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Q: How to import nested json into google big query I'm inserting JSON into Google Big Query.
At the bottom of the question is the schema of the JSON.
Below is an example JSON:
{
"_index":"data",
"_type":"collection_v1",
"_id":"548d035f23r8987b768a5e60",
"_score":1,
"_source":{
"fullName":"Mike Smith",
"networks":[
{
"id":[
"12923449"
],
"network":"facebook",
"link":"https://www.facebook.com/127654449"
}
],
"sex":{
"network":"facebook",
"value":"male"
},
"interests":{
},
"score":1.045,
"merged_by":"548f899444v5t4v45te9a4cc"
}
}
as you can see there's a "_source.fullName" field with "Mike Smith".
When I try to create a table with it, it errors out:
Array specified for non-repeated field: _source.fullName.
I believe this field is a one-time field for _source. How do I overcome this error?
here's the Schema:
[
{
"name": "_index",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "_id",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "_type",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "score",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "header",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "fullName",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "src",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "avatar",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "merged_by",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "cover",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "sex",
"type": "RECORD",
"mode": "NULLABLE",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "_source",
"type": "RECORD",
"mode": "NULLABLE",
"fields": [
{
"name": "fullName",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "links",
"type": "STRING",
"mode": "REPEATED"
},
{
"name": "birthday",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "phones",
"type": "STRING",
"mode": "REPEATED"
},
{
"name": "pictures",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "url",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "tab",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "contacts",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "id",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "fullName",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "tag",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "groups",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "id",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "Name",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "skills",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "relations",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "about",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "emails",
"type": "STRING",
"mode": "REPEATED"
},
{
"name": "languages",
"type": "STRING",
"mode": "REPEATED"
},
{
"name": "places",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "type",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "education",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "school",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "experience",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "start",
"type": "NUMERIC",
"mode": "NULLABLE"
},
{
"name": "company",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "title",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "networks",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "link",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "id",
"type": "STRING",
"mode": "REPEATED"
}
]
},
{
"name": "network",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "others",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "tag",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "books",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "tag",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "music",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "tag",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "games",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "tag",
"type": "STRING",
"mode": "NULLABLE"
}
]
},
{
"name": "spotify",
"type": "RECORD",
"mode": "REPEATED",
"fields": [
{
"name": "network",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "value",
"type": "STRING",
"mode": "NULLABLE"
},
{
"name": "tag",
"type": "STRING",
"mode": "NULLABLE"
}
]
}
]
}
]
}
]
A: You could import the full json row as if it was a CSV - basically a one column BigQuery table of json objects. Then you can parse the JSON at will inside BigQuery, with queries like this:
WITH j AS (
SELECT """{"_index":"data","_type":"collection_v1","_id":"548d035f23r8987b768a5e60","_score":1,"_source":{"fullName":"Mike Smith","networks":[{"id":["12923449"],"network":"facebook","link":"https://www.facebook.com/127654449"}],"sex":{"network":"facebook","value":"male"},"interests":{},"score":1.045,"merged_by":"548f899444v5t4v45te9a4cc"}}""" j
)
SELECT index
, STRUCT(
JSON_EXTRACT_SCALAR(source, '$.fullName') AS fullName
, [
STRUCT(
JSON_EXTRACT_SCALAR(source, '$.networks[0].id[0]') AS id
, JSON_EXTRACT_SCALAR(source, '$.networks[0].network') AS network
, JSON_EXTRACT_SCALAR(source, '$.networks[0].link') AS link)
] AS networks
) source
FROM (
SELECT JSON_EXTRACT_SCALAR(j.j, '$._index') index
, JSON_EXTRACT(j.j, '$._source') source
FROM j
)
See:
*
*https://medium.com/google-cloud/bigquery-lazy-data-loading-ddl-dml-partitions-and-half-a-trillion-wikipedia-pageviews-cd3eacd657b6
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,104 |
Dear Santa… & Cyber Monday!
Happy Monday, friends! This year brought many blessings for me personally, and I certainly have everything I need. I truthfully have a small 'wishlist' this year, relating to anything material-speaking for the holiday. Of course, there are a few things I wouldn't mind seeing under the tree… 😉 Little mementos for our upcoming wedding in 2018, or fitness-focused items, like a gift card or new activewear, would be wonderful. Do you have anything special on your own wishlist this year?
You can shop my gift ideas here, or click directly on the image above. Also, don't miss the best CYBER MONDAY deals below! | {
"redpajama_set_name": "RedPajamaC4"
} | 8,360 |
Delilah Announces New Single
After hitting number five in the charts with her debut album 'From the Roots Up', 21-year old singer-songwriter Delilah has announced the release of her new single 'Never Be Another'.
Delilah, AKA Paloma Stoeker, has had an exciting year, playing to packed crowds at festivals such as Lovebox, Camp Bestival, V Festival and Radio 1's Hackney Big Weekend, and recently scoring a nomination for Best Newcomer at the upcoming MOBO Awards.
The first track on her critically-acclaimed debut album, 'Never Be Another' will be released on 26th November. Stoeker commented that "'Never be Another' is about how being in love feels so right, even perhaps when it's with the wrong person." The single features London-based grime artist Devlin, who we interviewed and featured in our Freshers 2012 edition.
Delilah kicks off her UK headline tour on Saturday 20th October. Limited tickets are still available for the eight night tour, which will end in Bristol on 29th October.
The full list of dates for the tour is as follows:
20th October – Leicester O2 Academy 2
21st October – Birmingham Institute
23rd October – Manchester Academy 2
24th October – Newcastle Digital
25th October – Sheffield Plug
27th October – Brighton Concorde
28th October – London O2 Shepherds Bush Empire
29th October – Bristol O2 Academy | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,299 |
Q: Styling input password in HTML I have an input type password that only allow a six-digit number like this:
<fieldset>
<label for="password-input">Enter New Pin</label>
<input type="password" name="password" id="password-input" inputmode="numeric" minlength="6"
maxlength="6" size="6" value="">
<span class="hint">New pin must be 6 digit number only</span>
</fieldset>
It will show like this:
How can I style it so it can look like the following?
A: #Update
*
*Added a <input type='number'> which can adjust the root font-size: 8px to 84px.
#Relevant Points
*
*The input is stripped of border, outline, and background.
*Wrapped a label around the input as an overlay (technically it is an underlay? z-index: -1) which has a pseudo-class ::after with the content value of 6 underscores.
*Both input and overlay must have the following properties:
/* The values can anything as long as it is valid and are the same */
letter-spacing: 10px;
font-size: 1.2rem;
font-weight: 900;
*The overlay is display: table and the input is display: table-cell. This (along with absolute and relative positioning) keeps the input rigidly centered in the overlay.
*rem units are used so if you want to scale the font-size up or down, just change the font-size of the <html> tag and everything adjusts accordingly:
/* Change the 16px to whatever you want and everything scale to that value */
html,
body {
font: 400 16px/1.5 Consolas
}
##Demo
Note: Try keeping a key pressed continuously, and you'll see that there's no shifting.
var node = document.querySelector('#fSz');
node.oninput = setFontSize;
function setFontSize(e) {
var tgt = e.target;
var root = document.documentElement;
root.style.setProperty(`--${tgt.id}`, `${tgt.valueAsNumber}px`);
}
:root {
--fSz: 16px;
}
html,
body {
font-size: var(--fSz);
font-weight: 400;
line-height: 1.5;
font-family: Consolas, 'sans serif', monospace;
}
fieldset {
position: relative;
display: table;
min-height: 5.5rem;
padding: 0 0 0 0.3125rem;
margin-top: 2em;
overflow: visible;
}
fieldset * {
font-size: inherit;
font-weight: inherit;
line-height: inherit;
font-family: inherit;
-webkit-user-select: none;
-moz-user-select: none;
user-select: none;
}
legend {
font-size: 1.2rem;
}
.overlay {
display: table;
position: relative;
top: 0.3125rem;
left: 0.9375rem;
font-size: 1.2rem;
font-weight: 900;
}
.overlay::after {
content: '\ff3f\ff3f\ff3f\ff3f\ff3f\ff3f';
font-size: 1.2rem;
letter-spacing: 0.78rem;
}
@-moz-document url-prefix() {
.overlay::after {
content: '\2501\2501\2501\2501\2501\2501';
text-shadow: 0.65rem 0px 0px #222;
font-size: 1.37rem;
letter-spacing: 1.2rem;
line-height: 2;
}
}
.hint {
display: block;
position: absolute;
bottom: -2rem;
left: 0.625rem;
font-style: italic;
font-size: 0.75rem;
}
#password-input {
display: table-cell;
border: 0px none transparent;
outline: 0px none transparent;
background: transparent;
position: absolute;
left: 0px;
z-index: 1;
overflow: hidden;
line-height: 2;
transform: translate(0.25rem, -1rem);
letter-spacing: 1.25rem;
font-size: 1.35rem;
font-weight: 900;
}
sup {
padding-top: 0.25rem;
font-size: 0.65rem
}
.fc {
display: block;
position: fixed;
left: 0;
top: 0;
z-index: 3;
font: 400 16px/1.5 Consolas;
width: 50%;
}
#fSz {
display: inline-block;
padding-left: 8px;
width: 52px;
font: inherit;
text-align: center;
}
<label for='fSz' class='fc'>Font-Size:
<input id='fSz' type='number' min='8' max='84' value='16' step='0.5'> px
</label>
<fieldset>
<legend>Enter New Pin</legend>
<label for='chk' class='overlay'>
<input type="password" name="password" id="password-input" inputmode="numeric" minlength="6" maxlength="6" size="19" value="123456" placeholder='123456'>
</label>
<label for="password-input" class="hint"><sup>🞼</sup>New pin must be 6 digit number only</label>
</fieldset>
A: You can place an element containing "the mask" behind the input and set the background color of input to transparent. But pay attention to the following details:
*
*Use monospace font family so that the width of _ and • is always the same.
*End your font list with monospace so that OS can choose a fixed width font if all of the specified fonts are unavailable.
*User agent could choose a different font family, size and line height for input elements. It can also choose a different size and line height for monospace fonts (e.g. medium size could be computed as 13px instead of the usual 16px and normal line height is often off by 1px for two different fonts having same size). So make sure you specify these properties explicitly.
Here is the result:
body {
font-family: sans-serif;
}
fieldset label,
fieldset span {
display: block;
margin: .5em 0;
}
fieldset .input-wrapper {
/* positioning */
position: relative;
/* font */
font: 16px/1.5 monospace;
letter-spacing: .5em;
/* optional */
background-color: #EEE;
}
fieldset .input-wrapper::before {
/* positioning */
position: absolute;
/* masking */
content: "______";
}
fieldset input {
/* positioning */
position: relative;
/* font */
font: inherit;
letter-spacing: inherit;
/* masking */
background-color: transparent;
/* reset */
margin: 0;
border: 0;
padding: 0;
}
<fieldset>
<label for="password-input">Enter New Pin</label>
<div class="input-wrapper">
<input type="password" name="password" id="password-input" inputmode="numeric" minlength="6" maxlength="6" value="">
</div>
<span class="hint">New pin must be 6 digit number only</span>
</fieldset>
A: Since you can't use the ::after pseudo-element on your input box, use it on fieldset (or if you can alter the HTML, add an element). Then give it a content value using underscores, and position the elements where you want them. Finally, add letter-spacing and width to your input box, and give it a :focus of outline: none to get rid of the blue box.
fieldset {
color: #555;
font-family: sans-serif;
border: none;
position: relative;
}
fieldset > * {
display: block;
}
fieldset::after {
content: "___ ___ ___ ___ ___ ___";
display: block;
position: absolute;
top: 35px;
white-space: pre;
}
label {
font-size: 14px;
margin-bottom: 6px;
}
input#password-input {
position: relative;
font-size: 16px;
z-index: 2;
border: none;
background: transparent;
width: 300px;
text-indent: 9px;
letter-spacing: 25.6px;
font-family: Courier;
}
input#password-input:focus {
outline: none;
}
span.hint {
margin-top: 8px;
font-size: 12px;
font-style: italic;
}
span.hint::before {
content: "* ";
}
<fieldset>
<label for="password-input">Enter New Pin</label>
<input type="password" name="password" id="password-input" inputmode="numeric" minlength="6" maxlength="6" size="6" value="">
<span class="hint">New pin must be 6 digit number only</span>
</fieldset>
A: Try this:
input {
padding-left: 15px;
letter-spacing: 39px;
border: 0;
background-image: linear-gradient(to left, black 70%, rgba(255, 255, 255, 0) 0%);
background-position: bottom;
background-size: 50px 3px;
background-repeat: repeat-x;
background-position-x: 35px;
width: 280px;
font-size: 30px;
}
input:focus {
outline: none;
}
<fieldset>
<label for="password-input">Enter New Pin</label>
<input type="password" name="password" id="password-input" inputmode="numeric" minlength="6" maxlength="6" size="6" value="">
<span class="hint">New pin must be 6 digit number only</span>
</fieldset>
A:
This conventional solution may help for cross browser :
The HTML form :
<p class="text-center">Enter new pins</p>
<form role="form" method="post">
<div class="form-group text-center">
<input class="inputbox" maxlength="1" type="password" >
<input class="inputbox" maxlength="1" type="password" >
<input class="inputbox" maxlength="1" type="password" >
<input class="inputbox" maxlength="1" type="password" >
<input class="inputbox" maxlength="1" type="password" >
<input class="inputbox" maxlength="1" type="password" >
<small class="text-danger">New pin must be 6 digit number only</small>
</div>
<div class="form-group">
<button type="submit" class="btn btn-primary btn-lg btn-block">Verify Pin
</button>
</div>
<input id="code_hidden" maxlength="6" name="real_code" type="text" >
</form>
We can see the result on input name = real_code. It must be type = 'hidden' on production. Change this maxlength when more field is required.
Style CSS :
<style>
.inputbox {
background-color: #fff;
border: none;
border-bottom: thin solid gray;
width: 20px;
font-size: 24px;
margin-bottom: 20px;
margin-right: 5px;
}
</style>
Script part :
<script>
$(function() {
$(".inputbox").keyup(function () {
$(this).next('.inputbox').focus();
var value = [];
$('.inputbox').each(function() {
value += $(this).val();
});
$('#code_hidden').val(value);
});
});
</script>
| {
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} | 7,786 |
Сухотереша́нское се́льское поселе́ние — муниципальное образование в составе Николаевского района Ульяновской области. Административный центр — село Сухая Терешка.
Население
Состав сельского поселения
В состав поселения входят 5 населённых пунктов: 2 села и 3 деревни.
Примечания
Ссылки
Николаевский район
Сельские поселения Ульяновской области
Муниципальные образования Николаевского района Ульяновской области | {
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} | 9,785 |
Vietnamese rescuers Wednesday found the bodies of two of the seven fishermen who were missing after a collision between a Singaporean cargo vessel and a fishing boat earlier this week, taking the death toll to three.
The bodies were found nine nautical sea miles from the site of the accident that had occurred 54 miles off the coast of Vung Tau city Monday.
Authorities had earlier feared that the missing people were stuck in the fishing boat which broke into two and sank after the collision with the 20,000-ton plus Sima Sapphire.
Tuoi Tre newspaper quoted Le Van Chien, director of the Maritime Administration of Vung Tau, as saying the accident possibly happened because the ship was in 'autopilot' when it crashed into the anchored fishing boat.
Since it took place early in the morning, all 16 fishermen were probably sleeping without anyone on guard, he said.
The Singaporean ship's crew rescued eight people from the boat, and one body was retrieved later the same day.
The boat has been found 31-34 meters underwater south of Vung Tau.
It was trapped amid fishing nets and nearly 60 other fishermen have been trying to cut the nets to find the victims, Pham Hien, director of the Marine Search and Rescue Center No. 3, told Thanh Nien.
Though helicopters and rescue boats have been mobilized, heavy seas caused by a tropical depression and monsoon winds have hampered rescue efforts, authorities said.
Meanwhile, experts from the administration have taken Sima Sapphire's black box, sampled paint from its hull for testing, and questioned its captain and crew, Chien told Thanh Nien.
The ship, which had been headed for Malaysia, is anchored at Cai Mep Port in Vung Tau for investigation.
Authorities have also questioned the survivors, four of whom were sent to hospital for observation Tuesday. Some of them told the media they were exhausted after spending an hour in the water before being rescued.
Vo Van Thanh, 36, one of the survivors along with his son Vo Van Be, 13, told Thanh Nien he was sleeping when there was a big bang.
Everyone on board fell into the water, and the boat was totally destroyed and sank immediately, he said.
He managed to find an object to cling on to and rescue his son, who had been working aboard as a cabin boy for two years.
The boat's owner, Nguyen Van Hon, who lives in the Mekong Delta province of Tien Giang, told Thanh Nien that the vessel and crew had left July 26 and were expected to be at sea for two months. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,492 |
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Home Axwell, Axtone & Swedish House Mafia ...
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10 Years of Axtone: Looking Back On A Decade Of Music
Releases, remixes, unreleased music & projects.
Vinelli
I worship Axwell
Send private message https://soundcloud.com/axwell-forum-radio
Location: Rotterdam City Of Love, The Netherlands
Post Vinelli › 30 Dec 2015, 14:19
I say, let's continue the lookback till Axtone's anniversary year ends in may next year. There is still sooo much to tell
Post Vinelli › 05 Jan 2016, 12:32
AXT029 Hard Rock Sofa & Swanky Tunes - Here We Go
So 2015 just ended, but Axtone is still 10 till May! So like I said, I think it's a cool idea to continue this series until the very last day of their anniversary . A fitting track title to start this year off, is ofcourse Hard Rock Sofa's and Swanky Tune their collaboration 'Here We Go'.
https://www.youtube.com/watch?v=QlVJwlMTrqA
So this release marks the hat-trick for Hard Rock Sofa and the debut of Swanky Tunes. Russian producers had this, as Axtone put it themselves, 'oversized' big room sound that really felt fresh at the time. Arty, Hard Rock Sofa & Swanky Tunes were becoming names often found back in track list by Axwell and SHM. Where Swanky Tunes never returned to the label, Hard Rock Sofa grew on to become a rare Axtone artist signing (now in the form of Shapov).
https://www.youtube.com/watch?v=DYebxVetouc
Granted, I wasn't the biggest fan of this track when it came out, but looking back now I can definitely make more sense out of this release. It bares the same kind of energetic flow these current day Shapov tracks have. In fact, you can really hear his influence on his tracks when you know how his individual output sounds. I can't imagine what it must have sounded like hearing this monster live.
A tiny AXFACT might be that this track was featured in the movie 'Fast & Furious 6', alongside Quasar.
https://www.youtube.com/watch?v=p0sUxE1wpAM
Post Extensity › 05 Jan 2016, 13:38
I have been reading these posts even before I got to the forum and it's always nice to get back to some tracks or discover some unknown (to me) remixes. As I finally became a forum member, I just want to thank you Vinelli for finding some time to update this thread
"For the love of god, can you say INSERT, woman!"
DJ Gear: Denon DN-MC6000
VirtualDJ Pro
Post House5 › 05 Jan 2016, 13:55
Here We Go was a key track of Swedish House Mafia's One Last Tour (mashed with Resurrection and Together!), so I got to hear it live in Paris, it's a freaking beast, no wonder why Axwell signed it!
Hard Rock Sofa has become a really interesting act when Quasar got signed, before that they were good but not extraordinary I think, so Shapov & Denis owe a lot to Axwell
"You showed us, and the world, that Paris is much more than the Eiffel Tower and Mona Lisa..."
Axwell, Bercy @ Paris, Saturday, December the 8th 2012.
Luigi vs. House5...
Seveli13
Location: Belgrade, Serbia
Post Seveli13 › 05 Jan 2016, 15:33
This track is not that special...just another Big Room ''banger'' that started to get more popular at the time which eventually would lead to that Martin Garrix wave...this could've easily been a Spinnin' tune and no one would notice the difference...but because it's Axtone and SHM played it endlessly for a full year, literally every show, it's so ''fresh at the time''... Not every Axtone track is great...little objectivism would not hurt u guys...
Ax:O
Post Ax:O › 05 Jan 2016, 15:36
Seveli13 wrote: This track is not that special...just another Big Room ''banger'' that started to get more popular at the time which eventually would lead to that Martin Garrix wave...this could've easily been a Spinnin' tune and no one would notice the difference...but because it's Axtone and SHM played it endlessly for a full year, literally every show, it's so ''fresh at the time''... Not every Axtone track is great...little objectivism would not hurt u guys...
