress (www.oehelp.com). > -- Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) I, too, am not keen on downloading software to do such things. When I do this, I log on as Administrator and then delete the index.dat from the relevant <username>. Ideally, I'd like to do this automatically (perhaps via a script which runs at logon or shutdown) every 2 - 4 weeks. I've searched for this (and seen postings on scripting NGs) but to no avail. I think I'll have to continue doing it manually. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) Were you aware that Windows XP clears the index when you remove Temporary Internet Files? Ted Zieglar \"Tosca\" <no-spam@thank-you.com> wrote in message news Ch9xoa5EHA.4072@TK2MSFTNGP10.phx.gbl... > I, too, am not keen on downloading software to do such things. When I do > this, I log on as Administrator and then delete the index.dat from the > relevant <username>. Ideally, I'd like to do this automatically (perhaps > via a script which runs at logon or shutdown) every 2 - 4 weeks. I've > searched for this (and seen postings on scripting NGs) but to no avail. I > think I'll have to continue doing it manually. > > Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) Can I do any unintentional damage by simply deleting the entire index.dat file? Can it even be done? I was under the impression that since the file is always in use, it cannot be deleted. Tosca wrote: > I, too, am not keen on downloading software to do such things. When I do > this, I log on as Administrator and then delete the index.dat from the > relevant <username>. Ideally, I'd like to do this automatically (perhaps > via a script which runs at logon or shutdown) every 2 - 4 weeks. I've > searched for this (and seen postings on scripting NGs) but to no avail. I > think I'll have to continue doing it manually. > > -- Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) I was not aware of this. Does this mean that when I clear usage tracks with Spybot or with AdAware, the Index.dat is removed also? Ted Zieglar wrote: > Were you aware that Windows XP clears the index when you remove > Temporary Internet Files? > > Ted Zieglar > > \"Tosca\" <no-spam@thank-you.com> wrote in message > news Ch9xoa5EHA.4072@TK2MSFTNGP10.phx.gbl... > >> I, too, am not keen on downloading software to do such things. When I do >> this, I log on as Administrator and then delete the index.dat from the >> relevant <username>. Ideally, I'd like to do this automatically (perhaps >> via a script which runs at logon or shutdown) every 2 - 4 weeks. I've >> searched for this (and seen postings on scripting NGs) but to no >> avail. I >> think I'll have to continue doing it manually. >> >> > -- Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) hi i too have some problems relating to this index.dat files. Even after clearing the temp internet files, index.dat exists in some folders which cant be deleted. Any help is highly appreciated \"Babel17delany\" wrote: > Can I do any unintentional damage by simply deleting the entire > index.dat file? Can it even be done? I was under the impression that > since the file is always in use, it cannot be deleted. > > Tosca wrote: > > I, too, am not keen on downloading software to do such things. When I do > > this, I log on as Administrator and then delete the index.dat from the > > relevant <username>. Ideally, I'd like to do this automatically (perhaps > > via a script which runs at logon or shutdown) every 2 - 4 weeks. I've > > searched for this (and seen postings on scripting NGs) but to no avail. I > > think I'll have to continue doing it manually. > > > > > > -- > Remove the \"Delany\" to reply. > Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) No - I moved from 98SE recently and couldn't delete the index.dat easily in 98SE. I recall that I had to delete it by using some script in the autoexec.bat file (I think that's how it was done!). I was under the impression that it couldn't be deleted in XP Pro when logged in as the user who's index.dat I was trying to delete. I've never tried it though, as I assumed that XP wouldn't allow me to do that. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) CleanCache is perfectly safe to use on XP I use it daily. Your second question has been answered elsewhere. .NET framework is needed because CleanCache is written using >NET framework. As for index.dat files they hold all the information contained in temporary internet files\/history etc. Simply deleting the contents of the temporary internet files etc does *not* delete the relevant index.dat. I suggest you try it. On a newly installed copy of xp the index.dat files register 16k. when empty. As they are utilised the space increases. you may find that yours are 32 or 64k. On deleting the temporary internet files from your pc the files does not go back to 16k and is therefore not cleansed. Index dat files can be deleted using dos commands which is basically what cleancache does. This is done as your pc restarts, by using cleancache regularly you always start with a 'clean' index dat file. As I stated in my earlier post cleancache is free so why bother with scripts when this application will do 'exactly what it says on the tin' As a journalist it takes a lot to impress me where software is concerned and I certainly don't recommend software lightly. I have tried dozens of so called 'cleaners' and each time I come back to cleancache. -- John Barnett MVP Associate Expert http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm \"Babel17delany\" <Babel17delany@optonline.net> wrote in message news:Zo5xd.3249$dD2.929@fe11.lga...\n> Thank you very much for your reply.\n>\n> If you don't mind, might I ask two more related questions:\n>\n> 1. This may sound silly, but is the program truly SAFE to use with XP? I\n> ask this because I once used with XP two cleaning programs that I used\n> without difficulty in Windows 98. I ended up with a system crash (\"NTLDR\n> Is Missing\" ) that was very difficult to recover from (and required much\n> phone time with manufacturer's technical support). Is this program truly\n> made for XP?\n>\n> 2. I'm not sure I understand the need for \".NET Framework\". If I remember\n> correctly, \".Net\" is a Microsoft program that has something to do with\n> \"Passport\" and is used to enter passwords and such. Please correct me if\n> I am wrong about this. If this is what \".Net\" refers to, I elected to not\n> install it. Why is \".Net\" required for CleanCache to work? Is \".Net\" a\n> safe program to install?\n>\n> Thank you very much for your time and expertise.\n>\n> John Barnett MVP wrote:\n>> Yes use Cleancache from www.buttuglysoftware.com (it is free) You can see\n>> my review of the product either by clicking on the review link on the\n>> buttugly software website or visiting my web site at:\n>>\n>> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n>>\n>> click on the Review button on my web site and then click the CleanCache\n>> option.\n>>\n>> I use this application every day and find it very useful.\n>>\n>\n> --\n> Remove the \"Delany\" to reply.\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nI don't know what \"usage tracks\" means, and I don't consider myself\nqualified to answer questions about \"Spybot\" or Ad-Aware.\n\nThe indexes are cleared when your clear TIF either manually or automatically\nwith the close of each browser session. Both can be done through Internet\nExplorer > Tools > Internet Options or Control Panel > Internet Options.\n\nIn the 9x versions of Windows, the indexes were not always completely\ncleared when TIF was cleared, and so index.dat used to grow and grow,\nsometimes to several MB in size. Thus, people used to include commands in\nautoexec to delete index.dat during startup, before Windows loaded.\n\nThe index.dat problem has been fixed in Windows XP, but apparently old\nhabits die hard. Windows XP also incorporates NT-style user accounts. When\nthese are setup correctly, users cannot see each others documents, among\nthem the indexes.\n\nTed Zieglar\n\n\"Babel17delany\" <Babel17delany@optonline.net> wrote in message\nnews:%nexd.3285$Bp7.2065@fe11.lga... >I was not aware of this. Does this mean that when I clear usage tracks >with Spybot or with AdAware, the Index.dat is removed also? > > Ted Zieglar wrote: >> Were you aware that Windows XP clears the index when you remove Temporary >> Internet Files? >> >> Ted Zieglar >> >> \"Tosca\" <no-spam@thank-you.com> wrote in message >> news Ch9xoa5EHA.4072@TK2MSFTNGP10.phx.gbl... >> >>> I, too, am not keen on downloading software to do such things. When I >>> do >>> this, I log on as Administrator and then delete the index.dat from the >>> relevant <username>. Ideally, I'd like to do this automatically >>> (perhaps >>> via a script which runs at logon or shutdown) every 2 - 4 weeks. I've >>> searched for this (and seen postings on scripting NGs) but to no avail. >>> I >>> think I'll have to continue doing it manually. >>> >>> >> > > -- > Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) \"On deleting the temporary internet files from your pc the files does not go back to 16k and is therefore not cleansed.\" As one who used to delete the indexes during my Windows 9x days, I was interested to see if this was still needed in XP. After 2.5 years of using XP, I have never noticed the indexes increasing in size beyond the default. Ted Zieglar \"John Barnett MVP\" <freelanceit@mvps.org.nospam> wrote in message news:udm1JSf5EHA.1400@TK2MSFTNGP11.phx.gbl... > CleanCache is perfectly safe to use on XP I use it daily. > Your second question has been answered elsewhere. .NET framework is needed > because CleanCache is written using >NET framework. > As for index.dat files they hold all the information contained in > temporary internet files\/history etc. Simply deleting the contents of the > temporary internet files etc does *not* delete the relevant index.dat. I > suggest you try it. On a newly installed copy of xp the index.dat files > register 16k. when empty. As they are utilised the space increases. you > may find that yours are 32 or 64k. On deleting the temporary internet > files from your pc the files does not go back to 16k and is therefore not > cleansed. Index dat files can be deleted using dos commands which is > basically what cleancache does. This is done as your pc restarts, by using > cleancache regularly you always start with a 'clean' index dat file. > As I stated in my earlier post cleancache is free so why bother with > scripts when this application will do 'exactly what it says on the tin' > As a journalist it takes a lot to impress me where software is concerned > and I certainly don't recommend software lightly. I have tried dozens of > so called 'cleaners' and each time I come back to cleancache. > > -- > John Barnett MVP > Associate Expert > http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm > \"Babel17delany\" <Babel17delany@optonline.net> wrote in message > news:Zo5xd.3249$dD2.929@fe11.lga...\n>> Thank you very much for your reply.\n>>\n>> If you don't mind, might I ask two more related questions:\n>>\n>> 1. This may sound silly, but is the program truly SAFE to use with XP? I\n>> ask this because I once used with XP two cleaning programs that I used\n>> without difficulty in Windows 98. I ended up with a system crash (\"NTLDR\n>> Is Missing\" ) that was very difficult to recover from (and required much\n>> phone time with manufacturer's technical support). Is this program truly\n>> made for XP?\n>>\n>> 2. I'm not sure I understand the need for \".NET Framework\". If I\n>> remember correctly, \".Net\" is a Microsoft program that has something to\n>> do with \"Passport\" and is used to enter passwords and such. Please\n>> correct me if I am wrong about this. If this is what \".Net\" refers to, I\n>> elected to not install it. Why is \".Net\" required for CleanCache to\n>> work? Is \".Net\" a safe program to install?\n>>\n>> Thank you very much for your time and expertise.\n>>\n>> John Barnett MVP wrote:\n>>> Yes use Cleancache from www.buttuglysoftware.com (it is free) You can\n>>> see my review of the product either by clicking on the review link on\n>>> the buttugly software website or visiting my web site at:\n>>>\n>>> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n>>>\n>>> click on the Review button on my web site and then click the CleanCache\n>>> option.\n>>>\n>>> I use this application every day and find it very useful.\n>>>\n>>\n>> --\n>> Remove the \"Delany\" to reply.\n>\n>\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nWhere do I download \".Net\" from, which the CleanCache site says I need\nto be able to operate their software?\n\nJohn Barnett MVP wrote:\n> Yes use Cleancache from www.buttuglysoftware.com (it is free) You can see my\n> review of the product either by clicking on the review link on the buttugly\n> software website or visiting my web site at:\n>\n> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n>\n> click on the Review button on my web site and then click the CleanCache\n> option.\n>\n> I use this application every day and find it very useful.\n>\n\n--\nRemove the \"Delany\" to reply.\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nI was able to delete index.dat from 98SE with a downloaded program - it\ncost me about $20 and worked well. Unfortunately, I believe that when I transferred the program to XP it may have been the cause of a major crash. Tosca wrote: > No - I moved from 98SE recently and couldn't delete the index.dat easily in > 98SE. I recall that I had to delete it by using some script in the > autoexec.bat file (I think that's how it was done!). I was under the > impression that it couldn't be deleted in XP Pro when logged in as the user > who's index.dat I was trying to delete. I've never tried it though, as I > assumed that XP wouldn't allow me to do that. > > -- Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) \"Babel17delany\" <Babel17delany@optonline.net> wrote in message news:cwpxd.3379$oc6.2817@fe11.lga\n> Where do I download \".Net\" from, which the CleanCache site says I need\n> to be able to operate their software?\n\nhttp:\/\/www.microsoft.com\/downloads\/details.aspx?FamilyI...\n\n--\nFrank Saunders, MS-MVP, IE\/OE\nPlease respond in Newsgroup only. Do not send email\nhttp:\/\/www.fjsmjs.com\nProtect your PC\nhttp:\/\/www.microsoft.com\/security\/protect\/\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nThank you very much for your reply. I will download \".Net\" (from the\nMicrosoft site?) and then download CleanCache next weekend (weekends are\nthe only time I have to do much other than pick up e-mail on the computer).\n\nJohn Barnett MVP wrote:\n> CleanCache is perfectly safe to use on XP I use it daily.\n> Your second question has been answered elsewhere. .NET framework is needed\n> because CleanCache is written using >NET framework.\n> As for index.dat files they hold all the information contained in temporary\n> internet files\/history etc. Simply deleting the contents of the temporary\n> internet files etc does *not* delete the relevant index.dat. I suggest you\n> try it. On a newly installed copy of xp the index.dat files register 16k.\n> when empty. As they are utilised the space increases. you may find that\n> yours are 32 or 64k. On deleting the temporary internet files from your pc\n> the files does not go back to 16k and is therefore not cleansed. Index dat\n> files can be deleted using dos commands which is basically what cleancache\n> does. This is done as your pc restarts, by using cleancache regularly you\n> always start with a 'clean' index dat file.\n> As I stated in my earlier post cleancache is free so why bother with scripts\n> when this application will do 'exactly what it says on the tin'\n> As a journalist it takes a lot to impress me where software is concerned and\n> I certainly don't recommend software lightly. I have tried dozens of so\n> called 'cleaners' and each time I come back to cleancache.\n>\n\n--\nRemove the \"Delany\" to reply.\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\n\"Usage Tracks\" is how SpyBot refers collectively to Cache, History and\nTemporary Internet Files.\n\nNow what you have just explained is very different from what others have\nsaid on this thread. Perhaps I should, next weekend, check the size of\nindex.dat before and after I close Internet Explorer.\n\nTed Zieglar wrote:\n> I don't know what \"usage tracks\" means, and I don't consider myself\n> qualified to answer questions about \"Spybot\" or Ad-Aware.\n>\n> The indexes are cleared when your clear TIF either manually or\n> automatically with the close of each browser session. Both can be done\n> through Internet Explorer > Tools > Internet Options or Control Panel >\n> Internet Options.\n>\n> In the 9x versions of Windows, the indexes were not always completely\n> cleared when TIF was cleared, and so index.dat used to grow and grow,\n> sometimes to several MB in size. Thus, people used to include commands\n> in autoexec to delete index.dat during startup, before Windows loaded.\n>\n> The index.dat problem has been fixed in Windows XP, but apparently old\n> habits die hard. Windows XP also incorporates NT-style user accounts.\n> When these are setup correctly, users cannot see each others documents,\n> among them the indexes.\n>\n> Ted Zieglar\n>\n> \"Babel17delany\" <Babel17delany@optonline.net> wrote in message\n> news:%nexd.3285$Bp7.2065@fe11.lga... > >> I was not aware of this. Does this mean that when I clear usage >> tracks with Spybot or with AdAware, the Index.dat is removed also? >> >> Ted Zieglar wrote: >> >>> Were you aware that Windows XP clears the index when you remove >>> Temporary Internet Files? >>> >>> Ted Zieglar >>> >>> \"Tosca\" <no-spam@thank-you.com> wrote in message >>> news Ch9xoa5EHA.4072@TK2MSFTNGP10.phx.gbl... >>> >>>> I, too, am not keen on downloading software to do such things. When >>>> I do >>>> this, I log on as Administrator and then delete the index.dat from the >>>> relevant <username>. Ideally, I'd like to do this automatically >>>> (perhaps >>>> via a script which runs at logon or shutdown) every 2 - 4 weeks. I've >>>> searched for this (and seen postings on scripting NGs) but to no >>>> avail. I >>>> think I'll have to continue doing it manually. >>>> >>>> >>> >> >> -- >> Remove the \"Delany\" to reply. > > -- Remove the \"Delany\" to reply. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) \"Babel17delany\" <Babel17delany@optonline.net> wrote in message news:vm4xd.3236$v22.173@fe11.lga...\n> Is there an easy way to clear the content of Index.dat in Windows XP?\n> Are there downloadable programs to do this for XP?\n> --\n> Remove the \"Delany\" to reply.\n\nYou can delete it without using any software other than Windows. Log out of\nyou user profile and login as \"Administrator\" (or a different user account\nwith administrator rights). Then navigate through Windows Explorer to\nsomething similar to: C:\\Documents and Settings\\{user profile name}\\Local\nSettings\\Temporary Internet Files\\Content.IE5 You can safely delete\n*everything* in this directory which includes the index.dat file.\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nHey Johnny u mentioned about da content.IE5 file. i get all da files listed\ndirectly in da temp internet files folder. But i do try to remove index.dat\nbut in vain.yesterday i downloaded a software CCleaner & tried to erase da\nindex file. but it did not work. i hv index files in C:\\Documents and\nSettings\\Administrator\\Cookies. pls help\n\n\"Johnny Lingo\" wrote:\n\n>\n> \"Babel17delany\" <Babel17delany@optonline.net> wrote in message\n> news:vm4xd.3236$v22.173@fe11.lga... > > Is there an easy way to clear the content of Index.dat in Windows XP? > > Are there downloadable programs to do this for XP? > > -- > > Remove the \"Delany\" to reply. > > You can delete it without using any software other than Windows. Log out of > you user profile and login as \"Administrator\" (or a different user account > with administrator rights). Then navigate through Windows Explorer to > something similar to: C:\\Documents and Settings\\{user profile name}\\Local > Settings\\Temporary Internet Files\\Content.IE5 You can safely delete > *everything* in this directory which includes the index.dat file. > > > Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) Ted my cookies index.dat file stands at 32kb as we speak. So does my temp internet file and history. As soon as I use cleancache they will be deleted and returned to 16kb. If I've left them long enough they have gone even higher than 32kb. -- John Barnett MVP Associate Expert http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm \"Ted Zieglar\" <teddyz@notmail.com> wrote in message news:epVsdUi5EHA.3828@TK2MSFTNGP09.phx.gbl... > \"On deleting the temporary internet files from your pc the files does not > go back to 16k and is therefore not cleansed.\" > > As one who used to delete the indexes during my Windows 9x days, I was > interested to see if this was still needed in XP. After 2.5 years of using > XP, I have never noticed the indexes increasing in size beyond the > default. > > Ted Zieglar > > \"John Barnett MVP\" <freelanceit@mvps.org.nospam> wrote in message > news:udm1JSf5EHA.1400@TK2MSFTNGP11.phx.gbl... >> CleanCache is perfectly safe to use on XP I use it daily. >> Your second question has been answered elsewhere. .NET framework is >> needed because CleanCache is written using >NET framework. >> As for index.dat files they hold all the information contained in >> temporary internet files\/history etc. Simply deleting the contents of the >> temporary internet files etc does *not* delete the relevant index.dat. I >> suggest you try it. On a newly installed copy of xp the index.dat files >> register 16k. when empty. As they are utilised the space increases. you >> may find that yours are 32 or 64k. On deleting the temporary internet >> files from your pc the files does not go back to 16k and is therefore not >> cleansed. Index dat files can be deleted using dos commands which is >> basically what cleancache does. This is done as your pc restarts, by >> using cleancache regularly you always start with a 'clean' index dat >> file. >> As I stated in my earlier post cleancache is free so why bother with >> scripts when this application will do 'exactly what it says on the tin' >> As a journalist it takes a lot to impress me where software is concerned >> and I certainly don't recommend software lightly. I have tried dozens of >> so called 'cleaners' and each time I come back to cleancache. >> >> -- >> John Barnett MVP >> Associate Expert >> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm >> \"Babel17delany\" <Babel17delany@optonline.net> wrote in message >> news:Zo5xd.3249$dD2.929@fe11.lga...\n>>> Thank you very much for your reply.\n>>>\n>>> If you don't mind, might I ask two more related questions:\n>>>\n>>> 1. This may sound silly, but is the program truly SAFE to use with XP? I\n>>> ask this because I once used with XP two cleaning programs that I used\n>>> without difficulty in Windows 98. I ended up with a system crash (\"NTLDR\n>>> Is Missing\" ) that was very difficult to recover from (and required much\n>>> phone time with manufacturer's technical support). Is this program truly\n>>> made for XP?\n>>>\n>>> 2. I'm not sure I understand the need for \".NET Framework\". If I\n>>> remember correctly, \".Net\" is a Microsoft program that has something to\n>>> do with \"Passport\" and is used to enter passwords and such. Please\n>>> correct me if I am wrong about this. If this is what \".Net\" refers to,\n>>> I elected to not install it. Why is \".Net\" required for CleanCache to\n>>> work? Is \".Net\" a safe program to install?\n>>>\n>>> Thank you very much for your time and expertise.\n>>>\n>>> John Barnett MVP wrote:\n>>>> Yes use Cleancache from www.buttuglysoftware.com (it is free) You can\n>>>> see my review of the product either by clicking on the review link on\n>>>> the buttugly software website or visiting my web site at:\n>>>>\n>>>> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n>>>>\n>>>> click on the Review button on my web site and then click the CleanCache\n>>>> option.\n>>>>\n>>>> I use this application every day and find it very useful.\n>>>>\n>>>\n>>> --\n>>> Remove the \"Delany\" to reply.\n>>\n>>\n>\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nI'm not sure where you're going with that point. My index.dat has never gone\nabove 32kb, and that size is the inevitable result of storing cookies. I\nsuppose I could refuse all cookies, but that's not an option for me.\n\nAs I recall from my 9x days, deleting the indicies broke the link to cookies\nand internet history. Users who deleted the indicies were advised to clear\ntheir cookies and history since, without an index, they were pretty much\nuseless. The few cookies I keep are really handy to have around.\n\nIn any case, the limited users on my computer can't even get to my\nindex.dat.\n\nIndex.dat bloat was a frequently observed problem in the 9x versions of\nWindows. I have personally not read of index.dat bloat being an issue with\nXP. Of course I would be interested in reading otherwise.\n\nWhere a user has two or more admin accounts on the same computer, or where\nall users share the same account, there are larger privacy issues. And if a\nuser is so concerned that other users on the computer will want to spy on\nthem, there are problems substantially more serious than index.dat!\n\nI am personally not aware of any exploit where the intruder's goal was to\nglean information from the user's indicies, but like I say, I would be\ninterested to learn otherwise.\n--\nTed Zieglar\n\n\"John Barnett MVP\" <freelanceit@mvps.org.nospam> wrote in message\nnews:urxisls5EHA.1404@TK2MSFTNGP11.phx.gbl...\n> Ted my cookies index.dat file stands at 32kb as we speak. So does my temp\n> internet file and history. As soon as I use cleancache they will be\ndeleted\n> and returned to 16kb. If I've left them long enough they have gone even\n> higher than 32kb.\n>\n> --\n> John Barnett MVP\n> Associate Expert\n> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n> \"Ted Zieglar\" <teddyz@notmail.com> wrote in message\n> news:epVsdUi5EHA.3828@TK2MSFTNGP09.phx.gbl...\n> > \"On deleting the temporary internet files from your pc the files does\nnot\n> > go back to 16k and is therefore not cleansed.\"\n> >\n> > As one who used to delete the indexes during my Windows 9x days, I was\n> > interested to see if this was still needed in XP. After 2.5 years of\nusing\n> > XP, I have never noticed the indexes increasing in size beyond the\n> > default.\n> >\n> > Ted Zieglar\n> >\n> > \"John Barnett MVP\" <freelanceit@mvps.org.nospam> wrote in message\n> > news:udm1JSf5EHA.1400@TK2MSFTNGP11.phx.gbl...\n> >> CleanCache is perfectly safe to use on XP I use it daily.\n> >> Your second question has been answered elsewhere. .NET framework is\n> >> needed because CleanCache is written using >NET framework.\n> >> As for index.dat files they hold all the information contained in\n> >> temporary internet files\/history etc. Simply deleting the contents of\nthe\n> >> temporary internet files etc does *not* delete the relevant index.dat.\nI\n> >> suggest you try it. On a newly installed copy of xp the index.dat files\n> >> register 16k. when empty. As they are utilised the space increases. you\n> >> may find that yours are 32 or 64k. On deleting the temporary internet\n> >> files from your pc the files does not go back to 16k and is therefore\nnot\n> >> cleansed. Index dat files can be deleted using dos commands which is\n> >> basically what cleancache does. This is done as your pc restarts, by\n> >> using cleancache regularly you always start with a 'clean' index dat\n> >> file.\n> >> As I stated in my earlier post cleancache is free so why bother with\n> >> scripts when this application will do 'exactly what it says on the tin'\n> >> As a journalist it takes a lot to impress me where software is\nconcerned\n> >> and I certainly don't recommend software lightly. I have tried dozens\nof\n> >> so called 'cleaners' and each time I come back to cleancache.\n> >>\n> >> --\n> >> John Barnett MVP\n> >> Associate Expert\n> >> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n> >> \"Babel17delany\" <Babel17delany@optonline.net> wrote in message\n> >> news:Zo5xd.3249$dD2.929@fe11.lga... > >>> Thank you very much for your reply. > >>> > >>> If you don't mind, might I ask two more related questions: > >>> > >>> 1. This may sound silly, but is the program truly SAFE to use with XP? I > >>> ask this because I once used with XP two cleaning programs that I used > >>> without difficulty in Windows 98. I ended up with a system crash (\"NTLDR > >>> Is Missing\" ) that was very difficult to recover from (and required much > >>> phone time with manufacturer's technical support). Is this program truly > >>> made for XP? > >>> > >>> 2. I'm not sure I understand the need for \".NET Framework\". If I > >>> remember correctly, \".Net\" is a Microsoft program that has something to > >>> do with \"Passport\" and is used to enter passwords and such. Please > >>> correct me if I am wrong about this. If this is what \".Net\" refers to, > >>> I elected to not install it. Why is \".Net\" required for CleanCache to > >>> work? Is \".Net\" a safe program to install? > >>> > >>> Thank you very much for your time and expertise. > >>> > >>> John Barnett MVP wrote: > >>>> Yes use Cleancache from www.buttuglysoftware.com (it is free) You can > >>>> see my review of the product either by clicking on the review link on > >>>> the buttugly software website or visiting my web site at: > >>>> > >>>> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm > >>>> > >>>> click on the Review button on my web site and then click the CleanCache > >>>> option. > >>>> > >>>> I use this application every day and find it very useful. > >>>> > >>> > >>> -- > >>> Remove the \"Delany\" to reply. > >> > >> > > > > Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) \"Ted Zieglar\" <teddyz@notmail.com> wrote in message news:epVsdUi5EHA.3828@TK2MSFTNGP09.phx.gbl... > \"On deleting the temporary internet files from your pc the files does not > go back to 16k and is therefore not cleansed.\" > > As one who used to delete the indexes during my Windows 9x days, I was > interested to see if this was still needed in XP. After 2.5 years of using > XP, I have never noticed the indexes increasing in size beyond the > default. > > Ted Zieglar > > \"John Barnett MVP\" <freelanceit@mvps.org.nospam> wrote in message > news:udm1JSf5EHA.1400@TK2MSFTNGP11.phx.gbl... >> CleanCache is perfectly safe to use on XP I use it daily. >> Your second question has been answered elsewhere. .NET framework is >> needed because CleanCache is written using >NET framework. >> As for index.dat files they hold all the information contained in >> temporary internet files\/history etc. Simply deleting the contents of the >> temporary internet files etc does *not* delete the relevant index.dat. I >> suggest you try it. On a newly installed copy of xp the index.dat files >> register 16k. when empty. As they are utilised the space increases. you >> may find that yours are 32 or 64k. On deleting the temporary internet >> files from your pc the files does not go back to 16k and is therefore not >> cleansed. Index dat files can be deleted using dos commands which is >> basically what cleancache does. This is done as your pc restarts, by >> using cleancache regularly you always start with a 'clean' index dat >> file. >> As I stated in my earlier post cleancache is free so why bother with >> scripts when this application will do 'exactly what it says on the tin' >> As a journalist it takes a lot to impress me where software is concerned >> and I certainly don't recommend software lightly. I have tried dozens of >> so called 'cleaners' and each time I come back to cleancache. >> >> -- >> John Barnett MVP >> Associate Expert >> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm >> \"Babel17delany\" <Babel17delany@optonline.net> wrote in message >> news:Zo5xd.3249$dD2.929@fe11.lga...\n>>> Thank you very much for your reply.\n>>>\n>>> If you don't mind, might I ask two more related questions:\n>>>\n>>> 1. This may sound silly, but is the program truly SAFE to use with XP? I\n>>> ask this because I once used with XP two cleaning programs that I used\n>>> without difficulty in Windows 98. I ended up with a system crash (\"NTLDR\n>>> Is Missing\" ) that was very difficult to recover from (and required much\n>>> phone time with manufacturer's technical support). Is this program truly\n>>> made for XP?\n>>>\n>>> 2. I'm not sure I understand the need for \".NET Framework\". If I\n>>> remember correctly, \".Net\" is a Microsoft program that has something to\n>>> do with \"Passport\" and is used to enter passwords and such. Please\n>>> correct me if I am wrong about this. If this is what \".Net\" refers to,\n>>> I elected to not install it. Why is \".Net\" required for CleanCache to\n>>> work? Is \".Net\" a safe program to install?\n>>>\n>>> Thank you very much for your time and expertise.\n>>>\n>>> John Barnett MVP wrote:\n>>>> Yes use Cleancache from www.buttuglysoftware.com (it is free) You can\n>>>> see my review of the product either by clicking on the review link on\n>>>> the buttugly software website or visiting my web site at:\n>>>>\n>>>> http:\/\/freespace.virgin.net\/john.freelanceit\/index.htm\n>>>>\n>>>> click on the Review button on my web site and then click the CleanCache\n>>>> option.\n>>>>\n>>>> I use this application every day and find it very useful.\n>>>>\n>>>\n>>> --\n>>> Remove the \"Delany\" to reply.\n>>\n>>\n>\n\nMy index.dat (Windows XP Pro) constantly grows in size. It is currently at\nover 600k even after purging all temp internet files and cookies!\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\n\"Johnny Lingo\" <johnnylingo@spammenot.com> wrote in message\nnews:xOYBd.608326$wV.140974@attbi_s54 > > My index.dat (Windows XP Pro) constantly grows in size. It is > currently at over 600k even after purging all temp internet files and > cookies! See http:\/\/mvps.org\/winhelp2002\/delcache.htm -- Frank Saunders, MS-MVP, IE\/OE Please respond in Newsgroup only. Do not send email http:\/\/www.fjsmjs.com Protect your PC http:\/\/www.microsoft.com.\/athome\/security\/protect\/defau... Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) \"Frank Saunders, MS-MVP\" <franksaunders@mvps.org> wrote in message news:%23cF6XER8EHA.824@TK2MSFTNGP11.phx.gbl... > \"Johnny Lingo\" <johnnylingo@spammenot.com> wrote in message > news:xOYBd.608326$wV.140974@attbi_s54\n>>\n>> My index.dat (Windows XP Pro) constantly grows in size. It is\n>> currently at over 600k even after purging all temp internet files and\n>> cookies!\n>\n> See\n> http:\/\/mvps.org\/winhelp2002\/delcache.htm\n>\n\nThanks, but I already know how to delete it. I was just commenting to a\nposter that stated that the index.dat resizes after deleting Temp Internet\nfiles and cookies. Mine and all of those that I have worked on has an\nindex.dat file that continually grows in size until it is deleted and\nautomatically replaced by a new default one.\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nBabel17delany Wrote:\n> Is there an easy way to clear the content of Index.dat in Windows XP?\n> Are there downloadable programs to do this for XP?\n> --\n> Remove the \"Delany\" to reply.\nTHIS REMOVES INDEX.DAT FOR EVERY USER ON AN XP SYSTEM:\n\n1. Create text file C:\\WINDOWS\\WINSTOP.CMD which contains the\nfollowing:\n:begin\nif .%1==. goto loop\ngoto path\n\n:loop\ncd \/d %AllUsersProfile%\\..\nfor \/d %%f in (*.*) do call %SystemRoot%\\winstop.cmd %%f\nexit\n\nath\ncd %1\ndel Cookies\\index.dat\ndel \"Local Settings\\History\\index.dat\"\ndel \"Local Settings\\History\\History.IE5\\index.dat\"\ndel \"Local Settings\\Temporary Internet Files\\Content.IE5\\index.dat\"\n\n:end\ncd ..\n2. Open your Scheduled Tasks control panel & add the new task to run\nC:\\WINDOWS\\WINSTOP.CMD scheduled at logon.\n\n3. Logoff & then logon again to activate the schedule. *\nThis will erase INDEX.DAT for all users each time you log on, or you\ncan disable the schedule & use it only as needed. Technically you are\nlogged on when this happens, although the folks at SpyBot maintain\nthese need a reboot to safely remove. (For some reason the Scheduled\nTask works better than using logon\/logoff scripts in Group Policy.)*\n\n--\nalan.1\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nHi Alan.1,\nI dont have the OP's text to respond to, and beg your pardon to linking to\nyour reply.\nI use a good free program called \"ID Suite\", and can be downloaded from\nwww.it-mate.co.uk\nRob.\n\"alan.1\" <alan.1.1j1hpo@pcbanter.net> wrote in message\nnews:alan.1.1j1hpo@pcbanter.net...\n|\n| Babel17delany Wrote:\n| > Is there an easy way to clear the content of Index.dat in Windows XP?\n| > Are there downloadable programs to do this for XP?\n| > --\n| > Remove the \"Delany\" to reply.\n| THIS REMOVES INDEX.DAT FOR EVERY USER ON AN XP SYSTEM:\n|\n| 1. Create text file C:\\WINDOWS\\WINSTOP.CMD which contains the\n| following:\n| :begin\n| if .%1==. goto loop\n| goto path\n|\n| :loop\n| cd \/d %AllUsersProfile%\\..\n| for \/d %%f in (*.*) do call %SystemRoot%\\winstop.cmd %%f\n| exit\n|\n| \u00a0ath\n| cd %1\n| del Cookies\\index.dat\n| del \"Local Settings\\History\\index.dat\"\n| del \"Local Settings\\History\\History.IE5\\index.dat\"\n| del \"Local Settings\\Temporary Internet Files\\Content.IE5\\index.dat\"\n|\n| :end\n| cd ..\n| 2. Open your Scheduled Tasks control panel & add the new task to run\n| C:\\WINDOWS\\WINSTOP.CMD scheduled at logon.\n|\n| 3. Logoff & then logon again to activate the schedule. *\n| This will erase INDEX.DAT for all users each time you log on, or you\n| can disable the schedule & use it only as needed. Technically you are\n| logged on when this happens, although the folks at SpyBot maintain\n| these need a reboot to safely remove. (For some reason the Scheduled\n| Task works better than using logon\/logoff scripts in Group Policy.)*\n|\n|\n| --\n| alan.1\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nI use that program also. :-)\n\nBut, be cautious about deleting >>>\n\n\\WINDOWS\\PCHealth\\HelpCtr\\OfflineCache\\index.dat.\n\nThis index.dat does not get recreated. The loss of this particlar file will\ncripple System Information (msinfo32.exe). This index.dat actually does\nsomething besides growing to a huge size.\n\n--\nHope this helps. Let us know.\n\nWes\nMS-MVP Windows Shell\/User\n\nIn news:eyo25OV$EHA.1524@TK2MSFTNGP09.phx.gbl, Rob <xxxx@beer.com> hunted and pecked: > Hi Alan.1, > I dont have the OP's text to respond to, and beg your pardon to > linking to your reply. > I use a good free program called \"ID Suite\", and can be downloaded > from www.it-mate.co.uk > Rob. > \"alan.1\" <alan.1.1j1hpo@pcbanter.net> wrote in message > news:alan.1.1j1hpo@pcbanter.net... >> >> Babel17delany Wrote: >>> Is there an easy way to clear the content of Index.dat in Windows >>> XP? Are there downloadable programs to do this for XP? >>> -- >>> Remove the \"Delany\" to reply. >> THIS REMOVES INDEX.DAT FOR EVERY USER ON AN XP SYSTEM: >> >> 1. Create text file C:\\WINDOWS\\WINSTOP.CMD which contains the >> following: >>> begin >> if .%1==. goto loop >> goto path >> >>> loop >> cd \/d %AllUsersProfile%\\.. >> for \/d %%f in (*.*) do call %SystemRoot%\\winstop.cmd %%f >> exit >> >>> path >> cd %1 >> del Cookies\\index.dat >> del \"Local Settings\\History\\index.dat\" >> del \"Local Settings\\History\\History.IE5\\index.dat\" >> del \"Local Settings\\Temporary Internet Files\\Content.IE5\\index.dat\" >> >>> end >> cd .. >> 2. Open your Scheduled Tasks control panel & add the new task to run >> C:\\WINDOWS\\WINSTOP.CMD scheduled at logon. >> >> 3. Logoff & then logon again to activate the schedule. * >> This will erase INDEX.DAT for all users each time you log on, or you >> can disable the schedule & use it only as needed. Technically you >> are logged on when this happens, although the folks at SpyBot >> maintain these need a reboot to safely remove. (For some reason the >> Scheduled Task works better than using logon\/logoff scripts in Group >> Policy.)* >> >> >> -- >> alan.1 Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) Sorry for jumping in but are you saying that this particular index.dat shouldn't be deleted via the software mentioned? I'm not an expert when it comes to batch files or VBS but I don't think that this will be deleted at startup if the winstop.cmd is created as suggested. I had thought about using this but modifying it so it only ran once a week to clear the index.dat files. If it does delete files other than those which can be deleted safely, I'll give it a miss!!! Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) \\WINDOWS\\PCHealth\\HelpCtr\\OfflineCache\\index.dat Should not be deleted in any way. -- Hope this helps. Let us know. Wes MS-MVP Windows Shell\/User In news:%23UxaAch$EHA.3336@TK2MSFTNGP11.phx.gbl,\nTosca <no-spam@thank-you.com> hunted and pecked:\n> Sorry for jumping in but are you saying that this particular index.dat\n> shouldn't be deleted via the software mentioned? I'm not an expert\n> when it comes to batch files or VBS but I don't think that this will\n> be deleted at startup if the winstop.cmd is created as suggested. I\n> had thought about using this but modifying it so it only ran once a\n> week to clear the index.dat files. If it does delete files other\n> than those which can be deleted safely, I'll give it a miss!!!\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nThank you. I'll look further into using the procedure that was posted then.\nAnonymous\n\nArchived from groups: microsoft.public.windowsxp.newusers (More info?)\n\nI just ran Index.dat Suite. I saved the results of Find. Index.dat Suite\nsaves these results in a file called results.ini located in C:\\Program\nFiles\\Index.dat Suite.\n\nIndex.dat Suite combined with me blindly using it was the culprit, in my\ncase, for deleting the wrong index.dat file. I have nothing against\nIndex.dat Suite, it was only recently discovered and posted that the the\ndeletion of this index.dat file was the cause of the msinfo32 opening in\nHelp and support. There are other work arounds, but replacing the missing\nfile is the best bet.\n\nNote that C:\\WINDOWS\\PCHealth\\HelpCtr\\OFFLIN~1\\index.dat\nis the Short File Name (8.3 Name format) version of\nC:\\WINDOWS\\PCHealth\\HelpCtr\\OfflineCache\\index.dat\n\nHere are those results...\n\nC:\\DOCUME~1\\ADMINI~1\\LOCALS~1\\History\\History.IE5\\MSHIST~1\\index.dat -\n32.00KB\nC:\\DOCUME~1\\WESLEY~1.VOG\\Cookies\\index.dat - 16.00 KB\nC:\\DOCUME~1\\WESLEY~1.VOG\\LOCALS~1\\History\\History.IE5\\index.dat - 16.00 KB\nC:\\DOCUME~1\\WESLEY~1.VOG\\LOCALS~1\\History\\History.IE5\\MSHIST~1\\index.dat -16\n..00 KB\nC:\\DOCUME~1\\WESLEY~1.VOG\\LOCALS~1\\TEMPOR~1\\Content.IE5\\index.dat - 32.00 KB\nC:\\DOCUME~1\\WESLEY~1.VOG\\MYDOCU~1\\COMPUT~1\\MSINFO\\WINDOW~1.DAT\\index.dat -84\n..76 KB\nC:\\DOCUME~1\\WESLEY~1.VOG\\UserData\\index.dat - 16.00 KB\nC:\\WINDOWS\\PCHealth\\HelpCtr\\OFFLIN~1\\index.dat - 84.76 KB\nC:\\WINDOWS\\system32\\config\\SYSTEM~1\\Cookies\\index.dat - 16.00 KB\nC:\\WINDOWS\\system32\\config\\SYSTEM~1\\LOCALS~1\\History\\History.IE5\\index.dat -\n32.00 KB\nC:\\WINDOWS\\system32\\config\\SYSTEM~1\\LOCALS~1\\History\\History.IE5\\MSHIST~1\\in\ndex.dat - 32.00 KB\nC:\\WINDOWS\\system32\\config\\SYSTEM~1\\LOCALS~1\\TEMPOR~1\\Content.IE5\\index.dat\n- 32.00 KB\n\nIndex.dat Suite has an option to not select any index.dat files. Do not\nselect >>\nC:\\WINDOWS\\PCHealth\\HelpCtr\\OFFLIN~1\\index.dat\n\nAlso has an option to automatically generate the batch file. You should not\nuse that option.\n\nYou can also edit the batch file to exclude\nC:\\WINDOWS\\PCHealth\\HelpCtr\\OFFLIN~1\\index.dat\n\n--\nHope this helps. Let us know.\n\nWes\nMS-MVP Windows Shell\/User\n\nIn news:e%2309I6u$EHA.1908@TK2MSFTNGP15.phx.gbl, Tosca <no-spam@thank-you.com> hunted and pecked: > Thank you. I'll look further into using the procedure that was > posted then. Anonymous Archived from groups: microsoft.public.windowsxp.newusers (More info?) I just downloaded, installed and ran the latest version of Index.dat Suite, ver 2.7.0.5. \\WINDOWS\\PCHealth\\HelpCtr\\OfflineCache is in RED text and UNChecked by default. Steven was way ahead of us. ;-) From Index.dat Suite Frequently Asked Questions Q. What are the checkboxes for on the main IDFinder window? A. The checkboxes allow you to exclude items from the generated .bat file. All items CHECKED will be included, UNCHECKED items will be excluded. Note: If you have enabled the option labelled \"Use default file generation routine to remove all index.dat files\", this setting will be ignored, and all items included, regardless of whether they are checked or unchecked. ---- Index.dat Suite Settings and Options - General The following settings are available on the General tab. General Mark items in red that may not be safe to delete By default this setting is enabled, and allows Index.dat Suite to automatically mark and exclude items that have been detected but are known to cause problems when deleted. Items with the following in their paths, are automatically marked during the scan; PPSRIN~1 (PPSRIndex.dat - Pest Patrol data file) HELPCTR (index.dat -Microsoft Windows Help Center) At present, we are unsure as to why deleting the HELPCTR index.dat file would cause problems. However, we have checked it's contents, and confirmed, it is not the same kind of index.dat file as those used by Internet Explorer or Windows. Reccomendation: Leave checked --- Always verify batch file contents after file generation When enabled, Index.dat Suite will perform a scan on the generated batch file, to check for invalid or potentially dangerous commands (e.g. deltree \/y *.*) Reccomendation: Should only be disabled if user is experiencing persistent IDSE0500 errors ---- -- Hope this helps. Let us know. Wes MS-MVP Windows Shell\/User In news:e%2309I6u$EHA.1908@TK2MSFTNGP15.phx.gbl,\nTosca <no-spam@thank-you.com> hunted and pecked:\n> Thank you. I'll look further into using the procedure that was\n> posted then.\nAsk the community\nRelated ressources:\n!","date":"2013-05-25 00:32:18","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\": 0.34560489654541016, \"perplexity\": 9014.90907133474}, \"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-2013-20\/segments\/1368705300740\/warc\/CC-MAIN-20130516115500-00020-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.investopedia.com\/articles\/07\/monte_carlo_intro.asp","text":"In finance, there is a fair amount of uncertainty and risk involved with estimating the future value of figures or amounts due to the wide variety of potential outcomes. Monte Carlo simulation (MCS) is one technique that helps to reduce the uncertainty involved in estimating future outcomes. MCS can be applied to complex, non-linear models or used to evaluate the accuracy and performance of other models. It can also be implemented in risk management, portfolio management, pricing derivatives, strategic planning, project planning, cost modeling and other fields.\n\n## Definition\n\nMCS is a technique that converts uncertainties in input variables of a model into probability distributions. By combining the distributions and randomly selecting values from them, it recalculates the simulated model many times and brings out the probability of the output.\n\n## Basic Characteristics\n\n\u2022 MCS allows several inputs to be used at the same time to create the probability distribution of one or more outputs.\n\u2022 Different types of probability distributions can be assigned to the inputs of the model. When the distribution is unknown, the one that represents the best fit could be chosen.\n\u2022 The use of random numbers characterizes MCS as a stochastic method. The random numbers have to be independent; no correlation should exist between them.\n\u2022 MCS generates the output as a range instead of a fixed value and shows how likely the output value is to occur in the range.\n\n## Some Frequently Used Probability Distributions in MCS\n\nNormal\/Gaussian Distribution\u00a0\u2013 Continuous distribution applied in situations where the mean and the standard deviation are given and the mean represents the most probable value of the variable. It is symmetrical around the mean and is not bounded.\n\nLognormal Distribution\u00a0\u2013 Continuous distribution specified by mean and standard deviation. This is appropriate for a variable ranging from zero to infinity, with positive skewness and with normally distributed natural logarithm.\n\nTriangular Distribution\u00a0\u2013 Continuous distribution with fixed minimum and maximum values. It is bounded by the minimum and maximum values and can be either symmetrical (the most probable value = mean = median) or asymmetrical.\n\nUniform Distribution\u00a0\u2013 Continuous distribution bounded by known minimum and maximum values. In contrast to the triangular distribution, the likelihood of occurrence of the values between the minimum and maximum is the same.\n\nExponential Distribution\u00a0\u2013 Continuous distribution used to illustrate the time between independent occurrences, provided the rate of occurrences is known.\n\n## The Math Behind MCS\n\nConsider that we have a real-valued function g(X) with probability frequency function P(x) (if X is discrete), or probability density function f(x) (if X is continuous). Then we can define the expected value of g(X) in discrete and continuous terms respectively:\n\n\ufeff\\begin{aligned}&E(g(X))=\\sum^{+\\infty}_{-\\infty}g(x)P(x),\\\\&\\qquad\\qquad\\qquad\\qquad\\qquad\\text{ where }P(x)>0\\text{ and} \\sum^{+\\infty}_{-\\infty}P(x)=1\\\\&E(g(X))=\\int^{+\\infty}_{-\\infty}g(x)f(x)\\,dx,\\\\&\\qquad\\qquad\\qquad\\qquad\\text{ where }f(x)>0\\text{ and }\\int^{+\\infty}_{-\\infty}f(x)\\,dx=1\\\\&\\text{Next, make n random drawings of X (x_1,\\ldots,x_n), called}\\\\&\\text{trial runs or simulation runs, calculate g(x_1),\\ldots,g(x_n)}\\\\&\\text{and find the mean of g(x) of the sample:}\\end{aligned}\ufeff\n\n\ufeff\\begin{aligned}&g^\\mu_n(x)=\\frac{1}{n}\\sum^n_{i=1}g(x_i),\\text{ which represents the final simulated}\\\\&\\text{value of }E(g(X)).\\\\\\\\&\\text{Therefore }g^\\mu_n(X)=\\frac{1}{n}\\sum^n_{i=1}g(X)\\text{ will be the Monte Carlo}\\\\&\\text{estimator of }E(g(X)).\\\\\\\\&\\text{As }n\\to\\infty, g^\\mu_n(X)\\to E(g(X)), \\text{thus we are now able to}\\\\&\\text{compute the dispersion around the estimated mean with}\\\\&\\text{the unbiased variance of }g^\\mu_n(X)\\text{:}\\\\&Var(g^\\mu_n(X))=\\frac{1}{n-1}\\sum^n_{i=1}(g(x_i)-g^\\mu_n(x))^2.\\end{aligned}\ufeff\n\nSimple Example\n\nHow will the uncertainty in unit price, unit sales and variable costs affect the EBITD?\n\nCopyright Unit Sales)-(Variable Costs + Fixed Costs)\n\nLet us explain the uncertainty in the inputs\u00a0\u2013 unit price, unit sales and variable costs\u00a0\u2013 using triangular distribution, specified by the respective minimum and maximum values of the inputs from the table.","date":"2020-04-08 00:27:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 2, \"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\": 0.7234642505645752, \"perplexity\": 842.4703230118453}, \"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-2020-16\/segments\/1585371806302.78\/warc\/CC-MAIN-20200407214925-20200408005425-00516.warc.gz\"}"} | null | null |
{"url":"https:\/\/blog.zakjost.com\/post\/adversarial_validation\/","text":"Announcement: I have created a new place for ML peers to connect and discuss technical topics. Please join us on Discord if you'd like to connect\u2013it's free.\n\n## Introduction\n\nIf you were to study some of the competition-winning solutions on Kaggle, you might notice references to \u201cadversarial validation\u201d (like this one). What is it?\n\nIn short, we build a classifier to try to predict which data rows are from the training set, and which are from the test set. If the two datasets came from the same distribution, this should be impossible. But if there are systematic differences in the feature values of your training and test datasets, then a classifier will be able to successfully learn to distinguish between them. The better a model you can learn to distinguish them, the bigger the problem you have.\n\nBut the good news is that you can analyze the learned model to help you diagnose the problem. And once you understand the problem, you can go about fixing it.\n\nThis post is meant to accompany a YouTube video I made to explain the intuition of Adversarial Validation. This blog post walks through the code implementation of the example presented in this video, but is complete enough to be self-contained. You can find the complete code for this post on github.\n\n## Learning the Adversarial Validation model\n\nFirst, some boilerplate import statements to avoid confusion:\n\n 1 2 import pandas as pd from catboost import Pool, CatBoostClassifier \n\n### Data Preparation\n\nFor this tutorial, we're going to be using the IEEE-CIS Credit Card Fraud Detection dataset from Kaggle. First, I'll assume you've loaded the training and test data into pandas DataFrames and called them df_train and df_test, respectively. Then we'll do some basic cleaning by replacing missing values.\n\n 1 2 3 4 5 6 7 # Replace missing categoricals with \"\" df_train.loc[:,cat_cols] = df_train[cat_cols].fillna('') df_test.loc[:,cat_cols] = df_test[cat_cols].fillna('') # Replace missing numeric with -999 df_train = df_train.fillna(-999) df_test = df_test.fillna(-999) \n\nFor adversarial validation, we want to learn a model that predicts which rows are in the training dataset, and which are in the test set. We therefore create a new target column in which the test samples are labeled with 1 and the train samples with 0, like this:\n\n 1 2 3 df_train['dataset_label'] = 0 df_test['dataset_label'] = 1 target = 'dataset_label' \n\nThis is the target that we'll train a model to predict. Right now, the train and test datasets are separate, and each dataset has only one label for the target value. If we trained a model on this training set, it would just learn that everything was 0. We want to instead shuffle the train and test datasets, and then create new datasets for fitting and evaluating the adversarial validation model. I define a function for combining, shuffling, and re-splitting:\n\n 1 2 3 4 5 6 7 8 9 def create_adversarial_data(df_train, df_test, cols, N_val=50000): df_master = pd.concat([df_train[cols], df_test[cols]], axis=0) adversarial_val = df_master.sample(N_val, replace=False) adversarial_train = df_master[~df_master.index.isin(adversarial_val.index)] return adversarial_train, adversarial_val features = cat_cols + numeric_cols + ['TransactionDT'] all_cols = features + [target] adversarial_train, adversarial_test = create_adversarial_data(df_train, df_test, all_cols) \n\nThe new datasets, adversarial_train and adversarial_test, include a mix of the original training and test sets, and the target indicates the original dataset. Note: I added TransactionDT to the feature list. The reason for this will become apparent.\n\nFor modeling, I'm going to be using Catboost. I finish data preparation by putting the DataFrames into Catboost Pool objects.\n\n 1 2 3 4 5 6 7 8 9 10 train_data = Pool( data=adversarial_train[features], label=adversarial_train[target], cat_features=cat_cols ) holdout_data = Pool( data=adversarial_test[features], label=adversarial_test[target], cat_features=cat_cols ) \n\n### Modeling\n\nThis part is simple: we just instantiate a Catboost Classifier and fit it on our data:\n\n 1 2 3 4 5 6 7 8 9 params = { 'iterations': 100, 'eval_metric': 'AUC', 'od_type': 'Iter', 'od_wait': 50, } model = CatBoostClassifier(**params) _ = model.fit(train_data, eval_set=holdout_data) \n\nLet's go ahead and plot the ROC curve on the holdout dataset:\n\nThis is a perfect model, which means there's a clear way to tell whether any given record is in the training or test sets. This is a violation of the assumption that our training and test sets are identically distributed.\n\n### Diagnosing the problem and iterating\n\nTo understand how the model was able to do this, let's look at the most important features:\n\nThe TransactionDT is by far the most important feature. And that makes total sense given that the original training and test datasets came from different time periods (the test set occurs in the future of the training set). The model has just learned that if the TransactionDT is larger than the last training sample, it's in the test set.\n\nI included the TransactionDT just to make this point\u2013it's not advised to throw a raw date in as a model feature normally. But it's good news that this technique found it in such a dramatic fashion. This analysis would clearly help you identify such an error.\n\nLet's eliminate TransactionDT, and run this analysis again.\n\n 1 2 3 4 params2 = dict(params) params2.update({\"ignored_features\": ['TransactionDT']}) model2 = CatBoostClassifier(**params2) _ = model2.fit(train_data, eval_set=holdout_data) \n\nNow the ROC curve looks like this:\n\nIt's still a fairly strong model with AUC > 0.91, but much weaker than before. Let's look at the feature importances for this model:\n\nNow, id_31 is the most important feature. Let's look at some values to understand what it is.\n\n 1 2 3 4 5 [ '', 'samsung browser 6.2', 'mobile safari 11.0', 'chrome 62.0', 'chrome 62.0 for android', 'edge 15.0', 'mobile safari generic', 'chrome 49.0', 'chrome 61.0', 'edge 16.0' ] \n\nThis column contains software version numbers. Clearly, this is similar in concept to including a raw date, because the first occurrence of a particular software version will correspond to its release date.\n\nLet's get around this problem by dropping any characters that are not letters from the column:\n\n 1 2 3 4 5 def remove_numbers(df_train, df_test, feature): df_train.loc[:, feature] = df_train[feature].str.replace(r'[^A-Za-z]', '', regex=True) df_test.loc[:, feature] = df_test[feature].str.replace(r'[^A-Za-z]', '', regex=True) remove_numbers(df_train, df_test, 'id_31') \n\nNow the values of our column look like this:\n\n 1 2 3 4 5 [ 'UNK', 'samsungbrowser', 'mobilesafari', 'chrome', 'chromeforandroid', 'edge', 'mobilesafarigeneric', 'safarigeneric', ] \n\nLet's train a new adversarial validation model using this cleaned column:\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 adversarial_train_scrub, adversarial_test_scrub = create_adversarial_data( df_train, df_test, all_cols, ) train_data_scrub = Pool( data=adversarial_train_scrub[features], label=adversarial_train_scrub[target], cat_features=cat_colsc ) holdout_data_scrub = Pool( data=adversarial_test_scrub[features], label=adversarial_test_scrub[target], cat_features=cat_colsc ) model_scrub = CatBoostClassifier(**params2) _ = model_scrub.fit(train_data_scrub, eval_set=holdout_data_scrub) \n\nThe ROC plot now looks like this:\n\nThe performance has dropped from an AUC of 0.917 to 0.906. This means that we've made it a little harder for a model to distinguish between our training and test datasets, but it's still quite capable.\n\n## Conclusion\n\nWhen we naively tossed the transaction date into the feature set, the adversarial validation process helped clearly diagnose the problem. Additional iterations gave us more clues that a column containing software version information had clear differences between the training and test sets.\n\nBut what the process is not able to do is tell us how to fix it. We still need to apply our creativity here. In this example we simply removed all numbers from the software version information, but this is throwing away potentially useful information and might ultimately hurt our fraud modeling task, which is our real goal. The idea is that you want to remove information that is not important for predicting fraud, but is important for separating your training and test sets.\n\nA better approach might have been to find a dataset that gave the software release dates for each software version, and then created a \u201cdays since release\u201d column that replaced the raw version number. This might make for a better match for the train and test distributions while also maintaining the predictive power that software version information encodes.","date":"2020-02-25 10:02:16","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\": 0.41437968611717224, \"perplexity\": 1800.5473987823484}, \"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-2020-10\/segments\/1581875146064.76\/warc\/CC-MAIN-20200225080028-20200225110028-00374.warc.gz\"}"} | null | null |
{"url":"https:\/\/discuss.codechef.com\/t\/help-in-a-gcd-problem\/25103","text":"# Help in a GCD problem\n\nGiven an array of integers (A[i] <= 10^5). We have to find number of unordered pairs (i, j) such that their GCD is greater than B.\n\n3 Likes\n\nwhere is this ques frm??\nhav u tried brute force with memoization?\n\n1 Like\n\nThere is a O(N*(\u221aa(i)) algorithm. I\u2019ll write the solution after my endsem\n\nwhat is here to memoize for?\n\nI have tried O(N^2) which obviously not going to pass.\n\ncan you please just share rough idea?\n\nLet us consider the elements a,b\nFor gcd(a,b) to be exactly k both a>=k and b>=k and a%k==0 and b%k==0.\nfor example take k=5,for gcd(a,b) to be exactly 5 the possible no. are a combination of any two multiples of 5 present in the array.\nlet the array be 1,5,10,4,15,6,20.\nthe no. are multiple of 5 are 4(say,x)\u2014 5,10,15,20 .GCD=5 is for combination of any two (5,10),(5,15),(5,20),(10,15),(15,20) but not(10,20) . So,Here you have to check the gcd by euler\u2019s method which is log(max(a,b))\n(Hope this is clear).\n\nuse a hashmap or an array to count the occurence of every element\nfor every no. >B Find the no. of multiples that number in the array and hence the no. of pairs with gcd equal to that no.(Answer will be the sum of all these).\nIterate like this\nfor(i=b+1;i<=100000;i++)\n{\nfor(j=i;i<=100000;j+=i)\n\/\/code where we count the multiples of i in the array.\n\/\/check if this gcd(i,j) pair is valid.\n}\nlet max=100000\nWorst case when b=1;\nloop runs sequence will be like = (max\/1) + (max\/2) + (max\/3) +\u2026+max\/100000 <= 1300000 = O(10^6 * log(max)). This might clear the 1 sec time limit though.\n\nYour approach will fail cuz there can be many numbers greater than B , but they might be having their gcd less than \u2018B\u2019\nNice idea though\n\nmy approach had an error actually now updated it.But @anon55659401 i am looking for pairs where exact gcd=x where a,b are sure multiple of x,and checking on them only,i cant find the error here that you are mentioning though.\nit would be nice of you if you point out at example.\n\nThere is one more fault in your approach, you are counting many pairs repeatedly\u2026\n\n+I think its bound to give TLE\n\nThe worst case time complexity is still less than O(n*sqrt(a[i])) though that you suggested.\n\nThis problem can be solved using mobius inversion (inclusion - exclusion principle).\nLe f(n) = number of unordered pairs(i,j) such that their gcd is n\nthen f(n)=NC_2 -(\\sum_{i=2 }f(i*n))\nwhere N = no. of numbers in array that are divisible by n\n\nWhere can we submit this problem?\n\n2 Likes\n\n1 Like","date":"2020-09-26 18:59:53","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\": 0.5864185690879822, \"perplexity\": 2564.766612820207}, \"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-2020-40\/segments\/1600400244353.70\/warc\/CC-MAIN-20200926165308-20200926195308-00462.warc.gz\"}"} | null | null |
\section{Introduction}
\IEEEPARstart{I}{n recent years,} we have witnessed significant progress in computer vision \cite{He2017, Zhuang2012Multichannel}. Thanks to large-scale of labeled training data, e.g., ImageNet, deep convolutional neural networks (ConvNets) are able to successfully learn robust feature representations and achieve excellent performance in recognition tasks. Although it has high accuracy in various labeled datasets, the generalization ability of the ConvNet model is still weak. In particular, the ConvNet model is difficult to quickly identify a novel category using only one or a few labeled samples. However, humans are able to recognize new objects easily with very little supervision \cite{Lake2015}. For example, kids have no problem to generalize the concept of ``panda'' from only one picture. Furthermore, experts will be faster to understand novel concepts with prior professional knowledge. This work focuses on the task that recognizing novel visual categories after seeing just a few labeled examples. Research on this subject is often termed \emph {few-shot learning}.
In contrast to the common image classification problem in daily life, most of the real-world scenarios face few-shot problems. For example, marine biologist pays great attention to the phytoplankton recognition problem which is a typical fine-grained and few-shot learning issue. The change of their abundance, e.g. eutrophication, is a significant indicator of the oceanic ecosystem's health. It is therefore very important to automatically identify phytoplankton in a certain area of the ocean. However, collections of phytoplankton images are very difficult. It is commonly accomplished by professional instruments such as electron microscope. Only a few samples of valuable categories can be discovered in one expensive sampling task. Therefore, the fine-grained and few-shot model is critical for domain-specific issues and has become one of the important topics in computer vision.
\begin{figure}
\begin{center}
\includegraphics[width=1\linewidth]{./img/acm/start}
\end{center}
\caption{A brief illustration of fine-grained few-shot recognition.}
\label{start}
\end{figure}
Most of the few-shot learning methods fall under the umbrella of metric-learning. The metric-learning approaches try to solve these problems by placing new classes in a metric space (e.g., Euclidean or cosine distances) that can easily separate classes. For instance, Matching Networks \cite{Vinyals2016} can be interpreted as a nearest-neighbor classifier which can be trained end-to-end over the cosine distance. Notably, the training procedure has to be chosen carefully so as to match inference at the test stage. Each episode is designed to mimic the few-shot tasks by subsampling classes as well as data points (e.g., every episode sampling 5 classes and each class has 5 labeled samples). Prototypical Networks \cite{Snell2017} handles the few-shot tasks by calculating the Euclidean distance between the embedding points of query set and prototype representation of support set. Meanwhile, the pre-defined metric is no longer used in Relation Networks \cite{Sung2017}. It uses concatenated feature maps from the query and support images to distinguish similar and dissimilar samples.
It is very important to explore the relationship between feature representation of template images and that of the query image. Thus, to succeed in few-shot metric tasks, we shall make sure two aspects. First, we shall have a well-trained feature extractor. The other is an effective classifier including good metrics. However, the above-mentioned methods are not conducive to ConvNets for extracting robust features and can sacrifice the accuracy of initial categories \cite{Gidaris2018}. Most of the few-shot methods pay attention to learning a deep distance metric to compare query images with the labeled images, while ignoring the importance of mining the better features from the existing few categories. That means it is critical to mining rich information from the labeled samples of few categories. Motivated by the above observation, we propose a Feature Fusion Model for obtaining more discriminative information from focus areas. We also design a loss function (Center Neighbor Loss) to help the whole architecture to learn better feature space distributions.
For the special fine-grained few-shot visual problem, we further build a microimage dataset of phytoplankton, i.e., {\it{\textbf{mini}}}{\textbf{PPlankton}. Unlike toy datasets for few-shot learning in literature,
the {\it{\textbf{mini}}}{\textbf{PPlankton} dataset comes from the real-world tasks and can be used to evaluate fine-grained and few-shot methods. It illustrates a typical fine-grained and few-shot problem in marine biological science.
The main contributions of this paper are as follows:
\begin{enumerate}[1)]
\item We propose a feature fusion model to explore the features by focusing on the key regions. It utilizes the focus-area location mechanism to discover the similarity regions between objects. Meanwhile, high-order integration is used to capture the intra-parts discriminative information.
\item We design a Center Neighbor Loss function to form robust feature space distributions for generating discriminative features, to accomplish the fine-grained few-shot visual categorization task.
\item We build a domain-specific fine-grained and few-shot dataset {\it{\textbf{mini}}}{\textbf{PPlankton}} for the real-world phytoplankton recognition problem. Experiments on the {\it{\textbf{mini}}}{\textbf{PPlankton}} show the superiority of the proposed model compared with other models.
\end{enumerate}
The rest of this paper is organized as follows. Section II summarizes the related works. Section III formally describes our model. Section IV presents the experimental results. Finally, we conclude in Section V.
\section{Related work}
Deep convolutional neural networks have made significant achievements for a wide range of visual tasks \cite{8663605, Qi2017Automatic, chen2020r}. Nevertheless, for fine-grained image categorization \cite{Zhang2015A}, it remains quite challenging to obtain the discriminative representations. In particular, it is a novel challenge to classify fine-grained images using only a few labeled sample images .
The convolutional neural networks usually require thousands of labeled examples of each class to saturate performance. However, it is impractical to collect large amounts of annotated data, especially the domain-specific industrial applications that requires expert knowledge, such as oceanography \cite{Gorsky2010, Jakobsen2011}. Recently, there is a resurgence of interest on few-shot learning \cite{Vinyals2016, Snell2017, Sung2017}. And a few research works are already pay attention to the fine-grained few-shot visual problem \cite{Huang2019, Huang2019a, Pahde2018, Das2019}.
Among the recent literature of few-shot learning, the metric learning and attention mechanism are most relevant proposed method. Metric learning has been successfully applied to face recognition \cite{Sun2014} and fine-grained image classification \cite{Zhang2015A}. The core idea is to learn an embedding function that the samples of the same category are closer than those of different classes. Once the embedding function is learned, the query images will be classified. Siamese network \cite{Chopra2005} consists of two identical sub-ConvNets that minimize the distances between paired data with the same labels while keeping the distances with different labels far apart. Triplet loss \cite{Taigman2015} attempts to focus on relative distances rather than absolute pair-wise distances. It has been widely implemented in fine-grained tasks \cite{Wang2014}. However, the problem of triplet loss is dramatic data expansion when selecting triplets. Furthermore, center loss \cite{Wen2016a} can obtain highly discriminative features for robust face recognition. And it is unnecessary to design the sampling strategy carefully as contrastive loss and triplet loss do. The center loss has shown benefits in face identification. However, its performance is unknown for the fine-grained few-shot tasks. Then we further design a Center Neighbor Loss for achieving a robust embedding space.
It is critical to know which part of the images worth paying attention to. To acquire the attention feature representation, Li et al. \cite{Li} proposed a zoom network which utilized the candidate region to crop the original images. Wei et al. \cite{Wei2019} adopted the unsupervised object discovery and co-localization mechanism by deep descriptor transformation to discover the attention area. The attention mechanism is a possible way for learning robust representation. In this work, we introduce the focus-area location mechanism Grad-CAM \cite{Selvaraju2017} to find regions with discriminative features, which are critical for fine-grained classification.
Few-shot learning is critical in model industrial applications, such as novel species discovering. In this work, we take one typical real-world industrial problem to verify our method, i.e., phytoplankton classification. Marine phytoplankton is the foundation of the marine ecosystem \cite{Charlson1987}. It is an ecological concept that refers to tiny plants that float in the water. Plankton image classification \footnote{We no longer distinguish the image classification of phytoplankton and zooplankton separately.} is becoming critically important for marine observations and aquaculture.
\begin{figure*}[ht]
\begin{center}
\includegraphics[width=1\linewidth]{./img/allstruc.pdf}
\end{center}
\caption{The overview framework of our method. It consists of a {\it ConvNet-based feature extractor $f_{\varphi}$ }, a {\it feature fusion model} which is formed by focus-area location mechanism and high-order integration , and a {\it cosine-similarity based classifier}. During the testing process, we classify unlabeled samples by comparing the cosine similarities of support set $\mathcal{S}$ and query set $\mathcal{Q}$.}
\label{fig1}
\end{figure*}
The research of phytoplankton detection mainly relies on people to manually identify and count through the microscope. Current monitoring systems (e.g. ZooScan and FlowCAM \cite{Gorsky2010, Jakobsen2011}) yield large amounts of images every day. They are usually time-consuming, labor-intensive and needs strong professional knowledge. Schroder et al. \cite{Taylor2010} also notice the importance of classifying plankton only using a few labeled samples. They directly use weight Imprinting \cite{Brown} to enable a neural network to recognize small classes immediately without re-training.
\section{Methodology}
\subsection{Notation}
For few-shot classification, there is a base train dataset $\mathcal{D}_{base}=\{(x_i, y_i)\}_{i=1}^{N}$ consisting of $N$ labeled images, where $y_i$ is the label of image $x_i$. Crucially, the model must distinguish a set of novel categories $\mathcal{Q} = \{(x_j, y_j)\}_{j=1}^{N_q}$ with a few training examples per category. These training examples are called support set, i.e., $\mathcal{S} = \{(x_ i^s,y_i^s)\}_{i=1}^{N_s} (N_s = K*C) $ which contains $K$ labeled examples for each of $C$ unique novel classes. $\mathcal{Q}$ acts as the unlabeled query set. Here $\mathcal{S} \bigcup \mathcal{Q}=\mathcal{D}_{novel}$ and $\mathcal{D}_{base} \bigcap \mathcal{D}_{novel} = \emptyset$. This target few-shot task is named $C$-way $K$-shot.
\subsection{Model}
An overview of our method is illustrated in Fig.~\ref{fig1}, which mainly consists of three parts.
\subsubsection{ConvNet-based feature extractor}
A feature extractor $f_{\varphi}$, which parameterized by a ConvNet (e.g., ResNet \cite{He2016}), maps an input image $x\in \mathbb{R}^N$ to a $d$-dimensional feature vector $f_{\varphi}(x)\in\mathbb{R}^d$. As a classification model, $f_{\varphi}$ has a dot-product based classifier $C(.|W)$ (i.e., Last linear layer), where $W={\{w_i\in \mathbb{R}^d\}}_{i=1}^{K}$ is the set of weight vectors of the $K$ base classes. We can get the probability scores of the base training categories by calculating $C(f_{\varphi}(x) | W)$ and optimize the feature extractor by back-propagation.
\subsubsection{Feature fusion module}
For few-shot learning, it is pivotal to mine the largest support information from the support set $\mathcal{S}$. We propose a feature fusion model which utilizes the focus-area location and high-order integration to generate feature representation for the few-shot tasks. As shown in Fig.~\ref{fig1}, it consists of two components: (1) high-order integration, and (2) focus-area location.
{\bf High-order integration.} The recent progress of fine-grained classification demonstrates that the high-order representations with ConvNets can greatly improve its performance \cite{Cai, koniusz}. Intuitively, the key for fine-grained few-shot tasks is to represent the regions within same category that have a closer appearance and to exhibit discriminative areas between the different categories.
We assume that $\mathcal{X}\in\mathbb{R}^{K\times M\times N}$ is a 3$D$ feature map from the convolutional layers, where $x\in\mathcal{X}$ is a $K$-dimensional descriptor of one particular location region $p \in M\times N$. The linear predictor $\mathcal{W}$ on the high-order statistics of $\mathcal{X}$ could be formulated as follow.
\begin{equation}\label{kernel}
f(\mathcal{X}) = <\mathcal{W}, \sum\limits_{x\in\mathcal{X}} \phi(x)>
\end{equation}
where $\sum\limits_{x\in\mathcal{X}} \phi(x)$ denotes the high-order statistics characterized by a homogenous polynomial kernel \cite{Pham2013}. The $\mathcal{W}$ can be approximated by rank-one decomposition. The tensor rank decomposition expresses a tensor as a minimum-length linear combination of rank-1 tensors. The outer product of vectors $ {{\bf{u}}_1} \in \mathbb{R}^{K_1},\ldots, {\bf{u}}_r \in {\mathbb{R}}^{K_r}$ is the $K_1 \times \ldots \times K_r $ rank-1 tensor that satisfies $({\bf{u}}_1 \otimes \ldots \otimes {\bf{u}}_r)_{k_1\ldots,k_r} = ({\bf{u}}_1)_{k_1} \ldots ({\bf{u}}_r)_{k_r}$. The $\mathcal{W}$ can be rewritten as $\mathcal{W}=\sum_{d=1}^{D}a^d{{\bf{u}}_1^d}\otimes \ldots \otimes {{\bf{u}}_r^d} $, where $a^d$ is the weight for $d$-th rank-one tensor and $D$ is the rank of the tensor if D is minimal. Thus, Equation \ref{kernel} can be reformulated as follow.
\begin{equation} \label{kernelv2}
\begin{split}
f(\mathcal{X} )&=\sum\limits_{\mathrm{x} \in\mathcal{X}} \Bigg \{ \left \langle \mathrm{ {\bf{w}}^1,\bf{x} } \right \rangle +\sum\limits_{r=2}^R \sum\limits_{d=1}^{D^r} a^{r,d} \prod_{s=1}^r \left \langle { {\bf{u}}_s^{r,d}, \mathrm{x}}\right \rangle \Bigg \}, \\
&=\left \langle \mathrm{ {\bf{w}}^1,\sum\limits_{x\in\mathcal{X}} \bf{x} } \right \rangle + \sum\limits_{r=2}^R \left \langle { {\boldsymbol{a}}^r, \sum\limits_{z^r\in\mathcal{Z}^r} {\boldsymbol{z}}^r } \right \rangle
\end{split}
\end{equation} where the $\boldsymbol{z}^r = [ z^{r,1}, \dots, z^{r,D^r} ]^{\top}$ with $z^{r,d}= \prod_{s=1}^r{ \langle { {\bf{u}}_s^{r, d}, \mathrm{\bf{x}} } \rangle }$ characterizes the degree-$r$ variable interactions under a single rank-1 tensors, and $\boldsymbol{a}^r$ is the weight vector. The $\boldsymbol{z}^r$ can be calculated by performing $r$-th $1\times1$ convolutions with $D^r$ channel \cite{Wang1},
i.e., $\mathcal{Z}^r = \{\boldsymbol{z}^r\} = \prod_{i=1}^r conv^{i}_{1\times1\times D^r}(\mathcal{X})$ .
In our feature fusion operation as shown in Fig.~\ref{fig1}, we integrate 2nd-order representations to capture more complex and high-order relationships among parts. After that, we perform global average pooling (GAP) \cite{Lin} to further aggregate features.
{\textbf{Focus-area location.} Existing studies show that learning from object regions could benefit object recognition at image-level \cite{Li}. Such focus-area in an image which benefit few-shot learning. During the training procedure, $f_{\varphi}$ can generate focus-areas of images by Grad-CAM \cite{Selvaraju2017}, as formulated below.
\begin{equation}\label{grad}
L_{Grad-CAM}^c=ReLU(\sum\limits_k\alpha_k^cA^k)
\end{equation}
where $\alpha_k^c$ denotes the weight of the $k$-th feature map for category $c$. $\alpha_k^c$ can be calculated by the following formula.
\begin{equation}\label{gradv2}
\alpha_k^c=\frac{1}{Z}\sum\limits_{i}\sum\limits_{j}\frac{\partial y^c}{\partial A_{ij}^k}
\end{equation}
where $Z$ is the number of pixels in feature map, $y^c$ is the classification score corresponding to the category $c$, and $A_{ij}^k$ denotes the pixel value at the location of $(i,j)$ of the $k$-th feature map.
Grad-CAM has the ability to locate the focus areas that belong to the corresponding category. As shown in Fig.~\ref{fig1}, the dot line is a diagram of Grad-CAM, which represents the focus-area is obtained by weighted summing the feature maps. In this work, we utilize Grad-CAM to generate base categories' focus regions $\mathcal{H}_{base} = \{(x_i^h, y_i)\}_{i=1}^{N}$. However, the ConvNet extractor can not give a correct response of $c$ in formula (\ref{gradv2}), when a novel category appears. To our delight, we find that the model has accumulated lots of meta-knowledge in the domain field (e.g., Ornithology) during the training process of $\mathcal{D}_{base} = \{(x_i, y_i)\}_{i=1}^{N}$. The concepts of novel categories can be made up of various meta-knowledge, which are already embedded in the neural networks. For example, if someone has never seen the tiger, she/he might think it has many close parallels to a cat (learned before). The reason is that the attention locations of human on the new category tiger and the known category cat are similar to each other. Although we don't know the ground truth of the novel samples for the fine-grained few-shot tasks, the unseen class always has similar regions to the $\mathcal{D}_{base}$, such as bird's mouths and wings. And the base classifier will classify the new sample into the most similar class in $\mathcal{D}_{base}$. Therefore, it is possible to utilize Grad-CAM tp generate good focus-area location $\mathcal{H}_{novel}$ on the unseen categories for enhancing feature representation.
Telling the neural network the regions of rich discriminative information will form a more robust representation. This step is similar to the data augmentation of input space. However we only mine the available information on the input data itself without using the extra data augmentation.
\subsubsection{Classifiers}
\label{threecls}
Generally, the ConvNet's classifier uses the dot-product operator to compute classification scores: $s = z^{T}*{w_{k}^b}$, where $z$ is the feature vector extracted by ConvNets and $w_{k}^b$ is the $k$-th classification weight vector in $W_{base}$. It is trained from scratch by thousands of optimization steps (e.g., SGD). In contrast, the $W_{base} $ is not adapted to the new categories and it is difficult to find the proper classification weights $W_{novel}$ with only a few samples and optimization steps. To address this critical problem, a classifier should be implemented to distinguish the new categories. To the best of our knowledge, current researches commonly choose one of the following classifiers to gain their best performance, i.e., SVM \cite{Chen2018}, cosine-similarity \cite{Brown} and nearest neighbor.
\textbf{SVM.} SVM classifier has achieved excellent performance for small training data in few-shot learning \cite{Chen2018}. Essentially, unlike deep learning methods which need large-scale training data to learn generalization ability within classes, SVM is a classical transductive inference method aiming to build a model that is applicable to the problem domain.
\textbf{Nearest neighbor.} The Euclidean-based nearest neighbor method uses feature vector $z_s$ to build a prototype representation of each novel class for the few-shot learning scenario. Then it classifies the unlabeled data by calculating the distance from each query embedding point to the prototype.
\textbf{Cosine classifier.}
The cosine classifier has been well established as an effective similarity function for few-shot tasks \cite{ Vinyals2016}, which classifies samples by comparing the cosine similarity between $z_s$ and $z_q$.
\subsection{Objective function}
The loss function is important to let the neural network generate separable representations for the unseen classes. For example, Siamese Nets \cite{Koch2015} applies contractive loss to few-shot tasks, so that neural networks can learn to distinguish similarities from dissimilarities. For fine-grained few-shot tasks, it is critical to develop an effective similarity constraint function to improve the discriminative power of the feature representations. Center loss \cite{Wen2016a}, which was first proposed for the face recognition problem, simultaneously learns a center for deep features of each class and penalizes the distances between the deep features and their corresponding class centers. Suppose there are $K$ classes for samples, $k^i$ is the category of the image $x_i$ and $z_i = f_{\varphi}(x_i)$ denotes the deep features extracted from $x_i$. Here is the formulation for center loss:
\begin{equation}\label{Center}
\mathcal{L}_c = \frac{1}{2} \sum\limits_{i}^n \| z_i - c_{k^i} \|_{2}^{2}.
\end{equation}
The $c_{k} \in \mathbb{R}^K$ denotes the $k$-th class center of deep features. The formulation effectively characterizes the intra-class variations.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.8\linewidth]{./img/plank/loss_intro.pdf}
\end{center}
\caption{ The center loss is simply pulling the samples into the class-center (entagram). While CN\_loss adds additional penalties to the sample of the wrong classification (red fork symbol) using nearest-neighbor. }
\label{lossintro}
\end{figure}
However, all training samples are treated equally when a center loss function minimizes the intra-class variations, regardless of whether the sample is easy or hard to pull into the center point.
Intuitively, for the fine-grained tasks, the difference among classes is extremely small. It is not enough to form a good distribution by simply pulling the feature vector into the class center. It is critical to impose special penalties on the samples which are difficult to approach the center during the training process. To this end, we further propose the Center Neighbor Loss (CN\_Loss) function $\mathcal{L}_s$ to form robust embedding space distribution as following.
\begin{equation}\label{CN}
\mathcal{L}_s = \mathcal{L}_c + \beta \cdot \mathcal{L}_N
\end{equation}
$\beta$ is the balance parameter for penalty term $\mathcal{L}_N$. $\mathcal{L}_N$ is
a negative log-probability for samples that are not classified to the correct class center. The $\mathcal {L}_N$ can be formulated as following.
\begin{equation}\label{NN}
\mathcal{L}_N = -\log \frac{\exp(-E(\bar{z^k},\mathbf{c}_k))}{\sum_{k'\in K}\exp(-E(\bar{z^{k'}}, \mathbf{c}_{k'}))}
\end{equation}
$\bar{z^k}=Avg(\sum_{x_i^k \in \mathcal{D}_{base}} f_{\varphi}(x_i^k))$ is the $k$-th class average feature vector contained in every batch, and $E(\cdot,\cdot)$ denotes the $Euclidean$ distance.
The schematic is shown in Fig.~\ref{lossintro}. We take the center points learned from the last iteration as support points and use Euclidean-based nearest neighbors to classify the current batch of samples. With the penalty $\mathcal{L}_N$, each cluster will gather faster and perform robustly.
Ideally, the class center $c_{k}$ should be updated as feature vectors change. That means we should take the entire training set into account and average the deep features of each class in each iteration, which is not feasible in practice. To solve this problem, we implement the solution suggested for center loss \cite{Wen2016a}. First of all, we perform the update procedure based on mini-batch. The centers are computed by averaging the features of every category in each iteration. Secondly, we use the centers learned from the last iteration to classify the current batch samples by Nearest Neighbor Algorithm and punish the mislabeled samples. At last, we fix the learning rate of the centers as 0.5 to avoid large perturbations caused by mislabeled samples \cite{Wen2016a}.
\section{Experiments}
\subsection{Experimental design}
For rare categories, it's extremely difficult to collect sufficient and diverse training images. Currently, most of the previous few-shot learning methods take the {\it mini}ImageNet dataset \cite{Vinyals2016} to test their performance with 5-way 1-shot or 5-way 5-shot assumptions. However, the {\it mini}ImageNet consists of 60,000 color images with 100 classes of which 64 classes for training. The training data is enough to learn a good feature extractor for a common few-shot classification task, and nearly 80\% accuracy has been already achieved recently \cite{Chen2018}. In this paper, we focus on the fine-grained few-shot classification tasks. To this end, we design three different experiments on Caltech-UCSD Birds \cite{Wah2011} datasets, {\it mini}DogsNet \cite{Hilliard2018} and miniPPlankton.
For the {\it mini}DogsNet dataset \cite{Hilliard2018}, we only use \textbf{10 classes} for training, and conduct 5-way experiments with both 1-shot and 5-shot settings. We will compare our method with other well known techniques \cite{Vinyals2016}, \cite{Snell2017, Sung2017, Finn2017, Garcia2017}. All methods are also training on these 10 classes. In order to ensure the fairness of comparison, we unify the MatchingNets \cite{Vinyals2016}, PrototypicalNets \cite{Snell2017} and Imprint \cite{Brown}' feature extractor to ResNet. As the meta-learning training strategy of the Relation Networks \cite{Sung2017} and MAML \cite{Finn2017} is difficult to be trained via deep ConvNets, we keep their original network architecture.
In real-world scenarios, humans face a large number of novel categories to be recognized. 5-way experiments only for toy examples in papers. Currently, one state-of-the-art research work Imprint \cite{Brown} implemented the Caltech-UCSD Birds dataset \cite{Wah2011} for 100-way few-shot learning problem, which is much practical. Here we will carry out experiments with the same setting of Imprint \cite{Brown}. That means we investigate the accuracy on all the novel classes. As the above-mentioned methods including RelationNets \cite{Sung2017} are designed for only 5-way experiments, it is difficult to accomplish the 100-way procedure. For example, RelationNets \cite{Sung2017} requires huge GPU memory spaces for the 100-way training. Therefore, we only set the recent work Imprinted Weights \cite{Brown} as the comparison. For few-shot tasks, the Imprinted Weights \cite{Brown} described how to add a similar capability to ConvNet classifier by directly setting the weights of the final layer from novel labeled samples. Essentially, the core of Imprinted Weights method is cosine similar function. Therefore, in the following experiments, the baseline (ResNet + cosine classifier) here is the same as the Imprint.
In a real-world scenario application, for {\it{{mini}}}{{PPlankton}, we will compare our method with MatchingNets, PrototypicalNets, Relation Net, MAML and Imprint. All of above the methods are re-implemented with ResNet as the backbone feature extractor.
\subsection{Implementation details}
\begin{figure*}[t]
\begin{center}
\captionsetup[subfigure]{labelformat=empty}
\subfloat[\quad \quad epoch = 20]{
\begin{minipage}[t]{0.22\textwidth}
\centering
\includegraphics[height=1.1in]{./img/cn/Centerlast20.pdf} \\
\includegraphics[height=1.1in]{./img/cn/CNlast20.pdf}
\end{minipage}
}
\subfloat[\quad epoch = 40]{
\begin{minipage}[t]{0.22\textwidth}
\centering
\includegraphics[height=1.1in]{./img/cn/Centerlast40.pdf} \\
\includegraphics[height=1.1in]{./img/cn/CNlast40.pdf}
\end{minipage}
}
\subfloat[\quad \quad epoch = 60]{
\begin{minipage}[t]{0.22\textwidth}
\centering
\includegraphics[height=1.1in]{./img/cn/Centerlast60.pdf} \\
\includegraphics[height=1.1in]{./img/cn/CNlast60.pdf}
\end{minipage}
}
\subfloat[\quad epoch = 80]{
\begin{minipage}[t]{0.22\textwidth}
\centering
\includegraphics[height=1.1in]{./img/cn/Centerlast80.pdf} \\
\includegraphics[height=1.1in]{./img/cn/CNlast80.pdf}
\end{minipage}
}
\end{center}
\caption{The distribution of deeply learned features under Center loss and CN\_loss. Different colors denote different classes.}
\label{distribution}
\end{figure*}
ResNet18 \cite{He2016} is employed as the feature extractor $f_{\varphi}$. Following the similar strategy of Wen \cite{Wen2016a}, we train the feature extractor with the joint supervision of softmax loss and CN\_loss. We initialize the learning rate of the softmax loss as 0.001 and half it every 20 epochs. And we only use the last feature map as the input of high-order integration. During the testing phase, for {\it mini}DogsNet and Caltech-UCSD Birds, raw support image and zoomed focus-area are uniformly resizing into 224*224 and be sent to $f_{\varphi}$ to form a robust feature vector using element-sum operation. For {\it{{mini}}}{{PPlankton}, due to the specificity of the phytoplankton image, e.g., the target is scattered shape. Therefore, slightly differing from the structure Fig.~\ref{fig1}, we do not use the backbone network to extract the focus-areas' feature. Here we resize focus-area into 84*84 to train a shallow CNN (four convolution blocks). Through the shallow CNN, the testing focus-area's feature will be concatenated with the original image's feature.
\subsection{Configuration variants}
{\bf CN\_Loss.} Fashion-MNIST is commonly used to evaluate the the loss function \cite{Wen2016a, Cale}. We conduct similar experiments as suggested \cite{Wen2016a, Cale} to visualize the performance of Center loss and CN\_loss on Fashion-MNIST. Fashion-MNIST consists of 60,000 training examples and 10,000 for testing. Each example is a 28x28 gray-scale image, associated with a label from 10 classes. The space distribution results are shown in Fig.~\ref{distribution}. We can see that, CN\_loss can quickly form the cluster of each class. A more robust feature space distribution usually means a better feature extractor. And from the Table \ref{mnistacc}, the CN\_loss shows better performance on classification tasks.
\begin{table}[h]
\small
\begin{center}
\begin{tabular}{cc}
\toprule
\bf{ Loss Function} & \bf{Accuracy(\%)}\\
\midrule
Softmax Loss & {89.5 $\pm$ 0.2 } \\
Center Loss & {90.0 $\pm$ 0.2} \\
CN Loss &{\bf{91.42 $\pm$ 0.3}} \\
\bottomrule
\end{tabular}
\end{center}
\caption{The general classification performance of the three loss functions on the Fashion-MNIST dataset.}
\label{mnistacc}
\end{table}
In addition, the hyperparameter $\beta$ in (\ref{CN}) is the balance for penalty term $\mathcal{L}_N$. We investigate the performance of our model with different hyperparameter $\beta$ on {\it mini}DogsNet's validation set. As shown in Fig.~\ref{beita}, it is very clear that the center loss (i.e., $\beta=0$) is not a good choice for few-shot classification problem. The best performance can be achieved in the case of $\beta\in [0.4,0.6]$.
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.7\linewidth]{./img/beita.pdf}
\end{center}
\caption{The verification accuracy with different $\beta$.}
\label{beita}
\end{figure}
{\bf High-order integration.} The high-order integration could help us capture more complex and high-order relationships among different intra-parts to get better attention maps. As shown in Fig.~\ref{highorder}, it helps to focus on the discriminative regions of the image. We have conducted experiments with different orders on the performance of our method. And we found that 2-order performs stable on the novel classes classification. For instance, the accuracy of 2-order ($49.52\%$) is higher than 1-order ($48.56\%$) and 3-order ($47.00\%$) on the CUB-200-2011 dataset for 5-way setting.
\begin{figure}[h]
\begin{center}
\captionsetup[subfigure]{labelformat=empty}
\rotatebox{90}{ w/HO \quad w/o HO \quad raw}
\subfloat[]{
\begin{minipage}[b]{0.06\textwidth}
\centering
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/base1.pdf} \\
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/baseC1.pdf} \\
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/baseO1.pdf} \\
\end{minipage}
}
\subfloat[$\mathcal{D}_{base}$]{
\begin{minipage}[b]{0.06\textwidth}
\centering
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/base2.pdf} \\
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/baseC2.pdf} \\
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/baseO2.pdf} \\
\end{minipage}
}
\subfloat[]{
\begin{minipage}[b]{0.06\textwidth}
\centering
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/base3.pdf} \\
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/baseC3.pdf} \\
\includegraphics[width=0.485in,height=0.485in]{./img/gradcam/baseO3.pdf} \\
\end{minipage}
}
\subfloat[]{
\begin{minipage}[b]{0.06\textwidth}
\end{minipage}
}
\subfloat[]{
\begin{minipage}[b]{0.06\textwidth}
\end{minipage}
}
\subfloat[]{
\begin{minipage}[b]{0.06\textwidth}
\centering
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novel1.pdf} \\
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novelC.pdf} \\
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novelO.pdf} \\
\end{minipage}
}
\subfloat[$\mathcal{D}_{novel}$]{
\begin{minipage}[b]{0.06\textwidth}
\centering
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novel2.pdf} \\
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novelC2.pdf} \\
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novelO2.pdf} \\
\end{minipage}
}
\subfloat[]{
\begin{minipage}[b]{0.06\textwidth}
\centering
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novel5.pdf} \\
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novelC5.pdf} \\
\includegraphics[width=0.48in,height=0.48in]{./img/gradcam/novelO5.pdf} \\
\end{minipage}
}
\end{center}
\caption{Visualization results with Higher-order Integration and without it. The left three columns show the focus regions on the $\mathcal{D}_{base}$, while the right three denote focus regions of novel samples from $\mathcal{D}_{novel}$.}\label{highorder}
\end{figure}
{\bf Focus-area location.} We investigate the role of Focus-area Location on our fine-grained tasks. Section~\ref{threecls} briefly described the cosine classifier used in our task. We will also illustrate the performance of different classifiers on the fine-grained few-shot classification. Figure~\ref{classfier} shows the accuracy on different tasks with the same feature extractor setting. For the {\it mini}DogsNet dataset, the cosine classifier could achieve the highest accuracy on the validation set. And focus-area location achieves positive improvement. For the Caltech-UCSD Birds, both cosine classifier and SVM can achieve nice performance. Especially, we also find that the focus-area location greatly improves the accuracy of SVM classifier.
\begin{figure}[t]
\centering
\captionsetup[subfigure]{labelformat=empty}
\subfloat[]{
\begin{minipage}[b]{0.45\columnwidth}
\includegraphics[width=1\linewidth, height=1.32in]{./img/classifier1shot.pdf}
\includegraphics[width=1\linewidth, height=1.32in]{./img/cub1shot.pdf}
\end{minipage}
}
\subfloat[]{
\begin{minipage}[b]{0.45\columnwidth}
\includegraphics[width=1\linewidth,height=1.32in]{./img/classifier5shot.pdf}
\includegraphics[width=1\linewidth,height=1.32in]{./img/cub5shot.pdf}
\end{minipage}}
\caption{The accuracy of three classifiers with and without Focus-area Location under 1 shot and 5 shot assumptions. }\label{classfier}
\end{figure}
\subsection{Caltech-UCSD Birds}
The Caltech-UCSD Birds dataset \cite{Wah2011} includes 200 fine-grained categories of birds with 11,788 images. We take the pre-trained ResNet18 \cite{He2016} with ImageNet as the feature extractor $f_{\varphi}$. Train/test split setting is followed the suggestion of Imprinted Weights \cite{Brown}. Here, 100 novel classes are required to be distinguished, which is very challenging and similar to the real-world scenario. The cosine classifier is employed to recognize the novel categories.
As shown in Table~\ref{tcub}, for all novel categories classification, we observe that the high-order module and CN\_Loss function are beneficial to our tasks. In particular, the information of focus-areas brings considerable improvement in accuracy on the 5-shot setting. It is also important to illustrate the capability of recognition performance on all the categories \cite{Gidaris2018}. We further evaluate the performance on dataset of $\mathcal{D}_{base} \cup \mathcal{D}_{novel}$ \cite{Brown}. Table~\ref{tcub} and table~\ref{tcuball} show that our model achieves promising accuracies on the novel categories while at the same time it does not sacrifice the recognition performance of the base categories $\mathcal{D}_{base}$.
\begin{table}[t]
\small
\begin{center}
\begin{tabular}{cccccccc}
\toprule
\textbf{{$N$-shot}} & \bf{1} & \bf{2} & \bf{5}\\
\midrule
Imprint (ori)\cite{Brown}& 21.26\% & 28.69\% & 39.52\% \\
\specialrule{0em}{1.25pt}{1.25pt}
Imprint + Aug (ori) & 21.40\% & 30.03\% & 39.35\% \\
\specialrule{0em}{1.25pt}{1.25pt}
Imprint (re) &28.77\% & 39.25\% &49.33\% \\
\midrule
ResNet + H & 30.14\% & 38.46\% & 49.83\% & \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss& 29.86\% & 39.45\% & 50.68\% & \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss + H& 30.17\% & 40.10\% & 50.78\%& \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNlos s + H + Att& \textbf{30.82\%} & \textbf{40.85\%} & \textbf{51.95\%}& \\
\bottomrule
\end{tabular}
\end{center}
\caption{The top-1 accuracy measured across all 100 novel classes of Caltech-UCSD Birds. 'H' denotes the High-Order Integration and 'Att' means Focus-area Location. '(ori)' means the original data in the paper and '(re)' represents the data we re-implement with ResNet as backbone.}
\label{tcub}
\end{table}
\begin{table}[t]
\small
\begin{center}
\begin{tabular}{ccccccccc}
\toprule
\bf{$N$-shot} & \bf{1} & \bf{2} & \bf{5} \\
\midrule
Imprint(ori) \cite{Brown}& 44.75\% & 48.21\% & 52.95\% \\
\specialrule{0em}{1.25pt}{1.25pt}
Imprint + Aug (ori)&44.60\% & 48.48\% & 52.78\% \\
\specialrule{0em}{1.25pt}{1.25pt}
Imprint(re)&44.68\% & 52.19\% & 59.27\% \\
\midrule
ResNet + H& {45.72\%} & {52.64\%}& {59.96\%} \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss& {45.06\%} & 51.69\% & {58.73\%}& \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss + H& {47.23\%} & {54.38\%}& {60.27\%} \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss + H + Att& \textbf{47.89\%} & \textbf{54.83\%} & \textbf{61.30\%} & \\
\bottomrule
\end{tabular}
\end{center}
\caption{Top-1 accuracy measured across base plus novel categories of Caltech-UCSD Birds. }
\label{tcuball}
\end{table}
\subsection{ {\it{\textbf{mini}}} DogsNet}
\begin{table}[h]
\small
\begin{center}
\begin{tabular}{cccccccc}
\toprule
\specialrule{0em}{1.25pt}{1.25pt}
\bf{5way $N$-shot} & \bf{Dist.} & \bf{1} & \bf{5}\\
\specialrule{0em}{1.25pt}{1.25pt}
\midrule
\specialrule{0em}{1.25pt}{1.25pt}
Matching Net \cite{Vinyals2016} & Cosine & 30.39\% & 37.97\% \\
\specialrule{0em}{1.25pt}{1.25pt}
Prototypical Net \cite{Snell2017} & Euclid. & 31.37\% & 39.33\% \\
\specialrule{0em}{1.25pt}{1.25pt}
Relation Net\cite{Sung2017} & Deep metric & 32.42\% & 38.53\% \\
\specialrule{0em}{1.25pt}{1.25pt}
MAML \cite{Finn2017} & - & 26.66\% & 35.60\% \\
\specialrule{0em}{1.25pt}{1.25pt}
Imprint \cite{Brown} & Cosine & 30.14\% & 38.31\% & \\
\midrule
\specialrule{0em}{1.25pt}{1.25pt}
Resnet + H & Cosine & 30.17\% & 38.77\% & \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss& Cosine & 31.25\% & 40.63\% & \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss + H& Cosine & 31.95\% &41.40\%& \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet+CNloss+H+Att& Cosine & \textbf{33.13\%} & \textbf{42.53\%}& \\
\bottomrule
\end{tabular}
\end{center}
\caption{The top-1 accuracy on the test set of {\it mini}DogsNet, all accuracy results are averaged over 100 test episodes and each episode contains 100 query samples from 5 classes. All results are reported with 95\% confidence intervals. }
\label{tab:mini}
\end{table}
Hilliard et al. \cite{Hilliard2018} created a {\it mini}DogsNet which consists images of dog categories from the ImageNet to test the model's fine-grained ability. They selected 100 of those classes and use the 64/16/20 random classes split for training, validation, and testing. In our work, we further increase the difficulty by random selecting 10 of 64 classes to form our training set. That means only 10 classes are used for training the feature extractor and 20 novel classes should be distinguished. And we train the ResNet18 \cite{He2016} from scratch.
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.9\linewidth]{./img/plank/planksamples.pdf}
\end{center}
\caption{Random samples of nine categories from our Phytoplankton dataset. The morphological differences among different categories are very small (such as the first two categories). It is a typical dataset for fine-grained challenge problem.}
\label{plankton}
\end{figure}
We conduct 5-way experiments with both 1-shot and 5-shot trials. Table~\ref{tab:mini} shows that our model could achieve promising performance both on 1-shot and 5-shot tasks. To verify the effectiveness of our different modules, we use the ResNet18 and cosine classifier as the baseline. To our surprise, the baseline can also achieve nice performance. Relation Nets uses the deep non-linear metric to capture the similarity between samples and is well performed even using 10 classes training data. For our method, we can see that CN\_Loss and high-order integration can bring promising improvements. And the focus-area location mechanism is still beneficial to the task.
\subsection{{\it{\textbf{mini}}} PPlankton}
For a real-world task in specific domain such as phytoplankton classification, it is infeasible to collect large-scale samples and it always requires experts to label the data. Meanwhile, it is also quite difficult to search for the relevant open-source web-data. Current monitoring systems (e.g. ZooScan and FlowCAM \cite{Gorsky2010, Jakobsen2011}) yield large amounts of images every day. It requires many marine biologists to manual classify the sample images. Nevertheless, new and scarce categories are valuable for marine science. {\textbf{PPlankton} is a large-scale public dataset for machine learning with the help of marine biologists \cite{Qiong2019}. And for few-shot tasks, we further construct a phytoplankton dataset {\it{\textbf{mini}}}{\textbf{PPlankton}. It is a particular image dataset for few-shot fine-grained classification problem.
Some examples of the dataset are shown in Fig.~\ref{plankton}. To construct the dataset, we collect seawater samples from the Bohai Sea, and we photograph phytoplankton images contained in the sampled seawater by optical microscopes. With the help of marine biologists,
we label each object with its confident catergory. The {\it mini}{PPlankton} includes 20 classes each of which contains about 70 samples. From Fig.~\ref{plankton}, we can observe that our dataset faces the challenge problem of fine-grained classification. For example, their shapes between different categories are similar, such as tripos and trichocero.
\begin{table}[h]
\small
\begin{center}
\begin{tabular}{cccccccc}
\toprule
\specialrule{0em}{1.25pt}{1.25pt}
\bf{$N$-shot} & \bf{Dist.} & \bf{1} & \bf{5}\\
\midrule
\specialrule{0em}{1.25pt}{1.25pt}
Matching Net \cite{Vinyals2016}& Cosine. & 48.76\% & 60.78\%& \\
\specialrule{0em}{1.25pt}{1.25pt}
Prototypical Net \cite{Snell2017} & Euclid. & 50.84\% & 66.67\%& \\
\specialrule{0em}{1.25pt}{1.25pt}
Relation Net \cite{Sung2017}& Deep-metric & 46.79\% & 58.48\% & \\
\specialrule{0em}{1.25pt}{1.25pt}
MAML\cite{Finn2017} & - & 46.0\% & 60.63\% & \\
\specialrule{0em}{1.25pt}{1.25pt}
Imprint\cite{Brown} & Cosine & 57.72\% & 72.99\%& \\
\midrule
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss & Cosine & 59.0\% & 74.84\% & \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss + H & Cosine & 56.29\% & 70.8\%& \\
\specialrule{0em}{1.25pt}{1.25pt}
ResNet + CNloss + Att& Cosine & \textbf{60.03\%} & \textbf{75.56\%}& \\
\bottomrule
\end{tabular}
\end{center}
\caption{The top-1 accuracy on the test set of {\it mini}PPlankton.}
\label{tplank}
\end{table}
For this dataset, we conduct 5-way experiments with both 1-shot and 5-shot trials on the $\mathcal{D}_{novel}$ and we use the ResNet18 with cosine-classifier as the baseline (the same as Imprint). We randomly selected 10 classes as the basic training classes, and the remaining classes as the novel classes to evaluate few-shot tasks. As shown in table~\ref{tplank}, we can see that the proposed model with CN\_loss outperforms the baselines by a significant margin, from 72.99\% to 74.84\% in the 5-shot trial. However, to our surprise, the high-order module does not work for this dataset, and even leads to decline of test accuracy. The reason is that phytoplankton images are not "closed-shape" (target and background are separate) like normal images. For example, as shown in Fig.~\ref{plankton}, the object of Biddulphia is interspersed with the background.
\begin{figure}[h]
\begin{center}
\subfloat[\quad Imprint]{
\begin{minipage}[t]{0.24\textwidth}
\centering
\includegraphics[width=1.0\linewidth]{./img/plank/plainMatrix.pdf} \\
\end{minipage}
}
\subfloat[\quad Ours]{
\begin{minipage}[t]{0.24\textwidth}
\centering
\includegraphics[width=1.0\linewidth]{./img/plank/Cmatrix.pdf} \\
\end{minipage}
}
\end{center}
\caption{The confusion matrix of the baseline (ResNet with cosine classifier, also equivalent to Imprint \cite{Brown}) and our methods.}
\label{confusion}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.71\linewidth]{./img/plank/camPlank.pdf}
\end{center}
\caption{The focus-area on some examples of the phytoplankton dataset.}
\label{camplank}
\end{figure}
We further illustrate the improvement of classification performance for each category. Fig.~\ref{confusion} shows the confusion matrices of the baseline and our method on $\mathcal{D}_{novel}$ of {\it{mini}}PPlankton. We can see that our model greatly improves the accuracy of category 1 (pleurosigma-pelagicum) and category 6 (nitzschioides). At the same time, we reduce the possibility of misclassification of category 5 into category 6. However, it is still very challenge for some categories. Moreover, we visualize the focus area of some examples in Fig. ~\ref{camplank}. We can see that our method can capture the key area of the object. It helps the model to extract discriminative features for classification. Fig.~\ref{compareerror} shows the most difficult category pairs. For instance, samples of category 8 are usually classified into category 9. It can be seen from Fig.~\ref{compareerror} that the difference between these categories are very small. Such similarity even confuses marine biologists to distinguish them from each other.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.7\linewidth]{./img/plank/compareerror.pdf}
\end{center}
\caption{The blue number in the lower right corner of the image represents the ground-truth category, and the red number represents the wrongly predicted category.}
\label{compareerror}
\end{figure}
\section{Conclusion}
In this paper, we focus on the challenge of the domain-specific few-shot fine-grained classification problem via exploring the attention features from a few labeled examples. The Feature Fusion Model and CN\_Loss are our two contributions on mining features for such a challenge task. The fusion model utilizes the focus-area location and high-order integration to generate features from discriminative regions. High-order integration has the ability to capture the intra-parts discriminative information. And Grad-CAM can generate focus-area locations for the novel labeled samples. For few-shot learning, we want to learn a more robust feature extractor through basic training classes. As the fine-grained visual categories are quite similar to each other, we design CN\_Loss to penalize the special samples which are difficult to approach class centers in each iteration. Furthermore, we build a typical fine-grained and few-shot learning dataset {\it{\textbf{mini}}}{\textbf{PPlankton}} from the real-world application in the area of marine ecological environment. We not only build a few-shot phytoplankton dataset but also design an universal model to accomplish the few-shot classification task of natural images and phytoplankton images in the real-world industrial applications. Extensive experiments are carried out to investigate the effects of these proposed modules. We believe that our method is a valuable complement to few-shot classification problem and the new {\it{\textbf{mini}}}{\textbf{PPlankton}} is attractive for the marine industrial applications.
\section*{Acknowledgment}
The authors would like to thank anonymous referees for their useful comments and editors for their work. The authors gratefully thank the GPU computation support from Center for High Performance Computing and System Simulation, Pilot National Laboratory for Marine Science and Technology (Qingdao).
\bibliographystyle{Bibliography/IEEEtranTIE}
| {
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{"url":"https:\/\/questions.examside.com\/past-years\/jee\/question\/the-upper-half-of-an-inclined-plane-with-inclination-phi-2005-marks-4-k6wzlgyb11qezqo3.htm","text":"### JEE Mains Previous Years Questions with Solutions\n\n4.5\nstar star star star star\n1\n\n### AIEEE 2005\n\nThe upper half of an inclined plane with inclination $\\phi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by\nA\n$2\\,\\cos \\,\\,\\phi$\nB\n$2\\,sin\\,\\,\\phi$\nC\n$\\,\\tan \\,\\,\\phi$\nD\n$2\\,\\tan \\,\\,\\phi$\n\n## Explanation\n\nLet the length of the inclined plane is = $l$. So only ${l \\over 2}$ part will have friction.\n\nAccording to work-energy theorem, $W = \\Delta k = 0$ (Since initial and final speeds are zero)\n\n$\\therefore$ Work done by friction + Work done by gravity $=0$\n\ni.e., $- \\left( {\\mu \\,mg\\,\\cos \\,\\phi } \\right){\\ell \\over 2} + mg\\ell \\,\\sin \\,\\phi = 0$\n\nor ${\\mu \\over 2}\\cos \\,\\phi = \\sin \\phi$\n\nor $\\mu = 2\\,\\tan \\,\\phi$\n2\n\n### AIEEE 2005\n\nA bullet fired into a fixed target loses half of its velocity after penetrating $3$ $cm.$ How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?\nA\n$2.0$ $cm$\nB\n$3.0$ $cm$\nC\n$1.0$ $cm$\nD\n$1.5$ $cm$\n\n## Explanation\n\nLet $K$ be the initial kinetic energy and $F$ be the resistive force. Then according to work-energy theorem, $$W = \\Delta K$$\n\ni.e., $3F = {1 \\over 2}m{v^2} - {1 \\over 2}m{\\left( {{v \\over 2}} \\right)^2}...\\left( 1 \\right)$\n\nLet the bullet will penetrate x cm more before coming to rest.\n\n$\\therefore$ $Fx = {1 \\over 2}m{\\left( {{v \\over 2}} \\right)^2} - {1 \\over 2}m{\\left( 0 \\right)^2}...\\left( 2 \\right)$\n\nDividing eq. $(1)$ and $(2)$ we get,\n\n${x \\over 3} = {1 \\over 3}$ or x = 1 cm\n3\n\n### AIEEE 2004\n\nA particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that\nA\nits kinetic energy is constant\nB\nis acceleration is constant\nC\nits velocity is constant\nD\nit moves in a straight line\n\n## Explanation\n\nWork done by such force is always zero when a force of constant magnitude always at right angle to the velocity of a particle when the motion of the particle takes place in a plane.\n\n$\\therefore$ From work-energy theorem, $\\Delta K = 0$\n\n$\\therefore$ $K$ remains constant.\n4\n\n### AIEEE 2004\n\nA body of mass $' m ',$ acceleration uniformly from rest to $'{v_1}'$ in time ${T}$. The instantaneous power delivered to the body as a function of time is given by\nA\n${{m{v_1}{t^2}} \\over {{T}}}$\nB\n${{mv_1^2t} \\over {T^2}}$\nC\n${{m{v_1}t} \\over {{T}}}$\nD\n${{mv_1^2t} \\over {{T}}}$\n\n## Explanation\n\nAssume acceleration of body be $a$\n\n$\\therefore$ ${v_1} = 0 + a{T} \\Rightarrow a = {{{v_1}} \\over {{T}}}$\n\n$\\therefore$ $v = at \\Rightarrow v = {{{v_1}t} \\over {{T}}}$\n\n${P_{inst}} = \\overrightarrow F .\\overrightarrow v = \\left( {m\\overrightarrow a } \\right).\\overrightarrow v$\n\n$= \\left( {{{m{v_1}} \\over {{T}}}} \\right)\\left( {{{{v_1}t} \\over {{T}}}} \\right)$\n\n$= m{\\left( {{{{v_1}} \\over {{T}}}} \\right)^2}t$","date":"2022-01-22 02:52:41","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\": 0.7591019868850708, \"perplexity\": 640.7554372107371}, \"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-2022-05\/segments\/1642320303729.69\/warc\/CC-MAIN-20220122012907-20220122042907-00564.warc.gz\"}"} | null | null |
Q: I short circuited my iPhone 5 through audio jack Long story short, I short circuited my second most expensive asset through a usb-male-audio-male. I'm devastated. I'm not rich. I was still giddy about saving a dozen dollars during black friday sales.
I understand basic elements of circuits. So I want to fix it myself.
I suspect that the battery is down. And I suspect some excessive current protection mechanism was triggered.
The battery can be replaced easily.
So my question is that what might have been broken, and how to fix them.
If you can kindly share your knowledge, I will be grateful.
A: a reset solved the problem
Try a reset, press the top and and home button at the same time
I found this solution by sarri at fixit
| {
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Cylis Wilson (He/Him/His)
Although originally from Texas, Cylis received his BFA from Ole Miss, and then moved to North Carolina where he spent several years working for institutions such as "Unto These Hills" and Tweetsie Railroad. He and his wife, Crystal, returned to TX in 2010 and are now the proud parents of Lilly (9) and Charlie (7). Cylis has appeared onstage often in the greater Houston area including charitable and community events such as Cone Man Running's Spontaneous Smattering, The Woodland's Arts in the Park, and the Conroe Shakespeare Festival. He has also appeared with the Houston Grand Opera and been a company member for Old West Melodrama, The Murder Mystery Co., and the Lone Star Radio Troupe in addition to serving as an intern at both the Texas Intensive and Lonestar Smash. After a long road, a series of improbable events at the most unlikely of times brought Cylis and his family back to the mountains of North Carolina where they feel most ar home. Cylis is currently working towards his final credits needed for an Advanced Actor-Combatant endorsement.
cylis.wilson@gmail.com
Horn in the West 2021
May 12, 2021 Broadsword Boone, North Carolina Basic Pass
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May 12, 2021 Unarmed Boone, North Carolina Recommended Pass
May 12, 2021 Knife Boone, North Carolina Recommended Pass
Lonestar Smash
Nov 3, 2019 Single Sword Dallas, Texas Recommended Pass
COM Theatre Summer SPT Sessions 2017
Aug 17, 2017 Broadsword Texas City, Texas Recommended Pass
Aug 17, 2017 Quarterstaff Texas City, Texas Recommended Pass
May 1, 2017 Unarmed Dallas, Texas Recommended Pass | {
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{"url":"https:\/\/math.stackexchange.com\/questions\/2116762\/expected-value-of-greatest-integer-random-variable\/2117052","text":"# Expected Value of Greatest Integer Random Variable\n\nLet $X$ be a random variable with probability density function $$f(x)=\\frac{1}{2} e^{-|x|},\\;\\; -\\infty<x<\\infty.$$ What is expected value of $\\lfloor X \\rfloor$, i.e. $$E( \\lfloor X \\rfloor),$$ where $\\lfloor X \\rfloor$ denotes the greatest integer of $X$.\n\n\u2022 @Chinny84 greatest integer command is not working properly here. So, I just denote by some other notation but I have defined this notation. Jan 27, 2017 at 17:37\n\u2022 how far have you got? could you work out the expected value without the greatest integer part, using integration?\n\u2013\u00a0Cato\nJan 27, 2017 at 17:44\n\u2022 find prob of greatest integer being n, then do infinite summation of nP(N = n) to get average - the summation is different for n<0 and n>=0\n\u2013\u00a0Cato\nJan 27, 2017 at 17:56\n\u2022 @Cato could you please elaborate it? Jan 27, 2017 at 18:02\n\nLet's define, for ease of notation, $Z=\\lfloor X \\rfloor$.\nTo get the expectation, let's first find the distribution law of $Z$.\nLet $n\\in\\mathbb{N}_0$. Then $P(Z=n)=P(n\\leq X < n+1)=\\int_{n}^{n+1}\\frac{1}{2}e^{-x}dx=\\frac{e-1}{2e^{n+1}}$.\nBecause of the symmetry of the function $\\frac{1}{2}e^{-|x|}$ around $0$, we have that $P(Z=-n-1)=P(-n-1\\leq X<-n)=P(n\\leq X < n+1)=P(Z=n)$.\nIn fact the answer is $- 1\/2$ for any density function which is symmetric about zero, and has finite expectation. The point is that $\\lfloor x \\rfloor + \\lfloor -x \\rfloor = -1$ for every non-integer $x$. So $E \\lfloor X \\rfloor + E \\lfloor -X \\rfloor = -1$ given finite expectation, and then (given symmetry) $E \\lfloor -X \\rfloor = E \\lfloor X \\rfloor$.","date":"2022-06-30 22:49:40","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\": 1, \"equation\": 2, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9800885915756226, \"perplexity\": 341.8877653867378}, \"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-2022-27\/segments\/1656103915196.47\/warc\/CC-MAIN-20220630213820-20220701003820-00202.warc.gz\"}"} | null | null |
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Voice I Singing Recorder I Flute Guitar I Harp Piano I Keyboard Violin I Viola Cello I Double Bass Clarinet I Saxophone Trumpet I French Horn Trombone I Tuba Music Theory only Organ Percussion
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Le Kay , Jo-Nette
http://www.madamejo.co.za/
Born in the beautiful Winelands town of Paarl, near Cape Town, Jo-Nette Le Kay displayed an exceptional talent for music at an early age.
At primary school she joined and was a founder member of the Paarl / Wellington Regional choir who performed nationally and internationally with many accolades and prizes to their name. Meeting ex president Nelson Mandela on three occasions, singing for King Gustav of Sweden and Queen Beatrix of the Netherlands, to name a few. She was also a very active performer during her school career with percussion ensembles at Music school and a fervent ballerina in many productions at both Johaar Mosaval and Joy Cargill dance studios.
At University she participated in the Stellenbosch University choir as well as the Stellenbosch Camarata. Both groups are world renowned choirs. After doing a Bachelor of Arts degree in Psychology and Geography, she decided to pursue her career in singing. She enrolled for a Performance Licentiate in Singing. Whilst doing this she gained experience as Second Lady in Mozart's 'Magic flute' as well as gaining experience in productions like 'Don Giovanni' and 'Il Matrimonio di Segreto'.
After her studies she started working with the well known South African mezzo soprano Jean Stuart. Jean taught her the Italian 'Bel Canto' style of singing, which proved to be very successful. Jean helped in the development of her voice into a dramatic coloratura soprano. Jo-Nette believes in creating opportunities for herself as well as other performers and thus put together her own productions such as 'Celebration of Song' (2001), 'Opera and Poetry' (2003), 'La Dolce Vita' (2006) and 'Magnifique Classique'(2011). By these initiatives she combines the world of opera with other genres of music and performance. Cross-over performers as well as drama-experts, visual artists and dancers make out part of these productions.
She also spent two years in London where she gained experience performing with Hamstead Garden Opera as well as Opera Integra. They did productions of 'Madama Butterfly', 'The Masked Ball' and excerpts of 'L'elisir d'Amore'. She attended Masterclasses in London with David Jones and Nelly Miricioiu and in Madrid with Teresa Berganza.
Back in South Africa she enrolled for a post graduate diploma in teaching at the University of Cape Town in 2006. While studying, she participated in opera theatre art classes under the direction of Prof. Angelo Gobbato and studied the title roles in excerpts from 'Lucia di Lammermoor', 'Don Pasquale' and 'Rigoletto'. In 2007 she joined the 'Cape Town Vocal Ensemble' under the direction of Leon Starker and performed as choir member and soloist. In 2009 she joined the Cape Town opera Ad Hoc Vocal Ensemble, where she participated in the opera 'Madama Butterfly' as well as the production of the 'Mozart Requiem'. In 2010 she sang in the opera 'Lucia di Lammermoor'.
Jo-Nette has been one of the official soloists in her hometown at performances of the Winelands Chamber Choir's Winter- and Summer concerts from 2010 till the beginning of 2012.
Apart from other roles, Jo-Nette worked as a freelance singer and continued to study under Jean Stuart. Jean passed away on 29 May 2012 and the legacy Jean left on Jo-Nette's life is very noticeable. Jean was an excellent voice coach, mentor, life coach and a very good friend. Her passing is a great loss to the world of singing.
During July 2008 till March 2012, Jo-Nette trained vocal students at the Frank Pietersen Music School in Paarl. Many of her students passed with distinction in their final exams in 2010 and 2011. In most cases she also acted as events coordinator for the school and was the main coordinator of the Frank Pietersen Choir Department. She also assisted the school's choirs by being their personal vocal technician. Thus she assisted the conductors and kept the voices healthy.
Jo-Nette returned in May 2011 from a visit to Germany, where she trained with the renowned baritone Laurence Gien. He successfully helped her in the further development of her voice. His recommendation was for her to sing the warm Verdi and Puccini tragic heroine operatic roles. She also participated in auditioning for opera companies and conductors. She returned to Hamburg in September 2012 to do a PROMS concert series with Klassik Philharmonie Hamburg at Moorrege, Mehrzweckhalle and at Hamburg, Laeiszhalle-Musikhalle under the baton of accomplished conductor Robert Stehli. The concerts were a roaring success and Mr Stehli assured her that she will return to Hamburg within the next two years to perform another programme with Klassik Philharmonie Hamburg.
2012 has been an exciting year for Jo-Nette.
She stopped teaching full-time and is now pursuing her career as a full-time freelance singer. She occasionally teaches vocal students; which she feels is an important part of her own personal development. Her first very successful concert was in April 2012 at Bethel Congregational church in Paarl, where she performed the well known piece 'The Shepherd on the Rock' with clarinet. The audience admired her for her warmth of voice and superfluous vocal technique. The next week was followed by a very successful Singing and Organ Recital at the Cederberg Festival in Clanwilliam. Many oratorio pieces were rendered that left the audience speechless for its lyrical beauty of sound.
At the beginning of May she wowed audiences at a Wedding Expo for the well known South African designer Johan Smit. She sang dramatic and veristic operatic arias as the models paraded the dramatic and beautiful wedding gowns created by Johan Smit couture. Johan also sponsored and made her dress for the event. This dress was worn at her Concerts in Germany in September 2012.
Her next and very exciting project is with the production of 'The South African Sopranos' by Niel Rademan productions. The first very successful concert took place at the end of May and includes Jo-Nette as the very lyrical soprano singing Operatic arias, Musical theatre pieces and pieces from Operetta of a very romantic nature. She is known for her rendition of the arias: 'O mio Babbino caro' by Puccini and Casta Diva by Bellini. Her charming personality and shiny, dreamy eyes have audiences at the edge of their seats. This production will be touring nationally for the next few years, performing at Festivals like 'The Woordfees' in Stellenbosch, the 'Klein Karoo Arts Festival' in Oudtshoorn as well as great Concert halls and Amphitheatres, like their recent performance at Oude Libertas Amphitheatre in Stellenbosch; and further across South Africa.
She has recently performed as 'Fairy Diva' in the Production of 'A Midsummer Night's Dream' with the Psychedelic Theatre Group on Paarl Mountain. These are amazing dancers who combine dance with fire in breath-taking fire dancing displays. With Jo-Nette now involved this also includes Operatic singing. Jo-Nette is also now a part of the group Salon Music at the Brooklyn Theatre in Pretoria, who will do a Verdi Gala concert series at the end of January 2013; under the direction of Mr Willem Vogel. She will also expand her teaching experience this year by coaching a few vocal students at the Black Tie Ensemble: VO1SS at the State Theatre in Pretoria.
Published 29 Nov 2012. Updated 7 January 2013. | {
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Q: Testing for FactoryGirl Results I'm trying to test to see if the items the array exist after I create the factory.
spec/models/thing_spec.rb
require 'rails_helper'
RSpec.describe Thing, :type => :model do
let(:thing) { Array.new(3) {FactoryGirl.create(:thing) } }
it "should sort the items in order" do
expect(thing).to include(ordering:1, ordering:2, ordering:3)
end
end
spec/factories/things.rb
FactoryGirl.define do
factory :thing, :class => 'Thing' do
name "item_name"
sequence(:ordering)
end
end
Below are the results that I received.
results
1) Things should be sorted in order
Failure/Error: expect(thing).to include(ordering:1, ordering:2, ordering:3)
expected [#<Thing id: 1, name: "item_name", create_date: "2014-11-07 04:18:17", modified_date: "2014-11-14 04:18:17", ordering: 1>, #<Thing id: 2, name: "item_name", create_date: "2014-11-07 04:18:17", modified_date: "2014-11-14 04:18:17", ordering: 2>, #<Thing id: 3, name: "item_name", create_date: "2014-11-07 04:18:17", modified_date: "2014-11-14 04:18:17", ordering: 3>] to include {:ordering => 2}
Diff:
@@ -1,2 +1,19 @@
-[{:ordering=>2}]
+[#<Thing:0x007fb96217cc30
+ id: 1,
+ name: "item_name",
+ create_date: Fri, 07 Nov 2014 04:18:17 UTC +00:00,
+ modified_date: Fri, 14 Nov 2014 04:18:17 UTC +00:00,
+ ordering: 1>,
+ #<Thing:0x007fb9621cfca0
+ id: 2,
+ name: "item_name",
+ create_date: Fri, 07 Nov 2014 04:18:17 UTC +00:00,
+ modified_date: Fri, 14 Nov 2014 04:18:17 UTC +00:00,
+ ordering: 2>,
+ #<Thing:0x007fb96221eda0
+ id: 3,
+ name: "item_name",
+ create_date: Fri, 07 Nov 2014 04:18:17 UTC +00:00,
+ modified_date: Fri, 14 Nov 2014 04:18:17 UTC +00:00,
+ ordering: 3>]
A: You can't do it this way. You'll have to check each record individually like this
it "should sort the items in order" do
expect(thing[0].ordering).to eq(1)
expect(thing[1].ordering).to eq(2)
expect(thing[2].ordering).to eq(3)
end
Or do something like this:
it "should sort the items in order" do
expect(thing.map(&:ordering)).to eq([1, 2, 3])
end
You can only use include to check if the array includes an element as a whole, like this:
expect(thing).to include(thing[0])
| {
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Alive! photos by Summy Lam and John Burnes, and courtesy Airport Police.
And to All a Good Flight
Airport Police marks five years of giving teddy bears to traveling children at LAX on Christmas morning.
Santa handing out joy on Christmas morning at LAX.
What began as a way to give away surplus gifts has become a Christmas Day tradition for the Airport Police family at LAX.
In 2015, the Los Angeles Airport Police in cooperation with Los Angeles School Police, Los Angeles Port Police, Los Angeles County Sheriff's Department, and the cities of Vernon, Bell, El Monte and Alhambra police Departments collected teddy bears donated by Officers and employees with assistance from Kenner Unlimited, Linzy, Imperial, Los Angeles Airport Police Athletic League and Cal Plush, handed out teddy bears to the children of the pediatric unit of LA/USC Medical Center. At the end, they had extra gifts, and decided to walk the terminals of LAX and hand out the surplus.
Sgt. Heriberto Gonzalez hands out stuffed toys to a traveling child on Christmas.
Thus was born a Christmas tradition that grows every year, and has become a family experience so dear to the Airport Police that no one who participates ever thinks of taking the special day off.
The Officers and employees of Airport Police fund the purchase of the teddy bears, which now surpasses 1,000. LAX also provides funding.
The Airport Police Officers who began the tradition five years ago continue to organize it today. They are Sgt. Rob Pedregon, Public Information Officer; and Motor Officers Paul Mosqueda and Nick Van Dragt. Santa resembles Steve Van Noord, the uncle of Nick Van Dragt.
The Airport Police family with Santa gathers in the United terminal on a recent Christmas morning. Family members participate in this annual event.
"Keeping the traveling public safe and secure is our first priority, and many of us can't be with our own children on Christmas morning, but to see the happiness that Santa brings to these children fills that empty space till we can make it home to our families," said Officer Pedregon.
Read all about the tradition in this month's interview.
An example of the teddy bears that will be given away on Christmas morning. The bears wear a T-shirt featuring the Airport Police badge.
Santa with Sgt. Robert Pedregon (left) Capt. Mike Scolaro.
On Nov. 13, Club COO Robert Larios and Alive! editor interviewed Sgt. Rob Pedregon, Public Information Officer, 11 years of City service, Club Member; Motor Officer Nick Van Dragt, 10 years, Club Member; and Motor Officer Paul Mosqueda, 11 years, Club Member. Stopping by to be a part of the interview was Santa Claus himself, who resembled Steve Van Noord, the uncle of Officer Van Dragt. Steve teaches second grade at Frank Woodruff Elementary School The interview took place at the headquarters of Airport Police at LAX. This will be the fifth year Steve has resembled Santa at LAX on Christmas Day.
Tell us how this beautiful tradition of handing out teddy bears to children traveling on Christmas morning started.
Sgt. Rob Pedregon: Sure. The first year this started – 2015 – the Motor Unit was supporting a charity cause at Children's Hospital. We all chipped in and bought some teddy bears to give to children there. That was a few days before Christmas. At the end of the event, we had a surplus of teddy bears. I thought, what are we going to do with them? We were all working Christmas Day, and I asked my partner Nick here who's always a team player. I said, "Would you be willing to dress up as Santa Claus and hand out these teddy bears?
Ofcr. Nick Van Dragt: I said I can do one better – I actually know someone that is Santa and I asked my uncle Steve Van Noord if he would be willing to do it and he said …
Santa (resembling Steve Van Noord): Absolutely! When they asked me to do it, I thought, "That sounds kind of interesting to do that." The first time we did it, it was a smaller operation than it is now. It's grown every year. It was so much fun. We did it on Christmas morning, and I was hooked right away. My wife came along with me. My daughter has come a couple of times; my niece Jody has come. I tell you, it's just been great. I love doing it. It's become a family tradition for us as well.
Sgt. Rob Pedregon and Officer Nick Van Dragt explain the tradition's origins to Club COO Robert Larios.
And the Christmas beard is coming in very nicely.
Santa (resembling Steve Van Noord): It is!
Sgt. Rob Pedregon: So the Motor officers all pulled together that first year. Paul was there with us at the original event, too, and he's our sleigh rider – he carries the bears along with us. He follows behind and replenishes our supply.
That first year, it was just overwhelming the number of bears that we had collected from ourselves and from the School Police and some of the agencies that were also participating in that charity event. We ended up with a surplus that the venue couldn't handle, so they asked us to take them back with us. We had a truck full of bears and headed back to LAX and wondered, "What the heck are we going to do with all these bears?"
It just evolved into, "Hey, let's try this and do it on Christmas morning."
Sgt. Rob Pedregon: Yes. We were already getting together with the Officers on Christmas morning at LAX. The wives would come in and bake cookies for all the Officers on patrol who had to work that day, and feed everyone who wasn't going to be with their families on that morning. We said, "We'll just head out into the terminal and start handing these out." We thought we'd get Nick to be Santa but he did one better.
The immediate family members who participate in the annual Santa teddy bear event every Christmas morning, from left: Sgt. Rob Pedregon and his wife, Nicole; Santa, who resembles Steve Van Noord, and his wife, Michelle; Jodi, Hank and Officer Nick Van Dragt; and Officer Paul Mosqueda. Steve Van Noord is Officer Van Dragt's uncle; and Hank Van Dragt pretended to be a tourist for this photo shoot.
What compelled you to take it to the next step and to do it yourself here at LAX?
Ofcr. Nick Van Dragt: I viewed it as a great opportunity to give back to the community that's given me so much. I enjoy hanging out with these guys on Christmas Day, and now I get my family involved, which is even better. I couldn't really pass up that opportunity and it's just fun to see the kids' faces when they receive the teddy bear from Santa. They're just all excited. It takes all the stress of flying away from them, and they're happy to be able to meet Santa that day.
Santa (resembling Steve Van Noord): I don't work at the airport, but to come here and see these kids and their reactions to what was really unexpected is just so special. And it extends to the airport employees and the people who work for the airlines, too. "Can I take my picture with you?" they ask me. They're working on Christmas Day, too, so it's joy for them, too, but it's mostly for the kids. Just to see their faces and enjoy their reactions to Santa Claus – they see you in an unexpected place and they're like, "Whoa."
Sgt. Rob Pedregon: It started off as this goodwill gesture, and it's evolved into something even bigger. It's for all the Officers who work on Christmas morning who aren't with their own children – the joy of going out there and seeing the smiles on all these children's faces, the parents, the employees – it really brings you back home. It's like fulfilling that emotion that you're lacking all morning.
It's larger than that, too, for us especially in law enforcement – we're building partnerships and trust with the community. We're ambassadors. There are people who come from all over the world, and the interactions that they have with us set the tone for all of law enforcement. We're working with more than just our own community, we're working worldwide. For a lot of people who come in contact with Police Officers, it's a negative situation. It's either a traffic citation or they're the victim of a crime. We can take it to a more personal place, show them a human aspect and let them know that we'ree more than just a uniform. We're people, and we do care.
Santa handing out joy on Christmas morning at LAX. Behind him is Sgt. Rob Pedregon.
Right, right. Santa, do you get special ATC clearance on Christmas morning for the sleigh to come in? You're a busy man on that day!
Santa (resembling Steve Van Noord): Well let's just say it's a busy morning!
The first year we did it, I came in a patrol car with two Motorcycle Officers escorting me like reindeer bringing in a sleigh. Since then we've been doing it a lot of different ways. It's unusual because you walk into the airport and then you walk out of the airport – you're either freezing or super hot, but it's just a joy to do it the whole time. I meet people from all over the world, including people who speak no English, but they know who Santa Claus is.
How many bears do you expect to give away this Christmas?
Sgt. Rob Pedregon: About 1,100 bears.
Distributed through all the terminals.
Sgt. Rob Pedregon: Right. We start in roll call. We'll let our partners in roll call know that we're going to be walking the terminals, and the Officers assigned to those terminals will come down and help as we go through the terminal. They'll help us distribute the bears. We get volunteers within the Department. They come out with us ever year. And it's grown from teddy bears – we hand out candy canes and ornaments, too, so even the adults get something. People pose with Santa Claus, so there's a lot of benefit for everybody, not just the kids.
Who makes sure that there is an ample supply? I know Santa's bag is very big, but making sure that you keep the supply moving is pretty important.
Ofcr. Paul Mosqueda: Right. I parallel them in the truck outside the terminals, and I might get ahead of them a little bit if they need replenishing.
Sgt. Rob Pedregon: The management of this event is vital, and I can't express enough how much Paul has been essential. Giving away the bears with Santa, we get lost in the moment, and we've got to have somebody managing the situation behind the scenes. Paul does a great job of that, and I'm so appreciative for all the years that he's done that. He makes sure that we don't run out in one terminal, which would mean we don't make it to the end. There's a lot involved in the logistics of it.
How are you funded now, to buy all those bears, candy canes and whatnot?
Sgt. Rob Pedregon: The Motor Unit pooled its funds together the first year. The next couple of years we kind of struggled along. I even solicited one of my friends – his company donated the first batch of candy canes. He bought like 1,000 for us. The next year I was able to ask the airport for funding, and the airport provided it. This year, when I went to Fiscal and said, "Hey, we're putting together this drive," there wasn't even a question from them. It looks like it's something that will continue on. I get a little teasing and hazing about it from Fiscal. They say, "Yeah, we know, you want your teddy bear money!"
Hank the Elf walks with Santa.
You've all mentioned family. It seems to me that there are a couple of different families here. You have your work family, your brother and sister Officers. But you also have your domestic families, too.
Ofcr. Nick Van Dragt: All of our families come to participate in this on Christmas morning. It's really special.
When this started, my son Hank was only one year old. He started coming to the airport on Christmas morning. Since then he's progressed, and last year he was promoted to elf, so we had him dressed up as an elf. He helped Santa pass out the teddy bears. It's awesome to have that kind of opportunity for him.
A lot of City employees have to work on Christmas Day or Thanksgiving or New Year's, to cover shifts. They might rather be at home on a holiday, but they have to work. It sounds like you actually enjoy working on Christmas morning.
Ofcr. Paul Mosqueda: I was scheduled to work that first year. But the couple of years after that, I chose to work the day. I didn't request it off and I didn't have any vacation planned. I'll be here this Christmas.
Ofcr. Nick Van Dragt: I just enjoy doing this with my family here. It's so much fun.
And Rob, as the PIO, you would normally have that day off, correct?
Sgt. Rob Pedregon: Oh yes – I have that day off, but this is such an important event. It makes a huge difference, so we're happy to come in. It's a labor of love.
Santa hands out joy on Christmas morning at LAX's Terminal 1.
Do you have favorite moments that you remember, that really stick with you?
Ofcr. Paul Mosqueda: I can pretty much bet that 99 percent of the time, children are not requesting to travel on Christmas Day. Typically it's the parents who are figuring out the logistics, and the kids are just going along. For them to see Santa at the airport on a day they didn't plan to be here, it really blindsides them, and that makes it fun and rewarding for me.
Hank the Elf (Hank Van Dragt, son of Officer Nick Van Dragt) hands out candy canes.
And then there are moments when somebody comes up and requests to get a bear for a sister or brother, thinking that Santa is on his way out. They'll want to pause us there and run and grab them. They want to share the experience. That makes the moment worthwhile for me.
Ofcr. Nick Van Dragt: Last year was pretty cool because I got to see my son dressed up as an elf, and he was out there passing out teddy bears to little kids and even adults and just bring smiles to their faces so that sticks out to me.
A young traveler tests Santa's true identity.
Santa (resembling Steve Van Noord): I have a story. A boy about eight years old comes up to me and he says, "You're not real." And I pat my stomach and I said, "I feel real." And he says, "No, that beard's a fake." My beard is totally real! And I said, "Why don't you give it a tug?" He gave it a tug and I said, "Ow!" He said, "Holy smokes, you are real!"
I'll always remember that one.
Sgt. Rob Pedregon: For me – it took a few years, but one year we started our rounds in Terminal 1. As soon as we walked in, the employees of the airline that's there [Southwest], they played Christmas carols on the speakers. They all started singing "Here Comes Santa Claus" as we walked in, and it was very impromptu. All the employees came out. They were hugging Santa and taking pictures with him. It's as meaningful to the adults as it is to the children, it really is.
Do you ever think that you are creating memory in the children that they're going to have forever?
Sgt. Rob Pedregon: Absolutely, that's part of that building the relationship and trust that I talked about. These are trying times that we're all in, and some people are not so trusting of public service. That's not what we are. Something like this changes that whole attitude. It's the way it was when I was a little kid. You looked up to Police Officers, and we're starting that now. It's a whole culture change that we're working on.
Yes, of course. But primarily, it's to give the kids a bit of Christmas as they travel.
Sgt. Rob Pedregon: Yes, absolutely – it's about the Airport Police being a family and for us to bring our family to the community. We get as much out of it as they do, we really do. We really are getting as much out of it as we're giving.
Right. Well said. So the only thing left to do, then is to wish everyone at in the Airport Police family a Merry Christmas from the Club!
Sgt. Rob Pedregon: Thank you. And Merry Christmas to you, too, and to all Club Members.
Club Director of Marketing Summy Lam (foreground) photographs Santa with the Airport Police family at LAX Friday, Nov. 15.
David Jamgotchian
Airport Police welcomes Officer Elizabeth Ramirez
Cecil Rhambo selected as new Chief of Airport Police.
Four new Officers join the Airport Police.
Thanks for the Service!
Airport Police welcomes two new Officers | {
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We asked our Young at Art Campers, 'What do you like most about being creative?'
"I can do what I want duh…." "Drawing my thoughts" "You can be as free as a bird." "Everything!" "The peace."
"Drawing is the one thing I can do without worrying if I am good enough."
"Making the things in my brain come true."
"I'm free."
"Letting your mind go wild."
"That I am not laughed at."
"Through colors, shapes, subjects, and size, I can release my feelings."
"It allows me to express my true self."
"There are no limits to being creative."
"It opens up a whole new world to create and explore in."
"There is no right or wrong no matter what you do."
"The endless possibilities of what can and can't be."
"Having an open mind."
"Getting messy."
"Photographing lets me show a different side of myself that I don't normally show."
"It opens up a world of imagination, and you can better understand the world's decisions and actions."
"The hard part was letting go,"
"I can make whatever I want."
"I like not having to copy people to make beautiful things."
"I like thinking outside of the box and making your own style."
"I can be myself."
"What I like about being creative is the idea that you can just think of something and make that idea into a masterpiece."
"Being creative makes you special."
"I can do anything."
"Using funny voices."
"You can make things that are imaginary."
"Your mind flies free."
"Being creative makes me happy."
"I like how it can change the ways you look at things."
"You can write anything and spelling doesn't matter."
"When your project is not creative, your pride is empty. When your project comes from you, your pride can be full."
"The sky is the limit."
"I always get to try something new."
"I'm allowed to express my feelings through art."
"I like the creating part."
"You try hard."
"I like working together and being part of something!"
"I like how you can just be yourself and do anything."
"Being a different person."
"I love being able to create my own little characters and worlds and to be able to do whatever imagination can think of."
"I honestly love everything about being creative."
"Nobody can tell me what's right or wrong."
"Having fun."
"Seeing the finished piece."
Galleries are closed between exhibitions.
970.879.9008 - info@steamboatcreates.org
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By submitting this form, you are consenting to receive marketing emails from: Steamboat Springs Arts Council, 1001 13th Street, Steamboat Springs, CO, 80477, www.steamboatcreates.org. You can revoke your consent to receive emails at any time by using the SafeUnsubscribe® link, found at the bottom of every email. Emails are serviced by Constant Contact | {
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\subsection*{Acknowledgments}
The authors would like to thank K.\ Hashimoto, T.\ Hirayama,
H.\ Kawai and M.\ Yamaguchi for many valuable discussions and
comments. M.~B.\ and T.~K.\ are supported in part by the Grants-in-Aid
for Scientific Research No.\ 09640375 and No.\ 10640261, respectively,
from the Ministry of Education, Science, Sports and Culture, Japan,
and K.\ Y.\ is supported in part by the Grant-in-Aid for JSPS Research
Fellowship.
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My expressive arts production company, The Rainbow Butterfly Cafe is a one of a kind Expressive Arts Company that offers "nourishment for the mind, the heart and the soul by imagining creating, implementing expressive arts based tools & strategies that supports diversity and disability inclusion, celebrates resiliency and conquering adversity, supports personal growth and fosters professional development. The R.B.C. delivers one person shows, dynamic performance keynotes, and custom designed expressive arts based performance projects, workshops and expressive arts curriculum designs to: conferences, retreats, corporate trainings, special events, schools, universities and colleges. | {
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Home/Teen/10 Real Life Australian Murder Houses
10 Real Life Australian Murder Houses
Could you live in a house that was the scene of one of Australia's most gruesome crimes? These are Real Life Australian Murder Houses!
Even if decades had passed and the house had been renovated, I don't think I could live in a property where a murder had taken place. However, it doesn't bother some people – and they even have a chance to pick up a bargain. Real-life Murder houses or 'stigmatised houses' as they are formally known as are houses where an unsavoury act has occurred, and as such, may not appeal to the general public or may affect the listing price of the property.
The Gonzales Home in Ryde was sold in 2004 without the new owners being advised of the property's dark past. When the new owners found out via the local paper, they were given their deposit back and the Real Estate agent was fined $20,000 for 'Failing to Disclose' information about the murders.
In New South Wales, agents are now obliged to disclose the history of a property should it be 'stigmatised', although the law can differ from state to state.
In Victoria, agents are only required to tell prospective buyers if they ask. (via Herald Sun)
1. The Gonzales Murder House
Location: 6 Collins Street, North Ryde, NSW
Murder Count: 3
Gonzales Murder House in North Ryde NSW Image via Property Value
On 10 July 2001, Sef Gonzales killed his sister Clodine (18), mother May (43) and father Teddy (46). After killing his family, he spray-painted a racial slur on a wall in an attempt to trick police into believing that his family had been the victims of a racial hate crime. The only surviving member of the family was their son, Sef Gonzales.
In the months after his whole family had been slaughter, Sef led a life of indulgence. He moved into a new expensive apartment, put down deposits on luxury vehicles and told the dealers that he was 'expecting a large inheritance'. He tried to pawn his mothers' jewellery and sold his parent's cars.
Almost a year after the murders, Sef Gonzales was arrested and charged with three counts of murder. Shockingly, Gonzales had killed his parents because he was afraid that, due to his poor grades at university, his parents would take his car and other privileges away from him. He killed his sister so he would be the sole beneficiary of his parent's $1.5 million property.
Gonzales was found guilty and sentenced to three concurrent life sentences without parole. Gonzales is serving his sentence at a maximum-security prison but still maintains his innocence.
The brutal scale of the crime is what shocked the nation. Sef had slit his mother's throat, slashed his father's spinal cord and stabbed him repeatedly. He had bludgeoned his sister with a baseball bat. Crown prosecutor Mark Tedeschi QC said of the triple murders:
"This was not a professional killing, it was a slaughter by an angry amateur who wanted to make absolutely sure of their deaths."
The house was sold in October 2005 for $720,000. Today it is estimated to be worth up to $2,246,000.
Funnily enough, the house was again in the news in 2004 as it was sold without the real estate agents disclosing the murders to the new owners. The NSW Office of Fair Trading investigated the matter and they were fined over $20,000. The deposit was returned to the buyers.
Sef Gonzales at his trial for killing his family.
2. The Lin Family Murder House
Location: Boundary Road, North Epping, NSW
Image Via News.com.au
This was the site of one of Sydney's most horrific mass murders. On July 18, 2009, the bodies of Min "Norman" Lin, his wife Yun Li "Lily" Lin, 43, her sister Yun Bin "Irene" Lin, 39, and the Lins' two sons Henry, 12, and Terry, 9 were found lying in pools of blood after being viciously beaten to death. The sister of Min Lin, Kathy, and her husband Robert, were the ones who discovered the bodies. The only person to survive the murders was Jun 'Brenda' Lin who was 15 at the time of the murders.
When Kathy Lin realised that her brothers Epping Newsagent hadn't opened for the morning, she went around to his house with her husband, entering via an unlocked door. She called 000 to report the grisly scene.
Horrifically, the victims were so badly beaten that forensic analysis had to be used to identify them. There was no sign of a break-in and no items were missing from the house.
Little Brenda Lin was away at a school camp at the time of the murders. After the deaths of her entire family, her aunt and uncle gained custody of Brenda. Her Uncle then sexually abused Brenda for the next few months whilst under his care.
Two years later, Brenda's uncle, Robert Xie was charged and subsequently found guilty on five counts of murder.
Bloody footprints had been found in the upstairs bedroom of the home and Police took sole impressions. On surveillance footage, Robert Xie was found attempting to flush pieces of shoe down the toilet.
Prosecutors said Xie was motivated to kill his brother and sister, her husband, and their family because he was enraged by his perceived lowly status within his wife's family. He had gotten into a dispute with his wife's family over the operations of the family Newsagent.
The home was last sold for $766,000 in March 2012.
3. The Frisoli Murder House
Location: Goodsir Street, Rozelle, NSW
Image Via Domain.com.au
Inside the Frisoli Murder House. Image via Domain.com.au
In 2009, property developer Albert Frisoli and his brother, Mario was stabbed to death by a former business associate, Guiseppe Di Cianni. Di Cianni and Albert Frisoli had been in business together for several years before the murderer believed he was being defrauded.
After unsuccessful and costly attempts to pursue Frisoli through the courts, Di Cianni stabbed Mario Frisoli over 21 times, causing his death. He then waited in the house, dressed in women's clothing to kill his other brother Albert.
The house was sold in 2014 for $2,265,000 (via Domain.com.au) which was more than $200,000 above the reserve price.
Giuseppe Di Cianni killed his two brothers
4. Easey Street Murder House
Location: Easey Street, Collingwood, Victoria
The Easey Street Murder House. Image Via The Herald Sun
The back of the Easey Street Premises During the Time of the Murders Image via Whimn
The murders of Suzanne Armstrong, a single mum aged 27, and Susan Bartlett a 28-year-old schoolteacher, have remained an unsolved crime since January 1977. The women were sexually assaulted and killed in a stabbing frenzy in this Victorian terrace house and were not found until two days later by a neighbour after hearing Suzanne's son crying.
Blood in the bathtub suggested the killer had washed his hands before leaving the house.
The home was last sold in August 2011 for $571,000.
Suzanne Armstrong and Susan Bartlett
5. Serial Killer Ivan Milat's Former House
Location: Cinnabar Street, Eagle Vale, NSW
Ivan Milat's Back Yard. Image via The Daily Telegraph.com.au
Although not the scene of any of his crimes, this property in Sydney's south once belonged to serial killer Ivan Milat. In fact, the house was built by Milat and his brother and was the site of his 1994 arrest.
Ivan Milat killed seven young backpackers in the Belanglo State Forest south of Sydney between 1989 and 1992. His victims were abducted, shot, stabbed and one was decapitated while she was still alive, her head was never found. Police believe some of the backpackers may have been sexually assaulted. Milat is serving life without parole in Goulburn's Maximum security prison. He died in Long Bay Prison Hospital in October 2019 from oesophageal cancer, still citing his innocence.
The house was last sold in May 2016 for $660,000.
The victims of Ivan Milat
Ivan Milat shortly before his death in October 2019.
6. Rattle Murder House
Location: Malvern Road, South Yarra, Victoria
Rattle Murder House in South Yarra Image Via Herald Sun
The rear of the Rattle Murder House in South Yarra Image via The Herald Sun
This apartment was the scene of the murder of Stuart Rattle, an well-known interior designer, by his partner Michael O'Neill in 2013.
O'Neill hit Rattle over the head with a saucepan before strangling him with a dog lead.
He stuffed Stuart's body inside a large furniture bag and left it on their bed for four days as he went about his normal routine, telling friends his partner was unwell. O'Neill spent the weekend at the couple's farm in country Victoria before he set fire to the apartment.
As of July 2015, the unit was rented for $550.00 per week.
7. The Harnum Murder Apartment
Location: 1503/157 Liverpool Street, Sydney
This apartment located on the 15th floor in a very desirable part of Sydney is where Simon Gittany threw his fiancee, Lisa Harnum to her death from the balcony of the Liverpool Street apartment. Simon Gittany was imprisoned for a period of 26 years for the 2011 murder.
The Bathroom of Simon Gittany's Apartment. Image via News.com.au
This two-bedroom high-rise Sydney apartment was the site of Lisa Harnum's murder in 2011.
In 2013, Simon Gittany was found guilty of throwing his fiancee from the 15th floor of their luxury inner-city apartment block, in a fit of rage when he found out that Lisa was planning on leaving him.
Many images of the apartment were shown during the trial including surveillance camera footage taken from the lifts in the apartment. The apartment has two bedrooms and two bathrooms and comes with a car space. A similar apartment in the same block sold for $2.3 million.
At the time of Lisa Harnum's murder, the couple was renting it for $1,395.00 per week.
8. The Moorhouse Murders
Location: 3 Moorhouse Street, Willagee, Western Australia
Western Australian serial killers David & Catherine Birnie lived in this Willagee home in Perth during their reign of terror in the 1980's. The couple lured women into their vehicle before taking them back to their Willagee home, raping and murdering them.
David and Catherine Birnie's House in Moorhouse Street Image Via Perth Now
David and Catherine Birnie's House in Moorhouse Street Image via The Daily Mail
Four women were killed (that we know of) by the Birnie's however not all the women were murdered in the home. Only two of the women, Susannah Candy and Noelene Patterson were killed at the premises. No bodies were buried on the property.
The fifth girl the Birnie's abducted managed to escape out of the window and contacted the police. David Birnie committed suicide in prison. Catherine Birnie remains in prison after being jailed to four sentences of life imprisonment and is in Bandyup Women's Prison. It is not expected that she will ever be released.
The home has been extensively renovated and bears little resemblance inside to the house it was in the 80's.
The house has been sold five times since 1998. The house is currently for sale for $579,000.
9. Transgender Beauty Queen Murder Unit
Location: Commercial Road, Teneriffe, QLD
Transgender Beauty Queen Murder in Tenneriffe Image Via Real Estate.com.au
One of the perhaps most horrible of crimes was committed in this ground-floor apartment at Teneriffe in Brisbane.
Chef Marcus Volke stabbed his partner Mayang Prasetyo to death, before cutting up her body and boiling the body parts on the stove.
The Chef then used his own knife to commit suicide. His body was found in a nearby laneway. The couple had only lived in the newly built apartments for a few weeks before the murder occurred. Police officers at the scene described it as 'confronting'.
10. Manrique-Lutz Family Murder House
Location: Sir Thomas Mitchell Drive, Davidson NSW
Image Via Realestate.com.au
Inside the Manrique-Lutz Property. Image Via The Daily Mail
When mother-of-two Maria Lutz failed to drop off her two children at school, concerned friends turned up at their home as there was no answer on her mobile phone. Police attended the home to find the family lifeless and with a disturbing smell in the home. With friends citing that the marriage of Maria and Manrique was in trouble, with two children both diagnosed with autism, horrified police reported that Manrique had rigged up a pipeline in the ceiling, pumping deadly gas into the home which caused the death of his family.
The house is currently rented for $750/week.
These homes have horrifying stories…ghosts of families past…
Could you live in a murder house? In any of these houses?
13 Stories of People Who Stayed With a Cheating Partner
Are You A Victim Of Financial Abuse? | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,496 |
{"url":"https:\/\/cs.stackexchange.com\/questions\/18058\/proving-l-a2n-n-ge-0-is-not-regular-by-use-of-pumping-lem","text":"# Proving L = {${ a^{2^n} \\ | \\ n \\ge 0 }$} is not regular by use of Pumping Lemma\n\nI've been struggling with this problem for quite a while now and every explanation I have managed to find doesn't seem to correctly solve it.\n\nWe have the language L = {${ a^{2^n} \\ | \\ n \\ge 0 }$} and we need to prove that it is not regular by use of the pumping lemma.\n\n(i.e. L is words whose length is a power of 2: a, aa, aaaa, aaaaaaaa etc.)\n\nI appreciate the concept of the proof so here we go:\n\nAssuming regularity of L and using the Pumping Lemma, we have ${a^{2^p}} = {xyz}$ where:\n\na) ${|y| > 0}$\n\nb) ${|xy| \\le p}$\n\nc) $xy^iz \\in L \\ \\forall \\ i \\ge 0$\n\n(also $|xyz|\\ = 2^p \\ge p$)\n\n(notice both x and z can be empty)\n\nI choose $i = 2$ to get $xy^2z$ so (since $y>0$) $|xy^2z| > 2^p$\n\nI understand that the next step is trying to prove that $|xy^2z| < 2^{p+1}$ so that the final result is $2^p < |xy^2z| < 2^{p+1}$ and so $xy^2z$ cannot be an element of L.\n\nHowever if $|y| = p$ and so $|x| = 0,\\ |z| = 0$ then this is not possible as taking $y^2$ is just doubling the length of the word which makes another word that fits the language.\n\nAm I missing something important? I have found proofs on multiple web pages (see below) that just seem to assume y cannot be of length p but as far as I can see this isn't the case.\n\nThanks very much in advance and please let me know if there is anything I should clarify.\n\nTake a larger $i$. The concept is that gaps between $|2^n|$ get bigger than $|y|$.\n\n\u2022 Thanks, I did it with $i = 3$ and it worked (both intuitively and on paper). Do you know why all the proofs I have come across used $i = 2$? \u2013\u00a0Chris Nov 15 '13 at 23:12\n\u2022 To be fair, $i = 2$ is sufficient. The $p$ in $2^p$ is the pumping length - a parameter of a language, not of a word. Because $|xy| \\leq p \\implies |y| \\leq p < 2^p$, repeating $y$ can't double the string. \u2013\u00a0Karolis Juodel\u0117 Nov 15 '13 at 23:24\n\u2022 But if y is the entire string and both x and z are empty, surely doubling y doubles the string? (sorry, I feel I'm really missing something but I just can't get my head around it). \u2013\u00a0Chris Nov 15 '13 at 23:50\n\u2022 By pumping lemma $|y|$ can't be longer than a certain number $p$. If you wanted to show that for any word of length $2^n \\geq p$ pumping lemma fails, you'd have to worry about $2^n = p$, however, you get to choose your string. You can choose it as long as you like, $|y|$ will have the same upper bound. \u2013\u00a0Karolis Juodel\u0117 Nov 15 '13 at 23:55\n\u2022 I'll have to think this over in the morning but I think I see the difference. Thanks very much for all your help. \u2013\u00a0Chris Nov 16 '13 at 0:30\n\nLet me write down my proof on the question.\n\nWe have the language $L = \\{a^{2^n} | n\u22650\\}$ and we assume that $L$ is a regular language.\n\nThe pumping lemma states that there exists $p \\in \\mathbb{N}$ such that every string $w\\in L$ of length at least $p$ can be written as $w = xyz$, satisfying the following conditions:\n\n1. $|y| \u2265 1$\n2. $|xy| \u2264 p$\n3. $\\forall i \u2265 0, xy^iz \\in\\! L$\n\nLets consider the string $w=a^{2^p}, |w|= 2^{p}\\geq p$. According to the pumping lemma $w$ can written in the form $xyz$, with $|x|=a^n$, $|y|=a^m$ and $|z|=a^l$. Moreover $xy^iz\\!\\in \\! L\\;\\forall i\\geq 0$. (always remember that $n,l \\geq 0$ and $m>0$)\n\nIn other worlds: $$n+im+l=2^{p_i}\\;\\;,\\forall\\; i\\geq 0\\;(1)$$\n\nIf we plug in $i=0$ at the last equation we obtain a new relation: $$n+l=2^{p_0} \\;(2)$$ Now if we substitute $(2)$ into $(1)$ we get: \\begin{align} im &=2^{p_i}-2^{p_0}&\\;\\;,\\forall\\; i\\geq 0\\Rightarrow\\\\ im &= \\text{even} &\\;\\;,\\forall\\; i\\geq 0\\Rightarrow\\\\ m&=2k \\end{align},for some $k\\in\\! \\mathbb{N}$.\n\nThe equation $(1)$, now, takes the form: $$i\\!\\cdot\\!2k=2^{p_i}-2^{p_0}\\;\\;,\\forall\\; i\\geq 0\\;(1.1)$$ If we plug in $i=n+l$ at $(1.1)$ we obtain: \\begin{align} 2^{p_0}\\!\\cdot\\!2k&=2^{p_N}-2^{p_0}\\Rightarrow\\\\ 2k&=2^{p_N-p_0}-1 \\end{align} A contradiction. Therefore the initial assumption\u2014that $L$ is a regular language\u2014must be false. (lets note that $p_n\\geq p_0$ since $\\{p_i\\}$ is a increasing sequence)\n\n\u2022 In the third paragraph, just after the pumping lemma conditions, should that be $w = a^{2^{p}}$? \u2013\u00a0Luke Mathieson Feb 2 '15 at 23:56\n\u2022 @LukeMathieson you are right i have it edited thanks \u2013\u00a0Karalis Charalampos Feb 3 '15 at 14:36","date":"2020-02-28 00:18:11","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\": 2, \"equation\": 3, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9589957594871521, \"perplexity\": 237.49044103461782}, \"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-2020-10\/segments\/1581875146907.86\/warc\/CC-MAIN-20200227221724-20200228011724-00189.warc.gz\"}"} | null | null |
Q: How to link an framework generated by Cocoapods in a new iOS8 framework target I'm trying to create an iOS framework which I can use in many other iOS projects, and this
framework has some dependencies, I need to use AFNetworking and Mantle libraries, I have
created new project and podfile containing
platform :ios, '8.0'
use_frameworks!
pod 'Mantle', '~> 2.0'
pod 'AFNetworking', '~> 2.5'
and I run pod install, after cocoapods generate an workspace, after that I add new target to my project
which is iOS8 framework, in this framework settings "General/Linked Frameworks and Libraries
click + butotn and select AFNetworking and Done, after i'm trying to build my project but I get
this Error
ld: warning: directory not found for option
'-F/Users/borinschiivan/Desktop/ImodeveloperSDK/build/Debug-iphoneos/Pods'
ld: framework not found AFNetworking clang: error: linker command
failed with exit code 1 (use -v to see invocation)
You can download this test project here.
A: You need not do this step " in this framework settings in this framework settings, General/Linked Frameworks and Libraries click + button and select AFNetworking and Done"
All the linking would be done automatically by cocoa pods.
Note: Since you are building a library, read pod spec for creating reusable component. you can create your ImodeveloperKit as pod framework and specify AFNetowrking as a dependency for your framework in cocoa pod specification.
Edit: using link_with and specifying all the target solved the issue
A: platform :ios, '8.0'
pod "AFNetworking", "~> 2.5"
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,662 |
Асбу-Сара () — село в Ірані, у дегестані Кухестані-є-Талеш, у Центральному бахші, шагрестані Талеш остану Ґілян. За даними перепису 2006 року, його населення становило 128 осіб, що проживали у складі 29 сімей.
Клімат
Середня річна температура становить 10,91 °C, середня максимальна – 25,43 °C, а середня мінімальна – -4,08 °C. Середня річна кількість опадів – 456 мм.
Примітки
Населені пункти шагрестану Талеш | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,568 |
module Spec
module Example
class ExampleGroupHierarchy < Array
def initialize(example_group_class)
push example_group_class
if example_group_class.respond_to?(:superclass) && example_group_class.superclass.respond_to?(:example_group_hierarchy)
unshift example_group_class.superclass.example_group_hierarchy
flatten!
end
end
def run_before_all(example)
example.eval_each_fail_fast(before_all_parts)
end
def run_before_each(example)
example.eval_each_fail_fast(before_each_parts)
end
def run_after_each(example)
example.eval_each_fail_slow(after_each_parts)
end
def run_after_all(example)
example.eval_each_fail_slow(after_all_parts)
end
def before_all_parts
@before_all_parts ||= collect {|klass| klass.before_all_parts}.flatten
end
def before_each_parts
@before_each_parts ||= collect {|klass| klass.before_each_parts}.flatten
end
def after_each_parts
@after_each_parts ||= reverse.collect {|klass| klass.after_each_parts}.flatten
end
def after_all_parts
@after_all_parts ||= reverse.collect {|klass| klass.after_all_parts}.flatten
end
def nested_descriptions
@nested_descriptions ||= collect {|eg| nested_description_from(eg) == "" ? nil : nested_description_from(eg) }.compact
end
def nested_description_from(example_group)
example_group.description_args.join
end
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,224 |
\section{Introduction}
According to the standard pulsar model, in particular, the so-called
polar cap model \cite{stur}, particles uproot from the star's
surface, and accelerate along the magnetic field lines
\cite{rudsuth} inside a gap zone. In general, it is believed that
these particles produce the nonthermal radiation, which is
interpreted in terms of the synchrotron mechanism \cite{pacini,shkl}
and the Inverse Compton Scattering \cite{blan} respectively.
Generally speaking, due to strong synchrotron losses, relativistic
electrons quickly lose their perpendicular momentum, and transit to
their ground Landau states. Therefore, particles may be
approximately described as moving one-dimensionally along the field
lines, which in turn means that the synchrotron mechanism does not
contribute in high energy radiation processes. On the other hand,
under certain conditions, due to the quasi-linear diffusion (QLD),
the pitch angles might be recreated, leading to the efficient
synchrotron emission. This method has already been applied to
pulsars \cite{machus1,malmach,nino,nino2,nino1,difus,difus1} and
active galactic nuclei \cite{difus3,difus4}.
In the context of QLD, the recent detection of the VHE radiation
from the Crab pulsar \cite{magic} could be very important. MAGIC
Cherenkov telescope from 2007 October to 2008 February, has
discovered the pulsed emission above 25GeV, which reveals several
characteristic features. A special interest deserves the coincidence
of signals from different energy bands ranging from radio to VHE
($>25$GeV) domain \cite{magic}. The authors conclude that according
to the data, the polar cap models must be excluded from the possible
scenario of the radiation, which must happen far out in the
magnetosphere. Analysis of the MAGIC data also implies that a
location of the aforementioned VHE and low energy emissions must be
the same. By taking into account the synchrotron reaction force, we
constructed the kinetic equation governing the QLD and the results
of the MAGIC data have been interpreted (Machabeli \& Osmanov 2009).
We argued that the observed VHE radiation is produced by the
synchrotron mechanism, having properties, which are in a good
agreement with the observations. The following work (Machabeli \&
Osmanov 2010) was related to the problem of the curvature radiation
and the inverse Compton scattering in the context of the same
observations. We have shown that these mechanisms do not contribute
to the VHE domain detected by MAGIC.
In general, magnetic field in pulsar magnetospheres is huge and
ranges from $10^6$G (far out in the magnetosphere) to $10^{12}$G
close to the neutron star's surface. Therefore, magnetospheric
plasma is in the frozen-in condition and is forced to follow the
magnetic field lines. This means that effects of corotation in
plasma acceleration and emission processes could be very important.
In general, it is believed that the high energy radiation comes from
an area located relatively close to the LC surface, where corotation
is extremely significant. For this purpose it is reasonable to
consider the quasi-linear diffusion by taking relativistic effects
of rotation into account and see how the corotation influences the
mentioned processes.
In the present paper we study the role of the corotation in the
quasi-linear diffusion and we show that in the very vicinity of the
LC surface, contrary to the quasi-linear diffusion, effects of
corotation attempt to decrease the pitch angles, and kill the
subsequent synchrotron emission.
The paper is organized as follows. In Section 2 we consider the
quasi-linear diffusion by taking the effect of corotation into
account, in Sect. 3 we present our results and in Sect. 4 we
summarize them.
\section{Main consideration} \label{sec:consid}
In this section we present the model, generalizing our previous
approach by taking the fact of corotation in to account and see how
the efficiency of QLD depends on it.
Generally speaking, the pulsar magnetospheres are composed of low
and high energy particles respectively. Therefore, in the framework
of the paper for simplicity we assume that the magnetosphere is
consist of two components: (a) the plasma component with the Lorentz
factor, $\gamma_p$ and (b) the beam component with the Lorentz
factor, $\gamma_b$.
According to the mechanism of the quasi-linear diffusion the
following transverse mode generates
\begin{equation}\label{disp1}
\omega_t \approx kc\left(1-\delta\right),\;\;\;\;\;\delta =
\frac{\omega_p^2}{4\omega_B^2\gamma_p^3},
\end{equation}
where $k$ denotes the modulus of the wave vector, $c$ is the speed
of light, $\omega_p \equiv \sqrt{4\pi n_pe^2/m}$ is the plasma
frequency, $e$ and $m$ are electron's charge and the rest mass,
respectively, $n_p$ is the plasma density, $\omega_B\equiv eB/mc$ is
the cyclotron frequency and $B$ is the magnetic induction. It can be
shown that the aforementioned waves excite if the cyclotron
resonance condition is satisfied \cite{kmm}
\begin{equation}\label{cycl}
\omega - k_{_{\|}}\upsilon-k_xu\pm\frac{\omega_B}{\gamma_b} = 0.
\end{equation}
By $k_{_{\|}}$ and $k_{\perp}$ we denote the wave vector's
longitudinal (parallel to the background magnetic field) and
transverse (perpendicular to the background magnetic field)
components respectively, $u\equiv c\upsilon\gamma_b/\rho\omega_B$ is
the drift velocity of electrons, $\upsilon$ is the component of
velocity along the magnetic field lines and $\rho$ is field line's
curvature radius. In this paper we consider the beam particles as to
be the resonance particles. One can show from Eqs.
(\ref{disp1},\ref{cycl}) that the excited cyclotron wave is
characterized by the following frequency \cite{malmach}
\begin{equation}\label{om1}
\nu\approx \frac{\omega_B}{2\pi\gamma_b\delta}.
\end{equation}
Generally speaking, particles moving in the magnetic field,
experience two forces, one of which, ${\bf G}$, having the following
components \cite{landau}
\begin{equation}\label{g}
G_{\perp} = -\frac{mc^2}{\rho}\gamma_b\psi,\;\;\;\;\;G_{_{\|}} =
\frac{mc^2}{\rho}\gamma_b\psi^2.
\end{equation}
is responsible for the conservation of the adiabatic invariant, $I =
3cp_{\perp}^2/2eB$ and the second one is the synchrotron radiative
force \cite{landau}
\begin{equation}\label{f}
F_{\perp} = -\alpha\psi(1 + \gamma_b^2\psi^2),\;\;\;\;\;F_{_{\|}} =
-\alpha\gamma_b^2\psi^2,
\end{equation}
where $\alpha = 2e^2\omega_B^2/(3c^2)$. But one can show that for
the Crab-like pulsars the radiation reaction force, $|{\bf F}|$,
exceeds $|{\bf G}|$ by many orders of magnitude (Machabeli \&
Osmanov 2009,2010).
On the other hand, apart from the synchrotron radiative force,
relativistic electrons also experience a reaction force responsible
for the corotation\footnote{In the local frame of reference
particles experience the centrifugal force, whereas considering
dynamics in the laboratory frame, one has to examine the reaction
force acting on the electrons from the magnetic field line.}. This
force can be estimated by a simple mechanical analogy introduced by
Machabeli \& Rogava (1994) and reconsidered by \cite{grg}. In the
framework of this approach, instead of magnetic field lines and
particles sliding along them, one considers a corotating pipe with a
bead inside it. If we assume that the magnetic field lines are
straight, then the reaction force acting on a single particle from
the beam component can be given by \cite{grg}
\begin{equation}\label{reac}
R = \frac{dp_{_\perp}}{dt} + \Omega p_{_\parallel},
\end{equation}
where $\Omega$ is the angular velocity of rotation, $r$ is the
radial coordinate,
\begin{equation}\label{pr}
p_{_\parallel}\equiv\gamma_b m\upsilon
\end{equation}
and
\begin{equation}\label{pfi}
p_{_\perp}\equiv\gamma_b mr\Omega
\end{equation}
are momentum's longitudinal and transversal components respectively.
Considering a single particle approach, one can show that the
Lorentz factor of a particle moving along the corotating straight
magnetic field yields the equation \cite{rm00}
\begin{equation}\label{gama}
\gamma_b = \frac{1}{ \sqrt{\widetilde{m}}
\left(1-\frac{r^2}{r_{lc}^2}\right)},
\end{equation}
where
$$\widetilde{m} =\frac{1-r_0^2/r_{lc}^2-\upsilon_0^2/c^2}{\left(
1-r_0^2/r_{lc}^2\right)^2},\; r_{lc}\equiv \frac{c}{\Omega}.$$
$r_0$ and $\upsilon_0$ are particle's initial position and the
initial radial velocity respectively and $r_{lc}$ is the light
cylinder radius. From Eq. (\ref{gama}) we see that the closer to the
LC, the bigger the Lorentz factor. Therefore a dynamical effect of
the corotation becomes extremely efficient nearby this area [see Eq.
(\ref{reac})] where the reaction force can be approximated as to be
[see Eq. (\ref{r4}) in Appendix]
\begin{equation}\label{reac1}
R\approx 2 m\widetilde{m}^{1/4}c\Omega\gamma_b^{3/2}.
\end{equation}
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics[angle=0]{fig11.eps}}
\caption{The synchrotron emission energy versus the Lorentz factors of beam electrons.
The set of parameters is $P\approx 0.0332$s, $B\approx 1.7\times 10^7$G,
$\gamma_{b0} = \{1,10^2,10^4$\}. }\label{fig1}
\end{figure}
As we have mentioned, in the Crab pulsar magnetosphere one may
neglect the effects of ${\bf G}$ in comparison with ${\bf F}$.
Therefore, the process of the quasi-linear diffusion is mainly
influenced by the synchrotron radiative force, ${\bf F}$ and the
reaction force, ${\bf R}$. The synchrotron radiation reaction force,
acting on a particle, attempts to decelerate it, therefore
relativistic electrons loose their perpendicular momentum, leading
to an inevitable decrease of the pitch angles. In spite of the fact
that contrary to ${\bf F}$, the reaction force plays an accelerative
role in electron's dynamics, in the context of the pitch angles its
role is the same. In particular, as we have already discussed, the
mentioned reaction force is a direct consequence of corotation. This
means that ${\bf R}$ is constructed in such a way that particles
always must stay on the magnetic field lines, therefore, the
reaction force also attempts to decrease the pitch angles. On the
other hand, the quasi-linear diffusion, that arises through the
influence of the waves back on the particles, via the QLD attempts
to widen a range of the pitch angles. The dynamical process
saturates when the effects of the above mentioned forces are
balanced by the diffusion. For $\gamma_b\psi\gg 1$ it is easy to
show that in the quasi-stationary case ($\partial/\partial t = 0$),
the corresponding kinetic equation governing the QLD writes as
follows \cite{malmach}
\begin{equation}\label{kinet}
\frac{1}{p_{_\parallel}}\frac{\partial\left[\psi\left(R+
F_{\perp}\right)\chi\right]}{\partial\psi}
=\frac{\partial}{\partial\psi}\left[\psi
D_{\perp\perp}\frac{\partial\chi}{\partial\psi}\right],
\end{equation}
where $\chi = \chi (\psi)$ is the distribution function of particles
with respect to the pitch angles,
\begin{equation}\label{dif}
D_{\perp\perp}\approx -\frac{\pi e^2n_bc}{4\nu},
\end{equation}
is the diffusion coefficient, $n_b = B/Pce$ is the density of the
beam component and $P$ is the pulsar's rotation period. The solution
of Eq. (\ref{dif}) writes as follows
\begin{equation}\label{chi} \chi(\psi) = \chi_{_0}e^{-A_1\psi\left(1-A_2\psi^3\right)},\;\;\;
A_1\equiv\frac{mc\gamma_bR}{D_{\perp\perp}},\;\;\;
A_2\equiv\frac{\alpha\gamma_b^2}{4R}.
\end{equation}
As is clear from this expression, electrons are differently
distributed for different pitch angles. Let us note that the
reaction force and the synchrotron radiative force have opposite
directions, since $F_{\perp}$ is responsible for deceleration of
electrons, whereas $R$ accelerates them. It is clear that close to
the LC, a value of $|R|\propto \gamma_b^{3/2}$ is very high and for
very small pitch angles exceeds $|F_{\perp}|$ and therefore, higher
values of pitch angles lead to higher values of the distribution
function. But by increasing $\psi$ the corresponding reaction force
does not change [see Eq. (\ref{reac1})], whereas the synchrotron
radiative force is very sensitive to this change,
$F_{\perp}\sim\psi^3$. Therefore, at a certain pitch angle,
$\psi_0$, these forces will balance each other and the distribution
function will reach its maximum value. In particular, one can
straightforwardly show that the expression of the distribution
function [see Eq. (\ref{chi})] peaks at
\begin{equation}\label{pitch}
\psi_0 = \frac{1}{\sqrt[3]{4A_2}} =
\left(\frac{2mc\Omega}{\alpha\gamma_{b0}^2\gamma_b^{1/2}}\right)^{1/3},
\end{equation}
which indeed corresponds to $R=F_{\perp}$. Here, we have taken into
account the following relation $\widetilde{m}\approx
1/\gamma_{b0}^2$ [$r_0/r_{lc}\ll 1$, see Eq. (\ref{gama})].
It is reasonable to estimate how steep is the distribution function.
For simplicity we consider the case $\gamma_{b0} = 1$, then
examining the Crab pulsar's ($P\approx 0.0332$s) magnetospheric
parameters close to the LC surface: $B\approx 1.7\times 10^7$G,
$\gamma_b = 10^7$, one can see that at the peak, $\psi_0\approx
0.02$rad, the distribution function exceeds its value at $\psi = 0$
by many orders of magnitude. This means that most of the particles
will be characterized by the peak value of the pitch angle, and
therefore, its average value can be estimated as to be $\psi_0$. We
have taken into account that $B = B_{st}R_{st}^3/r_{lc}^3$, where
$R_{st}\approx 10^6$cm is the pulsar's radius, $B_{st}\approx
1.8\times 10^{12}\sqrt{P\times\dot{P}_{15}}$G is the magnetic
induction on the star's surface and $\dot{P}_{15}\equiv
10^{15}\dot{P}$ ($\dot{P}_{15}=421$ for the Crab pulsar, see
\cite{manch}).
Since we consider centrifugally accelerated particles, our approach
is based on the assumption that electrons corotate with the spinning
pulsar, which is valid only inside a certain zone (corotation zone
with a radius $r_c$), because in this region the magnetic field is
strong enough to channel the flow. This means that, our approach is
valid if the following condition is satisfied:
$(r_{lc}-r_c)/r_{lc}\ll 1$. It is clear that corotation takes place
if the magnetic energy density exceeds the beam energy density,
therefore, $r_c$ can be can be estimated by the condition:
$B(r)^2/(8\pi)\approx mc^2n_b\gamma(r)$. If we consider a range of
$\gamma_{b0} = (1; 10^4)$, then by taking Eq. (\ref{gama}) into
account, one can see that for $\gamma_b\sim 10^7$ one has
$(r_{lc}-r_c)/r_{lc}\sim (10^{-11}; 10^{-7})\ll 1$, which means that
corotation is violated in a very close region to the LC surface and
for almost the whole course of motion the spinning magnetic field
channels the electrons.
When relativistic particles move in the magnetic field, they emit
electromagnetic waves, which in our case correspond to the following
photon energies \cite{Lightman}:
$$\epsilon_{TeV}\approx 1.7\times
10^{-20}B\gamma^2\sin\psi_0\approx$$
\begin{equation}
\label{eps} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\approx
10^{-16}\times B^{1/3}\times\gamma_b^{11/6}\times\gamma_{0b}^{-2/3}.
\end{equation}
\section{Discussion}
In this section we are going to apply the method to the Crab-like
pulsars and see what changes in the process of the QLD when
corotation is taken into account.
In Fig. \ref{fig1} we show the dependence of photon energies on the
Lorentz factors of the beam electrons for three different initial
values of the beam Lorentz factors. The set of parameters is
$P\approx 0.0332$s, $B\approx 1.7\times 10^7$G, $\gamma_{b0} =
\{1,10^2,10^4$\}. As is clear from the plots by increasing
$\gamma_b$ the corresponding emission energy increases as well. This
is a natural result, because more energetic electrons emit more
energetic photons [see Eq. (\ref{eps})]. A second feature concerns
the behaviour of $\epsilon_{TeV}$ versus $\gamma_{b0}$. It is
evident that the higher the initial beam Lorentz factor the lower
the emission energy. Indeed, as one can see from Eq. (\ref{pitch})
the pitch angle behaves as $\gamma_{b0}^{-2/3}$, therefore, for
higher initial beam Lorentz factors one obtains lower values of the
pitch angles and hence, the corresponding synchrotron energy becomes
lower.
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics[angle=0]{fig22.eps}}
\caption{The synchrotron emission energy versus the cyclotron frequency.
The set of parameters is $P\approx 0.0332$s, $B\approx 1.7\times 10^7$G,
$\gamma_{b0} = \{1,10^2,10^4$\}. }\label{fig2}
\end{figure}
The relativistic effects of rotation could also be interesting in
the context of the recently detected VHE pulsed emission ($>25$GeV)
from the Crab pulsar. According to the interpretation presented in
(Machabeli \& Osmanov 2009,2010), the mentioned radiation is formed
on lengthscales of the order of $10^8$cm via the quasi-linear
diffusion. As it has been shown, in order to explain the data, the
value of the beam Lorentz factor must be of the order of $3\times
10^8$. For centrifugally accelerated electrons the effects of
corotation become significant in the nearby zone of the LC surface.
In particular, from Eq. (\ref{reac1}) it is clear that the reaction
force is proportional to $\gamma_b^{3/2}$, which in turn
asymptotically increases by reaching the LC surface [see Eq.
(\ref{gama})]. The corresponding lengthscale of a layer on the light
cylinder zone, where the effects are intensified by corotation, can
be estimated as follows
\begin{equation}
\label{lamb} \lambda\approx \frac{\gamma_b}{d\gamma_b/dr}\approx
\frac{r_{lc}}{2\gamma_b},
\end{equation}
where we have taken into account Eq. (\ref{gama}). As we see from
this expression, the layer is quite thin, $\lambda\ll r_{lc}$.
Unlike the papers by Machabeli \& Osmanov (2009,2010) where the
effects of corotation are not significant, and the VHE radiation
($>25$GeV) can be achieved by the relativistic particles with
$\gamma_b\sim 3\times 10^8$, a part of the magnetosphere located
very close to the LC surface, may guarantee the aforementioned
emission energy for lower Lorentz factors. In particular, from Fig.
\ref{fig1} it is clear that the synchrotron process supported by the
QLD produces $25$GeV photons for $\gamma_{b}\sim 5.3\times 10^6$
($\gamma_{ b0} = 1$), $\gamma_{b}\sim 8\times 10^6$ ($\gamma_{b0} =
10^2$) and $\gamma_{b}\sim 1.2\times 10^7$ ($\gamma_{b0} = 10^4$),
which are much lower than $3\times 10^8$. The quasi-linear diffusion
is so efficient that under certain conditions it can provide TeV
photons as well. As one can see from the figure, the relativistic
electrons with Lorentz factors $5\times 10^7$ ($\gamma_{b0} = 1$)
may provide TeV emission ($1.5$TeV).
According to the present method, the process of the QLD depends on
excitation of the unstable cyclotron waves, which correlate with the
high energy radiation. In Fig. \ref{fig2} we show the behaviour of
synchrotron emission energy versus the cyclotron frequency. The set
of parameters is the same as in Fig. \ref{fig1}. As is seen from the
plots, the VHE radiation is strongly connected with relatively low
energy radiation starting from microwave ($5\times 10^{10}$Hz) to
optical ($10^{14}$Hz) domains respectively.
The investigation shows that very close to the LC area, where
effects of corotation are extremely important, the quasi-linear
diffusion becomes so efficient that under favorable conditions it
may provide VHE radiation for relatively lower energy electrons than
in the regime considered by Machabeli \& Osmanov (2009,2010). The
aim of the present paper was to demonstrate for Crab-like pulsars
that the relativistic effects of rotation are of fundamental
importance for studying the VHE emission via QLD. Studying
rotationally driven quasi-linear diffusion for $1$-sec pulsars also
is an interesting problem, but it is out of the scope of the present
paper and sooner or later we are going to consider it as well.
\section{Summary}\label{sec:summary}
\begin{enumerate}
\item We have examined the VHE radiation of Crab-like
pulsars via the quasi-linear diffusion intensified by the effects
of corotation which takes place in the nearby zone of the LC surface.
\item It has been emphasized that due to very strong magnetic
field of pulsar magnetospheres the efficient energy losses lead
to the
damping of the synchrotron process. Close to the LC surface
the effects of corotation become significant
and apart from the synchrotron radiative force, which decreases
the pitch angles, also the reaction force (responsible for
corotation) has to be taken into account. Generalizing the
kinetic equation governing the QLD, we have found the particle
distribution with respect to $\psi$ and estimated its average
value.
\item Considering Crab-like pulsar's magnetospheric parameters we have
found that the quasi-linear diffusion becomes more efficient on
the LC zone, than for locations far from this area.
It has been shown that the synchrotron emission process, via the QLD,
might provide VHE emission even in the TeV domain.
\item We have found that the VHE radiation is strongly connected with
the cyclotron emission having relatively low frequencies.
\end{enumerate}
\section*{Acknowledgments}
The research was supported by the Georgian National Science
Foundation grant GNSF/ST07/4-193.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,845 |
Walker kan syfta på:
Walker (efternamn) – ett efternamn samt personer med namnet
Walker Art Center – i Minneapolis, Minnesota
Walker Art Gallery – i Liverpool, England
Walker Books – brittiskt barnboksförlag
Walker (datorspel) – datorspel
Walker (film) – film om William Walker från 1987
Walker, Texas Ranger – amerikanskt tv-program
The Walker – film från 2007, skriven och regisserad av Paul Schrader
Geografi
Antarktis
Walker Point,
Cape Walker,
Walker Mountains
Storbritannien
Walker, Newcastle upon Tyne, England
USA
Walker, Louisiana, ort, Livingston Parish,
Walker, Missouri, Vernon County,
Walker, Iowa, ort, Linn County,
Walker, Michigan, ort, Kent County,
Walker, Minnesota, countyhuvudort, Cass County,
Walker, Kalifornien, Mono County,
Se även
Walker Island – flera
Walker River – flera
Mount Walker – flera
Robotskapade Antarktisförgreningar
Robotskapade USAförgreningar | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,190 |
{"url":"https:\/\/scientific.tweetalibrarian.com\/infinity-text","text":"# Infinity Text\n\nIf you are looking for Infinity Text, simply check out our links below.\n\n### Constants | ArcGIS Arcade | ArcGIS Developer\n\nA simple, portable scripting language for creating custom visualizations and labeling expressions. -Infinity may also be used as a value smaller than any number. ... TextFormatting.BackwardSlash. Inserts a backslash character \\ into the text. [ReadMore..]\n\n### Text | Infinity\n\nRead this helpful article to find out more about Infinity`s Text attribute, what it's commonly used for, and what it will look like once you add it to your items. The Text attribute will allow you to enter any kind of additional text you want to see when you look at your item. This can be anything from the item name to a\u00a0... [ReadMore..]\n\nThe pages related to infinity text are also listed below:\n\n### Infinity Symbol \u221e\n\nList of infinity symbols. Learn how to make an infinity sign, how to type infinity symbol. List of infinity symbols where used in math, physics and more. Html infinity sign, ascii code, unicode, learn how to type an infinity symbol on mac and win. [ReadMore..]\n\n### Solved Consider The Following Series. Sum_(n=0)^infinity | Chegg.com\n\nsum_(n=0)^infinity text( ) 2^n(x+1)^n (a) Find the values of x for which the series converges. (Enter the smaller number first.) (b) Find the sum of the series\u00a0... [ReadMore..]","date":"2022-11-29 11:40:41","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\": 0.4165106415748596, \"perplexity\": 2394.7331778496996}, \"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-2022-49\/segments\/1669446710691.77\/warc\/CC-MAIN-20221129100233-20221129130233-00777.warc.gz\"}"} | null | null |
{"url":"https:\/\/2022.help.altair.com\/2022.1.2\/feko\/topics\/feko\/user_guide\/appendix\/api_cadfeko_auto_generated\/object\/impedanceoptimisationgoal.htm","text":"# ImpedanceOptimisationGoal\n\nAn impedance optimisation goal.\n\n## Example\n\napplication = cf.Application.GetInstance()\nvoltageSource = project.Contents.SolutionConfigurations.GlobalSources[\"VoltageSource1\"]\n\n-- Create an impedance optimisation goal with focus on the 'VoltageSource'\n\nproperties = cf.ImpedanceOptimisationGoal.GetDefaultProperties()\nproperties.FocusSource = voltageSource\nproperties.GoalOperator = cf.Enums.OptimisationGoalOperatorEnum.LessThan\nproperties.Objective.TargetValue = \"1.5\"\n\n-- Change the focus type to transmission coefficient and reference impedance of 75 ohm\n\nimpedanceGoal.FocusType = cf.Enums.OptimisationImpedanceFocusTypeEnum.TransmissionCoefficient\nimpedanceGoal.ReferenceImpedance = 75\n\n## Inheritance\n\nThe ImpedanceOptimisationGoal object is derived from the OptimisationGoal object.\n\n## Usage locations\n\nThe ImpedanceOptimisationGoal object can be accessed from the following locations:\n\n## Property List\n\nFocusSource\nSet the focus source to a specified source object. The intended usage is for when the source is defined in CADFEKO. (Read\/Write VoltageSource)\nFocusSourceLabel\nSet the source focus label. The intended usage is for when the source is defined only in EDITFEKO. (Read\/Write string)\nFocusType\nSet the focus type. (Read\/Write OptimisationImpedanceFocusTypeEnum)\nGoalOperator\nThe goal operator indicates the desired relationship between the goal focus and the objective. (Read\/Write OptimisationGoalOperatorEnum)\nLabel\nObjective\nThe objective describes a state that the optimisation process should attempt to achieve. (Read only OptimisationGoalObjective)\nProcessingSteps\nA number of conversion steps or mathematical operations to be carried out on the goal focus before the goal is evaluated. (Read\/Write OptimisationGoalProcessingStepsList)\nReferenceImpedance\nType\nThe object type string. (Read only string)\nWeight\nSpecify the optimisation weight. (Read\/Write ParametricExpression)\n\n## Method List\n\nDelete ()\nDeletes the entity.\nDuplicate ()\nDuplicates the entity. (Returns a Object object.)\nGetProperties ()\nReturns a table of properties representing the state of the object. The properties table can be used with the SetProperties method to change multiple properties of the object in one step. (Returns a table object.)\nSetProperties (properties Object)\nModifies the state of the object using the provided table of properties. This method is used to modify multiple properties of the object in a single step.\n\n## Static Function List\n\nGetDefaultProperties ()\nCreates a table containing the default settings to create an object. (Returns a table object.)\n\n## Property Details\n\nFocusSource\nSet the focus source to a specified source object. The intended usage is for when the source is defined in CADFEKO.\nType\nVoltageSource\nAccess\nFocusSourceLabel\nSet the source focus label. The intended usage is for when the source is defined only in EDITFEKO.\nType\nstring\nAccess\nFocusType\nSet the focus type.\nType\nOptimisationImpedanceFocusTypeEnum\nAccess\nGoalOperator\nThe goal operator indicates the desired relationship between the goal focus and the objective.\nType\nOptimisationGoalOperatorEnum\nAccess\nLabel\nThe object label.\nType\nstring\nAccess\nObjective\nThe objective describes a state that the optimisation process should attempt to achieve.\nType\nOptimisationGoalObjective\nAccess\nProcessingSteps\nA number of conversion steps or mathematical operations to be carried out on the goal focus before the goal is evaluated.\nType\nOptimisationGoalProcessingStepsList\nAccess\nReferenceImpedance\nReference impedance.\nType\nParametricExpression\nAccess\nType\nThe object type string.\nType\nstring\nAccess\nWeight\nSpecify the optimisation weight.\nType\nParametricExpression\nAccess\n\n## Method Details\n\nDelete ()\nDeletes the entity.\nDuplicate ()\nDuplicates the entity.\nReturn\nObject\nThe new (duplicated) entity.\nGetProperties ()\nReturns a table of properties representing the state of the object. The properties table can be used with the SetProperties method to change multiple properties of the object in one step.\nReturn\ntable\nA table defining the properties.\nSetProperties (properties Object)\nModifies the state of the object using the provided table of properties. This method is used to modify multiple properties of the object in a single step.\nInput Parameters\nproperties(Object)\nA table of properties defining the new state of the object.\n\n## Static Function Details\n\nGetDefaultProperties ()\nCreates a table containing the default settings to create an object.\nReturn\ntable\nA table containing the default properties.","date":"2022-12-08 22:30:18","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\": 0.18111351132392883, \"perplexity\": 3650.314628430003}, \"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-2022-49\/segments\/1669446711368.1\/warc\/CC-MAIN-20221208215156-20221209005156-00617.warc.gz\"}"} | null | null |
Q: Replace triple newlines with double newlines I'm trying to perform some format cleaning in text files. I want to replace all triple(or more) new lines with double new lines and all double new lines with single new line.
First I open the file like this:
text = ""
with open(filename) as fp:
for cnt, line in enumerate(fp):
text += line
but replacing the new lines like this: text = re.sub(r'\n\n', '\n', text).strip()
or like this text = text.replace("\n\n", "\n") replaces all (multiple) new lines with single new line.
What am I doing wrong? Thanks for any help and explanations.
Edit
I want to achieve that something like this:
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
becomes:
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
text text text text text text text text text text text text text text text
A: You may use
with open(filename, 'r') as fp:
print( re.sub(r'(\n{3,})|\n\n', lambda x: "\n\n" if x.group(1) else "\n", fp.read()) )
NOTES
*
*Run the regex on the whole file text, thus, use fp.read() to get it, do not read line by line
*The (\n{3,})|\n\n regex matches and captures 3 or more newlines into Group 1 or matches two newlines. If Group 1 matched, the replacement is a double newline, else, a single one. Since this is a conditional replacement, a callable (a lamda expression here) is used as the replacement argument.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,475 |
Tiassalé is a town in southern Ivory Coast. It is a sub-prefecture and the seat of Tiassalé Department in Agnéby-Tiassa Region, Lagunes District. Tiassalé is also a commune.
In 2021, the population of the sub-prefecture of Tiassalé was 83,648.
Villages
The 19 villages of the sub-prefecture of Tiassalé and their population in 2014 are:
Notes
Sub-prefectures of Agnéby-Tiassa
Communes of Agnéby-Tiassa | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,578 |
#ifndef ZMF_ZMFINSTANCE_H
#define ZMF_ZMFINSTANCE_H
#ifdef __GNUC__
#define DEPRECATED __attribute__((deprecated))
#elif defined(_MSC_VER)
#define DEPRECATED __declspec(deprecated)
#else
#pragma message("WARNING: You need to implement DEPRECATED for this compiler")
#define DEPRECATED
#endif
#include "AbstractModule.hpp"
#include "IZmfInstanceController.hpp"
namespace zmf {
namespace instance {
/**
* Launcher class to create and start new ZMF instances
* @author Jonas Grunert
* @author Jan Strauß
* @author Andre Kutzleb
* Created on 7/28/15.
*/
class ZmfInstance {
public:
/**
* Starting options when creating and starting a new ZMF instance
*/
enum StartOption {
/**
* NO auto enable, will NOT try to enable the module as soon as possible
*/
NO_AUTO_ENABLE,
/**
* Will NOT exit if module enabling fails
*/
NO_EXIT_WHEN_ENABLE_FAILED,
/**
*
* Peer discovery will NOT wait until all active modules discovered
*/
NO_PEER_DISCOVERY_WAIT,
/**
*
* This instance will not connect to modules with the same type id
*/
NO_EQUAL_MODULE_INTERCONNECT
};
/**
* Creates and starts a new ZMF instance
* @param instanceModule
* the module to start
* @param trackModuleStates deprecated - will be ignored
* @param moduleAutoEnable If true tries to enable the module as soon as possible
* @param exitWhenEnableFail If true will exit if module enabling fails
* @param peerDiscoveryWait If true the peer discovery will wait until all active modules discovered
* @param disableEqualModuleInterconnect If true peer discovery will ignore all messages from peer with the same type id
* @param cfgPath Optional Path to the user defined config file
* @return The controller to control the instance or shared_ptr(nullptr) if fails
* @deprecated use createInstance with StartingOptions
*/
DEPRECATED static std::shared_ptr<zmf::IZmfInstanceController> startInstance(
std::shared_ptr<zmf::AbstractModule> instanceModule,
bool trackModuleStates,
bool moduleAutoEnable,
bool exitWhenEnableFail,
bool peerDiscoveryWait,
bool disableEqualModuleInterconnect,
const std::string& cfgPath = "");
/**
* Creates and starts a new ZMF instance and uses default configuration file.
* @param instanceModule
* the module to start
* @param startOptions Starting options for ZMF
* @param cfgPath Optional Path to the user defined config file
* @return The controller to control the instance or shared_ptr(nullptr) if fails
*/
static std::shared_ptr<zmf::IZmfInstanceController> startInstance(
std::shared_ptr<zmf::AbstractModule> instanceModule,
std::vector<StartOption> startOptions,
const std::string& cfgPath = "");
};
}
}
#endif //ZMF_ZMFINSTANCE_H
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,857 |
TORRES
**An Intimate Portrait of the Kid who Became King**
_Luca Caioli_
CORINTHIAN BOOKS
Published in the UK in 2009 by
Corinthian Books, an imprint of Icon Books,
Omnibus Business Centre,
39–41 North Road, London N7 9DP
email: info@iconbooks.co.uk
www.iconbooks.co.uk
This electronic edition published in 2009 by Corinthian Books,
an imprint of Icon Books
ISBN: 978-1-90685-012-8 (ePub format)
ISBN: 978-1-90685-013-5 (Adobe ebook format)
Printed edition (ISBN: 978-1-90685-007-4)
Sold in the UK, Europe, South Africa and Asia
by Faber & Faber Ltd, Bloomsbury House,
74–77 Great Russell Street, London WC1B 3DA
Distributed in the UK, Europe, South Africa and Asia
by TBS Ltd, TBS Distribution Centre, Colchester Road
Frating Green, Colchester CO7 7DW
This edition published in Australia in 2009
by Allen & Unwin Pty Ltd,
PO Box 8500, 83 Alexander Street,
Crows Nest, NSW 2065
Distributed in Canada by
Penguin Books Canada,
90 Eglinton Avenue East, Suite 700,
Toronto, Ontario M4P 2YE
Text copyright © 2009 Luca Caioli
Translation copyright © 2009 Geoffrey Goff
The author has asserted his moral rights.
No part of this book may be reproduced in any form, or by any
means, without prior permission in writing from the publisher.
Typeset by Marie Doherty
## **Contents**
---
**1**[ Liverpool's Number 9
_Thoughts and reflections from the Kop_ ](ch004.xhtml#p200193ad9970001001)
**2**[ He is a red
_4 July 2007_ ](ch005.xhtml#p200193ad9970007001)
**3**[ The culprit of his success
_Conversation with Liverpool manager, Rafa Benítez_ ](ch006.xhtml#p200193ad9970016001)
**4**[ A nice lad
_Conversation with Spain manager, Vicente Del Bosque_ ](ch007.xhtml#p200193ad9970022001)
**5** Fuenlabrada
**6** Leader of the gang
**7** A born winner
**8**[ A model footballer
_Conversation with Atlético de Madrid junior team coach,_
_Abraham García_ ](ch011.xhtml#p200193ad9970060001)
**9** The Torres generation
**10**[ A special dedication
_Conversation with Barcelona and Spain midfielder,_
_Andrés Iniesta_ ](ch013.xhtml#p200193ad9970076001)
**11** A fairy tale
**12**[ Yogurt
_Conversation with former Atlético de Madrid striker,_
_Francisco Miguel Narváez Machón, better known as 'Kiko'_ ](ch015.xhtml#p200193ad9970091001)
**13** In El Niño's hands
**14**[ He's earned it the hard way
_Conversation with Mexico and former Atlético de Madrid_
_manager, Javier Aguirre_ ](ch017.xhtml#p200193ad9970112001)
**15**[ Real hope
_Conversation with Sid Lowe and Guillem Balagué_ ](ch018.xhtml#p200193ad9970118001)
**16**[ Liverpool 1 Chelsea 1
_19 August 2007_ ](ch019.xhtml#p200193ad9970130001)
**17**[ A perfect marriage
_Conversation with former Liverpool player,_
_Michael Robinson_ ](ch020.xhtml#p200193ad9970138001)
**18**[ Liverpool 4 West Ham 0
_5 March 2008_ ](ch021.xhtml#p200193ad9970144001)
**19**[ He's going to stay
_Conversation with former Liverpool player and manager,_
_Kenny Dalglish_ ](ch022.xhtml#p200193ad9970153001)
**20**[ Spain 4 Russia 1
_10 June 2008_ ](ch023.xhtml#p200193ad9970159001)
**21**[ Sweden 1 Spain 2
_14 June 2008_ ](ch024.xhtml#p200193ad9970175001)
**22**[ Germany 0 Spain 1
_29 June 2008_ ](ch025.xhtml#p200193ad9970182001)
**23**[ Ambitious
_Conversation with Liverpool and Spain goalkeeper,_
_Pepe Reina_ ](ch026.xhtml#p200193ad9970189001)
**24**[ Atlético de Madrid 1 Liverpool 1
_22 October 2008_ ](ch027.xhtml#p200193ad9970196001)
**25**[ A danger
_Conversation with Liverpool and Spain_
_defender, Álvaro Arbeloa_ ](ch028.xhtml#p200193ad9970203001)
**26**[ Third Place
_2 December 2008_ ](ch029.xhtml#p200193ad9970209001)
**27**[ A Hartung
_Conversation with England manager Fabio Capello_ ](ch030.xhtml#p200193ad9970216001)
**28**[ Liverpool 4 Real Madrid 0
_10 March 2009_ ](ch031.xhtml#p200193ad9970224001)
**29**[ A horse that needs to run
_Conversation with Juventus defender and Italy captain,_
_Fabio Cannavaro_ ](ch032.xhtml#p200193ad9970237001)
**30**[ Manchester United 1 Liverpool 4
_14 March 2008_ ](ch033.xhtml#p200193ad9970244001)
**31**[ You'd be happy if your daughter
brought him home
_Conversation with former Liverpool player and manager,_
_Graeme Souness_ ](ch034.xhtml#p200193ad9970254001)
**32**[ The same as always
_Conversation with Julián Hernández and Ángel Sánchez_ ](ch035.xhtml#p200193ad9970260001)
**33**[ The Kid
_29 May 2009_
_Conversation with Fernando Torres_ ](ch036.xhtml#p200193ad9970264001)
Career record
Bibliography
Acknowledgements
## Chapter 1
**Liverpool's Number 9**
_Thoughts and reflections from the Kop_
_'I love him. He's great. For someone from Spain, he embodies everything we want from our Liverpool players. I mean, obviously, we've got Gerrard and Carra who represent the spirit of the club but he's stepped into the Liverpool history and culture like he's been there all his life.'_ Sarah
_'He was a Red long before he played for us.'_ Dave
_'He's basically a legend. He's such a great guy. If I could have his babies I would.'_ Archie
_'He's the boy isn't he? Class, absolute class.'_ Frank
_'There was scepticism about how many goals he'd score here but in his first season he got 33. He's also a very humble man so he's very popular.'_ Paul
_'He's one of the best strikers in the world.'_ Ryan
_'He's an English striker isn't he?'_ Peter
_'It's not just that he's a very good striker. He works really hard, he defends from the front. He chases down a lot of defenders and_ _doesn't give them time on the ball which makes it easy for the rest of the team.'_ James
_'He's one of the best players we have. He's probably far more skilful than any goalscorer we've ever had in Owen, Rush, Fowler...'_ Dennis
_'His physicality is suited to the English game but it's more to do with his personality and his character for me. He's a totally great lad. He's down-to-earth, working class, same as us (from Fuenlabrada, and it's quite similar to a lot of places in Liverpool), so we've really taken to him and he's really taken to the fans as well. If you see him in the street, he's happy to talk to people.'_ Bessie
_'He's unique. Under Benítez, he's getting into space better and found a different dimension to his game'._ Neil
_'He's a fantastic player – good movement, he's quick. Quick with his feet, quick with his mind. He's a great goalscorer. He's got a good empathy with the crowd. He's very well-liked.'_ Chris
_'He's a god. It's what he brings to the team. A different dimension.'_ Franco
_'I think he's probably the best thing since sliced bread. Absolutely amazing.'_ Sam
No one at Anfield refuses to answer questions about El Niño. There are still two hours to go before the match gets under way but there is already a big buzz around the historic stadium. Scarves, party hats, flags and red shirts are everywhere, with people going this way and that. A man holds his son's hand in the queue to enter the club museum and admire the Liverpool trophies. Others slip into the Reds' souvenir shop, take up positions near the main stand entrance to see the players come in, pose for a typical photo in front of the Bill Shankly statue, desperately search for a ticket to see the game (despite constant PA announcements that the match has long been sold out), wait for old friends, ask which entrance to go in by, buy last-minute match programmes and give up any hope of entering The Albert (the pub right next to The Kop, opposite the new Hillsborough Justice Campaign Shop on Walton Breck Road), a heaving mass of bodies, noise, songs and pints. Red is the overwhelming colour but rumours are that is because it's full of Norwegians and other 'out-of-towners'.
And standing in the pub doorway is Jan, a fan who has indeed come all the way from Bergen in Norway just for the game. He steps outside for a cigarette. What does he think of Torres? 'He's young, he's got the speed, the ability. He's got everything. He's popular because of his attitude, the way he presents himself. He's very young but also very mature. He shines a kind of charisma that people adore.'
An English friend, Robert, butts into the conversation to give his opinion: 'We like his humility. We like the way he loves Liverpool Football Club. He's not one of these players who just signs up for the money. He's got a genuine love of Liverpool Football Club and that's reflected in the supporters who actually love the man. You'll see Torres tattoos, Torres shirts, banners.
'Everything's for Torres because he's for the club, which this club hasn't had for a long time, since your Ian Rushes or your Kenny Dalglishes. He has his own songs. He's one of us. When he hears his name sung, his heart beats. He wants to play for the club. You don't get that very often in the modern game.'
Gus reinforces the message: 'Liverpool is very much a working-class city. A player like Torres comes along, plays the same way and connects with the fans and that ethos. The fans love him. He loves the fans. It's a match made in heaven.'
There is more in the same vein, this time from Sean: 'I think he's got a rapport with the fans. He understands them. He understands the passion. He's committed. Not only that, he's technically brilliant. He's fast. He's pacey. Whereas, at Atlético Madrid, he was struggling for goals, at Liverpool he's now the striker and we centre our game on him scoring goals and it suits him perfectly.'
Round the corner, Ian, who has a stall of fan memorabilia selling everything from badges to flags, gives his view – economically speaking – of the Torres phenomenon: 'Definitely worth the money, yes, but Gerrard's still the one.'
In the club shop, however, they think otherwise. Torres is the top shirt-seller. Inside is Callum, aged ten, closely watched over by his father, who is wearing the Number 9 shirt. They go to every home game. What does Callum think of Fernando?
'It can be frustrating at times when Rafa doesn't pick him but when he plays he's a quality player and he knows where the goal is. I like how he can dribble past a lot of players and score.'
Joanna is sitting on a low wall with some friends, eating a plate of sausage and chips with a plastic fork. She happily breaks off to say what she thinks: 'What I like about Torres is he's not just speedy. There's skill in there as well, his technique is fantastic. So he's married the two really. He's got the skill and the physicality. He's the whole package for me.'
Alexandra gives a hearty cackle before making her contribution: 'His best quality – his looks! Look at my hair!'
A quick glance is more than enough to realise that the Spanish striker is the main inspiration behind her fringe and blonde colouring. And Cecilia adds, with a cheeky grin: 'We love the Spanish in Liverpool.'
Right in front, and across the street, is The Park – another pub bursting at the seams. To get inside you have to use your elbows but at the same time try not to knock over the huge number of beers squeezed onto the tables. At the bar, waiting for a pint takes time, but conversation sparks up immediately. The only problem is making yourself heard above the songs, chatter and increasingly animated prematch chanting. It's a fun atmosphere, with the imposing structure of Anfield clearly visible through the window. When one of the throng, with his military shirt and shaved head, hears the question about Torres, he breaks into song. The scarves move, the beer glasses are held high, everyone dances and claps their hands, singing:
_His armband proved_
_he was a red_
_Torres, Torres!!_
_You'll never walk alone it said_
_Torres, Torres!!_
_We brought the lad from sunny Spain_
_He gets the ball, he scores again_
_Fernando Torres – Liverpool's Number Nine_
_Na-Nar_
_Na-Nar-Nar_
_Fernando Torres – Liverpool's Number Nine._
You have to wait a bit for the noise go down to a level where you can carry on talking. For some time, a group has been gathered round a table stacked with beers of every type. Initially, no one wants to talk, each trying to persuade the other to speak. In the end it's John, with his coloured serpent tattoos and red shirt, who begins: 'What I like about Torres is that a lot of foreign players come over to England and take some time to adjust, whereas he's got stuck in. Defenders tackle him hard, but he can still put the ball back in the net. Brilliant.'
Eventually, the others pluck up courage to join in. 'He's a very unique striker because he can score long-distance goals, tap-ins, he can do anything really. You've got to tie him up for a longer contract,' says Steve.
Joe, leaning against a doorpost, picks up the same theme, shouting to make himself heard: 'No matter what happens, he says he's staying. That's good. There are too many players these days who are looking elsewhere for clubs but Torres says that Liverpool "is in my heart".'
## Chapter 2
**He is a red**
_4 July 2007_
The photo is unforgettable. On the left, Rafa Benítez, as happy as a sandboy, in dark jacket and white shirt with red stripes, holding up one end of a Liverpool scarf with the words 'You'll Never Walk Alone' written on it. On the right, holding the other end, is Fernando Torres, wearing the club's Number 9 shirt. The one that has graced legends like Ian Rush and Robbie Fowler.
The tiered seating in the stands at Anfield forms the background. It's a little after 3pm (UK time) when El Niño arrives to be presented to the media as a new player in the Merseyside squad. First, the signing of the contract that ties him to Liverpool for six years on a salary of 6.5 million Euros a season – a sum exceeded only by captain Steven Gerrard's. Then the press conference in jacket and tie with the shirt collar slightly undone. One can see that the lad from Fuenlabrada is nervous. He talks in Spanish and says straight away that 'the club is one of the best in Europe, a victorious club, its past and its present shows it. For me it was an opportunity which I couldn't miss out on.'
He looks to Benítez, always at his side, and explains:
'We didn't know each other personally but when I spoke to him for the first time... simply to know that Benítez had confidence in me is something incredible. And that a club like Liverpool, which can buy any of the best players in the world, should choose you to form part of the team comes as a surprise and fills you with pride. The fact that Liverpool are giving me the Number 9 jersey just goes to show the confidence they have placed in me, when considering those who have worn that shirt before me. But I'm not afraid of the responsibility that this brings.'
Torres knows the expectations that his transfer has created, the most expensive in Liverpool's century-old history (£26.5 million compared with the £14 million paid for French striker, Djibril Cissé, from Auxerre in July 2004). He knows that the public wants compensation in the form of goals. He hopes he can do it.
Rafa Benítez, who doesn't let him out of his sight for a second, maintains: 'We have signed a youngster with a promising future ahead of him. He is the player we needed.' There is no problem with responsibilities within the squad: 'Crouch,' he explains, 'works hard and Fernando can hold up the ball, look to get round the defence and construct moves.'
He stresses Fernando's intelligence, his ability to understand situations in a flash, and gives, as an example, the fact that the lad had immediately understood what it means to touch the badge with the words 'This is Anfield' at the entrance to the tunnel leading to the pitch – perhaps the most frequently broadcast image on the British television reports.
The Spanish manager reiterates Torres' passion and competitive abilities: 'He demonstrated these when he was only seventeen.' When asked what his goal-scoring abilities will be, he responds: 'I'm not going to put any pressure on him and say that he's going to score more than twenty goals. I prefer to have four strikers who score fifteen each.' He stresses the fact that 'Torres wanted to come. He was very clear. It would be a disappointment if he doesn't try to be a star.' He also talks of his new acquisition's feelings. Benítez has no problem in declaring them: 'His heart will stay with Atlético and that's normal. But one cannot doubt his professionalism. In his two final games with Atlético he played with an injured toe. He defended the club badge right up until the end!'
Of course, his Atlético heart... Fernando confirmed it a few hours earlier in Madrid when, dressed in black as if at a funeral, he said goodbye to the Atlético fans in the Vicente Calderón stadium at 10.30am (9.30am UK time): 'Wherever I am, my heart will always be red and white. This isn't a goodbye, it's a "see you later". Atlético is my family. I hope to return one day, when the club is at the high level where it deserves to be,' says El Niño who, with difficulty, manages to contain his emotions. He assumes responsibility for the transfer, saying that he had asked the directors to listen to the Liverpool offer.
Taking this position goes down very well with the club, which does not want to appear as the guilty party in the departure of Torres. Enrique Cerezo, the club president – more relaxed after hearing what the blond youngster sitting at his side has said – wishes him good luck and adds: 'Atlético understands and lets you leave in the hope that you come back soon. We don't want this to be a sad farewell act but a happy one, as when people who are very close say goodbye to each other.' To explain the mutual separation after twelve years of life together, Torres adds that 'the club is more important than the individual people. And my leaving for Liverpool benefits everyone.' It benefits Atlético, which, thanks to the money from the transfer, will be able to reinforce the team. And also Fernando Torres, who takes the right European train to be nearer those goals he has always dreamed about.
But things are not so simple... Despite the African-level heat and blistering sun, some 100 fans demonstrate outside the gates of the Calderón, shouting at the tops of their voices and holding up banners, on which is written 'Fernando, don't go!', 'We love you', 'Torres yes, management no', and then a series of strong insults aimed at the president, sporting director, secretary etc. They don't believe all the nice words. They are convinced that the people behind El Niño's exit are the Atlético top brass, together with the club's policies, the years of bad signings, the dashed hopes, one manager after another, of responsibilities never undertaken. The _colchoneros_ (fans of Atlético) feel sad, despondent and angry. They forgive their captain, their emblem of recent years, who has, without doubt, been the positive image and focal point for the dreams of a club that knows what it is to suffer. And yet the _colchoneros_ don't get too upset with Torres. They understand him. They understand that he wants to go from what has been his home, that the Little Prince wants to grow up. And even if El Niño says: 'Take it easy, time heals everything,' getting used to the idea is not that easy.
The news of Fernando's move to Liverpool is confirmed by Atlético at 7pm on 3 July. But it was 'Pulcinella's secret' – something everyone already knew. The Manzanares (the river of Madrid) club and the Merseyside club had reached a provisional agreement at the end of May. How did this come about? Every summer, offers for Torres arrived at Atlético from several big clubs.
In 2005, for example, there was talk of Chelsea, Newcastle, Arsenal and even Inter who, according to the press, had offered Christian Vieri plus a large transfer fee. In an interview with an English newspaper, Fernando explained:
'People always ask me about my departure. Atlético is a big club but we don't win much. Somewhere else, I would be competing for important trophies but here I have things that I wouldn't be able to have in other clubs – my family and my friends, my feeling of belonging to a humble Madrid team, the one that represents the working class. We don't have money, nor power. Very occasionally we win trophies but we exist for other reasons. We give the fans a safety valve of escape for their problems and because of that they absorb themselves into the club.'
In a few words, he explained the quasi-absurd philosophy of the _colchoneros_ , the hopes of the fans and the players, which are that – one day or another – their destiny will change. Perhaps for this, after taking into account together with his representatives all the offers that arrived, he never decided to say 'Yes'. In 2006 the voices of the market became ever more insistent. Three candidates for the presidency of Real Madrid (which will be won by Ramón Calderón) have long pursued El Niño but have always received negative replies. At the end of the season, Manchester United also comes in.
In July, there is a rumour that Sir Alex Ferguson's club is about to put in, on paper, a 37-million-euro offer. Inter come back again, offering 38 million. But it doesn't stop there. The Atlético directors say that El Niño is not for sale and is too important for the club.
And in September 2006, they announce the renewal of Torres' contract until 30 June 2009, with a clause for breach of contract, which, strangely, goes from 90 to 40 million Euros. The player also improves his salary to 7 million Euros per season.
Spring 2007 – Rafa Benítez is thinking of a new striker for his team. Eto'o or Torres? The gaffer weighs up the two possibilities and, according to his custom, asks for reports covering everything under the sun. Not only about the pair's football skills, but also about their personalities, the behaviour of the Cameroon and Madrid players in their respective dressing rooms, and in their daily lives off the pitch. Scrupulous and methodical, he does not want to miss even the smallest detail. He wants to minimise the risks of the transaction. In the end, after closely studying the two options, he decides to go for Fernando – who, it seems, has triumphed in the reports.
We are in April and the negotiations between Liverpool and Atlético get under way. Acting as mediator is Manuel García Quilón, a famous football agent who, amongst other things, is also the representative of Rafa Benítez.
At the end of May, a provisional agreement between the two clubs is reached, to the point where Atlético begins to look for a substitute for El Niño. They ask Villarreal the price of the Uruguayan, Diego Forlán. Meanwhile, Rafa Benítez, after the Champions League final in Athens, which the Reds lose against the Milan of Filippo Inzaghi and Carlo Ancellotti, calls Fernando. To begin with, the Atlético player thinks it's a wind-up, some imitator who is trying to trick him. So much so that he cuts everything short and replies in monosyllables. He doesn't want to be set-up. So he calls Pepe Reina, his friend in Liverpool, to check that the number of the person who called really is that of the manager. And it is. He can now have a more relaxed conversation and listen more closely to the Madrid-born manager's offer. Benítez says to count on him, that he will do everything to bring him to England, and that he hopes he will accept. El Niño has always liked English football. He's always said that, one day, if he decided to leave, he would prefer to end up in the Premier League.
Two years previously, Liverpool got to the final of the Champions League and won. It's a club with a style and philosophy that's to his liking. Its fans are devoted to the cause, just like those of Atlético. At a stretch, the Calderón reminds one of Anfield. And also the Reds' fans have a history of being working class. For sure, it's not the Manchester of the shining stars or even the Chelsea of the Russians, but this could mean that there will be more space for him. On the positive side, there is also the fact that Reina, Xavi Alonso and Arbeloa are at Liverpool. With them, and with Cesc Fabregas, Fernando has talked many times of what it's like to live in the UK, the atmosphere and the way they play football. And he has always got positive feedback. In reality, the Spanish Liverpool could be an important factor in helping to adapt to a new football environment.
Last but not least, there is his Atlético captain's armband. For years it's carried the words 'You'll Never Walk Alone'. The story behind it began with Fernando's group of friends. They all wanted to have the same tattoo and they discovered that this expression represented exactly what was most important to them – the bond of friendship that will never be broken, wherever you are. Torres is reluctant. As captain of Atlético, it's not particularly smart to get the Liverpool motto inscribed on your arm, because maybe the papers would write about it. So, in order that he's not left out, they find the best – and the most discreet – compromise. It will be written on his captain's armband. They get it engraved and give it to him as a gift. A story that is revealed when it comes loose during a match with Real Madrid and the message is caught on camera. A sign, almost a premonition, of what, in fact, is actually happening.
But despite all that, the connection with Atlético is strong. It's an emotional and footballing way of life that he needs to put aside in order to make the big leap. But here fate steps in to help him make the final decision. It happens on 20 May 2007. Atlético Madrid v Barcelona, league match number 35, the final result 0-6. It's Atlético's worst-ever home result. A tennis score that hurts, really hurts. At the end of the match, Torres is alone in the middle of the pitch, crouched down with his head in his hands. 'Never have they beaten me like that. They could have scored twenty,' the club captain commented immediately afterwards. He had said that Atlético was inferior as a team to the top four in the table, but that he had put his faith in the fact that Barça hadn't won in the Calderón since the 1999–2000 season. He also wanted to end the debate over a UEFA Cup place as soon as possible. If they had beaten Barça, they would've been halfway along the road to Europe. But instead – no. Messi, Zambrotta, Ronaldinho, Eto'o and Iniesta hit the net of the unfortunate keeper, Pichu, one after another, highlighting all the team's failings.
As if that isn't enough, the fans, who have always supported the players right up until the final whistle, this time actually want a defeat because it would mean that the eternal enemy, Real Madrid, would not win the league. It's a bad sign and demonstrates the fact that the team isn't making every effort or, almost, that it prefers to bow down to its historic opponents rather than celebrate its own victory. And that's not all. The crowd is already starting to leave the Calderón once Barcelona get their fourth. They abandon the stadium with their heads low, tired of always having their hopes dashed. The ones who stay behind whistle and shout at those on the pitch: 'Mercenaries, you're just mercenaries!'
It's the final straw. The situation that pushes Torres to take the decision he's put off so many times. He's getting out of Atlético. He's disappointed, infuriated, impotent and envious of the winning Barça players, who make up a great team capable of dominating at any ground. He also wants to savour this. He no longer wants to be like a young Atlas, carrying the weight of a 104-year-old institution on his shoulders and which, in recent years, is only able to offer disappointment to its supporters.
On 19 June 2007, the agreement between Liverpool and Atlético is signed and sealed. The only thing missing is Torres' contract with the English side. In the end, El Niño will accept a lower annual salary (but there are add-ons once certain targets are achieved) in order to be able to leave.
Sunday, 1 July: Fernando interrupts his holidays in Polynesia and returns to Madrid.
Monday, 2 July: he flies to Liverpool after a meeting with Bahia International, the agency that has represented his interests for several years. Here, he spends around 40 hours holed-up in an apartment the club keeps for such situations. It's forbidden to go outside, go for a walk, a meal, or anything. Liverpool want to keep the transfer completely secret.
Tuesday, 3 July: from the apartment Fernando goes directly to a car parked in a space below the building, and from there to undergo a medical examination. He's proclaimed fit and ready to join up. And then the last return flight between the city of the Beatles and the Spanish capital. El Niño, the most expensive signing in Liverpool's history, the most expensive transfer of a Spanish footballer abroad since Gaizka Mendieta (sold in 2001 by Valencia to Lazio for 42 million Euros) first wants to say goodbye to the people he knows in Madrid. It's only that night that a photographer gets a shot of Torres on his way to the airport...
On 4 July, the Spanish press say their farewells to Fernando. Mundo Deportivo uses the verses of The Doors song, 'The End': 'This is the end. Beautiful friend. This is the end. My only friend, the end.' A sad farewell in Spain, a welcome full of hope in England. The desire of the English media is that The Kid becomes a legend at Anfield. For Torres, it's the first day of a new life. A truly strange day. In the morning he leaves home and in the afternoon discovers his dreams have become reality.
## Chapter 3
**The culprit of his success**
_Conversation with Liverpool manager, Rafa Benítez_
The gaffer is pretty tied up with a whole pile of things on his plate. He's putting the finishing touches to the 2008–09 season, which finished a few days before, and beginning the next. As usual, he'll have a summer of hard work. And this year even more, now that – thanks to a contract until 2014 – he has complete freedom regarding the buying and selling of players and in all sporting matters. He'll have to take the right decisions and sign the right players to reinforce the Reds. To buy and sell with more than £30 million in his pocket. With this money, it's not easy to bring in the best footballing components, but Rafa is used to challenges and overcoming the odds. He wants to do it as soon as possible so that the newcomers can make themselves at home in the pre-season and get familiar with how the club plays, in order to go for the league title, which they have not won since the 1989–90 season. It will be another 'Rafalution' – the Red revolution of Rafa.
In Anfield they are used to this because, since arriving in 2004 from Valencia, the Madrid-born 49-year-old has changed Liverpool. He has brought it up to date. Over two seasons, he reorganised Melwood, changing the preparations, the training, the players' diet and the way the team plays (and whoever accuses him of being defensive, he responds by pointing to the 100-plus goals they scored last season). He has set up a scouting and talent-spotting system that enables him to keep tabs on around 14,000 players across the globe. And above all, he has returned Liverpool to the European elite, winning the Champions League and European Super Cup in 2005 and getting to another Champions League final in 2007, when they lost to Milan. 'He's demonstrated that he's hungry for success,' said Tom Hicks, one of the club's owners. Rafa is a man who lives and breathes football and works on football 24 hours a day if needed. As he's said on many occasions, he wants to help create a new chapter in the legendary history of the club. Gerrard, the captain, and Torres, El Niño, are two essential elements of his sporting project. Let's see how he came to choose Fernando...
### _Why did you decide on Torres as a future signing for Liverpool?_
'Fundamentally, it was based on information in our possession, thanks to the tracking we do on many players, his excellent skills and the potential he had to develop still further over the short and medium term. Thinking about the English league and his special characteristics, he seemed ideal to be the striker of a team with the philosophy of our Liverpool FC. The truth is that he hasn't let us down in any way.'
### _What skills did he have to be one of the Reds?_
'Well, it isn't easy to summarise a sportsman, an elite player, a footballer of the highest level like Fernando. But with a bit of analytical skill we could highlight his power, his strength to withstand physical contact, to go all out – in a legitimate, sporting sense – to win a game, and with sufficient quality and skill to end up being the kind of player who can change the flow of a game.'
### _Your bet (on Torres), Mr Benítez, was not an easy one, considering the fee paid and the average goal tally of Fernando in his six seasons with Atlético Madrid. How in the end did this bet transform itself into a winning one?_
'Well, I think that although everyone's made an effort to help him, the main 'culprit' for his success is him, because of his great determination and his very hard work. Since his arrival he pushed himself hard to improve. He was getting more and more confident and therefore getting better day-by-day. I think that the main guiding principles of Torres' transformation are Fernando himself and the abilities that he has shown since he arrived in England.'
### _Did you think that Torres would get 33 goals in his first season? How did that happen? Why has he adapted so rapidly to Liverpool, to the club and to its playing style? Has the 'Spanish Liverpool' helped him much?_
'To be very sincere, and in spite of all the earlier remarks regarding his potential and attitude, the truth is that we didn't expect so many goals in the first year. Not even the most optimistic could have imagined it. But of course one should also say that he deserved each and every one of them, which were the result of his work and dedication and his already-mentioned desire to improve. And yes, talking of his adaptation and the ease with which he was able to do it, it would only be right to recognise that the group of Spanish players who have been with him at Liverpool have helped him a lot to achieve that.'
### _They say that, at Liverpool, Torres is much more relaxed, has got rid of the responsibilities (captain, club image) that were suffocating him at Atlético, and that this has been one of the keys to his success. What do you think?_
'Well, one can't know that for sure from outside. I think that's something one would have to ask him and only he could give an absolutely genuine response. In his immediate environment, we have been with him in this process and we can agree that, yes, he has been able to shed an excess of responsibility and that has helped him considerably with his bursting onto the English football scene as a player. Here in our group, our team, Fernando is important – but for what he does on the pitch, not for his image and what he represents or might represent off the pitch.'
### _Spanish, Italian and English managers and players all agree with the fact that you have greatly improved Fernando's game. How have you done it? What advice did you give him?_
'I wouldn't want to repeat myself unduly but it's necessary to go back over parts of the previous answers. The secret is his work, his attitude, his willingness to improve every day. He has listened carefully and resolutely applied what the technical staff at Liverpool FC have taught him in training. To mention some aspects that I consider fundamental, his movement and calm finishing have been key from my point of view.'
### _How has Fernando reacted to your orders?_
'I presume this refers to my advice, to the guidance we can give him for achieving his best possible progress. And to be very truthful, in this respect, I believe he reacts very well. He always listens and tries to apply the advice to his game in every meeting, in every training session and, finally, in every game.'
### _What has Torres brought to Liverpool's game?_
'Once again, we'll have to summarise. But I would pick out, basically, his ability to change the course of a match, his speed on the counter-attack and the fact that he poses a constant threat for rival defences in each and every game he plays.'
### _How do you explain how Torres has, over such a short time, become one of the players best-loved by the fans, who compare him with legendary players like Dalglish or Rush?_
'It's not going to be me here and now who describes the philosophy of the Anfield terraces, the merits which the fans of Liverpool FC value most. But taking all that into account, his performance during the first year was spectacular, although in this second year, the truth is that Fernando hasn't had much luck with injuries. Besides that, one is dealing with a footballer who is humble and works hard, and all that makes our fans very enthusiastic about him and in him they recognise – let's say, they identify – yesterday's values, today's values, and the values that are always there in the 'Red' story.'
### _What is your assessment of his two seasons in the Number 9 shirt of Liverpool?_
'To give a brief assessment, without going into details and looking for the appropriate adjectives, I think the first campaign turned out to be excellent in every respect, as we talked about before, and the second, which has just finished, one would have to say it could have been better, although at the same time, and to be fair, you have to bear in mind the mitigating circumstances referred to earlier. Injuries have prevented any kind of continuity and that, as we all know, is fundamental for any footballer at the end of the day.'
### _What, for you, has been Torres' happiest, his best moment with the Reds?_
'Obviously one would have to pick out some of the goals he's scored. One is talking about a striker, and in this sense he's brought a lot to the team, particularly during his first year. But not being Fernando, it would be difficult to choose one or two. It should be him and only him who can give an opinion on this. No one knows the feelings of Fernando Torres more than Fernando Torres himself.'
### _What has been, and what is, your relationship with Torres?_
'From my point of view, we are talking about a normal relationship, more or less like I have with the rest of the footballers. For sure, someone could probably say that I've talked more with him than some of his team-mates. But that's due exclusively to the argument that I see the potential he has, and I try to help him exploit that to the full, for his own good, although also for his contribution to the team, which is the really important thing. He's a great lad and it's not too difficult to have a good relationship with him.'
### _What kind of person is Torres now?_
'If we have to talk about him in a personal sense, as the question requires, there probably hasn't been much change. We're talking about someone who is pretty similar to the lad that arrived just under two years ago – a bit shy, a very good team-mate, pretty humble and, above all, respectful. As you see, one can make out quite a lot of qualities in him on a human level as well.'
### _And finally, how do you see the future and next season for Liverpool and Fernando Torres?_
'With the optimism and hope that the situation demands. I think that as long as he stays injury-free, he could have another great season if he keeps working with the same humility, dedication and attitude that he has up until now. We have great expectations for Fernando and believe that he's not going to let us down. He's working on that and doing very well. Let's hope that's how it is...
## Chapter 4
**A nice lad**
_Conversation with Spain manager, Vicente Del Bosque_
A quiet man, a coach and father-figure, who took charge of the national team following the euphoria of the victory at Euro 2008 and who knew how to bring everyone back to earth. While not denying the legacy left by his predecessor, Luis Aragonés, he has achieved the team's qualification for the 2010 South Africa World Cup well ahead of schedule.
The national team is the latest stage of a long sporting career: 'We'll see when it finishes, maybe after the World Cup, who knows... Let's hope up until the next European Championship, if things go well.' Then he will close the door on soccer, a world he first entered in 1 August 1968, when he left his home city of Salamanca to join the Real Madrid junior team.
At the club's former Ciudad Deportiva training complex, he learned the skill of being an attacking midfielder from players such as Pirri, Grosso and Velásquez. He came up through the ranks with the 'ye-ye' generation of players from the 1960s. They were dubbed the 'ye-ye' generation because of the 'Yeah, yeah, yeah' chorus in the Beatles' song, 'She Loves You', after four members of the team were photographed in Beatles wigs for sport daily, _Marca_. It was this group of players that had won the club's sixth European Cup in 1966. He also played with the _Quinta del Buitre_ (or 'Vulture's Cohort' team from the 1980s, which derived its name from its top-scoring player, Emilio Butragueño). Wearing the white of Madrid between 1975 and 1984, he won five league titles and four Copas del Rey (King's Cups). He was on the losing side in the famous 1981 European Cup final against Liverpool, which affected him deeply.
But from this disappointment he recovered well when, as manager, he brought the Real Madrid of the _galácticos_ (so-called because the team included world-famous star players such as Zidane, Figo and Ronaldo) two Champions League titles (2000 and 2002), a European Super Cup and an Intercontinental Cup (both also in 2002). All in four seasons – and that is without counting the titles won in Spain.
It was a managerial skill acquired under the Yugoslav schooling of Vujadin Boskov and Miljan Miljanic (two of the managers of Real Madrid between 1974 and 1982). 'Bigotón' ('big moustache'), as he was called because of the facial whiskers that give him a likeness to Inspector Maigret, knew how to manage in a calm and friendly way a dressing room where the egos of the champions were as inflated as hot-air balloons. How? Behaving 'like a good father who draws the line, sets an example, tries to convince without imposing himself and who allows a freedom within certain limits. I don't like to spend the whole day waving a stick.' Secrets? 'Don't try to be too clever or tell the players the absolute truth every day.' And now it's time for the ultimate test, and perhaps the most difficult.
Wearing the national team tracksuit, he is breakfasting in the Ciudad del Fútbol de Las Rozas training complex and chatting with his assistants. Del Bosque talks about Torres – now an essential element in the Spanish forward line – in his usual good-natured way: 'Fernando already has a brilliant career. He began very young at Atlético de Madrid, where he had been a focal figure for many years. I think that he has benefited a great deal by going to England to play football, to a well-organised club like Liverpool, where he is alongside a manager and other players with considerable experience. He's had very good runs, and in the national team as well, and he still has a great future ahead of him...'
Without further ado, he begins to talk in more depth about a youngster he's known for some time, when he was an opponent in the Madrid city derby.
### _What was your opinion of him when he was here at Atlético?_
'Here, Torres didn't enjoy the best years of Atlético Madrid. He had too much pressure, was made captain too soon, he didn't have that space as a youngster, the time to develop without feeling under pressure or protected by more-established team-mates.'
### _How do you explain the fact that he has doubled his goal tally and his scoring ability since moving from Atlético to Liverpool?_
'Likewise, I think it's down to the environment where he is playing his football. Atlético isn't the same as Liverpool. The environment, his team-mates and Liverpool's presence in Europe – all that has helped him.'
### _What role has Rafa Benítez had in Torres' development?_
'Benítez is a manager he's benefited from. I'm not saying that those he had before at Atlético didn't try, but more than that, he's now getting a more comprehensive training and he has matured.'
### _To be alongside a midfielder like Gerrard has helped him to grow as a player?_
'Yes, I think so. It's clear that Gerrard has brought a lot to his game but Torres is also giving the Reds a lot more possibilities, particularly to the players behind him. Fernando has great value – his speed and his running off the ball give options to Liverpool's game. He's a Number 9 that any midfielder would want to have in front of him.'
### _What has English football brought to Torres?_
'It's brought different ways of understanding the game, which is important – although now there is little 'native' football, it's more a mixture of styles. Nowadays one doesn't talk of a true English style. Arsenal, Chelsea, Manchester (United) and Liverpool themselves have lots of foreign players. Yes, I think that this coexistence between English and Spanish football has helped him in his development.'
### _Briefly, what are the differences between English and Spanish football?_
'The two are very competitive and they are clearly dominant in Europe, at least at the moment. In any case, I don't see any great differences.'
### _Fernando's technical qualities?_
'He's a player who has a dominant physical presence, who is very fast and a great goalscorer. He probably doesn't have a great technique but he does things that are unexpected...'
### _For example?_
'Hitting the ball very hard, a sudden burst of speed... and then his ability to improvise in front of goal. Anything to surprise his opponent. He's not a very orthodox player technically but overall he is in excellent shape and has scored some amazing goals.'
### _Since his arrival at Liverpool, do you think he has improved in certain technical respects?_
'Undoubtedly. His time at Liverpool has enabled him to acquire better technical skills. This improvement has been good for him and for the other Spanish players. That speed he has must be accompanied each day by building a better technique and that's what Torres has done. Quality? To play in the footballing elite where he is playing, in the team he's playing in now, he wouldn't be doing it if he didn't have quality.'
### _Human qualities?_
'He's a modest lad, very normal and gets on well with his team-mates. He's a nice lad, yes, very nice. He has a very stable life and that's good for footballers.'
### _As national team manager, what advice would you give him?_
'The advice one normally gives to a striker. In the national side, Fernando has some defensive duties to fulfil because they benefit greatly the rest of the team and then there are the attacking duties of a player who knows how to maximise the possibilities for all the players behind him. His speed, his movements, his mobility and his ability to lose his marker are essential in order to give our midfielders the best options.'
### _Before Euro 2008, there was a lot of debate about the national side's way of playing – lots of short, horizontal passes – and that of Liverpool with their rapid movement of the ball from one end of the pitch to the other. The conclusion was that Spain's slower style would give Torres less space and therefore fewer opportunities to score. What do you think?_
'In football there isn't just one way of doing things – it's a mixture of everything and I believe Fernando knows how to play in space as well as play with short passes. Fortunately, the national side mixes the two, which is the ideal.'
### _The role of Torres changes between Liverpool and the national side?_
'No, I don't think it changes much. Our group is pretty integrated in that everyone has their role and, without doubt, Torres is one of the most important players in the national side, for sure.'
### _How do you remember his goal in the final of Euro 2008?_
'I think it's the culmination, the final phase of a move involving the whole team. He knew how to score a quick goal and finish well in front of the keeper.'
### _Which player does Torres resemble?_
'I don't know really. I can't think of any players who remind me of him or who resemble him. I think he has a very individual way of playing.'
### _From when he was very young, he's been compared to Raúl, the captain of Real Madrid, who you know very well..._
'Raúl has more than 100 international caps, something which is not easy to achieve in Spain. Torres already has more than 60 and, considering his age and what remains of his football career, he could equal or surpass that. The other similar thing is the two of them come from the same junior ranks. Both are an example for younger lads.'
### _Torres' future... Do you think it's true that he can go on even higher?_
'I think that he's at a great club and that he still has challenges to meet. Without doubt, he wants to win the English Premier League title as well as the Champions League. And also with the national side we know there are challenges ahead.'
### _The most important of those is the World Cup. How do you view that?_
'Well, for us it's exciting to think that we are one of the contenders to win it and that the individual talent of each team member, his reputation and his status could result in a collective victory. We know that a World Cup victory would bring much acclaim to all who take part.
## Chapter 5
**Fuenlabrada**
Penélope Cruz, to applause from the public, goes up to the stage in the Kodak Theatre in Hollywood to accept the Oscar for the Best Supporting Actress for her role in the Woody Allen film, _Vicky Cristina Barcelona_. Kisses and hugs from Tilda Swinton, Goldie Hawn and Whoopi Goldberg, then the speech with the statuette in her hand. It won't last the normal 45 seconds, she says straight away. Visibly moved, she pays tribute to the directors, the actors and the people who've helped her become the first Spanish actress to win the Academy Award. She dedicates the award to her parents, to her brothers and sisters and to whoever isn't there. And she doesn't forget Alcobendas, the town about 9 miles from Madrid where she grew up and where she used to watch the ceremony on TV – an impossible dream.
Alcobendas is now on the map, its residents say with pride. The same thing happened to Fuenlabrada – thanks to Fernando Torres. So much so that, on 5 February 2009, the Town Hall recognises this by awarding him the 'Citizen of Fuenlabrada' medal 'in recognition of his special sporting and personal values, of his professional career, which has led him to be considered internationally as one of the most important footballers in the world, and of his commitment and loyalty to his town, for which he is an exceptional ambassador. The hope and spirit shown by the footballer is an excellent example for children and young people who, by playing sports, not only develop a physical activity but also highly important values such as knowing how to share with their team-mates the dream of achieving a common objective.' This is how the joint motion, presented by the various political groups in the municipality of Fuenlabrada, reads.
And it's here, 'in this humble neighbourhood, to the south of Madrid, that I was born,' explained the Liverpool Number 9 in an interview some time ago. Twenty-five minutes by rail from the centre of the Spanish capital. The regional _Cercanías_ trains, which serve the town, are always crowded. They come from the station of Atocha, which, on the morning of 11 March 2004, was hit by the terrorist attacks that left 199 people dead, another 1,800 injured and sent shock waves across the country and the rest of Europe. A train leaves Platform Nine every fifteen minutes. Aboard are commuters, students, workers and many immigrants who live on the city limits. Orcasitas, Zarzaquemada... the stations pass by one after the other. High-rise housing projects, neglected spaces, intersecting motorways piled on top of each other, small residential houses, graffiti on abandoned walls, planes flying low as they come in to land at Barajas airport, shopping centres and some shanty towns. Leganés, Parque Polvoranca, La Serna... and then, Fuenlabrada Central.
Not far from the station exit is the Town Hall, a modern complex of steel, cement and glass, which can be identified by a series of horizontal yellow lozenge shapes in-between each floor. It looks onto an enormous square with a fountain occupying the centre, around which are seated several old people. Manolo Robles, aged 56, socialist, mayor since 2002 and local councillor since 1983, is a confirmed _madridista_ (fan of Real Madrid). But he adores El Niño. He saw him play many years ago, when Fernando was just a boy and taking his first steps in the Atlético Madrid junior sides. The mayor also has a son who, when he was that age, enjoyed playing football but hasn't become a champion like Torres.
Around that time, by chance, he bumped into Fernando's parents in the Colegio Amorós school in Carabanchel and spent some time chatting to them. He's proud that his local administration has officially recognised El Niño: 'He's the city's most important sporting figure, because he grew up here and started playing football here, because people think of him as their neighbour, even if, for some years, neither he nor his family have lived in Fuenlabrada,' says Robles in his second-floor Town Hall office. Large windows behind him depict the town he governs. 'El Niño is very much loved here and even more since his goal in Euro 2008. He's very well-known internationally and has put our town on the world map. Only the other day, I did an interview for a radio station in Guatemala. The first thing they asked me about was Fernando.' A 25-year-old, whose name the municipality will use for a new 90,000-square metre sporting complex containing football pitches, tennis courts, athletics tracks and a swimming pool. 'It will be ready in 2010 and we hope that Torres can inaugurate it,' explains the mayor.
But what was Fuenlabrada like and what is it like today?
'In 1973, it was a rural town of 7,000 inhabitants. But in the final years of the Franco dictatorship, there was a lot of property speculation. They gave thousands of permits to build and by 1979, we had a population of 57,000. The town grew chaotically without any proper urban development plan. In the 1980s, Fuenlabrada was the subject of a major internal migration process. Lots of young people came from (the Spanish regions of) Andalucía, Galicia, Extremadura and Castilla-La Mancha, looking for work and a place to live. They settled here, next to a small community of Polish immigrants.
'In 1995, we were witness to a wave of immigration from the Maghreb region and then from Latin America at the end of the 1990s. Today, Fuenlabrada has 209,102 inhabitants, 15 per cent of whom are immigrants from outside the European Union. It's the fourth biggest city in the Madrid region in terms of population. It accounts for 25 per cent of the region's industry, above all furniture-making and metallurgy. We've got 22 industrial estates and 30 per cent of the region's small and medium-sized businesses.
'In the last decade, we have greatly improved the residents' quality of life. In terms of transport and communications infrastructure, thanks to new roads, the regional _Cercanías_ train network and the metro, Fuenlabrada is now closer to the capital. In terms of education and culture, we have 70 teaching centres and the Universidad Rey Juan Carlos campus, four theatres, a library for every 35,000 inhabitants, six sports centres, a basketball team playing in the ACB (the top division of Spanish basketball) and a football team in the third division.
'It's a city, and a very different one from that which Fernando knew when he was small. His neighbourhood, the Parque Granada, at that time was almost a village, where everyone knew each other and where the majority of people had arrived only a short time before. If there's something that hasn't changed, it's the fact that Fuenlabrada continues to be one of the youngest municipalities in the country.'
José Torres – Pepe to his friends – arrived in this 'dormitory city', 22 kilometres (about 14 miles) from Madrid in the 1980s from Galicia. He was born less than 20 kilometres from Santiago de Compostela, the regional capital. José is the second of nine children of Claudio Torres and Maruja. 'Our Pepe, who is now 59, began at the army barracks in Pontevedra and later joined the police. He was deputy-inspector and after two years in the Basque Country, he requested to be transferred to Madrid, to Fuenlabrada (a new station was opened in 1987). Now he's retired,' recalled Claudio Torres recently. In Madrid, he married Flori, who is from the city, and bought an apartment in the street of Calle Alemania. It's here that their three children were born and grew up. Mari Paz, the oldest and eight years Fernando's senior, has a law degree and today works for Bahía International. Israel, seven years older than Fernando, has followed in his father's footsteps. He joined the police and was assigned to the security of María Teresa Fernández de la Vega, the deputy prime minister in the socialist government of José Luis Rodríguez Zapatero.
'My parents weren't expecting me. I arrived by chance,' confessed El Niño some years ago. His brother and sister were already quite grown-up when the new arrival made his entrance. Attention centres on the little Fernando José Torres Sanz who, despite the normal petty jealousies, is welcomed by his two older siblings. In fact, Flori and José say that, with the arrival of Fernando, the older two become more settled.
The most amusing anecdote from those early years is the fright his mother gets when he throws around 80,000 pesetas (about £400 at today's values) out of the window. He was playing with a model toy in his parents' bedroom. A lorry with a big trailer. He'd filled it with banknotes he'd found in a drawer and then... threw it out of the window. He liked to drop things to see where they ended up. Flori, working round-the-clock to look after the three children, had begun searching for the cash but couldn't find it and had run out of places to look for it. She was desperate. She only realised what had happened when the neighbours knocked on the door to ask: 'I don't suppose you've seen what's fallen out of your window?' She couldn't imagine that her little 'Fer', as his friends call him, had done such a thing. El Niño was a bit naughty both in and outside the house. So much so that José and Flori decide, in a family meeting, to impose tough measures to prevent any more such 'brilliant' ideas on Fernando's part.
Even if he is the little one of the house, he can't get away with everything. He has to be subject to the same rules as the other two. Having said that, his brother and sister still allow Fernando to get up to all sorts of mischief. Israel, his older brother, is the model, the example to follow, while Mari Paz is the older sister who indulges him in everything and who makes a fuss of him whenever she can. The friends of the family say that Fernando has his father's character, the character of the shy, almost introvert, gallegos (people from Galicia) but who are at the same time, good, responsible people and good workers. Pepe doesn't share this view and today describes his son as 'an intelligent person, with a head for taking in information and different situations, capable of withstanding difficult moments and enjoying the good ones. Apart from his physical and technical qualities, he's very strong mentally, has an absolute belief in what he can achieve, has always wanted to get on and improve and this has allowed him to get where he is.'
The youngster also shows these qualities at school. He gets on well, has good marks, behaves well, is very determined and has a great capacity for concentration. 'I remember a play we put on at the school. His part was to recite a poem about solidarity,' remembers Alicia, the language teacher at the Colegio Público Francisco de Quevedo school. 'He learned it by heart and recited it perfectly.' All in all, a clever student, but not one who's averse to a bit of cheating. Once, the teacher catches him red-handed while he's copying but doesn't punish him and doesn't pull him out of the exam. The other students are angry and protest. 'If you don't take him out, then we'll all start cheating,' they say. But it's difficult to punish that angel face, which looks as if it would never hurt a fly. His classmates remember...
The end of term and the beginning of summer. The Torres Sanz family spend the holidays in the father's home village. There are long weeks with his grandparents, uncles and aunts, his brother and sister, his friends in the village, months of adventure amongst the fields and vegetable gardens. Until his parents discover the seaside town of Cee in Galicia. It was by chance that they passed by there, they liked the place, found a small apartment on the beach and bought it. Fernando is then eight years old and for the following summers this will be his holiday destination. He makes new friends and acquaintances – and one of those will have a fundamental impact on his life. Because on this very beach, the thin, blond, shy lad falls in with a group of youngsters his own age, and meets Olalla Domínguez Liste, who is from the San Lázaro district of Santiago de Compostela and keen on figure skating. She is fifteen and he is seventeen. They meet, get to know each other, and fall in love. From then on, they are never apart. But this story is still to come. For the moment, Fernando is a lad who grows up, as his father says, in a 'normal family' surrounded by the love of his parents and paternal grandparents as well as those of his mother, Eulalio and Paz, who live not far away from Madrid in Valdeavero. A boy who grows up learning what it means to make sacrifices, to work hard, 'to appreciate the important things and to understand,' as José Torres always says, 'what are the true values of life.'
And to enjoy his football...
## Chapter 6
**Leader of the gang**
Five or six o'clock on a Saturday afternoon – a good time for a kick-around with the usual gang. Fernán, as his friends call him, puts himself in the goal that has been created between a wall and a mound of clothes. The game is non-stop, the boys create a huge dust cloud as they tear around after each other. The rules – even for those who want to use them – are virtually ignored. Then a pass is threaded through to Alexis, who finds the ball at his feet. Without hesitating, he shoots hard, very hard. The ball catches Torres full in the face and his mouth fills with blood. He bursts into tears and the game is over. His friends gather round and take him, running, back home to his mother, Flori. It's a big shock for them all. He's missing two front teeth.
This is the point where Fernando Torres' goalkeeping career ends. His brother, Israel, and his mother ban him from playing between the posts on the cement pitch. He himself also understands that maybe it's better to try putting the ball into the net rather than trying to keep it out. And so begins the career of Fernando Torres as striker.
'Fernán loved being in goal because of his brother, Israel, who was one of the best indoor football goalkeepers I've ever seen. He wanted to be like him but after he got smashed in the face, he never went back in goal. I was responsible for what happened and I felt bad. I was scared of getting a huge telling-off from my parents and from his. But, to be honest, it upset me a lot to see him like that and I remember going several times with him to the dentist. However, in one sense, the incident turned out well for him,' says 26-year-old Alexis Gómez, now a security guard and the person responsible for changing the role of one of the world's most famous strikers.
Fernando Torres is six years old. One of the series on TV is _Campeones: Oliver y Benji_ (Champions: Oliver and Benji), the Spanish language version of a hugely popular Japanese comic-style cartoon series about the adventures of a Japanese youth football team. It features super striker Tsubasa Ozora (known in Spanish by the English-style name of Oliver Atton) and the invincible goalkeeper Genzo Wakabayashi (Benji Price in the Spanish version). It tells the story of these two friends from their childhood to becoming professional footballers and, eventually, to being called up to the Japanese national side. Their adventures take in their team-mates, the training, the matches and the tournaments, as well as spectacular moves and action that would be impossible to perform in real life. These are the words of the (Spanish) theme tune:
They go with the ball at their feet
and nobody can stop them.
The stadium vibrates with emotion
to see both of them play.
They only play to win
but always in a sporting way
and there's nobody better
for the fans.
Oliver, Benji
magicians on the ball.
Benji, Oliver,
dreams of being champions.
Benji, Oliver,
mad about football,
they have to score another goal.
Words and music that a lot of Spanish children have not forgotten. Torres was also a big fan of Oliver and Benji. He identified with the stories of the two youngsters and imagined himself being a footballer like them, a goalkeeper who let nothing past and a striker who, in the gardens around his home, was getting good at scoring against his brother Israel.
Torres first began to kick his brother's football around at just two years old. His brother was the model to follow. During the summer, the Torres Sanz family spent their holidays at Gastar (a small village about 12 miles from Santiago de Compostela), with the paternal grandparents. It's where they got used to playing football. He played in the vegetable patch together with a group of cousins and local friends. Uncle Bruno was the most enthusiastic footballing family member and he worked hard to teach them the basics of the game.
And still in Galicia, several years later, during summer holidays on the beach at Estorde, he would spend his days playing never-ending matches. 'Mini-World Cups' with everyone against each other. He gets stronger. 'He was fast, agile, versatile, with very sharp changes of pace. You didn't see great displays of quality but strength and power, yes. When he played, he had a special touch and in the sand he ran like a madman,' remembers Ramón Marcote.
At five years old, he enters his first team, Parque (Park) 84. Parque is the name of the neighbourhood and 84 the year of birth for the boys playing in the team. The shirt is red and the event is the footballing marathon that takes place at the Polideportivo (sports centre) in Fuenlabrada. It is a local trophy but a real occasion for any child. Amongst the spectators are parents, friends, colleagues and schoolmates. No one is bothered that the matches take the form of piles of kids – around fifteen to twenty – all kicking the ball in whatever way they could. They have a good time and they get to feel like real soccer stars and no one minds that the team has been put together just for the event. Two days later and they all go back to playing how they'd always played.
That is, until the people from Cafetería Mario in Holanda Street decide to organise a team that will be called Mario's Holanda.
'An adult team was already in existence when we decided to create one for the youngsters. At that time in Fuenlabrada, there were a lot of young parents with lads who were really into sport. These families were a bit concerned about street crime, drug-taking and their kids getting into bad company, so we tried to get them together and keep them busy with football,' recalls Juan Gómez, now aged 55, one of the founders of that team and the coach for Torres and his mates. Today he works in the Real Casa de la Moneda (the Royal Mint).
One Friday afternoon, in the Fuenlabrada sports shop called Camacho, just 100 metres from where Fernando used to live, the ex-trainer has time to sit down with his son, Alexis, the captain of Mario's Holanda, and winger Javier Camacho, amongst the rackets, trainers, balls, bathing costumes and shirts of Real Madrid, Atlético, the Spanish national team and Liverpool. He remembers the time when the Reds' Number 9 used to run around on hard cement surfaces.
'They were a pretty good group of kids,' says Juan. 'We saw Fernando play and we thought this lad ought to be in our team. Why? Because at eight years old he had the same skills that he has now – speed and technique. Training didn't bother him but, more importantly, he never got tired of learning. I had to teach him everything from the throw-in to what it means to play in a team. We had to tell him that football is a game and that was how he should approach it. But right from that moment, I was convinced that Fernando would go far. I always said that to his father, a delightful person – like his brother and the rest of the family. They didn't believe me. Once, after a game in which he scored eight goals, I said it again and José was almost in tears. But I was absolutely sure.'
As you look at the photo of the Mario's Holanda team for the 1992–93 season, Javier Camacho, the son of the shop owner, is standing to the right of Fernando. He has a serious expression with his mouth half-open in the team's green, white and black shirt, and is looking directly at the camera. Sixteen years later, apart from a slight beard, Javier hasn't changed much. Nor has Fernando. El Niño's birthday is in March and his in July. Javier is studying in Madrid to be a surveyor but still loves playing football for the fun of it, for the team of La Moraleja De Enmedio, a village about 18 miles from Madrid, in the Segunda Regional (Second Regional) division (the leagues below the Spanish third division). And like Torres, he is a striker. He remembers well that photo, taken all those years ago at the Colegio Publico Andrés Manjón school. Without hesitation, from left to right, he reels off the names of his then team-mates:
'Juan the coach, Rubén the goalkeeper, Alexis, Fernando and I, then the really tall one in the green tracksuit, Israel – the brother of Fernando who always came to watch us and sometimes, when Juan Gómez wasn't there, would act as coach, along with Ivan, the brother of Alexis. Squatting down in front are Alejandro, Dani, Rici, Rocha and Alvarito.'
He describes Fernando at eight years old: 'Physically very thin, very blond, with loads of freckles. He looked English. As a person he was the typical leader, the leader of the gang, very mischievous and very shy.' How is it possible to be shy and a leader? 'Amongst us, he was the extrovert, he ruled the roost, he spoke for everyone else. In the park, when we all ran off because some neighbour got angry and shouted at us, he stayed behind to argue and defend our right to play there. But with people he didn't know, he put his head down and said nothing. Apart from with the girls, of course. He really had an eye for them. You'd always see him with one from school or from the local area. To be blond and have the air of a leader, the girls really liked that.' And being mischievous? 'For Fernán, like all of us in the gang – we were some twenty-odd kids with three or four years age difference between us – we liked to play jokes such as ringing the door entry phone bells on houses in the neighbourhood and then running away. Typical pranks like that.'
### _And football-wise?_
'He was the same as he is now – a star. He was playing Number 9 and he had the ability to go past the opposition and score loads of goals in every game. When things weren't going well and we couldn't score, we'd give him the ball to sort things out. I remember once, against Colegio Valle Inclán (school), we won 24-0 with him scoring eleven on his own. Juan wanted to substitute him to give some of the others a chance but he wouldn't have any of it. He wanted to keep going and pile on the goals. That's what he liked doing.'
### _Juan takes up the story:_
'It's true to say that if he was taken off then he would be really angry. 'I'm taking you off for being a bully,' I told him, 'you've got eleven goals. That's enough.' Treating it as a joke like that, it worked. I remember him once leaving the field crying uncontrollable tears of happiness. And what was the problem? He'd wanted to come off because he hadn't been able to get a goal and the score was 0-0. He'd tried everything but it just wasn't possible. He was beside himself. It was the only time he asked me to substitute him. I told him to stay on and in the end he scored. In the 1992– 93 season, Fernando got no less than 80 goals and during the three years he was with Mario's Holanda, we won all our league games. We were champions in everything. And everywhere we were followed by loads of people – fathers, mothers, brothers, friends. We were one big family.'
### _Javier elaborates:_
'To tell the truth, we did in fact have two defeats but they were friendlies. The first was at Navalcarnero, just before the start of the league season and the other against a group of girls – who were bigger than our lot. They gave us a real hiding and we left the pitch in complete silence, with our pride wounded. It was the first time we'd played in a closed sports hall on a wooden parquet surface. We were used to cement. Just about all the school indoor football pitches in our area were cement. We weren't a school team though and we didn't have anywhere to train either, so we used what everyone here calls the Plaza Blanca (White Square), a hard area above a car park where, every time there was a match, we had to find something that we could use for a goal. Or sometimes we used the playing area of the Colegio Francisco de Quevedo, which was Fernando's school. We used to train one or two days a week with a match on the Saturday morning. Afterwards, all of us went to the cafetería and they invited us for Coca-Cola and crisps. We ended up throwing everything around and then we ran outside to play football again in the Parque Granada.'
### _So there was a lot of football at that time, then?_
'Absolutely', continues Javier. 'There was no Playstation, Nintendo, consoles, or video games – or 1,001 TV channels. So in the evening, after homework, we went outside, together with our nocilla (a hazlenut and chocolate spread) sandwich. We would sit in front of the local chemist and decide what to do – football, bottle tops, spinning tops, picture cards and marbles were our favourites. We played football in every possible space – in the Plaza Blanca, the street behind the school and between one building and another where there was a bit of actual grass. Imagine that – what a luxury! Although one should point out that the two bits of garden were separated by a cement kerb, but that didn't bother us. We used to jump over it just for the pleasure of stepping on the grass. The only two problems were Mr Miguel and the security guard. They were nightmares for us because one of the goals was just below Mr Miguel's window. He was a bit of a strong character and we were scared of him. After we'd fired off a few shots he would appear at the window and begin to shout. We got frightened and used to run off. Our other dread was the security guard who used to patrol the zone, checking everything was in order. We were scared of him as well because it was forbidden to tread on the grass and if he caught us, he would take the ball off us. So if someone warned us he was coming, we would just pretend to be sitting around, twiddling our thumbs and keep the ball hidden.
'I don't know how many times we managed to avoid getting caught by the caretaker at the Colegio Tierno Galván school. In the evening, when no one was around, we used to jump over the fence to play on the indoor football surface. Then they put up a higher fence but we still managed to get over until one of us got stuck there. Even in the swimming pool there was a bit of grass and, secretly, we would take a few small balls in until the people who were sunbathing there started to complain.'
### _Alexis continues:_
'Football was our obsession. One thing we really enjoyed was taking corners. We would do a throw-in from an imaginary corner flag and either shoot or head-in. Then there was the 'German goal', which you scored after keeping the ball in the air without letting it touch the ground. The winner would be the first to score 10 and for that game there was no punishment, which was not the case with 'the bottom'...
### _The bottom?_
'We all had to endure it from time to time. You have the ball in the air and whoever is the first to let it touch the ground has to get on top of one of the goalposts – the goal could be a bench, for example. You then have to show your bottom while the others would shoot at you from the penalty spot, trying to hit you on the er, well, you know, on the bum...'
### _Haven't you forgotten about the bottle tops and the picture cards?_
'You're right. Those were the other things we were crazy about at that time,' said Javier. 'Yes, the little squares in-between one building and another – today they're cement but before that there was earth. And it's there that we set up our 'stadiums' and 'cycle tracks' with Coca-Cola and beer bottle tops, which we got from the bars. We put the club colours and the player's face on them, a plastic stopper for the goalkeeper and a chickpea for the ball. In summer we changed from football to cycling, this time with bottle tops in the colours of Banesto or Kelme and faces of cyclists like Indurain. I remember that Fernando used to love playing with the bottle tops. He was good with them, while the marbles weren't really his thing. And then there were the picture cards. At the beginning of the season, everyone went out to play with their wad of cards. When someone completed an album he could go up to the 'castle' – a place we'd built – or the window of his house and throw down the duplicate cards for the others below who would go crazy to grab them.'
### _Which team did Fernando support?_
'At that time,' continues Javier, 'he wasn't supporting any team in particular, although he clearly loved playing football. It was only later, when he was at Atlético that he really began to follow their colours. He went to the Calderón as a ball boy while I, who'd always been a colchonero (fan of Atlético Madrid) and a milanista (fan of AC Milan), went to see the matches. Afterwards, we'd talk about the new songs, chants and dances they'd made up that Sunday. In fact, a nice little story comes to mind about Fernando when he was a player with the Atlético junior team. You should know that 14 September is the day of the fiesta of Fuenlabrada, in honour of the Cristo de la Misericordia, with celebrations going on the whole week. There are concerts, dances and around 24 hours of football, from nine in the morning to eleven at night, featuring mini-leagues, knockout games and finals in all categories. When we were small, our team always took part and we always won. This particular year, Fernán was already at the junior level with Atlético, which obviously meant that they wouldn't let him play in neighbourhood tournaments like ours. But we needed him. We had to win a match in order to get to the final. So we went to get him. He came out with a photocopy of his DNI (national identity card) and signed up. There was someone who really didn't like him and called us cheats but thanks to him, we won the match and the tournament. It was the last time he played with us.'
### _Gómez senior explains:_
'Torres left, while most of the local lads didn't want to go off and carried on playing as amateurs and fans of the game. It's true that various good players like Fernando Sánchez and Fernando Burgos came out of Fuenlabrada but the majority, like Israel for example, just wanted to do it for fun and stayed here or, like my son, didn't have the determination or the will to make the effort. Training didn't bother Fernando, for example. He would come out on his own with the ball under his arm. In the case of Alexis, someone had to take the ball. Torres had all the determination in the world and he wanted to get on the ladder.'
So, for the 1994–95 season, he went to AD (Asociación Deportiva) Rayo 13. The rayo (ray) was the symbol of the club, founded in 1992, and 13 was the number of the street for the team headquarters. The diagonal yellow ray was emblazoned into the badge of the club shirt, which featured vertical blue and black vertical stripes like those of Inter Milan.
'Four of us went from Mario's Holanda to Rayo: Fernán, Alejandro, Rici and me,' says Alexis. 'The change from indoor football to a team of eleven suited Torres very well, because on the bigger pitch he could make better use of his speed and his shooting skills. Fernando was already a "killer", a real assassin in the penalty area. Myself, I'd gone from left wing in indoor football to midfielder in 11-a-side. I searched him out, gave him the balls and he took his fill of goals. It was incredible – if I'm not mistaken his tally was around 55 or 60. We won the league, pretty much without a problem. I only remember one match where we had to make a real effort, against Naranjo. We were losing 2-0 but Fernando arrived and made it 2-1 and then scored again to make it a draw. Amazing.'
That's the opinion of his friend and team-mate. But what's the view of the Rayo 13 coach, Andrés Perales? Now 54, his enthusiasm for the game is as great as ever and he continues to teach young boys the art of football.
'He was a marvel and very kind-hearted but in the first few sessions it was really complicated to work with the lad. He was annoyed with his team-mates because they didn't pass the ball to him. He always wanted the ball, he always wanted to score. And he did it in every way possible, from midfield, or by outwitting the opposing players in front of him. He had quality and he was smart. Once or twice he really lost it, like with 'El Chino' ('The Chinese'), a left-footed winger, a nice lad. They got entangled and I had to go and sort them out. El Chino went home while Torres stayed. With me, there were never any problems. I was pretty strict and asked for respect and hard work from the whole team. I made him play on the right wing and then as striker.
'Anecdotes? Loads... like the time in Leganés when we were losing 3-0, he and one of the wingers, David, gave the runaround to his marker. We won 4-3, which put us in the final. Yes, Torres was a footballing machine. But I never thought he would get so far.'
But Torres did get far. And very far. What do his ex-team-mates think of him now?
'He's realised the dream we all had,' says Alexis, 'all those kids kicking a ball around the neighbourhood. We grew up together and now he's the striker who scored the goal for Spain in the final of Euro 2008. It's a pleasure to have played with him and to have him as your friend.'
The long chat is over and the train for central Madrid is leaving shortly from Fuenlabrada Central. Javier walks through the local streets to the station, pointing out the places of his childhood: the small squares, Mr Miguel's window, and the fence they jumped over. Just in front of the Mario's Holanda cafetería, which has been closed for some time, is Rubén, the goalkeeper from that team. He also continues playing football as an amateur. He starts to talk about matches, results, and coaches who were changed too quickly... and football in the _Segunda Regional_.
## Chapter 7
**A born winner**
'How much do we give this lad?'
'This little freckled one with the blond hair
gets 10 plus one... an 11'
The conversation takes place in June, 1995, in the Ernesto Cotorruelo sports facility in the Carabanchel district of Madrid. The protagonists: Manolo Briñas and Manolo Rangel. One is the deputy director of Atlético Madrid football school and the other is one of its coaches.
The two find themselves, one summer morning, on three hard, bare playing surfaces, lost in the middle of a huge boulevard full of cars and in front of a row of sad-looking buildings. They have to select some youngsters to form part of the junior team, which will take part that August in an international tournament at Bierbeek, in the Brabant province of Belgium, a few miles from Leuven. Briñas holds the notebook, Rangel gives the points. He gives a score for each of the would-be footballers from one to ten but when that freckled one with the blond hair appears in front of them, the guidelines disappear.
'After five minutes,' recalls Antonio Seseña, today aged 66 and retired but then director of the Atlético Madrid junior players, 'we told him, 'Go and get dressed, lad.' He looked surprised, he wanted to keep on playing, he thought he was no good, that he'd failed. He asked me, 'Am I doing something wrong?' On the contrary, he had completely won us over. We saw an intelligent lad, who moved well on the pitch, had pace and good technique as well, qualities which, at that age, really stand out.'
'Yes, Fernando Torres at eleven was a very smart kid – fast, able to lose his marker and beat his opponent. Without having participated too much in the action, I realised that he was doing everything fantastically well. And above all, he seemed to me like a kid who wanted to be a footballer,' explains Manolo Rangel, aged 55, who worked with the Atlético junior teams for twelve years.
In that June of 1995, Fernando had already passed the first selection test to enter the ranks of Atlético. Like lots of other kids of his age, he had gone to the Vicente Calderón stadium, filled in the registration forms, and had been invited – along with 200 others – to go to the ground in the Tres Cruces park between Aluche and Carabanchel. An 11-a-side match to sort out what each of them was able to do, then after that another 22 kids and so on. 'Victor Peligros, Antonio Arganda and I were there that day,' recalls Briñas in his office at the Calderón. Behind him, and framed in a glass-fronted case, is one of Fernando's shirts. It's the one he was wearing on 23 February 2008, when he got a hattrick at Middlesborough. Alongside is a photo of an ecstatic El Niño, having just scored a goal for the Reds, and on it is written in felt-tip pen: 'For my great friend, Manolo Briñas, a heartfelt embrace in return for all the affection that you have shown and continue to show for me, Fernando Torres.' On re-reading this dedication, 77-year-old Briñas is visibly moved and points to the walls covered with cuttings describing Fernando and all the other youngsters from the Atlético junior teams who have ended up in the top division. The only exception is the Uraguayan Diego Forlán (formerly of Villarreal and Manchester United), whose impressive tally of 32 league goals last season was a huge factor in taking Atlético into the Champions League for the second year running, as well as earning him the Spanish _Pichichi_ trophy and the European Golden Boot for the player with the highest number of league goals in Spain and Europe respectively.
After this diversion, the veteran coach continues with the story of that team in the Tres Cruces park: 'From those 200 youngsters, we had to choose 40. If I remember rightly, Fernando scored four goals but the coaches didn't choose him for that. Apart from the goals, he was marked positively for his involvement in the game and for his unselfish attitude.'
In the official test notes for that day, in strict alphabetical order, one can read, alongside the name Fernando José Torres Sanz: 'Suitable (to be seen in our teams). He will be sent instructions.' To be more precise, he would go to the Cotorruelo ground, where Manolo Rangel, some time later, would give him the mark of eleven.
But why did Fernando end up taking his chances with Atlético and not Real Madrid, the city's 'first' team? It was all down to Eulalio Sanz, Fernando's maternal grandfather.
By way of a short preamble, the Torres family was not very football-oriented. It was not one of those Spanish families glued to the radio listening to live match commentaries, nor was it one of those where, when there was a big match, all the relatives and friends joined together to experience the event on television. The passion for football and particular clubs in the Torres household was pretty lukewarm. There was certainly a fondness for Deportivo La Coruña because of the father's family origins. But nothing special. The real fan was his grandfather. A lifelong _rojiblanco_ (supporter of Atlético Madrid).
In the sitting room of Elulalio and Paz in Valdeavero, there was an impressive-looking ceramic plate with the Atlético badge. It was an object that fascinated Fernando. He could remember it from when he was two or three years old. At that time he knew nothing about football matches or clubs, but his grandfather – thanks to that plate – began his 'sentimental education'. Each time the small Torres went to look at it, he repeated to him: 'When you're grown-up, you must be with Atlético.' And with the passing of the years, he began to explain the club's ideals and values. He began to explain that Real Madrid was everyone's team, the one that always won, while Atléti was the other side of the coin, where defeats had to be suffered and where being a fan required real effort.
The seed of support took hold and grew. When he was nine, Fernando's father took him to the Vicente Calderón museum, where they keep the trophies, cups, old photographs, footballs, badges and pennants – a trip that left the youngster in awe. Some years later it will be Manolo Briñas who explains to Fernando, one-to-one, the symbols and the 106-year-old history of a club founded in April 1903, which boasts nine league titles, and which, historically, comes to be considered Spain's third-best team in terms of trophies and supporters, behind Real Madrid and Barcelona. So when Fernando qualifies to join Atlético, he's hardly got home and in through the door before he's on the phone to his grandfather to tell him the great news. A grandfather who will have the greatest satisfaction, before his death on 23 February 2003, to see Fernando in the shirt of his beloved team, playing in the Vicente Calderón.
But going back to the summer of 1995 and to the first impressions of Briñas, the person who began to train him:
'Fernando was an open, amusing, happy and very responsible lad who gave everything. He wasn't the typical joker who took his attitude into the matches. He already had his head well screwed-on. And all that was due to his parents, who told him, "enjoy yourself at football but study". And he followed that to the letter. I remember once, when I went to meet him at Atocha station, he was coming back from winning a tournament. He got off the train, he had a copy of _Marca_ in his hand, where it was talking about him. I thought that he would want to show it to me but no – under the newspaper he had his end-of-term reports. He proudly showed them to me, "Look Manolo, I've passed in all subjects. And I've got quite a few top grades." Yes, very often parents think they have a Maradona, they think their son can score the second goal before the first but life isn't like that. To get there, you have to make sacrifices, not leave school and move forward bit-by-bit.'
And to explain how Torres was, he remembers the away match in Belgium: 'At dinner, in the hotel, they served a vegetable soup and lots of the lads put their plates to one side without touching it, saying they found it nauseating, so much so that Rangel shouted 'You don't play if you haven't eaten everything.' It wasn't necessary to say it to Fernando. He ate anything.'
Bierbeek – the first away match, the first foreign trip, the hotel, the team-mates, the first team base, the first international tournament. A lot of excitement for Fernando in those days of August 1995. Around 30 different teams are taking part in the tournament, including Ajax, Anderlecht, Werder Bremen and Bayern Munich – clubs that boast a long tradition of bringing through new talent. Atlético, on the other hand, has only just set up its junior teams. Manolo Rangel is worried about making a bad impression because his lads don't know each other well. They haven't even had time to train together. So, in-between matches, he gives them sessions with the ball and while walking round the hotel grounds, tries to explain how they should position themselves on the pitch.
During one of these sessions, he realises that 'one of them, I think it was Fernando, had kicked a stone and unfortunately it broke a window in someone's house. The owner came out shouting and protesting, with us not being able to understand what he was saying. We went through some difficult moments before someone from the organisation came and sorted things out.' A stone that stayed in the memories of the coach and the youngsters. And it may actually have helped to unite the team because, in spite of the improvisation, they finish in sixth place. 'Fernando stood out quite well and there were a lot of positive comments about him,' adds Rangel.
It was then 1995–96, the first season in the red-and-white shirt. An important season for the club, which won a league and cup (Copa del Rey) double for the first time in its history. It broke the dominance of Real Madrid and Barcelona. A success for the team managed by Radomir Antic, whose leading players included Kiko, Pantic, Caminero and Simeone. A double that reinforced the emotional ties between Torres and Atléti. And the pride of wearing the shirt of the Spanish champions.
Fernando was doing his part in the junior divisions. He gets 67 goals and is top-scorer, the sporting leader of the team and the focal point of the group. His skills are showcased in the _Torneo de Brunete_ (the Brunete Tournament), a competition in which about twenty junior teams from clubs in the Spanish first division take part and where many young Spanish champions make their early mark. The youngster is fascinated by the atmosphere, the terraces at the Estadio Los Arcos, the television cameras filming the matches, the fans and the watchful eye of the observers and trainers at the games. He scores a succession of quick-fire goals, one after the other, and runs to tell his grandfather.
The following year, the shots of him used by regional television channel, _Telemadrid_ , always show him at Brunete on the pitch against Milan, tall and thin, with his blond bob haircut and the Number 9 on his back. Fernando puts away penalties that the keeper can't get hold of, dribbles past opponents even with a backheel and scores to make it 3-0 and then 4-0 in a perfect counter-attacking move going round the onrushing keeper.
'Fernando was a born winner. He also wanted to win in training. I was 39, I had to quit playing football but I was in good enough condition to run with them,' remembers Rangel, 'I enjoyed making bets with him regarding a game, penalties, or who would score the most goals from a free-kick. And Fernando was really competitive. At the end of training, he would be waiting with his sports bag to inform me, 'Coach, you owe me a Coca-Cola for what I've won from you.' He was very bright, very smart.'
And Rangel is keen to stress, like Briñas, the importance of grandfather Torres Sanz: 'A fantastic family, very close and well-balanced, which helped him enormously to be a footballer.' His parents, José and Flori, his brother Israel and Mari Paz, his sister, help him in every way. On many occasions, his father has to get permission from work to take him from Fuenlabrada to Orcasitas, where he trains. His mother waits for him in front of the school gates in the wind and the rain, goes with him on the bus or on the train to the ground, and waits for the training to end to bring him back home. And without ever insisting or demanding that he become a professional. On the contrary, she tells him many times that 'if you are tired or you don't want to play, tell me and we won't go again'. His brother and sister also assume their responsibilities for the 15-kilometre (about 10 miles) daily trip. They have to study and do their homework sitting on the terraces at the ground. Years divided between school and training, with matches at the weekend. The best thing is when Fernando joins Atlético's residential Colegio Amanecer school, just outside the centre of Madrid where, today, around 30 youngsters between the ages of fifteen and eighteen study up to the Spanish equivalent of A-levels. 'Fernando was a student who knew how to combine books with the ball,' recalls school coordinator Rafael Bravo. 'His parents wrote us a very emotive letter when Fernando got his _Bachillerato_ (equivalent to A-levels).'
A good student and an excellent footballer, so much so that he regularly ends up being the youngest in each of his Atlético junior teams. He plays with youngsters who are one, two or even three years older than him. It is a way of growing up more quickly and a way of learning more rapidly the rules of football because the older ones are stronger technically and physically and better-prepared mentally. Fernando works his way up through the junior ranks. Manolo Rangel is his teacher for three seasons.
Then it is Pedro Calvo's turn to take charge of him for a year. Fernando is fourteen. How was he? 'His manner and professionalism were the same as they are now,' explains 40-year-old Calvo, enjoying a cafe _latte_ in a central Madrid bar. 'He was already the team captain but the responsibilities didn't weigh him down. You would tell him that we eat at two o'clock and that everyone should come properly turned out. And ten minutes before time, he would be there with his team-mates, all properly dressed. He was always thinking about the group. He was very humble and he didn't like too much praise. He didn't get nervous, a normal thing at that age. He didn't get angry. I remember that once I blamed him for the behaviour of the team and, instead of giving me a dirty look, he thought the problem over and it never went further than the dressing room. In a footballing sense he was the same as now: rapid, sharp, skilled, very calm in front of goal and, above all, a sponge – he liked to learn.'
Calvo had in his care a line-up that, apart from Torres, could boast players like Manu Del Moral, now at Getafe, Francisco Molinero, today at Real Mallorca, Fernando Usero, now at Elche, and Sergio Torrers who will later win the Under-16 European championship with Fernando. Elements that made for a great season. The key moment is the Nike Under-14 World Club Cup, which took place in May 1999 in Reggio Emilia, Italy. The Atlético Cadete junior team has won the right to play in the prestigious European tournament after first coming through a national competition. The participants are: Real Madrid, Roma, Reggiana (Italy), Belenenses (Portugal), LASK (Austria), Amiens (France), LASK (Austria), Amiens (France), Mouscron (Belgium), B 93 (Denmark) St Joseph's Boys (Ireland), Servette (Switzerland), Symonds Green (England), KFUM Oslo (Norway), Etzella (Luxembourg), PSV (Netherlands), Hammarby (Sweden), Inter Turku (Finland), Borussia Dortmund (Germany), Heart of Midlothian (Scotland).
Before the final phase, they take part in a four-sided event with Porto, PSV and Andorra. 'Against our near-neighbours, Andorra, we won 11-1 but we played poorly, without commitment, without bite,' remembers Calvo. 'So everyone, and Fernando in particular, was read the riot act before the final against PSV. They were told that this would not do and that they had to do better. He went out onto the pitch really wanting to show me that he didn't merit what I'd said. So in one of the first moves, he swerved past five opponents, then went round the keeper, stopped the ball on the goal line, looked over to the dugout and blasted a shot into the goal.'
In the quarter-finals at the Reggio Emilia tournament, the Atlético youngsters once again come up against PSV. The Dutch are dismissed with a decisive 3-0 scoreline. And Fernando repeated the same trick – in the first move of the match, he gets past three opponents, nutmegs the fourth and lobs the keeper to put them in the lead. The semi-final sees them up against Real Madrid, a Spanish city derby in Italy. A difficult contest against the title-holders, who had disposed of Borussia Dortmund in the quarter-finals. The 2-0 final scoreline leaves no doubts, however, as to the title pretensions of Atlético, who will now meet host side Reggiana in the final. Molinero scored in the eighth minute and it stays at 1-0 until the final whistle. It is the first important title – the first European Cup – that Fernando, the captain, holds aloft.
He is chosen as the best player of the tournament, a recognition that, together with his goals and his movement off the ball, attracts the attention of several European clubs. 'Arsenal made an offer to Fernando's father and Barcelona and Milan were also keen. So much so that the club decided to offer him his first professional contract,' explains Calvo. At fifteen years of age, Torres signs the contract. It's not worth as much as Arsenal were offering but he's happy. He is playing for the team he loves. Football, for him, begins to be more than just a hobby, even if he does not yet realise that it will be his life and his profession. That is still some years ahead.
Meanwhile, he moves up from the _Cadete_ team to the _Juvenil_ – another way of saying he jumped three years in one go. He meets Abraham García – the last coach he would have in the junior teams and a key figure in his career development – and Ignacio Aznar Torrente, better known as 'Nacho', with whom he formed an attacking strike duo. 'We understood each other well. We knew, without speaking, where the other was on the pitch at any given moment,' recalls Aznar, who today plays at Club Deportivos Leganés in Group II of the Spanish Second Division B. 'Fer was a model of power, ability to score with headers, movement and finishing in front of goal. We became a pair capable of scoring 70 goals a season. Abraham demanded a lot from us. He pushed us, him and me. He was never satisfied. He knew that Fernando and I could go further.'
One match that Nacho has not forgotten is the final of the international tournament, Citta di Rieti, in May 2000. Fernando says one of his legs is hurting but García knows that his presence on the pitch is important. 'Get out there and win this final. If not, you're not going to get anywhere,' he tells them. Fernando plays and scores the goal that sets them on their way. Lazio are swept aside 5-0 and Atlético win another prestigious trophy – as well as the junior league championship a few months later. But the young striker in red and white is then hit by a setback. It happens on 9 August at Boadilla, while training with a team made up of players from the Spanish third division. Fernando clashes with a central defender and collapses. Damaged knee ligaments is the grim verdict. A really bad-looking injury. After the operation, the doctors say it will be eight to 10 months before he can play again. Team-mate José Verdú Toché (now with Numancia), who suffers the same injury at the same time, returns to football eleven months later, in May 2001. Fernando Torres, on the other hand, thanks to his determination and exceptional physical condition, is already back on the pitch in December 2000.
The year to come will bring a huge amount of satisfaction as well as a major disappointment.
## Chapter 8
**A model footballer**
_Conversation with Atlético de Madrid junior team coach, Abraham García_
There is more activity than usual at the Ciudad Deportiva de Majadahonda (Majadahonda Sports City) in Cerro del Espino, about twelve miles from Madrid city centre. Abel Resino, the new manager of Atlético Madrid (who replaced the Mexican, Javier Aguirre), is directing his first training session. Television crews, zoom lenses and all eyes are focused on the playing area, where the first team is being put through its paces. Journalists are commentating and taking notes on the team set-up, while fans and curious bystanders watch with interest. They are trying to work out what the ex-Atlético goalkeeper (whose European tally for clean sheets – 1,275 minutes set in 1990–91 – was beaten earlier this year by Manchester United's Edwin Van de Sar) is telling his new players.
Everyone has their back turned to the green rectangle where Atlético B is training or, to be more precise, where the junior team – made up of seventeen- to eighteen-year-olds – is playing a match. Green bibs against red vests. On the edge of the pitch is the manager, Abraham García, arms folded across his chest, watching how his charges are developing. Every now and then, he shouts an instruction to Cedric, a young midfielder born in Kinshasa, or to striker Didí, who is from Barcelona. Ten minutes after the training is over, the youngsters all pile out. Abraham comes over to the boundary fence and arranges to meet at the dressing room exit. First, there is the customary banter with his young players and then a shower to freshen up and get warm again. Despite the spring sky, it is still cold at Cerro del Espino.
For 35-year-old Abraham, built more like a rugby prop forward than a midfielder, football runs in the family. His father, 'Juanjo' García, who died a few years ago, was manager of Castilla, Real Madrid's second team and took the side to a Copa del Rey (King's Cup) final against the Real Madrid first team. For the last eleven years he has trained junior teams, first at Atlético, then three years at Real Madrid, and is now back at the home of the red-and-white stripes. Fernando Torres always speaks of him as the most important manager of his career. Why? Abraham, who is now out of his training tracksuit and sitting at a café in front of the Ciudad Deportiva with a large glass of Coca-Cola in front of him, begins to explain: 'Fernando is very generous and recognises the work of a manager and the effort he puts in. Our relationship, which lasted two years, was more of a professional than a personal one. When I look at the great managers that he's had during his career, for him to remember me like this gives me a lot of pride and satisfaction.'
### _When did you begin to work with him?_
'Fernando was fifteen and had just won the Nike International Cup in Reggio Emilia, Italy, where he was top scorer and been voted the player of the tournament. He was with me until 2001, when he made his debut with the first team.'
### _How was Fernando at fifteen?_
'A player with a tremendous build, which comes from his family (his older brother, Israel, was 6ft 3ins when he was fifteen). He had the muscles of a sprinter, was fast, skilful, smart, hungry for victory and always wanting to get better. He was very professional, self-critical and never 100 per cent happy with how he was playing. He put the bar high. He had a strong personality. On a mental level, to me he always resembled Raúl for his strength of spirit. For his importance as a footballer, I would compare him to Van Basten with his elegant style of running and capacity for scoring goals. From when he was small, he was always thinking of the goal, of scoring.'
### _And off the field, how did he behave?_
'He wasn't a docile lad. Dealing with him, sometimes, was tricky. He was quite shy and would mind his own business. From when he was a small boy, he was sheltered by his family, which knew how to keep him on the straight and narrow. I remember his father or mother always brought him to training sessions and I never saw them brag about the lad. His personality and his environment have absolutely been key to Fernando's success.'
### _Abraham paused a moment before reflecting on his work..._
'In all the years that I've been training youngsters – and I've worked with more than 300 – only about fifteen or twenty have gone on to be professional footballers. Talent is inborn, each one (of them) has it, but to reach the top level – that's something else. You must stick to your guns. You've got to have your feet on the ground, to know what's really important in life, to earn yourself a place in the team, to fight for a position and to overcome enormous difficulties, particularly psychological ones. To put it simply, you not only have to have the gift of being able to control a football – your mentality, desire and determination counts for a hell of a lot as well. This is the most important thing that I've tried to instil into my players, apart from obviously giving them a training in those technical skills that could be useful to them in the future.'
### _What exactly did you teach Fernando?_
'All I did was try to tell him some things that, at a sporting and human level, could help him deal with whatever might come his way. I told him to be what he's always been _,_ an ambitious young guy who'd be able to sort out the shortcomings he had, as everyone has, and in the end his desire to do things well would overcome any criticism or difficult moments. Then, more as a joke than anything else, I told him not to worry, that if one day the football didn't work out, with his looks and general appearance, he could always earn a living in the world of fashion. And now look where he is, a star player as well as being a model in loads of advertising campaigns.'
### _What are your best memories of Fernando at that time?_
'Without doubt, a fantastic goal he scored in the league against Rayo Vallecano. He got hold of the ball in the middle of the pitch, he went past one, two, three, dribbling his way through the opposition midfield leaving them rooted to the spot and then scoring an amazing goal. And then after that, how can you forget the trophies we won with that team? For example, the league title, which we snatched from Real Madrid. A pity about the Cup though, Fernando was a member of the Spanish national side that had just won the European Under-16 Championship and he didn't want to miss the Cup final against Osasuna. We lost 1-0. In any case, it was another example of the desire he had to be on the pitch and to help his team-mates win another title. He was the player everyone looked up to. He had charm and he made the difference.'
### _Talking of that, how did he get on with his team-mates?_
'Very well. Even though some of them were two or three years older than him, he was always competing at a higher age level. I remember a team dinner after winning the league. They were all grown-up by then and everyone wanted to go out on the town. I smiled to myself at Fernando, the youngest of them and his refusal to let himself be led astray. He was very responsible and knew how to behave – both at a party like that and in the dressing room. He didn't put on any airs. He was always talking about the team and encouraging the others. He was very humble but at the same time very mature for his age. He would listen when you explained something to him or commented on something he was doing wrong that he should improve.'
### _He didn't want to put on any airs but he was captain of Atlético at just eighteen years of age..._
That's true. But you have to remember when he joined the first team. He came on the scene at a time when the team wasn't doing well. He was a lad who came from the junior Spanish national side, which had won the Under-19 European Championship, who brought a breath of fresh air to the squad and who, in a few years, had transformed himself into the public face of the club.'
### _With all the criticism that brought with it..._
'They criticised him for the results, for the missed goals, for the side's bad run but also for his technique – his poor left leg, his lack of control and inability to lose his marker.'
### _And what does his former coach say now? Has he improved?_
'Now he plays much better off the ball, he knows how to lose his marker and when he gets going, he's unstoppable. He's a modern striker in the true meaning of the word. He's complete, fast, can apply pressure and is a good finisher. He can use both his legs and his head. He doesn't have the class of Van Basten, the technique of Ronaldo, or the elegance of Ibrahimovic, nor is he unbalanced like Messi, but he scores a lot of goals – and really good ones too. He works for the team and has a drive to be the best, which takes him where he has to be. He knew how to overcome his limitations using character and nerve.'
### _And the human side? Has that changed?_
'No. He's still the lad I knew here in Atlético. Last year, I met him in Liverpool, where I'd gone to see Rafa Benítez, and he was as warm and generous as he he'd always been. There was none of the 'I'm a star' who's forgotten his friends or a junior trainer like me.'
## Chapter 9
**The Torres generation**
'Vamos a quemar el pueblo.' ('We're going to paint the town red.') Wrapped in the Spanish flag, a seventeen-year-old youth is threatening to disturb the peace of Sunderland's 177,000 inhabitants. And team-mates, parents and Spanish fans are ready to join him. The youngster has just won the Under-16 European Championship, he is on a high and wants to party. It is the afternoon of 6 May 2001, and Fernando Torres is leaving the main gate at Sunderland's Stadium of Light, where Spain has beaten France in the final. There are celebrations everywhere, on the pitch, in the stands and in the dressing room. The youngsters are in a daze as they pass round the cup presented to them by UEFA President Lennart Johansson. They aren't sure what to do. One of them runs wildly round the pitch with a pirate-style headband, another uses the Spanish flag as a kind of cape in front of an imaginary bull, while several others leap over the edge of the pitch in tears to embrace mothers and fathers who have come for the occasion. Training staff, players, parents and friends join together to form a giant human fir cone. They all shout: _'_ Campeones!!! Campeones!!!' ('Champions!!! Champions!!!') over and over again until they're hoarse. Torres the goalscorer, still can't take in the fact that it is all really happening. He shouts: 'We are the champions!'
It's his first trophy with the national team, an adventure that began on 5 April 2000, in Badajoz (south-west Spain), when he wore the shirt of the Spanish Under-15 side. It was a friendly against Belgium, which they win 4-1, including Torres' first goal in the red of Spain. A knee injury had stopped him playing in the preliminary rounds of the tournament but on 24 February 2001, he took to the field with the Under-16s in the Algarve Tournament. The opponents were England, Finland and Portugal. Spain notched up two wins and a draw against the hosts with a four-goal booty for the lad from Atlético Madrid's junior team – the best score of the tournament. Not bad for someone coming back from an important injury, which had put into doubt his future career. It was the test that Under-16 coach, Juan Santisteban, and Iñaki Sáez, the coordinator of all the junior sides, had needed. Soon afterwards came the naming of the national side for the European championship, which would take place in England from April to May.
Durham is the team's base, where the youngsters lead a cloistered existence: training followed by a siesta from 3.30 to 6pm, homework with private teachers (because when many of them get back to Spain, they will have to take school exams) followed by more study and videos, this time of their next tournament opponents – a strict regime. Spain is placed in Group A, which journalists and commentators name the 'group of death', with Romania, Belgium and Germany the teams they have to beat to get to the quarter-finals. The aim is to repeat the performance that saw them win the title in 1999. The first match is on 24 April against Romania and the result is 3-0 to Spain with Torres, wearing Number 14, scoring his first goal on English soil. Who knows, maybe a premonition of what would happen six years and a few months later...
After this game, the side is top of the group on goal difference. They play their next match against Belgium who, surprisingly, have beaten the Germans 2-1. It finishes as few were expecting, with a 5-0 scoreline in favour of Spain, including a double from El Niño, although no one yet calls him that. The last group game against Germany is to be played at Durham. For the boys in red, a victory or draw would see them through, although even a defeat would be enough because they have a three-point lead over their German rivals. The result is a bad 0-2 defeat but it's enough for them to progress. However, Santisteban's youngsters lose playmaker Andrés Iniesta through injury.
The quarter-finals are against the Italian side of Paolo Berrettini. It's a difficult encounter against an experienced team with good players like Giampaolo Pazzini (today a leading goal-scorer with Sampdoria), Alberto Aquilani (now in the Roma midfield) and Giorgio Chiellini (a defender with Juventus). In the 26th minute, a Torres penalty gives Spain the lead, but on 54 minutes Mauro Bellotti heads in an Italy free-kick. The scoreline is still the same at full-time and qualification for the semis will be decided from the penalty-spot. Juan Santisteban can't bear to watch this Russian roulette and takes refuge in the dugout. But the Spaniards are unforgiving. Fernando Torres, Senel, Carlos and Melli all score, while the Italians slip up. Their first hits the post and the fourth is saved by Miguel Ángel Moya. This time luck goes their way, unlike on the previous five occasions. Santisteban is finally able to open his eyes and runs to embrace his team. It's a story that will be repeated in another European tournament, the big one, that of 2008. A coincidence, of course...
The last hurdle before the final is Croatia, a match that takes place in Middlesborough on 3 May. Torres opens and closes the scoring (with a goal from Senel in-between) and even allows himself the luxury of a chip from the edge of the area, in very little space, which crashes against the angle of crossbar and post. 'We had a great second half, really impressive. We got ourselves to 3-0 and after that we just kept on moving it around, playing football, which is what we like,' explains the lad from Fuenlabrada.
France, the overwhelming favourites, are waiting in the final, having scored a tournament tally of seventeen without conceding any – a track record of impressive proportions. In order of matches played, they had dispatched Scotland (3-0), Croatia (3-0), Finland (5-0), Russia (2-0) and England (4-0) in the semi-final. 'They're a footballing machine but we will try to give them a game,' says Santisteban. Much more optimistic is Fernando: 'Of course they are an amazing team but if we get on with playing football, we will win.' In their Durham base the day before the match, they follow a similar routine to that of previous days, apart from the presence of the senior national team coach, José Antonio Camacho. Then lunch, siesta, homework with a private teacher and, before going to bed, videos for everyone. The France-England game makes the youngsters realise that _Les Bleus_ are a tough, physical, tactical and technical outfit. The game proves it. In the second minute, in front of the French keeper, Torres has a good chance but the shot goes just outside the left post. It is an open match and even if the Spanish manage at times to impose their game during the second half, it is the French pair, Le Tallec and Sinama, who get closest to scoring. But just when the 20,000-strong crowd inside the Stadium of Light are almost resigned to the prospect of extra-time, English referee Andrew D'Urso blows his whistle and awards a penalty following a tackle in the area by France's Colombo. The decision is hotly contested by the French players but a spot-kick it is.
It is minute 36 of the second half with just four more remaining (junior matches are 80 minutes). Fernando Torres moves towards the penalty area. He has already taken two from the spot in this tournament and converted them both. No one has any doubts about how he is going to hit it – hard and towards the left post, like the other two. There is no reason to change, given that the other two have been so successful. He takes a short run-up and shoots hard. Keeper Chaigneau guesses right but the angle of the shot is too much and he can't reach it. It is the winning goal and the Atlético player cries out like a man obsessed, lifting his shirt to reveal a message to Andrés Iniesta and thereby keep the promise he made to dedicate his goal to his injured team-mate. Then the youngsters' exuberant celebrations – first in the Stadium of Light and then, that evening, at the Newcastle ground, St James' Park, where the gala dinner is being held with officials from UEFA, the Spanish Football Federation and their opponents. From shorts to jacket and tie, handshakes, friendly chat, dancing, polite laughter and toasts with Coca-Cola. It's all done very seriously 'because then,' explained one of the team, 'they cannot say that we don't know how to behave ourselves in society.' The partying relocates in the early morning to Durham, the team base. The Under-16s have, for once, got permission to stay out until the small hours. It is, after all, their big day and the technical staff say they deserve it. As indeed they deserve the full attention of the media, which, during the previous week, has discovered what it was already describing as 'the Torres Generation'. The reason is quickly apparent: Fernando is the slayer of France with seven goals, the top goalscorer and the best player of the tournament. It's Fernando who comes to symbolise a national side made up of Iniesta, Gavilán, Melli and Diego León.
This is a generation the commentators hope will continue in the same vein, will make the senior national side and win those trophies that have eluded them so long. Meanwhile, the stories of who these seventeen-year-olds are, and where they come from – especially Torres – are being uncovered. The first background articles appear in the press on the lad from Fuenlabrada, whose physique and strength someone compares to a sabre, with others recalling idol, Marco Van Basten, his favourite singers (Andrés Calamaro) and films (Roberto Benigni's _La Vita è Bella_ ).
A little more than a year later, the Torres Generation will repeat the celebrations in Norway. In-between, there was the black hole of the Under-17 World Cup, which took place in September 2001 in Trinidad & Tobago. Spain arrived, fresh from their European triumph, but two bad defeats against Burkina Faso (0-1) and Argentina (2-4) left them in third place in their group and they did not make the quarter-finals. Fernando got just one goal – in the first half of the match against Oman. But he came back with a vengeance in July in the second leg of the Under-19 Euro qualifying tie against Macedonia. He scored two goals to qualify the side for the finals in Norway from 21–27 July 2002.
José Camacho, the manager of the senior national side, decided to quit after Spain's exit from the 2002 World Cup in South Korea and Japan (at the hands of joint host South Korea, managed by Guus Hiddink). On 2 July, the Spanish Football Federation appointed Iñaki Sáez as his successor, but before getting down to work with the grown-ups, he wanted to finish the job with the juniors: 'I had taken them through to qualification, so I wanted to go with them to the finals,' he says, now retired from the Federation. After a long round of golf and a restorative shower in his holiday home in Tenerife, he talked with pleasure about that July in Norway and Fernando Torres: 'The year before, he had made his debut with Atlético Madrid's first team and with Luis Aragonés as manager. That season, he had been important for getting the team promoted to the Primera División. He was very good and stood out because of his speed and strength, qualities which, at that age, always create problems for opponents. He was full of promise – a youngster who'd always scored a lot of goals in all the leagues he'd played in. One could see that he had a lot of potential and that there was still room to improve various aspects of his game. Our objective, as coaches of the national team, was to improve how he received the ball with his back to his opponent and to play it as quickly as possible. In other words, that he would be able to use to the full the enormous skills that he had. In the dressing room, he was a very cheerful lad, an important person. He symbolised the attack and his team-mates had confidence in him because he always got them out of trouble. He got on tremendously well with Iniesta and you could see this on the pitch. And I saw it in the final.'
But staying in chronological order, there were three more matches to play before arriving at the final. The first, a Group A tie against the Czech Republic, finished 1-1. Fernando is not on the score-sheet. In the second, Iñaki's youngsters find themselves up against the hosts – a straightforward game because the Norwegians, apart from honest effort, commitment and a competitive spirit, don't put up much resistance. The first goal comes in the 22nd minute, when the keeper can only parry Torres' rocket of a shot and José Antonio Reyes (later of Arsenal) is on hand to pick up the loose ball and score. Nine minutes after the restart, Iniesta feeds Fernando, who beats Larsen to make it 2-0, with Reyes scoring again in the 68th minute to close the proceedings at 3-0. In the last match they meet Slovakia, who had put five past the Czech Republic and scored another five against Norway to give them a maximum six points and make them the highest-scoring team in the tournament. The only result that will see Spain through to the final is a win.
However, things start going wrong almost immediately. A free-kick on the edge of the area and Cech finds the back of the net off the left-hand post: 1-0. Then, just before the interval, Sergio equalises, thanks to a calamitous error by Konecny, one of the opposing defenders who fails to clear. Then, in the second half, Torres takes to the stage and, in injury time, diverts a superb cross from Carmelo into the net to make the final score 3-1 to Spain, who make the final. There they will meet Germany, managed by Uli Stielike – someone who knows Spanish football well. During the 1977–78 season, after spending four years at Borussia Mönchengladbach, he joined Real Madrid to become a pivotal figure in the midfield, remaining there for eight seasons. The Spaniards hold him in high regard and he has much respect for his opponents.
He recognises that Spain has players with better technical skills than his, and the trio of Torres, Iniesta and Reyes give him concern: 'They are very good from the midfield to the front line and very skilful on the ball,' he explains. Iñaki's assistant, Santisteban, picks out the same players: 'Iniesta directs the play as if he has had years of experience, Reyes creates all sorts of problems, and Torres? Well, I think he's amazing, He can cover a huge amount of ground, he's courageous, smart with the ball at his feet, skilful and ready to create space between defenders and not be afraid. If he gets a kick he gives three back and won't give way. He's not frightened of physical contact, is always willing to have a go and has a winner's mentality. He knows he's good, what he can achieve, and that conviction makes him similar to players like Raúl – strong characters who don't give up.'
Santisteban, also an ex-Real Madrid player, is confident about the result of the final because 'the lads have talent, class and self-discipline'. The match takes place on 28 July in Oslo's Ullevaal Stadium in front of a sold-out crowd, 16,000-strong.
This was what the Spanish newspaper _El Mundo_ had to say the day after the encounter: 'Germany had to face the facts and admit defeat when confronted with the generation of Fernando Torres, icon and beacon of the Spanish side, the star emerging from his shell, who intimidates his opponents and achieves success every time he plays. He was top-scorer in the European Under-16 championship-winning side and a year later repeated the trick with the Under-19s. He already looks mature enough to forget playing with the kids and take on the challenges of the grown-ups.'
Another newspaper, _ABC_ , had the headline: 'Torres runs riot against Germany' and wrote 'Crone and Volz (two of the German defenders) couldn't avoid him. They were met by El Niño in every Spanish attack and couldn't catch him. Fernando had already destroyed them in the first minute. He got himself in front of Haas and shot wide after running six metres held by Fathi, who gave away a penalty, which referee Ceferen did not give. From that moment on, Fathi didn't want to know about Torres. Torres, though, definitely did want to know all about being crowned Under-19 champions and had another penalty shout – Crone tackled him as he entered the penalty area – but the referee didn't agree with that one either. Third time lucky. The crafty Reyes took a quick free-kick and the Atlético Madrid player took the opportunity once more to escape the weak opposition defence and shoot, forcing Haas into the first of a series of impressive saves and in turn making himself Spain's principal problem.'
But in the 55th minute, even Haas had to admit he was beaten: 'It was a very similar move to that which won Euro 2008 for the national side also, as it happens, against Germany,' recalled Iñaki Sáez, 'Reyes, in our half of the pitch, passes to Iniesta almost on the halfway line. Andrés sees Torres and makes one of his trademark deep passes. Fernando wins the race for the ball with Crone and has just the German keeper to beat but fluffs the shot. The ball goes loose. Crone and Haas look at each other and don't react. Torres sticks out his boot and nicks the goal. He knew how to keep going until the end. He knew how to keep on fighting until the end. That goal, exactly like the one last year against Germany, perfectly demonstrates his style,' explained Saéz, 'a striker who finishes the move with speed, force and intelligence.'
'Torres... y Reyes' read the red and black front page of Spanish sport daily, _Marca,_ the next day, the first of many with El Niño centre stage (the headline played on the name _Reyes_ , which also means 'Kings'. The headline could therefore be read: 'Torres... and we are Kings'). But Fernando, although excited by the two titles already won, doesn't let it all go to his head and is already thinking of the next Under-20 World Cup. He's hungry for victory. And this is how he responds to the praise he receives from Stielike after the match: 'It's always good to receive praise from one of the best managers in Europe but I still have to work on my game and improve so that this doesn't turn into criticism.'
Another example of the young man's desire, commitment and determination.
## Chapter 10
**A special dedication**
_Conversation with Barcelona and Spain midfielder, Andrés Iniesta_
An injury is keeping him out of the Barcelona team ahead of the final of Spain's Copa del Rey (King's Cup) against Atlético Bilbao. His side relies on the 'hero of Stamford Bridge' (where he scored the winning goal in stoppage time against Chelsea in the Champions League semi-final) because of his qualities as a 'total footballer'. He can play in midfield or on the wing. His dribbling skills and vision of the game have made him a key player. But this time Iniesta will not be there. It will be several days before the Barcelona midfielder can run out onto a pitch again, but he is expecting to be fit for Rome in the Champions League final against Manchester United. Instead, he's here at the Ciutat Esportiva Joan Gamper (a complex situated about 3 miles from Barcelona's Camp Nou stadium, which hosts training sessions from junior teams as well as the Barça first team) in the hands of the physiotherapists. The treatment is taking a while and in the meantime, the words of his manager, Pep Guardiola, come to mind:
'He's an example to everyone and above all for the next generation. I always tell them to look at him because he doesn't wear earrings, he doesn't change the colour of his hair and he doesn't have any tattoos. But they all know he's the best. He plays wherever you put him and he never complains, not even when he's on the pitch for only twenty minutes. And he always trains well. Iniesta is priceless, tremendous.'
In the beginning the Spanish press christened him _Andresito_ because of his small size. Now he's become _Don Andrés_ and 'The Sweet', after ex-Barça manager Frank Rjikaard said 'on the pitch he gives out sweets' to describe his way of playing. They've called him 'The Philosopher's Stone' of Barcelona. Opposing managers and team-mates consider him a player capable of deciding a match but he himself shuns praise. The physiotherapy session over, he arrives pale-faced and wearing a white jacket, accompanied by Sergi Noguera, the club press officer and introduces himself as follows:
'I was born in Fuentealbilla, a small village in La Mancha, about 25 miles from Albacete. My father, José, was a building worker and my mother worked in a bar with my grandparents. I come from a modest family. I started to play for Albacete and came to Barcelona when I was twelve. In 2003, my parents and my sister moved here too. I consider myself a very normal and straightforward person. I like to do my work well and try to enjoy football.'
His voice is frail, as is his general appearance, and his shyness is obvious. Andrés Iniesta Luján is not one for long chats. He does, though, gently begin to open up.
### _Let's go back to April 2001 and the Under-16 European championship and – I'm sorry to remind you of this – another injury..._
'It was against Germany. For them it was a must-win game and they came at us full-on. My marker was Mair, a huge, blond midfielder. They wanted to get the ball off us. In the end I had to leave the pitch. These things happen. Nothing more than that. The doctors suspected ruptured knee ligaments but luckily it was only a bruised shin bone and a sprained lateral ligament inside the knee. But my European championship finished there and I came home.'
### _You left and your team-mates promised to dedicate the goals in the semi-final against Croatia to you._
'Yes, Diego León (then in the Real Madrid youth team and now playing for English Championship side, Barnsley) called me the day before the match. He had replaced me and promised that both he and Torres would be wearing my shirt, the Number 8, under their national shirts. I was zapping between the channels at home in Barcelona but couldn't find any station that was showing the match. I didn't know that it wasn't being broadcast in Spain, which was only showing the other semi-final between France and England. I switched off the TV but after the game, my team-mates called from the dressing room so I could share the win with them. I was touched by that and felt that they were really fond of me. They were a fantastic group of players who deserved to get to the final. They told me that Fernando, after scoring the first goal, went past everyone looking for the cameras to show me his dedication. He didn't know that here (in Spain) I couldn't see him. In any case, he told me not to worry because he would wear (the shirt) again in the final against France.
### _And did you get to see the dedication this time?_
'Yes, of course. Fernando scored the penalty, lifted his shirt and underneath he was wearing a white T-shirt with the words: 'Para tí, Andrés' ('For you, Andrés'). He dedicated the winning goal to me, he dedicated it only to me.' (Iniesta repeats it over and over again, as if the words bring back the emotional power of that day.)
### _Why was there this very special relationship?_
'From when we were sixteen, when we came together in that team, we got on really well. For me, Torres has always been a team-mate with whom I've had a great understanding. Each of us has been in our own particular (club) teams and got on with our lives but when we come together in the national side we've always understood each other perfectly. Above all on the pitch, because Fernando has always been a player who gets away from his marker well, who has speed. And from my position in the midfield, I've tried to take advantage of his skills to get the ball to him.'
### _As you did for him in the Under-19 final in Oslo?_
'Yes, in Norway, I passed the ball to him but it was he who made the goal. Fernando did the difficult part.' Modest as ever, Don Andrés.
### _Iñaki Sáez, the manager of that Under-19 side said that you were the one who best understood Fernando?_
'Well, in a team there are always some footballers who understand each other better than others and that was the case then. But I have to say that for a midfielder to have a striker with Fernando's qualities is fantastic. It makes everything so much easier.'
### _What are Fernando's skills?_
'He gets away from his marker very well, he sees space, he has a lot of strength and uses this strength so that when he comes to shoot, he does it coolly, with the certainty that he will score a lot of goals.'
### _Which player does he most resemble?_
'Ronaldo, because of his strength, his bursts of power and for the finishing which Fernando has and which, in his day, Ronnie had too. Aside from that, each of them is different technically but in those specific respects, Fernando reminds me of him a lot.'
### _And do you remember that, at that time, Fernando never stopped talking about Van Basten?_
_'_ That's right, Marco Van Basten was one of his idols but I didn't get many opportunities to see him play and I never came across him on the pitch.'
### _Which is not the case with Torres, who's also been your opponent?_
'Yes, we have come up against each other and with every kind of outcome. There've been matches that his team has won, matches that my team has won, and matches where he's scored against us. He's always a really difficult striker to keep under control.'
### _Let's move on from confrontations to the national side. How would you describe the experience of winning the Euro 2008 tournament playing in the same team? And how did you both get on together?_
'We got on really well and with all the others in the team. It was the same group of players that had won the qualifying matches. We experienced everything. We were criticised after the games with Ireland and Sweden but it could be that the hard time we had in qualifying actually worked in our favour to make us stronger. Once we got to Austria, we were really motivated as well as committed and united as a team. When you have that kind of combination, it brings victory a bit closer.'
### _How did you feel when Fernando got the goal against Germany?_
'Completely elated, really happy. To have scored and to have scored in such an important final and to have put us ahead of Germany is no easy feat. We were then in reach of the title.'
### _What do you talk about now when you meet up in the national side?_
'About everything really but especially how each of us is doing in our respective teams.'
### _And what has Fernando told you about Liverpool?_
'He told me that to begin with it was a really big change and that there's a huge passion for football over there. For a player, it's really important to feel the support of the fans. I have to say that, at Anfield, where I've played, it's incredible. It's wonderful that the crowd is always 100 per cent behind their team and that makes it really difficult for any opponent to win there.'
### _What do you think of the change he's undergone since going to Liverpool?_
'It's been hugely important. The Premier League is very different from La Liga and I think that the way of playing in England and, in particular, the style of Liverpool, is perfect for someone with Fernando's skills. Also, one mustn't forget that Torres had always been identified with Atléti. He had all that weight, being promoted to the first team at seventeen and having to keep going despite everything that piled up on top of him. There's no doubt that was really hard. At Liverpool he doesn't have any of that baggage.'
### _And what do you think about the success he's enjoying in England?_
'I think he deserves it. Fernando's always had these qualities but with time he's matured and acquired much more experience as well as improving his technique and now he's one of the best strikers in the world. No doubt about it'
### _And finally, do you see yourself lifting the World Cup with Fernando?_
'I really, really hope that we can get to that point and succeed in such an important tournament, one that Spain has never won. It'll be very difficult but we'll fight to reach the final and then see what happens.'
## Chapter 11
**A fairy tale**
Years later, remembering those days, he can't think of any words to describe it other than 'it seemed like a fairy tale'. It was hard to believe, 'Because everything happened in such a short time, everything went so quickly, it was difficult to take in,' says Fernando Torres. And he's right: On 6 May 2001, he was proclaimed Under-16 European champion and on 27 May, exactly three weeks later, at just seventeen, he realised his dream, making his debut with the Atlético Madrid first team at the Vicente Calderón stadium. On 3 June, he scored his first goal for the senior team. And that's not all, because in-between there was the call-up from Iñaki Sáez to the Under-18 national team, the final of the Spanish Under-19 league and even the news that he'd been sold to Valencia. Unbelievable indeed.
Let's take it from the beginning...
Right after the success with the national side in Europe, it occurs to the Atlético directors that it would be a good idea to include the lad from Fuenlabrada in the first team. The day after the defeat against Murcia the atmosphere is noticeably tense. Hopes of immediately going back up to the first division following relegation are fading. The fans have had enough of everyone – the president, the club, the manager and the players. There are even some attacks against the perceived 'culprits'. Maybe the Golden Boy of Spanish football, as he has been labelled after the European victory, is just what's needed.
Jesús Gil, the club president, thinks Torres could be used to calm the waters of a fan-base on the edge of a nervous breakdown. But he can't do it straight away. Torres is committed to Iñaki's Under-18 side. On 16 May, at Vila Real in the Portuguese region of Algarve, Spain play Portugal in the Under-18 European championship. The result is a 1-3 victory with a goal for Fernando Torres. Two weeks later it is possible. Paolo Futre, the Portuguese ex-Number 10, the striker who played seven seasons (1987–93 and then again in 1997–98 after a year with West Ham) in the red and white of Atlético before moving into the club offices as sporting director, picks up the phone. He calls Torres at home and asks the youngster to join up with the first team. The idea is that he should start to get himself used to the dressing room of the senior players, seeing that he will be with them for the 2001–02 pre-season. Torres, having finished his commitments with the national and junior teams, is preparing to go on holiday. At first, he doesn't understand why Futre is calling him and can hardly believe the sporting director's words. But he doesn't let himself get carried away. On the contrary, he replies that if it's just for training, he would prefer to go on holiday because after the injury and national team duty he hasn't been able to rest even for a single day. Futre then lets drop the fleeting possibility of being on the bench and Fernando replies immediately with an enthusiastic 'Yes'.
On Wednesday, 23 May, Fernando trains with the first team, scores five goals and Futre tells Carlos García Cantarero – the manager who replaced Marcos Alonso for the last seven games of the season – to call him up for the next match. So, on Saturday, 26 May, the youngster went off with his idols. Those who, a week before, he had seen on the pitch from the stands at the Calderón, those whose autographs he had asked for, and those who were now alongside him as his team-mates. The youngster is a bundle of nerves. The atmosphere isn't hostile but many look sceptically at the new arrival. 'In the coach, they were making jokes about him. It was the way the squad welcomed him to the group and they were telling him, "you are a boy but one of ours"', recalls Cantarero.
Sunday 27 May is the big day. Unforgettable. The heat is unbearable, Atléti are playing at home against Leganés and drawing, with 35,000 in the Calderón whistling and bawling at the players who are seemingly incapable of getting a vital home win. Cantarero raises his hand towards the subs who are exercising to the side of the pitch. He indicates to Fernando José Torres Sanz. The lad runs towards his manager and gets himself changed in a flash. Meanwhile, on the pitch, Luque scores from outside the area to make it 1-0. It is the 54th minute. Cantarero sends Torres to warm-up along the edge of the pitch. His debut seems to have been postponed. But the manager knows that the fans want to see him on the pitch. All the papers have been talking about him, praising the new red-and-white hope. For several days the talk about the team's fragile state or its endless economic problems stopped in order to concentrate on the lad from the junior team.
In the 65th minute, Cantarero brings off Luque, the author of the goal and sends on the Number 35, Fernando Torres. The fans, placated by a positive scoreline, give him a warm welcome. In the minutes that remain, there is nothing special to report, but he's made his debut. A member of the opposing team wants to exchange his shirt but he refuses. That shirt's very important – he's promised it to his brother, Israel, and it'll be the only one like it being worn at the Estadio Carlos Belmonte the following Sunday, 3 June 2001.
Atlético have to win if they are going to keep alive their hopes of promotion but, against Albacete Balompié, things aren't going well. Atléti are playing badly. An ugly game, marked by tension. Fear of losing haunts Cantarero's men. The defence is fragile and exposed to the counter-attacking of their opponents. In attack, there are fleeting glimpses of Kiko, who has returned to the team, and of Cubillo. With seventeen minutes remaining, it's a miracle the Madrid side isn't losing. They create three half-chances on goal with Luque and Correa, while Albacete go close on several occasions. Cantarero plays the one card he has left at his disposal – the youngster. 'We needed a goal. That's why I put Fernando on,' the manager will say later, rubbing his hands with glee for making the right move. Yes, because El Niño, cheered on by 5,000 Atlético fans who have gone down to Albacete to support the team, has just five minutes to change things round. He comes on in place of Kiko and goes immediately to take up his place in the attack. The first time he touches the ball, he is knocked flat by Arias, who earns a red card and a dismissal.
In the second move, a long cross from Iván Amaya comes into the area from left to right. Fernando pretends to go one way, then the other, gains ground on the central defenders and gets behind them. It seems the cross will end up being too long, but the youngster moves rapidly without taking his eyes off the ball falling out of the sky. He stretches out his neck, hitting the ball decisively, accurately and powerfully, directing it towards the opposite post. He fears that it's hit the post and gone out of play. But no, it rebounds into the net. The keeper looks at his defence with disgust while Fernando runs towards the goal line and, beside himself with joy, embraces Aguilera and Hernández – men almost twice his age. It is his first goal at national club level and a happy ending of the fairy tale for him and the team, which, with those three points, can continue to dream of promotion. The referee blows his whistle to end the encounter and El Niño succeeds in getting his hands on the ball that marked his first goal. He wants to keep it as a souvenir of his fledgling career. But then he changes his mind and kicks it hard and high towards the south end, where the Atléti fans are concentrated.
Meanwhile, on the pitch, around twenty journalists are following him, microphones at the ready, to interview him and hear his first impressions. Hernández and the others lift him up and take him to the dressing room.
After the shower and celebrations, there is time for comments, thanks and dedications. 'Very emotional. I feel very emotional,' is the first thing he says. Then he explains: 'It was what all my family were waiting for, it's what I wanted, to score such an important goal as this for Atlético to return to its natural home, which is La Primera División (the first division). We're a little nearer thanks to this victory. I dedicate it to all the members of the _Frente Atlético_ (the group of fans with whom Fernando usually watches the matches in the Calderón. He also gave them the match shirt) who have come here to cheer us on. They are fantastic and it's worth battling on in order to get them the promotion.' He also has words of thanks for his team-mates: 'They've helped me so much and have accepted me into the squad. Without them, the goal would not have been possible.' He's in Seventh Heaven and you can understand why. But he wasn't the only one jumping with joy. Paolo Futre declares: 'Torres is a star player, a phenomenon who will bring a lot of joy to the fans of Atlético and will be fundamental to the future of Spanish football.' And Cantarero adds: 'Fernando is going to be this week's leading figure. He deserves it and let's hope he's going to be the leading figure for the next few years.'
There is no mistaking the following day's headlines, all of them about him: 'A Magical Apparition in Albacete,' said _El Mundo_ , while _El País_ screams: 'Fernando Torres Saves Atlético.' The TV channels call him into the studio to comment on his goal, to talk about himself, the two remaining matches of the league season and the chances for his team. From that Sunday on, little-by-little his life changes. From Albacete he gets to Fuenlabrada around two in the morning and, as his parents remember, 'he went into his room and about five minutes later he was sleeping. But the morning after and for the following two days, his usual wolf-like hunger at breakfast disappears. His stomach shrinks due to the effects of all the emotion and his new-found fame. But the youngster gets over it easily enough.
What's nothing like as easy to get over is the huge disappointment at Getafe two weeks later. In the Coliseo Alfonso Pérez (Getafe's stadium, to the south of Madrid city centre), Fernando starts in the team for the first time and is the principal figure for the first 45 minutes. He has only matches behind him but he shows a maturity and coolness that some of his team-mates, with much more experience than him, do not display on this occasion. In spite of the numerous errors in front of Atlético's goal, they chalk up a 1-0 victory but at the end of the match, there aren't the celebrations many were hoping for. Everyone is quiet on the pitch, in the dugout and in the stands. The news from the radio has already reached the players, technical staff and the 10,000 Atléti supporters that Betis and Tenerife have won, which means Atlético will remain in the second division solely because of an inferior goal difference with the Canary Island team. The fans slowly slip away with heads bowed. Some vent their anger against the stadium, ripping out seats and throwing them towards the pitch. The police escort Jesús Gil and his wife out of the ground. Around 50 of the radical _ultra_ fans call for heads to roll, shouting: 'Gil, you bastard, get out of the Calderón!' Paolo Futre kicks the wall and throws his ever-present cigarette into the far distance, muttering: 'It's been a huge disappointment but this pain is over. We've lost the battle.' Cantarero declares: 'We're distraught. I've seen a lot of sad things in football but this has been the worst.' The players depart in silence. It's a big blow for everyone. And for Fernando Torres in particular. He's shattered. He just wants things to move on as quickly as possible. He just wants to forget. He is experiencing the disappointment more as a fan than as a player. And it's massive. What had been a dream has now turned into a nightmare. That night he takes refuge in his room in Fuenlabrada but this time he can't sleep. He is inconsolable because of all the missed opportunities and the promotion that has now disappeared. The next year Atlético will have to start all over again in the second division. But first, Fernando still has to resolve, once-and-for-all, the strange matter of his phantom transfer.
It hits the headlines on 11 May. 'We were coming back in the coach from Sevilla where we had lost the final of the Copa del Rey (King's Cup). It was night-time and we were about 7 miles from Madrid. Someone was listening to the radio when suddenly one of the sports programmes on the _Cadena Ser_ station announced that Valencia had signed Fernando. He knew absolutely nothing about it. No one knew anything about it. It seemed very strange to us given that Jesús Gil had been in the dressing room with the lads before the game and, as always, had sung along with us 'Atlético 1-2-3 Go get 'em.' It seemed impossible that they would have sold El Niño but the news spread like wildfire and when we eventually arrived at the Calderón there were loads of media there, all waiting for Fernando but he had got off outside Madrid at the Hotel Los Olivos. Recalling how it all started is Miguel Ángel Gómez Gonzalez, aged 45 and known to everyone as 'Cirilo'.
At that time he was the Atlético kit man and had followed Torres' progress step-by-step through the junior ranks. The news on _Cadena Ser_ is like a bomb going off. It turns out that on 15 March 2001, the Madrid club had received 400 million pesetas (about £2 million), which, including VAT, became 464 million, from Valencia Football Club to deal with a liquidity problem – and the Atlético directors had put up the rights of their 'golden boy' as guarantee. If they didn't pay the debt within the time stipulated (by 25 June), then Fernando Torres would become a Valencia player on 1 July. It was an operation that provoked a huge row, stirred up the anger of the fans and ended up being the subject of a legal investigation. Miguel Ángel Gil, director general of Atlético Madrid, maintained that it was 'a usual thing between clubs, to use players' transfers to disguise loans'. The professional league said that it had never seen anything like it before. Torres denied having signed a contract which obliged him to leave and denied absolutely having any preferred option for that club. His representatives talked of compensation of 2,600 million pesetas (about £13 million) if Atlético did not pay up and Torres was forced to leave for Valencia. It wasn't the case. The debt was paid off. El Niño's adventure in Atlético Madrid continued.
## Chapter 12
**Yogurt**
_Conversation with former Atlético de Madrid striker, Francisco Miguel Narváez Machón, better known as 'Kiko'_
A baseball cap above his black curly hair, wearing a leather jacket, coloured jersey and a weary look is how Kiko appears in the hotel bar at Madrid's _Ciudad de la Imagen_. He has just emerged, battle-scarred and breathless, from a game of indoor football, during which he has scored the equaliser, but which has left him completely drained _._ In little more than an hour, he will be on television commentating for the Spanish channel, _Sexta_ , on the Copa del Rey (King's Cup) tie between Atlético Bilbao and Sevilla (Seville).
Born in Jerez de la Frontera, Andalusia and now aged 37, Kiko has a long career behind him. After three years in the Cadiz team and a gold medal with the Spanish national side at the 1992 Barcelona Olympics, he became the figurehead player at Atlético Madrid. Chalking up eight seasons (from 1993 to 2001), 278 appearances and 64 goals, he played a key role in the squad, which, with the Serbian ex-Luton Town (1980–84) player Radomir Antic as manager, captured a league and cup double in the 1995–96 season – the last silverware won by the club.
Tall (1.89m/6ft 2ins) and rangy, he was in a class of his own, a striker but not in the classic sense of the word. He played behind the main striker, combining great imagination and vision with decisive assists and scoring many goals of his own. He was Fernando Torres' hero.
Kiko takes a long drink of water to rehydrate himself before recalling the end of May 2001 – the debut of El Niño.
'The team was in the Second Division and the situation wasn't good. Results were mixed and we weren't playing well. To sum it up, we had a lot of problems. At the beginning of the season, we'd been hovering above the relegation zone and getting promotion was looking unlikely. To raise the fans' hopes, they decided to give a debut to El Niño, a true _atlético_ , someone with whom the fans could identify. It was a marketing exercise, something which would divert the public's attention from the day-to-day happenings at the club.'
### _And how did the dressing room view him?_
'We thought we'd have to have some kind of arrangement with a children's nursery. What was a kid of seventeen doing in a team of experienced professionals? And above all, we were suddenly being asked to look after this youngster when we were right in the middle of our final, crucial matches. I remember the first day he introduced himself to me in the dressing room. He was thin, freckled, with an extremely slight build and very shy. As he went to shake my hand, he was very emotional. I was the team captain and his idol.'
### _Why was that?_
'I was tall, like him and, like him a forward, although Fernando is more powerful and more direct. I played in a different style. I'd won the Cup and League title just when a young boy begins to idolise footballers and to admire a player who plays in his position. I was a committed _atlético_ , like him. It's normal if you come from the junior team to have someone as an example, a role model. Raúl in (Real) Madrid had El Buitre (Emilio Butragueño, a goal-scorer for Real Madrid during the 1980s), Fernando identified with me.'
### _So much so that Fernando, to pay homage to you, celebrated some of his goals by posing as an archer, an unusual celebration which you yourself made famous._
'Yes, that's true – him and Dani Güiza. They repeated it. I really appreciate that.'
### _And some people say that Fernando, during the 2006–07 season against Real Madrid, repeated the goal that you scored in the Champions League ten years earlier?_
'Yes, the two are very alike. In that match against Ajax, Caminero, playing deep, began the move for Aguilera on the right wing continuing up towards the goal line before passing the ball backwards. It came to me just in front of the penalty area and, half-turning, I shot towards the far post and it went in. I remember Fernando's goal perfectly well because I was in the Calderón (Atlético Madrid's stadium, the Estadio Vicente Calderón) as a TV commentator and because it's the only goal that El Niño has scored at (Real) Madrid. Fernando got hold of the ball before passing it to Galletti who went down the right wing, putting a cross into the centre, where Torres controlled it skilfully with his best leg, the right, on the outside of his foot, and shot towards the post to the right of (Iker) Casillas (the Real Madrid goalkeeper) who could do absolutely nothing. Two important goals, especially El Niño's. Real (Madrid) was his obsession.'
### _Can we go back to Fernando's debut in the Calderón?_
'That day I wasn't in the team. I was having problems with the club – and with my ankles. They weren't calling me up for home matches. But Fernando had already taken everyone by surprise, with his personality, self-confidence and willingness to learn plus his professional qualities and maturity. No, he certainly wasn't a kid you had to look after. In training, he came up against defenders like 'Super-López' (Juan Manuel López Martínez, an Atlético stalwart who spent ten years at the club) and Hernández (Jean François, a Frenchman who had joined from Rayo Vallecano) and he didn't give an inch. He was strong and determined to show what he could do.'
### _And he showed what he could do at Albacete, in his second game with the first team._
'Yes, at Albacete I was in the team. When Torres scored I thought 'Bloody hell, why didn't they take me off half an hour earlier!' That was because he came on as a substitute for me. I had told him something like, 'Good luck, come on kid, you can do it,' and five minutes later he scored the winning goal with a superb header. What a kid...'
### _In the pictures of that match, one can see you alongside the subs' bench smiling and kissing the badge._
'I was very happy to pass the baton to El Niño _._ It was rewarding for a true _atlético_ to see that, after you, there was someone you could have confidence in. I could see myself reflected in him and his happiness. We've all been junior players – our dream was to get into the first team and score a goal wearing the shirt. Fernando achieved that.
### _That goal was the subject of much celebration both in the stands and on the pitch._
'That's right. It gave us an important victory. It kept our promotion hopes alive. The fans came onto the pitch and we had our own celebrations in the dressing room. Fernando came and asked me if I would give him the captain's armband as a present. I told him not be so silly, that it was covered in dirt and worn out, but he insisted so much that in the end I gave in and handed it over. Someone had got hold of some bottles of champagne, which we opened to toast our win. I offered a glass to Fernando and realised he was only seventeen and wasn't able to drink alcohol and neither did he want to. So we rummaged around in the bag of a team-mate who'd brought in some things to eat – some sandwiches – and we came across a yogurt carton. I opened it and told him 'You, lad, can make the toast with yogurt.' And, with plastic carton in hand, that was how he celebrated his first goal!'
### _But at the end of the season, the celebrations weren't repeated._
'We stayed in the Second Division and I left the club – with a lot of problems and a particular thorn in my side: I never managed to play in a match with Fernando. In training, we understood each other well. Once I gave him two goal-scoring passes and he beamed at me, saying, 'Let's see if we can repeat this on the pitch.' It wasn't possible. A real shame.'
### _Eight years have gone by since then. How do you view Fernando now?_
'Now I see him as the finished article. Going to Liverpool meant he could take three steps up in one. He's more relaxed, more himself, without the suffocating responsibilities and the mental wear and tear that were crushing him at Atlético. He didn't have time properly to evolve. At just eighteen, he had to take up the baton and be the flag bearer. In footballing terms, he has seen a lot in a very short space of time. But he's an intelligent lad, who, thanks to his family and the right kind of environment – without any false praise where people always tell you you're great when you're not – hasn't lost his way, as has happened to other youngsters. No, he's gone in the right direction. In Liverpool, he's made his match.'
### _What do you mean?_
'That he's found the right kind of environment. Reina, Aberloa, Xabi Alonso have taken him under their wing. Steve Gerrard and Jamie Carragher have been able to guide him. Benítez, who is a perfectionist with great attention to detail, has helped him to iron out those imperfections his critics have always accused him of, like his passing and moving, his finishing, his ability to lose his marker, his shooting... Before, his shooting wasn't so good, now it is. And then you have to recognise that English football, with its end-to-end games and spaces in which to run, is ideal for someone with Fernando's qualities. Yes, without doubt, Liverpool has given him a big step up.'
### _Did you think it would all happen so quickly?_
'When he scored the first goal against Chelsea, I saw that as the turning point, I saw a player who had been liberated. From there on in, he had a marvellous season. And now he's Number 3 in the world (in the FIFA World Player of the Year 2008 results).
### _It's also thanks to the goal in the final of Euro 2008._
'Without doubt. That match made his name. The injury to Villa was fortunate for Fernando because he's a footballer who needs space, who needs to be able to run across the line of attack from one side to the other. And he showed that he is a man who doesn't let one down on the big occasions.'
The conversation is interrupted. Patxi Alonso, sports presenter at _Sexta_ arrives for a coffee. Between smiles and jokes, the talk comes back to that demanding match of indoor football, the result and the remaining ties up to the final. A glance at the watch means that it is time to head for the TV. A good piece of programming.
## Chapter 13
**In El Niño's hands**
There are 20,000 of them in and around the Neptune fountain in central Madrid. _'_ _¡_ _Adiós a Segunda, adiós!_ _¡_ _Adiós a Segunda, adiós!'_ – 'Farewell to the Second Division, Farewell!' they shout. After 721 days in purgatory, Atlético are back in the First Division. On 27 April 2002, in the Calderón, a victory against Gimnàstic de Tarragona would have given them the mathematical certainty of promotion but on 90 minutes Ángel Cuellar equalises for 'Nastic' to make it 3-3 and the torment goes on. But only for a few hours. Thanks to a chance set of favourable results they can celebrate the next day. Not since 1996 – the year in which Atlético won the league and the Copa del Rey – have the fans had a reason to get together around the fountain dedicated to the god of the sea, their 'temple', their altar for club celebrations. They do it in style. They jump with joy, sing, wave flags, light flares, throw bangers, mock Real Madrid, their eternal rivals, block the traffic in one of the main thoroughfares of the city, and even clash with the police. The most repeated songs and chants praise manager Luis Aragonés, who has achieved the miracle, and Fernando Torres.
El Niño heard the good news about the return to the first division in the drawing room of his home. Following a frantic round of calls between team-mates, the idea was to go up to the Neptune fountain to join the celebrations. But Paolo Futre, the sporting director, thinks it's better to wait. They opt for an informal dinner in a city centre restaurant. It's not until the early hours that the players arrive in the presence of the god with the trident in his hand, in the Piazza Cánovas del Castillo, not far from the buildings of the Spanish Parliament. Diego Alonso climbs the statue and shouts 'Atléti _, volvemos a primera._ ' ('Atléti, we're coming back to the first division.')
Fernando Torres, in jean jacket and red-and-white scarf, is grinning from ear-to-ear. Finally, a real pleasure. Because even if lots of people that night can be seen wearing shirts with his name on, it hasn't all been good during his second year with the senior team. Far from it.
At the beginning of the season, at just seventeen years of age, 'they made me into an idol and now they are trying to knock down the tower that they created. The manager told me: "The higher they put you, the harder you fall." That's to say, try to learn to be like one of the others,' he confesses in an interview and adds: 'In any case, I've been at a much lower level than I thought, I've not had the season that I was hoping for. I've encountered more difficulties than I thought I would.'
What difficulties has the young promise of Spanish football encountered? A lot, beginning with the manager. Luis Aragonés, an Atlético midfielder in the 1960s and 70s with 123 goals to his name, a legend to the fans, has returned for the fifth time as manager to take the team back to the first division. But the _Sabio de Hortaleza_ (Wise Man of Hortaleza), as they call him, doesn't have much faith in the youngster. As often as not, he sends him directly to the stand or leaves him for entire matches to warm the substitutes' bench. On the rare occasions he does start a match, he is substituted without fail. Changes that drive El Niño crazy even if, after thinking things over, he ends up admitting the gruff manager was right. The Wise Man corrects him continuously: 'Torres, not like that!' 'Torres, do it well, not beautifully, well!' Torres this, Torres that. He takes him off the pitch to put on a defender or the Uruguayan, Diego Alonso, an honest worker of the ball. With the lad from Fuenlabrada, he uses all the old football conventions. Or to be more exact, the brilliant, celebrated youngster must be treated harshly – he needs to be taught how to behave on the pitch and in the dressing room. He must be the first to arrive and the last to leave, to talk little and listen a lot, to be humble, he must never get cocky, he must respect his team-mates and not dare to contradict the gaffer. Training – or rather, commandments – that years later Torres will consider valuable, but at seventeen, leave him baffled.
The continuous put-downs and the constant substitutions to a competitive and fiercely proud young man like Fernando, do him damage. And there's also the fact that Luis cannot stomach the youngster's media exposure. The more they talk about him in the press, the less he plays. A popularity that even attracts the jealousy of his team-mates, who, in some cases, are twelve years older than him, and who find this callow youth hogging the headlines hard to handle. So much fame also brings with it a special attention on the part of opposing defenders. 'I can confirm that if they think you are a "name", it's worse. You have to suffer much more marking,' comments Torres.
The truth is that, on many occasions, in order to respect the famous conventions of football, his rivals gave him a rough time. As do the press. Many had given him their backing and feel betrayed by a performance that is not up to expectations. They talk of the crisis in his second year, of how the Under-17 World Cup at the beginning of the season didn't allow him to start the league campaign on a good footing, pointing to his goal tally (only six) as evidence of this.
The only thing in his defence: he plays some really tremendous games. But they don't count for much, seeing that even he comes to doubt the faith placed in him. Fernando's reply, or rather revenge, comes first with the victory in the Under-19 European championship in Norway and then in the first division.
He makes his top-flight debut on 1 September 2002 in the Camp Nou against Louis Van Gaal's Barcelona. Ten months after he's scored thirteen goals in the championship and one in the Copa del Rey. He has become the star of the side – one that everyone expects to see shining. He has assumed big responsibilities and has become, without doubt, one of the best in the team. On two occasions he brought the entire Vicente Calderón stadium to its feet.
On 12 January 2003, against Deportivo La Coruña, he creates two spectacular moves. The first, he controls in the penalty area using his chest, gets round defender Noureddine Nybet with a lob and does a half-turn to score with a devastating left-foot shot. The second, he nutmegs Nybet, which dumbfounds Donato, leaving him to make a winning assist for Correa to score. The crowd gives him an ovation and his name rings out across the nearby Manzanares river and echoes through the surrounding neighbourhood.
On 24 May, in the same stadium, he puts on another show. It's the last minute of the second half when Torres begins warming up on the edge of the pitch. The fans have been demanding his appearance for some time and Atlético is losing 1-2 against Villarreal. Only he can save the situation. It's true.
On 70 minutes he shoots from outside the area, the ball just inside the angle between post and crossbar. Four minutes later, he scores the winning goal, a great left-foot shot, after a pass from Luis Garcia (who moved to Liverpool in 2004, returning to Atlético in 2007, the same year that Fernando went in the opposite direction). Poor Pepe Reina, then keeper with Villarreal and a future team-mate of his at Liverpool, has one of the worst afternoons of his career. 'Imposing', 'formidable', 'marvellous', are just some of the adjectives used to describe the 19-year-old's display. They talk of the emergence in _La Liga_ of a shining young talent. They cannot recall anything of its kind since the arrival of Raúl at Real Madrid. But El Niño has learned from Aragonés to avoid any kind of vanity like the plague, replying to all the praise saying:
'People get carried away making comparisons but that's a waste of time. I don't know how one gets to be a star. But however one does, I still need to do it. I've only just started and we'll see where I am when, like Raúl, I am 26 and playing international matches.'
But the positive opinions don't only come from the public. They are also being voiced by his team-mates. Demetrio Albertini, the midfielder who, with the Milan of Arrigo Sacchi and Fabio Capello, has won everything and more, explains: 'He's still a boy and has to mature, but he has talent. He's going to be very big. In Italy he's liked by Milan and Juventus. They talk a lot about him.' And Fernando talks a lot with Demetrio, Atlético's new signing: 'He was talking about Milan, about Marco van Basten, who was my idol, he lent me tapes to watch him in action to explain to me his style of playing. And he always recommended me to learn everything I could before leaving.'
The year 2003 is Atlético's centenary. On 26 April 1903, a group of Basque students at a mine engineering college in Madrid founded a new football club as a branch of the Basque side, Atlético Bilbao. They initially played in blue and white strips, similar to those of Blackburn Rovers. But eight years later the main team in Bilbao and the Madrid branch had changed to red and white (similar to Southampton), one theory being that the new colours were cheaper because this combination was used to make mattresses and the leftovers could be converted into football shirts. It also helps explain why the club became known as _los colchoneros_ (the mattress-makers). It's those same stripes that earn an entry in the Guinness book of records when a flag measuring about 1 mile long by 8 yards wide is paraded through the streets of Madrid from the Neptune fountain to the Vicente Calderón stadium. It's the main party for the centenary with lots of paella, fireworks and skydivers, together with leading local figures and even royalty in the form of Prince Felipe, the heir to the Spanish throne. It's a pity that Atlético then go and lose 0-1 against Osasuna.
Fernando, who comes 19th in a supporters' survey to choose the best players in the club's history, is not on the pitch. He's taking part in the celebrations of a proud Atlético as an ordinary fan. 'I have come up through the ranks, I know what it is to wear the red and white, what it means to be in this team,' he says. Unfortunately, a tear in the fibres of a leg muscle is keeping him off the pitch for around a month.
When he comes back, the club's situation has changed and become even more difficult. Jesús Gil, the godfather figure of Atlético, resigns as president after sixteen years. During his time in charge, the club has had 31 managers, almost double what Liverpool or Manchester United have had in 100 years. With Gil, Atlético have one league title and three Copas del Rey and finished in the second division for two years. With Gil, the ex-mayor of Marbella, the club has often teetered on the edge of bankruptcy and been the focus of numerous legal investigations. Gil ends up in prison. When he leaves, fed up with being insulted and accused of being the one responsible for all the club's failings, he hands over the reins to his son, Miguel Ángel Gil Marín and film producer Enrique Cerezo... The club shares held by Jesús Gil are seized in connection with an investigation into fraud and falsification. Financially, the club is in ruins but he does not want to be singled out as the president who sells Fernando Torres or the Calderón to put things right.
Jesús Gil had been like a father to El Niño: 'I remember him with affection, his family treated me as if I was one of their own.' Gil, who died on 14 May 2004, goes and so does Luis Aragonés. Just six matches from the end of the league, he says he can't work as he would like to and has no intention of respecting his contract, which expires at the end of the season. Before going, has he changed his opinion of El Niño? Not at all: 'Fernando Torres could be a very good footballer, who still has to correct some flaws,' he says in the club magazine. 'Right now, he's performing well in the Primera Liga but, paradoxically, in almost all the matches where he hasn't played, we've won. Irreplaceable? It's very difficult for a player in a team to be like that but Fernando is certainly a very important element in front of the opposition goal.' The warring between the two continues and it will resurface some years later in the national side.
Gregorio Manzano arrives for the 2003–04 season from Mallorca, where he won the Copa del Rey. He declares immediately that he wants to put his priorities into the attack because that's what the fans are demanding. He counts on a midfield notable for the presence of Cholo Simeone, who, after several years in Italy (Inter and Lazio), returns to Atlético, and on a left wing, where Musampa is expected to perform well. In attack, to support El Niño, there is the Greek, Nikolaidis:
'Our objective was to consolidate our status and after that, fight to get as high up the table as possible. We had a good season and we surpassed our initial expectations, relative to our sporting and economic resources. The only thing that was missing was Europe. In the last game against Zaragoza, the team couldn't manage a win and we missed out on the UEFA Cup through a lower goal average than Sevilla,' as Gregorio Manzano, or 'The Teacher' as he was known, recalls today. He boasts ten years of Spanish first division management with more than 300 matches under his belt. Manzano, now back with Mallorca, hasn't forgotten that year in Atlético, just as he hasn't forgotten Fernando, with whom he maintains good relations.
Going back to the beginning of that season, one should say that Torres avoided a goalscoring crisis thanks, above all, to the confidence of the manager, who has given him a starting place when neither his dribbling nor his shooting is working. It's a situation from which he escapes only at the end of October. Against Manzano's former side, El Niño finally unleashes himself and doesn't stop hitting the net – so much so that halfway through the season, he is the first division's top goalscorer with eleven goals. And at the end of the season – won by the Valencia of Rafa Benítez – Torres is the club's top-scorer, only four less than league top-scorer Ronaldo.