Not sure where this is aimed at? I simply said it was fresh at the time, as it WAS a new sound 100 percent. If the track is good or not, is for yourself to judge
Seveli13 wrote: Not every Axtone track is great...little objectivism would not hurt u guys
So basically because some people happen to like tunes you don't like, they're not objective ?
You can't really be objective about well produced music, you either like it or you don't. And YES it's well produced
It's just not really made for home listening, but live you can definitely see why this was popular. And true it was fresh, meaning that there was not so many tracks like this before
House5 wrote:
@Vinelli Not at u man...it's just nothing special by Axtone standards...and for HOUSE5, by that logic Animals is the freshest track that has come in the last 3 , 3 and a half years...it started a whole new wave of ''music'' that rarely any track did (that much i mean)...and the same can be said for u man, just because u live every single crap Axwell and Axtone deliver that everyone must like it, it's going round in circles man And i didn't say it was bad produces, just that is nothing special and definitely hasn't got that Axtone vibe...
No no I said you either like it or you don't, so you have the right not to like it man it's alright, I don't judge hahaha! I never said you have to like it
Btw, Axtone standards are TREND + PRODUCTION QUALITY, something that Here We Go definitely had back then (Trend I mean, prod quality is still here), something that Shapov tracks also have even though we may not like all of them, something that Torn Apart has as well...
Axtone standards are not restricted to 1 kind of electronic music anymore and this is just the best thing that can happen to a label, being wide open-minded! So the Axtone vibe as you say is not restricted to this anymore :
https://www.youtube.com/watch?v=NwtLiTRb5s4
The fact u think Axtone standards are following trends and Shapov fits very nicely with that just speaks more loudly than anything else i can say
And they were never restricted to one kind of electronic music, it was just Ax's and his friends place to release some music from time to time, no money, no marketing, no trying to compete with other labels...just pure love for the music...that's the real Axtone and House vibe, and i can only say i feel sorry for u cuz' u probably never experienced those times...cheers mate, healthy talk...
Return to "Axwell, Axtone & Swedish House Mafia"
Axwell, Axtone & Swedish House Mafia
Production Board | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,448 |
2011 Volkswagen Passat official pictures and specs
2011 Volkswagen Passat - Click above for high-res image gallery
Volkswagen is slowly in the process of refreshing its entire product portfolio, and right on the heels of the recently introduced 2011 Jetta comes the seventh-generation Passat. The automaker's new corporate design language is in full force here, and observations of the new Passat looking like a big Jetta will not be disagreed with.
A full range of gasoline and diesel engines will be available when the Passat launches later this year. In North America, it's safe to assume that we'll receive the 207-horsepower, 2.0-liter turbocharged four-cylinder as well as the 296-horsepower, 3.6-liter V6, but we won't rule out the possibility of Volkswagen offering its well-liked 2.0-liter TDI diesel engine, as well. All engines can be mated to either a six-speed manual or dual-clutch automatic gearbox, and like previous Passats, 4Motion all-wheel drive should be available on top-end models.
The Passat will also be available with Volkswagen's XDS electronic differential, which first debuted on the GTI hatch. This system helps reduce understeer and improve overall traction in slippery conditions, and we imagine that it will quickly make its way to the vast majority of VW products. What's more, a new optional city emergency braking function automatically stops the car at speeds below 18 miles per hour when an imminent collision is detected, sort of like the self-stopping systems by Volvo (which, as we've seen, don't always work correctly).
Both the sedan and wagon Estate models go on sale in the UK next month, with North American availability coming shortly thereafter.
Press release: SEVENTH GENERATION PASSAT UNVEILED AT THE PARIS MOTOR SHOW
Following over 15 million sales in 37 years across 100 countries around the world Volkswagen has unveiled the seventh generation of the Passat at the Paris Motor Show. Establishing benchmarks in quality, design, economy and comfort the new Passat is not only the most advanced iteration yet but also the most efficient.
A completely new look styled by Klaus Bischoff (head of design, Volkswagen) and Walter de Silva (head of design, Volkswagen Group) establishes a fresh direction for the Passat saloon and Estate with clean surfaces and an elegant yet imposing stance. The front of the car, dominated by a new grille element with prominent horizontal chrome fins, features striking heavily contoured headlight units, set into which are LED running lights. At the rear a set of distinctive tail lights is joined by subtle chrome highlights that extend down the side of the car. Every body panel apart from the roof is new.
Measuring 4,769 mm in length (Estate 4,771 mm) the new Passat is marginally longer than the car it replaces (+4 mm) and at 1,820 mm wide and 1,474 mm tall (Estate 1,519 mm) it retains the same proportions.
The fresh look continues inside the seventh generation Passat with new seats that can be specified to both heat and cool their occupants and even feature a massage function for the driver and front seat passenger. A revised dashboard with new dials, trim finishes and an analogue clock are joined by subtle chrome inserts and the option of ambience lighting similar to that found in the Phaeton. The centre console has also been uprated with revisions to the minor controls as well as new door trims.
Powering the new Passat is a range of advanced and highly efficient petrol and diesel engines. The petrol line-up comprises a 1.4-litre TSI engine developing 122 PS, a 1.8-litre TSI unit with 160 PS, a 2.0-litre TSI 210 PS engine and a range-topping 3.6-litre V6 producing 300 PS.
The refined and frugal diesel range starts with the most efficient engine, the 1.6-litre TDI unit producing 105 PS. Equipped with this engine and the BlueMotion package of changes including aerodynamic modifications, Stop/Start and battery regeneration, the new Passat can achieve a combined 68.8 mpg while emitting just 109 g/km of CO2. This equates to a theoretical range of over 1,000 miles on a single tank of diesel. Joining the 1.6-litre TDI is a 2.0-litre TDI engine available in two power outputs – 140 PS and 170 PS. Each of the engine ranges can be specified with a choice of manual or DSG gearboxes.
The new Passat is available with many new safety and comfort technologies previously only seen in the Touareg and Phaeton luxury models.
The optional new City emergency braking function, a part of the Automatic Distance Control (ADC) system, automatically engages the brakes at speeds below 18 mph should an unavoidable collision be sensed by the vehicle. The system is also able to accelerate the vehicle automatically should it detect an imminent rear end collision providing the vehicle sees a clear space ahead.
In addition, the new Passat can be fitted with an automatic fatigue detection system that monitors the driver's inputs and automatically emits an audible and visual warning to recommend a break if required.
As with previous Passat models, the Electronic Stabilisation Programme (ESP) incorporates Trailer Stabilisation when a factory fitted towbar is specified.
Promising enhanced dynamics, the new Passat can be specified with the acclaimed XDS electronic transverse differential for the first time. The system, which is standard on the Golf GTI, acts to reduce understeer and improve traction in slippery conditions making the new Passat feel more responsive as a result.
Other new optional convenience systems include an innovative boot opening system for the saloon model: on vehicles specified with keyless entry, so long as you're carrying the key fob on your person a simple foot motion at the back of the car is enough to activate sensors that open the boot automatically – a useful function when your hands are full.
Both the saloon and Estate models are due to go on sale in the UK around the middle of October at which time pricing and specification details will be announced. First customer deliveries will take place in early January 2011.
Gallery: Volkswagen New Passat
2011 Volkswagen Passat unveiled ahead of Paris Motor Show originally appeared on Autoblog on Wed, 29 Sep 2010
xmachineheadx
I thought the Passat was gone, to be replaced by the NMS? The article says North American availability will be shortly thereafter.
The Passat is gone and that car pictured will not make it to North America. I really would like vented seats, the RNS 850 GPS system, and keyless access KESSY in my next car...
My guess is that the NMS will be similar to the Passat and have the RNS 510 GPS, maybe torsion beam rear suspension.
chittychittybangbang Sep 29, 2010 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,455 |
\section{Introduction}
Small noncoding RNAs (sRNAs) have
recently been discovered
as key components of genetic regulation
in systems ranging from bacteria to
mammals~\cite{G04,FGJLJLBB05,JBB06},
and this has spurred much
activity in understanding their functional advantages.
For example, degradation of sRNA with their target mRNAs has been
proposed as a mechanism to obtain
ultrasensitivity \cite{LMLKWB04}.
One particular system which has
been extensively studied is the Fe-Fur system in the bacterium
{\sl Escherichia coli} which contains the regulatory
sRNA RyhB~\cite{ARR03,MA05}.
This system is responsible for maintaining homeostasis of
Fe$^{++}$ ions, which are essential for cell functioning
but also poisonous at high concentrations.
During aerobic exponential growth, iron-using enzymes in {\sl E. coli}
utilize around $10^6$ Fe atoms
per cell generation, but more than
$10^4$ Fe$^{++}$ ions in free or loosely-bound form
is poisonous \cite{NOBOMKY99,KI96}.
Thus, the cell faces the problem of maintaining a huge flux
of Fe through a small reservoir, and at the same time
channeling this flux into its most essential functions
when the cell is starved of iron:
It needs to prioritize and sort the usage of a limited resource.
Reference \cite{SAKJMS06} describes a detailed model of the Fe
regulation in {\sl E. coli},
which incorporates several feedback mechanisms that
together secure the system against both
up and down shifts of the iron level.
In this paper, we focus on the
prioritization of the usage of iron
by the sRNA regulation and its role in sudden
iron depletion.
The model in \cite{SAKJMS06} is simplified
into a core ``motif" (Figure ~\ref{motifs}a)
describing the negative feedback used in iron homeostasis.
The motif consists of three variables,
$f$ the iron-activated Fur (Ferric uptake
regulator) protein complex
that senses the Fe$^{++}$ level, $r$, the sRNA RyhB, and $m$,
the mRNA of iron-using proteins.
The sRNA works by binding strongly to the mRNA, after which this
entire complex is rapidly degraded \cite{MG02,MEG03,MVG05}.
The sRNA is in turn transcriptionally repressed by $f$.
Thus, $f$ effectively activates $m$, through a double negative link
via the sRNA.
Interestingly, the regulation of iron homeostasis in the bacterium
{\sl Helicobacter pylori} differs from that of {\sl E. coli} in one
important respect: the regulation via the sRNA RyhB is replaced
by a direct transcriptional activation of the mRNA $m$ by $f$
(see Figure~\ref{motifs}b) \cite{DSRS01,DRDCRS06}.
These two bacteria motivate us to compare
the ``sRNA motif" with the corresponding ``transcription motif".
By studying these motifs, we demonstrate
the following interesting aspects of sRNA regulation:
(i) both motifs can be adjusted to have similar response times,
but the metabolic cost is different for the two motifs.
(ii) a single type of sRNA can
efficiently prioritize expression level of various
downstream target mRNAs,
thus prioritizing the usage of a limiting resource.
We also discuss possible experiments to test these results.
\begin{figure}[t]
\begin{center}
\includegraphics[width=8cm]{figure1.eps}
\end{center}
\caption{(a) The sRNA motif
found in {\sl E. coli}, consists of
three variables, $f$, the
Fe-Fur complex which depends on the amount of loosely bound iron,
$r$, the sRNA ryhB, and $m$,
the mRNA of iron-using proteins.
The red barred arrows between $r$ and $m$ represent
the formation of the $r-m$ complex and its subsequent
degradation. The other red barred arrow indicates
transcriptional repression of $r$ by $f$.
The influx of $f$, denoted by $C$, is divided into
the channel $A$, regulated by $m$ (green arrow),
and the non-regulated channel $B$.
(b) The transcription motif found in {\sl H. pylori}.
Here, $m$ is transcriptionally activated by $f$.
\label{motifs}}
\end{figure}
\section{The Two Motifs}
\subsection{sRNA motif}
In the motif of Figure~\ref{motifs}a we focus
on the case where sRNA
binds to mRNA and both RNAs in the complex are degraded.
In terms of an effective rate constant for the
overall degradation, $\delta$, the dynamics of the concentrations of
the sRNA ($r$) and its target mRNA ($m$)
can be described by
\begin{eqnarray}
\frac{dr}{dt} & = & \alpha_r - \frac{r}{\tau_r} - \delta \cdot r \cdot m\\
\frac{dm}{dt} & = & \alpha_m - \frac{m}{\tau_{mrna}} - \delta \cdot r
\cdot m
\end{eqnarray}
where $\alpha_r$ and $\alpha_m$ set the respective production rates,
and $\tau_r$ and $\tau_m$ define the background degradation
times.
We next rescale the parameters
by measuring concentrations in units
of $\alpha_m \tau_r$ and measuring time in units of $\tau_r$
\footnote{The equation are formally rescaled by replacing
$m\rightarrow m/(\alpha_m \tau_r )$,
$r\rightarrow r/(\alpha_m \tau_r )$
and $t\rightarrow t/\tau_r$. Thereby, a unit of time corresponds to the
degradation time of the sRNA, and the unit of production rates
corresponds to the production rate of the target mRNA.}.
To these rescaled equations we also add
an equation for $f$, a small-molecule-activated
transcription factor for the sRNA (as shown in
Figure~\ref{motifs}a).
We simplify this two step reaction from $f$ to regulation
by assuming that all bindings are first order, and by rescaling
binding constants such that $f=1$ results in half-repression
of the promoter of the sRNA gene.
Including the import and consumption of $f$
in analogy to the Fe-Fur system\cite{SAKJMS06},
the full dynamics of the motif becomes:
\begin{eqnarray}
\frac{df}{dt} &=&
\left\{
\begin{array}{ll}
C- A \cdot m\;
- B \cdot f \;\;\; & \mbox{when}\;\; f>0,
\label{fs}
\\
C \;\;\; & \mbox{when} \;\; f=0,
\end{array}\right. \\
\frac{dr}{dt} &=& \frac{\alpha}{1+f}- r
- \gamma r\cdot m \label{rs},
\\
\frac{dm}{dt} &=&1\; -\; \frac{m}{\tau_m}
- \gamma r\cdot m.\label{ms}
\end{eqnarray}
Here the dimensionless mRNA degradation time
$\tau_m=\tau_{mrna}/\tau_r$, and the
dimensionless degradation rate of the RNAs is related
to the dimensionfull parameters as follows:
\begin{equation}
\gamma = \delta \alpha_m \tau_r^2.
\end{equation}
In the absence of $m$, $r$ is
degraded relatively slowly because unbound sRNA are quite
stable {\sl in vivo} \cite{MEG03}.
This means that $\tau_r$, which is
our rescaled time unit in eqs. (\ref{fs})-(\ref{ms}), is
around $(25/\ln 2)$ min.
In the absence of $r$, $m$ is degraded with $\tau_m=0.2$,
the lifetime of RyhB target
mRNA in {\sl E. coli} from ref. \cite{MEG03}.
\begin{figure}[t]
\begin{center}
\includegraphics[angle=-90,width=8cm]{figure2.eps}
\end{center}
\caption{
Limits on rescaled sRNA-target mRNA coupled degradation rate
$\gamma=\delta \alpha_m \tau_r^2$.
The colour shading indicate
that the model takes longer (shorter) time
in a darker (yellow) region to be depleted 5-fold
after the small RNA is activated by setting $f$ from
40 to zero at $t=0$.
The green solid line shows the contour line of 3 min.
When production of mRNA is much faster than
production of sRNA the 5-fold reduction can be obtained by a small $\gamma$,
whereas a relatively small $\alpha=\alpha_m/\alpha_r$ makes production
of sRNA so slow that the mutual degradation must be very fast.
The response time is calculated based on the
degradation time of sRNA $\tau_r=(25/\ln 2)$min \cite{SAKJMS06}.
\label{parameters}}
\end{figure}
The most important parameters that
determine the dynamics of sRNA regulation are $\alpha$ and $\gamma$
in eqs.(\ref{rs}) and (\ref{ms}).
We can determine a reasonable range of values for
these two parameters using experimental data.
First, for the Fe-Fur system $\alpha$ and $\gamma$
are mutually constrained by the observation that the target mRNA, sodB,
is depleted around 5-fold within 3 minutes after
full induction of the RyhB promoter\cite{MEG03}. These 3 minutes
include the time required for RyhB production, set by $\alpha$, plus
the time for the produced RyhB to
bind to sodB message and to degrade the complex, set by $\gamma$.
For $\alpha<1$ there will never be enough RyhB to deplete
the message completely, whereas for $\alpha$ slightly higher than 1
an extremely high $\gamma$ is needed for efficient depletion.
Fig. \ref{parameters} illustrates this.
We simulate eqs. (\ref{rs}) and (\ref{ms})
to measure how long it takes for $m$ to be depleted 5-fold
after fully-activating sRNA at $t=0$
by changing $f$ manually from $40$ to zero.
The solid line in Fig. \ref{parameters}
shows values of $\gamma$ and $\alpha$ that
give a 3 minutes depletion-time for sodB mRNA.
With $\alpha$ values in the range from 3 to 10, we see that
physiological $\gamma$ values would need to be between 100 and 10000.
In addition, the reduction of iron consumption occurs
as soon as the sRNA-mRNA complex is formed, even before
the mRNA is degraded, but
the measurement of \cite{MEG03} does not
distinguish RNA species in complexes from the free form.
Thus, the effective $\gamma$ could be larger than the above estimate.
The value of $\alpha$ can be estimated from other
data in ref. \cite{MEG03} of
RyhB and sodB time series after induction and
repression of RyhB.
From these data, we estimate that $\alpha$
is between 2 and 5.
In the rest of the paper, we
explore the small RNA motif
for a range of $\alpha$ and $\gamma$ values,
around the estimates made above.
The three other parameters, $A$, $B$, and $C$,
in the iron flux equation (\ref{fs}), we set
using experimental data \cite{SAKJMS06},
as described in the appendix.
\subsection{Transcriptional motif}
To model the transcription motif (Figure~\ref{motifs}b) we
replace (\ref{rs}) and (\ref{ms}) by the single equation:
\begin{equation}
\frac{dm}{dt}
= D \; \cdot \frac{f^h}{f^h+K_t^h} \; -\; \frac{m}{\tau_m}.
\label{mt}
\end{equation}
The first term models the direct transcriptional
activation of $m$
production by $f$, where $D$ sets the
maximum production rate of $m$ and $K_t$ sets
the binding constant between $f$ and the DNA.
The ``Hill coefficient" $h$ sets
the steepness of the response, and is related to the
cooperativity in binding.
We use the same values of the influx $C$ and
two constants $A$ and $B$ in (\ref{fs})
as those used in the sRNA motif.
We choose $D$ and $K_t$ in the transcription
motif to have the identical steady state values of the $f$ and $m$
to the corresponding sRNA motif (parameterized by $\alpha$ and $\gamma$)
for high iron ($f=40$) and low iron ($f=5$).
It is not obvious that this is
possible for all values of $\alpha$ and $\gamma$.
In fact, we found that it is not possible
for $h\le 2$, but
when $h=3$, we can set $D$ and $K_t$
such that the above conditions are fulfilled for $\alpha\in[0,20]$ and
$\gamma\in [0,2000]$. Therefore, henceforth we keep $h=3$.
\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=13cm]{figure3.eps}
\end{center}
\caption{(a) The steady state level of
$r/(\alpha-1)$
(thin lines) and $m/\tau_m$ (thick solid lines) vs. $f$ for $\alpha=4$ with
$\gamma=15$ (red solid lines) and $\gamma=1500$ (green dashed lines)
in the sRNA motif.
(b) The steady state level
of $m/\tau_m$ (thick lines) vs. $f$ for the
corresponding transcription motif parameters (see text).
The time evolution of $f$ (divided by 200,
thin lines) and $m$ (thick lines)
for the systems in (a) and (b)
are shown in (c)
and (d), respectively, after
the sudden drop of $C$ at $t=0$.
}
\label{ss_and_dyn}
\end{figure}
\section{Results}
\subsection{Degradation times}
Figures~\ref{ss_and_dyn}a
and b show how the steady state values
of $r$ and $m$ depend on the steady state $f$ level,
in the sRNA motif for two different $\gamma$ values,
and, respectively, in the corresponding
transcription motif systems.
For the sRNA motif, a larger $\gamma$ results
in a much larger ratio between
maximum and minimum $m$ values, and a steeper drop between
them (Figures~\ref{ss_and_dyn}a).
This is expected because in the $\gamma\rightarrow\infty$
limit, $m = \max(O(1/\gamma),\tau_m[1-\alpha/(1+f)])$,
and this steepness in the sRNA regulation
is referred to as ``ultrasensitivity'' in \cite{LMLKWB04}.
For the transcription motif, on the other hand,
the dependence of $m$ on $f$ is weaker
and nearly unaffected by the corresponding change
in $D$ and $K_t$ (Figure~\ref{ss_and_dyn}b).