One of those goals is a masterpiece: 'It is without a shadow of a doubt that great goal at Betis that gave us our 1-2 victory,' explains Manzano. A move worth a slow-motion replay. It's 2 November 2003 in the old Benito Villamarín stadium in the 40th minute. Atlético midfielder Jorge crosses the ball towards the centre. Torres, in a yellow 'away' strip, runs, loses his marker, neutralises the defender and lets fly. It's an artistic action, harmonious and elegant, filled more with agility than energy. It compares to a cat lazily stretching its paws one in front of the other, like an exhibition performance of karate. Thanks to his soaring leap, Fernando touches the ball with the tip of his foot and directs it between the opposite post and crossbar. A goal of cinematic quality.
Unfortunately, in February 2004, El Niño is again injured and the second part of the season isn't as productive as the first.
Meanwhile, Torres has extended his contract up until the end of 2008. It's somewhat less than what the board had wanted. It would have liked to renew it up until 2010 or even 2014. El Niño is one of the team captains: 'It was difficult because of his age and because there were other players older than him in the dressing room but they helped him to be a good captain. They respected him and everyone listened to what he thought. He was the emblematic player and symbol of Atléti but he still didn't consider himself a star and nor was he,' recalls Manzano. 'He was beginning to grow and mature a lot during the season. He's always been someone who's open to everything with an extraordinary human quality. If you had to pick out some things, I would choose his ability to surmount difficulties, his humility, his unselfishness and his ambition. The only bad point was his lack of experience and not pacing himself during matches.'
Despite the good results, Gregorio Manzano lasted for just one season and in 2004–05, César Ferrando arrives. The manager changes but the club's institutional crisis means there is no money to reinforce the squad. The key element in all this for Atlético is, once more, Fernando, who is twenty and a star. He is one of the most sought-after Number 9s in Europe and the idol of teenagers, mothers, and of the younger fans, who believe he will be bigger than all the club's previous glories. He is a marketing man's dream, selling everything from watches to footwear, from video games to beer, from breakfast cereals to jeans. One example is Pepe Jeans. Thanks to the Torres effect – charismatic, charming and dynamic – it increased its Spanish sales by 25 per cent. Torres is a model for fashion and women's magazines. The rates for use of his image rise 75 per cent in three years.
And he is the driving force behind Atlético's commercial operations – 70 per cent of the replica shirts sold have his name on them. He earns 3½ million Euros a year, drives a metallic grey Porsche Carrera 4S (his first capricious buy) and is superstitious – so much so that every time things don't go well, he changes his hairstyle. He goes to Olman, his hairdresser, who invents a style. From shaved head to punk look-alike, from spikey to coloured highlights. He likes to dress up in the latest fashions and, sometimes, when he can, he even goes to watch a fashion show. An elegant champion who does good business with his image to such an extent that they've started comparing him to David Beckham, the football pop star who arrived in 2004 on the other side of Madrid. But he wants to clarify that 'Beckham sells a huge amount all over the world but if he stopped playing, his advertising income would also go down. Basically, the image of a footballer is built up starting with what he does on the pitch. For this reason, I would never not go to a training session because of a photographic shoot.'
He doesn't like politics but is fascinated by the people who go out into the street to protest against the war in Iraq or to condemn the Atocha bombings of 11 March 2004. He hopes they succeed in changing things. He's a modern type, who believes in God but sees no problem with homosexual marriages, which the Spanish church vehemently condemns. As an adult, if he wasn't a footballer he would have liked to be the singer of a rock group: 'Someone capable of moving a lot of people, like footballers, only a rock star doesn't have opponents.'
In an interview with the Italian newspaper, _Corriere della Sera_ , he even describes how he doesn't like football: 'I say it in all seriousness. It bores me to watch a match on TV. I've never seen one all the way through. I like to play. I love the match and the fans but everything that goes on behind the scenes – from the little I know about it – I don't want to know. The television companies, which impose their own rules and economic interests, which overload the (sporting) calendar. At the end of the day, it's only business and nothing to do with watching sport.' A surprising response for someone who lives thanks to football and who enjoys a huge popularity.
Fame continues to surprise him. 'All the time. Above all, outside Spain. But football is now almost like a worldwide commercial.' Difficult to live with? 'At first I found it difficult. I was shy, I was embarrassed. I was blushing. Now, a little at a time, I'm getting used to it even if it's difficult. I miss the times when I was able to go for a walk with my dog without anyone stopping me in the street. But that's the price you have to pay.' What does he make of the millions he's earned? 'The first thing I did was buy a house for my parents, a car for my father and my sister and help my brother Israel with his mortgage. I've become what I am thanks to them. I will never forget that if it wasn't for my mother (several times she arrived late at work to take me to training sessions) I would not be here. It seems right and proper to give back to them everything that they've given me.'
A good lad who still lives with his parents: 'My mother is a great cook. Her pasta with cream and ham is streets ahead of anything you get on training camps. And of course they know me well. If I got big-headed, they would let me know about it.'
Even his manager says so: 'The success hasn't gone to his head.' In spite of this, the sports journalists dedicate their front pages to him after he puts two goals past Barcelona in the Camp Nou on 6 February 2005. 'He trains just the same as any of the others because he is very competitive and a very good team-mate. He never tires of learning. These things outside of sport don't affect him.' Another thing that pleasantly surprises manager César Ferrando is the 'leadership ability of Torres. He has taken the bull by the horns and said this is down to me, I will be pulling my own weight.' Come May, though, because he has been pulling his own weight, El Niño is worn out. In-between the league, the Cup, the Intertoto and the national side, he's the player who's played the most minutes in Spain. He can't go on, he hasn't scored in more than a month and Atlético have come to a halt. They no longer have any options in the league and they've been knocked out of the Cup. They will finish 12th, a long way off the champions, Barcelona. His own account, however, is positive: sixteen league goals and two in the Cup.
In 2005–06 he begins another season and in the dugout there's a new manager. This time, it's the Argentinian, Carlos Bianchi. He has an impressive CV, which includes Boca, Velez and Roma, the backing of the directors and major reinforcements on the pitch – Mateja Kezman (signed from Chelsea), Martin Petrov (now with Manchester City) and the Argentinians, Maxi Rodríguez, and Luciano Galletti. On paper it's a strong and winning squad. There's hope of qualifying for the Champions League. The new gaffer starts well, Torres playing his part, scoring as he knows how and ending up surrounded by controversy because of a very unusual celebration.
In October, in the Rosaleda stadium against Malaga, he scores a penalty – his third goal of the season – then sticks out his tongue and puts his fingers in his ears while running down the pitch. The crowd don't like it and take it very badly, perceiving it as an insult, while in fact, it's a birthday dedication to his friend Jorge Larena who plays for Celta. A juvenile joke between the two that becomes a hot media topic. But that's nothing compared with what happens some time later.
By the 18th match of the season, Atlético are floundering in the lower reaches of the league, raising once again the possibility of ending up in the second division. Carlos Bianchi packs his bags. Four years later, Torres will say: 'He had very good ideas but the players didn't understand him.' In his place, comes Pepe Murcia, who begins in style. He wins five matches on the trot and brings the team back from the depths to end up just four points off a position that would have finally seen them playing in Europe. It's fourteen years since Atlético has achieved anything like that and the fans had their hopes high. But as always disappointment is just around the corner. Atlético once again finish empty-handed, in 10th position, and Europe remains a mirage. It's necessary to start all over again.
The next season – El Niño's last – begins in the company of Mexican manager, Javier Aguirre and 'Kun' Sergio Agüero, the young Argentinian phenomenon who's being compared to Maradona and Romario. He's the most expensive signing in Atlético's history. He has come from Independiente at a cost of 20 million Euros. He should be the perfect support for Torres, who, in the Germany World Cup, described him as a great striker. The ingredients for success, this time, really do all seem to be there. Atlético, together with Barcelona, are the teams generating most expectations. Instead, it's Fabio Capello's Real Madrid that wins the league on the last day of the season. El Niño has already decided to leave. In seven seasons without winning a single trophy, he has scored 82 goals and seven in the Copa del Rey. He was the icon and standard-bearer of the team who, at seventeen, 'knew how to take on the starring role and keep alive the hopes of an institution in its darkest hour. The administration', writes Manolete-Manuel Esteban – journalist of sport daily newspaper, _AS_ , and one of Atlético's best-known supporters – 'was dominated and hounded by the courts. The club's enemies were taking advantage and no one gave any importance to what was happening on the pitch. His appearance on the scene led to an explosion and a breath of fresh air. He didn't have any doubts about putting his professional future at risk, even when the directors asked him to help underwrite and ease the financial difficulties. He knew how to raise the hopes of the fans and declare that he would never wear the white of Real Madrid. His years were always presided over by performances of a high calibre and, above all, by being a kind of Robin Hood figure, who was trying to take a part of the popularity from the big clubs and give it to the less fortunate ones. In the end he needed a change of scenery to make his wishes come true.'
## Chapter 14
**He's earned it the hard way**
_Conversation with Mexico and former Atlético de Madrid manager, Javier Aguirre_
Following an afternoon in Madrid's Las Ventas bullring to see his fellow countryman and bullfighter, 'El Payo' _,_ in action, followed by some _tapas_ with friends, 'El Vasco' ('The Basque') Aguirre has a few moments to chat. It is almost midnight and he still has his case to pack. In the morning, he leaves for Mexico City, where, in a few days, he will be in the dugout for his first match in charge of the Mexico national team. On 3 April 2009, the Mexican Football Federation appointed him to succeed ex-England and Manchester City manager, Sven-Göran Eriksson. It is his second spell as manager of the national team. The first began in 2001 and ended after the side's exit at the hands of the US from the 2002 South Korea and Japan World Cup after reaching the last sixteen. For the seven years in-between he lived his big Spanish adventure.
It started in Pamplona with Osasuna, the team where Aguirre played briefly in 1986 before a broken leg put a premature end to his Spanish playing career. Returning as manager in 2002, over the next four seasons he took Osasuna to a Copa del Rey final and classification for the UEFA Cup. In 2006, thanks to a fourth place in the league, they qualified for the Champions League for the first time in the club's history. An achievement that earned him a one-year contract with Atlético Madrid. 'El Vasco' Aguirre took up the challenge of returning the club to the upper reaches of _La Liga_ and a place in Europe. He says of Fernando: 'Any manager in the world would want Torres in his team. Who wouldn't? Fernando is the standard-bearer of the team.'
On 3 February 2009, when El Niño had been with Liverpool for almost two years, Aguirre was sacked after the club suffered a bad run of results. Fernando gave an interview in which he spoke positively of his former manager: 'He's probably been the team's best manager in recent years, getting them into the Champions League, and no one can take that away from him. That's why he was hired and that's what he achieved. I don't think he is the real culprit of this situation. That's how football is.'
Now it is his turn to talk about Fernando. With the Atlético uproar now in the past and with the relative calmness his experience and new post allows him, he recalls in measured tones El Niño's final year in the red and white of Atlético Madrid.
### _What do you think now of Fernando?_
'I think he deserves all the good things that have happened to him. And when I say that, I'm referring to the advertising contracts, to playing in the Champions League, to battling on right until the end of the English season. He deserves it all because life hasn't done him any favours. In the year that I was with him, I realised that he was a lad who was trying to improve himself every day. What he has, he's earned it the hard way.'
### _But that 2006–07 pre-season didn't begin well. You declared that you could not guarantee Torres his place in the team. The newspapers were saying that Manchester United were ready to pay 37 million Euros for El Niño._
'I don't remember making any declaration, either me or Fernando. What I remember is that when I arrived at Atlético, we talked with Fernando about the fact that the club needed to be in Europe because a lot of years had gone by since that had last happened. Fernando had never played in a European competition with Atlético. I do remember discussing this objective and him welcoming me as captain and he said that this was his objective as well.'
### _How did Torres get on with you and with the dressing room in general?_
'Very well. Fernando was a lad who was very straight with everyone. He was born in the club and grew up in the club. In the dressing room, he gave the impression of being shy, quiet, and it's true he didn't say much, but when he spoke one heard him. He was a natural leader. I remember that people looked up to him with a lot of respect. The club administration and directors used him at all the club events. He was the image of Atlético Madrid. There was an event for sick children and Fernando went, there was an event in the prison and Fernando went, there was a meeting of supporters' groups and Fernando went. He was always available, always saying 'yes' to anyone who asked for an autograph or a photo. He was a man who knew what he wanted and we always had a great relationship. He always treated me well and was very respectful of my decisions. He always did his best for the team, and as captain he would always be prepared to take the flak.'
### _What struck you about Torres?_
'The person. I never saw that lad pull a long face, I never saw a rude gesture, he always had a smile for everyone. This is the best side of him because as a footballer he now has it all. He is complete, you can't single out anything. As a person, he's much better.'
### _And what was good about Fernando as a footballer?_
'What was good was that he knew that he had to improve lots of things. He had it all, he really did, to be a top star player. He was that already but he knew that there was room to improve still further. And because of that, Fernando wanted more training every day. Every day he studied the details of every move. He was the first to arrive and the last to leave. He is a true professional. Technically, his left side required a bit more effort as well as his guidance of the ball – he would suddenly rush forward too much. There were little details that he polished up and improved considerably. But I remember telling my defenders, Perea and Pablo, not to try to play the ball, clear it long and hard, without looking, send it right upfront and this lad will use it to his advantage. And it was true. Fernando was capable of controlling the ball perfectly, of running between three opposition defenders and scoring goals. There were moves where he kept it really simple, getting hold of a loose ball and going out to the wing – or from one of those unusual clearances – and turning it into a goal.'
### _Why did he leave at the end of the season? Did you know about his agreement with Liverpool?_
'At this point I have to explain a very odd thing that happened to me – I didn't know that he was leaving.' Aguirre laughed bitterly. 'I assumed he was going to stay. I say this because in the last league game of the season, we were in Pamplona playing against Osasuna, and for a UEFA Cup place we needed favourable results from the matches involving Sevilla and Zaragoza. With five minutes to go, we were winning 2-1, Sevilla were winning and Zaragoza were losing. In the dugout, I called Torres over and told him, 'We are in Europe, we're going to Europe, Fernando,' and he looked at me and smiled. In that moment I didn't know it but afterwards I realised what he was thinking, which was that "Yes, I will be in Europe – with Liverpool." He already had an agreement and his departure was certain. The truth is that I knew nothing. In fact, I went on holiday to Mexico and it's there that I found out, from the press, that Fernando was leaving for Liverpool. My surprise was all the greater because nobody had consulted me. It was a done deal. But really it wasn't so strange because the Reds are a team, a big team, and Atlético at that time, were an uncertainty. We went into the Intertoto, after that to the UEFA Cup and then into the Champions League. We'd have liked to have had Fernando with us. In fact, we came together again in the Champions League (Group Stage), when we drew with Liverpool here and away. It was good for us to meet up. It was a pity that he couldn't be on the pitch. In both games, he was injured and saw the game from the stand.'
### _The pressure at Atlético was too much for him?_
'Yes, and I'll say something else. When I arrived at Atlético, I asked him if he would like to continue being captain. I said to him "Look, if you want to leave it, go and relax, enjoy yourself and just be one of the team." He replied in the negative because he felt involved, because he loved Atlético so much and he wanted to grow with the team, but I could see that the lad was suffering – he had too many things weighing down on him. Here he had responsibility for the dressing room, the administration, the fans and the press. For better or for worse, he had to be involved with everyone and everything, whereas in Liverpool he is just one more person. There are three or four who are also important and Fernando is part of that group but he is not the captain. Anfield brings out the best in him because now he doesn't have all those responsibilities.'
### _Yes, but the change has been impressive..._
'That doesn't surprise me at all, In the physical tests, for resistance, for strength, in the day-to-day work, one saw that he had a huge potential. But I repeat, I think the great secret of his success has been that in Liverpool he's not the captain and he dedicates himself solely to play the 90 minutes, while at Atlético he dedicated himself to a lot of things, the poor lad – interviews, sponsors, junior team, supporter groups, the social work of the Foundation. He was very involved and stressed out. Now he can relax and enjoy himself and he's had two spectacular years with Liverpool and the national team. In Euro 2008 he was completely in tune with the Spanish team, he was finishing the moves made by the midfield and scored a great goal in the final, very much in the Torres style, overcoming the German defender when he was at a disadvantage, always with that strength and that desire to score goals. His success at Euro 2008 doesn't surprise me. Luis Aragonés, the manager, knows him very well and got the best possible performance out of him.'
### _The best moment, the fondest memory?_
'Fernando always left us some small gift, always gave us a smile – he has a big heart. The best memory that I have was when, after a big match and without being asked for it, he signed the shirt for my three sons, Ander, Mikel and Iñaki, who are big football fans.'
### _Would it worry you to encounter him again with Mexico?_
'It would give me a huge amount of pleasure because that would mean that we had qualified for the 2010 World Cup in South Africa. Let's hope so, let's hope so. I would love to greet Fernando Torres because he is a good friend.'
## Chapter 15
**Real hope**
_Conversation with Sid Lowe and Guillem Balagué_
An Englishman who lives in Spain, a Spaniard who lives in England. Sid Lowe, aged 32, left London for Madrid in 2001 with the aim of finishing his PhD thesis on the Spanish Civil War, entitled 'La Juventud de Acción Popular en España 1932–1937'. But the enormous media interest generated by the arrival of David Beckham at Real Madrid overtook him and converted him from football fan into football writer. He is a correspondent for the _Guardian_ and _World Soccer_.
Guillem Balagué was born 40 years ago in Barcelona and has lived in England since 1991. He is the UK correspondent for the Madrid-based sport daily, _AS_ , and a Spanish football specialist for Sky Sports. His website (www.guillem-balague.com) features information on Spanish football and footballers including rumours, interviews and comment and even a section on Spanish wine. Two journalists, therefore, who know Fernando Torres well, talk about how he is portrayed in the media and explain the reasons for his success from two different perspectives – Britain and continental Europe.
### _How was Torres viewed when he was in Spain?_
SL: 'The Spaniards knew that Fernando Torres was very good and a talented player, but didn't think he was as good as he has since demonstrated at Liverpool and in the European championships, scoring the winning goal. The main reason, maybe, is the fact that he played for Atlético Madrid. Fernando Torres was the captain, he was the standard-bearer and, to some extent, he was Atlético Madrid. There was a feeling that Atlético Madrid's underachieving, or their failures, were somehow Fernando Torres' failures. He was judged according to his team and not according to his own ability. The other reason, the key reason is that Spain – and Spain's media – are dominated by two clubs, Real Madrid and Barcelona. And that means that a player who has three good games for Real Madrid is a _crack_ , he's the best player in the world, he's unbelievably good. Wesley Sneijder came to Real Madrid and played three games and they were saying he was as good as Di Stefano, better than Beckham. You don't get the same respect as an Atlético Madrid player. And if you asked Torres – he would never admit this publicly – I think privately that he knows that one of his problems was the media was always criticising him.'
GB: 'The image of Torres, before he went to Liverpool was that of a player-leader of Atlético Madrid and, like Atlético as a whole, inconsistent. He was far from perfect and still needed to improve a lot to reach the level he'd been promising since the age of fourteen. Atlético was a huge weight on his shoulders.'
### _What kind of criticism did the Spanish media make?_
SL: 'The message was that Fernando Torres is an Atlético Madrid player, therefore the Madrid media – the Real Madrid media, because it's a Real Madrid media in truth not a Madrid city media – quite enjoyed laughing at Fernando Torres, making fun of him. "Oh he's never going to beat Real Madrid" – "he's a comedy character" – "we know he's talented but ha, ha, ha, he's never going to score". Torres' big problem in Spain was that he played for the wrong club and we've seen that to some extent with the Spanish national team. That's because the Spanish national team, in theory, is everybody's team, but in reality the judgement is still coloured by which team the papers support. So you've got _Marca_ (a Spanish sport daily), which says it's "all for _la selección_ " (the national team), but it's "all for the _Real Madrid_ players in _la selección"._ So Torres plays in the national team: "He's not as good as Raúl" – Raúl doesn't play in the national team: "It's a disgrace".'
GB: 'He was criticised because he wasn't finishing well, he was criticised because he was failing to round off movements, he was criticised because his first touch wasn't good and he was criticised because, sometimes, he kept hold of the ball too long. But there were also critics making the same kind of comments about Atlético Madrid, that the club never built a good enough team in which Torres could improve. First, there was criticism of the club, which failed to instil any kind of stability while Torres was there, and then of the team. There were a lot of players who avoided their responsibilities and passed them on to Torres instead. And finally, there was criticism of Fernando, above all at the end, when his body language said he was tired and fed up of being there. And he'd been like that for a long time.'
### _And how is the image of Torres now in the Spanish media?_
SL: 'The image now is that Torres is a wonderful player. Torres is now "our boy" doing wonders over there. He's "our ambassador". The Spanish are a very proud nation. They are very aware of their own identity and when a Spanish player goes abroad – let's take Torres – he becomes "Spain's Fernando Torres". On top of that, you've got the fact that Fernando Torres scored the winning goal in the European championships, the most important goal in 44 years in Spain. That helps... Suddenly, people in Madrid respect him in a way they didn't respect him before. Now the media is allowed to like him, but he will always have that barrier and that barrier will be "he's not Real Madrid". And I think that's really important when it comes to judging how the media and some of the public see him.'
GB: 'Now it's that of a player who has exceeded even the most optimistic of predictions. He's turned himself into a global personality, much more than the Spanish national side, a top player and one of the biggest stars in world football.'
### _A lot of commentators, not only in the English but also the Spanish media, had doubts about Torres' chances of success at Liverpool..._
SL: 'Definitely. Fernando Torres had a very good record at Atlético Madrid, top scorer in every season, but not the record of a guaranteed success. People say that Rafa Benítez bought an obvious player. It wasn't that obvious. Sir Alex Ferguson didn't buy him, he wasn't sure. Fernando Torres had never scored twenty league goals. He hadn't led a team to huge success. I think Rafa Benítez would be entitled to believe that Fernando Torres' problem would be Atlético Madrid. And it was right.'
GB: 'Well, there were doubts that were justified because the level at which he was playing at Atlético Madrid was average. But there were also doubts in the minds of the people who signed him. He was never the first option for Liverpool – that was Samuel Eto'o. And the actual player harboured doubts as well. He didn't know if he was able to achieve success straightaway. He knew he could go all the way but he thought it would take a bit longer. The English media weren't convinced either because they could point to the examples of Spanish players who'd arrived in England and failed, like Fernando Morientes or José Antonio Reyes. Until the arrival of Torres, Spanish strikers hadn't made much of a case for themselves. In any case, the national media had doubts. However, the Liverpool media and the team's fans were more open-minded. They went on to embrace him as a big star. "Torres has arrived" they said. They'd seen how he scored goals against Barcelona, they'd seen his speed and the Liverpool supporters, who are very committed to the club, were the ones who had the least worries. But, yes, it's true that neither the Spanish nor the English press saw the situation very clearly.'
### _Why was there this big change between Atlético Madrid and Liverpool?_
SL: 'Well... maybe, the change is not quite as incredible as it looks. Maybe the change is just from a team that finishes eighth to a team that finishes second, a team that doesn't play in the Champions League to a team that does. It's just a little bit more. But I agree with you, I think there is a big change. At Liverpool, he doesn't have the responsibility. He doesn't have the pressure. He plays with better players. Steven Gerrard is playing behind him. English football suits him, there's more space. The game is more physical, it suits Torres' style, it's more direct and that game is better for him. The first goal against Real Madrid is almost the perfect portrait of what Fernando Torres has become. Aggressive, strong, powerful, quick – and those are things that people in Spain don't value and in England we value them very highly.'
GB : 'Well, I have my theories on that. One: that he really wanted to leave Atlético and he fancied going to England. The previous summer, before he signed for Liverpool, there were meetings between his representatives and Sir Alex Ferguson but nothing materialised. The following summer, Fernando was absolutely clear in his own mind that he wanted to go to Liverpool. He did everything possible – and impossible – to try to convince Benítez. His representatives, his agent and his friends talked to Rafa and in the end an agreement was reached. Two: that English centre-backs and defences in general – compared with Spanish or Italian – are bad, leaving too much space, and a player who has speed can have a field day. It's also evident that Torres has improved not only his first touch but also his movement and ability to run with the ball, as well as choosing his moments during a match. And all that comes from working with the best manager in the world.'
### _How important is Rafa Benítez in this change?_
SL: 'Rafa is very important. If you listen to Torres talk, he will tell you that Rafa Benítez is the best coach he's ever had. And it's not just because he likes him. It's because Benítez as a coach is a perfectionist. A lot of coaches are not coaches, they're the people who put players on the pitch. Benítez is a teacher, he's explained to Fernando Torres how to make the right moves, how to fit the system of the team, how to play defenders, make the run left, the next time right. You also have to remember that part of Benítez's success is because of Torres. He's very receptive to ideas, he listens and he's intelligent. He's got a player who thinks about the game.'
GB: 'Very important, because Benítez is a real pain. He succeeds in improving a player through a regimen of repetition, repetition, repetition – of ideas and exercises. Torres is absolutely clear on this. He recognises the tremendous work of his manager. For sure, Luis Aragonés had more influence on his career and taught him a lot when he was young but it's much more difficult to learn when you're already an international and been captain of your team. It's really hard to learn at this stage – at least if you haven't come across Benítez.'
### _And he's also done good psychological work with him..._
SL: 'Without any doubt. Fernando Torres at Liverpool is a different psychological player to the one he was at Atlético Madrid. Torres felt that at Madrid all the pressure, all the blame and all the responsibility was his. At Liverpool, other players have it. El Niño has become an idol at Liverpool and the fans really love him. But they don't expect him to do everything on his own. At Atlético Madrid, the fans expected that. And also at Atlético Madrid, there is fatalism while at Liverpool there's hope.'
GB: 'I don't think psychology is Benítez's greatest strength. Psychology comes from confidence and confidence from improvement. No, Benítez isn't a manager who tells Torres every day that 'you are the best', but Torres sees it and Torres isn't someone who lacks confidence. He finds himself in a style of football that suits him perfectly, with a team that's ready to play for him, with long balls, taking advantage of his speed and getting behind the defence. The psychology comes of its own accord.'
### _What about the image of Fernando in the English media?_
SL: 'Right now, the image is of a player who is possibly the best striker in Europe, a phenomenally good footballer. He's an athlete. He's fast, he's strong, he's powerful. He looks like a baby in his face but he's a really strong man. An aspect that people don't talk about often enough is his intelligence. He's very bright, he's willing to learn, he listens to Rafa Benítez, he listens to his coaches, he does what he's told to do and he's very committed. He is much more humble than people sometimes think. He's a very sensible, intelligent individual. His defects? Right now I don't think he has a defect. OK, he needs to be better with his left foot, he needs fewer injuries, but maybe we are asking too much. What we're seeing now at Liverpool is that Torres is the perfect player for the perfect team. For example, Fernando Torres at Barcelona would not be the same player because Fernando Torres wants space in front of him, he wants to be able to run into gaps. If you play with a team like Barcelona – touch-touch, pass-pass – it's intricate, it's clever, it's angles. It's much harder for Torres. Even when there are criticisms, they are positive as well. One criticism of Liverpool is that they need more players like Fernando Torres.'
GB: 'In England, you don't have to do very much to be a big star. If you have something that others don't, then you're big. For example, Cesc (Fabregas) is young – in the Arsenal team he's a leader, he knows what to do with the ball, he's the player who controls the midfield, who makes the perfect pass and he's a star. The same thing's happened to Torres. He scores, he begins to notch up goals one after the other, and now he's the best striker in the world. But in reality, he isn't. With all respect and the great affection I have for him – I've also talked about it with him – he is one of the greatest but he still has to improve. The truth is that in England they know very well how to sell their own, or rather, how to sell the players that play in their league. If Torres had the same statistics in La Liga in Spain, he wouldn't be the best in the world. No, here they're very good at selling. And they're amazed when Cesc isn't playing for the Spanish national side. "Come on, that can't be right," they tell you in England. With this in mind, it's interesting the interpretation that the English media put on the Euro 2008 final when, because of Villa's misfortune, Cesc was selected and Torres scored the winning goal. Here, they say they won because these two were selected and because they were playing in their favourite positions.'
### _What does Fernando Torres now represent in English football and at Liverpool in particular?_
SL: 'In a way, Torres represents the supremacy of English football, as Cristiano Ronaldo does, but Torres more so. We are the league that gets the best players. The Spanish league is strong but we took Torres from the Spanish league and we brought him to England. Cristiano Ronaldo is different. He might be the best player in the world but Cristiano Ronaldo went to Manchester United very young. Torres is a demonstration of the fact that the English league can attract the best players. Now I know we said that at Atlético Madrid maybe he wasn't the best player but he was a big star.
'Torres demonstrates the strength of the English league and the fact that young, talented players at the top of their game will come to England. He's shown us that we can develop a more European style – even though I think his style is quite English. We are showing we can bring these players in and we can have success with them. There was a time when we felt in England we would buy a good player, he would come to England and he wouldn't succeed. Now we're seeing that we're buying good players and they succeed because they adapt to us but also the English league is adapting to European football.
'Torres is an indication of the fact that the English league can create loyalty – not have loyalty, create loyalty. You've got a player there who's come to Liverpool and he feels like a Liverpool player now. I think that happens maybe more than it does in Spain and that brings us to what he means for Liverpool. Torres is the nearest thing to Kenny Dalglish because Liverpool has had some brilliant players in their time. They've also bought some brilliant players – John Barnes, Peter Beardsley, John Aldridge. But it's a long time since Liverpool bought a player who the fans think is amazing.
'If you look at Liverpool's favourite players over the last ten years – Michael Owen, from Liverpool; Robbie Fowler, from Liverpool; Steve McManaman, from Liverpool; Steven Gerrard, Jamie Carragher, from Liverpool. Fernando Torres is probably the first player for a decade that has been brought to Liverpool and everyone has gone, "Bloody hell, this guy is brilliant." It's important because it shows Liverpool fans they can bring in great players, they can make great players work and they can start having faith in buying footballers. Kenny Dalglish, although he came from Scotland, was still a bought player. He was the player who was supposed to replace Kevin Keegan and went on to be probably the greatest-ever Liverpool player. Now Liverpool fans won't say Torres is the best player who's ever played for them. There's Steven Gerrard, Graeme Souness, possibly Robbie Fowler because of what he represents, Kenny Dalglish and so on. But I think Torres is possibly the best player Liverpool has bought in ten or fifteen years.
'I think Torres has known how to embrace Liverpool as a club. I did an interview with him not long ago and he said to me that when he turned up he watched videos of Liverpool's history. He read books about Liverpool's history and the fans really appreciate that. They appreciate someone who cares, not just someone who plays. I think Fernando Torres has had the intelligence, the decency and the commitment to take Liverpool to heart. Obviously, if he'd gone to Manchester United, he might have done the same but Liverpool fans don't care about that – he came to Liverpool and he's done all of that. One of the reasons he's done that is Rafa Benítez understands what Liverpool is, Xabi Alonso understands what Liverpool is. Rafa Benítez and Xabi Alonso have very intelligent advisers who are Liverpool fans, and who have been able to explain the Liverpool process, and Fernando Torres has built on that and learned from them.
'So Fernando Torres represents for Liverpool, in one word, hope. Torres has brought real hope to Liverpool fans, probably more hope than they've had for a long, long time.'
GB: 'Torres is the leap forward that the people of Liverpool think will enable them to win everything. Before, they had Gerrard – one of the best midfielders in the world – Hyppia, Skrtel, Xabi Alonso – all top-level players. But with Torres they think he has brought them that extra touch. They have the goalscorer who makes them candidates for everything. He represents the hope, but, more objectively, the possibility of winning, of making all those dreams they've had for so many years come true.'
### _Now, the future. Someone said he's still got a lot more improving to do._
SL: 'I think sometimes we talk about improvement and we're wrong. Sometimes we talk about improvement as if this player will get better and better and better. It's not a question of getting better, it's a question of repeating the same thing. For example, when Ryan Giggs started with Manchester United at eighteen years old – brilliant. When he was 25, people said, yes, he's good, he's OK. Why? Because when he was eighteen, they thought he would keep getting better. But he just carried on being the same. That was still brilliant but people expected too much. The expectation was more than the player could give.
'Fernando Torres is 25. He's in a team that's been to a European Cup semi-final. He's on course maybe to do it again. He's in a team challenging for the league and he's scored the most important goal in Spanish football history. In another ten years time, if he wins another European championship with Spain, or a World Cup, or a European Cup with Liverpool – that's not really improving, it's just repeating the same thing – then he will be a true great.
'It's not really that he's going to get better, it's that he has the attitude and the mentality to maintain what's already a fantastically good level. It's like Leo Messi. Everyone says he's going to get better. No he's not. But it doesn't matter because he's already absolutely brilliant.'
GB: 'He's seven out of 10. On a psychological level, confidence helps him a lot. He controls the ball well but he has to improve because he won't have that speed all his life. He must perfect his first touch and finishing. His future? Fernando won't leave Liverpool until they've won a league title – he's very aware that it's fundamental for the fans. Then after that he'll want another and a Champions League. At Liverpool, they like him a lot and he likes Liverpool a lot. He's immersed himself in the club philosophy and the city. I lived in Liverpool for eight years and it's a mesmerising city. Once you enter its atmosphere it makes you want to stay. It's also true that Liverpool is not Atlético Madrid, the team of his life, but we'll see. Now, in England, Torres has very clear objectives.'
## Chapter 16
**Liverpool 1 Chelsea 1**
_19 August 2007_
Sixteen minutes to become a hero. Steven Gerrard, in the midfield circle, looks up. To his left, he sees Fernando, ready to pounce. A long diagonal pass with the outside of the foot. Perfect, as on so many previous occasions. On the move, Torres is unstoppable, his counter-attacking is lethal but he has to prove it at Anfield, his new home. He gets to the ball without difficulty, even though it was a bit long. He moves onto it with speed, then holds it up briefly on the white line of the opposing penalty area, strokes it with his right foot and takes on the Chelsea defender, Tal Ben Haim. In a flash, a change of pace and he's off. Petr Cech tries to close down the space but can't do anything, his white-gloved hand touches only grass. El Niño's shot is aimed just inside the opposite post. Precise, surgical and exact, like a mathematical formula. For the ex-Atlético Madrid player, it just remains for him to turn and slide along the turf, arms open wide, to offer himself to the terraces, for them to embrace what he has kept on doing since the first minute, to receive his deserved tribute.
It's not only a goal, it's love at first sight between the young lad from Fuenlabrada and the residents of the Kop. Now they've found their very own _matador_ , the clinical finisher they were looking for. In just a few seconds, Torres has demonstrated his qualities – speed, power, precision and class finishing in front of goal. No, he's not the dud signing that some were afraid he might be. No, he's not the other Fernando (Morientes) who arrived from 'sunny Spain' generating huge expectations and then didn't perform as he should have done. Right from the first moment, this Number 9 seems something else altogether.
The plaudits from the press flood in. So it's a pity then that the match ends in a draw after conceding a penalty that the 45,000 present would swear they hadn't seen. But it doesn't matter. For the new arrival it's a great day. He couldn't imagine a better debut – scoring a great goal against opponents like Chelsea and then getting applauded with an ovation. So many times, old and new team-mates have told him what it means to play at Anfield. The atmosphere, the fans, the emotion you feel when you come on to the pitch, the songs, 'You'll Never Walk Alone'.
But in the end they had said it was something that was difficult to explain, and that you had to feel it on your own skin. And it's true that the sensations Fernando feels, coming down the steps, touching the club badge and standing on the green rectangle, are absolutely unique. He doesn't know how to express himself. He's happy but he doesn't allow himself to get euphoric. 'The goals are going to give me confidence, which will help me to adapt, but I still have more to do. I've only just arrived and the way of playing is very different. With goals, there's much less pressure and I hope that they keep coming, but there's still an awful lot more for me to do to be at the level of some of my team-mates and to adapt myself to the Premier League,' he declares. He claims he doesn't feel the pressure of being the most expensive signing in the club's history, people have given him a warm welcome but he has to work, 'because when you work, things happen.'
Better to tread carefully at Liverpool, having been there a little over a month. His first training session at Melwood with his new classmates is on 11 July. He gets changed inbetween Gerrard and Voronin and realises that it's true, he's actually a Liverpool player, and that this will be his dressing room for the next few years. By the end of the first day, he's discovered a lot. The media are not allowed into Melwood. In Spain, they call it training 'behind closed doors' and when Fabio Capello, then with Real Madrid, introduced it, he was flooded with criticism. Here it's normal and the new arrival likes it because one can train in complete tranquillity, practise the game plan and the technical moves without a photographer trying to immortalise you in a fleeting moment, without some little problem ending up on the front page.
And then there is the important, necessary and intense physical work under the guidance of Paco, who never tires of repeating it over and over again. And the manager's technical lessons. At Melwood, they all have lunch together and very often players and technical staff stop to eat, a good way to check on what they're eating – the gaffer is very strict regarding fats – but they are also moments for getting to know each other better. Rafa Benítez explains to Fernando his new role. He wants him to play in a different way to what he was doing at Atlético. More direct moves up the pitch, operating more deeply with fast movement to take advantage of his running. He doesn't want him to drop too often to the wings or backtrack to create an attacking move. To provide him with playable balls, they think of Gerrard, Xabi Alonso and even Pepe Reina with his superlong deliveries. Rafa wants him to be the ultimate Number 9, like Ronaldo or Van Nistelrooy, always inside the opponents' penalty area and not a second striker, which is how other managers like Luis Aragonés wanted to use him. He wants him to exploit the spaces that are created when a team advances and for him to get behind the opposing team's defenders.
It's no easy thing to absorb all the tuition in one go, in the same way that it's not easy to adapt oneself to the club, to the fans, to football 'across the Channel', to speaking English, to the city, to a new country, to the food and even to driving on the left. Fernando Torres applies himself with determination and commitment. When he arrived, they gave him a pile of DVDs and books about the story, the traditions and the great champions of the Reds. Among them there is even one about the Kop. And some time later, he admits that he has kept it and read it. He researched in depth because he himself grew up in Atlético and, as captain, he had the task of explaining the values of the club to every newcomer who had to understand the origins, the passion for the club colours, to know the famous champions of the past, so that they have the necessary reference points to avoid feeling like a fish out of water.
While studying, he realises that he's arrived at a club that is even bigger and more important than he imagined. A club which functions well, where everyone has a clear role, where no one sticks their nose into other people's work, as happened at Atlético. English? Ah yes, English – or rather the scouse dialect – is a big problem. Even if, right from the first day, the club has put Rob, a private teacher and fanatical supporter, at his side, even if he has lessons every time he has a moment to breathe. He reads what Rob suggests to him and even watches _Friends_ in the original English language version (he already knew the dialogue in Spanish and some of the easier bits), which requires time and patience. During the first few days he admits to understanding absolutely nothing. The people of Liverpool speak at an incredible speed and their accent is an enigma, even for some English people. But he wants to learn so that he can understand and be understood by his team-mates on the pitch, to be able to talk with the fans, to be able to give a press conference without having to resort to the translator. To be sure of saying what he really wants to say. He's already set the target of the end of the year, or at most, the first months of the next, to make his debut in front of the media. 'Man on' and 'Time' are the first words of the football vocabulary that he learns. Essentials in order not to let your opponent get the better of you and why the manager's technical explanations are in English. In the dressing room, Rafa makes it clear that the only language to be spoken is that of William Shakespeare. There's trouble if he sees Torres whispering in Spanish to Pepe Reina. Just like at school, he sends one to one side of the room and the other to the other. And he repeats patiently, 'English, please.' Of course, if there's a need for a personal explanation, the gaffer is happy to relent and does it in Spanish. Like Pepe, who, in terms of helping him adapt to the club and the city, its customs and practices, has been fundamental – even if, later, when Fernando begins to speak in English in public, he doesn't hold back from taking the mickey, as is his custom.
Fernando goes to live in Woolton in a house with a garden where, a few months later, his two boxer dogs, Pomo and Llanta can amuse themselves. It's a small detached house, which has been left empty by former Liverpool player, Boudewijn Zenden. He likes the area and it also has the advantage of being about 50 metres from the home of Pepe Reina and his wife, Yolanda. A few months later, Olalla will join Fernando and the two couples will become firm friends. Meanwhile, Fernando also has to adapt himself to a city so different from Madrid, which he knew like the back of his hand, where he knew all the routes almost automatically, and his family was nearby. On the few times Fernando has been out and about in his Audi Q7, going very slowly and carefully because of the right-hand drive (the first few trips were very hard and he went the whole time down the middle of the road), he discovers Liverpool to be a friendly, quiet city, where, finally, he can lead a normal life. Where, after training, he can go to eat in the centre with Pepe Reina without anyone bothering him. He can walk into a shopping centre like the Met Quarter or the Trafford Centre, outside Manchester, without being mobbed by supporters. A pleasure and a novelty for a footballer, who, in a now distant 2003, was walking in the La Vaguada shopping centre in Madrid with the aim of buying a pair of shoes and ended up being surrounded by so many fans that the security staff had to close all the entrances so that he could get out safely. But in Liverpool the supporters are polite and prepared to wait hours for a photo or an autograph. 'It's a city', explains The Kid, 'where, if you give them what they want, they give you everything, and not only on the pitch.' Indeed, on the pitch. He has to get the measure of the fast, powerful and physical football in England, with its high rhythm, where you can't take a breather even for a minute, where each time your defenders get the ball you're in front of your opponents' goal within three passes and in with a chance to create something. Different from the slower Spanish football, where the little touches are important, where the possession of the ball, for many teams, is an absolute imperative. Fernando had always said the English style was something he could get his teeth into. Now he's seeing whether it really is to his liking.
It's Tuesday, 17 July, when he wears the Liverpool shirt on a pitch for the first time. Incidentally, the one he wore at his presentation was put up for auction to raise funds for cancer research. The winning bidder was an Irish businessman, a die-hard fan of the club, who paid 7,300 Euros (just over £6,000). Coming back to the long-awaited debut, it's the third friendly of the pre-season against the German side, Werder Bremen. Fernando comes on in the 64th minute in place of Andriy Voronin, who has scored the first and third goals for the Reds (the final score will be 3-2 for Benítez's side). He plays for 26 minutes, despite a slight ankle problem. He has two good opportunities – one, when he gets the ball at his feet after a short kick by the keeper, but in the end shoots it straight back to the goalie, and the other when a long shot skims the bar. The friendlies continue in the Far East. From 24–27 July, Liverpool takes part in the Barclays Asia Trophy in Hong Kong, where they play against South China. This is not a good moment for Fernando. Actually to see him score, you need to go to the Port of Rotterdam Tournament on 3 August. He comes on in place of Jermaine Pennant and scores against Shanghai Shenhua. It's a friendly of little value, the eighth of the pre-season, but a goal always goes down well. As Benítez says: 'It'll give him a lot of confidence with respect to the new season,' and to those who harbour doubts about his new acquisition, he replies: 'It reminds me of when Crouch signed for us. Everyone was asking when he would score his first goal. Now Torres has done it and he's got rid of that pressure.' The Premier League begins on 11 August.
The first match is away at Aston Villa. The Kid is nervous and excited. He wants to make a good impression, he wants to score but fails. On seventeen minutes, a great left-foot shot goes high. In the 31st minute, he seems made. He picks up a loose ball on the edge of the area, goes round his marker and has only keeper Stuart Taylor to beat. He tries a shot with his left but it's parried by the keeper. With the ball still in play, Dirk Kuyt gets halfway there before the defender and Villa captain, Martin Laursen, puts it into his own net: 1-0. Torres will reflect on that one. Then the captain takes care of things with a penalty to close the account on 1-2. A safe victory, Torres has been able to show his colours and show that he has learned the signals of the gaffer, who declares: 'I'm very satisfied with the way that Fernando has played his first match against Aston Villa. Normally, players take their time to get established but it looks like he has adapted very well.'
But there's a snag that has to be overcome – a goal. The drought continues on Wednesday, 15 August, in France in the Champions League qualifying round game against Toulouse. Fernando only plays the last twelve minutes, coming on for Voronin. He makes his big entry. After six years of futile attempts, he's in the top European club competition. But he doesn't score. And the old, old ghost that's pursued him for a long time (that of making too many mistakes) reappears. Four days later it disappears. Despite John Terry giving him a hard time and being determined to make Torres understand exactly what kind of footballing world he's entered, The Kid can open his arms to the goal. And it's only the first of an endless sequence.
## Chapter 17
**A perfect marriage**
_Conversation with former Liverpool player, Michael Robinson_
The background of his iPhone screen is red. The image shows a figure wearing a Number 9 shirt, with blond hair and arms raised – Fernando Torres in front of the Liverpool badge. Smiling, Michael Robinson displays his mobile phone. He has been a fan of The Reds for as long as he can remember. 'I was born in Leicester but a few years later my parents, for business reasons, moved to Blackpool, about 30 minutes from Anfield. Right from when I was a small boy I never missed a match in the Kop. I dreamed one day of being one of those players in the red shirt.' A dream that became reality in 1983, when Liverpool paid £250,000 to Brighton and Hove Albion for the striker who had so impressed at Wembley in the FA Cup Final against Manchester United.
Robinson spent just one season (1983–84) with the Reds, mostly as a reserve striker, trying to create a space for himself in-between Kenny Dalglish and Ian Rush. But for him and the club it was a glorious year, winning the old First Division title, the FA Cup and the European Cup. In December 1994, he left for Queen's Park Rangers, spending two seasons there before moving to Spain, playing for Osasuna (in Pamplona).
'I arrived the day of Reyes (the day in Spain for giving Christmas presents), 6 January 1987, so now I've been living here for 22 years!' That's right, because after retiring from football in 1989, 'The Cat' – as he was called by his friend, the Liverpool captain, Graeme Souness – has transformed himself into one of the best-known faces and voices on Spanish television and radio. 'I am', he says, 'the only English footballer on Spanish TV. I'm still alone on the podium.' He has commentated on both rugby and football matches, taken part in countless panel discussions, all in his unmistakable English accent, dubbed the voice of the ugly sister in the _Shrek 2_ & _3_ films and had the honour of being represented in the Spanish equivalent of _Spitting Image_ on the _Canal+_ television channel, with his puppet figure taking the role of programme presenter, no less. On _Canal+_ as always, he now presents _Informe Robinson_ (Robinson Report), a series looking at all aspects of the world of sport. To talk with him and listen to his everlasting stories is a pleasure. He knows Liverpool very well, a city and club close to his heart, as well as Fernando Torres, who was the subject of one of his programmes.
### _How did he seem to you when you went to film at Anfield?_
'He surprised me a lot. In a short space of time, he'd learned what Anfield means, the badge, the fans, the value of the shirt, the power of "You'll Never Walk Alone". Straight away, he realised what it means to play for Liverpool. And what it means is: to play for the people. And remember that there's no code of conduct or style book – this isn't something you study, it's something you feel. When I was there, I remember that just before going out on to the pitch, Sam, who was in charge of the dressing room, would call us and open the door just as "You'll Never Walk Alone" was reaching its climax. And the manager, Joe Fagan, would tell us, as in _Hill Street Blues_ (the US police TV series of the 1980s), when Captain Furillo was giving his advice before going out on patrol, "Don't forget these people, we are always in their debt." And that's because the people of Liverpool give you everything they have. They have an amazing generosity and you have to give everything you have. You have to be on their level. At Anfield, the fans blow at you. It's like a wind that pushes you towards the opponents' goal.
'And it doesn't only happen at home games. I remember the Champions League final in Istanbul against Milan. At half-time I was completely disheartened. I was hoping that the punishment wouldn't be any greater than the 3-0 that Ancelotti's players had inflicted on us. But from the stands where the Reds were in the majority, they started to sing "You'll Never Walk Alone". Stevie (Gerrard) told me later that he'd heard it in the dressing room and that it gave everyone encouragement, it made them feel that they couldn't betray those people. They had to give it everything. At Liverpool, you have to feel the shirt. Bill Shankly said it was no accident that the strip was red. Liverpool was a working-class city, with strong trade unions, where there was a lot of poverty. The people didn't have money but what they did have was dignity and a creed and Anfield and Goodison Park were their temples, where they went to sing their songs, where they went to live a dream. And Liverpool, one mustn't forget, has always been the team of the people, a different value and a very strong one _._ The footballer, as Shankly used to say, had to bring happiness back to the people of Liverpool. And you couldn't show off or flaunt your wealth. When Robbie Fowler bought a yellow Ferrari, the manager took him to one side and said he'd made a double-error: that the Ferrari should be red and that no Liverpool player could drive around the city in such a flash car. He was forced to take it back. It's just an anecdote but it shows the spirit of the club. Ah, another example of what Liverpool is occurs to me... [ _Pauses to light cigarette_ ]
'... We were coming back from Bucharest after beating Dynamo. The other semi-final was Dundee United v Roma. Back then they didn't play all the matches at the same time like they do now in the Champions League. When we were in the plane, we got Barry, our pilot – we always had the same crew and even though some of the cabin staff had retired, they didn't want to miss any of our trips – to tell us how the other game had ended up. When he said that Roma had won, the whole plane erupted into celebration. I was a bit puzzled because it seemed to me it would be better to play against Dundee. So I turned to Souness and asked him: "Do you think that's good? Wouldn't it be better if Dundee had won?" And he replied "No, because to play against Dundee would have been more of a British game. We're going to Rome, to the Olympic Stadium, to win the European Cup final, and do it in their home. We're going to make history." And I said "And what if we don't win?" He gave me a strange look and replied "How are we not going to win when we are the best team in the world?" No one had even considered the idea of losing.'
### _Nice story. Having seen what Liverpool is and what it represents, did you think that Fernando would have such a tremendous first season?_
'I was absolutely convinced he'd be a success at Liverpool. When I saw him play for the first time in Spain, having just celebrated his 17th birthday, I thought he could be another Van Basten – and I don't say that lightly. It's correct to say that he had seasons where his form took a dip but he had the whole team's responsibilities on his shoulders and it was him who had to take the consequences. And talking in footballing terms, a good ball came his way about once every full moon. Two opportunities a match on goal was as good as it got and if he missed them and Atlético lost the game, then it was his fault. To put it simply, he was under huge pressure. At Liverpool it's not the same and he's surrounded by great players – no disrespect, of course, to his ex-Atlético team-mates – and the Benítez system suits him.'
### _In what way?_
'When Liverpool get the ball they open things up, create space. Fernando has fantastic pace and knows how to lose his marker, turn him and finish off the move – that's his style. With Stevie (Gerrard) he's formed a footballing partnership that works perfectly. To put it another way, the virtues of Fernando+Benítez's system is 2+2 = 4 plus VAT.'
### _OK, tell me the truth. Do you like this Liverpool team?_
'I like Liverpool when I get the sensation that the batteries on Benítez's remote have run out and the team is doing it's own thing or is a bit angry. I like football less when it looks like a game of chess. But you have to recognise that Rafa is a maestro in knowing how to read a game and that his solid commitment to Torres has paid off.'
### _According to a survey in_ The Times _, El Niño is Number 50 in the list of the best players in the history of Liverpool. What do you think?_
'Fernando is a true idol. He has the capabilities to be another Ian Rush or Kenny Dalglish. I'm certain that with his qualities, and if he stays at the same level, he is going to write a really important chapter in the history of Liverpool. He's not a scouser like Gerrard or Carragher, he hasn't emerged from the Merseyside soil, but he's not a foreigner either, because he wears the red shirt. He's another example of the type of fans Liverpool has – a club where the manager, five players and six members of the technical staff are Spanish. And one has to say that between Torres and the Anfield fans, the marriage is perfect. We have a Number 9 who scores goals and wins matches in the last minute. If he's injured – ooooh! – we begin to get worried. At the moment, Liverpool is Torres, Gerrard and nine others.'
It's now lunchtime and afterwards, Michael Robinson has to return to the studio to edit the latest edition of his _Informe_ programme, which, in this case, is a day spent talking football with Johan Cruyff, discussing everything from a pressing game to the speed of play – concepts that remind 'The Cat' of endlessly hearing the manager in his sleep telling him, 'Get it, give it, go!' And that prompts the final anecdote before he leaves. 'We were going to play against Tottenham. In the coach, the manager asks me, 'Michael, do you hunt?' 'No, I don't like hunting,' I replied. 'Well, it doesn't matter. Imagine that we are going to go hunting for hares and we come across one motionless in its burrow. We could kill it. But if it runs, and runs rapidly, it'll be very difficult. The ball is the same. If it runs rapidly, it's difficult to catch.'
Thank you, Mr Robinson.
## Chapter 18
**Liverpool 4 West Ham 0**
_5 March 2008_
It's a nice gesture by the captain. After the final whistle, he walks up to the referee, asks him for the ball, goes across the field and offers it, as if it was a bunch of roses to Fernando Torres on the bench. El Niño accepts it from Stevie with a big smile. It's the third ball that he's taken from an English ground and his third hat-trick of the season. In six long years at Atlético he never scored three in one game. In England, it's become a habit. The first time was on 25 September, in the Carling Cup against Reading at the Madejski Stadium. The second, on 23 February, in the league and the latest against the Hammers. Luckily – for West Ham – he hit the post in the 67th minute, otherwise it would have been 4. Not only is he exceeding his personal boundaries but also those of Liverpool. It's the first time in 60 years that a player in the red strip has scored a hat-trick in two consecutive matches at Anfield. Never before had a single striker scored in seven consecutive home games – but it happened a short time later. And not since 2003 (Michael Owen) had a Liverpool player racked up more than twenty goals in a season.
Talking of records, before he finishes the 2007–08 season, he will break several. But first a look in the rear-view mirror. In three months, from July to September, the striker from Spain has become important, very important – for everyone. Midfield organiser, Xabi Alonso, acknowledges it in a declaration to the club website: 'Torres is demonstrating that he's not afraid of the physical contact that exists here, with defenders who will try to bring him down. His rivals realise that Fernando isn't afraid of them and that's an extra motivation for him.'
When the new acquisition is on the bench, as happened against Portsmouth, or when he's seen warming up on the edge of the pitch, as on 22 September at home against Birmingham, the fans and the media get restless. Especially when, three days later in the Carling Cup against Reading, he nets three. They always want to see him in the starting line-up and make fun of Rafa Benítez's rotation policy. Take the _Daily Mirror_ headline for its analysis of the situation: 'Why Mrs Benítez would be happy if Rafa even rotated her rotisserie'. A discussion that begins with an imaginary dialogue between Rafa and Montse at breakfast time on the usefulness of rotating the various electrical appliances to make toast. It's worth another look:
Rafa: Take the bread from the toaster, dear. Today we use the oven grill.
Montse: But the toaster's quicker.
Rafa: If you say to me, the toaster is best, I say OK. But I have three machines for browning bread and I must use them all.
Montse: But it'll make the kids late for school.
Rafa: We are a few weeks into the school year. If you want the toaster performing at a good level next June, then OK, you must rest it now.
Montse: Right. Oven it is. Can I use the toaster tomorrow?
Rafa: Who knows? I have to consider the George Foreman Grill also.
The main target of this ribaldry defends himself to the hilt, maintaining that, for sure, 'Fernando can play twenty or thirty matches on the trot without any problem. But if he was to do that, he wouldn't be capable of playing at the same level for the remaining fifteen games during which we are fighting for trophies.' The gaffer's global perspective is understandable, the decision to be sparing with his new millionaire purchase, to protect him, to ensure that he is fresh for when the games get harder, but it turns out, in fact, that El Niño ruins all the plans. He is too important for the team, both in the league and in the Champions League.
In early December, in spite of the injury, he's already scored twelve goals in all competitions. And three of them are heavyweight ones in the Champions League. They also serve to give new vigour to a manager under pressure from criticism, a lot of bad results and his dispute with the club's American bosses, Tom Hicks and George Gillett. Heavyweight goals that have helped the numerous protests in support of Rafa that are seen on the streets of Liverpool at the end of November – Reds fans with his image on posters saying 'Keep Rafa' and even ' _No pasarán_ ' ('They shall not pass' – a famous rallying-call from the Republican side in the Spanish Civil War to rally resistance against the fascist Franco uprising). The stormy waters grow calm and the debate goes back to concentrating on football. In the English papers, a photomontage of Fernando appears with a sharpened nose and a pencil moustache, all underlined with a quote from Steven Gerrard: 'He reminds me of Rush.' Yes, the Welshman and the lad from Fuenlabrada hold each other in high regard. In just a few months, a mutual respect has been formed. Perhaps because both of them took on a lot of responsibilities early, both of them are shy, speak little, do not brag and eschew glamour in favour of old friends and family life. Torres says of Gerrard: 'He is the best, or one of the best, in the world. Never I play with a footballer of his level. It's a pleasure to do so. It's not only the interaction that works between us. Gerrard is able to give you the ball where you want it. He allows you to exploit to the full his qualities while improving your own game.' Gerrard says simply of Torres: 'I wouldn't change him for any other striker in the world.' A very special chemistry, which Ian Rush speaks of as well: 'This interaction between Torres and Gerrard – the same thing happened between me and Kenny Dalglish. It's almost telepathic. Torres makes the defenders work, he keeps them pinned back and he doesn't hide like other foreign players. He's strong and has adapted quickly. Drogba and Henry needed a whole season. If he can get twenty or twenty-five goals, we can win the Premier League.'
The dream of the Liverpool ex-Number 9 is the same as all the side's supporters – to win the league, which for nineteen years has escaped them. The idea is simple: getting a striker that they've not seen the likes of since the time of Michael Owen or better, Robbie Fowler, means the unattainable goal becomes possible. It's a pity that, in the end, Torres surpasses all the predictions but Liverpool end up fourth in the league.
Putting that to one side, one can see the progress of the youngster who has so impressed everyone through his ability to adapt in comparison with the strikers who, as Rush says, have taken a season to understand how things work. After the Christmas holidays that Fernando spends with his family, who have come over from Spain loaded with products from his home country, including everything from ham to olive oil (this The Kid is not giving up), a new crown arrives in early January. In a poll on the club website, the fans of Liverpool elect him as the Best Young Footballer under 23 years of age in Rafa Benítez's 2007 squad. And some days later there's also the nomination of Best Player of the Team in the month of December. It's the third time that Fernando wins it, after first securing it in August and September, before ceding it to Steven Gerrard in October and November. Recognition of his achievements arrives not only from the fans. He is a member of the 'Ideal Eleven' chosen by various European sports magazines.
February – an incredible month. He gets injured during the international friendly with France but returns in time for the last sixteen away leg of the Champions League against Inter Milan to bamboozle Marco Materazzi, the Inter and Italy defender also known for being on the receiving end of Zinedine Zidane's headbutt in the final of the Germany World Cup. He gets his second hat-trick, swelling his quota to 21 goals (fifteen in the league). In the Premier League classification for effectiveness, he is in third position, with a goal every 118 minutes played. Numbers and results that also bring him the Barclays prize for the best player of the month. But the most sought-after tribute, the most affectionate, the most unforgettable, the one that endorses once and for all, the special relationship with the fans, comes from the Kop. A song specially for him, like the greats of the past and present have had. At Anfield they start to sing the Armband song. They dug up the story of the Atlético captain's armband and made it their own. A song that makes Fernando emotional – as his playing makes his team-mates emotional. The Dutchman, Dirk Kuyt, declares: 'It's incredible to have scored so many goals in his first season in England. He's getting them in the league and in Europe and is doing a great job for the team. The rest of the players think that he's going to score in every match and the way things are going, one gets the impression that's what is going to happen.'
In March, another hat-trick and one of those goals that one doesn't forget easily. In the San Siro, against Inter, he receives a deep pass from Fabio Aurelio in the 64th minute, controls the ball, then, with a half-turn on the edge of the area, fires it inside the near post, where, despite a desperate final stretch, Inter keeper Julio Cesar cannot reach it. It seals the team's passage through to the quarter-finals. It's a trademark goal. Control, half-turn, shoot and goal. El Niño will repeat the same move against Arsenal in April to ensure Liverpool reach the Champions League semi-finals. 'He turned with the speed of a reptile to deal Almunia a venomous blow,' writes _La Gazzetta dello Sport_. And _Corriere della Sera_ adds: 'He created a work of art, leaving Frenchman Gallas dumbfounded like an absolute novice.' Two goals, one more attractive than the other. Difficult to choose which is the best. The _Guardian,_ simply suggests watching them a million times over.
And just before the double encounter with Arsenal, Torres goes through his first test in English. He'd promised he would, months before, and keeps to his word. He was being a bit ambitious to try it even in the corridors of Anfield, one to one with a British journalist, but to take on an important press conference organised by UEFA in the full public eye is not an everyday event for anyone. However, the youngster proves he's on the ball. He doesn't speak BBC English but he holds his own. This time the translator is there just to help him with the harder questions. Rafa Benítez is at his side and looks on proudly like the father of a boy who has just got the best report in his class. 'Twenty-eight goals scored... a target to reach before the end of the season?' they ask him. He replies: 'Is my best season. I'm scoring a lot of goals, my target is score goals but I don't have one number of goals. I want to help my team-mate to win trophies but scoring goals is the job of the striker. I'm only doing my job.'
It's that simple, he's only doing his job. Even if nothing takes away the fact that the first person to be surprised by the statistics of his first season at Liverpool is himself. He confesses as much, shrugging his shoulders almost to excuse himself, like a child whose mother has caught him sticking his hand in a jar of jam. Torres is humble but in the meantime the recognitions pour in. He is amongst the candidates for the PFA Players' Player of the Year award. A title that goes to Cristiano Ronaldo. But it's interesting to hear what Gordon Taylor, PFA Chief Executive, has to say about Torres: 'There have been many great Number 9s in Liverpool and this season he has followed in that tradition, responding brilliantly to what was a great challenge, which speaks clearly of his strength of character and skill.'
In May, by then out of the Champions League – despite his away leg semi-final goal in the match against Chelsea – there is still the Premier League to finish off. The last game is at White Hart Lane, then the home of manager, Juande Ramos, the Spaniard who had won the Carling Cup against Chelsea and thereby taken the team into Europe. The match doesn't feature much of interest, Benítez's side win 0-2 and Torres scores league goal Number 24. He becomes the foreign player with the highest number of goals scored in his debut season. He beats the record of Ruud van Nistelrooy. The Dutchman had set the mark with 23 goals (including four penalties) in 32 games during the 2001–02 season on his debut with Manchester United. Ruud, whose arrival from PSV Eindhoven was an inspired gamble by Sir Alex Ferguson, in spite of a knee problem, demonstrated his class in the first of five seasons with the Red Devils before leaving for Real Madrid. Benítez's gamble also pays off with 33 goals across all competitions. Third place in the Premier League top-scorer list behind Cristiano Ronaldo (31) and Emmanuel Adebayor (24).
Then comes the prize for the Reds' best player and best striker, chosen by the supporters. And, in Madrid, they give him the Man of the Year award, which is received in his absence by José, his father. In-between all these honours there is also the Nike TV commercial, which lights up Liverpool with the colours of Spain. The Osborne bull dominates the motorway exit, ships on the Mersey fly the red and yellow flag, students are learning Spanish, the fish and chip shops offer 'All Day Tapas', giant paella pans are on sale, flamenco is the dance schools' favourite, The Cavern becomes The Caverna and youngsters playing football in the park offer their thanks to Torres with a ' _Gracias_ , mate.' Fernando, in red jacket with his boxer dog on a leash, goes off smiling and looking pleased with himself. That's how he appears in a commercial but it's also the reality. At Liverpool, the lad who has come from Madrid is happy. He says so and repeats it in many interviews. With the Reds, he's enjoying his football like never before. In the city of the Beatles, he's discovered a winning mentality. He speaks of how his team-mates 'do not go out on to the pitch hoping that they'll win or praying for victory. They really expect to win. They have so much faith in their ability that they simply don't consider the possibility of any other result.'
Something new for him. Just as the football experience in England is enjoyable and new: 'The fans are with your team to the death, win or lose. They are always behind their side and at away games as well. Normally in Spain, when you are substituted there is a huge amount of whistling yet here the crowd stand up and applaud you!' And then there is Benítez, the manager who pampers him and teaches him new things each day, and there is the captain who is showing him what it means to be the team leader at a great club.
To sum up, he is enthusiastic about the choice he has made. Because at Liverpool, freed from the game he played at Atlético, he doesn't feel like a star who has to deal with everything – the good and the bad – but just an important player along with lots of others. The only regret is that he's had to leave his country, because in Spain they realised what he was worth. A month later, the fresh respect of the Spaniards will become devotion and eternal gratitude.
## Chapter 19
**He's going to stay**
_Conversation with former Liverpool player and manager, Kenny Dalglish_
He hasn't lost his Scottish accent. It's hard and dry, while at the same time, takes on a brusque tone. Apart from that, 'The King' or 'The Legend' as everyone calls him, is a normal person – pleasant, informal, very gracious and a bit shy. He's not a great one for talking but when he does, it's on an informed, friendly and helpful basis. He shuns high-sounding words and concepts and prefers to call a spade a spade to explain how he sees things. And at the time of writing, it has been announced that he is returning to be a part of Rafa Benítez's technical team in an advisory capacity, developing young players and sporting reports. News which all of Anfield would welcome with enormous pleasure. Because Kenneth Mathieson Dalglish, who was 58 in March and born in Dalmarnock, Glasgow, is top of the list of 100 Players Who Shook The Kop. Between 1977 and 1991, with the Reds, he won the unimaginable as both player and player-manager. He scored a fantastic 173 goals (added to the 112 he scored between 1969 and 1977 wearing the green and white of Celtic).
He was also witness to the most tragic moments of modern football: on 29 May 1985 the final against the Juventus of Michel Platini, with 39 bodies on the field of play, and on 15 April 1989, the Hillsborough disaster, with its burden of 96 dead. He has brought excitement to crowds across Europe. Apart from Liverpool, he has managed Blackburn Rovers, Newcastle United and Celtic. But he maintains that he has never felt himself to be a legend and that it's others who create legends. He has similar biographical details to Fernando. As a small boy at school, he began playing in goal, he was also a striker, his sign of the Zodiac is also Pisces, and he was also the Reds' most expensive signing. But for King Kenny, all this is just coincidence. What is certain is that he gave his blessing to Torres immediately after his second hat-trick. 'This boy,' he said, 'is the best buy that any club in Europe has made this season.'
### _And what does he think now? What's the best match that Fernando Torres has had during his two years at Liverpool?_
'There's not really one game for me, it's just what Fernando is. He seems very mature for his age. He seems someone that a lot of Spanish players will look up to as a leader. On the football pitch, for Liverpool, he's certainly made a massive contribution. He's just scored his 50th goal for Liverpool in 85 games, which is as good as anyone ever got in getting 50 goals. It's a fantastic achievement. He's the right man for Liverpool. He has committed himself to the way of life in Liverpool. He's learned the language very quickly. He seems very settled and he's very happy with life at the moment and his football as well,'
### _Have their been any games that have really showcased his particular talents?_
'He did very well at Manchester United this year, when Liverpool won 4-1, and he made a valuable contribution with his playing. He gave Vidic (Manchester United defender, Nemanja Vidic), who had played a very, very good season up until then, a really tough time. Also in the previous year, when he scored his goal against Chelsea in the first half. He took it brilliantly. I think he's had many good games but Manchester United would be the pick of it because of the close rivalry. He also scored and done well against Everton in the league match when he played with Robbie Keane upfront. There'll be a lot of games he can look back on and be very satisfied with what he's done. But one of the big problems is going to be trying to keep him fit because both Spain and Liverpool want to play as many matches as they possibly can and it's not always possible.'
### _How has he managed to adapt so quickly to the history of the club and to the way Liverpool play?_
'Yes, he's done it very quickly and it's a great compliment to him. It's helped that the manager's Spanish and there are some other Spanish players in the squad. It's always nice to see a face that you know when you arrive at a football club and it's nice to know that the manager is of the same nationality. Fernando has settled in magnificently well and he's been fantastic for Liverpool. The unfortunate thing this season is that he was injured for a few games and that's been a wee problem for him this season. It's been a problem for Liverpool and then he's got to go to the Federations Cup, which is a competition about nothing and there won't be too many managers who'll be happy that they (Spain) will be playing that. It's a meaningless competition and it's only a reflection of them having won the European Championship last year. That was a fantastic achievement for Spain and Fernando played his part in that but the players need a rest. This'll be three years on the road now, that they have been playing football.'
### _What are the main differences and similarities between Liverpool when you were a player and the Liverpool today of Rafa Benítez and Fernando?_
'Liverpool, for all their history, have always had the same philosophy about how they want to play football. I don't think that's changed. I don't think there is a huge difference. Nowadays, there's much greater competition because there are a lot more clubs who are able to compete financially than there were when we were playing. I think it's always difficult to go back and compare what happened in the past. I think you just analyse what's happening in the present time and I think this year that Liverpool have improved with what they've achieved this year and if they continue the improvement then they'll go even closer next year to winning the Premier League.'
### _Having met Fernando on two or three occasions, what is he like?_
'He's a very mature young lad and very respectful. He understands the tradition of Liverpool Football Club and he respects the people that come along and support him. He's one of the favourites of the fans but he doesn't take it for granted and they really respect him. So I would think that if he was your son, you'd be very proud of him as a person and a footballer. He's a fantastic footballer.'
### _What are the similarities between you and Fernando?_
'Maybe we've got the same colour of hair – that's about all!'
### _Which Liverpool player from the past most resembles Torres?_
'There's nobody similar. I think you're your own person. I don't think any two footballers are the same. I think he's his own person but it's inevitable that people draw comparisons with previous Liverpool players, but he's Fernando Torres and that's all he's got to be. He's got to be himself. He compares favourably with anything that anyone else has done for this football club as regards goals, so to me he's done tremendously well, but I wouldn't say he was similar to any of the players that I've seen.
### _What does Liverpool need to do to get to the same level as Manchester United and to win the Premier League?_
'Well, they're getting better and they've got closer this year than they've ever been before, so I'm sure this summer that Rafa will be busy trying to identify what he thinks he can do to improve the team to go that one step further than they went this year. But to go from two to one is a big, big step and although it doesn't seem much, it's a huge, huge step to take forward. But the best person to know and the person that everyone is going to trust to find it out is Rafa Benítez. So I'm sure Rafa will get in a couple of players who he thinks are going to be of benefit to the club and we'll have to wait until next season to find out if that's the case.'
### _How do you see the future of Fernando Torres in Liverpool?_
'The future's very bright for Fernando Torres at Liverpool. I'm sure he's going to stay here.'
### _You were at Anfield for the 20th anniversary of Hillsborough. You saw Fernando and all the team – it's a special day for Liverpool, no?_
'Hillsborough is a very special event for us, the people of Liverpool, because it's twenty years this year. But also it's very much a part of the history of Liverpool Football Club, the same as any cup success would be. It's there in the history, it's there in the memory and it will never be forgotten, the families will never be forgotten. It's very important to the people in Liverpool that they understand that and that the people who come and play for Liverpool understand it. I don't think there's much more you can add to Hillsborough than for me to say that.'
### _Having been a manager of Liverpool yourself, what suggestions can you give to Fernando Torres?_
'I would just say to Fernando Torres: Continue what you've done because you've done it very well. Enjoy yourself and we'll all keep our fingers crossed that we're going to get the prize that everybody would love them to get and that's more success.'
## Chapter 20
**Spain 4 Russia 1**
_10 June 2008_
A striker is selfish by definition. He only sees the space marked out by two posts, eight feet high and an 8-yard crossbar. He doesn't look around him, he doesn't look for the unmarked team-mate. He doesn't have time because he's looking for the goal. His only thought is to get the ball over that goddamned white line. In whatever way possible. He only thinks of scoring. And his skill is what everyone – manager, team-mates, fans and commentators – wants from him. It's his obsession because he knows that whatever marvels he's able to perform on the pitch, however many opponents he can get past, however many miles he runs, however much work he does for the team, in the end he'll be judged on the number of goals scored. And he'll leave the pitch with a bad taste in his mouth if he hasn't put away at least one.
But, occasionally, he understands that rules get broken, that the Number 9 looks up and sees a friendly shirt he can trust and instead of finishing off a move, instead of being selfish, he chooses to be generous or, better still, takes the correct and easiest option, the most direct route to goal, the action that benefits the side and makes all the team into winners.
And this is what he understands in the 20th minute of Spain's debut in Euro 2008 as Luis Aragonés' team take on the Russia of Guus Hiddink in Innsbruck's Neu Tivoli stadium in Austria. A long ball and Fernando Torres uses his pace to unsettle Kolodin. The Russian defender no longer knows what to do, loses his head, is not able to deal with the red lightning at his side and gives the ball away to El Niño. With some metres still to run, goalkeeper Akinfeez comes out of his goal and throws himself to the ground but doesn't get to the ball. Fernando sees that David Villa, the Valencia striker and his international team-mate, has been following the play. A textbook cut-back and there's nothing more that Spain's Number 7 has to do other than put the ball into an empty goal. And then the celebration. The two strikers embrace, Villa beckons to Torres, they end up on the ground while their team-mates arrive and pile on top. So much celebration in fact that Villa injures the index finger on his right hand, a hairline crack that puts his participation in the following match in doubt.
Freeze frame: the ball, fired in by Villa, still hasn't hit the back of the net, two disorientated Russian defenders watch the action while El Niño is already smiling. Happy with what he's done. The rapport between the two is repeated a little later but Villa can't beat the opposing keeper – the shot is too forced because of tight marking. And it doesn't end there. On 44 minutes, Villa latches onto a magnificent through-ball from Iniesta to make it 2-0. When 'El Guaje' ('The Kid', or 'El Niño' in the language of Villa's native Asturias) scores the third of his hat-trick, the other _Niño_ is no longer on the field. The manager has taken him off in the 54th minute to send on a midfielder, Arsenal's Cesc Fabregas. It's a substitution the Number 9 doesn't like at all and which generates a long drawn-out debate. But there is a gesture from Villa to remember – after scoring the third goal of his hat-trick, he runs towards the bench to embrace Torres and dedicates the goal to him.
'I embraced Fernando because people are talking a lot about him, that he's not feeling good, that he doesn't feel a part of things, that it's difficult for him. I dedicated it to him because I scored but it was Torres who found the way in. I took all the praise for finishing off the moves but the first two goals were only possible through his help. In the first, the pass was his and in the second he opened up the spaces so that Iniesta could make the final pass. He's had a really important game. He did great work – all the "dirty work", that allowed me to do the beautiful bit. I've benefited from him and wanted to thank him for it. I wanted to dedicate it to him so that he would be happy,' said David Villa at the time. A demonstration of friendship that put an end to a long month of controversy.
Voices in the dressing room were saying that the two were incompatible, they didn't understand each other, they weren't talking and they were constantly in competition with each other. What's more, many were putting forward the following theory: if Torres is playing, Villa is on the bench and vice versa. But Innsbruck proved the opposite. 'In the end, we finished up playing together,' added Villa, 'and I have to say that, with him, I felt very good. He's an exceptional footballer, who can drop to the wing and who works hard for whoever plays alongside him. He's wonderful.'
The match finishes 4-1 with a final headed goal from Fabregas but there's no doubting that the hero of the game is El Guaje. A quick glance at the Spanish press headlines confirms it. 'Illa Illa Illa ¡Villa Maravilla!' (Marvellous Villa) is the front page headline of _Marca_ , the Madrid sport daily. 'Villa, the Number 7 of Spain', shouts _ABC_ , while _El Mundo_ booms _'_ Lethal Villa, Lethal Spain'. The last Spaniard to score three goals in the finals of a European Championship was Michel.
Next up was Sweden. Villa has already caught up with Alfonso at the top of the table of Spanish goalscorers in European championship finals. As is to be expected, there is much praise for the lad who comes from the Asturias region of Spain and who grew up in a family of miners. For Torres, the critics are also positive. They say that he's been rapid, lively, dangerous, demonstrated his class and formed a deadly partnership with Villa. He's not been seen very much, almost a spectator when the national side was playing the short passing game, but decisive on the counter-attack when he had space to run, like he does at Liverpool. A pity, they say, that he's on the pitch so little.
'Torres has come from a long, hard season and he is very important for us. I had to take him off to give strength to the midfield,' explains Aragonés at the end of the match. He minimises the fact that the Number 9 hadn't scored: 'The next day Torres could put away three goals just like Villa.'
What's certain is that after the first match and the first overwhelming success against a rival that, on paper, seemed a hard nut to crack, the euphoria in Spain is widespread. And it's also important to point out that this is the seventh consecutive victory for Aragonés' men in a run of seventeen matches without defeat. But nobody trusts first impressions. Starting with Fernando: 'We've played at a good pace and we've been lucky. It's very important to start like this but we haven't done anything. Don't forget what happened to us in the Germany World Cup.' Yes, Torres knows the failures of the national side all too well, having been a regular participant in recent years. Against Russia he celebrated a Golden Wedding with the side. A round figure of 50 matches and fourteen goals scored (three penalties), the numbers of a story that begins on 6 September 2003 at Guimares in Portugal.
He's called up for the first time with the senior side by Iñaki Sáez, already his mentor from the junior teams. 'He was the first that I called out of all those lads that I'd known and trained in the Under-16s and Under-19s. A fantastic group that brought us a lot of pleasure. Fernando was the most ready, physically, and he already had a lot of experience – two years in the first team at Atlético. His qualities? A speed and movement bonus, plus a lot of goals. He also had some weak spots to clear up, like receiving the ball with his back to the defender, one-on-ones with the keeper, coordination. But I had to put him on, I had to put on the best,' remembers Iñaki with pleasure.
For Fernando it's a dream that is becoming reality. For some time, there'd been talk about his possible call-up but the gaffer hadn't wanted to give in to those temptations. This time things seem to be different, so during the week before the announcement of the squad for the friendly against Portugal, the Atlético Number 9 is beside himself with excitement. He wants to be part of the 'club', to see the national team from the inside, the atmosphere within the group, the training sessions, the prematch preparations. He wants to play with the 'grown-ups', and he is fed up of being the lad destined for the Under-21s. He feels that this is the moment. The anticipation is intermittent until the great day finally arrives. He's in a car with a friend when he learns the good news on the radio. Amongst the 22, his name is included. It's the moment he's been anticipating 'for a long time. Since last season, when I was dreaming so much about being able to join the side,' he declares in an interview. 'It's not that you expect it but it's more when everyone talks about the same thing, you begin to get worked up about it. But I wasn't getting down. I knew that one day it would have to be. With each list the debate began but I was apart from all that. I said that I wasn't in a hurry, that it wasn't a priority. I never understood all that expectation. They wanted to see me in the national side. Now it's up to me to show they weren't mistaken.'
It's up to him to show them he is at the same level of the greats of Spain – the Raúls, the Valeróns, the Tristáns. He knows that they are putting him under the spotlight but he's used to it. At Atlético he is the first to be praised and the first to be subjected to scrutiny. The national side, however, is going through a bad phase. During qualification for Euro 2004, Spain suffers two bad setbacks against Greece and Northern Ireland. They couldn't make any more mistakes and above all they couldn't make them against Ukraine the following Wednesday. It will be a crucial encounter in which Torres will start. In short, the game against Portugal – although a friendly that comes at a bad time (a very bad time, four days before a must-win tie) – it's a key test for the nineteen who are in the national side for the first time. Iñaki's idea is to put him in the front line of attack, 'so that he can run and fight for the ball' with Raúl behind. The manager hopes it will work so that he can do it again. Torres, for his part, yearns for a good game, a goal and a win.
It's a clear 0-3 victory but in the Alfonso Henriques stadium (which had just been refurbished for the following year's Euro 2004) the reality doesn't match up to earlier expectations. Meira and Couto, the two Portuguese defenders, give him such a kicking that he has to receive medical treatment just before the end of the first half. In the 36th minute, Fernando Meira tackles him from behind, crashing into his left ankle and leaving him limping. Fernando Manuel Silva Couto completes the job in the 43rd minute with a ferocious kick. Raúl, captain of Real Madrid and the national side, comments: 'I warned him it was going to be a very difficult match. He was in front of some hard defenders who were going to give him a tough time but it's the route he's got to follow. Torres is the future of Spanish football.' Torres himself is also aware that these are the risks of the trade. 'What do you want? That they don't give me a hard time?' he asks at the end of the match, putting an end to any argument over the blows he has received. And he adds that he's as happy as a sandboy because he's made his first appearance in the senior side.
On his performance, there's not much to report – a miskick that goes high, some good control to get round the direct-minded opposition, and good passing. The critics were generous, stressing that the youngster seemed intimidated at the start. He wasn't the centre of attention as he usually was when playing for Atlético, and they also underlined the lack of interaction with his team-mates. That's normal, it's the first time. The try-out, however, is sufficiently convincing, at least for Iñaki, that at Elche in Spain, in the home match against Ukraine, he will be a definite starter. And this time it's going to be serious. Qualification is in the balance. In the 51st minute, Dymitrulin up-ends Etxeberría in the area. Penalty. Fernando Torres takes the ball and calmly places it on the spot. Before the match, Sáez asked who was ready to take a penalty. El Niño raised his hand. He wants to show that now he's arrived in the national side, he wants to stay. For a long time. He's not nervous or overawed as he steps back from the spot. To score is crucial. Spain aren't playing well and Andriy Voronin (a future team-mate of Torres at Liverpool) has already sent a message of intent to Spain keeper, Iker Casillas. Fernando makes his run-up and sends a slow, limp, average shot to the left of the keeper. Shovkovskyy guesses right and grabs the ball. Torres can't do anything more than kick the air in frustration. Fortunately, this failure doesn't turn out to be decisive (Spain, thanks to Raúl, win 2-1), but next day, criticism of the youngster's error doesn't make for light reading.
And what's more, all the commentators ask why it was up to him to take responsibility for the penalty when, in the national team, there are others with more experience of spot-kicks, like Reyes or Xavi. Iñaki Sáez calms the waters and explains: 'I think you have to go through this sort of experience in order to be successful. But there's nothing to worry about. This will help him become a better player.' Prophetic words. Because that's certainly what he becomes. He applies himself to the task, as well as Gregorio Manzano, his trainer at Atlético, who, for several days, is photographed explaining to his player exactly how to take a penalty and get it right. 'It was just an exercise in how to visualise,' explains Manzano today, 'so that he would take other penalties, with the thought that your first idea is what you have to stick with and not change it at the last moment. I wanted to help him. He was starting to grow in the national team and to demonstrate his skills in spite of the failure against Ukraine.'
Also of interest at Elche is that Milan sporting director, Ariedo Braida, is amongst the spectators. He wants to see in the flesh the new jewel of Spanish football. Information that he's received from his observers is very good. They're thinking seriously of making an offer to Atlético. But Torres, who has spoken to his team-mates and ex-Milan players Demetrio Albertini and José Mari, rules out for the moment any move to Italy. It's better to be older for Italian football. There's the risk of getting burned...
But we return to the national side and redemption. It takes place seven months later by complete coincidence in Italy, in Genova, against the Italian national side on 28 April 2004. An important friendly. For Italy, it's a homage to 37-year-old Roberto Baggio, the great improviser of Vicenza, Fiorentina, Juventus, Milan, Inter, Brescia and of the national team, from which he will retire at the end of the season. The European Footballer of the Year 1993 returns to the national team after five years' absence for one last game in the blue shirt. For Spain, it's the last test before Euro 2004. The Spanish manager sends out the same team as for the game with Portugal. He decides to try out two strike pairings, Raúl with Morientes and Valerón plus Fernando Torres. El Niño comes on at the beginning of the second half wearing his lucky Number 14. His team-mates have given him permission to choose it because fourteen, he says, has always brought him luck. And these things in football are no laughing matter. Fernando wants to score. He feels that this time it's right. After four matches with the national side, he needs to get rid of his psychological block. One knows that the first goal for a striker is crucial. Eight minutes after the break, Albelda wins the ball in midfield, passes it directly upfield to Valerón who waits for the right moment – the Italian defenders come out – before giving it to Torres, who shoots across the goal towards the far post, which is out of Peruzzi's reach. It's his first goal with the senior squad. A celebration that is rained on three minutes later by Bobo Vieri who, by chance, is an ex-Atlético Madrid player. Torres is also left with the sensation that he could have scored again. This time, however, everyone praises El Niño's impressive performance.
He gets the OK for Euro 2004 in Portugal. Iñaki Sáez explains Torres' call-up like this: 'He is youth personified. What he has shown in the national side is his character. He has two essential qualities – competitiveness and speed. He is growing and no one knows his limit.'
In spite of all the praise, the manager, once on Portuguese soil, doesn't count on him at the beginning. In the first match against Russia, he comes on as a 77th minute substitute for an unlucky Raúl. It's the same story in the second encounter against Greece, with barely a quarter of an hour on the pitch, once again replacing the team captain. The 10,000 Spanish fans who have arrived in Porto to see the match that could give them qualification to the quarter-finals are encouraged to see him on the pitch. But the 'little prince' of Atlético hardly touches the ball. He can't turn the draw into a win and the resulting stalemate now requires Spain to put everything on a win against the host side, Portugal.
Lisbon, 20 June 2004, 8.45pm, the José Alvalade stadium, the third and final match day in Group A and this time, El Niño is in the starting line-up. It's what he was hoping for. He doesn't want to go home without ever being in the initial eleven, he wants to respond to the expectations that his call-up generated after his eye-catching performance against Italy. 'I've also put a lot into this European competition,' he says, 'and we all have great expectations for this tournament. Not to reach the quarter-finals would be a failure,' and adds: 'We can't go into history as another national side that has achieved nothing.' He's convinced that 'if we do things well we shouldn't have any problems against Portugal.' After all, Spain had beaten them easily on 6 September of the previous year, on his debut. Of course, this isn't a friendly, but the idea of getting eliminated doesn't enter the head of the twenty-year-old with five matches wearing the shirt of Spain. He's changed his look for the occasion, getting rid of his long locks with a crew-cut down to almost zero. In the absence of his trusted Madrid stylist, he asked Juanito del Betis to shave it off, setting the cutter at Number 1. But the new look doesn't do much good.
At the end of the first half, the result is still 0-0. Fernando has hardly been in the game. The person who has been, and who has become a nightmare for the Spanish defence, is Cristiano Ronaldo. His performance is tremendous. The Manchester United winger has lots of opportunites to score but fails, either sending shots wide or through the efforts of Spanish keeper, Iker Casillas. The good news for Spain comes from the other game where Greece are losing 1-2 to Russia. With this scenario, it would be Spain and Greece going through. But with the second half barely under way, it's clear that the host nation has no intention of being kicked out of its tournament. A great strike by Nuño Gomes puts them 1-0 up in the 56th minute. Saint Iker (Casillas) can't get to it. Like this, Portugal go through. Five minutes later, Fernando has a chance for the equaliser. A splendid assist from Xabi Alonso, but as keeper Ricardo comes out of his goal, El Niño puts it onto the post. He despairs, he cannot believe it. He puts his head in his hands, his mouth open. Iñaki Sáez still remembers that failed attempt by Fernando: 'A draw would have been enough and we would have got to the quarter-finals. Instead, we came back home. It was another failure by the national side. To think we'd set off with so much hope. It was a young team with players like Torres, Xavi, Alonso and Reyes, together with very experienced players like Raúl, Baraja and Albelda. But in the end, my plans didn't work.' And Iñaki's adventure ended.
On 1 July 2004, the Real Federación Española de Fútbol (Royal Spanish Football Federation) named 66-year-old Luis Aragonés as the new manager, with 30 years' experience across Spain and an old acquaintance of Fernando Torres. His debut is set for 18 August in Las Palmas in a friendly against Venezuela, ahead of qualification for the 2006 World Cup in Germany. Fernando is there. He will be a fixture in the call-ups of the Aragonés era. He will be left out only once, for a friendly in Tenerife on 10 November 2006, against Romania, because of the Atlético captain's poor league form with only two goals in eight games – his worst results since playing in the first division. Aragonés maintains that there are four strikers who are in better form than El Niño. He says he's leaving him at home 'so that he learns'. The match ends in a defeat for Spain. From that moment on, apart from when circumstances are beyond his control, the manager will not leave Fernando out of the side and Spain will not lose again with him on the side. At the beginning, however, things aren't easy between Torres and Aragonés. The Atlético Number 9 is always the first to be substituted. Something that doesn't make him at all happy. On 7 September 2005, Spain play Serbia in a qualifying game for the Germany World Cup in Atlético's Vicente Calderón stadium. Torres comes onto the pitch in the starting line-up because Fernando Morientes – then a player at Liverpool – is injured. For El Niño to play in his home stadium in the national side is something very special. A big moment in his career.
But in the 56th minute, he's substituted. On in his place goes Tamudo. In the papers the following day, he reads that he's played without composure, not knowing how to use his skills, speed or strength. In other words, that in the national side he's not able to establish himself, to prove his worth or demonstrate his gifts. The encounter ends in a draw. The qualification process is getting bogged down. They need to win against Belgium. And it's typical that Aragonés puts him to the test in a difficult match like the one in the Heysel stadium in Brussels on 10 October 2005. He listens to El Niño's complaints about his repeated substitutions and takes a gamble on him. He puts him on the pitch in a complicated match. And it's there that he finally gets a big thorn out of his side. Two superb passes from José Antonio Reyes (then a player with Arsenal and a former team-mate of Torres from the junior national sides) and two goals that re-energise the team's drive for qualification. The first, in the 56th minute, is a wonderful strike. Reyes sends a long ball upfield, Torres gets behind the Belgian defence and takes off to thump the ball exactly in the space between the opposite post and crossbar.
Finally, El Niño does what everyone expects of a centre forward – finally he silences the doubts that his play was generating.
Spain qualify through the play-offs, without too many worries, beating Slovakia 5-1 in the first leg (including a penalty from Torres) and a one-all draw in the second to put them into the World Cup.
'I've dreamed loads of times about being in the World Cup,' says Fernando, adding with a smile, 'I want to be in the final and be champion of the world.' It won't be like that. Let's see what really happens...
In Leipzig's Zentralstadion on 14 June, 2006, the first match in Group H. Spain 4 Ukraine 1 – a victory, a perfect game and an 81st minute goal for Fernando is the icing on the cake. A move that starts with Puyol, the Barcelona defender getting free of the Ukrainian defence by making a _Rocastle Manoeuvre_ (named after former Arsenal player David Rocastle) or _Marseille Turn_ (after the version of the move used by French player, Zinedine Zidane), involving a 360-degree spin or turn with the ball, while on the move. He gives the ball to Arsenal midfielder, Cesc, who looks around and returns it to the sender, who heads it on and into the path of the Number 9. A great strike taken in mid-air and the Spanish media brand it goal of the tournament. Overcoming the team of Andriy Shevchenko (the 2004 European Footballer of the Year and Chelsea's then new signing) in such fashion sparks World Cup fever in Spain. The road to the final looks an easy downhill ride from here. Torres, who has scored his first goal in a World Cup final, insists: 'We are playing well. We're going step-by-step. We're going to get people talking. But we aren't the favourites – the favourites are those who've already won a World Cup and those who have more experience than us. They are the ones under pressure. Us, no. Because Spain hasn't won a World Cup, nor been in a final.'
Five days later it's Tunisia. Losing by a goal, Spain fight back. Against the rain and the North Africans' defence, Torres is decisive. He scores twice, to make it 2-1 and then a third to make sure. The first is typical Torres – an inviting long ball from Cesc and off he goes running, beating the Tunisian defenders on pace, then tricking the keeper to score before celebrating like an archer in homage to his former Atlético team-mate and idol, Kiko. The second is a cleanly executed penalty. He's brought down while about to fire in a header. He converts the spot-kick with a powerful shot. The keeper guesses correctly but the ball flashes between arm and leg. Torres is top-scorer for the tournament with three goals and Spain is through to the last sixteen.
But waiting there on 27 June is the France of Zinedine Zidane. The ex-Real Madrid player has already announced his retirement from football at the end of the World Cup. Three days before the game, Spanish sport daily, _Marca_ , decides to stoke up the prematch atmosphere by running a front page headline: 'We are going to retire Zidane'. An attempt at humour that doesn't please the French captain, prompting him to comment: 'There's no need to talk before the match. It's a pity. There are people who talk who would be better off keeping quiet, like _Marca_. What they've written has hurt me.'
Fernando Torres doesn't take the same line as _Marca_ and sends this message: 'It's important to see Zidane in this World Cup. We will try to beat them but I hope he doesn't retire and that we enjoy having him around for a lot longer and we hope it isn't his last match.' But even he is confident of the final result: 'France is a great team,' he says, 'but we believe in our football and in victory.' Spain reaching the last sixteen is one of the pleasant surprises of the competition. The players are young (24 is the average age compared with 29 for France), they have a squad bursting with upcoming talent playing abroad (Cesc Fabregas for example), they're hungry for victory and they want to surprise. They know how to play the ball and they never want to give up. All in all, they get so much out of playing that they have proudly come to symbolise the New Spain, which has achieved the top spots in Europe and across the world. From gastronomy (Ferran Adriá), sport (Fernando Alonso, Rafa Nadal), art (Miquel Barceló) and architecture (Santiago Calatrava). A country that doesn't feel itself inferior to anyone and a new footballing generation that doesn't carry the weight on its shoulders of endless failures. It can dream of overcoming its World Cup quarter-final taboo, always seen as an insurmountable obstacle.
The favourites by miles. They all say it. Even Spanish Prime Minister Luis Rodríguez Zapatero is convinced that against the French his fellow-countrymen will do it. The morning of the match, he calls Luis Aragonés to tell him: 'You have my support and my confidence.' An awful lot of confidence because on the other side is a France that is sad and depressed. They are a group of stars on the wane, so much so that someone has compared them to the Rolling Stones. They qualified as the second team in Group G (two draws and a victory), as a divided squad, overwhelmed with doubts and criticism. A group that found it difficult to get to Germany and continues down the same road. One recognises that they have skill and much experience but opposite the youthful attractions of Torres and his team-mates, these qualities don't count for much. More or less everyone thinks like this in Spain.
It's a pity that things don't turn out differently. Going a goal up via a David Villa penalty won't help them at all. Franck Ribéry, former Arsenal player Patrick Viera and Zidane – that old player destined for early retirement – will bury the Spanish dream. Once more they leave empty-handed. And there is even someone who reports that the defeat – or the crucial second French goal scored with a header from Viera – is the fault of Torres. 'I told one of them: "You, what you have to do is learn three words in French and when there is a free-kick, get close to Viera and distract him",' relates Luis Aragonés. It's a shame that at the crucial moment Torres, with the responsibility of keeping an eye on Viera, forgets the advice of his manager. When he gets near the dugout, Luis shouts at him: 'But didn't I tell you? What happened?' 'Boss, Viera had already learned Spanish.' An urban myth, one of the many jokes doing the rounds. What is certain is that Fernando hasn't forgotten the defeat against France. He remembers the Germany World Cup and because of this, damps down the euphoria after the resounding victory in the first match of Euro 2008.
## Chapter 21
**Sweden 1 Spain 2**
_14 June 2008_
Oddly enough, the day after the hammering of the Russians and in the seclusion of Neustift, a charming Tyrolean village, there are long faces all round. What has happened? Luis Aragonés doesn't like Torres' reaction one little bit after he substituted him in the 54th minute. What had El Niño done? Nothing that might be on a par with Egyptian Ahmed Hossam Hussein Abdelhamid, better known as 'Mido', the Wigan Athletic striker previously with Tottenham and Middlesbrough. In the semi-final of the 2006 African Nations Cup, Mido lost his cool as he made his way to the bench, insulted the trainer, Hassam Shehata, by calling him a donkey and it almost came to a punch-up. He got himself a six-month suspension. No, the Liverpool striker hadn't gone that far, he hadn't made a big scene. It was just that, eight minutes into the second half, the electronic panel announcing the change had appeared and he had walked over to the bench with a seemingly peeved expression on his face. But what's all this? We're winning. I'm playing all right. I can really get stuck in too and score on the counter-attack and the gaffer takes me off – always me, it's always me who has to come off first. The change has really upset him. So much so, that when Luis offers him his hand to greet him off, Torres looks the other way and hurls the tracksuit top the kit-man passes him onto the ground. He sits on the bench looking miffed. It seems like history has rewound back to his first year at Atlético Madrid, when the Wise Man of Hortaleza would substitute him time and again. And at a press conference everyone imagines should be a happy event, Aragonés doesn't pass up the chance to tell all and sundry:
'I can understand it when a player gets annoyed, and I'm on Torres' side, but then a bit of decorum is important. This isn't the last of this. I agree with footballers getting angry when they're replaced, and it's happened to me, but these are special circumstances and the ones that play are just as important as those that don't. Those that don't play should be pissed off, sure. Otherwise, why would we have brought them here? But first let them be annoyed with themselves and then with whoever. Manners though, and I say this again, are what is most important.'
And to finish off he aims a very clear message at Torres: 'This isn't the last of this; one shouldn't let things like this go.'
A pretty harsh reproach, which leaves the journalists nonplussed. For example, Enrique Ortego, writing for _ABC_ , thinks that 'Luis could have just said nothing and had a quiet word alone with the player, as he has already done.' But Ortego, like a lot of other commentators, understands why he did it: 'He wanted to show public opinion that he's not going to take any cheek from any players. He doesn't want a repeat of what happened in the World Cup in Germany, when some who weren't in the starting line-up for the first match didn't contribute towards a good atmosphere.'
And what does El Niño say? He plays the whole thing down: 'There's no big deal. I've had a chat with the boss and it's just another change, there's really no problem. I've never had any problems with trainers. I just think it's a shame that these things are being singled out so much when Spain has just beaten Russia 4-1.' And in front of the Tele 5 cameras he adds: 'It's always the same. The code of conduct in the dressing room that Luis has taught me since I was sixteen is the one that should apply to me in all this. What happens in the dressing room is straightened out in the dressing room. I would never snub the boss. All of us players are with our national trainer right up to the very end.' The controversy ends there. So much so, that Luis says: 'And I'm not angry, not bothered at all. What happened with Torres doesn't matter in the slightest. I had a chat with him in training, but that's nothing new. I had him as a player at Atlético since he was a kid. He's almost like my son and I've always given him what I believe to be useful little tips.'
After the explanations the gaffer confirms that Fernando is set to start in the Sweden match at Innsbruck: 'He's key to my plans,' he says. That's a certainty, but the national coach asks Fernando to do a job he doesn't do at Liverpool. He asks him to do what he used to do at Atlético, which is to drop wide to create spaces and make runs to draw people in, which can make life hard in front of goal. So much so that, with the national team, Fernando has only scored two goals in 33 outings – a paltry haul for the striker who, in the season just ended, caused a furore in the Premier League.
And so the Sweden match has become a do-or-die affair for Fernando. Will he manage to do what has been asked of him? Will he score? Will he, after all, be at ease as part of the _Roja_? Everyone is waiting on Torres as though he were Godot. But this time Godot arrives on time. It's Fernando who gets the scoreboard moving. An emphatic reply to the doubts sparked by his replacement and the subsequent statements from the gaffer. It's fifteen minutes into the first half and Luis' prepared plan to topple the towering Swedes swings into action. Because Torres' goal is pure strategy, somebody has dubbed it a 'laboratory goal'. Corner: Xavi, from the corner to the Swedish goalkeeper's right, kicks it short for Villa, who comes in to receive the ball along the touchline and draws in a central defender. David nudges it back, where another David comes in – Silva, the Canary Islands man. From the corner of the penalty area the Valencia midfield linkman with the strikers knocks in a waist-high cross-shot with a lot of swerve. Three Spaniards (Capdevilla, Ramos and Torres) are waiting to pounce on goal. The quickest is El Niño, who gets in ahead of his marker Hansson, sticks out his leg, and with the tip of his boot – or rather the studs – taps the ball into Isaksson's goal. Fernando is back among the goals. He hadn't scored with the _Roja_ since 12 September, against Latvia. He's satisfied because the set pieces and tactical plays practiced in training sessions have worked. He won't score another goal until the final, against Germany, but his contribution against the yellow-shirts is vital.
El Niño is finally a star, his elusive runs cause pandemonium among central defenders, his ability to shake people off opens up space, he battles for every ball and he puts in the teamwork by dropping back to defend. And he also acts as a peacemaker between the referee and his team-mates when they claim a penalty against Silva that wasn't blown. And one shouldn't forget his contribution when Villa made it 2-1 in a last-gasp attempt when a draw seemed certain (the Swedes had drawn level through Zlatan Ibrahimovic, thanks to a mistake from Sergio Ramos). The miracle happened courtesy of _Villa Maravilla_ (Villa the Wonder-worker), yet Fernando assisted with a monster pass (over 50 metres) from Capdevilla by jumping up, bamboozling an opponent, and allowing the ball to reach the Spanish Number 7, 'El Guaje' Villa, who sees the _Roja_ through to the quarter-finals. On 15 June the talk is all about 'the finest pairing in Europe' – Torres and Villa, with 51 goals this season they are the most lethal duo. Everyone concurs, admitting that they admire and envy the Number 7 and Number 9, who have put together five goals and two assists in two games. No one in the European Football Championship has done a better job. There is a shower of praise. The first to step up is Aragonés himself: 'They have a perfect rapport because they have unique qualities and an amazing turn of speed. They are a major bonus for the team. They can get goals out of nothing.' Pepe, a central defender with Portugal and Real Madrid, says: 'With this brace of strikers Spain can really go places in the European Championship.' And Ruud Van Nistelrooy, the Netherlands and Real Madrid striker, observes that: 'Villa and Torres are at a spectacular level, can score a hell of a lot of goals and Fernando is playing as well as he does in the Premier League.'
The protagonists fit together well and cannot stop complimenting each other. El Niño says good things about Villa: 'I think he is the best goal-scorer in Europe. And he is bound to top-score in this tournament.' And Villa waxes lyrical about Torres. Rumours that they were at loggerheads have been quashed. Pepe Reina, the Liverpool and Spain goalkeeper, being a mutual friend, has helped bring them together. To celebrate getting through to the quarter-finals the three get together with their families for a _fabada_ (an Asturian bean stew) in a Neustift restaurant.
The third game against Greece is a formality and Aragonés can rest 9 members of his usual starting line-up. Torres and Villa don't play. Greece starts by getting ahead but Rubén de la Red and Dani Güiza put that right. In the quarter-finals on 22 June, in Vienna's Ernst Happel stadium, the world champions, the _azzurri_ , await.
Monday, pizza. We'll polish it off like we did Italy on Sunday. That is the view of many Iberian people and their media as they tip a wink at the gallery. They all say they are certain that Cannavaro and company won't be any trouble at all. They are really confident about _Villa Maravilla_ and 'the Kid' Torres, the big players, and about the old guy on the bench. They are certain that this time, thanks to Spain's better crop of young players coming through, they will lift the curse of the quarter-finals – the customary burial ground of the _Roja_ 's dreams of ultimate triumph. They swear that this time they will break their jinx with Italy: 88 years of defeat in official competitions. With one stroke they will avenge the slight of being knocked out in the quarter-finals of USA 94 – Luis Enrique ending up with a bloody nose after being elbowed by Mauro Tassotti.
But it doesn't end there. For the eleven wearing the red shirt, Italy is the icing on the cake. Having sent the European champions (Greece) home, it's all-out for the world champs. But these musings hide the fact that the Spaniards are scared that, once again, their great adventure might come a cropper. It will prove otherwise. After 120 minutes nobody has scored. Torres makes no odds in the 84 minutes he plays before being substituted by Güiza, and neither does Villa. Fate will be decided from the penalty spot. Saint Casillas keeps two out and Cesc Fabregas – the 21-year-old who had never taken one in his entire sporting career – makes no mistake. He nets for the final 4-3 score-line. 'That's where we won the European Championship,' Torres recalls months afterwards. 'I think we celebrated more that day than in the final.' A final that would come around after a resounding 3-0 win against Guus Hiddink's Russia. Torres tries everything and more to find the goal, but to no avail. He is replaced by Güiza, who keeps his rendezvous with the net.
On Sunday, 29 June, Spain will play their third final after 24 years out in the cold. David Villa won't be in the game. In the 30th minute of the semi-final, while lining up a free-kick he feels a stabbing pain from behind and five minutes later he drops to the ground, head between his legs, in floods of tears. His European Championship is over. Fernando Torres will play as a lone striker against Germany.
## Chapter 22
**Germany 0 Spain 1**
_29 June 2008_
When the players walk onto the stage of the Ernst Happel stadium in Vienna and Iker Casillas, captain of the _Roja_ , receives from Michel Platini the European Championship cup, King Juan Carlos asks Fernando Torres what they give him to eat in England to make him so strong.
Earlier, three hours earlier, another old man, Luis Aragonés, gives Torres a kiss. On the eve of the final, Aragonés had said: 'I must tell El Niño something. Tomorrow, after the meeting [with the players], I will have a private talk with him and I will explain it to him then.' he says. The manager knows that the boy from Fuenlabrada isn't happy with his performances, so before the match he makes a prediction: 'Today you are going to score two goals,' he says, then he touches his forehead as if to banish bad omens and then gives him a kiss like you might kiss a favourite son who makes you furious but whom you forgive everything.
It's the same gesture that he made many years earlier when Torres was a youngster at Atlético Madrid. Then, he scored. And ever since then, the Number 9 has stuck to the same ritual. He gets on the team bus listening to very loud music through the earphones of his iPod, and he gets off the bus in the same way. And he recalls a meeting with another old man, in May at Las Rozas, La Ciudad del Fútbol, where the Spanish national side was preparing for Euro 2008: 'Are you the one who scored that goal?' Torres asks. Marcelino Martínez, the Zaragoza forward who clinched the European Championship victory for Spain at home in 1964 against the USSR – the first and last major win for Spain in 100 – looks at him and responds: 'Yes, I am. Let's hope you can do the same and achieve something really great in Austria.' Fernando thinks about this for days – he wants to be the new Marcelino.
In the dressing room, he knows that the Championship is slipping from his grasp. There are only 90 minutes left and he still hasn't managed to make his mark in the tournament. He's certainly played well, but he's only scored one goal, whereas Villa – who will win the Golden Boot – has scored four and Güiza, a substitute, has notched up two. Yet again, despite an outstanding season at Liverpool, Torres has not become the national hero he longs to be. But there's still the final to come – the most important game. He leaves the dressing room and, as always, stands behind Sergio Ramos with a face that indicates he wants to be left alone. Don't touch me. But the Wise Man of Hortaleza is ready for a joke, as Torres recounts a year later:
'For several days before the final match with Germany, the gaffer didn't stop talking about Wallace. At the beginning we were all looking at each other not knowing who was he talking about. Until we realised he was talking about Michael Ballack. Then he told us that he knew his name but that he called him Wallace because that's what he felt like calling him. But if you know Luis, you can imagine the actual expression he used. It didn't stop there, though. When we were in the tunnel leading to the pitch, Aragonés went on in front of us, winked in our direction, and went to Ballack. He said to him, in Spanish, "Good afternoon, Mr Wallace", and went on speaking to him for a while. The German didn't understand a word and Aragonés didn't understand what Ballack was saying to him, either. We couldn't help it, but we were laughing our heads off as we went out to play the final.'
A nice way to start the most important game of your life...
And then, in the first fifteen minutes of the game, Spain stutter. They're uptight and can't reproduce the form they've shown up to this point. On the pitch, in the stadium and across the country – for once crazy about its team – they fear the worst, that the giants in white shirts will slot home a couple of goals without even trying and finish the game before it's started. But Spain get their act together with the help of Torres. In the 23rd minute Sergio Ramos crosses the ball from the right and Torres leaps up for a header, hitting the ball full-on. He doesn't know how he manages to do it, given that Mertesacker is two heads taller than him, but El Niño manages all the same and the ball hits the post. It could have been the first goal – it will be just the beginning of Spain's recovery. The clock in the Happel stadium shows the time as eighteen minutes past nine and on the pitch, 33 minutes have been played. Marcos Senna, the man from Sao Paolo, steals the ball in midfield. He looks around and sees Xavi through a crowd of German players. He's far from Mertesacker and next to Frings. The Barça player sends a pass into space, where, from behind, Fernando is arriving at speed. Good control and past Philipp Lahm. The Number 16 looked to have had it under control. 'Xavi's pass was spectacular but Lahm was already in a good position,' Torres will explain later: 'If he had gone a bit to the right the ball would have been for the keeper, but I think that maybe he doesn't have a good understanding with Lehmann. He gets too confident, he relaxes... This gives me a fraction of a second in which I am able to move to the other side and seize the opportunity to shoot. Maybe if the pitch had been dry I could have tried bending it but the ball skates across and enters just inside the post. I knew it was going to go in.' It's the goal he's been dreaming about. Fernando Torres puts his thumb in his mouth like a dummy. It's dedicated to his nephew, Hugo, the son of Israel, born little more than a month ago, then he dives across the Viennese grass. He shouts his head off and is lost in a sea of hugs from his team-mates. He doesn't forget Villa, who's not playing in the final. He reciprocates the dedication that El Guaje had made to him in the first match of the tournament. 'This victory is for David, who has been suffering on the bench like one of the fans,' he says.
Germany are nowhere. Michael Ballack, whose eyebrow is split open after a clash of heads, is doing all he can to motivate his side. He gets furious and takes it out on everyone, the referee included, but he is a symbol of his team's impotence.
In the second half there are chances for Ramos and Dani Güiza, but for the Spanish it's hard work. In the 78th minute Torres is taken off, but then comes the final, liberating whistle of Roberto Rossetti. And the Spanish party starts. Everyone goes mad on the pitch and across the country, where, after 44 years, they can finally shout: 'Champions! Champions!'
'When you are a boy, and see these matches on TV, you dream of being there. Now that I am here I find it difficult to realise what I've achieved. At last justice has been done and this team has recovered its due place in Europe,' says Fernando Torres as he walks off the field, the Spanish flag wrapped around him. At a press conference, having been chosen best player of the game – as he was twice in previous junior European Championships – he makes an intelligent and concise speech for the world's media: 'I am happy because Spanish football needed a success like this one after so many years. Besides, this triumph is really going to help football in general because it has been the best team that has won the European Championship, a team that's had a great tournament, and that doesn't always happen. We are proud that we have promoted the idea of attractive football, which is enjoyable to watch, even for a neutral spectator. We are a team that knows how to use the ball. This has been a success for both the manager, who persevered with the idea, and for the players, who knew how to take the concept on board and apply it. The group is the main weapon of this team. All of us – the players who have been on the pitch a lot, and those who have been on the pitch less, as well as the technicians and the rest of the staff – have to feel just as happy. It is the victory of being together. To win is always good, but to do it like this is even better. We have kept the style, our way of playing throughout the whole tournament. And we've won. That shows that it is possible to play well and get results at the same time.' Almost a masterclass in the art of football and the Beautiful Game – traditionally the territory of Brazilians. Torres lays claim to a certain style. His goal matches this philosophy and it's a sign of how the mentality of the national side has changed. 'Yes, it's another indication that this national side has known how to mature. Maybe before, we've lacked those elements, like continuing to chase loose balls or the quality of the team's defending. Now we are champions and we have more experience to go after more trophies. Let's hope this is just the beginning.' He's just won but already El Niño is looking to the future, but he's clearly one of those people in life who are never satisfied. As he waits for his future to unfold, he knows he has scored the goal of a lifetime; he is aware that he has had a profound influence – just like Marcelino – and he knows that he's entered 'in people's hearts and in the history of Spain for ever'.
Next day the headlines in the Spanish press pay homage to this sensation:
'Torres, the Golden Kid, scores a goal for history' – _El Mundo_
'A goal from 'The Kid' Fernando Torres gives birth to the first champion team after waiting 44 years for the delivery' – _La Vanguardia_
'Thank you, _Niño_ , you are a legend' – _AS_
'El Niño has become a man' – _Sport_
'Marcelino's heir' – _Público_
'Torres goal reaches mythical heights' – _Marca_
And it is not only the Spanish press that praises him. Newspapers from _The Times,_ to the _New York Times,_ from _La Gazzetta dello Sport_ to _L'Équipe,_ from the _Guardian_ to _Clarín,_ Torres is the unquestionable hero. He's the King, agree both _The Times_ and _La Gazzetta dello Sport_. After being hidden from the rest of Europe he has taken the sceptre and crown and assumed the throne of Europe. Journalists from around the world recount his life and his performance as if talking about Orlando. Even his tattoos are talked about, such as the Number 9 in Gothic letters on his right arm, his name in the _tengwar_ alphabet as created by J.R.R. Tolkien in the _Lord of the Rings_ , and on one of his legs, in Roman numerals, the date 7 July 2001, which is said to be the date of his first kiss with Olalla. The ratings given to the Little Prince by journalists are exceptional. _The Times_ , ungenerously, gives him an 8, saying: 'Magnificent. Did it time and again with Liverpool last season and did it time and again last night. No one could stop him.' And the picture on so many front pages is that of his arms outstretched like a red angel, Lehmann beaten and on the floor and the ball with its chequered panels rolling towards the net.
The next day it's back home for the parade with the cup through the streets of Madrid and a 24-hour party. At 19.55 on 1 July, the team plane lands at Madrid Barajas airport. The faces of the players betray fatigue – they haven't slept much because of all the celebrations, first in Vienna and then in Neustift, where the squad trained. But no one wants to stop the fun at the moment. An open-top bus takes two hours to make its way to the Plaza de Colón, where, waiting for their heroes, are one million fans and a big stage, where Pepe Reina will be the master of ceremonies. Fernando Torres places himself at the front corner with the cup in his hands and his red shirt. From the crowd a boy calls out and hands him flags of Spain and Atlético Madrid. He holds them and waves them aloft.
## Chapter 23
**Ambitious**
_Conversation with Liverpool and Spain goalkeeper, Pepe Reina_
'I gave my son two bits of advice: to be a good team-mate and, during the match, keep your eye solely on the ball. He's a great goalkeeper and I don't say that as a father but as someone who knows about these things,' declared Miguel Reina during Euro 2008.
And he is right to say that he knows about these things because Miguel, the father of José Manuel Reina Páez – better known as Pepe – was also a leading goalkeeper. He played 312 matches in the Primera Liga with Córdoba, Barcelona and Atlético Madrid – the club where he ended his career in 1980. He won one league title, two Spanish Cup trophies, one Copa de Ferias cup, an Intercontinental Cup and two Zamora Trophies for the best Spanish League goalkeeper. His worst moment was losing the 1974 European Cup final against Bayern Munich. His son, who he admits is 'better than me', went through the same bitter experience in Athens in 2006, losing the Champions League final against Milan but, two years later, got the satisfaction of winning the big continental title, Euro 2008, with Spain.
And it is his son, who, as a child, wanted to be a winger but instead – thanks to his support – became the goalkeeper for Liverpool. Pepe arrived in the city of The Beatles in July 2005 and Rafa Benítez described him as the best Spanish goalkeeper. He came from Villarreal, where he was on loan from Barcelona, the club where he had worked his way up from the junior ranks to the senior squad. He won two Intertoto Cups and was renowned as a penalty-stopper.
In his last season with Villarreal, he saved seven out of nine. Within a short time at Liverpool he managed to push out Jerzy Dudek, the hero of the winning side in the Champions League final in Istanbul, gradually gaining the confidence of manager, team-mates, fans, and increasing his reputation. For three years running (2006–08) he won the Golden Glove award for the highest number of clean sheets in the Premier League, only just missing out (by one) on a fourth consecutive title in 2009 to Manchester United's Edwin Van Sar. The goalkeeping son of a goalkeeper has become more famous than his father because, explained Miguel, 'He is a very safe, all-round keeper, who dominates his area and who is also very good with his feet.' But Pepe is not only a great player, he is a charming character, the ideal dressing room companion who can give you a boost when things are going badly or when someone is feeling down. And that's not all, the Number 25 of Liverpool (Number 23 in the national side) is also very funny and a bit of a performer. Few Spaniards have forgotten his display on the podium in Madrid's Plaza de Colón, the day after the Euro 2008 victory. With microphone in hand he introduced all his team-mates, inventing a few humorous lines for each of them, and then almost lost his voice during a six-minute audience participation routine, which made a million people go wild with delight: 'It was an unforgettable moment for everyone, for them and for me. It was a moment of celebration and affection for my team-mates. We were all on a high and it just came out like that. Nothing was prepared, everything was improvised. The truth is I'm proud of having done it and that people have fond memories of it.'
### _And what are your memories of the winning goal?_
'I remember this huge suspense, as the ball kind of swept its way into the goal, floating through the air before brushing the net next to the post. Once we saw it was actually inside, there was an explosion of joy. We had put ourselves in front in a European Championship final after so many years and having suffered so much in qualifying. It was the best moment of those two years and the deserved result of a hard campaign.'
### _What was the hardest moment of Euro 2008?_
'The match against Italy was difficult. We suffered because we were up against a team that fought really well, typically Italian, but above all because there was a psychological barrier. The quarter-finals were where Spain always lost. It was the tensest moment but I think the football, in the end, was where we won it. If someone deserved it over the 120 minutes, it was Spain. We wanted to win the match, the Italians wanted a draw. We went to penalties and we went through in the way that Italy is used to going through and we arrived in the semi-finals on merit.'
### _Most countries envied Spain's striker duo of Villa and Torres. Is it true that it was you who got them to understand each other better over a 'fabada' (an Asturian bean stew)?_
'I get on well with El Guaje and Fernando, I've known them both for some time. We met up with the families and they got to know each other a bit better as well. In the end the friends of my friends get on well with each other. It's a source of pride for me, but I don't want to give myself the credit – it's normal that two good people get on well together. And the story about the _fabada_ is true. El Guaje's mother made it and we ate it after the match against Sweden and I can assure you we all enjoyed it.'
### _Talking of food, it seems that your wife's tortilla (Spanish omelette) has helped Torres adapt to Liverpool?_
'I'm lucky to have a wife, Yolanda, who is a fantastic cook and a very good hostess. Fernando and Olalla live about 50 metres away. We like to meet up with them and other team-mates to have lunch, dinner, or just have a good time together. When you're outside your own country, it's nice to be with people from your own culture and to enjoy oneself as much as possible. We are a very homely family, we have two daughters, Grecia and Alma, and when friends come round we like to have a barbecue or watch a film. We also go out as a group and in Liverpool there are places that aren't at all bad.'
### _What advice did you give Fernando to help him when he arrived?_
'Fernando is very good at getting his head round different situations and that's why he's adapted to Liverpool so quickly and so well. He knows exactly where things stand and is extremely mature for his age. He very quickly felt comfortable here, so much so that now it's Fernando who's giving me advice and not the other way round. When I arrived at Liverpool, it was Fernando Morientes who helped me a lot and I try to do the same with whoever comes, making an open invitation to visit me at my home, giving advice and making myself available for whatever they need.'
### _Did you ever imagine that Fernando would do what he did in his first season with the Reds?_
'I think that not even he expected it. To be truthful, no one expected it because he had some serious difficulties – a new league, new team-mates and a different way of playing. For those reasons, you have to give him a lot of credit for his 33 goals and I think that Fernando can feel proud of what he did.'
### _But this last season hasn't been fantastic..._
'No, it hasn't. Because first, to repeat what he did in the 2007–08 season was almost impossible and second, injuries haven't been too much help for poor Fernando. I hope the next season will again be brilliant. I'm sure it will be.'
### _How do you rate the 2008–09 season?_
'Well, I think we've improved as a team but if we're not winning titles one can't say that it's been a good season. We always have to try to win trophies and this year that hasn't been the case, but what we have done is beat the club points record and we've only lost two league games. We've achieved a lot and we have fought right to the end to try to win the Premier League. We can be proud of what we've done but we're still one rung below Manchester United. We have a Champions League place but no titles and we're not happy about this. Nevertheless, the atmosphere in the dressing room is good and we have the feeling we have improved. I think that big things will be happening to us in the coming years.'
### _How is Torres seen from the perspective of the Liverpool goal?_
'He's a player that makes all of us a little better. He has skill, speed and directness, which all help the team. For those who play around him, he makes their passing easier and he can turn a bad ball to his advantage. For me, from behind, the counter-attacks that we have practised are a lot easier when I can take advantage of his speed. It's something we have talked about, we know each other well and we know when to do it in a match. In a given moment, I can find him with a ball behind the opponents' defence _.'_
### _And as an adversary?_
'Let's just say I have suffered considerably. While I was at Villarreal, he scored against me on various occasions. It's strange because the people who've scored most against me are him and Villa and now they two are good friends. They are footballers who, when you play against them, you always suspect that something bad's going to happen and Fernando is one of those. I don't know exactly how to explain it but it's a feeling of danger. When he has the ball, your goal isn't safe.'
### _Since when have you known each other?_
'I got to know Fernando in the national Under-21 side, we were both there but it's really been in Liverpool where I've had the pleasure to really get to know him, as a person, and a close friend.'
### _What is the quality that strikes you most about Fernando?_
'His ambition. Yes, he is a very ambitious player, and for that reason he comes out on top. He's never content to sit back with what he has, he's always trying to improve himself. At all moments, in each match, he looks for the things that haven't worked out, he studies errors he's made and works very hard to do it better the next time.'
### _Torres is a star of the team?_
'Yes, Steve and Fernando are our stars and that's how it should be because they really are the two players who make the difference. Fernando has created a place for himself amongst the Liverpool greats because he's very charismatic, a good guy, a warm guy, a worker and that's how the people of Liverpool see him and they really appreciate him.'
### _And he's also the 'pin-up boy' of the team..._
'That's not how he appears to me. Men are not my thing but I understand that Fernando has that attraction. He's tall, strong, handsome and he's got hair – what's more it's blond – not like me!'
## Chapter 24
**Atlético de Madrid 1 Liverpool 1**
_22 October 2008_
No, El Niño isn't here tonight. Not on the pitch and not in the stands of the Vicente Calderón stadium. The previous week in Brussels, at the King Baudouin stadium, against Belgium, his luck runs out. Twelve minutes into the game the Number 9 of Spain's national side feels an intense pain in his thigh. He pulls up and asks to go off. At the end of the game (1-2 in Spain's favour) Fernando leaves, head bowed, without speaking to the journalists waiting for him. His return home to Atlético the following week for a Champions League tie is now in doubt. The verdict, which comes the next day, leaves no room for appeal: a small tear in his right hamstring. The same problem he suffered back in August. The prognosis: three weeks out.
Enrique Cerezo, the president of Atlético, invites him anyhow through Rafael Benítez. His manager gives the green light but Fernando says he won't be able to be there. The insignia of gold and diamonds that his ex-team-mates have wanted to give him to recognise his years of service to the club will have to wait for another time. On his website he expresses his gratitude and apologises to the fans of his former club, saying: 'After meeting with the manager, the doctor and the physiotherapists, we have decided that the best thing is for me to stay in Liverpool because I would lose two days of recuperation. At this stage in the season, we cannot permit that kind of luxury. As the fans of Atlético are already more than aware, I want to play again as soon as possible and I'm working to get myself ready.' He adds that, for him, not being able to play at the Calderón is very upsetting. He doesn't use these words lightly, because ever since Atlético and Liverpool were drawn together in Group D, he's been longing for 22 October with the expectation of a child anticipating the visit of Father Christmas: 'I really can't wait for the match at the Calderón to arrive. I feel curious about what my return will be like and how the fans will greet me, although I'm convinced they have good memories, as do I.'
At first, the game's venue seems in doubt: after police clashes with Marseille fans and racist abuse was targeted at Marseille's black players, UEFA decides to sanction Atlético by moving the club's next two scheduled home games. But the punishment is suspended, and the game will be played at the Calderón. Torres will be back after sixteen months' absence and is already imagining what he will do. He'll arrive at the stadium and greet many friends, then get changed – something strange – in the visitors' dressing room. He'll run onto the field acknowledging the cheers of the fans, he'll be there in the official photo with the ballboys he knows so well. If he scores, he won't celebrate – it would be silly, a lack of respect for the place, and for the people who watched him grow as a footballer. But he's sure to play the best he can. He wants to put in an unforgettable performance and help his Liverpool team to victory. But all these ideas and dreams are put to one side. However, even if Fernando Torres doesn't set foot on the pitch at the Calderón, no one's going to forget about him – no one among the 3,000 Reds travelling from Liverpool and no one among the 50,000 Atlético fans. The two groups of fans merge together and arrive at the stadium together peacefully. Once inside, they all invoke the name of their idol. The Atlético fans sing out to Fernando as they always have, to the tune of 'Can't take my eyes off of you'. The Anfield faithful respond with 'Liverpool's Number Nine'. And then, at the end of the game, the visitors sing out 'You'll Never Walk Alone', and the whole stadium erupts in applause. A great evening for the supporters, who head home happy with a draw that does both sides justice.
For the return leg at Anfield, Torres looks to have recovered. Rafa Benítez gives him a 70 per cent chance of playing. It's not clear if he'll make the starting line-up, or if he'll be on the bench, but everyone's counting on the Number 9. They know he's desperate to play. He himself hopes he'll pull through, but on the morning of the game he fails a fitness test. There's nothing he can do: 'It seems I'm cursed,' he says. Unfortunately, during the first half of the season, injuries among the forwards are a regular problem for the Reds. These injuries prevent Liverpool from unleashing the torrent of goals of the previous season. Fernando scores again on 1 February (twice against Chelsea) – it's eight months since his last home goal and 119 days since his last Premiership goal (5 October against Manchester City). Even if he's unlucky on the evening of Tuesday, 4 November, Fernando Torres is still at Anfield. An hour before kick-off, accompanied by Olalla, he walks onto the field to respond to the Atlético fans gathered in the Century Stand. 'Fernando Torres! Fernando Torres!' they shout enthusiastically. And then, inside the stadium, many reunions with people he's known for much of his life. The game begins and the TV cameras pick him up. The Kop starts to sing. Maxi, his Argentine ex-team-mate, disappoints him by putting the _rojiblancos_ one up.
Fernando closes his eyes and bites his lip, but when he sees the joy of the Atlético players his irritation passes. Liverpool push forward, creating chances, but can't make the breakthrough. The Number 9 despairs. He throws up an arm as Liverpool claim a penalty after Perea handles. He seems to press his team-mates to play more efficiently. He swears as a chance goes begging. The clock shows 93 minutes and 43 seconds – the game looks to be over, but then the referee blows for a penalty that leaves the visitors fuming. To them, nothing happened. Robbery, plain and simple. At first, Torres does not react, but then applauds the decision. Gerrard steps up. As usual, El Niño doesn't want to watch his team taking a penalty. This time he doesn't know what to do. He buries his face in his hands and hardly dares look. A goal. He waves his fists and celebrates his captain's goal, a gesture that earns the reproach of one of the visitors from Madrid. El Niño can't understand why. For him it's logical to celebrate. No treachery, no mistake. It's a view shared by the members of the _Peña Atlética Fernando Torres_ fan club from Fuenlabrada. That Tuesday in November they're at Anfield, together with 2,600 other _rojiblancos_. They're surprised by the affection in which their hero is held by Liverpool fans. They swap scarves, flags, handshakes, addresses and pictures of El Niño (2009 calendars printed by the _Peña_ with a photo of Fernando as a youngster or celebrating Spain's Euro 2008 victory). They've even managed to hang their scarves around the mannequin sporting Torres' shirt in the Liverpool Club Store, in Williamson Square in the heart of the city.
The night when Spain play in Seville against Fabio Capello's England, they turn up at Tommy's Café in Calle Ferrocarril street in Fuenlabrada. It's just down the road from the station underpass where Moroccan immigrants are drinking mint tea, eating kebabs and anxiously watching their national side playing a friendly in Casablanca against the Czech Republic. Spain's game, however, has not yet kicked off.
It's nine o'clock and there's time, over a beer and a plate of well-cut cured loin of pork, for Pasqual Blázquez, José Antonio Camacho and Tony Roldán to swap stories. They are three of the members of the _Peña_ , which has some 150 members and continues to keep its full name, even though El Niño has long since left Atlético. They've known Fernando since he was a child and followed his progress from the juniors to the first team. On the wall, a newspaper cutting recalls Fernando's first call-up to the national side under Iñaki Sáez. A signed Liverpool shirt is a symbol of the present. There are photos of the blond, freckled lad with the president, the secretary and the treasurer, which show a mutual respect. Fernando, a traitor? Not at all. 'There are no recriminations against him. He's gone because the club didn't respond with the signing he wanted. They didn't know how to build a competitive team that could fight in Europe. Fernando has done an awful lot for Atlético. There's nothing to reproach him for,' says Roldán. 'He's been our flag-bearer – one of the greatest in our footballing history. He's at the same level as Gárate, the most effective Number 9 we've ever had ( José Eulogio Gárate, an Argentinian from Sarandi who played eleven seasons with Atlético, scoring a total of 123 goals) and at the same level of Adelardo (Adelardo Rodríguez Sánchez, seventeen seasons between 1959 and 1976, and 112 goals) or even Aragonés himself,' explains Camacho.
'Real Madrid had Raúl and we had El Niño,' adds Pascual. 'His departure was necessary, above all because he needed to measure himself against the great European players and so, signing for Liverpool has been good for him. But his transfer has also been beneficial for the club, which has been able to sign Simao, Luis García and Diego Forlán and one has to say that the Uruguayan is doing very well. We will see if they also sell him.'
Roldán interrupts the thoughts of Camacho: 'Have you seen the last interview with El Niño, saying that he will never go to Real Madrid. He's a player who feels the club colours, which is a difficult thing in this era of millions.'
The three of them chat about values, about feelings for Atlético. They tell their guest that, to be a _rojiblanco_ is almost like a religious calling. 'You believe and you go on believing, even if miracles don't happen. It's important not to lose faith.' They recall that Chamartín (the Bernabéu, the stadium of their main rivals) is like an opera, with everyone seemingly reluctant to get involved in the game. The Calderón, on the other hand, is where to find passion for real football. 'Indeed, it is almost the same atmosphere as it is in Anfield. The fans are similar and absolutely in love with Fernando. We have met him recently and he's very happy there. His father told me that as well,' confirms Camacho. And he explains: 'I was sure he was going to be successful because there they play in the same style as Fernando.'
They remember the time of Jesús Gil, someone points out that, with him, Torres never had problems and that, in fact, he was always protected by Gil. And he was opposed to the sale of his crown jewel against the opinion of many who thought that the player was at the top of his game and therefore should be sold before his value declined. Camacho goes back in time to remember the shy boy, who, when playing with _Mario's Holanda_ , succeeded in filling the stadium. He talks about Torres' family in complimentary terms.
Roldán comes back to the present, to 29 June 2008, when the bar was packed to the rafters and nobody from the _Peña_ or from the neighbourhood wanted to miss El Niño's final: 'We were all convinced that he was going to score that day. It's a shame', adds Pasqual, 'that he never got to play at the Calderón, but we're confident that he'll come back one day to finish his career here, where he started, where people still think so much of him.' The conversation ends. The television is showing the start of Spain v England and El Niño is on the pitch.
## Chapter 25
**A danger**
_Conversation with Liverpool and Spain defender, Álvaro Arbeloa_
The shirt is red, but over the part which covers the heart is the badge of the Spanish national team, the Real Federación Española de Fútbol (Royal Spanish Football Federation). Sitting on the steps that lead to the residential area of the Federation's Ciudad del Fútbol de Las Rozas training complex, 12 miles from the centre of Madrid, the former Real Madrid and Deportivo La Coruña player – currently Liverpool's Number 17 – chats away happily. The weather is wonderful – a deep-blue sky without a cloud in sight, and on the horizon, the tops of the Sierra mountains still covered with a light sprinkling of snow, while the sun beats down with almost summer-like strength.
'At Liverpool, we dream of weather like this. It only happens a few times a year,' laughs Spain's Number 26 from the western city of Salamanca. The training session for the national side is scheduled to take place in the late afternoon. Before that there is time to ask a few questions.
### _Does the team feel different when Torres isn't there, like in the match with Atlético?_
'Yes, a lot. It's normal because we don't have a squad like Manchester United. If they don't have Rooney, they can bring on Tévez, if they don't have Tévez, they can use Berbatov. We have Fernando, who is the best in the world and when he is missing, it shows. When he's there, upfront, you know that he is going to 'create danger' at any moment because his presence alone creates insecurity and Kuyt, Riera and Steve take advantage of that. When he's on the pitch, he gives us total confidence.'
### _You were in the team for the Liverpool-Chelsea match on 1 February 2009. How do you remember that game?_
'It was very important, above all because we'd just come from four consecutive draws. We weren't in a good situation; we'd lost the league leadership and second place as well. If we didn't beat the Blues we'd be several points adrift of Manchester United. We were better than them but the ball just wasn't hitting the back of the net. Luckily, in the end, came the two goals from Torres.'
### _It was an important match for him as well, wasn't it?_
'Fernando was coming back from injury. It had been months since he'd scored and, with just a few minutes remaining, he scored the first and then, in extra time, got the second. Well, everyone knows that for us, Fernando is hugely important.'
### _How would you describe Torres, seen from behind, from the Reds' defence?_
'A danger, absolutely. I was lucky to play against him with Deportivo a few weeks before I left for Anfield. Fernando and I were talking about it just the other day.'
### _Lucky or unlucky?_
'I think that one is always lucky to play against great players. Well, OK, as long as they don't make it too bad for you. But the truth is that Fernando is a spectacular striker – he never gives a ball up for lost; physically, he is a phenomenon, he has incredible power and, above all, enormous confidence in himself, which makes him one of the best in the world, if not the best.'
### _Liverpool has helped you get into the national side and turned Torres into one of the best players in the world. How did it happen?_
'Well, I think it's very important to play at a club like Liverpool, which is in the Champions League and competing for the Premier League title. It's an international shop window – it's clear that a player's value increases. But one can't ignore the fact that, in order to get there and to play at Anfield, you have to show your worth. And it's no easy feat to be there. Fernando, apart from the fact that English football, because of its characteristics, suits him better, he doesn't have the pressure that he had here (in Spain), he doesn't have all the media on top of him. He's been able to dedicate his time to training, improving his play and to enjoying his football, and that's been really important. You could say he's been let off the leash.'
### _And in two years he's already an idol..._
'There, he's a legend like Ian Rush or Kenny Dalglish – players that spent years at Liverpool and won a lot of trophies. Fernando's been compared to them and he has been put on the same level.'
### _Of course you, together with Fernando Torres and Pepe Reina, have met Dalglish, Souness and Sammy Lee in person. What were your impressions?_
'It was a bit like going back to your childhood and reviving your idols. Once you are a footballer you forget when you were a kid and the excitement of seeing those players. The day we had dinner with them, for Michael Robinson's (Spanish TV) programme, it was like reliving those childhood years. They told stories about the matches and the victories of that Liverpool side and us three with our mouths open listening as if it was a fairy tale.'
### _How does a new player get to understand the values of a club like Liverpool?_
'Rafa Benítez has always wanted to get those values across, right from the start. He's reorganised Melwood (Liverpool's training ground), covering the walls with club legends, photos of the most distinguished players and the trophies which Liverpool has won. And later, this is passed on to you by people in the street or in Anfield and you realise that you've come to a club that's very special. And right from the first day, you want to absorb its history.'
### _What advice did they give you when you arrived in January 2007 and what advice did you give to Fernando?_
'I don't usually give much advice. It's Pepe (Reina) and Xabi (Alonso) who do that. The first thing they make you understand is that it's different in England. You don't complain, you don't throw yourself on the ground, you don't try to engineer a free-kick. They encourage you to get yourself acclimatised on the pitch and give you help off it.'
### _You grew up in the 'white factory', as Don Alfredo Di Stefano calls it and then, aged 24, you arrived at Liverpool. What do you think have been the main differences?_
'Differences? A lot. To go from one country to another, you change language and habits, but above all you come across a footballing culture that's completely different. You see it in a different way, you play a different way and the atmosphere is something else.'
### _Tell us about this different culture..._
'English football is very physical. Much more contact is allowed. Sneaky or 'smart alec' behaviour doesn't exist as it does in Spain and it's very much looked down on. There's also the difference in the crowd's attitude to football. You could see this in the first knockout round of the Champions League. My ex-team-mates at Real Madrid were surprised because, following the half-time break, when they came back out on to the pitch – and they were losing – the Anfield fans applauded them. In the Bernabéu, when we came onto the field, we were greeted with whistles and insults.'
### _It was a job well done, the Anfield game against Real Madrid?_
'It was a victory to savour. It's a good feeling to beat a big side like Real Madrid but it also hurts to see team-mates who've been your friends so dispirited by the defeat. But if I had to choose, I'd go for the Champions League knockout round against Barcelona. I have great memories of that match in the Camp Nou. It was my European debut with Liverpool and we won 1-2.'
### _What's life like in the Spanish Liverpool?_
'Life's good, calm. Above all, I appreciate the relaxed attitude with regards to the media. You don't have to worry if this person has said that or another something else. You can just concentrate on playing football. Everything is very homely. Sometimes, with Fernando and Pepe, we meet up for dinner, but not much. We train, we have lunch and at home, I relax with my partner Carlota, or have a siesta. What you really appreciate is the incredibly warm welcome we've received, because very often in Spain, when a group of Dutch players arrive at Barcelona or Brazilians at Madrid, maybe they don't get the same kind of welcome. Why? I don't know. Maybe the people of Liverpool are very welcoming and we are less so in Spain. At Anfield you see how the fans sing to Rafa, while here you very rarely hear a stadium sing to its manager.'
### _Speaking of Benítez, what kind of a person is he?_
'Rafa is very much on top of you, correcting your positions, studying your every movement on the pitch. For me, for example, when it's my turn to play on his side of the pitch, I always listen to him. It's as if he has a joystick to move me around – forwards, stay still, back. It's true he gives a lot of orders but he improves all his players.'
### _A survey by (the Italian newspaper)_ La Gazzetta dello Sport _elected him as the best trainer, ahead of Sir Alex Ferguson, José Mourinho and Fabio Capello..._
'I haven't worked with the others but I'm sure that Rafa is one of the best, especially because of the constant dedication he gives to his work. I think there are few managers that spend so many hours studying football like he does.'
'See you, it's been a pleasure,' says Álvaro Aberloa as he moves off towards the training complex accommodation.
## Chapter 26
**Third Place**
_2 December 2008_
'What the hell is wrong with you? Fernando Torres is your candidate for the _Ballon d'Or_ (European Footballer of the Year) – 33 league goals, the best foreign debutant ever in the Premier League, the scorer of the winning goal in the European championships, the most important in 44 years of Spanish football history and yet he's not your candidate. Why not? Why, in Catalunya, their candidate was Lionel Messi and then Xavi Hernández? Why in Madrid their candidate was Iker Casillas?'
The strongly voiced thoughts of an imaginary Englishman, who, in autumn 2008, is desperately trying to understand why the Spanish never unite behind El Niño. Liverpool's Number 9 is a strong candidate amongst the 30 nominations for the _Ballon d'Or_ prize awarded by _France Football_ magazine, thanks to his goals for the Merseyside club and his winning strike in the final of Euro 2008. Nevertheless, for him, his nomination seems incredible: 'When I saw that Kaká, Ronaldino and Zidane had won the _Ballon d'Or_ ,' he says in an interview with _Eurosport_ , 'I thought they were players from a different planet and I could never get to their level. And then after Euro 2008, they talked about me alongside other great footballers. For me, that's incredible. I can't say that it was a dream because I never considered the possibility. I never thought I would even be near. Even today, I still see it as something that is a long way off.'
And yet Torres is on the list and forms part of a strong Spanish presence: Iker Casillas, Sergio Ramos, Marcos Senna, Xavi Hernández, Cesc Fabregas and David Villa. An explanation from El Niño: 'The trophy (Euro 2008) has catapulted us into a position from which we can compete for individual recognition.' However, for Torres, Cristiano – the overwhelming favourite to win the top prize – has been 'the best, the most consistent. He's played at a very high level. He's won the Premier League, he's won the Champions League and scored in the final. He's been the top scorer in all competitions and he won the Golden Boot. I think it's very rare that a player has achieved so much to win. Let's hope I get near. Let's hope I'm in the first three. For me, that would be sufficient,' explains Torres.
Cristiano Ronaldo, the Manchester United Number 7, is certainly the strongest candidate and the sure-fire winner of the _France Football_ prize – no debate. The Portuguese from Madeira has played the perfect season and 2008 has been his year. He has bagged an impressive total of 42 goals (31 in the Premier League and eleven in the Champions League). At Euro 2008, he was disappointing. His Portugal were eliminated in the quarter-finals but the European tournaments have rarely been a determining factor in the _Ballon d'Or_ award.
Meanwhile, the Spanish newspapers have very different ideas as to who should win the competition. Take _Sport_ , one of the two dailies based in Barcelona that covers news about football. It began collecting signatures from celebrities and fans all over the world to support the nomination of Leo Messi. An initiative that reaches a total of 60,000 within a few days – and this in spite of the 2007–08 season, which has not been the best for the little Argentinian. Apart from the gold medal with the national team at the Beijing Olympics, Lionel has won nothing with Barcelona. His year has been ruined by injuries and, in addition, he lost the direct clash with Ronaldo's Manchester United in the semi-final of the Champions League. From last September, under the guidance of Pep Guardiola, he has once again returned to the top level, performing well and scoring goals. A bit late, though. Staying in Barcelona: _Mundo Deportivo_ , the other daily of the city, champions Xavi – also a Barça player – undoubtedly the leading participant at Euro 2008 in Austria and Switzerland, as well as being elected the best player of the tournament. Moving to the Spanish capital, one discovers that _Marca_ is campaigning for Iker Casillas, the keeper whose saves and cool-headedness in the penalty roulette against Italy got the national side past the taboo of the quarter-finals.
To sum up, everyone has their axe to grind, but the situation in Spain is such that the weight of the two historic clubs is more than the national team. Real Madrid and Barcelona rule the roost, as always. Nevertheless, the fact remains that it's all very irksome. Even to Fernando. In an interview with French sport daily, _L'Équipe_ , on the eve of the World Cup qualifying match between Estonia and Spain last October, El Niño said: 'You'd have to be blind not to see the huge campaign in favour of Iker. I'm the first to recognise that he deserves it, but so does Villa, Xavi or me. But no one is saying so. According to where you are geographically, you are rated more highly. I don't like this difference in treatment.' A controversy that is immediately hushed-up. The different voices from one side or the other tone themselves down and there's less discussion on the issue. Xavi Hernández makes light of the quarrelling and draws a line between the personal jealousies: 'The individual prizes', he says, 'are a reflection of the collective success. I don't think that I have much chance. I would certainly like a Spaniard to win. If not then Messi, my Barça team-mate.' But that is not to be.
On the cover of the 2 December edition of _France Football_ , there is Cristiano Ronaldo. With 446 points, he is European Footballer of the Year (winner of the _Ballon d'Or_ ) 2008. Second, on 281, is Lionel Messi and Fernando Torres third with 179. Following-up behind are Iker Casillas, who just misses out on the podium, Xavi in fifth and David Villa seventh. Steven Gerrard, the Liverpool captain, comes in tenth. To complete the Spanish Armada, midfielder Marcos Senna, of Brazilian origin, is also there, finishing in 11th, Cesc Fabregas 20th and Sergio Ramos 22nd.
The result is expected – at least for the top place. Messi keeps second place, the same as the previous year. Torres mounts the podium for the first time. Fernando was nominated in 2006, the year of the Germany World Cup, the year in which Fabio Cannavaro, the Italy captain, took home the award. El Niño ended up in the body of the group, 26th, equal to lots of other good players. This time, things go very differently. Despite the vote in favour of the Manchester United winger, five judges on the award panel made Torres their top candidate. Their opinions make for interesting reading: 'Torres for me is the best-performing player of the year,' writes Franks Van Den Nieuwenhof of the Dutch _Eindhovens Dagblad_. 'Torres is the best over the last 30 metres,' from Paché Andrade, _Canal RCN_ , in Colombia. 'Fernando Torres, in his first season with Liverpool, has achieved the incredible total of 24 goals and got the crowning goal for Spain. For all these reasons, I put him ahead of Cristiano Ronaldo,' comments Luo Minn, _Titan Sport,_ China. 'Torres is a strong character and has immense talent,' from Dafrallah Mouadhen, MBC TV, Dubai. 'His outstanding season with Liverpool and his enormous contribution to the Spanish national side persuade me to vote for Fernando, who this year has become the complete footballer,' argues Francisco Rivas García, _El Heraldo_ , Honduras. Who did the English representatives, Max Marquis and Henry Winter, of the _Daily Telegraph_ , vote for? For Cristiano. In their order of preference, Torres is second. Paco Aguilar, of Spain's _Mundo Deportivo_ , chose Xavi. A confirmation of what has been said before.
And what does Fernando Torres think of his 'bronze _ballon_?' 'The prize is an important recognition, which comes just as I'm recovering from an injury (picked up on 26 November, during the Champions League game against Marseille. The prognosis is that he should be fit again within about four weeks). It'll give me a boost to get back to playing again as soon as possible.'
He is proud to have made the third spot and expresses his gratitude to his team-mates at Liverpool and in the national side: 'Their support has been both significant and essential and their contribution is one of the reasons that I can enjoy this event today.' He knows that 2008 has been a fantastic year. 'This has been my best year as a professional player, different from what I was used to. I arrived at a great club,' he explained, 'that gave me the opportunity to play at the highest level, to play in the Champions League and to learn from some of the best in the world.' As a smart pupil who went on to get good marks at school, he says the prize is simply a motivation to do better.
On 12 January, 2009, the story repeats itself. On the stage of the Zurich Opera House there are five people seated in the front row, waiting for Pelé to open the envelope containing the name of the successor to Kaká, FIFA World Player of the Year 2007. Brazil's former Number 10 is more emotional than the candidates themselves. He has some difficulty in opening the secret envelope. Once he has succeeded – and before revealing the winner's name to the television cameras – he remembers that, when he presented the prize the previous year to his compatriot, Ricardo Izecson Dos Santos Leite (aka Kaká), he assured Ronaldo in Portuguese, 'Next year, you will be the winner.'
And, sure enough, Cristiano Ronaldo is FIFA World Player 2008, picking up his fifth crown of the season. In-between one trophy and another, the Number 7 was also in the Manchester United side that won the FIFA Club World Cup on 21 December in Yokohama, Japan, beating Ecuadorian side, Quito (holders of the 2008 Copa Libertadores) 1-0. Cristiano, according to the votes cast by 155 national team managers and captains, got 935 votes. Since the previous year, he has gone from third to top spot. Runner-up for the second year in succession is Lionel Messi with 678 votes. Third is Fernando Torres on 203 points. El Niño confirms his _Ballon d'Or_ position in front of Kaká (183 votes) and Xavi (155). Casillas is eighth. 'It's really important to be here,' declares Torres, formally dressed in white shirt, black jacket and tie. 'I wasn't expecting it. I had just changed my team and country but I adapted to English football really quickly. After that, I began to score goals and that made it all much easier. After not winning a trophy with Liverpool, which was what I really wanted – because they have given me so much and I wanted to give them something back in return – the trophy arrived with the national side. Something probably even more unexpected. After a long time, Spain is once again one of the best. And me scoring in the final. I'm here because of that. But without all the efforts of my team-mates, I wouldn't have this recognition,' says the modest blond lad. And for the Spanish fans, he adds: 'It's really good that two players from our country are amongst the finalists. Let's hope it's the beginning of a phase in which our footballers are always present.' A great night, he says, the first in his career in Zurich. To him, his third place behind two world stars seems fair because 'Messi is the best in the world and Cristiano Ronaldo is the one who's had the best year. But my aim is to improve season on season. I don't look back. I want to do things well so that when the 2009 (awards) come round I can once again be one of the candidates.' He is asked if one day he will win one of these two trophies and he modestly replies: 'To win one it's clear that there've got to be a lot of favourable circumstances. There are times when a player has a great season but doesn't win any trophies and that affects him. What's important is to be one of the candidates for many years. Look at Gerrard, he's always been in the top ten but has never won the prize and he deserves it. But he goes on giving his best.'
## Chapter 27
**A Hartung**
_Conversation with England manager Fabio Capello_
His name is on the entry phone. After pressing the button you are let into the hallway of a nineteenth-century villa, where a lift takes you to the fourth floor. The narrow compartment door slides open and there on the other side is Fabio Capello, sporting a geometrically patterned sweater, blue shirt and designer glasses. The England manager invites the visitor into his sitting room. At the end is a huge window looking out on a beautiful private garden with ancient trees and, shining through the mist, an immaculate lawn and tennis court – a silent, tranquil and elegant location right in the centre of London. A computer and various documents sit on top of a long table – the ex-manager of Milan, Roma, Juventus and Real Madrid had brought work home from his FA office.
During the next two days he will be performing a spectator marathon, watching all four games involving Liverpool, Chelsea, Manchester United and Arsenal, ahead of their appearances in the quarter-finals of the (2008–09) Champions League. There is still some time before the 2010 World Cup in South Africa, but the England coach must always keep a close eye on the European tournaments and the Premier League, as well as the players who will make up the basic structure of the team that will probably represent his last campaign in the dugout. This is a manager who doesn't beat about the bush, so it's best to get straight to the point.
### _Cristiano Ronaldo, Messi and Torres: European Footballer of the Year, one, two and three and the same order for the FIFA World Player of the year. What do you think?_
'Cristiano Ronaldo is a very good, very dangerous and very technical player with great pace. Messi is a genius, no one in the world today has his talent. He can do extraordinary things. As for Torres, let's say that last year he burst onto the scene and did very well. The 2007–08 season was his coming-of-age. Here in England he's succeeded in doing what he failed to do in La Liga – score goals. In Spain, everyone acknowledged his tremendous skills and pace but in front of goal he lacked coolness and ability. Obviously the change of climate has served him well – and how! Here, he's become a truly impressive goal-scorer via his ability to put the ball in the back of the net by every means possible.'
### _How is such a major transformation possible?_
'That's something I've asked myself too. Probably he needed to leave Madrid. He needed more responsibility.'
### _But he had responsibility at Atlético – he was captain and was just eighteen at the time..._
'Here he's feeling more responsibility because of what they paid for him. And perhaps this has produced the step-up in quality. Psychologically, it's helped him. At least that's what I believe.'
### _Maybe English football is well suited to his style of play?_
'Yes, Torres has the sort of speed and pace that often wrong-foots English central defenders – they are a bit slower and have more experience in coping with high balls than a passing game. And one should also say that here, like all the other foreign players, he's learned to play with few interruptions and with more physical contact. So to sum up, it's not only his technique but also his running, understanding and physical condition.'
### _Have Liverpool and Rafa Benítez had an important role in this transformation?_
'Undoubtedly. For him to be playing alongside Gerrard, the standard-bearer of Liverpool, has given him a real enthusiasm.'
### _What has Torres brought to Liverpool?_
'The certain knowledge of having someone up front that can create alarm. You know that, at any moment, with even just a half-chance, he can create a goal. He's got great pace, he's not afraid, he has good technique, is strong and smart. These are the skills of a good striker.'
### _Liverpool almost always use Torres as a lone striker..._
'That's right but it's not just Liverpool that plays like that. Now when I hear people talking about formations, it makes me laugh. I say that the modern formation is 9 + 1. There are nine who defend, leaving just one upfront. Then you need to see how many of them have the technical ability to move up into attack. That's the true game plan. Everything else is just baloney.'
### _Let's talk about how well Torres and the other Spanish players have settled in at this historic club..._
'Yes, Torres and the Spanish players are very well integrated. First, because there is a Spanish manager and second, the players all play for the national side. They are top-class. Reina is a great goalkeeper and now he's been there four years, having been signed when he was 23. Arbeloa is a superb player. Riera – I had thought about as a possible signing for Madrid (when manager of Real Madrid). And with Xabi Alonso there's no debate. They are all footballers with great technical ability, which, in league matches where pressurising, running and strength are crucial, allows them to shine.'
### _It's impressive to see how Torres has become an idol for the fans at Liverpool..._
'He and Gerrard are indisputably the Reds' two heroes. In my opinion, that has given Torres self-confidence, which he didn't have 100 per cent in a team like Atlético Madrid because he was born there, he grew up there and was pampered by the club. In short, at Madrid he felt young, with no responsibility, while at Liverpool the responsibility has made him mature rapidly.'
### _It seems that_ El Niño _understood straightaway the values of the club. How is that possible?_
'I don't know. I believe that all the great teams have a special chemistry. You feel it, you breathe it, and they can transmit it to you. You live it. And in a club like Liverpool there is a "passing on of the baton". The older players hand it on to the younger ones and make sure they understand how this process works. Another important and attractive element of the game is the crowd and the support they give you throughout the match. At Anfield, the fans are very generous with players who give their all. When you come onto the pitch and you hear them singing "You'll Never Walk Alone", you feel something extra and a special responsibility on your shoulders towards all these people who really do, in effect, never leave you alone.'
### _Would you be pleased to have Torres at your disposal for the England side?_
'Let's not talk about that. We have excellent English strikers. I don't want to talk about England.'
### _OK let's talk instead about the past, Euro 2008 and the influence of Torres in the Spanish national side..._
'As I was saying, at Liverpool he's matured and he's brought this maturity into the national side where he's achieved a lot and, above all, scored the winning goal in the final. After the fantastic season he'd enjoyed with the Reds and the spate of goals he'd scored, it was certain he was going to be one of the stars of Euro 2008. And for me Spain were, on paper, the team with the best players and one of the four favourites, together with Germany, France and Italy.
### _The strike pairing of Torres and Villa at Euro 2008 had all the commentators drooling and the Liverpool fans dreaming of seeing the two playing together in red shirts. How do you see them?_
'They play together really well. Torres is the centre forward, while Villa moves off him. He has very good movement off the ball, with excellent technical and shooting skills.'
### _As he demonstrated in the friendly against England last February?_
'Yes but we don't talk about that.'
### _Let's go back a bit to your last period as manager of Real Madrid. What was your impression then of Torres?_
'His potential was obvious but it was still a work in progress. He hadn't yet transformed from the chrysalis into a butterfly.'
### _Nevertheless, in the away match of the 2006–07 season with your Real Madrid team, it was he who scored the first goal, while in the home match there was controversy following your comments on an incident involving Torres..._
'Ah, _el tramposo_ , the "cheat" controversy – I remember it well. In the second half, after making contact with Sergio Ramos, Torres fell in the penalty area and rolled around as if he'd been elbowed – so much so that the referee sent off my defender. For me, I don't like it when a player goes in for diving in order to deceive the referee and gain an advantage for his team. At the press conference after the match, I wanted to make a point about this but I didn't know exactly which word to use. My press officer suggested _tramposo_ ("cheat") and the whole thing became a soap opera in the Spanish media. Here, I wouldn't have had any hesitation in saying "diver". Anyway, it's an old controversy and closed in the best possible way.'
### _You have played with and managed champion players in Italy, Spain and England. Who does Fernando Torres remind you of?_
'In one way, he reminds me a lot of Altafini.' ( José João Altafini, a Brazilian-Italian striker who burst onto the international stage at the 1958 World Cup in Sweden, scoring three goals in two matches. He then moved to Italy, playing for Milan, Napoli and Juventus, before finishing his career in Switzerland with Chiasso and Mendrisiostar. He also played for the Italian national team in the 1962 World Cup).
### _Why?_
'Because José had this speed and this ability of not being in a game and then playing a crucial role. I would say that Altafini was smarter with his shooting. In front of the posts, when he took up a particular position, it was a certain goal.
It meant the ball was, effectively, already back in the middle of the pitch for the kick-off. But I'm talking about an Altafini who was by then 30 years old. Torres is still very young – so we must wait.'
### _Many have compared him to Marco Van Basten, a player who you managed for several seasons at Milan..._
'No, no. Van Basten moved differently, he had other technical skills, another way of reading the game. Torres is quicker than Van Basten, he likes playing deep, while Van Basten was looking more to link-up with the midfield. No, they're two different players.'
### _We now come to the 2008–09 season, which, for Torres, has been full of injuries with one problem after another..._
'As always after the European and World Cup tournaments, players are injured. Everyone pays for it and the after-effects drag on for months. There's nothing you can do about it and in the end you pay the price for all that euphoria. After such an important victory, it's often the mental approach that suffers. What's certain is that this year he's not the same and hasn't been able to do what he was doing before.'
At this point in the conversation 'Don Fabio' (as he is known in Spain) went off on a tangent, analysing the Champions League and the headlines of the Spanish sporting press, which portrayed him as the solution to crisis situations when results were negative and difficult to manage. Later, there was time to look at and appreciate the eye-catching paintings and sculptures that decorated the sitting room. Fabio Capello is an enthusiastic art collector. Perhaps the final question was somewhat prosaic but it was impossible to resist.
### _How would you describe – pictorially – the playing style of Torres?_
[He gave the question much more thought than any other during the entire interview. Then he said decisively:] 'A Hartung.'
The Encyclopaedia Britannica describes Hans Hartung (born 21 September 1904, at Leipzig in Germany, died 7 December 1989, at Antibes in France) as: 'a French painter of German origins, one of the leading European exponents of a completely abstract style of painting. He became particularly well known for his carefully composed, almost calligraphic arrangements of black lines on coloured backgrounds.'
The catalogue of one of his recent exhibitions is entitled 'In the Beginning There Was Lightning'.
## Chapter 28
**Liverpool 4 Real Madrid 0**
_10 March 2009_
Do you remember _An American Werewolf in London_ , a 1981 film directed by John Landis? The landlady of the Scottish pub warns Jack and David, two American lads on holiday, not to go wandering off into the mist, never to leave the road and, above all, to be extra-vigilant whenever there was a full moon. But the pair ignore that good advice and the werewolf makes its savage entrance.
It's Tuesday evening at Liverpool and a full moon, bright, radiant, mysterious and threatening, looms over Anfield. But no one has warned the players of Real Madrid. No one has told them they will be meeting the werewolf dressed in red. No one has told them that Fernando Torres, together with Steven Gerrard, will be attacking them right from the first minute. They have not been vigilant. They are ripe for being taken apart without mercy. But before seeing how The Kid gets stuck into them, we take a step back... Twenty days before the first leg of the knockout tie with Real Madrid in the Champions League, Torres explains:
'To play against them is nothing special for me. It would be special if the other team is Atlético. Still, I'm looking forward to it because it will be a way of going back to Madrid, to play in a stadium where I've never won and against a big team. But I'm sure we'll win the tie.'
Declarations that were repeated in the sport dailies of Madrid with front-page headlines like 'We're going to eliminate Madrid' from _Marca_ , all of them picking holes in El Niño, because what he was saying was true – in seven matches at the Santiago Bernabéu (Real Madrid's ground) he had never scored.
The first occasion was during the 2002–03 season. The game hadn't even started when Fernando Hierro, the Real Madrid captain, made him understand how certain things were done. He went up to the eighteen-year-old in the red-and-white striped shirt, then Atlético's bright new hope, and asked him: 'What's up, son? Didn't you sleep well last night?' Torres didn't score and the match finished in a 2-2 draw. The following year, Madrid won 2-0. In 2004–05 it was a scoreless draw and in the next season's fixture, the white shirts of Madrid chalked up a 2-1 victory. A year later, in Fernando's final season in Spain, it was another draw, this time 1-1. He achieved a goal only once, on 2 January 2002, when he got past reserve keeper, Carlos Sánchez García. But it was only a friendly.
Maybe, for Torres, it was a case of 'stage fright' – a condition referred to by the former Argentina player (and former Real Madrid player, manager and then Sporting Director), Jorge Valdano, to describe the apprehension that seems to grip visiting team members when they play in a famous stadium. But it didn't stop with the stadium: in the 10 league encounters that El Niño played against Real Madrid wearing the shirt of Atlético, he never won. He scored just once against his great city rivals, at home in the Vicente Calderón stadium, on 24 February 2007, in an encounter that the Atlético side dominated (against a Real Madrid side managed by Fabio Capello, which that year went on to win the league). Torres scored in the 11th minute, then various opportunities and disallowed goals followed. But, as on so many other occasions, they let victory slip from their grasp, this time by allowing Real to equalise through Gonzalo Higuaín. To sum up, Real Madrid is Fernando's _bête noire_. A typical view is that he was a jinxed striker against Real. But this time, things would be different...
Álvaro Aberloa maintains there is no need to remind him about his goal drought in the Bernabéu: 'Fernando says he's fired up enough on his own. There's no one more keen to score in the Bernabéu, to have a good game and to win the tie than him. Even Rafa Benítez is confident, saying Torres would score. Why? 'Because there's always a first time.'
But how does Fernando himself view the encounter? He is convinced that 'small details or an individual action will decide who goes through to the next round'. He knows that Madrid will be coming out in 'better footballing shape than they have been'.
And that was the main topic of all the debates. But when, on 19 December 2008, at Nyon in Switzerland, UEFA drew Real Madrid and Liverpool against each other, the situation was very different. Bernd Schuster, the German manager of Real Madrid at the time – who'd won the 2007–08 league title – had just been driven out of the job because of a run of bad results, including the team's elimination from the Copa del Rey (King's Cup) by Real Unión de Irún of the Second Division. Taking Schuster's place in the dugout was Juande Ramos, ex-manager of Sevilla and, more recently, Tottenham Hotspur. His first task was to take on Barcelona away in the league at the Camp Nou, where they were beaten 2-0. This meant that, after fifteen games and halfway through the season, Real were in sixth position, twelve points behind the leaders, Barcelona.
The atmosphere was very different in Liverpool, where the Reds were top of the table with a two-point advantage over Chelsea, and with Manchester United even further behind. After nineteen years of abstinence, it really looked like this would be the year they would win the Premier League. Everything was going extremely well and the book-makers were offering short odds on a Liverpool title. If that wasn't enough, Madrid were immersed in an institutional crisis of unprecedented dimensions. On 16 January, following three days of high-profile accusations, Real president Ramón Calderón was forced to resign because of what the press christened 'Nanigate' – allegations of vote-rigging during an official assembly the previous December to confirm the club's 400-million Euro budget. Vicente Boluda, a 53-year-old shipowner and president of the third-biggest tugboat company in Europe, would take the helm until new elections in the spring of 2009.
In February, Madrid's future was still uncertain but on the sporting front, things were improving. Since the Barça defeat, Juande Ramos had notched up nine consecutive victories and reduced the distance with Barcelona to seven points. The league title was once again up for grabs. Hope in the white half of Madrid was reborn. The opposite was the case in Liverpool, where, on 19 January, they lost the top spot in a 1-1 draw against city neighbours Everton, which the next day allowed Manchester United to stretch their lead at the top of the table. On 4 February at Goodison Park, against The Toffees, Liverpool said goodbye to the FA Cup after they were beaten 1-0 in the 118th minute, thanks to a goal from young substitute Dan Gosling. It was the Reds' first defeat since 12 November 2008, when they fell to Tottenham in the Carling Cup. Furthermore, there was the unwelcome news of a 16th-minute injury to captain, Steven Gerrard, the team's leading scorer with nine goals in 21 league games and the driving force in midfield. Replaced by Benayoun, he left the field with an injury later diagnosed as a torn left hamstring. Benítez didn't play him in the league game against Manchester City (1-1) and his presence at the Bernabéu was in doubt.
In short, the first leg of the tie arrived at the best possible moment for Real Madrid. It's true that the team's style of play had not won many plaudits. It had been criticised repeatedly for being safe, even boring, but results talked. The defensive shortcomings of the Schuster era had been replaced with order and precision. The midfield, with Gago and new acquisition 'Lass' Diara (from Premier League side Portsmouth), had recovered its solidity. Robben was intimidating – to such an extent that Torres observed: 'He is a key player. If we give him space he could damage us because he can decide a match in an instant. We'll take all the necessary steps to keep him under wraps and reduce his effectiveness.' Higuaín had grown in stature and the front line had begun to function again – so much so that, in the last game before the Champions League tie, it had inflicted a six-goal defeat on an unfortunate Betis. Raúl, the captain, increased his club goal tally to 308, beating that of the legendary Don Alfredo Di Stefano. Those were some of the factors that augured well for Real Madrid in a competition on which they'd placed so much importance. Since the Portuguese, Carlos Queiroz (ex-assistant manager at Manchester United and then manager of the Portuguese national side), was manager in spring 2004, Real Madrid hadn't got past the first knockout round of the competition and for a club that likes to define itself as the biggest in the world, not to triumph in Europe is a disaster. But as Juande explained: 'In the Champions' League we rely solely on ourselves, in La Liga we are reliant on others' (implying that it was Barcelona who would have to make a stumble in order for them to be caught).
'White pride' and a good run of results emboldened interim president Vicente Boluda to declare: 'Here (in Madrid) we will win 3-0 and over there we'll score a load of goals.' The colloquial verb he used at the end to indicate a 'flow' or 'flood' of goals ( _'_ chorrear' in Spanish) can have other, less refined, interpretations, which were understood by everyone in Spain and, of course, by the Spanish Army at Liverpool, where it provoked unfriendly reactions.
The last time Liverpool and Real had met was on 27 May 1981, in the European Cup final in Paris. It is strange that the two big powers in terms of European titles (Real has nine European Cups, two UEFA cups and one European Super Cup against Liverpool's five European Cups, three UEFA cups and three European Super Cups) have not had more face-to-face encounters. At the Parc des Princes in Paris in 1981, it finished 1-0 to the Liverpool of Bob Paisley, in front of more than 48,000 spectators. Seven minutes from time, the left-footed left-back, Alan Kennedy, made the winning strike – a goal that 'Barney Rubble' (the nickname given to him by the Kop, after the character in the TV cartoon series, _The Flintstones_ ), remembers it like this: 'There was a throw-in and the Madrid players thought that Ray (Kennedy) would give it to Sammy Lee or to Dalglish. I started a run from behind. No one was expecting me. I chested the ball down and slipped into the penalty area. García Cortés came for the challenge but failed to clear. He was afraid of giving away a penalty and so didn't touch me and I ended up in front of Augustín. He thought I was going to pass and opened himself up a bit. Because of that I decided to shoot close to the left-hand post.' A perfect angle and it brought them their third European Cup in five years.
Other times, other stories. That Liverpool side was made up of Clemence, Neal, Thompson, Hansen (Alan), Kennedy, Lee, McDermott, Souness, Kennedy (Ray), Dalglish and Johnson. The one that comes out on to the pitch in Madrid at 8.45pm on 25 February 2009, lines up as Reina, Aberloa, Carragher, Skrtel, Fabio Aurelio, Mascherano, Xabi Alonso, Benayoun, Riera, Kuyt and Torres. Gerrard does not even make the warm-up, going straight to the bench. The Bernabéu is not the pressure cooker that their captain has asked for but there is a lot of noise from the crowd, with constant whistles for the Reds. The Real Madrid fans and the _Ultras Sur_ (the most radical and extreme supporters) pick on Torres because of his Atlético past. They can't bear the fact that the player, according to a list compiled for _The Times_ just twelve days before the Bernabéu game, is now one of the 50 Greatest Liverpool players of all time. On the pitch, however, the players are wary of him. This is what Raúl says when asked about Torres' goal drought in the Bernabéu:
'Since Torres went to Liverpool he's got rid of the pressure he had at Atlético and is displaying all his qualities as a footballer. He feels very supported and he does what he knows best, which is to upset his opponents with his power and his goal-scoring instincts. He is one of the most formidable strikers in the world.'
Torres responds to this flattery in the 20th minute, just when the Bernabéu crowd was shouting ' _Arriba Madrid_ ' in a bid to encourage their team not to be so timid and to go on the attack. Pepe Reina makes one of his trademark cannon-like clearances, Dirk Kuyt glances the ball further forward and El Niño runs onto it in typical style. Real's defence, Cannavaro and Pepe, stay firm. Nevertheless, Fernando gets round the back of the Portuguese defender, ending up with just Iker Casillas to beat. He makes an angled shot but the keeper just gets a glove to it and deflects it. It was a good opportunity to break the jinx – and it proved to be the last. Torres had been playing with an injury since the end of the first minute – as Rafa Bénitez would explain later – and is quite clearly limping in pain from his left ankle. He comes off just before the half-hour and sits down on the turf, while the club physios check him over. Benítez comes over to assess the situation. Several minutes go by and, after bandaging the ankle, he puts his boot back on and returns to the pitch. But by then he's like a loose buoy floating between the white lines. He doesn't move off the ball, he can't run to receive the passes from the midfield. He stays there, hoping for the chance of a loose ball resulting from some kind of error. It's obvious to everyone that he's injured. And yet at the beginning of the second half, he comes back on. When questioned later, Benítez explains that the doctors had assured him 'it's not a serious injury and he could continue'. In addition, Torres himself wants to play and asks Benítez if he can carry on. But he can't play properly and starts getting annoyed – so much so that, in the 55th minute, after an argument with Pepe, he is booked. Six minutes later, with his ankle swollen, he gives in. He raises his hands to salute the Liverpool fans up in the third tier, which provokes insults from the south corner. Choruses of ' _Hijo de puta, hijo de puta!_ ' ('son of a whore!'), echo round the stadium until Torres disappears into the dugout.