This is because the steepness of the curve in the transcription
motif is determined by the Hill coefficient $h$,
which is set to be relatively high value 3 but
still not enough to give as sharp slope as the
sRNA motif with $\gamma=1500$.
The importance of $\gamma$ is also evident
in the dynamical response of the motifs
to a sudden depletion in the external
iron source $C$ (Figures~\ref{ss_and_dyn}c and d).
For the sRNA motif, Figure~\ref{ss_and_dyn}c shows that a larger $\gamma$
results in a faster drop in $m$ level, and a quicker approach to the
new steady state level. The same is true for the $f$ level also.
That is, a large $\gamma$ naturally ensures a faster removal of all excess $m$,
while also allowing $f$ and
$m$ to climb back to non-zero steady levels even after $f$ drops almost to zero
during the initial shock.
In contrast, the transcription motif displays approximately
the same timescale of mRNA drop for the two corresponding cases
because a drop in $m$ takes
a time proportional to $\tau_m$, independent of other parameters.
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{figure4.eps}
\end{center}
\caption{The contour plot of sRNA motif response time, $\Delta t$,
at which $f$ recovers to and subsequently remains within
95\% of the final steady state value.
The corresponding transcription motif systems show a
faster response in the shaded region.
\label{contour}
}
\end{figure}
We investigate this further by quantifying the response time.
Looking at Figure~\ref{ss_and_dyn}c, we see that the $f$ level drops
very sharply and then rises towards its final steady state value.
During this rise, at some time, $\Delta t$, $f$ reaches within
95\% of the final steady state value. We use $\Delta t$ as a measure of the response speed
of the system. In Figure~\ref{contour} we show a contour plot
of $\Delta t$ for a range of values of $\alpha$ and $\gamma$.
The corresponding transcription motif systems show a faster
response than the sRNA motif in the shaded region.
The comparison indicates that sRNA based translational regulation
produces a faster response than transcriptional regulation
when $\alpha\gtrsim 2$ (and $\alpha$ is not too large
compared to the investigated range of $f$)
and $\gamma$ is larger than a critical level, around 150
(the unshaded region in Figure~\ref{contour}).
\subsection{Metabolic cost}
The relatively slow response of the transcription motif is, of
course, because its response timescale is set by $\tau_m$, which we
keep constant. We emphasize that it is possible
to achieve a fast response in the transcription motif also by
decreasing $\tau_m$. There are some costs associated with this
alternative strategy though. Faster mRNA turnover due to lower
$\tau_m$ requires a higher production to maintain the same
homeostatic levels of $f$. At high $f$ levels, where mRNA is high,
the sRNA motif secures a low degradation rate of mRNA, whereas the
transcription motif produces the mRNA at its maximum rate. On the
other hand, at low $f$ the sRNA motif maintains a high rate of mRNA
degradation, while the transcription motif saves resources by
reducing mRNA production. Therefore, for a given response speed to
sudden iron starvation, the sRNA motif is less costly if the
bacterium usually lives in iron-rich conditions, whereas the
transcription motif is preferable if the organism mostly lives in
iron-poor conditions.
\subsection{sRNA prioritize downstream protein levels}
\subsubsection{Prioritization in the iron feedback motif}
The properties of sRNA regulation can be
used in an interesting way when more than one kind
of mRNA is under regulation \cite{MVG05}.
Different mRNA can have
hugely different binding strengths to the regulating sRNA, and thereby
very different effective degradation timescales.
This is because the
binding strength of the $r$-$m$ complex is, to a first
approximation, an exponential
function of the number of matching base-pairs, which can vary by
an order of magnitude across different mRNA:
The free-energy gain per matching
base-pair is around 1 to 2 kcal/mol,
which can give the difference in
statistical weight $\exp(\Delta G/k_B T)\approx 5$ to 30.
Because of this property,
sRNA regulation could be used to prioritize the degradation
of different mRNA.
We illustrate this by adding a second mRNA to the sRNA motif:
\begin{eqnarray}
\frac{dr}{dt} &=&
\frac{\alpha}{1+f}- r
- r \cdot \left(\gamma_1 m_1+\gamma_2 m_2\right)
\label{2rs}
\\
\frac{dm_1}{dt}&=&\alpha_{m_1}-\frac{m_1}{\tau_m}
- \gamma_1 r m_1,\label{2m1s}\\
\frac{dm_2}{dt}&=&\alpha_{m_2}- \frac{m_2}{\tau_m}
- \gamma_2 r m_2. \label{2m2s}
\end{eqnarray}
For $f$, we use (\ref{fs}),
replacing $m$ by $(m_1+m_2)$.
The two mRNAs, $m_1$ and $m_2$, have different effective
degradation rates, $\gamma_1$ and $\gamma_2$, resulting in
different steady state levels for a given $C$ value. Other parameters
are set as in the case with a single mRNA.
Figure~\ref{sorting} shows the
behavior of this system.
The steady state level in Figure~\ref{sorting}a
shows that $m_2$, the mRNA with larger $\gamma$,
is suppressed more than $m_1$ on depletion of $f$.
\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=13cm]{figure5.eps}
\end{center}
\caption{
Investigation of mRNA prioritization by the sRNA motif.
(a) The steady state level of
$r/(\alpha-1)$
(blue dotted line), $m_1/(\tau_m\alpha_{m_1})$
(red solid line), and $m_2/(\tau_m\alpha_{m_2})$ (green dashed line)
vs. $f$ for $\alpha=4$, $\gamma_1=150$,
and $\gamma_2=1500$.
(b) The time evolution of $f$ (divided by 400, blue dotted line),
$m_1$ (red solid line), and $m_2$ (green dashed line)
after the sudden drop of $C$ at $t=0$.
\label{sorting}
}
\end{figure}
The prioritization behavior is easily understood by considering the extreme
case where both $\gamma$s are very large but $\gamma_2\gg\gamma_1$.
Then, depending on the level of $f$, the steady state is such that
either (i) both mRNAs are near-zero, (ii) only $m_1$ is non-zero,
(iii) both $m_1$ and $m_2$ are non-zero.
Taking into account finite $\gamma$ values, the prioritization
efficiency becomes, respectively,
\begin{itemize}
\item[(i)]
$m_1\approx O(1/\gamma_1)$ and $m_2\approx O(1/\gamma_2)$ for small
$f$, i.e. $f\lesssim \frac{\alpha}{\alpha_{m_1}+\alpha_{m_2}}-1$,
\item[(ii)]
$m_1\approx \tau_m(\alpha_{m_1}+
\alpha_{m_2}-\frac{\alpha}{1+f})$ and $m_2\approx
O(\gamma_1/\gamma_2)$ for intermediate $f$, i.e.
$\frac{\alpha}{\alpha_{m_1}+\alpha_{m_2}}-1\lesssim f\lesssim
\frac{\alpha}{\alpha_{m_2}}-1 $,
\item[(iii)]
$m_1\approx \tau_m \alpha_{m_1} $ and $m_2\approx
\tau_m(\alpha_{m_2}-\frac{\alpha}{1+f})$ for large $f$, i.e.
$\frac{\alpha}{\alpha_{m_2}}-1 \lesssim f$.
\end{itemize}
where the $O(x)$ are some functions that
are small and proportional to $x$ for small $x$.
Case (ii) is what we refer to as the ``prioritized state", where only one of
the mRNA (the one with smaller $\gamma$) is present and the other's
level drops to near-zero. Clearly, the larger the difference between
the $\gamma$ values of the mRNAs, the better the prioritization;
the order of magnitude difference in $\gamma$ is important
to have the clear prioritization.
In addition, $\alpha$, the sRNA production rate, determines the range
of $f$ for which the sRNA is affected, and a larger $\alpha$ results
in prioritization being effective for a wider range of $f$.
In addition, the dynamics in Figure~\ref{sorting}b shows that,
when $C$ is suddenly dropped,
the mRNA with a larger $\gamma$ value is rapidly depleted while the
other mRNA stays at a higher level.
That is, the sRNA is not only able to
prioritize the mRNA steady
state levels, but is also able to remove the ``unwanted'' mRNA $m_2$
much quicker than the ``wanted'' mRNA $m_1$.
\subsubsection{Prioritization of multiple mRNAs}
\begin{figure}
\begin{center}
\includegraphics[angle=-90,width=7cm]{figure6a.eps}
\includegraphics[angle=-90,width=7cm]{figure6b.eps}
\end{center}
\caption{
Prioritization of mRNAs by (a) sRNA regulation
and (b) transcriptional regulation.
The steady state level of mRNAs normalized by their maximum value
is plotted against $\beta$.
(a) The prioritization by sRNA regulation, for
$\alpha_{m_1}=\alpha_{m_2}=\alpha_{m_3}=\alpha_{m_4}=0.25$,
and $\gamma_1=10^2, \gamma_2=10^3,\gamma_3=10^4,\gamma_4=10^5$.
The value of $\gamma_i$ are chosen to be large and
have 10-fold difference between different mRNAs, so that
the separation becomes clear.
(b) Transcriptional regulation, where the transcription factor
has concentration $\beta$ and acts as a repressor.
The Hill coefficient $h$ is 3.
The binding constants are
$K_1=1$, $K_2=0.75$, $K_3=0.5$, and $K_4=0.25$.
The values of $K_i$ are chosen to be
$K_i=\sum_{j=i}^4 \alpha_i$, so that
the value of $\beta$ at which the mRNA starts to be significantly degraded
is the same for the two motifs.
}
\label{SortingSimple}
\end{figure}
It is clear that the prioritization can be generalized to the case of
more than two kinds of mRNAs regulated by a single type of sRNA.
To illustrate this we ignore feedback through $f$ and consider the
following general system with $n$ different types of mRNAs:
\begin{eqnarray}
\frac{dr}{dt}&=&\beta-r-\sum_{i=1}^n \gamma_i r m_i,
\label{mrss}\\
\frac{dm_i}{dt}&=&\alpha_{mi}-\frac{m_i}{\tau_m}-
\gamma_i r m_i
\quad \mbox{for}\quad i=1,n.
\end{eqnarray}
Here, to focus on the prioritization, the production term of
sRNA in (\ref{2rs}) which contains
feedback from iron concentration is replaced by a constant $\beta$.
We assume
$\gamma_1<\gamma_2<\cdots<\gamma_i<\gamma_{i+1}<\cdots<\gamma_n$
without loss of generality,
and rescale all variables to be dimensionless
such that $\sum_{i=1}^n\alpha_{m_i}$ and
the degradation time of sRNA are unity.
Figure \ref{SortingSimple}a shows the normalized
steady state level of mRNAs, $m_i /(\alpha_{m_i}\tau_m)$,
versus the production rate of the sRNA, $\beta$.
As $\beta$ becomes larger, sRNA increases and more
mRNAs are degraded. As shown in Figure \ref{SortingSimple}a,
the $n$-th mRNA with the largest $\gamma$ is degraded
first. This also ``protects'' other mRNAs from degradation because
the sRNAs are also degraded together with
the $n$-th mRNAs. The ($n-1$)-th mRNA starts to be
degraded when the level of $n$-th mRNA becomes low enough,
which occurs roughly at $\beta\approx \alpha_n$.
The ($n-2$)-th mRNA starts to be degraded when $\beta\approx
\alpha_{n}+\alpha_{n-1}$, and so on, and
finally all the mRNAs are almost completely
degraded when $\beta\approx \sum_{i=1}^n\alpha_{i}=1$.
The separation of the level between the ($k+1$)-th mRNA
and the $k$-th mRNA for
$\sum_{i=k+1}^{n}\alpha_{mi}<\beta<\sum_{i=k}^{n}\alpha_{mi}$
becomes clearer for larger
difference between $\gamma_{i+1}$ and $\gamma_i$%
\footnote{
In the case $\gamma_{i+1}/\gamma_i\ll 1$ for any $i$,
the steady state level of mRNA for
$\sum_{i=k+1}^n\alpha_{m i}<\beta<\sum_{i=k}^n\alpha_{m i}$
is estimated as follows:
$m_{i}/(\tau_m \alpha_{mi})\approx 1$ for $i<k$,
$m_{k}/(\tau_m \alpha_{mk})
\approx (\sum_{i=k}^n\alpha_{m i}-\beta)/\alpha_{mk}$,
and $m_i/(\tau_m\alpha_i)\ll 1$ for $i\ge k+1$.
}.
This multistep-switch-like degradation
upon changing the value of $\beta$
is the characteristic feature of the sRNA regulation.
This prioritization mechanism is schematically
presented in Figure \ref{sortfig}, where the mRNAs are
degraded in descending order of the value of $\gamma$.
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{figure7.eps}
\end{center}
\caption{Schematic picture of the prioritization of
various kinds of mRNAs by a single type of sRNA.
Different kinds of mRNAs are represented by different
colors, and have different value of $\gamma$ (left boxes).
(a) When a small amount of sRNAs is produced, the mRNAs with larger
$\gamma$ are degraded (shaded region in the right box),
while the levels of mRNAs with small $\gamma$
are scarcely affected.
(b) As more sRNA is produced,
the mRNAs with smaller $\gamma$ are also degraded.
}\label{sortfig}
\end{figure}
We note that it is possible to
have different steady state of mRNAs in the transcriptional
motif also.
Suppose $r$ is the concentration of the
repressor with a production rate $\beta$.
Then the simplest model for the mRNA level is
\begin{eqnarray}
\frac{dr}{dt}&=&\beta-r,\\
\frac{dm_i}{dt}&=&\frac{\alpha_{m_i}}{1+(r/K_i)^h}-\frac{m_i}{\tau_m}
\quad \mbox{for}\quad i=1,n.
\end{eqnarray}
with a Hill coefficient $h$ and binding constants $K_i$;
we assume $K_1>K_2>\cdots >K_n$ without loss of generality.
Here, the variables are rescaled to be dimensionless such that
$K_1$ and the degradation time of $r$ are unity.
The normalized steady state level is given by
$m_i/(\alpha_{m_i}\tau_m)=\frac{1}{1+(\beta/K_i)^h}$:
The levels decrease as $\beta$ increases with the slope
determined by the Hill coefficient $h$, and the characteristic
value of $\beta$ where the $m_i$ level becomes half of its
maximum is given by $K_i$.
Figure~\ref{SortingSimple}b shows the
separation of the steady state by transcription regulation
with a relatively high value of the Hill coefficient $h=3$
and various values of $K_i$.
We see that the separation of the $m_i$ level
is not as sharp as with sRNA regulation,
and $m_i$ does not change much upon changing $\beta$
especially for large $K_i$.
The sRNA regulation is more effective
in the sense that the prioritization of the mRNAs
is sensitive to small changes in $\beta$.
\section{Discussion}
Our analysis pinpoints three features that are particular to sRNA
regulation in a feedback system. First, as sRNAs act through
degradation, the regulation can, in principle, be very fast,
generating a near instant response. Second, as the sRNA motif
uses a double negative link, instead of a direct
activation regulation, it has a higher metabolic cost for conditions where
downstream targets are repressed. Third, and most interestingly, it
has the capability of efficiently prioritizing the usage of downstream target
genes.
It is essential for the prioritized
expression of downstream targets that the sRNA as
well as the mRNAs are degraded together after they form a complex.
In the large $\gamma$ limit, the effective prioritization occurs because
the degradation of $m_2$ interferes with the degradation of $m_1$ by
sequestering $r$, leaving less unbound $r$ to bind $m_1$.
Indeed, if the sRNA simply catalyzed the degradation of the mRNAs without
itself being degraded (i.e., no $\gamma_i m_i$ terms in
(\ref{2rs}) or (\ref{mrss})), the ``protection" of $m_1$ is also lost.
The degradation of different mRNAs doesn't interfere
as in the previous case, and thus the prioritization
is less effective.
The switch-like behavior due to the
``ultrasensitivity'' of the sRNA regulation \cite{LMLKWB04}
together with the prioritization suggested in this work opens
the possibility of more sophisticated regulation of gene
expression. In particular, if each mRNA is targeted by
several kinds of sRNAs, the combinatorics allows
one to realize various logic gates.
For example, if different kinds of sRNAs
can bind to the same part of the targeted mRNA
to trigger the regulation, it behaves as an ``OR'' gate.
Such an example is known in {\sl V. cholerae},
where four different sRNAs regulate HapR and
any one of them is enough for regulation\cite{LMLKWB04}.
It is also, in principle, possible that one mRNA has multiple binding sites
for different sRNAs \footnote{
The authors do not know of an established example,
but there exists an mRNA that has multiple binding sites
for the same micro RNA in eukaryotic cells \cite{H04,CJFLH04}}.
In this case, if binding of all the sRNAs is
necessary to trigger the regulation, it realizes an ``AND'' gate.
The concentration dependent prioritization
can add more
complicated functions to the logic gates.
It is an interesting future issue to explore the possibility of
combinatoric regulation by sRNAs.
We have tested numerically that the results of this paper do not
strongly depend on the specific form of (\ref{fs}) for $f$. As
long as in- and out-fluxes are large enough to allow a much faster
response of $f$ than of $m$, then $m$ is the rate-limiting factor.
Another thing to note is that we assumed that the Hill coefficient
for the repression of sRNA by $f$ is 1, though we introduced a Hill
coefficient $h=3$ in the transcription motif to achieve the sharp
contrast in $m$ at high and low $f$. If we put a Hill coefficient
$H>1$ in the sRNA motif by replacing the production term of $r$ with
$\alpha/(1+f^H)$, the $m$ vs. $f$ curve becomes even steeper, which
makes the response sharper.
\section{Experimental tests}
The suggested prioritization possibility for downstream mRNAs invites
experimental tests. One key quantity of interest is the degradation
parameter $\gamma$, which in fact sets the efficiency of the whole
sRNA regulatory system. For large $\gamma$, the sRNA
regulation works as a step function: when production of sRNA is
larger than production of downstream targets, these are instantly
removed. Therefore it is essential to measure degradation times of
downstream targets under various expression levels of the sRNA.
These degradation times are tightly coupled to the steady state
level of downstream mRNA, and could therefore be obtained from bulk
measurements, using for example microarrays for both RyhB and
downstream targets. For a given $r$ (=sRNA) in the steady state, the
downstream mRNA level is $m_i(r)=\alpha_{m_i}/(1/\tau_m+\gamma_i
r)$, and therefore the slope of $m_i(0)/m_i(r)-1$ versus $r$ gives
$\gamma_i \tau_m$.
An experimental test of the prioritization capability of the RyhB system is
to consider homeostasis, and compare wild type with any mutant where
the RyhB binding part of a downstream target gene is highly
over-expressed. The over-expressed genes should be constructed such
that they do not produce proteins that can bind Fe,
and thereby indirectly influence the free/loosely bound Fe pool.
For a given low level of external iron, the prioritized usage implies
that for mutants where the over-expressed gene
has small $\gamma$ the expression levels of other genes
would be almost the same as in wild type.
For the remaining, there will be large changes associated to
RyhB being depleted by the over-expressed gene with large $\gamma$.
If the difference in $\gamma$ between different target mRNA
is of an order of magnitude, i.e., enough to have clear
prioritization, the influence
of the over-expressed gene should be quite sharp.
Further, our prioritization scheme implies that as the external Fe
is depleted further, the number of downstream genes
which influence homeostasis should diminish monotonically.
\section{Conclusion}
Using the well characterized homeostatic response system for iron in
bacteria, we analyzed the pros and cons of sRNA versus transcription
regulation. The investigated negative feedback motif of
Fe $\rightarrow$ FeFur $\rightarrow$ proteins $\rightarrow$ Fe brings out
the functional similarities and differences between the two
alternative strategies of regulating downstream targets. For
sufficiently high Hill coefficients, transcriptional regulation can
reproduce the same steady state behavior as the sRNA regulation.
Further, both regulations can in principle provide a fast response
to sudden decreases in externally available iron. However, their
functional capabilities differ in two important aspects.
\begin{itemize}
\item
First, adjusting parameters to obtain similar response times, the
sRNA motif results in more turnover of target mRNAs in iron-poor
conditions, whereas the transcription motif results in more
turnover in iron-rich conditions.
\item
Second, the sRNA allows a prioritization of expression level of
downstream targets, thus efficiently regulating the usage of a limiting
iron resource. At the same time, unwanted mRNA is degraded more rapidly.
This observation fits with the fact that the
transcription motif is found in {\sl H. pylori}, a bacterium with a
small genome and limited capacity for genome regulation, while {\sl
E. coli}, which has a larger genome and can benefit from fine tuning
of mRNA levels, has an sRNA motif.