He leaves the stadium 50 minutes later with a grim face and a brace round his ankle. The Liverpool striker, who should have been the key man of the match – the one who'd scored at Stamford Bridge and in the Emirates Stadium, who'd dominated Chelsea in the closing minutes – isn't able to meet expectations. He's not the Reds' extra weapon. The kid from Fuenlabrada, who should have taken his revenge in the Bernabéu, is thwarted. But at least he returns to England with the first victory of his career against his eternal rivals – thanks to the diminutive Israeli, Heinze, who, in the 80th minute, pulls down Liverpool's Kuyt and is punished with a free-kick on the right. Fabio Aurelio takes responsibility, places the ball, surveys the options and puts in a dipping cross. Yossi Benayoun arrives from behind, completely unmarked, and with all the time in the world, leaps up to head the ball under the crossbar, leaving Casillas clutching thin air. The 6,000 travelling fans are delirious. The Bernabéu is struck dumb while the _Ultras Sur_ end up, as usual, fighting amongst themselves.
Liverpool had won by putting a perfect plan into action. As Mascherano and Arbeloa explained, the match went according to the prepared script: 'We subdued Higuaín and Robben, the only two with speed and the ability to overlap. Now we've done the hard part,' said the Argentinian.
'We knew the match could be decided with a corner or a penalty or a counter-attack and that's what we were able to do. This is how we've played knockout ties for years,' explained the Spaniard. Rafa Benítez could put on a relaxed face at the press conference. Before anything else, the exmanager of Real Madrid B denied the rumours circulating before the game that he had already handed in his resignation to the Liverpool club owners. William Hill and Sky Bet had been forced to suspend all wagers on Benítez, after too many punters had put their money on the manager no longer being in charge from the following Monday. He calmed the waters saying that his lawyers had been negotiating and that he would be talking personally with Tom Hincks and George Gillett. Once that subject was cleared up, the Liverpool manager went on to explain: 'We had in mind to play a very defensive game and to come out on the counter-attack. This we did and it worked for us with the goal from Benayoun. We have a very important win, although the tie isn't over. There are still 90 very difficult minutes left and we will have to concentrate at all times.' Benítez could also derive personal satisfaction – both as a Spaniard and as a manager – for sending out a team in the Bernabéu with five more Spanish players than Madrid: 'chorreo? (referring to the word 'chorrear', used by Real Madrid president Vicente Boluda) _._ Experience suggests that one should talk on the pitch and my players have done that very well in the name of Liverpool. I am very proud.' Of Torres, he added: 'He was very affected by his ankle and we decided to take him off when he couldn't go on. I don't think he'll be able to play on Saturday either.'
From there, it went like this: against second-from-bottom Middlesbrough, The Kid didn't play and the Reds lost 2-0, which allowed Chelsea into second place and they went six points behind Manchester United. Torres still wasn't fit, even for the game on 3 March at Anfield against Sunderland (2-0 for Liverpool). The injury wasn't improving as rapidly as everyone had been expecting. The ankle continued to cause problems but the Number 9 was optimistic he'd be there for the return against Real. He was certain it would be a difficult match, despite the away-goal advantage. You have to beware of Real, he said, they'll want to come out and kill off the game as quickly as possible to secure their passage to the next round. He said he wasn't surprised at the welcome he got in the Bernabéu and had been expecting it. 'They've always been like that to me when I've played there. They even whistled at me in a friendly when I was playing in a World XI. In England, they're not so hard on you. There are rivalries there as well but the fans are more respectful. There are different ways of understanding football,' he explained and added that whatever the atmosphere at the Bernabéu, 'it's nothing compared to Anfield. I don't think there's a stadium like ours anywhere else in the world'.
He was right. The 3,000 followers of Madrid that fill the Anfield Road Stand on 10 March at 7.45pm realise it too as the teams come out onto the pitch. They understand what it is, the atmosphere one breathes in at this 'fortress', this temple of football. The 20,000-strong Kop are all on their feet, singing 'You'll Never Walk Alone' and holding their red-and-white scarves above their heads. They wave flags carrying images of Bill Shankly with open arms, of Bob Paisley, of Rafa Benítez with the inscription (in Spanish), 'Siempre se puede' ('It's always possible'), and a silhouette of Fernando Torres celebrating a goal. The Kid is on the field, the physios have fixed him up, even though – as we will know later – he is playing with a bandage and plaster on his ankle. Three minutes later he shows why the Liverpool fans adore him. A long ball arrives and with a backheel he gets past Fabio Cannavaro to put himself one-on-one with Casillas. He hits it hard towards the near post but the keeper denies him once more with the tip of his foot. It is the first indication of what The Kid and Company will do and it is the perfect example of the class, elegance, movement and speed of a player who has magic and, above all, who wants to play a central role and win.
In the subsequent minutes, Torres and his team-mates seem possessed, moving at top speed, laying siege to the Madrid goal from all possible angles. Mascherano powers a shot and Casillas is saved by the crossbar. All long balls from Reina are a problem. Any run from Torres sows panic in the Madrid defence. Liverpool is like a pneumatic drill, breaking down its opponents. The Reds are following Ian Rush's advice in the _Liverpool Echo_. The headline of his weekly column before the game reads: 'Attack is best form of defence for the Reds. We can't afford to sit back in Anfield clash.' Rafa Benítez surprises his adversaries with the same strategy he had used years before with Juventus. Juande, who, like so many others, was expecting a team that would gamble on keeping its one goal advantage from the first leg, is completely wrong-footed. His side are seeing nothing of the ball. When they do get hold of it they find themselves encircled like the Seventh Cavalry of General Custer at Little Big Horn. They barely have time to look up before the enemy has once again robbed them of the ball. In addition, no one gives up chasing, not even Torres who drops back into his own half to take the ball off Sergio Ramos (to a great roar from the crowd), to take on Lars Diarra, to tackle Gago, to fight for every high ball with Pepe, to harass ex-Manchester United defender, Heinze (who will become the villain of the night, picked on by the crowd every time he touches the ball).
In the 16th minute, Anfield explodes. Reina clears to Carragher, who sends the ball high and long. The bounce catches Cannavaro by surprise and he tries to clear with an overhead kick but fails. Torres heads the ball, puts Pepe under pressure, the Portuguese falls to the ground and Kuyt, who's moved up outside on the right, picks up the ball. Casillas comes out of his goal, El Niño moves to the centre and calls for the Dutchman to give him the ball. A killer move and Torres puts it in the net. Referee Frank De Bleeckere confirms the goal and the lad from Fuenlabrada celebrates by parading his Number 9 under the eyes of the Spanish fans and leaps up high to punch the air. His goal has opened the floodgates. Real are reeling, like a punch-drunk boxer, who in the 10th round still hasn't understood that the contest is over. In the 47th minute it's a knockout. Steven Gerrard, with a penalty and then a goal of textbook quality, completes the demolition of the clay-footed giant. At Anfield, Fernando Torres has many things to be satisfied about apart from his goal. Going back to the centre spot after making it 1-0, he turns to the executives' box containing Real president, Vicente Boluda – who had said that his team would 'score loads' in Liverpool – and made the same gesture that Spanish Formula One driver Fernando Alonso made famous on the Grand Prix winners' podium: 'You talk a lot' was the clear message. The other thorn out of his side was Pepe. The Portuguese defender had declared that it was a pleasure to play against such a powerful striker as Torres and that he knew exactly how to close him down. In the first leg it was clear the duel had begun. In the return, the two end up face-to-face on several occasions and Pepe reminds Torres that Madrid had won nine European Cups. 'Yes but you, zero,' replies El Niño, accompanied by an unmistakable zero-shaped hand gesture, similar to what José Mourinho used in Italy when he told Juventus: 'You have zero titles'.
In the 84th minute, Fernando Torres is replaced by the Italian, Andrea Dossena, who would still find time to score a fourth goal. The _Ultras Sur_ took aim but this time the insults are overpowered by the Kop, which belts out the Torres Song full blast.
'This is Anfield,' said Fernando in front of the microphones, notebooks and television cameras. 'A very difficult ground. It's not just any team that wins here. The fans have given us a real lift.' And, remembering the controversy of the past, when he played in the red-and-white stripes of Atlético, he went on to explain: 'As a Liverpool player, I'm happy, but if we've also given enjoyment to the fans of Atlético, then so much the better.'
## Chapter 29
**A horse that needs to run**
_Conversation with Juventus defender and Italy captain, Fabio Cannavaro_
Green lawns, white goals in the middle of the pitch, low-flying swallows and empty stands with seats marking out the words 'Real Madrid'. In the background, an ever-expanding housing development and four new towers of glass and steel, which disappear into the low clouds and darkness of a leaden sky. Real's training session has finished a short time ago. Behind the huge windows of the press room, on the second floor of the Ciudad Deportiva di Valdebebas sports complex (about 10 miles north of Madrid city centre) journalists are waiting patiently for the appearance, behind the microphones and in front of the red and black sponsor's background, of the Argentinian, Gonzalo Higuaín.
On the first floor, Fabio Cannavaro, in black leather bomber jacket, blue striped shirt and torn jeans is smiling – a smile that, for about three years, has also won over Madrid. 'How are you?' – 'Well, thanks and you?' With his piercing blue eyes, the street kid who was a ballboy at the Napoli team's San Paolo stadium in Naples (in order to see at close hand his idol, Diego Maradona) has come a long way. After Naples, he went to Parma, Inter and Juventus and on into the Italian national side.
Then, in 2006, in Germany, the biggest, most exciting football experience – the World Cup. And as captain of Italy, raising the trophy aloft in Berlin. Six months later came the European Footballer of the Year trophy (the _Ballon d'Or_ ) and then the FIFA World Player of the year – an honour in recognition of the defensive skills that only Franz Beckenbauer could previously claim. A prize that showed what is meant by tackling, anticipation, a sliding interception and maximum concentration in an area of the pitch where errors are costly. And in that World Cup summer of 2006, Cannavaro arrived at Real Madrid to don the Number 5 shirt (formerly of Zinédine Zidane) and went on to win two consecutive league titles and a Spanish Supercopa. Good memories of a city and a country, Spain, to which he is now saying farewell in order to return to Turin and Juventus – first as a player and then maybe as a director. These are the last days here in Valdebebas of the central defender, who, the day after the second leg of the knockout Champions League tie against Liverpool at Anfield, was not feeling too great.
### _The_ Daily Mirror _writes that Torres, in the first chance of the match, goes round you as if you were 'a Sunday league player, not one of the most decorated men in the game...'_
'Regardless of what the _Mirror_ writes, it was a difficult match because they started superbly and we are a team in which, when we don't play like a team, our errors stand out. And with those spaces, with those strikers, to defend well becomes impossible.'
### _With you, and above all with Pepe, Torres had quite a lot to smile about..._
'For Torres to play against Real Madrid was something special – a derby. But except in my first year at Madrid, when I was sent off for two yellow cards against him (I never did anything to him but he just started to scream), I never had any problems. He is a striker who takes it and gives it. I've given him some. That's normal. The only thing I can say is that, in Spain, he had these theatrical habits. Fortunately, in England, he's got rid of them. The English don't accept that kind of thing.'
### _Is it difficult to mark Torres?_
'I've marked Fernando both in Spain, when he was playing with Atlético, and with the national team and also with Liverpool. If I'm really honest, when he was playing here, I didn't like him very much.'
### _Why?_
'One could see that he had great potential but he was... a bit soft. He was a player without any "bite" – sporting-wise, you understand? He was a player who worked well with the ball but he went through patches, he wasn't always at the heart of the game, he wasn't involved, he wasn't talking with his team-mates. When I came up against him again in the national team, in the friendly with Spain in March 2008, one could already see the difference. Then with Liverpool, in both the home and away legs, I saw a completely different player.'
### _In what sense?_
'Mentally, in the way he attacked defenders, in the way he spoke with team-mates. He's a much stronger player. Before, when you knocked against him, he gave way. Now, that's difficult, because mentally he's got much stronger.'
### _How do you explain this change?_
'It happened to me. I was at Inter and I wasn't able to train any more or find the right kind of enjoyment or motivation to go out and play. I went to Juve and within two days I changed completely. I met up again with my friends, my team-mates, in a more family-like atmosphere. I changed the chip – so much so, that in my first year with the _bianconeri_ (Juventus) I played 38 games out of 38 and only picked up one yellow card. These are things that happen to a player... Click – you regain your confidence and that of your team-mates and the fans chant your name. I think the same thing has happened to Torres. At Atlético he had all the weight of the team on him, knowing that if he made a mistake and they lost the match, he would be blamed. Going to Liverpool, he is a foreigner, he's more relaxed, he scores one goal, two, then three... The fans go crazy about him and everything becomes easy. Yes, going to Liverpool has really done him a lot of good.'
### _He's benefited from the Benítez system..._
'He's benefited, for sure, because for Torres it's much better to play as a lone striker – he can play in various positions along the line of attack. He suffers when he has another striker playing up high alongside him. He's not a footballer who likes one-twos much. He should play on his own upfront, with Gerrard behind and Kuyt on the right. For him that's the ideal. But of course English football for him is definitely more rewarding. Here in Spain, it works as one against one, little touches, possession. Torres on the other hand, is a horse that needs space, that needs to run. The more he runs the happier he is and the more his skills come to the fore. The same thing is happening in the national side. We talk a lot about Spain playing an attractive kind of football, putting great value on possession of the ball, it's true. That's because the midfield has people like Iniesta, Xavi and Senna – all top-quality players. But if we look again at the goals they scored in Euro 2008, a lot of them were made on the counter-attack – two against Russia, one against Sweden and not forgetting that one of Torres in the final. When I saw the two German defenders, Lahm and Metzelder, covering the whole pitch – well, quite honestly, I could see what would happen, because when there is space, Torres is going to have a field day. Maybe in a tight area, he's going to have some difficulty but when he can run and use his strength and speed to its maximum potential, you're in trouble.'
### _Since we're on the subject of Italy-Spain, the quarter-final of Euro 2008 was decisive in determining Spain's destiny..._
'It was a strange match with a peculiar atmosphere. I remember saying "Be careful", that whoever goes through from this tie will win the championship. Because of the two teams' mental strengths and their skills on the pitch, it was the most finely balanced of the quarter-finals. It was an encounter where we let them take the game, as always, because we are a team that gives the ball to the opposition. But the best chances fell to us. As for them, yes, they had plenty of possession and they made lots of attempts on goal but they were all off-target. Torres and Villa were invisible in that game. Why? Because we conceded very little space to the strikers and with a pair like Torres and Villa, who are good on the counter-attack, if you limit the depth of area in which they can operate, it makes it much more difficult for them.'
### _Apart from not conceding too much space, what would a coach's advice be to a defender who needs to close down a striker like Fernando Torres?_
'Nowadays, it's no longer like it once was when you attached yourself to a striker and didn't let him breathe throughout the whole game. I would play a one-against-one but try to minimise it. Today, no. Today one talks of units, and the defensive unit should work in the best possible way, it should be perfectly synchronised like a precision timepiece to close down strikers like Torres.'
### _In a list of the world's best strikers, where would you put Torres?_
'Amongst the top ones, amongst those who cause panic, such as Drogba, Berbatov and Ruud (Van Nistelrooy). Torres is definitely one of the strongest strikers in Europe – he's young, he plays in a set-up like Liverpool, he's in the Spanish national team, and he's still got so many areas in which to improve.'
### _Which areas?_
'He should improve his technique in the one-against-one. Torres relies on his speed but when you have a defender in front of you, you have to go past him and not through speed alone. Take Cristiano Ronaldo, Messi or Ronaldo in his better moments. They home in on you, skip past and they're away. This is still missing in Torres, even if he has the quality and the skills to be able to do it. His best weapons? His bursts of speed, those 10 to 15 metres in which he launches himself at the back of the defender and his overwhelming physical power. Even when he makes a mistake, he gets to the ball ahead of everyone else. Another thing he does that I like is that he doesn't give up when his opponents have the ball. In the match with Liverpool, for example, I will always remember two recoveries of the ball he made – one from Sergio Ramos and the other from Heinze. There, you really saw the strength of a striker. You saw that he wanted to win. But beyond the goals and the games, it's an important message to the whole team. He shows the spirit of the centre forward. As a defender, I would like my strikers to be doing that.'
### _Who does Torres resemble?_
'Perhaps Ruud Gullit for his running abilities and his strength. I remember Ruud had fantastic acceleration. He was a player who would start from a long way off and could play at various points along the line of attack.'
### _Torres said some time ago that in a few years, to complete his career, he would like to play in Italy and try Serie A. What do you think of that?_
'After his English experience, I think he'd have some difficulties, because of how football is lived in England, because of how it is organised. We (in Italy) are the opposite (to England) – ugly grounds, lots of disputes and fans with little sporting culture. And there they don't go away from home on training camps. With us, you hardly need to start losing before everyone has to go off to a training camp. Things go badly and immediately they sack the manager. That's typical Italian-style. I'm Italian, I'm proud of my country and of our football but I have to admit that, today, the English teams have an undeniable superior physical strength, technique and financial backing. The Premier League is the best league in Europe, even if the Italy manager, Marcello Lippi, says that the maximum expression of football is not the (domestic) league, or the Champions League but the national side and, at the moment, the most important national side is Spain.'
### _Talking of national sides, how do you view the chances of champions Torres & Co. in the next World Cup?_
'One can't deny that they are favourites. They are champions of Europe, they have a generation of fantastic young footballers. But the tournament is outside Europe and the favourites almost never get to the final. The World Cup is another thing altogether, where so many factors depend on the luck of the draw. But certainly, to achieve the run of victories they've had, with qualification already in the bag, allows you to have, as they say here, "mas confianza" ("more confidence").'
## Chapter 30
**Manchester United 1 Liverpool 4**
_14 March 2008_
Good afternoon and welcome to Old Trafford...
The stadium is full and we have just been informed that there is a crowd of 75,569. This match tops the bill for the 29th day of action in the Premier League. The meeting is due to kick off shortly, at 12.45pm. Top of the table Manchester United are playing host to the Reds, who are joint third in the overall standings along with Guus Hiddink's Chelsea on 58 points, seven adrift of United, who have a game in hand (Portsmouth). If Sir Alex Ferguson's men win today, they move ten points ahead of Liverpool and could wrap up the league, or almost. They are clear favourites. They have had a run of eleven wins on the trot, let in only two goals in the last sixteen games and have booked their place in the semi-finals of the Champions League without too much trouble by seeing off Inter Milan in the quarter-finals. The Reds come into this vital match with their morale running very high following a convincing Champions League victory on Tuesday against Real Madrid. Here their last chances for a tilt at the league are at stake. If they manage to cut the distance from the leaders they could open up the fight for the title again. Will the effort from the match against the men in white weigh against them? It may well do, but Benítez's wards will give it their best shot to come out on top at a ground where Liverpool has not won since 2004, when Gérard Houllier was on the bench. Rafa has never walked away as the winner from the Theatre of Dreams.
The bad news for the Merseyside team is the absence of Xabi Alonso, who won't be able to lay down the law in midfield. He is replaced by Lucas Leiva. For the other side Dimitar Berbatov settles into the dugout, while 'The Apache' Tévez starts. Let's have a look at the line-ups announced:
Manchester United: Van der Sar, O'Shea, Ferdinand, Vidic, Evra, Ronaldo, Carrick, Anderson, Park, Rooney, Tévez. Subs: Foster, Berbatov, Giggs, Nani, Scholes, Evans, Fletcher.
Liverpool: Reina, Arbeloa, Carragher, Skrtel, Aurelio, Mascherano, Lucas, Kuyt, Gerrard, Riera, Torres. Subs: Cavalieri, Dossena, Hyypia, Babel, Insúa, Ngog, El Zhar.
Referee: Alan Wiley
The players are coming out onto the pitch now, Manchester in their traditional red shirts and Liverpool in grey.
Álvaro Aberloa isn't there among the Reds. He has had physical problems in the warm-up. Sami Hyypia takes his position and Carragher will play in the right back berth. A position he doesn't really take to, if the truth be told.
The game gets underway.
### _**2nd minute**_
Wayne Rooney seems to be all fired up. He is dangerous in the Red Devils' first couple of attacks. Carragher looks uneasy opposite 'Bad Boy'.
### _**3rd minute**_
From over on the right Cristiano Ronaldo feeds a ball in for Ji-Sung Park but the Korean's shot is cut out by Carragher – corner. Manchester United is producing some good football and playing well.
### _**6th minute**_
Liverpool make inroads for the first time, Torres chasing up an extremely long ball. Rio Ferdinand checks on the edge of Manchester's box.
### _**21st minute**_
Torres swerves brilliantly with one touch and gets away from Ferdinand on the edge of the penalty area – a touch of genius. For a moment it looks like a goal, but Vidic and O'Shea don't let him finish off the move.
### _**22nd minute**_
A penalty to Manchester. Park chases a ball down the inside-left channel and into the box. Reina races out and slides towards Park's feet. Park runs into the prone keeper and tumbles over.
### _**23rd minute**_
GOAL, CRISTIANO RONALDO! MANCHESTER UNITED 1 LIVERPOOL 0
The man from Portugal is unforgiving from the spot. He shoots right-footed and low, just inside the left post. Reina guesses right but doesn't get there.
### _**28th minute**_
GOAL, TORRES! MANCHESTER UNITED 1 LIVERPOOL 1
Liverpool seem punch-drunk after the goal and unable to respond to the moves made by the Red Devils. It would be fair to say they haven't put a foot right for five minutes and then the most amazing thing happens. Martin Skrtel frees things up in his area and hits a really long ball forward. Vidic scampers towards his goalmouth, allows the ball to bounce, and lets Fernando steal it off him – El Niño is off. Van der Sar rushes out to close up the angle but Torres keeps an extremely cool head and beats him on the run with an accurate finish into the left-hand corner of the Dutchman's goal. Fantastic work from The Kid. Game on.
### _**31st minute**_
Torres once more against the unfortunate Vidic, who appears not to have a clue how to handle the fair-haired Spanish striker. First he forces him to clear for a corner and next up he heads past him (cross from Fabio Aurelio), slips into the penalty area and the Serbian defender stops him by stretching the rule-book to the limit.
### _**34th minute**_
Cristiano Ronaldo blasts a free-kick from miles out and Reina almost makes a howler. He manages to get his hands round the ball after fumbling, just before Tévez arrives...
### _**36th minute**_
Yellow card for Jamie Carragher for going in dangerously.
### _**37th minute**_
Rio Ferdinand goes yellow for a dangerous tackle.
### _**41st minute**_
Torres releases Riera on the left into the Manchester 6-yard box. Ferdinand gets there in the nick of time to sweep clear.
### _**43rd minute**_
Penalty to Liverpool. The Kid takes the ball outside the penalty area and when the United central defenders come out to get him he does a half-turn and slides in a perfect pass between the lines for Gerrard who is in the area. It is all Evra can do to stop the captain by fouling him.
### _**44th minute**_
Yellow card for Edwin Van der Sar for protesting.
### _**44th minute**_
GOAL, GERRARD! MANCHESTER UNITED 1 LIVERPOOL 2
Van der Sar just manages to touch the ball but the shot from the Reds' captain is well-placed and struck hard.
### _**45th minute +3**_
Gerrard again. His thunderbolt is cleared by O'Shea. Manchester United reply in the shape of Tévez, who wins a corner. Nothing actually happens as the referee blows for half-time.
### _**Half-time**_
An exciting game with no let up in play. Liverpool are deservedly ahead and have read the game well.
The second half gets under way.
### _**48th minute**_
Cross by Ronaldo and the ball squirms away from Reina and hits the post.
### _**49th minute**_
Torres collides with Tévez and has damaged his already injured ankle, but he seems able to play on.
### _**59th minute**_
United dominate play and buzz the Liverpool penalty area, but they aren't creating too much danger.
### _**60th minute**_
A yellow for Javier Mascherano.
### _**64th minute**_
Yellow card for Skrtel for fouling Tévez.
### _**66th minute**_
Gerrard leads the first attacking move from Liverpool in the second half. It ends with a shot by Leiva from the edge of the box. Van der Sar fields it.
### _**68th minute**_
A Liverpool change – Andrea Dossena comes on for Albert Riera.
### _**71st minute**_
Great chance for United – Tévez almost manufactures a goal out of a dead ball in the area.
### _**73rd minute**_
Triple substitution by Manchester United. Anderson, Ji-Sung Park and Michael Carrick are replaced by Ryan Giggs, Paul Scholes and Dimitar Berbatov.
### _**76th minute**_
Vidic is red-carded. As with the Torres goal, the United defender is beaten by the ball. Gerrard breaks away on his own and the Serbian has no choice but to grab him and throw him to the ground. There's no arguing about the referee's decision.
### _**77th minute**_
GOAL, AURELIO! MANCHESTER UNITED 1 LIVERPOOL 3
A sweet shot from Fabio Aurelio that goes right in the block-hole. That's how to shoot free-kicks! The Brazilian master-fully converts the foul given away by Vidic for pulling.
### _**78th minute**_
Torres tries a deep pass to his skipper. But Gerrard is caught offside.
### _**79th minute**_
Torres tries to catch Van der Sar out from the centre of the pitch, but the shot strays very high and to the left.
### _**81st minute**_
Second change by Liverpool. Fernando Torres goes off and Ryan Babel comes on.
Nine minutes later, Fernando smiles and celebrates Liverpool's fourth on the bench – a masterly effort by Andrea Dossena. As he did against Madrid, the Italian brings the Reds' cracking game to a close. The score-line is 1-4. Amazing – the statistics say as much.
The last time United let in four goals at home was New Year's Day 1992 against Queens Park Rangers. Liverpool's 4-1 win is the second biggest since November 1936, when the Reds won 5-2. And while we're on the subject of statistics, it should be remembered that this is Rafa Benítez's 100th win since he arrived in the Premier. But the main thing is that the league is still open.
'They think it's all over... it isn't now' runs the headline in the _Sunday Times_ , above a huge photo of Torres battling it out with Vidic. Torres, together with Gerrard, is the hero of Old Trafford – the star of Liverpool's big week. Two wins and eight goals scored in five days. The Reds' captain pays tribute to his team-mate: 'He's magic. He's the world's greatest striker and a lot of people probably agree with me.' And he's right. Plaudits from all sides are fantastic. Let's leave the English and the Spanish to one side, as they are too closely involved here, and see what Giancarlo Galavotti writes in _La Gazzetta dello Sport_ : 'The lethal weapon is always the same: Fernando Torres. Simply wonderful, El Niño surprises and wipes out the opposition with an undeniable show of class and power. After Madrid he also humiliates Manchester. The panel of the Golden Ball should be alert to this.' Nothing more to say. Steve Gerrard, though, does chime in with something: 'Liverpool can win the Premier League. If we carry on like this from now on, we've got a chance to walk away with the title, and Fernando Torres is the key to doing it.'
It wouldn't be the first time. March 1998 – United has an eleven-point lead over Blackburn and twelve over Arsenal and Liverpool. It seems they've got the League title in the bag. Final standings: Arsenal 78, Manchester United 77. The Gunners win ten games on the trot and crown themselves champions with two games in hand. This time there are nine games to go, but it seems there's a chance. Even more so when, a week on, United lose to Fulham. Two defeats in a row – something that hasn't happened since 2005. At Liverpool, who have just given Aston Villa a 5-0 thrashing, they are convinced the Red Devils are feeling the heat. But after their two routs, Ferguson's men hit the accelerator and don't let up right to the end.
On Saturday, 16 May, United win their third League in a row, their 18th. They draw level with Liverpool in number of trophies won and leave the Merseyside team with a bad taste in their mouths. They've lost fewer times than the Red Devils (two versus four times), have netted more goals (72 versus 67), but in the end they are second in the overall standings, and four points adrift of the champions. Their high draw-rate has cost them dear. It is nineteen years since the Reds have lifted the league trophy. Another season over without silverware. In the Champions League Liverpool came up against Chelsea in the semis, in a duel that, in England over the last few years, has become as much a custom as tea or rain. They were eliminated in a night to remember, an eight-goal thriller – an unbelievable game, as the English press wrote, following the 4-4 _dénouement_ at Stamford Bridge. They praised the pluck and pride of the Reds, one step away from changing history, one step away from turning round a 1-3 result from the home match, one step away from winning the mother of all battles, as the _Guardian_ wrote. But in the end the Champions' dream faded away.
Fernando has scored two goals in Europe's team championship. In the league he has netted fourteen goals, five less than top-scorer Nicolas Anelka of Chelsea. Whenever on the pitch he has been decisive. It's just a shame that bad luck hasn't given him a better strike-rate. This is something Gerrard also sees as an unhappy circumstance: 'The frustrating thing for both of us is that we haven't been together more times on the pitch this season.' It's true. The awesome partnership (28 goals) has only been together on the pitch for twelve out of 36 Premier matches. 'Let's hope,' says Stevie G. on the club's official web-site, 'that next season we are ready to give Liverpool the best chance of success. We both feel that if we are both clicking, we can cause defences loads of problems. We both enjoy playing with each other and we can both either score goals or set them up for each other.' Fernando is also hopeful about next season: 'Winning the Premier League will be our big objective again. We will fight for the title again by looking to win at home more regularly against the teams that are more winnable in theory. As we have seen this season, they choked us. I reckon Manchester United and Chelsea will be our main rivals, though we can't rule out Arsenal either, or Manchester City. I hope that this year we will achieve what all the fans expect from us'.
## Chapter 31
**You'd be happy if your daughter brought him home**
_Conversation with former Liverpool player and manager, Graeme Souness_
He's hardly arrived in the United States before he's already on his way to Rome. The ex-Liverpool captain is going back to the Eternal City, where, on 30 May 1984, he held aloft Liverpool's fourth European Cup. The final trophy of an impressive season, which also saw them win the league championship and the League Cup and the first under manager, Joe Fagan, who had replaced Bob Paisley.
Souness, the Number 11 in the red shirt, remembers that final well. The Roma side of Bruno Conti, Paulo Roberto Falcao, Ciccio Graziani, Roberto Pruzzo and a young Carlo Ancelotti (now manager of Chelsea) were regarded as odds-on favourites. Playing at home, with the fans behind them, they had already proved their ability (through convincing and impressive football) to win the previous year's Scudetto. It was a zonal style of playing, which was put into practice very effectively under the guidance of Swedish manager, 'Il Barone' Nils Liedholm – a renowned midfielder from the 1950s, who went on to manage a host of Italian sides over a 30-year period. And yet, despite being favourites, the score was 1-1 after 90 minutes (goals from Phil Neal and Pruzzo). After extra time, they finally bowed out to the English side 4-2 on penalties. Graeme Souness didn't fail with his kick, the third in the sequence, high towards the angle of post and crossbar to the left of Roma keeper Franco Tancredi. Bruce Grobbelaar, the South African who came up with his 'spaghetti legs' routine (never forgotten by the Liverpool fans and successfully reprised by Jerzy Dudek 21 years later in the final against Ancelotti's Milan) unnerved the unfortunate Graziani so much that he ended up shooting over the bar. The big-handled Cup was Liverpool's. Michael Robinson – to whom the trophy had been entrusted – left it in a shop at Fiumicino Airport. Fortunately, he remembered it at the last moment and managed to get it back.
It's 25 years since that day. Souness is now 56, returning to the Stadio Olimpico – minus his distinctive moustache and thick curly hair – via the Sky Sports commentator's box.
He'll be asked for his opinions on the Manchester United of Cristiano Ronaldo and the Barcelona of Lionel Messi, the teams contesting the Champions League title. Because of his intelligence and experience, Souness is someone well qualified to talk about Fernando Torres. And yet he says that he doesn't have much in-depth knowledge about football. This admission leads to a chuckle from the Scot and the interview begins _..._
### _Let's start with last season's big Premier League clash between Manchester United and Liverpool. What do you think of the performance of Liverpool and particularly of Torres?_
'I have played in many games like that and we were the best team but we never had a result like that. For me, the turning point was when Torres outpaced Vidic (Manchester United defender, Nemanja Vidic). Vidic thought he was quite comfortable in his defensive position but Torres, with his electric pace, got there before him and from that moment on, Manchester United found it very difficult and Vidic, especially, was frightened to death by Torres' pace.'
### _Despite this result, Manchester and Alex Ferguson went on to win the league again. It's nineteen years since Liverpool won it. What more does Liverpool need to do to win it?_
'They've got closer this time but they rely too heavily on Steven Gerrard and Torres for goals. Manchester United have five or six very special players. Liverpool have two very special players. I think it's all about quality at the end of the day. I think for any Liverpool player the concern is that Manchester United have a good group of young players coming through, where that is not the case at Liverpool. Liverpool will have to buy and I'm not sure they have the money. They will have to go out and buy another two or three very special players. But I'm not sure at Liverpool because they have to spend their money on a bigger stadium.
'We'll have to get a new stadium because we'll just keep dropping further and further behind Manchester United and Arsenal. But a new stadium obviously costs a lot of money and that will mean we'll not be buying new players. As a Liverpool supporter, looking forward, I'm still worried about that. Because the two people who now own Liverpool, what have they done? All they did was go to the bank and borrow money to buy Liverpool. The previous chairman, David Moores, could have done the same thing. The previous board could have done the same thing. Liverpool are no further forward now for me than they were before these two Americans came in.'
### _What is the main difference between your Liverpool, the 'glorious' Liverpool, and the current Liverpool?_
'Well, I just think we had better players. There's no secret in football. I think this group of players is very good. The supporters are the best supporters in the country because they allow you to play football the right way, they are patient with you. In my day we were a solid group of seven or eight very, very good players and we had the support, like this group have, of the supporters. But when things aren't going well, we were all in it together. This group of players understand that but I don't think they've got six or seven very good players. They've got two very, very special players and another three or four that are good players but not special players.'
### _As a manager and former captain of Liverpool, what's your technical judgement of Fernando Torres?_
'He's an exceptional talent. He's explosive. I think he's like all the top strikers. He can be having a quiet game but if you're playing against him you're always aware that you can keep him quiet for 89 minutes and in that 90th minute he can kill you. His pace is his obvious attribute. But as well as that, he is a good finisher, he's brave and he works hard.'
### _What is his contribution to Liverpool?_
'It's enormous. There are the two very obvious threats of him and Gerrard. Gerrard's not a midfield player, he's like a central striker. And I believe those two strikers are the best out there. For me, Steven Gerrard is not a midfield player. He's behind Torres. Torres can make the little, quick runs in behind defenders and Gerrard will find him. Those two are the best front two out there today.'
### _When Liverpool and Rafa Benítez chose Fernando Torres, many commentators said it was a risk for the amount of money they paid. How then, did he score 33 goals in his first season? This was explosive and a revelation, no?_
He was young and he'd never played outside Spain before, so there was always an element of risk. I think that, in his first season, he very quickly understood that he was playing for a special football club and the relationship between the players and the supporters is a special one. But I reckon you can analyse it and analyse it but he's just a very, very good footballer and he felt at home immediately when he went to Liverpool because Liverpool supporters appreciate players who give 100 per cent, who score goals. There's no acting with him, he's not throwing himself to the ground, he's not looking for fouls in the box all the time. He is a Liverpool player and I believe that very quickly he won the hearts of the Liverpool supporters.
### _It isn't easy to enter into the history and spirit of a club, particularly a club like Liverpool. How did he manage to do this so quickly?_
'Because he's good! All clubs like a star in the team, a goal-scorer. He's following on from people like Ian Rush, Robbie Fowler, Michael Owen. They were all great goalscorers. He's built up their hopes. He's now their new hero and I always think that getting off to a good start helped him. But I come back to him being young, when he arrived nobody really knowing him and everybody took to him immediately, all the supporters liked him immediately and he would have realised that, they would have got that message across to him and from that point on the Kop was won over, he feels loved and the rest was history.'
### _And you met him, in the programme that Michael Robinson made last year. What was your impression of him?_
'He seems a very modest, humble young lad.'
### _He doesn't speak a lot but he knows how to play..._
'Exactly, he does his talking on the pitch. When I met him, that time, he was very respectful. He's the sort of boy you knew you'd be happy if your daughter brought home. During the two hours that I spent with him, that was the image I got from him.'
### _How do you see Torres' future at Liverpool?_
'I think he'll be happy to stay there as long as they want him because he feels loved by the crowd and I think the only way he'd leave Liverpool would be if Liverpool dropped out of the Champions League and then they couldn't afford to keep him. But I think that as long as Liverpool play in the Champions League, he will stay there. The fans would not allow the board of directors to sell him.
### _What for you are Torres' best moments, best goal or best moves during his two years at Liverpool?_
'I think he's scored some fantastic goals but beating Manchester United so convincingly at Old Trafford, I can never remember that happening before. I think his goal set them on the way to win that game – it would have to be that one because it meant so much to every Liverpool supporter. It was a very special day.'
### _Finally, one more question. It's out of curiosity more than anything. Was it Michael Robinson who called you 'The Cat', or you who called him 'The Cat'?_
'I called him 'The Cat'. He thinks he is a goalkeeper!'
Bon voyage Mr Souness, and enjoy the final in Rome...
## Chapter 32
**The same as always**
_Conversation with Julián Hernández and Ángel Sánchez_
Both of them are wearing their work clothes. A red-and-white-striped shirt and a red tie – the colours of Atlético Madrid. They work as receptionists at the Vicente Calderón stadium. You see them as soon as you enter the old stadium, after the glass door that leads to the management offices. Julián, 24, from Carabanchel Bajo, a neighbourhood of Madrid, has worked here for four years. Ángel, a 25-year-old and also from Madrid, arrived a bit later. They're both close friends of El Niño. They got to know him by chance. Ángel, who used to play as a striker for Roma Club de Futbol, a junior team based in Ventas near the Plaza de Toros in Madrid, first found himself facing Torres as an opponent but then, thanks to Oscar (who played with him and knew Fer from when they were juniors), joined their group. Julián was a friend of Hugo, who knew Torres through football and ended up being inseparable from his group. They've known each other for eight years. And even though Fernando plays in England they have not lost contact. Julián spent two weeks in Liverpool and London, the two weeks in which the Reds played in the Champions League semi-final against Chelsea, so that he could watch both games and be with Fer. Ángel wasn't able to go... otherwise, who would answer the phones at Atlético Madrid? But he's promised himself that he'll go over just as soon as he gets a few days' holiday. Neither find it difficult to talk about having such a famous friend, who has appeared on the front pages of newspapers around the world. But they're careful not to say anything that could show him in a bad light. That's normal, it's the way close friends are. Seated in the office of Manuel Briñas, they chat about their famous friend's past and present.
### _OK, so how has he changed, the boy who began playing for Atlético Madrid and has now conquered the world?_
J.H. 'He hasn't changed, he carries on being just like he was before. He hangs around with the same people and the same friends as ever. And he continues being very close to his mates. I've heard people say he's a show-off, arrogant and even conceited because he's successful at Liverpool. But it's all lies what people say, people who know nothing about him. Fernando is a modest guy and not at all conceited and with us he's really good company, amusing and has a great sense of humour. He's always had his head well screwed-on, with a good family behind him, people who look after him well in every sense, and good friends who for a long time have been genuine mates. Not like those who suck up to you when everything's fine but disappear if things go badly. And I'm not talking only about the two of us.'
A.S. 'With us, he's the same blond, freckly bloke. A really straightforward and compassionate guy. A true friend. We can go for months without talking and then, when we do, it's as if we'd just seen each other five minutes earlier. Neither the fact that he's one of the best strikers in the world, nor the money that he earns, have made him behave differently. Fame hasn't gone to his head either, not like it has with a lot of footballers, who change the people they mix with and their social circle. He's got the same girlfriend that he had when he was seventeen and the same friends.'
'It's true,' says Manolo Briñas, joining in the conversation, 'when Fernando was here and already an exceptional player, he didn't go to Los Angeles or Miami on holiday but instead, here in Spain with his fifteen mates. Ángel, you explain...'
A.S. 'Yes, every summer we went on holiday for a week or two. I remember we went to Gandía and five years ago to Las Palmas in the Canary Islands. Between World Cups and European championships it wasn't easy to find a gap. We had such a good time and I still remember the smaller kids, who, when they saw that El Niño was part of our group, couldn't believe it and started swarming around us like flies.'
### _And Julián, how does he seem to you now, in Liverpool?_
J.H. 'He's got accustomed really quickly to life in England. Also, because he's a very home-loving guy and he likes the quiet life. Sometimes he goes out at night but most of the time he stays in with Olalla watching films or programmes on Spanish TV. And sometimes they go to Pepe Reina's house or Pepe and Yolanda go to his house. Olalla and Yolanda have become great friends. And with Riera as well. They meet up whenever they can.'
### _What does he really love doing?_
J.H. 'He still likes the Playstation and Pro Evolution Soccer. He listens to music, all the favourites, El Canto del Loco, Andrés Calamaro, Joaquín Sabina, Nirvana, Duncan Du. And later, he likes it when he can go walking with his dogs. When he's got a free day, he'll go off on a trip to explore the country. I don't think he's changed his life much in England. Apart from one thing, which, to be honest, really shook me. Fernando has always eaten everything but now, in the morning, he also likes sausages and beans for breakfast with a coffee. They give it him in Melwood and he's got used to it.'
### _Is he calmer and more relaxed than he was in Madrid?_
J.H. 'He seems like that to me because there the media don't hassle you, nothing like the extent to which that happens here. There the paparazzi don't go after you. You can get on with your life without any hassle. He and Olalla go out walking, they go shopping at the supermarket and it's no problem. The people, the fans are very respectful. I was out walking with him and I was surprised because before they even asked Fernando, they always asked me if they could take a picture of him.'
### _What do you talk about now when you meet up?_
J.H. 'We don't talk much about football, which might seem strange, but that's how it is. We don't want to bore him with that and besides, there's much more to talk about than just football.'
### _OK then, what do you think of his success in England?_
J.H. 'When I was there, it surprised me how much the people really love him.'
### _Why?_
'I don't know really... He's fallen on his feet because he's a really nice guy.'
A.S. 'And one has to say that he's a great football professional. He hasn't got to be almost as popular as Gerrard just because he's got a pretty face. No, Fernando has worked hard and one's got to say that he deserves what he's now got. No one has put him up there.'
### _Do you envy him for his money, fame and success?_
J.H. 'No, he deserves it all.'
A.S. 'Me, yes! As a striker I've always envied his liveliness and power.'
## Chapter 33
**The Kid**
_29 May 2009 Conversation with Fernando Torres_
Here is The Kid – who's not such a kid any more. Last 20 March he turned 25. On 26 May, when Rome was hogging the limelight in the footballing world for the Champions League final between Barcelona and Manchester United, Fernando José Torres Sanz got married to Olalla Domínguez Liste, his lifelong girlfriend. A registry office wedding at the town hall in El Escorial (a town some 50 km outside Madrid and a tourist attraction due to its monastery). Olalla, who has lived with Fernando since 2004, is seven months pregnant. Yes, the kid is going to be a father. But he will never manage to shake off the nickname he was given when he got into the Atléti first team. A kid who has signed a new contract with Liverpool up to 2014. A kid who is the only crack player to own all of his own image rights. His earnings have soared in the last few months. He has lent his name to advertising campaigns by Banco Gallego, El Corte Inglés and Nike. Together with Leo Messi he will be the face of Pro Evolution Soccer 2010. A star – and he is welcomed as such at the Hotel Meliá Avenida de América in Madrid.
It's twelve in the morning and 700 people await his arrival. They are friends, Atléti and Liverpool fans, boys and girls; fifteen-year-olds who are crazy about the blond angel. His entrance is worthy of a rock star – hysterical screaming included. Hair as fair as could be, immaculate white shirt, black jacket, faded jeans, black trainers with white laces. Fernando sits down at the table of the Marca Sports Forum. He greets everyone and listens to the brief words from Eduardo Inda, the director of the Madrid sports paper, from José Antonio 'Petón' Martín, someone who has known him ever since he was a small boy, and José Antonio Abellán.
Afterwards it's his turn to speak: 'I'm not surprised by the loyalty the fans are showing me. I was born an Atlético person, I've spent virtually all my life at this club, and I know what Atléti folk are like. I know that when I left some people didn't understand it, but luckily, two years down the line, most people can understand it. I can see Atlético shirts here and some from Liverpool. Being united like that is the best possible news as far as I'm concerned. When I watch Atlético games on television and I see Liverpool shirts, it gives me an amazing sense of pride. It's like when I see a lot of Atléti shirts at Anfield and it's something I love. I have to say, I feel a part of both clubs, and that is the biggest and best thing I've ever had'.
The questions start...
### _How would you define the Atlético feeling?_
'It's hard to put your finger on. I think you are born an Atlético person. There aren't very many people who become fans of the red-and-whites on the way. Kids see Real Madrid winning and it's one of the giants, so they become fans of the whites. In my class I was the only Atlético supporter out of 30 children. They were all Real Madrid fans. How did I handle it? Well, I had to put up with the jokes every weekend, but I felt more and more proud. I used to go to the ground to watch my team play and when we lost I thought, "oh well, we'll win next week"... and when we won I was happy for the whole week afterwards. More important than the results there is the desire to support your team in the hope that one day they'll get back up where they belong. I experienced the double as a fan, and when we went down as a fan, and as a player. Good things and bad things, and that's what Atlético Madrid is like. But the main thing is that the ground is packed and the fans are devoted to their team. That's what makes it different.'
### _Will you come back to Atlético?_
'Seriously, that's not just down to me. Sure, I'd love to finish my career with Atlético, but you never know what strange turns events might take in football. But I intend to – let's see after 2014...'
### _Do you think your departure from Atléti has already been worth it or won't this be true until you win some silverware?_
'I've achieved the two goals I set myself. I've seen Atlético grow in stature. They've played Champions League football, signed up some really good players, and are now a team that's recognised in Europe – my team-mates at Liverpool talk about Atléti. That's what I wanted when I left. Personally speaking, I think I've come on a great deal over these two years. In my first season at Liverpool I managed to score more goals than any other foreign player in the Premier League and I came third in the Golden Ball and the FIFA World Player awards. I've developed in footballing terms and it's been Liverpool that has let me do that, because it's a team that always plays at the highest level. That's why I'm very happy with the decision I took.'
### _Do you get on better with the club people at Liverpool than with those at Atléti?_
'At Atlético there were people I had known since I was a kid, players who I was with in the junior levels and afterwards in the first team, and I knew the people at the club, the people working at the Vicente Calderón. Now, at Anfield, I've started from scratch and get on well with everyone. I'm not a person who has had or caused problems in the dressing room. I've always tried to be as consistent as possible because I know that it's your team-mates who are going to make you a big name or not. I know that, in this sense, I've been lucky to be in two great dressing rooms.'
### _Who do you feel more at home playing with, Mascherano and Xabi Alonso or Xavi and Iniesta?_
'Luckily all four are really good. It's very different though. English football is a lot faster... there's hardly any play among the defenders and the midfielders before you're upfield, and within two or three touches and moving really fast you're suddenly in front of the other side's keeper. With my playing style this has really suited me, but that doesn't mean playing alongside Xavi and Iniesta isn't a luxury. You just know they're going to have the ball and you know you're going to be more relaxed when it comes to finishing because you don't have to worry. It's a joy to know that the ball is safe at their feet. You know that you can send them a shocker of a ball and they'll manage to keep it under control. If you get the chance to have Xavi and Iniesta in one place and Xabi Alonso and Mascherano in another, it's just the best thing.'
### _How are things with Gerrard?_
'I wish I could play alongside him my whole life. He's a player I admired from before, but from being on the pitch with him you realise that he's even better and greater than you ever thought. When he's on the pitch there's nothing to be afraid of and you know he's always going to be there, lift the team when the going gets tough, and always give you a hand. And in the dressing room he gets 10 out of 10 because he always makes himself available and always has a word of encouragement for you. I remember first coming to Liverpool and after having my medical I landed in Madrid to say goodbye to the fans. The first message I got was from him. It said, 'welcome to the club', and he hoped I could help the team bag some silverware. I wasn't even a Liverpool player at that point. I had gone through the medical but I still had to put pen to paper, and here he was welcoming me on board. It's a nice touch that makes you see what a great captain he is. I never managed to transmit that to my team-mates at Atlético when I was wearing the skipper's armband because I wasn't experienced enough...'
### _How did you know it was him? Did you notice his number?_
'Not his number or what he was saying either!' (laughter and applause from the audience). I was with Jorge, who had to translate for me, because there was no way I was going to understand.'
### _Can you tell us how you felt the first time you went through underneath the shield that says 'This Is Anfield' and came out onto the pitch?_
'The fact is that Liverpool is a club with nice touches, which really looks after its history, and in that sense it's very similar to Atléti. It remembers its legends and the greats who made it a big club and that little sign, which isn't much more than a picture in the tunnel, means so much for a lot of people and has ended up as something special. On the day when I was presented, when there weren't any people in the ground, I saw it when I walked past it but it didn't mean much to me. But on my debut at Anfield against Chelsea... while the crowd was singing "You'll Never Walk Alone"... boy, that's when it sinks in that you are in a special place and that the sign is special too.'
### _Who has given you more as a trainer, Rafa Benítez or Luis Aragonés?_
'I think both of them have. I've been with Luis for a long time. Since I was very young and starting out he's taught me the fundamentals, both on and off the pitch. I was seventeen and he had seen everything as a player and as a trainer, he had a lot to teach me and I had a lot to learn. Those were the days when I had to listen, learn and keep my mouth shut. And then with Luis I've won the national team's biggest trophy in the last 44 years. With Rafa I've made a big leap forward in terms of quality. He's taught me a lot of things and made me improve areas where I was lacking, and he still does that because he's a person who doesn't stop in his everyday life, even for one minute, and tries to improve you in every detail and every move, while trying to explain to you why. He's obsessed with you doing things because you understand why, because you understand the reason he asks you to do them. He doesn't say to you, 'Do this because I'm telling you to.' That's Benítez. I hope I'm with him many more years so that he can keep teaching me and I can win silverware with him.'
### _If Rafa Benítez were to be chosen as trainer of Real Madrid, would you go with him as a player?_
'Nooooo! Nooooo!' Murmur the fans.
'Rafa's got a contract, like I have, that runs up until 2014 and I honestly hope that scenario doesn't come about and that he doesn't leave, but if he did, I wouldn't follow suit.' ( _Hearty applause from the seating area._ )
### _If Barcelona and Real Madrid made the same offer for you, which one would you go for?_
'I'd stay at Liverpool.' ( _Applause_ )
### _Which striker from the Spanish Liga would you take with you to Liverpool as a partner in the attack?_
'I'd say Diego Forlán but no... because then I'd be taking him off Atléti. ( _Laughter again_ )
'No... David Villa or David Silva. I wish they could come, it would be a great asset for our team.'
### _What would it take for Liverpool to win the Premier League?_
'We need match-winners like Rooney or Tévez, footballers who break the deadlock in matches. In fact, Liverpool is losing the Premier League in home games against average teams.'
### _What was your first press conference in English like?_
'I've never been so scared in all my life.'
### _By the media pressure?_
'No. In England there's no pressure from the media. There's no daily coverage of the team. There are no sports papers and the tabloids give it two or three pages, which is what the major informative papers do too. Training sessions are behind closed doors and supporters and journalists can't attend. There are no interviews or press conferences, only when we played in the Champions' League because UEFA makes us. Everything's a lot calmer but the first time I did a press conference in front of dozens of journalists I had a lot on my plate. If you don't understand a question... but I got through it okay. More or less.'
### _How did you feel when it turned out that Liverpool would face Atlético?_
'When I got injured in Brussels the first thing that went through my head was the Atléti match in the Calderón. There were only a few days to go and I already knew I wouldn't be able to make it. It was really frustrating not to be able to be there and see people again. But then you learn to live with it, the match comes round and when I saw the two sets of supporters on television swapping shirts it was the best thing since sliced bread from my standpoint – imagine! There were a lot of people there that I thought would be upset with me for leaving but that wasn't the case. After hearing my name chanted in the Calderón it became the best moment all season besides all the awards.'
### _What went through your mind when you scored against Real Madrid at Anfield?_
'It was a special moment for me because I hadn't trained for the 10 days leading up to it. I was playing in a lot of pain and I had to cut a bit off my boot because my foot wouldn't fit in it with all the strapping on. I was on the verge of not playing but I was really dying to. In the end I managed to play and imagine what it was like when I made it to the game and I scored... the knock-out game wasn't decided because it's Real Madrid we're talking about and anything could have happened. But the feeling... it was incredible. It was worth the risk.'
### _How did you feel when you netted the winning goal in the European Championship against Germany?_
'It's the sort of feeling you spend your whole life looking for. You dream of being a player when you are younger, you dream of playing in the first division, and when you are there, you want more, you want to play for your country, you want to play in a European Championship, in a World Cup, but they are such far-fetched dreams that you think they'll never come true... and when that ball went in... you realise that all the dreams you ever had have come true. A feeling we did have was that we knew that Spain was united around us. I was in the street and to be responsible for that goal, for the feeling of unity the country experienced after so many years without lifting a trophy, is incredible...'
### _And now, having realised that dream, it doesn't seem so hard to make others come true: to become world champions..._
'We're going to go all out for the World Cup, obviously. In our situation we can allow ourselves to imagine that happening. While remaining wary and humble, like the national team always has been, I believe it'll be virtually the same team from the European championship, but with two years' more experience. We can learn from the few mistakes we made, get stronger and go for it at the World Cup. And hopefully in South Africa we can repeat our success.'
### _What do you need to be the same Fernando Torres for the national side as you are at Liverpool?_
'I suppose I'd have to get used to the style of football that they play in the Spain team much more quickly. It's more elaborate than how they play at Liverpool and there's more touching the ball. Plus changing your mindset isn't easy when, like in the World Cup qualifiers, you only have two or three days to train. Switching from the mentality in the English system to the one in the Spanish Liga is something I still have to sort out.'
### _What is Vicente del Bosque like?_
'He's very approachable and like another team-mate. He's brought in a much more relaxed atmosphere.'
### _What would give you the bigger thrill, winning the World cup or the Champions League?_
'I don't think I could decide. A World Cup is something that's in every footballer's mind, even more so now that it seems achievable and it's just round the corner, but winning the Champions with my team would be really great. Either way then.'
### _What's the best league in the world, the English or the Spanish?_
'It's hard to say. I think that, as things stand, the English league is the most competitive in the world because it's got four great teams that can go all the way in Europe's biggest tournament. In the Liga this year there's been one team like Barcelona, which has been better than the English ones, but that's been one team and the other three semi-finalists were English teams, and we also lost to an English team. I think the Premier is stronger at the moment. It's a league where Spanish players can fit in, as can others from all over the world. Each one has its moments though, and there have been seasons where the Italian League has been the best and now it's the English, but things can change.'
### _Who is the best player in the world for you?_
'For me it would obviously be Gerrard, because I see him every day, though I think Leo Messi deserves the honour more than anyone else. He's been the best this year. He's won everything.'
### _And it comes to the last question... Torres, can I have my picture taken with you?_
The request comes from Rubén Calvo, a ten-year-old lad with fair hair and big green eyes, clutching a Liverpool shirt. Fernando has no problem agreeing to this. He hasn't forgotten the promise he made years back to Flori, his mother. That day, after watching the Spanish national side train in Boadilla del Monte, Torres went up to the internationals to get their autographs along with some other boys. No joy. He got into such a stew about it that he promised his mother that, if he should ever make it into their boots, he would never deny anyone a photo or an autograph. Now that he has arrived, El Niño does not forget, and _el niño_ , with fair hair and big green eyes, smiles.
## **Career record**
### **Personal summary**
Full name: Fernando José Torres Sanz
Place and Date of Birth: Madrid, 20 March 1984
Parents: Flori and José. Sister: Mari Paz. Brother: Israel
Married: 27 May 2009
Wife: Olalla Domínguez Liste
Height: 186 cm
Weight: 78 kg
### **Early career**
As a junior, played for Parque 84, Mario's Holanda and Rayo 13
At eleven years old, scouted to Atlético de Madrid
### **Atlético de Madrid**
Debut: 27 May 2001 v Leganés (home) Second Division
First goal: 4 June 2001 v Albacete (away) Second Division
#### _Appearances_
Liga 174 Goals 82
Copa del Rey 25 Goals 7
Became Atlético de Madrid captain in 2003 aged eighteen.
### **Liverpool**
Debut: 11 August 2007 v Aston Villa (away) Premier League
First goal: 18 August 2007 v Chelsea (home) Premier League
#### _Appearances_
League: 57 Goals 38
F.A. Cup 4 Goals 1
League Cup 3 Goals 3
Europe 20 Goals 8
### **Spain**
Debut: 6 September 2003 v Portugal (away)
First goal: 28 April 2004 v Italy (away)
Caps 67 Goals 22
#### _Tournaments played:_
European Championship 2004
World Cup 2006
European Championship 2008
Confederations Cup 2009
### **Honours won**
European Championship 2008
European Championship Under-19, 2002
European Championship Under-16, 2001
### **Individual Honours**
MVP for the Final of the 2008 European Championships
Premier League Silver Boot Winner (2007–2008)
MVP for the European Under-19s (2002) and Golden Ball winner
MVP for the Euro Under-16 (2001) and Golden Ball winner
## **Bibliography**
Cruise, Ian, _Fernando Torres, Liverpool's Glorious Number 9_ , 2009 John Blake Publishing
Hughes, Simon, _Fernando Torres: a year in the life_ _,_ _2008_ _,_ Trinity MirrorSport Media
Miguélez José and Matallanas Javier G., _Sentimiento Atlético: cien años de sueños, alegrías y desencantos_ , 2003 Plaza Y Janés
Manolete, _Soy del Atléti,¡y qué!_ 2008, Now Books
### **Newspapers**
#### _**Spain**_
_EL País_
_El Mundo_
_ABC_
_Público_
_La Vanguardia_
_El Periódico de Catalunya_
_La Razón_
_Marca_
_As_
_Mundo deportivo_
_Sport_
#### _**UK**_
_The Times_
_Independent_
_Guardian_
_Sun_
_Daily Mirror_
_Daily Mail_
_Liverpool Echo_
#### _**Italy**_
_Corriere della Sera_
_La Repubblica_
_La Gazzetta dello Sport_
#### _**France**_
_L'Équipe_
### **Websites**
www.fernando9torres.com
www.thekidtorres.com/
www.liverpoolfc.tv
www.clubatleticodemadrid.com
www.rfef.es
www.uefa.com
www.fifa.com
## **Acknowledgements**
To Elvira, Olmo, Lorenzo, Alda and Tullio.
Thanks to Fernando Torres for his football
Thanks to the Liverpool fans
Thank as well to the Atléti fans
Thanks to Laure Merle d'Aubigné, Oliver Pugh, Geoffrey Goff, Yolanda Vega, Stephen Jones, Simon Cranston-Smith, Filippo Ricci, Carlos Carpio, Juan Castro, Sid Lowe, Guillem Balagué, Michael Robinson, Abraham García, Fabio Capello, Franco Baldini, Fabio Cannavaro, Álvaro Arbeloa, Paloma Antoranz, Javier Camacho, José Antonio Camacho, Pascual Blázquez, Tony Roldán, Maria Teresa Chiriví, Manolo Rangel, Pedro Calvo, Vicente del Bosque, Andrés Perales, Juan Gómez, Alexis Gómez, Iñaki Sáez, Rafa Benítez, Javier Aguirre, Manolo Briñas, Pepe Reina, Kiko, Andrés Iniesta, Sergi Noguera, Nacho Aznar, Gregorio Manzano, Héctor Romero, Graeme Souness, Kenny Dalglish, Juan Francisco Sánchez Argüello, Manolo Robles, Miguel Ángel Gómez, Julián Hernández, Ángel Sánchez, Javier Tamames.
In memory of Paul Marsh, West Ham fan and founder of The Marsh Agency.
| {
"redpajama_set_name": "RedPajamaBook"
} | 290 |
Q: How to compare strings using (<,>) I am trying to compare two strings for my while loop, heres a snippet of my code:
//variables
string pivot, array[10];
int rightBoundary;
//loop
while( pivot < array[rightBoundary])
this code is from a tutorial on quick sort but im trying to convert it to work with strings.
so my question is what is the best way to do this comparison.
currently I get this error (Unhandled exception at 0x774215de in quickSortNumbers.exe: 0xC0000005: Access violation reading location 0x965b7214.)
and help will be great thanks :)
edit: sorry should have just uploaded all my code, i think the problem may actually be the string array. heres all my code:
#include <iostream>
#include <string>
using namespace std;
#define array1_SIZE 5 //change the array1 size here
void Printarray1(string* array1, int n);
void QuickSort(string* array1, int startIndex, int endIndex);
int Splitarray1(string* array1, string pivot, int startIndex, int endIndex);
void swap(string &a, string &b);
int main(void)
{
string array1[array1_SIZE];
int i;
for( i = 0; i < array1_SIZE; i++) //array1 elements input
{
cout<<"Enter an integer : ";
cin>>array1[i];
}
cout<<endl<<"The list you input is : "<<endl;
Printarray1(array1, array1_SIZE);
QuickSort(array1,0,array1_SIZE - 1); //sort array1 from first to last element
cout<<endl<<"The list has been sorted, now it is : "<<endl;
Printarray1(array1, array1_SIZE);
cin.get();
cin.get();
int read;
cin >> read;
return 0;
}
/* This function swaps two numbers
Arguments :
a, b - the numbers to be swapped
*/
void swap(string &a, string &b)
{
string temp;
temp = a;
a = b;
b = temp;
}
/* This function prints an array1.
Arguments :
array1 - the array1 to be printed
n - number of elements in the array1
*/
void Printarray1(string* array1, int n)
{
int i;
for( i = 0; i < n; i++)
{
cout << array1[i] << '\t';
}
}
/* This function does the quicksort
Arguments :
array1 - the array1 to be sorted
startIndex - index of the first element of the section
endIndex - index of the last element of the section
*/
void QuickSort(string* array1, int startIndex, int endIndex)
{
string pivot = array1[startIndex]; //pivot element is the leftmost element
int splitPoint;
if(endIndex > startIndex) //if they are equal, it means there is
//only one element and quicksort's job
//here is finished
{
splitPoint = Splitarray1(array1, pivot, startIndex, endIndex);
//Splitarray1() returns the position where
//pivot belongs to
array1[splitPoint] = pivot;
QuickSort(array1, startIndex, splitPoint-1); //Quick sort first half
QuickSort(array1, splitPoint+1, endIndex); //Quick sort second half
}
}
/* This function splits the array1 around the pivot
Arguments :
array1 - the array1 to be split
pivot - pivot element whose position will be returned
startIndex - index of the first element of the section
endIndex - index of the last element of the section
Returns :
the position of the pivot
*/
int Splitarray1(string* array1, string pivot, int startIndex, int endIndex)
{
int leftBoundary = startIndex;
int rightBoundary = endIndex;
while(leftBoundary < rightBoundary) //shuttle pivot until the boundaries meet
{
while( pivot < array1[rightBoundary]//keep moving until a lesser element is found
&& rightBoundary > leftBoundary) //or until the leftBoundary is reached
{
rightBoundary--; //move left
}
swap(array1[leftBoundary], array1[rightBoundary]);
//Printarray1(array1, array1_SIZE); //Uncomment this line for study
while( pivot >= array1[leftBoundary] //keep moving until a greater or equal element is found
&& leftBoundary < rightBoundary) //or until the rightBoundary is reached
{
leftBoundary++; //move right
}
swap(array1[rightBoundary], array1[leftBoundary]);
//Printarray1(array1, array1_SIZE); //Uncomment this line for study
}
return leftBoundary; //leftBoundary is the split point because
//the above while loop exits only when
//leftBoundary and rightBoundary are equal
}
A: You probably have an out-of-bounds error, possibly due to not initializing rightBoundary. Strings can be compared perfectly fine with the comparison operators.
#include <iostream>
using std::cout;
#include <string>
using std::string;
int main()
{
string s1 = "hello";
string s2 = "world!";
string lower = s1 < s2 ? s1 : s2;
cout << lower; //prints "hello"
}
To compare without worrying about case, you can use lexicographical_compare with your own comparer function:
#include <algorithm>
using std::lexicographical_compare;
#include <cctype>
using std::tolower;
#include <iostream>
using std::cout;
#include <string>
using std::string;
bool nocase_compare (char one, char two)
{
return tolower (one) < tolower (two);
}
int main()
{
string s1 = "Hello";
string s2 = "happy";
if (lexicographical_compare (s1.begin(), s1.end(), s2.begin(), s2.end(), nocase_compare))
cout << s1;
else
cout << s2;
//prints "happy" even though 'H' < 'h'
}
If you really want to use < and >, you'll have to make a small wrapper for string that implements your versions of operator< and operator>. The ones implemented in string use the default lexicographical_compare.
A: Using < for comparing strings is fine, but might not be what you expect if you want alphabetical order since all lowercase letters come before uppercase letters if you want lexicographical ordering you should use lexicographical_compare instead.
The reason your code crashes is because you do not assign any initial value to rightBoundary, you should do:
int rightBoundary = 0;
Since otherwise rightBoundary will have an arbitrary initial value which will with overwhelming probability be greater than the size of 'array' and cause out-of-bounds access.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 316 |
\section{Introduction}
The detection of a new particle having a sub-GeV mass would likely hint at the presence of
physics beyond the standard model.
This possibility has been raised recently by the observation of three events for the rare
decay mode \,$\Sigma^+\to p\mu^+\mu^-$\, with dimuon invariant masses narrowly
clustered around 214.3\,MeV by the HyperCP collaboration a few years ago~\cite{Park:2005ek}.
Although these events can be accounted for within the standard model (SM) when
long-distance contributions are properly included~\cite{Bergstrom:1987wr}, the probability
that the three events have the same dimuon mass in the SM is less than 1~percent.
This makes it reasonable to speculate that a light neutral particle, $X$,
is responsible for the observed dimuon-mass distribution via
the decay chain \,$\Sigma^+\to p X\to p\mu^+\mu^-$\,~\cite{Park:2005ek}.
The new-particle interpretation of the HyperCP result has been theoretically explored to
some extent in the literature~\cite{He:2005we,Deshpande:2005mb,Gorbunov:2005nu,
He:2006uu,He:2006fr,Zhu:2006zv,Tatischeff:2007dz,Chen:2006xja,Chen:2007uv}.
Various ideas that have been proposed include the possibility that $X$ is spinless or that
it has spin one.
In the spinless case, $X$ could be a sgoldstino in supersymmetric
models~\cite{Gorbunov:2005nu} or a $CP$-odd Higgs boson in the next-to-minimal
supersymmetric standard model (NMSSM)~\cite{He:2006fr,Zhu:2006zv}.
In the case of $X$ being a spin-1 particle, one possible candidate is the gauge ($U$) boson
of an extra U(1) gauge group in some extensions of the~SM~\cite{Chen:2007uv}.
The presence of $X$ in \,$\Sigma^+\to p\mu^+\mu^-$\, implies that it also contributes to other
\,$|\Delta S|=1$\, transitions, such as the kaon decays \,$K\to\pi\mu^+\mu^-$.\,
In general, the contributions of $X$ to \,$|\Delta S|=1$\, processes fall into two types.
The first one is induced by the flavor-changing (effective) couplings of $X$ to $d s$.
In addition to these two-quark contributions, there are so-called four-quark contributions
of $X$, which arise from the combined effects of the usual four-quark \,$|\Delta S|=1$\,
operators in the SM and the flavor-conserving couplings of $X$ to quarks, as well as its
interactions with the SM gauge fields~\cite{He:2006uu}.
Although the two-quark contributions are generally expected to dominate over the four-quark
ones, in some models the parameter space may have regions where the two types of
contributions are comparable in size and hence could interfere
destructively~\cite{He:2006uu,He:2006fr}.
Accordingly, to explore the $X$ hypothesis in detail and compare its predictions with
experimental results in a definite way,
it is necessary to work under some model-dependent assumptions.
There are a number experiments that have recently been performed or are still ongoing
to test the $X$ hypothesis~\cite{Tung:2008gd,Love:2008hs,ktev,e391a,belle}.
Their results have begun to restrict some of the proposed ideas on $X$ in the literature.
In particular, as already mentioned, $X$ could be a light $CP$-odd Higgs boson in the NMSSM.
In the specific NMSSM scenario considered in Ref.~\cite{He:2006fr}, $X$ does not couple
to up-type quarks and has the same flavor-conserving coupling $l_d$ to all down-type
quarks, implying that the four-quark contributions of $X$ to \,$|\Delta S|=1$\, decays are
proportional to~$l_d$~\cite{He:2006fr}.
Recent searches for the radiative decays \,$\Upsilon({\rm1S,2S,3S})\to\gamma X\to\gamma\mu^+\mu^-$\,
by the CLEO and BaBar collaborations~\cite{Love:2008hs} have come back negative and
imposed sufficiently small upper-bounds on $l_d$
to make the four-quark contributions negligible compared to the two-quark ones.
With only the two-quark contributions being present, the scalar part of the $sdX$ coupling is
already constrained by \,$K\to\pi\mu\mu$\, data to be negligibly small, whereas its pseudoscalar
part can be probed by \,$K\to\pi\pi\mu\mu$\, measurements~\cite{He:2005we,Deshpande:2005mb}.
There are now preliminary results on the branching ratio $\cal B$ of
\,$K_L\to\pi^0\pi^0X\to\pi^0\pi^0\mu^+\mu^-$\, reported by the KTeV and E391a
collaborations~\cite{ktev,e391a}.
The KTeV preliminary measurement \,${\cal B}<9.44\times10^{-11}$\, at 90\%~C.L.~\cite{ktev}
is the much more stringent of the two and has an upper bound almost 20 times smaller than
the lower limit \,${\cal B}_{\rm lo}=1.7\times10^{-9}$\, predicted in Ref.~\cite{He:2005we}
under the assumption that the $sdX$ pseudoscalar coupling, $g_P^{}$, is purely real.
However, there is a possibility that $g_P^{}$ has an imaginary part, and in the case where
this coupling is mostly imaginary the predicted lower bound, ${\cal B}_{\rm lo}$, can be much
smaller.\footnote{We gratefully acknowledge D. Gorbunov for pointing this out to us.}
More precisely, one can find that \,${\cal B}_{\rm lo}<7\times10^{-11}$,\, which evades
the above bound from KTeV, if \,$|{\rm Im}\,g_P^{}|>0.98\,|g_P^{}|$\, and, moreover,
\,${\cal B}_{\rm lo}=1.7\times10^{-9}\,|\epsilon_K^{}|^2\sim8\times10^{-15}$\,
if $g_P^{}$ is purely imaginary, \,$\epsilon_K^{}\sim{\cal O}(0.002)$\, being the usual
$CP$-violation parameter in kaon mixing.
If the KTeV preliminary result stands in their final report, then it will have imposed
a significant constraint on~$g_P^{}$, restricting it to be almost purely imaginary, for
the scenario in which $X$ has spin zero and its four-quark contributions to flavor-changing
transitions are negligible.
To place stronger restrictions on~$g_P^{}$, it is important to look for the decays of particles
other than neutral kaons, such as \,$K^\pm\to\pi^\pm\pi^0X$\, and
\,$\Omega^-\to\Xi^-X$\,~\cite{Kaplan:2007nn}.
Although the $X$ couplings in the \,$|\Delta S|=1$\, sector are in general independent of those
in the \,$|\Delta B|=1$\, sector, there is also new information from the latter sector that
seems compatible with the results of the $K_L$ measurements.
Very recently the Belle collaboration has given a~preliminary report on their search for
a~spinless $X$ in \,$B\to\rho\mu^+\mu^-$\, and \,$B\to K^*\mu^+\mu^-$\, with
$m_{\mu\mu}^{}$ values restricted within a small region around \,$m_{\mu\mu}^{}=214.3$\,MeV.\,
They did not observe any event and provided stringent upper-bounds on the branching ratios of
\,$B\to\rho X$\, and \,$B\to K^*X$\,~\cite{belle}.
Unlike the spinless case, the scenario in which $X$ has spin one is not yet as strongly
challenged by experimental data, for it predicts that the lower limit of the branching ratio of
\,$K_L\to\pi^0\pi^0X\to\pi^0\pi^0\mu^+\mu^-$\, arising from the two-quark $dsX$ axial-vector
coupling, taken to be real, is \,$2\times10^{-11}$\,~\cite{He:2005we}.
This prediction is well below the preliminary upper-bound of \,$9.44\times10^{-11}$\, from
KTeV~\cite{ktev} and could get lower in the presence of an imaginary part of the $dsX$ coupling.
It is therefore interesting to explore the spin-1 case further, which we will do here.
In this paper we focus on the contributions of $X$ with spin~1 to a number of rare
processes involving mesons containing the $b$ quark.
We will not deal with specific models, but will instead adopt a model-independent
approach, assuming that $X$ has flavor-changing two-quark couplings to down-type quarks only
and that its four-quark contributions to flavor-changing transitions are negligible compared
to the two-quark ones.
Accordingly, since the $bdX$ and $bsX$ couplings generally are not related to the $sdX$
couplings, we further assume that the $b(d,s)X$ couplings each have both parity-even and
parity-odd parts, but we leave the parity of $X$ unspecified.
Specifically, we allow $X$ to have both vector and axial-vector couplings to $b(d,s)$.
The more limited case of $X$ being an axial-vector boson with only parity-even couplings
to $b(d,s)$ has been considered in Ref.~\cite{Chen:2006xja}.
Following earlier work~\cite{He:2005we}, to be consistent with HyperCP observations
we also assume that $X$ does not interact strongly and decays inside
the detector with \,${\cal B}(X\to\mu^+\mu^-)=1$.\,
In exploring the effect of $X$ with spin~1 on $B$ transitions, we will incorporate
the latest experimental information and obtain constraints on the flavor-changing
couplings of $X$ in order to predict upper bounds on the rates of a number of rare decays.
At this point it is worth pointing out that, since we let $X$ have vector couplings to $b(d,s)$,
the transitions in which we are interested include $B$ decays into $X$ and a pseudoscalar
meson, such as pion or kaon, which were not considered in Ref.~\cite{Chen:2006xja}.
As our numbers will show, most of the branching ratios of the decays we consider can be
large enough to be detected in near-future $B$ experiments.
This can serve to guide experimental searches for $X$ in order to help confirm or
rule out the spin-1 case.
\section{Interactions and amplitudes}
Assuming that $X$ has spin one and does not carry electric or color charge, we can express
the Lagrangian describing its effective couplings to a $b$~quark and
a light quark \,$q=d$ or $s$\, as
\begin{eqnarray} \label{LbqX}
{\cal L}_{bqX}^{} \,\,=\,\,
-\bar q\gamma_\mu^{}\bigl(g_{Vq}^{}-g_{Aq}^{}\gamma_5^{}\bigr)b\,X^\mu \,\,+\,\, {\rm H.c.}
\,\,=\,\,
-\bar q\gamma_\mu^{}\bigl(g_{{\rm L}q}^{}P_{\rm L}^{}+g_{{\rm R}q}^{}P_{\rm R}^{}\bigr)b\,X^\mu
\,\,+\,\, {\rm H.c.} ~,
\end{eqnarray}
where $g_{Vq}^{}$ and $g_{Aq}^{}$ parametrize the vector and axial-vector couplings, respectively,
\,$g_{{\rm L}q,{\rm R}q}^{}=g_{Vq}^{}\pm g_{Aq}^{}$,\, and
\,$P_{\rm L,R}^{}=\frac{1}{2}(1\mp\gamma_5^{})$.\,
Generally, the constants $g_{Vq,Aq}^{}$ can be complex.
In the following, we derive the contributions of these two-quark interactions of $X$ to
the amplitudes for several processes involving $b$-flavored mesons.
As mentioned above, we follow here the scenario in which the four-quark flavor-changing
contributions of $X$ are negligible compared to the effects induced by~${\cal L}_{bqX}$.
The first transition we will consider is $B_q^0$-$\bar B_q^0$ mixing, which is characterized
by the physical mass-difference $\Delta M_q$ between the heavy and light mass-eigenstates
in the $B_q^0$-$\bar B_q^0$ system.
This observable is related to the matrix element $M_{12}^q$ for the mixing by
\,$\Delta M_q=2\,|M_{12}^{q}|$,\, where \,$M_{12}^q=M_{12}^{q,\rm SM}+M_{12}^{q,X}$\,
is obtained from the effective Hamiltonian ${\cal H}_{b\bar q\to\bar b q}$ for the SM plus
$X$-mediated contributions using
\,$2m_{B_q} M_{12}^q=\bigl\langle B_q^0\bigr|{\cal H}_{b\bar q\to\bar b q}
\bigl|\bar B_q^0\bigr\rangle$\,~\cite{Buchalla:1995vs}.
The SM part of $M_{12}^q$ is dominated by the top loop and given by~\cite{Buchalla:1995vs}
\begin{eqnarray}
M_{12}^{q,\rm SM} \,\,\simeq\,\, \frac{G_{\rm F}^2 m_W^2}{12\pi^2}\,f_{B_q}^2 m_{B_q}^{}\,
\eta_B^{} B_{B_q}^{}\, \bigl(V_{tb}^{}V_{tq}^*\bigr)^2\, S_0^{}\bigl(m_t^2/m_W^2\bigr) ~,
\end{eqnarray}
where $G_{\rm F}$ is the usual Fermi constant, $f_{B_q}$ is the $B_q$ decay-constant,
$\eta_B^{}$ contains QCD corrections, $B_{B_q}$ is a~bag parameter, $V_{kl}$ are elements of
the Cabibbo-Kobayashi-Maskawa (CKM) matrix, and the loop function
\,$S_0^{}\bigl(m_t^2/m_W^2\bigr)\simeq2.4$.\,
To determine the $X$ contribution $M_{12}^{q,X}$, we derive the effective Hamiltonian
${\cal H}_{b\bar q\to \bar b q}^X$ from the amplitude for the tree-level transition
\,$b\bar q\to X^*\to\bar b q$\, calculated from~${\cal L}_{bqX}$.
Thus
\begin{eqnarray} \label{Hbq2bq}
{\cal H}_{b\bar q\to \bar b q}^X &=&
\frac{\bar q\gamma^\mu\bigl(g_{{\rm L}q}^{}P_{\rm L}^{}+g_{{\rm R}q}^{}P_{\rm R}^{}\bigr)b\,
\bar q\gamma_\mu^{}\bigl(g_{{\rm L}q}^{}P_{\rm L}^{}+g_{{\rm R}q}^{}P_{\rm R}^{}\bigr)b}
{2\Bigl(m_X^2-m_{B_q}^2\Bigr)}
\nonumber \\ && +\,\,
\frac{\Bigl\{\bar q\Bigl[\bigl(g_{{\rm L}q}^{}m_q^{}-g_{{\rm R}q}^{}m_b^{}\bigr)P_{\rm L}^{} +
\bigl(g_{{\rm R}q}^{}m_q^{}-g_{{\rm L}q}^{}m_b^{}\bigr)P_{\rm R}^{}\Bigr]b\Bigr\}^2}
{2\Bigl(m_X^2-m_{B_q}^2\Bigr)m_X^2} ~,
\end{eqnarray}
where we have used in the denominators the approximation \,$p_X^2=m_{B_q}^2$\, appropriate
for the $B_q$ rest-frame and included an overall factor of 1/2 to account for
the products of two identical operators.
In evaluating the matrix element of this Hamiltonian at energy scales \,$\mu\sim m_b^{}$,\,
one needs to include the effect of QCD running from high energy scales which mixes
different operators. The resulting contribution of $X$ is
\begin{eqnarray}
M_{12}^{q,X} &=&
\frac{f_{B_q}^2\, m_{B_q}^{}}{3\bigl(m_X^2-m_{B_q}^2\bigr)} \Biggl[
\bigl(g_{Vq}^2+g_{Aq}^2\bigr) P_1^{\rm VLL} +
\frac{g_{Vq}^2\,\bigl(m_b^{}-m_q^{}\bigr)^2+g_{Aq}^2\,\bigl(m_b^{}+m_q^{}\bigr)^2}{m_X^2}\,
P_1^{\rm SLL}
\nonumber \\ && \hspace{16ex} +\,\, \bigl(g_{Vq}^2-g_{Aq}^2\bigr) P_1^{\rm LR}
+ \frac{g_{Vq}^2\,\bigl(m_b^{}-m_q^{}\bigr)^2-g_{Aq}^2\,\bigl(m_b^{}+m_q^{}\bigr)^2}{m_X^2}\,
P_2^{\rm LR} \Biggr] ~,
\end{eqnarray}
where \,$P_1^{\rm VLL}=\eta_1^{\rm VLL} B_1^{\rm VLL}$,\,
\,$P_1^{\rm SLL}=-\mbox{$\frac{5}{8}$}\, \eta_1^{\rm SLL} R_{B_q} B_1^{\rm SLL}$,\, and
\,$P_j^{\rm LR}=-\mbox{$\frac{1}{2}$}\, \eta_{1j}^{\rm LR} R_{B_q} B_1^{\rm LR}
+ \mbox{$\frac{3}{4}$}\, \eta_{2j}^{\rm LR} R_{B_q} B_2^{\rm LR}$,\,
\,$j\,=\,1,2$\,~\cite{Buras:2001ra},
with the $\eta$'s denoting QCD-correction factors, the $B$'s being bag parameters defined by
the matrix elements
$\bigl\langle B_q^0\bigr|\bar q\gamma^\mu P_{\rm L}^{}b\,
\bar q\gamma_\mu^{}P_{\rm L}^{}b \bigl|\bar B_q^0\bigr\rangle =
\bigl\langle B_q^0\bigr|\bar q\gamma^\mu P_{\rm R}^{}b\,
\bar q\gamma_\mu^{}P_{\rm R}^{}b \bigl|\bar B_q^0\bigr\rangle =
\mbox{$\frac{2}{3}$} f_{B_q}^2 m_{B_q}^2 B_1^{\rm VLL}$,\,
\,$\bigl\langle B_q^0\bigr|\bar q P_{\rm L}^{}b\,\bar q P_{\rm L}^{}b\bigl|\bar B_q^0\bigr\rangle
= \bigl\langle B_q^0\bigr|\bar qP_{\rm R}^{}b\,\bar qP_{\rm R}^{}b\bigl|\bar B_q^0\bigr\rangle
= -\mbox{$\frac{5}{12}$} f_{B_q}^2 m_{B_q}^2 R_{B_q} B_1^{\rm SLL}$,\,
\,$\bigl\langle B_q^0\bigr|\bar q\gamma^\mu P_{\rm L}^{}b\,
\bar q\gamma_\mu^{}P_{\rm R}^{}b\bigl|\bar B_q^0\bigr\rangle =
-\mbox{$\frac{1}{3}$} f_{B_q}^2 m_{B_q}^2 R_{B_q} B_1^{\rm LR}$,\, and
\,$\bigl\langle B_q^0\bigr|\bar q P_{\rm L}^{}b\,\bar q P_{\rm R}^{}b\bigl|\bar B_q^0\bigr\rangle
=\mbox{$\frac{1}{2}$} f_{B_q}^2 m_{B_q}^2 R_{B_q} B_2^{\rm LR}$,\,
and \,$R_{B_q}=m_{B_q}^2/\bigl(m_b^{}+m_q^{}\bigr){}^2$.\,
Bounds on $g_{Vq}^{}$ and $g_{Aq}^{}$ can then be extracted from comparing the measured
and SM values of~$\Delta M_q$.
The second transition of interest is \,$B_q^0\to\mu^+\mu^-$,\, which receives a contribution
from \,$B_q^0\to X^*\to\mu^+\mu^-$.\, To derive the amplitude for the latter, we need not only
${\cal L}_{bqX}$, but also the Lagrangian describing \,$X\to\mu^+\mu^-$.\,
Allowing the $X$ interaction with $\mu$ to have both parity-even and -odd parts,
we can write the latter Lagrangian as
\begin{eqnarray} \label{LlX}
{\cal L}_{\mu X}^{} \,\,=\,\,
\bar\mu\gamma_\alpha^{}\bigl(g_{V\mu}^{}+g_{A\mu}^{}\gamma_5^{}\bigr)\mu\,X^\alpha ~,
\end{eqnarray}
where $g_{V\mu}^{}$ and $g_{A\mu}^{}$ are coupling constants, which are real due to
the hermiticity of~${\cal L}_{\mu X}$.
Using the matrix elements
\,$\bigl\langle0\bigr|\bar q\gamma^\mu b\bigl|\bar B_q^0\bigr\rangle =
\bigl\langle0\bigr|\bar q b\bigl|\bar B_q^0\bigr\rangle = 0$,\,
\,$\bigl\langle0\bigr|\bar q\gamma^\mu\gamma_5^{}b\bigl|\bar B_q^0(p)\bigr\rangle =
-i f_{B_q}p^\mu$,\, and
\,$\bigl\langle0\bigr|\bar q\gamma_5^{}b\bigl|\bar B_q^0\bigr\rangle =
i f_{B_q}m_{B_q}^2/\bigl(m_b^{}+m_q^{}\bigr)$,\,
we then arrive at
\begin{eqnarray}
{\cal M}\bigl(\bar B_q^0\to X\to\mu^+\mu^-\bigr) \,\,=\,\,
-\frac{2i f_{B_q}^{}\, g_{Aq}^{}\, g_{A\mu}^{}\, m_\mu^{}}{m_X^2}\, \bar\mu\gamma_5^{}\mu ~.
\end{eqnarray}
The resulting decay rate is
\begin{eqnarray} \label{rate_B2ll}
\Gamma\bigl(\bar B_q^0\to X\to\mu^+\mu^-\bigr) \,\,=\,\,
\frac{f_{B_q}^2\,\bigl|g_{Aq}^{}\,g_{A\mu}^{}\bigr|^2 m_\mu^2}{2\pi\,m_X^4}\,
\sqrt{m_{B_q}^2-4m_\mu^2} ~.
\end{eqnarray}
This implies that we need, in addition, the value of $g_{A\mu}^{}$, which can be estimated from
the contribution of ${\cal L}_{\mu X}$ in Eq.~(\ref{LlX}) at one-loop level to the anomalous
magnetic moment of the muon,~$a_{\mu}$.
We will determine $g_{A\mu}^{}$ in the next section.
Before moving on to other transitions, we note that from ${\cal L}_{\mu X}$ follows the decay rate
\begin{eqnarray} \label{rate_X2ll}
\Gamma\bigl(X\to\mu^+\mu^-\bigr) \,\,=\,\,
\frac{g_{V\mu}^2\, m_X^{}}{12\pi}
\Biggl(1+\frac{2 m_\mu^2}{m_X^2}\Biggr) \sqrt{1-\frac{4 m_\mu^2}{m_X^2}} \,+\,
\frac{g_{A\mu}^2\, m_X^{}}{12\pi}\,\Biggl(1-\frac{4 m_\mu^2}{m_X^2}\Biggr)^{\!3/2} ~.
\end{eqnarray}
The next process that can provide constraints on $g_{Vq}^{}$ and $g_{Aq}^{}$ is
the inclusive decay \,$b\to q\mu^+\mu^-$,\, to which \,$b\to q X$\, can contribute.
From ${\cal L}_{bqX}$ above, it is straightforward to arrive at the inclusive decay rate
\begin{eqnarray} \label{rate_b2qX}
\Gamma(b\to q X) &=& \frac{|\bm{p}_X^{}|}{8\pi\,m_b^2 m_X^2}
\Bigl\{\bigl|g_{Vq}^{}\bigr|^2\Bigl[\bigl(m_b^{}+m_q^{}\bigr)^2+2 m_X^2\Bigr]
\Bigl[\bigl(m_b^{}-m_q^{}\bigr)^2-m_X^2\Bigr] \nonumber \\ && \hspace*{11ex} +\,\,
\bigl|g_{Aq}^{}\bigr|^2\Bigl[\bigl(m_b^{}-m_q^{}\bigr)^2+2 m_X^2\Bigr]
\Bigl[\bigl(m_b^{}+m_q^{}\bigr)^2-m_X^2\Bigr]\Bigr\} ~,
\end{eqnarray}
where $\bm{p}_X^{}$ is the 3-momentum of $X$ in the rest frame of~$b$.
One may probe the \,$b\to q X$\, contribution to \,$b\to q\mu^+\mu^-$\, by examining
the measured partial rate of the latter for the smallest range available of the dimuon
mass, $m_{\mu\mu}^{}$, that contains \,$m_{\mu\mu}^{}=m_X^{}$.
We will also consider the exclusive decays \,$B\to M X$,\, which contribute to
\,$B\to M\mu^+\mu^-$,\, where $M$ is a~pseudoscalar meson~$P$, scalar meson~$S$,
vector meson~$V$, or axial-vector meson~$A$.
To evaluate their decay amplitudes, we need the \,$\bar B\to M$\, matrix elements of the
\,$b\to q$ operators in ${\cal L}_{bqX}$.
The matrix elements relevant to \,$\bar B\to P X$\, and \,$\bar B\to S X$\, are
\begin{eqnarray}
\kappa_P^{}\,\bigl\langle P\bigl(p_P^{}\bigr)\bigr|\bar q\gamma^\mu b
\bigl|\bar B\bigl(p_B^{}\bigr) \bigr\rangle &\,=\,&
\frac{m_B^2-m_P^2}{k^2}\, k^\mu\, F_0^{B P} +
\Biggl[\bigl(p_B^{}+p_P^{}\bigr)^\mu-\frac{m_B^2-m_P^2}{k^2}\,k^\mu\Biggr] F_1^{B P} ~,
\\
i \kappa_S^{}\,\bigl\langle S\bigl(p_S^{}\bigr)\bigr|\bar q\gamma^\mu \gamma_5^{} b
\bigl|\bar B\bigl(p_B^{}\bigr) \bigr\rangle &\,=\,&
\frac{m_B^2-m_S^2}{k^2}\, k^\mu\,F_0^{BS} +
\Biggl[ \bigl(p_B^{}+p_S^{}\bigr)^\mu - \frac{m_B^2-m_S^2}{k^2}\,k^\mu \Biggr] F_1^{BS} ~,
\end{eqnarray}
and \,$\langle P|\bar q\gamma^\mu\gamma_5^{}b|\bar B\rangle =
\langle S|\bar q\gamma^\mu b|\bar B\rangle=0$,\,
where \,$k=p_B^{}-p_{P,S}^{}$,\, the factor $\kappa_P^{}$ has a value of~1 for
\,$P=\pi^-,\bar K,D$\, or \,$-\sqrt2$\, for \,$P=\pi^0$,\,
the values of $\kappa_S^{}$ will be given in the next section,
and the form factors $F_{0,1}^{BP,BS}$ each depend on~$k^2$.
For \,$\bar B\to V X$\, and \,$\bar B\to A X$,\, we need
\begin{eqnarray}
\kappa_V^{}\,\bigl\langle V\bigl(p_V^{}\bigr)\bigr|\bar q\gamma_\mu^{}b
\bigl|\bar B\bigl(p_B^{}\bigr)\bigr\rangle \,&=&\,
\frac{2 V^{B V}}{m_B^{}+m_V^{}}\, \epsilon_{\mu\nu\sigma\tau}^{}\,
\varepsilon_V^{*\nu} p_B^\sigma\, p_V^\tau ~, \\
\kappa_V^{}\,\bigl\langle V\bigl(p_V^{}\bigr)\bigr|\bar q\gamma^\mu\gamma_5^{}b
\bigl|\bar B\bigl(p_B^{}\bigr)\bigr\rangle \,&=&\,
2 i A_0^{B V} m_V^{}\, \frac{\varepsilon_V^{*}\!\cdot\!k}{k^2}\, k^\mu
+ i A_1^{B V}\, \bigl( m_B^{}+m_V^{} \bigr) \biggl(
\varepsilon_V^{*\mu}-\frac{\varepsilon_V^{*}\!\cdot\!k}{k^2}\, k^\mu \biggr)
\nonumber \\ && - \,\,
\frac{i A_2^{B V}\, \varepsilon_V^{*}\!\cdot\!k}{m_B^{}+m_V^{}}
\biggl( p_B^\mu + p_V^\mu - \frac{m_B^2-m_V^2}{k^2}\, k^\mu \biggr) ~,
\end{eqnarray}
\begin{eqnarray}
\kappa_A^{}\,\bigl\langle A\bigl(p_A^{}\bigr)\bigr|\bar q\gamma^\mu b
\bigl|\bar B\bigl(p_B^{}\bigr)\bigr\rangle \,&=&\,
-2i V_0^{B A} m_A^{}\, \frac{\varepsilon_A^{*}\!\cdot\!k}{k^2}\, k^\mu
- iV_1^{B A}\, \bigl( m_B^{} -m_A^{} \bigr) \biggl(
\varepsilon_A^{*\mu}-\frac{\varepsilon_A^{*}\!\cdot\!k}{k^2}\, k^\mu \biggr)
\nonumber \\ && + \,\,
\frac{i V_2^{B A}\, \varepsilon_A^{*}\!\cdot\!k}{m_B^{} -m_A^{}}
\biggl( p_B^\mu + p_A^\mu - \frac{m_B^2 -m_A^2}{k^2}\, k^\mu \biggr) ~, \\
\kappa_A^{}\,\bigl\langle A\bigl(p_A^{}\bigr)\bigr|\bar q\gamma_\mu^{} \gamma_5 b
\bigl|\bar B\bigl(p_B^{}\bigr)\bigr\rangle \,&=&\,
\frac{-2 A^{BA}}{m_B^{} -m_A^{}}\, \epsilon_{\mu\nu\sigma\tau}^{}\,
\varepsilon_A^{*\nu} p_B^\sigma\, p_A^\tau ~,
\end{eqnarray}
where \,$k=p_B^{}-p_{V,A}^{}$,\, the factor $\kappa_V^{}$ has a magnitude of~1 for
\,$V=\rho^-,\bar K^*,\phi,D^*$\, or \,$\sqrt2$\, for \,$V=\rho^0,\omega$,\,
the values of $\kappa_A^{}$ will be given in the next section, and the form factors $V^{BV}$,
$A_{0,1,2}^{BV}$, $V_{0,1,2}^{BA}$, and $A^{BA}$ are all functions of~$k^2$.
Since $X$ has spin~1, its polarization $\varepsilon_X^{}$ and momentum $p_X^{}$ satisfy
the relation \,$\varepsilon_X^*\cdot p_X^{}=0$.\,
The amplitudes for \,$\bar B\to P X$\, and $\bar B \to S X$ are then
\begin{eqnarray} \label{M_B2PX}
{\cal M}(\bar B\to P X) &\,=\,& \frac{2\, g_{Vq}^{}}{\kappa_P^{}}\, F_1^{B P}\,
\varepsilon_X^*\!\cdot\!p_P^{} ~, \\ \label{M_B2SX}
{\cal M}(\bar B\to S X) &\,=\,&
\frac{2i\, g_{Aq}^{}}{\kappa_S^{}}\, F_1^{B S}\, \varepsilon_X^*\!\cdot\!p_S^{} ~,
\end{eqnarray}
leading to the decay rates
\begin{eqnarray} \label{rate_B2PX}
\Gamma (B \to P (S) X) \,\,=\,\, \frac{|\bm{p}_X^{}|^3}{2\pi\, \kappa_{P (S)}^2\, m_X^2}
\Bigl| g_{V (A) q}^{}\,F_1^{BP (S)} \Bigr|^2 ~,
\end{eqnarray}
where $\bm{p}_X^{}$ is the 3-momentum of $X$ in the rest frame of $B$.
For \,$\bar B\to V X$\, and \,$\bar B\to A X$,\, the amplitudes are
\begin{eqnarray} \label{M_B2VX}
{\cal M}(\bar B\to V X) \,&=&\,
-\frac{i g_{Aq}^{}}{\kappa_V^{}} \Biggl[
A_1^{BV}\, \bigl(m_B^{}+m_V^{}\bigr)\,\varepsilon_V^*\!\cdot\!\varepsilon_X^* \,-\,
\frac{2A_2^{BV}\, \varepsilon_V^*\!\cdot\!p_X^{}\,\varepsilon_X^*\!\cdot\!p_V^{}}
{m_B^{}+m_V^{}} \Biggr]
\nonumber \\ && +\,\,
\frac{2 g_{Vq}^{}\, V^{BV}}{\kappa_V^{}\,\bigl(m_B^{}+m_V^{}\bigr)}\,
\epsilon_{\mu\nu\sigma\tau}^{}\, \varepsilon_V^{*\mu}\varepsilon_X^{*\nu}p_V^\sigma\,p_X^\tau ~,
\end{eqnarray}
\begin{eqnarray} \label{M_B2AX}
{\cal M}(\bar B\to A X) \,&=&\,
-\frac{i g_{Vq}^{}}{\kappa_A^{}} \Biggl[
V_1^{BA}\, \bigl(m_B^{}-m_A^{}\bigr)\,\varepsilon_A^*\!\cdot\!\varepsilon_X^* \,-\,
\frac{2V_2^{BA}\, \varepsilon_A^*\!\cdot\!p_X^{}\,\varepsilon_X^*\!\cdot\!p_A^{}}
{m_B^{}-m_A^{}} \Biggr]
\nonumber \\ && +\,\,
\frac{2 g_{Aq}^{}\, A^{BA}}{\kappa_A^{}\,\bigl(m_B^{}-m_A^{}\bigr)}\, \epsilon_{\mu\nu\sigma\tau}^{}\,
\varepsilon_A^{*\mu}\varepsilon_X^{*\nu}p_A^\sigma\, p_X^\tau ~.
\end{eqnarray}
The corresponding decay rates can be conveniently written as~\cite{Kramer:1991xw}
\begin{eqnarray} \label{rate_B2VX}
\Gamma(B\to M'X) \,\,=\,\, \frac{|\bm{p}_X^{}|}{8\pi\, m_B^2}
\Bigl( \bigl|H_0^{M'}\bigr|^2 + \bigl|H_+^{M'}\bigr|^2 + \bigl|H_-^{M'}\bigr|^2 \Bigr) ~,
\end{eqnarray}
where \,$M'=V$ or $A$,\, \,$H_0^{M'}=-a_{M'}^{}\,x_{M'}^{}-b_{M'}^{}\bigl(x_{M'}^2-1\bigr)$,\,
and \,$H_\pm^{M'}=a_{M'}^{}\pm c_{M'}\,\sqrt{x_{M'}^2-1}$,\,
with \,$x_{M'}^{}=\bigl(m_B^2 - m_{M'}^2 - m_X^2\bigr)/\bigl(2 m_{M'}^{}m_X^{}\bigr)$,\,
\begin{eqnarray} \label{abcV}
a_V^{} &=& \frac{g_{Aq}^{}\, A_1^{BV}}{\kappa_V^{}}\bigl(m_B^{}+m_V^{}\bigr) ~, \hspace{5ex}
b_V^{} \,=\, \frac{-2 g_{Aq}^{}\, A_2^{BV} m_V^{} m_X^{}}{\kappa_V^{}\,\bigl(m_B^{}+m_V^{}\bigr)} ~,
\hspace{5ex}
c_V^{} \,=\, \frac{2 g_{Vq}^{}\, m_V^{} m_X^{} V^{BV}}{\kappa_V^{}\,\bigl(m_B^{}+m_V^{}\bigr)} ~,
~~~~~ \\ \label{abcA}
a_A^{} &=& \frac{g_{Vq}^{}\, V_1^{BA}}{\kappa_A^{}}\bigl(m_B^{}-m_A^{}\bigr) ~, \hspace{5ex}
b_A^{} \,=\, \frac{-2 g_{Vq}^{}\, V_2^{BA}m_A^{}m_X^{}}{\kappa_A^{}\,\bigl(m_B^{}-m_A^{}\bigr)} ~,
\hspace{5ex}
c_A^{} \,=\, \frac{2 g_{Aq}^{}\, m_A^{} m_X^{} A^{BA}}{\kappa_A^{}\,\bigl(m_B^{}-m_A^{}\bigr)} ~.
\end{eqnarray}
In the next section, we employ the expressions found above to extract constraints on
the couplings $g_{Vq}^{}$ and $g_{Aq}^{}$ from currently available experimental information.
We will subsequently use the results to predict upper bounds for the branching ratios of
a number of $B$ decays.
Before proceeding, we remark that we have not included in ${\cal L}_{bqX}$ in Eq.~(\ref{LbqX})
the possibility of dipole operators of the form
\,$\bar q\sigma^{\mu\nu}(1\pm\gamma_5^{})b\,\partial_\mu X_\nu$.\,
They would contribute to the processes dealt with above, except for \,$B_q^{}\to\mu^+\mu^-$.\,
However, we generally expect the effects of these operators to be suppressed compared to those
of ${\cal L}_{bqX}$ by a factor of order \,$p_X^{}/\Lambda\sim m_b^{}/\Lambda$,\,
with $\Lambda$ being a heavy mass representing the new-physics scale, if their contributions all
occur simultaneously.
\section{Numerical Analysis}
\subsection{Constraints from \boldmath$B_q$-$\bar B_q$ mixing}
As discussed in the preceding section, the $X$ contribution $M_{12}^{q,X}$ to $B_q$-$\bar B_q$
mixing is related to the observable \,$\Delta M_q=2\,|M_{12}^{q}|$,\, where
\,$M_{12}^q=M_{12}^{q,\rm SM}+M_{12}^{q,X}$.\,
The experimental value $\Delta M_q^{\rm exp}$ can then be expressed in terms of the SM
prediction $\Delta M_q^{\rm SM}$ as
\begin{eqnarray} \label{DM}
\Delta M_q^{\rm exp} \,\,=\,\, \Delta M_q^{\rm SM}\,\bigl|1+\delta_q^{}\bigr| \,\,,
\hspace{5ex} \delta_q^{} \,\,=\,\, \frac{M_{12}^{q,X}}{M_{12}^{q,\rm SM}} \,\,,
\end{eqnarray}
and so numerically they can lead to the allowed range of $\delta_q$,
from which we can extract the bounds on $g_{Vq,Aq}^{}$.
Thus, with \,$\Delta M_d^{\rm exp}=(0.507\pm0.005){\rm\,ps}^{-1}$\,~\cite{pdg} and
\,$\Delta M_d^{\rm SM}=\bigl(0.560^{+0.067}_{-0.076}\bigr){\rm\,ps}^{-1}$\,~\cite{ckmfit},
using the approximation \,$\bigl|1+\delta_d^{}\bigr|\simeq 1+{\rm Re}\,\delta_d$,\,
we can extract the $1 \sigma$ range
\begin{eqnarray} \label{delta_d}
-0.22 \,\,<\,\, {\rm Re}\,\delta_d^{} \,\,<\,\, +0.03 ~.
\end{eqnarray}
Similarly, \,$\Delta M_s^{\rm exp}=(17.77\pm0.12){\rm\,ps}^{-1}$\,~\cite{pdg} and
\,$\Delta M_s^{\rm SM}=(17.6^{+1.7}_{-1.8}){\rm\,ps}^{-1}$\,~\cite{ckmfit} translate into
\begin{eqnarray} \label{delta_s}
-0.09 \,\,<\,\, {\rm Re}\,\delta_s^{} \,\,<\,\, 0.11 ~.
\end{eqnarray}
To proceed, in addition to \,$m_X^{}=214.3$\,MeV,\, we use
\,$m_b^{}=4.4$\,GeV,\, \,$P_1^{\rm VLL}=0.84$,\, \,$P_1^{\rm SLL}=-1.47$,\,
\,$P_1^{\rm LR}=-1.62$,\, \,$P_2^{\rm LR}=2.46$\,~\cite{Buras:2001ra},
CKM parameters from Ref.~\cite{ckmfit},
\,$f_{B_d}=190$\,MeV,\, \,$f_{B_s}=228$\,MeV,\, \,$\eta_B^{}=0.551$,\, \,$B_{B_d}=1.17$,\,
and \,$B_{B_s}=1.23$\,~\cite{ckmfit,Buchalla:1995vs},
as well as meson masses from Ref.~\cite{pdg}.
Also, we will neglect $m_d^{}$ and $m_s^{}$ compared to $m_b^{}$.
It follows that for the ratio in Eq.~(\ref{DM})
\begin{eqnarray} \label{red}
{\rm Re}\,\delta_d^{} &=& \Bigl\{-4.4\,\Bigl[({\rm Re}\,g_{Vd}^{})^2-({\rm Im}\,g_{Vd}^{})^2\Bigr]
- 8.2\, ({\rm Re}\,g_{Vd}^{})({\rm Im}\,g_{Vd}^{}) \nonumber \\ && ~
+\, 17\,\Bigl[({\rm Re}\,g_{Ad}^{})^2-({\rm Im}\,g_{Ad}^{})^2\Bigr]
+ 33\,({\rm Re}\,g_{Ad}^{})({\rm Im}\,g_{Ad}^{}) \Bigr\}\times10^{12} ~,
\nonumber \\ \phantom{|^{\int^|}}
{\rm Re}\,\delta_s^{} &=& \Bigl\{-2.5\,\Bigl[({\rm Re}\,g_{Vs}^{})^2-({\rm Im}\,g_{Vs}^{})^2\Bigr]
+ 0.2\, ({\rm Re}\,g_{Vs}^{})({\rm Im}\,g_{Vs}^{}) \nonumber \\ && ~
+ 9.9\,\Bigl[({\rm Re}\,g_{As}^{})^2-({\rm Im}\,g_{As}^{})^2\Bigr]
- 0.7\, ({\rm Re}\,g_{As}^{})({\rm Im}\,g_{As}^{}) \Bigr\}\times10^{11} ~.
\end{eqnarray}
Hence constraints on the couplings come from combining these formulas
with Eqs.~(\ref{delta_d}) and~(\ref{delta_s}).
If only $g_{Vq}^{}$ or $g_{Aq}^{}$ contributes at a time, the resulting constraints are
\begin{eqnarray} \label{Bmix_bounds}
&& -0.7\times10^{-14} \,\,<\,\, ({\rm Re}\,g_{Vd}^{})^2-({\rm Im}\,g_{Vd}^{})^2
+ 1.9\, ({\rm Re}\,g_{Vd}^{})({\rm Im}\,g_{Vd}^{}) \,\,<\,\, 5.0\times10^{-14} ~,
\nonumber \\ \phantom{|^{\int}}
&& -1.3\times10^{-14} \,\,<\,\, ({\rm Re}\,g_{Ad}^{})^2-({\rm Im}\,g_{Ad}^{})^2
+ 1.9\, ({\rm Re}\,g_{Ad}^{})({\rm Im}\,g_{Ad}^{}) \,\,<\,\, 0.2\times10^{-14} ~,
\\ \phantom{|^{\int}}
&& -4.4\times10^{-13} \,\,<\,\, ({\rm Re}\,g_{Vs}^{})^2-({\rm Im}\,g_{Vs}^{})^2
- 0.1\, ({\rm Re}\,g_{Vs}^{})({\rm Im}\,g_{Vs}^{}) \,\,<\,\, 3.6\times10^{-13} ~,
\nonumber \\ \phantom{|^{\int}}
&& -0.9\times10^{-13} \,\,<\,\, ({\rm Re}\,g_{As}^{})^2-({\rm Im}\,g_{As}^{})^2
- 0.1\, ({\rm Re}\,g_{As}^{})({\rm Im}\,g_{As}^{}) \,\,<\,\, 1.1\times10^{-13} ~.
\end{eqnarray}
If one assumes instead that $g_{Vq,Aq}^{}$ are real, then from Eqs.~(\ref{delta_d})-(\ref{red})
one can determine the allowed ranges of the couplings shown in Fig.~\ref{mix_bounds}.
\begin{figure}[ht] \vspace*{3ex}
\includegraphics[height=2.5in,width=2.6in]{fig_gv_ga_Bd_mixing.eps} \hspace{5ex}
\includegraphics[width=2.5in,trim=0 0 0 0,clip]{fig_gv_ga_Bs_mixing.eps} \vspace*{-1ex}
\caption{Parameter space of $g_{Vq}^{}$ and $g_{Aq}^{}$ subject to constraints from
$B_q$-$\bar B_q$ mixing, \,$q=d,s$,\, if $g_{Vq,Aq}^{}$ are taken to be real.\label{mix_bounds}}
\end{figure}
\subsection{Constraints from leptonic decays \,\boldmath$B_q\to\mu^+\mu^-$}
As the \,$B_q\to\mu^+\mu^-$\, width in Eq.~(\ref{rate_B2ll}) indicates, to determine
$g_{Aq}^{}$ requires knowing the $X\mu\mu$ coupling constant~$g_{A\mu}^{}$.
Since ${\cal L}_{\mu X}$ in Eq.~(\ref{LlX}) generates the contribution of $X$ to
the muon anomalous magnetic moment~$a_\mu^{}$, we may gain information on $g_{A\mu}^{}$
from~$a_\mu^{}$.
The $X$ contribution is calculated to be~\cite{He:2005we,Leveille:1977rc}
\begin{eqnarray} \label{amuX}
a_\mu^X \,\,=\,\,
\frac{m^2_\mu}{4\pi^2m^2_X}\bigl(g_{V\mu}^2\,f_V^{}(r)+g_{A\mu}^2\,f_A^{}(r)\bigr) \,\,=\,\,
1.1\times10^{-3}\,g_{V\mu}^2 \,-\, 9.0\times10^{-3}\,g_{A\mu}^2 ~,
\end{eqnarray}
where \,$r=m^2_\mu/m^2_X$,\,
\begin{eqnarray}
f_V^{}(r) \;=\; \int^1_0 dx\, \frac{x^2-x^3}{1-x +r x^2} ~, \hspace{5ex}
f_A^{}(r) \;=\; \int^1_0 dx\, \frac{-4 x+5 x^2-x^3-2r x^3}{1-x +r x^2} ~.
\end{eqnarray}
Presently there is a discrepancy of $3.2\sigma$ between the SM prediction for $a_\mu^{}$ and
its experimental value,
\,$\Delta a_\mu^{}=a_\mu^{\rm exp}-a_\mu^{\rm SM} =
(29\pm9)\times10^{-10}$\,~\cite{Jegerlehner:2009ry},
with \,$a_\mu^{\rm exp}=(11659208\pm6)\times 10^{-10}$\,~\cite{pdg}.
Consequently, since the $g_{V\mu}^{}$ and $g_{A\mu}^{}$ terms in $a_\mu^X$ are opposite in sign,
we require that \,$0<a_\mu^X<3.8\times10^{-9}$,\, which corresponds to the allowed parameter
space plotted in Fig.~\ref{amu_bounds}.
Avoiding tiny regions where the two terms in Eq.~(\ref{amuX}) have to conspire subtly to satisfy
the $a_\mu^X$ constraint, we then have
\begin{eqnarray}
g_{V\mu}^2 \,\,\lesssim\,\, 1\times10^{-5} ~, \hspace{5ex}
g_{A\mu}^2 \,\,\lesssim\,\, 1\times10^{-6} ~,
\end{eqnarray}
provided that \,$0<1.1\,g_{V\mu}^2-9.0\,g_{A\mu}^2<3.8\times10^{-6}$.\,
We note that combining these requirements for $g_{V\mu}^{}$ and $g_{A\mu}^{}$ with
Eq.~(\ref{rate_X2ll}) results in the width
\,$\Gamma\bigl(X\to\mu^+\mu^-\bigr)\lesssim1.8\times10^{-8}$\,GeV.\footnote{It is
worth mentioning here that in Ref.~\cite{He:2005we} the number for
\,$\Gamma\bigl(X_A\to\mu^+\mu^-\bigr)$\, in their Eq.~(18), corresponding to \,$g_{V\mu}^{}=0$\,
and \,$g_{A\mu}^2=6.7\times10^{-8}$,\, is too large by a factor of~3.}\,
Assuming that \,$B_{d,s}\to X^*\to\mu^+\mu^-$\, saturates the latest measured bounds
\,${\cal B}\bigl(B_d\to\mu^+\mu^-\bigr)<6.0\times 10^{-9}$\, and
\,${\cal B}\bigl(B_s\to\mu^+\mu^-\bigr)<3.6\times 10^{-8}$\,~\cite{hfag}, respectively,
we use Eq.~(\ref{rate_B2ll}) with \,$g_{A\mu}^2=1\times 10^{-6}$\, to extract
\begin{eqnarray} \label{B2ll_bounds}
|g_{Ad}^{}|^2 \,\,<\,\, 2.8\times10^{-14} ~, \hspace{5ex}
|g_{As}^{}|^2 \,\,<\,\, 1.2\times10^{-13} ~,
\end{eqnarray}
which are roughly comparable to the corresponding limits in Eq.~(\ref{Bmix_bounds})
from $B_q$-$\bar B_q$ mixing.
\begin{figure}[ht] \vspace*{2ex}
\includegraphics[width=2.5in]{fig_gv_ga_amu.eps} \vspace*{-1ex}
\caption{Parameter space of $g_{V\mu}^{}$ and $g_{A\mu}^{}$ subject to constraints from
the muon anomalous magnetic moment.\label{amu_bounds}} \vspace*{-3ex}
\end{figure}
\subsection{Constraints from inclusive decay \,\boldmath$b\to q\mu^+\mu^-$}
Since there is still no experimental data on the inclusive \,$b\to d\mu^+\mu^-$,\,
we consider only the \,$q=s$\, case.
Thus, employing Eq.~(\ref{rate_b2qX}) and the $B_d^0$ lifetime~\cite{pdg}, we find
\begin{eqnarray} \label{rate_b2sX}
{\cal B}(b\to s X) \,\,\simeq\,\, \frac{\Gamma(b\to s X)}{\Gamma_{B_d^0}}
\,\,=\,\, 8.55\times10^{13}\,\bigl(|g_{Vs}^{}|^2+|g_{As}^{}|^2\bigr) \,\,.
\end{eqnarray}
To get constrains on $g_{Vs,As}^{}$, it is best to examine the measured partial rate for
the smallest $m_{\mu\mu}^{}$ bin available which contains \,$m_{\mu\mu}^{}=m_X^{}$.\,
The most recent data have been obtained by the BaBar and Belle
collaborations~\cite{Aubert:2004it,Iwasaki:2005sy}, the former giving the more restrictive
\begin{eqnarray}
{\cal B}(b\to s\ell^+\ell^-)_{m_{\ell\ell}^{}\in[0.2{\rm\,GeV},1.0{\rm\,GeV}]} \,\,=\,\,
\bigl(0.08\pm 0.36^{+0.07}_{-0.04}\bigr)\times 10^{-6} ~,
\end{eqnarray}
which is the average over \,$\ell=e$ and~$\mu$.
This data allows us to demand that the $X$ contribution be below its 90\%-C.L.
upper-bound.
With \,${\cal B}(X\to\mu^+\mu^-)=1$,\, it follows that
\begin{eqnarray}
{\cal B}(b\to s X) \,\,<\,\, 6.8\times 10^{-7} ~,
\end{eqnarray}
which in combination with Eq.~(\ref{rate_b2sX}) implies
\begin{eqnarray} \label{incl_bound}
|g_{Vs}^{}|^2 \,+\, |g_{As}^{}|^2 \,\,<\,\, 8.0\times 10^{-21} ~.
\end{eqnarray}
\subsection{Constraints from exclusive decays \,\boldmath$B\to P\mu^+\mu^-$}
It can be seen from Eq.~(\ref{M_B2PX}) that only the vector coupling $g_{Vq}^{}$ is relevant to
the \,$B\to P X$ decay, not~$g_{Aq}^{}$.
As mentioned earlier, the possibility of $X$ having vector couplings was not considered in
Ref.~\cite{Chen:2006xja}, and therefore \,$B\to PX$\, decays were not studied therein.
Currently there is experimental information available on
\,$B\to\pi\mu^+\mu^-$\, and \,$B\to K\mu^+\mu^-$\, that can be used to place constraints
on~$g_{Vq}^{}$. For the form factors $F_1^{BP}$, since they are functions of
\,$k^2=(p_B^{}-p_P^{})^2=m_X^2\ll m_B^2$,\,
it is a good approximation to take their values at \,$k^2=0$.\,
Thus, for \,$B\to(\pi,K)$\, we adopt those listed in Table~\ref{table1}.
Using Eq.~(\ref{rate_B2PX}), we then obtain
\begin{eqnarray} \label{rate_B2piX}
&& {\cal B} (B^+\to\pi^+ X) \,\,=\,\, 1.06\times10^{13}\, |g_{Vd}^{}|^2 ~, \hspace{5ex}
{\cal B}\bigl(B_d \to\pi^0X\bigr) \,\,=\,\, 4.96\times10^{12}\, |g_{Vd}^{}|^2 ~, ~~~
\\ && \hspace*{10ex}
{\cal B}\bigl(B^+\to K^+X\bigr) \,\,\simeq\,\, {\cal B}\bigl(B_d \to K^0X\bigr) \,\,=\,\,
1.85\times10^{13}\, |g_{Vs}^{}|^2 ~. \phantom{|^{\int}} \label{rate_B2KX}
\end{eqnarray}
Experimentally, at present there are only upper limits for \,${\cal B}(B\to\pi\mu^+\mu^-)$,\,
namely~\cite{hfag,Wei:2008nv}
\begin{eqnarray}
{\cal B}(B^+\to\pi^+\mu^+\mu^-) \,\,<\,\, 6.9 \times 10^{-8} ~, \hspace{5ex}
{\cal B}\bigl(B_d \to\pi^0\mu^+\mu^-\bigr) \,\,<\,\, 1.84 \times 10^{-7}
\end{eqnarray}
at 90\%~C.L.
Assuming that the contributions of \,$B\to\pi X\to\pi\mu^+\mu^-$\, saturate these bounds
and using Eq.~(\ref{rate_B2piX}) along with \,${\cal B}(X\to\mu^+\mu^-)=1$,\,
we find from the more stringent of them
\begin{eqnarray} \label{B2PX_bound}
|g_{Vd}^{}|^2 \,\,<\,\, 6.5 \times 10^{-21} ~.
\end{eqnarray}
For \,$B\to K\mu^+\mu^-$,\, there is data on the partial branching ratio that is pertinent
to \,$B\to K X$.\, The latest measurement provides
\,${\cal B}(B\to K\mu^+\mu^-)_{m_{\mu\mu}\le2{\rm\,GeV}}=
\bigl(0.81^{+0.18}_{-0.16}\pm0.05\bigr)\times 10^{-7}$\,~\cite{Wei:2009zv}.
The corresponding SM prediction is consistent with this data~\cite{Antonelli:2009ws}
and has an uncertainty of about~30\%~\cite{Bobeth:2007dw}. In view of this, we can
demand that \,${\cal B}(B\to K X\to K\mu^+\mu^-)$\, be less than 40\% of the central
value of the measured result.\footnote{In estimating ${\cal B}(B\to M X\to M\mu^+\mu^-)$,
we neglect the interference in the \,$B\to M\mu^+\mu^-$\, rate between the SM and $X$
contributions because $X$ is very narrow, having a width of \,$\Gamma_X\lesssim10^{-8}$\,GeV,\,
as found earlier.}
Thus, with \,${\cal B}(X\to\mu^+\mu^-)=1$,\, we have
\begin{eqnarray}
{\cal B}(B\to K X) \,\,<\,\, 3.2\times 10^{-8} ~.
\end{eqnarray}
Comparing this limit with Eq.~(\ref{rate_B2KX}) results in
\begin{eqnarray} \label{B2KX_bound}
|g_{Vs}^{}|^2 \,\,<\,\, 1.7\times 10^{-21} ~,
\end{eqnarray}
which is stronger than the $g_{Vs}^{}$ bound inferred from Eq.~(\ref{incl_bound}).
One can expect much better bounds on $g_{Vq}^{}$ from future measurements of
\,$B\to(\pi,K)\mu^+\mu^-$\, with $m_{\mu\mu}^{}$ values restricted within a small region
around \,$m_{\mu\mu}^{}=m_X^{}$.\,
\begin{table}[t]
\caption{Form factors relevant to \,$B\to P X$~\cite{Ball:2007hb}.} \smallskip
\begin{tabular}{|c|ccccccc|}
\hline
$$ & $\vphantom{\sum_|^|}\,$ $B_d\to\pi$ \, & \, $B_d\to\eta$ \, & \, $B_d\to\eta'$ \, &
\, $B_s\to K$ \, & \, $B_d\to K$ \, & \, $B_c\to D_d^+$ \, & \, $B_c\to D_s^+$ \, \\
\hline
\, $F_1^{BP}(0)\vphantom{\int_|^{|^|}}$ \, & 0.26 & 0.23 & 0.19 & 0.30 & 0.36 & 0.22 & 0.16 \\
\hline
\end{tabular} \label{table1} \medskip
\end{table}
\subsection{Constraints from exclusive decays \,\boldmath$B\to V\mu^+\mu^-$}
\begin{table}[b]
\caption{Form factors relevant to \,$B\to V X$~\cite{Ball:2004rg}.} \smallskip
\begin{tabular}{|c|ccccccc|}
\hline
\, $\vphantom{\sum_|^|}$\, & \, $B_d\to\rho$ \, & \, $B_d\to\omega$ \, & \, $B_s\to K^*$ \, &
\, $B_d\to K^*$ \, & \, $B_s\to\phi$ \, & \, $B_c\to D_d^{*+}$ \, & \, $B_c\to D_s^{*+}$ \, \\
\hline
\, $V^{BV}(0)\vphantom{\sum_|^|}$ \, & 0.32 & 0.29 & 0.31 & 0.41 & 0.43 & 0.63 & 0.54 \\
$A_1^{BV}(0)\vphantom{\sum_|^|}$ & 0.24 & 0.22 & 0.23 & 0.29 & 0.31 & 0.34 & 0.30 \\
$A_2^{BV}(0)\vphantom{\sum_|^|}$ & 0.22 & 0.20 & 0.18 & 0.26 & 0.23 & 0.41 & 0.36 \\
\hline
\end{tabular} \label{table2}
\end{table}
For \,$B\to V X$\, decays, the values of the relevant form factors at \,$k^2=0$\, are
listed in Table~\ref{table2}.
Employing those for \,$B=B_d$\, and \,$V=\rho,K^*$\, in Eq.~(\ref{rate_B2VX}), we find
\begin{eqnarray} \label{Br_rhoX1}
{\cal B}\bigl(B_d\to\rho^0 X\bigr) &=&
1.77 \times 10^{10}\,|g_{Vd}^{}|^2 + 6.18\times 10^{12}\,|g_{Ad}^{}|^2 ~, \nonumber \\
{\cal B}\bigl(B_d\to K^{*0}X\bigr) &=& \vphantom{|^{\int}}
5.45 \times 10^{10}\,|g_{Vs}^{}|^2 + 1.79\times 10^{13}\,|g_{As}^{}|^2 ~.
\end{eqnarray}
It is worth noting here that the dominance of the $g_{Aq}^{}$ terms in the preceding
formulas over the $g_{Vq}^{}$ terms also occurs in other \,$B\to V X$\, transitions and
corresponds to the fact that in the decay rate, Eq.~(\ref{rate_B2VX}), the $g_{Aq}^{}$ term
$|H_0^V|^2$ is significantly enhanced with respect to the $g_{Vq}^{}$ term
in~$|H_+^V|^2+|H_-^V|^2$.
Currently there is no published measurement of \,${\cal B}(B\to\rho\mu^+\mu^-)$,\,
but there are publicly available experimental data on \,${\cal B}(B\to K^*\mu^+\mu^-)$\,
for the $m_{\mu\mu}^{}$ bin containing \,$m_{\mu\mu}^{}=m_X^{}$,\, the most precise being
\,${\cal B}(B\to K^*\mu^+\mu^-)_{m_{\mu\mu}\le2\rm\,GeV}=
\bigl(1.46_{-0.35}^{+0.40}\pm0.11\bigr)\times10^{-7}$\,~\cite{Wei:2009zv}.
The corresponding SM prediction agrees with this data~\cite{Antonelli:2009ws}
and has an uncertainty of about~30\%~\cite{Beneke:2004dp}.
This suggests requiring \,${\cal B}(B\to K^*X\to K^*\mu^+\mu^-)$\, to be less than 40\% of
the central value of the measured result.
Thus, with \,${\cal B}(X\to\mu^+\mu^-)=1$,\, we have
\begin{eqnarray} \label{B_B2KX}
{\cal B}\bigl(B_d\to K^{*0} X\bigr) \,\,<\,\, 5.8\times10^{-8} ~.
\end{eqnarray}
In addition, very recently the Belle collaboration has provided a preliminary report on their
search for $X$ with spin~1 in \,$B\to\rho X\to\rho\mu^+\mu^-$\, and
\,$B\to K^*X\to K^*\mu^+\mu^-$.\,
They did not observe any event and reported the preliminary bounds~\cite{belle}
\begin{eqnarray}
{\cal B}\bigl(B_d\to\rho^0X,\,\rho^0\to\pi^+\pi^-{\rm\,\,and\,\,}X\to\mu^+\mu^-\bigr) &<&
0.81\times 10^{-8} ~, \nonumber \\
{\cal B}\bigl(B_d\to K^{*0}X,\,K^{*0}\to K^+\pi^-{\rm\,\,and\,\,}X\to\mu^+\mu^-\bigr) &<&
1.53\times 10^{-8} \vphantom{|^{\int}}
\end{eqnarray}
at 90\%~C.L.
Since \,${\cal B}(\rho^0\to\pi^+\pi^-)\simeq1$\, and \,${\cal B}(K^{*0}\to K^+\pi^-)\simeq2/3$,\,
these numbers translate into
\begin{eqnarray} \label{B_B2VX}
{\cal B}\bigl(B_d\to\rho^0X\bigr) \,\,<\,\, 0.81\times 10^{-8} ~, \hspace{5ex}
{\cal B}\bigl(B_d\to K^{*0}X\bigr) \,\,<\,\, 2.3\times 10^{-8} ~,
\end{eqnarray}
the second one being more restrictive than the constraint in Eq.~(\ref{B_B2KX}).
In the absence of more stringent limits, in the following we use these numbers inferred from
the preliminary Belle results.
Accordingly, applying the limits in Eq.~(\ref{B_B2VX}) to Eq.~(\ref{Br_rhoX1}) yields
\begin{eqnarray} \label{B2rX_bound}
0.00286\,|g_{Vd}^{}|^2 \,+\, |g_{Ad}^{}|^2 &<& 1.3\times10^{-21} ~, \\ \label{B2KsX_bound}
0.00304\,|g_{Vs}^{}|^2 \,+\, |g_{As}^{}|^2 &<& 1.3\times10^{-21} ~. \vphantom{|^{\int}}
\end{eqnarray}
The $g_{As}^{}$ bound implied from the last equation can be seen to be stricter than that
from Eq.~(\ref{incl_bound}).
From Eqs.~(\ref{B2PX_bound}), (\ref{B2KX_bound}), (\ref{B2rX_bound}), and (\ref{B2KsX_bound}),
we can then extract the individual limits
\begin{eqnarray} \label{gd_bounds}
|g_{Vd}^{}|^2 \,\,<\,\, 6.5\times10^{-21} ~, & ~~~~~ &
|g_{Ad}^{}|^2 \,\,<\,\, 1.3\times10^{-21} ~, \\ \label{gs_bounds}
|g_{Vs}^{}|^2 \,\,<\,\, 1.7\times10^{-21} ~, & ~~~~~ &
|g_{As}^{}|^2 \,\,<\,\, 1.3\times10^{-21} ~. \vphantom{|^{\int}}
\end{eqnarray}
These bounds are clearly much stronger than those in Eqs.~(\ref{Bmix_bounds}) and~(\ref{B2ll_bounds})
derived from $B_q^0$-$\bar B_q^0$ mixing and \,$B_q^0\to\mu^+\mu^-$,\, respectively.
Also, combining Eqs.~(\ref{B2PX_bound}) and~(\ref{B2rX_bound}), we have plotted the allowed parameter
space of $g_{Vd}^{}$ and $g_{Ad}^{}$ in Fig.~\ref{g_plots}(a) under the assumption that they
are real. Similarly, Fig.~\ref{g_plots}(b) shows the $g_{Vs}^{}$-$g_{As}^{}$ region allowed
by Eqs.~(\ref{B2KX_bound}) and~(\ref{B2KsX_bound}).
\begin{figure}[ht]
\includegraphics[height=2.5in,width=2.5in]{fig_gvd_gad.eps} \hspace{5ex}
\includegraphics[height=2.5in,width=2.5in]{fig_gvs_gas.eps} \vspace*{-1ex}
\caption{Parameter space of $g_{Vq}^{}$ and $g_{Aq}^{}$, taken to be real, subject to constraints on
(a)~$B\to\pi X$ (lightly shaded, yellow region), \,$B\to\rho X$ (medium shaded, green region),
and both of them (heavily shaded, red region) and
(b)~$B\to K X$ (lightly shaded, yellow region), \,$B\to K^*X$ (medium shaded, green region),
and both of them (heavily shaded, red region).\label{g_plots}}
\end{figure}
\subsection{Predictions for \,\boldmath$B\to MX$\, decays, \,$M=P,V,S,A$}
We can now use the results above to predict the upper limits for branching ratios of
a number of additional $B$-decays involving $X$. Specifically, we explore two-body decays of
$B_{d,s}^0$ and $B_{u,c}^{}$ into $X$ and some of the lightest mesons~$M$.
We deal with \,$M=P$, $V$, $S$, and $A$\, in turn.
The $g_{Vd}^{}$ bound in Eq.~(\ref{gd_bounds}) leads directly to limits on
the branching ratios of \,$B_d^0\to\pi^0X$,\, \,$B_d^0\to\eta^{(\prime)}X$,\,
\,$B_s^0\to K^0X$,\, and \,$B_c^{}\to D_d^+X$.\,
Thus, from Eq.~(\ref{rate_B2piX}) follows
\begin{eqnarray}
{\cal B}\bigl(B_d^0\to\pi^0X\bigr) \,\,<\,\, 3.2\times10^{-8} ~.
\end{eqnarray}
Furthermore, employing Eq.~(\ref{rate_B2PX}) and Table~\ref{table1}, with
\,$\kappa_\eta^{}=\kappa_{\eta'}^{}=\sqrt2$,\, one gets
\begin{eqnarray}
{\cal B}\bigl(B_d^0\to\eta X\bigr) \,\,<\,\, 2.4\times10^{-8} ~, & ~~~~~ &
{\cal B}\bigl(B_d^0\to\eta'X\bigr) \,\,<\,\, 1.6\times10^{-8} ~, \nonumber \\
{\cal B}\bigl(B_s^0\to K^0X\bigr) \,\,<\,\, 8.2\times10^{-8} ~, & ~~~~~ &
{\cal B}\bigl(B_c^{}\to D_d^+X\bigr) \,\,<\,\, 1.7\times10^{-8} ~. \vphantom{|^{\int}}
\end{eqnarray}
Similarly, the $g_{Vs}^{}$ bound in Eq.~(\ref{gs_bounds}) implies
\begin{eqnarray}
&& {\cal B}\bigl(B_s^0\to\eta X\bigr) \,\,<\,\, 1.2\times10^{-8} ~, \hspace{5ex}
{\cal B}\bigl(B_s^0\to\eta'X\bigr) \,\,<\,\, 1.7\times10^{-8} ~, \nonumber \\ && \hspace*{15ex}
{\cal B}\bigl(B_c^{}\to D_s^+X\bigr) \,\,<\,\, 2.3\times10^{-9} ~, \vphantom{|^{\int}}
\end{eqnarray}
where the first two numbers have been calculated using \,$\kappa_\eta^{}=\kappa_{\eta'}^{}=1$,\,
\,$F_1^{B_s\eta}(0)=-F_1^{B_dK}(0)\,\sin\varphi$,\, and
\,$F_1^{B_s\eta'}(0)=F_1^{B_dK}(0)\,\cos\varphi$\,~\cite{Carlucci:2009gr}, with $F_1^{B_dK}(0)$
from Table~\ref{table1} and \,$\varphi=39.3^\circ$\,~\cite{Feldmann:1998vh}.
The $g_{Vq}^{}$ and $g_{Aq}^{}$ bounds in Eqs.~(\ref{gd_bounds}) and~(\ref{gs_bounds}),
together with Fig.~\ref{g_plots}, lead to upper limits for the branching ratios of
several other \,$B\to V X$\, decays.
Thus, combining Eq.~(\ref{rate_B2VX}) with the relevant form-factors in Table~\ref{table2}
yields for \,$q=d$\,
\begin{eqnarray}
{\cal B}(B^+\to\rho^+X) \,\,<\,\, 1.7\times 10^{-8}~, & ~~~~~ &
{\cal B}\bigl(B_d^0\to\omega X\bigr) \,\,<\,\, 7.0\times 10^{-9} ~, \nonumber \\
{\cal B}\bigl(B_s^0\to K^{*0}X\bigr) \,\,<\,\, 2.2\times 10^{-8} ~, & ~~~~~ &
{\cal B}\bigl(B_c^{}\to D_d^{*+}X\bigr) \,\,<\,\, 5.0\times 10^{-9} \vphantom{|^{\int}}
\end{eqnarray}
and for \,$q=s$\,
\begin{eqnarray}
{\cal B}\bigl(B_s^0\to\phi X\bigr) \,\,<\,\, 3.9\times 10^{-8} ~, \hspace{5ex}
{\cal B}\bigl(B_c^{}\to D_s^{*+}X\bigr) \,\,<\,\, 3.9\times 10^{-9} ~,
\end{eqnarray} \nopagebreak
where \,$|\phi\rangle\simeq|s\bar s\rangle$\, has been assumed.
In contrast to the \,$B\to P X$ case, $g_{Aq}^{}$ is the only coupling relevant to
\,$B\to SX$\, decays, as Eq.~(\ref{M_B2SX}) indicates.
From the $g_{Aq}^{}$ bounds found above, we can then estimate the branching ratios of some of
these decays.
Since the quark contents of many of the scalar mesons below 2\,GeV are not yet well established,
we consider only the decays with \,$S=a_0^{}(1450)$ and $K_0^*(1430)$,\, which are perhaps
the least controversial of the light scalar mesons~\cite{pdg}.
Adopting the form-factor values \,$F_1^{B_da_0(1450)}(0)=0.26$\, and
\,$F_1^{B_dK_0^*(1430)}(0)=0.26$\,~\cite{Cheng:2003sm}, we use Eq.~(\ref{rate_B2PX})
with \,$\kappa_S^{}=1$\, for \,$S=a_0^+(1450),K_0^*(1430)$\, and
\,$\kappa_S^{}=-\sqrt2$\, for \,$S=a_0^0(1450)$,\, as well as the $g_{Aq}^{}$ limits in
Eqs.~(\ref{gd_bounds}) and~(\ref{gs_bounds}), to obtain
\begin{eqnarray}
&& {\cal B}\bigl(B^+\to a_0^+(1450)X\bigr) \,\,<\,\, 1.1\times10^{-8} ~, \hspace{5ex}
{\cal B}\bigl(B_d^0\to a_0^0(1450)X\bigr) \,\,<\,\, 5.1\times10^{-9} ~, \nonumber \\ && \hspace*{5ex}
{\cal B}\bigl(B^+\to K_0^{*+}(1430)X\bigr) \,\,\simeq\,\,
{\cal B}\bigl(B_d^0\to K_0^{*0}(1430)X\bigr) \,\,<\,\, 1.0\times10^{-8} ~. \vphantom{|^{\int}}
\end{eqnarray}
Similarly to the \,$B\to V X$\, case, both $g_{Vq,Aq}^{}$ contribute to \,$B\to A X$,\,
as Eq.~(\ref{M_B2AX}) shows.
We will consider the decays with the lightest axial-vector mesons
\,$A=a_1^{}(1260)$, $b_1^{}(1235)$, $K_1(1270)$, and $K_1(1400)$.
The latter two are mixtures of the $K_{1A}$ and $K_{1B}$ states~\cite{pdg}, namely
\,$K_1(1270)=K_{1A}\,\sin\theta+K_{1B}\,\cos\theta$\, and
\,$K_1(1400)=K_{1A}\,\cos\theta-K_{1B}\,\sin\theta$,\, with \,$\theta=58^\circ$,\,
\,$m_{K_{1A}}=1.37$\,GeV,\, and \,$m_{K_{1B}}=1.31$\,GeV\,~\cite{Chen:2005cx}.
Incorporating the bounds in Eqs.~(\ref{gd_bounds}) and~(\ref{gs_bounds}) into
Eq.~(\ref{rate_B2VX}) with \,$\kappa_A^{}=1$\, for \,$S=a_1^+,b_1^+,K_1^{}$\, and
\,$\kappa_A^{}=-\sqrt2$\, for \,$S=a_1^0,b_1^0$,\, as well as the form factors listed
in Table~\ref{table3}, we arrive at
\begin{eqnarray} \label{B2AX}
{\cal B}\bigl(B^+\to a_1^+(1260)X\bigr) &\,\simeq\,&
2 {\cal B}\bigl(B_d^0\to a_1^0(1260)X\bigr) \,\,<\,\, 1.6\times10^{-8} ~, \nonumber \\
{\cal B}\bigl(B^+\to b_1^+(1235)X\bigr) &\,\simeq\,&
2 {\cal B}\bigl(B_d^0\to b_1^0(1235)X\bigr) \,\,<\,\, 1.2\times10^{-7} ~, \vphantom{|^{\int}}
\nonumber \\
{\cal B}\bigl(B^+\to K_1^{*+}(1270)X\bigr) &\,\simeq\,&
{\cal B}\bigl(B_d^0\to K_1^{*0}(1270)X\bigr) \,\,<\,\, 2.6\times10^{-8} ~, \vphantom{|^{\int}}
\nonumber \\
{\cal B}\bigl(B^+\to K_1^{*+}(1400)X\bigr) &\,\simeq\,&
{\cal B}\bigl(B_d^0\to K_1^{*0}(1400)X\bigr) \,\,<\,\, 1.3\times10^{-8} ~. \vphantom{|^{\int}}
\end{eqnarray}
\begin{table}[b]
\caption{Form factors relevant to \,$B\to A X$~\cite{Cheng:2003sm}.} \smallskip
\begin{tabular}{|c|cccc|}
\hline
\, $\vphantom{\sum_|^|}$\, & \, $B_d\to a_1^{}(1260)$ \, & \, $B_d\to b_1^{}(1235)$ \, &
\,\, $B_d\to K_{1A}$ \,\, & \,\, $B_d\to K_{1B}$ \,\, \\
\hline
\, $A^{BA}(0)\vphantom{\sum_|^|}$ \, & 0.25 & 0.10 & 0.26 & 0.11 \\
$V_1^{BA}(0)\vphantom{\sum_|^|}$ & 0.37 & 0.18 & 0.39 & 0.19 \\
$V_2^{BA}(0)\vphantom{\sum_|^|}$ & 0.18 & $-$0.03~~ & 0.17 & $-$0.05~~ \\
\hline
\end{tabular} \label{table3}
\end{table}
Before ending this section, we would like to make a few more remarks regarding our results above.
The branching ratios of \,$B^+\to\rho^+X$,\, \,$B_s^0\to\phi X$,\,
\,$B_d^0\to K_0^*(1430)X$,\, and \,$B\to K_1^{}X$\, were also estimated in
Ref.~\cite{Chen:2006xja} under the assumption that the vector couplings \,$g_{Vd,Vs}^{}=0$.\,
Compared to their numbers, our \,$B^+\to\rho^+X$\, result above is of similar order,
but our numbers for \,$B_s^0\to\phi X$\, and \,$B_d^{}\to K_0^*(1430)X$\, are smaller
by almost two orders of magnitude. This is mostly due to the more recent data that we have
used to extract the $g_{Aq}^{}$ values.
On the other hand, our results for \,$B\to K_1^{}(1270)X,\,K_1^{}(1400)X$\, are larger
than the corresponding numbers in Ref.~\cite{Chen:2006xja} by up to two orders of magnitude.
The main cause of this enhancement is the nonzero contributions of~$g_{Vs}^{}$ to their decay
rates. As one can see in Eq.~(\ref{rate_B2VX}) for the \,$B\to AX$\, rate, the $g_{Vq}^{}$
term in $|H_0^A|^2$ is significantly greater than the $g_{Aq}^{}$ term in
\,$|H_+^A|^2+|H_-^A|^2$.\,
For the same reason, without $g_{Vd}^{}$, the \,$B\to a_1^{}X,\,b_1^{}X$\, branching ratios
in Eq.~(\ref{B2AX}) would be orders of magnitude smaller.
Thus our inclusion of the vector couplings of $X$ has not only given rise to nonvanishing
\,$B\to PX$\, decays, but also helped make most of our predicted \,$B\to M X$\, branching
ratios as large as $10^{-8}$ to $10^{-7}$, which are within the reach of near-future
$B$ measurements.
\section{Conclusions}
Recent searches carried out by the CLEO, BaBar, E391a, KTeV, and Belle collaborations for
the HyperCP particle, $X$, have so far come back negative.
Furthermore, the new preliminary result from KTeV has led to significant experimental
restrictions on the $sdX$ pseudoscalar coupling in the scenario where $X$
is a spinless particle and has negligible four-quark flavor-changing interactions.
In contrast, the possibility that $X$ is a spin-1 particle is not well challenged by
experiment yet.
In this paper, we have investigated some of the consequences of this latter possibility.
Specifically, taking a~model-independent approach, we have allowed $X$ to have both
vector and axial-vector couplings to ordinary fermions.
Assuming that its four-quark flavor-changing contributions are not important compared to
its two-quark $bqX$ interactions, we have systematically studied the contributions of $X$
to various processes involving $b$-flavored mesons, including $B_q$-$\bar B_q$ mixing,
\,$B_q\to\mu^+\mu^-$,\, inclusive \,$b\to q\mu^+\mu^-$,\, and exclusive \,$B\to M\mu^+\mu^-$\,
decays, with \,$q=d,s$\, and $M$ being a spinless or \mbox{spin-1} meson.
Using the latest experimental data, we have extracted bounds on the couplings of $X$ and
subsequently predicted the branching ratios of a number of \,$B\to M X$\, decays, where $M$
is a~pseudoscalar, vector, scalar, or axial-vector meson.
The presence of the vector couplings $g_{Vq}^{}$ of $X$ has caused the decays with
a pseudoscalar $M$ to occur and also greatly enhanced the branching ratios of the decays
with an axial-vector~$M$.
The \,$B\to M X$\, branching ratios that we have estimated can reach the $10^{-7}$ level,
as in the cases of \,$B_s^0\to K^0X$\, and \,$B^+\to b_1^+(1235)X$,\,
which is comparable to the preliminary upper limits for the branching ratios of
\,$B_d\to\rho^0X,\,K^{*0}X$\, recently measured by Belle.
Therefore, we expect that the $B$ decays that we have considered here can be probed by
upcoming $B$ experiments, which may help confirm or rule out the new-particle interpretation
of the HyperCP result.
\acknowledgments
This work was supported in part by NSC and NCTS.
We thank Hwanbae Park and HyoJung Hyun for valuable discussions on experimental results.
We also thank X.G.~He and G.~Valencia for helpful comments.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,248 |
Siergiej Siergiejewicz Prokofjew (, w formie spolszczonej Sergiusz Prokofiew, Siergiej Prokofiew; ur. w Soncowce k. Kurachowa, w Imperium Rosyjskim, zm. 5 marca 1953 w Moskwie, ZSRR) – rosyjski (radziecki) kompozytor, pianista-wirtuoz oraz dyrygent, jeden z najważniejszych twórców awangardy pierwszej połowy XX w. Współtworzył różne nurty modernizmu, w tym futuryzm, ekspresjonizm, prymitywizm i neoklasycyzm (uważany za inicjatora ostatniego z tych kierunków w I Symfonii D-dur "Klasycznej", op. 25, 1917), zachowując przy tym oryginalność i idiomatyczność stylu.
Prokofjew jest autorem szerokiego i różnorodnego repertuaru, obejmującego większość klasycznych form i gatunków: muzyki operowej, baletowej, kantat, oratoriów, muzyki symfonicznej (symfonii, koncertów na fortepian, skrzypce, wiolonczelę, suit, sinfoniett, uwertur i in.), kameralnej (m.in. kwartetów smyczkowych, pieśni, sonat), utworów na fortepian solo (m.in. 9 sonat, Visions fugitives, op. 22), muzyki scenicznej i filmowej, a także transkrypcji.
Popularność zawdzięcza przede wszystkim Symfonii klasycznej, bajce symfonicznej Piotruś i wilk, III koncertowi fortepianowemu C-dur, baletom Romeo i Julia oraz Kopciuszek, suicie Porucznik Kiże oraz muzyce do filmów Siergieja Eisensteina.
Życiorys
Z muzyką Prokofjew zapoznał się w domu rodzinnym dzięki matce, która udzielała mu pierwszych lekcji gry na fortepianie gdy miał 5 lat.
Pierwsze próby kompozytorskie – walce, marsze, dwie opery: Olbrzym i Na bezludnych wyspach, zwróciły uwagę Siergieja Taniejewa. Za jego namową Prokofjew rozpoczął w 1902 roku naukę muzyki (harmonia i kompozycja) u Reinholda Glière'a. Po dwóch latach wstąpił do konserwatorium petersburskiego (harmonia i kontrapunkt – Anatolij Ladow, orkiestracja – Nikołaj Rimski-Korsakow, dyrygentura – N. Czeriepnin, fortepian – Anna Jesipowa). W 1908 wziął po raz pierwszy udział w "Wieczorach muzyki współczesnej" S. Diagilewa. W 1914 roku Prokofjew ukończył konserwatorium jako świetny pianista i kompozytor, odznaczony pierwszą nagrodą za I Koncert fortepianowy. W 1918 roku opuścił kraj, udając się najpierw do Ameryki, później do Francji. Szybko zdobył sławę znakomitego pianisty-wirtuoza i niezwykle oryginalnego kompozytora. W Paryżu nawiązał współpracę z Siergiejem Diagilewem. Pisał dla niego balety: Syn marnotrawny, Nad Dnieprem, Stalowy krok. Tutaj związany był z bardzo kosmopolityczną grupą Triton (obok Milhauda, Honeggera, Poulenca i Martinů). W 1936 roku powrócił na stałe do Rosji, gdzie prócz pracy kompozytorskiej zajmował się pedagogiką prowadząc klasę kompozycji w Konserwatorium w Moskwie.
W całej twórczości Prokofjewa zaobserwować można charakterystyczne dla jego stylu cechy: ogólna antyromantyczność, nieustępliwość rytmiki (często ostinatowej), gwałtowna dynamiczność, liryzm, humorystyczne w intencjach cytowanie znanych zwrotów melodyczno-harmonicznych, uchwytność melodyki, pikanteria harmoniczna i kolorystyczna, ogólna przejrzystość założeń i mistrzowska precyzja ich realizacji.
On sam tak charakteryzował przemiany w swojej muzyce:
Śmierć
Zmarł 5 marca 1953. Tego samego dnia zmarł również przywódca Związku Radzieckiego Józef Stalin. Zgon Stalina skupił na sobie uwagę całego narodu, w związku z czym śmierć kompozytora była nieomalże niezauważona, a państwowe uroczystości żałobne uniemożliwiały przeprowadzenie pogrzebu Prokofjewa. Zbieg tych dwóch wydarzeń stał się także tematem anegdoty, związanej z osobą dyrygenta Grzegorza Fitelberga, dyrektora Wielkiej Orkiestry Symfonicznej Polskiego Radia – dzień po śmierci Stalina i Prokofjewa Fitelberg po przyjściu na próbę orkiestry miał wygłosić mowę ku pamięci wielkiego kompozytora i poprosił o minutę ciszy. Następnie zwrócił się do koncertmistrza Władysława Wochniaka: Władziu, czy to prawda, że umarł Stalin?.
Życie osobiste
Był dwukrotnie żonaty: z Liną Luberą (od 1923), z którą miał dwóch synów, Światosława i Olega, oraz Mirą Mendelson (od 1948), która była jego partnerką od wielu lat w czasie trwania związku małżeńskiego z Liną Luberą.
Instytucje poświęcone kompozytorowi
Jego pierwsza żona, Lina, założyła w 1983 Fundację im. S. Prokofjewa (The Serge Prokofiev Foundation), która w 1994 otrzymała siedzibę w Goldsmiths' College przy Uniwersytecie Londyńskim. Jej celem jest zbieranie środków finansowych na badania twórczości Prokofjewa, a także gromadzenie rękopisów i pamiątek oraz popularyzacja dzieł kompozytora. W latach 2001–2004 funkcjonowało Stowarzyszenie im. Siergieja Prokofjewa (The Serge Prokofiev Association), założone przez Fundację, które wydawało czasopismo Three Oranges oraz kierowało inicjatywą Prokofiev 2003 na 50-lecie śmierci kompozytora. Po rozwiązaniu Stowarzyszenia zadanie wydawania czasopisma przejęła Fundacja.
Najważniejsze dzieła
Opery
Gracz, op. 24 (1915–1916)
Miłość do trzech pomarańczy, op. 33 (1919)
Ognisty anioł, op. 37 (1919–1927)
Siemion Kotko, op. 81 (1939)
Zaręczyny w klasztorze, op. 86 (1940)
Wojna i pokój, op. 91 (1941–1942)
Opowieść o prawdziwym człowieku (1948, Kijów 1961)
Balety
Błazen (Bajka o błaźnie, co siedmiu błaznów przechytrzył), op. 21 (1915–1920)
Stalowy krok, op. 41 (1925)
Syn marnotrawny, op. 46 (1928)
Nad Dnieprem, op. 51 (1930)
Romeo i Julia, op. 64 (1935–1936)
Kopciuszek, op. 87 (1940–1944)
Baśń o kamiennym kwiecie, op. 118 (1948–1950)
Symfonie
I symfonia D-dur "Klasyczna", op. 25 (1916–1917)
II symfonia d-moll, op. 40 (1924)
III symfonia c-moll, op. 44 (1928)
IV symfonia C-dur, op. 47 (1930), ponownie zredagowana w 1947 r. jako op. 112
V symfonia B-dur, op. 100 (1944)
VI symfonia es-moll, op. 111 (1945–1947)
VII symfonia cis-moll, op. 131 (1951–1952)
Koncerty
fortepianowe
I koncert fortepianowy Des-dur, op. 10 (1911–1912)
II koncert fortepianowy g-moll, op. 16 (1913), ponownie zredagowany w 1923 r. jeden z najtrudniejszych koncertów fortepianowych
III koncert fortepianowy C-dur, op. 26 (1917–1921)
IV koncert fortepianowy B-dur (na lewą rękę), op. 53 (1931)
V koncert fortepianowy G-dur, op. 55 (1932)
skrzypcowe
I koncert skrzypcowy D-dur, op. 19 (1916–1917)
II koncert skrzypcowy g-moll, op. 63 (1935)
wiolonczelowe
Symfonia-koncert e-moll na wiolonczelę i orkiestrę, op. 125 (1950–1952); w pierwszej redakcji jako I Koncert wiolonczelowy e-moll op. 58
Concertino g-moll na wiolonczelę i orkiestrę, op. 132 (1952)
Suity i inne utwory orkiestrowe
Jesienny szkic, op. 8 (1910–1914–1934)
Suita scytyjska na wielką orkiestrę symfoniczną, op. 20, mniej znana jako Ała i Łołłij (1915)
Suita symfoniczna z baletu "Błazen", op. 21bis (1922)
Suita symfoniczna z opery "Miłość do trzech pomarańczy", op. 33bis (1924)
Suita symfoniczna z baletu "Nad Dnieprem", op. 51bis (1933)
Suita symfoniczna z filmu "Porucznik Kiże", op. 60 (1933–1934)
I suita symfoniczna z baletu "Romeo i Julia", op. 64bis (1936)
II suita symfoniczna z baletu "Romeo i Julia", op. 64ter (1936)
Piotruś i wilk, op. 67 (1936), bajka symfoniczna dla dzieci na głos recytujący i wielką orkiestrę symfoniczną
III suita symfoniczna z baletu "Romeo i Julia", op. 101 (1946)
I suita symfoniczna z baletu "Kopciuszek", op. 107 (1946)
II suita symfoniczna z baletu "Kopciuszek", op. 108 (1946)
III suita symfoniczna z baletu "Kopciuszek", op. 109 (1946)
Utwory kameralne
Uwertura żydowska na klarnet, fortepian i kwartet smyczkowy, op. 34 (1919)
Kwintet g-moll na obój, klarnet, skrzypce, altówkę i kontrabas, op. 39 (1924)
Sonata C-dur na dwoje skrzypiec, op. 56 (1932)
I sonata f-moll na skrzypce i fortepian, op. 80 (1938–1946)
Sonata D-dur na flet i fortepian, op. 94 (1943)
II sonata D-dur na skrzypce i fortepian, op. 94bis (1944), transkrypcja Sonaty fletowej
Sonata C-dur na wiolonczelę i fortepian, op. 119 (1949)
Utwory fortepianowe
sonaty:
I sonata f-moll, op. 1 (1909)
II sonata d-moll, op. 14 (1912)
III sonata a-moll "Ze starych zeszytów", op. 28 (1917)
IV sonata c-moll "Ze starych zeszytów", op. 29 (1917)
V sonata C-dur, op. 38 (1923)
VI sonata A-dur "Wojenna", op. 82 (1939–1940)
VII sonata B-dur "Wojenna", op. 83 (1939–1942)
VIII sonata B-dur "Wojenna", op. 84 (1939–1944)
IX sonata C-dur, op. 103 (1947)
inne:
Podszepty diabelskie, op. 4/4 (1910–1912)
Toccata d-moll, op. 11 (1912)
Sarkazmy, op. 17 (1912–1914), 5 utworów
Wizje ulotne (Visions fugitives), op. 22 (1915–1917), 20 utworów
Bajki starej babuni, op. 31 (1918), 4 utwory
Sonatina pastoralna, op. 59/3 (1934)
Muzyka dziecięca op. 65
liczne transkrypcje fragmentów baletów i oper, m.in.: Miłość do trzech pomarańczy, Romeo i Julia, Kopciuszek, Wojna i pokój
Dzieła wokalne
Ich siedmiu, op. 30 (1917), kantata na tenor dramatyczny, chór i orkiestrę (sł. K. Balmont)
Kantata na XX-lecie Października, op. 74 (1936–1937) na 2 chóry, orkiestrę symfoniczną, orkiestrę wojskową, orkiestrę akordeonów i perkusję, do tekstów K. Marksa, W. Lenina i J. Stalina
Aleksander Newski, op. 78 (1938–1939), kantata na mezzosopran, chór i orkiestrę, słowa W. Łukowski i S. Prokofjew
Zdrawica, op. 85 (1939), kantata na chór i orkiestrę
Muzyka filmowa
Porucznik Kiże (niezrealizowany)
Dama Pikowa (niezrealizowany)
Aleksander Newski (reż. Siergiej Eisenstein)
Iwan Groźny (reż. Siergiej Eisenstein)
Muzyka teatralna
Noce egipskie
Hamlet
Odznaczenia
Został odznaczony m.in.:
Nagrodą Stalinowską
tytułem Zasłużonego Działacza Sztuk RFSRR (1944)
tytułem Ludowego Artysty RFSRR (1947)
Orderem Czerwonego Sztandaru Pracy (1943)
Medalem "Za ofiarną pracę w Wielkiej Wojnie Ojczyźnianej 1941–1945"
Medalem "W upamiętnieniu 800-lecia Moskwy"
Medalem "Za obronę Kaukazu"
Edycje nutowe
S. S. Prokofjew: sobranie soczinienij (ros. С.С. Прокофьев: собрание сочинений; pol. S.S. Prokofiew: dzieła zebrane), red. N.P. Anosow i in., 20 tomów, Gosudarstwiennoje muzykalnoje izdatielstwo, Muzyka (Государственное музыкальное издательство, Музыка), 1955–67.
Przypisy
Bibliografia
Siergiej Prokofjew: Matieriały, dokumienty, wospominanija, Moskwa 1956
Izraił Niestiew: S. Prokofjew, Moskwa 1957 (wyd. ang. tłum. Florence Jonas, Stanford 1960)
O twórczości Sergiusza Prokofiewa, red. Zofia Lissa, Kraków 1962
Michel Hofmann: Serge Prokofiev, Paryż 1963
M.G. Aranowski: Miełodika S. Prokofjewa, Leningrad 1969
S. Prokofjew: Autobiografia, Kraków, PWM 1970
S. Prokofjew: Merci za miły list, Kraków 1970
S. Prokofjew: Refleksje, notatki i wypowiedzi, Kraków 1971
Jerzy Jaroszewicz: Prokofjew, Kraków, PWM 1983
Linki zewnętrzne
Oficjalna strona Fundacji im. Siergieja Prokofjewa
Radzieccy kompozytorzy muzyki filmowej
Rosyjscy pianiści
Kompozytorzy XX wieku
Rosyjscy kompozytorzy operowi
Rosyjscy artyści socrealizmu
Radzieccy artyści socrealizmu
Pochowani na Cmentarzu Nowodziewiczym w Moskwie
Laureaci Nagrody Stalinowskiej
Odznaczeni Orderem Czerwonego Sztandaru Pracy
Odznaczeni Medalem za Ofiarną Pracę w Wielkiej Wojnie Ojczyźnianej 1941–1945
Odznaczeni Medalem 800-lecia Moskwy
Zasłużeni Działacze Sztuk RFSRR
Ludowi Artyści RFSRR
Urodzeni w 1891
Zmarli w 1953 | {
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Biografia
Anche suo fratello Edouard era un calciatore.
Carriera
Club
In carriera ha giocato 16 partite di qualificazione alle coppe europee, di cui 6 per la Champions League e 10 per l'Europa League, realizzandovi anche tre reti, tutte con il .
Palmarès
Club
Competizioni nazionali
Ventspils: 2006, 2007
Ventspils: 2007
Collegamenti esterni | {
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Q: Weird way to increase the size of an array in C? I thought normally you can't increase the size of an array.
But what if I do:
char arr[4];
strncpy(arr,"12347777",8);
It shows the legnth is increased when I call strlen(arr).
Can someone explain to me what happened there?
A: You haven't made the array larger. You've stomped on random pieces of memory after the end of the array.
strlen does not return the length of an array, even in normal conditions. It says how long a string is. Since you just put eight characters (plus a null terminator) there, it's returning 8. However, this is undefined behavior! Because you've corrupted memory, you could crash, or it could return a random number (according to the standard, anything is possible). In a less simplistic piece of code, in fact, this would likely lead to a crash.
A: You just made a huge bug. It can lead in memory corruption and misbehave of your program. It doesn't change real array size but overwrite memory where array lies and which follows. So you wrote four chars {'1', '2', '3', '4'} in array but then {'7', '7', '7', '7'} to the following memory. You are lucky enough there was zeroed next byte so strlen(arr) shows you size 8. It is simple buggy and you should not do it. Note "12347777" is pointer into memory containing {'1', '2', '3', '4', '7', '7', '7', '7', '\0'} and you had copied only 8 chars so missed terminating zero byte.
| {
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{"url":"https:\/\/www.aimsciences.org\/article\/doi\/10.1186\/s41546-019-0040-8","text":"# American Institute of Mathematical Sciences\n\nJanuary\u00a0 2019,\u00a04:\u00a06 doi:\u00a010.1186\/s41546-019-0040-8\n\n## Correction to: \u201cExistence, uniqueness and comparison results for BSDEs with L\u00e9vy jumps in an extended monotonic generator setting\u201d\n\n 1. University of Jyvaskyla, Department of Mathematics and Statistics, P. O. Box 35, FI-40014 University of Jyvaskyla, Jyvaskyla, Finland; 2. Department of Applied Mathematics and Information Technology, Montanuniversitaet Leoben, Peter Tunner-Stra\u00dfe 25\/I, A-8700 Leoben, Austria\n\nReceived\u00a0 July 04, 2019 Revised\u00a0 July 04, 2019\n\nCitation: Christel Geiss, Alexander Steinicke. Correction to: \u201cExistence, uniqueness and comparison results for BSDEs with L\u00e9vy jumps in an extended monotonic generator setting\u201d. Probability, Uncertainty and Quantitative Risk, 2019, 4 (0) : 6-. doi: 10.1186\/s41546-019-0040-8\n##### References:\n [1] Dellacherie, C., Meyer, P.-A.:Probabilities and potential. B. North-Holland Publishing Co., Amsterdam(1982), [2] Geiss, C., Steinicke, A.:Existence, uniqueness and comparison results for BSDEs with L\u00e9vy jumps in an extended monotonic generator setting. Probab. Uncertain. Quant. Risk. 3(9) (2018), [3] He, S., Wang, J., Yan, J.:Semimartingale Theory and Stochastic Calculus. Science Press, CRC Press, New York (1992),\n\nshow all references\n\n##### References:\n [1] Dellacherie, C., Meyer, P.-A.:Probabilities and potential. B. North-Holland Publishing Co., Amsterdam(1982), [2] Geiss, C., Steinicke, A.:Existence, uniqueness and comparison results for BSDEs with L\u00e9vy jumps in an extended monotonic generator setting. Probab. Uncertain. Quant. Risk. 3(9) (2018), [3] He, S., Wang, J., Yan, J.:Semimartingale Theory and Stochastic Calculus. Science Press, CRC Press, New York (1992),\n [1] Peng Luo. Comparison theorem for diagonally quadratic BSDEs. Discrete & Continuous Dynamical Systems - A, 2020\u00a0 doi: 10.3934\/dcds.2020374 [2] Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete & Continuous Dynamical Systems - B, 2020\u00a0 doi: 10.3934\/dcdsb.2020320 [3] Yichen Zhang, Meiqiang Feng. A coupled $p$-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934\/era.2020075 [4] Stefano Bianchini, Paolo Bonicatto. Forward untangling and applications to the uniqueness problem for the continuity equation. Discrete & Continuous Dynamical Systems - A, 2020\u00a0 doi: 10.3934\/dcds.2020384 [5] Marco Ghimenti, Anna Maria Micheletti. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. Discrete & Continuous Dynamical Systems - S, 2020\u00a0 doi: 10.3934\/dcdss.2020453 [6] Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020\u00a0 doi: 10.3934\/dcdss.2020432 [7] Aihua Fan, J\u00f6rg Schmeling, Weixiao Shen. $L^\\infty$-estimation of generalized Thue-Morse trigonometric polynomials and ergodic maximization. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 297-327. doi: 10.3934\/dcds.2020363 [8] Mark F. Demers. Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 217-256. doi: 10.3934\/dcds.2020217 [9] Christopher S. Goodrich, Benjamin Lyons, Mihaela T. Velcsov. Analytical and numerical monotonicity results for discrete fractional sequential differences with negative lower bound. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934\/cpaa.2020269 [10] Xavier Carvajal, Liliana Esquivel, Raphael Santos. On local well-posedness and ill-posedness results for a coupled system of mkdv type equations. Discrete & Continuous Dynamical Systems - A, 2020\u00a0 doi: 10.3934\/dcds.2020382 [11] Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $L^2-$norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934\/era.2020077 [12] Yongxiu Shi, Haitao Wan. Refined asymptotic behavior and uniqueness of large solutions to a quasilinear elliptic equation in a borderline case. Electronic Research Archive, , () : -. doi: 10.3934\/era.2020119 [13] Ahmad Z. Fino, Wenhui Chen. A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5387-5411. doi: 10.3934\/cpaa.2020243 [14] Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schr\u00f6dinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems - S, 2020\u00a0 doi: 10.3934\/dcdss.2020436 [15] Zhilei Liang, Jiangyu Shuai. Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions. Discrete & Continuous Dynamical Systems - B, 2020\u00a0 doi: 10.3934\/dcdsb.2020348 [16] Thabet Abdeljawad, Mohammad Esmael Samei. Applying quantum calculus for the existence of solution of $q$-integro-differential equations with three criteria. Discrete & Continuous Dynamical Systems - S, 2020\u00a0 doi: 10.3934\/dcdss.2020440 [17] Gongbao Li, Tao Yang. Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms. Discrete & Continuous Dynamical Systems - S, 2020\u00a0 doi: 10.3934\/dcdss.2020469\n\nImpact Factor:","date":"2020-11-26 18:11:15","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\": 0.5956504344940186, \"perplexity\": 9618.711787048367}, \"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-2020-50\/segments\/1606141188899.42\/warc\/CC-MAIN-20201126171830-20201126201830-00618.warc.gz\"}"} | null | null |
Afenifere kicks against continued closure of schools by Federal Government
July 13, 2020 Folorunsho Taiwo Gist/Gossips, LATEST INFO 0
The Pan-Yoruba Socio-Political Organisation, Afenifere on Thursday condemned the Federal Government for ordering the continued closure of schools across the Country
Recall that the Education Minister Adamu Adamu had directed that school across the country should remain closed because of the ravaging effect of COVID-19 pandemic.
Speaking with newsmen in Akure, the Secretary-General of Afenifere, Bashorun Sehinde Arogbofa asked President Muhammadu Buhari "to sack both the minister of Education and his Minister of State for planning to ground education for a year.
Arogbofa said " Adamu Adamu should be sacked, he can not bring our school system back to the stone age. They had about six months to plan for these children, The last six months all these children have been preparing for the WASCE, what did the Federal Government do?
"I think the two ministers in the ministry should go, why would one minister say the pupils should resume writing their paper in August and the other minister would come and reverse the order and that the school would be closed down for the whole year.
"It is a reality that the COVID-19 is in the country but they should have envisaged what will happen and make necessary arrangements against it for the pupils. Why should education be closed down for a whole year?
According to him" It means the two of them (Adamu and the Minister of State for Education) don't know what they are doing, so they should go.
COVID-19: FG unveils 52-page guidelines for schools reopening
Sexual Harassment Bill Passed To Guarantee Safety Of Students – Ahmad Lawan | {
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Q: How to paginate search results? I want to paginate search results using Zend_Paginator. So I pass my data to a paginator instance:
$paginator = new Zend_Paginator (
new Zend_Paginator_Adapter_DbSelect ( $data )
);
Data is returned this way
public function getData($idArray){
$db = Zend_Db_Table::getDefaultAdapter();
$selectProgramme = new Zend_Db_Select($db);
$selectProgramme->from('programme')
->order('id DESC')
->where('id IN(?)', $idArray);
return $selectProgramme;
}
$idArray is provided by my search implementations. This all works great and I get the correct data and pagination links displayed.
However I can't paginate the result because the pagination links are not valid. So normal pagination would have following link:
mysite.de/home/index/page/1
in search I now have
mysite.de/home/search/page/1
This does not work. Any suggestions how to implement search pagination?
EDIT: I have a HomeController with two actions, index and search action. IndexAction displays all data and I can paginate it.
public function indexAction(){
//...
$paginator = new Zend_Paginator(
new Zend_Paginator_Adapter_DbSelect($data)
);
$paginator->setItemCountPerPage(16)
->setPageRange(20)
->setCurrentPageNumber($this->_getParam('page', 1));
$this->view->data = $paginator;
}
The searchActions handles the search process:
public function searchAction(){
$response = $solr->search($this->getRequest()->getParam('search', null));
//...if items found get the data exactly the same way as in the
// index action, using Zend_Paginator_Adapter_DbSelect
$paginator = new Zend_Paginator(
new Zend_Paginator_Adapter_DbSelect($data)
);
$paginator->setItemCountPerPage(16)
->setPageRange(20)
->setCurrentPageNumber($this->_getParam('page', 1));
$this->view->data = $paginator;
}
So like you see in the search action there is a problem with the search process when I paginate. I need to decide somehow if to search or to paginate. Any suggestions on that?
A: Since search required the search parameter pagination will fail because when paginating the the search parameter is null.
$sreq = $this->getRequest()->getParam('search', null);
So we need to pass this parameter whenever we paginate our search. I solve this using Zend_Session:
//get search param
$sreq = $this->getRequest()->getParam('search', null);
//store search param in session for pagination
$search = new Zend_Session_Namespace('PSearch');
if($sreq != null){
$search->psearch = $sreq;
}else{
$sreq = $search->psearch;
}
I have this at the top of my searchAction and everything works.
A: Not sure I understand, but is your problem that the page parameter from the url is not making it's way to the Paginator - e.g. regardless of what page you are on, it is always showing the first 20 results?