\end{itemize}
Our analysis suggests new ways to analyze other systems where
multiple sRNAs regulate a more complicated response, including for
example quorum sensing~\cite{LMLKWB04}. There, mutual binding inhibition
between the sRNAs and a central regulator (LuxR mRNA in {\sl V.
harveyi} \cite{LMLKWB04}, HapR mRNA in {\sl V. cholerae} \cite{JH97},
and the translational regulator RsmA in Pseudomonas \cite{PWHHHCHW01}),
may allow signals from adhesion and host factors to differentiate
the sRNAs and thereby their downstream targets. Overall, our
analysis suggests that sRNAs or micro RNAs
may allow a near-digital reorganization
of cellular composition, an observation which concurs with their
ubiquity in regulatory processes associated with development.\\
\ack
This work was funded by the Danish National
Research Foundation. NM thanks the Yamada Science Foundation for
supporting her stay at the NBI. SS is grateful for the Janos Bolyai
Research Fellowship of the Hungarian Academy of Sciences.
\section*{Appendix:
Parameters in the flux equation}
We set the parameters $A$, $B$ and $C$ in eq. (3)
using data on the uptake and usage of Fe in
{\sl E. coli} and {\sl H. pylori}.
These systems are characterized by a huge
flux of free $Fe^{++}$, where the fluxes $C$, $A$ and $B$ are so large that
the pool is replenished about 100 times per cell generation.
In more detail,
the constant incoming flux, $C$, is partitioned into two channels, A
and B, that are motivated by the two separate ways of using iron in
the Fe-Fur system. Flow through channel A is regulated, i.e., it can
be reduced during iron-starvation, and is proportional to the mRNA
level, but independent of $f$
when there is any substantial amount of $f$ in the system
~\cite{SAKJMS06}%
\footnote{
When we simulate eq.(\ref{fs}),
we used the form $df/dt=C-A\cdot m\cdot
[f/(f+K_{cut})] -B\cdot f$
with $K_{cut}=0.1$ to avoid the numerical difficulty
due to the singularity at $f=0$. This expression
agrees with eq.(\ref{fs}) in the limit of $K_{cut}\to 0$.
}.
In contrast,
flow through channel B is proportional to $f$. In the case of the full
Fe-Fur system~\cite{SAKJMS06} the regulation of this flux by other
proteins becomes important when extracellular iron increases
suddenly, but here we focus on the regulation by sRNA and therefore
keep flow through channel B unregulated. That is, our motif is
designed to respond to depletion of $f$. Our ``minimal" motif cannot
do without this B channel because removing it results in robust
oscillations, for which there is no evidence in {\sl E. coli}
\cite{ARR03}.
The parameters in (\ref{fs}) are set
as follows \cite{SAKJMS06}:
For conditions where extracellular iron is plentiful, we demand that
the internal Fe$^{++}$ level is such that $f=40$
\cite{SAKJMS06} in steady state,
while at the same time the net in- and out-flux
per cell generation is approximately 100 times larger,
representing the fast turnover
and high usage of Fe \cite{ARR03,SAKJMS06}.
In addition, we assume that the iron flux
is equally partitioned between
the A and B channels,
because we found it best fulfills the
homeostatic requirements
in our full model~\cite{SAKJMS06}.
These conditions set the value of two parameters
$C=4572$ (i.e. $C=114\times f$~\cite{SAKJMS06})
and $B=57$.
The value of $A$ is completely determined by
the steady state level of $m$, which depends on the parameters
in the regulation part of the motif
(i.e., $\alpha$ and $\gamma$ in the sRNA motif,
or $D$ and $K_t$ in the transcription motif).
For iron-starvation we demand that $f=5$ \cite{SAKJMS06},
keeping the value of $B$
and $A$ constant.
This condition is achieved by reducing $C$,
reflecting the reduction in extracellular iron.
The $C$ change needed to get $f=5$ is dependent on
the values of the regulation part of the motif.
Note that, for a given regulatory motif,
the steady state value of $f$ is
a unique function of the influx $C$.
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| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,265 |
ISL78302A is a high-performance dual LDO capable of sourcing 300mA current from each output. It has a low standby current and very high PSRR and is stable with output capacitance of 1µF to 10µF with ESR of up to 200mΩ.
The device integrates an individual Power-On Reset (POR) function for each output. The POR delay for VO2 can be externally programmed by connecting a timing capacitor to the CPOR pin. The POR delay for VO1 is internally fixed at approximately 2ms. A reference bypass pin is also provided for connecting a noise-filtering capacitor for low noise and high-PSRR applications.
The quiescent current is typically only 47µA with both LDOs enabled and active. Separate Enable pins control each individual LDO output. When both Enable pins are low, the device is in shutdown, typically drawing less than 0.3µA.
The ISL78302A is AEC-Q100 qualified. The ISL78302A is rated for the automotive temperature range (-40°C to +105°C). | {
"redpajama_set_name": "RedPajamaC4"
} | 1,175 |
Q: Global Array not saving a change made to it Public Sub changePoints(ByVal Name As String, StartPoint As Boolean, Point As Integer)
Locations(Point).Name = Name
If StartPoint = True Then
For i = 0 To 19
Locations(i).StartPoint = False
Next
End If
Locations(Point).StartPoint = StartPoint
DrawGraph()
End Sub
Private Sub SaveButton_Click(sender As Object, e As EventArgs) Handles SaveButton.Click
GraphicalPlot.changePoints(PointNameBox.Text, MakeStart.Checked, LoadedPointValue)
End Sub
So i have 2 forms. The first form, when clicked with a point selected, brings up the second form with details of the point in an editable textbox. When you click the save button on the second form to save details, the 2nd subroutine above runs, and calls the subroutine in the first form that holds the global variable.
The information passes to the subroutine in the first form correctly. When i check the value of the global array immediately after changing it (right after the line Locations(Point).Name = Name), it says the value has been changed properly.
However, after the subroutine finishes, the global array returns to the value it had before the subroutine was called, and there is no trace of the information i input to the second form.
If it helps, the global array is of a structure:
Structure EnteredPoint
Dim Xcoord As Integer 'Stores X co-ordinate of point
Dim Ycoord As Integer 'Store Y co-ordinate of point
Dim Name As String 'Stores name of point, used to check if point is unused
Dim StartPoint As Boolean 'Checks if the point is the start point
Dim Selected As Boolean 'Checks if the point is currently being hovered over the mouse
Dim nextPoint As Integer 'Used to implement a linked list, making deleting and recreating points easier
End Structure
The name changing back to what it was shouldn't be possible; the only time my program changes the name outside of initialization (which sets it to "unused", or the number of points that have been created) is here.
I've googled it, showed it to my teacher, and a friend, and we couldn't find anything despite playing with it for hours. Any help would be much appreciated, since this is for my Comp4 coursework!
Edit: added for vbnet3d
Sub DrawGraph()
'Used to draw the current state.
G = Me.CreateGraphics
G.Clear(Color.White) 'Sets entire background to white
Dim placeholder As Integer = 0 'Used to store the current point being checked.
If UsedLocations > 0 Then 'This part will only run if any points have been made
Do Until Locations(placeholder).nextPoint = 0 'Loops until all points have been drawn
If Locations(placeholder).StartPoint = True Then 'will only draw this if it is the starting point
G.FillEllipse(Brushes.LightBlue, Locations(placeholder).Xcoord - 3, Locations(placeholder).Ycoord - 3, 16, 16)
End If
If Locations(placeholder).Selected = True Then 'Will only draw this if it is the currently selected point
G.FillEllipse(Brushes.LightGreen, Locations(placeholder).Xcoord - 3, Locations(placeholder).Ycoord - 3, 16, 16)
End If
'Draws the actual Point
G.FillEllipse(Brushes.Black, Locations(placeholder).Xcoord, Locations(placeholder).Ycoord, 10, 10)
If UsedLocations <= 20 Then
placeholder = Locations(placeholder).nextPoint 'Gets the next point to be checked.
End If
Loop
If UsedLocations = 20 Then
If Locations(placeholder).Selected = True Then 'Will only draw this if it is the currently selected point
G.FillEllipse(Brushes.LightGreen, Locations(placeholder).Xcoord - 3, Locations(placeholder).Ycoord - 3, 16, 16)
End If
'Draws the actual Point
G.FillEllipse(Brushes.Black, Locations(placeholder).Xcoord, Locations(placeholder).Ycoord, 10, 10)
End If
End If
End Sub
A: The problem is that you are using a value type (Structure) in your array. When you access the array element, you are getting a copy of the item so your changes are only made on the copy.
You will have to get the EnteredPoint from the array, change the properties as needed and then reassign the point back to the array:
Public Sub changePoints(ByVal Name As String, StartPoint As Boolean, Point As Integer)
Dim pointToChange As EnteredPoint = Locations(Point)
pointToChange.Name = Name
If StartPoint = True Then
For i = 0 To 19
Dim tmp As EnteredPoint = Locations(i)
tmp.StartPoint = False
Locations(i) = tmp
Next
End If
pointToChange.StartPoint = StartPoint
Locations(Point) = pointToChange
DrawGraph()
End Sub
If you wish to keep your original syntax, then you can change EnteredPoint to a class and it will work as you expect.
A: Your issue is being caused by default form references. (See comment by @Plutonix) What this means is that you have a base class instance called "GraphicalPlot" but you also have an active instance of "GraphicalPlot" which is a separate instance. These two classes are identical in form, but do not share in-memory data (one is a model for the other). When you make the following call, it references the model form instead of the active form:
Private Sub SaveButton_Click(sender As Object, e As EventArgs) Handles SaveButton.Click
GraphicalPlot.changePoints(PointNameBox.Text, MakeStart.Checked, LoadedPointValue)
End Sub
You need to create a reference to the active form (GraphicalPlot), and pass it to GraphicsMenu using Me as the current instance reference. Something along the lines of:
GraphicsMenu.Load(Me, PointName, PointNum)
And in GraphicsMenu:
Dim GP As GraphicalPlot
Public Sub Load(ByVal PlotForm As GraphicalPlot, ByVal Name As String, pointnumber As Integer)
GP = PlotForm
End Sub
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,299 |
\section{Introduction}
The degree--diameter problem asks for the maximum number of vertices in a graph of maximum degree $\Delta\ge 3$ and diameter $k\ge 2$. For general graphs the {\it Moore bound}, \[M(\Delta, k):=1+\Delta+\Delta(\Delta-1)+\ldots+\Delta(\Delta-1)^{k-1}= (1+o(1))(\Delta-1)^k (\text{for fixed $k$}),\] provides an upper bound for the order of such a graph. de Bruijn graphs provide a lower bound of $\floor{\Delta/2}^{k}$ \cite{Bru46}. For background on this problem the reader is referred to the survey \cite{MS05a}.
If we restrict our attention to particular graph classes, better upper bounds than the Moore bound are possible. For instance, a well-known result by Jordan \cite{Jordan1869} implies that every tree of maximum degree $\Delta$ and fixed diameter $k$ has at most $(2+o(1))(\Delta-1)^{\lfloor k/2\rfloor}$ vertices. For a graph class $\mathcal{C}$, we define $N(\Delta,k,\mathcal{C})$ to be the maximum order of a graph in $\mathcal{C}$ with maximum degree $\Delta\ge 3$ and diameter $k\ge 2$. We say $\mathcal{C}$ has {\it small order} if there exists a constant $c$ and a function $f$ such that $N(\Delta,k,\mathcal{C})\le c(\Delta-1)^{\floor{k/2}}$, for all $\Delta\ge f(k)$. The class of trees is a prototype class of small order.
For the class $\mathcal{P}$ of planar graphs, Hell and Seyffarth \cite[Thm.~3.2]{HS93} proved that $N(\Delta,2,\mathcal{P})=\floor{\frac{3}{2}\Delta}+1$ for $\Delta\ge 8$. Fellows {\it et al.}~\cite[Cor.~14]{FHS95} subsequently showed that $N(\Delta,k,\mathcal{P})\le ck\Delta^{\lfloor {k}/{2}\rfloor}$ for every diameter $k$. Notice that this does not prove that $\mathcal{P}$ has small order. Restricting $\mathcal{P}$ to even diameter graphs assures small order, as shown by Tishchenko's upper bound of $(\frac{3}{2}+o(1))(\Delta-1)^{{k}/{2}}$, whenever $\Delta \in\Omega(k)$ \cite[Thm.~1.1, Thm.~1.2]{Tis2011}. Our first contribution is to prove that $N(\Delta,k,\mathcal{P})\le c(\Delta-1)^{\lfloor {k}/{2}\rfloor}$ for $k\ge 2$ and $\Delta \in\Omega(k)$. That is, we show that the class of planar graphs has small order.
\begin{comment}
{Constructions by Fellows {\it et al.} \cite{FHS95,FHS98} imply that
\[N(\Delta,k,\mathcal{P})\ge\begin{cases}
\tfrac{3}{2}\Delta^{\lfloor {k}/{2}\rfloor}& \text{if $k$ is even}\\
\tfrac{9}{2}\Delta^{\lfloor {k}/{2}\rfloor}& \text{if $k$ is odd.}
\end{cases}\]\end{comment}
We now turn our attention to the class $\mathcal{G}_\Sigma$ of graphs embeddable in a surface\footnote{A {\it surface} is a compact (connected) 2-manifold (without boundary). Every surface is homeomorphic to the sphere with $h$ handles or the sphere with $c$ cross-caps \cite[Thm~3.1.3]{MohTho01}. The sphere with $h$ handles has {\it Euler genus} $g:=2h$, while the sphere with $c$ cross-caps has {\it Euler genus } $g:=c$. For a surface $\Sigma$ and a graph $G$ embedded in $\Sigma$, the (topologically) connected components of $\Sigma-{G}$ are called {\it faces}. A face homeomorphic to the open unit disc is called {\it 2-cell}, and an embedding with only 2-cell faces is called a {\it 2-cell embedding}. Every face in an embedding is bounded
by a closed walk called a {\it facial walk}.} $\Sigma$ of Euler genus $g$. For diameter 2 graphs, Knor and \v{S}ir\'a\v{n} \cite[Thm.~1, Thm.~2]{KS97} showed that $N(\Delta,2,\mathcal{G}_\Sigma)=N(\Delta,2,\mathcal{P})= \floor{\frac{3}{2}\Delta}+1$, provided $\Delta\in\Omega(g^2)$. \v{S}iagiov\'a and Simanjuntak \cite[Thm.~1]{SR04} proved for all diameter $k$ the upper bound \[N(\Delta,k,\mathcal{G}_\Sigma)\le c(g+1)k(\Delta-1)^{\left\lfloor {k}/{2}\right\rfloor}.\]
The main contribution of this paper, Theorem~\ref{theo:GralSurface} below, is to show that the class of graphs embedded in a fixed surface $\Sigma$ has small order.
\begin{thm}\label{theo:GralSurface}
There exists an absolute constant $c$ such that, for every surface $\Sigma$ of Euler genus $g$,
\[N(\Delta,k,\mathcal{G}_\Sigma)\le\begin{cases}
c(g+1)(\Delta-1)^{\lfloor {k}/{2}\rfloor}& \text{if $k$ is even and $\Delta\ge c(g^{2/3}+1)k$,}\\
c(g^{3/2}+1)(\Delta-1)^{\lfloor {k}/{2}\rfloor}& \text{if $k$ is odd and $\Delta\ge 2k+1$.}
\end{cases}\]
\end{thm}
We now prove a lower bound on $N(\Delta,k,\mathcal{G}_\Sigma)$ for odd $k\geq3$ (see \cite{FerPin13} for a more complicated construction that gives the same asymptotic lower bound.)\ Let $g$ be the Euler genus of $\Sigma$. It follows from the Map Colour Theorem \cite[Thm~4.4.5, Thm.~8.3.1]{MohTho01} that $K_p$ embeds in $\Sigma$ where $p\geq \sqrt{6g+9}$. Let $T$ be the rooted tree such that the root vertex has degree $\Delta-p+1$, every non-root non-leaf vertex has degree $\Delta$, and the distance between the root and each leaf equals $(k-1)/2$. Observe that $T$ has $(\Delta-p+1)(\Delta-1)^{(k-3)/2}$ leaf vertices. For each vertex $v$ of $K_p$ take a copy of $T$ and identify the root of $T$ with $v$. The obtained graph embeds in $\Sigma$, has maximum degree $\Delta$, and has diameter $k$. The number of vertices is at least $p(\Delta-p+1)(\Delta-1)^{(k-3)/2}$. It follows that for odd $k$, for all $\epsilon>0$ and sufficiently large $\Delta\geq\Delta(g,\epsilon)$,
\begin{equation}
\label{LowerBound}
N(\Delta,k,\mathcal{G}_\Sigma)\geq(1-\epsilon)\sqrt{6g+9}\,(\Delta-1)^{(k-1)/2}.
\end{equation}
This lower bound is within a $O(g)$ factor of the upper bound in Theorem~\ref{theo:GralSurface}. Moreover, combined with the above upper bound for planar graphs, this result solves an open problem by Miller and \v{S}ira\v{n} \cite[Prob.~13]{MS05a}. They asked whether Knor and \v{S}ir\'a\v{n}'s result could be generalised as follows: is it true that, for each surface $\Sigma$ and for each diameter $k\ge 2$, there exists $\Delta_0:=\Delta_0(\Sigma,k)$ such that $N(\Delta,k,\mathcal{G}_\Sigma)=N(\Delta,k,\mathcal{P})$ for $\Delta\ge \Delta_0$?
We now give a negative answer to this question for odd $k$.
Equation~\eqref{LowerBound} says that $N (\Delta, k, \mathcal{G}_\Sigma)/(\Delta-1)^{\lfloor{k/2}\rfloor}\ge c\sqrt{g}+1$, while Theorem~\ref{theo:GralSurface} with $g=0$ says that $N (\Delta, k, \mathcal{P})/(\Delta-1)^{\lfloor{k/2}\rfloor}\le c'$, for absolute constants $c$ and $c'$. Thus $N(\Delta,k,\mathcal{G}_\Sigma)> N(\Delta, k, \mathcal{P})$ for odd $k\ge 3$ and $g$ greater than some absolute constant.
In the literature all upper bounds for $N(\Delta,k,\mathcal{P})$ or $N(\Delta,k,\mathcal{G}_\Sigma)$ rely on graph separator theorems. Fellows {\it et al.} \cite[Cor.~14]{FHS95} used the graph separator theorem for planar graphs by Lipton and Tarjan \cite[Lem.~2]{LT79}, while Tishchenko used an extension of Lipton and Tarjan's theorem proved by himself in \cite[Cor.~3.3]{Tis2011a}. In the same vein, \v{S}iagiov\'a and Simanjuntak \cite{SR04} made use of Djidjev's separator theorem \cite[Lem.~3]{Dji85} for graphs on surfaces. Our proofs rely on a new graph separator theorem, also proved in this paper, which extends Tischenko's separator theorem to all surfaces, and is of independent interest.
In this paper we follow the notation and terminology of \cite{Die05}. The remainder of the paper is organised as follows. Section~\ref{sec:l-separators} proves a separator theorem for graphs on surfaces. Section~\ref{sec:surface-graphs} is devoted to the proof of Theorem~\ref{theo:GralSurface}.
Finally, Section~\ref{sec:conclusion} discusses some open problems arising as a result of our work.
\begin{comment}
Hereafter, the letter $n$ denotes the number $|V(G)|$ of vertices in a graph $G$ which is clear from context. We often denote by $|G|$ the number of vertices in $G$
Let $V_{\le l}(u)$ be defined as the set $\{v\in V(G): \dist(u,v)\le l\}$, and naturally extend this notion to $V_{=l}(u)$. Note that, for any integer $l\ge1$,
\begin{align}
|V_{= l}(u)|&\le \deg(u)(\Delta-1)^{l-1}\le\Delta(\Delta-1)^{l-1}, \textrm{and}\label{rmk1a}\\
|V_{\le l}(u)|&\le 1+\deg(u)\frac{(\Delta-1)^l-1}{\Delta-2}\le\frac{\Delta(\Delta-1)^l-2}{\Delta-2}=:M(\Delta,l)\label{rmk1b},
\end{align}
where $M(\Delta,l)$ is the Moore bound.
\end{comment}
\section{$\ell$-Separators in multigraphs on surfaces}
\label{sec:l-separators}
A \emph{triangulation} of a
surface $\Sigma$ is a multigraph (without loops) embedded in $\Sigma$ such
that each face is bounded by exactly 3 edges. Let $\ell\in \mathbb{Z}^+$ and let $\Sigma$ be a surface of Euler genus $g$ and let $G$ be an $n$-vertex triangulation of $\Sigma$. The aim of this section is to find a ``small'' subgraph $S$ of $G$ with $\ell$ faces such that each face of $S$ contains ``many'' vertices of $G$.
A well-known result by Lipton and Tarjan {\cite[Lem.~2]{LT79} states that if $\ell=2$ then there exists a subgraph $S$ of order at most $(\ell-1)(2r+1)$ in every plane triangulation $G$ such that each face of $S$ contains at least $\frac{n}{2\ell-1}-|S|$ vertices of $G$. Here $r$ denotes the radius of $G$. Tishchenko \cite[Thm.~1.1,Thm.~1.2]{Tis2011} found such a subgraph $S$ in a plane triangulation for every $\ell\ge2$. Tishchenko \cite{Tis2011} called such subgraphs {\it $\ell$-separators} by virtue of its number of faces. Our result extends Tishchenko's result to all surfaces.
\begin{comment}
{\color{blue}{David the condition $n\ge (\ell+2)b0$ was not right. We need $n\ge \alpha(\ell)n_0 $ for some function $\alpha$ such that
\begin{enumerate}
\item $\alpha(\ell)\ge \ell+1$ (for $\ell\ge0$) for the tree to have at least $\ell$ edges, and
\item $n'\ge \alpha(\ell-1)n_0$.
\end{enumerate}
I am now finding a family of functions $\alpha$ satisfying (2). We know that \begin{align*}
n'&\ge \frac{(2\ell-1)n-n_0}{2\ell+1}\ge \frac{(2\ell-1)\alpha(\ell)n_0-n_0}{2\ell+1}=\frac{(2\ell-1)\alpha(\ell)-1}{2\ell+1}n_0\\
&\ge \frac{(2\ell-1)\alpha(\ell)-1}{2\ell+1}n_0\ge \alpha(\ell-1)n_0
\end{align*}
To make our life easier we look for functions $\alpha$ such that
\[\frac{(2\ell-1)\alpha(\ell)-1}{2\ell+1}= \alpha(\ell-1)\]
Then we find that $\alpha(\ell)=\ell+\tfrac{1}{3}(2\ell+1)c$ for a constant $c$ are solutions. For (1) to work we must have
\[\ell+\tfrac{1}{3}(2\ell+1)c\ge \ell+1, \quad\text{$\ell\ge0$}\]
that is, every $c\ge 3$ works. Let us then pick $c=3$, and \[\alpha(\ell)=3\ell+1.\]
}}
\end{comment}
A \emph{tree decomposition} of a multigraph $G$ is a pair $(T,\{B_z:z\in V(T)\})$ consisting of a tree $T$ and a collection of sets of vertices in $G$ (called \emph{bags}) indexed by the nodes of $T$, such that:
\begin{enumerate}
\item $\bigcup\{B_z:z\in V(T)\}=V(G)$, and
\item for every edge $vw$ of $G$, some bag $B_z$ contains both $v$ and $w$, and
\item for every vertex $v$ of $G$, the set $\{z\in V(T):v\in B_z\}$ induces a non-empty (connected) subtree of $T$.
\end{enumerate}
For a subtree $Q$ of $T$, let $G[Q]$ be the subgraph of $G$ induced by $$\bigcup\big\{B_z:z\in V(Q)\big\}\setminus\bigcup\big\{B_z:z\in V(T)\setminus V(Q)\big\}.$$
Thus a vertex $v$ of $G$ is in $G[Q]$ whenever $v$ is in some bag in $Q$ and is in no bag outside of $Q$.
Our approach to finding an $\ell$-separator in an embedded multigraph is based on the following lemma for finding a separator in a multigraph with a given tree decomposition.
\begin{lem}
\label{lem:TreeDecompSeparator}
Let $\ell\geq0$ and $b\geq2$ be integers. Let $G$ be a multigraph with $n\geq (3\ell+1) b$ vertices. Let $(T,\{ B_z : z \in V(T) \})$ be a tree decomposition of $G$, such that $T$ has maximum degree at most 3, and $|B_z|\leq b$ for each $z\in V(T)$. Then there is a set $R$ of exactly $\ell$ edges of $T$ such that for each of the $\ell+1$ components $Q$ of $T-R$,
$$|G[Q]|\geq \frac{n-\ell b}{2\ell+1}.$$
\end{lem}
\begin{proof} We proceed by induction on $\ell\geq0$. The base case with $\ell=0$ and $R=\emptyset$ is trivially true. Now assume that $\ell\geq1$. Observe that $|E(T)|\ge \ell$ since $n\ge (3\ell+1)b$ and each bag has size at most $b$.
Consider an edge $xy$ of $T$. Let $T(x,y)$ and $T(y,x)$ be the subtrees of $T$ obtained by deleting the edge $xy$, where $T(x,y)$ contains $x$ and $T(y,x)$ contains $y$.
Let $G(x,y):=G[T(x,y)]$ and $G(y,x):=G[T(y,x)]$.
By part (3) of the definition of tree decomposition, each vertex of $G$ is in either $G(x,y)$ or $G(y,x)$ or $B_x\cap B_y$. Orient each edge $xy$ of $T$ by $\overrightarrow{xy}$ if $$|G(x,y)|<\frac{n-\ell b}{2\ell+1}.$$
{\bf \noindent Case 1.} Some edge $xy\in E(T)$ is oriented in both directions: Then $|G(x,y)|<\frac{n-\ell b}{2\ell+1}$ and
$|G(y,x)|<\frac{n-\ell b}{2\ell+1}$. Thus $$n=|G(x,y)|+|G(y,x)|+|B_x\cap B_y|< 2\left(\frac{n-\ell b}{2\ell+1}\right)+b.$$ Hence
$n(2\ell+1)< 2(n-\ell b)+b(2\ell+1)=2n+b$ and
$n(2\ell-1)< b$, which is a contradiction.
Now assume that each edge is oriented in at most one direction. A vertex $x$ of $T$ is a \emph{sink} if no edge incident with $x$ is oriented away from $x$. (Note that some edges incident with a sink might be unoriented.)\ Let $J$ be the subforest of $T$ obtained as follows: every sink is in $J$, and if $xy$ is an unoriented edge incident with a sink $x$, then $y$ and $xy$ are in $J$. Note that the vertex $y$ is also a sink and so every vertex in $J$ is a sink. Since $T$ is acyclic, $V(J)\neq\emptyset$.
{\bf \noindent Case 2.} $E(J)=\emptyset$: Thus $J$ contains an isolated vertex $y$.
Let $x_1,\dots,x_d$ be the neighbours of $y$, where $d\leq 3$. Since $y$ is a sink and is isolated in $J$, each edge $x_iy$ is oriented $\overrightarrow{x_iy}$. Thus $|G(x_i,y)|< \frac{n-\ell b}{2\ell+1}$. Every vertex not in $\bigcup_i G(x_i,y)$ is in $B_y$. Thus $$n\leq b+\sum_i|G(x_i,y)|< b+3\left(\frac{n-\ell b}{2\ell+1}\right).$$
Thus $n(2\ell+1)< b(2\ell+1)+3(n-\ell b)=3n-\ell b + b$ and $0\leq n(2\ell-2)< b(1-\ell)\leq 0$, which is a contradiction.
{\bf \noindent Case 3.} $E(J)\neq\emptyset$: Let $x$ be a leaf vertex in $J$. Thus $x$ is a sink and is incident with exactly one unoriented edge $xy$. Let $x_1,\dots,x_d$ be the other neighbours of $x$ in $T$, where $d\leq 2$. Thus $x_ix$ is oriented $\overrightarrow{x_ix}$.
Let $T':=T(y,x)$ and $G':=G(y,x)$ and $n':=|G'|$. Then $(T',\{B_z\setminus(B_x\cap B_y):z\in V(T')\})$ is a tree-decomposition of $G'$.
Since $x_ix$ is oriented $\overrightarrow{x_ix}$,
$$n\leq |B_x|+ n' + \sum_i|G(x_i,x)| \leq b+n'+ 2\left(\frac{n-\ell b}{2\ell+1}\right).$$
It follows that
\begin{align*}n' \geq \frac{(2\ell-1)n-b}{2\ell+1}\ge \frac{(2\ell-1)(3\ell+1)b-b}{2\ell+1}=(3(\ell-1)+1)b.\end{align*}
By induction, there is a set $R'$ of $\ell-1$ edges of $T'$ such that for each component $Q'$ of $T'-R'$,
\begin{align*}
|G'[Q']| \geq \frac{n'-(\ell-1)b}{2\ell-1}.
\end{align*}
We now prove that $R:=R'\cup\{xy\}$ satisfies the lemma. By definition, $|R|=\ell$. Each component of $T-R$ is either $T(x,y)$ or is a component of $T'-R'$. Since $xy$ is unoriented, $|G(x,y)|\geq\frac{n-\ell b}{2\ell+1}$, as required. For each component $Q'$ of $T'-R'$,
\begin{align*}
|G[Q']| \,=\, |G'[Q']|
\,\geq\, \frac{n'-(\ell-1)b}{2\ell-1}
\,\geq\, \frac{n}{2\ell+1} - \frac{b}{(2\ell+1)(2\ell-1)}-\frac{(\ell-1)b}{2\ell-1}
\,=\, \frac{n-\ell b}{2\ell+1},
\end{align*}
as required. Hence $R$ satisfies the lemma.
\end{proof}
\begin{thm}
\label{thm:SeparatorSurface}
Let $\ell \in \mathbb{Z}^+$. Let $\Sigma$ be a surface with Euler genus $g$. Let $G$ be a triangulation of $\Sigma$ with radius $r$ and order $n\ge(3\ell+1)((3+2g)r+1)$. Then $G$ has a subgraph $S$ with at most $(2r+1)(g+\ell)$ edges, such that the induced embedding of $S$ in $\Sigma$ is 2-cell with $\ell+1$ faces, and each face of $S$ contains at least $$\frac{n-\ell (3+2g)r-\ell}{2\ell+1}$$ vertices of $G$ in its interior.
\end{thm}
\begin{proof}
Let $u$ be a centre of $G$. Let $T$ be a breadth-first spanning tree of $G$ rooted at $u$. Thus $\dist_T(u,v)=\dist_G(u,v)\leq r$ for each vertex $v$ of $G$. Let $T_v$ be the $uv$-path in $T$.
Various authors \cite{Big71,RicSha84,Sko92} proved that there is a set $X$ of exactly $g$ edges in $G-E(T)$ such that the induced embedding of $T\cup X$ in $\Sigma$ is 2-cell and has exactly one face. Let $F(G)$ be the set of faces of $G$. If $T^*$ is the graph with vertex set $F(G)$, where faces $f_1$ and $f_2$ of $G$ are adjacent in $T^*$ whenever $f_1$ and $f_2$ share an edge in $E(G)\setminus(E(T)\cup X)$, then $T^*$ is a tree with maximum degree at most 3. For each face $f=xyz$ of $G$, let
$$B_f:=V(T_x\cup T_y\cup T_z)\,\cup\,\bigcup_{pq\in X}V(T_p\cup T_q).$$ Dujmovi\'c et al. \cite[Thm.~7]{DujMorWoo13} proved that $(T^*,\{B_f:f\in V(T^*)\})$ is a tree decomposition of $G$. Clearly, $T^*$ has maximum degree at most 3, and $|B_f|\leq (3+2g)r+1$ for each $f\in V(T^*)$ (since each $T_v$ has at most $r+1$ vertices, one of which is $u$).
By Lemma~\ref{lem:TreeDecompSeparator} with $b=(3+2g)r+1$, there is a set $R$ of $\ell$ edges of $T^*$ such that
$|G[Q]| \geq \frac{n- \ell (3+2g)r-\ell}{2\ell+1}$ for each of the $\ell+1$ components $Q$ of $T^*-R$.
Let $L$ be the set of edges $vw$ of $G$, such that for some edge $f_1f_2$ of $T^*$ in $R$, we have that $vw$ is the common edge on the faces $f_1$ and $f_2$ in $E(G)\setminus(E(T)\cup X)$. Thus $|L|=|R|=\ell$.
For each edge $vw$ of $G-E(T)$, let $Y_{vw}:=T_v\cup T_w\bigcup\{vw\}$. Note that $Y_{vw}$ has at most $2r+1$ edges. Let $S:=\bigcup\{Y_{vw}:vw\in X\cup L\}$. Thus $S$ has at most $(2r+1)(g+\ell)$ edges. Starting from the 2-cell embedding of $T\cup X$ with one face, the addition of each edge in $L$ splits one face into two, giving $\ell+1$ faces in total. Thus $S$, which is obtained from $T\cup X\cup L$ by deleting pendant subtrees, also has $\ell+1$ faces, and is 2-cell embedded.
The faces of $S$ are in 1--1 correspondence with the components of $T^*-R$. Let $\Phi$ be the face of $S$ corresponding to some component $Q$ of $T^*-R$. Let $v$ be one of the at least $\frac{n- \ell (3+2g)r-\ell}{2\ell+1}$ vertices in $G[Q]$.
If $v$ is not strictly in the interior of $\Phi$, then $v\in B_f$, where $f$ is a face of $G$ that is outside of $\Phi$ and incident with $v$, contradicting that $v$ is in $G[Q]$.
Hence each face of $S$ contains at least $\frac{n- \ell (3+2g)r-\ell}{2\ell+1}$ vertices in its interior.
\end{proof}
The case of planar graphs is worth particular mention, and is similar to a result by Tishchenko \cite[Cor.~33]{Tis2011a}.
\begin{cor}
\label{cor:SeparatorPlanar}
Let $\ell \in \mathbb{Z}^+$. Let $G$ be a triangulation of the sphere with radius $r$ and order $n\ge(3\ell+1)(3r+1)$. Then $G$ has a subgraph $S$ with at most $\ell(2r+1)$ edges, such that the induced embedding of $S$ is 2-cell with $\ell+1$ faces, and each face of $S$ contains at least $$\frac{n-(3r+1)\ell}{2\ell+1}$$ vertices of $G$ in its interior.
\end{cor}
\section{Proof of Theorem~\ref{theo:GralSurface}}
\label{sec:surface-graphs}
We start the section with a well-known lemma.
\begin{comment}
The following lemma is a consequence of Euler's formula \cite[pp.~85]{MohTho01}.
\begin{lem}\label{lem:EulerFormula}
Let $G$ be a multigraph with minimum degree $\delta\ge 3$ which is embedded in a surface $\Sigma$ of Euler genus at most $g$. Then
\begin{align*}
|V(G)|\le \frac{2}{\delta-2}\left(|F(G)|+g-2\right)\;\text{and}\;|E(G)|&\le \frac{\delta}{\delta-2}\left(|F(G)|+g-2\right)
\end{align*}
\end{lem}
\end{comment}
\begin{lem}[Euler's formula, {\cite[pp.~95]{MohTho01}}]\label{lem:EulerFormula}
Let $G$ be a multigraph which is embedded in a surface $\Sigma$ of Euler genus $g$. Then
\[|V(G)|-|E(G)|+|F(G)| \ge 2-g,\]
where $V(G)$, $E(G)$, and $F(G)$ denote the set of vertices, edges, and faces of $G$, respectively. Equality is achieved when the multigraph embeds 2-cellularly in $\Sigma$.
\end{lem}
Let $S$ be a connected multigraph with minimum degree at least 2 and maximum degree at least 3 which is embedded in a surface $\Sigma$. We define a multigraph $H$ from $S$ as follows: if there is an edge $e$ with a degree-2 endvertex then contract $e$, and repeat until the minimum degree is at least $3$. The multigraph so constructed is called the {\it simplified configuration} of $S$ \cite{Tis2011}. During the edge contraction we do not allow a facial walk to vanish; that is, a facial walk can become a loop but not a point. Note that any two sequences of edge contractions result in isomorphic multigraphs and that $H$ could also be defined as the minimal multigraph such that $S$ is a subdivision of H. We call a vertex of $S$ or $H$ a {\it branch vertex} if it has degree at least three in $S$ or $H$, respectively; every vertex in $H$ is a branch vertex. Also, $H$ may have faces of length 1 (the loops) and faces of length 2, and it is connected. See Fig.~\ref{fig:Goodregions} for an example.
\begin{figure}[!ht]
\begin{center}
\includegraphics[scale=0.9]{GoodRegions}
\caption{($a$) A 5-separator in the plane. ($b$) The associated simplified configuration $H$. Branch vertices are represented by a square.}
\label{fig:Goodregions}
\end{center}
\end{figure}
Our Theorem~\ref{theo:GralSurface} follows from the following technical result.
\begin{thm}\label{theo:mainSurface} Let $G$ be a graph embeddable in a surface with Euler genus at most $g$, maximum degree $\Delta\geq 3$, and diameter
$k\geq 2$. Then
\[|V(G)|< (2\ell+1)c(\Delta-1)^{\left\lfloor{k}/{2}\right\rfloor}+(2\ell+1)(2k+1)(g+\ell)M+\ell(3+2g)k+\ell,\]
where $M=M(\Delta,\lfloor k/2\rfloor-1)$ and \[(\ell,c):=\begin{cases}(\ceil{g^{2/3} + g^{1/2}}+6,2 g^{1/3}+ 6)&\text{if $k$ is even}\\
(\ceil{\sqrt{42g}}+33, 2\ell+2g-1)&\text{if $k$ is odd}.\end{cases}\]
\end{thm}
Note that the assumed lower bounds on $\Delta$ in Theorem~\ref{theo:GralSurface} ensure that the secondary term $(2\ell+1)(2k+1)(g+\ell)M+\ell(3+2g)k+\ell$ in the upper bound on $N(\Delta,k,\mathcal{G}_\Sigma)$ in Theorem {\ref{theo:mainSurface} is not dominant.
\begin{proof}[Proof of Theorem {\ref{theo:mainSurface}}]
By \cite[Prop.~3.4.1, Prop.~3.4.2]{MohTho01}, we may
assume that $G$ is 2-cell embedded in a surface $\Sigma$ of Euler genus $g$. Suppose for the sake of contradiction that \begin{equation}\label{eq:order}|V(G)|\ge (2\ell+1)c(\Delta-1)^{\left\lfloor{k}/{2}\right\rfloor}+(2\ell+1)(2k+1)(g+\ell)M+\ell(3+2g)k+\ell.\end{equation}
It follows that $|V(G)|\ge (3\ell+1)((3+2g)k+1)$. Thus, we may
apply Theorem~\ref{thm:SeparatorSurface} to a triangulation $G'$ of $G$. Note that $G'$ may be a multigraph. Let $S$ be a subgraph of $G'$ satisfying Theorem~\ref{thm:SeparatorSurface}. Thus $|E(S)|\le (2k+1)(g+\ell)$, and the induced embedding of $S$ in $\Sigma$ has exactly $\ell+1$ faces $R_1,\ldots,R_{\ell+1}$ such that
\begin{equation}\label{eq:TheoFunCycSep}
|V(G)\cap R_i|\ge \frac{|V(G)|}{2\ell+1}-\frac{\ell(3+2g)k+\ell}{2\ell+1},\; \text{for $i\in [1,\ell+1]$.}
\end{equation}
For each face $R_i$ of $S$, let $\partial(R_i)$ be the subgraph of $S$ consisting of the vertices and edges embedded in the boundary of $R_i$. A vertex in $V(G)\cap R_i$ is {\it deep} if it is at distance at least $\lfloor k/2\rfloor$ in $G$ from $\partial(R_i)$.
Our proof proceeds as follows. We first give a lower bound of $c(\Delta-1)^{\lfloor{k}/{2}\rfloor}$ for the number of deep vertices in each face of $S$. This implies that for every pair of distinct faces $R_i$ and $R_j$ of $S$ either $\partial(R_i)$ and $\partial(R_j)$ intersect or there exists an edge of $G$ with an endvertex in $\partial(R_i)$ and another endvertex on $\partial(R_j)$. Then we show that the embedding of $G$ restricts the number of pairs of faces of $S$ whose boundaries share an edge; these are our good pairs of faces. We bound the number of good pairs by a function linear in $\ell$. It follows that the number of pairs of faces of $S$ whose boundaries do not share an edge is quadratic in $\ell$; these are our bad pairs of faces. The existence of deep vertices in each face forces edges between the boundaries of each bad pair of faces; these are our jump edges. The proof ends when we show that this quadratic (in $\ell$) number of jump edges is inconsistent with a surface embedding. In the following we detail these ideas formally.