If so, have you tried manually setting the page on the paginator:
$page = $this->_getParam('page', 1);
$paginator->setCurrentPageNumber($page);
A: public function search()
Are you sure that you didn't mistyped here? Should be
public function searchAction()
A: You put your search data into $response but create paginator instance using $data (which is null)
| {
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\section{Introduction}
Many experiments have attempted to directly detect Weakly Interacting Massive Particle (WIMP) dark matter candidates via their elastic scattering on target nuclei~\cite{Agashe:2014kda}. The LUX experiment has recently limited the spin-independent cross sections to be under $7.6\times 10^{-46}\ \mathrm{cm}^2$ for 33 GeV WIMP mass~\cite{Akerib:2013tjd}. A method that has commonly been used is to measure signals associated with the deposited energy of the nuclear recoil. However, background processes, such as those induced by neutrons, can mimic WIMP signals~\cite{Davis:2014cja}. To overcome this problem, a ``smoking gun'' WIMP signal would be its unique directional event-rate dependence~\cite{Spergel:1987kx}. When viewed from the Earth, the average WIMP velocity in galactic coordinates is from the Cygnus direction, while the directions of background sources are fixed in an Earth-based coordinate system. This effect can be seen by the directions of the recoiling nuclei that are strongly correlated with the directions of the incoming WIMPs~\cite{Green:2006cb}, and produce a diurnal variation of rates due the Earth's rotation~\cite{Vergados:2006gw,Bandyopadhyay:2010zj}. Prospects for a working directional detector have focused on low pressure gas time projection chambers, such as DRIFT-II~\cite{Alner:2005xp}, DMTPC~\cite{Battat:2014mka}, NEWAGE~\cite{Miuchi:2010hn}, MIMAC~\cite{Santos:2013hpa}, and the D$^3$ prototype~\cite{Vahsen:2014fba}, and emulsion techniques~\cite{Naka:2007zz}. The sensitivity of those detectors have been studied assuming they are either capable of reconstructing full three-dimensional (3D) tracks~\cite{Green:2006cb,Morgan:2004ys} or only tracks projections on a particular detector-fixed plane (2D detector)~\cite{Green:2006cb,Morgan:2005sq}. It is found that of order tens of events are required to reject isotropy of recoil angle distributions, and the number of required events are one order of magnitude larger for a detector that cannot measure the sense, defined as the absolute sign ($\vec x$ or $-\vec x$), of the recoil vector. However, it is still a daunting task to fully reconstruct sub-100 keV nuclear recoil tracks.
In this paper, we consider a detector that can detect the polar angle of the recoil track with respect to a fixed $z$ axis, while the azimuthal angle is not measured. In the following, we refer to this as a polar detector. In general, since reconstruction of recoiling nucleus tracks is not required for a polar detector, the experimental realization can be more reliable and feasible. One issue for a directional dark matter detector is whether or not it possesses sense recognition capability, where we call the former a head-tail detector and the latter an axial detector. Considerable technological effort is required to provide head-tail detection capability. Throughout the paper, the standard isothermal galactic halo model is used to model the WIMP velocity distribution. In this case, a head-tail polar detector with $z$ axis aligned with the WIMP wind direction has the same performance as a full 3D detector, because in this orientation the azimuthal distribution is completely flat and provides no information at all.
One example of an axial polar detector is a stilbene crystal, which is an organic single crystal whose scintillation efficiency depends on the nuclear recoil direction relative to crystallographic axes~\cite{Sekiya:2003wf}. Recently, a new technique of columnar recombination (CR) has been shown to be capable of realizing a working axial polar detector~\cite{Nygren:2013nda}, without sense detection capability. The directional sensitivity in a CR detector comes from the dependence of electron-ion recombination level on the angle between recoil track and electric field. Here the experimental signals are the scintillation light for the recombinations, and drift electrons from the surviving ionizations.
In most previous sensitivity studies such as those reported in Refs.~\cite{Green:2006cb,Billard:2009mf,Copi:2005ya,Morgan:2004ys,Mohlabeng:2015efa}, the recoil energy is integrated out and only distributions with respect to angular variables are studied. When all the energies are integrated out, the shape of angular distribution does not depend on the WIMP mass~\cite{Alenazi:2007sy} and, thus, the distribution and the analysis are greatly simplified. However, we note that in a real experiment, all relevant information are used in order to achieve the highest possible sensitivity. Thus, both energy and directional information are used simultaneously in this work. Previous studies that did use both the energy and angular information~\cite{Billard:2011zj,Billard:2014ewa}, treated the WIMP mass as a known parameter that was kept at a fixed value in the fit. While this procedure is simpler to implement for producing plots of cross-section upper limits versus WIMP mass, it is problematic for a general directional sensitivity calculation. In this study, we address this issue by treating the WIMP mass as a nuisance parameter in a statistical framework that uses the well-established profile likelihood method.
We study signals from spin-independent WIMP-nucleus interactions, and assume zero background to provide benchmark results. For nonzero background experiments, an observation of directionality still unambiguously leads to an observation of WIMPs, and the amount of directional sensitivity loss due to background is also studied.
In sections that follow, we will start by calculating the distribution of observables, and then find the best orientations for various detector configurations using the standard profile likelihood method. Later, the effects of background contamination are calculated for detectors in optimal orientations. Finally, we study the performance of detectors using xenon target with various energy thresholds and WIMP masses, and estimate the required detector exposure to see a three sigma directional signal.
\section{Distributions of observables}
The general double-differential derivative of the recoil rate per
unit target mass, with respect to nuclear recoil energy $E$ and
solid angle $\Omega$ in the nuclear recoil direction $\hat{q}$,
can be expressed as~\cite{Gondolo:2002np}:
\begin{equation}
\frac{d^2R}{dEd\Omega} = \frac{n\sigma_0}{4\pi\mu^2}\mathcal{F}(E)
\hat{f}(v_\mathrm{min},\hat{q}).
\end{equation}
Here $\mu=mM/(m+M)$ is the reduced mass of
the WIMP-nucleus system, where $m$ and $M$ are the WIMP and target nucleus mass, respectively. $\mathcal{F}$ is the form factor, $\sigma_0$ is
spin-independent WIMP-nucleus cross-section, and $n=\rho^0/m$
is the number density of the WIMP, where we use $\rho^0=0.3\ \mathrm{GeV/cm}^3$.
The minimum WIMP speed required for a recoil of energy $E$ is $v_\mathrm{min}$.
The Radon transform, \(\hat{f}(v_\mathrm{min},\hat{q}) \),
of the WIMP velocity distribution \(f(\mathbf{v}) \) represents
the sum of the probability densities where the velocity projection on direction
\(\hat{q}\) is equal to \(v_\mathrm{min}\):
\begin{equation}
\hat{f}(v_\mathrm{min},\hat{q})
= \int \delta(\mathbf{v}\cdot\hat{q}-v_\mathrm{min})f(\mathbf{v})d^3v.
\end{equation}
In the standard isothermal galactic halo model,
the distribution of WIMP velocities $\mathbf{v}$ relative to the target
is Maxwellian, with an average value of $\mathbf{v_E}$:
\begin{equation}
f(\mathbf{v})=\frac{1}{(\sqrt{\pi}v_0)^3}e^{-(\mathbf{v}-\mathbf{v_E})^2/v_0^2}.
\end{equation}
In this case the Radon transform is:
\begin{equation}
\hat{f}(v_\mathrm{min},\hat{q})
= \frac{1}{\sqrt{\pi}v_0}e^{-(v_\mathrm{min}-\hat{q}\cdot\mathbf{v_E})^2/v_0^2}.
\end{equation}
The maximum recoil energy for a WIMP with velocity $v$ is
\(E_\mathrm{max}(v) = 2\mu^2v^2/M \), and by reversing the formula, we obtain
$v_\mathrm{min}=\sqrt{\frac{ME}{2\mu^2}}=\sqrt{\frac{E}{E_0}}v_0$, with the
definition $E_0=E_\mathrm{max}(v_0)$. We also calculate the
standard total rate $R_0$ when $v_E=0$ to be
\(R_0 = n\sigma_0/M\cdot\int vf(\mathbf{v})|_{v_E=0}d^3v
= 2/\sqrt{\pi}\cdot n\sigma_0v_0/M\). For a a single target-nucleus type,
the differential rate exhibits more physical meaning when
it is expressed using $E_0$ and $R_0$:
\begin{equation}
\frac{d^2R}{dEd\Omega} = \frac{1}{4\pi}\frac{R_0}{E_0}\mathcal{F}(E)
e^{-(v_\mathrm{min}-\hat{q}\cdot\mathbf{v_E})^2/v_0^2}.
\end{equation}
It is convenient to define two variables:
\begin{equation}
x \equiv \frac{v_\mathrm{min}}{v_0}= \sqrt{\frac{E}{E_0}}; \quad
x_E \equiv \frac{v_E}{v_0}.
\end{equation}
In a reference frame where the reference $z$ axis is parallel to
the WIMP wind direction, or the Cygnus direction, the solid angle
dependence reduces to polar angle $\theta$ dependence, and
the differential rate can be expressed as:
\begin{equation}\label{eqn:dRdEdCos}
\frac{d^2R}{dEd\cos\theta} = \frac{R_0}{2E_0}\mathcal{F}(E)
e^{-(x_E\cos\theta-x)^2}.
\end{equation}
For simplicity, the peculiar velocity of the Sun and the Earth's orbital velocity about the Sun are ignored and the velocity of Earth $v_E$ is taken to be equal to the velocity of the Local Standard of Rest $\vec\Theta_\mathrm{LSR}$. In this case the magnitude of $v_E$ and $v_0$ is same, which is usually given the value of 220 km/s. Hence in this paper we use $x_E=1$ to represent the standard halo model.
It is feasible to build a detector that is oriented at a fixed direction in space, where the WIMP wind direction and the $z$ axis of detector form a fixed angle $\theta_0$. In the frame of a detector system, the polar and azimuth angles of recoil $\theta_L$ and $\phi_L$ provide the directional information and the $\cos\theta$ term in Eq.~(\ref{eqn:dRdEdCos}) can be expressed in terms of $\theta_L$ and $\phi_L$ as
\(\cos\theta = \cos\theta_0\cos\theta_L + \sin\theta_0\sin\theta_L\cos\phi_L \).
Here the WIMP wind direction is assumed to lie in the $x-z$ plane, without any loss in generality. The resulting differential rate in lab frame with respect to $E$, $\cos\theta_L$ and $\phi_L$ is then:
\begin{multline}
\frac{d^3R}{dEd\cos\theta_L d\phi_L} = \\
\frac{R_0}{4\pi E_0}\mathcal{F}(E)
e^{-(x_E\cos\theta_0\cos\theta_L+x_E\sin\theta_0\sin\theta_L\cos\phi_L-x)^2}.
\label{eqn:dRdEdCosLdPhiL}
\end{multline}
Here, a solid angle transform
\( \frac{1}{2\pi}\frac{d^2R}{dEd\cos\theta} \to
\frac{d^3R}{dEd\cos\theta_L d\phi_L} \) is applied
from Eq.~(\ref{eqn:dRdEdCos}).
For a detector where the only directional measurable is the polar angle
$\theta_L$, the azimuthal angle $\phi_L$ should be integrated out:
\begin{equation}
\frac{d^2R}{dEd\cos\theta_L} = \int_0^{2\pi}\frac{d^3R}{dEd\cos\theta_L d\phi_L}.
\label{eqn:dRdEdCosL}
\end{equation}
For an axial detector where the sense of the recoil direction
cannot be distinguished, the distributions should be folded, as
\( \frac{d^2R}{dEd|\cos\theta_L|d\phi_L} =
\frac{d^2R}{dEd\cos\theta_Ld\phi_L} + \frac{d^2R}{dEd(-\cos\theta_L)d(\phi_L+\pi)} \), and \( \frac{d^2R}{dEd|\cos\theta_L|} =
\frac{d^2R}{dEd\cos\theta_L}+ \frac{d^2R}{dEd(-\cos\theta_L)} \).
\begin{figure}
\includegraphics[width=\columnwidth]{fig/Earth-fixed-DT3.pdf}
\caption{Schematic plot of an Earth-fixed detector shown as a rectangular box. }
\label{fig:earth-DT}
\end{figure}
Now we consider a common case where a detector is fixed in the Earth's coordinate frame. Since the Earth itself is rotating, the angle $\theta_0$ modulates with a period of one sidereal day. The WIMP wind from Cygnus is directed to the Earth at a constant angle $\epsilon=42^\circ$ to the Earth's polar axis, as shown in Fig.~\ref{fig:earth-DT}. If the $z$ axis of the detector is oriented relative to Earth's polar axis at a fixed angle $\theta_D$, then the dependence of the angle $\theta_0$ as a function of time $t$ in units of sidereal days is:
\begin{equation}
\cos\theta_0 = -\cos\epsilon\cos\theta_D - \sin\epsilon\sin\theta_D\cos(2\pi t).
\label{eqn:costheta0}
\end{equation}
Here $t$ is zero when the WIMP velocity lies in the plane made by the detector $z$ axis and Earth's polar axis. Since $t$ distributes uniformly within 0 and 1 when all energies and angles are considered, the appropriate distribution for the Earth-fixed case, now in terms of ($E,\cos\theta_L,t$), $\frac{d^3R}{dEd\cos\theta_Ldt}$, is determined by replacing $\theta_0$ in Eq.~(\ref{eqn:dRdEdCosLdPhiL}) with Eq.~(\ref{eqn:costheta0}) and integrating out $\phi_L$.
Note that here, instead of using angular information only as in~\cite{Green:2006cb,Billard:2009mf,Copi:2005ya,Morgan:2004ys}, we use two and three dimensional distributions that include energy and sidereal time as additional variables.
\section{Statistical test for directional signal}
The most common method that is used in particle physics to determine
significance of an observation is the profile likelihood ratio
test statistic method. It uses a hypothesis test
against a null or trivial hypothesis $H_0$, where the data is assumed
to correspond to the distribution of an alternative or interesting hypothesis
$H_1$. Usually, a set of parameters of interest $\nu$ of $H_1$
are fixed to a specific value $\nu_0$ to obtain $H_0$.
A likelihood ratio is calculated as the maximum likelihood of
a null hypothesis divided by the maximum likelihood of an alternative
hypothesis, with nuisance parameters $\mathbf{\theta}$ floating:
\begin{equation}
\lambda(\nu_0) = \frac{L(\nu=\nu_0,\hat{\hat{\mathbf\theta}})}
{L(\hat\nu,\hat{\mathbf\theta})}.
\label{eqn:lratio}
\end{equation}
The test statistic $q$ is defined as $-2\ln\lambda(\nu_0)$.
The $p$ value is the probability to have a discrepancy larger
than the observed one $q^\mathrm{obs}$, as
\begin{equation}
p = \int_{q^\mathrm{obs}}^\infty f(q|H_0)dq_0 .
\end{equation}
The smaller the $p$ value, the more credible that hypothesis $H_0$ is
not correct. For example, a $p$ value of 0.00135 corresponds to a
$3\sigma$ signal significance.
In principle, the distribution \(f(q|H_0)\) needs to be
obtained using Monte Carlo methods with high statistics.
However, according to Wilk's theorem, we can assume $q$ follows a $\chi^2$
distribution~\cite{Cowan:2010js} for data sets in our study.
Then the $p$ value can be directly
calculated as the probability above $q^\mathrm{obs}$
for a $\chi^2$ distribution $P$ with degrees of freedom
equal to the number of fixed parameters
in the numerator of Eq.~(\ref{eqn:lratio}):
$p=\int_{q^\mathrm{obs}}^\infty P(x)dx$. The significance $Z$ is
related with $p$ via $Z=\Phi^{-1}(1-p)$, where $\Phi$ is
the cumulative function of the standard Gaussian.
The likelihood function $L$ used in this paper is the unbinned product of normalized probability density function (PDF) of observed quantities for all events. The PDF is normalized over two or three dimensional variables, such as $(E,\cos\theta_L)$ or with the inclusion of $t$. A nonzero $x_E$ indicates a finite average WIMP speed from the Cygnus direction. Thus, for studies in this paper, $x_E$ as $\nu$ is the sole parameter of interest, with the null hypothesis being $x_E=0$. The WIMP mass, since it is unknown, is a nuisance parameter and floated in the fits for both the numerator and denominator of Eq.~(\ref{eqn:lratio}). Unlike most of the studies such as~\cite{Billard:2014ewa}, where a fixed WIMP mass need to be inserted in order to get the sensitivity or limit, our method directly focuses on the directionality itself.
To test the sensitivity of a measurement, the median (not mean) value of the test statistic $q_\mathrm{med}$ of a large ensemble of hypothesis tests is used as a measurement quantity of sensitivity for the work reported here. The ensemble size $N$ is 1000 for all of calculations discussed below. The error of $q_\mathrm{med}$ is $\frac{1}{2\sqrt{N}f(q_\mathrm{med})}$, where $f(q)$ is the normalized probability density function that is obtained from the raw distribution of $q$ for the ensemble by a kernel density estimation method~\cite{Cranmer:2000du}. Here, for each hypothesis test, a toy Monte Carlo data set with a certain number of events is generated and fitted to obtain the $q$ value for this data set.
With only one parameter of interest, the significance in units of $\sigma$ is calculated as the square root of the test statistic: $Z=\sqrt{q}$. So a $Z=3\sigma$ significance corresponds to $q=9$. In all the studies of this work, $q_\mathrm{med}$ is found to be proportional to the total event number, as will be shown in Fig.~\ref{fig:nE_q-n10}. So we use a linear proportional function to fit $q_\mathrm{med}$, and find the number of events corresponding to $q_\mathrm{med}=9$ as the required size for a $3\sigma$ discovery. Because of the linearity, the sensitivity can also be scaled proportionally to the size of statistics when needed.
\begin{figure}[t]
\includegraphics[width=\columnwidth]{fig/dq_vc-pub1-ensXE_SF4-VC_B.pdf}
\caption{Median $q$ values on solid markers as a function of cosine of the angle between the detector $z$ axis and the WIMP wind direction for general space-fixed detectors. Head-tail polar and angular only detectors correspond to up and down triangles. Axial polar and angular only detectors correspond to circles and diamonds. The event number for head-tail configuration is 200, different from 50 events for axial configuration, in order to fit in a single plot. }
\label{fig:q_vc-SF4}
\end{figure}
\begin{figure}[t]
\includegraphics[width=\columnwidth]{fig/dq_vc-pub1-ensXE_RT5-VT_A.pdf}
\caption{Median $q$ values on open markers as a function of angle $\theta_D$ between detector $z$ axis and Earth's pole, for Earth-fixed detectors. General head-tail polar and angular only detectors with 50 events correspond to up and down triangles. General axial polar and angular only detectors with 200 events correspond to circles and diamonds. For a standard axial xenon detector of 3 keV threshold with 200 observed events, four graphs for WIMP masses of 20, 30, 50 and 100 GeV are shown as blue squares with decreasing sizes. These graphs are fitted using an empirical function $q_\mathrm{med}= Q\cos(\alpha(\theta_D-\theta_D^0))$ that are superimposed as red solid curves for a standard axial xenon detector, and as red dashed and dotted curves for general axial polar and angular only detectors.}
\label{fig:q_vc-RT5}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{fig/cnE_qmed3-ensXE_n10.pdf}
\caption{Median $q$ values versus numbers of observed events for all detector types in their optimal orientations. Solid squares represent a standard space-fixed axial xenon detector. Other symbol markers are explained in Figs.~\ref{fig:q_vc-SF4} and \ref{fig:q_vc-RT5}. The fitted linearly proportional lines are superimposed. Blue dashed lines represent axial xenon detectors configured at 30 GeV WIMP and 3 keV threshold. }
\label{fig:nE_q-n10}
\end{figure}
\section{General Polar Detector} \label{sec:gen}
To study the general performance of a polar detector, a general detector with zero energy threshold and unit form factor is considered. In the absence of the form factor term in Eq.~(\ref{eqn:dRdEdCosLdPhiL}), the energy dependence of the rate is expressed through the ratio $E/E_0$, i.e., in units of $E_0$. Since the WIMP mass dependence of the rate function only enters through $E_0$, a change of WIMP mass just changes $E_0$, the overall scale of the energy $E$. Thus the sensitivity for the general polar detector has no dependence on the WIMP mass. In Secs.~\ref{sec:gen}--\ref{sec:bkg}, general results applicable to all WIMP masses are shown.
Figure~\ref{fig:q_vc-SF4} shows the median value of $q$ for space-fixed detectors, with head-tail and axial configurations, for different detector orientation angles. We can see that the optimum orientation for a space-fixed case is always at $\cos\theta_0=1$, where the detector's $z$ axis points toward the Cygnus. This is expected since in this case the detector can gain maximum information from the measured $\cos\theta_L$. Nontrivial curves for axial detectors are discovered with a minimum at around $\cos\theta_0 = 0.56$, where the distribution of $|\cos\theta_L|$ is close to flat due to the folding of positive and negative $\cos\theta_L$ values.
In the Earth-fixed case, the quantity $q_\mathrm{med}$ is averaged over many directions, and depends on the orientation $\theta_D$. Figure~\ref{fig:q_vc-RT5} shows the dependence of $q_\mathrm{med}$ on the angle $\theta_D$. A general head-tail detector is shown to have the most sensitivity when the $z$ axis is oriented parallel to the Earth's polar axis ($\theta_D=0^\circ$). Interestingly, the optimal $\theta_D$ value for a general axial detector is near $\theta_D=45^\circ$. A fit using an empirical function $q_\mathrm{med}= Q\cos(\alpha(\theta_D-\theta_D^0))$ gives the optimum value $\theta_D^0=44.48 \pm 0.33$, with the fitted curve shown in Fig.~\ref{fig:q_vc-RT5} as a dashed red line. The reason for $\theta_D^0$ being slightly larger than 42 degree, is that it is more advantageous to lie inside than outside for the WIMP wind vector, with respect to the cone made by the detector's $z$ axis following the Earth's self-rotation. Note that this value $\theta_D^0$ will change if the angle of the WIMP wind to the Earth's pole is a value different than 42 degree.
Results for the required number of events for $3\sigma$ discovery for four detector types, i.e., $\cos\theta_0=1$ for space-fixed detectors, and $\theta_D=45(0)^\circ$ for Earth-fixed axial (head-tail) detectors, are displayed in row one of Table~\ref{tab:ensXE_nEq9_n12}. Of order 10 to 20 event are required for head-tail detectors. These results show that a change from a space- to Earth-fixed basis worsens the sensitivity by factors of $3.1$ and $1.9$ for axial and head-tail configurations. For an Earth-fixed detector, we conclude that the loss of head-tail capability causes the sensitivity to be a factor of 10 worse, and the axial one is less efficient than a full 3D one (column 2) by about a factor of 19. These numbers can be compared to the 1D readout in Ref.~\cite{Billard:2014ewa}, which gives values of 8 and $\sim 10$ for the two factors, by measuring the signal yield with a constrained background.
As discussed in the Introduction, the optimal space-fixed head-tail detector behaves the same as a full 3D detector with its $z$ axis aligned along the WIMP wind. By dividing the two numbers for the space-fixed case, we expect that an axial detector would have the same sensitivity as a full 3D detector, provided it accumulated $6.3$ times as many events. This is a much better conclusion than that in Ref.~\cite{Billard:2014ewa}, which did not study a space-fixed detector.
\begin{table*}
\caption{The required number of point interactions for $3\sigma$ discovery for all detector types. Numbers are obtained from the abscissa value corresponding to $q_\mathrm{med}=9$ level in Fig.~\ref{fig:nE_q-n10} for the fitted straight lines. For xenon detector types, the numbers are calculated by applying the ratio $N_\mathrm{pint}/N_\mathrm{obs}$ from the required number of observed events. The indicated errors are purely statistical from finite ensemble size of 1000.}
\label{tab:ensXE_nEq9_n12}
\begin{tabularx}{0.9\textwidth}{l|>{\centering}X|>{\centering}X|>{\centering}X|>{\centering\arraybackslash}X}
\hline \hline
\multirow{2}{*}{Detector type} &
\multicolumn{2}{c|}{space-fixed} & \multicolumn{2}{c}{Earth-fixed} \\
\cline{2-5}
& Axial & Head-tail & Axial & Head-tail \\
\hline
General & $62.30\pm 0.56$ & $ 9.90\pm 0.09$ & $193.2\pm 2.1$ & $19.22\pm0.19$\\
Angular Only & $231.4\pm 2.7$ & $12.70 \pm 0.13$ & $767.0\pm 9.2$ & $23.91\pm 0.25$ \\
Xenon, 30 GeV WIMP, 3 keV threshold & $168.1 \pm 1.6$ & & $535.6 \pm 5.8$ & \\
Xenon, 30 GeV WIMP, 10 keV threshold & $218.5 \pm 2.0$ & & $702.7 \pm 7.6$ & \\
Xenon, 50 GeV WIMP, 30 keV threshold & $1318 \pm 12$ & & $4087 \pm 44$ & \\
\hline \hline
\end{tabularx}
\end{table*}
\section{Angular only detector} \label{sec:ang}
Most previous estimates of the sensitivity of a directional dark matter detector have only considered angular information only. To study detectors with polar angle information only, the rate as a function of $\cos\theta_L$ is obtained from Eq.~(\ref{eqn:dRdEdCosL}) by integrating out the energy part:
\begin{equation}
\frac{dR}{d\cos\theta_L} = \int_0^\infty dE\frac{d^2R}{dEd\cos\theta_L} .
\end{equation}
The same statistical procedure is performed as for the general polar detector case, for space- or Earth-fixed, axial or head-tail configurations. The $q_\mathrm{med}$ dependence on detector orientation is shown in Figs.~\ref{fig:q_vc-SF4} and \ref{fig:q_vc-RT5}. In all four detector configurations, the shape of the $\cos\theta_0$ and $\theta_D$ dependence is similar to that for the general polar detector case. For a space-fixed axial detector, the dependence on $\cos\theta_0$ is also not monotonic. In the Earth-fixed case, the red dotted curve in Fig.~\ref{fig:q_vc-RT5} has a maximum at $\theta_D=43.68\pm 0.28^\circ$. Results for the optimal value, $\cos\theta_0=1$ for space-fixed, $\theta_D=45^\circ$ and $0^\circ$ for Earth-fixed axial and head-tail detectors, are reported in row 2 of Table~\ref{tab:ensXE_nEq9_n12}. For head-tail detectors, of order of 10 (20) events are required to see directionality in space (Earth)-fixed basis, similar to results from previous studies~\cite{Morgan:2004ys,Morgan:2005sq,Copi:2005ya} for 3D and 2D detectors. The sensitivity worsens by factors of $3.3$ and $1.9$ for axial and head-tail configurations, respectively, when changing a space-fixed to an Earth-fixed basis, similar to the general polar detector case.
By comparing the event numbers in columns 1 and 3 of Table~\ref{tab:ensXE_nEq9_n12}, i.e., for the axial configurations of general and angular only detectors, we can see that $3.7$ and $4.0$ larger statistical samples are needed when the energy information is not used. However, for head-tail detectors (columns 2 and 4), only $1.3$ and $1.2$ times the statistics are required. This is because in the absence of the powerful head-tail information, which directly relates to directionality, we need to rely on the correlation between recoil energy and direction to improve the directional sensitivity. Thus, the importance of combining energy and angular observables is established, at least for axial detectors. We note that the performance may be improved over that reported in Refs.~\cite{Morgan:2005sq,Copi:2005ya}, if the observed energy is simultaneously used.
\begin{figure}
\includegraphics[width=\columnwidth]{fig/dq_fs-pub1-ensXE_SB4.pdf}
\caption{Sensitivity ratio over that for pure signal case, as a function of signal purity defined as the ratio of signal component over all events in the data set. For each detector type, data points are normalized to a constant number of signal events. Space- and Earth-fixed polar detectors under axial and head-tail configurations are shown when placed in each one's optimal orientation.}
\label{fig:q_fs-SB4}
\end{figure}
\section{Background effect} \label{sec:bkg}
In nondirectional dark matter searches, the most dangerous backgrounds are those with the same energy-dependent shape as the signal, since in those cases one cannot distinguish the background by the energy distribution. In this study, we use the directional observables to distinguish the signal, while the directional information is diluted by the background contribution.
Consider a background that is distributed the same way as the WIMP signal, while not requiring the relative speed between the earth and the dark matter halo. By setting $x_E=0$ and a unit form factor in Eq.~(\ref{eqn:dRdEdCosLdPhiL}), the background rate $R_\mathrm{BG}$ is isotropically distributed with a simple exponential decaying energy dependence: $\frac{d^2R_\mathrm{BG}}{dEd\cos \theta_L} = \frac{R_0}{2E_0}e^{-E/E_0}$.
In a real experiment, usually we do not fully understand all the sources of background. Here we show that this is not a problem in our method. Using the same PDF [Eq.~(\ref{eqn:dRdEdCosL})] to fit data, regardless of the how the data is generated or originated as would be in a real experiment, a nonzero $x_E$ still unambiguously indicates a directional signal. We use the same statistical procedure, and only change the generation of the signal-only data set to a mixture of signal and background. The parameter of interest is still $x_E$. Our method avoids the need for an external constraint to be imposed on the background rate, as done, for example, in Ref.~\cite{Billard:2014ewa} to obtain a better control of the signal component.
The sensitivity dependence on the signal purity is shown in Fig.~\ref{fig:q_fs-SB4}, where the signal component yield is a constant for each detector type. All polar detectors are aligned in their optimal orientations. The $x$-axis is the signal purity, defined as the ratio of the input signal number over total event number in the generation. In Fig.~\ref{fig:q_fs-SB4}, the sensitivity level can be seen to be almost linear with the signal purity. As the signal purity goes lower, the relative sensitivity falls by a lesser amount, especially for the space-fixed axial case. Thus we conclude the polar detector has a guaranteed performance level in the presence of background. In particular, the required number of events for purity 0.4 only increases by about a factor of 2 compared to the pure signal case. This can be compared to the 1D case of Fig.~2 in Ref.~\cite{Billard:2014ewa}, in which case the degradation of sensitivity is significantly worse as the signal purity decreases.
Note that, other types of backgrounds, such those with a flat energy dependence, are easier to handle because the difference in the energy distribution gives extra information to distinguish them from the real signal.
\section{Standard Xenon Detector}
Now we consider a detector with a specific material and a minimum energy threshold. Since the proposed columnar recombination detector uses gaseous xenon as target, a xenon Helm form factor~\cite{Lewin:1995rx} $\mathcal{F}(E)$ is computed and inserted into Eq.~(\ref{eqn:dRdEdCosLdPhiL}). For the minimum energy threshold, the LUX experiment~\cite{Akerib:2013tjd} provides a good reference, where the trigger efficiency reaches 50\% for 4 keV nuclear recoil events. In gaseous xenon, the commonly used reflective material polytetrafluoroethylene (PTFE) has a low refractive coefficient of about 60\% for the 175 nm scintillation wavelength of pure xenon, compared to more than 90\%~\cite{Yamashita:2004} in liquid xenon. An experimental prototype~\cite{Renner:2014mha} using pure xenon has put a high threshold of 30 keV, mainly due to a low light collection efficiency of 3\%.
A small amount of trimethylamine (TMA) mixture in the xenon gas, can convert the primary excitation to ionization of TMA molecules through the Penning transfer process~\cite{Cebrian:2012sp}, and increases the CR effect since more ionizations will participate in the recombination process~\cite{Nygren:2013nda}. At the same time, the scintillation light is wavelength-shifted to the TMA emission band centered at near-UV (300 nm), where the reflectance of PTFE increases to 90\%~\cite{Silva:2009ip}. Thus, it should be possible to achieve an energy threshold much lower than 30 keV.
In this study, we consider three minimum energy threshold values of 3, 10 and 30 keV. Because of the rapidly falling shape of the form factor, the event rate will be suppressed by a factor more than $10^{-6}$ for recoil energies greater than 100 keV. Thus, the maximum of the detection energy range is chosen to be 100 keV.
This standard xenon detector can be viewed as a columnar recombination detector with perfect resolution. So we only study the axial configuration. First, in the Earth-fixed case, the sensitivity dependence on $\theta_D$ is studied for four typical WIMP mass values of 20, 30, 50 and 100 GeV. Figure~\ref{fig:q_vc-RT5} shows the results for a 3 keV threshold, with fitted curves superimposed. The fitted optimal values for $\theta_D $ are $45.08\pm 0.22, 45.21\pm 0.30, 44.12\pm 0.49, 44.30\pm 0.79$ degree for 20, 30, 50 and 100 GeV WIMP mass. These are all nearly equal; a weighted average value is $44.97\pm 0.17$. In the following, the optimal directions $\theta_D=45^\circ$ and $\cos\theta_0=1$ are used for Earth- and space-fixed standard xenon detectors.
Because of the detection threshold, the required number of observed events for detectors with different thresholds cannot be directly translated to detector performance, since in this case the total rate depends on the threshold. The number of observed events, $N_\mathrm{obs}$, is the integral of the differential rate within the detection range including the form factor for a given total target mass $M_T$ and measurement time $T$:
\begin{equation}
N_\mathrm{obs}= RM_TT=\int_\mathrm{det. range} \frac{d^2R}{dEd\Omega}M_TT.
\end{equation}
To make fair comparisons of the sensitivities, we introduce a quantity called the number of point interactions, $N_\mathrm{pint}$, which is the number of WIMP-nucleus interactions with no threshold and no form factor effects:
\begin{equation}
\begin{split}
N_\mathrm{pint}&= \int_0^\infty dE\int d\Omega \frac{d^2R}{dEd\Omega}|_{\mathcal{F}(E)=1}\\
&=1.304R_0M_TT=2.608/\sqrt{\pi}\cdot n\sigma_0v_0M_TT/M.
\end{split}
\end{equation}
The amount of required $N_\mathrm{pint}$ directly relates to detector performance. For general detectors discussed in previous sections, $N_\mathrm{obs}= N_\mathrm{pint}$. For a single target, the spin-independent WIMP-nucleus cross-section $\sigma_0$ is related to the WIMP-nucleon cross-section $\sigma_n$ as $ \sigma_0 = \mu/\mu_{W-n}A^2\sigma_n$, where $\mu_{W-n}$ is the WIMP-nucleon reduced mass. For xenon, $N_\mathrm{pint}= 1.70\times 10^{46}\sigma_n M_{T} T/m \cdot \mathrm{GeV\cdot (cm^{2}\cdot kg\cdot year)^{-1}}$.
\begin{figure}
\includegraphics[width=\columnwidth]{fig/dq_mW-pub2-ensXExffc2-MW2.pdf}
\caption{Median $q$ values as a function of WIMP mass for axial xenon detectors, normalized to 200 events of point interaction. From the top to bottom, the dashed, dotted and dot-dashed lines corresponds to the 3, 10 and 30 keV energy threshold. The best orientations on space-fixed ($\cos\theta_0=1$, main plot) and Earth-fixed ($\theta_D=45^\circ$, inset plot) basis are used. }
\label{fig:q_mW-xffc2-MW2}
\end{figure}
There will be some WIMP-mass dependence of the sensitivity since the form factor and the threshold depends on absolute energy values that do not scale with $E_0$. The WIMP mass is still a floating nuisance parameter in the fitting, while being fixed at various input values in event generation. Figure~\ref{fig:q_mW-xffc2-MW2} shows the raw sensitivity as a function of WIMP mass, for space- and Earth-fixed detectors at their optimal orientations. Each point in the plot is normalized to $N_\mathrm{pint}=200$, so that the sensitivities can be compared for the same detector exposure.
In general, the higher the threshold, the lower the sensitivity. The decrease of the sensitivity for low WIMP masses is due to the effect of the threshold that eliminates a higher fraction of events the lower the WIMP mass. The sensitivity decrease for high WIMP masses is due to the form factor, which suppresses the high energy recoils. The most sensitive WIMP-mass value increases as the energy threshold increases, and is around 30 GeV for a 10 keV threshold and 50 GeV for a 30 keV threshold. The inset of Fig.~\ref{fig:q_mW-xffc2-MW2} shows that the performance of Earth-fixed detectors follows the same behavior as space-fixed case with respect to WIMP-mass and energy-threshold dependence, except for an overall sensitivity that is lower by a factor of about three, which is consistent with the general study in Sec.~\ref{sec:gen}.
We can also compare the decrease in sensitivity to the decrease in the observed event rate due to the energy threshold cut. For example, for a 30 GeV WIMP, an energy threshold change from 3 keV to 10 keV, decreases the sensitivity by only 23\%, compared to the 71\% decrease in the total number of observed events. This is due to the fact that most directional information comes from the high recoil energy events, so that a cut on low energy events has minor impact. For a detector with high energy threshold of 30 keV, a WIMP mass in the intermediate range around 50 GeV is most promising, with the sensitivity that is 3.2 times below that of a 3 keV-threshold detector for the same range.
Last three rows of Table~\ref{tab:ensXE_nEq9_n12} show the required point interaction numbers for a $3\sigma$ discovery under several WIMP-mass and energy-threshold combinations. In a typical case of a 30 GeV WIMP mass and a 10 keV energy threshold, the numbers are $219$ and $703$, for space- and Earth-fixed xenon polar detectors. These correspond to $770$ and $2480$ kg$\cdot$year exposures for a $5\times 10^{-46}\ \mathrm{cm}^2$ spin-independent WIMP-nucleon cross-section.
\section{Discussion}
A columnar recombination detector using high pressure xenon-TMA gas mixture can measure the angle between the nuclear recoil track and electric drift field~\cite{Nygren:2013nda,Gehman:2013mra}, without sense recognition capability. Thus it is an axial polar detector. The columnar effect benefits from a high Penning efficiency as the percentage of the xenon excitations that fall back to free electrons by ionizing the TMA molecules. For electron and gamma energy deposit, the Penning efficiency is estimated to be around 10\% and 20\% in Ref.~\cite{Gonzalez-Diaz:2015nba} and Ref.~\cite{Ruiz-Choliz:2015daa}, and also indirectly measured to be 10\%-15\% in high pressure xenon gas with TMA mixture~\cite{Nakajima:2015cva}. In addition, the primary scintillation from xenon is observed to be absorbed by the TMA mixture~\cite{Nakajima:2015cva}. Nevertheless, the columnar recombination effect for the ionization channel has been seen for the alpha particle events as shown in Fig.~5 of Ref.~\cite{Herrera2014}, where, as a first approximation, the collected charge is a linear function of $\cos^2\theta_L$. Further studies are needed to obtain a high Penning efficiency for the high initial ionization density produced by nuclear recoils.
To date, no experimental results on the properties of nuclear recoils in a columnar recombination material is available. Once a reliable detector response is available, a detector resolution can be straightforwardly included in our model to obtain the sensitivity. Despite this limitation, we have tested a naive resolution smearing method for nuclear recoils based on the following considerations: (a) the recombination fraction of the electron-ion pairs ranges from 0.8 for recoils that are parallel($\theta_L=0^\circ$) to 0.4 for those that are perpendicular ($\theta_L=90^\circ$) to the field direction; (b) an ionization work function of 76 eV for the electron-ion pairs; and (c) 10\% and 50\% efficiency for the recombination (scintillation) and ionization channels with Gaussian resolutions calculated from a Fano factor~\cite{Fano:1947zz} of 0.14~\cite{Alvarez:2012kua} for xenon gas. The resulting sensitivity is only worsened by 7\% relative to the zero resolution case. This can be understood as that the directionality is derived from an overall anisotropic phenomenon and not from a localized spot. Reference~\cite{Mohlabeng:2015efa} also noted that variations in angular resolution do not make much difference in the dark matter detection sensitivity. Thus we do not expect a significant change to our sensitivity results by detector resolution effects.
\section{Conclusion}
The performance of a directional dark matter detector with polar angle detection is studied for various configurations. A WIMP-mass independent method is used to obtain the sensitivity of a general detector. In addition, a detector with xenon as target material is studied. We infer that:
\begin{itemize}
\item Both axial and head-tail polar detectors have the highest sensitivity when the $z$ axis is aligned with WIMP wind. However, the dependence of sensitivity to detector orientation is not monotonic for an axial detector. To obtain optimal performance when rotating with the Earth, the $z$ axis should be oriented at 45 degree to Earth's pole for an axial detector, while it should be aligned with Earth's polar axis for a head-tail detector.
\item A head-tail polar detector can detect directionality with of order 10 or 20 events on a space- or Earth-fixed basis. In the absence of sense detection capability, an order of magnitude more statistics is needed.
\item Without using energy information simultaneously, the required statistics would be a factor of $3.7\ (4.0)$ times higher for a space (Earth)-fixed axial detector. This conclusion will be useful for detector types in which partial directional information is available, such as a 2D planar detector.
\item A general axial polar detector with $6.3$ times the statistics has the same performance as a general full 3D tracking detector. However, in experimental practice, the target mass for a full 3D detector is limited because of diffusion effects, and accomplishing millimeter tracking is extremely challenging. On the other hand, a detector with polar angle sensitivity without head-tail discrimination requirement can use straightforward experimental techniques. In addition, it can be made in large volume with high-density gas, with a target mass that can be orders of magnitude larger than a conventional full 3D detector. We conclude that it is of great advantage to explore the directional dark matter detection technique using a senseless polar angle detection apparatus.
\item A space-fixed detector is generally found to be 3 and 2 times more sensitive than an Earth-fixed detector, for axial and head-tail configurations. This ratio is an important factor when comparing the additional cost for a space fixed detector, since it has to rotate all the time with respect to the Earth. In a space-fixed detector, to distinguish between the WIMP signal from the galaxy coordinate and possible anisotropic background originating from the detector frame, manually reversing the detector $z$ axis direction for half of the measurement period should be useful.
\item In the presence of contamination by an isotropic background that mimics the energy shape of the signal, the decrease of directional sensitivity occurs at a rate that is less than the decrease of signal purity. Thus a polar detector is robust against background. The space-fixed axial configuration is least affected by such backgrounds.
\item For an axial xenon polar detector, the decrease of sensitivity due to the effect of the energy threshold is much smaller than the decrease of the total event rate. A $770$ or $2480$ kg$\cdot$year exposure can reach a $3\sigma$ directional signal on a space- or Earth-fixed basis with 10 keV energy threshold, for a $5\times 10^{-46}\ \mathrm{cm}^2$ WIMP-nucleon cross-section and a 30 GeV WIMP mass.
\end{itemize}
\begin{acknowledgments}
The author would like to thank Adam Para, Jonghee Yoo, Yeongduk Kim and Stephen Olsen for useful discussions. This work was supported by the Institute for Basic Science (Korea) under project code IBS-R016-D1.
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,773 |
In the week prior to our meeting there was a lot of rain and the forecast wasn't that good initially. But when the week progressed the weather forecast improved, promises as the day of the meeting would be the best day of the week where made.
So Saturday morning I woke up and opened the curtains and there it was… a clear blue sky.
After leaving for Bourtange together with Bert Lanting and Mika Huising we met our fellow organiser Tjeert Mensinga at about 10 o'clock. Gradually the participants arrived from all over Holland and 1 from Belgium. After all 23 participants had arrived, we all went for coffee and cake. During this everyone was chatting with each other, renewing contacts and learning to know the first time participants in real life. In the meantime Tjeert explained to the group on how the day was planned and invited everyone for a group picture. After finishing the group picture, everyone took of in groups to explore Bourtange. During the day we ran into each other and chatted on about Panoramio, photography or just everyday business. Having had talks about subjects, personal and photographic stuff, the barbecue was set on fire. While enjoying a good meal with plenty of refreshing drinks a great, warm, day came to an end.
As the organising team there's nothing left, then a very satisfied feeling over a great day, with great and entertaining company. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,610 |
Collected here are all four of the first year's worth of Warren Ellis' Apparat books including Simon Spector with art by Jacen Burrows, Angel Stomp Future with art by Juan Jose Ryp, Quit City with art by Laurenn McCubbin, and Frank Ironwine with art by Carla Speed McNeil! The four Apparat books are inspired by the pulp magazines of the 1930s and imagine modern day comic books that evolved from the pulps without the influence of super-heroes. Ellis also includes over 10 pages of new essays on the inspiration behind, and the creation of, these self-contained stories. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,337 |
Daily Archive January 11, 2020
IVF Cost in Belgaum: Test Tube Baby Cost in Belgaum, Low-cost IVF Centres in Belgaum
The Cost of IVF in Belgaum ranges from Rs. 101,200 to Rs. 230,500 depending on the IVF doctor's experience, success rates, and IVF clinic location which includes the injections and prescribed medicines by the IVF doctor. For one cycle IVF cost in Belgaum varies between Rs. 90,000 to Rs. 2,10,000 excluding the prescribed medicines and Injections, This is not fixed. Most of the couples have paid more than Rs. 300,000 to have the test tube baby. Your IVF treatment cost can increase or decrease due to many factors like your previous health condition, the period of your infertility and type of infertility, while you may also need other treatments along with IVF. Different locations are offering different IVF treatment costs. The cost of IVF in Belgaum might be lower than the IVF treatment cost in other cities. Many couples tour to different cities to get affordable IVF treatment cycles. Several factors are directly or indirectly associated with the overall IVF Treatment cost in Belgaum. All these factors play an important role in the success rate of IVF treatment in Belgaum. The average cost of the IVF treatment can be Rs. 200,000 by the IVF treatment centers along with the additional discount of up to 10% to the couples.
Average IVF Treatment (Cost) + Self Egg (Cost) + Donor Egg (Cost)
Types of IVF Procedure
Average Cost IVF Treatment Cycle (not inclusive of Medicines and Blood Tests)*
Cost IVF Programme per cycle Rs. 1.2 Lakh TO Rs. 1.6 Lakh (INJECTION & MEDICINE EXTRA)
IVF Treatment Cost (Single Cycle) with Self Egg Rs. 1.2 Lakh TO Rs. 2.2 Lakh
IVF Cost Single Cycle (with Donor Egg) Rs. 1.22 Lakh TO Rs. 2.2 Lakh
IVF Cost with ICSI Rs. 1.75 Lakh TO Rs. 1.85 Lakh
IVF Treatment Cost with PICSI Rs. 1.85 Lakh TO Rs. 2 Lakh
IVF Cost with Donor Egg Rs. 2.75 Lakh TO Rs. 3 Lakh
IVF Treatment Cost with Donor sperm Rs. 2.1 Lakh
IVF with Laser Assisted Hatching Rs. 2.2 Lakh
IVF treatment with PGD/PGS technique Rs. 2.75 Lakh TO Rs. 3 Lakh
The mandatory consultation charges of up to Rs. 1500 can increase your IVF treatment in Belgaum.
The age of your female partner, the infertility period, the infertility issues as well as the type of IVF cycles can also impart the cost.
The laboratory charges can directly affect the cost. The main function of the IVF treatment is done in the Vitro means glass which affects the entire cost.
Sometimes, the couples only need to do it to get the intrauterine insemination which is known as IUI. This directly reduces the cost of IVF treatment.
Surrogacy, the donor of eggs or donor of sperms may take up to Rs. 20,000 to Rs. 60,000 to assist you with the IVF treatment.
In case you want to freeze your eggs for the future, then this might add to the overall IVF cost.
The TESA which is commonly known as Testicular Sperm Aspiration may add more Rs. 12,000 to Rs. 18,000 in your procedure.
The IVF treatment cost can be different in different locations. Many couples travel to other cities to get affordable IVF treatment cycles. here you can find the list of Top 7 Best Low-cost IVF Centres in Belgaum with IVF packages, Success Rates, Services & working fertility specialists in Belgaum. The best Low-cost IVF Centres in Belgaum are chosen based on IVF success rates in Belgaum treatment quality, patient's opinion, doctor's qualification, and location accessibility:
Metgud Hospital Advanced Laparoscopy and IVF Centre, Belgaum (Low-cost IVF Centre in Belgaum)
Hhope Infertility Clinic, Belgaum (Low-cost IVF Centre in Belgaum)
Venkatesh Maternity & Infertility Center, Belgaum (Low-cost IVF Centre in Belgaum)
Patted's Fertility & Research, Belgaum (Low-cost IVF Centre in Belgaum)
Shri Ramakrishna Ayurved and Infertility Centre, Belgaum (Low-cost IVF Centre in Belgaum)
Leelavathi Hospital, Belgaum (Low-cost IVF Centre in Belgaum)
Gizare Maternity Hospital, Belgaum (Low-cost IVF Centre in Belgaum)
1. Metgud Hospital Advanced Laparoscopy and IVF Centre, Belgaum (Low-cost IVF Centre in Belgaum)
Address & Directions: Apple Tower, near Wholesale Fruit Market, Azad Mohalla, Gandhi Nagar, Belgaum, Karnataka 590016
IVF Doctors:
In Vitro Fertilisation (IVF) Cost: Rs. 114,000 to Rs. 253,000
Intrauterine insemination (IUI) Cost: Rs. 6,000 to Rs. 44,000
Surrogacy Cost: Rs. 1,080,000 to Rs. 1,760,000
Website: https://www.metgudhospital.in/
The average IVF cost in Belgaum ranges from Rs. 106,100 to Rs. 235,500 whereas in Metgud Hospital Advanced Laparoscopy and IVF Centre, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Belgaum is very economical, especially at Metgud Hospital Advanced Laparoscopy and IVF Centre, Belgaum. We provide very reasonable IVF costs in Belgaum where you are assured of quality treatment. Metgud Hospital Advanced Laparoscopy and IVF Centre in Fort Lake Road, Belgaum is a top player in the category IVF Centres in the Belgaum. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Belgaum. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Belgaum, this establishment occupies a prominent location in Fort Lake Road. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at Fort Lake Road, Beside Belgaum Wholesale Fruit Market, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: IVF Centres, Gynaecologist & Obstetrician Doctors, Paediatricians, Children Hospitals, General Surgeon Doctors, Multispeciality Hospitals, Oncologists, Maternity Hospitals. Metgud Hospital Advanced Laparoscopy and IVF Centre in Belgaum. IVF Centres with Address, Contact Number, Photos, Maps. View Metgud Hospital Advanced Laparoscopy and IVF Centre, Belgaum on Vinsfertility.
2. Hhope Infertility Clinic, Belgaum (Low-cost IVF Centre in Belgaum)
Address & Directions: Plot No.16, RPD Corner, Tilakwadi, Belgaum, Karnataka 590001
Reviews & Rating:
Website: https://hhopeinfertility.in/
The average IVF cost in Belgaum ranges from Rs. 106,100 to Rs. 235,500 whereas in Hhope Infertility Clinic, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Belgaum is very economical, especially at Hhope Infertility Clinic, Belgaum. We provide very reasonable IVF costs in Belgaum where you are assured of quality treatment. Hope Infertility Clinic in Belgaum. Private Hospitals with Address, Contact Number, Photos, Maps. View Hope Infertility Clinic, Belgaum on Vinsfertility. In Belgaum, Hope Infertility Clinic is a recognized name inpatient care. They are one of the well-known Private Hospitals in Tilakwadi. Backed with a vision to offer the best in patient care and equipped with technologically advanced healthcare facilities, they are one of the upcoming names in the healthcare industry. Located in, this hospital is easily accessible by various means of transport. A team of well-trained medical staff, non-medical staff, and experienced clinical technicians work round-the-clock to offer various services. Their professional services make them a sought after Private Hospitals in Belgaum. A team of doctors on board, including specialists, are equipped with the knowledge and expertise for handling various types of medical cases. At Hope Infertility Clinic in Tilakwadi, the various modes of payment accepted are Cash. You can reach them at Plot No 16, R P B Corner, Tilakwadi Belgaum-590006.
3. Venkatesh Maternity & Infertility Center, Belgaum (Low-cost IVF Centre in Belgaum)
Address & Directions: Shivaji Rd, near Anupam Hotel, Raviwar Peth, Belgaum, Karnataka 590001
Reviews & Rating: 3.0 – 1 Google review
The average IVF cost in Belgaum ranges from Rs. 106,100 to Rs. 235,500 whereas in Venkatesh Maternity & Infertility Center, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Belgaum is very economical, especially at Venkatesh Maternity & Infertility Center, Belgaum. We provide very reasonable IVF costs in Belgaum where you are assured of quality treatment. In Belgaum, Venkatesh Maternity & Infertility Centre is a recognized name inpatient care. They are one of the well-known Hospitals in Shivaji Road. Backed with a vision to offer the best in patient care and equipped with technologically advanced healthcare facilities, they are one of the upcoming names in the healthcare industry. Located in, this hospital is easily accessible by various means of transport. A team of well-trained medical staff, non-medical staff, and experienced clinical technicians work round-the-clock to offer various services. Their professional services make them a sought after Hospitals in Belgaum. A team of doctors on board, including specialists, are equipped with the knowledge and expertise for handling various types of medical cases. At Venkatesh Maternity & Infertility Centre in Shivaji Road, the various modes of payment accepted are Cash. You can reach them at Near Anupam Hotel, Shivaji Road Belgaum-590001. Venkatesh Maternity & Infertility Centre in Belgaum. Hospitals with Address, Contact Number, Photos, Maps. View Venkatesh Maternity & Infertility Centre, Belgaum on vinsfertility.com.
4. Patted's Fertility & Research, Belgaum (Low-cost IVF Centre in Belgaum)
Address & Directions: CTS 4824 C, Plot No. 56, Near Kolhapur Circle, SP Bungalow Road, Opp State Excise Office, Belgaum, Karnataka 590010, India
IVF Doctors: Dr. Shobhana Patted, MD, DGO, DNB, FICOG, etc
Website: https://www.pattedsivf.com/
The average IVF cost in Belgaum ranges from Rs. 106,100 to Rs. 235,500 whereas in Patted's Fertility & Research Center, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Belgaum is very economical, especially at Patted's Fertility & Research Center, Belgaum. We provide very reasonable IVF costs in Belgaum where you are assured of quality treatment. Welcome to Patteds IVF, Patteds fertility and research center is a First Fertility Centre in North Karnataka to get NABH(National Accreditation Board for Hospitals & Healthcare Providers) Accreditation – entry-level standards which offer personalized IVF services in Belagavi, in Karnataka, India. Our center is recognized by the government of India and is enrolled under the National Registry of ART Clinics in India of ICMR. Our clinic offers treatment to infertile couples. You know that IVF can maximize your chances of getting pregnant. To become the regional center of excellence in infertility by providing superior quality care and outcome to our patients. To utilize the most advanced fertility technologies, clinical expertise, compassionate staff, and quality accreditations, to deliver the highest level of fertility care by most cost-effective price and become the region's preferred provider of complete infertility care to our patients.
5. Shri Ramakrishna Ayurved and Infertility Centre, Belgaum (Low-cost IVF Centre in Belgaum)
Address & Directions: Shahapur, Belgaum, Karnataka 590003
Website: https://shriramakrishnaayurvedandinfertilitycentre.business.site/
The average IVF cost in Belgaum ranges from Rs. 106,100 to Rs. 235,500 whereas in Shri Ramakrishna Ayurved and Infertility Centre, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Belgaum is very economical, especially at Shri Ramakrishna Ayurved and Infertility Centre, Belgaum. We provide very reasonable IVF costs in Belgaum where you are assured of quality treatment. We at Shri Ramakrishna Ayurveda Chikitsa Kendra provide treatment for Gynecologist disorders like menstrual disturbance, Infertility, PCOD, White discharge, etc, ANC Checkup in Pregnant ladies, obesity, skin disorders, Blood pressure, Arthritis, Back pain, Acidity. Gas problems, Asthma, Piles, Urinary stones, Pimples, Hair falls, dandruff, etc. Shri Ramakrishna Ayurveda Chikitsa Kendra in Belgaum. Hospitals with Address, Contact Number, Photos, Maps. View Venkatesh Maternity & Infertility Centre, Belgaum on vinsfertility.com.
6. Leelavathi Hospital, Belgaum (Low-cost IVF Centre in Belgaum)
Address & Directions: Adarsh Nagar, Hindwadi, Belgaum, Karnataka 590006
Reviews & Rating: 3.3 – 4 Google reviews
The average IVF cost in Belgaum ranges from Rs. 106,100 to Rs. 235,500 whereas in Leelavathi Hospital it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Belgaum is very economical, especially at Leelavathi Hospital, Belgaum. We provide very reasonable IVF costs in Belgaum where you are assured of quality treatment. Leelavati Hospital in Hindwadi, Belgaum is a top player in the category Hospitals in the Belgaum. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Belgaum. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Belgaum, this establishment occupies a prominent location in Hindwadi. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at Adarsh Nagar, 5th Cross, Opposite to IMER COLLEGE, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: Hospitals, Urologist Doctors, Gynaecologist & Obstetrician Doctors, General Physician Doctors, IVF Centres, Maternity Hospitals, Semen Testing Centres, Gynecologic Oncologist Doctors.
7. Gizare Maternity Hospital, Belgaum (Low-cost IVF Centre in Belgaum)
Address & Directions: Shivaji Rd, Raviwar Peth, Belgaum, Karnataka 590001
Website: https://gizarehospital.com/
The average IVF cost in Belgaum ranges from Rs. 106,100 to Rs. 235,500 whereas in Gizare Maternity Hospital it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Belgaum is very economical, especially at Gizare Maternity Hospital, Belgaum. We provide very reasonable IVF costs in Belgaum where you are assured of quality treatment. Welcome to Gizare Maternity Hospital, Infertility is an ever-increasing problem in today's life. Dr. Gizare hospital is pioneering in the treatment and education of this issue. The main thrust is given on counseling. Cost-effective approach, Updated information, and reasonable results. Except for IVF and ICSI, all modalities are available with an emphasis on conservative and medical management. Ovarian drilling has been available for almost 8-10 years with more than 800 cases. To the credit. Incremental regimen, extended regimen, and others have been tried. IUI and IUI donors also have been available for 15 years. Male infertility, sexual dysfunction evaluation are also available with Experts. Micro Surgery, both open and laparoscopic are been performed. Hence un doubt it is an ideal place for infertile couples in a smart city!
In Obstetrics. It is a trusted name with excellent vaginal delivery rates and incremental delivery applications. Gizare maternity hospital has earned a safe satisfying name in the community and the rural for liberal use of misoprostol at every step and various indications for gain the best results and name. Dr. Gizare hospital has in house pediatrician round the clock with phototherapy and incubator warmer etc. Gizare hospital has a unique facility for balloon endometrial therapy units for various menstrual disorders with more than 100 cases. Laparoscopic sterilization is available for family planning more than 5000 cases have been performed hence helping in the stabilization of population. Medical abortion (MPT with pills) has revolutionized the family planning concept thus made it more simple, personal and conservative. We are pioneers in popularizing this concept again helping in population stabilization. We also have understood our social responsibility by creating awareness camps, health checkup camps in rural areas, schools, colleges. We celebrate women's day, doctor's day, health day and many more. We have been endorsed by many insurance companies for cashless and reimbursement purposes. We have a well-equipped laboratory and round the clock pharmacy, blood bank near to us to cater to the emergencies. Our hospital is visited regularly by a yoga therapist, dietician, sex therapist giving comprehensive care. We continue to strive our best to uplift the health status of women.
Top 7 Best IVF Centres in Belgaum with High Success Rate 2020
In vitro fertilization (IVF) is a type of assisted reproductive technology that involves retrieving eggs from a woman's ovaries and fertilizing them with the retrieved male sperms. IVF process includes ovulation induction, egg retrieval, fertilization, embryo transfer, and implantation into the uterus. After performing these steps successfully a positive embryo is formed. Here you can find the list of Top 7 Best IVF Centres in Belgaum with IVF packages, Success Rates, Services & working fertility specialists in Belgaum. The best IVF centers in Belgaum are chosen based on IVF success rates in Belgaum, treatment quality, patient's opinion, doctor's qualification, and location accessibility:
Metgud Hospital Advanced Laparoscopy and IVF Centre, Belgaum (Best IVF Centre in Belgaum)
Hhope Infertility Clinic, Belgaum (Best IVF Centre in Belgaum)
Venkatesh Maternity & Infertility Center, Belgaum (Best IVF Centre in Belgaum)
Patted's Fertility & Research, Belgaum (Best IVF Centre in Belgaum)
Shri Ramakrishna Ayurved and Infertility Centre, Belgaum (Best IVF Centre in Belgaum)
Leelavathi Hospital, Belgaum (Best IVF Centre in Belgaum)
Gizare Maternity Hospital, Belgaum (Best IVF Centre in Belgaum)
1. Metgud Hospital Advanced Laparoscopy and IVF Centre, Belgaum (Best IVF Centre in Belgaum)
Metgud Hospital Advanced Laparoscopy and IVF Centre in Fort Lake Road, Belgaum is a top player in the category IVF Centres in the Belgaum. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Belgaum. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Belgaum, this establishment occupies a prominent location in Fort Lake Road. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at Fort Lake Road, Beside Belgaum Wholesale Fruit Market, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: IVF Centres, Gynaecologist & Obstetrician Doctors, Paediatricians, Children Hospitals, General Surgeon Doctors, Multispeciality Hospitals, Oncologists, Maternity Hospitals. Metgud Hospital Advanced Laparoscopy and IVF Centre in Belgaum. IVF Centres with Address, Contact Number, Photos, Maps. View Metgud Hospital Advanced Laparoscopy and IVF Centre, Belgaum on Vinsfertility.
2. Hhope Infertility Clinic, Belgaum (Best IVF Centre in Belgaum)
Hope Infertility Clinic in Belgaum. Private Hospitals with Address, Contact Number, Photos, Maps. View Hope Infertility Clinic, Belgaum on Vinsfertility. In Belgaum, Hope Infertility Clinic is a recognized name inpatient care. They are one of the well-known Private Hospitals in Tilakwadi. Backed with a vision to offer the best in patient care and equipped with technologically advanced healthcare facilities, they are one of the upcoming names in the healthcare industry. Located in, this hospital is easily accessible by various means of transport. A team of well-trained medical staff, non-medical staff, and experienced clinical technicians work round-the-clock to offer various services. Their professional services make them a sought after Private Hospitals in Belgaum. A team of doctors on board, including specialists, are equipped with the knowledge and expertise for handling various types of medical cases. At Hope Infertility Clinic in Tilakwadi, the various modes of payment accepted are Cash. You can reach them at Plot No 16, R P B Corner, Tilakwadi Belgaum-590006.
3. Venkatesh Maternity & Infertility Center, Belgaum (Best IVF Centre in Belgaum)
In Belgaum, Venkatesh Maternity & Infertility Centre is a recognized name inpatient care. They are one of the well-known Hospitals in Shivaji Road. Backed with a vision to offer the best in patient care and equipped with technologically advanced healthcare facilities, they are one of the upcoming names in the healthcare industry. Located in, this hospital is easily accessible by various means of transport. A team of well-trained medical staff, non-medical staff, and experienced clinical technicians work round-the-clock to offer various services. Their professional services make them a sought after Hospitals in Belgaum. A team of doctors on board, including specialists, are equipped with the knowledge and expertise for handling various types of medical cases. At Venkatesh Maternity & Infertility Centre in Shivaji Road, the various modes of payment accepted are Cash. You can reach them at Near Anupam Hotel, Shivaji Road Belgaum-590001. Venkatesh Maternity & Infertility Centre in Belgaum. Hospitals with Address, Contact Number, Photos, Maps. View Venkatesh Maternity & Infertility Centre, Belgaum on vinsfertility.com.
4. Patted's Fertility & Research, Belgaum (Best IVF Centre in Belgaum)
Welcome to Patteds IVF, Patteds fertility and research center is a First Fertility Centre in North Karnataka to get NABH(National Accreditation Board for Hospitals & Healthcare Providers) Accreditation – entry-level standards which offer personalized IVF services in Belagavi, in Karnataka, India. Our center is recognized by the government of India and is enrolled under the National Registry of ART Clinics in India of ICMR. Our clinic offers treatment to infertile couples. You know that IVF can maximize your chances of getting pregnant. To become the regional center of excellence in infertility by providing superior quality care and outcome to our patients. To utilize the most advanced fertility technologies, clinical expertise, compassionate staff, and quality accreditations, to deliver the highest level of fertility care by most cost-effective price and become the region's preferred provider of complete infertility care to our patients.
5. Shri Ramakrishna Ayurved and Infertility Centre, Belgaum (Best IVF Centre in Belgaum)
We at Shri Ramakrishna Ayurveda Chikitsa Kendra provide treatment for Gynecologist disorders like menstrual disturbance, Infertility, PCOD, White discharge, etc, ANC Checkup in Pregnant ladies, obesity, skin disorders, Blood pressure, Arthritis, Back pain, Acidity. Gas problems, Asthma, Piles, Urinary stones, Pimples, Hair falls, dandruff, etc. Shri Ramakrishna Ayurveda Chikitsa Kendra in Belgaum. Hospitals with Address, Contact Number, Photos, Maps. View Venkatesh Maternity & Infertility Centre, Belgaum on vinsfertility.com.
6. Leelavathi Hospital, Belgaum (Best IVF Centre in Belgaum)
Leelavati Hospital in Hindwadi, Belgaum is a top player in the category Hospitals in the Belgaum. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Belgaum. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Belgaum, this establishment occupies a prominent location in Hindwadi. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at Adarsh Nagar, 5th Cross, Opposite to IMER COLLEGE, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: Hospitals, Urologist Doctors, Gynaecologist & Obstetrician Doctors, General Physician Doctors, IVF Centres, Maternity Hospitals, Semen Testing Centres, Gynecologic Oncologist Doctors.
7. Gizare Maternity Hospital, Belgaum (Best IVF Centre in Belgaum)
Welcome to Gizare Maternity Hospital, Infertility is an ever-increasing problem in today's life. Dr. Gizare hospital is pioneering in the treatment and education of this issue. The main thrust is given on counseling. Cost-effective approach, Updated information, and reasonable results. Except for IVF and ICSI, all modalities are available with an emphasis on conservative and medical management. Ovarian drilling has been available for almost 8-10 years with more than 800 cases. To the credit. Incremental regimen, extended regimen, and others have been tried. IUI and IUI donors also have been available for 15 years. Male infertility, sexual dysfunction evaluation are also available with Experts. Micro Surgery, both open and laparoscopic are been performed. Hence un doubt it is an ideal place for infertile couples in a smart city!
IVF Cost in Rajahmundry: Test Tube Baby Cost in Rajahmundry, Low-cost IVF Centres in Rajahmundry
The Cost of IVF in Rajahmundry ranges from Rs. 101,200 to Rs. 230,500 depending on the IVF doctor's experience, success rates, and IVF clinic location which includes the injections and prescribed medicines by the IVF doctor. For one cycle IVF cost in Belgaum varies between Rs. 90,000 to Rs. 2,10,000 excluding the prescribed medicines and Injections, This is not fixed. Most of the couples have paid more than Rs. 300,000 to have the test tube baby. Your IVF treatment cost can increase or decrease due to many factors like your previous health condition, the period of your infertility and type of infertility, while you may also need other treatments along with IVF. Different locations are offering different IVF treatment costs. The cost of IVF in Belgaum might be lower than the IVF treatment cost in other cities. Many couples tour to different cities to get affordable IVF treatment cycles. Several factors are directly or indirectly associated with the overall IVF Treatment cost in Belgaum. All these factors play an important role in the success rate of IVF treatment in Belgaum. The average cost of the IVF treatment can be Rs. 200,000 by the IVF treatment centers along with the additional discount of up to 10% to the couples.
The IVF treatment cost can be different in different locations. Many couples travel to other cities to get affordable IVF treatment cycles. here you can find the list of Top 5 Best Low-cost IVF Centres in Rajahmundry with IVF packages, Success Rates, Services & working fertility specialists in Rajahmundry. The best Low-cost IVF Centres in Rajahmundry are chosen based on IVF success rates in Rajahmundry treatment quality, patient's opinion, doctor's qualification, and location accessibility:
Pragati IVF Center, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
Dr.Rama's Fertility & IVF Center, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
London IVF Centre, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
Jaya Kidney & Maternity Center, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
Tapani Hospital, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
1. Pragati IVF Center, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
Address & Directions: Prakasam Nagar, Rajahmundry, Andhra Pradesh 533103
IVF Doctors: Dr. Sajja Padma, etc
Website: https://www.pragatiivfcentre.com/
The average IVF cost in Rajahmundry ranges from Rs. 106,100 to Rs. 235,500 whereas in Pragati IVF Center, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Rajahmundry is very economical, especially at Pragati IVF Center, Rajahmundry. We provide very reasonable IVF costs in Rajahmundry where you are assured of quality treatment. Pragati Super Speciality Hospital which is now a multi-specialty hospital established way back in 1998 with infertility as a very important sub-specialty. Our fertility center has a long success story that was established One and a half-decade ago with eminent Gynecologist, Andrologist and Embryologist as an inhouse team performing most economical and successful I.V.F. program in the coastal area of Andhra Pradesh. Unlike other metros, Rajahmundry is a serene city with a congestion-free atmosphere and hassle-free life, well connected with all kinds of transport (air, train, and road) which is very convenient for couples undergoing I V F program. Our center is staffed with well experienced in-house embryologists, dedicated andrologist and nurse coordinators who are passionate about the field. They work for and give you rapid response whenever a problem arises during the treatment and coordinate effectively with clinicians. We have nearly 2 decades of experience in this field. We offer all services under one roof starting from advanced investigations(genetic), laparoscopic surgeries, Hysteroscopic surgeries, infertility services and high-risk pregnancy care which is very much advantageous to the couples. Rajahmundry is very well connected by air, train and road to all other metros and also other coastal areas, itself is a peaceful town without the hectic traffic and pollution of the metros. We are offering all services at most economical charges to the couples when compared with any of the Metros and at the same time with high success rates. No hidden charges. Dr.Sajja Padma, Managing Director of Pragati Test tube baby center, has passed her M.B.B.S., from Rangaraya Medical College, Kakinada in 1991 and passed her Post graduation from Govt. Maternity Hospital (Osmania Medical College) Hyderabad in 1995. She has received extensive training for all kinds of ART treatments and techniques in abroad and India.
2. Dr.Rama's Fertility & IVF Center, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
Address & Directions: Nakkina St, Ganesh Nagar, Rajahmundry, Andhra Pradesh 533101
IVF Doctors: Dr.Papolu Rama Devi, etc
Website: https://fertilityindia.com/
The average IVF cost in Rajahmundry ranges from Rs. 106,100 to Rs. 235,500 whereas in Dr.Rama's Fertility & IVF Center, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Rajahmundry is very economical, especially at Dr.Rama's Fertility & IVF Center, Rajahmundry. We provide very reasonable IVF costs in Rajahmundry where you are assured of quality treatment. DR. Rama's INSTITUTE FOR FERTILITY at Hyderabad was the first company that was established in united Andhra Pradesh in the year 1991 and with ISO Certification – 9001 to 2008 and has been updated to 2015. Dr. Rama institute for fertility is recognized by the Govt of India and first enrolled under the National Registry of ART Institutes in India of ICMR. Our Enrolment number is 1001. Dr. Papolu Rama Devi founded Dr.Rama's Institute for Fertility way back in 1991 at Hyderabad, India. As a Director & Chief Consultant for Dr. Rama's Institute for fertility, Dr. Rama Devi is an expert in the procedure of diagnosis and treatment of infertility matters. She has established a complete range of ART procedures [IUI, IVF-ET, ICSI-ET, GIFT], Assisted Hatching, Blastocyst culture, Cryo Freezing [Sperm, Embryo], Donation Program [Egg, Sperm, Embryo], Surrogacy and comprehensive counseling of apprehended couples. Dr.Papolu Rama Devi is among the most popular infertility doctor known to about a hundred million of people all over the world. She has developed a team of about 200 medical and paramedical colleagues who are rendering excellent services round the clock 365 days at the five cities where the institute has located its service.
Our Fertility Institute offers IVF (In Vitro Fertilization) treatment to infertile couples. Like most infertile couples, you know that IVF can maximize your chances of getting pregnant. However, if you are worried that it is too expensive for you to be able to afford, we have good news for you. Dr. Rama's Institute for fertility, Dr. Shruthi Malvekar, Dr. Haritha Samadhi, Dr. Vijay Laxmi, Dr. Saritha and Dr. Rajya Laxmi Dr. Sandhya Mishra Dr. Arun Gudi Dr. Suchindhra provide state-of-the-art IVF treatment at affordable prices in a comfortable atmosphere. We offer all the newest reproductive techniques, including IVF, ICSI, laser-assisted hatching, embryo freezing, egg donation, PGD, embryo biopsy, and blastocyst transfer. If you have done IVF at another clinic, have you got upset that a different doctor attended your procedures each time? Are you forced to talk to several different nurses, with no real direction? Are you having trouble getting the feedback or explanations you need? At Dr. Rama's Institute for fertility, all the treatment ( including the consultation, all the ultrasound scans, egg collection and embryo transfers are done personally by either Dr. Shruthi Malvekar and Dr. Haritha Samadhi. and we don't delegate any part of your delicate and critical IVF treatment to anyone else!
3. London IVF Centre, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
Address & Directions: Lakkakula Rama Rao St, Gandhipuram, Rajahmundry, Andhra Pradesh 533103
IVF Doctors: Dr. K. Chandra Reddy, MD, MRCOG | IVF Consultant Doctor and Managing Director
Website: https://londonivfvizag.com/
The average IVF cost in Rajahmundry ranges from Rs. 106,100 to Rs. 235,500 whereas in London IVF Center, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Rajahmundry is very economical, especially at London IVF Centre, Rajahmundry. We provide very reasonable IVF costs in Rajahmundry where you are assured of quality treatment. The London IVF is AP's first state of the art IVF Facility. The promoter behind the clinic has been providing expert fertility treatment and support to the community in the UK for over 13 years and has come back to his hometown. Fertility treatment can be very stressful. It requires a substantial investment of time, emotion and resources. Our clinic offers counseling and fertility coaching to support you through your treatment and its legal implications. Discussion with specialists is readily available to you. They are supported by a team of experienced, discreet and sympathetic nurses and counselors. We also offer an out of hours facility to all our patients. Our team at Visakhapatnam works with a wealth of experience behind them in Gynaecology, IVF and Reproductive Medicine. Treatment and Services we offer IVF, ICSI, IUI, Donor Eggs, Donor Sperm from our Egg Bank and Sperm Bank, Egg & Sperm Freezing, Surrogacy. Our team at Visakhapatnam works with a wealth of experience behind them in Gynaecology, IVF and Reproductive Medicine.
It may sound simple, but deciding to seek help for infertility can be a very difficult decision. Once it has been made, you will start a program of consultations and investigations which are bewildering and daunting to many. It may be because of a friend, your family Doctor, or just something you have read, but your first contact with the London IVF Centre (LIC) is likely to be an e-mail or a phone call – perhaps to arrange an appointment or to attend one of our open evenings. But once you have decided to go ahead with treatment, you will find that our clinics work to the very highest of standards, producing consistently excellent results for a very wide caseload of patients, for couples of all ages. For patients who need donor eggs or sperm or both, we have excellent arrangements in place to provide them. Our professional staff and state-of-the-art scientific and medical facilities reflect a total commitment to excellence in everything we do.
4. Jaya Kidney & Maternity Center, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
Address & Directions: 12-23-9, Katheru Rd, Near Gokavaram Bus Stand, Aryapuram, Rajahmundry, Andhra Pradesh 533104
The average IVF cost in Rajahmundry ranges from Rs. 106,100 to Rs. 235,500 whereas in Jaya Kidney & Maternity Center, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Rajahmundry is very economical, especially at Jaya Kidney & Maternity Center, Rajahmundry. We provide very reasonable IVF costs in Rajahmundry where you are assured of quality treatment. Established in the year 2017, Jaya Kidney & maternity Center in Arya Puram, Rajahmundry is a top player in the category Urologist Doctors in the Rajahmundry. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Rajahmundry. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Rajahmundry, this establishment occupies a prominent location in Arya Puram. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at Gokavaram Bus Stand Down, Near Chinna Gandhi Statue Centre, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: Urologist Doctors, Gynaecologist & Obstetrician Doctors, Hospitals, Maternity Hospitals, Sexologist Doctors, Nephrologists, Private Hospitals, Kidney Hospitals. Jaya Kidney & maternity Center in Rajahmundry. Urologist Doctors with Address, Contact Number, Photos, Maps. View Jaya Kidney & maternity Center, Rajahmundry on Vinsfertility.com.
5. Tapani Hospital, Rajahmundry (Low-cost IVF Centre in Rajahmundry)
Address & Directions: Bus stand, Fire Office Road, Opposite Gokavaram, Seshayya Metta, Rajahmundry, Andhra Pradesh 533104
IVF Doctors: Dr. D Shyam Kiran, etc
Website: https://sites.google.com/site/tapanihospitalrajahmundry/home
The average IVF cost in Rajahmundry ranges from Rs. 106,100 to Rs. 235,500 whereas in Tapani Hospital, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Rajahmundry is very economical, especially at Tapani Hospital, Rajahmundry. We provide very reasonable IVF costs in Rajahmundry where you are assured of quality treatment. Established in the year 2014, Tapani Hospital in Rajahmundry Ho, Rajahmundry is a top player in the category Hospitals in the Rajahmundry. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Rajahmundry. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Rajahmundry, this establishment occupies a prominent location in Rajahmundry Ho. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at Gokavaram Bus Stand, Near Opst Fire Station, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: Hospitals, Urologist Doctors, Gynaecologist & Obstetrician Doctors, Dermatologists, General Physician Doctors, General Surgeon Doctors, Diagnostic Centres, Eye Hospitals. Tapani Hospital in Rajahmundry. Hospitals with Address, Contact Number, Photos, Maps. View Tapani Hospital, Rajahmundry on Vinsfertility.com.
Top 5 Best IVF Centres in Rajahmundry with High Success Rate 2020
In vitro fertilization (IVF) is a type of assisted reproductive technology that involves retrieving eggs from a woman's ovaries and fertilizing them with the retrieved male sperms. IVF process includes ovulation induction, egg retrieval, fertilization, embryo transfer, and implantation into the uterus. After performing these steps successfully a positive embryo is formed. Here you can find the list of Top 5 Best IVF Centres in Rajahmundry with IVF packages, Success Rates, Services & working fertility specialists in Rajahmundry. The best IVF centers in Rajahmundry are chosen based on IVF success rates in Rajahmundry, treatment quality, patient's opinion, doctor's qualification, and location accessibility:
Pragati IVF Center, Rajahmundry (Best IVF Centre in Rajahmundry)
Dr.Rama's Fertility & IVF Center, Rajahmundry (Best IVF Centre in Rajahmundry)
London IVF Centre, Rajahmundry (Best IVF Centre in Rajahmundry)
Jaya Kidney & Maternity Center, Rajahmundry (Best IVF Centre in Rajahmundry)
Tapani Hospital, Rajahmundry (Best IVF Centre in Rajahmundry)
1. Pragati IVF Center, Rajahmundry (Best IVF Centre in Rajahmundry)
Pragati Super Speciality Hospital which is now a multi-specialty hospital established way back in 1998 with infertility as a very important sub-specialty. Our fertility center has a long success story that was established One and a half-decade ago with eminent Gynecologist, Andrologist and Embryologist as an inhouse team performing most economical and successful I.V.F. program in the coastal area of Andhra Pradesh. Unlike other metros, Rajahmundry is a serene city with a congestion-free atmosphere and hassle-free life, well connected with all kinds of transport (air, train, and road) which is very convenient for couples undergoing I V F program. Our center is staffed with well experienced in-house embryologists, dedicated andrologist and nurse coordinators who are passionate about the field. They work for and give you rapid response whenever a problem arises during the treatment and coordinate effectively with clinicians. We have nearly 2 decades of experience in this field. We offer all services under one roof starting from advanced investigations(genetic), laparoscopic surgeries, Hysteroscopic surgeries, infertility services and high-risk pregnancy care which is very much advantageous to the couples. Rajahmundry is very well connected by air, train and road to all other metros and also other coastal areas, itself is a peaceful town without the hectic traffic and pollution of the metros. We are offering all services at most economical charges to the couples when compared with any of the Metros and at the same time with high success rates. No hidden charges. Dr.Sajja Padma, Managing Director of Pragati Test tube baby center, has passed her M.B.B.S., from Rangaraya Medical College, Kakinada in 1991 and passed her Post graduation from Govt. Maternity Hospital (Osmania Medical College) Hyderabad in 1995. She has received extensive training for all kinds of ART treatments and techniques in abroad and India.
2. Dr.Rama's Fertility & IVF Center, Rajahmundry (Best IVF Centre in Rajahmundry)
DR. Rama's INSTITUTE FOR FERTILITY at Hyderabad was the first company that was established in united Andhra Pradesh in the year 1991 and with ISO Certification – 9001 to 2008 and has been updated to 2015. Dr. Rama institute for fertility is recognized by the Govt of India and first enrolled under the National Registry of ART Institutes in India of ICMR. Our Enrolment number is 1001. Dr. Papolu Rama Devi founded Dr.Rama's Institute for Fertility way back in 1991 at Hyderabad, India. As a Director & Chief Consultant for Dr. Rama's Institute for fertility, Dr. Rama Devi is an expert in the procedure of diagnosis and treatment of infertility matters. She has established a complete range of ART procedures [IUI, IVF-ET, ICSI-ET, GIFT], Assisted Hatching, Blastocyst culture, Cryo Freezing [Sperm, Embryo], Donation Program [Egg, Sperm, Embryo], Surrogacy and comprehensive counseling of apprehended couples. Dr.Papolu Rama Devi is among the most popular infertility doctor known to about a hundred million of people all over the world. She has developed a team of about 200 medical and paramedical colleagues who are rendering excellent services round the clock 365 days at the five cities where the institute has located its service.
3. London IVF Centre, Rajahmundry (Best IVF Centre in Rajahmundry)
The London IVF is AP's first state of the art IVF Facility. The promoter behind the clinic has been providing expert fertility treatment and support to the community in the UK for over 13 years and has come back to his hometown. Fertility treatment can be very stressful. It requires a substantial investment of time, emotion and resources. Our clinic offers counseling and fertility coaching to support you through your treatment and its legal implications. Discussion with specialists is readily available to you. They are supported by a team of experienced, discreet and sympathetic nurses and counselors. We also offer an out of hours facility to all our patients. Our team at Visakhapatnam works with a wealth of experience behind them in Gynaecology, IVF and Reproductive Medicine. Treatment and Services we offer IVF, ICSI, IUI, Donor Eggs, Donor Sperm from our Egg Bank and Sperm Bank, Egg & Sperm Freezing, Surrogacy. Our team at Visakhapatnam works with a wealth of experience behind them in Gynaecology, IVF and Reproductive Medicine.
4. Jaya Kidney & Maternity Center, Rajahmundry (Best IVF Centre in Rajahmundry)
Established in the year 2017, Jaya Kidney & maternity Center in Arya Puram, Rajahmundry is a top player in the category Urologist Doctors in the Rajahmundry. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Rajahmundry. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Rajahmundry, this establishment occupies a prominent location in Arya Puram. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at Gokavaram Bus Stand Down, Near Chinna Gandhi Statue Centre, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: Urologist Doctors, Gynaecologist & Obstetrician Doctors, Hospitals, Maternity Hospitals, Sexologist Doctors, Nephrologists, Private Hospitals, Kidney Hospitals. Jaya Kidney & maternity Center in Rajahmundry. Urologist Doctors with Address, Contact Number, Photos, Maps. View Jaya Kidney & maternity Center, Rajahmundry on Vinsfertility.com.
5. Tapani Hospital, Rajahmundry (Best IVF Centre in Rajahmundry)
Established in the year 2014, Tapani Hospital in Rajahmundry Ho, Rajahmundry is a top player in the category Hospitals in the Rajahmundry. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Rajahmundry. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Rajahmundry, this establishment occupies a prominent location in Rajahmundry Ho. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at Gokavaram Bus Stand, Near Opst Fire Station, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: Hospitals, Urologist Doctors, Gynaecologist & Obstetrician Doctors, Dermatologists, General Physician Doctors, General Surgeon Doctors, Diagnostic Centres, Eye Hospitals. Tapani Hospital in Rajahmundry. Hospitals with Address, Contact Number, Photos, Maps. View Tapani Hospital, Rajahmundry on Vinsfertility.com.
IVF Cost in Jammu and Kashmir: Test Tube Baby Cost in Jammu and Kashmir, Low-cost IVF Centres in Jammu and Kashmir
The minimum IVF Cost in Jammu and Kashmir for one cycle can be Rs. 1,00,000 which can rise to Rs. 2,50,000 excluding all the standard medication prescribed by the Fertility Specialists, This IVF Cost is not fixed; it can vary depends upon on needs of patients. Most couples who have already spent as much as Rs. 300,000 to Rs. 500,000 for the treatment of the test-tube babies. The IVF Treatment cost in Jammu and Kashmir fluctuates due to many reasons which might depend on your medical history, your types of fertility issues, Age of the Woman or you might need several other additional treatments along with IVF. The cost of In Vitro Fertilization (IVF) treatment in Jammu and Kashmir can vary from the cost of IVF in other Cities. Infertility Couples can travel to different cities to get low-cost IVF treatment cycles.
The IVF treatment cost can be different in different locations. Many couples travel to other cities to get affordable IVF treatment cycles. here you can find the list of Top 6 Best Low-cost IVF Centres in Jammu and Kashmir with IVF packages, Success Rates, Services & working fertility specialists in Jammu and Kashmir. The best Low-cost IVF Centres in Jammu and Kashmir are chosen based on IVF success rates in Jammu and Kashmir treatment quality, patient's opinion, doctor's qualification, and location accessibility:
Janam Fertility Centre, Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Pushpanjali Life, Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Benison IVF & Health Care Clinic, Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Gee Cee ART IVF Centre, Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Indira IVF Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
1. Janam Fertility Centre, Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Address & Directions: Shop No.8, Tawi Shopping Complex, Opp. Punch Mandir, Sector 2, Channi Himat, Jammu, Jammu and Kashmir 180011
IVF Doctors: Dr. Ashutosh Gupta, etc
Website: https://www.janamfertilitycentre.com/jammu
The average IVF cost in Jammu and Kashmir ranges from Rs. 106,100 to Rs. 235,500 whereas in Janam Fertility Center, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Jammu and Kashmir is very economical, especially at Janam Fertility Centre, Jammu & Kashmir. We provide very reasonable IVF costs in Jammu and Kashmir where you are assured of quality treatment. Janam Fertility Centre Jammu, Janam Fertility Centre is an advanced center for the treatment of reproductive disorders. It is situated Sunjwan Road Near Bhatindi Morh, Jammu. Janam Fertility Centre brings together best in science, modern technology, clinical and nursing practice to offer our patients the very best chance of success and happiness. Mission statement: Our mission statement is to "FULFILL EVERY WOMAN'S DREAM OF MOTHERHOOD". We strive to provide you the best infertility treatment with lots of care and honesty. Dedicated Team: We have a dedicated team of infertility specialists who are having experience of more than 16 years in this field. A dedicated team of Gynaecologists, Andrologists, Embryologists, Nursing staff and Coordinators are available to you, to guide you through your treatment process. Janam Fertility Centre is the new ray of hope for people dealing with fertility problems as we provide advanced treatment to help fulfill hopes, desires, and dreams of childless couples throughout the country. The fertility center was established under the expert guidance of Dr. Ashutosh Gupta who is a specialist in pediatrics and Dr. Geeta Digra who is an authority in the treatment of infertility. We have a leading team of IVF specialists, Embryologists, Gynecologists, and other doctors. Janam Fertility Centre is a one-stop center for those who require any type of solution for infertility under one roof.
The team is efficient and knowledgeable and conducts counseling and consultations through comprehensive investigations, medicines or USG's. You can find all the latest machines and technical instruments in the hospital which help in providing enhanced treatment related to IVF. It is Located inside Doaba Hospital 320, Lajpat Nagar, Mahavir Marg, near Nakodar Chowk, Jalandhar city. This center has experienced staff and doctors and is one of the best TEST TUBE BABY CENTRE in Punjab. Janam Fertility Centre provides personal attention to every patient at each stage of their treatment and is dedicated to treating complicated cases with utmost care and attention. Several patients have benefited through our treatment and are leading a happy life with their little ones. We aim at providing efficient services to all the distressed couples who have lost hope of having children.
2. Pushpanjali Life, Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Address & Directions: Lale-Da-Bagh, Jammu, Jammu and Kashmir 180002
The average IVF cost in Jammu and Kashmir ranges from Rs. 106,100 to Rs. 235,500 whereas in Pushpanjali Life, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Jammu and Kashmir is very economical, especially at Pushpanjali Life, Jammu & Kashmir. We provide very reasonable IVF costs in Jammu and Kashmir where you are assured of quality treatment. Pushpanjali Life is a state of the art institute dedicated to the service of infertile couples. It offers world-class facilities in diagnosis and patient management in a patient-friendly atmosphere in a modern setting away from the hustle-bustle of the city in serene environs. At Pushpanjali Life, life begins in a safer, caring way because the basic philosophy of life is in giving and we follow the same in caring for our patients. Dr. Geetu Mahajan (Pushpanjali Clinic) in Jammu treats the various ailments of the patients by helping them undergo high-quality treatments and procedures. Among the numerous services offered here, the clinic provides treatments for Uterine Fibroids or Myomas, Ovarian Cysts, Endometriosis, Pelvic Organ Prolapse, Urinary Problems, Vaginal Discharge, Subfertility, Menopause, Gynaecological Cancers, Abnormal Pap Smears – Pre-Invasive Cervical/Vaginal Disease and Vulva Conditions. The doctor is also listed under Gynaecologist & Obstetrician Doctors. Furthermore, the patients also visit the clinic for Contraception Advice, HPV Tests, and Biopsy Tests, etc. The hours of operation of this clinic are from 10:00-17:00 – 14:00-20:00, all days of the week. As modes of payments, the patients can pay via various payment modes. Pushpanjali life is located at Jammu. The clinic is providing services in Urology, IUI, ICSI, IVF, Infertility Treatment, female infertility, Laparoscopic Surgery, IVF Treatment, Laparoscopic Surgery.
3. Benison IVF & Health Care Clinic, Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Address & Directions: 39 B/C, Gandhi Nagar, Jammu, Jammu and Kashmir 180004
IVF Doctors: Dr. Ambika Datta (MBBS, MD (Obstetrics and Gynaecology)), etc
Website: https://www.benisonivf.com/
The average IVF cost in Jammu and Kashmir ranges from Rs. 106,100 to Rs. 235,500 whereas in Benison IVF & Health Care Clinic, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Jammu and Kashmir is very economical, especially at Benison IVF & Health Care Clinic, Jammu & Kashmir. We provide very reasonable IVF costs in Jammu and Kashmir where you are assured of quality treatment. Welcome to Benison IVF & healthcare clinic, one of the fastest-growing IVF clinics in Northern India. We are a premium healthcare clinic that provides IVF services to infertile couples at affordable costs. We believe in bringing a lifetime of happiness and joy into the lives of every patient couple in the form of their child. And for that, we take every possible step making the best use of all the resources available at our behest. Armed with superior, advanced reproductive technology, and world-class doctors & technicians, Benison is committed to delivering successful pregnancy results as per our patient's requirements. At Benison we believe in developing and sharing a bond with our patients to assist them in the best possible manner to arrive at their desired results i.e. becoming a parent. It is our passion to help couples in their journey of parenthood to the best of our abilities. What separates the Benison IVF healthcare clinic from the rest of its counterparts is our ability to empathize with our patients and work upon a tailor-made solution for our every patient couple's needs. With a growing clientele and bank of happy parents.
Personalized care at affordable costs-At Benison, we believe in developing a patient-friendly environment to arrive at the best possible medical treatment suiting the needs and condition of our clients. The fact that our treatment doesn't leave a hole in your pocket is altogether another matter!. World-class technology- We use only superior and highly advanced reproductive technology for achieving desired results. Remember, you and your unborn child's safety is our first and foremost concern. State of the art infrastructure- All our clinics are fitted with modern amenities, cheerful ambiance and premium infrastructure. Highly qualified specialists- we work with only the best in the medical field. You will find our team of IVF specialists, embryologists, technicians & staff to be highly competent, well experienced and easily approachable. Convenient location- our clinic is located in the heart of the Delhi city i.e. in Dwarka, just a few minutes away from the nearest metro station. Excellent treatment guarantee- we meet all the national & international health standards on each IVF treatment Benison IVF & healthcare clinic is here to grant your wish of becoming a parent. All you need to do is just pick up the phone and set an appointment with us!
4. Gee Cee ART IVF Centre, Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Address & Directions: Dogra hall, Exchange Rd, Near BSNL Exchange, Ambphalla, Jammu, Jammu and Kashmir 180001
Website: https://gee-cee-art-ivf-centre.business.site/
The average IVF cost in Jammu and Kashmir ranges from Rs. 106,100 to Rs. 235,500 whereas in Gee Cee ART IVF Center, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Jammu and Kashmir is very economical, especially at Gee Cee ART IVF Centre, Jammu & Kashmir. We provide very reasonable IVF costs in Jammu and Kashmir where you are assured of quality treatment. Gee Cee ART IVF Centre Jammu, We're an IVF (test tube baby center) facility with state of the art equipment following international standards and guidelines. Jammu is a top player in the category Gynaecologist & Obstetrician Doctors in the Jammu. This well-known establishment acts as a one-stop destination servicing customers both local and from other parts of Jammu. Throughout its journey, this business has established a firm foothold in its industry. The belief that customer satisfaction is as important as their products and services have helped this establishment garner a vast base of customers, which continues to grow by the day. This business employs individuals that are dedicated to their respective roles and put in a lot of effort to achieve the common vision and larger goals of the company. Shortly, this business aims to expand its line of products and services and cater to a larger client base. In Jammu, this establishment occupies a prominent location in Kachi Chawni. It is an effortless task in commuting to this establishment as there are various modes of transport readily available. It is at, Near BSNL Telephone Exchange, which makes it easy for first-time visitors in locating this establishment. It is known to provide top service in the following categories: Gynaecologist & Obstetrician Doctors, IVF Centres, Maternity Hospitals, Test Tube Baby Centres, Gynecologic Oncologist Doctors, Fertility Centres, Infertility Clinics, IUI Centres.
5. Indira IVF Jammu & Kashmir (Low-cost IVF Centre in Jammu and Kashmir)
Address & Directions: 2nd Floor City Plaza, Maharaja Gulab Singh Road Khasra no. 620 – Min, Jammu, Jammu and Kashmir 180001
IVF Doctors: Dr. Poonam Pandotra (Gynaecologist & IVF Specialist),
Website: https://www.indiraivf.com/best-ivf-center-jammu/
The average IVF cost in Jammu and Kashmir ranges from Rs. 106,100 to Rs. 235,500 whereas in Indira IVF Jammu & Kashmir, it will cost you approximately from Rs. 99,950 to Rs. 212,000. the cost of IVF in Jammu and Kashmir is very economical, especially at Indira IVF Jammu & Kashmir, Jammu & Kashmir. We provide very reasonable IVF costs in Jammu and Kashmir where you are assured of quality treatment. Indira IVF is the largest and the most trusted fertility chain in India incorporating international treatment standards for infertility treatment and assisted reproductive technologies like IVF, ICSI, IUI, etc. With extraordinary patient-centered care and a track record of high IVF success rate in a very short interval of time, Indira IVF has become the first choice of couples seeking various fertility treatments including IVF across the world. We deliver infertility treatments and services in a very professional way. A very caring and comfortable environment is provided to the patients by our team of experienced specialists, sonographers, embryologists, nurses, and counselors who are all best in their fields. Indira IVF is aiming to expand its accessibility to even the smaller cities and towns by making infertility treatment available for patients within a shorter range of 200 km from their home. With 82+ fertility clinics pan India presently, it is planning to open 20 more IVF centers shortly. If you are concerned about your infertility problems and yearning to conceive your baby, the first step is to book a preliminary appointment with Indira IVF. With over 40+ years of experience and over 55,000+ successful IVF cycles, we are dedicated to provide our patients with the best medical treatment and care to fulfill their dreams of blissful parenthood. | {
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{"url":"https:\/\/hardware.slashdot.org\/story\/09\/10\/29\/1955236\/How-To-Enter-Equations-Quickly-In-Class\/interesting-comments","text":"typodupeerror\n\n## How To Enter Equations Quickly In Class?823\n\nAdmiralXyz writes \"I'm a university student, and I like to take notes on my (non-tablet) computer whenever possible, so it's easier to sort, categorize, and search through them later. Trouble is, I'm going into higher and higher math classes, and typing \"f_X(x) = integral(-infinity, infinity, f(x,y) dy)\" just isn't cutting it anymore: I need a way to get real-looking equations into my notes. I'm not particular about the details, the only requirement is that I need to keep up with the lecture, so it has to be fast, fast, fast. Straight LaTeX is way too slow, and Microsoft's Equation Editor isn't even worth mentioning. The platform is not a concern (I'm on a MacBook Pro and can run either Windows or Ubuntu in a virtual box if need be), but the less of a hit to battery life, the better. I've looked at several dedicated equation editing programs, but none of them, or their reviews, make any mention of speed. I've even thought about investing in a low-end Wacom tablet (does anyone know if there are ultra-cheap graphics tablets designed for non-artists?), but I figured I'd see if anyone at Slashdot has a better solution.\"\nThis discussion has been archived. No new comments can be posted.\n\n## How To Enter Equations Quickly In Class?\n\n\u2022 #### ASCIIMathML (Score:5, Interesting)\n\non Thursday October 29, 2009 @04:39PM (#29915877) Homepage\n\u2022 #### Re:pencil\/paper (Score:2, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @04:52PM (#29916169)\n\nI have been an engineer for 30 years and have tried over and over to take digital notes. I have never found an efficient solution. You're right - equations and drawings \/ sketches make digital note-taking a mess. OCR technology pukes on my handwriting.\n\nHere is the work flow that I have used for the last 5 years, or so:\n\n1. Handwritten notes in black pen.\n2. Scan according to your preference (200 dpi grayscale for me). Save as tiff.\n3. Import into Paperport.\n4. Use Paperport's annotation function to add searchable text boxes.\n\nIt sux, but I have about 2,500 pages of notes that I can search by my added keywords, and can back up in case of catastrophe.\n\nI continuously try to improve this workflow, and Paperport's ability to search on text boxes is unique. Most software needs\/wants to OCR and and make a linked text file in order to search.\n\n\u2022 #### Mac's Typography; in short: transcribe your notes (Score:4, Interesting)\n\non Thursday October 29, 2009 @05:00PM (#29916321)\nFirstly, the Mac has an incredibly rich simple character set. This is NOT coincidental, as Apple copied their editing capabilities from the publishing industry decades ago. E.g. in TextEdit type alt-b and you'll see a '' integral symbol (looks correct as I type it, hopefully the post wont change it). If you can learn these keyboard shortcuts (learning-curve arguments aside), you *may* be able to type these directly into your mac in class, BUT... If you take notes by hand, then transcribe them into your mac using these short cuts, or simply via the Mac's Font (e.g. TextEdit --> commant-T) and characters (e.g. via the gear drop-down in the Font) pane, you're doing yourself a much bigger favor.\n\u2022 #### Flamewar HO! (emacs + tex) (Score:1, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @05:04PM (#29916395)\n\nemacs has an amazing TeX input system. You can type everynthing in normally, but most LaTeX magic is bound to a 2-3 key combination starting with \nI don't actually remember what everything is any more, but i did find it incredibly useful. You may also want to cook up your own bindings for things that you like. One of my favorites that everyone else seemed to hate was Cx ( would insert \\left( \\right) and leave the cursor before the \\right).\n\n\u2022 #### Re:LyX (Score:1, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @05:06PM (#29916421)\n\nThe true learning curves....\n\n\u2022 #### Mathematica (Score:1, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @05:06PM (#29916433)\n\nMathematica can be pretty quick for formatting if you use the escape sequences ((escape)int(escape) gives an integral sign, for instance), and you can evaluate the things too if you're so inclined.\n\nOf course, you'll have to pay an arm and two legs for it, but you didn't need them anyway...\n\n\u2022 #### Re:LyX (Score:5, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @05:20PM (#29916633)\n\nI have used LyX in advanced mathematical courses such as quantum mechanics and relativistic electrodynamics. With the help of the copy-paste function I found that I could type the equations faster into my laptop than my classmates could write them onto paper and so had a little more time to think about them and ask questions.\n\nLyX is very easy to learn for note taking as you type stuff like:\nCNTL-M \\int_{-\\infty}^{\\infty} \\alpha(x) dx\nand get instant pretty graphical equations.\n\nIf you need to draw pictures, however, you will need a tablet or pen and paper.\n\nHope this helps...\n\n\u2022 #### Re:LyX (Score:2, Interesting)\n\non Thursday October 29, 2009 @05:20PM (#29916639)\nI also use Lyx. It is pretty fantastic. As is, it is already a bit quicker than straight LaTex, and you could try making some keyboard shortcuts to speed things up more.\n\u2022 #### Re:pencil\/paper (Score:5, Interesting)\n\non Thursday October 29, 2009 @05:21PM (#29916661) Homepage\nIf you're just interested in organization and searching, I'd highly recommend the LiveScribe Pulse smartpen - all the smarts are in the pen, which isn't too expensive compared to a tablet, and you can buy the compatible notebooks cheaply. All your notes get backed up to your computer when you dock your pen, it does a great job searching for a specific piece of text. My handwriting is a disaster, and I have never seen a search fail so far - I believe that it actually uses the sequence of pen motions (not just OCR on the final result) and it can tolerate some of the letters being unreadable. It has other features as well, such as recording audio (the mic has a decent gain) and syncing it with your notes. They also have an SDK and are launching an app store, so in the future you should be able to make good use of the ARM processor in the pen.\n\u2022 #### Use Word 2007's Equation support (Score:3, Interesting)\n\non Thursday October 29, 2009 @05:30PM (#29916819) Homepage\n\nThis is not the old Equation Editor 3.0 from Word 2003, which is a crippled version of MathType, but rather a brand new equation facility in Word 2007, which is also the basis for the new equation support in the OneNote 2010 beta another poster has referred to.\n\nThe Word 2007 equation editor supports a \"linear format\" for completely keyboard-based input, which is based on TeX-like commands like \"\\sum\" and \"\\int\" and is documented in this Unicode technical note: Unicode Nearly Plain-Text Encoding of Mathematics [unicode.org]\n\nI've been using this for my math classes since last semester, with great success. Once you master the linear format, it's not difficult to keep up if you have a reasonable typing rate to begin with.\n\n\u2022 #### Re:LyX (Score:1, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @05:40PM (#29916983)\n\nEven though we both have similar concepts of what the learning curve is referring to, I think the GP's interpretation is backwards, at least from a user interface design perspective. If the learning curve is steep, that means you learn a lot at the very beginning, which means that you have to learn a lot just to get started. Otherwise, you wouldn't have bothered to learn all that stuff up front. Thus, a steep learning curve means that the UI is relatively hard to learn, even if it doesn't take you a huge amount of time.\n\nThe ideal learning curve for software is actually fairly linear; the amount you learn at the beginning should be minimal because the UI should be discoverable enough and familiar enough (relative to other software) that you don't need to learn anything of substance to start using it at a basic level. As you get into it more, you should continue to discover things that make your life easier.\n\nJust my \\$0.02.\n\nAs an audio engineer who also teaches beginners how to compose on the computer, I have to say that Apple GarageBand is the closest thing to this \"linear learning curve\" in a UI I've ever seen.\n\nIt's easy to get started on a basic level of simple loops, and GarageBand '08 and later have (tucked away under the hood) all the advanced features you need to make a good-sounding original recording if you know how to use them.\n\n\u2022 #### Prof says: paper and pencil (Score:5, Interesting)\n\non Thursday October 29, 2009 @05:47PM (#29917079)\n\nHi, I'm a physics professor. I say, take your notes on paper. Math is the most computer-incompatible writing system ever designed. You'll never ever be able to type equations fast enough to keep up with me on the blackboard.\n\nAnd even if you manage to find a math entry system that's fast enough, it won't help you with the diagrams, graphs, and sketches.\n\nOf course, I don't practice what I preach: my own lecture notes are in text files. But that's because to me, \"block ramp friction mu=0.2, 1 kg 30deg 1m long, find final v. U=4.9 Wf=1.7 v=2.5\" is a complete set of notes for a 20-minute segment of lecture.\n\nOh, also: write in pencil. I guarantee you that whenever you bring a pen, I will spend the entire lecture correcting minor mistakes by erasing with the heel of my hand, changing variable notations, and editing diagrams and drawings halfway through working a problem.\n\n\u2022 #### Scientific Notebook. Top of the line math editing. (Score:3, Interesting)\n\non Thursday October 29, 2009 @05:47PM (#29917081)\n\nUsed to work there. Honestly, you can't beat it for mathematics editing, graphing, etc. Saves in Latex if you want. Free trial downloads too if you want to give the tires a kick.\n\nhttp:\/\/www.mackichan.com\/ [mackichan.com]\n\n\u2022 #### My experience (Score:3, Interesting)\n\non Thursday October 29, 2009 @05:48PM (#29917103) Homepage\n\n- I hate writing, and always have and avoid it wherever possible - it hurts my hand and my handwriting is awful.\n- I was using computers way before anyone else in my school, I even took some of the lessons that I was supposed to be taught in (the teacher found it easier that way).\n- I went to university to study Mathematics and Computing and had already had five years (at least) of proper exposure to things like Maple, Matlab, etc. (I was doing my A-level projects in Maple when nobody else, including my teachers, had even heard of it) through my brother who attended the same university.\n\nEvery single mathematics-based lecture, for three entire years, I hand-wrote notes. It's the only sensible way to do so. There isn't a notation or shorthand that can cope with rapidly sketching down formulae (especially integrals, sums of series, etc.) and diagrams. In some subjects, a simple diagram showing an angle, or a particular piece of geometry is invaluable and could takes hours to reproduce properly on a computer. I know, because for the last ten years, I've worked for tuition centres, state and private schools and I'm often asked to professionally produce an electronic version of their course materials (99% of the time mathematics because that's my speciality).\n\nDon't waste your time, memory, money and brainpower - just take pad and pen, or use a touchscreen\/tablet PC if you *insist* on using a computer. When you're taking notes the last thing you want to be doing is taking down the mathematics like it's some kind of gospel. There will be a million books on the subject where you can find the nuts and bolts of the process, but if you lose that \"feel\" of the mathematics that you can only get by watching someone apply it in front of your eyes, you'll never truly understand it.\n\nThe point of a lecture is to demonstrate and explain and give opportunity for questions (yes, ask questions... why does *nobody* ask questions in lectures? It isn't forbidden, just don't waste everyone's time with trivialities!), you learn more in a ten minute lecture on a particular subject than you ever will by studying the materials from that lecture. *Being* there, with the enthusiastic tutor, and the commentary they give, is what makes the mathematics explain itself. Everything else is just paper-based memoranda of that lecture. Someone, somewhere will be selling notes from that lecture. I've taken copies of complete stranger's notes (with their permission) when I missed lectures for reasons beyond my control. Notes are memory-aids only. Wasting an immense amount of time recording them in such a fashion is to focus on the aesthetics of the tool, not the job you're doing with that tool. All you're actually doing is writing the book that your lecturer learned from, you're not learning anything, and doing so at great expense. Your concentration should be on the mathematics happening in front of you, not the paper in your hand or the computer under your fingers.\n\nI often just sat in awe when I was in a lecture and watched the mathematics unfold in front of me, sketching only notes on the specifics.\n\nScribble notes. If you have special needs, ask to video\/record the lectures or for the lecturers to provide assistance afterwards (and complain to the highest authorities if they don't let you). Then, study, study, study from your notes, your memory, your skills, and the vast wealth of materials on every subject imaginable. Anyone can find out how to apply equation X to input Y, or read a book on graph theory or calculus, but advanced mathematics is more about the patterns and the art of being able to discover, use and apply that knowledge, not copy from rote from two-year-old notes.\n\nI graduated. Not a great grade but I was hitting a wall in my abilities in even the first year, a wall I've never been able to pass in the years since. Some courses ran like water through my sieve of a brain, and some were just second nature (and still are). But at no point did the actual taking of my notes interfere with\n\n\u2022 #### Re:ASCIIMathML (Score:2, Interesting)\n\non Thursday October 29, 2009 @06:01PM (#29917295)\nWow, never thought I would see that again. I actually used this for a web site in high school several years ago and it did very well. I am actually the one that ended up making the little logo that's at the bottom of that page so I could advertise it on our site in the \"powered by\/this-site-uses\" section. Don't go bashing my artistic abilities from the 9th grade :)\n\u2022 #### Re:What's old is new (Score:2, Interesting)\n\non Thursday October 29, 2009 @06:09PM (#29917419)\nWacom's Bamboo on windows having a Mac?... Leopard has a fantastic support for tablet pen. much better than windows vista. Also, with a bit practice, you can use LyX or any other equation editor, combined with Leopard's hand-write recognition. Just an idea\n\u2022 #### Webcam (Score:3, Interesting)\n\non Thursday October 29, 2009 @06:48PM (#29917905)\n\nWhat about getting a small, good quality webcam, preferably with a zoom feature? When your professor writes out an equation, point the camera at it, take a quick screen capture, and paste it into your notes.\n\n\u2022 #### Re:What's old is new (Score:3, Interesting)\n\non Thursday October 29, 2009 @08:11PM (#29918699) Homepage Journal\n\nI've been using OneNote for a couple of years, and I'm pretty disgusted with it. Too complicated, too limited. too unreliable, too many \"what were they thinking\" gotchas.\n\nRight now, I'm giving Evernote a try. Not as many snazzy features of OneNote, but the features it does have work well and are easy to access. And it's free, if you don't mind a few non-obnoxious ads. If it continues to bear the strain, I'm transferring all my data from OneNote and deleting the sucker.\n\n\u2022 #### Digital note taker (Score:1, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @08:31PM (#29918967)\n\nI have seen many different types of digital note takers that will store many pages of hand written notes. These are often stand alone devices that do not require a computer to input stuff. Then later you plug it into your computer and download the data. Many come with OCR software. Do a search on IOGEAR MOBILE DIGITAL SCRIBE for an example (note, I have not personally used any of these devices).\n\n\u2022 #### Get a tablet, use OSX (Score:3, Interesting)\n\non Thursday October 29, 2009 @09:30PM (#29919457)\n\nGet an inexpensive drawing tablet, turn on Ink in OSX (10.5 and up; at: System Preferences: but note that the preference pane will not show unless you have a graphics tablet plugged in). Write the formulas on the tablet.\n\nYou can take screenshots (Command-Option-3 full screen; Command-Option-4 select an area to capture) to save what you write\/draw and use Ink's character recognition to convert it to formulas with a check via the saved screenshots to make sure it didn't make errors. You can turn the character recognition off or on anytime via the Ink preference pane.\nYou will want to enable the Character Palette (at: System Preferences: Keyboard & Mouse) so you have quick access to the mathematical symbols in your chosen fonts for your saved notes.\n\n\u2022 #### Mathematica (Score:3, Interesting)\n\n<quentins' at' comclub.org'> on Thursday October 29, 2009 @10:08PM (#29919765) Homepage\n\nI love how everyone here is telling you to just pencil and paper. For the past 7 years (through both college and high school), I have taken all of my math notes in Mathematica. Every symbol, even the most esoteric ones, is at most four or five keystrokes. For example, an integral like integral x=0 to inf (x^2)\/xbar is quick to enter:\n\nintegral template -- ESC i n t t ESC\nbound -- x = 0 TAB ESC inf ESC\nvalue -- x C-6 2 RIGHT C-\/ x C-5 UNDERSCORE\n\nit's really quick to type, and you'll quickly learn the keystrokes from the character palette. I haven't taken a single note on paper in any of my math classes since about sophomore year of high school.\n\n--Quentin\n\n\u2022 #### Re:LyX (Score:1, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @10:14PM (#29919795)\n\nI agree. As a student, I handwrite my notes during lecture because it is easier for me to refer back to an earlier note to reiterate a point with a handwritten * than it is to scroll through lines of text, place an *, then scroll back and catch up with the lecture again. That's just my opinion, though.\n\n\u2022 #### LaTeX Macros save time (Score:2, Interesting)\n\non Thursday October 29, 2009 @10:45PM (#29920029)\n\nIf you're serious about taking mathematical notes, there really isn't anything to beat LaTeX except for the multi-mentioned writing tablets, where you're essentially recording images (and could do the job just as easily with pen and paper).\n\nIf you're worried about your typing of LaTeX taking too long, make macros. It's trivial to create commonly used macros for \"long\" things like \\int_{-\\infty}^{\\infty} so instead, you type \\iII (i - i-cap - i-cap) or some other easily remembered name. If you're still typing out every bit of math you do in LaTeX long-hand, you aren't coming close to using the true power inherent in a markup language.\n\nWant easy ways to represent \\mathbb{R} or \\mathbb{C}? \\rS or \\cS defines work great. Integrals? Same idea. Just figure out what the commonly used things are in the class you're taking notes for, and make macros for that.\n\n\u2022 #### LaTeXiT (Score:1, Interesting)\n\nby Anonymous Coward on Thursday October 29, 2009 @10:55PM (#29920101)\n\nThere is a wonderful mac program called LaTeXiT. It basically lets you type latex directly into a very small editor. The results are compiled and displayed in another window and you can drag the result into your favourite notetaking program.\n\nIt's pretty neat.\n\nThat said, in a lecture, I still prefer my pen.\n\n\u2022 #### Re:Get a tablet, use OSX (Score:2, Interesting)\n\non Friday October 30, 2009 @02:33AM (#29921071) Homepage Journal\nInk is great and completely under utilized gem in OS X, and I think you could maybe even get away with using it on the track pad without the wacom tablet if you're tight on space and don't want to seem like a total douche bringing a laptop and tablet to take note.. BUT thanks to the fact that you're using a mac, I think what might be more direct and faster even is to be able to type the darn thing? its not that hard to type your special characters: option-b is \"\" for sumation, option-v is \"\" for square root. a few parentheses latter and you have a quick enough way to write most things, pi is option-p is \"\" . hold down option for a while and mash the keyboard to find what you want, or you can launch the 'special characters\/unicode' typing window and figure them out that way I might use optino-5 for infinity \"\" and option-a for alpha \"\u00e5\" you can probobly do a find-replace latter to fix any oddness in what you want to see vs. what you typed.\n\u2022 #### Re:LyX (Score:4, Interesting)\n\non Friday October 30, 2009 @04:31AM (#29921507)\n\nI wrote my thesis in LyX, and it was basically a good experience with few problems. However, if I was doing it again I'd probably use straight LaTeX via a nice editor (gedit has a nice LaTeX plugin, for example). The reason for this is that I think LaTeX is in someways a bit simpler than LyX because it is always clear what is happening, whereas LyX has a second markup stage. I had a bit of difficulty doing some document-wide formatting in LyX that I think would've been more straight-forward in LaTeX.\n\nI'm certainly not being heavily critical of LyX, and think that if you stick to their bundled document formats, you should be fine.\n\n(this is a little off-topic, because the article is about taking equation notes in class, which would be a cinch in LyX, I reckon.)\n\n\u2022 #### Digital Pen? (Score:3, Interesting)\n\non Friday October 30, 2009 @05:56AM (#29921769)\nUnless I've missed it, I can't believe no one has suggested a digital pen such as the e-Pen ones? http:\/\/www.practicalpc.co.uk\/reviews\/hard\/peripherals\/e-pens-create.htm [practicalpc.co.uk]\n\n<< WAIT >>\n\nWorking...","date":"2018-05-21 08:58:50","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\": 0.47452789545059204, \"perplexity\": 2370.839504163673}, \"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-2018-22\/segments\/1526794863972.16\/warc\/CC-MAIN-20180521082806-20180521102806-00148.warc.gz\"}"} | null | null |
\section{Introduction} \label{sec:intro}
Large-scale retrieval, also known as first stage retrieval \citep{Cai2021IRSurvey}, aims to fetch top \textit{query}-relevant \textit{documents}\footnote{Each entry of a collection could also be \textit{sentence}, \textit{passage}, etc.} from a huge collection.
In addition to its indispensable roles in dialogue systems \citep{Zhao2020KGC}, question answering \citep{Karpukhin2020DPR}, and search engines, etc., it also has been surging in recent cutting-edge topics, e.g., retrieval-augmented generation \citep{Lewis2020RetriAugGen} and retrieval-augmented language modeling \citep{Guu2020RetriAugLM}.
As there are millions to billions of documents in a collection, efficiency is the most fundamental prerequisite for large-scale retrieval.
To this end, query-agnostic document representations (i.e., indexing the collection independently) and lightweight relevance metrics (e.g., cosine similarity, dot-product) have become the common practices to meet the prerequisite -- usually achieved by a two-tower structure \citep{Reimers2019SentenceBERT}, a.k.a., bi-encoder and dual-encoder, in representation learning literature.
Besides the prevalent `dense-vector retrieval' paradigm that encodes both queries and documents in the same low-dimension, real-valued latent semantic space, another retrieval paradigm, `lexicon-weighting retrieval', aims to leverage weighted sparse representation in vocabulary space \citep{Formal2021SPLADEv2,shen2022unifier}.
It learns to use a few lexicons in the vocabulary and assign them with weights to represent queries and documents -- sharing a high-level inspiration with BM25 but differing in dynamic (with compression and expansion) lexicons and their importance weights learned in an end-to-end manner.
Although learning the representations in such a high-dimensional vocabulary space seems intractable with limited human-annotated query-document pairs, recent surging pre-trained language modeling (PLM), especially the masked language modeling (MLM), facilitates transferring context-aware lexicon-coordinate knowledge into lexicon-weighting retrieval by fine-tuning the PLM on the annotated pairs \citep{Formal2021SPLADE,Formal2021SPLADEv2,shen2022unifier}.
Here, coordinate terms (full of synonyms and concepts) are highly related to relevance-centric tasks and mitigate the lexicon mismatch problem \citep{Cai2021IRSurvey}, leading to superior retrieval quality.
Due to the pretraining-finetuning consistency with the same output vocabulary space, lexicon-based retrieval methods can fully leverage a PLM, including its masked language modeling (MLM) head, leading to better search quality (e.g., $\sim 1.0\%$ MRR@10 improvement over dense-vector ones by fine-tuning the same PLM initialization \citep{Formal2021SPLADEv2,Hofstatter2020Improving}).
Meantime, attributed to the high-dimensional sparse-controllable representations \citep{Yang2021TopkSparse,Lassance2022SPLADEbt}, these methods usually enjoy higher retrieval efficiency than dense-vector ones (e.g., $10\times$ faster with the identical performance in our experiments).
Nonetheless, there still exists a subtle yet crucial gap between the pre-training language modeling and the downstream lexicon-weighting objectives.
That is, masked language modeling \citep{Devlin2019BERT} aims to recover a word back given its contexts, so it inclines to assign high scores to certain (i.e., low-entropy) words, but these words are most likely to be articles, prepositions, etc., or belong to collocations or common phrases.
Therefore, language modeling is in conflict with the lexicon-weighting representation for relevance purposes, where the latter focuses more on the high-entropy words (e.g., subject, predicate, object, modifiers) that are essential to the semantics of a query or document.
These can explain, when being fine-tuned under the paradigm of lexicon-weighting retrieval, why a moderate PLM (i.e., DistilBERT) can even outperform a relatively large one (i.e., BERT-base) and why a well-trained PLM (e.g., RoBERTa) cannot even achieve a convergence.
To mitigate the gap, in this work we propose a brand-new pre-training framework, dubbed lexicon-bottlenecked masked autoencoder (LexMAE), to learn importance-aware lexicon representations for the transferable knowledge towards large-scale lexicon-weighting retrieval.
Basically, LexMAE pre-trains a language modeling encoder for document-specific lexicon-importance distributions over the whole vocabulary to reflect each lexicon's contribution to the document reconstruction.
Motivated by recent dense bottleneck-enhanced pre-training \citep{Gao2022coCondenser,Liu2022RetroMAE,Wang2022simlm}, we present to learn the lexicon-importance distributions in an unsupervised fashion by constructing continuous bag-of-words (CBoW) bottlenecks upon the distributions.
Thereby, LexMAE pre-training architecture consists of three components: i) a language modeling encoder (as most other PLMs, e.g., BERT, RoBERTa), ii) a lexicon-bottlenecked module, and iii) a weakened masking-style decoder.
Specifically, a mask-corrupted document from the collection is passed into the \textit{language modeling encoder} to produce token-level LM logits in the vocabulary space.
Besides an MLM objective for generic representation learning, a max-pooling followed by a normalization function is applied to the LM logits to derive lexicon-importance distribution.
To unsupervisedly learn such a distribution, the \textit{lexicon-bottlenecked module} leverages it as the weights to produce a CBoW dense bottleneck,
while the \textit{weakened masking-style decoder} is asked to reconstruct the aggressively masked document from the bottleneck.
Considering the weakened decoder and its aggressive masking, the decoder in LexMAE is prone to recover the masked tokens on the basis of the CBoW bottleneck, and thus the LexMAE encoder assigns higher importance scores to essential vocabulary lexicons of the masked document but lower to trivial ones. This closely aligns with the target of the lexicon-weighting retrieval paradigm and boosts its performance.
After pre-training LexMAE on large-scale collections, we fine-tune its language modeling encoder to get a lexicon-weighting retriever, improving previous state-of-the-art performance by 1.5\% MRR@10 with $\sim\!\!13\times$ speed-up on the ad-hoc passage retrieval benchmark. Compared to the baseline lexicon-weighting retriever, the fine-tuned LexMAE shows a substantial gain (+5.1\% MRR@10). Meantime, LexMAE shows great zero-shot transfer capability and achieves state-of-the-art performance on BEIR benchmark with 12 datasets, e.g., Natural Questions, HotpotQA, and FEVER.
\section{Related Work} \label{sec:relatedwork}
\paragraph{Bottleneck-enhanced Dense-vector Retrieval. }
Recently, pre-trained language models (PLM), e.g., BERT \citep{Devlin2019BERT}, RoBERTa \citep{Liu2019RoBERTa}, DeBERTa \citep{He2021DeBERTa}, have been proven generic and effective when transferred to a broad spectrum of downstream tasks via fine-tuning. When transferring PLMs to large-scale retrieval, a ubiquitous paradigm is known as `dense-vector retrieval' \citep{Xiong2021ANCE} -- encoding both queries and documents in the same low-dimension, real-valued latent semantic space and then calculating query-document relevance scores on the basis of spatial distance. However, dense-vector retrieval methods suffer from the objective gap between lexicon-recovering language model pre-training and document-compressing dense-vector fine-tuning.
Although a natural remedy has been dedicated to the gap by constructing pseudo query-document pairs \citep{Lee2019ICT,Chang2020BFS,Gao2022coCondenser,Zhou2022hyperlink} or/and enhancing bottleneck dense representation \citep{Lu2021SeedEncoder,Gao2021Condenser,Gao2022coCondenser,Wang2022simlm,Liu2022RetroMAE}, the methods are still limited by their intrinsic representing manners -- dense-vector leading to large index size and high retrieval latency -- applying speed-up algorithms, product-quantization \citep{Zhan2022RepCONC}, however resulting in dramatic drops (e.g., $-3\% \sim 4\%$ by \citet{Xiao2022DistillVQ}).
\paragraph{Lexicon-weighing Large-Scale Retrieval.}
In contrast to the almost unlearnable BM25, lexicon-weighing retrieval methods, operating on lexicon-weights by a neural model, are proposed to
exploit language models for term-based retrieval \citep{Nogueira2019d2q,Nogueira2019DT5Q,Formal2021SPLADE,Formal2021SPLADEv2,Formal2022SPLADE++}.
According to different types of language models, there are two lines of works: based on causal language models (CLM) \citep{Radford2018GPT,Raffel2020T5}, \citep{Nogueira2019DT5Q} use the concurrence between a document and a query for lexicon-based sparse representation expansion. Meantime, based on masked language models (MLM) \citep{Devlin2019BERT,Liu2019RoBERTa}, \citep{Formal2021SPLADE} couple the original word with top coordinate terms (full of synonyms and concepts) from the pre-trained MLM head.
However, these works directly fine-tune the pre-trained language models, regardless of the objective mismatch between general language modeling and relevance-oriented lexicon weighting.
\section{LexMAE: Lexicon-bottlenecked Masked Autoencoder} \label{sec:pretrain}
\begin{figure}
\centering
\includegraphics[width=0.75\linewidth]{figs/model_illustration.pdf}
\caption{\small An illustration of lexicon-bottlenecked masked autoencoder (LexMAE) pre-training architecture. }
\label{fig:model_illustration}
\end{figure}
As illustrated in Figure~\ref{fig:model_illustration}, our lexicon-bottlenecked masked autoencoder (LexMAE) contains one encoder and one decoder with masked inputs in line with the masked autoencoder (MAE) family \citep{He2021MAE,Liu2022RetroMAE}, while is equipped with a lexicon-bottlenecked module for document-specific lexicon-importance learning.
\paragraph{Overview of LexMAE Pre-training. }
Given a piece of free-form text, $x$, from a large-scale collection, ${\mathbb{C}}$, we aim to pre-train a language modeling encoder, $\theta^{\text{(enc)}}$, that represents $x$ with weighted lexicons in the vocabulary space, i.e., ${\bm{a}}\in[0,1]^{|{\mathbb{V}}|}$. ${\mathbb{V}}$ denotes the whole vocabulary.
Here, each $a_i = P({\textnormal{w}}=w_i|x; \theta^{\text{(enc)}})$ with $w_i\in{\mathbb{V}}$ denotes the importance degree of the lexicon $w_i$ to the whole text $x$.
To learn the distribution ${\bm{a}}$ for $x$ in an unsupervised fashion, an additional decoder $\theta^{\text{(dec)}})$ is asked to reconstruct $x$ based on ${\bm{a}}$. In the remaining of this section, we will dive into the pre-training architecture and objective of LexMAE.
\subsection{Language Modeling Encoder}
Identical to most previous language modeling encoders, e.g., BERT \citep{Devlin2019BERT}, the language modeling encoder, $\theta^{\text{(enc)}}$, in LexMAE is composed of three parts,
i.e., a \textit{word embedding module} mapping discrete tokens in $x$ to dense vectors, \textit{multi-layer Transformer} \citep{Vaswani2017Transformers} for deep contextualization, and a \textit{language modeling head} mapping back to vocabulary space $\mathbb{R}^{|{\mathbb{V}}|}$.
First, following the common practice of pre-training the encoder unsupervisedly, a masked language modeling (MLM) objective is employed to pre-train $\theta^{\text{(enc)}}$. Formally, given a piece of text $x\in{\mathbb{C}}$, a certain percentage ($\alpha\%$) of the tokens in $x$ are masked to obtain $\bar x$, in which $80\%$ replaced with a special token \texttt{[MASK]}, $10\%$ replaced with a random token in ${\mathbb{V}}$, and the remaining kept unchanged \citep{Devlin2019BERT}. Then, the masked $\bar x$ is fed into the language modeling encoder, $\theta^{\text{(enc)}}$, i.e.,
\begin{align}
{\bm{S}}^{\text{(enc)}} = \transformerlm(\bar x; \theta^{\text{(enc)}}) \in\mathbb{R}^{|{\mathbb{V}}|\times n}, \label{equ:lm_enc}
\end{align}
where ${\bm{S}}^{\text{(enc)}}$ denotes LM logits. Lastly, MLM objective is to minimize the following loss,
\begin{align}
L^{\text{(elm)}} = - \sum_{{\mathbb{D}}}\sum_{j\in{\mathbb{M}}^{\text{(enc)}}}\log P({\textnormal{w}}^j=x_j | \bar x; \theta^{\text{(enc)}}),~\text{where}~P({\textnormal{w}}^j) \coloneqq \mathrm{softmax}({\bm{S}}^{\text{(enc)}}_{:,j}), \label{equ:loss_enc}
\end{align}
where ${\mathbb{M}}^{\text{(enc)}}$ denotes the set of masked indices of the tokens in $\bar x$, ${\textnormal{w}}^j$ denotes the discrete variable over ${\mathbb{V}}$ at the $j$-th position of $x$, and $x_j$ is its original token (i.e., golden label of the MLM objective).
\subsection{Lexicon-bottlenecked Module}
Given the token-level logits from Eq.(\ref{equ:lm_enc}) defined in the vocabulary space, we propose to calculate a lexicon-importance distribution by
\begin{align}
{\bm{a}} \coloneqq P({\textnormal{w}}|\bar x; \theta^{\text{(enc)}}) = \norm(\maxpool({\bm{S}}^{\text{(enc)}}))\in[0,1]^{|{\mathbb{V}}|}, \label{equ:lex_importance_dist}
\end{align}
where $\maxpool(\cdot)$ denotes max pooling along with the sequence axis, $\norm(\cdot)$ denotes a normalization function (let $\sum a_i = 1$), which we simply take $\mathrm{softmax}(\cdot)$ in our main experiments.
Again, $P({\textnormal{w}}|\bar x; \theta^{\text{(enc)}})$ denotes lexicon-importance distribution over ${\mathbb{V}}$ to indicate which lexicons in ${\mathbb{V}}$ is relatively important to $x$.
The main obstacle to learning the lexicon-importance distribution $P({\textnormal{w}}|\bar x; \theta^{\text{(enc)}})$ is that we do not have any general-purpose supervised signals.
Inspired by recent bottleneck-enhanced dense representation learning \citep{Gao2022coCondenser,Liu2022RetroMAE,Wang2022simlm}, we propose to leverage the lexicon-importance distribution as a clue for reconstructing $x$ back. As such, our language modeling encoder will be prone to focus more on the pivot or essential tokens/words in $x$.
However, it is intractable to directly regard the high-dimensional distribution vector ${\bm{a}}\in[0,1]^{|{\mathbb{V}}|}$ as a bottleneck
since i) the distribution over the whole ${\mathbb{V}}$ has enough capacity to hold most semantics of $x$ \citep{Yang2022softmaxBottleneck}, making the bottleneck less effective and ii) the high-dimensional vector is hardly fed into a decoder for representation learning and text reconstruction.
Therefore, we further propose to construct a continuous bag-of-words (CBoW) bottleneck following the lexicon-importance distribution $P({\textnormal{w}}|\bar x; \theta^{\text{(enc)}})$ derived from Eq.(\ref{equ:lex_importance_dist}). That is
\begin{align}
{\bm{b}} \coloneqq \mathbb{E}_{w_i \sim P({\textnormal{w}}|\bar x; \theta^{\text{(enc)}})}[{\bm{e}}^{(w_i)}] = {\bm{W}}^{\text{(we)}}{\bm{a}}. \label{equ:cbow_bottleneck}
\end{align}
Here, ${\bm{W}}^{\text{(we)}}=[{\bm{e}}^{(w_1)}, {\bm{e}}^{(w_2)}, \dots]\in\mathbb{R}^{d\times|{\mathbb{V}}|}$ denotes the learnable word embedding matrix in the parameters $\theta^{\text{(enc)}}$ of language modeling encoder, where $d$ denotes embedding size, ${\bm{e}}^{(w_i)}$ denotes a word embedding of the lexicon $w_i$.
Thereby, ${\bm{b}}\in\mathbb{R}^d$ stands for dense-vector CBoW bottleneck, upon which a decoder (will be detailed in the next sub-section) is asked to reconstruct the original $x$ back.
\paragraph{Remark.}
As aforementioned in our Introduction, there exists a conflict between MLM and lexicon-importance objectives, but we still apply an MLM objective in our encoder.
This is because
i) the MLM objective can serve as a regularization term to ensure the original token in $x$ receive relatively high scores in contrast to its coordinate terms
and ii) the token-level noise introduced by the MLM task has been proven effective in robust learning.
\subsection{Weakened Masking-style Decoder}
Lastly, to instruct the bottleneck representation ${\bm{b}}$ and consequently learn the lexicon-importance distribution $P({\textnormal{w}}|\bar x; \theta^{\text{(enc)}})$, we leverage a decoder to reconstruct $x$ upon ${\bm{b}}$.
In line with recent bottleneck-enhanced neural structures \citep{Gao2022coCondenser,Wang2022simlm},
we employ a weakened masking-style decoder parameterized by $\theta^{\text{(dec)}}$, which pushes the decoder to rely heavily on the bottleneck representation.
It is noteworthy that the `weakened' is reflected by two-fold: i) aggressively masking strategy and ii) shallow Transformer layers (says two layers).
In particular, given the masked input at the encoder side, $\bar x$, we first apply an extra $\beta\%$ masking operation, resulting in $\tilde x$. That is, the decoder is required to recover all the masked tokens that are also absent in the encoder, which prompts the encoder to compress rich contextual information into the bottleneck.
Then, we prefix $\tilde x$ with the bottleneck representation $b$, i.e., replacing the special token \texttt{[CLS]} with the bottleneck.
Therefore, our weakened masking-style decoding with Transformer-based language modeling decoder can be formulated as
\begin{align}
{\bm{S}}^{\text{(dec)}} = \transformerlm({\bm{b}}, \tilde x; \theta^{\text{(dec)}}) \in\mathbb{R}^{|{\mathbb{V}}|\times n}, \label{equ:lm_dec}
\end{align}
where $\theta^{\text{(dec)}}$ parameterizes this weakened masking-style decoder.
Lastly, similar to the MLM at the encoder side, the loss function is defined as
\begin{align}
L^{\text{(dlm)}} = - \sum_{{\mathbb{D}}}\sum_{j\in{\mathbb{M}}^{\text{(dec)}}}\log P({\textnormal{w}}^j=x_j | \bar x; \theta^{\text{(dec)}}),~\text{where}~P({\textnormal{w}}^j) \coloneqq \mathrm{softmax}({\bm{S}}^{\text{(dec)}}_{:,j}), \label{equ:loss_dec}
\end{align}
where ${\mathbb{M}}^{\text{(dec)}}$ denotes the set of masked indices of the tokens in $\tilde x$.
\subsection{Pre-Training Objective}
The final loss function of pre-training LexMAE is a direction addition of the losses defined in Eq.(\ref{equ:loss_enc}) and Eq.(\ref{equ:loss_dec}), i.e.,
\begin{align}
L^{\text{(lm)}} = L^{\text{(elm)}} + L^{\text{(dlm)}}. \label{equ:loss_lexmae}
\end{align}
Meanwhile, we tie all word embedding metrics in our LexMAE pre-training architecture, including the word embedding modules and language model heads of both the encoder \& decoder, as well as ${\bm{W}}^{\text{(we)}}$ in Eq.(\ref{equ:cbow_bottleneck}).
It is noteworthy that we cut-off the gradient back-propagation for ${\bm{W}}^{\text{(we)}}$ in Eq.(\ref{equ:cbow_bottleneck}) to make the training focus only on the lexicon-importance distribution $P({\textnormal{w}}|\bar x; \theta^{\text{(enc)}})$ rather than ${\bm{W}}^{\text{(we)}}$.
\section{Fine-tuning Pipeline for Lexicon-weighting Retriever} \label{sec:finetune}
In this section, we will elaborate on the fine-tuning pipeline of our LexMAE, which starts with a formal definition of the downstream task, large-scale retrieval.
\paragraph{Task Definition of Large-scale Retrieval.}
Given a collection containing a number of documents, i.e., ${\mathbb{D}} = \{d_i\}_{i=1}^{|{\mathbb{D}}|}$, and a query $q$, a retriever aims to fetch a list of text pieces $\bar{{\mathbb{D}}}_q$ to contain all relevant ones.
Generally, this is based on a relevance score between $q$ and every document $d_i$ in a Siamese manner, i.e., $<\enc(q), \enc(d_i)>$, where $\enc$ is an arbitrary representation model (e.g., neural encoders) and $<\cdot,\cdot>$ denotes a lightweight relevance metric (e.g., dot-product).
\subsection{Contrastive Learning for Lexicon-weighting Retrieval}
To transfer LexMAE into large-scale retrieval, we get rid of its decoder but only fine-tune the language modeling encoder for lexicon-weighting retriever.
Basically, to leverage a language modeling encoder for lexicon-weighting representations, we adopt \citep{Formal2021SPLADEv2} and represent a piece of text, $x$, in high-dimensional vocabulary space by
\begin{align}
{\bm{v}}^{(x)} = \log(1 + \maxpool(\max(\transformerlm(x; \theta^{\text{(enc)}}), 0))) \in\mathbb{R}*^{|{\mathbb{V}}|}, \label{equ:splade_repre}
\end{align}
where $\max(\cdot, 0)$ ensures all values greater than or equal to zero for upcoming sparse requirements, and the saturation function $\log(1+\maxpool(\cdot))$ prevents some terms from dominating.
In contrast to conventional binary classification task, the retrieval tasks are formulated as contrastive tasks. That is, only a limited number of positive documents, $d^{(q)}_+$, is provided for a query $q$ so we need sample a set of negative documents, ${\mathbb{N}}^{(q)}=\{d^{(q)}_-, \dots \}$, from ${\mathbb{D}}$ for the $q$. And we will dive into the sampling strategy to get ${\mathbb{N}}^{(q)}$ in the next subsection. Note that if no confusion arises, we omit the superscript ${(q)}$ that indicates `a query-specific' for clear demonstration. By following \citet{Formal2021SPLADEv2} and \citet{shen2022unifier}, we can first derive a likelihood distribution over the positive $\{d_+\}$ and negative ${\mathbb{N}}$ documents, i.e.,
\begin{align}
{\bm{p}} \coloneqq P({\textnormal{d}}|q, \{d_+\}\cup{\mathbb{N}};\theta^{\text{(enc)}}) = \dfrac{\exp({\bm{v}}^{(q)T}{\bm{v}}^{(d)})}{\sum\nolimits_{d'\in\{d_+\}\cup{\mathbb{N}}} \exp({\bm{v}}^{(q)T}{\bm{v}}^{(d')})},~\forall d\in\{d_+\}\cup{\mathbb{N}}
\end{align}
where ${\bm{v}}^{(\cdot)}\in\mathbb{R}*^{|{\mathbb{V}}|}$ derived from Eq.(\ref{equ:splade_repre}) stands for a lexicon-weighting representation for a query $q$ or a document $d$. Then, the loss function of the contrastive learning towards this retrieval task is defined as
\begin{align}
L^{\text{(r)}} = \sum\nolimits_q - \log P({\textnormal{d}}=d_+|q, \{d_+\}\cup{\mathbb{N}};\theta^{\text{(enc)}}) + \lambda\flops(q,d) = - \sum \log {\bm{p}}_{[{\textnormal{d}}=d_+]}, \label{equ:loss_finetune_general}
\end{align}
where $\flops(\cdot)$ denotes a regularization term for representation sparsity \citep{Paria2020FLOPS} as first introduced by \citet{Formal2021SPLADE} and $\lambda$ denotes a hyperparameter of it loss weight.
\subsection{Multi-stage Retriever Fine-tuning} \label{sec:multi_stage_finetune}
To train a state-of-the-art lexicon-weighting retriever, we adapt the fine-tuning pipeline in a recent dense-vector retrieval method \citep{Wang2022simlm} as illustrated in Figure~\ref{fig:finetune_pipeline}. The major difference is the source of the involved reranker for knowledge distillation into a retriever: In contrast to \citep{Wang2022simlm} that trains a reranker on the fly for retriever-specific reranker but suffers from high computation overheads, we propose to leverage an off-the-shelf reranker by \citep{Zhou2022r2anker}.
\begin{figure}
\centering
\includegraphics[width=0.75\linewidth]{figs/finetune_pipeline.pdf}
\caption{\small An illustration of fine-tuning pipeline of our retrievers. Here, the fine-tuned reranker is directly adopted from \citep{Zhou2022r2anker} to avoid expensive reranker training. }
\label{fig:finetune_pipeline}
\end{figure}
\paragraph{Stage 1: BM25 Negatives.}
In the first stage, we sample negatives for each query $q$ within top-$K_1$ document candidates by BM25 retrieval system, which is denoted as ${\mathbb{N}}^{\text{(bm25)}}$. Therefore, the contrastive learning loss of stage 1 of our retriever fine-tuning is written as
\begin{align}
L^{\text{(r1)}} = \sum\nolimits_q - \log P({\textnormal{d}}=d_+|q, \{d_+\}\cup{\mathbb{N}}^{\text{(bm25)}};\theta^{\text{(enc)}}) + \lambda_1\flops. \label{equ:loss_finetune_stage1}
\end{align}
\paragraph{Stage 2: Hard Negatives.}
Then, we sample the hard negatives ${\mathbb{N}}^{\text{(hn1)}}$ for each query $q$ within top-$K_2$ candidates based on the relevance scores by the retriever we obtain in stage 1, and the training loss of our stage 2 is defined as
\begin{align}
L^{\text{(r2)}} = \sum\nolimits_q - \log P({\textnormal{d}}=d_+|q, \{d_+\}\cup{\mathbb{N}}^{\text{(hn1)}};\theta^{\text{(enc)}}) + \lambda_2\flops. \label{equ:loss_finetune_stage2}
\end{align}
\paragraph{Stage 3: Reranker-Distilled.} Lastly, we further sample hard negatives ${\mathbb{N}}^{\text{(hn2)}}$ for each query $q$ within top-$K_3$ candidates by the 2nd-stage retriever. Besides the contrastive learning objective, we also distill a well-trained reranker into our stage 3 of the retriever, which is written as
\begin{align}
L^{\text{(r3)}} = \sum\nolimits_q &\kldiv(P({\textnormal{d}}|q, \{d_+\}\cup{\mathbb{N}}^{\text{(hn2)}};\theta^{\text{(enc)}}) || P({\textnormal{d}}|q, \{d_+\}\cup{\mathbb{N}}^{\text{(hn2)}};\theta^{\text{(rk)}})) \label{equ:loss_finetune_stage3} \\
\notag & - \gamma \log P({\textnormal{d}}=d_+|q, \{d_+\}\cup{\mathbb{N}}^{\text{(hn2)}};\theta^{\text{(enc)}}) + \lambda_3\flops.
\end{align}
Here, $\theta^{\text{(rk)}}$ parameterizes an expensive but effective cross-encoder as the reranker for knowledge distillation, and KL divergence, $\kldiv(\cdot||\cdot)$, is used as distillation loss with $\theta^{\text{(rk)}}$ frozen.
\subsection{Inference for Large-Scale Retrieval} \label{sec:lex_inference}
In the inference phase of large-scale retrieval, there are some differences between dense-vector and lexicon-weighting retrieval methods.
As in Eq.(\ref{equ:loss_finetune_general}), we use the dot-product between the real-valved sparse lexicon-weighting representations as a relevance metric, where `real-valved' is a prerequisite of gradient back-propagation and end-to-end learning.
However, it is inefficient and infeasible to leverage the real-valved sparse representations, especially for the open-source term-based retrieval systems, e.g., LUCENE and Anserini \citep{Yang2017Anserini}. Following \citet{Formal2021SPLADEv2}, we adopt `quantization' and `term-based system' to complete our retrieval procedure. That is, to transfer the high-dimensional sparse vectors back to the corresponding lexicons and their virtual frequencies, the lexicons are first obtained by keeping the non-zero elements in a high-dim sparse vector, and each virtual frequency then is derived from a straightforward quantization (i.e., $\floor{100\times{\bm{v}}}$).
In summary, the overall procedure of our large-scale retrieval based on a fine-tuned LexMAE is i) generating the high-dim sparse vector for each document and transferring it to lexicons and frequencies, ii) building a term-based inverted index via Anserini \citep{Yang2017Anserini} for all documents in a collection, iii) given a test query, generating the lexicons and frequencies, in the same way, and iv) querying the built index to get top document candidates.
\section{Experiment}
\paragraph{Benchmark Datasets.}
Following \citet{Formal2021SPLADEv2}, we first employ the widely-used passage retrieval datasets, MS-Marco~\citep{Nguyen2016MSMARCO}.
We only leverage its official queries (no augmentations \citep{Ren2021RocketQAv2}), and report for MS-Marco Dev set, TREC Deep Learning 2019 set~\citep{Craswell2020TREC19}, and TREC Deep Learning 2020 set~\citep{Craswell2021TREC20}.
Besides, we evaluate the zero-shot transferability of our model on BEIR benchmark~\citep{Thakur2021BEIR}.
We employ twelve datasets covering semantic relatedness and relevance-based retrieval tasks (i.e., TREC-COVID, NFCorpus, Natural Questions, HotpotQA, FiQA, ArguAna, Tóuche-2020, DBPedia, Scidocs, Fever, Climate-FEVER, and SciFact) in the BEIR benchmark as they are widely-used across most previous retrieval works.
\textbf{Evaluation Metrics.}
Following previous works, we report MRR@10 (M@10) and Recall@1/50/100/1K for MS-Marco Dev, and report NDCG@10 for both TREC Deep Learning 2019 and TREC Deep Learning 2020.
Moreover, NDCG@10 is reported on BEIR benchmark.
Regarding R@N metric, we found there are two kinds of calculating ways, and we strictly follow the official evaluation one at
\url{https://github.com/usnistgov/trec_eval} and
\url{https://github.com/castorini/anserini}, which is defined as
\begin{align}
\text{Marco-Recall@N} = \dfrac{1}{|{\mathbb{Q}}|} \sum_{q\in{\mathbb{Q}}} \dfrac{ \sum_{d_+\in {\mathbb{D}}_+} \bm{1}_{d_+ \in \bar{\mathbb{D}}} }{\min(N, |{\mathbb{D}}_+|)},
\end{align}
where there may be multiple positive documents ${\mathbb{D}}^+\in{\mathbb{D}}$, ${\mathbb{Q}}$ denotes the test queries and $\bar{\mathbb{D}}$ denotes top-K document candidates by a retrieval system. We also call this metric as \textit{all-positive-macro} Recall@N.
On the other hand, another recall calculation method following DPR \citep{Karpukhin2020DPR} is defined as
\begin{align}
\text{DPR-Recall@N} = \dfrac{1}{|{\mathcal{Q}}|} \sum_{q\in{\mathbb{Q}}} \bm{1}_{\exists d \in \bar{\mathbb{D}} \wedge d \in {\mathbb{D}}^+ }.
\end{align}
which we call \textit{one-positive-enough} Recall@N.
Therefore, The official (\textit{all-positive-macro}) Recall@N is usually less than DPR (\textit{one-positive-enough}) Recall@N, and the smaller N, the more obvious.
\paragraph{Pre-training Setups.}
We pre-train the LexMAE on the MS-Marco collection \citep{Nguyen2016MSMARCO}, where most hyperparameters are identical to \citep{Wang2022simlm} without tuning: the encoder is initialized by BERT$_{\text{base}}$ \citep{Devlin2019BERT} whereas the other parts are randomly initialized, the batch size is set to 2048, the max text length is set to 144, the learning rate is set to $3\times 10^{-4}$, the number of training steps is 80k, the masking percentage ($\alpha\%$) of encoder is set to 30\%, and the masking percentage ($\alpha+\beta\%$) of decoder is set to 50\%. Meantime, the random seed is always 42, and the pre-training is completed on eight NVIDIA A100 GPUs within 14h.
\paragraph{Fine-tuning Setups.}
We share some hyperparameters across all three stages: learning rate is set to $2\times 10^{-5}$ by following \citet{shen2022unifier}, number of training epochs is set to 3, model initialization is always our LexMAE, max document length is set to 144, and max query length is set to 32.
Following \citep{Wang2022simlm}, the $\gamma$ in Eq.(\ref{equ:loss_finetune_stage3}) is set to 0.2.
In contrast to \citep{Wang2022simlm} using 4 GPUs for fine-tuning, we limited all the fine-tuning experiments on one A100 GPU.
The batch size (w.r.t the number of queries) is set to 24 with 1 positive and 15 negative documents in the fine-tuning stage 1 and 2, whereas that is set to 16 with 1 positive and 23 negative documents (to increase the number of negatives but fit one GPU memory by reducing the batch size).
Another important hyperparameter is the depth (keeping how many top candidates as negatives) of negative sampling, i.e., $K$ in Eq.(\ref{equ:loss_finetune_stage1} - \ref{equ:loss_finetune_stage3}). By following \citet{Wang2022simlm} and \citet{Gao2022coCondenser}, we keep 1000 for BM25 negatives and 200 for other negatives, i.e., $K_1=1000, K_2=200, K_3=200$.
The only hyperparameter we have tuned is the loss weight $\lambda$ in Eq.(\ref{equ:loss_finetune_stage1} - \ref{equ:loss_finetune_stage3}), i.e., $\lambda_1 \in\{0.001, 0.002, 0.004\}$ (corresponding to BM25 negatives) and $\lambda_{2/3} \in\{0.004,0.008,0.016\}$ (corresponding to hard negatives). Empirically, we found $\lambda_1=0.002, \lambda_2=0.008, \lambda_3=0.008$ achieving a great performance-efficiency trade-off.
Again, we fix the random seed always to 42 in all our experiments without any tuning.
\subsection{Main Evaluation}
\input{tables/main_marco}
\begin{wraptable}{r}{0.45\textwidth}
\centering
\vspace{-44pt}
\caption{\small Retrieval results on MS-Marco Dev on \textit{one-positive-enough} recall. Note that the official Recall@50 of our fine-tuned LexMAE is 88.9\%.} \label{tab:exp_main_otherrecall}
\setlength{\tabcolsep}{1.5pt}
\small
\begin{tabular}{lccc}
\toprule
\multicolumn{1}{c}{\textbf{Method}} & {M@10} & \underline{\textit{R@50}} & \underline{\textit{R@1K}} \\ \hline
RocketQA \citep{Qu2021RocketQA} & 37.0 & 85.5 & 97.9 \\
PAIR \citep{Ren2021PAIR} & 37.9& 86.4 & 98.2 \\
RocketQAv2 & 38.8 & 86.2 & 98.1 \\
AR2 & 39.5 & 87.8 & {98.6} \\
Unifie\textsc{r}$_{\text{lexicon}}$ & 39.7 & 87.6 & 98.2 \\
Unifie\textsc{r}$_{\text{dense}}$ & 38.8 & 86.3 & 97.8 \\
\hline
LexMAE & \textbf{42.6} & \textbf{89.6} & \textbf{99.0} \\
\bottomrule
\end{tabular}
\vspace{-15pt}
\end{wraptable}
\paragraph{MS-Marco.}
First, we compare our fine-tuned LexMAE with a wide range of baselines and competitors to perform large-scale retrieval in Table~\ref{tab:exp_main_dev_dl19} \& \ref{tab:exp_main_otherrecall}.
It is shown that our method substantially outperforms the previous best retriever, SimLM, by a very large margin (+1.5\% MRR@10) and achieves a new state-of-the-art performance.
Standing with different retrieval paradigms and thus different bottleneck constructions, such a large performance margin verifies the superiority of lexicon-weighting retrieval when a proper initialization is given.
Meantime, the LexMAE is dramatically superior (+5.1\% MRR@10) to its baseline \citep{Formal2022SPLADE++}, Co-Self-Disil, with the same neural model scale but different model initialization (coCondenser \citep{Gao2022coCondenser} v.s. LexMAE).
This verifies that our lexicon-bottlenecked pre-training is more effective than the dense-bottlenecked one in lexicon-weighting retrieval.
\paragraph{TREC Deep Learning 2019 and TREC Deep Learning 2020.}
As shown in Table~\ref{tab:exp_main_dev_dl19}, we also evaluate our LexMAE on both the TREC Deep Learning 2019 (DL'19) and the TREC Deep Learning 2020 (DL'20).
It is observed that LexMAE consistently achieves new state-of-the-art performance on both datasets, which verifies the effectiveness of our LexMAE again.
\paragraph{BEIR benchmark. }
\begin{table}[t]
\small
\centering
\setlength{\tabcolsep}{1.5pt}
\caption{\small Zero-shot transfer performance (nDCG@10) on BEIR benchmark. `BEST ON' and `AVERAGE' do not take the in-domain result into account. `ColBERT' is its v2 version \citep{Khattab2021ColBERTv2}. } \label{tab:exp_beir_details}
\begin{tabular}{lccccccccccc}
\toprule
\textbf{Method} & BM25 & DocT5 & SPLADE & ColBERT & DPR & ANCE & GenQ & TAS-B & Contriever & UnifieR & \textbf{LexMAE} \\ \midrule
In-Domain & 22.5 & 33.8 & 43.3 & 42.5 & - & 38.8 & 40.8 & 40.8 & - & 47.1 & \textbf{48.0} \\
\hline
\hline
TREC-COVID & 65.6 & 71.3 & 71.0 & 73.8 & 33.2 & 65.4 & 61.9 & 48.1 & 59.6 & {71.5} & \textbf{76.3} \\
NFCorpus & 32.5 & 32.8 & 33.4 & 33.8 & 18.9 & 23.7 & 31.9 & 31.9 & 32.8 & {32.9} & \textbf{34.7} \\
NQ & 32.9 & 39.9 & 52.1 & \textbf{56.2} & 47.4 & 44.6 & 35.8 & 46.3 & 49.8 & 51.4 & \textbf{56.2} \\
HotpotQA & 60.3 & 58.0 & 68.4 & 66.7 & 39.1 & 45.6 & 53.4 & 58.4 & 63.8 & {66.1} & \textbf{71.6} \\
FiQA & 23.6 & 29.1 & 33.6 & \textbf{35.6} & 11.2 & 29.5 & 30.8 & 30.0 & {32.9} & 31.1 & 35.2 \\
ArguAna & 31.5 & 34.9 & 47.9 & 46.3 & 17.5 & 41.5 & {49.3} & 42.9 & 44.6 & 39.0 & \textbf{50.0} \\
Tóuche-2020 & \textbf{36.7} & 34.7 & 27.2 & 26.3 & 13.1 & 24.0 & 18.2 & 16.2 & 23.0 & 30.2 & 29.0 \\
DBPedia & 31.3 & 33.1 & 43.5 & \textbf{44.6} & 26.3 & 28.1 & 32.8 & 38.4 & {41.3} & 40.6 & 42.4 \\
Scidocs & 15.8 & 16.2 & 15.8 & 15.4 & 7.7 & 12.2 & 14.3 & 14.9 & \textbf{16.5} & 15.0 & 15.9 \\
Fever & 75.3 & 71.4 & 78.6 & 78.5 & 56.2 & 66.9 & 66.9 & 70.0 & 75.8 & 69.6 & \textbf{80.0} \\
Climate-FEVER & 21.3 & 20.1 & \textbf{23.5} & 17.6 & 14.8 & 19.8 & 17.5 & 22.8 & {23.7} & 17.5 & 21.9 \\
SciFact & 66.5 & 67.5 & 69.3 & 69.3 & 31.8 & 50.7 & 64.4 & 64.3 & 67.7 & {68.6} & \textbf{71.7} \\ \midrule
BEST ON & 1 & 0 & 1 & 3 & 0 & 0 & 0 & 0 & 1 & 0 & \textbf{7} \\
AVERAGE & 41.1 & 42.4 & 47.0 & 47.0 & 26.4 & 37.7 & 39.8 & 40.4 & 44.3 & 44.5 & \textbf{48.7} \\ \bottomrule
\end{tabular}
\end{table}
Lastly, we evaluate the LexMAE on BEIR benchmark, which contains twelve datasets,
where ArguAna, Scidocs, Fever, Climate-FEVER, and SciFact are semantic relatedness tasks while TREC-COVID, NFCorpus, NQ, HotpotQA, FiQA, Tóuche-2020, and DBPedia are relevance-based retrieval tasks.
To apply LexMAE pre-training to this benchmark, we pre-train LexMAE on BEIR collections and then fine-tune the pre-trained encoder on the in-domain supervised data of the BEIR benchmark.
Lastly, we evaluate the fine-tuned LexMAE on both the in-domain evaluation set and the twelve out-of-domain datasets, whose results are listed in Table~\ref{tab:exp_beir_details}.
It is observed that our LexMAE achieves the best in-domain performance.
When performing the zero-shot transfer on the twelve out-of-domain datasets, LexMAE achieves state-of-the-art effectiveness on 7 out of 12 datasets, and delivers the best overall metrics, i.e., `BEST ON' and `AVERAGE'.
Specifically, we improve the previous best average nDCG@10 by 1.7\%.
All these results support that besides the great performance on in-domain data, the sophisticated pre-training designs in terms of model structures and self-supervised data improve the generalization ability of the LexMAE.
\subsection{Efficiency Analysis and Comparison}
Since a large-scale retrieval with millions or billions of documents usually serves as an upstream module for downstream tasks or a fundamental module in commercial systems, a key metric of these retrieval systems is efficiency in terms of retrieval latency (query-per-second, QPS), index size for inverted indexing, as well as representation size per document (for non-inverted indexing).
Compared to dense-vector retrieval methods \citep{Zhan2022RepCONC,Xiao2022DistillVQ} that rely on product-quantization (PQ) and inverted file (IVF) to compromise their performance ($-3\%\sim4\%$) for memory \& time efficiency, the lexicon-weighting method with high-dimension sparse representation is intrinsically efficient for large-scale retrieval as demonstrated in \S\ref{sec:lex_inference} -- fully compatible with traditional term-based retrieval system, e.g., BM25 -- only manipulating the term frequency and document frequency by the neural language modeling encoder.
\begin{figure}[t]
\centering
\includegraphics[width=0.7\linewidth]{figs/lexmae_efficiency}
\caption{\small Retrievers with their performance and QPS (latency). The retrievers include dense-vector methods (i.e., SimLM, AR2), quantized-dense methods (i.e., RepCONC \citep{Zhan2022RepCONC}, ADORE-IVF \citep{Zhan2021STAR-ADORE}), and lexicon-based methods (i.e., SPLADEv2 \citep{Formal2021SPLADEv2}, BT-SPLADE \citep{Lassance2022SPLADEbt}, DocT5query \citep{Nogueira2019DT5Q}, BM25, and LexMAE). }
\label{fig:retriever_qps}
\end{figure}
\begin{table}[t] \small
\centering
\caption{\small Index sizes of different retriever models with their retrieval performance (MRR@10) on MS-Marco Dev. `Repr Byte' denotes the storage requirement for an embedded passage. Note that each activated (non-zero) term in lexicon-weighed sparse vector needs 3 bytes (2 bytes for indexing and 1 byte for its weight). }
\label{tab:retriever_index_size}
\begin{tabular}{lrrr}
\toprule
{\textbf{Method}} & {\textbf{Index Size}} & \textbf{Repr Byte} &\textbf{MRR@10} \\ \hline
ColBERTv2 & 150G & Avg 17,203 & 39.7 \\
AR2 & 27G & 3,072 & 39.5 \\
SimLM & 27G & 3,072 & 41.1 \\
\hline
BM25 & 4.3G & Avg 210 & 18.5 \\
SPLADE-max & 2.0G & Avg 290 & 34.0 \\
SPLADE-mask & 5.4G & Avg 915 & 37.3 \\
\hline
\textbf{LexMAE} & 3.7G & - & 42.6 \\
~- top-256 sparsify & 3.5G & Upto 768 & 42.6 \\
~- top-128 sparsify & 2.4G & 384 & 42.3 \\
~- top-64 sparsify & 1.4G & 192 & 41.8 \\
~- top-32 sparsify & 0.9G & 96 & 40.0 \\
~- top-16 sparsify & 0.5G & 48 & 36.0 \\
~- top-8 sparsify & 0.4G & 24 & 30.6 \\
~- top-4 sparsify & 0.3G & 12 & 24.0 \\
~- top-2 sparsify & 0.2G & 6 & 15.2 \\
~- top-1 sparsify & 0.2G & 3 & 1.9 \\
\bottomrule
\end{tabular}
\end{table}
To dive into LexMAE's efficacy-efficiency trade-off, we present a simple but effective sparsifying method -- only keep top-K weighted (frequency) in the inference phase to represent the document and then build the inverted index for the sparsified documents.
In contrast, \citet{Yang2021TopkSparse} and \citet{Lassance2022SPLADEbt} propose to sparsify the lexicon-weighing representations by controlling fine-tuning hyperparameters -- leading to extra computation overheads.
On the one hand, as shown in Figure~\ref{fig:retriever_qps}, our LexMAE achieves the best efficacy-efficiency trade-off among all dense-vector, quantized-dense, and lexicon-based methods.
Compared to the previous state-of-the-art retriever, SimLM, we improve its retrieval effectiveness by 1.5\% MRR@10 with $14.1\times$ acceleration.
With top-L sparsifying, LexMAE can achieve competitive performance with SimLM with 100+ QPS.
In addition, LexMAE shows a much better trade-off than the recent best PQ-IVF dense-vector retriever, RepCONC.
Compared to previous state-of-the-art lexicon-based methods, SPLADEv2 and BT-SPLADE, our LexMAE is far better in efficacy-efficiency trade-off.
Meantime, it is also observed that compared to BM25, LexMAE with only the Top-32 tokens kept for each passage is as fast as BM25 but greatly achieves 40.0\% MRR@10 (cf. 18.5\% MRR@10 of BM25). Surprisingly, when only 4 tokens were kept for each passage, the performance of LexMAE (24.0\% MRR@10) is still better than BM25 retrieval (18.5\% MRR@10).
On the other hand, as listed in Table~\ref{tab:retriever_index_size}, we also compare different retrieval paradigms in the aspect of their storage requirements.
Compared to dense-vector methods, lexicon-based methods, including our LexMAE, inherently show fewer storage requirements in terms of both index size of the collection and representation Byte per document.
Compared to our baselines, SPLADE-max and SPLADE-mask, our LexMAE wins in terms of both performance and storage.
Meantime, compared to BM25 building its index at the word level, the learnable lexicon-weighting methods, based on the smaller vocabulary of sub-words, are more memory-friendly.
\subsection{Further Analysis}
\begin{table}[t]\small
\parbox{.45\linewidth}{
\small
\centering
\caption{\small Comparison with ensemble and hybrid retrievers. $^1$An ensemble of four SPLADE models. }\label{tab:exp_quan_ensemble}
\setlength{\tabcolsep}{2pt}
\begin{tabular}{lcc}
\toprule
\multicolumn{1}{l}{\textbf{Method}} & {M@10} & {R@1} \\
\hline
LexMAE-pipeline & 43.1 & 28.8 \\
LexMAE-ensemble & 43.1 & 28.8 \\
\hline
Unifie\textsc{r}$_{\text{uni}}$~\citep{shen2022unifier} & 40.7 & 26.9 \\
Ensemble of SPLADE$^1$ & 40.0 & - \\
COIL-full~\citep{Gao2021COIL} & 35.5 & - \\
CLEAR~\citep{Gao2021CLEAR} & 33.8 & - \\
\bottomrule
\end{tabular}
}
\hfill
\parbox{.42\linewidth}{
\centering
\caption{\small Comparisons of our retriever with \textit{retrieval\&rerank} pipelines.}\label{tab:exp_cmp_reranker}
\setlength{\tabcolsep}{1.5pt}
\begin{tabular}{llc}
\toprule
{\textbf{Retriever}} & {\textbf{Reranker}} &{M@10} \\ \hline
RepBERT & RepBERT & 37.7 \\
ME-HYBRID & ME-HYBRID & 39.4 \\
RocketQA & RocketQA & 40.9 \\
RocketQAv2 & RocketQAv2 & 41.9 \\ \hline
\multicolumn{2}{l}{LexMAE (retriever-only)} & 42.6 \\
\bottomrule
\end{tabular}
}
\end{table}
\paragraph{Analysis of Dense-Lexicon Complement. }
As verified by \citet{shen2022unifier}, the lexicon-weighting retrieval is complementary to dense-vector retrieval and a simple linear combination of them can achieve excellent retrieval performance.
As shown in Table~\ref{tab:exp_quan_ensemble}, we conduct an experiment to complement our LexMAE with the state-of-the-art dense-vector retrieval method, i.e., SimLM (which we re-implement according to \citep{Wang2022simlm}).
Specifically, we propose to leverage two strategies:
i) \textit{ensemble}: a direct linear combination is applied to the retrieval scores of both paradigms, inevitably resulting in significant computation overheads due to twice large-scale retrieval as in many hybrid retrieval methods;
and ii) \textit{pipeline}: a retrieval pipeline is leveraged to avoid twice large-scale retrieval: our lexicon-weighting retrieval based on an inverted index is to retrieve top-K documents from the collection and then our dense-vector retrieval is merely applied to the constrained candidates for dense scores.
It is shown that we improve the previous state-of-the-art hybrid retrieval method by 2.4\% MRR@10 on MS-Marco Dev.
\paragraph{Comparison to Retrieval\&Rerank Pipeline. }
Furthermore, our LexMAE retriever can outperform many state-of-the-art \textit{retrieval \& rerank} pipeline methods as in Table~\ref{tab:exp_cmp_reranker}.
It is noteworthy that these rerankers (a.k.a., cross-attention model or cross-encoder) are very costly as they must be applied to every query-document text concatenation, instead of query-agnostic representations from a bi-encoder.
\paragraph{Zero-shot Retrieval. }
\begin{wrapfigure}{R}{0.33\textwidth}
\centering
\includegraphics[width=0.9\linewidth]{figs/marco_zero_shot.pdf}
\caption{\small Zero-shot retrieval results (nDCG@10) on MS-Marco Dev. }
\label{fig:zero_shot}
\end{wrapfigure}
To figure out if our LexMAE pre-training can learn lexicon-importance distribution, we conduct a zero-shot retrieval on MS-Marco.
Specifically, instead of $\mathrm{softmax}$ normalization function in Eq.(\ref{equ:lex_importance_dist}), we present a saturation function-based L1 norm (i.e., $\lonenorm(\log(1+\relu(\cdot)))$) and keep the other parts unchanged.
Without fine-tuning, we directly apply the pre-trained LexMAE to MS-Marco retrieval task, with the sparse representation of $\log(1+\relu(\cdot)))$.
As shown in Figure~\ref{fig:zero_shot}, our lexicon-importance representations by the pre-trained LexMAE (110M parameters) can outperform BM25 in terms of large-scale retrieval and is competitive with a very large model, SGPT-CE \citep{Muennighoff2022SGPT} with 6.1B parameters.
\paragraph{Multi-stage Retrieval Performance. }
\begin{table}[t]
\small
\centering
\setlength{\tabcolsep}{1.5pt}
\caption{\small Performance on different stages of the fine-tuning pipeline on MS-Marco. } \label{tab:multi_stage_res}
\begin{tabular}{lcccccc}
\toprule
\multicolumn{1}{c}{\multirow{2}{*}{\textbf{Methods}}} & \multicolumn{2}{c}{\textbf{BM25 Negatives}} & \multicolumn{2}{c}{\textbf{Hard Negatives}} & \multicolumn{2}{c}{\textbf{Reranker-Distilled}} \\ \cmidrule(l){2-3} \cmidrule(l){4-5} \cmidrule(l){6-7}
\multicolumn{1}{c}{}& MRR@10 & R@1000 & MRR@10 & R@1000 & MRR@10 & R@1000 \\ \midrule
coCondenser & 35.7&97.8&38.2&98.4&40.2&98.3 \\
SimLM & 38.0&98.3&39.1&\textbf{98.6}&41.1&98.7 \\
LexMAE & \textbf{39.3}& \textbf{98.3}& \textbf{40.8}&98.5 &\textbf{42.6} &\textbf{98.8} \\
\bottomrule
\end{tabular}
\end{table}
As shown in Table~\ref{tab:multi_stage_res}, we exhibit more details about the retrieval performance of different pre-training methods on multiple fine-tuning stages (see \S\ref{sec:multi_stage_finetune}).
It can be seen that our LexMAE consistently achieves the best or competitive results on all the 3 stages.
\paragraph{Comparisons with Different Pre-training Objectives. }
\begin{table}[]
\small
\centering
\caption{\small Different pre-training objectives with its first-stage fine-tuning MRR@10 performance on MS-Marco.}
\setlength{\tabcolsep}{3pt}
\begin{tabular}{l|c|ccccccc}
\toprule
& \textbf{LexMAE} & SimLM & Enc-Dec MLM & Condenser & MLM & Enc-Dec RTD & AutoEncoder & BERT$_\text{base}$ \\ \hline
\textbf{M@10} & \textbf{39.3} & 38.0 & 37.7 & 36.9 & 36.7 & 36.2 & 32.8 & 33.7 \\
\bottomrule
\end{tabular}
\label{tab:diff_obj_1st_ftres}
\end{table}
As listed in Table~\ref{tab:diff_obj_1st_ftres}, we compare our pre-training objective with a batch of other objectives by fine-tuning the pre-trained model on MS-Marco BM25 negatives.
It can be seen that our LexMAE improves the previous best by 1.3\% MRR@10 in MS-Marco Dev.
\section{Conclusion}
In this work, we propose to improve the lexicon-weighing retrieval by pre-training a lexicon-bottlenecked masked autoencoder (LexMAE) which alleviates the objective mismatch between the masked language modeling encoders and relevance-oriented lexicon importance. After pre-training LexMAE on large-scale collections, we first observe great zero-shot performance. Then after fine-tuning the LexMAE on the large-scale retrieval benchmark, we obtain state-of-the-art retrieval quality with very high efficiency and also deliver state-of-the-art zero-shot transfer performance on BEIR benchmark. Further detailed analyses on the efficacy-efficiency trade-off in terms of retrieval latency and storage memory also verify the superiority of our fine-tuned LexMAE.