Let $V_i:=V(G)\cap R_i$ and let $D_i$ be the set of deep vertices in $R_i$. Since $\partial(R_i)$ has at most $(2k+1)(g+\ell)$ vertices and since the number of vertices at distance at most $\floor{k/2}-1$ from a given vertex is at most $M(\Delta,\floor{k/2}-1)$,
\[|V_i|\le (2k+1)(g+\ell)M+|D_i|.\]
By (\ref{eq:order}) and (\ref{eq:TheoFunCycSep}),
\begin{align*}|V_i|\ge c(\Delta-1)^{\left\lfloor {k}/{2}\right\rfloor}+(2k+1)(g+\ell)M+\frac{\ell(3+2g)k+\ell}{2\ell+1}-\frac{\ell(3+2g)k+\ell}{2\ell+1}.\end{align*}
Thus, $c(\Delta-1)^{\left\lfloor k/2\right\rfloor}+(2k+1)(g+\ell)M\le (2k+1)(g+\ell)M+|D_i|$, implying
\begin{equation}
\label{eq:DeepVertSurf} |D_i|\ge c(\Delta-1)^{\left\lfloor {k}/{2}\right\rfloor}.
\end{equation}
Let $H$ be the simplified configuration of $S$. Since $S$ is a connected multigraph with at least $3$ faces, $S$ has minimum degree at least 2 and maximum degree at least 3. The multigraph $H$ has minimum degree at least 3 and $\ell+1$ faces, and it may include faces of length 1 or 2. It is connected and embeds 2-cellularly in $\Sigma$. We use the multigraph $H$ to count the branch vertices of $S$. Since $3|V(H)|\le 2|E(H)|$, Lemma~\ref{lem:EulerFormula} gives
\begin{align}\label{eq:SurfaceH}
|V(H)|\le 2\ell+2g-2\; \text{and}\;|E(H)|&\le 3\ell+3g-3.
\end{align}
Distinct faces $R_i$ and $R_j$ of $S$ are a {\it good} pair if their boundaries share an edge in $S$; otherwise they are a {\it bad} pair.
Since the number of good pairs of faces of $S$ is at most $|E(H)|$, the number of bad pairs of faces of $S$ is at least
\begin{align}
\label{eq3} {\ell+1 \choose 2}-(3\ell+3g-3).
\end{align}
Let $R_i$ and $R_j$ ($i\ne j$) be a bad pair of faces of $S$. Let $I_{ij}$ be the set of vertices in $\partial(R_i)\cap \partial(R_j)$.
We first prove the theorem for even $k$. Note that $I_{ij}\ne \emptyset$ for each bad pair of regions, since $D_i$ and $D_j$ are nonempty. For each $i$, let $\ell_i$ be the number of bad pairs in which $R_i$ is involved. Choose $i$ so that $\ell_i$ is maximum, then $\ell_i\ge 2\frac{{\ell+1 \choose 2}-(3\ell+3g-3)}{\ell+1}=\frac{\ell^2-5\ell-6g+6}{\ell+1}\ge 1$, since $\ell=\ceil{g^{2/3} + g^{1/2}}+6$. For simplicity of notation, assume the faces $R_1,\ldots,R_{\ell_i}$ are involved in those pairs, and $i\not\in\{1,\ldots,\ell_i\}$.
Let $\Lambda$ be the multigraph formed from $\cup_{j=1}^{\ell_i} \partial(R_j)\cup \partial(R_i)$ by contracting each edge not incident to two vertices of $\cup_{j=1}^{\ell_i} I_{ij}$; see Fig.~\ref{fig:IntSurf}. Thus $\Lambda$ has vertex set $\cup_{j=1}^{\ell_i} I_{ij}$ and edge set formed by the edges left after the contractions.
\begin{figure}[!ht]
\begin{center}
\includegraphics[scale=1]{IntSurf}
\caption{A possible configuration for the multigraph $\Lambda$.}
\label{fig:IntSurf}
\end{center}
\end{figure}
Since $|F(\Lambda)|\le |F(S)|=\ell+1$ and since every vertex of $\Lambda$ has degree at least 4, Lemma~\ref{lem:EulerFormula} gives
\begin{align}\label{eq:Iij-1}
|V(\Lambda)|=|\cup_{j=1}^{\ell_i} I_{ij}|\le \ell+g-1\quad \text{and} \quad|E(\Lambda)|\le 2(\ell+g-1).
\end{align}
Each face $R_j$ ($j\in \{1,\ldots,\ell_i\}$) of $\Lambda$ has $|I_{ij}|$ vertices, and thus has $|I_{ij}|$ edges. Each such edge is in at most two such faces. Furthermore, the face $R_i$ of $\Lambda$ has $|V(\Lambda)|$ edges and shares no edge with a face $R_j$ ($j\in \{1,\ldots,\ell_i\}$). Thus
\begin{align}\label{eq:Iij-2}
2|E(\Lambda)| \geq 2|V(\Lambda)| +\sum_{j=1}^{\ell_i} |I_{ij}| \geq 2|V(\Lambda)|+\ell_i |I_{ij*}|,
\end{align}
where $I_{ij*}$ is a set $I_{ij}$ of minimum size.
Combining (\ref{eq:Iij-1}) and (\ref{eq:Iij-2}),
\begin{align*}
|I_{ij*}|&\le\frac{4(\ell+g-1)-2|V(\Lambda)|}{\ell_i}\le \frac{4(\ell+g-1)}{\ell_i}-\frac{2|I_{ij*}|}{{\ell_i}} \quad\text{(since $|V(\Lambda)|\ge |I_{ij*}|$)},\\
|I_{ij*}|\left(1+\frac{2}{\ell_i}\right)&\le\frac{4(\ell+g-1)}{\ell_i},\\
|I_{ij*}|&\le\frac{4(\ell+g-1)}{\ell_i+2}\le \frac{4(\ell+g-1)(\ell+1)}{\ell^2-3\ell-6g+8}\quad\text{(since $\ell_i\ge \tfrac{\ell^2-5\ell-6g+6}{\ell+1}$).}\end{align*}
For $x\in D_i$ and $y\in D_{j*}$ every $xy$-path of length $k$ includes some vertex in $I_{ij*}$. Thus every vertex in $D_i\cup D_{j*}$ is at distance $k/2$ from $I_{ij*}$. Since the number of vertices at distance $t$ from a fixed vertex is at most $(\Delta-1)^t$, by (\ref{eq:DeepVertSurf}), \[2c(\Delta-1)^{{k}/{2}}\le |D_i|+|D_{j*}|\le|I_{ij*}|(\Delta-1)^{{k}/{2}}\le \frac{4(\ell+g-1)(\ell+1)}{\ell^2-3\ell-6g+8}(\Delta-1)^{{k}/{2}},\]
which is a contradiction for $\ell=\ceil{g^{2/3} + g^{1/2}}+6$ and $c=2 g^{1/3}+ 6$.
Now assume that $k$ is odd. Consider any two faces $R_i$ and $R_j$ of $S$, then an edge $xy$ in $G$ with $x\in \partial(R_i)-\partial(R_j)$ and $y\in \partial(R_j)-\partial(R_i)$ is called a {\it jump edge between} $R_i$ and $R_j$. We say that two jump edges are {\it equivalent} if they connect the same set of pairs of faces.
\smallskip
\noindent {\bf Case 1:} There is no jump edge between some bad pair of faces $R_i$ and $R_j$.
We follow the reasoning of the even case. Let $\Lambda$ be the multigraph formed from $\partial R_i\cup \partial R_j$ by contracting each edge not incident to two vertices of $I_{ij}$. Thus $\Lambda$ has vertex set $I_{ij}$ and edge set formed by the edges left after the contractions. Since $D_i\ne \emptyset$ and $D_j\ne \emptyset$ and since there is no jump edge between $R_i$ and $R_j$, we must have $I_{ij}\ne \emptyset$. It follows that $|F(\Lambda)|\le |F(S)|=\ell+1$ and that the minimum degree of $\Lambda$ is at least 4. Thus, by Lemma~\ref{lem:EulerFormula}, $|V(\Lambda)|\le \ell+g-1$.
For $x\in D_i$ and $y\in D_j$, since $\text{dist}(x, \partial(R_i))\ge \lfloor k/2\rfloor$ and $\text{dist}(y, \partial(R_j))\ge \lfloor k/2\rfloor$ and because there is no jump edge between $R_i$ and $R_j$, every $xy$-path of length at most $k$ includes some vertex in $I_{ij}$. If $\text{dist}(x, I_{ij})\ge \lfloor k/2\rfloor+1$ and $\text{dist}(y, I_{ij})\ge \lfloor k/2\rfloor+1$ for some $x\in D_i$ and $y\in D_j$, then $\text{dist}(x,y)\ge k+1$. Thus, without loss of generality, every vertex in $D_i$ is at distance exactly $\lfloor k/2\rfloor$ from $I_{ij}$. By (\ref{eq:DeepVertSurf}),
\[c(\Delta-1)^{\left\lfloor {k}/{2}\right\rfloor}\le|D_i|\le|I_{ij}|(\Delta-1)^{\left\lfloor {k}/{2}\right\rfloor}\le(\ell+g-1)(\Delta-1)^{\left\lfloor {k}/{2}\right\rfloor},\]
which is a contradiction since $c=2\ell+2g-1$.
\smallskip
\noindent {\bf Case 2:} Now assume that between every bad pair of faces there is a jump edge.
A jump edge $xy$ is {\it normal} if neither $x$ nor $y$ is a branch vertex in $S$, otherwise it is {\it special}. Observe that a normal jump edge connects exactly one pair of regions. (This is not true for special jump edges.)
Let $X$ be the multigraph consisting of $S$ plus the jump edges. The multigraph $X$ is connected and may have more than $\ell+1$ faces. Now define a multigraph $Y$ obtained from $X$ by contracting an edge whenever it is not a jump edge and no endvertex is a branch vertex of $S$. During the edge contraction we do not allow the facial walk of a face to vanish; that is, a facial walk may become a loop but not a point. See Fig.~\ref{fig:EdgeCont}. Also, a set of jump edges running (in ``parallel'') between the same set of pairs of regions are replaced by a single edge.
\begin{figure}[!ht]
\begin{center}
\includegraphics[scale=1]{EdgeCont.eps}
\caption{Contraction of edges which are ends of jump edges. ($a$) various jump edge ends (in dashed lines). ($b$) The resulting edges in Y.}
\label{fig:EdgeCont}
\end{center}
\end{figure}
Observe that $Y$ can be obtained from a subdivision of $H$ by adding the jump edges, where each edge of $H$ is subdivided at most once. Thus \begin{align*}
|V(Y)|\le & |E(H)|+|V(H)|\le 5\ell+5g-5.
\end{align*}
The multigraph $Y$ may have faces of length 1 or 2, and it is connected and of minimum degree at least 3.
Denote by $F_{1}(Y)$ and $F_{2}(Y)$ the set of faces of $Y$ of length 1 or 2, respectively. Then $|F_{1}(Y)|+|F_{2}(Y)|\le \ell+1$; this is the case because $Y$ has no multiple jump edges, and therefore, faces of length 1 and 2 can only arise from the initial faces of $H$. The handshaking lemma for faces gives $3(|F(Y)|-|F_1(Y)|-|F_2(Y)|)+|F_1(Y)|+2|F_2(Y)|\le 2|E(Y)|$. Thus,
\begin{align*}
|F(Y)|&\le \tfrac{2}{3}|E(Y)|+\tfrac{1}{3}(2|F_{1}(Y)|+|F_{2}(Y)|)\le \tfrac{2}{3}E(Y)|+\tfrac{2}{3}(\ell+1).
\end{align*}
Consequently, Lemma~\ref{lem:EulerFormula} gives that
\begin{align*}
|E(Y)|\le 3|V(Y)|+2\ell-4+3g& \le
17\ell+18g-19.
\end{align*}
The number of bad pairs of faces of $S$ that are connected by normal jump edges equals the number of normal jump edges, and hence, is at most $|E(Y)|$.
Since the number of bad pairs of faces of $S$ is at least ${\ell+1 \choose 2}-(3\ell+3g-3)$ and since $\ell=\ceil{\sqrt{42g}}+33$, the number of bad pairs of faces of $S$ that are not joined by a normal jump edge is at least \begin{equation}\label{eq5}{\ell+1\choose 2}-(3\ell+3g-3)-(17\ell+18g-19)\ge 1.\end{equation}
Hence, there is at least one bad pair of faces $R_i$ and $R_j$ of $S$ that is not joined by a normal jump edge.
Recall the number of branch vertices in $S$ equals the number of vertices of $H$, which is at most $2\ell+2g-2$. Thus, the number of deep vertices in each of $D_i$ and $D_j$ at distance $
\lfloor k/2\rfloor$ from a branch vertex in $\partial(R_i)\cup \partial(R_j)$ is at most
\[(2\ell+2g-2)(\Delta-1)^{\left\lfloor {k}/{2}\right\rfloor}.\]
By Equation (\ref{eq:DeepVertSurf}), $|D_i|\ge c(\Delta-1)^{\floor{k/2}}$ and $|D_j|\ge c(\Delta-1)^{\floor{k/2}}$. Since $c>2\ell+2g-2$ there are vertices $\beta_i$ and $\beta_j$ in $D_i$ and $D_j$ respectively at distance at least $\lfloor k/2\rfloor+1$ from each branch vertex of $H$. Thus a shortest path of length $k$ between $\beta_i$ and $\beta_j$ must use a normal jump edge between $R_i$ and $R_j$. This is a contradiction and completes the proof of the theorem.
\end{proof}
\section{Concluding remarks}
\label{sec:conclusion}
We believe the asymptotic value of $N(\Delta,k,\mathcal{G}_\Sigma)$ is closer to the lower bound in
Equation~\ref{LowerBound}
than to the upper bound in Theorem~\ref{theo:GralSurface}.
\begin{conjecture}\label{conj1}
There exist a constant $c$ and a function $\Delta_0:=\Delta_0(g,k)$ such that, for $\Delta\ge \Delta_0$,
\[N(\Delta,k,\mathcal{G}_\Sigma)\le\begin{cases}
c(\Delta-1)^{\lfloor {k}/{2}\rfloor}& \text{if $k$ is even}\\
c(\sqrt{g}+1)(\Delta-1)^{\lfloor {k}/{2}\rfloor}& \text{if $k$ is odd.}
\end{cases}\]
\end{conjecture}
\begin{comment}
For a surface $\Sigma$ of Euler genus $g$ define its {\it chromatic number }$\gamma$ as follows:
\[\gamma(\Sigma)=\begin{cases}6& \text{if $\Sigma$ is the Klein bottle}\\ \frac{7+\sqrt{1+24g}}{2}& \text{otherwise.}\end{cases}\]
Let $\Sigma$ be any surface of Euler genus $g$ and let $h:=\gamma(\Sigma)+1$. From the Map Colour Theorem \cite[Thm~4.4.5, Thm.~8.3.1]{MohTho01} it follows that the complete graph $K_h$ on $h$ vertices does not embed in $\Sigma$. Then every graph embedded in $\Sigma$ is $K_h$-minor-free. Theorem~\ref{theo:GralSurface} then implies that, for $\Delta\ge \Delta_0$ with $\Delta_0:=c(h,k)$,
\[N(\Delta,k,\mathcal{G}_\Sigma)\le \begin{cases}
c_0(\Delta-1)^{\lfloor {k}/{2}\rfloor}
& \text{if $k$ is even}\\
c_1(\Delta-1)^{\lfloor {k}/{2}\rfloor}
& \text{if $k$ is odd}
\end{cases}\] for some constants $c_0:=c(h^{2})$ and $c_1:=c(h^3)$.
\end{comment}
A generalisation to the class $\mathcal{G}_H$ of $H$-minor-free graphs, with $H$ a fixed graph, was studied in {\cite{PVW12}}. The current best upper bound of $$N(\Delta,k,\mathcal{G}_H)\le 4k(c|H|\sqrt{\log{|H|}})^k\Delta^{\lfloor k/2\rfloor}$$ was given in {\cite[Sec.~4]{PVW12}}. Note that if $H$ is planar, then $\mathcal{G}_H$ has bounded treewidth, and thus has small order {\cite[Thm.~12]{PVW12}}.
\begin{comment}
Let $G\in \mathcal{G}_H$, then it is $K_{|H|}$-minor-free. Thus, when dealing with $H$-minor-free graphs, it suffices to consider fixed complete graphs. Furthermore, if a graph $G$ has bounded tree-width, a positive answer for Problem~\ref{prob:H-minor} follows from \cite[Thm.~12]{PVW12}. If instead $G$ embeds in a fixed surface of bounded genus, a positive answer follows from our Theorem~\ref{theo:GralSurface}. Thus, in Problem~\ref{prob:H-minor} we can assume that $G$ has unbounded tree-width and unbounded genus. Furthermore, it is known that an $H$-minor-free graph has bounded tree-width iff $H$ is planar \cite{Robertson1986b}. Consequently, we could take $H:=K_h$ with $h\ge5$ in Problem~\ref{prob:H-minor}.
\end{comment}
\section*{Acknowledgments}
We would like to thank Roi Krakovski for discussions that led to improvements in the paper presentation.
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57 but turned away and acted treacherously like their fathers; they twisted like a deceitful bow.
58 For they provoked him to anger with their high places; they moved him to jealousy with their graven images.
59 When God heard, he was full of wrath, and he utterly rejected Israel.
61 and delivered his power to captivity, his glory to the hand of the foe.
62 He gave his people over to the sword, and vented his wrath on his heritage. | {
"redpajama_set_name": "RedPajamaC4"
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{"url":"https:\/\/www.gamedev.net\/forums\/topic\/64373-recving-entire-packets\/","text":"\u2022 ### Popular Now\n\n\u2022 9\n\u2022 13\n\u2022 10\n\u2022 18\n\u2022 19\n\n#### Archived\n\nThis topic is now archived and is closed to further replies.\n\n# Recving entire packets\n\nThis topic is 5987 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.\n\n## Recommended Posts\n\nI'm having a pretty frustrating problem, and I'm pretty sure it is occuring because packets aren't getting completely sent. I'm using winsock with SOCK_STREAM sockets. Well, I'm using winsock wrapped in my own socket class. I'm pretty sure the class is not the problem. A more detailed explanation: I have a \"logon\" struct, that holds a packet ID, username (char[20]) and password(char[20]).\n struct \/\/logon packet { BYTE id; char username[21]; char password[21]; } logon; \nNow, from the client, I do some initialization and send the packet:\n logon.id = PID_LOGON; \/\/denotes that this is a login packet strcpy(logon.username,\"riley riley\"); strcpy(logon.password,\"howdy\"); clientSocket.send((char *)&logon, sizeof(logon), 0); \nThen, in the server, I recv the packet, but not everything comes through.\n \/\/packet is defined above to have the same structure as logon from the client memset(&packet, 0, sizeof(packet)); \/\/zero out the packet int bytesReceived = socket.recv((char *)&packet, sizeof(packet), 0); \nbytesReceived comes out being 16.. but only the id and username get transmitted. No part of password is transmitted. My question is, how do I get the rest of this packet? How do I even make sure it all got sent - MSDN warns that send isn't guaranteed to send all of the data I give it. And if I send another round of data later, how do I attach it to the end of the data already received in the server? Thanks for any help -riley Edited by - rileyriley on October 22, 2001 11:30:14 PM\n\n##### Share on other sites\nHi.\n\nI''m probably not qualified to answer blablabla, but anyway..\n\nIn short, I think you need to call recv several times in order to get the whole packet.\n\nSo the receiving machine needs to know how long a packet is. If the received amount of bytes is less than the packet length call recv again. Thus, either you have a fixed packet length or send the packet length in some kind of header in each packet.\n\nYou might also need to call send several times if you see that not the whole packet was sent.\n\nI think this is how its done, haven''t done any serious tcp\/ip. So someone correct me if I''m wrong!\n\nCheers\n\n##### Share on other sites\nOk, thanks, yeah that makes sense. I''d thought about that before, but I was thinking that it would be possible for some packets to arrive out of order - but SOCK_STREAM specifies that all the data arrives in the order it was sent, right?\n\nThanks,\n-riley\n\n##### Share on other sites\nOn thinking about what you said some more, I''ve come apon a little catch - if you''re using variable sized packets and send the size _in_ the packet, how can you be guaranteed that the server will even get the whole size?\n\n##### Share on other sites\nsockets (and most streamed reads) shoudl be double-buffered at some point. You packet protocol should probably be wrapped in control characters (STX and ETX are the standard) so that you can process thusly:\n\nDefine a buffer around 8k. This is your primary recv buffer. As long as read() returns data, append it to this primary buffer. You may need to use select() or wouldblock() to see if more data is available after the read(), but once all data is read, sweep the buffer for your control characters and then memmove() each COMPLETE packet (STX thru ETX) into your packet struct and move on to the next chunk.\n\nSound good? It may seem like a lot of bloat but TCP\/IP is NOT ASSURED DELIVERY, meaning it only ensures the packets will be IN ORDER, not that they will ALWAYS GET THERE. A very important distinciton.\n\n---------\n-WarMage\n...my sensei is a tcp\/ip ninja...\n\n##### Share on other sites\nI ended up writing all of the data recved to a buffer, like you suggested. But instead of then sweeping the buffer for control \"packet boundary\" characters, I do the following:\n\nI have a boolean variable that reflects whether or not my program is in \"mid packet.\" If it is not mid-packet, I read a single byte, the ID of what kind of packet is being sent, and set midpacket to true. Then, from that single byte received, I look up the size of that kind of packet and call it totalPacketSize.\n\nEvery time select notifies my program that the socket has incoming data waiting, I call recv again, with totalPacketSize - lengthOfDataAlreadyRead as the requested number of bytes to read. I add however many bytes are received to lengthOfDataAlreadyRead (actually called dataLen), and repeat the process until dataLen equals totalPacketSize, so I know that the whole packet has been received. Then I copy the buffer to the appropriate packet structure (I actually have a bunch unioned into one generic PACKET). Then I set midpacket to false again, and dataLen to 0, and the process can start over for the next packet.\n\n PACKET packet; int bytesReceived; if (!midPacket) { midPacket = true; \/\/we just want to read a single byte, the id of the packet, and then figure out wth to do with the rest bytesReceived = socket.recv((char *)buffer, 1, 0); if (bytesReceived == 1) \/\/this will always be true but whatever { totalPacketSize = getPacketSize(buffer[0]); \/\/remember buffer[0] now holds the packet ID if (totalPacketSize == -1) cout << \"ERROR: Invalid packet type sent!!\" << endl << flush; dataLen = 1; } } bytesReceived = socket.recv((char *)buffer + dataLen, totalPacketSize - dataLen, 0); dataLen += bytesReceived; if (bytesReceived == 0) { cout << socket.ip << \" disconnected :(\\n\" << flush; socket.disconnect(); active = false; \/\/deactivate myself return; } if (dataLen >= totalPacketSize) \/\/if we've gotten the whole packet { \/\/copy the buffer to the packet memcpy(&packet, buffer, dataLen); midPacket = false; switch(packet.id) \/\/decide how to interpret the data: { case PID_LOGON: cout << \"User \" << packet.logon.username << \" has logged on.\\n\" << flush; break; \/\/and etc...\n\nThis seems like it shoudl work fine for me. The only problem would be if packets could come partially, which is something that I still don't know about - can the first part of a packet come and then the start of another before the end of the first packet?\n\nThanks\n-riley\n\nEdited by - rileyriley on October 23, 2001 3:23:53 PM\n\n##### Share on other sites\nquote:\nOriginal post by rileyriley\nThe only problem would be if packets could come partially, which is something that I still don''t know about - can the first part of a packet come and then the start of another before the end of the first packet?\n\nNo, that''s a function of the TCP layer of the implementation. If separate segments of datagrams are received in overlapping fashion, the TCP layer can either queue or discard the offending segment(s) on continue assembling the first datagram. I believe what happens is that the driver dumps the segment and responds to the remost system that the packet was not recieved.\n\n---------\n-WarMage\n...this is a job for rm -rf!...\n\n##### Share on other sites\nThanks - is that also true of streams?\n\n##### Share on other sites\nquote:\nOriginal post by rileyriley\nThanks - is that also true of streams?\n\nI would say no, because a Winsock stream is a specialized stream, and streams in general cnnot be out of order. Winsock just happens to have to implement TCP\/IP, which stipulates that packets may be recievd out of order. Read up on the spec for TCP\/IP and it will be much clearer\n\n---------\n-WarMage\n...it''s a party in your mouth...\n\n##### Share on other sites\nBeing a streamed protocol, TCP has the following features:\n\n1) Guaranteed delivery. As long as the connection doesn''t break, all bytes sent will be received. No bytes will be duplicated.\n\n2) In-order delivery. All bytes will be received in the order they were sent.\n\n3) There are no packet boundaries.\n\nThis has the following implications:\n\n- when you call to recv(), you might only receive the beginning of a structure the server send()s as a whole\n\n- two blocks of data that are send() seperately may be received by a single call to recv()\n\n- you do not have to have any special packet boundary markers (like the STX and ETX previously mentioned) or length indicator if your packets are fixed in size. If your packets vary in size, you need a header giving the length of the packet before the actual data\n\n- you don''t need to introduce sequence numbers for your packets\n\nIf you were to use anything like sequencing or packet boundary marker, you''d just duplicate the efforts that are already done in the TCP layer, wasting both processing speed and network bandwidth.\n\ncu,\nPrefect\n\nOne line of sourcecode says more than a thousand words.","date":"2018-03-20 14:24:57","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\": 0.17852598428726196, \"perplexity\": 3337.307008043203}, \"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-2018-13\/segments\/1521257647475.66\/warc\/CC-MAIN-20180320130952-20180320150952-00026.warc.gz\"}"} | null | null |
In Massachusetts, all home improvement contractors are required to register with the Board of Building Regulations and Standards (BBRS). It is very important to check if your state has a registration requirement. If so, you must check to see if your contractor is registered. If not, do not hire him or her! It has been shown tht there are far more incidents of problems with unregistered contractors. In fact, contractors may incur criminal penalties for failing to register. This is an easy tip to follow, and homeowners can save themselves a great amount of trouble if they do. | {
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Q: Use OrmLite in every class which doesn't extand OrmLiteBaseActivity or Activity I use OrmLite and I want to get the helper class (and then get a dao class) in a class which doesn't extend OrmLiteBaseActivity.
I read the documentation on using with Android and I looked at their no base class example.
As my class isn't an Activity :
*
*it isn't a Context, so OpenHelperManager.getHelper can't work.
I know I can get the context from every part of my application using the application but is there a better way ?
*it doesn't have a onDestroy to override.
I can put the logic at the end of my function :
if (databaseHelper != null) {
OpenHelperManager.releaseHelper();
databaseHelper = null;
}
But if my class become more complex, what is the good behaviour ?
Regards.
A: The general rule of thumb is that you should create a single helper object and then release it when all of the parts of your program are done with it. This means that if you have different threads that are using the helper, you'll need to keep some sort of usage counter -- maybe with AtomicInteger. As each class asks for the helper, the first time it is created but every time afterwards the counter is increased. As they are done with the helper they decrement the counter. When the counter goes to 0 you release it from OpenHelperManager.
it isn't a Context, so OpenHelperManager.getHelper can't work.
You are going to need to get the Context somehow. Using the application should be fine as long as it works.
it doesn't have a onDestroy to override
But part of your program does have onDestroy. You are going to have to application the other parts of your application from the places that do have onDestroy -- maybe by calling a static destroy() method.
But if my class become more complex, what is the good behaviour?
I don't see any problems with the above even with complex applications. If you'd like maybe setup a register/unregister type of config so as your classes construct they register with some central class which then shuts them down at the end.
Hope some of this helps.
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{"url":"https:\/\/www.storyofmathematics.com\/which-operation-could-we-perform-in-order-to-find-the-number-of-milliseconds-in-a-year\/","text":"Which operation could we perform in order to find the number of milliseconds in a year?\n\n\u2022 $60\\cdot 60\\cdot 24\\cdot 7\\cdot 365$\n\u2022 $1000\\cdot 60\\cdot 60\\cdot 24\\cdot 365$\n\u2022 $24\\cdot 60\\cdot 100\\cdot 7\\cdot 52$\n\u2022 $1000\\cdot 60\\cdot 24\\cdot 7\\cdot 52$\n\nThe goal of this question is to convert a year into milliseconds by selecting a suitable formula from the list provided.\n\nFor this operation, disregard the use of months in the calculation. They have irregular days, which complicates the operation. Let us start with days, hours, minutes, seconds, and milliseconds. A normal year has $365$ days and one day has $24$ hours, in addition, there are $60$ minutes in an hour and $60$ seconds in a minute.\n\nWe need to figure out how many milliseconds there are in a year.\n\nTo begin with the solution, milli means thousandth, so one second incorporates $1000$ milliseconds.\n$1\\, s=1000\\, ms$\n\nFollowing that, there are $60$ seconds in a minute, so the number of milliseconds in one\u00a0minute can be calculated by multiplying the number of milliseconds in one\u00a0second by the number of seconds in one\u00a0minute.\n\n$1\\,min=60\\,s=1000\\cdot60\\,ms$\n\nFollowing this, there are $60$ minutes in an\u00a0hour, so the number of milliseconds in one\u00a0hour can be calculated by multiplying the number of milliseconds in one\u00a0minute by the number of minutes in one\u00a0hour.\n\n$1\\,h=60\\,min=1000\\cdot60\\cdot60\\,ms$\n\nAlso, a day has\u00a0$24$ hours, so the number of milliseconds in one\u00a0day is calculated by multiplying the number of milliseconds in one\u00a0hour by the number of hours in one\u00a0day.\n\n$1\\,day=24\\,h=1000\\cdot60\\cdot60\\cdot24\\,ms$\n\nFinally, we make the assumption that a year has 365 days. After that, the number of milliseconds in one\u00a0year is calculated by multiplying the number of milliseconds in one\u00a0day by the number of days in one\u00a0year.\n\n$1\\,year=365\\,days=1000\\cdot60\\cdot60\\cdot24\\cdot365\\,ms$\n\nSo, from the given options, it can be seen that:\n\n$1000\\cdot 60\\cdot 60\\cdot 24\\cdot 365$\n\nis the correct option.\n\nExample $1$\n\nConvert $6$ days and $7$ hours into hours.\n\nSince $1$ day is equal to $24$ hours,\n\nthis means $6$ days $7$ hours will be equal to:\n\n$(6\\times 24)\\,h+7\\, h$\n\n$=151\\,h$\n\nExample $2$\n\nConvert $2$ years into seconds.\n\n$2$ years is equal to $2(365)=730\\, days$\n\n$1$ day is equal to $24\\,h$\n\n$1\\,h$ is equal to $60$ minutes,\n\nand $1$ minute is equal to $60$ seconds\n\nHence, $2$ years $= 730 \\cdot 24 \\cdot 60 \\cdot 60 = 63,072,000\\,s$","date":"2023-03-20 09:41:46","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\": 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\": 0.4792763590812683, \"perplexity\": 428.8105054203885}, \"config\": {\"markdown_headings\": false, \"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\/1679296943471.24\/warc\/CC-MAIN-20230320083513-20230320113513-00640.warc.gz\"}"} | null | null |
Tough times on the high street as Blockbuster goes in to administration
Craft market in St James Ave with Blockbuster on the right corner
Hot on the heels of Jessops and HMV the next high street chain to go in to administration is Blockbuster UK, though it appears it will keep trading whilst a buyer is sought. Blockbuster has a shop in West Ealing on the corner of the Uxbridge Road and St James Ave. This spot is a key one for WEN and others who are working on ideas to reclaim the dead space at the top end of St James Avenue. WEN has run a monthly craft market here since April and OPEN Ealing may move its arts centre to the building above Blockbuster. In addition, there may be TfL money to improve this pedestrianised area at the top of St James Avenue and the Council is putting in a bid for 'pocket park' funds to add to the Tfl ones. What happens to Blockbuster on this corner could have an impact on these plans. So we'll be watching events carefully to see what happens.
Traders and residents invited to hear about plans for West Ealing centre
On Tuesday 22 January 2013 at 5:30pm at SiLVA Cafe, 148 Broadway, West Ealing local traders are being invited to hear about plans to re-invigorate our High Street.
Anyone can attend – just turn up. The more the merrier. We all need to hear and discuss everyone's views.
David Highton, Chair of WEN, will be discussing current and future WEN initiatives as well as outlining some London Borough of Ealing (LBE) proposals, which WEN and other local stakeholders have been working on. These include vacant shop initiatives, a business hub, pop up businesses, events and markets.
Eric Leach, Chair of West Ealing Centre Neighbourhood Forum (WECNF), will be discussing the forum's programme to create a detailed, 15 year spatial plan for the centre of West Ealing. These include policies for social provision, movement, Crossrail, housing and of course the High Street. LBE has a set of movement proposals; WECNF has its own plans; and local businesses have their own ideas too! Initiatives to be discussed include increased car parking, pedestrian improvements, accommodating cyclists, improved bus services, taking full advantage of the arrival of West Ealing Crossrail and better traffic flows.
Matthew McMillan Chief Executive of Ealing Broadway Business Improvement District (EBBID) will explain what a BID is all about. West Ealing Traders' Association (WETA), WEN. WECNF and LBE are all keen for local traders to form a West Ealing Centre BID organisation.
Barn dance, West Ealing, St James's Church, Sat 16th March, 2013
Stabbing at West Ealing bus stop
According to a story on the Ealing Today website, a fight this morning at the bus stop outside The Gym (old Daniels building) led to one man being stabbed. It doesn't sound life threatening fortunately. The police have increased foot patrols in the area. Unfortunately, there has been a run of serious incidents in West Ealing over the past months with the most recent – a fight between two gangs – just before Christmas. The whole question of local law and order will be looked at in WEN's January newsletter which will be published on Friday and will be on our website from then.
New stuff for January and beyond at OPEN
West Ealing's very own arts centre has much to offer. For a full programme, including a quiz night, book club, pass on a poem, a talk on Hindi cinema, and guided trips to inspirational building interiors, go to www.openealing.com .
'Under her skin' – great show at the Drayton in January
Laurel Swift (the one with the double bass) teaches her long-running folk workshop to local folkies at the Drayton on Monday nights, and now offers to West Ealing:
'Under Her Skin'
Directed by John Wright
The Drayton Court, The Avenue, West Ealing ** 15-17 January 2013 ** 7:45pm ** £5
An epic tale, a modern twist, two voices, four feet and eight strings.
Debs Newbold and Laurel Swift bring a rich and innovative collision of forms to their first full-length collaboration – a story of loss and regret that is also funny, irreverent, moving and dripping with streetwise credibility. Combining dynamic performance storytelling with the effusive energy of traditional dance and music, Under Her Skin sweeps audiences into a rich imaginative landscape.
"…a glorious, raucous, joyful show which manages seamlessly to combine the raw energy of dance, the earthiness of social realism and the magic and wonder of myth into an entirely integrated, expertly realised evening's entertainment."
GILES ABBOTT
This is storytelling crafted especially for adults. Based on an ancient British Selkie (seal people) folktale and set firmly in the here and now, it is an integrated show, inventive and theatrical yet with no fourth wall to get in the way of any mischief! Debs Newbold's highly acclaimed and charismatic storytelling voice joins the double bass, fiddle and clog dynamism of Laurel Swift to create an explosion of joy. Under Her Skin plays freely with the conventions of storytelling and gives an ancient British folktale a strong contemporary retelling.
Laurel Swift is an Associate Artist of the English Folk Dance and Song Society
www.debsandlaurel.co.uk
www.morrisoffspring.co.uk
www.gadarenemusic.com
www.gloworms.org.uk
Anyone else having problems with waste collection?
Hi, I've phoned Ealing Council about 20 times since April to report missed collections and have had 4 letters acknowledging my complaints but nothing improves. About 25% of the time all the recycling and black bag rubbish goes on the right day. About 50% of the time, one or two categories (varies which ones) are not picked up; when I report it to the call centre the next day, whatever didn't get collected is then collected. About 25% of the time, two categories are missed and the recollection only picks up one of the missed categories and the other one stays till I ring again or the next collection day.
I spoke to one of the recollection gang today and they said it was because the new contractors, Enterprise, had reduced the number of waste vehicles available by 16, and increased the size of the remaining ones – and this means they can't get round some of the street corners.
Thinks: if that's the case, why don't the operatives move the rubbish up to the nearest accessible street corner and collect from there?
The recollecters said that they had hundreds of tasks on their log-sheets – and they think it's more expensive to recollect than collect correctly the first time.
I asked the call centre at Ealing council how I can escalate my complaint but have heard nothing yet (only rang yesterday).
Is anyone else having problems?
Had enough of cooking over Christmas? Give yourself a break and come along to Sally and Steff's Supper Club on Saturday
If you've seen enough of your kitchen stove and sink this Christmas and New Year then give yourself a break and come along to Sally and Steph's Supper Club at the W7Emporium in Hanwell on Saturday. Sally and Steff met at OPEN Ealing and out of this was born the supper club. It's a chance to get out and enjoy someone else's cooking in good company and accompanied by music from two musicians from one of West Ealing's best bands – Blushing Bones.
Their three course menu is based on the recipes of Yotam Ottolenghi with live acoustic folk-based music from singer Tess and guitarist Jibs, of the Blushing Bones.
Date: Saturday January 5th 2013
Time: 7.30p.m. for 8.00p.m.–11.30p.m.
Place: W7 Emporium, 60b,Boston Rd,Hanwell,London W7 3TR (Opposite Wickes)
Price: £30 per head for welcome glass of Prosecco and nibbles, 3 courses + coffee.
Wine and cheese at an additional charge will be provided by the local W7 cheesemonger Claire.
Booking: Please contact Sally on sashrubsall@aol.com Stephanie on s.sundle@btinternet.com or book through the W7 Emporium directly. Please mention when booking if you have special dietary requirements (e.g. vegetarian or allergies) so that we can take this into consideration. N.B Some recipes contain nuts, and will be present in the food preparation areas.
Menu available shortly from W7 Emporium Facebook page. | {
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Q: Can some explain what this property does? Can some explain what this property does?
ClientProperites.FEATURE_AUTO_DISCOVERY_DISABLE
"jersey.config.disableAutoDiscovery.client"
I am trying to figure out the actual meaning of it.
http://javadox.com/org.glassfish.jersey.core/jersey-client/2.6/org/glassfish/jersey/client/ClientProperties.html#FEATURE_AUTO_DISCOVERY_DISABLE
A: There is an interface AutoDiscoverable, that when implemented, allows features to be discovered, registered, and configured automatically. Be default, this auto-discoverable feature is turned on. If you turn it off, then you will lose a lot of features that would have been automatically registered. You will need to register them yourself.
One example would be the Jackson JSON support. Just by adding the jersey-media-json-jackson dependency, it comes with a JacksonAutoDiscoverable that registers the JacksonFeature (which provides all the JSON support), and we would not have to register it explicitly.
Unless you have a real necessity to disable this feature, you should leave it. One reason you would want to disable it would be because you do not want to have a certain feature enabled that is enabled by autodiscovery.
The property is suffixed with client because you can do the same for the server; disable all the auto-discovered features. That property is suffixed with server.
There's a small section in the docs about Auto-Discoverable Features.