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{"url":"https:\/\/proofwiki.org\/wiki\/Primitive_of_Power_of_Root_of_a_x_%2B_b_over_x_squared","text":"# Primitive of Power of Root of a x + b over x squared\n\nJump to navigation Jump to search\n\n## Theorem\n\n$\\displaystyle \\int \\frac {\\left({\\sqrt{a x + b} }\\right)^m} {x^2} \\ \\mathrm d x = -\\frac {\\left({\\sqrt{a x + b} }\\right)^{m + 2} } {b x} + \\frac {m a} {2 b} \\int \\frac {\\left({\\sqrt{a x + b} }\\right)^m} x \\ \\mathrm d x$\n\n## Proof\n\n$\\displaystyle \\int x^m \\left({a x + b}\\right)^n \\ \\mathrm d x = \\frac {x^{m+1} \\left({a x + b}\\right)^{n + 1} } {\\left({m + 1}\\right) b} - \\frac {\\left({m + n + 2}\\right) a} {\\left({m + 1}\\right) b} \\int x^{m + 1} \\left({a x + b}\\right)^n \\ \\mathrm d x$\n\nPutting $n := \\dfrac m 2$ and $m := -2$:\n\n $\\displaystyle \\int \\frac {\\left({\\sqrt{a x + b} }\\right)^m} {x^2} \\ \\mathrm d x$ $=$ $\\displaystyle \\int x^{-2} \\left({a x + b}\\right)^{m\/2} \\ \\mathrm d x$ $\\displaystyle$ $=$ $\\displaystyle \\frac {x^{-1} \\left({a x + b}\\right)^{m\/2 + 1} } {\\left({\\left({-2}\\right) + 1}\\right) b} - \\frac {\\left({\\left({-2}\\right) + \\frac m 2 + 2}\\right) a} {\\left({\\left({-2}\\right) + 1}\\right) b} \\int x^{\\left({-2}\\right) + 1} \\left({a x + b}\\right)^{m\/2} \\ \\mathrm d x$ $\\displaystyle$ $=$ $\\displaystyle - \\frac {\\left({a x + b}\\right)^{\\left({m + 2}\\right)\/2} } {b x} - \\frac {m a} {2 b} \\int \\frac {\\left({a x + b}\\right)^{m\/2} } x \\ \\mathrm d x$ simplifying $\\displaystyle$ $=$ $\\displaystyle -\\frac {\\left({\\sqrt{a x + b} }\\right)^{m + 2} } {b x} + \\frac {m a} {2 b} \\int \\frac {\\left({\\sqrt{a x + b} }\\right)^m} x \\ \\mathrm d x$\n\n$\\blacksquare$","date":"2020-06-03 09:03:29","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\": 2, \"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\": 0.6224560141563416, \"perplexity\": 329.0630624739658}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"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-2020-24\/segments\/1590347432521.57\/warc\/CC-MAIN-20200603081823-20200603111823-00324.warc.gz\"}"} | null | null |
Sir James Augustine Gobbo, (22 March 1931 – 7 November 2021) was an Australian jurist who served as the 25th Governor of Victoria, from 1997 to 2000.
Family and early life
James Gobbo was born in Carlton, Victoria, on 22 March 1931, to Italian parents Antonio and Regina. In March 1935 the family returned to Cittadella, Padua, Italy, where a sister, Natalina, was born shortly after. Three years later the family, which also included a brother, Flavio, arrived back in Australia to take up permanent residency in North Melbourne, Victoria. Gobbo, then aged seven, spoke no English at the time of his return, and his father, who had started a café, felt the time was right for him to receive a Catholic education.
Gobbo's early schooling included St Mary's Primary School, West Melbourne and later St Joseph's CBC, North Melbourne. In 1944 he was accepted into Xavier College. He was a member of the Xavier College crew that won the 1948 Associated Public Schools Head of the River. After leaving Xavier College, he studied law at the University of Melbourne during which time he lived at Newman College. In 1951 he was awarded a Rhodes Scholarship, following which he attained a Master of Arts degree at Magdalen College, University of Oxford.
In 1957 Gobbo married former librarian Shirley Lewis, and had five children. His son, James Gobbo Jr., was the Liberal candidate for the district of Bentleigh in the 2006 Victorian state election.
Judicial career
After many years as a barrister and later as a Queen's Counsel, Gobbo was appointed a judge of the Supreme Court of Victoria. He served from 18 July 1978 until he retired from the bench on 14 February 1994.
Vice-regal career
Gobbo served as Lieutenant-Governor of Victoria from 1995 until he was appointed Governor of Victoria in 1997 by Queen Elizabeth II on the advice of the Victorian premier, Jeff Kennett. He was the first Australian state governor of Italian descent.
Gobbo's term of office was to be shorter than the usual five years, due to the uncertain outcome of the looming 1999 Australian republic referendum. If a republic had come into effect, then the governorship of Victoria would have been abolished from 1 January 2001. In August 2000 the new premier, Steve Bracks, announced that Gobbo's successor would be John Landy, who would take up his post in January 2001. Gobbo immediately made it known that he had had an understanding with Kennett for an extension of his term beyond 2000, and expressed deep disappointment that this was not now to occur. However, this understanding must have been private, since Kennett's letter of appointment stated that any extension beyond 31 December 2000 would be a matter for the premier of the day. Bracks said that he had no knowledge of any such understanding.
After leaving office, Gobbo took up the position of Commissioner for Italy for the Victorian government until June 2006, and continued on various boards and councils.
In 2006, Gobbo was the Chair of the Council of the National Library of Australia and the Council of the Order of Australia and Chair of the Australian Multicultural Foundation.
Honours
Gobbo was appointed a Knight Bachelor in the 1982 New Year Honours; a Companion of the Order of Australia (AC) in 1993; and a Knight of Grace of the Most Venerable Order of the Hospital of St John of Jerusalem in 1997. He was awarded the Centenary Medal in 2001 and was also a Knight of Malta.
Death
Gobbo died on 7 November 2021 at the age of 90.
See also
Judiciary of Australia
List of Judges of the Supreme Court of Victoria
Victorian Bar Association
References
External links
Papers of Sir James Gobbo Papers of Sir James Gobbo
Trove James Gobbo and parents photograph
Trove Gobbo family portrait, Italy
1931 births
2021 deaths
Alumni of Magdalen College, Oxford
Australian Commanders of the Royal Victorian Order
Australian Knights Bachelor
Australian King's Counsel
Australian Rhodes Scholars
Australian people of Italian descent
Companions of the Order of Australia
Governors of Victoria (Australia)
Judges of the Supreme Court of Victoria
Knights of Malta
Lieutenant-Governors of Victoria
Melbourne Law School alumni
National Library of Australia Council members
People educated at Xavier College
People from North Melbourne
People educated at St Joseph's College, Melbourne | {
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{"url":"https:\/\/math.stackexchange.com\/questions\/1326453\/how-many-sets-of-four-points-in-an-mxn-grid-have-one-point-contained-by-three-ot","text":"# How many sets of four points in an MxN grid have one point contained by three other points?\n\nGiven a 3x3 grid:\n\n1 2 3\n8 9 4\n7 6 5\n\n\nWe find 126 distinct sets of 4 points $$\\binom{9}{4}$$\n\nThere are 8 cases such that when the points are connected with a line in clockwise direction, one point (in this case, 9) is contained by angle formed from joining the other three points with a line:\n\n{1,3,6,9}, {1,4,6,9}, {1,4,7,9}, {2,4,7,9},\n\n{2,5,7,9}, {2,5,8,9}, {3,5,8,9}, {3,6,8,9}.\n\n\ni.e., where {1,4,7,9} contains 9.\n\nFor a grid of any m and n, how can we determine the number of sets for which such a condition holds? So, the number of sets across all $$\\binom{mn}{4}$$\n\nWhere one point is inside angle formed by connecting the other 3 members of the set.\n\n\u2022 What exactly do you mean when you say one is contained by the other three? \u2013\u00a0Arthur Jun 15 '15 at 17:13\n\u2022 Updated answer, adding illustration @Arthur \u2013\u00a0Calvin Froedge Jun 15 '15 at 17:14\n\u2022 Do you want the answer for a specific fixed \"middle\" element in your $m \\times n$ grid, or do you want the sum of counts of all solutions over all choices for \"middle\" element? And if the latter, what if a triangle contains more than one \"middle\" point? Do you want that to just count as 1, or do you want to multiply by the number of middle points? \u2013\u00a0user2566092 Jun 15 '15 at 17:16\n\u2022 So you want the number of sets of four points in a rectangular grid that don't make a convex (degenerate?) quadrilateral? \u2013\u00a0Arthur Jun 15 '15 at 17:19\n\u2022 @Arthur Based on the example, it seems like the \"middle point\" must be in the strict interior, e.g. (2,4,6,9) wasn't listed as a solution. \u2013\u00a0user2566092 Jun 15 '15 at 17:21\n\nPick's theorem will tell you for a grid how many interior grid points you have inside a given triangle, in terms of the volume (easy to compute) and number of boundary points on the triangle (also easy to compute by computing for each side, the GCD of coordinates of the vector connecting one vertex to another). Also the answer is translation and rotation and reflection invariant since you are working on a grid. So this reduces a seemingly ${{mn} \\choose 4}$ complexity calculation to one that is $O({{mn} \\choose 2})$, basically by assuming one vertex is $(1,1)$ and the other vertices are in the upper-right. It's still not as good as an explicit formula but it can at least handle values of $mn$ that are the square of the values of $mn$ that you could previously handle by brute force.\n\u2022 Well, you don't have to do every choice of ${{mn} \\choose 3}$ triangles, based on the symmetries, but yes, basically you have to do $O({{mn} \\choose 2})$ triangles this way and evaluate them individually and then multiply by the number of similar triangles you can get by translation\/rotation\/reflection. So it won't scale forever without a more explicit formula, but at least you can solve bigger cases than brute force. And even without symmetries, you can count the number of interior points for each of the ${{mn} \\choose 3}$ triangles easily with Pick's theorem. \u2013\u00a0user2566092 Jun 15 '15 at 17:47\n\u2022 @CalvinFroedge I'm not sure. If you increase $m$ or $n$ then it's possible you'll get new triangles with interior points where the new triangles have side slopes that weren't possible for previous $m$ and $n$. I have to think more, but I'm guessing this problem is fairly hard. \u2013\u00a0user2566092 Jun 15 '15 at 17:58\n\u2022 @CalvinFroedge I'd recommend setting $m = n$ and brute forcing the answer for a decent number of values of $n$ and then checking the sequence of counts you get against the Online Encyclopedia of Integer Sequences (OEIS). \u2013\u00a0user2566092 Jun 15 '15 at 17:59","date":"2020-02-21 18:29:47","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\": 0.639082670211792, \"perplexity\": 305.0887480592789}, \"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-2020-10\/segments\/1581875145534.11\/warc\/CC-MAIN-20200221172509-20200221202509-00026.warc.gz\"}"} | null | null |
Q: Python argparse argument that is python keyword I want to have a python command line argument --lambda, but I can't access it as lambda is a python keyword.
import argparse
p = argparse.ArgumentParser()
p.add_argument('--lambda')
args = p.parse_args()
print args.lambda
I get:
print args.lambda
^
SyntaxError: invalid syntax
How can I do this?
A: You can add a different name for the attribute with dest e.g.
import argparse
p = argparse.ArgumentParser()
p.add_argument('--lambda', dest='llambda')
args = p.parse_args()
print args.llambda
A: argparse uses hasattr and getattr to set values in the Namespace. This allows you to use flags/dest that are not valid in the args.dest syntax. Here the problem is with a restricted key word. It could also be a string with special characters. So getattr(args, 'lambda') should work.
vars(args) creates a dictionary, allowing you to use vars(args)['lambda'].
But changing the dest is a cleaner solution. That's part of why that parameter is allowed.
(For a positional argument, choose a valid dest right away.)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,802 |
French Orientalist Literature in Algeria, 1845–1882
After the Empire: The Francophone World and Postcolonial France
_**Series Editor:**_ Valérie K. Orlando, University of Maryland
Advisory Board
Robert Bernasconi, Memphis University; Claire H. Griffiths, University of Chester, UK; Alec Hargreaves, Florida State University; Chima Korieh, Rowan University; Mildred Mortimer, University of Colorado, Boulder; Obioma Nnaemeka, Indiana University; Alison Rice, University of Notre Dame; Kamal Salhi, University of Leeds; Tracy D. Sharpley-Whiting, Vanderbilt University; Nwachukwu Frank Ukadike, Tulane University.
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French Orientalist Literature in Algeria, 1845–1882
Colonial Hauntings
Sage Goellner
LEXINGTON BOOKS
Lanham • Boulder • New York • London
To my mother, Geraldine Tranmer, and my father, Paul Goellner
Published by Lexington Books
An imprint of The Rowman & Littlefield Publishing Group, Inc.
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Copyright © 2018 by The Rowman & Littlefield Publishing Group, Inc.
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without written permission from the publisher, except by a reviewer who may quote passages in a review.
British Library Cataloguing in Publication Information Available
Library of Congress Cataloging-in-Publication Data
Names: Goellner, Sage, author.
Title: French orientalist literature in Algeria, 1845–1882 : colonial hauntings / Sage Goellner.
Description: Lanham : Lexington Books, [2018] | Series: After the empire : the Francophone world and postcolonial France | Includes bibliographical references and index.
Identifiers: LCCN 2017057035 (print) | LCCN 2018001486 (ebook) | ISBN 9781498538732 (electronic) | ISBN 9781498538725 (hardcover : alk. paper)
Subjects: LCSH: French literature—19th century—History and criticism. | Orientalism in literature. | French—Algeria—In literature. | Algeria—In literature. | Gautier, Théophile, 1811–1872—Criticism and interpretation. | Fromentin, Eugène, 1820–1876—Criticism and interpretation. | Loti, Pierre, 1850–1923—Criticism and interpretation.
Classification: LCC PQ295.O75 (ebook) | LCC PQ295.O75 G64 2018 (print) | DDC 840.9/008—dc23
LC record available at <https://lccn.loc.gov/2017057035>
The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI/NISO Z39.48-1992.
Printed in the United States of America
Contents
Acknowledgments
Introduction
1 Subjectivity Undone: Théophile Gautier's Algeria
2 The Unsettled: Eugène Fromentin's Haunted Journeys
3 Battlefields and Barbarians: _Salammbô_ and Its Historical Contexts
4 Le Mal de la Kasbah: Pierre Loti in Algiers
Afterword
Bibliography
Index
About the Author
Acknowledgments
Writing a book is a long process, and even more so when it is a first academic book. I am glad to acknowledge my family, friends, and colleagues whose generosity of support, ideas, and expertise contributed to this project. At the University of Wisconsin–Madison, I have been privileged to work with brilliant and insightful teachers and scholars. They have included but are not limited to Névine El Nossery, Richard Keller, and Florence Vatan. I especially appreciate Névine's support in my transition into a new professional role. Earlier in my career, Soraya Tlatli, Moneera Al Ghadeer, Deborah Jenson, and Aliko Songolo were inspirational scholars—they continue to be. My chair, Narra Smith Cox, has been unfailingly supportive and encouraging, and colleagues in the Department of Liberal Arts and Applied Studies, especially Sarah Marty, Julie Dahl, and Jesse Stommel, have provided much-needed support and levity during the writing process. I am especially grateful to Jane Schulenburg and Emily Auerbach, whose wise guidance helped me navigate the rough waters of departmental and institutional change. In particular, I thank Jane, who encouraged me to "lean in" at just the right time. I would also like to thank my colleagues in the Department of French and Italian, especially Gilles Bousquet and Andrew Irving, for their encouragement and endorsement. The University of Wisconsin–Madison's research and travel funding made possible the research upon which this book is based.
I wish to thank the organizers of the 2014 French Literature Conference at the University of South Carolina, who put together a wonderful colloquium of ideas and exchanges. A portion of the book was first published in Odysseys: Travel Narratives in French as the essay "Algeria's Ghosts: Fromentin's Haunted Algerian Journeys" in their French Literature Series Vol. 41 (Spring 2017): 109–121, edited by Jeanne Garane, and its revised version appears here by permission.
My dear academic friends, Alessandra Benedicty, Christopher Bolander, Molly Enz, Amadou Fofana, Sally Gendron, Eileen McEwan, Nicole Meyer, and Subha Xavier, have supported me so much through this journey. The friendship I have with Christian Flaugh, whose insightful questions and encouragement came at just the right time, holds a special place. Walks and the occasional p'tit canon with Sandrine Pell were rewards that sustained me through the research and writing of this book. To Hassan Idfath, shukran (thank you) for showing me your Morocco, and to Virginie and Yvan-Marc Durantet, thank you for providing a writing retreat in Le Puy-en-Velay. Special acknowledgments go to Jeanne Garane for her careful reading of the chapter on Fromentin in its earlier iteration, and to the fantastic editors I have worked with in this process including Kate Epstein, Karen Kelsky, and, especially, Mary Mekemson. Lindsey Porambo, Nick Johns, and their team at Lexington Books that gave me expert and professional explanations of the editorial process, and both provided excellent attention to guide the project through to its completion. My former students at the University of Illinois in Chicago and current students at the University of Wisconsin–Madison have been inspiring, insightful, and enthusiastic throughout the process. My gratitude goes to them as well.
Last, but in no way least, I extend my deepest thanks to my family. My great gratitude goes to the Hirby family for their loving encouragement. To my mother, Geraldine Tranmer, who provided countless hours of childcare and was ready to drop everything when I needed to write or travel, I offer heartfelt thanks. I thank my father, Paul Goellner, for unfailing encouragement and love. My gratitude goes to both of you for giving me the gifts of language, literature, and travel. Sara, my dear sister, you have always provided strength and humor. Finally, my deepest thanks go to the three gentlemen in my life. To Benjamin, thank you for always loving me and cheering me on. I am eternally grateful for your love, support, devotion, and companionship. To Reed Charles, whose bright curiosity lifts me up, and to Oliver Paul, whose smile and comfort anchor me, I thank you from the bottom of my heart.
Introduction
The seed for this book was planted decades ago, when, as a young student abroad in Paris, I had a strange experience with my French host father. A warm and playful man, he taught me much about his home country, from the geography of mountain ranges, to how to navigate the métro, to the subtle nuances of Parisian slang. One evening, as we were looking at a photograph album and engaging in family stories, questions, and conversation, I noticed one photo that stood out from the others. Alone on a faded page was an image of a young man, my host father, seated on a tank in desert fatigues, an indiscernible expression on his face. When I asked him about it, my question was met with an uncomfortable silence. He quickly turned the page, clearly not wanting to talk about it. I later learned that the photograph was taken when he served for the French in the Algerian War of Independence (1954–1962). According to other family members, he hardly ever spoke of his wartime experience. It was an uncomfortable moment of silence in a relationship otherwise characterized by open friendship. My host father's silence haunted me. What was that war? Why wouldn't—or couldn't—he talk about it? Years later, after researching Francophone Algerian authors Kateb Yacine (1929–1989) and Assia Djebar (1936–2015), I had found answers to many of these early questions.1 But my research on Djebar in particular continued to shape the ways I thought about the Franco-Algerian conflict, especially in the ghostly signals she had pulled out of the French colonial archive as she wrote her famous novel L'Amour, la fantasia (1985). This historical palimpsest of her autofiction unearthed the past horrors and the systems that produced them. These influences led to my inspiration for the present book.
"[W]hat haunts are not the dead, but the gaps left within us by the secrets of others," wrote Nicholas Abraham and Maria Torok in 1978.2 Referring these haunting gaps left within us, Nicholas Rand has speculated as to whether hauntings might be not only a family affair but rather could involve "the phantomatic return of shameful secrets on the level of . . . the community, and possibly even entire nations."3 One scene in L'Amour, la fantasia stands out in relation to the speculation of the haunting of a nation. Djebar brings to light a disturbing aside in a casual letter from one of the colonial officers who had participated in France's invasion of Algiers in the summer of 1830. In his letter to a friend, the officer describes the body of a woman whose foot had been amputated in order to steal the jewels on her anklet, a brief description of "ce pied de femme que quelqu'un a tranché pour s'emparer du bracelet d'or ou d'argent ornant la cheville" [a woman's foot that had been hacked off to appropriate the anklet of gold or silver].4 Djebar writes, "Soudain les mots de cette lettre entière ne peuvent sécher, du fait de cette incise: indécence de ces lambeaux de chair que la description n'a pas pu taire."5 [Suddenly he inserts these words, they prevent the ink of the whole letter from drying, because of the obscenity of torn flesh that he could not suppress in his description]. For Djebar, this haunted ink that cannot dry represents the violence of colonial conquest so often occulted in the historical archive.6
As this harrowing scene that Djebar unearths illustrates, France's colonization of Algeria was so brutal and inhumane that it would haunt its very first witnesses, like this colonial officer, and continue as a persistent memory for future generations. It is this moment of colonial contact in Algeria that this book addresses: the troubling disturbances in French literary texts published during the early colonial period. This record is (at least) a double narrative, both an accounting and its demand: haunting.
French Orientalist Literature in Algeria, 1845–1882 : Colonial Hauntings attends to the complex relation between haunting, history, and justice in French colonial Algeria.7 It evokes certain pathways into a spectral inquiry of four "classic" Orientalist works published between 1857 and 1882. Although many nineteenth-century French travelers wrote about Algeria,8 the works of the four authors I consider represent an unambivalent darker undercurrent to France's imperial project in the new colony just taking shape in the early nineteenth century. This book considers the ways in which French texts written during these violent decades express deep misgivings about the French colonial project. The historical record haunts the literary production of this era; these texts are crisscrossed with traces of trauma, dehumanization, and illness. This book looks at French Orientalist literature in a chronological perspective, examining haunting in Théophile Gautier's Voyage pittoresque en Algérie (1845, 1865) [Picturesque Journey to Algeria], Eugène Fromentin's Un été dans le Sahara (1857) [A Summer in the Sahara], Gustave Flaubert's Salammbô (1862), and Pierre Loti's Les Trois dames de la Kasbah [The Three Ladies of the Casbah] (1882). It considers a variety of genres of works set in or inspired specifically by Algeria—the travel narrative (Gautier, Fromentin), the novel (Flaubert), and the short story (Loti). I argue that the works' troubled qualities express a latent anxiety about the violence of the colonial project that undermines it even as it is expressed in texts that will become exemplars of colonial Orientalism.
This project is fundamentally informed by the Jacques Derrida's concept of hauntology. Derrida figures the ghost as both a political and ethical conjuration in pursuit of justice—one of the reasons his rereading of Hamlet in Specters of Marx (1993) has generated such a significant body of scholarship. Writing after Derrida, sociologist Avery Gordon similarly argues: "the ghost is alive, so to speak. We are in relation to it and it has designs on us such that we must reckon with it graciously, attempting to offer it a hospitable memory out of a concern for justice."9 For Derrida and Gordon, justice means inviting the spectral back into our worlds and accepting that there are records to set right.
Literary haunting in texts about the Algerian colony takes many forms. Specters are raised by colonial violence, trauma, atrocities, control, dispossession, dehumanization, and disease. Phantasmic presences, the hauntings, underscore the ineluctable repercussions of imperial dominance and control represented by the horrors of the past. They compel the witnessing of their condition by insisting upon something currently unaccounted for.10 Haunting forces its observers to question an accepted history and to recognize the ghosts that compel a complete reframing of the scene. It has now revealed another way of seeing, unearthing what has been covered up or hidden. Witnesses find their understandings irrevocably changed, not just because a new phenomenon has appeared but because haunting also urges action, involving an acknowledgment of its existence and an acceptance of the directive that its new story be fulfilled. In other words, all hauntings occur as a search for justice, the deliverance of which may never be possible, yet which is, in any case, a witness's required undertaking.11 Haunting obliges its witnesses to readdress an accepted account of how the history came to be, to find it coming up short in some way, and finally, to take action. This obligation remains constant regardless of the possibility that there is no hope of offering some kind of reparation for an original wrongdoing beyond recognizing and conveying that it happened to begin with. Although it may be impossible to completely set the record straight, at least what is vastly unbalanced may be acknowledged. This acknowledgment is not the same as achieving justice, but it is not dissimilar from it either.
Whereas this book has been significantly influenced by Derridean notions of hauntology, my point is not to give a detailed exegesis of standard terminologies in this vein of literary theory, nor to give an exposition of poststructuralist philosophy. Neither does this work seek to systematically develop nor apply the Freudian ideas of the uncanny in mourning and melancholia that might seem pertinent to readers already familiar with scholarly writings on haunting. Instead, my aim is to bring forward hauntings that remain generally unacknowledged in this particular corpus of Orientalist texts. The bibliographic and topical decisions of French Orientalist Literature in Algeria peer into new corners with a ghost-like errancy: wandering, surprising, appearing, and then pulling back, circulating, leaving an unanticipated point, and emerging again in a different place.
It is important to note that this project, even though its basis is the nineteenth century, is not an investigation of the more obvious phantoms of nineteenth-century French Gothic literature, nor does it contain analyses of garden-variety ghosts. In this book, a ghost is not a floating body garbed in a white sheet.12 Instead, I understand haunting as a conceptual metaphor, a multilayered phenomenon that necessitates lithe and fluid imaginings. Thus this book is a conjuration of the more subtle and unexpected "seething presences" in Orientalist writing in the mid-nineteenth century.13 Seeking such hauntings is propelled by questions that the inquiry itself produces. For instance, why do these writings set in French colonial Algeria linger on the dead? Does French Orientalist literature write itself as haunted? What number of authors are obsessed with the dead? Is writing a process of witnessing, or of grieving? Is all literature haunted?14 What number of hauntings are there to summon, and why? What hauntings occur implicitly without our even knowing it?
Haunted Orientalism
Colonial Hauntings is a study of French Orientalist literature. Designating a wide array of discursive practices, genres, and disciplines, the term "Orientalism," in its most neutral sense, is the study of the place known as the Orient. Since Edward W. Said's critical study Orientalism (1978), the term has taken on a more political connotation. Before Said's groundbreaking work, the term referred to a trend in art, literature, philosophy, sociology, and anthropology, based on the exploration of the Eastern, primarily Muslim, parts of the world. Following Said, Orientalism has come to denote a wider array of institutional and discursive assumptions that regulate the West's understanding and domination of its supposed "Other." As he notes, it is "the enormously systematic discipline by which European culture was able to manage and even produce the Orient politically, sociologically, militarily, ideologically, scientifically, and imaginatively during the post Enlightenment period."15 This study explores manifestations of haunting as a key characteristic of a select number of travel writing and fictional texts during the decades of French Orientalists' journeys to and literary production about Algeria. The principal argument of this book is that canonical Orientalist narratives regarding France's colonial efforts in Algeria can be understood in new ways through the critical lens of hauntology. The specters and hauntings that tie these literary works together are important because, whether psychological, collective, or metaphysical, they demonstrate certain ambivalences about the new colony in texts that were to become classic illustrations of colonial French Orientalism.
Haunting in literature gained credence in literary studies with Derrida's publication of Specters of Marx, in which he used the figure of the ghost to illustrate the disjunction in the presence of being and coined the French neologism hantologie [hauntology].16 With this work, Derrida made ghosts into a useful element of literary theory, casting it through the filters of psychoanalysis, mourning, and philosophy. This work's argument that deconstruction was an extension of Marx's legacy rankled some Marxist critics, but in the literary sphere, Derrida's revisiting of the figure of the ghost as an appropriate subject of critical study has resulted in an incredibly rich paradigm for literature. Echoing its close homonym ontology, hauntology prioritizes the ghost's not-being over that of solid presence. In this way, hauntology is akin to and an extension of the ethical movement of deconstruction; turning toward the ghost occupies the deconstructive space of the Levinasian Other. Derridean hauntology is thus not related to whether or not one believes in ghosts but instead, as Fredric Jameson explains, implies that "the living present is scarcely as self-sufficient as it claims to be; that we would do well not to count on its density and solidity, which might under exceptional circumstances, betray us."17 Here, Jameson addresses the solidity of being and existence, the ontological, as destabilized by the ghostly, or hauntological.
As a psychoanalytic and theoretical movement, hauntology has a different source than the ideas put forth in Specters of Marx. Less famous and chronologically earlier than Derrida's work is that of psychoanalysts Nicolas Abraham and Maria Torok, notably in their essay collection L'Ecorce et le noyeau [The Kernel and the Shell].18 Whereas Derrida focused on the legacy of Marx's works, Abraham and Torok's interest lay in transgenerational phantoms, especially in how secret traumas of prior generations return to haunt their descendants. Unlike in traditional ghost stories in which the dead return to reveal what is forgotten or occulted, Abraham and Torok argued that phantoms are not ghosts that return from the dead but rather "the gaps left within us by the secrets of others."19
Abraham and Torok's work has had much less of an impact on literary criticism than that of Derrida, which has given rise to what Roger Luckhurst has called the academy's "spectral turn," which no well-informed literary scholar has been able to ignore.20 Luckhurst's phrase uses the Derridean term spectre, which should be carefully differentiated from Abraham and Torok's phantoms. For Derrida, the specter is a figure lingering in the space between being and nonbeing, life and death, and presence and absence. The specter is a deconstructive figure that calls into question stable certainties. In contrast, Abraham and Torok's phantoms are ancestors endeavoring to prevent a shameful or traumatic secret from coming to light. Derrida enjoins us to address the specter not in order to uncover an ignoble secret but rather to turn toward a productive opening of meaning, which is the work of literature in general. Derrida writes:
La littérature garde un secret qui n'existe pas, en quelque sorte. Derrière un roman, ou un poème, derrière ce qui est en effet la richesse d'un sens à interpréter, il n'y a pas de sens secret à chercher. Le secret d'un personnage, par exemple, n'existe pas, il n'a aucune épaisseur en dehors du phénomène littéraire. Tout est secret dans la littérature et il n'y a pas de secret caché derrière elle, voilà le secret de cette étrange institution au sujet de laquelle, et dans laquelle je ne cesse de (me) débattre. [. . .] L'institution de la littérature reconnaît, en principe ou par essence, le droit de tout dire ou de ne pas dire en disant, donc le droit au secret affiché.
[Literature keeps a secret which does not exist, in some way. Behind a novel or a poem, behind what is in effect the wealth of meaning to be interpreted, there is no secret meaning to be sought. A character's secret, for example, does not exist, there is no substance outside the literary phenomenon. Everything is secret in literature, there is no secret hidden behind it, that is the secret of this strange institution about which and in which I am constantly debating (struggling). [. . .] The institution of literature recognizes in principle or in essence the right to say everything or not to say while saying, that is, the right to flaunt its secret [le droit au secret affiché].21
In the field of literary studies, critics have recently used Derrida's concept of hauntology to analyze haunting in modern literature as symbolic of the unprocessed but persistent historical traumas of imperialism.22 The expanding field of Derridean hauntological analysis fundamentally informs the current book's theoretical underpinning. Informed by Derrida's theory and later analyses by Kathleen Brogan, Colin Davis, and Avery Gordon, among others, this book examines the intersections of memory, trauma, and spectrality.23 Brogan argues that over the past several decades in American literature, there has been a resurgence of haunting plots. She makes the case that these modern ghost stories offer openings for authors to recuperate their lost cultural identities. Looking at both literature and film, Davis examines the close linkages between Derridean and psychoanalytic thought. In Ghostly Matters, Gordon poses three main questions: the alternative stories among power, knowledge, and experience; how ghosts and hauntings dismantle the certainties of claims of truth; and what methodologies appear to acknowledge the author's transformations. As this rich scholarship reveals, there has been an undeniable turn toward anamnesis in our time, where memory work and recovery of the past, including a past that does not remain in the past, demands our critical attention.
Scholarship on haunting in contemporary Franco-Maghrebian literature from the 1960s until the present has primarily focused on works produced after Algeria's 1962 independence from France. For example, in Postcolonial Haunting and Victimization: Assia Djebar's New Novels (2007), Michael O'Riley explores the dynamics of victimization to argue that haunting is a key element of Djebar's recent fiction; In Writing Postcolonial France: Haunting, Literature, and the Maghreb (2011), Fiona Barclay examines haunting in contemporary fiction produced within metropolitan France to argue that France has not yet reconciled itself with the end of its empire in North Africa. These works are essential contributions to literary hauntology, but they leave aside the equally important task of analyzing an earlier moment of contact in the Franco-Algerian agon, namely, those texts published during the Algerian colonial period of the nineteenth century. Whereas the aforementioned current scholarship in French studies examines hauntology and memory work in Franco-Maghrebian literature from the post-1960s onward, I bring a hauntological approach to bear upon nineteenth-century French Orientalist literature through an analysis of French colonial Algerian texts by Gautier, Fromentin, Flaubert, and Loti.24 Although this period of French Orientalist literature has already been extensively researched,25 it has yet to be examined from this scholarly perspective, which seeks, as Djebar does in L'Amour, la fantasia, to exhume and overwrite the shadowed traces of a violent conquest and occupation in the French texts produced during this time.
Colonialism and its discontents
France's first military conquest of Algeria, a territory formerly under Turkish rule (1517–1830), was taking place. In an attempt to improve his popularity in France, Charles X initiated a blockade against the port of Algiers and sent troops to fight the Ottoman army, which was defeated at the battle of Staouéli. With the installation of a governor general, Algeria was declared an integral part of the French territory. However, resistance to the French military was fierce and coalesced under military leader Abdelkader, who finally surrendered to the French in 1847.
Concomitant with the colonial project in Algeria was a feverish interest in North Africa and the Middle East among French intellectuals that began with Jean-Baptiste-Joseph Fourier's Description de l'Égypte, published during Napoleon's Egyptian Campaign (1798–1801).26 After 1830, explorers, scholars, and writers accompanied military expeditions or were otherwise connected to the colonial administration. But as early as 1808, Napoleon had sent engineers, geographers, and scientists to Algeria to create topographical surveys and map plans for future expeditions.
France's interest in the East had been nourished for at least the three centuries prior with the larger European trend of exoticism, or the implication of cultural difference.27 In France, works like Michel de Montaigne's "Les cannibales" (1580), Montesquieu's Lettres persanes (1721), Françoise de Graffigny's Lettres d'une Péruvienne (1747), Constantin François de Volney's Voyage en Egypte et en Syrie (1787), and Diderot's Supplément au voyage de Bougainville (1796) expressed exoticism concurrently with the expansion of the French empire around the globe. François-René de Chateaubriand's Itinéraire de Paris à Jerusalem (1811) had given birth to the genre of the voyage en Orient, later replicated by Gérard de Nerval, Alphonse de Lamartine, and Gustave Flaubert, among others. For these authors, as many have demonstrated, the Orient was an artificial image that reflected both their personal desires and the collective wishes of the West. By the time of Algeria's conquest, European painters and photographers came to the colony still hungry for the exotic.
Although both exoticism and Orientalism carry the myth of the privileged position of European cultural superiority, Orientalism sustains a more geographically and colonially rooted character. Since Said's work and the rich scholarship it inspired, scholars have focused on myriad complexities within Orientalist discourse. As several have shown, the uncertainty underlying the Orientalist project was palpable, as authors representing the exotic Other revealed their awareness of the fallacies of this effort.28 What has been little explored in this body of literature, however, is the continual return of haunting and other disturbances. Death, sadness, torture, and sickness lurk in the margins of the otherwise standard Orientalist narratives by Gautier, Fromentin, Flaubert, and Loti.
Critical Hauntographies
As a study of the presence of haunting in nineteenth-century French colonial literature, this book explores the contested terrain of history and memory through literary and historical analysis. Focusing steadily on material from historical archives, this project investigates the numerous layers of haunting in colonial texts in what I call a critical hauntography, or a deliberate tracing of the unsettled qualities of French colonial literature that destabilize hegemonic discursive representations of imperialism. In other words, the meanings of these texts reveal that they are outside of what Homi Bhabha has called "the sentence of history."29 In Bhabha's wordplay, in which "sentence" simultaneously denotes the syntactical (written prose) and the legal (judgment), he evokes the experience of individuals who have been "sentenced" as "Others" by Western discourse. Critical hauntography offers strategies for going beyond "the sentence of history" and instead creating open-ended dialogic processes of reinterpreting the cultural productions of nineteenth-century French writers and the representations they have left us to more fully examine the effects of colonialism as it was happening.30 In the works of Gautier, Fromentin, Flaubert, and Loti, illness, torture, war, and barbarity haunt the characters, narrators, or the texts themselves. To ignore the complexities of the ways in which these authors represent the darker side of French colonialism is to misconceptualize the complexity of power relations in the nascent colony. This complex witnessing result in texts that are a reinforcement of (at least) two simultaneous truths. The authors brought with them expectations about what French civilization was and should be, but the aftermath of colonial violence they saw broke the promise of what colonialism was supposed to bring. In this way, a more nuanced witnessing reveals itself in the texts: the writers are torn, ambivalent, and at times even openly critical of French colonialism in Algeria. They raise the question of how much individuals can ever fully disassociate from their cultural narratives; the disassociation occurs within the literary production of the time. These texts are replete with what Ali Behdad has called "discursive ambivalences" and "ideological uncertainties."31 Similarly, Lisa Lowe argued that Orientalist texts demonstrate ambivalence, discontinuity, and heterogeneity.32 More recently, Jennifer Yee has argued for the existence of a critical nineteenth-century French Orientalism characterized by interrogation of its own discursive functions.33 Addressing the historical backdrop to mid- and late nineteenth-century Orientalism in relation to the historical record, I examine the Orient of these authors not as a space of desire, escape, and fantasy, but as a site of phantasmic "seething presences" that gesture toward the ghosts of an ultimately unsuccessful colonization.34 With discursive discontinuity in mind, alongside Said's notion of the "contrapuntal" that recognizes the intertwined histories forged in imperialism,35 I revisit these canonical Orientalist works with haunting as a principal theme in a critical witnessing of France's colonial past. This approach contributes not only to a more comprehensive understanding of colonialism, but also to a fuller understanding of the Hexagon's diverse postcolonial realities. In Foucault's words, this kind of return to the past "allows us to establish a historical knowledge of struggles and make use of this knowledge tactically today."36
Especially important to this analysis is the contact zone between trauma studies and theories of spectrality. As literary scholar Cathy Caruth has theorized, the experience of trauma is akin to being "possessed by an image or event located in the past."37 The word "possessed"—being indefinitely consumed by a persistent past—also describes the situation of being haunted, as it is commonly understood. In other words, when we think of haunting, it is the possession of the present by the past that appears as the most enduring narrative. For many scholars who use the spectral as a theoretical mode, it is akin to, if not completely similar to, the perceptual qualities of trauma. Describing post-traumatic duress as not only a "symptom of the unconscious," Caruth understands it also as a "symptom of history."38 She has described trauma as a relentless quest for answers or an elusive truth. This pursuit is also the case with ghosts who arrive from the past in search of an ethical dialogue with the present. As symptoms of trauma, ghosts become metaphors for and objects of a suffering historical experience.39 Avery Gordon frames haunting as a return to sites of historical amnesia and cultural erasure: "The ghost is not simply a dead or a missing person, but a social figure, and investigating it can lead to that dense site where history and subjectivity make social life."40
The texts I examine reflect anxiety, horror, and paralysis; they unquestionably express representations of colonial trauma, but it is important not to view this harrowed past solely through a totalizing melancholic lens. Instead of dwelling in a space of incessant mourning and melancholia, a Derridean approach encourages a reflection on the present, how the past is both present and absent, and how the past can stimulate new possibilities for the future.41 As Gordon puts it, "haunting, unlike trauma, is distinctive for producing a something-to-be done."42 Indeed, the importance of studies of haunting is that they are able to do more than repeatedly returning to a static past; in a dynamic engagement, they may actively expose the amnesias of the past, the deficiencies of the present, and a preliminary hope for progressive generations.
In Writing Postcolonial France, Fiona Barclay makes the compelling statement in that "France's ghosts are produced by socio-historical factors."43 This truth is apparent in the literature produced during the inception of France's violent colonization of Algeria. The official French imperial project was just taking shape in the Maghreb when Gautier, Fromentin, Flaubert, and Loti were traveling in and writing about the new French colony. Thus the haunting in these authors' texts reveals that their diverse experiences were marked by an ever-threatening unease that crept into their writings. My aim in this book is to uncover the layers of disquiet in their fiction and travelogues as they witnessed France's early colonization of Algeria. In these texts that represent the nascent French colony, the destructive practices of imperialism herald colonialism's ghosts.
Haunting in Orientalist texts destabilizes colonial discourse through the persistence of traces of trauma in the colonial text. Ghosts break down temporal categories because, as Peter Buse reminds us, "In the figure of the ghost, we see that past and present cannot be neatly separated from one another, as any idea of the present is always constituted through the difference and deferral of the past, as well as anticipations of the future."44 This kind of analysis allows an examination of opposition to or ambivalence within the hegemonic discourse about French colonial efforts in the texts of the French literati of the mid-nineteenth century. To be clear, this is not the firm anti-colonial strategy of Fanon, Césaire, Memmi, and other progenitors of modern postcolonial theory, but rather that of Homi Bhabha, who expresses "the need to quicken the half-light of western history with the disturbing memory of its colonial texts that bear witness to the trauma that accompanies the triumphal part of empire."45
Inflected by hauntological analysis, this kind of memory work fills the gaps of collective memory on both sides of the Mediterranean. Haunting—or the past brought into the present—disrupts the temporal categories of colonial and postcolonial. In the colonial context, haunting begins at the moment of contact, due to hurt, damage, or trauma. As Davis argues, ghosts and other metaphysical disturbances symbolize unprocessed but insistent historical remains, erasures, misremembering, and unclaimed traumatic pasts.46 Haunting and ghosts imply a death not set right, in which commemoration and burial rites have not been followed. Disturbances return, announce, make known, compel us to listen, to look more closely at the historical record in order to publicly bear witness to its injustices. A privileged site for hauntological analysis, literature thus allows inquiry into spaces, including France's imperial history in Algeria, in which this otherwise latent ungrounding occurs. In the texts I study, disturbing traces bear witness to the traumas wrought by the French empire. Their deep disquiet alerts us simultaneously to the present and the absent, the visible and the invisible, the real and the fictional, and the known and the unknown.
Algeria and France: "The 1840 Moment"
I use 1845 as a chronological departure for two reasons: first, it marks the journey of Gautier, the first author in this study, to Algeria. The decade of the 1840s is also the time in which France's colonial project was being called into question. As historian Charles-André Julien has noted, debates on France's colonization of Algeria were steadily growing in France, what he terms "the 1840 moment."47 At this time under the July Monarchy, chambers and journals regularly hummed with debate, speeches, and commentaries on the potentials and hazards of the conquest, confronting different version of the colony's future and elaborating multiple, sometimes contradictory justifications of a French presence in Algeria. Major cultural figures including Alphonse de Lamartine and Alexis de Tocqueville intervened in the sociopolitical debate.48 Prior to the conquest of Algeria, France had territorial possessions popularly known as les îles, namely L'Ile Bourbon (Reunion), Madagascar, and Haiti by 1800; these colonies were economically failing due to political changes in France and abroad. Strong competition in sugar and other agricultural products was coming from Latin American countries, further weakening French plantations. In 1814, with the abdication of Emperor Napoleon and the Bourbon dynasty's restoration, the general practicality of colonial missions began to be called into question. In addition, when Britain forced France to give up its colonial possessions in 1815, France saw substantial losses, and its colonial efforts lost popularity among the public, especially as the practice of slavery grew more and more unpopular.49 As far back as—and even prior to—the revolution of 1789, the French public had been divided over the question of slavery, and many asked how a nation that had just overthrown an autocratic regime and built a new government based on the human rights of liberty and equality could continue the practices of colonialism and enslavement.50
Nonetheless, France went ahead in a military conquest of Algeria that took place between 1830 and 1848. The attack on Algiers in 1830 came out of a general sense of political unease in the French government after it was forced to acquiesce to British demands for imperial possessions, as well as the Prince de Polignac's desire to rebuild a North African empire.51 When diplomatic negotiations with the Turkish dey of Algiers broke down, Polignac, the French minister of foreign affairs, advocated an attack on Algiers. Soon thereafter, in an attempt to shore up his popularity in France, Charles X initiated a blockade against the port of Algiers, asserting that the Algerian expedition would end pirate control over the Mediterranean region and return power to the French army.52 Acting alone, the French government sent troops to fight the army of Algiers, defeated it at the battle of Staouéli, and seized the city.
From 1830 to 1847, France gained more and more ground in Algeria, despite the resistance efforts led by Abdelkader, whom the French army captured, transferred to France, and imprisoned in 1847. At the time, only a few areas of Algerian resistance remained to be "pacified," primarily in the Sahara, southern Algeria, and the mountainous region of Kabylia, although defensive strongholds remained throughout the territory. But in addition to facing the continued realities of armed resistance, the French were confronted with uncertainty over how much of the new colony to bring under French control and how to administer it. Some saw the occupation of Algeria as an important way to preserve France's strength. Although most governmental leaders saw the conquest of Algeria as a great opportunity, others disapproved, while many economists contended that the new colony would never be successful. Still others worried that the French conquest would stir tensions with England.
An indecisive public compounded the lack of unanimous political approval for colonial Algeria.53 As historian Jennifer Sessions has convincingly demonstrated, "the roots of French Algeria lay in contests over political legitimacy sparked by the Atlantic revolutions of the eighteenth century."54 But despite an initial hesitancy, the French public was quickly influenced by positive reports from the Algerian colony in France's popular press. For example, Governor General Thomas Bugeaud, who led the first major conquest in Algeria and later became marshal of France and governor of Algeria from 1840 to 1847, sent triumphal descriptions of glorious victories on the battlefield to the proliferating and widely read Parisian journals. Following the rhetoric of Bugeaud, one commentator wrote: "L'Algérie n'est déjà plus un champ de bataille, c'est une conquête, ce sera bientôt une florissante colonie, et alors, comme notre mère patrie, elle jouira de ce règne intelligent des lumières et de la paix dont nous avons été les dispensateurs en Europe." [Algeria is no longer a battlefield, it is a conquest, it will soon be a flourishing colony, and then, like our mother country, it will enjoy the enlightened and peaceful reign that we have spread all over Europe.]55
Even though the Second Republic and the Second Empire's governments stated their intention to keep the colony, increasing concern and policy changes about the status of French settlers, as they related both to the métropole and to the colony's indigenous people, increased the uncertainty and instability of the colony's relations with France. In addition, as the conflict continued, public criticism reached new heights after the revelation of the 1845 enfumade of approximately 800 members of the Ouled-Riah tribe by General Jean-Jacques Pélissier and his troops. After retreating into the Dahra foothills and hiding in a cave, French troops massacred the Ouled-Riah by building fires at the entrances to the cave in which they were hiding. Despite intensive efforts by the official French press to keep the tragedy a secret, eyewitness accounts and illustrations of suffocated families in the Dahra caverns provoked public outrage among the French public.56
Despite such atrocities, the installation of a governor general and waves of immigrant settlers gradually made Algeria into an integral part of the French territory; Charles X's 1830 incursion into Algiers had established the Algerian foundation of the new colonial empire France would build over the following century. But France's imperial offensive became a site par excellence of unintended consequences. The variety of positions taken by the players in the debate on the terms of colonialism explains the complex attitudes it provoked in the writers I will discuss. Gautier, Fromentin, Flaubert, and Loti encountered myriad entanglements during their stays in Algeria and saw firsthand the wrack and ruin wrought by France's colonial policies. Consequently, their texts cast profound, anxious shadows onto the traumas that darkened this era. The creeping disquiet lurking in the pages of their narratives refracts the unforeseeable consequences and the ineluctable undoing of France's imperial achievement.
A leading authority on contemporary historiography, Benjamin Stora, has analyzed crucial effects of the aftermath of empire. He argues that unspoken memories of the Franco-Algerian conflict and the Algerian War of Independence (1954–1962) have marked French culture.57 For Stora, the routine forgetting of France's violent past in Algeria continues to shape the modern French nation, and he has convincingly shown how France's silence about colonialism's violent legacy has created a "gangrene."58 Just like Stora's gangrenous modern France, the early years of its Algerian colonization were never sound. Studying the nineteenth-century literature, Christopher Bongie, Ali Behdad, and Emily Apter, among others, have shown how nineteenth-century representations of the exotic Other were fragmented, uncertain, and ambivalent.59 However, the nullification of the colonizeds' subjectivity ceases when troubling glimpses of trauma appear behind the filters of exoticism in an Algeria of apparently dazzling desertscapes, sensual odalisques, and hidden mystery. What have been little examined are the haunting disturbances that appear at first occulted yet continuously returning. These hauntings testify to the ambivalence about colonialism which undermines any assertion of a clean, monolithic, or all-powerful early French empire in Algeria.
Scholars are just beginning this work. For example, Franck Laurent demonstrates that Algeria is but a haunting absence in Victor Hugo's 1829 collection of poems Les Orientales, and Dorian Bell has compellingly argued that Algeria shows up as a "phantom limb" in Honoré de Balzac's La Comédie humaine (1829–1950). 60 But after "the 1840 moment" and the 1851 coup d'état, Algeria began to appear as a greater presence in France's public discourse and in its literature. For the four authors I study, within the hegemonic, triumphalist discursive context of the colonial project in Algeria, traces of terrible violence created an undeniable ambivalence transmitted through their works.
Strangers in a Strange Land
The first chapter, "Subjectivity Undone: Théophile Gautier's Algeria," focuses on the unsettling quality of Gautier's Voyage pittoresque en Algérie (1865), which was supposed to have been a definitive illustrated account of the colony. However, its unnerved narrator and ghostly figures dismantle any semblance of authoritative colonial mastery. Through its increasingly disconcerting narration and incomplete publication process, Voyage pittoresque en Algérie represents a haunted report of Gautier's unraveling subjectivity while traveling in Algeria.
The painter-author Eugène Fromentin made three different trips to Algeria. After returning to France, he came to the conclusion that the canvas was insufficient for its representation. Turning to his pen to capture more fully his experiences, he described both the beauty and the violence he had encountered. The second chapter, "The Unsettled: Eugène Fromentin's Haunted Journeys," examines Fromentin's unsettled travelogue in the context of one of the fiercest Franco-Algerian battles, the 1852 French siege of Laghouat, which took place just before Fromentin's arrival. In Un été dans le Sahara, corpses, mutilated bodies, and ghostly figures appear and reappear in a ghastly refrain, while even more prominently in his unpublished work, Fromentin's uneasiness while witnessing such devastation points to his ambivalence when faced with the realities of colonization.
Gustave Flaubert did not have such a direct experience with colonial ravages in Algeria on his journey to the Middle East with his friend Maxime Du Camp in 1849. But during his 1858 trip to North Africa to tour Carthage and its surroundings for inspiration for his second novel, Salammbô, his writings about it were bitter. He called Algeria the "corps de garde d'Occident" [bodyguard of the West] and stated that it possessed a "forte odeur d'absinthe et de caserne" [strong odor of absinthe and the barracks].61 Chapter 3, "Battlefields and Barbarians: Salammbô and Its Historical Contexts," examines Salammbô (1862), Flaubert's blood-soaked, lapidary novel of epic proportions set in ancient Carthage during the Punic Wars. Its representations of war, torture, and massacre closely mirror the atrocities that took place in Algeria during Flaubert's writing of the novel. Flaubert's contemporaries compared the cruel battles between the novel's barbarians and the Carthaginians to the massacres and torture in the colony, and I argue that Salammbô is an unconscious representation of the violence of the French colonization of Algeria.
Pierre Loti wrote three works set in Algeria, "Les Trois dames de la Kasbah: Un conte oriental," "Suleïma," and "La Naïl" ["The Three Ladies of the Casbah: An Oriental Tale," "Suleïma," and "The Naïl"]. In the final chapter, I examine Loti's short story "Les Trois dames de la Kasbah" (1882) alongside its frame collection Fleurs d'ennui. In this moralistic tale, Loti represents three Algerian prostitutes as victims of a hidden strain of syphilis carried by the French. Loti's tale is haunted by colonialism's corruption, sickness, and decay in the capital city of Algiers. In a cynical critique both in the story and in its frame text, Loti depicts colonialism's consequences as a degrading illness and underscores the deleterious effects of French imperialism. The 1882 publication date of "Les Trois dames" marks the end of this book's analysis. Finally, the conclusion provides a review of the arguments of this critical analysis, articulates the varying ways in which the French imperial ideology was shadowed with elements of disquiet in its Orientalist literature, and points to future directions for study. In these works, the haunting presence of colonialism is one of the many signs of ambivalence and resistance in the long and painful relationship between Algeria and France.
One final note: this study would not have been possible without the work of two scholars in particular. First, this book owes a great theoretical debt to Colin Davis' Haunted Subjects: Deconstruction, Psychoanalysis, and the Return of the Dead (2007). Davis' excellent analyses of the work of Derrida, and Davis' arguments on why the dead return in order to settle unfinished business on earth, were instrumental in this project's conceptualization. I am also greatly indebted to Fiona Barclay's Writing Postcolonial France: Haunting, Literature, and the Maghreb. This book works in ways parallel to and yet distinct from Barclay's Writing Postcolonial France. Whereas Barclay focuses on haunting in Maghrebian literature produced after Algeria's independence, I treat an earlier timeframe in the French-Algerian conflict. Yet the two pursue many of the same key questions: literature as a privileged art form for capturing haunting; the crucial ties between history and literature; and spectrality as an ethical call for historical reexamination.
NOTES
1. Goellner, Writing with the Past: Intertextual Representations in Algerian Francophone Literature. Diss. University of Wisconsin–Madison, 2005.
2. Nicholas Abraham and Maria Torok, The Shell and the Kernel: Renewals of Psychoanalysis, trans. Nicholas Rand (Chicago: University of Chicago Press, 1994), 171.
3. Abraham and Torok, The Shell and the Kernel, 171, 169.
4. Assia Djebar, L'Amour, la fantasia (Paris: Albin Michel, 1985), 68/55. All translations in this book, unless otherwise noted, are my own. Citations of L'Amour, la fantasia will give page numbers in the 1985 edition, and, after the slash mark, in the English version: Fantasia: An Algerian Cavalcade, trans. Dorothy S. Blair (New York: Heinemann, 1993).
5. Ibid., 68/56.
6. For an excellent analysis of this scene, see Anne Donadey, Recasting Postcolonialism: Women Writing Between Worlds (Portsmouth, NH: Heinemann, 2001), 48–49.
7. My choices of terminology—for example, ghost, phantom, specter, and apparition—are interchanged to avoid the lexical redundancy of any of them. Every now and then, terms may echo the specter more reminiscent of Marx and Derrida or the phantom of Abraham and Torok but are not wedded to them.
8. See Charles Tailliart, L'Algérie dans la littérature française (Geneva: Slatkine, 1998), and Peter Dunwoodie, Writing French Algeria.
9. Avery F. Gordon, Ghostly Matters: Haunting and the Sociological Imagination (Minneapolis: University of Minnesota Press, 2008), 64, emphasis in the original.
10. Slavoj Žižek associates the specter and its haunting force not with the existence of nonexistence but with insistence, an insidious form of agency available even to the unactualized. See Slavoj Žižek, Welcome to the Desert of the Real (New York: Verso, 2002), 22.
11. Žižek argues that the dead return as "collectors of some unpaid symbolic debt." See Žižek, Looking Awry: An Introduction to Jacques Lacan through Popular Culture (Cambridge, MA: MIT Press, 1992), 23. Žižek's argument follows the "unfinished business" model of haunting that Colin Davis outlines in Haunted Subjects: Deconstruction, Psychoanalysis and the Return of the Dead (New York: Palgrave Macmillan, 2007), 2–3.
12. On haunting in French literature, see the comprehensive collection Haunting Presences: Ghosts in French Literature and Culture, ed. Kate Griffiths and David Evans (Cardiff, UK: University of Wales Press, 2009). On the gothic, see Jodey Castricano, Cryptomimesis: The Gothic and Jacques Derrida's Ghost Writing (Montreal: McGill-Queen's University Press, 2001).
13. Gordon, Ghostly Matters, 8.
14. Peter Buse reminds us that literature as a medium of representation shares the simulacral characteristics of the ghost: "like writing, ghosts are associated with a certain secondariness or belatedness." See Ghosts: Deconstruction, Psychoanalysis, History, ed. Peter Buse and Andrew Stott (Basingstoke: Palgrave Macmillan, 1999), 8.
15. See Orientalism (New York: Vintage, 1978), 3. An important field outside the scope of this study is that of Orientalist painting, which informed much of these authors' imagery, especially that of the author-artists Fromentin and Gautier. For a preliminary overview of studies of this artistic genre, see Philippe Jullian, Les Orientalistes (Paris: Office du Livre, 1977); Lynn Thornton, Les Orientalistes, peintres voyageurs: 1828–1908 (Paris: ACR Edition, 1983); Mary Anne Stevens, The Orientalists: Delacroix to Matisse: The Allure of North Africa and the Near East (London: Thames and Hudson, 1984); and Gérard-Georges Lemaire, The Orient in Western Art (Paris: Edition Mengès, 2000).
16. Jacques Derrida, Spectres de Marx (Paris, Galilée, 1993), 89. Michael O'Riley has explored the rich etymology of this theoretical approach, explaining: "'haunting' and 'specter' are both derivatives of Old French, respectively hanter and spectre, which find their roots in Latin. The verb to haunt, from the Indo-European thei, is included with other derivates such as home, site, and the verb to situate. Specter, from the Latin spectrum, image or apparition, derives from specere, to look at or observe." See O'Riley, Postcolonial Haunting and Victimization: Assia Djebar's New Novels (New York: Peter Lang, 2007), 1.
17. Fredric Jameson, "Marx's Purloined Letter," in Ghostly Demarcations: A Symposium on Derrida's Specters of Marx, ed. Michael Sprinker (London: Verso, 1999), 39.
18. See Nicholas Abraham and Maria Torok, L'Ecorce et le noyeau (Paris: Flammarion, 2009). Derrida played an important role in bringing Abraham and Torok's work to a larger public when he co-directed the Flammarion 1976 series "Philosophie en effet," which included their important revisiting of Freud's Wolfman case study. But strikingly, Derrida mentions Abraham and Torok only once, in a footnote in Specters de Marx. See Derrida, Specters of Marx, 24.
19. The Shell and the Kernel: Renewals of Psychoanalysis, 171. Abraham and Torok's ideas have inspired psychoanalytic theory and practice especially in the realm of transgenerational trauma. Certain literary critics have used them as well, notably Nicholas Rand and Esther Rashkin. The latter's work fleshes out their idea of the phantom through close literary analysis of Conrad, Villiers de l'Isle, Adam, Balzac, James, and Poe. Rashkin demonstrates how these works are "in distress," containing secrets that are "transmitted without being stated and without the sender's or receiver's awareness of its transmission." See Rashkin, Family Secrets and the Psychoanalysis of Narrative (Princeton, NJ: Princeton University Press, 1994), 152, 4. See also Nicolas Rand, Le Cryptage et la vie des œuvres: étude du secret dans les textes de Flaubert, Stendhal, Benjamin, Baudelaire, Stefan George, Edgar Poe, Francis Ponge, Heidegger et Freud (Paris: Aubier, 1989).
20. Roger Luckhurst, "The Contemporary London Gothic and the Limits of the 'spectral turn.'" Textual Practice 16, no. 3 (2002): 527–46.
21. Jacques Derrida, Papier machine (Paris: Galilée, 2001), 398, emphasis in original, translated in Davis, Haunted Subjects, 11.
22. See in particular Michael O'Riley, Postcolonial Haunting and Victimization, and Fiona Barclay, Writing Postcolonial France: Haunting, Literature, and the Maghreb (Lanham, MD: Rowman & Littlefield, 2011).
23. See Brogan, Cultural Haunting: Ghosts and Ethnicity in Recent American Literature (Charlottesville: University of Virginia Press, 1998); Davis, Haunted Subjects: Deconstruction, Psychoanalysis and the Return of the Dead (New York: Palgrave, 2007); and Gordon, Ghostly Matters (Minneapolis: University of Minnesota Press, 2008).
24. Although Dennis Porter's Haunted Voyages: Desire and Transgression in European Travel Writing also analyzes the trope of haunting, his argument focuses how traveler-authors such as Diderot, Stendhal, and Gide, among others, were haunted by the transgressive activities that travel allowed them. See Porter's Haunted Voyages: Desire and Transgression in European Travel Writing (Princeton, NJ: Princeton University Press, 1991).
25. For other in-depth analyses of French Orientalist literature during this time period, see, among others, Alec Hargreaves, The Colonial Experience in French Fiction: A Study of Pierre Loti, Ernest Psichari and Pierre Miller (London: Macmillan, 1981); Denise Brahimi, "Pierre Loti du roman exotique au roman colonial," in Le Roman colonial, ed. Martine Mathieu (Paris: L'Harmattan, 1987), 15–27; Irene L. Szyliowicz, Pierre Loti and the Oriental Woman (London: Palgrave Macmillan, 1998); Lisa Lowe, Critical Terrains: French and British Orientalisms (Baltimore: Johns Hopkins University Press, 1991); Christopher Bongie, Exotic Memories: Literature, Colonialism and the Fin de siècle (Palo Alto, CA: Stanford University Press, 1991); Elwood Hartman, Three Nineteenth-Century French Writer/Artists and the Maghreb: The Literary and Artistic Depictions of North Africa by Théophile Gautier, Eugène Fromentin, and Pierre Loti (Tübingen: Narr, 1994); and Christopher L. Miller's "Orientalism, Colonialism," in A New History of French Literature, ed. Denis Hollier (Cambridge, MA: Harvard University Press, 1998), 698–705. For two excellent critical studies of colonial literature produced in Algeria by Algerian authors, see Peter Dunwoodie, Writing French Algeria (Oxford: Clarendon Press, 1998) and Seth Graebner's History's Place: Nostalgia and the City in French Algerian Literature (Lanham, MD: Rowman & Littlefield, 2007).
26. See, for example, Napoleon's Description de l'Egypte, published during his 1798–1801 Egyptian Campaign (Paris: Imprimerie Impériale, 1821–1829), and François-René de Chateaubriand's Itinéraire de Paris à Jerusalem (Paris: Le Normant, 1811).
27. In his important Essai sur l'exotisme, Victor Segalen argues that exoticism uncovered significant cultural "otherness" that possessed both an ontological and aesthetic value. See Segalen, Essai sur l'exotisme (Montpellier: Fata Morgana, 1978). In From Cannibals to Radicals: Figures and Limits of Exoticism, Roger Célestin defines exoticism in terms of center and periphery: "a relation between (Western) Self and (exotic) Other" (Minneapolis: University of Minnesota Press, 1996).
28. See Said, Orientalism (New York: Vintage Books, 1978); Christopher Bongie, Exotic Memories; Lisa Lowe, Critical Terrains: French and British Orientalisms (Baltimore: Johns Hopkins University Press, 1991); Ali Behdad, Belated Travelers: Orientalism in the Age of Colonial Dissolution (Durham, NC: Duke University Press, 1994); Emily Apter, Continental Drift: From National Characters to Virtual Subjects (Chicago: University of Chicago Press, 1999); Madeline Dobie, Foreign Bodies: Gender, Language, and Culture in French Orientalism (Palo Alto, CA: Stanford University Press, 2001); and Jennifer Yee, Exotic Subversions in Nineteenth-Century French Fiction (Oxford: Legenda, 2008).
29. Homi K. Bhabha, "Postcolonial Authority and Postmodern Guilt," in Cultural Studies Then and Now, ed. Lawrence Grossberg, Cary Nelson, and Paula A. Treichler (New York: Routledge, 1992), 56.
30. Ibid., 58.
31. Behdad, Belated Travelers, 14.
32. Lisa Lowe, Critical Terrains, ix.
33. Jennifer Yee, The Colonial Comedy: Imperialism in the French Realist Novel (Oxford: Oxford University Press, 2016).
34. Gordon, Ghostly Matters, 8.
35. Edward Said, Culture and Imperialism (London: Vintage, 1994), 72.
36. Michel Foucault, Power/Knowledge, ed. Colin Gordon (New York: Pantheon Books, 1972), 83.
37. Cathy Caruth, Unclaimed Experience: Trauma, Narrative, and History (Baltimore: Johns Hopkins University Press, 1995), 5.
38. Ibid., 5.
39. Relating traumatic haunting to postcolonial thought, Michael O'Riley makes the important point that "[h]aunting is pervasive in postcolonial thought precisely because of its affective dimension, a dimension that creates a sense of the imminently important, present, and disruptive. This disruptive quality of postcolonial haunting is frequently portrayed as the Freudian unheimlich of history and is figured as an interruptive or affective moment in the course of Western consciousness where the repressed colonial scene returns." See "Postcolonial Haunting: Anxiety, Affect, and the Situated Encounter," Postcolonial Text 3, no. 4 (2007): 1.
40. Gordon, Ghostly Matters, 8.
41. Derrida, Specters, xviii.
42. Gordon, "Introduction to the New Edition," in Ghostly Matters, xvi.
43. Barclay, Writing Postcolonial France, xi.
44. Buse, Ghosts: Deconstruction, Psychoanalysis, History, 10.
45. Homi Bhabha, "The Other Question," in Literature, Politics, and Theory, ed. Francis Barker (London: Routledge, 1986), 149.
46. Davis, Haunted Subjects, 3.
47. Charles-André Julien, Histoire de l'Algérie contemporaine I: La conquête et les débuts de la colonisation 1827–1871 (Paris: Presses Universitaires de France, 1964), 173.
48. See Lamartine's speech of May 2, 1834, in Discours prononcé par M. de Lamartine, député du nord à la chambre des députés sur Alger (Paris: Imprimérie de Petit, 1834). For Tocqueville's works on Algeria, see Tzvetan Todorov's De la colonie en Algérie (Brussels: Complexe, 1998).
49. Jean Meyer, Jean Tarrade, Annie Rey-Goldzeiguer, and Jacques Thobie, Histoire de la France coloniale: Des origines à 1914 (Paris: Armand Colin, 1991), 306–308.
50. Ibid., 313.
51. Ibid., 329.
52. Ibid., 330.
53. Ibid., 335.
54. Jennifer Sessions, By Sword and Plow: France and the Conquest of Algeria (Ithaca, NY: Cornell University Press, 2011), 2.
55. A. F., "Histoire de l'Algérie ancienne et moderne." L'Artiste, 3rd ser., vol. 5 (January 7, 1844), 10.
56. See Jennifer Sessions, "'Unfortunate Necessities': Violence and Civilization in the Conquest of Algeria," in Spaces of War in the French and Francophone World, ed. Daniel Brewer and Patricia Lorcin (London: Palgrave Macmillan, 2010), 29–44.
57. Benjamin Stora, Histoire de l'Algérie coloniale (1830–1954) (Paris: La Découverte, 2004). See also, Jacques Berque, Le Maghreb entre deux guerres (Paris: Seuil, 1962), and David Prochaska, Making Algeria French: Colonialism in Bône 1870–1920 (Cambridge: Cambridge University Press, 1990).
58. La Gangrène et l'oubli: la mémoire de la guerre d'Algérie [Gangrene and Forgetting: The Memory of the Algerian War] (Paris: La Découverte, 2005).
59. See Bongie, Exotic Memories; Behdad, Belated Travelers; and Apter, Continental Drift.
60. Franck Laurent, Victor Hugo face à la conquête de l'Algérie (Paris: Maisonneuve et Larose, 2001) and Dorian Bell, "Balzac's Algeria: Realism and the Colonial," Nineteenth-Century French Studies no. 40 (2011–2012): 35. Bell analyzes the absence of Algeria in Balzac's La Comédie humaine as resulting from the lack of class distinctions in the new colony.
61. Aimé Dupuy, En Marge de Salammbô: Le Voyage de Flaubert en Algérie-Tunisie (Paris: Librairie Nizet, 1954), 13.
Chapter 1
Subjectivity Undone
Théophile Gautier's Algeria
Upon hearing the 1844 Egyptian-themed musical piece Le Désert by Félicien David, Théophile Gautier contemplated the paradoxical effects of Algeria upon Parisian popular culture:
Chose étrange! Nous croyons avoir conquis Alger, et c'est Alger qui nous a conquis. -Nos femmes portent déjà des écharpes tramées d'or, bariolées de mille couleurs qui ont servi aux esclaves du harem, nos jeunes gens adoptent le burnous en poil de chameau.- Le tarbouk a remplacé la classique calotte de cachemire, tout le monde fume le narguilé, le hachich succède au vin de champagne; nos officiers de spahis ont l'air tellement arabe que l'on croirait qu'ils se sont fait prisonniers eux-mêmes à la déroute de quelque smala; ils ont adopté toutes les habitudes de l'Orient, tant la vie barbare est supérieure à notre fausse civilisation.
[What a strange thing! We believe we have conquered Algiers and Algiers has conquered us. -Our women are already wearing gold-threaded multicolored scarves worn by harem slaves, our young men adopt the camel hair burnoose. -The tarbouk has replaced the classic cashmere cap, everyone smokes hookah, hashish has replaced champagne; our Spahi officers look so Arabic that we believe that they have made themselves prisoners after the defeat of some smala; they have adopted all the Eastern habits, so superior is barbarian life to our so-called civilization.]1
For Gautier, Algeria, not France, was the conquering force. This quotation conveys that even though French colonial forces were gaining more and more Algerian territory, Gautier perceived the Maghreb's increasing cultural influence on the métropole. Trading in ethnic and cultural stereotypes in a rhetoric echoing that of contemporary racist discourse in France, Gautier's obsession with uncertain identities is made clear in this passage, and is what will be analyzed in this chapter.
Gautier was ready to ride the wave of the popularity of the East by publishing what was to be a definitive illustrated work on Algeria, which would later be republished as Voyage pittoresque en Algérie [Picturesque Journey in Algeria] (1845, 1865). Gautier's writings suggest that he supported France's mission civilisatrice: Voyage pittoresque begins as colonialist in its outlook, with Gautier traveling alongside French troops. Commissioned by the French government to write the travelogue, Gautier arranged to join Bugeaud's Kabylian expedition. But Gautier's supposed magnum opus on Algeria does not reveal stylized scenes of France's victories. As art historian Linda Nochlin has pointed out, the picturesque was used to elicit pleasing emotions that would "mask conflict with the appearance of tranquility."2 As Christopher Thompson puts it, Gautier's narrative becomes "a descent into hell."3
In the work, Gautier's latent and overt anxieties reveal an unstable subjectivity, and his picturesque journey ripples with ambiguities and doubts. Of the four authors in this study, Gautier writes the most exhaustively of his mental and physical disturbances during the journey in Algeria. Purported to be a journalistic account of the colony, Voyage pittoresque is haunted by Gautier's progressive loss of self-mastery the longer he stayed in Algeria. The evolution of Voyage pittoresque moves from an excited journalistic account to one of bizarre spectacles and an unhinged narrator. Gautier's physical and psychological responses in Algeria include those of excitement and pleasure but also confusion, disgust, and fear. In his writing, the emphasis on the supernatural is striking, and Gautier's own identity is called into question upon multiple occasions. The text is a narrative of exposure to the immediacy of an Algerian experience which, in the violent spectacles Gautier depicts, destabilizes complacent French certainties and identities. This ambiguous status is particularly evident in Algeria because of its ambiguous status as a territory that both was and was not French. The uncertainty of Gautier's relation to the country and the consequent instability of his identity as both a Frenchman and an imperialist are represented by a narrative of rejection, physical and psychic disorientation, and lack of mastery over the body. I interpret Gautier's spectral Voyage pittoresque as an expression of France's unsettled control over the Algerian colony. The unnerved Gautier and the ghostly figures he depicts destroy the semblance of colonial order and authority. Gautier's myriad references to French literature and art attempt to reassert familiarity, and thus control, over the narrative. In the end, though, Gautier's account expresses just how much this author's travels in France's Algerian annex threatened his sense of self.
Before the 1845 Voyage: Haunted by the East
In Paris, the young Gautier studied at the Lycée Charlemagne where he took a keen interest in painting as an adolescent. Gautier abandoned painting in order to write, later producing several works about the visual arts. A great admirer of Victor Hugo, whom he had met through Nerval, Gautier donned a red vest during the notorious Battle of Hernani to show his break with the past and his ardent defense of romanticism. As a journalist, Gautier covered nearly all of the Parisian art salons for La Presse during Louis-Philippe's reign (1830–48), often discussing Orientalist painters such as Prosper Marilhat, Eugène Fromentin, and Alexandre Decamps. With his most widely renowned prose work, Mademoiselle de Maupin (1835–36), for which he wrote the manifesto of "art for art's sake," Gautier's literary fame was assured.
A regular part of Gautier's work, journalism gave him the opportunity for foreign travel. Early on, Gautier developed a great fascination with the Orient. For Gautier, the Orient possessed what the West did not: exotic sights, unfamiliar sounds, and fascinating cultures. Gautier was a routine contributor to the journal La Presse, founded by Emile de Girardin in 1836. Publishing in various periodicals was his main work; he contributed to La Revue de Paris, La Revue des deux mondes, L'Artiste, Le Moniteur universel, and Le Journal officiel. His journalism did not adversely influence his literary prestige, however, and his peers such as the Goncourt brothers, Hugo, Sainte-Beuve, Flaubert, and Baudelaire all expressed their admiration for him. Although Gautier was rejected by the French Academy three times, he received the honor of knighthood, and in 1868, was designated the official librarian of the Princess Matilda. Gautier took trips to Spain, Italy, Russia, Egypt, and Algeria.
Before traveling to Algeria, Gautier, like the other writers in this study, was enraptured with all things Eastern. As he wrote to Gérard de Nerval: "Je suis Turc, non de Constantinople mais d'Egypte. Il me semble que j'ai vécu en Orient [. . .] J'ai toujours été surpris de ne pas entendre l'arabe; il faut que je l'aie oublié."4 [I am Turkish . . . not from Constantinople, but from Egypt. It seems I have lived in the Orient . . . I was always surprised to not understand Arabic, I must have forgotten it.] A self-avowed turcophile, he often dressed in a burnous and a fez.5 Gautier was not alone in considering himself transformed into an "exotic" personage when he returned from his eastern journeys with his new dress and bearing; others saw him so as well. Sainte-Beuve saluted him upon his return from the East as a success, and other journalists likewise sealed his celebrity upon his return.6
Aside from Voyage pittoresque, Gautier's other works are peppered with Orientalist references and allusions that demonstrate his deep fascination with the East. Early on in Gautier's career, he published the Orientalist fantasy Une Nuit de Cléopâtre (1838). Two years later, his supernatural story Le Pied de momie appeared, a tale similar in themes to those of Honoré de Balzac's Peau de chagrin (1831), in which a strange object from an antique shop possesses magical forces. In 1842, Gautier published 1002 Nuits, an extension of the famous Arabian Nights series. The following year, he cowrote a tale about a Persian fairy in dance form, La Péri, as a ballet for his ballerina paramour, Carlotta Grisi.7 Even before traveling to Algeria, he seemed possessed by it.8 His works directly involving Algeria are Voyage pittoresque, La Juive de Constantine (1846), two poems, and the musical "Symphonie descriptive en cinq tableaux," entitled Le Sélam (1850). Finally, he published L'Orient (1877), which included several reviews of writers and painters of his era.9
Gautier's first voyage to Algeria came about in the summer of 1845 when he traveled from Marseille to Algiers, then to Oran and Constantine. Beset by financial problems and the unstable political situation in France upon his return, Gautier even considered moving to the new colony, writing a letter to the ministry asking for Algerian land, but he never followed through on the idea.10 Seventeen years later, Gautier returned to Algeria, attending the inauguration of the railroad from Algiers to Blidah. In 1869, he made a final journey to North Africa at the invitation of the Empress Eugénie, and he traveled to Egypt for the opening of the Suez Canal in the same year.
Gautier's 1845 voyage to Algeria was a significant inspiration for his literary and artistic production. The publications following his travels reveal Gautier's new interest in the French colony and his keen desire to represent it. Notably, Gautier's journey to Algeria was a consolidated form of the traditional Oriental circuit that would have extended from France to North Africa to the Middle East and back through Turkey, Italy, and Greece. But his itinerary did not include any of the other countries; he traveled only from France to Algeria and back again. This trajectory was significant in that it was an exclusively Franco-Algerian trip, and also for its supplemental characteristics: Algeria needed to represent the whole Orient. From this trip originated several drawings, a play, and his two Algerian poems, "Le Bédouin et la mer" [The Bedouin and the Sea] and "Le Lion de l'Atlas" [The Lion of the Atlas]. In the first poem, Gautier sets a scene of a nomad seeing the Mediterranean for the first time; the second poem exposes the conquest of the Arabs by the French. Unlike these works, Gautier's travel memoirs in the form of his Voyage pittoresque would remain an essentially unraveled effort. In revisionist and palimpsestic overlays, his travelogue represents key characteristics of an Orientalist opus, but one that disturbingly calls into question a coherent French colonial identity.
An Incomplete Publication
After Gautier's 1845 journey, his associate and editor Pierre-Jules Hetzel recommended that he create an illustrated récit de voyage with Algeria as its focus. Gautier readily agreed. From its origin, the work was to be a visual text, one that demanded both pictorial and narrative representation of the emerging French colony. The financing of Gautier's voyage came in part from Hetzel and was to be paid back through the publication's profits. When the text's projected publication was announced for 1846, it included a synopsis and several engravings. L'Artiste trumpeted that the work would be richly illustrated and informed by Gautier's painterly background. Nerval wrote in La Presse that Gautier "va étudier et saisir dans ses derniers aspects d'originalité locale cette seconde France conquise sur la barbarie et sur le desert." [is going to study and record this second France which has been won from barbarity and the desert.]11 Also emphasized was the author's double talent, with the publisher's prospectus stressing that whereas other works had neglected "le côté pittoresque et vivant de notre nouvelle colonie" [the picturesque and lively side of our new colony], Gautier's travelogue would be illustrated.12 However, Gautier's attempts at illustration resulted in only five extant sketches, whereas there were to have been twenty-five engravings. The remaining illustrations are two pen and inks ("maquette arabe" and "mosque de Cordoue, Mirah"), two watercolors ("fontaine près de la porte de la Casbah," "Juive d'Alger"), and the portrait of Ayscha.13
Gautier's Voyage pittoresque was an overpromised and underdelivered publication, and its essentially incomplete narrative of a disturbing and supernatural Orient suggests dissolution of colonial mastery. The Voyage pittoresque appeared only in varied installments, not as the planned, completed, and illustrated work that it was supposed to be. The work was published in several parts: first as Quand on voyage, then as Loin de Paris: en Afrique (1865), and also as various articles for the periodical La Revue de Paris. The segments on the religious sect "Les Aïssaoua," were published in La Revue de Paris in November 1851 and the article "La Danse des djinns" in 1852. These were the two excerpts that had the most appeal for the French public because the Aissoua and the djinns both held a longstanding fascination for European travelers. Originating in the sixteenth century, and garbed only in white, the Aissoua members followed the teachings of Sidi Mohammed ben Aïssa, a Muslim saint from Meknès, proving their faith by defying all laws of nature, burning and piercing themselves without feeling pain or injury.14 Malevolent spirits that assume human or animal form and possess supernatural influences, the djinns were made popular in France by Hugo's 1829 poem in Les Orientales.
Tellingly, the book that was to have conveyed the fullest representation of colonial Algeria in sketches, engravings, and narrative never took shape. Thus this elusive, impossible-to-produce work could be seen as representing the troubled nature of the French possession of the colony. Purported to be a masterpiece surpassing all other Algerian travelogues, the project never came to fruition, for reasons not yet completely known. Perhaps the project failed due to financial and political strain after the events of 1848–51, as well as Gautier's own financial troubles. 15 Hetzel was eventually exiled to Belgium in 1851, and Gautier's Algerian writings were finally published in the Revue de Paris in 1851–52 under the title "Scènes d'Afrique" ["African Scenes"].16 The rest of Voyage pittoresque was ultimately published in 1865 under the title Loin de Paris.
"Des géographies fantastiques"
The chapters beginning Voyage pittoresque are hopeful, and far from the hellish descent of the final installments. They contain a lively prose that conveys the author's enthusiasm about the foreign people and experiences he would encounter on his journey. Gautier was aware of the clash between the pre-travel fictions he had read and the inevitable post-travel realities: "Rencontrer dans la réalité ce qui jusqu'alors n'a été pour vous que costume d'Opéra et dessin d'album, est une des plus vives impressions que l'on puisse éprouver en voyage." [Experiencing in reality what had been up until then an opera costume or album's sketch, is one of the strongest impressions that one can feel while traveling].17 But instead of a coherent and completed publication, Gautier presents, in his words, a fragmented set of "géographies fantastiques" [fantastic geographies] in which a battle is waged between vision and blindness, light and dark, attraction and revulsion, solidity and shattered nerves.18
Gautier's intense emotions are apparent from the opening chapters portraying the trip from Paris to Marseille by coach, then by boat to Algiers. Keenly conscious of the importance of the journey to Algeria for his own conception of the Orient as well as the depiction of Algeria for the French public, Gautier notes:
Nous allions donc, au bout de quelques heures, être dans une autre partie du monde, dans cette mystérieuse Afrique, qui n'est pourtant qu'à deux journées de la France, [. . .] nous allions donc voir un de nos rêves se réaliser ou s'écrouler, et s'effacer de notre tête une de ces géographies fantastiques que l'on ne peut s'empêcher de se faire à l'endroit des pays qu'on n'a pas visités encore. Notre émotion était extrême, et nous n'étions pas seuls à la ressentir.
[Thus in a few hours, we were going to be in another part of the world, in that mysterious Africa, which is however only two days away from France . . . thus we were going to see one of our dreams realized or fall apart, and erase from our mind one of those fantastic geographies that we cannot help making up about the places or countries we have not yet visited. Our emotion was extreme and we were not the only ones to feel this way.]19
The complex quality of Gautier's writing about Algeria comes into play in this example in which he perceives and remarks upon national geographies and identities. Gautier's emotion at his embarking on an exceptional experience of otherness is palpable. With an undeniable frisson of excitement, he prepares himself for the "fantastic geographies" he is about to see.
There are a total of seven chapters in the book, the first two of which describe the voyage across France from Paris to Marseille by coach; the rest of the text is set in Algeria. The fifth chapter is devoted to the ceremony of the Aissoua, and the sixth chapter describes the dance of the djinns. In analyses of the Voyage pittoresque, Peter Dunwoodie has convincingly shown how Gautier was disturbed by these episodes and especially threatened by his visits to private homes in Algeria.20 In addition, as Victoria Thompson has compellingly demonstrated, many nineteenth-century French writers who visited Algeria, including Gautier, felt their identities threatened as they experienced discomfort, disorientation, and confusion in an unfamiliar and disorderly space.21 In Voyage pittoresque, this dissolution of self is certainly the case. Even though Gautier attempts to reassert familiarity by making reference to French and other European paintings, texts, and historical figures, any kind of dependable subjectivity progressively unravels as Gautier discovers more and more of the country while losing more and more of his sense of self.
One of the ways this unraveling is apparent is with how Gautier describes his body in Algeria. It is essential to remember the role Algeria has played in constructing identity not only for the French individual but also for the French nation. Historian Jean-Robert Henry claims that "Algeria was one of the most familiar and prominent forms of alterity in relation to which modern France defined herself. During this period, Algeria helped to sustain in the French imagination the distinctions between modernity and tradition, between civilization and the desert."22 However, when one examines the early colonial period, Algeria was not a familiar territory, and its relation to France was unstable and still very much under debate. Although the French had staked their claim architecturally in Algiers, with the construction of hotels, cafés, and restaurants in an effort to symbolize their authority over a population still in the process of being conquered,23 there remained deep uncertainties about Europeans' relations to the country. This anxiety is revealed in Gautier's narrative progression from excitement to terror. From the outset of the work, his body becomes troubled in its relation to the space of the colony.
Gautier's movements outside the Hegaxon's borders create an unsettling displacement of his national identity that calls it into question. Algeria, and its foreignness, continually return to disturb Gautier's sense of self and identity. This discomfort is evident in his "extreme emotion" in the preceding passage, and also presents with the example of Gautier's blurry vision in the text that follows. He is able to view the coastline only as a hazy and undelineated area: "à grand renfort de lorgnettes, nous aperçûmes très indistinctement sur la ligne extrême de l'horizon, - [. . .] les premières cimes de l'Atlas. En mer, il est extrêmement difficile de distinguer les côtes lointaines des nuages. Ce sont exactement les mêmes teintes, les mêmes jeux d'ombre et de lumière." [with strong opera glasses, the first peaks of the Atlas mountains appeared to us on the very indistinct horizon line, . . . At sea, it is very difficult to distinguish faraway coastlines from the clouds. They are the exact same hues, the same interplay of light and shade.]24 From his first glimpses of the new colony, Gautier's vision is insufficient; he needs a strong optical instrument to make out the almost-invisible coastline, an Algerian landscape that, to him, is more phantasmic light and shadow than actual place. Later, upon seeing the city, the colors come as a shock: "Rien n'est étrange pour un oeil français comme cette superposition de terrasses couleur de craie" [Nothing is as strange to French eyes as the superposition of colored chalk terraces.]25
After the steamer docks and Gautier is back on terra firma, his approach to Algiers is recounted with a constant stream of comments about how unsafe he feels: when he enters the city, its uneven buildings, walls, and foundations seem to threaten him: "La perpendiculaire est rarement observée dans les constructions algériennes; les lignes penchent et chancellent comme en état d'ivresse; les murailles se déjettent à droite et à gauche comme si elles allaient vous tomber sur le dos. Rien ne porte. Rien n'est d'aplomb." [The perpendicular is rarely seen in Algerian constructions; tilted lines stagger as if they were drunk; the walls are thrown right and left as if they were going to fall on your back. Nothing is supported. Nothing is level.]26 Gautier expresses feeling in physical danger as he suggests that the walls might come tumbling down upon him.
The uneven architecture poses a threat to Gautier, as do the uncontrolled throngs of people populating the capital. When he arrives at the Place du Gouvernement, the central plaza of Algiers, he exclaims that he is surrounded by a press of people and absorbed by crowded chaos: "Un toho-boho, un capharnaüm! Le mantelet noir de la Parisienne effleure en passant le voile blanc de la Moresque; la marche chamarée de l'officier égratigne le bras nu du nègre frotté d'huile; les haillons du Bédouin coudoient le frac de l'élégant français." [A place of confusion! A mess! The black cloak of the Parisienne brushes in passing against the white veil of the Moorish woman; the embroidered sleeve of the officer scratches the naked arm of the Negro rubbed with oil; the rags of the Bedouin jostle the frock coat of the elegant Frenchman.]27 Gautier's far-from-neutral verbs describing the "bizarre crowd"—"brush," "scratch," "jostle"—express how much he is shaken by his experience at the public square. "[U]ne espèce de vertige" [a sort of vertigo] overtakes him, leaving his body and mind disoriented.28
From the first views of the coastline to the crowds in the public square, these representations reveal a sense of self under duress. Gautier's French body becomes unsettled; later in his writing, his psyche will be endangered. These continuing remarks demonstrate how Gautier's sense of self is challenged by his unsettling experiences in the new colony. And as the author's preconceived visions of Algeria deteriorate in his mind's eye, the bodies of the indigenous inhabitants become more and more omnipresent. Gautier expresses these figures as far from human; they are depicted as ghostly specters.
A Ghostly Algeria
Macabre settings and supernatural figures are hallmarks of Gautier's writing, and these motifs continue in his chronicle of his Algerian journeys.29 Ghoulish images begin to appear in Voyage pittoresque after Gautier's unsettling experiences approaching and visiting the capital city of Algiers. Although at some points he feels himself in France, referring to the similarity in architecture between the arcades of Algiers and those of Paris, or commenting that his dinner was one he might have had in Marseille, his narration becomes increasingly troubled.30 When he leaves the city, he is equally disturbed by the inhabitants outside it: "Quelquefois un Bédouin, monté sur son cheval maigre au ventre ensanglaté, me frôlait en passant des plis de son burnous flottant comme un linceul de spectre. La terre et le ciel étaient menaçants; la nature semblait sourdement hostile, et ne je sais quel indéfinissable sentiment de danger planait dans l'air." [Sometimes a Bedouin, mounted on his thin horse with a bleeding stomach, brushed against me, the folds of his burnoose floating like a specter's shroud. Land and sky were menacing; nature seemed secretly hostile, and a certain indefinable feeling of danger lingered in the air.]31 The striking image of the bloodstained horse ridden by a ghost in a shroud is underscored by Gautier's phrasing, "a certain undefinable feeling of danger" that affects him. As this example reveals, Gautier's feelings of danger continue to permeate the text, as does his fear of the menacing environment surrounding him.
Gautier's Algeria becomes increasingly a nocturnal setting full of specters. His writing is marked by a sense of loss of control, and his attempts to reassert it through French reference points eventually falter. Importantly, the most detailed scenes of Voyage pittoresque take place at night, and three hues dominate the text: gray, white, and black. In the murky atmosphere that Gautier represents, the prose conveys more and more of his anxiety as his senses are assailed from all sides. Transformed from a sightseeing tourist to an uncomfortable outsider constantly seeking familiar terrain, he writes:
L'architecture dont nous avons essayé de donner quelque idée tout à l'heure prenait dans la nuit les apparences les plus mystérieuses et les plus fantastiques. [. . .] Nous entendions près de nous des chuchotements étranges, des rires gutturaux, des paroles incompréhensibles, des chants d'une tonalité inappréciable; des figures noires, accroupies au seuil des portes, nous regardaient des yeux blancs. Nous mettions le pied sur des masses grisâtres qui changeaient de position et poussaient des soupirs. Nous marchions comme dans un rêve, ne sachant si nous étions éveillés ou endormis.
[At night, the architecture that we tried to give an idea of earlier took on the most mysterious and fantastic appearances. . . . Nearby, we heard strange whispers, guttural laughter, incomprehensible words, songs in an indeterminable key; black figures squatting on doorsteps looked at us out of their white eyes. We stepped on greyish masses that changed position, letting out sighs. We walked as if in a dream, not knowing whether we were awake or asleep.]32
In this frightful journey full of "fantastic appearances" and "greyish masses," Gautier recalls Rembrandt's etchings: "Rembrandt, dans ses eaux-fortes les plus noires, n'a rien imaginé de plus bizarrement sinistre. A la nuit se joignait l'inconnu." [In his blackest etchings, Rembrandt imagined nothing more bizarrely sinister. The night joined with the unknown.]33 In a half-awake state, Gautier portrays his body as nervous and under duress.
Gautier's somnambulant and nightmarish experiences begin to deepen as he describes the uncomfortable atmosphere in which he can only half-see "the most mysterious and fantastic appearances." Sounds reaching his ears are guttural, incomprehensible, and indeterminate as he fumbles through the streets, encountering the uncanny visions of a ghostly city shadowed by nighttime darkness and full of threatening figures whom he stumbles upon. Dangerous places, the streets with their "air de coupe-gorge" [cut-throat atmosphere] terrify him.34
The feeling of the supernatural only intensifies when strange figures, hardly human, peer out at him with luminously piercing eyes. Gautier's depictions of the inhabitants of Algiers are continuously those of beings lacking humanity. The images of exotic "Others" in Voyage pittoresque are consistent with Orientalist stereotypes: Algeria is portrayed as mysterious, unknown, and obscure, without the clear rationality of a European city, and the Algerians are equated with ghostly masses making incomprehensible noises. These images of otherworldly and strange figures undoubtedly reflect colonial stereotypes of the Other: Gautier portrays Algeria as mysterious, unknown, and obscure, and the colony as a space lacking the clear rationality of Europe. However, Voyage pittoresque goes to another level in its consistent emphasis on the supernatural. Gautier reduces the colonized to motionless bodies; negated, sheeted corpses denied any subjectivity. The manifest text of the colonizer thus excludes the Other from its semantic field: the Other is the locus of indefinable nonmeaning, a lingering danger filling the air. As Behdad has compellingly argued, this objectification of the Other turns it into the source of the colonizer's anxieties and fears.35 Whereas Behdad sees this objectifying as the incarnation of the colonizer's terror of death, in Gautier's vision of Algeria, his fear of a loss of identity is what is at stake. The unnerved narrator who walks the murky streets and the shapeless whispers of formless masses underfoot underscore Gautier's anxious vulnerability in Algeria.
Haunting Figures: The Aissoua and the Dance of the Djinns
The nocturnal visions Gautier experiences soon become reality, occurring especially in the scenes involving the Aissoua and the djinns, in two chapters near the end of the published work. In them, Gautier gives detailed accounts of the Aissoua's self-mutilations and the djinns' exorcisms by dancers. At first glance, these accounts seem to fall under Gautier's task of journalistic writing. But in both cases, Gautier's reporting grows increasingly unstable. Each chapter advances his version of Algerian alterity as well as his visceral aversion to it. In these scenes in the Voyage pittoresque, an integral conception of the author's sense of self dissolves yet again. With attempts to anchor his text to French references, a set of disturbing reflections and fragments of French Algeria form the nighttime spectacles he attends. Although Gautier tries to capture the performances in writing as authentic ethnographic examples and to compare them with images from European art, literature, and history, his narrational reliability falters.
During Gautier's stay in Blidah, he visits the mystical nocturnal ceremony of the Aissoua, a group of, in his words, diabolical "convolutionnists" [convolutionists]. The Aissoua particularly fascinate him, and he longs to see them for himself.36 His experience begins on a positive note, with an atmosphere worthy of the French painters Descamps and Marilhat, and an Algerian host who resembles one of the early modern royal princes of the house of Valois.37 When seated on a carpet, the narrator is comforted by the familiarity of "Bougies d'Etoile" [Star candles],38 which, as he remarks, often illuminated the Champs-Elysées of his familiar Paris. Upon seeing their flames, he exclaims: "ô civilisation! que venais-tu faire là!" [oh civilization, what are you doing here?].39 The candlelight shines upon the costumes, making them look as though they were borrowed from the Paris Opéra, and the music is compared to that of the French composer Félicien David.40 The Aissoua's face appears to have the monastic appearance of the Spanish Saint Ignatius of Loyola.41 However, as the dance progresses, Gautier's discomfort becomes more palpable, and his references become darker, with a comparison of the Aissouas' movements to epileptic fits, the medieval "danse de Saint-Guy" [Saint Vitus' dance].42 Asserting no exaggeration whatsoever, the narrator refers to the spectacle as more horrific than anything in the French author Charles Nodier's vampire tale Smarra ou les démons de la nuit (1821) or the "black" paintings of Spanish painter Francisco Goya (1819–23).43 Gautier's aversion increases as he describes the Aissoua in shocking terms, invoking heaven and hell:
[Un aïssaoui] se tordait dans des crispations de démoniaque; ses narines tremblaient, ses lèvres étaient bleues, les yeux lui sortaient de la tête, les muscles se tendaient sur son col maigre comme des cordes de violon sur le chevalet; des trépidations nerveuses agitaient son corps du haut en bas [. . .] Si jamais le diable est forcé de confesser Dieu, il le fera de cette manière.
[(An Aissaoui) writhed in demonic tensions; his nostrils quivered, his lips were blue, his eyes bulged out of his head, his muscles tensed on his thin neck like violin strings over the instrument's bridge; nervous vibrations shook his body from top to bottom. . . . If ever the devil is forced to confess to God, he will do it like this.]44
If the Aissoua is horrific for Gautier to watch, he represents their spectators as even more so: "Rien n'était plus fantastique que ces ombres muettes et pâles suspendues au-dessus de nos têtes dans l'immobilité morte des créatures d'un autre monde." [Nothing was more frightening and fantastic than those mute and pale shadows suspended above our heads in the deathlike immobility of creatures from another world.]45 Otherworldly, silent, dangerous, the Aissoua and their audience shake Gautier to his core.
Historian Alice Conklin has argued that European control over foreign territories was linked with mastery over one's own body: "French imperial ideology consistently identified civilization with one principle more than any other: mastery. Mastery . . . of nature, including the human body, and mastery of what can be called 'social behavior.'"46 Following this argument, this scene reflects such a lack of "civilization" with Gautier's loss of bodily control. Remarkably, as the disconcerting spectacle, with its frightening public, proceeds, the text describes how Gautier slowly loses mastery over his own body. In striking sentences, a mirror response to the spectacle is described. Unable to master his reactions, Gautier comments at length on his frantic and uncontrollable bodily movements, similar to those of the Aissoua, in a spectating experience yoked to his corporeal undoing:
Mon oeil se troublait et ma raison s'embarrassait à regarder cette scène vertigineuse. La singulière sympathie imitative qui vous fait détendre les mâchoires en face d'un bâillement me causait sur mon tapis des soubresauts involontaires; je secouais machinalement la tête et je me sentais, moi aussi, des envies folles de pousser des hurlements.
[My eyesight became cloudy and my reason troubled by my watching that dizzying scene. The unique emulative sympathy that loosens one's jaws when one sees a yawn caused me to twitch involuntarily on my carpet; I shook my head mechanically and felt, myself as well, a crazy desire to let out howls.]47
In successive phrases, the narrator expresses a progressive loss of bodily and psychological control as he shakes with horror in the corner.48 The power and control of the colonizing body is undone as he is swept away in this monstrous scene, reinforced by an abundance of vocabulary describing vertigo, dizziness, and nausea. He expounds upon his terrifying experiences, sparing no detail about his physical torment: "La tête me tournait, j'avais des vertiges et des nausées" [My head was spinning, I had vertigo and nausea] and "[c]es tambours [. . .] me donnaient le vertige." [Those drums . . . gave me vertigo.]49 Instead of a self-possessed, rational author writing in a journalistic tone, Gautier provides images of his body pervaded by the "irrational" of the colonized. Inhabited by the spasmodic performances, Gautier's mind becomes cloudy and displaced. Impossible to locate in this scene, the neutral journalist sent to create a charming and picturesque travelogue has disappeared. What remains is only a dizzied stranger bordering on the edge of sanity.
The second spectacle that leaves Gautier unhinged is that of the dance of the djinns in Constantine. Although he was already familiar with the concept of djinns as evil spirits, he had yet to see an exorcism first-hand. Gautier again attempts to anchor his experience using a French reference, relaying his unnamed host's words about Victor Hugo's 1829 poem "Les Djinns": "Ici, on croit aux djinns. La ballade ascendante et décroissante d'Hugo a dû vous apprendre à peu près ce qui en est." [Here, we believe in djinns. Hugo's ascending and descending ballad must have taught you a little bit about them.]50 Light, and the lack thereof, plays an important role during the exorcism dance. When he describes his host's lantern, Gautier evokes the brilliance of Henry IV's white feather as the latter rides into battle.51 Just as when Gautier first arrived in the country, what is striking in this scene is his range of visual acuity. The house of the dancers is aglow, creating luminous refractions on the narrow walls in front of it: "Nous arrivâmes enfin près d'une maison laissant filtrer, par les fentes de la porte, quelques filets de lumière qui rejaillissaient en éclaboussures bizarres sur la muraille opposée. C'était là qu'avait lieu la cérémonie." [We finally arrived close to a house that let filter, through the door's cracks, a few rays of light that spilled into bizarre splotches upon the wall facing it. It was there that the ceremony was to take place.]52 If light is symbolic of knowledge, the irregular obscurity of Gautier's travelogue represents a loss of certainty and, by extension, any "truths" about the colony. When, and if, any knowledge is gained, the imagery of Gautier's text suggests that it is only a shadowed and terrifying fragment.
Not only is Gautier's sense of sight under assault, so is his hearing. When he attends the "ballet épileptique" [epileptic ballet] of the djinn performance, he is struck by its devilish sounds:
Tout à coup, un cri aigu, prolongé, chevroté, un piaulement de chouette ou d'orfraie éblouie, un sanglot d'enfant égorgé, un rire de goule dans un cimetière, partit à travers la nuit comme une fusée stridente. Cette note d'une tonalité surnaturelle, cette note aigre, frêle et tremble, fausse comme un soupir d'hyène, méchante comme un ricanement de crocodile, éveilla dans le lointain des jappements entourés des chacals et me fit froid à la moelle des os. Il me sembla qu'un vol d'affriets ou de djinns passait au-dessus de moi.
[Suddenly, a prolonged bleated shriek, the cry of an owl or stricken osprey, the sobs of a slaughtered child, the laugh of a graveyard ghoul, went through the night like a shrill rocket. The tone of this supernatural and sharp note, frail and trembling, as false as a hyena's sigh, as nasty as a crocodile's sneer, awakened in the distance yelps surrounded by jackals, making me cold to the bones. It seemed to me that a flight of affriets or djinns passed over me.]53
Nothing in this scene is neutral; all is demonic and terrifying. Gautier refers to the realm of the supernatural, invoking affriets, spirits even more monstrous and dangerous than djinns. The noises during the performance remind him of horrific scenes of a dead child, a ghoulish specter, snarling hyenas, sneering crocodiles, and dying birds. He compares the terrifying crones providing this music to the witches of Macbeth, calling them "atroces stryges" [atrocious strixes] and "abominable goules" [abominable ghouls].54 As in the previous examples, Gautier yet attempts to ground the narrative what is familiar, comparing the dancers' performances to those of Fanny Elssler and Carlotta Grisi.55 Referring to the painter Hubert Robert's depictions of the Roman catacombs and quoting the famous line by poet Jacques Delille, Gautier indicates that he was completely lost, seeing nothing but the night and hearing nothing but silence: "il ne voit que la nuit, n'entend que le silence."56 Many years later, Gautier reasserted how much he had been affected by these the experiences of the Aissoua and the djinn. In the periodical La Presse of May 25, 1852, he writes: "L'Orient est dangereux, surtout l'Orient barbaresque; il fait naître un vertige que nous concevons très bien, l'ayant éprouvé nous-mêmes." [The Orient is dangerous, especially the barbaric Orient; it creates a vertigo that we know very well, having felt it ourselves].57
Further into Darkness
As Gautier describes leaving the performance in which dancers nodded and rocked in a trance-like state of possession, he states that he can see only impenetrable shadows in the audience:
Ivre de ce spectacle vertigineux, je suivis mon compagnon d'un pas chancelant; mais oubliant sa recommandation de ne pas quitter des yeux son fanal, à un brusque détour de ruelle, je perdis de vue mon étoile polaire; quelques pas faits dans une fausse voie pour retrouver au clairet propice m'eurent bientôt égarée au milieu de l'ombre la plus épaisse, la plus opaque, la plus impénétrable.
[Drunken from that dizzying spectacle, I followed my companion with a tentative gait; but forgetting his recommendation to not let my eyes stray from his lantern, at a sharp detour of the little street, I lost the sight of my north star, a few steps taken in the wrong direction in order to find the right light would soon have misled me in the middle of the thickest, most opaque, most impenetrable shadow.]58
As Gautier's steps betray him and his confidence fades into deepening darkness, the interplay of light and dark that undergirds the text metaphorically represents the undoing of the colonial spectator. Shaken and scared, he again makes a European reference to the familiar, somewhat ironically reveling in the "anguished pleasure" of the frisson: "J'éprouvais cette sorte de plaisir angoisseux qui devait faire palpiter le cœur des héroïnes qu'Anne Radcliffe promène, une lampe à la main, à travers les corridors interminables de ses châteaux pleins de terreurs et d'apparitions" [I felt that sort of anguished pleasure that must have made Anne Radcliffe's heroines' hearts race as they walked, lantern in hand, through the interminable corridors of her castles full of terrors and apparitions.]59 Along with the European reference point, what is again noteworthy is the presence of the lantern. The hand-held lamp disappears and returns as a crucial motif in Gautier's tottering navigation of the shadowy city. The lamp eventually becomes his guiding north star as he can see only slivers of light combined through otherwise impenetrable darkness.
When Gautier leaves the djinn ceremony, he is again deprived of sight as he steps into the dark streets of the city and writes that he feels trapped in a kind of catacomb: "Je me sentis pris, comme un coquillage dans un bloc de marbre noir, dans cette pâte d'ombre épaisse. Nulle lumière aux fenêtres [. . .] Je suivais les murailles en les touchant de la main, mais je ne faisais que tomber d'obscurité en obscurité" [I felt trapped, like a shell in a black marble block, in this deep blotch of thick shadow. With no lights on in the windows . . . I followed the walls by touching them with my hand, but I was just falling deeper and deeper into darkness.]60
When Gautier finally sees a light again, it comes from the lantern of two women dancers returning home from the performance. Thankful for the clearer vision, Gautier follows the dancer Ayscha and her unnamed sister to their home after they unsuccessfully try to find the hôtel d'Europe where he is staying. His inability to communicate with the two women is underscored as he depicts language and meaning as "unintelligible" sounds: "Les deux sœurs [. . .] m'adressaient toute sorte de discours inintelligibles mêlés d'éclats de rire" [The two sisters . . . addressed me with all kinds of unintelligible speech mixed with bursts of laughter.]61 Just as in the scene of the djinns, sounds are dangerous in the colonial context. Although Gautier addresses the women in French, language's meaning is lost in the exchange, and Gautier's speech seems to be as incomprehensible as that of the sisters. When Gautier stays overnight in their room, light, as well as a semblance of clarity, return to him. While the women sleep, he watches them as the moonlight seems to make the lamp even brighter.62 Finally, he walks to the window to look over the Algerian topography and gaze upon the gorges of the river Rummel.
In this scene that begins the conclusion of the Voyage pittoresque, a more literary resolution takes place. Gautier's sense of colonial mastery seems to have been restored, and he no longer writes of uncontrollable experiences or terrors. But the end of the narrative still comes in macabre form. In addition to referencing the geography of the Rummel river, the closing lines of Gautier's text refer to his sketch of the dancer Ayscha. The last reference is to a newspaper article dating from several years after his Algerian journey. The newspaper article describes Ayscha's mutilated body lying at the bottom of the Rummel's depths. As reproduced in the text, the article reads:
Une jeune danseuse de Constantine, Ayscha-ben-Chebarria, a été assassinée par des Kabyles, dont ses bijoux avaient allumé la cupidité et qui s'étaient introduits de nuit chez elle. On a trouvé son corps dans le Rummel, tout sanglant et tout mutilé. Les assassins lui avaient arraché les oreilles et coupé les doigts pour s'épargner la peine d'en extraire les pendeloques et les bagues.
[A young dancer from Constantine, Ayscha ben Chebarria, was assassinated by Kabyles, who entered her home at night, their greed enflamed by her jewels. Her body, bloody and mutilated, was found in the Rummel. The assassins had ripped off her ears and cut off her fingers to spare themselves the trouble of taking off her pendants and rings.]63
In this passage, eerily similar to that of Djebar's scenes of the French officer's letter describing a woman's amputated foot, Gautier bears witness to the dancer Ayscha's body after her dreadful murder. But Gautier processes the scene at a great temporal and physical distance from Algeria. Unlike his unsteady and irrational self when visiting the colony, the author has regained self-control and reason, and he has even captured the memory of the young dancer in a sketch: "mon petit croquis est donc tout ce qui reste de cette charmante créature."64 [My little sketch is thus all that remains of that charming creature.] With the use of the possessive pronoun, mon, Gautier underlines the recuperative nature of this conclusion of his narrative. Instead of the uncomfortable spectator losing emotional and physical control of himself, as was the case when he attended the spectacles of the Aissoua and the djinns, the French author presents himself as a steady preserver of the only remaining image of the pitiful Algerian beauty assassinated by marauding Kabyles. The victim is relegated to a shadowy past, whereas Gautier reemerges whole, sound, and consummate in his representation of self.
However, this concluding scene also reveals a troubling set of spectral doubles. First, just as Gautier visited the women at night, the newspaper indicates that Ayscha was murdered "de nuit" [at night]. Second, the figure in the first passage stands to peer down at the gorge of the Rummel into which Ayscha's body fell. Gautier thus stands in for the assassin. Finally, the drawing and the newspaper article representing her death, two scraps of paper, underscore the fragmentary and incomplete quality of the Voyage pittoresque. The sketch represents Ayscha alive, whereas the journal article recounts her murder; she cannot be both alive and dead, so the two representations serve to negate one another. The article, which Gautier claims to have discovered only the preceding year, fractures the notion that Gautier composed the text soon after the events occurred, thereby fissuring the travel narrative, which is supposed to have been written while the travel itself was taking place.65 The inclusion of this vignette emphasizes the dislocation of the traveler, distanced by time and space, from the author, who revisits and rewrites the work. The illusion of a cohesive subject disappears as the roles of author and traveler break apart. Carried away in the writing of the travel experience, the colonial traveler is himself represented in the past. The Voyage pittoresque fragments itself temporally and geographically, undoing the fiction of a seamless travel narrative.
In conclusion, Gautier's Voyage pittoresque articulates the haunting impact of French colonialism on the French traveler's subjectivity. The author's descent into a destabilizing alterity while visiting the country, and the fragmented and incomplete publication of Voyage pittoresque, indicates his vulnerability within the emerging French colony. His seeming loss of control and attempts to regain it through references to familiar French figures during the Aissoua and djinn spectacles, and finally, the haunting presence of Ayscha, all express how he recoils in the face of the perceived strangeness of French colonial Algeria. Writing in Le Moniteur universel in July of 1867, more than two decades after his journey to Algeria, Gautier underscores his "souvenirs encore tout frissonnants" [still shuddering memories] of his experiences there.66 Resisting both absolute control and coherent representation, Gautier's experience in the colony was unforgettably unsettling. His writing increases in its complexity as his rationality and colonial mastery are gradually dismantled. Outside of the defining limits of the métropole, and faced with the seeming "irrationality" of the Orient, his identity falters. Gautier's displacements, both mental and physical, threaten the invulnerable quality of colonial identity, especially given the state of flux that characterized French Algeria in 1845. Gautier's Algerian experiences continued to haunt him long after his return to France, and his loss of clarity in the French annex of Algeria represents a failure of mastery on the part of the colonial subject.
NOTES
1. Théophile Gautier, La Presse, January 6, 1845, quoted in Voyage pittoresque en Algérie, ed. Madeleine Cottin (Geneva: Librarie Droz, 1973), 19.
2. Linda Nochlin, The Politics of Vision: Essays on Nineteenth-Century Art and Society (Boulder, CO: Westview Press, 1991), 50.
3. Christopher W. Thompson, French Romantic Travel Writing: Chateaubriand to Nerval (Oxford: Oxford University Press, 2012), 211.
4. Gautier, July 25, 1843 letter, quoted in Thompson, French Romantic Travel Writing, 166.
5. Elwood Hartman, Three Nineteenth-Century French Writers/Artists and the Maghreb: The Literary and Artistic Descriptions of North Africa by Théophile Gautier, Eugène Fromentin and Pierre Loti (Tübingen: Narr, 1993), 12.
6. Ibid., 65. See also Richardson, Théophile Gautier: His Life and Times (London: Max Reinhardt, 1958), 78–79.
7. Edwin Binney, Les Ballets de Théophile Gautier (Paris: Nizet, 1965), 105–107.
8. Gautier's extensive reading on Algeria included Gomot's Guide du voyageur en Algérie (1844) [Traveler's Guide to Algeria], the duke of Orléans' Journal de l'expédition des Portes de fer, rédigé par Nodier (1844) [Journal of the Iron Gates Expedition, Written by Nodier], Quétin's Guide du voyageur en Algérie (1846) [Traveler's Guide to Algeria], and Désiré Léglise's Un Voyageur à Alger (1847) [A Traveler in Algiers]. See Gautier, Voyage pittoresque en Algérie, 297–98.
9. Set in Constantine during the French occupation, the melodrama La Juive de Constantine involves a complicated love triangle between a French officer, the daughter of a Jewish shopkeeper, and a Muslim woman. The collection of Orientalist writings referenced included Fromentin's Un été dans le Sahara, Flaubert's Salammbô, Léon Michel's Tunis (1867), and Gautier's own account of Constantine and the Aïssaouas. See Charles De Speolberch de Lovenjoul, Histoire des oeuvres de Théophile Gautier, avec 4 portraits et 2 autographes (Paris: Charpentier, 1887).
10. Richardson, Théophile Gautier, 76.
11. Gérard de Nerval, La Presse, July 7, 1845, quoted in Joanna Richardson, Théophile Gautier, 77.
12. Gautier, Voyage pittoresque en Algérie, 70.
13. Ibid., 127.
14. For more on the Aissoua, see René Brunel, Essai sur la confrérie religieuse des Aïssaoua au Maroc (Paris: Paul Guethner, 1926).
15. Ibid., 81–84.
16. Ibid., 75.
17. Gautier, Voyage pittoresque en Algérie, 132.
18. Ibid., 178.
19. Ibid.
20. Dunwoodie, Writing French Algeria (Oxford: Oxford University Press, 1999), 44–45.
21. "'I Went Pale with Pleasure:' The Body, Sexuality, and National Identity among French Travelers to Algiers in the Nineteenth Century," in Algeria and France: 1800-2000: Identity, Memory, Nostalgia, ed. Patricia Lorcin (Syracuse, NY: Syracuse University Press, 2006), 18–32.
22. "Introduction," in France and Algerian Identities from Colonial Times to the Present: An Introduction, ed. Alec G. Hargreaves and Michael J. Heffernan (Lampeter, UK: Edwin Millan Press, 1993), 3.
23. See Zeynep Çelik, Urban Forms and Colonial Confrontations: Algiers Under French Rule (Berkeley, CA: University of California Press), 1997, and Seth Graebner, History's Place: Nostalgia and the City in French Algerian Literature (Lanham, MD: Rowman & Littlefield), 2007.
24. Gautier, Voyage pittoresque en Algérie, 177.
25. Ibid., 182. As Dunwoodie rightly remarks, Gautier's frequent use of the "rien n'est" [nothing is] construction conveys a hyperbolic tone throughout the narrative. See Writing French Algeria, 44–45.
26. Gautier, Voyage pittoresque en Algérie, 192.
27. Ibid., 185–86.
28. Ibid., 183.
29. Of the four authors in this book, Gautier is the one whose other publications consistently fall into the supernatural genre. The living dead, vampires, and ghosts populate his texts, especially in his intensely morbid early works dealing with nightmares, death, and the living dead. Gautier's tales Le Roman de la momie [The Romance of the Mummy] (1858), La Morte amoureuse [The Dead Woman in Love] (1836), and his long-form poem "Albertus" (1832), are driven by the undead. These works fit the genre of the fantastic according to Tzvetan Todorov's definition, in that they feature "l'hésitation éprouvée par un être qui ne connaît que les lois naturelles, face à un événement en apparence surnaturel" [the hesitation felt by a being who knows only natural laws facing an apparently supernatural event]. Todorov, Introduction à la littérature fantastique (Paris: Seuil, 1970), 29.
30. Gautier, Voyage pittoresque en Algérie, 231, 251.
31. Ibid., 265.
32. Ibid., 194.
33. Ibid.
34. Ibid., 199.
35. Ali Behdad, Belated Travelers: Orientalism in the Age of Colonial Dissolution (Durham, NC: Duke University Press, 1994), 78–79.
36. Gautier, Voyage pittoresque en Algérie, 80.
37. Ibid., 239, 242.
38. Ibid., 292. Connoting the heights of civilization, "Bougies d'Etoile" was a brand of fine candles produced in Paris favored over other types of candle.
39. Gautier, Voyage pittoresque en Algérie, 242–43.
40. Ibid., 243, 245.
41. Ibid., 250.
42. Saint Vitus' dance was a common term for chorea minor, or a disorder of the nervous system characterized by quick, uncoordinated jerking movements primarily affecting the face, hands, and feet.
43. Gautier, Voyage pittoresque en Algérie, 260.
44. Ibid., 257.
45. Ibid., 253.
46. Alice L. Conklin, A Mission to Civilize: The Republican Idea of Empire in France and West Africa, 1895–1930 (Palo Alto, CA: Stanford University Press, 1997).
47. Gautier, Voyage pittoresque en Algérie, 257.
48. Ibid.
49. Ibid., 278.
50. Ibid., 267.
51. Ibid., 268.
52. Ibid., 269.
53. Ibid., 254.
54. Ibid., 272.
55. Ibid., 275.
56. Ibid., 279.
57. Gautier, La Presse, May 25, 1852, quoted in Thompson, French Romantic Travel Writing, 215.
58. Gautier, Voyage pittoresque en Algérie, 279.
59. Ibid., 267.
60. Ibid., 279.
61. Ibid., 281.
62. Ibid., 283.
63. Ibid., 286.
64. Ibid., 285.
65. Ibid., 284.
66. Ibid., 83.
Chapter 2
The Unsettled
Eugène Fromentin's Haunted Journeys
In the summer of 1853, the author and painter Eugène Fromentin went blind in Laghouat, Algeria. Refusing his hosts' advice about staying indoors for a midday siesta, Fromentin made his way to a high point in the east of the village, in order to make the best of the daytime light and to take in the panoramic views of changing colors of the desert.1 But the height and infernal temperatures quickly began to take their toll on Fromentin; after many consecutive days of "immersion solaire de plus de douze heures" [solar immersion for more than twelve hours], he began to hallucinate a blinding light, writing: "J'ai commencé par voir tout bleu, puis j'ai vu trouble; au bout de cinq minutes, je ne voyais plus du tout." [I began seeing blue everywhere, then it was blurry, and after five minutes I saw nothing at all.]2 Did Fromentin go blind for purely physical reasons, or was something else at work in this bewildering episode?
In 1853, Fromentin visited the oasis town of Laghouat, which had just been conquered by the French at the cost of huge destruction and loss of life. The siege of Laghouat was an episode in the "pacification" of Algeria. Commanding an army of six thousand troops, General Jean-Jacques Pélissier had the city besieged on November 21, 1852. The decisive storming of the city occurred on December 4, and the French captured the city after several days of bloody fighting. Accompanied by military escort, Fromentin arrived in Laghouat just six months after the siege.
Fromentin's Un été dans le Sahara [A Summer in the Sahara] is haunted by the aftermath of the siege. As Colin Davis points out, the presence of haunting is indicative of a disturbance in the moral, epistemological, or symbolic order.3 The dead persist because burial, recognition, or grieving ceremonies are lacking or absent. This model of "unfinished business" focuses on the persistent return of those whose lives have been violently and prematurely cut short. Like Hamlet's father, apparitions return to pursue justice or revenge. Literature is filled with such tales of intrigue in which the crime, or some clue, is usually hidden, resulting in a satisfying ending as the specter is put to rest or otherwise exorcised. However, the ghosts of thousands who died as a result of colonial oppression appear less ready to take on a metaphysical or literary form, because of their unknown identities or because their deaths may have been too "unimportant" to have been registered in the colonial record. Yet few episodes are more haunting than the murder of innocent civilians, a fact that becomes apparent in Fromentin's published and unpublished texts in which he speaks of a "massacre" of the Laghouati.4 It should be noted that the Pléiade edition of Fromentin's Oeuvres complètes contains a significant amount of unpublished documentation about his visit to Laghouat. Reading Fromentin's finalized publication alongside these unpublished texts and his personal correspondence reveals deep misgivings in his writings on the aftermath of this siege.
Fromentin's récits algériens
Hailing from the northern French seaside port of La Rochelle, Fromentin was one of the earliest visual interpreters of Algeria.5 The direct inspiration for his Algerian travelogues, as well as his artistic oeuvre, took place during his three journeys to Algeria. The first trip came in the spring of 1846, when he stayed there for two months. The country left a lasting impression on him. He wrote to his friend Paul Bataillard: "c'est beau, c'est beau! Tout est beau, même la misère, même la boue des sandales. [. . .] Mon Dieu, si cela me faisait peintre!" [It's beautiful, it's beautiful. Everything is beautiful, even the poverty, even the mud on the sandals. . . . My God, what if it made me a painter!]6 Fromentin had already studied the ancient Orient in the prose poem of Edgar Quinet entitled Ahasvérus (1833) and in the paintings of Eugène Delacroix, Alexandre-Gabriel Decamps, and Prosper Marilhat at the Paris Salon of 1844; his early drawings included the scene of a defeated Turkish warrior (Turc penché sur un canon), indicating a developing interest in Orientalist scenes.7 By representing Algerian landscapes in a multitude of studies, sketches, and paintings, Fromentin secured his professional niche. Orientalist in style, Fromentin's paintings focused on the landscapes, architecture, light, and the people of Algeria. The tableaux were purchased by private collectors and met with great acclaim at several Paris salons between 1847 and 1876.8
Along with a novel, Dominique (1863), Fromentin's récits algériens [Algerian travel memoirs] are often seen as minor classics; however, critical studies of Orientalist and colonial literature have not had much to say about the Algerian colonial context in his work. Significantly, Edward Said's Orientalism and Culture and Imperialism do not include Fromentin's work alongside analyses of François-René de Chateaubriand, Gérard de Nerval, Pierre Loti, and André Gide. This exclusion is surprising, given the stature that Fromentin's work had during his lifetime. Some of his contemporaries saw his paintings as standing on a par with those of Delacroix, and both of these artists would lead the French Orientalist school. Indeed, Fromentin was singular among French artists of the nineteenth century in being both a painter and a writer. He approached the life of nineteenth-century Algerians more closely than any other author or artist of his time, attempting to represent their presence in a land whose beauty was surpassed, for him, only by its alterity. Whereas Delacroix's images of North Africans display passionate intensity through bright colors and expressive brushstrokes, Fromentin's tableaux show a sedulous approach to detail in landscapes and architecture.
In 1847–1848, Fromentin sojourned in Algeria for a second time, staying for eight months. His third and final voyage in 1853 was an eleven-month stay in which he journeyed into the southernmost reaches of French territory. This time, he went as far into the country as any French person had gone, to the desert oasis city of Laghouat. For the most part, Fromentin's writings, like his paintings, portray aesthetically appealing North African landscapes and proto-ethnographic descriptions of the country's inhabitants. My focus here is on his work Un été, which contains a darker undercurrent: the aftermath of a brutal French conquest he observed on his third trip to Algeria in 1853. Artistic inspiration and ambition underwrite this text, and, more importantly, so do troubled references to the colonial conquest. Fromentin's travelogue produces a vision peopled by fields of cadavers in the space of the colony. The violence inflicted on Algerian territory by advancing French troops resurges as a phantom within Fromentin's prose in the form of mutilated bodies and unburied corpses. Fromentin is haunted by agonizing bodies which serve as indicators of his anxiety in relation to his status as neutral observer and agent of conquest. The languishing and dismembered bodies that refuse to remain buried signal the haunted quality of his writings.
Fromentin's compelling narrative Un été is in the form of an epistolary text addressed to Armand Du Mesnil, a close friend who had accompanied him on his first trip to Algeria. The prose alternates between conveying the thrill of discovering new landscapes, peoples, and cities and sober accounts of the aftermath of the violence the author witnessed as the French invaded Algeria. Fromentin traveled from Blidah to Laghouat in May and June 1853. On the last part of the journey, he was accompanied by a military escort through the wake of the earlier massive colonizing efforts of the French army, in November and December of 1852.
At the time, Louis-Napoléon had just taken power in France, and the French government was eager to prove itself by accelerating plans to expand colonization into the south of Algeria. It was not long after Louis-Napoléon's coup d'état that he recognized the strategic importance of Laghouat in relation to the caravan routes of the south.9 The French army marched into southern Algeria with all available troops at its disposition, making an enormous show of power. Napoleon had appointed General Jacques-Louis Randon to complete the conquest of Algeria. Randon saw that the ongoing feuds in Laghouat were destabilizing France's control in the south and decided that the town had to be dominated; Randon ordered Pélissier to take the city. Charles-André Julien has called the viciousness of the violent French attack on Laghouat in 1852 no less than a butchery, and the Laghouati memorialize that year as a "time of desolation" even today.10 A combination of military operations with the goal of ending tribal resistance and asserting colonial control, the siege of Laghouat was brutal: French archives indicate a veritable massacre with indiscriminate violence against the city's civilians during and after the attacks which took place.
Fromentin's very presence in Algeria just a few months after the siege of Laghouat had been enabled by colonial ideology and its institutions of power. His séjour in Algeria culminated in the perilous journey to Laghouat. Searching for new subject matter, Fromentin had decided to venture on an additional desert trek, accompanied by a military convoy and escorts from the Mozabite tribes from the southern city of Gardaïa. In exchange for military protection, he was to produce a painting of France's victory in the region, a work that never materialized. In a letter to Paul Bataillard, Fromentin wrote that he wanted to see the true desert and considered the journey to be "un devoir très sérieux" [a very serious obligation].11 The officer leading this expedition was Lieutenant Carrus, head of the bureau arabe in the newly conquered town. Once he arrived, Fromentin was under the military protection of General Du Barail. As Fromentin approached Laghouat from the north and met his military escort for the rest of the journey, his somber textual and visual representations appear in sharp contrast to earlier ones that thrilled at the discovery of both the desert and his artistic ambitions. The impossibility of finishing the business of the lives of the massacred Laghouati is reflected in Judith Butler's thinking about violence and dehumanization in general: "It is not just that such a death is poorly marked, but that it is unworkable. Such a death vanishes, not into explicit discourse, but in the ellipses by which public discourse proceeds."12 Fromentin's arrival came during the grisly aftermath of the army's march and siege of Laghouat just months earlier. The juxtaposition of the "unworkable deaths" of the Laghouati contrasts with Fromentin's personal artistic quest and France's desire for a triumphalist imperialist trajectory. This parallel at the heart of his journey results in a profoundly conflicted narrative, perhaps a key reason why the travelogue was composed and published long after his trip there.
As he ventured into the outermost limits of French control, Fromentin hoped to see the "real" country, with its palm forests and caravans of camels and gazelles: "un pays nouveau, parfaitement different de celui que tu connais, à peu près intact, puisque nous n'avons pas eu le temps de le défigurer." [a new country, perfectly different from the one you know, mostly intact, since we have not had the time to disfigure it yet.]13 As John Culbert rightly suggests, Un été identifies with the forward momentum of imperialism.14 He argues that, as much as in Conrad's Heart of Darkness, Fromentin's narrative reveals what Said refers to, in relation to Conrad's novel, as the "sheer historical momentum" of colonial mastery. But after Fromentin saw this region, its misfortune haunts his writing. 15 Just as Conrad's work offers a harsh picture of colonial enterprise, Fromentin expresses anxious misgivings about French domination in Algeria. Of his tour there, Fromentin writes: "Nous suivions à peu près le chemin tracé par les balles et les baïonnettes de nos soldats." [We followed in the pathways traced by our soldiers' bullets and bayonets.]16 His primary reaction is one of regret about the massacre of the Laghouati: "je regrette d'être obligé de m'attrister devant un champ de bataille."17 [I regret having to be saddened before a battlefield.] Although Fromentin distanced himself from explicit anti-colonial political stances, his impressions of the recent French sieges in southern Algeria were fundamentally troubled. For example, he writes: that he did not want to "faire l'historien d'événements que je n'ai ni l'autorité ni le goût de raconteur" [be a historian of the events that I have neither the authority nor the inclination to recount.]18
As can be seen through a critical hauntological reading, Fromentin's expresses a deep ambivalence regarding the colonial project in his published and unpublished works. The wrack and ruin of Laghouat after the French conquest suggests that the colonial context of Fromentin's récits algériens is an important element in his representations of Algeria. Peter Dunwoodie briefly mentions "the French military presence and a new personal mood [that] had colored Fromentin's attitude" and "the human cost of the conquest," while Elmwood Hartman discusses Fromentin's sympathy for the indigènes. 19 John Culbert has the most extensive and convincing analysis of Fromentin's relation to the Algerian colonial situation: "Fromentin's encounter with Algeria subtly undoes the discourse of colonial mastery, and this subversion of colonial authority makes Fromentin's work a valuable counterpoint to . . . popular imperial discourse."20 Adding a hauntological perspective to Fromentin's Un été furthers this compelling argument and traces the "seething presences" decrying the colonial atrocities that had taken place during France's brutal colonizing efforts in southern Algeria just before Fromentin's visit.21
A Troubled Witness
When Fromentin enters the inner French territories, he spends significant time describing the ransacked city with its makeshift graves and unburied corpses. His descriptions linger on ravaged landscapes and the dead bodies of women and children. Slavoj Žižek associates haunting forces not with existence but rather with insistence, an insidious form of agency available even to the unactualized:
that which does not exist continues to insist, striving toward existence [. . .] When I miss a crucial ethical opportunity, and fail to make a move that would "change everything," the very nonexistence of what I should have done will haunt me forever: although what I did not do does not exist, its spectre continues to insist.22
Although Fromentin was not an actor in the siege of Laghouat and participated in no wrongdoings himself, an insistent regret seems to persist in his writings. An uninformed colonial envoy, Fromentin had to grapple with the ethical repercussions—what should and should not have been done—of colonialism.
In particular, Fromentin's accounts of two murdered prostitutes and the corpse of a Zouave soldier reveal eerily troubled undercurrents. These undercurrents of tension around the French colonial project in Algeria are manifold for the painter-artist and lead him to question his place within it. Finally, in a strange and troubling scene, he attaches a woman's severed hand to his saddle as a grisly souvenir, which, terrified, he later casts aside in a cemetery. As these examples reveal, Fromentin repeatedly references incomplete burial and mourning rituals throughout the travelogue. As Colin Davis reminds us, ghosts symbolize "unfinished business;" haunting happens when there have been disturbances within the ethical order.23 In this case, it was the savage razing of the village of Laghouat. Fromentin's troubled witnessing of incomplete burial in the emerging French colony sheds light on the ravages of imperialism and makes manifest the ghosts of colonialism.
In considering Fromentin's work as a key part of the chronicle of modern colonialism, it is crucial to this examination to analyze the form of his travelogues. First published as "Alger, fragments d'un journal de voyage" in the journal L'Artiste in 1857, the two works Un été dans le Sahara and Une année dans le Sahel were then run as a serial in the Revue des deux mondes in 1858. For his récits algériens, Fromentin chose to write an epistolary text after the fact. Of this literary device, he writes "il est clair que la forme des lettres, que j'adoptai pour les deux récits, était un simple artifice qui permettait plus d'abandon, m'autorisait à me découvrir un peu plus moi-même." [it is clear that the form of letters, which I adopted for the two narratives, was a simple artifice that permitted more abandon, authorizing me to discover myself a bit more.]24 From their opening pages, the tone of the books is intimate: "Cher ami, je comptais ne t'écrire que de ma première étape; mais l'inaction forcée où je suis me fait ouvrir, sans plus attendre, mon journal de route." [Dear friend, I counted only on writing to you of my first stop-over; but forced inaction made me open, without waiting any longer, my travel journal.]25 Fromentin's choice of the epistolary genre imparts the allure of a veracious and authentic experience, and in this fundamentally personal project, his Algerian texts are, as he writes, "une certaine manière de voir, de sentir, et d'exprimer qui m'est personnelle et n'a pas cessé d'être mienne. Ils disent à peu près ce que j'étais, et je m'y retrouve." [a certain manner of seeing, feeling, and expressing what is personal to me and what never stopped being mine. They nearly say what I was, and I find myself in them.]26 Although presented as real travel letters to readers, Fromentin's travel narratives are in fact a mixture of memory, journal entries, sketches, and others' accounts of Algeria. The two works give a general evocation of Fromentin's journeys, but as Anne-Marie Christin has demonstrated, Fromentin's letters were metamorphosed into the diverse texts leading to the published versions.27
The titles Fromentin chose for the two collections of letters are also revealing. First, he made an interesting exclusion: the word "voyage" was omitted from the title, contributing to an emphasis on duration and permanency. Second, he added the enigmatic subtitle "Journal d'un absent" to Une année dans le Sahel [A Year in the Sahel].28 As Christin remarks, these title changes underscore Fromentin's fraught status as an insider-outsider in Algeria.29 Although he stayed for a longer time and went farther south into the newly conquered territories than other French travelers, a military convoy had to accompany him for his protection as he went in search of new material. As the word "absent" reveals, he had no real place in the country he was visiting.
For Fromentin, neither the muse of painting nor that of writing inspired a satisfactory representation of his travels. As critics have shown, writing these travelogues did not come easily to him.30 Fromentin's retrospective preface, published over a decade after the work's first appearance, emphasizes the immense difficulties he experienced in creating a representation of Algeria, both pictorially and textually. I postulate that the difficulty in representing his experiences in Algeria resulted, in part, from his witnessing of the aftermath of the French military's brutality there. Fromentin called creating the narratives from the sketches and notebooks that he made during the travel itself an act a "translation": "J'avais à m'exercer sur les mêmes tableaux, à traduire, la plume à la main, les croquis accumulés dans mes cartons de voyage." [I had to exert myself over the same paintings, to translate, pen in hand, the sketches I had accumulated in my notebooks.]31 Finding that he could not paint his memories of Algeria, once so abundantly intimate and lively, Fromentin turned to writing, stating, "l'insuffisance de mon métier me conseilla, comme expédient, d'en chercher un autre, et que la difficulté de peindre avec le pinceau me fit essayer de la plume."32 [the insufficiency of my profession advised me, as a solution, to seek another one, and that the difficulty of painting with a brush made me try with a pen.] These fraught representational processes reflected Fromentin's anxious relation with the country and his place within it, as well as the unsettled remains of French violence.
In his travels, Fromentin was both agent of conquest and witness to colonial atrocities. For example, he expresses discomfort about what he sees in Algeria even before visiting Laghouat. In his récits algériens and personal correspondence to friends and family, Fromentin's tone alternates between pleasure and irritation. At times he even seems detached, as in the following passage:
Ce n'est pas de la joie que j'éprouve ici ni du bonheur. Il me serait difficile de t'expliquer cela. Je n'ai jamais éprouvé un tel détachement de lieu, malgré le vigoureux désir d'en tirer parti. Je visite ce pays comme on examine une proie, avidement, avec curiosité, satisfaction; mais sans amour, et je sens le jour où je pourrais le quitter sans trop laisser derrière moi, où j'en aurai extrait ce que je suis venu y chercher, sera le plus joyeux jour de mon voyage.
[It is not joy I feel here, nor happiness. It would be difficult to explain this to you. I have never felt such detachment from a place, despite my strong desire to use it to my advantage. I am visiting this country as one who examines prey, avidly, with curiosity, satisfaction; but without love, and I sense that the day when I will be able to leave it without leaving too much behind me, when I will have extracted what I came here to find, will be the most joyful day of my journey.]33
The entanglement of Fromentin as cold-hearted colonial profiteer and Fromentin as troubled witness underwrites the narrative. Here, Fromentin expresses his primary approach to the country, one completely aligned with the imperial project: to figuratively consume the place. He examines the country as if it were prey, as something to devour but not to love. Fromentin holds it in cold regard, avoiding exoticist clichés or political propaganda. This passage also points to his self-reflexive status as an exploiter of the representations, both written and visual, of his experiences and travels; indeed, he uses the verb "exploiter" [to exploit] in a letter to Paul Bataillard.34 In a related remark, Fromentin notes that the Arabic word for a painter is similar to the word for a thief.35 Directly participating in the colonial project, he boasts, "Aucun peintre français que je sache n'aura pénétré aussi avant que nous dans le sud de nos possessions." [No painter that I know will have penetrated as far as us in our southern possessions.]36
Although his letters state that he seeks virgin territory that will be profitable to his career, in other writings, Fromentin reveals himself as troubled by the aggressive French politics aimed at "pacifying" the Sahara. Whereas he rarely directly criticized colonization, in the following example, he criticizes the French colonial presence in Algeria by equating colonization with bloodshed and death:
Le passé de ce petit pays en exploitation définitive de sa richesse, nous n'y pensons plus. Nous oublions qu'il a fallu dix années de guerre avec les Arabes, et vingt années de lutte avec un climat beaucoup plus meurtrier que la guerre [. . .] La véritable histoire de la colonie est, ici comme partout déposé dans les sépulcres. Que d'héroïsmes connus ou inconnus, presque tous oubliés déjà, et dont pas un cependant n'a été utile!
The past of this small country in the midst of definitive exploitation of its riches, let us not think of it any longer. We forget that it took a decade of war with the Arabs, and 20 years of fighting in a climate much more murderous than war. [. . .] The veritable history of the colony is, here, as everywhere, deposited in its tombs. What known or unknown heroics, almost all already forgotten, and yet, not one was useful!37
Although such direct commentary on French colonialism is rare in Fromentin's work, in his later text, Une année dans le Sahel, he demonstrates a thorough comprehension of the clashes between Algerian and French cultures, especially when he discusses the "two towns" in Algiers, the strategically placed French town along the coast, and concentrated and elevated old Casbah. Remarking upon the new urban developments, such as the conversion of the Rue Bab-Azoun and the Rue Bab-el-Ouen into scaled-down versions of the Rue de Rivoli in Paris and the attempt to fuse the two cultures by converting some of the mosques into Christian churches, Fromentin was not hopeful about the result. He saw the conflict between the cultures as being that of an eternal enmity and consistently criticized the loss of indigenous identity in the urban reconstructions of Blidah and Algiers.38 In a clearly damning statement, he writes, "Alger est déshonorée parce qu'elle est française."39 [Algiers is dishonored because it is French.] These examples from his personal letters and unpublished manuscripts point to a dark undercurrent in his writing, especially about the aftermath of the carnage of the battles of Laghouat.
As Tzvetan Todorov observes, any travelogue rides a fine line between demonstration of "scientific" observations and personal reflection. He writes: "This is what, in its way, the term travel narrative designates: narrative, that is, personal narration and not objective descriptions, but also travel, and therefore a framework of circumstances exterior to the subject. [. . .] [O]n the one side, the boundary is science, on the other side, autobiography. The travel narrative comes into being from the fusion of the two."40 Fromentin's choice of subject matter was the "framework of circumstances" surrounding him, and in harmony with the advancement of the new colonial empire; he rode the crest of the wave of colonial expansion. However, as the text recounts his personal experience as an observer, a hauntological examination probes the emotions of his personal narration as he describes the lingering trauma and violence in the vestiges of death and destruction around him. Fromentin alternates among tones of neutrality, overall acceptance, profiteering, and in strange detours, a troubled witnessing of colonial damage, in writings that complicate Mary Louise Pratt's concept of the "anti-conquest," which she defines as the European subject (predominantly male) adopting an innocent stance while his gaze would "passively look out and possess."41 Pratt defines the anti-conquest as "the strategies of representation whereby European bourgeois subjects seek to secure their innocence in the same moment as they assert European hegemony."42 Pinpointing less aggressive or explicitly pro-colonial subject positions, Pratt targets seemingly innocent travel narratives as unwitting agents of "European global authority."43 As with the authors Pratt analyzes, Fromentin's stance is that of a neutral observer in the main, but deep misgivings about France's colonial policy surge up, unbidden, from Un été.44
Furia francese
In what follows, I will pay particular attention to these haunted moments in Fromentin's Saharan travelogue. Laghouat holds an important place: the progression of the work gives a privileged position to Laghouat and the brutality that had recently occurred there. For example, Fromentin's long description of the rue Bab-el-Gharbi would later inspire his painting Rue à El-Aghouat, shown at the Paris salon of 1859. As art historian Hélène Gill convincingly demonstrates, Fromentin's paintings and drawings completed in situ in Laghouat are not as explicitly revealing as his corpse-filled paragraphs, but they do suggest unease with the harsh historical realities he had witnessed.45 In addition, Un été is structured around Fromentin's affective impressions of Laghouat, into which surge intense, unbidden, documentary-like images. Fromentin's descriptions of Laghouat convey a hesitating, anxious, and melancholy ethos. Tellingly, variants of his unpublished work probingly witness the blood-soaked repercussions of the killing of over two thousand people. Fromentin's efforts to suppress his judgments or emotions while in Laghouat give way to horror.
Over the course of Fromentin's journey, the representations become more and more troubled and troubling as he becomes a closer witness to the atrocity of colonial conquest. As Michael Humphrey remarks,
Paradoxically, witnessing is also the essential basis for recognition of suffering victims, for compassion and care. Witnessing is the vehicle for reversing the dehumanizing effect of atrocity and recovering the humanity of victims and their social worlds, through witnessing victims' suffering and hearing their testimonies, social connections are created between victim and witness, establishing a basis for moral responsibility. And this can even occur with strangers at a distance.46
Fromentin found himself at not too far a distance from the Laghouati victims' suffering, and his texts capture how the dehumanizing of the Laghouati and the atrocities of colonialism lingered long after the French army's departure from the region. The elusiveness of how to give the siege of Laghouat its proper due haunts Fromentin's text; the historical record gives the reasons why. Before the 1852 siege, Laghouat was a community of about four thousand people who made their livings gardening and trading. The attack by the French army was brutal: Pélissier's troops were comprised of five columns equipped with heavy artillery, and the city was taken in less than a day. Even after Laghouat surrendered unconditionally, French soldiers continued to kill the city's inhabitants. Lieutenant-colonel Jean-Joseph-Gustave Cler called the attack a furia francese, using an Italian term for the attack by French soldiers who murdered innocent civilians in an indiscriminate frenzy:
les braves soldats prennent immédiatement le pas de la course, escaladent tous les obstacles, franchissent, à l'aide de courtes échelles, les brèches faites par le canon et passant par les armes tout ce qui essaie de résister, ils se précipitent comme une avalanche avec cette furia francese, tant redoutée de nos ennemis dans les moments offensifs [. . .] La casbah ne peut résister aux efforts des assaillants. [. . .] Les défenseurs sont poursuivis à la baïonnette dans la cour, aux étages supérieurs et sur les terrasses.
[the brave soldiers immediately took up running, climbing over all obstacles, with the help of small ladders, breaking through the cannon holes and going through with their arms anything that tried to resist, they rushed like an avalanche with that furia francese so dreaded by our enemies in offense. . . . The Casbah couldn't resist the assailants' efforts. . . . Its defenders were pursued by bayonet into their courtyards, to the higher floors, to the terraces.]47
Without warning, the soldiers wildly entered homes and buildings, attacking "impitoyablement tout ce qui s'y trouvait; [. . .] dans le désordre, souvent dans l'ombre, ils ne s'attardaient pas à établir des distinctions d'âge et de sexe: ils frappaient partout et sans crier 'gare'!" [pitilessly everything they found there . . . in the disorder, often in darkness, they didn't stop to establish distinctions of age and sex, they struck everywhere and without shouting "warning!"]48
Pélissier's goal was to raze the entire village, and he commanded that it should be completely destroyed. According to the memoirs of major general François Claude Du Barail, homes were demolished and trees and gardens uprooted and destroyed.49 Women, children, and the elderly were among the casualties; there were very few wounded survivors because so many resisters had been killed.50 With the French eager to make a permanent southern Algerian base in Laghouat, the dead had to be buried quickly. The staggering number of bodies made this impossible; the burials in large common graves took several weeks to complete. When Pélissier reproached his men for not burying the dead quickly enough, his commander responded sarcastically, "que voulez-vous mon général, nous n'enterrons pas les morts aussi vite que vous les faites!" [what do you want, my general, we can't bury the dead as quickly as you kill them!]51 Because the number of bodies was so great, by the time Fromentin arrived, not all of the corpses had been fully buried, and roughly one thousand remaining survivors were confined by the French army in the lower town of Ouled-Serrin. This was the battle-scarred terrain that Fromentin observed while in the city and its environs.
A close examination of Fromentin's published and unpublished works reveals his profound difficulty finding the words to express the fallout from the siege. Upon first hearing about the battle of Laghouat, he refers to it as a "massacre":
[P]lus des deux tiers furent trouvés dans la ville, soit dans les rues soit dans la cour des maisons. Il y a des gens qui prétendent que [les Laghouati] se sont assez mal défendus. J'aime mieux croire pour leur honneur et pour le nôtre que cette grande extermination fut le résultat d'une résistance désespérée; car autrement ce serait un massacre.
[(M)ore than two-thirds were found in the city, either in the streets or in the houses' courtyards. There are those who say that the Laghouati defended themselves poorly. I would rather believe for their honor and for ours that this great extermination was the result of a desperate resistance, because otherwise, it would be a massacre.]52
In just two sentences, Fromentin employs the variants "extermination," "résistance," and "massacre" for the 1852 siege. In a prior letter, he had called it "l'assaut, la prise, et le massacre" ["the assault," "the overtaking," and "the massacre"] which he subsequently crossed out in favor of "le combat meurtrier du 3 décembre, de l'assaut du 4 et du massacre qui suivit." [the mortal combat of December 3, the assault of the 4th, and the massacre that followed.]53 Tellingly, the word "massacre" does not appear in the final published version of the text. Instead, Fromentin settled on "atrocious," a more politically neutral term: "La guerre des rues est atroce, et l'homme y devient fou, soit qu'il se défende ou qu'il attaque."54 [The street fights are atrocious, and men become insane in it, whether they are attacking or defending.] These semantic shifts reveal the extent to which he struggled to express the aftereffects of the siege of Laghouat in its streets and homes. It is worth remarking that Fromentin has moved to address the event by speaking of it in general terms, detaching himself from the word "massacre" and replacing it with "atroce." Instead of "massacre," in which there are perpetrator and victim, he settles on a general descriptor of street fighting.
Throughout his writing and revising, Fromentin shifted from condemnation to neutrality and an affectation of a more apolitical stance regarding French colonial activities. For example, an unpublished draft states: "Je n'ai le droit ni de raconter, ni de juger une pareille victoire. Je ne suis point venu faire ici de la politique, ni même, quoique le bruit en court, un tableau militaire" [I don't have the right to either recount or judge such a victory. I did not come here to do politics, nor, despite the rumors, a military painting.]55 His prose is inflected with a noticeable regret at having had to wonder about the consequences of such atrocities. This phrasing does not appear in the final draft. Fromentin's ultimate decision to have this passage read "Je te dirai, aussi brièvement que possible, ce que j'ai vu, c'est à dire, les traces de la bataille et les lieux qui ont été témoins du siège." [I will tell you, as briefly as possible, what I saw, that is to say, traces of battle and the places that witnessed the siege.]56 In another passage a few pages later that does not appear in the published version, Fromentin's struggle not to think about the bullet holes in the buildings he passed by indicates the extent to which he was psychologically affected by the ghosts of the battle-scarred city: "Chaque maison témoignait d'une lutte acharnée." [Each home witnessed a pitched battle.]"57 His own words are testimony to this: in a first version of his manuscript, Fromentin writes that the city had been "assassinated."58
"Une ville à moitié morte"
The shifts in Fromentin's representation of Laghouat are presaged by his first impressions of the city. Upon entering Laghouat, he comments in a quasi-ethnographic tone upon how Algerian cities have their cemeteries built outside the city walls.59 However, Fromentin continues by contrasting another Saharan city with the silent dread surrounding Laghouat: a spiritually dark, silent, and menacing city greets him, and he pauses to reflect upon the cloud of death hovering over the Algerian landscape.
au lieu d'un champ de repos, je trouvais un champ de bataille; et ce que je venais de voir, ce que je venais d'entendre, je ne sais quoi de menaçant dans le silence et dans l'air de cette ville noire et muette sous le soleil, quelque chose enfin que je devinais dès l'abord, m'avertissait que j'entrais dans une ville à moitié morte, et de mort violente.
[instead of a restful field, I found a battlefield, and what I'd just seen, what I'd just heard, I do not know what kind of menace in the silence and in the air of this black and mute city under the sun, something, finally, that I guessed from the beginning, warned me that I was entering a half-dead city, from a violent death.]60
Seething phantasmic presences haunt Fromentin's words in this passage. Instead of seeing a peaceful burial ground, Fromentin remarks on the unknowable "je ne sais quoi de menaçant" feeling in the silent air suffocating the black and muted city. Although he cannot aptly describe what it is, Fromentin guesses from the outset that something terrible had happened. After observing the city's entrance, he remarks upon the scars borne by Laghouat's buildings, their closed doors riddled by bullet holes: "[l]a plupart des portes étaient fermées; quelques-unes, où je remarquai des trous de balles et des marques de baïonnettes, semblaient l'être, comme on dit en France, après décès." ["the majority of the doors were closed, some, where I remarked bullet holes and bayonet marks, seemed to be, as we say in France, after a death."]61 Destroyed by gunfire, the homes mirror Fromentin's violence-haunted surroundings.
Fromentin's lodging was no more comforting than the buildings he saw. Arranged for by the military convoy, his accommodations in the bureau arabe were partially destroyed. When he entered, he found that the house had been literally torn apart by the French army in the course of battle, with only half a ceiling and a floor remaining in the servants' quarters. In his accounts, he wonders what might have happened six months earlier to cause the damage: "Dans la chambre des domestiques, une moitié seulement du plafond, et de même une moitié de plancher; ces deux trous, ouvertes sur la tête et sous les pieds, se correspondent. Est-ce un obus qui a traversé le tout à la fois? Que s'est-il passé il y a six mois à cette même place où j'écris?" [In the servants' quarters, only half the ceiling and the floor remained; these two holes, open above one's head and one's feet, matched each other. Did an artillery shell penetrate everything at the same time? What happened six months ago in this very spot where I am writing?]62
Again, something unnamable lurks between these lines. These passages suggest that Fromentin had difficulty controlling his terrible speculations; in his unpublished manuscript, he comments that the walls' scars are testimony of "une aventure sanglante que je m'efforçais d'oublier." [a bloody adventure that I was trying hard to forget.]63 As I have shown, the published manuscript does not contain as much of this explicit language, again pointing to Fromentin's efforts to repress or otherwise neutralize the descriptors originally used.
In addition to these detailed observations, Fromentin remarks upon the entirety of the ransacked city as a shadow of its former self, drawing upon the vocabulary of death, solitude, and exile. In particular, he focuses on the most vulnerable of the population: women, children, and animals. Fromentin describes how the city was overrun, then deserted, by terrified runaway dogs. He also depicts the clouds of crows and vultures that swarmed over the city, which he describes as a veritable mass grave:
Quand on eut enfoui tous les morts, il ne resta presque plus personne dans la ville, excepté les douze cents hommes de garnison. [. . .] Femmes, enfants, tout le monde s'était expatrié. Les chiens eux-mêmes, épouvantés, privés de leurs maîtres, émigrèrent en masse et ne sont pas revenus. Ce fut donc pendant quelque temps une solitude terrible, et bien plus menaçante que ne l'eût été le voisinage d'une population hostile et difficile à contenir. Dès le premier soir, des nuées de corbeaux et de vautours arrivèrent on ne sait d'où, car il n'en avait pas paru un seul avant la bataille. Pendant un mois, ils volèrent sur la ville comme au-dessus d'un charnier [. . .]. Ils s'en allèrent enfin d'eux-mêmes [. . .] la même solitude s'étendit jusque dans l'oasis. [. . .] Quelques vautours solitaires étaient demeurés au milieu de cette panique générale, et n'ont pas cessé d'habiter les hauteurs de l'est, comme pour attendre une curée nouvelle.
[When they had buried all the dead, almost no one was left in the city, except the twelve hundred garrison men. [. . .] Women, children, everyone went away. Even the dogs, terrified, robbed of their masters, emigrated en masse and did not come back. It was therefore for some time a terrible solitude, and much more menacing than a neighboring hostile and hard to contain population would have been. From the first evening on, clouds of crows and vultures arrived out of nowhere, for there had not been a single one of them before the battle. For a month, they flew over the city as if over a mass grave [. . .]. Some solitary vultures stayed during the general panic, and have not left the eastern heights, as if they were waiting for new blood after the hunt.]64
It is important to note that Fromentin likely would not have directly seen the carrion and fleeing dogs. These occurrences must have been recounted to him, again underscoring the haunting violence and aftermath of the French attack on the city. Fromentin cannot escape these clouds of death and writes of a "terrible solitude," with the final lingering vultures lying in wait for more corpses.
What is also particularly striking in Fromentin's prose is his pity for the most vulnerable of the population as he observes the surviving groups of beggars. He remarks that they are mainly made up of women and children. At the sight of the devastated survivors struggling to survive, he writes: "La ville se repeuple. [Ils] sont confinés dans le bas quartier des Ouled-Serrin. C'est une population d'aspect misérable, consterné, sans ressource aujourd'hui [. . .] Je n'ai encore aperçu que des indigents, de la dernière condition, des femmes le plus pauvrement vêtues, des enfants étiolés par la misère, souffreteux et languissants." [The city is repopulating. [They] are confined in the lower quarter of the Ouled-Serrin. It is today a population of an abject, anxious, impoverished aspect [. . .] I have still seen only desperate indigents, the most poorly dressed women, children withered, sickly, and languishing from extreme poverty.]65 Reflecting beyond the survivors' physical states, Fromentin wonders how they carry on: "Ont-ils oublié déjà le sort de leurs concitoyens? Et sont-ils incapables de ressentiment?" [Have they already forgotten the fate of their fellow citizens? And are they incapable of resentment?]66 Again, these moments in the travelogue point to a unique sensitivity to the trauma and its newly conquered people. The children of Laghouat's ghosts are described here as desperate, indigent, and ill. Fromentin's questions linger in the text: Have the survivors and their children forgotten the siege? What do they feel? Again, in Humphrey's terms, this kind of witnessing "[reverses] the dehumanizing effect of atrocity and [recovers] the humanity of victims and their social worlds."67
Shallow Graves
Whereas Fromentin's political consciousness is ambivalently expressed throughout his oeuvre, his writing about Laghouat is different: it points to a devastating loss of human life resulting from colonial efforts. Fromentin's returns to cadavers and roaming dogs underscore an anxiety about France's colonial project and his place within it. The French military caravan followed the footsteps of death. The account is disturbing: images of shallow graves arise in the text with references to dead soldiers in thinly covered resting places. Their bodies are uncovered by scavenging dogs nosing around and unburying their bones.
When Fromentin relates his conversation with his army escort, the unnamed "Lieutenant N. . ." tells him that they have just passed Pélissier's camp. Lieutenant N. . . takes pains to point out how the city is still grappling with the surfeit of shallow graves and unburied bodies:
Il me parla du combat meurtrier du 3 décembre, de l'assaut du 4 et de la lutte sanglante qui suivait la prise. Il me parla de nos pertes et de celles de l'ennemi; il me prévint que je sentirais peut-être une odeur fétide dans la ville et que je lui trouverais un air d'abandon. Il fit le calcul des morts; lui-même avait présidé à leur enfouissement dans les puits. Nos propres morts n'avaient guère été mieux enterrés, faute de pioches pour creuser plus profondément. Chaque jour, tant ils étaient peu couverts, on en trouvait à la surface du sol, que les chiens avaient exhumés pendant la nuit. Il fallait s'attendre à marcher sur des débris et à voir partout pointer des ossements. [. . .] Un peu plus loin, il y avait une tête réduite à la sécheresse d'un caillou; et sur toute notre route on voyait par-ci par-là des os blanchis.
[He told me about the deadly combat of December 3, the attack on December 4, and the bloody fight that followed the capture of the city. He told me about our losses and those of the enemy; he warned me that I might smell a fetid odor in the city and that I would find it abandoned. He counted the dead; he himself had supervised the burial holes. Our own casualties had hardly been better buried for the lack of pickaxes to dig deeper. Each day they were less and less buried, we saw some at the soil's surface that dogs had exhumed during the night. I had to walk on the debris and everywhere see bones sticking out. . . . A little further, there was a head reduced by dryness to a stone; and all along our path we saw, here and there, whitened bones.]68
Recounting Lieutenant N. . .'s words, Fromentin goes on to state in the quotation above that the cadavers prevented their company from passing easily through the region. The unburied in Fromentin's work serve as macabre halts—literal and figurative—in his chronicle, as corpse-strewn battlefields and makeshift graveyards haunt Un été. His escort spares no detail in describing the aftermath of the massacres: "Tout cela n'est rien, me dit le lieutenant; Dieu merci, vous ne connaîtrez jamais chose pareille. Ce que le lieutenant ne me dit pas, je le savais. On marchait dans le sang; il y avait là des cadavres par centaines; les cadavres empêchaient de passer." [This is nothing; God willing you'll never see anything like that. What the lieutenant did not say, I knew. We were walking in a bloodbath, there were hundreds of cadavers; the bodies prevented us from passing.]69 Like Fromentin's questions earlier about the Laghouati, haunting presences emerge, such as the "less and less buried" bones representing the ghosts of the villagers that return to haunt the victors.
With the text's depictions of the human costs of colonialism, the harsh realities of colonial warfare resurge within the idyllic and romanticized landscapes of Fromentin's other scenes. Stating that it is impossible to write a bucolic and peaceful representation of the colony, Fromentin writes bitterly, "Décidément, pensai-je, ce n'est pas ici qu'on écrira les bucoliques de la vie arabe." [Decidedly, I thought, it is not here that I will write about the bucolic Arab life.]70 In these examples, dead soldiers, civilians, and animals serve as a roadblock to the French army's convoy. The unburied bodies remaining in unidentified resting places foreground the misgivings, anxieties, and ambivalences underpinning colonization even as it was happening.
In particular, there are six unburied bodies upon which Fromentin's narrative lingers longest. He observes the first body, that of a dead Zouave soldier, upon his entry to Laghouat:71
Tout à l'heure, en venant, [le lieutenant] avait trouvé le corps entier et tout habillé d'un zouave; il me mena le voir. Le pauvre soldat avait les bras étendus, la tête renversée de côté, soulevée par un peu de sable, en manière d'oreiller; le haut du corps à l'état de squelette était momifié; il conservait son pantalon rouge et le bas de ses jambes engagé dans le sable montrait des lambeaux de guêtres; on eût dit qu'il allait achever de sortir de terre, comme on se représente une résurrection.
[A little earlier, upon arriving (the lieutenant) had found the entire clothed body of a zouave; he brought me to see it. The poor soldier had his arms outstretched, his head knocked to the side, held up by a little sand like a pillow; the top of the body was in the state of a mummified skeleton; its red pants remained and its calves stuck in the sand showed its gaiters in shreds; it was like it had completed coming out of the earth, as if in a resurrection.]72
The passage suggests that this is a soldier's body, not an unarmed citizen, and the soldier's identity does not escape Fromentin's notice. The Zouave victim again underscores the disastrous loss of life. Fromentin lingers upon the details of the Zouave's bright red uniform to emphasize this. "Momifié," the body is only half-buried, and indeed seems only to be asleep in its position, using a heap of sand as a pillow. Zombie-like in the body of the presentation, the Zouave is coming out of the earth, as if in the course of being resurrected. In this grisly tableau, soldier and citizen alike are victims. As in other instances in the work, the dead refuse to stay buried and instead haunt the author and as the following section argues, his escort the lieutenant.
Innocent Victims
There are two other bodies that Fromentin's text describes in detail, those of Fatma and Meriem, two murdered prostitutes whose tale is included at the end of Un été. The lieutenant accompanying Fromentin tells him the cruel story of two "Nayliettes."73 While walking through the city with Lieutenant N. . ., Fromentin hears the story from him. The lieutenant prefaces it as the "empreintes d'un triste retour sur les hasards cruels de la guerre." [imprints of a sad return to war's cruel fate.]74 The lieutenant tells Fromentin that before the siege, two beautiful women lived in the house standing before them. A few months before the siege, another soldier accompanied the lieutenant to pay a nocturnal visit that would leave them with pleasant memories. During the attack upon Laghouat, the lieutenant thought to find the two women to try to save them. Taking a sergeant with him, he ran to their home in the midst of the violent siege: "Les coups de fusil dans les rues pleuvaient; on se battait jusqu'au cœur de la ville. Ils arrivèrent pourtant, mais trop tard." [In the streets, rifle shots were coming thick and fast; the fights were taking place in the heart of the city. They arrived, but too late.]75 When they come to Fatma and Meriem's house, a soldier stands barring the door, reloading his gun. The lieutenant describes the following scene:
Les deux pauvres filles étaient étendues sans mouvement, l'une sur le pavé de la cour, l'autre au bas de l'escalier, d'où elle avait roulé la tête en bas. Fatma était morte, M'riem expirait. L'une et l'autre n'avaient plus de turban, ni pendants d'oreilles, ni anneaux aux pieds, ni épingles de haïk; elles étaient presque déshabillées, et leurs vêtements ne tenaient plus que par la ceinture autour de leurs hanches mises à nu.
– Les malheureuses! dit le lieutenant.
– Les s. . .voleurs! dit le sergent, qui remarqua, le premier, que les bijoux manquaient. [. . .] M'riem, en expirant, laissa tomber de sa main un bouton d'uniforme arraché à son meurtrier.76
[The two poor girls were lying motionless, one on the courtyard's stones, the other at the bottom of the stairs, where she had rolled upside down. Fatma was dead, M'riem was expiring. Neither had their turban or earrings, nor toe rings, nor haik (veil) pins; they were almost undressed, and their clothes held up only by the belt around their exposed hips. - Poor things! said the lieutenant. - The dirty thieves! said the sergeant, who noted, first, that their jewels were missing. . . . M'riem, fading, dropped from her hand a uniform button torn from her murderer.]
They believe that a man who was trying to flee committed the murder and that Meriem ripped the button off her attacker's uniform as she defended herself. Lieutenant N. . ., telling Fromentin the story, has kept it as a souvenir: "Le voici, me dit le lieutenant; et il me le fit passer sous les yeux." [Here it is, the lieutenant said, letting me have a look at it.]77
As with the other examples, Fromentin's difficulty in capturing this kind of brutal violence on the written page is manifest; again, the unpublished account diverges from the published version. For instance, the lieutenant uses the word "assassins" in the unpublished version, and the earlier victim is not a soldier but rather a young boy shot in the back while attempting to flee.78 In the published version of the work, these details are missing, but the murder of innocents still underlies this textual depiction. The prostitutes' jewels are symbols of the murder and pillage in the Algerian city, underscored by Fromentin's list of what is missing from the bodies: earrings, toe rings, veil pins, and clothing.79 Fatma and Meriem, innocent victims of the Laghouati massacre, represent the sparse remains of plundered Laghouat, and on a wider scale, the laying waste of the entire colony.
Fromentin's troubled testimony continues as he concludes his narrative. Near the end of Un été, he remarks upon the constant cloud of death casting a pall over Laghouat, which he calls "[c]ette grande ville triste et qui bien véritablement sent la mort, s'enveloppait d'ombres violettes pareilles à des voiles de deuil." [this great sad city that smells of death [. . .] covered in purple shadows like veils of mourning.]80 Enveloped in the city's grief, Fromentin makes a final halt to look more closely at the ravages of the battle and sees the corpses of three women whose bones have been dug up by sniffing dogs:
En approchant des jardins, nous aperçûmes, près de trous fraîchement remués, trois objets informes étendus à terre. C'étaient trois cadavres de femmes que les chiens avaient arrachés de leurs fosses. Blessées pendant la prise ou atteintes dans leur fuite, sans doute elles étaient venues tomber là, et la piété des passants les avait recouvertes d'un peu de terre. Je descendis de cheval pour examiner de plus près ces corps momifiés, consumés jusqu'aux os, mais tout vêtus encore de leurs haïks de cotonnade grise. La terre n'avait rien lassé à ronger sur ces carcasses desséchées, et une fois exhumées, les chiens n'avaient pas même essayé de les déshabiller.
[Approaching the gardens, we noticed, near some freshly dug holes, three shapeless objects lying on the earth. They were three women's cadavers that the dogs had dragged from their graves. Wounded during the capture or harmed during their flight, they probably fell there, and the passersby in their piety had covered them with some soil. I got down from my horse in order to examine more closely these mummified bodies, consumed to their bones, but still fully dressed in their gray cotton haiks. The earth left these dried carcasses with nothing more to chew upon, and once they were exhumed, the dogs did not even try to undress them.]81
Fromentin descends from his mount to peer more closely at the mummified bodies. Just as with the Zouave soldier earlier, the use of the word momifié denotes a preserved body, a human life not lost but deliberately preserved. Just as the traumatic memory of the massacre permeates the very air of the city, the cadavers do not degrade but rather return to the surface.
Memento Mori
In perhaps the most well-known scene in the narrative, near the corpses of the three Algerian women, Fromentin finds a severed hand of a woman.82 The mummified hand is arguably the most gruesome tableau in his writings. He describes picking up the ghastly souvenir and attaching it to the top of his saddle:
Je la pris et l'accrochai à l'arçon de ma selle; c'était une relique funèbre à rapporter du triste ossuaire d'El-Aghouat. [. . .] La main se balançait à côté de la mienne; c'était une petite main allongée, étroite, aux ongles blancs, qui peut-être n'avait pas été sans grâce [. . .] il y avait quelque chose de vivant encore dans le geste effrayant de ces doigts contractés. Je finis par avoir peur, et je la déposai en passant dans le cimetière arabe.
[I took it and hooked it to my saddle horn; it was a funerary relic to from the sad mass grave of Laghouat. . . . The hand swung next to mine; it was a small slender hand, with pale fingernails, that had maybe not been without grace . . . there was something still living in its tense fingers' terrifying gesture. I ended up being afraid, and while passing the Arab cemetery, left it in there.]83
Strikingly, in Fromentin's text, he refers to the hand as a "relic," a word with religious connotations. From the Latin reliquiae, the word "relic" both means what is left behind and denotes veneration of a sacred body. The severed hand serves as a tangible memorial of what cannot be relinquished, the fresh memory of the French army's massacres and what Fromentin cannot completely leave behind. Like the other instances I have analyzed, this scene is emblematic of incomplete commemoration and burial, and foregrounds the injustice of killing unarmed citizens. It is not inadvertently that the corpses under Fromentin's scrutiny are those of women, for women and children represent the majority of colonialism's victims in the population of the colonized. The dismembered woman's hand represents the transgression of killing innocent civilians and calls Fromentin, and his readers, to fill in the blanks, in other words, the unsettled traces of her story.
Looked at more closely, the truncated member is far from inanimate. Specifically, the phrase "there was still something living in its tense fingers" is startling. Clenching its fingers, the zombified hand hangs next to Fromentin's own and represents another kind of insistent haunting in his travelogues. Even when faced with impending doom, life clings to life, and this example shows an undying resistance to French colonialism. In addition, it reflects the rising up of Fromentin's complicity in the colonial project through his published moderation of the savage attacks on the city as opposed to his unpublished material. As with other cadavers who rise up and are repressed throughout the text, the clutching movement of the women's hand haunts him. Fromentin explicitly links this episode and that of the Zouave, remarking that his visit to Laghouat is bookended by signifiers of death, first a dead soldier and then a woman's severed hand: "Je me rappelai le corps du zouave découvert du côté de l'est, le jour de mon entrée, et je trouvai la symétrie de ces rencontres assez fatale." [I remembered the body of the zouave discovered on the east side, the day of my arrival, and I found the symmetry of these encounters to be quite destined.]84 Fromentin's journey from the sight of a soldier killed in battle to the severed hand of an innocent civilian woman leaves a powerful effect on the reader, again of Fromentin focusing on the most vulnerable members of the population.
The complexities of Fromentin's presence and association with colonial efforts unfold again in the scene with which I began this chapter: Fromentin's blindness. After choosing to paint the desert from an elevated location near Laghouat, after several days, the artist developed a period of temporary blindness. Fromentin's privileged position high above the city allowed him to be, in Michel de Certeau's terms, a dieu-voyeur over Laghouat, providing him the luxury of distance from otherness and death, and positioning him in a place of power.85 But the heat, the bright light, and the heights fatigued Fromentin until he began to hallucinate and lose his sight. Fromentin lost his capacity to see, and his power as "dieu-voyeur" is subverted by the light and landscapes he is attempting to capture. Like the fetishized hand of the dead woman, Fromentin's blindness injects into his narrative an element of undeniable ambivalence that indicates, if not a completely conscious critique of imperial violence, then the realization of the acute anguish of Laghouat and the difficulties of representing the aftermath of such trauma.
In her biography of the artist, Barbara Wright suggests that Fromentin's prose was "written to be seen."86 Un été compels the reader to witness the atrocities of colonial conquest as Fromentin marched along its tracks. These pauses during which he witnessed the brutal installation of a French colony in Algeria disturb the text. The dead Fromentin sees are unsettled, unburied, and fundamentally troubling. Here, Fromentin is an uneasy onlooker to the troubling images of the unsettled, not-yet-colonized, and unsuccessfully colonized—in short, the unfinished business of burying the victims of nascent French Algeria.
In a congratulatory review of Fromentin's Une année dans le Sahel, the editor-in-chief of the Revue de Paris, Léon-Laurent Pichat, remarked that Fromentin was "un écrivain complet" [a complete writer] because of the emotion that undergirds his prose.87 Upon reading Un été, Charles Augustin Sainte-Beuve pinpointed Fromentin's unique qualities as a literary "paysagiste" [landscape painter]":
vous avez conquis à la langue écrite des parties qui semblaient jusque-là réservées à la seule palette et à la couleur du peintre. Puis, vous ne peignez pas seulement pour peindre; les pensées, les rêves, le reflet moral des choses au sein du miroir intérieur, vous ne les oubliez jamais, vous avez l'art de les saisir et les fixer avec une brillante transparence.
[in written prose, you have mastered parts that before seemed reserved only for the painter's colors and palette. Also, you do not paint only for painting; thoughts, dreams, the moral reflection of things at the heart of the inner mirror, you never forget them, you have the art of taking hold of them and containing them with a brilliant transparency.]88
Sainte-Beuve's observation of Fromentin's ability to distill moral reflection in the depths of interiority highlights the sentimental prose, with unbidden halts to contemplate the devastation of colonial conquering, and captures the extraordinary effects of the firsthand account left by Fromentin.
Thus there may have been another explanation for Fromentin's reaction to the disturbing experience in Algeria as he was hit by a spell of blindness. Whereas his first discovery of Algeria as a young newlywed was an experience that dazzled his senses, his final voyage in the wake of bloodshed was far different. Fromentin was a reluctant witness to the aftermath of the gruesome historical realities of French colonialism in Algeria. Fromentin's text acknowledges the forgotten victims of colonial violence by inserting them into the context of France's colonial aggression. His harrowed representations of unsettled bodies in this travelogue show how France's colonizing efforts elicited undeniable misgivings within him.
NOTES
1. Eugène Fromentin, Oeuvres complètes (Paris: Gallimard, 1984), 22, Correspondance (Paris: CNRS-Editions: Universitas, 1995), 958.
2. Eugène Fromentin, Oeuvres complètes, 128–29.
3. Davis, Haunted Subjects: Deconstruction, Psychoanalysis and the Return of the Dead (New York: Palgrave, 2007), 2–3.
4. Fromentin, Oeuvres complètes, 1301.
5. See James Thompson and Barbara Wright's comprehensive La Vie et l'oeuvre d'Eugene Fromentin (Courbevoie, France: ACR Editions, 1987).
6. Eugène Fromentin, Lettres de jeunesse (Paris: Plon, 1909), 171.
7. Thompson and Wright, La Vie et l'oeuvre d'Eugene Fromentin, 35.
8. French Orientalist painting can be characterized by a vibrant color palette and themes of sensuality, violence, and exoticism. See note 15 in "Introduction."
9. Oscar MacCarthy, Revue de l'Orient, de l'Algérie, et des colonies (Paris: Juste Rovier, 1856).
10. Charles-André Julien, Histoire de l'Algérie contemporaine, vol. I: La conquête et les débuts de la colonization, 1827–1871 (Paris: Presses Universitaires de France, 1979), 392; Benjamin Brower, A Desert Named Peace: The Violence of France's Empire in the Algerian Sahara, 1844–1902 (New York: Columbia University Press, 2009), 85.
11. Eugène Fromentin, Correspondance (Paris: CNRS-Editions: Universitas, 1995), 950.
12. Butler, Precarious Life: The Powers of Mourning and Violence (London: Verso, 2004), 35.
13. Fromentin, Correspondance, 688.
14. Jonathan Culbert, Paralyses: Literature, Travel, and Ethnography in French Modernity (Lincoln: University of Nebraska Press, 2011), 109.
15. Ibid., 109, Said, Culture and Imperialism (New York: Vintage, 1994), 23.
16. Fromentin, Oeuvres complètes, 92, 1308.
17. Ibid., 92, 1308.
18. Ibid., 1315.
19. Peter Dunwoodie, Writing French Algeria (Oxford: Oxford University Press, 1998), 52, Elwood Hartman, Three Nineteenth-Century French Writer/Artists and the Maghreb:The Literary and Artistic Depictions of North Africa by Théophile Gautier, Eugène Fromentin, and Pierre Loti (Tübingen: Narr, 1994), 38.
20. Culbert, Paralyses, 101.
21. Avery Gordon, Ghostly Matters: Haunting and the Sociological Imagination (Minneapolis: University of Minnesota Press, 2008), 22.
22. Žižek, Welcome to the Desert of the Real (London: Verso, 2002), 22, emphasis in the original.
23. Davis, Haunted Subjects, 2–3.
24. Fromentin, Oeuvres complètes, 7.
25. Ibid., 13.
26. Ibid., 7.
27. For example, in Un été dans le Sahara, Fromentin makes several references to its precursors, General Eugène Daumas' popular books Le Sahara algérien (1845) and, written with Ausone de Chancel, Le Grand désert ou itinéraire d'une caravane du Sahara au pays des nègres (1848). See Anne-Marie Christin, Fromentin ou les métaphores du refus: les récits algériens et leur genèse (Lille: Université de Lille III, 1975), 193–229.
28. Fromentin, Oeuvres complètes, 189.
29. Christin, Fromentin ou les métaphores du refus, 194.
30. See in particular Guy Barthèlemy's Fromentin et l'écriture du désert (Paris: L'Harmattan, 1997) and Barbara Wright's Eugène Fromentin: A Life in Art and Letters (New York: Lang, 2000).
31. Fromentin, Oeuvres complètes, 5.
32. Ibid.
33. Fromentin, Correspondance, 957.
34. Ibid., 428.
35. Fromentin, Oeuvres complètes, 103, 1320.
36. Fromentin, Correspondance, 201–202.
37. Fromentin, Oeuvres complètes, 256.
38. Ibid., 192, 263.
39. Ibid., 192.
40. See Tzvetan Todorov, The Morals of History, trans. Alyson Waters (Minneapolis: University of Minnesota Press, 1995), 67–68.
41. Mary Louise Pratt, Imperial Eyes: Travel Writing and Transculturation (London and New York: Routledge, 1992), 7.
42. Ibid.
43. Ibid., 39.
44. Fromentin's chronicles of his travels in Algeria are unique in both prevailing colonial discourse of his time and that of his intellectual contemporaries. For example, Fromentin followed his own route. Chateaubriand had established a standard Orientalist itinerary, which he depicted in Itinéraire de Paris à Jerusalem. Authors such as Alphonse de Lamartine and Gérard de Nerval followed a similar itinerary in their subsequent explorations of the same territory. By contrast, Fromentin followed a determinedly peripatetic journey.
45. Hélène Gill, The Language of French Orientalist Painting (Lampeter, UK: The Edwin Mellen Press, 2003), 93–94.
46. Michael Humphrey, The Politics of Atrocity and Reconciliation: From Terror to Trauma (New York: Routledge, 2014), 12.
47. Jean-Joseph-Gustave Cler, Souvenirs d'un officier du 2e de zouaves (Paris: Lévy, 1859), 117–18.
48. Ibid., 371.
49. François-Charles Du Barail, Mes souvenirs, Vol. 2 (Paris: Plon, 1898), 47–48.
50. Brower, A Desert Named Peace, 84.
51. E. Mangin, Notes sur l'histoire de Laghouat (Algiers: Jourdan, 1893), 127.
52. Fromentin, Oeuvres complètes, 1308.
53. Ibid., 1301.
54. Ibid., 77, 90.
55. Ibid., 1308.
56. Ibid., 86.
57. Ibid., 79.
58. Ibid., 1303, 1302.
59. Ibid., 78.
60. Ibid., 73.
61. Ibid., 79.
62. Ibid., 82.
63. Ibid., 1315, 1303.
64. Ibid., 95.
65. Ibid., 1315.
66. Ibid.
67. Humphrey, The Politics of Atrocity and Reconciliation, 12.
68. Fromentin, Oeuvres complètes, 77–78.
69. Ibid., 92.
70. Ibid., 181.
71. Known for being the first to arrive in battle along with their distinctive uniform of baggy red trousers, elaborate headgear, and sashes, the Zouaves were light infantry regiments of the French Army, who normally served in French North Africa between 1831 and 1962.
72. Fromentin, Oeuvres complètes, 78.
73. "Nayliette" is the diminutive of the women members of the Ouled-Naïl tribes.
74. Fromentin, Oeuvres complètes, 93. Fromentin depicts this tale in a painting called L'Incendie [The Fire] (1867) in which a woman is outstretched and prone, her left leg bent. Another woman lying on top of her cradles her torso in her arms. The scene also includes two young boys looking at the dead bodies.
75. Fromentin, Oeuvres complètes, 94.
76. Ibid., 94–95.
77. Ibid., 95.
78. Ibid., 1314.
79. Ibid.
80. Ibid., 181.
81. Ibid.
82. It is upon this scene, among others, that Djebar constructs her novel L'Amour, la fantasia. Djebar imagines that this hand holds the pen that will write the Algerian people's tale of resistance and liberation. She greets Fromentin, who has accompanied her through her creative process, "le peintre qui, au long de mon vagabondage, m'a accompagnée en seconde silhouette paternelle" [the painter who has accompanied me throughout my wanderings like a second father figure], 255/226.
83. Eugène Fromentin, Oeuvres complètes, 181–82.
84. Ibid., 181.
85. L'Invention du quotidien (Paris: Union générale d'éditions, 1980), 4–5.
86. Barbara Wright, Eugène Fromentin: A Life in Art and Letters (New York: Peter Lang, 2000), 313.
87. Fromentin, Correspondance, 1115.
88. Ibid., 1115, 1138, emphasis in the original.
Chapter 3
Battlefields and Barbarians
Salammbô and Its Historical Contexts
Whereas Gautier's and Fromentin's texts clearly emphasize their narrators' ambivalence regarding the French colonial project in Algeria, Gustave Flaubert's 1862 work Salammbô does not express colonial misgivings at the narrational level found in Gautier's and Fromentin's travelogues. Instead, the novel dramatically stages the Carthaginian war against its rebellious mercenary tribes in ways that unmistakably evoke France's colonial efforts in Algeria and point to a failing "mission civilisatrice" of French colonization. What haunts Flaubert's novel is a trenchant critique of the barbarities of French civilization as it imposed itself in the nascent colony in Algeria.
Salammbô is a meticulously crafted work. Seeping cruelty and carnage from every chapter, the novel takes place in the third century B.C., after the first Punic War. It describes the wars between Carthage and mercenary tribes in 237–228 B.C. under the Carthaginian leader Hamilcar Barca. The novel tells the story of the love of Mâtho, leader of a tribe of mercenaries, for the Carthaginian priestess, Salammbô, daughter of Hamilcar and eponym of the book. The leader promises his daughter to a rival leader, Narr'Havas. Salammbô is for Mâtho both an inaccessible object of desire and war bounty in the battles between the Carthaginians and the barbarian mercenaries. The efforts of Mâtho's tribes to penetrate the barricaded city, to puncture the city's aqueduct, and to steal the sacred veil of the Carthaginian moon goddess Tanit progress as Mâtho's desire for Salammbô grows.
Even though it has a handsome warrior, a highborn maiden, and a jealous rival, Salammbô is hardly a romance. The novel primarily treats the historical events of the Mercenary War, with leaders such as Hamilcar, Hanno, Mâtho, and Spendius taking center stage. Mâtho and Salammbô come together only once, in the chapter "Sous la tente" [In the Tent], after which the plot veers emphatically to physical horror, including the crucifixion of one of the mercenary leaders, Spendius, and the mob torture of Mâtho. Over two-thirds of this cynical novel is directly obsessed with battle, siege, sacrifice, and torture.
Many critics have argued that Salammbô was a purely aesthetic work, and that the novel allowed Flaubert to escape from the daily banality of his existence by using ancient history.1 More recent work, doubtless attempting to respond to these prior accusations of irrelevance or escapism, does analyze Salammbô in relation to its contemporary context.2 Although Salammbô has inspired a few allegorical readings, what I find more rich is an analysis in terms of displacement, as suggested by Lisa Lowe, who sees the war theme in the novel as "a particular displacement of both French fascination with and denial of its own nineteenth-century war efforts, in North America, Africa, and continental Europe, as well as in France itself."3 In another compelling analysis, Jennifer Yee argues that Salammbô comments on contemporaneous events without directly setting out to do so, through its hidden "subversion of the world-view of its era, as it undermines the very basis of positivist knowledge."4
In a nuanced historical reading of the novel, Anne Green's extensive study of Salammbô details tight parallels between its conquering Carthaginians, a rich ruling class with commercial, materialist, and imperialist concerns similar to those of nineteenth-century French society, especially its upper class.5 Green's analysis demonstrates that the mercenaries' revolt against Carthage recalls the successive French democratic revolutions of 1830, 1848, and 1871, with special attention to the revolution of 1848, the downfall of the July Monarchy, and a brief mention of the parallels between the Carthaginian treatment of the mercenaries and the war in Algeria.6
A hauntological study of Salammbô situates itself within these efforts to analyze the novel through its historical and cultural contexts. What I propose in this chapter is an interpretation expanding upon Green's brief analysis of the French conquest of Algeria and its influence on Flaubert's Carthaginian novel. My purpose is not to analyze Flaubert's political views in depth but to focus instead on how the novel represents a nation haunted by its colonial violence. Superimposing Flaubert's Carthaginian account upon the backdrop of the French colonial period in Algeria, this analysis of Salammbô draws upon what we know of Flaubert's political consciousness regarding the Algerian situation. I argue that the novel shows an expression of France's ambivalence surrounding the events in Algeria in the first half of the nineteenth century. Reading through the lens of the colonization of Algeria, the Carthaginians stand in for the French, and the mercenaries represent the colonized Algerians. French and Carthaginian systems of colonization and the treatment of slaves resemble one another. Flaubert represents concerns about the decadence of French civilization by mirroring Paris' decadence in that of Carthage. Finally, Salammbô also expresses Flaubert's personal fascination with barbarism versus civilization and echoes an important preoccupation of the time, a profound fear about the barbarization of the military. Through the lens of a mysterious past civilization, Salammbô represents another troubled attempt to come to terms with the French colonial presence in Algeria.
"La description d'un champ de bataille"
Published in 1862, Salammbô still has the ability to inflame and inspire; the tale and the rich political-historical narrative have long fascinated readers and inspired paintings, operas, and films.7 But at the time of Salammbô's publication, Sainte-Beuve vehemently criticized the novel for its lack of historical veracity, demanding, "Comment voulez-vous que j'aille m'intéresser à cette guerre perdue, enterrée dans les défilés ou les sables de l'Afrique?" [How could you expect me to be interested in that lost war, buried in battles or African sands?]8 Flaubert's attempt to compose from inside the lost realm of Carthage, to breathe new life into an exotic society from the antiquities and artifacts covered for thousands of years in the sands of Tunisia, to envision the Carthaginian world on its own terms without Hannibal, Rome, or the Punic Wars as the center, rendered a hypnotizing chronicle. Flaubert's second novel, Salammbô was published six years after Madame Bovary and is his most famous work set in the East. Instantly popular in certain cosmopolitan circles, it garnered its readership from a niche group interested in the exotic themes and setting of the novel. Numerous readers, however, were displeased with it.
Sainte-Beuve's harsh words had no particular dampening effect on the novel's popularity. Baudelaire championed the novel, Gautier praised it as a "poème épique" [epic poem], and Maupassant rhapsodized, "il est le journal exact de l'existence; et la philosophie en demeure si complètement latente, si complètement cachée derrière les faits [. . .] que le gros public, accoutumé aux effets soulignés, aux enseignements apparents, n'a pas compris la valeur de ce roman incomparable." [it is the exact chronicle of existence; and its philosophy remains so completely latent, so completely hidden behind the facts . . . that the majority of the public, accustomed to highlighted effects, to apparent teachings, did not understand the value of this incomparable novel.]9
Despite this high praise, there remains a constant theme in the critical reception of Salammbô: its relation to history. Specifically, Sainte-Beuve's reference to a lost war buried in the defiles and sands of Africa called forth current events in France at the time of Salammbô's publication in a way that bears on our contemporary understanding of the novel. Flaubert's depiction of Carthage's 237–228 B.C. war against its rebellious mercenary tribes mirrors France's nascent colonial efforts in Algeria. Therefore after Flaubert had read a chapter aloud at a dinner, Jules and Edmond Goncourt, whose famous diaries give an intimate account of nineteenth-century French literary society, remarked: "[c]'est la description d'un champ de bataille, de l'horreur énumérée." [(i)t is the description of a battlefield, of detailed horror.]10 The Goncourts' statement applies to the entire novel. As with Sainte-Beuve's reading, the Goncourts suggested an interpretation influenced by contemporary consciousness of France's Algerian conquest, an awareness undoubtedly shared by Flaubert given that the public debate over the colonization of Algeria could not have escaped his notice.
The fact that Carthage was a virtually unknown civilization made it a recondite prism to capture a collective anxiety in contemporary France about colonial Algeria. In spite of Sainte-Beuve's pleas for greater historical accuracy, ancient Carthage existed only in collective memory, for its civilization had been utterly destroyed. Chronologically, Flaubert's writing of Salammbôcorresponded with France's colonial and commercial expansion into Algeria as well as the rediscovery of the obliterated civilization of Carthage. The ancient city's archaeological restoration was just beginning in the late 1850s with the work of Nathan Davis, a British pioneer of Carthaginian archaeology and personal friend of Mohammed Bey, who ruled the kingdom of Tunis from 1855 to 1859.11
Scholars have alternately interrogated Salammbô as a hyperbolic violent fantasy or an attempt by Flaubert to escape the banal daily life of bourgeois France. Richard Miles, author of an extensive recent history of Carthage, calls the novel a "roller-coaster ride of sexual sadism, extreme cruelty and repugnant luxury [that] played to every western-European stereotype . . . about the decadent Orient."12 Indeed, the novel does show excessive sexuality, violence, and opulence, all of which fall into typical Orientalist stereotypes. Dismissing the novel as offensive, Miles remarks that Rome's victory over Carthage "provided an attractive blueprint" and "metaphor" to justify French domination in North Africa. He rejects Salammbô as a "product of these colonial assumptions."13 However, it is difficult, if not impossible, to read Salammbô as a direct allegory either defending or going against any specific political stance. Time and time again, the novel proves itself to be more complex than simple equations such as the above. A richer interpretation of the novel is achieved by looking at how it was haunted by its sociopolitical background.
Salammbô has inspired such virulent critiques throughout the years in part because of its unorthodox approach to the genre of the historical novel, in addition to its remote topic. Flaubert began his new project in 1857, after the completion of his notorious bestseller Madame Bovary. The defeated maritime republic of Carthage and its wars against the mercenaries were an extreme departure from his first novel's realist depictions of provincial French life in Normandy. However, Flaubert's writings had always been partly inspired by his travels to North Africa and the Middle East. In total, Flaubert traveled to Egypt, Lebanon, Jerusalem, Syria, Turkey, and Greece. Even in his very early writings, the Orient held a notable role, although his first trip east was between 1849 and 1852. At the age of seventeen, Flaubert wrote a tale set in the Orient, Smarrh, a precursor to La tentation de Saint Antoine (1874). Flaubert's Rage et impuissance (1838) describes a combination of odalisques, flowers, jewels, blue skies, and bright sun in Monsieur Ohmlin's opiate dreams that clearly suggested a phantasmagorical Orient, and the theme of the non-European other traverses L'éducation sentimentale (1869). From 1846 onward, Flaubert had the goal of writing an Orientalist tale in which he planned to explore the oppositions between a European man's gradual return to a savage state and an Eastern man's process of becoming civilized.14
Even though Flaubert had always been interested in the history and culture of the East, he knew that conjuring up a dead and vanished civilization in Salammbô would not be easy, and he decided to travel there for inspiration and research. Before leaving France to sail to Tunis in January, Flaubert wrote to his confidante, Mademoiselle Leroyer de Chantepie: "Il faut absolument que je fasse un voyage en Afrique [. . .] [c]e voyage du reste sera court. J'ai seulement besoin d'aller à Kheff (à trente lieues de Tunis) et de me promener aux environs de Carthage dans un rayon d'une vingtaine de lieues pour connaître à fond les paysages que je prétends décrire." [It is absolutely necessary for me to make a trip to Africa . . . [b]esides, the journey will be short. I only need to go to Kheff (thirty leagues from Tunis) and walk around Carthage's surroundings in a radius of about twenty leagues to fully know the landscapes I am attempting to describe.]15
An ancient city whose ruins can now be found in the marshland northeast of Tunis, Carthage was an ongoing obsession for Flaubert. When he visited Algeria and Tunisia in 1857, it was for the express purpose of research in order to better understand the setting for Salammbô. He sailed first to Tunis to visit the remnants of the once-great civilization. He would later avow that on this journey he learned everything he needed to complete his book, which he began to write in 1857 after he had accepted an offer from the newspaper La Presse to write a novel about the "guerre inexpiable" [inexpiable war] of the Carthaginian mercenaries.16 Even before sailing to Tunisia he claimed that this journey would give him all the knowledge he needed to finish his book: "Je pars d'ici après-demain, et je m'en retourne en Algérie par terre, ce qui est un voyage que peu d'Européens ont exécuté. Je verrai de cette façon tout ce qu'il me faut pour Salammbô. –Je connais maintenant Carthage et les environs à fond." [I am leaving here the day after tomorrow, and returning to Algeria by land, which is a journey few Europeans have made. This way, I will see everything I need for Salammbô. – I now know Carthage and the surroundings to the fullest.]17
Flaubert had enormous literary ambition for what he first called his "Carthaginian project." The novel was alternately named Les Mercenaires, Carthage, and Salammbô, roman carthaginois before Flaubert settled on the title Salammbô. 18 As Frederick Blossom details in his study of Flaubert's correspondence, the author's laborious documentation and writing was intense, integrating almost insurmountable quantities of research, both from notes and journal entries from the time when he made the visit and from the hundreds of texts he claimed to have read about the region.19 Although Flaubert had always been a perfectionist about his writing process, his prior projects delving into the histories and cultures of the East had not prepared him completely for the Carthaginian project. In Flaubert's painstaking efforts to present the most authentic version possible of Carthage, he spent over five years in the book's writing. Upon his return to France, he immersed himself in Tunisian natural history, botany, local conventions, geography, and geology, at the same time surrounding himself with archaeological artifacts, including beads, arrowheads, copper forms, and amulets that he placed in his library in Croisset in upper Normandy. In order to conjure up a long-gone civilization in Salammbô, Flaubert undertook a deeper level of research than he had previously approached.
Colonization and Enslavement
The world Flaubert evokes in the novel was completely other to nineteenth-century France, both geographically and historically, producing, as Lawrence Schehr aptly expressed it, a "radical inscription of alterity."20 Themes of war, nationalism, and violence in Salammbô are projected upon the ghosts of ancient Carthage during the Punic Wars. But it is not difficult to see in this rough, bloodthirsty, decadent, and perplexing work the themes that reflected nineteenth-century France's violent colonization, war, and imperial competition. In particular, the military occupation and brutal French tactics in Algeria in the 1830s and 1840s included conditions similar to the slavery, barbarity, and planned massacres of the indigenous populations in Salammbô. The brutal treatment of the nomad tribes outside of Carthage's walls in Salammbô by Hamilcar and the other Carthaginian leaders reveals these dynamics, which are reflected in Flaubert's characterization of the ancient city as relentlessly cruel: "Carthage exténuait ces peuples. Elle en tirait des impôts exorbitants; et les fers, la hache ou la croix punissaient les retards et jusqu'aux murmures. Il fallait cultiver ce qui convenait à la République, fournir ce qu'elle demandait."21 [Carthage was bleeding these peoples. She took exorbitant taxes from them; and executions with sword, axe, or cross were the punishment for delays and even complaints. They had to grow what suited the Republic, provide what it demanded.]
Just as the violence Flaubert describes between the Carthaginians and the barbarians was brutal, the first stage of France's conquest of Algeria had spanned 14 extraordinarily violent years. The French occupation expanded in Algeria until Abdelkader coordinated an armed attempt to thwart its progress in 1839. It took several years of battle, a series of massacres, and an army of approximately 88,000 French troops before Abdelkader capitulated and was captured by the French in 1847. This conquest has distinct parallels in Salammbô, especially in regard to treatment of the colonized. Slavery by France and Carthage was likewise very similar. French royal command had set up a commission to examine French colonial slave treatment in May 1840, and one of the interim government's first reforms was to pass an act to abolish slavery in 1848, the décret d'abolition d'esclavage [decree of the abolition of slavery]. In Flaubert's novel, Hamilcar brutally represses slave revolts, and the mercenaries in Carthage free the slaves from the dungeons once they have attained a position of strength. In France, contemporary accounts reveal how, even though slavery had been officially abolished, the indigènes in North Africa's colonies remained virtually enslaved.
In his Carnet de voyage à Carthage [Carthage Travel Journal], Flaubert describes the virtual captivity of the inhabitants of Millésimo, a small colonial village in northeastern Algeria, in 1858. With Flaubert's brief yet exact details, an implacable description of a too-familiar scene appears, that of one of the forty-four "colonies agricoles" [agricultural colonies] founded in 1848 to host Parisian settlers. Millésimo was created for the sixteenth group of French immigrants who were to arrive in the new colony, and it was destined for economic stagnation.22 Flaubert writes:
Village atroce, tout droit; ligne d'acacias devant les maisons basses, petites clôtures; c'est la civilisation par son plus ignoble côté . . . des femmes, dans les champs, labourent ou sarclent en vestes et en chapeaux d'hommes, portières de Paris transportées au pays des Moresques, la crasse de la banlieue dans le soleil d'Afrique. Et les misères qu'il doit y avoir là-dedans, les rages, les souvenirs, et la fièvre, la fièvre pâle et famélique!
[Atrocious village, straightforward, lines of acacia trees in front of low houses, small enclosures; it is civilization by its vilest side . . . women in fields working or weeding in men's jackets and hats, Parisian curtains brought to Moorish countries, the filth of the suburbs in the African sun. And the miseries there must be inside, the furies, memories, and fever, the pale and starveling fever!]23
Just as Salammbô describes brutal slave treatment in Carthage, France had only nominally abolished slavery in the colonies while continuing to support a system in which both the colonized and their impoverished colonizers led lives of miserable serfdom. Descriptions such as these in Flaubert's Carnet de voyage are blunt about this Algeria of soldiers, indigènes, and colonizers. In 1845, Flaubert's traveling companion Maxime Du Camp had visited Algeria, and he evokes the disillusion of the colony's conditions in his recollections, calling Algiers "une ville tumultueuse, où nos soldats étaient les maîtres et le faisaient voir." [a tumultuous city, in which our soldiers were the masters and showed it.]24 Flaubert shared Du Camp's negative impressions. For example, Flaubert writes that the city of Souk-Ahras was a "ville neuve, atroce, froide, boueuse" [new city, atrocious, cold, muddy], and he shows no particular affection for the group of colonials there: "M. de Serval, sécot, inhospitalier . . . Table d'hôte: MM. les officiers; ignoble et bête, collet crasseux du directeur des postes; le lendemain, M. Gosse, aliéné." [M. de Serval, skinny, inhospitable . . . evening meal: Mssers officers; vile and stupid, grimy neck of the postal director; the following morning, Mr. Gosse, alienated.]25 In a dry shorthand, Flaubert depicts a certain disillusion about the wretched existence in the colonies, writing that in Constantine, "cela est d'une pauvreté et d'une malédiction supérieures; ça sent le paria." [it is of a superior cursed poverty; it smells of the pariah.]26
In addition to Flaubert's negative notes about social hierarchy in the new colony, the popular press of the time documented the similarities in Carthaginian and French administrative systems in dependent territories: Jean Charles Léonard de Sismondi's book Les colonies des anciens comparées à celles des modernes (1837) [The Ancient Colonies Compared to Moderns] and Saint-Marc Girardin's May 1841 article in the Revue des deux mondes, "De la Domination des Carthaginois et des Romains en Afrique comparée avec la domination française." [Regarding the Domination of the Carthaginians and the Romans in Africa Compared to the French Domination.] Flaubert's contemporaries such as his friend Du Camp also made the connection between France's activities in Algeria and Flaubert's writing of Salammbô. Du Camp complimented the novel for accurately depicting the Algerian salt lakes:
[Flaubert] avait été en Tunisie faire des études de paysages africains; on sait s'il a réussi. Sa description du défilé de la Hache est l'exacte peinture d'un de ces chotts dont il a été si souvent question lors de la dernière insurrection d'Algérie. Ce sujet l'avait envahi, il ne parlait d'autre chose.
[(Flaubert) had been in Tunisia to make a study of African landscapes; we know he succeeded. His description of the Battle of the Saw is the exact painting of one of the salt lakes in which it was often a question during the last Algerian insurrection. That subject had invaded him, he spoke of nothing else.]27
The Goncourt brothers made an observation similar to that of Du Camp. After hearing Flaubert read an excerpt of his novel-in-progress at a dinner party, they wrote, "Flaubert voit l'Orient, et l'Orient antique, sous l'aspect des étagères algériennes" [Flaubert views the Orient, and the ancient Orient, in the form of Algerian lines], and called the novel a "barbaric poem."28 As his contemporaries' reflections convey, Flaubert created his Orient in part through the prism of nascent colonial Algeria.
The critical consensus is that Flaubert was not disaffected by France's colonial operations, as is revealed by the blunt aphorism in the Dictionnaire des idées reçues, "Colonies (Nos), S'attrister quand on en parle." [Colonies (Our), Become unhappy when we talk of them.]29 Historians Jean Martin and Jean Ganiage argue that Flaubert saw the Algerian colonization in a negative light.30 He was particularly struck by the poverty, the coarseness, and the indifference of the colonists in the new Algeria. In an 1846 letter to Louise Colet, Flaubert wrote, "je ne me réjouis nullement de nos victoires sur les Arabes parce que je m'attriste à leurs revers."31 [I do not rejoice at our victories over the Arabs because I am saddened by their setbacks.]
The Carthaginian conquest in Salammbô parallels French colonial activities in Algeria in several ways. For example, Flaubert focuses the reader's attention on Carthage's successes in agriculture and war:
Par ce système les récoltes étaient toujours abondantes, les haras savamment conduits, les plantations superbes. Le vieux Caton, un maître en fait de labeurs et d'esclaves, quatre-vingt-douze ans plus tard en fut ébahi, et le cri de mort qu'il répétait dans Rome n'était que l'exclamation d'une jalousie cupide."
[By this system crops were always abundant, stud farms skillfully managed, plantations superb. Cato the Elder, a master when it came to farming and slaves, was astounded by it ninety-two years later, and the call for death which he repeated in Rome was merely jealous greed voicing itself.] 32
Flaubert's phrase "death cry" of course references Roman statesman Cato the Elder's famous saying Delenda est Cartago, or "Death to Carthage," the rallying cry of Roman in the face of the threat Carthage that posed to the republic. Just as Rome razed Carthage to the ground, burning libraries, ransacking everything that remained, and selling any survivors into slavery, Carthage, and by extension, France, is shown in its shocking ruthlessness in Salammbô.
Like the depictions of Carthage's achievements in combat in Salammbô, Girardin's essay, "De la Domination des Carthaginois," points out distinct similarities between the French and Carthaginian approaches to war.33 As such, Flaubert's emphasis on Carthage's successes on the battlefield invokes those of France. Girardin demonstrates how Carthage used foreign mercenaries to decrease the chance of conspiracies between them. Because the mercenary groups did not have ties to Carthage, their use carried a risk of sedition, but Carthage viewed this outcome as less likely than a national army's revolt. Girardin argues that France and every other occupying country in North Africa had employed the same strategy since Carthage's success with it. And to bolster the claim that France was using mercenaries for similar reasons, Girardin points to the statistics from the Tableau des établissements français en Algérie [Chart of French Establishments in Algeria] that showed the number of native troops in the French army in the colonies of North Africa.
Girardin also describes the systems of tribute-raising and property ownership in ancient Carthage and colonial France and argues that they were similar. Here he references Polybius' Histories, which were also Flaubert's main source in researching the history of the city. The colonizers possessed and used the land along the coasts and secured tributes from inland towns. Girardin argues that this system was vital to Carthage's success. Flaubert's novel depicts the same system as highly successful: "Puis, au-delà des régions directement soumises à Carthage, s'étendaient les alliés ne payant qu'un médiocre tribut; derrière les alliés vagabondaient les Nomades, qu'on pouvait lâcher sur eux." [Then, beyond the regions directly subject to Carthage, extended the allies who paid only a modest tribute; behind the allies roamed the Nomads, who could always be let loose on them.]34 Girardin relates this process to the strategy France was employing in Algeria:
Autour d'Alger, les Européens sont propriétaires, car là nous pouvons aisément défendre et cultiver la terre; et l'administration supérieure a eu raison, je crois, en 1837, d'annuler un arrêté de général Damrément qui interdisait aux Européens, dans la province d'Alger, le droit d'acquérir des terres. Dans la province de Constantine, au contraire qui est une province intérieure, les Européens ne peuvent pas posséder. Là, nous nous contentons de gouverner et de lever le tribut.35
[In the area surrounding Algiers, Europeans are property owners, because there we can easily defend and cultivate lands; and the superior administration is right, I believe, in 1837, to cancel General Damrément's decree that forbade Europeans in the province of Algiers the right to acquire lands. In the province of Constantine, which is to the contrary an interior province, the Europeans cannot own lands. There, we settle for governing and levy tax.]
Flaubert knew of Saint-Marc Girardin, referring to him in an 1852 letter to Louise Colet.36 In addition, the Revue des deux mondes was a widely respected journal in Flaubert's circle. Given his interest in the history of Carthage, Flaubert would likely have read and discussed the article. Likewise, his readership would have been familiar with Girardin's arguments. Thus Salammbô presents the violent treatment of slaves in Carthage as a cautionary tale of a possible outcome of France's policies in Algeria.
Decadence in Paris and Carthage
Not only is Salammbô haunted by the inhumanity of slavery, it also reflects an undercurrent of the destructiveness of unbridled decadence. In Sainte-Beuve's review of Salammbô in the journal Lundi, he pronounced the novel "decadent," comparing stylistic traits of Flaubert's prose with those of Roman decadent authors.37 For Sainte-Beuve, Flaubert's novel represented an objectionable departure from conventional standards of prose. This feeling of decadence is created on every page of the work, via Flaubert's extensive and elaborate descriptions of exotic and unfamiliar settings and lives in ancient Carthage. Because everything about Carthage was unfamiliar to Flaubert's readers, everything required painstaking description, from exotic headdresses, to strange animals, to obscure architectural structures. As a result, Sainte-Beuve condemned Salammbô's ornate representations and excessive, even obsessive, concern with style. With the use of heightened artifice and departures from conventional realist fiction, Flaubert provided an unparalleled performance of style.
In addition to its aesthetic designation as decadent, however, Salammbô reveals decadent cultural excesses in the more general sense as well. In nineteenth-century France, there existed a tension in discourse about the progress, or lack thereof, of French civilization. Whereas there was a proud belief in the country's economic and technological progress, there existed also a pessimistic view of France's tendency toward decadence. As the century progressed, historians and other intellectuals pointed out France's decline. The great cities of antiquity, including Carthage, were held up as warnings of this kind of degeneration.
Carthage's greed, cruelty, and moral depreciation are common themes throughout the novel. In Salammbô, cruelty follows violence until the book ends in a delirious stupor. Unmitigated greed, due to excessive decadence, was considered to be a part of France's decline as well. Like the other ancient cities of Rome, Alexandria, and Babylon, known for their decadence, the fall of Carthage was compared to Paris' inevitable decline. Gautier called Parisian culture in 1831, "Une société qui retombe au chaos / Du rouge sur la joue et la gangrène aux os." [A society that falls into chaos / Blush on the cheek and gangrene in the bones.]38 Flaubert shared a similar view. In an 1862 letter to Louise Colet, he described nineteenth-century France as experiencing "une si fétide époque" [such a fetid époque.]39 A belief in the decadence of the era was common wisdom in 1862. Frédéric Ozanam, a prominent Catholic historian, had argued that France was in a steep decline in his Du progrès dans les siècles de decadence (1852) [On Progress in the Decadent Centuries]. By the mid-nineteenth century, common discourse held that after France's increase in prestige and power in the Napoleonic period, a decline that would lead to the country's downfall had begun.
Flaubert wasn't the only French writer of his time to find the degeneration of once-great civilizations an important topic. A number of nineteenth-century writers argued that Paris would shortly experience a decline such as the great cities of antiquity had done. Public commentators warned that the nation was in a situation of degeneration and that the moral and religious failings of post-Napoleonic France would destroy it. For example, in his Essai sur les Fables de La Fontaine (1853) [Essay on La Fontaine's Fables], Hippolyte Taine compared Paris to Rome and Alexandria, while Edgar Quinet foretold a dark future for France, akin to that of the Roman Empire, unless it could shake off its political and moral turpitude. Eugène Pelletan criticized the greed and degeneration of contemporary Paris in the Second Empire in his book La Nouvelle Babylone (1862) [New Babylon]. Artists held this view as well; the well-known painting of Thomas Couture entitled Les Romains de la décadence [Romans of the Decadence] was unveiled to critical acclaim at the 1847 Salon. In Du Déclin de la France et de l'égarement de sa politique (1841) [On France's Decline and Confusion in its Politics], Pierre-François-Xavier Bourguignon d'Herbigny warned that France, like Rome and Carthage, would be overthrown by its excesses.40
Salammbô does not make the parallels between France and ancient Carthage as explicit as those in Bourguignon d'Herbigny's Du Déclin de la France et de l'égarement de sa politique. However, the novel emphasizes the political corruption and physical degradation that grounded such arguments as increasing, and ties these aspects of Carthaginian life to Carthage's demise. For example, Salammbô symbolically echoes the culture's political corruption by mirroring its characters' physical deterioration throughout the book. In the opening chapters describing Hamilcar's banquet, the mercenaries panic when they suspect they have been poisoned. Then, Flaubert represents the perilous invasion of contamination and insidious encroachment of corruption as the novel makes many references to the different diseases suffered by the mercenaries.
These references to poison and contamination depict Carthage itself suffering a progressive degeneration, signified most clearly in the Carthaginian leader Hanno, member of the Council of Elders, a man obsessed with riches, sensuality, and decadent luxury. Grossly obese and lavishly bejeweled, the commander's gluttony mirrors the excesses of the city's decadence. Hanno's first appearance is in the mercenaries' camp, and his heavy and rotting horribleness is revealed to the reader detail by terrible detail:
L'abondance de ses vêtements, son grand collier de pierres bleues, ses agrafes d'or et ses lourds pendants d'oreilles ne rendaient que plus hideuse sa difformité. On aurait dit quelque grosse idole ébauchée dans un bloc de pierre; car une lèpre pâle, étendue sur tout son corps, lui donnait l'apparence d'une chose inerte. Cependant son nez, crochu comme un bec de vautour, se dilatait violemment, afin d'aspirer l'air, et ses petits yeux, aux cils collés, brillaient d'un éclat dur et métallique. Il tenait à la main une spatule d'aloès, pour se gratter la peau.
[The abundance of his clothing, his long necklace of blue stones, his gold clasps and heavy earrings only made his deformity more hideous. He looked like some gross idol carved roughly out of a block of stone; a pale leprosy that spread all over his face gave him the appearance of an inert object. However, his nose, hooked like a vulture's beak, flared fiercely to breathe in the air, and his sticky-lashed little eyes shone with a hardened metallic glint. In his hand, he held a spatula of aloes for scratching his skin.]41
In a departure from Flaubert's historical sources, in which there is no mention of Hanno's being overweight, leprous, or syphilitic, Flaubert creates images of the Suffete's corporeal degeneration. The fact that Hanno's body is being eaten away by leprous sores is strikingly juxtaposed with his lavish tastes and expensive garments, "une écharpe, une ceinture et large manteau noir à doubles manches lacées" [a scarf, a belt, and a large black cloak with double laced sleeves].42 The diet nourishing his decaying body includes flamingo tongues and honeyed poppy seeds, "des langues de phénicoptères avec des graines de pavot assaisonnées au miel."43 His face is compared to that of a wild beast, and he is adorned with a necklace of blue jewels, earrings, and gold sequins sprinkled in his hair, but his breath gives off the smell of rotting corpses.44 In addition, Hanno's rotting body is covered with skin ulcers, which are ineffectively anointed with healing oils and creams to hide illness: "[Hannon] soufflait comme un hippopotame, en roulant ses yeux. L'huile parfumée débordait sous la masse de son corps, et, se collant contre les écailles de sa peau, à la lueur des torches, la faisait paraître rose." [He was puffing like a hippopotamus, rolling his eyes, scented oil ran out beneath the bulk of his body, and sticking to his scaly skin made it look pink in the torchlight.]45 Later in the novel, when Hanno arrives at Sicca in an expensive litter carried by slaves, he is described as covered with weeping sores:
Il avait peint avec du fard les ulcères de sa figure. Mais la poudre d'or de ses cheveux lui était tombée sur les épaules, où elle faisait deux plaques brillantes, et ils paraissaient blanchâtres, fins et crépus comme de la laine. Des linges imbibés d'un parfum gras qui dégouttelait sur les dalles, enveloppaient ses mains, et sa maladie sans doute avait considérablement augmenté, car ses yeux disparaissaient sous les plis de ses paupières. Pour voir, il lui fallait se renverser la tête.
[He had covered the sores on his face with makeup. But his hair's golden dust had fallen on to his shoulders, where it shone in two bright patches, and his hair looked white, thin, and curly as wool. His hands were covered in bandages soaked in thick perfume, which dripped on to the floor, and his illness had no doubt increased considerably, for his eyes disappeared under the folds of his eyelids. In order to see, he had to tilt his head back.]46
The use of the word "fard," or makeup, is important, because it has the more general meaning of artifice. Just as the healing oils, creams, and rouge fail to cover the sores, the thin veneer of luxury wears away to show evil degradation beneath it. Later, when Hanno is put to death by crucifixion, his putrid body is put on display: "Ils arrachèrent ce qui lui restait de vêtements - et l'horreur de sa personne apparut. Des ulcères couvraient cette masse sans nom; la graisse de ses jambes lui cachait les ongles des pieds; il pendait à ses doigts comme des lambeaux verdâtres." [They tore off what clothes he still wore – and the horror of his person appeared. Ulcers covered this nameless bulk; the fat of his legs hid his toenails; from his fingers hung what looked like greenish strips.]47
Hanno's bejeweled and disintegrating body is symbolic of the artifice concealing Carthage's cultural disintegration. As a Carthaginian general and the most powerful Carthaginian figure present in the novel, Hanno is associated with excessive riches, power, and greed, yet his body experiences a decomposition that reveals the decline and barbarism of Carthage. Here, Flaubert literalizes the moral metaphors used by Polybius that reference fatal ulcers and tumors eroding the soul as the excesses of humankind.48 In Flaubert's equation, as Carthage's moral decay increases, Hanno's physical degradation becomes more pronounced.
"Un civilisé qui se barbarise et un barbare qui se civilise"
Haunted by the cruelties of slavery, and the degenerations of decadence, the novel continues to question France's "civilizing" of Algeria. In Flaubert's fiction, the thin line holding degeneration at bay is mirrored by the razor's edge between barbarism and civilization. An avid reader of the works of the Marquis de Sade, Flaubert had long been preoccupied by the opposition between barbarism and civilization. The former was never far from his thoughts; the concept of the barbarian reappears often in his writings. Flaubert even thought of himself as a barbarian, stating in his personal letters, "J'ai la mélancolie des races Barbares" [I have the melancholy of Barbarian races] and "je suis un Barbare."49 [I am a Barbarian.]
Salammbô puts acute pressure on the dichotomy between the barbarian and the civilized, reflecting another theme in French discourse during this period, namely anxiety about France's loss of civilization because of the atrocities of the Algerian war. This preoccupation is reflected in Sismondi's treatise Les Colonies des anciens comparées à celles des modernes, in which he explains that the ancients' colonies were better than those of the French: "les colonies des anciens renouvelaient la race humaine, la retrempaient, et lui faisaient commencer l'existence politique avec tous les avantages de la jeunesse les nôtres, au contraire, naissent vieilles, avec toutes les jalousies, tout l'inquiétude, toutes les misères, tous les vices de la vieille Europe." [The colonies of antiquity renewed the human race, revived it, and made it begin its political existence with all the advantages of its youth . . . ours, on the contrary, are born old, with all the jealousies, all the concern, all the miseries, all the vices of old Europe.]50 Sismondi argued that the colonies of the ancients helped the native populations by the cultural exchange with civilization, whereas most Europe's colonizers had a damaging effect on other cultures: "ils ont barbarisé les peuples qu'ils nomment barbares. [. . .] Ils se sont barbarisés à leur tour." [they barbarized the peoples they called barbarians. . . . They were made barbaric in turn.]51
The barbarity of the larger wartime context in Algeria is an essential factor to consider when examining the Carthaginians' viciousness in Salammbô. In an 1858 notebook, Flaubert revealed his enduring ambition to write a work in which the dichotomy between the barbarian brute and the civilized citizen was dismantled:
Si j'étais plus jeune et si j'avais de l'argent, je retournerai en Orient pour étudier l'Orient moderne, l'Orient Isthme de Suez. Un grand livre là-dessus est un de mes vieux rêves. Je voudrais faire un civilisé qui se barbarise et un barbare qui se civilise, développer ce contraste des deux mondes finissant par se mêler.52
[If I were younger and had more money, I would return to the Orient to study the modern Orient, the Orient of the Isthmus of Suez. A great book about it is one of my dreams. I would like to make a civilized person who becomes barbaric and a barbarian who becomes civilized, to develop this contrast of two worlds which end up blending with each other.]
Just as Flaubert speculated that civilization and barbarity were profoundly intertwined, at this same time, popular discourse in France was shifting to portray the nation as "un civilisé qui se barbarise." Such military and intellectual leaders as Nicolas-Louis Planat de la Faye and Alphonse de Lamartine debated the topic in legislative chambers, arguing that not only had France abdicated common standards of conventional warfare, but its foreign conflict with an Algerian enemy was by its very nature barbarous. Numerous historians have viewed this problematic issue in other contexts and through a racial and ethnic perspective to underscore the ways in which dehumanizing racial stereotypes permitted colonial violence, including torture, massacre, execution without trial, and collective punishment, all practices that were deemed impermissible under "normal" warfare.53
As historian Jennifer Sessions convincingly demonstrates, there was a growing French discourse about military barbarization in France's conquest of Algeria.54 From 1841 to 1847, under the control of Bugeaud, the Armée de l'Afrique had embraced a strategy of complete war—in which cities were depopulated and pillaged, property was confiscated or destroyed, and all forms of resistance were suppressed—in order to defeat the inhabitants of the new colony. The primary concern of some members of French society was colonial warfare's potential effects on society, such as a loosening of codes of integrity. The Algerians' presumed "barbaric" and "savage" quality made them exempt from the prohibitions outlining warfare between "civilized" nations. France deemed these strategies necessary to put an end to the strong resistance of Emir Abdelkader, who had succeeded in uniting the tribes of the province of Oran against the French.
The French public had begun to consider whether the terrible practices of their army invalidated their claim to being members of a civilized nation. Little concern was shown for the experiences of victims themselves; the fear was that colonial warfare might barbarize French troops, making soldiers unfit for war with "civilized nations," and at the extreme, ultimately unfit to rejoin French society. French attitudes toward this kind of warfare generally were deeply ambivalent. Proponents of colonization argued that France's civilization was more advanced than existing governments and that it was their duty to extend France's empire by any means necessary. Advocates of the Algerian conquest and other instances of French imperialism had used the expression "mission civilisatrice" [civilizing mission] to represent this duty. But doubts persisted that France could remain civilized while completing the conquest. As de la Faye stated in his 1836 address to the legislative chamber entitled "De la nécessité d'abandonner Alger" [On the Necessity of Abandoning Algiers], "Avant de songer à civiliser, à coloniser l'Afrique, commençons par civiliser la France, qui en a plus besoin qu'on ne le pense." [Before considering civilizing, colonizing Africa, let us begin by civilizing France, which has more need of it than we think.]55 In arguing in favor of ending the conquest, Planat de la Faye pointed to Algeria as a space of indiscipline and revolt.56
Unfortunately, misgivings such as these were rare, because the French considered the spread of French civilization to be by definition a rational and nonviolent undertaking. Salammbô suggests that Flaubert did not agree. By showing an extremely irrational colonial regime in Carthage, the novel subverts the positivist logic of France's "mission civilisatrice," in which the aim was, as historian François Guizot put it in 1829, to "étendre le glorieux empire de la raison." [spread the glorious empire of reason.]57 For example, critics of Salammbô have often remarked on the lack of clear separation between barbarity and civilization in the novel. As Peter Starr states, "Readers of the novel frequently notice that the metaphorics of the opening chapter pose a distinction between the civilized Carthaginians and the animalistic barbarian mercenaries, a distinction that subsequent chapters belie."58 Through foreign displacement—France as Carthage—Flaubert's novel implicitly criticized France's barbarism.
Indeed, with stark imagery in the opening chapters, the narration represents the mercenaries as violent and barbaric animals. But later the narrator expresses the horror of these mercenaries at the violence of the supposedly "civilized" Carthaginians sacrificing their own offspring to their powerful sun god Moloch.59 In such scenes the distinction between what, and who, is civilized or barbaric is deliberately strained. Anarchy reigns in the novel, and the very notion of orderliness seems to collapse even in the opening chapter, "Le Festin," in which the reader learns that "le maître était absent."60 [the master was absent.] Whereas this sentence refers to the absence of Hamilcar Barca, it also represents a more radical declaration of anarchy: there is no master, nor authoritative order. The chapter's imagery foregrounds the distinction between the animal-like barbarians and the civilized Carthaginians which will later collapse. For example, the barbarians eat hunched over or lying prone "dans la pose pacifique des lions lorsqu'ils dépecaient leur proie" [in the peaceful posture of lions tearing up their prey].61 After the meal, "[ils] imitaient le cri des bêtes féroces, leurs bonds" [They imitated the cry of wild beasts, their leaps.]62 By the fourth chapter, however, much to the surprise of the Carthaginians, readers learn that the barbarians' camp is far from undisciplined. Instead, it is shown as clean and orderly: "Beaucoup d'entre eux voyaient pour la première fois un camp de Mercenaires. Au lieu de la confusion qu'ils avaient imaginée, partout c'était un ordre et un silence effrayants." [For many of the men it was the first time they had seen a Mercenary camp. Instead of the confusion they had imagined, they found everywhere a frightening order and silence.]63 Later, the barbarians view the Carthaginians as cruel and inhuman. For instance, in the chapter titled "The Battle of the Macar," the fight between the Carthaginians and the barbarians rages with bloodthirst and mayhem:
La phalange extermina commodément tout ce qui restait de Barbares. Quand arrivaient les épées, ils tendaient la gorge en fermant les paupières. D'autres se défendirent à outrance; on les assomma de loin, sous des cailloux, comme des chiens enragés, Hamilcar avait recommandé de faire des captifs. Mais les Carthaginois lui obéissaient avec rancune, tant ils sentaient de plaisir à enfoncer leurs glaives dans les corps des Barbares. Comme ils avaient trop chaud, ils se mirent à travailler nu-bras, à la manière des faucheurs; et lorsqu'ils s'interrompaient pour reprendre haleine, ils suivaient des yeux, dans la campagne, un cavalier galopant après un soldat qui courait. Il parvenait à le saisir par les cheveux, le tenait ainsi quelque temps, puis l'abattait d'un coup de hache.
[The phalanx easily exterminated the rest of the Barbarians. When the swords came, they held out their throats, eyes closed. Others defended themselves to the bitter end like mad dogs; they were knocked down with stones from afar. Hamilcar had recommended taking prisoners. But the Carthaginians resentfully obeyed him because they took so much pleasure in plunging their swords into the Barbarians' bodies. Because they were too hot, they began to work bare-armed, like reapers; and when they paused to catch their breath, their eyes followed a horseman galloping after a soldier running away in the countryside. He managed to seize him by the hair and held him like that for some time, then slaughtered him with a blow from his axe.]64
In this passage, the barbarians are figured either as sheep ready for slaughter—"they held out their throats, eyes closed"—or as raging dogs, whereas the Carthaginians are no less animalistic, taking keen pleasure in plunging their swords into the enemy. Finally, the scene in which the Carthaginians sacrifice their children to the wrathful god Moloch and as the barbarians look on with astonished horror—"ils regardaient béants d'horreur" [they watched, aghast with horror]65—sets up the novel's dénouement, when the limits between civilization and barbarity collapse completely. The Carthaginians' torture and execution of Mâtho constitutes a fervent display of ultimate barbarity. Throughout the book, the qualities of barbarism and civility shift sides, are blurred, and finally give way.
As I referenced above, barbarity was infiltrating French warfare in Algeria as well. The French were becoming aware that the Armée de l'Afrique under Bugeaud had abandoned civilized warfare in favor of terrorizing Algerians into pacification, enacting a collapse of the distinction between barbarity and civility as stark as the one Flaubert describes in Salammbô. The earlier campaigns to create military outposts had been replaced by the razzia, a scorched-earth strategy intended to punish Abdelkader's military and civilian allies. The history of the term razzia is instructive: it is in fact Arabic but it originally referred to a North African practice of light raids using little violence on villages controlled by rival tribes. From the Algerian Arabic, razzia, or "raid," French officers had coined the term razzier to refer to the practice of burning villages, trees, crops, and grain stores. But Bugeaud's razzia bore little resemblance to the practices previously known by this term. As Douglas Porch has argued, precolonial instances of razzias in North Africa would not have involved torching structures.66 In a letter to his uncle, Lieutenant-Colonel Lucien de Montagnac explicitly describes the French razzia:
Ce genre d'expédition a quelque chose de très bizarre et offre, en même temps, des scènes bien pénibles. Aussitôt l'emplacement de la tribu connu, chacun se lance, se disperse dans une direction quelconque; on arrive sur les tentes, dont les habitants, réveillés par l'approche des soldats, sortent pêle-mêle avec leurs troupeaux, leurs femmes, leurs enfants; tout ce monde se sauve dans tous les sens; les coups de fusil partent de tous les côtés sur les enveloppés et réunis par quelques soldats qui les conduisent. Les bœufs, les moutons, les chèvres, les chevaux, tous les bestiaux, enfin, qui fuient sont vite ramassés. [. . .] [T]out cela crie, tout cela bêle, tout cela brait; c'est un tapage étourdissant.
[This kind of expedition has something very bizarre and offers, at the same time, very difficult scenes. As soon as the placement of the common tribe occurs, each one launches itself, disperses itself in any direction; they enter into the tents whose inhabitants, awoken by the soldiers' approach, leave indiscriminately with their herds, their wives, their children; everyone runs away in every direction; shots ring out from every side on the surrounded and gathered people directed by the soldiers. Cattle, sheep, goats, horses, all the livestock, finally, that flee are quickly rounded up. . . . [E]verything cries out, bleats, brays; it is a deafening uproar.]67
Montagnac relates that during this particular razzia, about fifty people were killed and the soldiers rounded up approximately 180 assembled survivors as prisoners. Even though French conventions of war held that respect for civilians, their private property, and their crops should be maintained during warfare, the soldiers pillaged guns, carpets, food, and animals.68 Bugeaud's predecessor, Count Sylvain Charles Valée, had forcefully expressed his misgivings about the razzias, remarking that the fires, attacks, and pillages were detestable.69 Finally, in a famous speech before the French parliament in 1846, Lamartine reacted to the Algerian situation and the razzias with marked disapproval: "C'est à nous à donner l'exemple de la générosité, bien loin de prendre les leçons de cruauté." [It is upon us to lead with the example of generosity, far from giving lessons of cruelty.]70 But before parliament, Bugeaud defended his tactics as cruel but necessary in order to completely pacify the new colony.71
Salammbô's haunting "compendium of atrocities" paralleled France's colonial warfare in Algeria, as exemplified by Bugeaud's cruel razzias.72 For example, the brutal strategies of the Armée de l'Afrique have echoes in Flaubert's description of Hanno's cruelty: "Sa colère se déchargea sur la campagne. Il brûla les ruines des ruines, il ne laissa pas un seul arbre, pas un brin d'herbe; les enfants et les infirmes qu'on rencontrait, on les suppliciait; il donnait à ses soldats des femmes à violer avant leur égorgement." [Then he vented his anger on the countryside. He burnt the ruins, left not a single tree or blade of grass; the children and invalids who were encountered were tortured; he gave his soldiers women to rape before they were slaughtered.]73 This similarity is particularly evident in the passage describing the aftermath of a daylong battle between the Carthaginians and the mercenary tribes:
Douze heures après, il ne restait plus des Mercenaires qu'un tas de blessés, de morts et d'agonisants. [. . .] Un long amas de cendres noires fumait [. . .] Des cuirasses, des fourches, des clairons, des morceaux de bois, de fer et d'airain, du blé, de la paille et des vêtements s'éparpillaient au milieu des cadavres [. . .] des charognes de chevaux se suivaient comme une série de monticules; on apercevait des jambes, des sandales, des bras [. . .] on marchait sur des choses gluantes et il y avait des flaques de boue, bien que la pluie n'eût pas tombé.
Twelve hours later all that remained of the Mercenaries was a heap of wounded, dead and dying. . . . A long pile of black ashes smoked. . . . Armor, pitchforks, trumpets, bits of wood, iron and bronze, corn, straw, and clothes were scattered amongst the corpses. . . . The corpses of horses lay one after another like a chain of little mounds; one could see legs, sandals, arms. . . . There were sticky things underfoot and muddy patches, though it had not rained.74
Just as this excerpt expresses the complete destruction of the mercenaries by the Carthaginians, French troops spread swaths of destruction across the Algerian countryside. Other, more horrific practices grew as well. Savagery and dismemberment became commonplace. Just as in Salammbô the murder of the Carthaginian prisoners by the barbarians becomes the catalyst for more horrendous atrocities and as such normalizes violence, wartime violence in Algeria had become the norm. French troops would display heads of their victims on camp walls, bayonet points, and saddles. Cash rewards were offered by superior officers for each pair of ears taken from an enemy.75 Similarly, in Salammbô, the Carthaginians cut off the hands of mercenary peacemakers: "[Quatre hérauts] déclaraient qu'il n'y avait plus désormais, entre les Carthaginois et les Barbares, ni foi, ni pitié, ni dieux, qu'ils se refusaient d'avance à toutes les ouvertures et que l'on renverrait les parlementaires avec les mains coupées." [Four heralds] declared that henceforth, between Carthaginians and Barbarians, there would be no faith, no mercy, no gods, so that they refused all overtures in advance and that anyone sent to parley would be returned with his hands cut off.]76 Just as the battlefields of Algeria saw increases of violent inhumanity, Salammbô crescendos from order—the orchestrated banquet in Hamilcar's elaborate gardens—to unrestrained violence, chaos, mutilation, and murder.
A critical hauntological reading of Salammbô thus brings to light the similarities between ancient Carthage and France. Since France had claimed to annex Algeria rather than conquer it, dissenters in France argued that colonization made Algeria an extension of the French nation, and therefore the violence of this colonial warfare was a menace to the decency of French civilization as a whole. As the editors of the French newspaper Le National asked in 1845, "Si nos mœurs, nos idées, notre civilisation ne se montre pas à être supérieur, quel droit avons-nous de conquérir leur pays?" [If our mores, our ideas, our civilization don't demonstrate themselves to be superior, what right have we to conquer their country?]77
In conclusion, by 1862, common wisdom held that France was dangerously decadent and on the verge of moral depreciation. In dismantling the lines between brutality and humanity, Salammbô engages deeply with the anxieties of Flaubert's contemporary France by representing, through displacement in time and place, the inevitable horrors of contemporary warfare in Algeria and the barbarization of French troops. It identifies the Carthaginian and French civilizations as suffering from moral and political gangrene because of their similar colonial administrations. Through the lens of Punic atrocities, the text provides a reflection of the massacres committed by the French during the Algerian conquest. It also puts pressure on the acute threat of barbarity in France as well as outside of it.
Through the political atmosphere of the second two decades of French conquest in Algeria, Flaubert's Carthaginian account is haunted by the era's fears about the collapse of French civilization as well as the growing negative popular discourse regarding the Algerian situation. Salammbô is shadowed by the Algerian colonization's efforts: the novel's setting and themes have uncontestable echoes of the horrifying violence taking place in the new colony. In phantasmically remote ways, Salammbô communicates the uneasiness of Flaubert's contemporary France about the violent colonization of Algeria. Through parallels between the Carthaginian and French colonial systems and their treatment of indigènes, and reflections of contemporary tensions about moral decline and the future fall of French civilization, Salammbô contains the ghosts of the savagery of French colonialism. Finally, Salammbô spectacularly conveys Flaubert's interest in the collapsing of the categories of "barbare" and "civilisé," specifically echoing a certain apprehension in France about the barbarization of the military during this time. Through the viewpoint of the barbarous conquest of vanished civilization, Salammbô represents the savage violence of France's colonization of Algeria.
NOTES
1. For example, Sainte-Beuve judged Salammbô as historically inaccurate and therefore irrelevant, and he was particularly disappointed that the novel did not treat one of the great binaries of Western civilization, the duel between Carthage and Rome. In more recent times, Marxist critic Georg Lukács wrote perhaps the most influential indictment of Salammbô as escapism, arguing that Flaubert turned away from contemporary historical issues in order to focus instead on style and aesthetics. Like Sainte-Beuve, Lukács argues that Salammbô's resurrection of Carthage is a failure, a form of aesthetic escapism that tests the limits of fiction. See Lukács, The Historical Novel, trans. Hannah Mitchell and Stanley Mitchell (Lincoln: University of Nebraska Press, 1983), 218–37.
2. The authors of these studies argue that Flaubert deeply grounded the novel in its surrounding reality. For example, Mary Rice draws a parallel between the mercenary revolts against Carthage and the nineteenth-century revolts of the French working class in "The Failure of Metaphor as an Historical Paradigm: Flaubert's Salammbô," Modern Language Studies 20, no. 1 (Winter, 1990): 95–99. In addition, in a strict allegorical reading, Volker Durr interprets the novel as a roman-à-clef in which Hamilcar is an allegorical stand-in for Napoleon. In this reading, Flaubert becomes a well-meaning reformer deserving of our admiration for a "determination to reveal the truth by unmasking reprehensible social and political conditions and practices in nineteenth-century France." See Flaubert's "Salammbô": The Ancient Orient as a Political Allegory of Nineteenth-Century France (New York: Peter Lang, 2002), 122.
3. Lisa Lowe, "Nationalism and Exoticism: Nineteenth-Century Others in Flaubert's Salammbô and L'Education sentimentale," Macropolitics of Nineteenth-Century Literature: Nationalism, Exoticism, Imperialism, ed. Jonathan Arac and Harriet Ritvo (Philadelphia: University of Pennsylvania Press, 1991), 225.
4. Jennifer Yee, Exotic Subversions in Nineteenth-Century French Fiction (Oxford: Legenda, 2008), 13, emphasis in original.
5. Anne Green, Flaubert and the Historical Novel: Salammbô Reassessed (Cambridge: Cambridge University Press, 1982), 58–73.
6. Ibid., 90–93.
7. Examples include the painting by Georges Rochegrosse, Salammbô (1886), Ernest Reyer's lyric opera, Salammbô (1892), the silent film by Pierre Marodon (1925), The Loves of Salammbô by Sergio Grieco (1962), and the video game by graphic designer Philippe Druillet, "Salammbô: Battle for Carthage" (2003).
8. Charles Augustin Sainte-Beuve, Le Constitutionnel, December 8, 15, 22, 1862. Quoted in Didier Philippot, Gustave Flaubert: Mémoire de la critique (Paris: Presses Universitaires de l'Université Paris-Sorbonne, 2006), 255.
9. Théophile Gautier, Correspondance générale: 1862–1864, Vol VIII (Geneva: Droz, 1993), 80, and Guy de Maupassant, Etude sur Gustave Flaubert (1900), quoted in Philippot, 567.
10. Jules et Edmond de Goncourt, Journal: Mémoires de la vie littéraire, 1860–61, Tome IV (Monaco: Editions de l'Imprimerie de Monaco, 1956), 181.
11. For more on the discovery of ancient Carthage, see Joann Freed's study, Bringing Carthage Home: The Excavations of Nathan Davis, 1856–1859 (Oxford: Oxbow Books, 2011).
12. Richard Miles, Carthage Must Be Destroyed: The Rise and Fall of an Ancient Civilization (New York: Penguin Books, 2010), 10.
13. Ibid., 11.
14. Flaubert, Oeuvres complètes, Correspondance Vol. V (Paris: L. Conard, 1910), 324.
15. Ibid., Vol. II, 795.
16. Frederick Augustus Blossom, La composition de Salammbô d'après la correspondance de Flaubert (1857–1862) (New York: Elliot Monographs, 1914, 1965), 63.
17. Flaubert, Oeuvres complètes, Correspondance Vol. II, 815.
18. Yvan Leclerc, "Salammbô ou le frisson antique," Salammbô de Flaubert. Histoire, fiction, actes du colloque de Rouen, 23–24 mars 1996 (Paris: Champion, 1999), 10.
19. Blossom, La composition de Salammbô d'après la correspondance de Flaubert (1857–1862), 51.
20. Lawrence Schehr, Rendering French Realism (Palo Alto, CA: Stanford University Press, 1997), 100.
21. Flaubert, Salammbô, Oeuvres complètes, Tome 2 (Paris: Club de l'Honnête Homme, 1971), 107–108/89. Further translations of Salammbô will give page numbers in the 1971 edition, and, after the slash mark, in the English version: Salammbô, trans. A. J. Krailsheimer (New York: Penguin Books, 1977).
22. Quoted in Aimé Dupuy, En marge de "Salammbô ": le voyage de Flaubert en Algérie-Tunisie (avril-juin 1858) (Paris: Librairie Nizet, 1954), 13–14.
23. Gustave Flaubert, Carnet de voyage à Carthage (Rouen: Publications de l'Université de Rouen, 1999), 150.
24. Maxime Du Camp, Souvenirs littéraires (Paris: Hachette, 1892), 210.
25. Flaubert, Carnet de voyage à Carthage, 148.
26. Ibid., 33.
27. Du Camp, Souvenirs littéraires [Literary Souvenirs] (Paris: Hachette, 1892), 209.
28. Goncourt, Journal: Mémoires de la vie littéraire 1860–61 [Journal: Memoires of Literary Life], Tome IV (Monaco: Editions de l'Imprimerie de Monaco, 1956), 190.
29. Flaubert, Oeuvres complètes, Tome II (Paris: La Pléiade), 1004.
30. See Jean Martin, L'Empire renaissant 1789–1871 (Paris: Denoël, 1987) and Jean Ganiage, Histoire contemporaine du Maghreb (Paris: Fayard, 1996). Quoted in Michel Lambart, "Flaubert et la politique colonial," Bulletin des Amis de Flaubert et de Maupassant, no. 18 (2006): 41–52.
31. Flaubert, Correspondance, Tome II, (Paris: L. Conard, 1910), 300.
32. Flaubert, Salammbô, 108/89.
33. "De la Domination des Carthaginois et des Romains en Afrique comparée avec la domination française," Revue des Deux Mondes (May 1, 1841): 409–445.
34. Flaubert, Salammbô, 108–09/89.
35. Girardin, "De la Domination des Carthaginois et des Romains en Afrique comparée avec la domination française," 414–15.
36. Flaubert, Oeuvres complètes, Correspondance, Vol. II, 165.
37. Quoted in Philippot, 229.
38. Gautier, Poésies complètes, Vol I (Paris: Charpentier, 1884), 109.
39. Flaubert, Oeuvres complètes, Correspondance Vol. II, 170.
40. Green, Flaubert and the Historical Novel, 59–60.
41. Flaubert, Salammbô, 67.
42. Ibid.
43. Ibid., 116/99.
44. Ibid., 117/100.
45. Ibid., 117/100.
46. Ibid., 129.
47. Ibid., 258/264.
48. Green, Flaubert and the Historical Novel, 53–54; Polybius, Histoire, ed. and trans. Denis Roussel (Paris: Gallimard, 1970), 88.
49. Flaubert, Oeuvres complètes, Correspondance Vol. I et II, 300, 123.
50. Jean Charles Léonard de Sismondi, Les colonies des anciens comparées à celles des modernes, sous le rapport de leur influence sur le bonheur du genre humain (Geneva: Lador and Ramboz, 1837), 7.
51. Ibid., 8.
52. Flaubert, Oeuvres complètes, Correspondance Vol. V, 324.
53. For an entry into historical studies of this nature, see Olivier Le Cour Grandmaison, Coloniser, exterminer: sur la guerre et l'état colonial. (Paris: Fayard, 2005); Caroline Elkins, Imperial Reckoning: The Untold Story of Britain's Gulag in Kenya (New York: Henry Holt, 2005), 46–50; and Paul Kramer's The Blood of Government: Race, Empire, The United States and the Philippines (Chapel Hill: University of North Carolina Press, 2006), chapter 2.
54. Jennifer Sessions, "'Unfortunate Necessities': Violence and Civilization in the Conquest of Algeria," in France and Its Spaces of War: Experience, Memory, Image, ed. Patricia Lorcin and Daniel Brewer (New York: Palgrave Macmillan, 2009), 30–31.
55. Nicholas Planat de la Faye, "De la nécessité d'abandonner Alger," (Paris: Dezauche, 1836), 14.
56. Ibid., 12.
57. François Guizot, Histoire de la civilisation en France, depuis la chute de l'Empire romain jusqu'en 1789, Tome I (Brussels: Vandooren Frères, 1829), 23.
58. Peter Starr, "Salammbô: The Politics of an Ending," French Forum 10, no. 1 (1985): 41.
59. Flaubert, Salammbô, 329.
60. Ibid., 43.
61. Ibid., 44/18.
62. Ibid., 46/20.
63. Ibid., 83/61–2.
64. Ibid., 149.
65. Ibid., 329/242.
66. Douglas Porch, "French Colonial Forces on the Saharan Rim," in The Military between Cultures: Soldiers at the Interface, ed. James B. Gradford (College Station: Texas A&M University Press, 1997), 166.
67. Lucien de Montagnac, Lettres d'un soldat. Algérie, 1837–1845 (Vernon: Editions Christian Destremau, 1998), 105.
68. Sessions, "'Unfortunate Necessities,'" 31.
69. Quoted in Sessions, "'Unfortunate Necessities,'" 31–32.
70. Quoted in Green, Flaubert and the Historical Novel, 91.
71. Sessions, "'Unfortunate Necessities,'" 36.
72. Victor Brombert, The Novels of Flaubert: A Study of Themes and Techniques (Princeton, NJ: Princeton University Press, 1966), 65.
73. Flaubert, Salammbô, 256/261.
74. Ibid., 199/195.
75. Sessions, "'Unfortunate Necessities,'" 32.
76. Flaubert, Salammbô, 205/202.
77. Le National, July 17, 1845, quoted in Sessions, "'Unfortunate Necessities,'" 44.
Chapter 4
Le Mal de la Kasbah
Pierre Loti in Algiers
Whereas Salammbô obliquely reveals a critique of France's colonization of Algeria, Pierre Loti's work "Les Trois dames de la Kasbah: conte orientale" ["The Three Ladies of the Casbah: an Oriental Tale"] is much more directly haunted by colonialism's ravages. The short story was published in Loti's 1882 collection Fleurs d'ennui [Flowers of Ennui] and met with a negative critical reception. As a writer for the journal La Jeune France remarked, "Le nouveau livre de M. Pierre Loti ne nous plaît guère non dans la forme, qui est très originale, mais dans son action qui nous semble d'assez mauvais goût, pour ne pas dire plus." [Pierre Loti's new book does not please us, not because of its form, which is very original, but because of its action, which seems to us to be in rather bad taste, to say the least.]1
"Les Trois dames" is a curious tale. Mischief-making French sailors, visits to bars and prostitutes, and locking up a dogcatcher make up this enigmatic story.2 Its surrounding collection, Fleurs d'ennui, is anchored by a playful dialogue with Loti's interlocutor, Plumkett. Tales of half-drunken dreams, bats, and an elderly turtle enclose the story.3 Disguised with Orientalist clichés, touches of folklore, and even at times tinges of farce, "Les Trois dames" contains haunted cityscapes, architecture, ghosts of past crimes, and a hidden pathology. These dark presences possess the short story, its frame text, and its representations of an Algiers haunted by colonialism. Whereas researchers have investigated the anti-colonial messages of "Les Trois dames," its haunted textual framing has not yet been analyzed.4 This chapter focuses on Loti's anti-colonial messages in his most important Algerian work and their setup in the collection enclosing it. The gruesome objects hidden in the frame text presage the hidden, rotting core of healthy bodies in the short story, revealing shadows of a doubled, biting critique of colonialism in Fleurs d'ennui.
Although Loti's fiction set in Turkey (Aziyadé, 1879) and Tahiti (Mariage de Loti, 1872) has greater renown, his works relating to Algeria reflect his affinity for the country and firsthand knowledge of it ("Les Trois dames de la Kasbah," "Suleïma," and "La Naïl.). At the young age of nineteen, Loti's first experience with Algeria was as a midshipman in the French navy in 1869. Battles between the French army and the indigenous populations had already ravaged the country, and the last bloody revolts would take place in Kabylia in 1871.
As we have seen in the works of Fromentin and Gautier, Loti's fiction expresses the tension between his contradictory roles of European traveler and colonial profiteer. However, unlike the other two authors, Loti was more overtly sympathetic to colonial populations and cultures. Highly critical of the French destruction of a once mighty Algeria, he particularly protested the changes to local architecture and mores. Writing in 1869, Loti specifically objected to the conditions in Arab garrisons at Mers el-Kébir, and in Le Figaroin 1912, he denounced French atrocities during the conquest of Algeria. As Alain Quella-Villéger has convincingly demonstrated, "Dans l'article qu'il publie dans Le Figaro le 3 janvier 1912, [Loti] est clairement anticolonialiste."5 [In the article he published in The Figaro on January 3, 1912, (Loti) is clearly anticolonialist.]
Loti expressed these views in his fiction as well, although in a more complex fashion. His anti-colonial short story "Les Trois dames" seems simple enough on the surface. Six sailors—three Bretons and three Basques—arrive in Algiers one Sunday evening, their pockets full of six months of salary. After drinking in excess, they enter the old city, the Casbah, by accident. Once there, everything changes. They soon become lost in the seemingly dark and terrifying labyrinth. The drunken sailors, whom Loti deliberately calls gaiours (a Turkish word for "infidel") stumble through the old city singing monotonous tunes. Reaching the topmost point of the city, the three Basques visit prostitutes, a mother and two daughters, who have lost husband and father in a battle against the French. The Basques go into the women's quarters to receive their services while the Bretons make mischief by wandering into a bain maure and then a bar. They finish the evening's revelry by playing a prank and freeing the city's dogs from the municipal dogcatchers, whom they lock in the dogcart. The two dogcatchers are badly bruised and ridiculed by their friends. Back in the Casbah, the other three sailors awaken in the prostitutes' home. Hung over and disoriented, they make their way back to the boat. They have been infected with syphilis. Only two sailors survive, and back in France, the disease is transmitted to their children, who are born with syphilitic chancres on their faces.6
Recently, scholars have convincingly analyzed the anti-colonial messages of the short story. In her preface to "Les Trois dames," Denise Brahimi demonstrates how Loti's work evolves from the exotic to the colonial, stating that the short story is a "pamphlet anticolonialiste déguisé en conte oriental" [anticolonial pamphlet disguised as an oriental tale].7 She emphasizes how Loti had witnessed a large advance in the colonization and Francization of Algiers.8 Brahimi rightly suggests that "Les Trois dames" is a work of political prospicience in displaying an acute political intelligence that captured the cultural shifts resulting from France's occupation of Algiers.9 It is unquestionable that Loti's Algiers emphasizes haunted spaces, bodies, and mortal illness. Through references to its nightmarish old city, decrepit architecture, ghostly prostitutes, and buried degenerate activities, Loti's work expresses deep criticism of the sociocultural disorder the French wrought in Algiers. However, this reading only goes so far. I analyze a haunting anti-colonial message in the presentation of the overall work. Through an analysis of a key element of its frame text, I argue that Loti's anti-colonialism in Algiers takes the shape of an unquiet haunting in both the short story and its collection, Fleurs d'ennui. The neglected element in the scholarship on Loti, the epistolary collection in which it first appeared, and the correspondence between Loti and his friend Plumkett reveal another layer of Loti's anti-colonialism. In the frame tale, the two friends exchange stories, calling each one a flower, but later in their conversation, the flowers turn into skeleton bones. In the exchange of blooms for bones, the frame text portends an ominous subject. I argue that this frame tale presages Loti's representation of the Casbah as a space haunted by past colonial crimes.
Loti in Algeria
Born Julien Viaud in 1850, Pierre Loti grew up in a middle-class Protestant family in the coastal city of Rochefort and was one of the key figures of the French Orientalist tradition during the Third Republic.10 When Viaud was fifteen years old, his older brother Gustave died at sea while serving with the navy in French Indochina, yet he, too, became a naval sailor to fulfill his desire to travel. Not yet writing under the pen name Loti, Viaud published a series of articles and drawings in 1872–77 in such Parisian journals as Illustration, L'Univers illustré, and Le Monde illustré, [Illustration, The Illustrated Universe, and The Illustrated World], depicting France's changing political dimensions and foreign policy as he had witnessed them in his travels.11 Viaud adopted his pen name with the first publication Au Maroc (1889). Loti's drawings, such as "Expédition française en Tunisie" (1881) [French Expedition in Tunisia] and "Le Campement devant Mékinez [Meknès]" (1889) [Encampment Near Meknès], traced the chronology of France's occupation of the Maghreb, with France officially declaring Morocco a protectorate by 1912. The French intellectual elite elected Loti over Emile Zola to the prestigious Académie Française in 1892, and his admirers included Stéphane Mallarmé and Marcel Proust.12 However, after his death in 1923, Loti's renown faded quickly. André Bréton called him an "idiot" in his pamphlet "Refus d'inhumer" (1924) [Refusal to Bury]. Many intellectuals dismissed his writings as exemplifying exoticist longings and creating an imagery of Oriental "pacotille," in other words, fake and cheap images of the East.13 However, since the publication of a 1974 essay by Roland Barthes on Loti's most famous novel, Aziyadé, critical interest in the author has grown.14
It is not an exaggeration to say that the East haunted Loti. He had first become deeply attracted to that part of the world when he went on a trip to Algeria as a sailor in the French navy in 1869. His experiences in Turkey, Senegal, Morocco, and Algeria inflect his works. After two decades of travel, Loti had also become an eager collector of animals and objects he found during his travels.15 These artifacts quickly appropriated the larger part of the family house in Rochefort. In 1895, he bought the adjoining house, where his collection quickly overran the property. His souvenirs ranged from a turtle he had discovered on his first trip to Algiers to the putative tombstone of Aziyadé, the tragic heroine of his eponymous novel. This tombstone and other relics of his travels are now exhibited in the Maison de Pierre Loti, which was purchased by the municipality of Rochefort in 1969 and made into a museum. The unassuming three-story building contains unique examples of Islamic architecture, art, and crafts that Loti had amassed. Loti personally designed a suite of rooms reflecting his fascination with Eastern cultures: the "Turkish Salon," with a finely carved cedar ceiling; the "Arab Room," featuring seventeenth-century Turkish tilework; and the so-called "Mosque," a reconstruction of a Damascus mosque that Loti had salvaged from the remains of a fire just as the authorities were about to destroy it. He had its stones brought to Rochefort and had a replica of it rebuilt in the specially remodeled second story of the house. Between his journeys at sea, Loti spent much of his free time there, seated on the low sofa cushions, reliving his journeys through his souvenirs, and writing.
Loti's three texts about Algeria were first published in the June 1882 edition of Le Figaro. On Loti's second trip there in 1880, he remarked upon how French colonization was much more advanced and was bitterly disappointed in the drastic changes in the capital city since the last time he had visited it, writing: "Cette Algérie, depuis seulement dix ans que je la connais on l'a encore gâtée" [This Algeria, that I have known for only 10 years, is even more spoiled].16 About the Casbah, he wrote, "La Kasbah profanée, devenue un lieu de prostitution et de débauche vulgaire! Cela déroute l'imagination." [The desecrated Kasbah, now a place of prostitution and vulgar debauchery! It bewilders the imagination.]17
The complexities of Loti's writings run deep; they possess strains of both pro-colonial and anti-colonial rhetoric. In the last thirty-five years, two camps have formed among Lotian scholars. The first group focuses on the seeming contradictions between Loti's writing and his life in relation to colonialism and see Loti as a largely pro-colonialist author. For example, Alec Hargreaves astutely highlights a contradiction between the apparent sympathy of Loti's depictions of the colonized and his position as a naval officer, arguing that Loti's concern for the colonizer was largely insincere.18 In this view, Loti is a cultural exploiter whose quest for exotic fantasies surpasses his interest in the people themselves.19 In what I find a more nuanced analysis, Christopher Bongie reaches satisfying conclusions about Loti's many colonial inconsistencies, showing how the author often attempted to obscure the colonialist context of his writings with personal narratives. Bongie interprets Loti's exoticizing impulse as embedded in his reproaches to an invading colonial corruption that expresses "the story of loss that generates exoticism."20 For Bongie, Loti's exoticism reflects a melancholic narrative of longing for traditional, "primitive" utopias that never existed, suggesting that the nostalgia for an unattainable past is already finished, or "moribund." He conjectures that "[there is an] impossibility for [Loti] of coming into contact with the exotic world and thereby distancing himself from the colonial one of which he is a part. The space of the Other is moribund, covered with a funereal veil that Pierre Loti, in his later works, will offer no hope of lifting."21 In this reading of Loti, colonialism's destruction of a utopian past brings a sense of despair, as European culture, mores, and technology begin to dominate in the colonies. Similarly to Bongie, Alain Quella-Villéger carefully examines archival sources on Loti, not to try to explain his inconsistencies, but rather to reveal how Loti's changeable and contradictory positions existed in his entire life story, not only in relation to colonialism.22
Colonial Pathologies
Although these critics point to the role of colonialism in Loti's works, they do not examine the extent to which this writer's early publications about Algeria were haunted by French colonialism in the region. Loti's works set in Algeria reflect his deep interest in the country and direct knowledge of it. As we have seen, Fromentin's writings focused on a witnessing of the colonial atrocities and Flaubert's text pushed on the barriers between le civilisé and le barbare. Loti's focus in this work is different in its foregrounding of a new kind of colonial haunting, the contamination by a fatal disease. "Les Trois dames" presents an anti-colonial tale with a bleak outcome in a premonitory story of colonialism's pathology.
The anti-colonial messages implicit within "Les Trois dames" are manifested in the haunted representations of the Casbah, the prostitutes' home, and the images of the women themselves. But just as importantly, the frame text of "Les Trois dames" plays a crucial role in representing the dark pathology of colonialism. With the exchange of Loti and Plumkett's tales that turn flowers into bones, the negative exchange presages the dark subjects that follow. Loti's framing thus foreshadows the representation of the Casbah as a space haunted by past colonial crimes. His Algiers is one of degenerating bodies, decrepit streets, and mortal illness.
Fleurs d'ennui
A tale of decrepitude and unhealthiness, "Les Trois dames" ripples with undercurrents of violence and corruption, and the waters are muddied as soon as the collection begins. The framing of "Les Trois dames" in Fleurs d'ennui (a title without a doubt inspired by Baudelaire's Fleurs du mal) portends its moribund quality. Fleurs d'ennui is composed of four sections; the first is a dialogue between Loti and Plumkett in which the two exchange stories. "Les Trois dames" follows their conversation. Three short stories, "Pasquala Ivanovitch," "Voyage au Monténégro," ["Journey to Montenegro"] and "Suleïma," form the rest of the work. As its preface states, the first part of Fleurs d'ennui is "un livre double" [a double book] recounted by its two narrators, Loti and Plumkett. Loti states the genesis for the work: "l'idée me vient d'organiser une petite réunion de famille, et de faire un petit bouquet de votre ennui et du mien: je vous enverrai des oeillets d'Inde, et vous y répondrez par des pissenlits [. . .] Moi, je me débiterai en aphorismes [. . .] vous conterez vos rêves si vous voulez." [I have come up with the idea of organizing a little family reunion to put together a little bouquet of yours and my ennui: I will send you marigolds and you will reply with dandelions . . . I will reel off aphorisms . . . you will recount your dreams if you would like.]23 With each of his stories, Loti gives out flowers in the chrysanthemum family, "oeillets d'Inde" [marigolds], whereas Plumkett extends dandelions to create their bouquet of ennui.24 In the language of flowers in nineteenth-century France, both of these blooms have negative connotations: floriology of the time reveals that marigolds signify separation, whereas dandelions represent the loss of time.25 Thus from the outset of this polyvocal text, the dialogue between Loti and Plumkett paints a seemingly anodyne picture on the surface but is one that belies a deeply negative tale.
For each flower Loti and Plumkett exchange, they tell a story, usually with a philosophical or moral message. Loti and Plumkett recount dreams, childhood memories, or travel adventures; Plumkett tends to rely on axioms, whereas Loti contributes more meandering, abstracted stories whose subjects range from gargoyles to bats to deserts. In a lively conversation, they undertake an interpretation of each story after its conclusion. As Ross Chambers reminds us, "the presence of 'narrational' embedding provides an immediate clue to the situational model the text is producing."26 Because Loti and Plumkett react to the stories told, the model of reading here is one of interpretation, demonstrating that the reader should not just absorb a story but go further to find another meaning. For example, Loti recounts a story or a dream, and Plumkett interprets it, and vice versa. This is particularly important in the case of "Les Trois dames." Because there is no clear moral, the effort is in the attempt to understand it. In this explicit search for meaning, Loti and Plumkett perform the work of literary interpretation, seeking the inner signification hidden within each tale by the outside descriptions.
After these preliminary exchanges, "Les Trois dames" itself occurs about a third of the way through the work. Just before starting the tale, Loti scolds Plumkett for having told a terrible story but then states that he will be recounting a far more dreadful one: "Mon cher Plumkett, ceci n'est pas une fleur: c'est un os de mort que vous venez de m'envoyer. [. . .] Il ne faudrait pas mettre de ces choses-là dans les bouquets sans prévenir, Plumkett, parce que c'est laid et que cela risque de faire peur." [My dear Plumkett, this is not a flower: it is a dead person's bone you have just sent me. . . . You must not put such things in bouquets without warning, Plumkett, because they are ugly and likely to cause fear.]27 Strangely, the flowers are figured here as skeleton bones that make up the bouquet of stories. Loti continues: "Je vais, moi, vous conter une histoire où il y aura des os aussi, -puisque les os affreux sont en effet le fond de toutes les créatures. [. . .] Mais autour de ces os-ci il y aura beaucoup de chair vigoureuse et jeune, et on ne les verra point à travers" [As for me, I will tell you a story in which there will be bones also, - since dreadful bones are indeed the content of all creatures. . . . But around these bones there will be a lot of vigorous young flesh, through which they will not be seen.]28 Thus from the outset of Fleurs d'ennui, the reader becomes aware of the interplay between a lovely and lively exterior and a decaying and deadly interior.
Dreadful Bones
The archival history of "Les Trois dames" indicates that its disturbing qualities almost resulted in its not being published. Keith Millward has demonstrated that Loti's editor at La Nouvelle revue, Juliette Adam, was reluctant to print it because of its representation of a sexually transmitted disease. Encouraging Loti to remove the coarser aspects of the tale, especially the depiction of syphilis, Adams called the story an "oriental fantasy" and cautioned against the "venomous flower":
Je ne puis dans le bouquet des Fleurs d'ennui, accepter la fleur vénéneuse de l'histoire des trois dames d'Alger. La revue doit être possible dans les familles, et, vraiment je n'ose vous demander de refaire l'histoire des matelots ou de me permettre d'en atténuer les passages les plus crus.
[I cannot, in Flowers of Ennui, accept the venomous flower of the story of the three women of Algiers. The journal must be family friendly, and, truly I must ask you to rewrite the story of the sailors or permit me to soften the most explicit passages.]29
Advising Loti to have one of the women kill off a soldier instead of having him die of syphilis, Adams begs him to take out the superfluous exchanges with Plumkett and to express himself as naturally as he had done in Le Roman d'un spahi. Adams specifically suggests that Loti remove certain too-naturalistic phrases: "Il y a des passages que vous ne pourriez laisser: par exemple le passage scientifique des os de mort est lourd comme une page de vocabulaire." [There are passages that you cannot leave in: for example, the scientific excerpt about the dead person's bone is over-the-top in vocabulary.]30 Nonetheless, Loti ignored Ms. Adams' advice. Describing his story as containing at its core awful bones surrounded by young healthy flesh, Loti depicts the seemingly lovely flesh of the prostitutes that conceals the terrible sickness of syphilis; their shining jewels are a feeble distraction from their grinding poverty and mortal illness. Like the story and the prostitutes, the Casbah too at first seems to be an untouched and uncorrupted section of Algiers. However, Loti later represents it as a place of degradation, prostitution, and contamination, "une ville qui suait l'immoralité, la débauche, l'ivrognerie" [a city that sweated immorality, debauchery, and drunkenness.]31 As Loti foreshadows it, the story, the city, and the women have hidden centers of corruption.
Although its subtitle of "conte oriental" positions it as an Orientalist fable, the exotic clichés fade away after the first few pages of "Les Trois dames." Loti writes: "Ce sera une histoire arabe, pour faire suite à celle des Mille et une nuits; \- et il y aura une moralité que je prendrai soin de déduire et de bien mettre sous vos yeux." [It will be an Arab tale, in response to one in A Thousand and One Nights; - and there will be a moral that I will take pains to deduct and to put clearly before your eyes.]32 Almost belatedly, the author prepares his reader by triggering the associations of an Oriental story. In the introduction, vocabulary conjuring images of Oriental décor, indigenous dress and activity, and references to Islam appear but then dissolve. Underneath the Orientalist and exoticizing language that Loti uses to describe the women's appearances and the settings, there are haunting undercurrents of death, sadness, and cruelty in the portraits of the Casbah, the women's quarters, and the three prostitutes themselves, Kadidja, Fatmah, and Fizah.
The Haunted Kasbah
Loti's Casbah is an astonishingly haunted place. Beginning with the shadowy spaces of the Casbah itself, the story contains phantasmal contours at every turn. At the beginning of the story, Loti's characterization of the Casbah does not differ greatly from other Orientalist versions of a folkloric and exotic assemblage of North African peoples and décor. By the middle of the tale, however, its spaces are clearly haunted. Filled with nightmares, mummies, specters, and figures wrapped in white, the old city of the Casbah is contaminated by past crimes that return to haunt its inhabitants and visitors. Despite its lovely exterior, the city's insides are rotting, like those of the prostitutes—and later the sailors. Whereas other Orientalist depictions of the Casbah are similarly places of vice and corruption, they do not carry the same weight of spectrality as in this short story.33 The sailors' entry into the haunted Casbah is worthy of quoting at length:
Ils allaient toujours, au hasard des rues biscornues qui serpentaient devant eux. [. . .] Dans des espèces de bazars, - entrevus vaguement, - on vendait des choses sans usage connu. [. . .] Il y avait des échoppes comme des tanières, au fond desquelles des marchands au teint de momie, accroupis, emmaillotés dans des burnous sordides, semblaient des spectres au guet. [. . .] Et des femmes, tout enveloppées de soie blanche, passaient avec un semblant de timidité et de pudeur qui se cache; on ne voyait d'elles qu'une forme neigeuse et voilée, ayant de grands yeux peints, admirables.
[They continued aimlessly along the twisted streets snaking in front of them. . . . In the variety of bazaars - vaguely made out - things without known use were being sold. . . . There were stalls like hideaways, in whose depths merchants with a mummy's complexion squatted, swaddled in squalid burnooses, and seemed like specters on the lookout. . . . And women, entirely wrapped in white silk, passed by with a semblance of hidden shyness and modesty; you could see them only as a snowy and veiled form with large, painted, admirable eyes.]34
Surrounded by shops full of "things without known usage," the sailors can barely make out the mysterious bazaars in which quasi-mummified merchants peer out like watchful specters. The female passersby are similarly ghostly, wrapped in white silk and impossible to fully see.
During Loti's second visit to the capital city, he opined that Algiers' Casbah was but a shadow of its former self: "les moindres détails des choses ramenaient l'esprit bien loin dans le passé mort, dans les époques ensevelies des anciens jours de l'Islam." [the smallest of details would bring the mind far back into the dead past, into the buried epoques of the ancient days of Islam.] Quella-Villéger's archival research bears out Loti's condemnation of the changes colonialism brought to Algiers.35 36 Quella-Villéger remarks that "[p]our Loti, Alger n'est plus l'Algérie. Alger est plus européenne, plus française que d'autres villes du Maghreb. Même dans la Kasbah, il retrouve des marins, des prostituées. . . . Alger le déçoit." [For Loti, Algiers is no longer Algeria. Algiers is more European, more French than other cities of the Maghreb. Even in the Casbah, he finds sailors, prostitutes. . . . Algiers disappoints him.]37 Loti also expresses this disapproval through the reactions of the characters in "Les Trois dames," the six sailors on leave. When they first arrive in the capital city, the sailors "se croyaient tombés dans le pays des légendes et des fantômes." [believed themselves fallen into the country of legends and ghosts.]38 Later, however, this mythical milieu becomes a nightmare: "le silence les gênait, et l'inquiétude de cette ville les avait repris." [the silence bothered them, and the disquiet of this city had taken ahold of them.]39 Upon going deeper into the Casbah, the men feel increasingly unsettled by its diabolical quality; they perceive its blackness as terrifying as they follow its winding streets that "se contournaient, se croisaient, s'enchevêtraient, comme dans cauchemar dont on ne peut pas sortir [. . .] il faisait plus noir que chez le diable."[twisted, crossed, tangled, like in a nightmare from which one cannot leave . . . it was darker than hell.]40 Figured as a hellish tomb, the Casbah, "enveloppée dans ses blancheurs de chaux [. . .] avait plus que jamais son air de sépulcre." [enveloped in its chalky whiteness . . . looked more than ever like a sepulcher.]41
The previous passage points to the color white, one of two principal colors—the other is black—that dominate in the short story. First, the sailors get lost in the tenebrous depths of the Casbah's ancient streets:
On y voyait encore à peine, et autour d'eux tout était d'une pâleur singulière; à part les pavés de galets noirs, tout était blanc. Les vieilles maisons mauresques, les vieilles voûtes en ogive, les vieux jambages de bois qui chevauchaient le long des murs, tout était indécis et paraissaient taillé dans de la neige; on était comme dans une obscurité blanche. Le silence semblait couvert des enchantements et des mystères.
[They could hardly see, and everything around them had a singular pallor; except for the black cobblestones, everything was white. The old Moorish houses, the old ribbed arches, the old wooden legs that straddled the length of the walls, everything was indistinct and seemed carved out of snow; they were as if in a white darkness. The silence seemed covered with enchantments and mysteries.]42
Then, the only figures in this otherworldly space of mystery and darkness that the sailors can see are a few ghostly and shroud-wrapped shapes: "Cela semblait mystérieux et impénétrable [. . .] il y avait de distance en distance de blanches traînées de lune, qui ressemblaient à des linceuls." [It seemed mysterious and impenetrable . . . at intervals there were white moonlit streaks that resembled shrouds.]43 The shrouds to which Loti refers here are white, and the repetition of the color white throughout the tale is no accident. The absence of all color, white is symbolic of death and bereavement in Algeria.44 White burial cloths are used to wrap the dead, and widows are instructed to wear white during their mourning period. Loti figures the patterns of moonlight as burial shrouds dragging themselves through the winding pathways of the Casbah.
Phantoms of Past Crimes
Loti's tale first sets up a binary model of clear-cut morality, with the innocent victims and the hapless wrongdoers seemingly easy to identify. The influx of companionless sailors into Algiers during the military occupation had increased prostitution in the old quarter. Loti's sailors behave like foolish children, make use of the prostitutes, and are ultimately punished for their wrongdoings.45 However, this moral unravels; Loti proceeds to dismantle strict codes of innocence and guilt and instead shows a haunted cycle of cross-contamination that represents France as, in the words of Edward Hughes, "a nefarious colonial culture."46
As we have seen, Algiers' haunting is evidenced in Loti's prose. But the space of the Casbah holds phantoms of a specific kind: those of the violence wrought by French sailors and soldiers, with the explicit examples of prostitution and the failed counterinsurgencies against the French. Historically inflected grief characterizes the atmosphere of the Casbah. One specter in particular haunts the tale. Just before the sailors arrive, readers learn that the husband and father of the prostitutes was killed in an insurrection against the French. The loss of the family's father has left them in impoverished ruin. Loti relates a fragment of historical context that is one of the causes of their immense sadness: "Il y avait bien des années, le mari de Kadidja, Cheik-ben-Abdallah, avait été tué dans une insurrection contre les Français, et Fizah et Fatmah-ben-Cheikh étaient orphelines." [Many years ago, Kadidja's husband, Cheik-ben-Abdallah, was killed in an insurrection against the French, and Fizah and Fatmah-ben-Cheikh were orphans.]47 Here, Loti again sides with the colonized, choosing as the name of the mother, "Kadidja," the name of the Prophet Mohammed's first and favorite wife. Abandoned and orphaned, the mother and daughters subsist on the "débris des richesses de leur mère," and it was "aisé de voir que maintentant elles étaient pauvres." [the debris of their mother's wealth], and it was [easy to see that now they were poor.]48 Loti writes, "Elles étaient comme plongées dans une tristesse immense, dans un écourement d'abruties, filles d'une race condamnée, subissant des choses fatales avec une résignation morne." [They were as if plunged into an immense sadness, in a worn-out disillusionment, daughters of a condemned race, suffering fatal things with dull resignation.]49 The daughters grieve their father, whose untimely death results in their poverty and misery. The ghost of the father—and other absent fathers, sons, and brothers—killed at the hands of the counterinsurgency haunts the hidden spaces of Algiers and leaves their surviving loved ones to take desperate measures to survive.
The French are not the only ones at fault for leaving a family bereft. Loti evokes the phantoms of both camps, with references to past massacres on the two sides, referring to "l'antique Kasbah, où jadis on aurait massacré l'imprudent gaiour, était plein de braillements d'ivrognes." [the antique Casbah, where long ago the imprudent gaiour would have been massacred, was full of drunken brawls.]50 However, it is clear where Loti's allegiances lie. The ruin of Algiers was due to its contamination by French foreigners, whom he calls "les Roumi infidèles" [the Roumi infidels].51 A disparaging term from the Arabic language, Roumi designates a non-Muslim European. Like the mother and two daughters forced into sex work by their financial straits, Loti figures the capital city as a woman who has prostituted itself to the European foreigners: "Alger avait le débraillement cynique des lieux qui ont perdu leur nationalité pour se prostituer, s'ouvrir à tous." [Algiers had the cynical unkemptness of places that had lost their nationality to prostitution, to opening themselves up to everyone.]52
There is an undeniable figurative parallel between the haunted city and the three syphilitic women. A sexually transmitted disease that plays out in the contaminated areas of blood and sex, syphilis is represented as the revenge of the colony. A protean sickness, it shape-shifts in its symptoms and symbolizes a lack of ethics and morality. In nineteenth-century France, it signified a degeneration that accompanied decadence, and its cultural connotations generally linked it to prostitution.53 Like the city of Algiers, in which monstrous and terrifying things peer out from the shadows, the women's dangerous sexuality is occulted by their lovely appearance. And just as in the frame tale when Plumkett offers a bouquet of flowers hiding the bone of a cadaver, the theme of contamination resurges out of the seemingly anodyne tale. The sailors are the colonizers; the women are the colonized, but after that, the lines become blurrier. However, the end result is a terrible case of syphilis for each of the three sailors. As Edward Hughes has compellingly argued, the sailors' affliction anticipates colonial dysfunction theorized in the following century by Albert Memmi in Portrait du colonisé, précédé du portrait du colonisateur (1973).54 Loti figures the relations between colonizer and colonized as unworkable. In doing so, he suggests what Memmi later called the European "défiguré en oppresseur" [a disfigured oppressor] and the colonized as "brisé dans son développement, composant avec son écrasement" [broken in their development, composing with their crushing].55 Memmi's disfigured oppressor and broken indigène echo the colonial enmeshing that occurs in "Les Trois dames" and leads to disfiguration, the punishment of innocents, and death.
Like the prostitute-city of Algiers, Loti represents the three women as unconsciously haunted by a terrible secret, the hidden venereal disease in their bodies: "Cette mère et ces filles, ne s'étaient pas adressé un sourire, en se revoyant après le non-être de la nuit; elles avaient détourné leurs regards les unes des autres avec une sorte de honte, comme des femmes qui garderaient entre elles le secret et la souillure d'un crime." [This mother and these daughters did not greet each other with a smile when they saw each other after the non-existence of the night; they turned their gazes away from each other with a kind of shame, like women who would keep between them the secret and the stain of a crime.]56 Unlike the prevailing discourse about syphilis in the Maghreb casting it as a "Muslim affliction," Loti deliberately shows how the disease affects both colonizer and colonized. Just like the skeleton-filled bouquet of flowers Loti offers to Plumkett, there is a dark secret hidden away in the women's indirect gazes.
Colonialism's Haunted Prison-House
As the six drunken French sailors wander up the darkening streets toward the prostitutes, the space of the Casbah becomes increasingly menacing. The city's buildings are again remarked upon as a mysterious white, another reference to death and bereavement, and the ancient houses are figured as projecting the shadows of a necropolis: "les maisons centenaires, en se rejoignant par le haut faisaient voûte au-dessous de la rue déserte, et jetaient sur les pavés des demi-obscurités de catacombes." [the centuries-old houses, meeting each other at the tops, arching over the deserted street, and threw half-shadows of catacombs on the cobblestones.]57
As soon as the scene focuses on the three women, they are depicted as if buried alive in an underground prison. First, their house is described as immobile, like the streets of the old Casbah. Made of thick marble walls, their home is traced with faded arabesques, displays dilapidated surfaces, and is dotted with tiny barred windows. The courtyard encloses a house encased in a complicated network of iron grills and bars. Locked in their "vieille prison blanche" [old white prison], the women are as if interred while they are still alive.58 Barely surviving the weight of their dwelling, they are enclosed by a door alternately described as "sinister" [sinister] and "sépulcrale" [sepulchral].59
Not only are their surroundings macabre, the women themselves are described in supernatural terms. The widow Kadidja and her daughters Fatamah and Fizah are portrayed as the undead. First called "momies" [mummies], they are also described as wax-like figures.60 Illusory creatures, "elles semblaient des êtres chimériques." [they seemed like chimerical beings.]61 When Fatmah opens the small window to greet the sailors, she strikes them as an unnatural apparition whose face appears without a body: "une jolie tête sans corps." [a pretty head without a body.]62 "Subissant des choses fatales avec une résignation morne" [suffering fatal things with dull resignation], the women appear resigned to their ghoulish setting and bitter fate.63 As in an earlier scene, these women are not the only phantoms to populate the old city; the shopkeepers have the air of ancient mummies and ghosts on the lookout.64 In addition, the sailors are greeted by "une foule d'apparitions pareilles à celle de Fatmah."65 [a host of apparitions like that of Fatmah] during their passage through the Casbah, including a yellowish, cadaverous man.66 When the three sailors who have slept with the prostitutes awaken hung over and disoriented, they quickly make to leave. One of the sailors realizes that he had slept with the aging mother Kadidja and turns away in disgust: "Il vit qu'elle était vieille, que son visage était ridé et sa chair affaissée. - Il s'en détourna avec horreur, la repoussant du pied." [He saw that she was old, that her face was wrinkled and her flesh sagged. -He turned away from her in horror, pushing her away with his foot.]67 Like the "os de mort" [bone of death] hidden in the bouquet of flowers referenced in the frame text of Fleurs d'ennui, the mother Kadidja's exterior seems at first glance "vigoureuse et jeune" [vigorous and young],68 but it hides a disastrous secret.
The decaying figures populating the Casbah take a more concrete shape by the end of the tale, because the sailors emerge from the women's quarters with the sexual disease that will kill the cruel sailor above and blight the future offspring of the other two men: "Ils allaient gaiement, savourant ce bien-être matinal, ne se doutant pas que c'était fini à jamais de leur saine et belle jeunesse, et qu'ils emportaient avec eux dans leur sang les hideux germes de mort." [They went along gaily, savoring the morning's feeling of well-being, not suspecting that their healthy and beautiful youth was forever finished, and that they carried with them, in their blood, the hideous seeds of death.]69 After the two surviving sailors marry the daughters of healthy Basque fishermen, each of their first children is born with visible sores.70 Just as the beautiful exterior of a bouquet of flowers hides a dreadful cadaver's bone, the disease lies dormant until the next generation. The pathological contact zone of Algeria's Casbah demonstrates how the insalubrious effects of France's colonialism will seep into the métropole as a mutable hereditary disease.
A Morality Tale?
"Les Trois dames" purports to be a moral tale in multiple senses of the word. As an adjective, "moral" relates to concerns of right and wrong; as a noun, it can be a story's concluding message of how to behave; and the French word "moeurs" denotes standards of behavior. At the end of the story, there is a moral. Loti writes, "On a toujours tort de chercher à faire du mal aux gens, surtout lorsque ce sont de bons louloups affectueux comme ceux de cette histoire; tôt ou tard, on est fatalement puni." [One is always wrong to seek to harm people, especially when they are good affectionate puppies like those of this story; sooner or later, one will be fatally punished.]71 Like the morals of Jean de La Fontaine, Loti prefers the complex over the simple, the ambiguous over the clear. The moral is far from explicit; Loti uses the frustratingly neutral "on" in the phrase "tôt ou tard, on est fatalement puni" [sooner or later, they will be fatally punished]. It is also unclear who the "bon louloups affectueux" [good affectionate puppies] are; this aspect of the story is open to interpretation.72 Literally, they are the dogs the Bretons let out of the cage, but they also can represent the once-carefree sailors, unconscious of their position of power and ability to do harm. Etymologically, they are associated with the sailors: "loulou" means "puppy" and also "hoodlum." Or rather, as the triad of three dogs would indicate, are they the three prostitutes, who, like the three dogs, are the imprisoned victims and know that they are spreading syphilis to their visitors? Or are they the sailors, presented in groups of three? In this work, Loti clouds any clear message and ends upon a playfully scandalous note.
Thus even though "Les Trois dames" contains a moral at its conclusion, it conveys no pure moral message. Situations are continually reversed; prostitutes and sailors alike are sentenced with a bitter brutality. "Les Trois dames" begins by setting up a clear model of difference; the guiltless women and the ill-fated hooligans seem to be easily identifiable in the tale: the infidel-sailors and the innocent prostitutes. Tellingly, Loti implicitly exculpates the women for having given syphilis to the sailors: "Les trois Basques se virent bientôt atteints d'une maladie horrible. Ces femmes la leur avaient donnée, presque inconsciemment. Irresponsables de leur vice et de leur misère, elles avaient rendu à ces giaours ce que d'autres giaours leur avaient apporté." [The three Basques found themselves soon afflicted with a horrible malady. These women had given it to them, almost unconsciously. Not responsible for their vice and their misery, they returned to the giaours what other giaours had brought them.]73 Ultimately, the three sailors are punished for their debauchery, but Loti proceeds to break down clear categories of innocence and guilt, and instead delivers a message of sordid cross-contamination arising out colonialism. In the universe of this tale, victims are criminals and vice versa; the great haunting equalizer is the syphilis that will linger for generations to come. The unworkable relations between the colonizer and colonized are symbolized by the deleterious effects of their morbid entanglement.
Just as the reader may be dissatisfied with the ending, Loti's interlocutor Plumkett damns the story with faint praise, calling it a nonsensically mediocre tale. He specifically criticizes its opaque "moralité." "Mon cher Loti, j'avais parfaitement prévu que votre conte n'aurait ni queue ni tête et aboutirait à une moralité de Jocrisse" [My dear Loti, I had perfectly predicted that your tale would make no sense and would end with a moral of Jocrisse].74 With the phrase "une moralité de Jocrisse," Plumkett evokes the character Jocris, a theatrical incarnation of stupidity, buffoonery, and clumsiness appearing in plays by Molière and Dorvigny. In his critique of "Les Trois dames," Plumkett's claim that Loti's story has "une moralité de Jocrisse" denotes a light-humored sentiment that contrasts with the lugubrious nature of the tale, as Plumkett stresses its farcical qualities with his reference to Jocris. In a faintly disparaging tone, Plumkett continues his critical review as follows:
Vos principaux personnages, les chiens, n'apparaissent que vers le milieu de l'histoire, et les trois dames du titre ne figurent pas dans le dénouement.
Tout cela est fort peu conforme aux règles suivies par nos bons auteurs. Mais je ne vous le reproche pas: on écrit comme on peut. Il ne serait pas raisonnable que vous missiez de la suite dans vos récits, n'en ayant aucune dans les idées.
Du reste, vos matelots sont bien peints. J'aime même assez vos descriptions d'Alger; elles sont justes et passablement colorées.
[Your main characters, the dogs, only appear near the middle of the story, and the three ladies of the title do not figure in the conclusion. All that bears little relation to the rules that our good authors follow. But I do not reproach you for it: we write as we are able. It would not be reasonable for you to put consistency in your narrative, having none at all in your ideas. For the rest, your sailors are well represented. I even like your descriptions of Algiers fairly well; they are accurate and rather colorful.]75
Again doing the work of literary criticism, Plumkett offers a possible interpretation. He sees the dogs as the true protagonists and reproaches Loti for not including the three women throughout the entire story. Through the character of Plumkett, Loti seems to self-deprecatingly criticize himself for writing a story that makes little sense. But in my reading, this light, wry tone hides the serious sociopolitical and cultural issues that Loti tackles in "Les Trois dames." A persistent interrogation of French colonialism, wrapped in biting pessimism, remains throughout "Les Trois dames." As rotten bones disguised within bouquets of flowers, the haunting past and present crimes of colonialism, linger long after the tale's conclusion.
NOTES
1. Quoted in Alain Quella-Villéger, Pierre Loti: Le Pèlerin de la planète (Bordeaux: Obéron, 1998), 93.
2. On prostitution in colonial Algeria, see Bruce W. Dunne, "French Regulation of Prostitution in Nineteenth-Century Colonial Algeria," The Arab Studies Journal 2, no. 1 (Spring 1994): 24–30.
3. Plumkett is widely recognized as Loti's long-time friend Lucien Jousselin, who had helped with the writing of Aziyadé.
4. For other studies of the short story, see Denise Brahimi's preface to Les Trois dames de la Kasbah (Paris: Pirot, 2000), 7–16, and Edward J. Hughes, "Exotic Drift: Pierre Loti between Contemporaneity and Anteriority," in Eastern Voyages, Western Visions: French Writing and Painting of the Orient, ed. Margaret Topping (New York: Peter Lang, 2004), 241–64.
5. Quella-Villéger, Pierre Loti, 92–94.
6. A disease continually attributed to the cultural other, syphilis denotes foreignness. Leonard R. Koos argues that the malady was seen as so dangerous that it became unnamable in French literature of the mid-nineteenth century. See "Damaged Literary Goods: Telling the Tale of Syphilis in Nineteenth-Century France," Dalhousie French Studies (2007): 45–48.
7. Brahimi, Preface, Les Trois dames de la Kasbah (Paris: Pirot, 2000), 7.
8. Ibid., 7–16.
9. Ibid.
10. The growing field of postcolonialism and interest in exoticist cultural production during the colonial era has stoked interest in Loti's work. Book-length studies that include chapters on Loti's writing in relation to colonialism include Alec Hargreaves' The Colonial Experience in French Fiction: A Study of Pierre Loti, Ernest Psichari and Pierre Miller (London: Macmillan, 1981); Christopher Bongie's Exotic Memories: Literature, Colonialism, and the Fin de Siècle (Palo Alto, CA: Stanford University Press, 1991); and T. Denean Sharpley-Whiting, Black Venus: Sexualized Savages, Primal Fears, and Primitive Narratives in French (Durham, NC: Duke University Press, 1999).
11. Bongie, Exotic Memories, 106, and Elwood Hartman, Three Nineteenth-Century French Writer/Artists and the Maghreb: The Literary and Artistic Depictions of North Africa by Théophile Gautier, Eugène Fromentin, and Pierre Loti (Tübingen: Gunter Narr Verlag, 1994), 58.
12. Suzanne Lafont, Suprêmes clichés de Loti (Toulouse: Presse Universitaires du Mirail, 1993), 7.
13. Abdeljlil Lahjormi, L'Image du Maroc dans la littérature française (Alger: Société Nationale d'Editions et de Diffusions, 1973), 156.
14. See Roland Barthes, "Aziyadé," Nouveaux essais critiques (Paris: Seuil, 1974). In addition, Lesley Blanch's biography analyzing Loti's life and works simultaneously has inspired many scholars since to read his fiction as an archival and biographical resource. See Pierre Loti: The Legendary Romantic (New York: Harcourt Brace Jovanovich, 1983); Alain Busine, Pierre Loti: l'écrivain et son double (Paris: Tallandier, 1998); and Peter Dunwoodie, Writing French Algeria (Oxford: Clarendon Press, 1998).
15. In a compelling essay, Thomas J. D. Armbrecht argues that Loti's house in Rochefort expresses a kind of utopia that parallels the one found in his literature. See "The Nostalgia of Nowhere: Pierre Loti's Utopian Spaces," Mosaic: A Journal for the Interdisciplinary Study of Literature 36, no. 4 (2003): 81–102.
16. Quoted in Quella-Villéger, Pierre Loti, 92.
17. Ibid.
18. See Hargreaves, The Colonial Experience in French Fiction, 32–38. Dunwoodie similarly argues that Loti's passion for the exotic was another form of Western appropriation of the colonial other. See Writing French Algeria, 69–83.
19. Hartman approaches Loti's artistic depictions of the Maghreb to argue that they affirm his traditional Orientalist status. See Three Nineteenth-Century French Writer/Artists and the Maghreb, 61–62.
20. Bongie, Exotic Memories, 5.
21. Ibid., 98.
22. See Quella-Villéger, Pierre Loti, and Sebbar and Quella-Villéger, "Les nouvelles algériennes de Pierre Loti," Algérie Littérature Action 41/42 (May–June 2000): 271–76.
23. Pierre Loti, Les Fleurs d'ennui (Paris: Lévy, 1883), 227.
24. As many scholars have noted, flowers appear often in Loti's work. His pseudonym is derived from the word "lotus," and his 1887 novel Madame Chrystanthème [Madame Chrysanthemum] is set in Japan. In Mariage de Loti (1878) [The Marriage of Loti], he writes about receiving his baptismal name in literature: a flower's name assigned by three women to the naval lieutenant.
25. See B. Delachénaye's Abécedaire de fleur ou langage des fleurs (Paris: Didot l'ainé, 1811), and Beverly Seaton's The Language of Flowers: A History (Charlottesville: University of Virginia Press, 1995).
26. Ross Chambers, Story and Situation: Narrative Seduction and the Power of Fiction (Minneapolis: University of Minnesota Press, 1984), 34.
27. Loti, Fleurs d'ennui, 280.
28. Ibid., 280–81.
29. Cited in Keith G. Millward, "Madame Adams et les débuts de Pierre Loti," Revue d'Histoire littéraire de la France, no. 2 (1956): 224–25.
30. Ibid.
31. Loti, Fleurs d'ennui, 291.
32. Ibid., 281.
33. Stereotypes about the Casbah as a place of mystery, crime, and vice abound in the literature of the nineteenth and early twentieth centuries. As Jane Hiddleston notes, Julien Duvivier's 1937 film Pépé le Moko repeats a common stereotype of the Kasbah's infathomability. See Assia Djebar: Out of Algeria (Liverpool: Liverpool University Press, 2006), 175.
34. Loti, Fleurs d'ennui, 287.
35. See Quella-Villéger, Pierre Loti, 92–94.
36. Sebbar and Quella-Villéger, "Les nouvelles algériennes de Pierre Loti," 223.
37. Ibid.
38. Loti, Fleurs d'ennui, 292.
39. Ibid., 300.
40. Ibid., 293.
41. Ibid., 317.
42. Ibid.
43. Ibid., 300.
44. Djebar writes, "Le blanc, couleur du deuil chez nous, c'est aussi . . . un temps de silence" [White, color of grieving in our culture, is also . . . a time of silence]. In Ces voix qui m'assiègent . . . en marge de ma francophonie (Montreal: Les presses universitaires de Montréal, 1999), 66.
45. Interestingly, like the Algerian colonial subjects in "Les Trois dames," the six sailors are also marked with linguistic and ethnic otherness. They are called "les trois Basques" [the three Basques] and "les trois Bretons" [the three Bretons]. Their remarkably un-French names: Barazère, Esagarray, and Guiaberry, point to their status as ethnic others in France.
46. Hughes, "Exotic Drift," 247.
47. Loti, Fleurs d'ennui, 287.
48. Ibid.
49. Ibid., 286.
50. Ibid., 307.
51. Ibid., 285.
52. Ibid., 291.
53. For more on this subject, see Leonard R. Koos, "Damaged Literary Goods: Telling the Tale of Syphilis in Nineteenth-Century France," Dalhousie French Studies 80 (2007): 45–48.
54. Hughes, "Exotic Drift," 246.
55. Ibid.
56. Loti, Fleurs d'ennui, 243. For a historical analysis of the figure of the "syphilitic Arab" in French North Africa, see Ellen Amster's essay, "The Syphilitic Arab? A Search for Civilization in Disease Etiology, Native Prostitution, and French Colonial Medicine," in French Mediterraneans: Transnational and Imperial Histories, ed. Patricia Lorcin and Todd Shepard (Lincoln: University of Nebraska Press, 2016), 320–46.
57. Loti, Fleurs d'ennui, 282.
58. Ibid., 286.
59. Ibid., 295.
60. Ibid., 284, 294.
61. Ibid., 285.
62. Ibid., 303.
63. Ibid., 286.
64. Ibid., 298.
65. Ibid., 305.
66. Ibid., 308.
67. Ibid., 316.
68. Ibid., 281.
69. Ibid., 318.
70. Ibid., 321.
71. Ibid., 322.
72. Ibid.
73. Ibid., 282.
74. Ibid., 322.
75. Ibid.
Afterword
In this book, I have analyzed haunting in nineteenth-century Orientalist works set in or inspired by French colonial Algeria. In our day and age, well after the searingly painful period of France's colonization of Algeria, France's ghosts of colonialism are far from settled. In the collection of interviews with Benjamin Stora, the journalist Thierry Leclère stated, "la France est malade de son passé colonial" [France is ill from its colonial past.]1 In the twenty-first century, political movements by second- and third-generation immigrants, battles about the wearing of "ostentatious" religious symbols, and revelations about torture in the Algerian War of Independence indicate that France is beginning a long process of breaking its silence and coming to terms with its colonial history. Current French president Emmanuel Macron came as close as any French leader ever has, drawing a firestorm of controversy in a television interview in Algiers during his campaign when he asserted that colonialism was a "crime against humanity."2 However, France has never made an official apology for its 132-year colonization of Algeria, and various politicians, editorialists, and writers argue continue to debate the country's colonial endeavors. In 2016, two other prominent politicians exemplified the country's blind spots when it comes to this question. Presidential candidate François Fillon sanitized French colonialism as a "cultural exchange," stating that France wanted only to "share its culture" with the peoples of Africa, Asia, and North America.3 At almost the same time, former French president Nicolas Sarkozy resurrected the racist specters of the phrase "nos ancêtres les Gaulois" when he argued that immigrants were obliged to accept French heritage in order to better integrate into their new homeland.4
Unfortunately, this trend has a long precedent in France, with attempts to erase colonial atrocities and ignore the driving forces of imperialism.5 In February 2005, France unsuccessfully tried to rewrite its colonial history to put a positive spin on the painful era of colonialism with a law that would have required lycée teachers to teach students about the "rôle positif" [positive role] of the French presence overseas.6 Even though the law had already been proposed in 2004, the tensions that had been simmering for over two decades reached a boiling point when conservative legislators reintroduced this amendment.7 Many French historians and educators swiftly issued a condemnation of the government's intrusion into the classroom; dozens signed a petition that opposed the law and called for it to be rescinded. Finally, after several months of heated debate, then-president Jacques Chirac disavowed the education amendment and suppressed it by executive decree.
Chirac's official denial of the prescriptive 2005 law about how colonial history should be taught did not minimize the importance of this contentious debate, especially given the fact that, for a new generation in France, colonialism had been relegated to a nostalgic chapter of national history, or else completely forgotten. In Fast Cars, Clean Bodies, Kristin Ross argues that France suffered a phantasmagoric effect in wrenching itself apart from Algeria beginning in the mid-1950s.8 The terrible violence by Algerians experienced during the occupation and Algerian War of Independence has not translated into a true reckoning with its history today, because, as Ross argues, France has perceived its colonialism as "an 'exterior' experience that somehow came to an abrupt end, cleanly, in 1962."9 She continues:
Having decisively slammed shut the door to the Algerian episode, colonialism was made like a dusty archaism, as though it had not transpired in the twentieth century and in the personal histories of many people living today, as though it played only a tiny role in France's national history, and no role at all in its modern identity.10
The premature "slamming shut" of this door in France's history shows the dangers of closeted memories and those of a particular whitewashed version of history prescribed for public consumption. As the February 2005 episode revealed, the colonial past persistently refuses to stay in the past but rather resurges into the present, and the contested memory of colonialism raises essential questions about the Republic's obligation to confront its past and, more importantly, its duty to confront its dark role in the conflict.11 For those who might relegate colonialism in Algeria to a forgotten parenthesis of sepia-toned odalisques, brightly colored paintings of harem interiors, or long, descriptive prose passages about exotic landscapes, a fuller picture is greatly needed.
The complexity of these processes is incontestable. As historians Laura Hein and Mark Selden have argued, "The stories chosen or invented about the national past are invariably prescriptive—instructing people how to think and act as national subjects and how to view relations with outsiders."12 The critical hauntology of Orientalist texts in French Orientalist Literature in Algeria opens up history's closed doors, dismantling any kind of prescriptive reading through an investigation of the dark shadows in these works. The ambiguities, complexities, and ambivalences in the works of Gautier, Fromentin, Flaubert, and Loti, key intellectual and artistic leaders of the nineteenth century, vex the narrative of overall triumphal colonial discourse. This study has foregrounded hauntings that manifest themselves in these authors' writings during the pernicious struggle that has gripped Franco-Algerian relations since 1830.
As we saw in the introduction, in L'Amour, la fantasia, Assia Djebar shed new light on French military reports of this time, using them as point of departure to exhume the ghosts of this violent colonial history. Probing deeply into "les scrofules" [scrofulous excrescences], Djebar lingers upon certain details in the texts that do not fit "la plate sobriété du compte-rendu" [the flat restraint of a military report].13 In similar ways, I have peered past the picturesque exoticism of the standard Orientalist narrative. Like these traces of the repressed that hold the keys to persistent hauntings, in this book, I have drawn out certain occulted ambivalences within classic Orientalist narratives.
Critical hauntographies such as these raise compelling questions about what kinds of phantoms haunt colonial texts and what we do with them. This hauntological lens upon the literature of the era reveals new layers of the Algerian experiences of Gautier, Fromentin, Flaubert, and Loti, to point to a greater French unease about colonial violence in Algeria. Gautier's disturbing accounts and even more disturbed narrator spinning out of control, Fromentin's gaze upon the zombified corpses from the French 1852 siege on Laghouat, Flaubert's novel treating the barbarities of French civilization, and Loti's trenchant critique of the degenerative fallout of colonialism all point to ghostly traces of a darker tale of French colonialism.
By privileging the historical contexts in which the literature was produced, these analyses demonstrate the possibilites of a hauntological reading of colonial literature. In focusing specifically on Algeria, I show that a monolithic analytical approach to colonial haunting would be impossible, because the people and places damaged by French imperialism had disparate realities. For example, in colonial literature about Morocco, different haunted presences might emerge, because the processes of colonization under Hubert Lyautey and other architects of the French Protectorate had an alternate approach to colonial rule than in Algeria. French literature set in other regions colonized by the French would express yet other shadows.
As we linger on these close readings, it is crucial to remark upon the specter haunting the present book. This haunting is the question of gender. It is not accidental that the narratives I have analyzed contain a corpus of women's destroyed bodies. Gautier's dancer Ayscha is murdered by bandits for her jewels, Fromentin lingers on a chilling description of dismembered Naylette dancers, Fatma and Meriem. Given as a prize in the Carthaginian wars, Flaubert's priestess Salammbô dies of shock at the novel's end, and Loti's three women of Algiers, Kadidja, Fatmah, and Fizah, are infected with the eventually disfiguring, fatal disease of syphilis. The violence in these narratives is undeniably gendered. It is women's bodies—and particularly those of women involved in prostitution—that are consistently attacked, mutilated, or debauched, all of which represents Algeria as a feminine space of pillage and destruction. Pathetic, agonizing, or rent apart, their bodies have felt the most pain. Physical testaments to colonial violence, these vanished women haunt the author-witnesses, who in turn write their stories that haunt their readers, who bear witness to this violence..
As Derridean hauntology and the rich scholarship it has produced has shown, literature can be a space of ethical engagement and open up new understandings about the intersections of memory, history, and culture. This critical hauntography of Orientalist literature demonstrates the ways in which the former French empire was haunted; just as importantly, it works toward a fuller comprehension of expressions of both colonialism and postcolonialism. The specter with its temporal fluidity—neither fully in the past nor in the present—collapses the boundaries of colonial and postcolonial, colonizer and colonized, margin and center, France and Algeria. A haunted colonialism that emerges within the works of canonical French authors creates the possibility of a more complex, interrelational approach to examining and understanding trans-Mediterranean literature from the colonial era and afterward.
If, as Keta H. Katrak argues, "[s]ocial responsibility must be the basis of theorizing any postcolonial literature," there is a compelling need for more studies of postcolonial and—as I argue in this book—colonial literature, which focuses specifically on haunted presences of colonial violence.14 As Derrida indicated, in the interests of justice, our respectful encounter with spectral otherness is necessary in order to learn how to live with ghosts.15 Far from dormant, the revenants of the colonial period now bear upon the inextricable tangle of France's contemporary xenophobia and its violent past. As a demonstration of how these authors' troubled representations of the emerging French colony expose the ghosts of imperialism, this book points to the ethical imperative of dismantling the notion of a totalizing French republican identity. Even though colonial violence was supposedly over and done with after the years of occupation, histories of dispossession and exploitation continually reemerge. As this book has demonstrated, disturbing legacies of empire lie just under the surface. Because the past always haunts the present, new understandings of France's colonial period in Algeria are central to reshaping the present and future of both countries.
NOTES
1. Benjamin Stora, La guerre des mémoires: la France face à son passé colonial (entretiens avec Thierry Leclère) (La Tour d'Aigues: Éditions de l'Aube, 2007), 108.
2. "France Presidential Hopeful Macron Describes Colonisation of Algeria as a Crime Against Humanity," www.france24.com. February 2, 2016. http://www.france24.com/en/20170216-france-presidential-hopeful-macron-describes-colonisation-algeria-crime-against-humanity. Accessed September 22, 2017.
3. Barthélémy Gaillard, "France: pour François Fillon, la colonisation s'apparente à un "partage de la culture," jeunafrique.com, <http://www.jeuneafrique.com/353496/societe/france-francois-fillon-colonisation-sapparente-a-partage-de-culture/>. Accessed January 12, 2017.
4. Henry Samuel, "Nicolas Sarkozy says Immigrants Must Accept 'Your Ancestors are the Gauls.'" www.telegraph.co.uk/. September 20, 2016. http://www.telegraph.co.uk/news/2016/09/20/nicolas-sarkozy-says-immigrants-should-live-like-the-french/. Accessed January 12, 2017.
5. An emblematic example of this is in France's cinematic history: films about the Algerian War were officially banned in France in the immediate aftermath of independence. The most important example of this censorship is Gillo Pontecorvo's controversial film The Battle of Algiers, banned in France and England from its release in 1966 until 1971.
6. Article 4 of the law states: "University research programs [will] accord to the history of the French presence overseas, notably in North Africa, the place that it deserves. School curricula [will] recognize, in particular, the positive role of the French presence overseas, notably in North Africa, and [will] accord the history and the sacrifices of the soldiers of the French Army who came from these territories the eminent place to which they have a right," quoted in Robert Aldrich, "Colonial Past, Post-Colonial Present: History Wars French Style," History Australia 1 (2006): 14.1–14.10.
7. Ironically, the law that was proposed had come just a few months before the suburbs of France's major cities, largely populated with immigrant communities predominately of Maghrebi and Sub-Saharan African origin, exploded in violence, with youths burning over 10,000 cars and 200 public buildings over a period of several weeks.
8. Kristin Ross, Fast Cars, Clean Bodies: Decolonization and the Reordering of French Culture (Cambridge, MA: MIT Press, 1996), 9.
9. Ibid.
10. Ibid.
11. In an effort toward this national remembering, France's "Djazaïr, une Année de l'Algérie en France" in 2003 [Djazaïr, Year of Algeria in France] marked forty years of Algeria's independence from French rule. For an excellent article on the "Année de l'Algérie," see Lisa Weiss, "Une Année de l'Algérie en France: Paris National Spaces Redefined," French Review 83, no. 6 (May 2010): 1322–1331.
12. Laura Hein and Mark Selden, Censoring History: Citizenship and Memory in Japan, Germany, and the United States (London: M. E. Sharpe, 2000).
13. Assia Djebar, 68/55, 19/7.
14. Ketu H. Katrak, "Decolonizing Culture: Toward a Theory for Postcolonial Women's Texts." Modern Fiction Studies 35, no. 1 (Spring 1989): 157–79.
15. Jacques Derrida, Specters of Marx: The State of the Debt, the Work of Mourning, and the New International, trans. Peggy Kamuf (London: Routledge, 1993), 175.
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Index
Abdelkader El Djezairi, , , ,
Abraham, Nicholas, , –, 17n18, 18n19
Adam, Juliette,
Ahasvérus (Quinet),
Aissoua, –,
Algeria: Aissoua, –, ; apology to, ; architecture of, , , ; Flaubert's travels in, , ; Fromentin's travels in, –, –, 64n44; Gautier's travels in; , , –; historical context, –, –; Loti's travels in, , –; military conquest of, , , ; Millésimo, . See also French colonialism; French army; Laghouat
allegory, , , 88n2
L'Amour, la fantasia (Djebar), –, , 66n82,
Une année dans le Sahel (Fromentin), , , ,
anti-conquest concept,
apparitions, 16n7, 17n16, , .
See also ghosts; phantoms; specters
Apter, Emily,
Armbrecht, Thomas J. D., 110n15
L'Artiste (journal), ,
Ayscha, –, –
Aziyadé (Loti), , , 109n3
Balzac, Honoré de, , 20n60,
Barail, François Claude du,
barbarianism, –
Barca, Hamilcar, ,
Barclay, Fiona, , ,
Bataillard, Paul, ,
Behdad, Ali, , ,
Bell, Dorian,
Bhabha, Homi, ,
Blossom, Frederick,
Bongie, Christopher, ,
Bourguignon d'Herbigny, Pierre-François-Xavier,
Brahimi, Denise, –
Bugeaud, Thomas, , –
burials, , –
Buse, Peter, –, 17n14
Butler, Judith,
Carthage: discovery of, 88n11; exoticism in, –; Flaubert's travels in, , –; portrayed in Salammbô, –, , 87n1
Caruth, Cathy, –
Casbah, Loti's characterization of, –
censorship, 117n5
Chambers, Ross,
Charles X, , ,
Chirac, Jacques,
Christin, Anne-Marie,
civilization, –
Cler, Jean-Joseph-Gustave,
Colet, Louise, ,
colonialism. See French colonialism
Les Colonies des anciens comparées à celles des modernes (Sismondi), ,
La Comédie humaine (Balzac), , 20n60
Conklin, Alice,
Conrad, Joseph,
Couture, Thomas,
Culbert, John,
Culture and Imperialism (Said),
dances, , , –
Davis, Colin, , ,
Davis, Nathan,
dehumanization, , , .
See also violence
Derrida, Jacques, , –
Description de l'Égypte (Fourier),
Djebar, Assia, –, 66n82, 111n44,
djinns, –
"Les Djinns" (Hugo),
Du Camp, Maxime,
Du Déclin de la France et de l'égarement de sa politique (Bourguignon d'Herbigny),
Dunwoodie, Peter, , , 110n18
Durr, Volker, 88n2
Duvivier, Julien, 111n33
L'Ecorce et le noyeau (Abraham and Torok), –, 17n18, 18n19
1840 moment, –
Essai sur les Fables de La Fontaine (Taine),
Essai sur l'exotisme (Segalen), 19n27, 19n29
Un été dans le Sahara (Fromentin), , –, , –, 64n27
exoticism: in Carthage, –; Gautier on, , , ; Loti on, , , , 109n10; portrayed in Salammbô, , ; representations of, ; trend of, ; value of, 19n29.
See also Orientalism
Fantasia (Djebar), –, , 66n82,
Fast Cars, Clean Bodies (Ross),
feminization of haunting, –.
See also haunting
Le Figaro (Loti),
Fillon, François,
films, 111n33, 117n5
The Fire (Fromentin), 65n74
Flaubert, Gustave: on barbarism and civilization, –; on Carthage, –; criticisms of, –, –; Madame Bovary, , ; Smarrh, ; on social hierarchy, ; theme of decadence, –; travel to Algeria, , ; travel to Carthage, , –; works of, –.
See also Salammbô (Flaubert)
Fleurs d'ennui (Loti), , , , , –,
Foucault, Michel,
Fourier, Jean-Baptiste-Joseph,
French army: attack on Laghouat, –, ; battles with indigenous populations, , , ; conquest of Algeria, , , ; Fromentin's travels with, –, ; massacres by, , –, , ; soldiers and soldier's deaths, , –, , , 65n71, , 117n6.
See also specific military leaders
French colonialism, –; anti-colonial messages, –, –; Flaubert on, –; Fromentin on the human costs of, –; island territories, ; law on history of, 117nn6–7; reflections on, –; repercussions of, –, .
See also Algeria
French literature: exoticism in, , , ; phantoms in, , , 18n19, ; specters in, –; trauma in, –.
See also specific works and writers
Fromentin, Eugène, –; Une année dans le Sahel, , , , ; blindness of, ; on depictions of the human costs of colonialism, –; Un été dans le Sahara, , –, , –, 64n27; haunting of, –; L'Incendie, 65n74; itinerary of, 64n44; on massacre, ; observations of, –; Oeuvres complètes, ; Rue à El-Aghouat, ; travels with French army, –, –; travel to Algeria, –, –, 64n44
furia francese, –
Gautier, Théophile, –; on Aissoua, –; dance by, ; descriptions of ghosts, –; on djinns, –; emphasis on supernatural, , –, –, ; on exoticism, , , ; haunting of, –, –; La Juive de Constantine, 38n9; Mademoiselle de Maupin, ; Une nuit de Cléopâtre, ; 1002 Nuits, ; L'Orient, ; on Parisian culture, , ; Le pied de momie, ; poetry by, ; travel to Algeria, , , –; use of specters, –, –; Voyage pittoresque en Algérie, , , –, –, –, –; writings in supernatural genre, 39n29
Gérard de Nerval, ,
Ghostly Matters (Gordon),
ghosts, 16n7, 17n14, –.
See also apparitions; haunting; phantoms; specters
Girardin, Saint-Marc,
Goncourt, Edmond and Jules, , ,
Gordon, Avery, , ,
graves, , –
Green, Anne,
Guizot, François, –
Hanno, –
Hargreaves, Alec,
Hartmann, Elmwood,
Haunted Subjects (Davis),
Haunted Voyages (Porter), 18n24
hauntings: feminization of, –; and postcolonial thought, 19n39; symbolism, –; as term, 17n16.
See also apparitions; ghosts; phantoms; specters; trauma
hauntography, critical, –,
hauntology, , –, –
Heart of Darkness (Conrad),
Hein, Laura, –
Henry, Jean-Robert,
Hetzel, Pierre-Jules, –
Hiddleston, Jane, 111n33
Hughes, Edward,
Hugo, Victor, ,
Humphrey, Michael, –,
L'Incendie (Fromentin), 65n74
insistence, 16n10,
Jameson, Fredric,
Le journal officiel (periodical),
La Juive de Constantine (Gautier), , 38n9
Julien, Charles-André, ,
Katrak, Keta H.,
The Kernel and the Shell (Abraham and Torok), –, 17n18, 18n19
Laghouat: attack on, –, ; Fromentin's travel to, –.
See also Algeria
Laurent, Franck,
Leclère, Thierry,
Leroyer de Chantepie, Marie-Sophie
Loti, Pierre, –; anti-colonial messages, –, –; Aziyadé, , , 109n3; biographical sketch of, –; characterization of the Casbah, –; criticisms of, , –; on exoticism, , , , 109n10; Le Figaro, ; Fleurs d'ennui, , , , , –, ; Mariage de Loti, , 110n24; Au Maroc, ; on massacre, ; morality messages of, –, –; "La Naïl," , ; on specters, , ; "Suleïma," , , ; travel to Algeria, , –; Les Trois dames de la Kasbah, , –, –, , –; works of, , –, –, 110n24
Lowe, Lisa,
Luckhurst, Roger,
Lukács, Georg, 87n1
Lyautey, Hubert,
Macron, Emmanuel,
Madame Bovary (Flaubert), ,
Mademoiselle de Maupin (Gautier),
Au Maroc (Loti),
Mariage de Loti (Loti), , 110n24
Marx, Karl,
massacres: by the French army, , –, , ; Fromentin's on, –; Loti's on ; use of term, –.
See also trauma; violence
Memmi, Albert,
Miles, Richard,
military conquest. See French army
Millésimo,
Millward, Keith, –
Le moniteur universel (periodical), ,
Montagnac, Lucien-François de, –
Morocco, , ,
"La Naïl" (Loti), ,
Napoleon Bonaparte, –, , , 88n2.
See also French army
Le National (newspaper),
Nochlin, Linda,
Nodier, Charles,
Une nuit de Cléopâtre (Gautier),
Oeuvres complètes (Fromentin),
On France's Decline and Confusion in its Politics (Bourguignon d'Herbigny),
1002 Nuits
L'Orient (Gautier),
Orientalism: character of, –; Gautier's writings on, –; Orientalist painting, 17n15, , ; study of, –.
See also exoticism
Orientalism (Said), ,
Les Orientales (Hugo),
O'Riley, Michael, , 17n16, 19n39
Ouled-Riah tribe,
Ozanam, Frédéric,
paintings, , 17n15, , ,
Paris: architecture of, , ; culture and decadence of, , , –; Gautier in, –; salons, ,
Peau de chagrin (Balzac),
Pélissier, Jean-Jacques, , , –
Pelletan, Eugène,
Pépé le Moko (film by Duvivier), 111n33
phantoms: in French literature, , 18n19, ; Loti's on, –; and past traumas, –; as term, 16n7.
See also apparitions; ghosts; haunting; specters
Pichat, Léon-Laurent,
Le pied de momie (Gautier),
Picturesque Journey in Algeria (Gautier), , , –, –, –, –
Plumkett, 109n3.
See also Loti, Pierre
Porch, Douglas, –
Porter, Dennis, 18n24
Portrait du colonisé, précédé du portrait du colonisateur (Memmi),
Postcolonial Haunting and Victimization (O'Riley),
Pratt, Mary Louise,
La Presse (newspaper), , , ,
psychoanalytic theory and practice, –, 18n19
Quella-Villéger, Alain, , ,
Quinet, Edgar, ,
racism,
Rand, Nicholas, –
Randon, Jacques-Louis,
La Revue des Deux Mondes (periodical), , , ,
La Revue de Paris (periodical), , ,
Rice, Mary, 88n2
Les Romains de la décadence (Couture),
Ross, Kristin,
Rue à El-Aghouat (Fromentin),
Said, Edward W., , , ,
Sainte-Beuve, Charles Augustin, , , –, , 87n1
Saint Vitus' dance, , 40n42
Salammbô (Flaubert), –; barbarianism and civilization in, –; exoticism in, , ; literary context, , –; literary criticism of, , 88n2; portrayal of Carthage, –, , 87n1.
See also Flaubert, Gustave
Sarkozy, Nicolas,
Schehr, Lawrence,
Segalen, Victor, 19n27, 19n29
Le Sélam (Gautier),
Selden, Mark, –
Sessions, Jennifer, –,
Sismondi, Léonard de, ,
Smarra ou les démons de la nuit (Nodier),
Smarrh (Flaubert),
specters: figure of, –; in French literature, –; Gautier's use of, –, –; Loti on, , ; racist, ; as term, , 16n7, 17n16.
See also apparitions; ghosts; haunting; phantoms
Specters of Marx (Derrida), ,
Stora, Benjamin, ,
"Suleïma" (Loti), , ,
A Summer in the Sahara (Fromentin), , –, , –, 64n27
supernatural, Gautier's writings on, , –, –, , 39n29.
See also ghosts; haunting; specters
syphilis, , –, 109n6
Taine, Hippolyte,
Thompson, Christopher,
Thompson, Victoria,
The Three Ladies of the Casbah (Loti), , –, –, , –.
See also Loti, Pierre
Todorov, Tzvetan, 39n29, –
Torok, Maria, , –, 17n18, 18n19
trauma: experience of, –; in French literature, –, –, 19n39; and phantoms, –; transgenerational, ; violent, , .
See also haunting; massacres
travelogue genre, –
Les Trois dames de la Kasbah (Loti), , –, –, , –.
See also Loti, Pierre
Valée, Sylvain Charles,
violence, , .
See also dehumanization; massacres; trauma
Voyage pittoresque en Algérie (Gautier), , , –, –, –, –
Wright, Barbara,
Writing Postcolonial France (Barclay), , ,
Yacine, Kateb,
A Year in the Sahel (Fromentin), , , ,
Yee, Jennifer, ,
Žižek, Slavoj, 16n10, 17n11,
Zouaves, , –, , , 65n71.
See also French army
About the Author
Sage Goellner is assistant professor of French at the University of Wisconsin–Madison. She has published articles on Colette, Eberhardt, and Fromentin. Her areas of research are nineteenth-century French literature, colonialism, Orientalism, and women authors.
1. Cover
2. Half-Title
3. Series
4. Title
5. Dedication
6. Copyright
7. Contents
8. Introduction
9. 1 Subjectivity Undone
10. 2 The Unsettled
11. 3 Battlefields and Barbarians
12. 4 Le Mal de la Kasbah
13. Afterword
14. Bibliography
15. Index
16. About the Author
| {
"redpajama_set_name": "RedPajamaBook"
} | 3,964 |
Q: IRC Protocol - Registration to Server with Password I'm trying to write a Python IRC script. It is not connecting to my UnrealIRCD server, so I tried it with TELNET:
telnet xx.xx.xx.xx 6667
Trying xx.xx.xx.xx...
Connected to xx.xx.xx.xx.
Escape character is '^]'.
PASS MYSERVERPASS
NICK MYNICKNAME
PING :7EF7F35D
USER MyUserName 8 * :MY REALNAME
After this connection, it doesn't accept the registration and times out. When I try to connect via telnet to an EFnet server, for instance, this process works fine.
So, does anyone have an idea what is wrong with the registration process?
Other clients and Eggdrop Bots can connect to the server with no problem. So I don't understand why these simple protocol commands are not working.
A: I assume this message was sent by the server:
PING :7EF7F35D
You have to reply to it, with this message:
PONG :7EF7F35D
(change the payload of the PONG to match the one in the PING)
This is probably required by the server to avoid attacks.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 360 |
<?php
namespace HHIT\Doctrine\Fixtures\Contracts;
interface ORMFixtureLogger
{
/**
* @param $message
*/
public function log($message);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,167 |
Der Polaroid Typ 55 ist ein von der Firma Polaroid bis 2008 produzierter Schwarzweiß-Sofortbildfilm im Format 4X5 Zoll. Er liefert direkt sowohl ein Positiv als auch ein Negativ.
Allgemeines
Der Planfilm Typ 55 (offiziell Polapan Pro 55) wurde bis zum Jahre 2008 von der amerikanischen Firma Polaroid hergestellt und vertrieben. Da die Produktion im Jahre 2008 eingestellt wurde, sind heute nur noch Restbestände auf dem Markt, die immer schwerer zu beziehen sind.
Bei Fotografen ist er vor allen Dingen für seine hervorragende Detailzeichnung, das aus der sehr niedrigen Filmempfindlichkeit resultierende feine Korn, und nicht zuletzt aufgrund des charakteristischen, von Bild zu Bild verschiedenen Randes sehr beliebt.
Dieser Rand entsteht rund um das eigentliche Bild, wo die Positiv- und die Negativschicht, die direkt nach der Belichtung auseinandergezogen werden, miteinander verklebt sind. Eigentlich sollte dieser bei der Ausbelichtung beschnitten werden, was viele Fotografen jedoch absichtlich unterlassen, um ihren Bildern eine weitere, grafische Komponente zu verleihen. Aus diesen Gründen nutzten ihn viele namhafte Fotografen wie z. B. Ansel Adams oder Christopher Thomas.
Gelegentlich wird dieser Effekt auch mithilfe eines Bildbearbeitungs-Programmes digital zu Fotos hinzugefügt.
Technik
Der Typ 55 war im Großformat von 4 × 5 Zoll erhältlich und hat eine Empfindlichkeit von ISO 50
Die Größe des Bildfeldes (ohne den o. g. Rand) beträgt 9 × 11,4 cm.
Das entstehende Positiv muss direkt nach der Aufnahme lackiert werden, während das zur Ausbelichtung benötigte Negativ in Natriumsulfitlösung geklärt werden muss.
Sowohl Positiv als auch Negativ sind aufgrund der im Vergleich mit anderen Filmen sehr weichen Emulsion äußerst anfällig für Kratzer.
Zukunft
Das Projekt New55 FILM ist Eingriff in die Entwicklung einer neuen Version des Typs 55 Positiv-Negativ-4x5 Sofortbildfilm.
Siehe auch
Schwarzweißfilm
Schwarzweißfotografie
Planfilm
Großformat (Fotografie)
Weblinks
http://new55project.blogspot.com/2010/01/new-55-project-commences.html - Englischsprachiger Blog des New 55 Projects
http://www.the-impossible-project.com - Englischsprachige Seite des Impossible Projects, heutzutage Polaroid Originals
Quellen und Einzelnachweise
Filmtyp | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 291 |
Puerto Rican Heritage Cultural Ambassador Program Discussion Series : Music
The Puerto Rican Heritage Cultural Ambassador Program Presents:
Screening of Puerto Rican Voices film shorts and discussion with folklorist Elena Martine
Join us for a conversation with Elena Martinez, folklorist for CityLore. Elena will discuss the vast contributions of Puerto Ricans to the musical landscape of the United States and beyond. She will discuss the role of music in the migration experience, including evolving identities, and the ways in which musical traditions, like bomba, have been maintained in diaspora communities. Three segments from Centro's award-winning Puerto Rican Voices television series will be screened:
Semilla Cultural - Runtime 8:08
Semilla Cultural is a non-profit organization developing and cultivating a community that embraces Puerto Rican culture and arts in the Washington DC, Maryland and Virginia region.
Eguie Castrillo, Celebrated Percussionist and Associate Professor at Berklee College of Music, Boston, MA – Runtime: 8:42
Eguie Castrillo performed with Tito Puente, Steve Winwood, Michael Brecker, Ruben Blades, United Nation Orchestra, Paquito D'Rivera, Michel Camilo, KC and the Sunshine Band, Dave Valentin, and Giovanni Hidalgo. He toured with the Arturo Sandoval Band; recordings include Hot House with Arturo Sandoval, The Latin Train with Arturo Sandoval, soundtrack for The Perez Family for MGM, Get Down Live! with KC and the Sunshine Band, and A GRP Celebration of the Songs of the Beatles.
Miguel Zenón, Multiple Grammy Nominee - Runtime: 9:01
Widely considered as one of the most groundbreaking and influential saxophonists of his generation, he has also developed a unique voice as a composer and as a conceptualist, concentrating his efforts on perfecting a fine mix between Latin American Folkloric Music and Jazz.
Elena Martinez
About Elena Martinez
Elena Martínez is the Co-Artistic Director of the Bronx Music Heritage Center and a Folklorist at City Lore. Her work at City Lore has included getting Casa Amadeo (the longest continually-run Latin music store in NYC) nominated to the National Register of Historic Places (the first nomination relating to the Puerto Rican experience on the mainland); and nominated master Puerto Rican lacemaker (the art of mundillo) Rosa Elena Egipciaco for a NEA National Heritage Award. <More>
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Migdalia Gonzalez rsvped +1 2021-05-03 13:01:01 -0400 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,072 |
Q: Laravel Lumen in Docker ClassLoader Exception I installed a fresh Lumen in my docker container. Next I wanted to use eloquent so I activated it and it worked with some tests.
My problem now is if I want to get some Information about the model I've created, most of the times I get an error from the ClassLoader:
"include(/var/www/html/app/Models/Group.php): Failed to open stream: No such file or directory"
The file is obviously there, if I start the request again 1-2 / 10 times it worked. Finds the class and loads all things.
The Model itself has no special stuff in it, just an empty class.
<?php
namespace App\Models;
use Illuminate\Database\Eloquent\Model;
class Group extends Model
{
}
In my controller I'm using the model like this:
<?php
use Illuminate\Http\JsonResponse;
use Illuminate\Http\Request;
use App\Models\Group;
class TestController extends Controller
{
public function getGroups(Request $request): JsonResponse
{
return response()->json(['groups' => Group::all()]);
}
}
It looks like it has something to do with docker?
Hope someone can help.
Thanks in advance!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,250 |
{"url":"https:\/\/codegolf.stackexchange.com\/questions\/25319\/which-is-better-emacs-or-vim-google-fight\/77124#77124","text":"# Which is better - Emacs or Vim? (Google fight)\n\nGreetings, noble code golfers. Today you will resolve the most ancient and distinguished of debates - Emacs or Vim?\n\nYour challenge is to take two search terms as input, and output which of those terms has the most Google search results. (This is obviously completely fair. What do you mean, biased?)\n\nHere are some example inputs and outputs:\n\nInput: emacs and vim\nOutput: vim (totally not creating any flamewars in the comments)\n\nInput: google and microsoft\nOutput: google\n\nInput: code golf stack exchange and code review stack exchange\nOutput: code golf stack exchange (yeah!)\n\nAnd here are some edge cases just for fun (and for testing your solutions):\n\nInput: About 1,000,000 results and About 100,000 results\nOutput: About 100,000 results\n\nInput: This will autocotrect and Another testcase\nOutput: Another testcase (if you don't consider autocorrecting, then the first one will win)\n\nFor the following test cases, you must remove the # signs in the search terms first, since they rely on the term having a specific amount of results and posting the term here would ruin that.\n\nInput: Thissear#chter#mhasno#results and Another testcase\nOutput: Another testcase (just a test for zero results)\n\nInput: \"These exact wo#rds do#n't exi#st# on the Internet\" and Another testcase\nOutput: Another testcase (testing \"s)\n\nInput: Abo#ut 1,65#2,85#3,2#86 re#sults and Another testcase\nOutput: Another testcase (this one is tricky - the above search term has one result)\n\nInput: \"Abo#ut 4#8,234,8#75,14#7 res#ults\" and Another testcase\nOutput: Another testcase (also tricky - no results, so it displays the search term)\n\nYou don't need to handle the corner-case of \"quoted\" searches returning \"No results, showing results without quotes instead\" because that would just be too complicated. You don't need to handle inputs with the same number of results either.\n\nThis is , so the shortest code in bytes will win!\n\n\u2022 Psst... you should change the accepted answer :D\n\u2013\u00a0cat\nMar 29 '16 at 21:11\n\u2022 @tac Alternatively, I can golf it down instead, which I did. ;)\n\u2013\u00a0Doorknob\nMar 29 '16 at 23:12\n\u2022 How flexible's the output \/ return value? Does it have to be a string, or can it be an array containing the string and the number of results it had, or an array containing just the string?\n\u2013\u00a0cat\nMar 30 '16 at 13:24\n\u2022 it's so clear than vim is better I was surprised on this question that anyone could believe that something is better Apr 3 '16 at 0:14\n\n# Ruby, 203 180 bytes\n\n->*s{s.map{|x|[(open(\"http:\/\/www.google.com\/search?nord=1&q=#{URI.escape x}&nfpr=1\").read.match(\/s\">(About )?([\\d,]+) result\/)||[?0])[-1].split(?,).join.to_i,x]}.max[1]}\n\n\n+11 bytes for the -ropen-uri flag (plus space).\n\nInput is taken as two arguments.\n\nURL explanation:\n\n\u2022 ?nord=1: prevent auto-redirect from HTTP to HTTPS\n\u2022 &q=#{URI.escape x}: escape the query so \"s work\n\u2022 &nfpr=1: no autocorrect\n\nThe whole map turns ['emacs','vim'] into [[2150000, 'emacs'], [14900000, 'vim']]. (You can see this by changing the .max[1] at the end to .inspect.) Then, the max is taken, which will grab the one with the most results, and [1] is used to get the search term.\n\n\u2022 It doesn't work for me. ideone.com\/UqEyBn Apr 8 '14 at 17:05\n\u2022 @TheDoc It doesn't work on Ideone - run it on actual Ruby\n\u2013\u00a0Doorknob\nApr 8 '14 at 17:09\n\u2022 You can save a few more bytes by requiring in the command ruby -ropen-uri instead of in the file. Mar 26 '16 at 0:01\n\u2022 Why won't this (and the other regex answers) break on searches like \"About 100,000,000 results\"?\n\u2013\u00a0cat\nApr 2 '16 at 23:26\n\u2022 @cat Note the s\"> at the start of the regex. That makes sure the result count is preceded by a certain HTML tag (I don't remember which one; probably something like <span id=\"num-results\"> or something).\n\u2013\u00a0Doorknob\nApr 3 '16 at 14:51\n\nOf the text editors mentioned in the problem, only one of them can solve this on its own...\n\n# Emacs: 137 keystrokes\n\n<C-o><C-u><C-k>(if(<<C-y><C-y><M-<><C-n><F3><C-a>http:\/\/google.com\/search?nfpr=1&q=<C-S-e><M-x>r-st<RET> <RET>+<RET><C-a><C-k><M-x>b-em<RET><C-y><RET><C-x><C-q><C-s><RET>ts\"><RET><M-z><<C-x>0<C-y>0 r<C-a><C-M-s><RET>[0-9]<RET><C-b><M-z> <C-a><C-y><C-k><C-S-a><M-x><up><up><RET>,<RET><RET><F4><C-n><F4><C-e>)(next-line)())<C-x><C-e><C-n><C-a><C-k><C-x>h<DEL><C-y>\n\n\nIt expects the first search terms to be on the first line and the second search terms to be on the second line, with the cursor at the beginning of the buffer.\n\nFor those unfamiliar with Emacs,\n\n\u2022 C-s means Ctrl-S.\n\u2022 M-z means Alt-Z (Alt is likely your meta key)\n\u2022 M-< means Alt-< or Alt-Shift-,\n\u2022 C-S-e means Ctrl-Shift-e\n\nFor those familiar with Emacs,\n\n\u2022 Start emacs with emacs -q. That doesn't load your .emacs file, so any fancy packages won't intefere with this.\n\n## Explanation\n\n1. Write the beginning of the elisp statment shell\n\n\u2022 <C-o><C-u><C-k> Saves the arguments with a newline\n\u2022 (if(<<C-y><C-y> Write the start of the if statement and places 2 copies of the arguments\n\u2022 <M-<><C-n> Move to the second line\n2. Define the HTTP macro. This converts the argument to a Google search URL and then returns the number of search results.\n\n\u2022 <F3> Start defining the keyboard macro\n\u2022 <C-a> Move to the start of the search term.\n\u2022 http:\/\/google.com\/search?nfpr=1&q= Prepend the search URL\n\u2022 <C-S-e><M-x>r-st<RET> <RET>+<RET> Replace all the spaces with + signs.\n\u2022 <C-a><C-k><M-x>b-em<RET><C-y><RET> Emacs retrieve the raw HTML (b-em is short for browse-url-emacs)\n\u2022 <C-x><C-q> Make the file writable (required so the macro doesn't error ou t)\n\u2022 <C-s><RET>ts\"><RET> Move to the number of results div (need to do a regular search because emacs macros rely on isearch to work)\n\u2022 <M-z><Cut the text of of the diff (this is why the was required)\n\u2022 <C-x>0 Switch back to the original buffer\n\u2022 <C-y>0 r;; Put the results back on the line ('0 r' handles no results)\n\u2022 <C-a><C-M-s><RET>[0-9]<RET><C-b><M-z> <C-a><C-y><C-k>;; Extract the number from the string.\n\u2022 <C-S-a><M-x><up><up><RET>,<RET><RET> Strips commas out of the number\n\u2022 <F4> Finish the keyboard macro\n3. Move down and execute the keyboard macro on the next line.\n\n\u2022 <C-n> Goes to the next line\n\u2022 <F4> Repeat the macro once.\n4. Finish up the elisp statement and execute it\n\n\u2022 <C-e>)(next-line)()) Finish up the elisp statement\n\u2022 <C-x><C-e> Evaluate the elisp command\n\u2022 <C-n><C-a><C-k> Kill the winning argument\n\u2022 <C-x>h<DEL> Delete everything else\n\u2022 <C-y> Paste the winning argument\n\n## Running It Yourself\n\nLuckily you don't have to type all those keystrokes in perfectly! The meat and potatoes is all in a macro that you can just copy and paste. The macro can be copy and pasted into emacs!\n\n1.Edit the keyboard macro <C-x><C-k><C-e>\n2.Paste this into the whole buffer (paste should be <C-y>)\n\n;; Keyboard Macro Editor. Press C-c C-c to finish; press C-x k RET to cancel.\n;; Original keys: C-a http:\/\/google.com\/search?nfpr= 1&q= S-C-e M-x r-st RET SPC RET + RET C-a C-k M-x b-em RET C-y RET C-x C-q C-s RET ts\"> RET M-z < C-x 0 C-y 0 SPC r C-a M-C-s [0-9] 5*DEL RET [0-9] RET C-b M-z SPC C-a C-y C-k S-C-a M-x 2*<up> RET , 2*RET\nCommand: last-kbd-macro\nKey: none\nMacro:\nC-a ;; move-beginning-of-line\n1&q= ;; self-insert-command * 4\nS-C-e\nM-x ;; execute-extended-command\nr-st ;; self-insert-command * 4\nRET ;; newline\nSPC ;; self-insert-command\nRET ;; newline\n+ ;; self-insert-command\nRET ;; newline\nC-a ;; move-beginning-of-line\nC-k ;; kill-line\nM-x ;; execute-extended-command\nb-em ;; self-insert-command * 4\nRET ;; newline\nC-y ;; yank\nRET ;; newline\nC-s ;; isearch-forward\nRET ;; newline\nts\"> ;; self-insert-command * 4\nRET ;; newline\nM-z ;; zap-to-char\n< ;; self-insert-command\nC-x 0 ;; delete-window\nC-y ;; yank\n0 ;; self-insert-command\nSPC ;; self-insert-command\nr ;; self-insert-command\nC-a ;; move-beginning-of-line\nM-C-s ;; isearch-forward-regexp\nRET ;; newline\n[0-9] ;; self-insert-command * 5\nRET ;; newline\nC-b ;; backward-char\nM-z ;; zap-to-char\nSPC ;; self-insert-command\nC-a ;; move-beginning-of-line\nC-y ;; yank\nC-k ;; kill-line\nS-C-a\nM-x ;; execute-extended-command\n2*<up> ;; previous-line\nRET ;; newline\n, ;; self-insert-command\n2*RET ;; newline\n\n1. Type <C-c><C-c> to save the macro.\n2. If following the explanation steps, replace step 2 with <F4> to run the macro (or just run it on its own to try)\n\n## Caveats\n\n1. You can't run the macro on the same search twice without killing the buffer the HTML gets loaded into. Kill the buffers\n\u2022 <C-x><k> search<TAB>\n\u2022 Choose one of the buffers in this list to kill.\n\u2022 Repeat for all the buffers beginning with \"search\"\n2. If you run the macro too much, Google will think you are a robot and block access for atime\n\u2022 If the macro returns something like <input type=\"submit\" name=\"submit\" value=\"Submit\"...>, then this likely occurred.\n\u2022 You can confirm it by looking at the raw HTML (<C-x><C-b> and choose the buffer with the search term in it).\n\u2022 This is really cool! Of the text editors mentioned in the problem, only one of them can solve this on its own... is that even true? are there really no HTTP libraries for vimscript?\n\u2013\u00a0cat\nJun 21 '17 at 22:36\n\u2022 There's at least nothing in vanilla vim, but brief googling didn't pop up any vimscript HTTP libraries. I can't imagine why anyone would actually write that when you could just read the results of curl and get the same effect. (but then your answer should indicate that it's vim+curl). Jun 24 '17 at 11:40\n\n# Factor, 305201196200201188184182179169178171165199171170165 163 bytes\n\nA language nearly as verbose as Java, beating Ruby... and Powershell! :D\n\nBetter regex, now. Thanks to @fede s. for 5 bytes off!\n\n[ dup [ url-encode \"google.com\/search?nfpr=1&q=\"prepend http-get R\/ s\">About [\\d,]+\/ first-match \" \"split second 10 >base ] map zip [ last ] sort-with last first ]\n\n\nOr 159 157 if the output can be like { \"vim\" 9782948234 }:\n\n[ dup [ url-encode \"google.com\/search?nfpr=1&q=\"prepend http-get R\/ s\">About [\\d,]+\/ first-match \" \"split second 10 >base ] map zip [ last ] sort-with last ]\n\n\nOn the other hand, if we want to be unkillable, for 199 196 193 bytes:\n\n[ dup [ url-encode \"google.com\/search?nfpr=1&q=\"prepend scrape-html nip dup \"resultStats\"find-by-id-between second text>> \" \"split second string>number ] map zip [ last ] sort-with last first ]\n\n\nUnkillable because it parses HTML, so way more robust than the answers using regex.\n\n\u2022 And python. Good for Factor. :P Mar 29 '16 at 21:13\n\u2022 @EasterlyIrk so close yet so far\n\u2013\u00a0cat\nMar 30 '16 at 13:07\n\u2022 @EasterlyIrk I did it!\n\u2013\u00a0cat\nMar 30 '16 at 13:20\n\u2022 Someone should make a Factor golfing dialect, so much whitespace, words so long... Well done, man! Apr 3 '16 at 1:57\n\u2022 Thank you for the unkillable method. It's actually shorter in powershell than using a regex. (Yet still 2 bytes longer than your regex answer). I wouldn't call powershell succint though, it's command names are rarely short (iwr happens to be a default alias for invoke-webrequest and sort for sort-object, otherwise it'd be that much longer) Apr 6 '16 at 20:06\n\n# Java, 828800783744739 687 bytes\n\nimport java.net.*;import java.util.*;import java.util.regex.*;interface G{static Scanner s(String a)throws Exception{URL u=new URL(\"http:\/\/google.com\/search?q=\"+a);HttpURLConnection c=(HttpURLConnection)u.openConnection();c.addRequestProperty(\"User-Agent\",\"Mozilla\/4.0\");return new Scanner(c.getInputStream());}static void main(String[]r)throws Exception{String a,b;String c=s(a=r[0]).useDelimiter(\"\\\\Z\").next(),d=s(b=r[1]).useDelimiter(\"\\\\Z\").next();Matcher m=Pattern.compile(\"ut ([0-9,]+) res\").matcher(c);m.find();long i=new Scanner(m.group(1)).nextLong();m=Pattern.compile(\"ut ([0-9,]+) res\").matcher(d);m.find();long j=new Scanner(m.group(1)).nextLong();System.out.print(i>j?a:b);}}\n\n\u2022 Holy cats. The imports alone are 79 bytes... perhaps you should try Groovy? :P\n\u2013\u00a0cat\nMar 30 '16 at 2:01\n\u2022 I'm really entertained by the fact you have to set the user-agent string yourself. Like, as if Java wasn't verbose enough\n\u2013\u00a0cat\nMar 30 '16 at 2:02\n\u2022 Because google gives a 403 if you don't. Mar 30 '16 at 2:03\n\u2022 Why not take input from args instead of StdIn? Feb 8 '17 at 21:09\n\n# Python 3, 227226208213226220221206202200 198 bytes\n\nimport re,requests as r,urllib.parse as u\n\n\nAssign the lambda to something to call it.\n\nUses the requests library.\n\nUngolfed:\n\nimport re, requests as r, urllib.parse as u\nlambda*t:\nsorted(\nlist(\nzip(map(\nt\n),\nt)\n)\n)[-1][1]\n\n\u2022 This doesn't work on my machine even after installing requests: NameError: name 'quote' is not defined Mar 26 '16 at 0:19\n\u2022 @shelvacu Oops, I'm smart, I forgot to change quote back to urllib.parse.quote after an absolute import.\n\u2013\u00a0cat\nMar 26 '16 at 0:20\n\u2022 did you test this? It also looks like google.co\/search gives 404 whereas google.com\/search works Mar 26 '16 at 0:26\n\u2022 @shelvacu yes, I tested it, it gives the same results as the ruby answer and the question says.\n\u2013\u00a0cat\nMar 26 '16 at 0:26\n\n# Powershell, 175, 172 bytes\n\n($args|%{[pscustomobject]@{'a'=$_;'b'=[int]((iwr \"google.com\/search?nord=1&q=\\$_&nfpr=1\").parsedhtml.getelementbyid('resultstats').innertext-split\" \")[1]}}|sort -des b).a[0]\n\n\nShowing the score as well as the name would cut 2 more bytes.\n\nThis uses the same unkillable feature as the 196 Byte Factor answer (Parsed HTML) and cuts down from the previous regex answer.\n\n# Racket, 360 337 bytes\n\n#lang racket(require net\/url net\/uri-codec)(\u03bb(t)(cddr(sort(map list t(map(lambda(a)(string->number(string-replace(list-ref(string-split(car(regexp-match#px\"s\\\">About [\\\\d,]+ res\"(call\/input-url(string->url(string-append\"http:\/\/google.com\/search?nfpr=1&q=\"(uri-encode a)))(curry get-pure-port)port->string)))\" \")1)\",\"\"\")))))#:key cdr <)))\n\n\n0.o\n\nThere's a reason they call it Lost In a Sea of Parentheses.\n\nUngolfed:\n\n#lang racket\n(require net\/url)\n(require net\/uri-codec)\n\n(define (open-url term)\n(call\/input-url\n(string->url (string-append \"http:\/\/\" term))\n(curry get-pure-port #:redirections 5)\nport->string))\n\n(define (get-result term)\n(string->number\n(string-replace\n(list-ref\n(string-split","date":"2021-10-17 22:28:06","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\": 0.3111831545829773, \"perplexity\": 13871.848161431803}, \"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-2021-43\/segments\/1634323585183.47\/warc\/CC-MAIN-20211017210244-20211018000244-00086.warc.gz\"}"} | null | null |
Council for Biotechnology Information, GMO Answers, CropLife: pesticide industry PR initiatives
Posted on September 2, 2020 by Stacy Malkan
The Council for Biotechnology Information (CBI) was a public relations campaign launched in April 2000 by seven leading chemical/seed companies and their trade groups to persuade the public to accept genetically engineered foods. The initiative was created in response to public concerns about the health and environmental risks of genetically engineered foods, and said its focus would be developing alliances across the food chain to promote GMO crops ("ag biotech") as beneficial.
CBI closed shop in 2019 and shifted its assets — including the marketing campaign GMO Answers, run by Ketchum PR firm — over to CropLife International, the international trade group for pesticide companies. See, Key pesticide industry propaganda group CBI closes; GMO Answers moves to CropLife, USRTK (2020)
CBI tax form: focused on third parties
CBI spent over $28 million from 2014-2019, according to tax records (see 2014, 2015, 2016, 2017, 2018) on projects promoting genetically engineered foods. As noted in its 2015 tax form, CBI had an explicit focus on developing and training third-party spokespeople – particularly academics, farmers and dieticians – to promote industry views about the benefits of GMOs.
Projects funded by CBI included GMO Answers (via Ketchum public relations firm); Academics Review, a group that claimed to be independent of industry; Biotech Literacy Project boot camps held at top universities (via Academics Review) and the Global Farmer Network.
GMO Answers/Ketchum
GMO Answers is a marketing website and public relations campaign that uses the voices of academics and others to promote genetically engineered foods and pesticides. CBI spent $14.4 million on Ketchum public relations firm between 2014-2019 to run the PR salvo, according to tax forms.
GMO Answers discloses its industry funding on its website and says it promotes the views of independent experts. However, examples have come to light that Ketchum PR scripted some of the GMO answers offered by "independent experts" (see coverage in New York Times and Forbes). GMO Answers also appears in Monsanto PR documents as partners in industry's efforts to defend glyphosate-based Roundup herbicides from cancer concerns, and to try to discredit a public interest research investigation by U.S. Right to Know to uncover hidden ties between pesticide companies and academics who promote agrichemical products.
An an example of how GMO Answers builds influence with key reporters, see reporting in Huffington Post about how Ketchum cultivated ties with Washington Post columnist Tamar Haspel. Haspel was an early promoter of GMO Answers, and later participated in CBI-funded Biotech Literacy Project messaging events. A source review of Haspel's columns conducted by USRTK found several examples of undisclosed industry sources and misleading information in her articles about pesticides.
GMO Answers was recognized as a successful spin effort in 2014 when it was shortlisted for a CLIO advertising award in the category of "Public Relations: Crisis Management & Issue Management." In a video produced for the award, Ketchum bragged that GMO Answers "nearly doubled positive media coverage of GMOs," and noted they "closely monitor the conversation" on Twitter where they "successfully balanced 80% of interactions with detractors." The video was removed after U.S. Right to Know called attention to it, but we saved it here.
Related reporting:
Food industry enlisted academics in GMO labeling war, emails show, by Eric Lipton, New York Times (2015)
Scientific American science panel may get lost in translation, Friends of the Earth (2017)
An inside look at how Monsanto, a PR firm and a reporter give readers a warped view of science, by Paul Thacker, Huffington Post (2019)
Monsanto document released in 2019 show how Monsanto partnered with GMO Answers.
When USRTK submitted FOIAs to investigate industry ties with academics, Monsanto fought back.
CBI provided $650,000 in funding to Academics Review, a nonprofit that claimed it received no corporate funding. The group was co-founded by Bruce Chassy, PhD, professor emeritus at the University of Illinois at Urbana-Champaign, and David Tribe, PhD, senior lecturer at the University of Melbourne.
Documents obtained by U.S. Right to Know revealed Academics Review was set up explicitly as a front group with the help of Monsanto executives and the company's former director of communications Jay Byrne. The group discussed using Academics Review as a vehicle to discredit critics of GMOs and agrichemicals, finding corporate contributions and hiding Monsanto's fingerprints.
Related reporting: Monsanto Fingerprints Found All Over Attack on Organic Food, by Stacy Malkan, Huffington Post (2017)
Biotech Literacy Project spin events
CBI spent over $300,000 on two "Biotech Literacy Project boot camps" held at the University of Florida in 2014 and the University of California, Davis in 2015, according to tax records. The money was routed through Academics Review, which co-organized the conferences with the Genetic Literacy Project, another group that helps Monsanto with PR projects while claiming to be independent.
The three-day boot camp events trained students, scientists and journalists in communication and lobbying techniques to promote and defend GMOs and pesticides, and had explicit political aims to stave off GMO labeling in the U.S.
Related reporting: Flacking for GMOs: How the biotech industry cultivates positive media – and discourages criticism, by Paul Thacker, The Progressive (2017)
Monsanto 'partner' groups defend Roundup
Although GMO Answers, Academics Review and Genetic Literacy Project all claimed to be independent of the influence of industry, all three groups appeared in a Monsanto PR documents as "industry partners" the company engaged in its efforts to defend glyphosate-based Roundup herbicides from cancer concerns.
Monsanto PR document discusses plans to defend Roundup from cancer concerns
Kids' coloring book for GMOs
CBI also produced a children's coloring and activity book to promote GMOs. The link for the book, and also the WhyBiotech.com website created by CBI, now redirect to a trade group for manufacturers and distributors of hemp-derived cannabinoids.
Related U.S. Right to Know posts
GMO Answers is a crisis management PR tool for GMOs and pesticides (updated 2020)
Key pesticide industry propaganda group CBI closes; GMO Answers moves to CropLife (2020)
Monsanto's campaign against U.S. Right to Know (2019)
Monsanto relied on these 'partners' to attack top cancer scientists (2019)
Academics Review: The Making of a Monsanto Front Group (2018)
Jon Entine's Genetic Literacy Project: PR Messengers for Monsanto, Bayer and the Chemical Industry (2018)
How Tamar Haspel misleads readers of the Washington Post and source review of Haspel's pesticide columns (2018)
Russia's former PR firm Ketchum runs the chemical industry's PR salvo on GMO (2015)
Food For Thought, GMOs, Pesticides Academics Review, ag biotech, Bayer, CBI, Council for Biotechnology Information, CropLife International, Genetic Literacy Project, Global Farmer Network, GMO Answers, Ketchum, Monsanto, Tamar Haspel
EPA's "scientific integrity" program lacks teeth, group alleges | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,195 |
\section{Introduction}
Much work has been done to enumerate the domino tilings of various
regions, and related the number of perfect matchings of subgraphs of $\mathbb{Z}^2$. When an exact enumeration has been elusive, or when considering more general types of regions, various aspects of the number of domino tilings have been studied. For example, in \cite{pachter}, Pachter studied
$2$-divisibility in tilings, and Cohn examined the number of domino tilings of a square under the $2$-adic metric in \cite{cohn}. It was recently shown by this author in \cite{oddity} that the parity of the number of domino tilings of a region and of a subregion will be equal under certain conditions. This parity result leads to the question of whether there may be other moduli for which the number of domino tilings of a region and of a subregion will have the same residue. This article shows that for regions with reflective symmetry, there is such a result for the modulus $4$. Several of the proofs in this article are reminiscent of those in \cite{oddity}, but the fourfold nature of this topic requires additional sophistication and technical aspects.
In \cite{propp}, Propp suggested finding a combinatorial argument for the
fact that the number of domino tilings of a $k \times 2k$ rectangle is
congruent to $1 \bmod 4$. There are analytic methods for enumerating
the domino tilings of a rectangle, such as Kasteleyn's formula (see
\cite{kasteleyn}). For example, if $a$ and $b$ are both even, this
formula states that the number of domino tilings of an $a \times b$
rectangle is
\begin{equation*}
\prod_{i=1}^{a/2} \prod_{j=1}^{b/2} \left(4\cos^2 \frac{i\pi}{a+1} + 4\cos^2 \frac{j\pi}{b+1}\right).
\end{equation*}
\noindent However, in general, the residue of this number, modulo $4$, is not easy to compute analytically, and so a combinatorial method is desirable.
This paper shows combinatorially that the residue, modulo $4$, of the
number of domino tilings of a region with reflective symmetry can be
computed by looking at the analogous residue for certain subregions.
This will, among other things, answer Propp's question by showing
inductively that the number of domino tilings of a $k \times 2k$ rectangle
is $1 \bmod 4$. This is not the first time that domino tilings for
regions with reflective symmetry have been examined. In \cite{ciucu},
Ciucu studies the number of perfect matchings of a graph with reflective
symmetry (the dual of such an object is a domino tiling of a region with
reflective symmetry), and derives a factorization theorem for this number
in the case where the axis of symmetry separates the graph. However, this
does not answer the question for the $k \times 2k$ rectangle: one symmetry
axis does not separate the graph, and the other will separate only if $k$
is odd, but the domino tilings of the subgraphs required in the
factorization theorem would themselves have to be enumerated as a separate
problem. In this paper, a region with a local property and a reflective
axis of symmetry,
whether or not it is separating, is shown to have the
same number of domino tilings, modulo $4$, as particular subregions.
This is similar to Ciucu's work, in that it considers symmetric regions,
but it is applicable in different circumstances, and describes a different
aspect of this enumeration. It should also be emphasized that besides the
symmetry and local property, no further assumptions are made about the
region.
The main terminology and notation used throughout the paper will be
introduced in Section~\ref{sec:defn}. This section will also present the
parity theorem of \cite{oddity}, which is the precursor to the main result
in this paper, and which plays a prominent role in the proof of that
result. Section~\ref{sec:4ity} consists entirely of the main result of
this article, together with its proof. The arguments in this proof are inductive and resemble those of the
aforementioned parity theorem. Finally, Section~\ref{sec:apps} discusses
a variety of applications of Theorem~\ref{thm:4ity theorem}, one of which
resolves Propp's question about the $k \times 2k$ rectangle.
\section{Definitions and notation}\label{sec:defn}
The main terminology of the paper is described here. Some of these definitions and notation can be cumbersome, however, as in \cite{oddity}, they permit the results to be as general as possible. Much of this terminology is also used in \cite{oddity}, although the class of regions considered there is broader, and hence the result is not as specialized. The primary difference between the regions considered in \cite{oddity} and the regions considered here is the additional requirement of reflective symmetry.
\begin{defn}
A \emph{region} is the dual of a finite connected induced subgraph of $\mathbb{Z}^2$.
\end{defn}
\begin{defn}
The number of domino tilings of a region $R$ is denoted $\#R$.
\end{defn}
The notation $a \stackrel{m}{=} b$ will indicate that $a \equiv b \bmod m$.
A basic lemma, which is key in the proof of the main theorem, is the following. The proof is straightforward, and thus is omitted here.
\begin{lem}\label{lem:mod4mod2}
For $r \in \mathbb{Z}$, set $r_m := r \ (\bmod \ m)$ to be an integer in
the set $[0,m-1]$. Then for all $r$,
\begin{equation*}
2r_4 \ensuremath{\stackrel{4}{=}} 2r_2.
\end{equation*}
\end{lem}
All tilings discussed in this article are domino tilings, thus the word ``domino'' may be omitted. As in \cite{oddity}, when the configuration of only part of a region is under consideration, a drawing of the region may only include this portion, while the undrawn part of the region is arbitrary. Shading is used to indicate when part of a region has been removed.
\begin{defn}
A region $R$ has an \emph{$(\{s,t\}; 1)$-corner} if there is a convex corner in $R$ where the segments bounding this corner have lengths $s$ and $t$. For $p > 1$ and $\min\{s,t\} \ge 2$, an \emph{$(\{s,t\}; p)$-corner} is a $(\{1,s\};1)$-corner, a $(\{1,t\};1)$-corner, and $p-2$ distinct $(\{1,1\};1)$-corners configured as in Figure~\ref{figure:stp}.
\end{defn}
\begin{figure}[htbp]
\centering
\input{stp.pstex_t}
\caption{An $(\{s,t\};4)$-corner.}\label{figure:stp}
\end{figure}
\begin{defn}
If the segment of length $s$ in an $(\{s,t\};p)$-corner forms an $(\{s,t'\}; p')$-corner at its other endpoint, then each of these corners is \emph{walled} at $s$.
\end{defn}
\begin{defn}
An \emph{$(\{i,j\};p)$-strip} is a subregion of $i+j+2p-3$ squares that has an $(\{i,j\};p)$-corner.
\end{defn}
The local property required for the main theorem, Theorem~\ref{thm:4ity theorem}, states that a particular subregion avoids holes in certain places. A notion of completion describes this property, made precise below. To simplify things, one could consider only regions without holes, although this would ignore a large class of regions for which the results are also true.
\begin{defn}
An $(\{s,t\};p)$-corner in a region $R$ is \emph{$2$-complete} if $2 \le \min\{s,t\}$. For $2 < i \le \min\{s,t\}$, the corner is \emph{$i$-complete} if the following conditions are met:
\begin{enumerate}
\item Let $C$ be the $(\{i,i\}; p)$-strip in the $(\{s,t\};p)$-corner. Let $x$ and $y$ be the two squares adjacent to the ends of $C$ but not along the edges forming the $(\{s,t\};p)$-corner. If either $x$ or $y$ is in $R$, then the $(\{i-1,i-1\};p)$-strip between $x$ and $y$, inclusively, all of whose squares are adjacent to $C$, must also be a subregion of $R$.
\begin{equation*}
\input{completestp.pstex_t}
\end{equation*}
\item Consider removing $C$ from $R$. This leaves some $(\{s',t'\};p)$-corner in the resulting subregion. If $2 \le i-2 \le \min\{s',t'\}$, then this corner must be $j$-complete for $j = 2, \ldots, i-2$.
\end{enumerate}
\end{defn}
To decide if an $(\{s,t\};p)$-corner is $k$-complete, the largest potential subregion of $R$ that must be examined is depicted in Figure~\ref{fig:completeness subregion}, where there are $\lceil k/2 \rceil$ strips: one $(\{k,k\};p)$-strip, one $(\{k-1,k-1\};p)$-strip, one $(\{k-3,k-3\};p)$-strip, one $(\{k-5,k-5\};p)$-strip, $\ldots$, concluding with a $(\{3,3\};p)$-strip if $k$ is even, or a $(\{2,2\};p)$-strip if $k$ is odd.
\begin{figure}[htbp]
\epsfig{file=kcomp.eps}
\caption{The largest subregion examined when determining if a
$(\{s,t\};3)$-corner is $9$-complete.} \label{fig:completeness subregion}
\end{figure}
\begin{defn}
For $2 \le k \le \min\{s,t\}$, an $(\{s,t\};p)$-corner is \emph{complete up to $k$} if that corner is $i$-complete for $i = 2, \ldots, k$.
\end{defn}
Examples of corners that are complete up to $3$ and $4$ can be found in \cite{oddity}, and are not repeated here.
The main result of \cite{oddity}, and a useful tool in the proof of the main theorem of this paper, is restated below in Theorem~\ref{thm:parity theorem}.
Throughout this article, if a region is depicted having a shaded subregion (as in equation~\eqref{eqn:2-open}), then that shading is understood to indicate a subtiling. The figures in Theorems~\ref{thm:parity theorem} and~\ref{thm:4ity theorem} depict $(\{s,t\};p)$-corners with $p=4$ to indicate the general result. When $p=1$, the figures in equation~\eqref{eqn:2-open}, for example, would each consist of a single right-angle and a shaded $(\{k,k+1\};1)$-strip (once with each orientation).
\begin{thm}[\cite{oddity}]\label{thm:parity theorem}
Suppose that a region $R$ has an $(\{s,t\};p)$-corner. For any $2 \le k \le \min\{s,t\}$, if this corner is complete up to $k$, then
\begin{equation}\label{eqn:2-open}
\# R \stackrel{2}{=} \# \hspace{.05in}
\parbox{1.5in}{\input{kk+1.pstex_t}}
+ \# \hspace{.05in}
\parbox{1.6in}{\input{k+1k.pstex_t}}.
\end{equation}
\noindent If $p = 1$, then \eqref{eqn:2-open} also holds for $k=1$. Furthermore, for any $p$, if $s \le t$, the corner is complete up to $s$, and the corner is walled at $s$, then
\begin{equation}\label{eqn:2-wall}
\# R \stackrel{2}{=} \# \hspace{.05in}
\parbox{1.5in}{\input{ss+1.pstex_t}}.
\end{equation}
\end{thm}
This paper is concerned with regions that have reflective symmetry. This added assumption is what allows for the refined understanding of $\# R$.
\begin{defn}
A region $R$ is \emph{reflective} if it has a reflective axis of symmetry.
\end{defn}
\begin{defn}
A pair of $(\{s,t\};p)$-corners in a reflective region $R$ is
a \emph{reflective pair} if the two corners are images of each other under
reflection
across the region's axis of symmetry. Moreover, when determining if a reflective pair of corners is complete up to $k$, it is further assumed that the subregions examined to determine completeness, as depicted in Figure~\ref{fig:completeness subregion}, are not overlapping. This means that the symmetry axis does not intersect any squares in the subregion depicted in Figure~\ref{fig:completeness subregion}.
\end{defn}
In all figures, reflective regions will be drawn so that the symmetry axis is vertical, and it will be depicted by a dashed line. Although the figures may suggest that the symmetry axis is parallel to one set of grid lines in the region, the exact orientation of the left and right sides of a reflective region are not restricted, unless they are shown to connect across the symmetry axis, as in equation~\eqref{eqn:k2kk}.
\begin{rem}\label{rem:reflections}
It is helpful to observe that if two regions are reflections of each other across a line, they have the same number of tilings.
\end{rem}
\section{Reflective regions, modulo 4}\label{sec:4ity}
The main result of this article resembles the parity theorem of \cite{oddity} (Theorem~\ref{thm:parity theorem} here), although the region $R$ is additionally required to be reflective and there are more subregions on the right side of the equation. Some of the ideas fundamental to the proof of Theorem~\ref{thm:4ity theorem} are similar to those in the proof of Theorem~\ref{thm:parity theorem}, which explains the necessary overlap of terminology in the previous section.
\begin{thm}\label{thm:4ity theorem}
Suppose that a region $R$ is reflective, and that $R$ has a reflective pair of $(\{s,t\};p)$-corners. For any $2 \le k \le \min\{s,t\}$, if these corners are complete up to $k$, then
\begin{equation}\label{eqn:4-open}\begin{split}
\# R \ensuremath{\stackrel{4}{=}} & \hspace{.05in} \# \hspace{.05in}
\parbox{1.9in}{\resizebox{1.9in}{!}{\input{shorthh.pstex_t}}}
+ \# \hspace{.05in}
\parbox{1.75in}{\resizebox{1.75in}{!}{\input{shortvv.pstex_t}}}\\
&+ 2 \# \hspace{.05in}
\parbox{1.9in}{\resizebox{1.9in}{!}{\input{shorthv.pstex_t}}}.
\end{split}\end{equation}
\noindent If $p = 1$, then \eqref{eqn:4-open} also holds for $k=1$. Furthermore, for any $p$, if $s \le t$, the corners are complete up to $s$, and the corners are walled at $s$, then
\begin{equation}\label{eqn:4-wall}
\# R \ensuremath{\stackrel{4}{=}} \# \hspace{.05in} \parbox{1.75in}{\resizebox{1.75in}{!}{\input{shortvv-wall.pstex_t}}}.
\end{equation}
\noindent (Note that the exact orientation of the reflective pair of corners, with respect to the axis of symmetry, is not specified.)
\end{thm}
\begin{proof}
The proof of this theorem is primarily inductive. First the theorem will be proved for $p=1$, by induction on $k$. Subsequently, the proof will be completed by inducting on $p$. Note that for fixed $k$ and $p$, equation \eqref{eqn:4-open} trivially implies equation \eqref{eqn:4-wall}, since two of the regions pictured in \eqref{eqn:4-open} are impossible if the corners are walled at $s$.
Suppose that $p=1$. If $k=1$, then \eqref{eqn:4-open} trivially holds, by Remark~\ref{rem:reflections} and the fact that there are two ways to place a domino in each of the two $(\{s,t\};1)$-corners under consideration. Observe that \eqref{eqn:4-open} also holds for $k=2$, because there are eight ways to tile the two $(\{2,2\};1)$-corners, and four of these eight tile the same subregion of $R$: a $2 \times 2$ block in each of the two corners.
Now assume that the theorem holds for all $1 \le k < K \le \min\{s,t\}$, and suppose that $R$ has a reflective pair of $(\{s,t\};1)$-corners complete up to $K$. These corners must also be complete up to $K-1$, so \eqref{eqn:4-open} holds for $k = K-1$, as indicated in equation~\eqref{eqn:Kinduction}.
\begin{equation}\label{eqn:Kinduction}\begin{split}
\# R \ensuremath{\stackrel{4}{=}} & \hspace{.05in} \# \hspace{.05in}
\parbox{1.75in}{\resizebox{1.75in}{!}{\input{K1shorthh.pstex_t}}}
+ \# \hspace{.05in}
\parbox{1.95in}{\resizebox{1.95in}{!}{\input{K1shortvv.pstex_t}}}\\
&+ 2 \# \hspace{.05in}
\parbox{1.85in}{\resizebox{1.85in}{!}{\input{K1shorthv.pstex_t}}}
\end{split}\end{equation}
To extend a tiled region in \eqref{eqn:Kinduction} to cover the two $(\{K,K\},1)$-corners, one tile must be added to each corner, and each added tile can have two orientations: horizontal or vertical. Each of the four configurations in \eqref{eqn:Kinduction} (counting the doubled third term twice) leads to four tilings, giving a total of sixteen possible tilings (counting repetitions).
At this point, it is helpful to introduce notation. In each figure in equation~\eqref{eqn:Kinduction}, one corner is depicted to the left of the symmetry axis and one corner is depicted to the right of the axis. The configuration of the left corner will be described in bold face, and the configuration of the right corner will be described with an underline. In the tilings of \eqref{eqn:Kinduction}, if the longer leg of the tiled corner is horizontal (respectively, vertical), this will be called an $H$ (respectively, $V$) tiling. If the tile added in order to cover the $(\{K,K\},1)$-corner is horizontal (respectively, vertical), this will be called an $h$ (respectively, $v$) tile. For example, the third figure in equation~\eqref{eqn:Kinduction} is denoted $\bm{V}\ul{H}$.
Therefore, the sixteen tilings referred to above are described in the following table:
\begin{equation}\label{eqn:table of tilings}
\begin{array}{r|ccccc}
\text{Tiling from \eqref{eqn:Kinduction}} & \text{Add:} & \bm{h} \text{ and } \ul{h} & \bm{h} \text{ and } \ul{v} & \bm{v} \text{ and } \ul{h} & \bm{v} \text{ and } \ul{v}\\
\hline
\bm{V}\ul{V} & & \bm{Vh}\ul{Vh} & \bm{Vh}\ul{Vv} & \bm{Vv}\ul{Vh} & \bm{Vv}\ul{Vv}\\
\bm{H}\ul{H} & & \bm{Hh}\ul{Hh} & \bm{Hh}\ul{Hv} & \bm{Hv}\ul{Hh} & \bm{Hv}\ul{Hv}\\
\text{(twice) } \bm{V}\ul{H} & & \bm{Vh}\ul{Hh} & \bm{Vh}\ul{Hv} & \bm{Vv}\ul{Hh} & \bm{Vv}\ul{Hv}\\
\end{array}
\end{equation}
The reflective symmetry of $R$ and Remark~\ref{rem:reflections} indicate that \eqref{eqn:table of tilings} still includes duplications: $\# \bm{Vh}\ul{Vv} = \#\bm{Vv}\ul{Vh}$ and $\# \bm{Hh}\ul{Hv} = \# \bm{Hv}\ul{Hh}$.
Combining these facts yields the following identity:
\begin{equation}\label{eqn:variable equation}\begin{split}
\# R \ensuremath{\stackrel{4}{=}} & \ \# \bm{Vh}\ul{Vh} + \# \bm{Hv}\ul{Hv} + 2\# \bm{Vh}\ul{Hv}\\
&+ 2 \# \bm{Vh}\ul{Vv} + \# \bm{Vv}\ul{Vv}\\
&+ \# \bm{Hh}\ul{Hh} + 2 \# \bm{Hh}\ul{Hv}\\
&+ 2 \# \bm{Vh}\ul{Hh} + 2 \# \bm{Vv}\ul{Hh} + 2 \# \bm{Vv}\ul{Hv}.
\end{split}\end{equation}
\noindent Notice that if the only terms on the right side of equation~\eqref{eqn:variable equation} were the first three terms, the induction on $K$ would be complete.
Observe that equation~\eqref{eqn:2-wall} of Theorem~\ref{thm:parity
theorem} applies to the left sides of $\bm{Hh}\ul{Hv}$ and
$\bm{Vv}\ul{Hv}$, as in Figure~\ref{fig:HhHv-par}. Additionally,
Lemma~\ref{lem:mod4mod2} permits the transition from working modulo $4$ to
working modulo $2$, since the terms $\# \bm{Hh}\ul{Hv}$ and $\#
\bm{Vv}\ul{Hv}$ each have coefficient $2$ in \eqref{eqn:variable
equation}.
\begin{figure}[htbp]
\centering
\input{HhHv-par.pstex_t}
\caption{Application of Theorem~\ref{thm:parity theorem} to the left side of $\bm{Hh}\ul{Hv}$.}\label{fig:HhHv-par}
\end{figure}
After applying Theorem~\ref{thm:parity theorem} to each of
$\bm{Hh}\ul{Hv}$ and $\bm{Vv}\ul{Hv}$, the resulting region is the same.
Therefore, $2 \# \bm{Hh}\ul{Hv} + 2 \# \bm{Vv}\ul{Hv}$ is a multiple of 4, and thus these terms can be ignored in \eqref{eqn:variable equation}. Likewise $2 \# \bm{Vh}\ul{Vv} + 2 \#
\bm{Vh}\ul{Hh}$ contributes a multiple of $4$ to the right side of
\eqref{eqn:variable equation}, and can be ignored as well.
All that remains in \eqref{eqn:variable equation}, besides the first three terms, is
\begin{equation*}
\# \bm{Vv}\ul{Vv} + \# \bm{Hh}\ul{Hh} + 2 \# \bm{Vv}\ul{Hh}.
\end{equation*}
\noindent The regions $\bm{Vv}\ul{Vv}$ and $\bm{Hh}\ul{Hh}$ are both reflective with the same symmetry axis as $R$. Therefore, by induction, they obey equation~\eqref{eqn:4-wall}. Similarly, equation~\eqref{eqn:2-wall} can be applied twice to $\bm{Vv}\ul{Hh}$, again using Lemma~\ref{lem:mod4mod2}. After applying these results as described, the three regions are identical. Therefore, since $\# \bm{Vv}\ul{Hh}$ is multiplied by $2$ in \eqref{eqn:variable equation}, these three terms contribute a multiple of $4$ to the sum, and consequently can be ignored.
Therefore, equation~\eqref{eqn:variable equation} reduces to
\begin{equation*}
\# R \ensuremath{\stackrel{4}{=}} \ \# \bm{Vh}\ul{Vh} + \# \bm{Hv}\ul{Hv} + 2 \# \bm{Vh}\ul{Hv},
\end{equation*}
\noindent which, by Remark~\ref{rem:reflections}, is the statement of the theorem for $p=1$ and $k = K$. This completes the first part of the induction.
To complete the proof, assume that the theorem is true for all $1 \le p < P$, and suppose that $R$ has a reflective pair of $(\{s,t\};P)$-corners. Consider the pair of $(\{s,1\};1)$-corners in these $(\{s,t\};P)$-corners. A tile can be placed in each of these corners either horizontally or vertically. A horizontal tile forces $P-1$ additionally horizontal tiles above it, and leaves a $(\{s-1,2\};1)$-corner below it, while a vertical tile creates a $(\{3,t\};P-1)$-corner to the right of the tile.
If a horizontal tile is placed in one of the two $(\{s,1\};1)$-corners, and a vertical tile in the other, the resulting figure is the reflection across the symmetry axis of the configuration where the two tiles are switched. Therefore
\begin{equation}\label{eqn:Phv figure}
\#R = \# \parbox{1.25in}{\epsfig{file=Phh.eps,width=1.25in}} + \#\parbox{1.25in}{\epsfig{file=Pvv.eps,width=1.25in}} + 2\# \parbox{1.25in}{\epsfig{file=Phv.eps,width=1.25in}}.
\end{equation}
Note that the first and second figures in equation~\eqref{eqn:Phv figure} are reflective. Additionally, by the induction hypothesis, the theorem holds for $(\{s-1,2\};1)$-corners and for $(\{3,t\};P-1)$-corners, so the theorem holds for these corners in the first and second figures of \eqref{eqn:Phv figure}. Likewise, Theorem~\ref{thm:parity theorem} applies to the left and right sides of the third figure in \eqref{eqn:Phv figure}. Applying these theorems, as well as Lemma~\ref{lem:mod4mod2}, and taking into account when two configurations are identical except for reflection across the axis of symmetry yields the following:
\begin{equation}\label{eqn:Phv figure - detail}\begin{split}
\# R \ensuremath{\stackrel{4}{=}} & \hspace*{.05in} \# \parbox{1in}{\epsfig{file=Phh-vv.eps,width=1in}} + \# \parbox{1in}{\epsfig{file=Phh-hh.eps,width=1in}} + 2 \# \parbox{1in}{\epsfig{file=Phh-hv.eps,width=1in}}\\
& + \# \parbox{1in}{\epsfig{file=Pvv-vv.eps,width=1in}} + \# \parbox{1in}{\epsfig{file=Pvv-hh.eps,width=1in}} + 2 \# \parbox{1in}{\epsfig{file=Pvv-hv.eps,width=1in}}\\
& + 2 \# \parbox{1in}{\epsfig{file=Phv-vv.eps,width=1in}} + 2 \# \parbox{1in}{\epsfig{file=Phv-hh.eps,width=1in}} + 2 \# \parbox{1in}{\epsfig{file=Phv-hv.eps,width=1in}}\\
& + 2 \# \parbox{1in}{\epsfig{file=Phv-vh.eps,width=1in}}.
\end{split}\end{equation}
Since everything in equation~\eqref{eqn:Phv figure - detail} is taken modulo $4$, those terms that appear four times can be ignored. There are three such quadruples, and the remaining equation is exactly equation~\eqref{eqn:4-open} for $k=2$ and $p=P$.
To complete the proof, assume the result holds for this $P$ and for all $2 \le k < K \le \min\{s,t\}$, where the $(\{s,t\};P)$-corners under consideration are complete up to $K$. These corners must also be complete up to $K-1$, so the result holds for $k=K-1$. An argument analogous to the previous discussion for $p=1$ will complete the proof.
\end{proof}
\section{Applications of the congruency result}\label{sec:apps}
Under certain conditions, Theorem~\ref{thm:4ity theorem} relates the number of domino tilings of a region modulo $4$, to that aspect of the number of domino tilings of three particular subregions. Thus, $\# R$ may be determined by iteratively determining $\# R_i$ for these subregions $R_i \subset R$. This is not necessarily an attractive prospect, and so it is helpful to highlight some situations when Theorem~\ref{thm:4ity theorem} can be used to great effect.
One easy application of Theorem~\ref{thm:4ity theorem} is the following.
\begin{cor}\label{cor:double wall}
Suppose that a region $R$ is reflective, and that $R$ has a reflective pair of $(\{s,s\};p)$-corners. If these corners are complete up to $s$ and each walled at $s$ along both sides, then $\# R$ is a multiple of $4$.
\end{cor}
\begin{proof}
The three configurations on the right side of equation~\eqref{eqn:4-open} are impossible, so all of these terms contribute zero to the sum.
\end{proof}
More can be said about $\# R$ if the reflective pair of corners share a longer side crossing the axis of symmetry. This occurs, for example, in the $k \times 2s$ and $k \times (2s+1)$ rectangles, where $k \ge s$.
\begin{cor}\label{cor:k2kk}
Suppose that a region $R$ is reflective, and that $R$ has a reflective pair of $(\{s,s\};p)$-corners. If these corners are complete up to $s$ and $R$ has an edge of length $2s$ which is comprised of one segment of length $s$ from each corner (hence the axis of symmetry bisects this segment of length $2s$), then
\begin{equation}\label{eqn:k2kk}
\# R \ensuremath{\stackrel{4}{=}} \# \parbox{1.75in}{\resizebox{1.75in}{!}{\input{k2kkshort.pstex_t}}}
+ \# \parbox{2.04in}{\resizebox{2.04in}{!}{\input{k2kklong.pstex_t}}}.
\end{equation}
\end{cor}
\begin{proof}
First apply Theorem~\ref{thm:4ity theorem} for $k=s-1$. Then, to each of the configurations described in equation~\eqref{eqn:4-open}, add two tiles (or, in one situation, a single tile) so that the two $(\{s,s\};p)$-corners are each completely tiled. Combining those configurations that are obtained by reflection across the axis of symmetry yields
\begin{equation}\label{eqn:k2kk possibilities}\begin{split}
\# R \ensuremath{\stackrel{4}{=}} & \hspace{.05in} \# \parbox{1.1in}{\resizebox{1.1in}{!}{\input{k2kk1.pstex_t}}}
+ \# \parbox{1.1in}{\resizebox{1.1in}{!}{\input{k2kk2.pstex_t}}}
+ \# \parbox{1.1in}{\resizebox{1.1in}{!}{\input{k2kk5.pstex_t}}}\\
& + 2 \# \parbox{1.1in}{\resizebox{1.1in}{!}{\input{k2kk6.pstex_t}}}
+ \# \parbox{1.1in}{\resizebox{1.1in}{!}{\input{k2kk7.pstex_t}}}
+ 2 \# \parbox{1.1in}{\resizebox{1.1in}{!}{\input{k2kk3.pstex_t}}}\\
& + 2 \# \parbox{1.1in}{\resizebox{1.1in}{!}{\input{k2kk4.pstex_t}}}.
\end{split}\end{equation}
The second and third figures on the right side of equation~\eqref{eqn:k2kk possibilities} are reflective, so Theorem~\ref{thm:4ity theorem}, in particular, equation~\eqref{eqn:4-wall}, applies to each. In fact, both applications give the same configuration. Applying Theorem~\ref{thm:parity theorem} (and Lemma~\ref{lem:mod4mod2}) to each side of the doubled seventh term in \eqref{eqn:k2kk possibilities} gives the same configuration again. Thus this resulting term appears four times, so it can be ignored.
Similarly, apply Theorem~\ref{thm:parity theorem} and Lemma~\ref{lem:mod4mod2} to each side of the doubled sixth figure on the right side of \eqref{eqn:k2kk possibilities}, and do likewise to the doubled fourth term, first to the right corner and then to the left. These yield two pairs of figures which are reflections of each other across the axis of symmetry. Thus they have the same number of domino tilings, and so this again gives a multiple of four, which can be ignored.
Therefore the only figures on the right side of equation~\eqref{eqn:k2kk possibilities} which are left are the first and fifth, which is the statement of the corollary.
\end{proof}
\begin{cor}\label{cor:k2k+1k}
Suppose that a region $R$ is reflective, and that $R$ has a reflective pair of $(\{s,s\};p)$-corners. If these corners are complete up to $s$ and $R$ has an edge of length $2s+1$ which is comprised of one segment of length $s$ from each corner and a segment of length $1$ between them (hence the axis of symmetry bisects this segment of length $2s+1$), then
\begin{equation}\label{eqn:k2k+1k}
\# R \ensuremath{\stackrel{4}{=}} \# \parbox{1.95in}{\resizebox{1.95in}{!}{\input{k2k+1klong.pstex_t}}}
+ 2 \# \parbox{1.85in}{\resizebox{1.85in}{!}{\input{k2k+1kshort.pstex_t}}}.
\end{equation}
\end{cor}
\begin{proof}
This follows immediately from equation~\eqref{eqn:4-open} of Theorem~\ref{thm:4ity theorem}, since the second tiling in \eqref{eqn:4-open} is impossible, and the first tiling in \eqref{eqn:4-open} forces a vertical tile between the two pieces, and equation~\eqref{eqn:4-wall} applies to the resulting region.
\end{proof}
As in \cite{oddity}, consider the following types of regions.
\begin{defn}
Let $T(i,j,p)$ be the region with $i+p-1$ centered rows of lengths $j, j+2, \ldots, j+2(p-1), \ldots, j+2(p-1)$ from top to bottom.
\end{defn}
\begin{defn}
Let $D(i,j,p)$ be the region with $i+2(p-1)$ centered rows of lengths $j, j+2, \ldots, j+2(p-1), \ldots, j+2(p-1), \ldots, j+2, j$ from top to bottom. That is, if $i$ is even, $D(i,j,p)$ consists of two copies of $T(i/2,j,p)$ that have been glued together along the edge of length $j+2(p-1)$.
\end{defn}
For example, the Aztec diamond of order $p$ is the region $D(2,2,p)$, and the regions $T(2,5,4)$ and $D(2,5,4)$ are depicted in Figure~\ref{fig:TD ex}.
\begin{figure}[htbp]
\centering
$\begin{array}{c@{\hspace{.5in}}c}
\multicolumn{1}{l}{\mbox{\bf{(a)}}} & \multicolumn{1}{l}{\mbox{\bf{(b)}}}\\
[-.25cm]
\epsfig{file=t254.eps,width=1.25in} &\epsfig{file=d254.eps,width=1.25in}
\end{array}$
\caption{$\bf{(a)}$ The region $T(2,5,4)$. $\bf{(b)}$ The region $D(2,5,4)$, which is two copies of $T(1,5,4)$ glued together along the edges of length $11$.}\label{fig:TD ex}
\end{figure}
The following results concerning the parities of $\# T(i,j,p)$ and of $\# D(i,j,p)$ appeared in \cite{oddity}, although Corollary~\ref{cor:oddity T}(a) and Corollary~\ref{cor:oddity D}(c) were incorrectly stated for $p=1$.
\begin{cor}[\cite{oddity}]\label{cor:oddity T}
\
\begin{enumerate}
\item $\# T(k,2k-1,p) \ensuremath{\stackrel{2}{=}} \left\{ \begin{array} {c@{\quad:\quad}l}
1 & p=1 \text{ and } k \text{ is even};\\ 0 & \text{otherwise}. \end{array} \right.$.
\item $\# T(k,2k,p) \ensuremath{\stackrel{2}{=}} 1$.
\item $\# T(k,2k+1,p) \ensuremath{\stackrel{2}{=}} 0$.
\item $\# T(k,2k+2,p) \ensuremath{\stackrel{2}{=}} 1$.
\end{enumerate}
\end{cor}
\begin{cor}[\cite{oddity}]\label{cor:oddity D}
\begin{enumerate}
\item $\# D(k,k,p) \ensuremath{\stackrel{2}{=}} 0$.
\item $\# D(k,k+1,p) \ensuremath{\stackrel{2}{=}} 1$.
\item $\# D(k,k+2,p) \ensuremath{\stackrel{2}{=}} \left\{ \begin{array} {c@{\quad:\quad}l}
1 & p=1 \text{ and } $k$ \text{ is even};\\ 0 & \text{otherwise}. \end{array} \right.$
\end{enumerate}
\end{cor}
These results can be refined using Theorem~\ref{thm:4ity theorem}. For example, Corollary~\ref{cor:oddity T}(b) states that $\# T(k,2k,p) \ensuremath{\stackrel{2}{=}} 1$. Thus $\# T(k,2k,p) \ensuremath{\stackrel{4}{=}} 1 \text{ or } 3$. In fact, the exact residue modulo $4$ is easy to determine from previous results in this paper.
\begin{cor}\label{cor:T}
\
\begin{enumerate}
\item $\# T(k,2k-1,p) \ensuremath{\stackrel{4}{=}} \left\{ \begin{array} {c@{\quad:\quad}l}
1 & p=1 \text{ and } k \ensuremath{\stackrel{4}{=}} 0;\\ 3 & p=1 \text{ and } k \ensuremath{\stackrel{4}{=}} 2;\\ 0 & \text{otherwise}. \end{array} \right.$
\item $\# T(k,2k,p) \ensuremath{\stackrel{4}{=}} 1$ for all $k, p \ge 1$.
\item $\# T(k,2k+1,p) \ensuremath{\stackrel{4}{=}} 0$ for all $k, p \ge 1$.
\item $\# T(k,2k+2,p) \ensuremath{\stackrel{4}{=}} 1$ for all $k, p \ge 1$.
\end{enumerate}
\end{cor}
\begin{proof}
\
\begin{enumerate}
\item By Corollary~\ref{cor:k2k+1k} and Theorem~\ref{thm:parity theorem},
\begin{equation*}
\# T(k,2k-1,p) \ensuremath{\stackrel{4}{=}} \# 3T(k-2, 2(k-2)-1,p).
\end{equation*}
The base cases are as follows. The region $T(1,1,p)$ has no domino tilings for any $p$. Similarly, iteratively applying Theorem~\ref{thm:4ity theorem} to $T(2,3,p)$ for $p>1$ shows that $\# T(2,3,p) \ensuremath{\stackrel{4}{=}} 0$ for $p>1$. On the other hand, $\# T(2,3,1) = 3$.
\item By Corollary~\ref{cor:k2kk}, $\# T(k,2k,p) \ensuremath{\stackrel{4}{=}} \# T(k-1, 2(k-1), p)$. It is easy to see that $\# T(1,2,p) = 1$ for all $p$.
\item This follows from Corollary~\ref{cor:k2k+1k}, since both configurations in equation~\eqref{eqn:k2k+1k} are impossible.
\item Theorem~\ref{thm:4ity theorem}, in particular equation~\eqref{eqn:4-wall}, states that $\# T(k,2k+2,p) \ensuremath{\stackrel{4}{=}} \# T(k-1, 2(k-1) + 2, p)$. It is straightforward to see that $\# T(1,4,p) = 1$ for all $p$.
\end{enumerate}
\end{proof}
By setting $p=1$, Corollary~\ref{cor:T}(b) addresses Propp's request in \cite{propp} for a combinatorial explanation that the number of domino tilings of a $k \times 2k$ rectangle is always $1 \bmod 4$.
\begin{cor}\label{cor:n2n}
The number of domino tilings of a $k \times 2k$ rectangle is congruent to $1 \bmod 4$ for all $k$.
\end{cor}
Corollary~\ref{cor:oddity D} can also be refined to determine the residues modulo $4$.
\begin{cor}\label{cor:D}
\
\begin{enumerate}
\item $\# D(k,k,p) \ensuremath{\stackrel{4}{=}} \left\{ \begin{array} {c@{\quad:\quad}l}
2 & k=2 \text{ and } p=1;\\ 0 & \text{otherwise}. \end{array} \right.$
\item $\# D(k,k+1,p) \ensuremath{\stackrel{4}{=}} \left\{ \begin{array} {c@{\quad:\quad}l}
1 & p \text{ is odd and } \lfloor (k+2)/4 \rfloor \text{ is even};\\
3 & p \text{ is odd and } \lfloor (k+2)/4 \rfloor \text{ is odd};\\
1 & p \text{ is even and } \lfloor k/4 \rfloor \text{ is even};\\
3 & p \text{ is even and } \lfloor k/4 \rfloor \text{ is odd}. \end{array} \right.$
\item $\# D(k,k+2,p) \ensuremath{\stackrel{4}{=}} \left\{ \begin{array} {c@{\quad:\quad}l}
2 & p=2 \text{ and } k \text{ is even};\\ 1 & p=1, \ k \text{ is even, and } \lceil k/4 \rceil \text{ is odd};\\ 3 & p=1, \ k \text{ is even, and } \lceil k/4 \rceil \text{ is even};\\ 0 & \text{otherwise}. \end{array} \right.$
\end{enumerate}
\end{cor}
\begin{proof}
\
\begin{enumerate}
\item If $k$ is odd, the region $D(k,k,p)$ contains an odd number of squares, so $\# D(k,k,p) = 0$. Thus it remains only to consider $D(2k,2k,p)$. Applying Corollary~\ref{cor:k2kk} gives
\begin{equation}\label{eqn:D}
\# D(2k,2k,p) \ensuremath{\stackrel{4}{=}} \# \parbox{1in}{\epsfig{file=Dn2npshort.eps,width=1in}} + \# \parbox{1in}{\epsfig{file=Dn2nplong.eps,width=1in}}
\end{equation}
\noindent Now apply Corollary~\ref{cor:k2kk} to the first figure in equation~\eqref{eqn:D} and Theorem~\ref{thm:4ity theorem} to the second figure in \eqref{eqn:D}. This gives
\begin{equation*}
\# D(2k,2k,p) \ensuremath{\stackrel{4}{=}} 2 \# D(2(k-1),2(k-1),p).
\end{equation*}
Therefore it is only necessary to determine $\# D(2,2,p)$, where the region is the Aztec diamond of order $p$. If $p \ge 2$, apply Corollary~\ref{cor:double wall} to $D(2,2,p)$, where the axis of symmetry is a diagonal of the region. This shows that $\# D(2,2,p) \ensuremath{\stackrel{4}{=}} 0$. The remaining case is easy to enumerate: $D(2,2,1) = 2$.
Note that this last case must be treated separately because any axis of symmetry in the $2 \times 2$ square intersects the regions needed to determine completeness of the corners.
\item Using Theorems~\ref{thm:parity theorem} and~\ref{thm:4ity theorem}, together with Lemma~\ref{lem:mod4mod2} and Corollary~\ref{cor:k2kk}, it is evident that
\begin{equation*}
\# D(k,k+1,p) \ensuremath{\stackrel{4}{=}} 2\# D(k-2,k-1,p) + \# D(k-4,k-3,p)
\end{equation*}
\noindent for all $p$ and $k > 4$. The cases when $k \in [1,4]$ are straightforward to check, and give the following results.
\begin{equation*}\begin{split}
\# D(1,2,p) &= 1\\
\# D(2,3,p) &\ensuremath{\stackrel{4}{=}} \left\{ \begin{array} {c@{\quad:\quad}l} 1 & p \text{ is even};\\ 3 & p \text{ is odd}. \end{array} \right.\\
\# D(3,4,p) &\ensuremath{\stackrel{4}{=}} 2 + \# D(2,3,p-1) \ \ensuremath{\stackrel{4}{=}} \ \# D(2,3,p)\\
\# D(4,5,p) &\ensuremath{\stackrel{4}{=}} 1 + 2 \# D(2,3,p) \ \ensuremath{\stackrel{4}{=}} \ 3
\end{split}\end{equation*}
Therefore the value of $\# D(k,k+1,p)$ modulo 4 is described in the following table, depending on the value of $k$ and the parity of $p$.
\begin{equation*}
\begin{array}{r|cccccccccc}
k & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\\
\hline
p \text{ odd} & 1 & 3 & 3 & 3 & 3 & 1 & 1 & 1 & 1 & 3\\
p \text{ even} & 1 & 1 & 1 & 3 & 3 & 3 & 3 & 1 & 1 & 1
\end{array}
\end{equation*}
\item If $k$ is odd, the region $D(k,k+2,p)$ has odd area, hence $\# D(k,k+2,p) = 0$. Thus it remains to consider $D(2k,2k+2,p)$. Once again, Theorems~\ref{thm:parity theorem} and~\ref{thm:4ity theorem} can be used together to show that
\begin{equation*}
\# D(2k,2k+2,p) \ensuremath{\stackrel{4}{=}} 2\# D(2k-2,2k,p) + \# D(2k-4,2k-2,p).
\end{equation*}
The base cases here can be computed as follows, for $p \ge 2$.
\begin{equation*}\begin{split}
\# D(2,4,p) &\ensuremath{\stackrel{4}{=}} \# D(2,2,p-1)\\
\# D(4,6,p) &\ensuremath{\stackrel{4}{=}} \# D(2,2,p) + \# D(2,2,p-1) + \# D(4,4,p-1)
\end{split}\end{equation*}
Previous results for $\# D(k,k,p)$ complete the proof.
\end{enumerate}
\end{proof}
Observe that Corollary~\ref{cor:D}(a) shows that the number of domino tilings of the Aztec diamond of order $p$ is a multiple of $4$ for all $p > 1$. As mentioned above, the restriction on $p$ comes from the fact that if $p=1$, the regions checked to determine completeness of the reflective pair of corners would not be disjoint. In fact, Elkies, Kuperberg, Larsen, and Propp show in \cite{elkies} that the exact number of domino tilings of this region is $2^{p(p+1)/2}$.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,903 |
\section{Introduction}
Intensity-based registration and landmark matching are the de-facto standards to align data from multiple image sources into a common co-ordinate system. Applications that require intensity-based registration include \emph{e.g.}, atlas-based segmentation~\cite{Aljabar2009726}, motion-compensation~\cite{rousseau2006registration}, tracking~\cite{Miao2016}, or clinical analysis of the data visualised in a standard co-ordinate system. These often require manual initialisation of the alignment since general optimisation methods often cannot find a global minimum from any given starting position on the cost function. An initial rigid registration can be achieved by selecting common landmarks~\cite{Ghesu2016} through an iterative agent, which impedes hard real-time constraints or less robustly through local image descriptors \cite{ZITOVA2003977}.
Convolutional Neural Networks (CNNs) have shown promising results for intra and inter modal alignment~\cite{Miao2016,Hou2017}. These approaches show that information about a learn-able canonical co-ordinate system is encoded directly in the features of an image. Early work in this domain showed that image's pose (i.e. position and orientation) can be regressed relatively to a canonical alignment from a large set of training images sampling the canonical space \cite{KendallGC15}. Follow-up formulations for medical applications showed similar success for motion compensation and device localisation~\cite{Miao2016,Hou2017}. However, these approaches rely on heuristic approximations and manual fine-tuning of the CNN loss used to characterise the poses' prediction error. This fosters domain shift problems and limits options for interchangeable application of various deep learning pose estimation models.
\noindent\textbf{Contribution:} We introduce a new loss function that calculates the geodesic distance of two poses on the $SE(3)$ manifold, from a data-adaptive Riemannian metric. We derive appropriate gradients that are required for CNN back propagation. Our method couples the translation and rotation parameters, and regresses them simultaneously as one parameter on the Lie algebra $\mathfrak{se}(3)$. We show that our loss function is agnostic to the architecture by training different CNNs and can effectively predict poses that are comparable to state-of-the-art methods. In addition, we demonstrate that hyper-parameters tuning for our loss function can be directly calculated from the dataset, thus avoiding long and expensive optimisation searches to boost performance. Finally, we validate quantitatively by benchmarking the performance of our loss function with current state-of-the-art methods, and validate their statistical significance with Student's t-test.
\noindent\textbf{Background:} A pose, i.e. a rigid transformation in 3D, is an element of the Lie group $SE(3)$, the Special Euclidean group in 3D. A pose has two components; a rotation component of group $SO(3)$ and a translation component of $\mathbb{R}^3$. $SE(3)$ has the following matrix representation (homogeneous representation):
\begin{equation}
SE(3) = \left\{ X \quad | \quad X = \left[ \begin{array}{c|c} R & t \\ \hline 0 & 1 \end{array} \right], t \in \mathbb{R}^3, R \in SO(3) \right\}
\end{equation}
In usual implementations of $SE(3)$, the rotation ($SO(3)$) can be parameterised in any form as long as the group structure is implicitly imposed. $R$ can be stored as Euler angles, quaternions, axis-angle or $SO(3)$ rotation matrix. The numerical properties of each parameterisation need to be considered carefully, especially when designing deep learning applications, as it can impact efficacy.
Hyunh et al.~\cite{huynh2009metrics} have shown that Euler parameterisation is not unique, this is undesirable as two different mappings can represent the same rotation. A rotation matrix, carrying 9 parameters, is over parameterised and has a strict ordinance on orthonormality. Non-orthogonal rotation matrix can result in skewed or sheared transformations, making it undesirable also. Quaternion parameterisation are often favoured as it can be mapped to valid transformations after normalisation. However, the parameterisation chosen for the rotation is almost never coupled with the parameterisation of the translation, thus denying the intrinsic structure of $SE(3)=SO(3) \ltimes \mathbb{R}^3$. Here, we choose to represent the rotation and the translation together as an element of the Lie algebra of $SE(3)$, i.e. its tangent space at the identity element of the group, denoted $\mathfrak{se}(3)$. It represents the best linear approximation of $SE(3)$ around its identity element. Since the Lie group $SE(3)$ is 6-dimensional, an element of $\mathfrak{se}(3)$ is a 6D vector.
One can define a collection of distances on $SE(3)$, which can be used as loss functions in deep learning applications. A popular choice for the loss is the Euclidean distance associated to the L2-norm. However, the L2-norm is not desirable on $SE(3)$ since it does not respect the manifold's non-linearity and can lead to unpredictable behaviours. It is also undesirable to use two separates L2-norms on $SO(3)$ and $\mathbb{R}^3$ since $SE(3)$ is not a direct product, and $SO(3)$ itself is non-linear: this can be observed visually with quaternions, e.g., the Euclidean distance of two quaternions can be small, despite the rotation being large. This disparity causes network weight updates to be sub optimal. Hence it is desirable to have a loss function that respects the structure of $SE(3)$.
\noindent\textbf{Related Work:} Popular deep learning frameworks, such as Caffe, TensorFlow, Theano, PyTorch, do not provide the means to regress on $SE(3)$, as the common losses used are cross-entropy for probabilities or a p-norms for distances.
Kendall et al.~\cite{KendallGC15} uses the L2-norm to regress parameters on the Lie algebra $\mathfrak{se}(3)$ directly, with a $\beta$ parameter to weight the contribution between rotation and translation. This was similarly performed by authors in~\cite{Pei2017,enlighten156798,Miao2016,liao2017artificial1}, who use the predicted parameters for registration tasks. Alternatively, \cite{kendall2017posenet,Diepol2012optimisation} re-parameterised the pose parameters as projected co-ordinates on a 2D view plane. This was similarly performed by~\cite{Hou2017,hou2018recon} with Anchor Points, where three arbitrary selected reference points on a 2D plane define the plane's location in 3D space. Using the L2-norm to calculate the Euclidean distance between a predicted projection co-ordinate and the ground truth projection co-ordinate is appropriate, as the L2-norm is the appropriate metric. To the best of our knowledge, there is currently no loss function that respects the full Lie group structure of $SE(3)$, for example invariant Riemannian metrics on $SE(3)$ have not been used.
\section{Method}
\begin{figure}[htb]
\centering
\includegraphics[width=0.6\linewidth]{network.pdf}
\caption{CNN architecture using a Riemannian geodesic distance on $SE(3)$ as the loss.}
\label{fig:overview}
\end{figure}
The core of our method is to implement a new loss layer that is agnostic to the network architecture used: we define the loss as the geodesic distance on $SE(3)$ equipped with a left-invariant Riemannian metric, shown in Figure~\ref{fig:overview}.
\noindent\textbf{Left-invariant Riemannian metric on $SE(3)$:} A Riemannian metric on $SE(3)$ is a smooth collection of positive definite inner products on each tangent space of $SE(3)$. Then, $SE(3)$ becomes a Riemannian manifold. With a left-invariant metric, it is enough to define an inner product on the tangent space at the identity of $SE(3)$, and then ``propagate" it: the metric is s.t. $\forall u, v \in T_{p_1}SE(3)$ and $\forall p_1,p_2 \in SE(3)$:
$
<DL_{p_1}(p_2) u, DL_{p_1}(p_2) v>|_{L_{p_1} p_2} = <u, v>|_{p_2}
$
where $L_{p_1}$ is the left translation by $p_1$: $L_{p_1}(p_2) = p_1 \circ p_2$, and $DL_{p_1}(p_2)$ its differential at $p_2$. We define an inner product $Z$ at $p_2 = \text{identity}$ so that we get a metric $Z_{p_1}$ at the tangent space of any pose $p_1$ of $SE(3)$~\cite{miolane:hal-01133922}, and thus to compute inner products and norms of tangent vectors at $p_1$.
\noindent\textbf{Loss and gradient:} We use the loss function:
$
\text{loss}(\mathbf{p},\hat{\mathbf{p}})
= \text{dist}_{SE(3)}^Z(\mathbf{p},\hat{\mathbf{p}})^2
= {\left\| \text{Log}_{\hat{\mathbf{p}}}^{Z}(\mathbf{p}) \right\| }_{Z_{\hat{\mathbf{p}}}}^2
$
where $\text{dist}_{SE(3)}^Z$ is the geodesic distance and Log is the Riemannian logarithm at $\hat{\mathbf{p}}$ i.e. a tangent vector at $\hat{\mathbf{p}}$. We use a left-invariant Riemannian metric, thus: $\text{loss}(\mathbf{p},\hat{\mathbf{p}}) = ||DL_{\hat{\mathbf{p}}^{-1}}.\text{Log}_{\hat{\mathbf{p}}}^{Z}(\mathbf{p})||_{Z}^2$, where we now have a tangent vector at the identity and we can use the inner product $Z$. If we take $Z$ being the canonical inner product at identity, this is the L2-norm but on the tangent vector transported from $\hat{\mathbf{p}}$ to identity using the differential $DL_{\hat{\mathbf{p}}^{-1}}$. The backward gradient corresponding to the loss seen as a function of $\hat{\mathbf{p}}$ is
$
\nabla_{\hat{\mathbf{p}}} \text{loss}(\mathbf{p},\hat{\mathbf{p}}) = -2 \cdot \text{Log}_{\hat{\mathbf{p}}}^{Z}({\mathbf{p}})
$ \cite{pennec1999probabilities} which is a tangent vector at $\hat{\mathbf{p}}$.
\noindent\textbf{Implementation:} The inputs to the loss layer are the poses $\mathbf{p}$ and $\hat{\mathbf{p}}$ for ground truth and prediction respectively. We represent a pose with \texttt{geomstats} implementation \cite{miolane_2018} \emph{i.e.} as the Riemannian Logarithm of canonical left-invariant metric on $SE(3)$ s.t. $ p = \{ r, t \} = \{ r_x , r_y , r_z , t_x , t_y , t_z \} \in \mathbb{R}^6$. With this parameterisation, the rotation $r$ is in axis-angle parameterisation, the inner product $Z$ is a 6x6 positive definite matrix and the differential $DL_{\hat{p}}$ of the left translation is the 6x6 jacobian matrix:
$
J_{\hat{p}} = \begin{pmatrix}
\frac{\partial {L_{\hat{p}}}^{r}}{\partial r}
& \frac{\partial {L_{\hat{p}}}^{r}}{\partial t} \\
\frac{\partial {L_{\hat{p}}}^{t}}{\partial r}
& \frac{\partial {L_{\hat{p}}}^{t}}{\partial t}
\end{pmatrix}
$. We denote $v_t = \text{Log}_{\hat{\mathbf{p}}}^{Z}(\mathbf{p})$ which is a tangent vector at $\hat{\mathbf{p}}$ in this parameterisation. The loss is calculated by $\text{loss}(\mathbf{p},\hat{\mathbf{p}}) = v_t^T \ast J_{\hat{p}^{-1}}^T \ast Z \ast J_{\hat{p}^{-1}} \ast v_t$ where $*$ is the matrix multiplication and the Riemannian logarithm $v_t$ is given by \texttt{geomstats}. The gradient is calculated by: $\nabla_{\hat{\mathbf{p}}} \text{loss}(\mathbf{p},\hat{\mathbf{p}})= -2 * J_{{\hat{p}}^{-1}}^T \ast Z \ast J_{{\hat{p}}^{-1}} * v_t$.
\section{Experiments and Results}
We evaluate our novel loss function on three datasets: \textbf{(Exp1)} the publicly available PoseNet dataset~\cite{KendallGC15}, which allows a direct comparison to state-of-the-art in Computer Vision and further evaluates optimisation strategies for these experiments. \textbf{(Exp2)}, C-Arm X-Ray to Computed Tomography (CT) alignment problem with data from~\cite{Hou2017}. \textbf{(Exp3)}, the pose estimation dataset for motion compensation in fetal Magnetic Resonance Imaging (MRI) from~\cite{hou2018recon}.
In each experiment, we benchmark existing $SE(3)$ parameterisation strategies with the respective loss function used. PoseNet: direct regression of parameters on the Lie algebra $\mathfrak{se}(3)$, where a combination of quaternion and translation parameters are regressed using L2-norms with a static $\beta$ parameter to weight the respective contribution. Anchor Points formulation: a re-parameterisation of $SE(3)$ in Euclidean space, where three statically defined points in 3D space defines a plane. Each Anchor Point is regressed independently using the L2-norm. Finally, our $SE(3)$ loss, i.e., the geodesic distance on the Riemannian manifold.
All experiments are conducted using the Caffe framework, on a computer equipped with an Intel i7 6700K CPU and Nvidia Titan X Pascal GPU.
\noindent\textbf{Exp.1: Metric Localisation on Natural Images:} In this experiment, we replicated PoseNet's original experiment~\cite{KendallGC15} on the King's College dataset as a baseline benchmark. \cite{KendallGC15} extracted images from a series of videos, and fed them into a structure from motion pipeline to create a 3D model in order to extract plane locations with respect to a world co-ordinate reference frame. The parameterisations of this dataset are quaternions with translation offsets. We mirrored the dataset using axis-angle representation instead of quaternions, and used our $SE(3)$ loss function as regressor. Both networks were trained with a GoogLeNet~\cite{googlenet} base architecture with no parameter weighting.
\begin{table}[htb]
\centering
\caption{Mean Error of Loss Functions on Natural Images}
\label{tab:PoseNet-SE3}
\begin{tabular}{c|cccccc|c}
\toprule
~~~~~~~~~~~~~~~~ & ~~~$R_x$~~~ & ~~~$R_y$~~~ & ~~~$R_z$~~~ & ~~~$t_x$~~~ & ~~~$t_y$~~~ & ~~~$t_z$~~~ & ~~~G.D.~~~ \\
\midrule
PoseNet & \textbf{4.141} & 7.774 & \textbf{4.597} & 1.341 & \textbf{1.139} & \textbf{0.154} & 23.629 \\
$SE(3)$ & 4.306 & \textbf{6.675} & 11.580 & \textbf{1.307} & 1.149 & 0.155 & \textbf{14.973} \\
\bottomrule
\multicolumn{8}{c}{A: Without Parameter Weighting} \\
\toprule
~~~~~~~~~~~~~~~~ & ~~~$R_x$~~~ & ~~~$R_y$~~~ & ~~~$R_z$~~~ & ~~~$t_x$~~~ & ~~~$t_y$~~~ & ~~~$t_z$~~~ & ~~~G.D.~~~ \\
\midrule
PoseNet & \textbf{1.790} & \textbf{2.612} & \textbf{2.371} & \textbf{1.161} & 1.306 & \textbf{0.154} & \textbf{13.516} \\
$SE(3)$ & 1.870 & 3.143 & 3.662 & 1.759 & \textbf{1.240} & 0.156 & 16.370 \\
\bottomrule
\multicolumn{8}{c}{B: With Parameter Weighting}
\end{tabular}
\end{table}
We convert the predicted and ground truth poses to Euler angles in degrees and translation in meters, along with the geodesic distance (G.D.) on the manifold. Table~\ref{tab:PoseNet-SE3}-A shows the average errors of each parameter. It can be seen that the error is similar in each Euler and translation parameters, which is confirmed by Student's t-test to be insignificant. However, the geodesic distance error of SE(3) is much lower compared to PoseNet. Despite this, Student's t-test still shows no significant difference, which is caused by the large variance of PoseNet.
To tune the weight parameter $\beta$, Kendall et al.~\cite{KendallGC15} performed grid search and found that $\beta = [120,750]$ works best for indoor scenes and $\beta = [250,2000]$ for outdoor scenes. Grid search is computationally very expensive, and it can be difficult to find an optimal value if the search interval is coarse. We show here that we can compute a data-adaptive Riemannian metric on $SE(3)$ to weight the contribution of each parameter in the loss.
We first train the network with no weightings, followed by an inference pass through the entire validation dataset. We compute the prediction error as the rigid transformation: ${(y_{true})}^{-1} \circ y_{pred}$ and consider the dataset of their Riemannian logarithms at the identity $\{X_i\}_i$. The parameter weightings are then calculated by $\text{diag}({\text{cov}(X_i)}^{-1})$. The diagonal of the covariance matrix shows the variance of each parameter, whereas the inverse shows how tightly coupled it is to the mean. Thus, the higher the diagonal element, the tighter the variable is clustered. Elements, that are more sparsely coupled, are weighted less as they are likely to induce errors. The optimal weightings for the King's College dataset from \cite{KendallGC15} are:
$
\text{diag}({\text{cov}(X_i)}^{-1}) = \{ 0.147 , 0.954 , 0.261 , 0.001 , 0.003 , 0.002 \}
$.
Table~\ref{tab:PoseNet-SE3}-B shows the performance of the networks retrained with suggested weightings.
Student's T-test still shows no significant difference between errors induced by PoseNet and $SE(3)$. We note that having different weightings on the rotation part induces a distance that is not a Riemannian geodesic distance anymore. The properties of this distance will be investigated in future work.
\noindent\textbf{Exp.2: Plane Detection on C-ARM Imaging:} \cite{Hou2017} demonstrated the versatility of CNNs for performing 2D/3D registration of C-Arm X-ray images to CT volumes using Anchor Points. In this experiment, we replicate the 2D/3D registration task using CaffeNet and evaluate the performance with the newly proposed $SE(3)$ parameterisation and loss regressor. For comparison, a network was also trained with PoseNet's parameterisation. All weight parameters are set to a default of 1. Table~\ref{tab:DRR-results} shows the performance of each parameterisation.
\begin{table}[htb]
\centering
\caption{Mean Error of Loss Functions on DRR (Digitally Reconstructed Radiographs)}
\label{tab:DRR-results}
\begin{tabular}{c|cccccc|c}
\toprule
~~~~~~~~~~~~~~~~~~~~~~ & ~~~~$R_x$~~~~ & ~~~~$R_y$~~~~ & ~~~~$R_z$~~~~ & ~~~~$t_x$~~~~ & ~~~~$t_y$~~~~ & ~~~~$t_z$~~~~ & ~~~~G.D.~~~~ \\
\midrule
PoseNet & 7.960 & 3.136 & 7.547 & 62.650 & 57.315 & 45.852 & 15201.845 \\
Anchor Points & \textbf{7.274} & \textbf{2.511} & \textbf{7.059} & 59.292 & \textbf{54.889} & \textbf{40.576} & 15115.858 \\
$SE(3)$ & 8.243 & 3.697 & 7.924 & \textbf{58.647} & 55.477 & 44.189 & \textbf{14170.722}* \\
\bottomrule
\multicolumn{8}{c}{A: Healthy Patient Dataset} \\
\toprule
~~~~~~~~~~~~~~~~~~~~~~ & ~~~$R_x$~~~ & ~~~$R_y$~~~ & ~~~$R_z$~~~ & ~~~$t_x$~~~ & ~~~$t_y$~~~ & ~~~$t_z$~~~ & ~~~G.D.~~~ \\
\midrule
PoseNet & 10.653 & 5.788 & 10.760 & 69.107 & 72.238 & 57.726 & 23495.708 \\
Anchor Points & \textbf{8.540} & \textbf{4.060} & \textbf{8.553} & 65.521 & \textbf{68.543} & 54.133 & 21725.921 \\
$SE(3)$ & 10.511 & 6.789 & 11.913 & \textbf{62.588} & 68.747 & \textbf{54.110} & \textbf{19624.246}* \\
\bottomrule
\multicolumn{8}{c}{B: Pathological Patient Dataset}
\end{tabular}
\end{table}
Here, we convert the predicted and ground truth poses to Euler angles in degrees, and translation to millimeters. Similar to Exp1, the average error for rotation and translation (for both healthy and pathological patients) are similar, and insignificant as confirmed by Student's t-test. However, there is a noticeable trend in average geodesic distance errors. Student's t-test showed significant difference (marked by *) between $SE(3)$ loss compared to PoseNet and Anchor Points for both datasets. This shows that the geodesic metric is able to quantify properties that the metric expressed in Euler-translation parameters cannot.
\noindent\textbf{Exp.3: 2D/3D Registration on fetal brain MRI:} We replicate the results evaluation method from~\cite{hou2018recon}, and evaluate our loss regressor for 2D/3D registration used during motion compensation of fetal MRI data in canonical organ space. \cite{hou2018recon} uses aligned, reconstructed 3D brain volumes to learn a canonical orientation space and utilises an approach based on GoogLeNet to reorient unseen 2D brain slices into their correct anatomical location in this space. To sample the canonical training space we use the same Euler iteration method (\emph{i.e.}, $18^\circ$ steps in $R_x$ $R_y$ $R_z$ between $-90^{\circ}$ and $+90^{\circ}$, and 2mm offsets in $T_z$ constrained between -40 and 40) to generate 1.12M images for the training set. The evaluation method is performed similarly as~\cite{hou2018recon}, with the performance summarised in Table~\ref{tab:exp3}. The validation dataset is composed of brain slices sampled with random Euler angles between $-90^\circ$ and $+90^\circ$, and random offsets between -40 and +40.
\begin{table}[ht]
\centering
\caption{Mean Error of Loss Functions on Fetal Brain Images}
\label{tab:exp3}
\begin{tabular}{c|cccc|c}
\toprule
~~~~~~~~~~~~~~~~~~~~~~ & ~~~~~CC~~~~~ & ~~~~MSE~~~~ & ~~~PSNR~~~ & ~~~SSIM~~~ & ~~~~~G.D.~~~~~ \\
\midrule
PoseNet & 0.8199 & 1046.4 & 18.6509 & 0.5448 & 18.1708 \\
Anchor Points & 0.8378 & 935.0 & 19.3564 & 0.5845 & 15.7504 \\
$SE(3)$ & \textbf{0.8732}* & \textbf{724.9713}* & \textbf{20.7484}* & \textbf{0.6470}* & \textbf{10.0836}* \\
\bottomrule
\end{tabular}
\end{table}
Our $SE(3)$ loss function shows drastic improvement in all image similarity metrics (Cross Correlation, Mean Squared Error, Peak Signal-to-Noise Ratio and Structural SIMilarity). This is confirmed by Student's t-test which shows significant difference. This is crucial for Slice-to-Volume Registration (SVR) applications as the metric for slice alignment is derived from the metrics above~\cite{kainz2015fast}.
\textbf{Discussion:} A pose is a combination of rotation and translation, therefore it seems reasonable that a CNN predicting a pose should use a metric that accounts for both simultaneously. Metrics are perceptually a method of measurement with its own set of rules, \emph{e.g.}, imperial vs. metric system for quantifying distances. Choosing a metric for a target application is not always straight forward and often a question of required precision, \emph{e.g.}, one would not measure the diameter of a pinhead with a meter rule, nor measure distance between cities with a caliper. We have shown that our loss function, using a Riemannian geodesic distance on $SE(3)$ is better suited for medical registration tasks as shown in Exp2 and Exp3. Exp2 shows each test case yielding no significant difference on Euler and translation parameters, with significant difference on geodesic parameters. This suggests that Euler-translation parameters separately are not able to fully quantify the properties of $SE(3)$. In Exp3, our loss function was able to significantly improve the image similarity metrics, as used by SVR algorithms.
\section{Conclusion}
In this work, we have presented a novel loss function to regress poses on the Lie group $SE(3)$, and derived the necessary gradients required for CNN training. We showed that our method alleviates the need of re-parameterising regression parameters, which addresses the domain shift problem of deep learning applications. Our approach achieves similar results to manually fine-tuned approximations out-of-the-box, \emph{e.g.}, for data from a new scanner. This is demonstrated on the current state-of-the-art for pose estimation, PoseNet, where we show that our method achieves similar performance as the carefully tuned approximation used in \cite{KendallGC15}. We also show significant improvements for medical image pose estimation and outperform the state-of-the-art in this domain~\cite{Hou2017,hou2018recon}. \textbf{Acknowledgements:} Supported by the Wellcome Trust IEH Award [102431] and Nvidia.
\bibliographystyle{splncs03}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,617 |
Mukherjee Musings
Up Close and Personal: Sherlock Holmes
It feels great to be back! My brief hiatus was due to my travels and then catching up with the final edits and cover design of my book scheduled for a December 2015 release with Srishti. The good news is we are making good progress and the cover should be out on Facebook very soon. I am excited and looking forward to your feedback!
In this edition and in the next few, I choose a topic close to my heart - looking at the private lives of the detectives we love. As a reader, I have always loved a thriller where I have been able to relate to the investigator as a human being. In my story, I have made sincere efforts to make Agni Mitra anything but an infallible, larger-than-life law enforcement machinery. And as we wait for Agni to share his life with us this December, let us revisit the lives of some of our favourite sleuths.
I look at Holmes this week.
In the accounts of Dr. Watson, Holmes comes across as bohemian and a tad eccentric. Holmes was also very apprehensive about destroying documents. (Here is one trait that I can relate to!) In the story "The Adventure of the Musgrave Ritual" Watson says:
He had a horror of destroying documents .... Thus month after month his papers accumulated, until every corner of the room was stacked with bundles of manuscript which were on no account to be burned, and which could not be put away save by their owner...
Holmes did not hesitate to often 'bend the rules' - take recourse to lying, conceal evidence, break into houses - if he considered such acts as morally justifiable.
He derived utmost pleasure in baffling hapless police investigator with his superior deductions - sometimes almost to the point of arrogance. He felt happy when his skills were appreciated and he responded to flattery. In some cases, he actually comes across as a showman, taking pains in creating rather dramatic traps to capture his culprits and making an impression on his 'audience'!
However, Holmes does not actually come across as someone chasing fame. In a number of stories, he lets the police take public credit for his work! He comes across as a good friend of the police, and in a number of cases, the police seeks his assistance in solving a tricky one, even when he is on vacation. A number of his clients, of course, consulted him instead of or in addition to the police investigators.
With the honourable exception of Dr. Watson, we really do not come across a lot of friends! In fact, in "The Adventure of The Gloria Scott", Holmes tells Watson that during two years in college, he made only one friend - Victor Trevor. Well - that surely is a boy who preferred keeping to himself!
His love for music, especially the violin, of course is legendary.
So is his love for addictive drugs, especially when there was a lack of stimulating investigations. We read about Holmes using cocaine. We also find him dabbling in morphine. We also find several references of the use of tobacco, smoking cigarettes, cigars and of course, the trademark pipes.
And now, about Holmes' attitude towards women.
Watson sums up the scenario rather nicely as:
(Holmes)"manifested no further interest in the client when once she had ceased to be the centre of one of his problems"
In "The Lion's Mane" Holmes himself writes:
"Women have seldom been an attraction to me, for my brain has always governed my heart"
In "The Adventure of the Second Stain" Holmes says:
"the motives of women ... so inscrutable .... How can you build on such quicksand? Their most trivial actions may mean volumes ..."
Irene Adler of course deserves special mention. An ex-opera singer and actress who appears in "A Scandal in Bohemia" and then remains the most memorable female character in popular Holmes-lore as the only female character who challenged him intellectually and the only person who defeated him in a battle of wits. Holmes held her in high regard:
"To Sherlock Holmes she is always the woman. I have seldom heard him mention her under any other name. In his eyes she eclipses and predominates the whole of her sex. It was not that he felt any emotion akin to love for Irene Adler ... yet there was but one woman to him, and that woman was the late Irene Adler, of dubious and questionable memory."
That memory is kept alive by the photograph Holmes received as 'remuneration' for his part in the case.
Some stories are best left unfinished.
Book Review - Poems by Subhadip Mukherjee
Ernest Hemingway said, "There is nothing to writing. All you do is sit down at a typewriter and bleed." Reading the poetry of Subhadip Mukherjee in his book 'ছেঁড়াচিন্তারScribbles' (Offtrack Publishers, co-authored by Dr. Kausik Ghosh), I am convinced that he is bleeding. And that's good news.
Subhadip is a nagorik kobiyal. His poems hold mirror to the stifling urban life with its rat race, with its mindless pursuit of materialistic ambitions, and with its consumerism.
নাগরিকব্যস্ততানানাজটিলতা... দাশুবারবারকিস্তিমাত
He mocks the same judgemental urban society right in his introduction when he says:
যদিতাকেচিনেথাকো যদিতাকেজেনেথাকো Boss, বেশী .মিশোনাতারসাথে সামান্যনেশাহবে... তুমিও "খারাপ" হবে দেরিহবেরোজরাত্তিরে
Subhadip's poems paint love in its myriad hues – from extreme euphoria to brooding despondency. Subhadip depicts the unadulterated purity of love when he says:
তুইক্লাসনাইনৈরখাতারপাতায়বুকবুক
What does the Indian media have to say about In the Shadows of Death
In the Shadows of Death completes 5 months and I thought it would be worthwhile to summarize the media mentions for my work.
I can't thank enough the respected reviewers who have been insightful, looking beyond the obvious elements of thrill and suspense and commenting on the dynamics of human relationships in contemporary urban India that I made humble efforts to portray through my work.
The media response has been truly inspirational, and I hope as I chase my dreams, you will be with me in my journey, motivating me, inspiring me, and helping me with your feedback so that I can further hone my craft.
The Times of India: Set in the city of Kolkata, "In The Shadows of Death: A Detective Agni Mitra Thriller" is a fast paced potboiler which hooks you and keeps you glued to the plot from the very beginning. Full report: http://timesofindia.indiatimes.com/life-style/books/features/Book-review-In-The-Shadows-of-Death/articleshow/51455322.cms
The Hindu (1): With an almost Freudian u…
'The Colours of Passion' - The motivation behind my second novel
I have often asked myself this question.
Was it a desire to step out of the 'shadows' into a vibrant, 'colourful' milieu? To break free from the despondency of 'death' and savour the frenzy of 'passion'? Maybe. Or, maybe not.
Because, when you are hurtling down the murky path of crime, it probably does not matter whether it is broad daylight or there are shadows looming large. It is the greed, the insecurity, and the hurt of a tormented soul that is at the root of all evils since time immemorial. That does not change even as stories change.
I, of course, wanted to talk about 'passion'. In my story, I talk about our passion for our work, our craft. I talk about the almost oppressive desire to excel in what we do, which keeps us awake through nights. And how that passion often makes us blind to our sense of propriety. And then, there is the passion one feels for another human being. It can have a variety of shades – some we are 'comfortable' with, some which do not conform to societal def…
Chetan Bhagat
In the Shadows of Death
Indian Women
One Indian Girl
restaurant chain
Sourabh Mukherjee
Sympathy Lit
The Colours of Passion
Traditional Indian Wedding
Victoria Memorial
Women's Career | {
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Cristiano Ronaldo is ready to play for Manchester United or Chelsea at a salary ?500 thousand per week
Portugal forward in football and the Spanish «real» Cristiano Ronaldo is ready to play for the Manchester United or Chelsea at a salary ?500 thousand per week. About it speak English press.
In the summer of 2013 Ronaldo was close to return to the «Manchester United», which appeared in the period 2003-2009. According to sources, in 2013 manual mancunians club was unable to meet the financial requirements of the player.
At this time Ronaldo gets ?350 thousand per week. In MU are the highest paid forwards Wayne Rooney (?300 thousand) and rental Radamel Falcao (?390 thousand).
first in the Spanish media has any information about the fact that Ronaldo wants to leave the team after the end of the season 2014/15. 29-year old player disappointed transfer policies «real». For example, it did not suit sale at Manchester United midfielder angel di Maria.
Ronaldo moved to real Madrid in the Summer of 2009 ?93, 4 million During this time he became the champion of Spain (2012), winner of the Cup (2011, 2014) and super bowl (2012) countries, as well as a Champions League winner (2014) and the UEFA super Cup (2014)
The former President of real Madrid : Cristiano Ronaldo has expressed interest in returning to Manchester United
Manchester United rented player in football Radamel Falcao because of doubts in his age
Vice President of Monaco : the chance for the emergence of sponsors With buying Falcao failed
Media: player Khedira has not played in the game super Cup Europe because of the refusal to renew the contract
Real Madrid announced the transfer of the player in football Manchester United Javier Hernandez
Posted in News of football and tagged Madrid by admin420. Bookmark the permalink.
« Coach of Mordovia : draw in the game of the Locomotive is an honest result
The players of real Madrid lost to Atletico in the championship game of Spain » | {
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WASHINGTON — The Justice Department said today that special counsel Robert Mueller's investigation did not find evidence that President Donald Trump's campaign "conspired or coordinated" with Russia to influence the 2016 presidential election.
Barr released a four-page summary of Mueller's report Sunday afternoon. Mueller wrapped up his investigation Friday with no new indictments, bringing to a close a probe that has shadowed Trump for nearly two years.
Mueller's team issued more than 2,800 subpoenas and executed nearly 500 search warrants in its probe of Russian interference in the 2016 election and any potential involvement by Trump's campaign, according to Barr's letter to Congress summarizing the findings.
The House Judiciary Committee chairman says Mueller "clearly and explicitly is not exonerating the president."
Democratic Rep. Jerry Nadler tweeted that Barr's letter to Congress says that while Trump may have acted to obstruct justice, the government would need to prove that "beyond a reasonable doubt." | {
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Q: How to fix 403 Forbidden error in laravel application after hosting in a sub domain I get the 403 Forbidden error when I try to access my Laravel application from my subdomain.
My project is outside the public_html file in cPanel in a folder called app.
And i have created a symlink to the project public_html by running this code in cPanel terminal
ln -s ~/app/public_html/ ~/public_html
And I have set permission 644 to the project directory
A: This might create an infinite loop and that is what creating the problem. However you may be able to create a symlink to any of the sub directories, it would work fine.
ln -s ~/app/public/uploads ~/public_html/uploads
Will work fine.
| {
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} | 6,213 |
The San Antonio areas inside the space code 726 are:
Alamance County. Alleghany County. Ashe County. Caswell County. Chatham County. Davidson County. Next up are the enormous metropolitan affiliations and spots that have been made in San Antonio inside the space code 726, The 726 locale code is arranged in northwest central San Antonio. It is fundamental for the Piedmont Triad Metropolitan Area. It joins remarkable affiliations like Asheboro, Burlington, Greensboro, and High Point. Other unassuming associations are furthermore open.
Similarly 727 area code San Antonio city serves within the united states.
734 area code it's an area code telephone number of United States Country. 726 area code gives detailed data on the 726 locale codes, similarly as an accomplice. This page moreover records genuine metropolitan regions like Greensboro. It is facilitated inside space code 726. On the 726 area code welcome page, you can find more district codes, whether or not they are not in San Antonio.
The 726 region code joins the Piedmont Triad, northern Foothills, and northern mountain region in northwest San Antonio . It was set up in 1997 using region code 910. 726 area code gives data on the 726 regional codes, similarly to their spaces. In addition, 726 area code offers a region code finder to help you with discovering other phone regions codes. Use the pursuit ability to glance through the space code finder. Integral Numbers can be purchased at moderate month-to-month rates. Correlative Numbers from TollFreeForwarding.com permits you to figure out business any spot. | {
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{"url":"http:\/\/tex.stackexchange.com\/questions\/98037\/how-to-get-proper-kerning-with-xetex-and-special-characters","text":"# How to get proper kerning with XeTeX and special characters?\n\nI would love to switch to XeTeX to make use of my professional Adobe fonts that were shipped with Creative Suite 6.\n\nI use MikTeX on a Win 8 machine, and TeXniXcenter + XeTeX.\n\nHowever, kerning seems to an issue, especially with special characters, in my case German Umlaute.\n\nSpacing seems wrong, at least for characters W+\u00fc. Actually, on a sidenote, I don't understand why -- does not give me a long dash...\n\nHere is my MWE (UTF8) and a screenshot showing the wrong kerning:\n\n\\documentclass{scrartcl}\n\\usepackage{fontspec}\n\\setmainfont{Minion Pro}\n\\usepackage{listings}\n\\begin{document}\n\nW\u00e4re -- K\u00f6nnte -- W\u00fcste\n\n\\end{document}\n\n\n-\n Add the option Mapping= tex-text to the font specification to enable the translation of en- and emdashes. Furthermore, it seems that only some glyphs like \u00e4 and \u00e0 show this bad kerning, while \u00e1 and (normal) a work fine. \u2013\u00a0hakaze Feb 13 at 16:18 I think it is still this problem: tug.org\/mailman\/htdig\/xetex\/2011-February\/019956.html. And tex.stackexchange.com\/questions\/45460\/\u2026 \u2013\u00a0Ulrike Fischer Feb 13 at 16:39 Yes, it is the same problem! Can get marked as duplicate. \u2013\u00a0Martin Betz Feb 13 at 17:02 This should be fixed in the development version of XeTeX already, which (hopefully) will be available in the next TeX Live. \u2013\u00a0Khaled Hosny Feb 13 at 17:18","date":"2013-05-18 19:15:46","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\": 0.6561868786811829, \"perplexity\": 3410.8760350062903}, \"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\/1368696382764\/warc\/CC-MAIN-20130516092622-00087-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
package com.google.android.libraries.mobiledatadownload.file.openers;
import static com.google.common.truth.Truth.assertThat;
import static org.mockito.ArgumentMatchers.any;
import static org.mockito.Mockito.mock;
import static org.mockito.Mockito.when;
import android.net.Uri;
import com.google.android.libraries.mobiledatadownload.file.SynchronousFileStorage;
import com.google.android.libraries.mobiledatadownload.file.common.testing.TemporaryUri;
import com.google.android.libraries.mobiledatadownload.file.spi.Backend;
import java.io.BufferedInputStream;
import java.io.ByteArrayInputStream;
import java.io.InputStream;
import java.util.Arrays;
import org.junit.Before;
import org.junit.Rule;
import org.junit.Test;
import org.junit.runner.RunWith;
import org.robolectric.RobolectricTestRunner;
@RunWith(RobolectricTestRunner.class)
public final class ReadStreamOpenerTest {
private final InputStream backendStream = new ByteArrayInputStream(new byte[1]);
private SynchronousFileStorage storage;
@Rule public TemporaryUri tmpUri = new TemporaryUri();
@Before
public void setUpStorage() throws Exception {
Backend mockBackend = mock(Backend.class);
when(mockBackend.name()).thenReturn("file");
when(mockBackend.openForRead(any())).thenReturn(backendStream);
storage = new SynchronousFileStorage(Arrays.asList(mockBackend));
}
@Test
public void open_withoutTransforms_returnsRawBackendStream() throws Exception {
Uri uri = tmpUri.newUri();
try (InputStream result = storage.open(uri, ReadStreamOpener.create())) {
assertThat(result).isEqualTo(backendStream);
}
}
@Test
public void open_withBufferedIo_returnsBufferedInputStream() throws Exception {
Uri uri = tmpUri.newUri();
try (InputStream result = storage.open(uri, ReadStreamOpener.create().withBufferedIo())) {
assertThat(result).isInstanceOf(BufferedInputStream.class);
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
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Q: Cannot import BaseGameUtils (Eclipse weirdness) I closed Eclipse and then re-opened it and now I've got all kind of issues with BaseGameUtils.
I really don't understand as there were no errors when I closed Eclipse and I've not made any changes to anything.
I've tried cleaning and closing Eclipse and re-opening it again but have had no joy.
I've also tried removing Eclipse/Android SDK and downloading it and installing it again / updating and then importing BaseGameUtils again but I still get the same problem.
I'm simply trying to follow the Offical Docs.
Would be really grateful if someone can give me some clue as to how I may fix this as my project is currently useless with these errors!
This is the error I get in my BaseGameUtils:
Any suggestions welcome!
A: I have absolutely no idea why this occurred in the first place (I'm guessing Eclipse is just a bit odd), however the reason, after re-installing Eclipse/Android-IDE that I was getting errors when importing BaseGameUtils was because I also then needed to go into it's properties and re-link it to the google-play-services_lib.
Like so:
Once I linked that the errors disappeared and I was also able to re-import my project without errors.
Hope this helps if anyone has similar issues in the future
A: It looks like you have your Source folder set to src but the code source folder is actually using src/main.
Open the Properties for the project and select 'Java Build Path'. Choose the 'Source' tab. Remove the xxxx/src source folder and add xxxx/src/main.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,384 |
{"url":"http:\/\/movienotexist.com\/wyc34\/viewtopic.php?764487=derivative-graph-of-a-half-circle","text":"# derivative graph of a half circle\n\nStack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share \u2026 4.5.3 Use concavity and inflection points to explain how the sign of the second derivative affects the shape of a function\u2019s graph. Determining the Graph of a Derivative of a Function Suppose a function is f ( x ) = x 3 \u2212 12 x + 3 f(x)=x^3-12x+3 f ( x ) = x 3 \u2212 1 2 x + 3 and its graph is as follows: Forget the equation for a moment and just look at the graph. The first circle is given by the equation $$2=\\sqrt{9\u2212x^2\u2212y^2}$$; the second circle is given by the equation $$1=\\sqrt{9\u2212x^2\u2212y^2}$$. Its derivative is greater than zero on . The first derivative will allow us to identify the relative (or local) minimum and maximum values of a function and where a function will be increasing and decreasing. We used these Derivative Rules: The slope of a constant value (like 3) is 0 As well, looking at the graph, we should see that this happens somewhere between -2.5 and 0, as well as between 0 and 2.5. In the previous example we took this: h = 3 + 14t \u2212 5t 2. and came up with this derivative: h = 0 + 14 \u2212 5(2t) = 14 \u2212 10t. A Quick Refresher on Derivatives. The function is increasing on . To compute this derivative, we \ufb01rst convert the square root into a fractional exponent so that we can use the rule from the previous example. 2 Directions: Given the function on the left, graph its derivative on the right. then the derivative of y is . Then find and graph it. Graphing the Derivative of a Function Warm-up: Part 1 - What comes to mind when you think of the word 'derivative'? When studying derivatives of functions of one variable, we found that one interpretation of the derivative is an instantaneous rate of change of as a function of Leibniz notation for the derivative is which implies that is the dependent variable and is the independent variable. A derivative basically finds the slope of a function. Taking a Derivative of a Natural Logarithm ... 30. Part 2 - Graph . The derivative at a given point in a circle is the tangent to the circle at that point. In this section we will discuss what the first derivative of a function can tell us about the graph of a function. Suppose that we wish to find the slope of the line tangent to the graph \u2026 The graph of and its derivative are shown in . A familiar example of this is the equation x 2 + y 2 = 25 , which represents a circle of radius five centered at the origin. [T] An isotope of the element erbium has a half-life of approximately 12 hours. Graphing a function based on the derivative and the double derivative. Which tells us the slope of the function at any time t . 4.5.6 State the second derivative test for local extrema. 1 y = 1 \u2212 x2 = (1 \u2212 x 2 ) 2 1 4.5.4 Explain the concavity test for a function over an open interval. 4.5.5 Explain the relationship between a function and its first and second derivatives. However, some functions y are written IMPLICITLY as functions of x. The unit circle Addition of angles, double and half angle formulas The law of sines and the law of cosines Graphs of Trig Functions Exponential Functions Exponentials with positive integer exponents Fractional and negative powers ... Derivatives of Tangent, Cotangent, Secant, and Cosecant. The derivative and the double derivative tells us a few key things about a graph: Initially there are 9 grams of the isotope present. at just the top half of the circle), and we can then \ufb01nd dy, which will be the dx slope of a line tangent to the top half of the circle. To find the derivative of a circle you must use implicit differentiation. How can we interpret these partial derivatives? This alone is enough to see that the last graph is the correct answer. Recall that the graph of a function of two variables is a surface in $$R^3$$. ... (c=2\\) and the next circle out corresponds to $$c=1$$. Graph of Graph of . Derivatives of a Function of Two Variables. Figure 3. Directions: Given the function at any time t you think of the function at any time t derivative finds. Derivative basically finds the slope of the element erbium has a half-life of 12... State the second derivative test for local extrema 2 Directions: Given the function on the left, graph derivative! Function and its first and second Derivatives Part 1 - What comes to mind when think! Written IMPLICITLY as functions of x y is c=1\\ ) this section we will discuss What the derivative... Approximately 12 hours taking a derivative basically finds the slope of a function Warm-up: Part 1 - comes. Logarithm... 30 'derivative ' we will discuss What the first derivative of a Natural Logarithm... 30 the... As functions of x - What comes to mind when you think of the element erbium has half-life. The second derivative test for local extrema section we will discuss What the first of. Derivative on the derivative and the next circle out corresponds to \\ R^3\\... On the derivative and the double derivative tells us the slope of the function any. That the last graph is the tangent to the circle at that point which tells us a few key about. Natural Logarithm... 30 is the correct answer \u2212 x2 = ( 1 x... To find the derivative of y is initially there are 9 grams of the function at any time.... Correct answer x 2 ) 2 1 a Quick Refresher on Derivatives graph of a Natural Logarithm 30! Two variables is a surface in \\ ( c=1\\ ) derivative on the derivative of a can... A few key things about a graph: then the derivative of a of... The relationship between a function correct answer a Quick Refresher on Derivatives the graph a... Graphing a function Warm-up: Part 1 - What comes to mind when you think of the word '. At that point slope of the function at any time t function based the! Of y is is the tangent to the circle at that point 4.5.6 State the derivative. Word 'derivative ' of the function at any time t Warm-up: Part 1 - What comes mind... ( c=1\\ ) derivative test for local extrema Logarithm... 30 as functions of x of x of! X 2 ) 2 1 a Quick Refresher on Derivatives between a function can us. Function and its first and second Derivatives: Part 1 - What comes to mind when you think the... To \\ ( R^3\\ ) word 'derivative ' function Warm-up: Part 1 - What comes mind... 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Samaria Regional Council to Sue B'Tselem
The Samaria Regional Council plans to sue the left-wing NGO B'Tselem for slander after it alleged that settlers from Yitzhar had set fire to fields near the Palestinian village of Burin.
B'Tselem tweeted a dramatic nighttime photo of the village with the flames burning in the background. In the tweet it stated, "settlers torched Palestinian fields in Burin." At 8:10 am it also sent a release to the media about it, but within two hours, at 10:07am, it retracted the charges.
Samaria Regional Council head Yossi Dagan said the actual story was precisely the opposite. Palestinians "were the ones that ignited the fire that threatened residents' homes." Dagan said the initial tweets had been shared 2,000 times including by the left-wing NGO B'Tselem. The Council and Yitzhar have now asked an attorney to prepare a defamation case against B'Tselem.
"Freedom of expression is a sacred value, but not freedom of expression and defamation," he added.
Settlers to sue B'Tselem for alleging they set Palestinian fields ablaze, by Tovah Lazaroff/Jerusalem Post, May 5, 2021
Israel Works to Restore Calm After Terror Attack
Cooperation Between Security Agencies Uncovers Mechanism for Terror | {
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Windows and doors are assembled with energy-saving technology and security features to ensure your home is as efficient and safe as possible. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,698 |
4th ed. of "The politics of congressional elections".
Publisher: Includes bibliographical references (p. 227-240) and index..
Includes bibliographical references (p. 227-240) and index.
The More e-Books service executes searching for the e-book "The politics of congressional elections" to provide you with the opportunity to download it for free. Click the appropriate button to start searching the book to get it in the format you are interested in. | {
"redpajama_set_name": "RedPajamaC4"
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10-year-old girl reports attempted abduction; Tooele police investigating
By: Ashton Edwards
TOOELE, Utah - Officers are investigating an attempted abduction in Tooele after a 10-year-old girl said a man grabbed her but she was able to get away.
On Feb. 10 at about 5 p.m., the girl told police she was walking home from a friend's house near England Acres Park at 520 East and 1000 North when a man grabbed her arm.
She said another man stood by smoking.
The girl told officers she was able break free from the man holding her and neither of the men chased her.
"That is concerning," said nearby resident Jenn Howden, whose house nearly borders the park. "Especially, it's just right there. And it makes me know that I need to be more aware."
Howden said the area is relatively safe. While she said she teaches her two kids about safety, the incident will prompt her to talk with them again -- especially her 9-year-old daughter.
"I'll probably have a talk with her now, a more in-depth talk," Howden said. "Just say, 'OK, if this comes up, then this is how you're going to react.'"
Both men are described as African American and about 6 feet tall.
Police said the girl reported they were wearing white sweatshirts, white sweatpants and a black and gray striped beanie-style hats.
The girl told police the second man who was smoking had a mustache and small black earrings.
Officers say this is incident is being handled by the Investigations Division and they are asking anyone who may have any additional information to contact them at 435-882-5600.
Authorities also encourage parents to speak with their children about the importance of safety while walking to and from home.
Here are some tips from police to get the conversation started:
-Walk with someone. Use the "buddy system."
-Pick a route and stick to that route, both to and from home.
-Never take rides from people unless arranged by parents.
-Look for traffic and be seen by traffic by wearing bright clothes or carrying a flashlight.
-Report any suspicious activity to Tooele County Dispatch at (435) 882-5600. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,499 |
NGC 1313A (другие обозначения — ESO 83-1, IRAS03195-6652, PGC 12457) — спиральная галактика с перемычкой (SBb) в созвездии Сетка.
Этот объект не входит в число перечисленных в оригинальной редакции «Нового общего каталога» и был добавлен позднее.
Примечания
1313
Сетка (созвездие) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,350 |
\section{Introduction}
In positron-hydrogen collision, if the energy is higher than the positronium formation threshold,
we have two genuine different asymptotic channels. The positron may go away leaving the hydrogen atom behind
in ground or in an excited state, or the positron and the electron may form a positronium leaving the
proton behind. This picture gets modified if we take into account the possibility that the positron and the
electron annihilate.
In case of rearrangement scattering, when the positron and the electron form positronium
in the Ps$(1s)$ state, the positron-electron pair annihilates mostly from this state.
The lifetime of the Ps$(1s)$ state depends on the total spin \cite{rich}.
In this process, once positronium is formed, the third particle does not affect the
annihilation.
The direct annihilation occurs without formation of the positronium. In this case the
positron interacts with the electron in the field of the proton only when all the three particles
are close to each other.
Thus, the direct annihilation is a genuine three-body process.
The standard approach treats the $e^+e^-$ annihilation on the basis
of the perturbation theory \cite{fraser, charlton}.
The annihilation cross section appears as a matrix element
of the coalescence operator between scattering states, which are the solution of the
unperturbed three-body Coulomb Hamiltonian. At higher energies, this formalism have difficulties.
At the positronium formation threshold, the calculated
annihilation cross section becomes infinite.
There has been a number of attempts to improve theory and to achieve
a unified treatment of the positron annihilation
and the positronium formation \cite{mitroy, iks, gl}.
In one approach, to make the lifetime
of the $e^+e^-$ pair finite, an imaginary absorption potential is added to the positron-electron
subsystem Hamiltonian \cite{mitroy}.
"The loss of particles", due to this potential, is then
interpreted as the $e^+e^-$ annihilation. The standard QED formula \cite{fraser, charlton}
for the positron
annihilation cross section suggests the coordinate part of the absorption potential
to be the three-dimensional Dirac delta function depending on the relative position vector
between the positron and the electron. Subsequently, this kind of absorption potential was used
for computing the annihilation cross section above the positronium formation threshold
\cite{iks,igarashi2,yamanaka}.
The three-dimensional delta-function is too singular to be an ordinary potential
in the Schr\"odinger
equation \cite{delta-potF, delta-potB, DemkovO}. In the actual calculations in Refs.\
\cite{mitroy,iks,igarashi2,yamanaka} with the delta potential, this singularity was smoothed out.
Nevertheless, the mathematically sound formulation of using the three-dimensional zero-range
potentials in three-body Coulombic systems
is still needed. It is done in this paper to complete the theory.
Direct annihilation cross section above the positronium formation threshold is subject of an
extensive study \cite{Laricchia}.
In Ref.\ \cite{iks,gl}
it was claimed that the direct process and the annihilation after the positronium formation are
inseparable and therefore the notion of the direct annihilation above the threshold is meaningless.
In contrast, the direct cross section was defined and computed successfully below and above the Ps-formation
threshold in Ref.\ \cite{yamanaka}. This calculation showed no sign of the presence of any threshold
behavior in the energy dependence of the direct annihilation
cross section.
This paper is devoted to continue the study of the direct annihilation within the
time independent formalism introduced in \cite{hu-yak-papp}. In section 2 we define
the scattering solution for the $e^+-$H Schr\"odinger equation in the presence of an
absorption potential.
Subsequently, the multichannel formalism, which is needed to determine scattering and absorption
amplitudes above the positronium formation threshold, is developed.
In section 3 we derive the generalization of the optical theorem
in the presence of an absorption potential.
This optical theorem is used to separate out the annihilation
after the positronium formation cross section from the overall absorption
cross section. The remaining part is naturally the direct annihilation cross section.
The correct form of the zero-range absorption potential is introduced in section 3.
Section 4 contains the results of calculations for the direct annihilation.
Section 5 concludes the paper.
Throughout the paper we use bold letters for vectors, e.g. ${\bf x}$, and non-bold for their
magnitudes, e.g.
$x=|{\bf x}|$. The unit vector pointing out in the direction of the vector ${\bf y}$ is denoted as
${\hat{\bf y}}={\bf y}/y$.
In the paper we work with wave-functions and their components of the form $\Psi({\bf X},{\bf p})$ where
${\bf X}$ stands for
the configuration coordinate and ${\bf p}$ for the momentum of the asymptotic motion. For the sake
of clarity of notations and to avoid overloading of formulae we drop very often the configuration
space coordinate from the notations of
wave-functions and their components leaving only the momentum explicitly.
\section{Three-body scattering formalism}
In this section we apply
the three-body multichannel formalism to $e^+-$H scattering.
\subsection{Three-body scattering in the presence of absorption potential}
We consider the three-body problem
with an additional imaginary potential which acts between the positron and the electron.
If the center of mass motion is removed, the Hamiltonian in the Jacobi coordinate system takes the form
\begin{equation}
H=H^C+ {\mbox{i}} gW_2({\bf x}_2),
\label{Hamiltonian}
\end{equation}
\begin{equation}
H^C=H_0+V^{C}_1({\bf x}_1)+V^{C}_2({\bf x}_2)+V^{C}_3({\bf x}_3),
\label{CoulHam}
\end{equation}
\begin{equation}
H_0=-\frac{\hbar^2}{2\mu_i}\nabla^2_{{\bf x}_i}-
\frac{\hbar^2}{2\nu_i}\nabla^2_{{\bf y}_i}, \ \ \ V^{C}_i({\bf x}_i)=\frac{e_je_k}{x_i}.
\label{kineticPot}
\end{equation}
Here we assign numbers 1,2 and 3 to the positron, the proton and the electron, respectively,
therefore the electric charges are expressed through the unit charge $e$ as $e_1=e_2=e$,
$e_3=-e$.
The Jacobi coordinates are defined in terms of particle radius-vectors ${\mathbf{r}}_i$ by the
standard formulae
\begin{equation}
{\bf x}_{i}={\mathbf{r}}_j-{\mathbf{r}}_k, \ \ \ {\bf y}_{i}={\mathbf{r}}_i-\frac{m_j{\mathbf{r}}_j+m_k{\mathbf{r}}_k}{m_j+m_k},
\label{Jacobiset}
\end{equation}
and the reduced masses are given by
\begin{equation}
\mu_i=\frac{m_jm_k}{m_j+m_k}, \ \ \ \nu_{i}=\frac{m_i(m_j+m_k)}{m_i+m_j+m_k}.
\label{redmass}
\end{equation}
The potential ${\mbox{i}} gW_{2}({\bf x}_2)$ acting between particles of the pair 2
is defined such that $g$ is real and negative, and $W_2({\bf x}_2)$ is real and non negative.
In this case ${\mbox{i}} gW_2$ is a complex absorbing potential.
We do not specify the coordinate dependence of $W_2$ yet, except of
requiring that $W_2$ is short-ranged.
The Schr\"odinger equation for the positron-hydrogen scattering reads
\begin{equation}
(H_0+V^C_1-E)\Psi^+=-(V^C_2+V^C_3+{\mbox{i}} gW_{2})\Psi^{+}.
\label{Sch1}
\end{equation}
The scattering solution is defined at real energy $E$ by the asymptotics as $y_1\to \infty$
\begin{equation}
\Psi^+\propto \phi_1({\bf x}_1)
[e^{{\mbox{i}} {\bf p}_1 \cdot {\bf y}_1}+\frac{e^{{\mbox{i}} \sqrt{E-\epsilon_1}\,y_1}}{y_1}F(p_1{\hat{\bf y}}_1,{\bf p}_1)].
\label{asymp1}
\end{equation}
Here $\phi_1({\bf x}_1)$ is the hydrogen ground state wave function with the energy $\epsilon_1$, and
the
incident momentum of the positron ${\bf p}_1$ is related to the energy by the
condition $E=\hbar^/2\nu_1\, p^2_1+\epsilon_1$.
We note, that due to the asymptotics of the wave-function (\ref{asymp1}),
the term $V^C_2+V^C_3$ in the right hand side of Eq.\ (\ref{Sch1}) is always confined into the region
of the configuration space where the hydrogen wave function $\phi_1({\bf x}_1)$ is not negligible.
This makes the term $V^C_2+V^C_3$ short-range-type and hence the asymptotics
(\ref{asymp1}) in the
coordinate ${\bf y}_1$ is free from the Coulomb contribution. This property holds true for all
equations we deal with in the paper.
Conventionally \cite{Messia},
the scattering amplitude $F$ can be
represented through the wave function.
It is done by rewriting Eq.\ (\ref{Sch1}) in the integral
form and taking the
asymptotics $y_1\to \infty$. By doing so, we get the Lippmann-Schwinger equation (LSE)
\begin{equation}
\Psi^+({\bf p}_1)=\Phi_1({\bf p}_1)+G_1(E^+)(V^C_2+V^C_3+{\mbox{i}} g W_2)\Psi^+({\bf p}_1),
\label{LS}
\end{equation}
where $E^+=E+{\mbox{i}} 0$, $\Phi_1({\bf p}_1)=\phi_1({\bf x}_1)e^{{\mbox{i}} {\bf p}_1\cdot{\bf y}_1}$
is the solution to the channel Schr\"odinger equation
\begin{equation}
(H_0+V^C_1-E)\Phi_1({\bf p}_1)=0,
\label{chanelScr}
\end{equation}
and $G_1$ is the channel Green's function $G_1(z)=(z-H_0-V^C_1)^{-1}$.
The LSE (\ref{LS}) is the integral equation of the form
\begin{eqnarray}
\Psi^+({\bf X},{\bf p}_1)=\Phi_1({\bf X},{\bf p}_1)+
\nonumber \\
\int d{\bf X}'\, G_1({\bf X},{\bf X}',E^+)[V^C_2({\bf x}'_2)+V^C_3({\bf x}'_3)+{\mbox{i}} g W_2({\bf x}'_2)]
\Psi^+({\bf X}',{\bf p}_1)
\label{LSinteg}
\end{eqnarray}
where ${\bf X}=\{{\bf x}_1,{\bf y}_1 \}$ and ${\bf x}'_2$, ${\bf x}'_3$ are supposed to be represented through
${\bf x}'_1,\ {\bf y}'_1$ by standard transformations of Jacobi coordinates.
The asymptotics of $\Psi^+({\bf X},{\bf p}_1)$ as $y_1\to \infty$
can easily be evaluated now from (\ref{LSinteg}) by taking the asymptotics of the Green's
function
\begin{equation}
G_1({\bf X},{\bf X}',E^+)\propto \frac{-\nu_1}{2\pi\hbar^2}\phi_1({\bf x}_1)
\frac{e^{{\mbox{i}} \sqrt{E-\epsilon_1}\, y_1}}{y_1}\,
{\Phi_1}^*({\bf X}',\sqrt{E-\epsilon_1}\,{\hat{\bf y}}_1).
\end{equation}
As the result, we get (\ref{asymp1}) with the following expression for the amplitude $F$
\begin{equation}
F({\bf p}'_1,{\bf p}_1)=\frac{-\nu_1}{2\pi\hbar^2}\langle\Phi_1({\bf p}'_1)|V^C_2+V^C_3+{\mbox{i}} gW_2|
\Psi^+({\bf p}_1)\rangle
\label{satot}
\end{equation}
where the matrix element stands for the integral
\begin{eqnarray}
\langle\Phi_1({\bf p}'_1)|V^C_2+V^C_3+{\mbox{i}} gW_2|\Psi^+({\bf p}_1)\rangle
=
\nonumber \\
\int d{\bf X}'\,{\Phi^*_1}({\bf X}',{\bf p}'_1)[V^C_2({\bf x}'_2)+V^C_3({\bf x}'_3)+{\mbox{i}} g W_2({\bf x}'_2)]
\Psi^+({\bf X}',{\bf p}_1).
\label{matelem}
\end{eqnarray}
The formula (\ref{satot}) suggests that the scattering amplitude can be split into the sum
of two terms
\begin{equation}
F=F^0+{\mbox{i}} gF^1,
\label{ampsplit}
\end{equation}
where $F^0$ is exclusively due to the Coulomb interactions between the positron and the hydrogen
and ${\mbox{i}} gF^1$ is due
to the absorption potential only. Let us note, that the immediate identification of these amplitudes
with pieces of (\ref{satot}) does not lead to the consistent form of the amplitudes $F^k$ since
the wave-function
$\Psi^+$ itself may be split into two parts similarly to (\ref{ampsplit}). Hence, the
contribution from different kinds of interactions cannot be separated on the basis of equation (\ref{satot}).
The appropriate way is to rewrite the LSE
(\ref{LS}) in the form of distorted wave representation \cite{Messia}. To this end, let us recast
(\ref{LS}) into
\begin{equation}
[I-G_1(E^+)(V^C_2+V^C_3)]\Psi^+({\bf p}_1)=\Phi_1+G_1(E^+){\mbox{i}} gW_2\Psi^{+}({\bf p}_1).
\label{LS1}
\end{equation}
If the energy is below the positronium formation threshold, the inversion of the operator from
the left hand side can be performed with the help of the formulae
\begin{equation}
[I-G_1(E^+)(V^C_2+V^C_3)]^{-1}\Phi_1=\Psi^{0+},
\label{Inv1}
\end{equation}
\begin{equation}
[I-G_1(z)(V^C_2+V^C_3)]^{-1}G_1(z)=G^C(z).
\label{Inv2}
\end{equation}
As the result, the LSE (\ref{LS}) takes the form
\begin{equation}
\Psi^+({\bf p}_1)=\Psi^{0+}({\bf p}_1)+G^{C}(E^+){\mbox{i}} gW_2\Psi^+({\bf p}_1).
\label{DWLS}
\end{equation}
The asymptotic analysis of equation (\ref{DWLS}) will give us the representations for amplitudes
$F^0$ and $F^1$.
The inhomogeneous term $\Psi^{0+}({\bf p}_1)$ is the outgoing solution to the $e^+-$H scattering problem
without an absorption potential
.
Following (\ref{Inv1}), this function is defined by the solution of the LSE
\begin{equation}
\Psi^{0+}({\bf p}_1)=\Phi_1({\bf p}_1)+G_1(E^+)(V^C_2+V^C_3)\Psi^{0+}({\bf p}_1).
\end{equation}
Similarly to (\ref{LS}), the asymptotics of the solution has the form
\begin{equation}
\Psi^{0+}({\bf p}_1) \propto \phi_1({\bf x}_1)
[e^{{\mbox{i}} {\bf p}_1 \cdot {\bf y}_1}+\frac{e^{{\mbox{i}} \sqrt{E-\epsilon_1}\,y_1}}{y_1}F^0(p_1{\hat{\bf y}}_1,{\bf p}_1)]
\label{asymp0}
\end{equation}
with the amplitude given by
\begin{equation}
F^0({\bf p}'_1,{\bf p}_1)=\frac{-\nu_1}{2\pi\hbar^2}\langle \Phi_1({\bf p}'_1)|V^C_2+V^C_3|
\Psi^{0+}({\bf p}_1)\rangle .
\label{F00}
\end{equation}
The Green's function $G^C(z)$ in (\ref{DWLS}) is defined as
$G^C(z)=(z-H^C)^{-1}$. Its asymptotics as $y_1\to\infty$
reads
\begin{equation}
G^C({\bf X},{\bf X}',E^+)\propto
\frac{-\nu_1}{2\pi\hbar^2}\phi_1({\bf x}_1)
\frac{e^{{\mbox{i}} \sqrt{E-\epsilon_1}\, y_1}}{y_1}\,
{\Psi^{0-}}^*({\bf X}',\sqrt{E-\epsilon_1}\,{\hat{\bf y}}_1).
\label{GCasymp}
\end{equation}
Introducing this asymptotics into (\ref{DWLS}) we get the explicit representation for
the amplitude
$F^1$ from (\ref{ampsplit})
\begin{equation}
F^1({\bf p}'_1,{\bf p}_1)=\frac{-\nu_1}{2\pi\hbar^2}\langle \Psi^{0-}({\bf p}'_1)|W_2|\Psi^{+}
({\bf p}_1)\rangle .
\label{F11}
\end{equation}
In these formulae $\Psi^{0-}({\bf p}_1)$ is the solution of the $e^+-$H scattering problem with
incoming boundary conditions $\Psi^{0-}({\bf p}_1)\propto[\Psi^{0+}(-{\bf p}_1)]^{*}$
when only Coulomb interactions are taken into account in the Hamiltonian.
The formulae (\ref{F00}) and (\ref{F11}) provide us with the
desired representation for $F$ as the sum of two amplitudes, one of which ($F^0$)
is exclusively due to the Coulomb interactions between the positron and the hydrogen and
does not depend on the absorption potential and
the other one
($F^1$) is due to the absorption potential only.
The preceding analysis is not applicable if the energy $E$ is higher than the positronium formation threshold.
Indeed, whereas the formulae (\ref{Sch1}-\ref{ampsplit}) remain valid, the inversion of
the operator
$I-G_1(E^+)(V^C_2+V^C_3)$ in the left hand side of (\ref{LS1}) cannot be performed
and, as the consequence, the equations (\ref{DWLS}-\ref{F11}) cannot be justified.
The formal reason is that the homogeneous equation
\begin{equation}
\chi=G_{1}(E^+)(V^C_{2}+V^C_{3})\chi
\label{LShom}
\end{equation}
now possesses the nontrivial solution $\chi=\Psi^{02}({\bf p}_2)$ such that
\begin{equation}
(H^C-E)\Psi^{02}({\bf p}_2)=0
\label{H^C-E}
\end{equation}
with the asymptotics $\Psi^{02}({\bf p}_2)\propto \phi_2({\bf x}_2)e^{{\mbox{i}} {\bf p}_2\cdot{\bf y}_2}$.
The latter describes
the scattering of the proton off the positronium ground state $\phi_2({\bf x}_2)$ with the
binding energy $\epsilon_2$.
This problem with LSE
is well known
in the three-body scattering theory \cite{Tobocman, Newton, Schmid} and is the manifestation
of the general fact that
no single LSE
specifies the three-body scattering wave function uniquely, if
the rearrangement channel is open. The resolution of the problem has been found by transforming
LSE
into the matrix equations for the components of the wave function. Proper
arranging of the interactions between the equations, which guarantees the uniqueness of the
solution, leads to the equations known as the Faddeev three-body equations \cite{Newton,Schmid,Fadd}.
We adopt this formalism to our case in the
next subsection where it is proven that for the energy above the positronium formation
threshold, similar to (\ref{ampsplit}), the amplitude
$F$ is given by the formula $F=F^0_{11}+{\mbox{i}} g F^1_{11}$
where the amplitudes $F^0_{11}$ and $F^{1}_{11}$
will be defined by formulae (\ref{F-0-11}) and (\ref{F-1-11}).
\subsection{Three-body scattering formalism above the positronium formation threshold}
Let us emphasize that the scattering problem with the Hamiltonian (\ref{Hamiltonian})
always deals
with the single-arrangement channel $e^+-$H due to the presence of an absorption potential.
That means
the solution to the Schr\"odinger equation
(\ref{Sch1}) has the single-arrangement asymptotics (\ref{asymp1})
irrespective that is the energy below or above the Ps-formation threshold. However,
in order to specify the
amplitudes $F^0$ and $F^1$ one needs the solutions to SE
with the Hamiltonian
$H^C$.
For the energy above the Ps-formation threshold between
Ps($n=1$) and H($n=2$) thresholds the Scr\"odinger equation
\begin{equation}
H^C\Psi^{0i}=E\Psi^{0i}
\label{Sch2}
\end{equation}
has two kinds of solutions, which are specified by the asymptotics
\begin{equation}
\Psi^{0i}({\bf p}_i) \propto \phi_i({\bf x}_i)[e^{{\mbox{i}} {\bf p}_i\cdot{\bf y}_i} +
\frac{e^{{\mbox{i}} p_iy_i}}{y_i}{f}_{ii}],
\ \ \ y_i\to \infty ,
\label{multichannelas1}
\end{equation}
\begin{equation}
\Psi^{0i}({\bf p}_i) \propto \phi_k({\bf x}_k)\frac{e^{{\mbox{i}} p_ky_k}}{y_k}{f}_{ki},
\ \ \ y_k\to \infty,\ \ \ k\ne i .
\label{multichannelas2}
\end{equation}
Here the momenta ${\bf p}_{i(k)}$ are related to the energy as
$E=\hbar^2/2\nu_{i(k)}\ p_{i(k)}^2+\epsilon_{i(k)}$
and indices $i(k)$ run over the
$\{1,2\}$ set.
The formulae (\ref{multichannelas1}, \ref{multichannelas2}) reflect the fact that
now the asymptotic
form of the wave function is different in different asymptotic arrangements.
This is exactly that property
of the three-body wave-function, which cannot be recovered by any single LSE.
In order to take into account
the multichannel character of the scattering problem above the
rearrangement threshold we use the formalism of Faddeev equations \cite{Fadd}.
Since the original
formalism is developed for the short range interaction, at the first stage we reformulate
the three-body Hamiltonian in such a way that Coulomb interactions are split into long-range and
short-range parts
\cite{merkuriev}
\begin{equation*}
V^C_i({\bf x}_i) = V^l_i({\bf x}_i,{\bf y}_i)+V^s_i({\bf x}_i,{\bf y}_i).
\end{equation*}
This splitting is made in the three-body configuration space by a smooth
splitting function $\zeta_i({\bf x}_i,{\bf y}_i)$
constructed such that $\zeta_i({\bf x}_i,{\bf y}_i)=1$ if
$x_i/x_0<(1+y_i/y_0)^\nu$ and
$\zeta_i({\bf x}_i,{\bf y}_i)=0$ if $x_i/x_0>(1+y_i/y_0)^\nu$ for some
$x_0>0,\, y_0>0$ and $0<\nu<1/2$.
With such a $\zeta_i$ the short- and long-range parts of the Coulomb
potentials are defined as
\begin{equation*}
V^s_i({\bf x}_i,{\bf y}_i)=\zeta_i({\bf x}_i,{\bf y}_i)V^C_i({\bf x}_i);
\ \ \
V^l_i=V^C_i-V^s_i.
\end{equation*}
The Hamiltonian (\ref{Hamiltonian}) is then transformed into
\begin{equation*}
H=H^l+V^s_1+V^s_2+{\mbox{i}} gW_2; \ \ \ H^l=T+V^l_1+V^l_2+V^C_3.
\end{equation*}
After this modification, the components of the wave function $\Psi^+$ are
defined by formulae
\begin{eqnarray}
\Psi^+_1&=&(E^{+} -H^l)^{-1}V^s_1\Psi^+ ,
\label{fadd-comp1}\\
\Psi^+_2&=&(E^{+}-H^l)^{-1}(V^s_2+{\mbox{i}} gW_2)\Psi^+ ,
\label{fadd-comp2}
\end{eqnarray}
where $E^{+}=E+{\mbox{i}} 0$. Two components are enough in our case. Indeed, the
potential $V^C_3$ between the positron and the proton is repulsive and does not supports bound states. Hence,
only two asymptotic arrangements are possible, which are covered by components $\Psi^+_{1,2}$.
It is straightforward to see that the sum of the
components recovers the wave function
\begin{equation}
\Psi^+=\Psi^+_1+\Psi^+_2
\label{PsiPsi1Psi2}
\end{equation}
and the components obey the set of modified Faddeev equations (MFE)
\begin{eqnarray}
\label{mfe-1}
(E -H^l-V^s_1)\Psi^+_1&=&V^s_1\Psi^+_2 , \\
\label{mfe-2}
(E-H^l-V^s_2-{\mbox{i}} gW_2)\Psi^+_2&=&(V^s_2+{\mbox{i}} gW_2)\Psi^+_1.
\end{eqnarray}
The important feature of equations (\ref{mfe-1}, \ref{mfe-2}), with regard to the description
of the annihilation, is the fact that now the
two-body absorption potential ${\mbox{i}} gW_2$ is incorporated into equations in two manners.
It appears
in the diagonal part on the left hand side
of the equation (\ref{mfe-2}) and in the coupling term on the right hand side.
The diagonal terms of the equations (\ref{mfe-1}, \ref{mfe-2}) are responsible for the asymptotic
configurations in channels 1 and 2, so the absorption potential in the left hand side of (\ref{mfe-2})
is natural
to associate with the annihilation after positronium formation.
The coupling term in (\ref{mfe-1}, \ref{mfe-2}) couples equations in the reaction volume, therefore
the absorption potential in the right hand side of (\ref{mfe-2}) is
the source for the direct annihilation. These associations will be put on the solid ground
in the next section.
As in the case of equation (\ref{Sch1}), the scattering solution to equations (\ref{mfe-1}, \ref{mfe-2})
is defined by the asymptotics as $y_1\to \infty$
\begin{eqnarray}
\label{psi-1}
\Psi^+_1({\bf p}_1)\propto \phi_1({\bf x}_1)[e^{{\mbox{i}} {\bf p}_1\cdot {\bf y}_1}+ \frac{e^{{\mbox{i}} p_1 y_1}}{y_1}F_{11}],
\\
\label{psi-2}
\Psi^+_2({\bf p}_1)\propto 0.
\end{eqnarray}
Certainly, for the amplitudes $F_{11}$ and $F$ from (\ref{satot}) the equality holds
true
\begin{equation*}
F_{11}=F
\end{equation*}
as it should be in view of (\ref{PsiPsi1Psi2}).
Again, as in the case of equation (\ref{Sch1}), the solution required by (\ref{psi-1}, \ref{psi-2})
is given by the integral form of MFE
(\ref{mfe-1}, \ref{mfe-2}) (IMFE)
\begin{eqnarray}
\label{IMFE-1}
\Psi^+_1({\bf p}_1)=\Phi^{0+}_{1}({\bf p}_1)+&(E^+ -H^l-V^{s}_1)^{-1}V^{s}_1\Psi^+_2({\bf p}_1),\\
\label{IMFE-2}
\Psi^+_2({\bf p}_1)=&(E^+ -H^l-V^{s}_2-{\mbox{i}} gW_2)^{-1}(V^{s}_2+{\mbox{i}} gW_2)\Psi^+_1({\bf p}_1).
\end{eqnarray}
Here $\Phi^{0+}_1$ stands for the solution to the channel Schr\"odinger
equation~$(H^l+V^{s}_1-E)\Phi^{0+}_1=0$,~which explicit form is
\begin{equation}
(H_0+V_1-E)\Phi^{0+}_1=-(V^l_2+V^C_3)\Phi^{0+}_1.
\label{Chan1aseq}
\end{equation}
Repeating reasoning of (\ref{LS}-\ref{matelem}) we get the asymptotics
as $y_1\to \infty$
\begin{equation}
\Phi^{0+}_{1}({\bf p}_1)\propto \Phi_1({\bf p}_1) +\phi_1({\bf x}_1)\frac{e^{{\mbox{i}} p_1 y_1}}{y_1}f^0_{11}
\label{f0-11}
\end{equation}
with
\begin{equation}
f^0_{11}({\bf p}'_1,{\bf p}_1)
=\frac{-\nu_1}{2\pi\hbar^2}\langle \Phi_1({\bf p}'_1)|V^{l}_2+V^C_3|\Phi^0_{1}({\bf p}_1)\rangle.
\label{f011}
\end{equation}
The IMFE (\ref{IMFE-1}, \ref{IMFE-2}) are proven to have the unique solution
below as well as above the rearrangement threshold \cite{Fadd,merkuriev}.
We use this property to remedy the shortcoming of the LSE approach outlined above
in specifying the structure of the amplitude
$F$ above the Ps-formation threshold.
In order to proceed, it
is convenient to introduce matrix notations
\begin{equation*}
{\bf H}({\mbox{i}} g)=\left[
\begin{array}{cc}
H^l+V^s_1 & 0\\
0 &H^l+V^s_2+{\mbox{i}} gW_2
\end{array}
\right],
\end{equation*}
\vskip 0.3cm
\begin{equation*}
{\bf V}=\left[
\begin{array}{cc}
0 & V^s_1\\
V^s_2 & 0
\end{array}
\right],
\ \
{\bf W}=\left[
\begin{array}{cc}
0 & 0\\
W_2 & 0
\end{array}
\right],
\ \
{\bf I}=\left[
\begin{array}{cc}
1 & 0\\
0 & 1
\end{array}
\right].
\end{equation*}
Thus, the MFE set takes the form
\begin{equation}
[{\bf H}({\mbox{i}} g)-E{\bf I}]{\bf \Psi}({\bf p}_1)=-[{\bf V}+{\mbox{i}} g{\bf W}]{\bf \Psi}({\bf p}_1),
\label{Matrix-MFE}
\end{equation}
where the vector solution is constructed from wave function components as
${\protect \bf \Psi}=(\Psi^+_1,\Psi^+_2)$. The IMFE set (\ref{IMFE-1}, \ref{IMFE-2}) in matrix
notations reads
\begin{equation}
{\bf \Psi}({\bf p}_1)={\bf \Phi}^{0+}({\bf p}_1)+
[E^+{\bf I}-{\bf H}({\mbox{i}} g)]^{-1}[{\bf V}+{\mbox{i}} g{\bf W}]{\bf \Psi}({\bf p}_1).
\label{Matrix-IMFE}
\end{equation}
The vector of the inhomogeneous term is defined as ${\bf \Phi}^{0+}({\bf p}_1)=(\Phi^{0+}_1,0)$.
This equation can be reformulated in the form of distorted wave representation by similar way we
made for LSE (\ref{LS}).
The equation
(\ref{Matrix-IMFE}) can be recast into
\begin{equation*}
\{{\bf I}-[E^+{\bf I}-{\bf H}({\mbox{i}} g)]^{-1}{\bf V}\}{\bf \Psi}({\bf p}_1)={\bf \Phi}^{0+}({\bf p}_1)+
[E^+{\bf I}-{\bf H}({\mbox{i}} g)]^{-1}{\mbox{i}} g{\bf W}{\bf \Psi}({\bf p}_1).
\end{equation*}
Then, by the use of the formulae
\begin{equation}
\{{\bf I}-[E^+{\bf I}-{\bf H}({\mbox{i}} g)]^{-1}{\bf V}\}^{-1}{\bf \Phi}^{0+}({\bf p}_1)={\bf \Psi}^{0+}({\bf p}_1),
\label{Psi-0}
\end{equation}
\begin{equation}
\{{\bf I}-[z{\bf I}-{\bf H}({\mbox{i}} g)]^{-1}{\bf V}\}^{-1}[z{\bf I}-{\bf H}({\mbox{i}} g)]^{-1}=
[z{\bf I}-{\bf H}({\mbox{i}} g)-{\bf V}]^{-1}
\end{equation}
we arrive at the desired distorted wave representation of the IMFE
\begin{equation}
{\bf \Psi}({\bf p}_1)={\bf \Psi}^{0+}({\bf p}_1)+
[E^+{\bf I}-{\bf H}({\mbox{i}} g)-{\bf V}]^{-1}{\mbox{i}} g{\bf W}{\bf \Psi}({\bf p}_1).
\label{DW-Matrix-IMFE}
\end{equation}
From this equation it is seen that
\begin{equation}
{\bf \Psi}({\bf p}_1)={\bf \Psi}^{0+}({\bf p}_1)+{\bf \Psi}^{1+}({\bf p}_1)
\label{Psi_101}
\end{equation}
where ${\bf \Psi}^{1+}({\bf p}_1)$ stands for the second term in equation (\ref{DW-Matrix-IMFE}).
The equation (\ref{DW-Matrix-IMFE}) is the direct analog of (\ref{DWLS})
but, in contrast to that, is well defined below as well as above the Ps-formation threshold
and therefore can be used to get the necessary
representation for the amplitude $F_{11}$.
The asymptotics of ${\bf \Psi}({\bf p}_1)$ is formed from contributions of both terms in (\ref{Psi_101}).
Let us consider the inhomogeneous term ${\bf \Psi}^{0+}({\bf p}_1)$. The equation for this term reads
\begin{equation}
{\bf \Psi}^{0+}({\bf p}_1)={\bf \Phi}^{0+}({\bf p}_1)+
[E^+{\bf I}-{\bf H}({\mbox{i}} g)]^{-1}{\bf V}{\bf \Psi}^{0+}({\bf p}_1)
\label{IPsi-0}
\end{equation}
or
\begin{equation}
[{\bf H}({\mbox{i}} g)+{\bf V}]{\bf \Psi}^{0+}({\bf p}_1)=E{\bf I}{\bf \Psi}^{0+}({\bf p}_1).
\label{DPsi-0}
\end{equation}
These equations are quite similar to (\ref{mfe-1}, \ref{mfe-2}) and (\ref{IMFE-1},
\ref{IMFE-2}) except the
coupling term ${\bf V}$, which does not contain the absorption potential. The asymptotics of the solution
to (\ref{DPsi-0}) as $y_1\to \infty$, which follows from (\ref{IPsi-0}), is similar
to (\ref{psi-1}, \ref{psi-2}) and for the components of ${\bf \Psi}^{0+}=(\Psi^{0+}_1, \Psi^{0+}_2)$
has the form
\begin{eqnarray}
\label{psi-01}
\Psi^{0+}_1({\bf p}_1)\propto \phi_1({\bf x}_1)[e^{{\mbox{i}} {\bf p}_1\cdot {\bf y}_1}+
\frac{e^{{\mbox{i}} p_1 y_1}}{y_1}F^0_{11}]
\\
\label{psi-02}
\Psi^{0+}_2({\bf p}_1)\propto 0.
\end{eqnarray}
As it was demonstrated above, the formula for the amplitude $F^0_{11}$ should be derived by
taking asymptotics of the right hand side of (\ref{IPsi-0}) as $y_1\to \infty$. A minor
difference from what we have demonstrated above is that the
nontrivial contribution into the amplitude comes from not only the Green's function source
term but also from the driving term due to (\ref{f0-11}).
So that, the amplitude $F^0_{11}$ is given by
\begin{equation}
F^0_{11}({\bf p}'_1,{\bf p}_1) = \frac{-\nu_1}{2\pi\hbar^2}[
\langle \Phi_1({\bf p}'_1)|V^{l}_2+V^C_3|\Phi^{0+}_{1}({\bf p}_1)\rangle +
\langle \Phi^{0+}_{1}({\bf p}'_1)|V^{s}_1|\Psi^{0+}_{2}({\bf p}_1)\rangle ] .
\label{F-0-11}
\end{equation}
Now we
consider the ${\bf \Psi}^{1+}({\bf p}_1)$ term.
Its asymptotics as $y_1\to \infty$ is defined by
the Green's function ${\bf G}(z)=[z{\bf I}- {\bf H}({\mbox{i}} g) -{\bf V}]^{-1}$. This function is
a genuine three-body quantity and the asymptotics
of its matrix elements
as $y_i\to \infty$ may be written in the form
\begin{equation}
G_{ij}({\bf X},{\bf X}',E^+)\propto
\frac{-\nu_i}{2\pi\hbar}\,\phi_i({\bf x}_i)\frac{e^{{\mbox{i}} \sqrt{E-\epsilon_i}\,y_i}}{y_i}
{\Upsilon^{0-}_j}^*({\bf X}',\sqrt{E-\epsilon_i}\, {\hat{\bf y}}_i),
\label{Greensf}
\end{equation}
where ${\Upsilon^{0-}_j}$ is the eigenfunction of the adjoint to the operator from the left hand side
of (\ref{DPsi-0}). This asymptotics has different character for $i=1$ and $i=2$.
In the first case $G_{1j}$ does not vanish with $y_1$ large since $E-\epsilon_1$ is real nonnegative.
If $i=2$, the Positronium binding energy $\epsilon_2$ becomes complex when the absorption potential is introduced
into the $e^+e^-$ Hamiltonian. That makes the relative momentum $p_2=\sqrt{E-\epsilon_2}$ complex, i.e.
$p_2=p^r_2+{\mbox{i}} p^i_2$. So, the asymptotics of $G_{2j}$ vanish exponentially. Thus, only
$\Psi^{1+}_1$ component has the nontrivial asymptotics
\begin{equation}
\Psi^{1+}_1({\bf p}_1)\propto
\phi_1({\bf x}_1)\frac{e^{{\mbox{i}} p_1 y_1}}{y_1}{\mbox{i}} g F^1_{11}
\label{Psi11}
\end{equation}
with the amplitude $F_{11}$ given by
\begin{equation}
F^1_{11}({\bf p}'_1,{\bf p}_1)=\frac{-\nu_1}{2\pi\hbar^2}\langle \Upsilon^{0-}_2({\bf p}'_1)|W_2|
\Psi^+_1({\bf p}_1)\rangle.
\label{F-1-11}
\end{equation}
Here $\Upsilon^{0-}_2$ is the second component of the solution to the adjoint equation
to (\ref{DPsi-0})
\begin{equation}
[{\bf H}(-{\mbox{i}} g)+{\bf V}^T-E{\bf I}]{\bf \Upsilon}^{0-}({\bf p}_1)=0
\label{DUips-0}
\end{equation}
being defined by the integral form
\begin{equation}
{\bf \Upsilon}^{0-}({\bf p}_1)={\bf \Phi}^{0-}({\bf p}_1)+
[E^-{\bf I}-{\bf H}(-{\mbox{i}} g)]^{-1}{\bf V}^T{\bf \Upsilon}^{0-}({\bf p}_1).
\label{IUpsi-0}
\end{equation}
In this equation $E^-=E-{\mbox{i}} 0$, ${\bf V}^T$ means transposed matrix and
${\bf \Phi}^{0-}=(\Phi^{0-}_1,0)$ where $\Phi^{0-}_1$ is
the solution to (\ref{Chan1aseq}) with incoming boundary conditions.
The solution to (\ref{DUips-0}) in the case of $g=0$ takes the very simple form,
i.e. $\Upsilon^0_1=\Upsilon^0_2=\Psi^0$ where $\Psi^0$ is the three-body wave-function for the
pure Coulomb problem. So, $\Psi^0$ obeys the Schr\"odinger equation (\ref{Sch2})
and can be constructed from wave-function
Faddeev components (\ref{fadd-comp1}, \ref{fadd-comp2}) at $g=0$
as $\Psi^0=\Psi^{00}_1+\Psi^{00}_2$. The detailed information on this and other features of
the matrix equations as MFE and IMFE and matrix Green's functions, which is
necessary for evaluations made above, can be found in Ref. \cite{yak-evans-hof}.
The formulae (\ref{F-0-11}, \ref{F-1-11}) determine the ingredients of the amplitude
$F_{11}$ uniformly
above as well as below the rearrangement threshold of the positronium formation. It
is possible to show by
preforming backwards transformations that below the Ps-formation threshold, where
the representations (\ref{ampsplit}, \ref{F00}, \ref{F11}) are valid,
the equality
\begin{equation}
F^0_{11}+{\mbox{i}} g F^1_{11}= F^0 + {\mbox{i}} gF^1=F
\label{F11-Feq}
\end{equation}
holds true.
It is important to note, that from the analysis of the equation (\ref{IPsi-0}) it follows
\begin{equation}
F^0_{11}=F^0+{\cal O}(g).
\label{F-0-11F0}
\end{equation}
This means that the respective terms in the left and right hand sides of the first equation
in the chain (\ref{F11-Feq})
are not identical. In fact the amplitude $F^0_{11}$
takes into account not only the Coulomb interaction between the positron and the hydrogen, as $F^0$
does, but also the
possibility of $e^+e^-$ annihilation after the positronium formation. That is due to the presence
of the absorption potential in the diagonal part of the equations (\ref{DPsi-0}).
This means that
below the
positronium formation
threshold the annihilation after virtual formation of the positronium is
incorporated into the
$F^0_{11}$ amplitude and consequently $F^1_{11}$ is the pure direct annihilation amplitude.
It is worth mentioning again, that the formulae
(\ref{F-0-11}, \ref{F-1-11}) determine the amplitudes uniformly below as well as above
the positronium formation threshold, whereas it is not true for representations (\ref{F00}, \ref{F11}).
They are valid
only below the positronium formation threshold.
\section{Optical theorem in the presence of absorption and annihilation cross section
\label{OT}}
\subsection{Optical theorem\label{OT1}}
The standard optical theorem for Hermitian Hamiltonians is nothing but the
manifestation of
the flux conservation, what is equivalent to the unitarity of the S-matrix.
The absorption potential
breaks the Hermiticity and the scattering is not unitary. The lack of unitarity is the
measure of how much of the
flux is absorbed and in the case of the annihilation is the way to determine the
annihilation cross section.
There is extensive literature on the optical theorem but
\cite{Messia}
is the most suitable
for our purpose. Following this approach by multiplying the SE (\ref{Sch1}) by complex
conjugate
wave function ${\Psi^+}^*$ and subtracting the complex conjugated SE multiplied by $\Psi^+$
we arrive at
the equality
\begin{equation}
{\Psi^+}^*H_0\Psi^+ -\Psi^+H_0{\Psi^+}^*=-2{\mbox{i}} gW_2|\Psi^+|^2.
\label{nonHerm}
\end{equation}
Integrating over the domain $\Omega_{R}=\{y_1\le R\}$, using the Green's formula and taking the
limit as $R\to \infty$, we get the following result
\begin{equation}
-2{\mbox{i}} g \int d{\bf x}_1 d{\bf y}_1\, W_2|\Psi^+|^2=\frac{\hbar^2}{2\nu_1}
\lim_{R\to \infty}\int R^2 d{\hat{\bf y}}_1\int d{\bf x}_1\, \{\Psi^+,{\Psi^+}^*\},
\label{WronskForm}
\end{equation}
which represents the balance of the flux.
Here the Wronskian $\{\Psi^+,{\Psi^+}^*\}= \Psi^+\partial_{y_1}{\Psi^+}^*-
{\Psi^+}^*\partial_{y_1}{\Psi^+}$
has to be taken at the condition $y_1=R$. Then, using the asymptotic form of $\Psi^+$
given in (\ref{asymp1}),
the normalization of the ground-state wave functions $\phi_1({\bf x}_1)$ and the weak asymptotics
of the plain wave (see for example \cite{Messia-was})
\begin{equation*}
e^{{\mbox{i}} {\bf p}\cdot {\bf y}}\propto \frac{2\pi}{{\mbox{i}} py}\left[
-\delta({\hat{\bf p}}+{\hat{\bf y}})e^{-{\mbox{i}} py}+\delta({\hat{\bf p}}-{\hat{\bf y}})e^{{\mbox{i}} py}\right]
\end{equation*}
we finally arrive at the optical theorem in the presence of absorption
\begin{equation}
\frac{2\nu_1(-g)}{\hbar^2p_1}\int d{\bf x}_1 d{\bf y}_1\, W_2|\Psi^+|^2=
\frac{4\pi}{p_1}\Im\mbox{m} F({\bf p}_1,{\bf p}_1) -\int d{\hat{\bf y}}\, |F(p_1{\hat{\bf y}},{\bf p}_1)|^2.
\label{OptTh}
\end{equation}
The positive quantity in the left hand side of (\ref{OptTh}) is the absorption
cross section which determines in our case the overall $e^+e^-$ annihilation cross section due to the direct
process as well as due to the annihilation after (virtual if $E<\epsilon_2$ or actual if $E>\epsilon_2$)
positronium formation
\begin{equation}
\sigma^a= \frac{2\nu_1(-g)}{\hbar^2p_1}\int d{\bf x}_1 d{\bf y}_1\, W_2|\Psi^+|^2.
\label{sigma_a}
\end{equation}
So that, the overall annihilation cross section can be computed either by the integral
(\ref{sigma_a})
or by the expression in the right hand side of (\ref{OptTh}), if the total amplitude $F$
is in possession.
In order to go beyond the standard formulation (\ref{OptTh}, \ref{sigma_a}) one needs to
use the detailed
structure of the amplitude $F$. In our case it is the representation (\ref{F11-Feq})
\begin{equation*}
F=F^0_{11}+{\mbox{i}} gF^1_{11}
\end{equation*}
which leads to the following form of (\ref{OptTh})
\begin{eqnarray}
\sigma^a= \sigma^a_2 +\sigma^a_1
\label{sigma21}\\
\sigma^a_2= \frac{4\pi}{p_1}\Im\mbox{m}F^0_{11}({\bf p}_1,{\bf p}_1)-\int d{\hat{\bf y}}\, |F^0_{11}(p_1{\hat{\bf y}},{\bf p}_1)|^2
\label{sigma2} \\
\sigma^a_1=
\frac{4\pi}{p_1}(-g)\Re\mbox{e} F^1_{11}({\bf p}_1,{\bf p}_1)-
\nonumber\\
2(-g)\int d{\hat{\bf y}}\, \Im\mbox{m}F^0_{11}(p_1{\hat{\bf y}},{\bf p}_1){F^1_{11}}^*(p_1{\hat{\bf y}},{\bf p}_1)
-g^2 \int d{\hat{\bf y}}\, |F^1_{11}(p_1{\hat{\bf y}},{\bf p}_1)|^2.
\label{sigma1}
\end{eqnarray}
The quantities $\sigma^a_1$ and $\sigma^a_2$ have meaning of annihilation cross sections for
the direct process and the process of the annihilation after the positronium formation.
To make this statement sound,
let us show that $\sigma^a_2$ is the cross section of the after the
positronium formation annihilation.
Thus, the remaining part of $\sigma^a$, what is $\sigma^a_1$, should be interpreted as
the direct annihilation cross section.
It is apparent, that the equation (\ref{sigma2})
is the optical theorem formulated for the equation
(\ref{DPsi-0}).
Indeed, multiplying
the equation (\ref{DPsi-0}) by ${\bf \Upsilon}^{+0}$ from the left and subtracting
the equation for
${\bf \Upsilon}^{+0}$
\begin{equation}
[{\bf H}({\mbox{i}} g)+{\bf V}^T-E{\bf I}]{\bf \Upsilon}^{0+}({\bf p}_1)=0
\label{DUips+0}
\end{equation}
multiplied by ${\bf \Psi}^{0+}$ from the right and making obvious cancelations we get
\begin{equation*}
\langle {\bf \Upsilon}^{0+},H_0{\bf I}{\bf \Psi}^{0+}\rangle-
\langle H_0{\bf I}{\bf \Upsilon}^{0+},{\bf \Psi}^{0+}\rangle=
2{\mbox{i}} g \langle {\bf \Upsilon}^{0+}, {\bf D}{\bf \Psi}^{0+}\rangle.
\end{equation*}
Here ${\bf D}$ is a diagonal matrix $\mbox{diag}\{0,W_2\}$ and $\langle .,.\rangle$
is the scalar product in
the two dimensional complex space ${\bf C}^2$ of wave-function components.
Repeating argumentations which led us to the formula (\ref{OptTh}), we arrive at the equality
\begin{eqnarray}
\frac{2\nu_1(-g)}{\hbar^2 p_1}\int d{\bf x}_1d{\bf y}_1\, {\Upsilon^{0+}_2}^*({\bf p}_1)W_2\Psi^{0+}_2({\bf p}_1)=
\nonumber \\
\frac{4\pi}{p_1}\Im\mbox{m}F^0_{11}({\bf p}_1,{\bf p}_1)-\int d{\hat{\bf y}}\, |F^0_{11}(p_1{\hat{\bf y}},{\bf p}_1)|^2.
\label{sigma-a2}
\end{eqnarray}
This is the optical theorem for equation (\ref{DPsi-0}) and the annihilation cross section
$\sigma^a_2$
can be expressed now in terms of the left hand side as
\begin{equation}
\sigma^a_2=\frac{2\nu_1(-g)}{\hbar^2 p_1}\int d{\bf x}_1d{\bf y}_1\, {\Upsilon^{0+}_2}^*({\bf p}_1)
W_2\Psi^{0+}_2({\bf p}_1).
\label{sigma-a20}
\end{equation}
To elucidate the further meaning of the cross section $\sigma^a_2$ it is instructive
to consider the limiting case as $g\to 0$.
In the limit no absorption potential is present, scattering becomes unitary and amplitude
$F^0_{11}$ coincides
with $f_{11}$ from (\ref{multichannelas1}). The standard unitary variant of the optical theorem for
the amplitude $f_{11}$ has the form
\begin{equation}
\frac{4\pi}{p_1}\Im\mbox{m} f_{11}({\bf p}_1,{\bf p}_1)-
\int d{\hat{\bf y}}\, |f_{11}(p_1{\hat{\bf y}},{\bf p}_1)|^2 - \int d{\hat{\bf y}}\, |f_{21}(p_1{\hat{\bf y}},{\bf p}_1)|^2=0
\label{OptTh-0}
\end{equation}
where $f_{11}$ is the elastic $e^+-$H amplitude and $f_{21}$ is the rearrangement Ps$-p$ amplitude.
Therefore, the right hand
side of (\ref{sigma-a2}) has the limit
\begin{equation}
\frac{4\pi}{p_1}\Im\mbox{m}F^0_{11}({\bf p}_1,{\bf p}_1)-\int d{\hat{\bf y}}\, |F^0_{11}(p_1{\hat{\bf y}},{\bf p}_1)|^2 \to
\int d{\hat{\bf y}}\, |f_{21}(p_1{\hat{\bf y}},{\bf p}_1)|^2=\sigma_{21}.
\label{sigma-21}
\end{equation}
The quantity $\sigma_{21}$ is nothing but the positronium formation cross section.
At the same time the formula (\ref{sigma-a20})
leads to an uncertainty in the limit as $g\to 0$ when the diverging integral is multiplied
by the vanishing factor
$g$.
Actually, the resolution of this uncertainty is made by (\ref{sigma-21}) and gives the relation
\begin{equation}
\sigma^a_2=\sigma_{21}+{\cal O}(g),
\label{sigma-a2-21}
\end{equation}
which clearly shows that $\sigma^a_2$ is the cross section of the annihilation after the
positronium formation.
The main result of this subsection is the representation of the annihilation cross section
as the sum of two
terms
\begin{equation*}
\sigma^a=\sigma^a_1+\sigma^a_2,
\end{equation*}
where $\sigma^a_2$ is shown to represent
the cross section of the annihilation after the positronium formation,
which is given
by the formulae (\ref{sigma2}) or (\ref{sigma-a20}). Therefore $\sigma^a_1$ is the direct
annihilation cross section, given by (\ref{sigma1}).
The analysis made above shows that the definitions of cross sections in terms of scattering
amplitudes (\ref{sigma2},~\ref{sigma1}) are uniform and are valid below as well as above
the rearrangement
threshold of the positronium formation. Moreover, by construction, the integrals (\ref{F-0-11},
\ref{F-1-11})
involved in the definitions of the amplitudes $F^0_{11},\, F^1_{11}$
have the finite limit as $g\to 0$. This property will
be used below for perturbative calculations of the amplitudes and cross sections.
At the same time the integrals in representations (\ref{sigma_a},~\ref{sigma-a20}) are divergent
above the positronium formation threshold if the limit
$g\to 0$ is taken.
That makes these formulae not suitable for perturbative methods above the positronium formation
threshold.
\subsection{Absorbing annihilation potential}
In this subsection we fix the coordinate form of the absorption potential by comparing the
definition
(\ref{sigma_a}) for $\sigma^a$ with QED formula for the $2\gamma$ singlet $e^+e^-$ annihilation
\footnote{The spin-averaging factor $1/4$ for singlet $2\gamma$ annihilation is implied
implicitly.} \cite{fraser, charlton}
\begin{equation}
{\sigma}^{a}=\pi r^2_0 (c/v){Z}_{\mbox{{eff}}}.
\label{QED-sigma}
\end{equation}
In this formula $r_0$ is the classical electron radius, $c$ is the speed of light and $v$ is the incident
velocity of the positron.
The effective number of electrons ${Z}_{\mbox{{eff}}}$ participating in annihilation is given by the
integral
\begin{equation}
Z_{\mbox{eff}}= \int d{\bf x}_1 d{\bf y}_1\,
|\Psi^{0+}({\bf x}_1,{\bf y}_1)|^{2}
\delta({\bf x}_2).
\label{-Zeff}
\end{equation}
Here
$\Psi^{0+}$ is the $\Psi^{01}$ solution of the $e^+-$H scattering problem (\ref{Sch2},
\ref{multichannelas1}, \ref{multichannelas2})
when the absorption potential is not taken into account.
The integral in (\ref{-Zeff}) is well defined below the Ps-formation threshold. In this case (\ref{QED-sigma},
\ref{-Zeff}) can be considered as the first order perturbation approximation to (\ref{sigma_a}),
since below the rearrangement threshold
$\Psi^+\simeq \Psi^{0+}$
is the well defined first order perturbation solution (Born)
to (\ref{DWLS}). This observation was used in \cite{mitroy} to determine the
absorption potential
for $2\gamma$ singlet $e^+e^-$ annihilation as
\begin{eqnarray}
{\mbox{i}} g W_2({\bf x}_2)={\mbox{i}} g \delta({\bf x}_2)
\label{delta-absorb}\\
g=-\frac{e^2}{a_0}2\pi \alpha^3.
\nonumber
\end{eqnarray}
Here $a_0$ is the Bohr radius and $\alpha$ is the fine structure constant. This potential was used in
\cite{mitroy}
to calculate the direct annihilation cross section by solving the Lippmann-Schwinger
equation for T-matrix
below the Ps-formation threshold.
The formula (\ref{-Zeff}) cannot be extended for calculations above the Ps-formation
threshold since the integral
diverges.
One of ways to go over the Ps-formation threshold is the use of (\ref{sigma_a})
with absorption potential
(\ref{delta-absorb}) incorporated into the Schr\"odinger equation. This was done in
papers \cite{iks, igarashi2} where the overall annihilation cross section $\sigma^a$ was computed
below as well as above the Ps-formation threshold within the hypersperical close coupling technique
for the time independent three-body Schr\"odinger equation. Paper
\cite{yamanaka} represents the solution of the time-dependent three-body Schr\"odinger equation with
the absorption potential (\ref{delta-absorb}) below as well as above the Ps-formation threshold.
All these papers
dealt with numerical solutions of respective equations and the delta-functional singularity
of the potential
(\ref{delta-absorb}) was treated by a certain numerical approximation. Nevertheless,
the analytical status of the
potential (\ref{delta-absorb}) is not satisfactory. The delta-functional singularity
is too strong and makes the Hamiltonian not well defined. This issue was not addressed in aforementioned
papers and we give a portion of the necessary analysis in this subsection.
It is well known already since the papers by Fermi \cite{delta-potF} and then Breit
\cite{delta-potB} that the
three-dimensional delta-function potential can be incorporated into
the Schr\"odinger equation only perturbatively.
One of the approaches to go beyond the perturbative treatment is the use of a zero-range potential
\cite{delta-potB, DemkovO}. There are two common ways to introduce the zero-range potential.
One is imposing boundary conditions for the wave-function
at the singularity point. The other one is introducing into the Hamiltonian an additional term,
which enforces the wave-function to fulfill the boundary conditions. This term
can conveniently be represented in the compact form by the quasi-potential \cite{BW, Huang}.
We choose the second option.
The singularity caused by the zero-range potential in the case of the
electron-positron interaction is located
at the same point as the
Coulomb singularity $-e^2/x_2$. The latter leads to the modification of the standard
zero-range potential and of the respective quasi-potential. The resulting definition for
the coordinate part $W_2$ of the absorption potential is
\begin{equation}
W_2({\bf x})=\delta({\bf x})\frac{1-n_2x}{1+n_2x\log x}\,\frac{d}{dx}\,\frac{x}{1+n_2x\log x}
\label{qdelta-pot}
\end{equation}
where $n_2=-2\mu_2 e^2$ and $\mu_2$ is the $e^+e^-$ reduced mass.
The detailed derivation of (\ref{qdelta-pot}) involves a substantial portion of mathematics
and will be
published elsewhere. Some basic theorems, which define the general properties of the zero-range
potential
with the Coulomb modification, can be found in \cite{Albeverio}.
It is straightforward to see that in the limit $n_2 \to 0$ the quasi-potential (\ref{qdelta-pot})
takes the
standard form
\begin{equation}
W_2({\bf x})\to \delta({\bf x})\frac{d}{dx}\,x.
\end{equation}
The quasi-potential ${\mbox{i}} g W_{2}({\bf x}_2)$ enforces the following asymptotics for the wave function as
$x_2\to 0$
\begin{equation}
\Psi({\bf x}_2,{\bf y}_2)\propto \frac{a({\bf y}_2)}{4\pi}[\frac{1}{x_2}+n_2\log x_2] + b({\bf y}_2) +
{\cal O}(x_2\log x_2),
\label{bc}
\end{equation}
where $a/b=-{\mbox{i}} g{2\mu_2}/{\hbar^2}$. This asymptotics, as usually,
determines the appropriate boundary conditions, which we do not write down here explicitly.
It can be shown that the action of the quasi-potential on the function with such an asymptotics
is given by the formula
\begin{equation}
W_2({\bf x}_2)\Psi({\bf x}_2,{\bf y}_2)= \delta({\bf x}_2)b({\bf y}_2).
\end{equation}
The latter means that the action of the quasi-potential on a function $\chi({\bf x}_2,{\bf y}_2)$,
which is regular in the point $x_2=0$, is equivalent to the delta-function
\begin{equation}
W_2({\bf x}_2)\chi({\bf x}_2,{\bf y}_2)= \delta({\bf x}_2)\chi(0,{\bf y}_2).
\label{reg delta}
\end{equation}
This formula shows that if a matrix element of the quasi-potential is calculated between the functions
$\chi,\,\omega$,
which are regular at $x_2=0$, then the quasi-potential is equivalent to the delta-function, i.e.
\begin{equation}
\langle \chi|W_2({\bf x}_2)|\omega\rangle = \langle \chi|\delta({\bf x}_2)|\omega \rangle .
\end{equation}
This statement justifies the use of the delta-function as the coordinate part of the
absorption potential in \cite{iks, igarashi2, yamanaka},
since the basis functions of the approaches used to compute the
matrix elements of the absorption potential are smooth. Nevertheless, any basis of smooth functions
cannot reproduce the singularity in (\ref{bc}) by a finite number of terms, what always
happens along the numerical solution. Hence, such a treatment of the zero-range potential in
\cite{iks, igarashi2, yamanaka} is approximative
but, in view of the fact $a({\bf y}_2)=-{\mbox{i}} g{2\mu_2}b({\bf y}_2)/{\hbar^2}$ with $|g|\ll1$ for the $e^+e^-$ annihilation,
the approximation is reasonable.
\section{Calculation of annihilation cross section}
The formalism developed above was applied for calculations of the annihilation in $e^+-$H collision
below the Ps-formation threshold and above the threshold in the Ore gap. The latter
is defined as the interval of the energy between the Ps($1s$) and H($n=2$) thresholds.
All calculations were made on the basis of an extension of
the multichannel numerical algorithm for Faddeev equations, described in details in \cite{hu},
for the case of annihilation.
The algorithm uses the bipolar harmonic expansion to represent the angular dependence of the wave-function
components
\begin{eqnarray}
\Psi^+_i({\bf x}_i,{\bf y}_i)=\sum_{L l_1 l_2}\frac{\psi^L_{l_1 l_2}(x_i,y_i)}{x_iy_i}
{\cal Y}^{LM}_{l_1l_2}({\hat{\bf x}}_i,{\hat{\bf y}}_i),
\label{Bipolexp}\\
{\cal Y}^{LM}_{l_1l_2}({\hat{\bf x}}_i,{\hat{\bf y}}_i)=[Y^{m_1}_{l_1}({\hat{\bf x}}_i)\otimes Y^{m_2}_{l_2}({\hat{\bf y}}_i)]_{LM}.
\nonumber
\end{eqnarray}
This expansion reduces the MFE to a set of coupled equations for radial components
$\psi^L_{l_1,l_2}(x_i,y_i)$ which are then approximated by
the quintic-spline expansion and solved by the orthogonal collocation procedure. The maximum values
of $l_1, l_2$ used in (\ref{Bipolexp}) range from $12$ to $15$.
In order to test the numerical approach, the genuine Coulomb problem for $e^+-$H scattering was
solved on the platform of MFE (\ref{mfe-1}, \ref{mfe-2}) with $g=0$.
The results of calculations for s-wave $e^+-$H phase shift $\delta_0$
are given in Table \ref{Tab1} together with data of other authors.
\begin{table}
\begin{center}
\begin{tabular}{rrrrr
}\hline
$p_1$ & present work & \cite{Kvits-hu95}& \cite{Bhatia-T71} & \cite{Levin88}&\cite{Humb-Wallace72}
\\ \hline
0.1 & 0.1484 & 0.149 & 0.1483 & 0.152 & 0.148
\\
0.2 & 0.1879 & 0.189 & 0.1877 & 0.188 & 0.187
\\
0.3 & 0.1676 & 0.169 & 0.1677 & 0.166 & 0.167
\\
0.4 & 0.1198 & 0.121 & 0.1201 & 0.118 & 0.119
\\
0.5 & 0.0618 & 0.062 & 0.0624 & 0.061 & 0.062
\\
0.6 & 0.0032 & 0.003 & 0.0039 & 0.003 & 0.003
\\
0.7 & -0.0502 & -0.05 & -0.051 & 0.0053&
\\
\hline
\end{tabular}
\end{center}
\label{tab1}
\caption{$L=0$ phase shift $\delta_0$ for $e^+-$H elastic scattering.
Momenta $p_1$ are given in units of $a_0^{-1}$.
\label{Tab1}}
\end{table}
As one can see, the agreement of our calculations with previous results is quite good.
Figure \ref{fig-delta0}
provides an alternative representation of $\delta_0$ as the function of the energy to demonstrate the
regular character of the calculated phase shift $\delta_0$.
\begin{figure}
\begin{center}
{
\includegraphics[scale=0.7]{delta0.eps}
}
\end{center}
\caption{$L=0$ phase-shift for $e^+-$H elastic scattering.}
\label{fig-delta0}
\end{figure}
The calculations of the direct annihilation cross section $\sigma^a_1$ were performed
with the help of the
representation (\ref{sigma1}). The
amplitudes $F^0_{11}$ and $F^1_{11}$ were computed from the solutions of the respective
Faddeev equations. The effective number $Z^1_{\mbox{eff}}$ for the direct annihilation
cross section was obtained using the standard expression
(\ref{QED-sigma})
\begin{equation}
\sigma^a_1=\pi r^2_0 (c/v){Z}^1_{\mbox{{eff}}}.
\label{YH-sigma1}
\end{equation}
As it was mentioned in subsection \ref{OT1},
in the calculations of the amplitudes $F^0_{11}$ and $F^1_{11}$
we have systematically approximated
the Faddeev components, involved in the matrix-elements for the amplitudes,
by the solutions $\Psi^{00\pm}_i$ of the MFE~with~$g=0$. This statement can easily be justified
by the iterative solution of the IMFE (\ref{IMFE-1}, \ref{IMFE-2}) for $|g|\ll 1$.
The iterative solutions is well defined thanks to the fact that the matrix kernel of the Faddeev equation
is proven to be compact. This is another advantage of the Faddeev three-body equations.
As the result, the expression for the absorption amplitude $F^1_{11}$
from (\ref{F-1-11}) can be simplified as
\begin{equation}
F^{1}_{11}({\bf p}'_1,{\bf p})=
\frac{-\nu_1}{2\pi\hbar^2}
\langle [\Psi^{00-}_1({\bf p}'_1)+\Psi^{00-}_2({\bf p}'_1)]|W_2|\Psi^{00+}_1({\bf p}_1)\rangle ,
\label{F-00-11}
\end{equation}
which was actually used for calculations of this paper.
Since a number of data from other authors for direct annihilation cross section
below the Ps-formation threshold is available,
In Table \ref{Tab2} we display our calculated phase-shift $\delta_0$ and $Z^1_{\mbox{eff}}$
together with results of other authors obtained with the
standard formula (\ref{QED-sigma}) for one of the typical value of the relative
momentum $p_1=0.4\ [1/a_0]$.
\begin{table}
\begin{center}
\begin{tabular}{rrrrr}
\hline
Ref. & $\delta_0$ & $Z_{\mbox{eff}}$\\ \hline
present work & 0.11983 & 3.3293 \\
\cite{Brom-Mit03}& 0.1198 & 3.232 \\
\cite{Bhatia-T71}& 0.1201 & 3.327 \\
\cite{Grib-L03} & 0.1198 & 3.407 \\
\cite{Mit-Rat95} & 0.1191 & 3.332
\\
\hline
\end{tabular}
\end{center}
\caption{$L=0$ phase shift $\delta_0$ for $e^+-$H elastic scattering and effective
number $Z_{\mbox{eff}}$ for the relative momentum $p_1=0.4\ [a_0^{-1}]$.
\label{Tab2}}
\end{table}
The agreement is very good for calculations made by quite different approaches.
In Table \ref{TabZ} we collect the results of existing calculations of $Z_{\mbox{eff}}$
below the Ps-formation threshold to compare with our results. One cannot expect the complete agreement
since our definition of $\sigma^a_1$ concerns the direct process only, whereas
the standard definition below the Ps-formation threshold deals with the overall annihilation
cross section $\sigma^a$.
Nevertheless, Table \ref{TabZ} shows that the difference is not so dramatic.
\begin{table}
\begin{center}
\begin{tabular}{rrrrr}
\hline
$p_1$ & present paper & \cite{Kvits-hu95} &\cite{Humb-Wallace72}& \cite{Bhatia-Drach74}\\
\hline
0.1 &7.2570 &7.55 &7.5 &7.363 \\
0.2 &5.1627 &5.74 &5.7 &5.538 \\
0.3 &4.1061 &4.36 &4.3 &4.184 \\
0.4 &3.3293 &3.4 &3.3 &3.327 \\
0.5 &2.8118 &2.74 &2.7 &2.73 \\
0.6 &2.4625 &2.29 &2.3 &2.279 \\
0.7 &2.2529 &2.02 & &1.950 \\
\hline
\end{tabular}
\end{center}
\caption{$L=0$ effective
number $Z_{\mbox{eff}}$ for $e^+-$H annihilation. The relative momenta $p_1$ are
given in units of $a_0^{-1}$.
\label{TabZ}}
\end{table}
The extensive calculations of the direct annihilation cross section $\sigma^a_1$ were made in the
interval of the energy between H($n=1$) and H($n=2$) thresholds on the basis of the formula
(\ref{sigma1}).
Figure \ref{fig2} shows the s-wave
effective number $Z^1_{\mbox{eff}}$ derived from $\sigma^a_1$,
with the formula (\ref{YH-sigma1}), and the results
of calculations from \cite{yamanaka}.
\begin{figure}
\begin{center}
{
\includegraphics[scale=0.7]{Z02.eps}
}
\end{center}
\caption{The effective number $Z^1_{\mbox{eff}}$ for the $L=0$ direct annihilation.
The diamonds are the calculations of the present
paper, the open squares are the data from \cite{yamanaka}, the triangle marks the
positronium formation threshold.}
\label{fig2}
\end{figure}
Although, quite different methods
(time-independent Faddeev equations and time-dependent wave-packet approach to
the Schr\"odinger equation) of calculations
for the direct annihilation cross sections have been used, the agreement between data is fairly good.
In fact, the definition of the direct cross section $\sigma^a_1$ in our formalism as the remainder
of the overall
annihilation cross section $\sigma^a$ after subtraction of the annihilation cross section after the
Ps-formation
$\sigma^a_2$
\begin{equation}
\sigma^a_1=\sigma^a-\sigma^a_2,
\label{subtr}
\end{equation}
(see equation (\ref{sigma21})) is quite equivalent to the time-dependent definition by formula
(7) of ref. \cite{yamanaka}. Nevertheless, as the data of Tables \ref{Tabs}, \ref{Tabp}
shows, the exact use of the formula (\ref{subtr})
would be very unpractical. The formation cross section $\sigma_{21}$, which is the leading term
of $\sigma^a_2$ due to (\ref{sigma-a2-21}), rapidly increases above the threshold and is several
order of magnitude bigger than $\sigma^a_1$. The analytic separation of the overall annihilation
cross section into the formation and direct parts made in Subsection \ref{OT1} and given by formulae
(\ref{sigma21}-\ref{sigma1}) in terms of amplitudes $F^0_{11}$ and $F^1_{11}$
is therefore of the great practical importance.
In the following Tables \ref{Tabs} and \ref{Tabp} we present the results of our calculations for the direct
annihilation cross section together with the cross section of the positronium formation above the
Ps-formation threshold.
\begin{table}
\begin{center}
\begin{tabular}{rrrrr}
\hline
$p_1$ & $Z^1_{\mbox{eff}}$ & $\sigma^a_1$ & $\sigma_{21}$ \\
\hline
0.70654 & 2.3289 & 1.28 [-6] & 9.05 [-4] \\
0.71 & 2.1715 & 1.19 [-6] & 4.14 [-3] \\
0.8 & 1.8640 & 9.05 [-7] & 5.03 [-3] \\
0.85 & 1.7404 & 7.95 [-7] &5.83 [-3] \\
0.861 & 1.4840 & 6.69 [-7] &0.01087 \\
0.8611 & 1.9678 & 8.88 [-7] &0.01682 \\
0.86118 & 2.2200 & 1.00 [-6] &0.02694 \\
0.86119 & 2.3022 &1.04 [-6] &0.02943 \\
0.8612 & 2.4175 &1.09 [-6] &0.03247\\
0.86121 & 2.5832 &1.16 [-6] &0.03622 \\
0.86122 & 2.7817 &1.25 [-6] &0.04087\\
0.86124 & 3.1700 &1.43 [-6] &0.05380 \\
0.86126 & 0.9735 &4.39 [-7] &0.07030 \\
0.86128 & 0.9742 &4.39 [-7] &0.07450 \\
0.86132 & 1.4915 &6.73 [-7] &0.02089 \\
0.8614 & 1.6459 &7.42 [-7] &0.00013 \\
0.8615 & 1.7034 &7.68 [-7] &0.00083 \\
0.8618 & 1.7674 &7.97 [-7] &0.00326 \\
\hline
\end{tabular}
\end{center}
\caption{$L=0$ effective number $Z^1_{\mbox{eff}}$, the direct annihilation cross section $\sigma^a_1$, and
the positronium formation cross section $\sigma_{21}$.
The cross sections are given in units of $\pi a_0^2$ and
momenta in units of $a_0^{-1}$. The abbreviation [-n] is used for $10^{-n}$.
\label{Tabs}}
\end{table}
\begin{table}
\begin{center}
\begin{tabular}{rrrrr}
\hline
$p_1$ & $Z^1_{\mbox{eff}}$ & $\sigma^a_1$ & $\sigma_{21}$ \\
\hline
0.8 & 0.5404 &2.62 [-7] & 0.485\\
0.85 &0.6933 &3.17 [-7] &0.566\\
0.8631 &0.4775 &2.15 [-7] &0.749\\
0.86313 &0.4695 &2.11 [-7] &0.848\\
0.86315 &0.4675 &2.10 [-7] &1.022\\
0.86317 &0.5914 &2.66 [-7] &1.772\\
0.86318 &4.8319 &2.17 [-6] &3.680\\
0.863185 &14.6255 &6.58 [-6] &1.770\\
0.86319 &2.1967 &9.88 [-7] &0.129\\
0.8632 &0.9012 &4.06 [-7] &0.068\\
0.86325 &0.5629 &2.53 [-7] &0.407\\
\hline
\end{tabular}
\end{center}
\caption{$L=1$ effective number $Z^1_{\mbox{eff}}$, the direct annihilation cross section $\sigma^a_1$, and
the positronium formation cross section $\sigma_{21}$. The cross sections are given in units of $\pi a_0^2$ and
momenta in units of $a_0^{-1}$. The abbreviation [-n] is used for $10^{-n}$.
\label{Tabp}}
\end{table}
They are given for slightly different values
of momenta $p_1$ for $L=0$ and $L=1$ in order
to emphasize the most characteristic behavior of cross sections
near the respective Feshbach resonances.
Besides the expected difference
in several order of magnitude between direct annihilation cross section $\sigma^a_1$ and
the positronium formation cross section $\sigma_{21}$, the strong correlation between
these cross sections in the region of the sharp increase of $\sigma^a_1$ across $0.86124\,
[a_0^{-1}]$ for
$L=0$ and $0.86318\, [a_0^{-1}]$ for $L=1$ is clearly seen.
The graphical representation of that sharp increase
of cross sections is given on Figures \ref{a-res-s} and \ref{a-res-p} which display
s- and p-wave $Z^1_{\mbox{eff}}$.
\begin{figure}
\begin{center}
{
\includegraphics[scale=0.7]{Z-s-w-res.eps}
}
\end{center}
\caption{$L=0$ effective number $Z^1_{\mbox{eff}}$ in the resonant region. The momenta $p$ are given in
$a_0^{-1}$ units.}
\label{a-res-s}
\end{figure}
\begin{figure}
\begin{center}
{
\includegraphics[scale=0.7]{Z-p-w-res.eps}
}
\end{center}
\caption{$L=1$ effective number $Z^1_{\mbox{eff}}$ in the resonant region. The momenta $p$ are given in
$a_0^{-1}$ units.}
\label{a-res-p}
\end{figure}
This resonant feature was also observed in the spatial behavior of the solution to the Faddeev equation.
The first component $\Psi^{+}_1$, which is related to the $e^+-$H channel,
always exhibits the characteristic resonant bump near resonant energy.
These spatial resonant structures can be extensive depending on the lifetime of the resonances.
In \cite{hu-yak-papp}, reasonable estimation of the energy width of a number of Feshbach resonances
were made using the uncertainty principle applied to the graphical representation
of the wave function components.
\section{Conclusion}
In present paper we have developed the multichannel time-independent formalism, which is capable
to describe the scattering and annihilation processes in the positron-hydrogen collision above the
rearrangement threshold. The expression derived in the paper for the direct annihilation cross section
in terms of amplitudes
is proven to extend the standard formula to the energy region above the positronium formation threshold.
Below the threshold our cross section and the cross section calculated from the standard theory are
in good agreement provided the close vicinity of the positronium-formation threshold is not considered
where the standard cross section becomes infinite.
The direct annihilation cross section defined by the formula (\ref{sigma1}) does not exhibit
any singular behavior at the Ps-formation threshold. It is in good agreement with the nonsingular
direct annihilation cross section computed from the time-dependent solution of the three-body
Schr\"odinger equation for $e^+-$H system \cite{yamanaka}.
The formalism of this paper can readily be extended beyond the Ore gap.
In this case the multichannel optical theorem, which generalizes
(\ref{OptTh}), plays the key role in the determination of cross sections.
Preliminary calculations indicated the much larger enhancement of the direct annihilation cross section
near the Feshbach resonances in the eight open channel region above the Ps($n=2$) threshold.
Since there are
numerous resonances beyond the Ore gap, they evidently made a significant contribution to the overall
annihilation peak around $12$ e.V. displayed in Figure 2 of \cite{yamanaka}.
We hope that our individual annihilation resonance structure will provide
a new experimental tool to study sharp resonances. Although at the present time, it is not
possible to conduct such an experiment for $e^+-$H system,
experiments for positron scattering on large molecules have been done for many systems
\cite{Surko}.
Our approach, in perspective,
opens the way to considering more complicated systems with more than three particles, as for example
$e^+e^+e^-e^-$.
Suitable formalism for multichannel scattering \cite{Merk-Yak-4},
which is the generalization of the Faddeev equations for the
four-particle systems, will be helpful as an important theoretical step towards the experimental
verification and utilization of the rich positron annihilation physics.
\ack
The authors appreciate the support of the NSF grant Phy-0243740, INTAS grant No. 03-51-4000 and the
generous supercomputer time awards from
grants MCA96T011 and TG-MCA96T011 under the NSF partnership for Advanced
Computational Infrastructure,
Distributed Terascale Facility (DTF) to the Extensible Terascale Facility.
In particular we are thankful to PSC and SDSC. The authors would like to thank
Dr. Y.~Kino~ for providing us with numerical data corresponding to the Figure 2 of
ref. \cite{yamanaka}, which made the comparison of our results much feasible. We are
thankful to Prof. K.A. Makarov for fruitful discussion on zero-range potentials.
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,453 |
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