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{"url":"https:\/\/rstudio-pubs-static.s3.amazonaws.com\/619192_c3a671b1fc494de88ec3109ec7e5630d.html","text":"library(tidyverse)\n## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --\n## v ggplot2 3.3.0 v purrr 0.3.4\n## v tibble 3.0.1 v dplyr 0.8.5\n## v tidyr 1.0.2 v stringr 1.4.0\n## v readr 1.3.1 v forcats 0.5.0\n## -- Conflicts ------------------------------------------ tidyverse_conflicts() --\n## x dplyr::filter() masks stats::filter()\n## x dplyr::lag() masks stats::lag()\n\n### Problem 1. Using R, generate a random variable X that has 10,000 random uniform numbers from 1 to N, where N can be any number of your choosing greater than or equal to 6. Then generate a random variable Y that has 10,000 random normal numbers with a mean of mu = sigma = \uf06d\uf03d\uf073\uf03d(N+1)\/2.\n\n# Set seed\nset.seed(42)\n\n# Set number of draws, maximum for the uniform draws, mean and standard deviation for the normal draws\ndraws<-10000\nN<-7\navg<-(N+1)\/2\nstdev<-(N+1)\/2\n\n# Generate random uniform variable\nX<-runif(draws,1,N)\nlength(X)\n## [1] 10000\n# Generate random normal variable\nY<-rnorm(draws,mean=avg,sd=stdev)\n\n### Probability: Calculate as a minimum the below probabilities a through c. Assume the small letter \u201cx\u201d is estimated as the median of the X variable, and the small letter \u201cy\u201d is estimated as the 1st quartile of the Y variable. Interpret the meaning of all probabilities. a. P(X>x|X>y) b. P(X>x,Y>y) c. P(X<x|X>y)\n\n(x<-median(X))\n## [1] 3.999024\n(y<-quantile(Y,0.25))\n## 25%\n## 1.261755\n\nCombine the variables into a data frame and add boolean columns to store the conditional values for greater than and less than.\n\ndf<-data.frame(X,Y)\ndf$Xgtx<-(X>x) df$Xgty<-(X>y)\ndf$Xltx<-(X<x) df$Ygty<-(Y>y)\n\ndf$Xlty<-(X<y) df$Ylty<-(Y<y)\ndf$Yltx<-(Y<x) df$Ygtx<-(Y>x)\ndim(df)\n## [1] 10000 10\nhead(df)\n## X Y Xgtx Xgty Xltx Ygty Xlty Ylty Yltx Ygtx\n## 1 6.488836 4.284890 TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE\n## 2 6.622452 7.881160 TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE\n## 3 2.716837 5.240141 FALSE TRUE TRUE TRUE FALSE FALSE FALSE TRUE\n## 4 5.982686 3.441806 TRUE TRUE FALSE TRUE FALSE FALSE TRUE FALSE\n## 5 4.850473 2.694755 TRUE TRUE FALSE TRUE FALSE FALSE TRUE FALSE\n## 6 4.114576 3.524762 TRUE TRUE FALSE TRUE FALSE FALSE TRUE FALSE\n\nFrom Bayes theorem, P(X>x|X>y) = P(X>x and X>y)\/P(X>y)\n\n(p.Xgtx.given.Xgty<-sum(X>x&X>y)\/sum(X>y))\n## [1] 0.5244389\n\nFor P(X>x,Y>y)\n\n(sum(X>x)\/length(X))*(sum(Y>y)\/length(Y))\n## [1] 0.375\n\nFor P(X<x|X>y)\n\n(p.Xltx.given.Xgty<-sum(X<x&X>y)\/sum(X>y))\n## [1] 0.4755611\n# This is the complement of the previous problem in 1.a. So it should be same as 1 minus probability computed in 1.a\n(1-p.Xgtx.given.Xgty)\n## [1] 0.4755611\n\n### Investigate whether P(X>x and Y>y)=P(X>x)P(Y>y) by building a table and evaluating the marginal and joint probabilities.\n\n(sum(X>x&Y>y)\/length(X))\n## [1] 0.3732\n#length(df$Xgtx) #length(df$Xgty)\ntb<-table(df$Xgtx, df$Ygty, dnn=c('Xgtx','Ygty'))\ntb\n## Ygty\n## Xgtx FALSE TRUE\n## FALSE 1232 3768\n## TRUE 1268 3732\nprop.tb<-prop.table(tb)\nprop.tb\n## Ygty\n## Xgtx FALSE TRUE\n## FALSE 0.1232 0.3768\n## TRUE 0.1268 0.3732\nprob.Xgtx.and.Ygty<-prop.tb[2,2] # Joint probability\nprob.Xgtx<-prop.tb[2,1]+prop.tb[2,2] # Marginal probability\nprob.Ygty<-prop.tb[1,2]+prop.tb[2,2] # Marginal probability\n#(prop.tb[2,1]+prop.tb[2,2])*(prop.tb[1,2]+prop.tb[2,2])\n(prob.Xgtx.and.Ygty)\n## [1] 0.3732\n(prob.Xgtx*prob.Ygty)\n## [1] 0.375\n\nThis is a check for independence of 2 events. From the above, it can be seen that the joint probability of both X greater than x and Y greater than y i.e.\u00a00.3732 is close to but not exactly equal to the product of the 2 marginal probabilities respectively i.e.\u00a00.375. While these 2 events should be independent, it is likely that there is some spurious correlation reflected because of the random number generation.\n\n### Check to see if independence holds by using Fisher\u2019s Exact Test and the Chi Square Test. What is the difference between the two? Which is most appropriate?\n\n# Fisher's test\nfisher.test(tb)\n##\n## Fisher's Exact Test for Count Data\n##\n## data: tb\n## p-value = 0.4189\n## alternative hypothesis: true odds ratio is not equal to 1\n## 95 percent confidence interval:\n## 0.8780932 1.0546192\n## sample estimates:\n## odds ratio\n## 0.9623146\n#Chi square test\nchisq.test(tb)\n##\n## Pearson's Chi-squared test with Yates' continuity correction\n##\n## data: tb\n## X-squared = 0.65333, df = 1, p-value = 0.4189\n\nBoth tests give a p-value of 0.4189 at the 95% confidence level, which is quite large - thereby preventing rejection of the Null Hypothesis that the 2 events are independent, as should be expected. Fisher\u2019s test is appropriate for sample sample sizes. In this case, the Chi-squared test is most appropriate because the sample size is large, and the smallest marginal probability is 0.25 resulting in 2,500 outcomes favorable to the event Y less than y. This is way more than the threshold of 5 suggested as the criterion for applying the Chi-squared test.\n\n### Problem 2. You are to register for Kaggle.com (free) and compete in the House Prices: Advanced Regression Techniques competition. https:\/\/www.kaggle.com\/c\/house-prices-advanced-regression-techniques .I want you to do the following. Descriptive and Inferential Statistics. Provide univariate descriptive statistics and appropriate plots for the training data set. Provide a scatterplot matrix for at least two of the independent variables and the dependent variable. Derive a correlation matrix for any three quantitative variables in the dataset. Test the hypotheses that the correlations between each pairwise set of variables is 0 and provide an 80% confidence interval. Discuss the meaning of your analysis. Would you be worried about familywise error? Why or why not?\n\n#Load packages\nlibrary(tidyverse)\nlibrary(corrplot)\n## corrplot 0.84 loaded\nlibrary(MASS)\n##\n## Attaching package: 'MASS'\n## The following object is masked from 'package:dplyr':\n##\n## select\nlibrary(gmodels)\nlibrary(psych)\n##\n## Attaching package: 'psych'\n## The following objects are masked from 'package:ggplot2':\n##\n## %+%, alpha\nlibrary(matrixcalc)\nlibrary(Hmisc)\n## Loading required package: lattice\n## Loading required package: survival\n## Loading required package: Formula\n##\n## Attaching package: 'Hmisc'\n## The following object is masked from 'package:psych':\n##\n## describe\n## The following objects are masked from 'package:dplyr':\n##\n## src, summarize\n## The following objects are masked from 'package:base':\n##\n## format.pval, units\nlibrary(PerformanceAnalytics)\n## Loading required package: xts\n## Loading required package: zoo\n##\n## Attaching package: 'zoo'\n## The following objects are masked from 'package:base':\n##\n## as.Date, as.Date.numeric\n##\n## Attaching package: 'xts'\n## The following objects are masked from 'package:dplyr':\n##\n## first, last\n##\n## Attaching package: 'PerformanceAnalytics'\n## The following object is masked from 'package:graphics':\n##\n## legend\nlibrary(gmodels)\nlibrary(pracma)\n##\n## Attaching package: 'pracma'\n## The following object is masked from 'package:Hmisc':\n##\n## ceil\n## The following objects are masked from 'package:psych':\n##\n## logit, polar\n## The following object is masked from 'package:purrr':\n##\n## cross\n#Load the training dataset from Kaggle\ntrain<-read.csv(\"C:\/Jagdish\/MastersPrograms\/CUNY\/DS605 Computational Mathematics\/Final Project\/train.csv\")\n# Conduct basic checks on the size and structure of the data\ndim(train)\n## [1] 1460 81\nstr(train)\n## 'data.frame': 1460 obs. of 81 variables:\n## $Id : int 1 2 3 4 5 6 7 8 9 10 ... ##$ MSSubClass : int 60 20 60 70 60 50 20 60 50 190 ...\n## $MSZoning : Factor w\/ 5 levels \"C (all)\",\"FV\",..: 4 4 4 4 4 4 4 4 5 4 ... ##$ LotFrontage : int 65 80 68 60 84 85 75 NA 51 50 ...\n## $LotArea : int 8450 9600 11250 9550 14260 14115 10084 10382 6120 7420 ... ##$ Street : Factor w\/ 2 levels \"Grvl\",\"Pave\": 2 2 2 2 2 2 2 2 2 2 ...\n## $Alley : Factor w\/ 2 levels \"Grvl\",\"Pave\": NA NA NA NA NA NA NA NA NA NA ... ##$ LotShape : Factor w\/ 4 levels \"IR1\",\"IR2\",\"IR3\",..: 4 4 1 1 1 1 4 1 4 4 ...\n## $LandContour : Factor w\/ 4 levels \"Bnk\",\"HLS\",\"Low\",..: 4 4 4 4 4 4 4 4 4 4 ... ##$ Utilities : Factor w\/ 2 levels \"AllPub\",\"NoSeWa\": 1 1 1 1 1 1 1 1 1 1 ...\n## $LotConfig : Factor w\/ 5 levels \"Corner\",\"CulDSac\",..: 5 3 5 1 3 5 5 1 5 1 ... ##$ LandSlope : Factor w\/ 3 levels \"Gtl\",\"Mod\",\"Sev\": 1 1 1 1 1 1 1 1 1 1 ...\n## $Neighborhood : Factor w\/ 25 levels \"Blmngtn\",\"Blueste\",..: 6 25 6 7 14 12 21 17 18 4 ... ##$ Condition1 : Factor w\/ 9 levels \"Artery\",\"Feedr\",..: 3 2 3 3 3 3 3 5 1 1 ...\n## $Condition2 : Factor w\/ 8 levels \"Artery\",\"Feedr\",..: 3 3 3 3 3 3 3 3 3 1 ... ##$ BldgType : Factor w\/ 5 levels \"1Fam\",\"2fmCon\",..: 1 1 1 1 1 1 1 1 1 2 ...\n## $HouseStyle : Factor w\/ 8 levels \"1.5Fin\",\"1.5Unf\",..: 6 3 6 6 6 1 3 6 1 2 ... ##$ OverallQual : int 7 6 7 7 8 5 8 7 7 5 ...\n## $OverallCond : int 5 8 5 5 5 5 5 6 5 6 ... ##$ YearBuilt : int 2003 1976 2001 1915 2000 1993 2004 1973 1931 1939 ...\n## $YearRemodAdd : int 2003 1976 2002 1970 2000 1995 2005 1973 1950 1950 ... ##$ RoofStyle : Factor w\/ 6 levels \"Flat\",\"Gable\",..: 2 2 2 2 2 2 2 2 2 2 ...\n## $RoofMatl : Factor w\/ 8 levels \"ClyTile\",\"CompShg\",..: 2 2 2 2 2 2 2 2 2 2 ... ##$ Exterior1st : Factor w\/ 15 levels \"AsbShng\",\"AsphShn\",..: 13 9 13 14 13 13 13 7 4 9 ...\n## $Exterior2nd : Factor w\/ 16 levels \"AsbShng\",\"AsphShn\",..: 14 9 14 16 14 14 14 7 16 9 ... ##$ MasVnrType : Factor w\/ 4 levels \"BrkCmn\",\"BrkFace\",..: 2 3 2 3 2 3 4 4 3 3 ...\n## $MasVnrArea : int 196 0 162 0 350 0 186 240 0 0 ... ##$ ExterQual : Factor w\/ 4 levels \"Ex\",\"Fa\",\"Gd\",..: 3 4 3 4 3 4 3 4 4 4 ...\n## $ExterCond : Factor w\/ 5 levels \"Ex\",\"Fa\",\"Gd\",..: 5 5 5 5 5 5 5 5 5 5 ... ##$ Foundation : Factor w\/ 6 levels \"BrkTil\",\"CBlock\",..: 3 2 3 1 3 6 3 2 1 1 ...\n## $BsmtQual : Factor w\/ 4 levels \"Ex\",\"Fa\",\"Gd\",..: 3 3 3 4 3 3 1 3 4 4 ... ##$ BsmtCond : Factor w\/ 4 levels \"Fa\",\"Gd\",\"Po\",..: 4 4 4 2 4 4 4 4 4 4 ...\n## $BsmtExposure : Factor w\/ 4 levels \"Av\",\"Gd\",\"Mn\",..: 4 2 3 4 1 4 1 3 4 4 ... ##$ BsmtFinType1 : Factor w\/ 6 levels \"ALQ\",\"BLQ\",\"GLQ\",..: 3 1 3 1 3 3 3 1 6 3 ...\n## $BsmtFinSF1 : int 706 978 486 216 655 732 1369 859 0 851 ... ##$ BsmtFinType2 : Factor w\/ 6 levels \"ALQ\",\"BLQ\",\"GLQ\",..: 6 6 6 6 6 6 6 2 6 6 ...\n## $BsmtFinSF2 : int 0 0 0 0 0 0 0 32 0 0 ... ##$ BsmtUnfSF : int 150 284 434 540 490 64 317 216 952 140 ...\n## $TotalBsmtSF : int 856 1262 920 756 1145 796 1686 1107 952 991 ... ##$ Heating : Factor w\/ 6 levels \"Floor\",\"GasA\",..: 2 2 2 2 2 2 2 2 2 2 ...\n## $HeatingQC : Factor w\/ 5 levels \"Ex\",\"Fa\",\"Gd\",..: 1 1 1 3 1 1 1 1 3 1 ... ##$ CentralAir : Factor w\/ 2 levels \"N\",\"Y\": 2 2 2 2 2 2 2 2 2 2 ...\n## $Electrical : Factor w\/ 5 levels \"FuseA\",\"FuseF\",..: 5 5 5 5 5 5 5 5 2 5 ... ##$ X1stFlrSF : int 856 1262 920 961 1145 796 1694 1107 1022 1077 ...\n## $X2ndFlrSF : int 854 0 866 756 1053 566 0 983 752 0 ... ##$ LowQualFinSF : int 0 0 0 0 0 0 0 0 0 0 ...\n## $GrLivArea : int 1710 1262 1786 1717 2198 1362 1694 2090 1774 1077 ... ##$ BsmtFullBath : int 1 0 1 1 1 1 1 1 0 1 ...\n## $BsmtHalfBath : int 0 1 0 0 0 0 0 0 0 0 ... ##$ FullBath : int 2 2 2 1 2 1 2 2 2 1 ...\n## $HalfBath : int 1 0 1 0 1 1 0 1 0 0 ... ##$ BedroomAbvGr : int 3 3 3 3 4 1 3 3 2 2 ...\n## $KitchenAbvGr : int 1 1 1 1 1 1 1 1 2 2 ... ##$ KitchenQual : Factor w\/ 4 levels \"Ex\",\"Fa\",\"Gd\",..: 3 4 3 3 3 4 3 4 4 4 ...\n## $TotRmsAbvGrd : int 8 6 6 7 9 5 7 7 8 5 ... ##$ Functional : Factor w\/ 7 levels \"Maj1\",\"Maj2\",..: 7 7 7 7 7 7 7 7 3 7 ...\n## $Fireplaces : int 0 1 1 1 1 0 1 2 2 2 ... ##$ FireplaceQu : Factor w\/ 5 levels \"Ex\",\"Fa\",\"Gd\",..: NA 5 5 3 5 NA 3 5 5 5 ...\n## $GarageType : Factor w\/ 6 levels \"2Types\",\"Attchd\",..: 2 2 2 6 2 2 2 2 6 2 ... ##$ GarageYrBlt : int 2003 1976 2001 1998 2000 1993 2004 1973 1931 1939 ...\n## $GarageFinish : Factor w\/ 3 levels \"Fin\",\"RFn\",\"Unf\": 2 2 2 3 2 3 2 2 3 2 ... ##$ GarageCars : int 2 2 2 3 3 2 2 2 2 1 ...\n## $GarageArea : int 548 460 608 642 836 480 636 484 468 205 ... ##$ GarageQual : Factor w\/ 5 levels \"Ex\",\"Fa\",\"Gd\",..: 5 5 5 5 5 5 5 5 2 3 ...\n## $GarageCond : Factor w\/ 5 levels \"Ex\",\"Fa\",\"Gd\",..: 5 5 5 5 5 5 5 5 5 5 ... ##$ PavedDrive : Factor w\/ 3 levels \"N\",\"P\",\"Y\": 3 3 3 3 3 3 3 3 3 3 ...\n## $WoodDeckSF : int 0 298 0 0 192 40 255 235 90 0 ... ##$ OpenPorchSF : int 61 0 42 35 84 30 57 204 0 4 ...\n## $EnclosedPorch: int 0 0 0 272 0 0 0 228 205 0 ... ##$ X3SsnPorch : int 0 0 0 0 0 320 0 0 0 0 ...\n## $ScreenPorch : int 0 0 0 0 0 0 0 0 0 0 ... ##$ PoolArea : int 0 0 0 0 0 0 0 0 0 0 ...\n## $PoolQC : Factor w\/ 3 levels \"Ex\",\"Fa\",\"Gd\": NA NA NA NA NA NA NA NA NA NA ... ##$ Fence : Factor w\/ 4 levels \"GdPrv\",\"GdWo\",..: NA NA NA NA NA 3 NA NA NA NA ...\n## $MiscFeature : Factor w\/ 4 levels \"Gar2\",\"Othr\",..: NA NA NA NA NA 3 NA 3 NA NA ... ##$ MiscVal : int 0 0 0 0 0 700 0 350 0 0 ...\n## $MoSold : int 2 5 9 2 12 10 8 11 4 1 ... ##$ YrSold : int 2008 2007 2008 2006 2008 2009 2007 2009 2008 2008 ...\n## $SaleType : Factor w\/ 9 levels \"COD\",\"Con\",\"ConLD\",..: 9 9 9 9 9 9 9 9 9 9 ... ##$ SaleCondition: Factor w\/ 6 levels \"Abnorml\",\"AdjLand\",..: 5 5 5 1 5 5 5 5 1 5 ...\n## $SalePrice : int 208500 181500 223500 140000 250000 143000 307000 200000 129900 118000 ... summary(train) ## Id MSSubClass MSZoning LotFrontage ## Min. : 1.0 Min. : 20.0 C (all): 10 Min. : 21.00 ## 1st Qu.: 365.8 1st Qu.: 20.0 FV : 65 1st Qu.: 59.00 ## Median : 730.5 Median : 50.0 RH : 16 Median : 69.00 ## Mean : 730.5 Mean : 56.9 RL :1151 Mean : 70.05 ## 3rd Qu.:1095.2 3rd Qu.: 70.0 RM : 218 3rd Qu.: 80.00 ## Max. :1460.0 Max. :190.0 Max. :313.00 ## NA's :259 ## LotArea Street Alley LotShape LandContour ## Min. : 1300 Grvl: 6 Grvl: 50 IR1:484 Bnk: 63 ## 1st Qu.: 7554 Pave:1454 Pave: 41 IR2: 41 HLS: 50 ## Median : 9478 NA's:1369 IR3: 10 Low: 36 ## Mean : 10517 Reg:925 Lvl:1311 ## 3rd Qu.: 11602 ## Max. :215245 ## ## Utilities LotConfig LandSlope Neighborhood Condition1 ## AllPub:1459 Corner : 263 Gtl:1382 NAmes :225 Norm :1260 ## NoSeWa: 1 CulDSac: 94 Mod: 65 CollgCr:150 Feedr : 81 ## FR2 : 47 Sev: 13 OldTown:113 Artery : 48 ## FR3 : 4 Edwards:100 RRAn : 26 ## Inside :1052 Somerst: 86 PosN : 19 ## Gilbert: 79 RRAe : 11 ## (Other):707 (Other): 15 ## Condition2 BldgType HouseStyle OverallQual ## Norm :1445 1Fam :1220 1Story :726 Min. : 1.000 ## Feedr : 6 2fmCon: 31 2Story :445 1st Qu.: 5.000 ## Artery : 2 Duplex: 52 1.5Fin :154 Median : 6.000 ## PosN : 2 Twnhs : 43 SLvl : 65 Mean : 6.099 ## RRNn : 2 TwnhsE: 114 SFoyer : 37 3rd Qu.: 7.000 ## PosA : 1 1.5Unf : 14 Max. :10.000 ## (Other): 2 (Other): 19 ## OverallCond YearBuilt YearRemodAdd RoofStyle ## Min. :1.000 Min. :1872 Min. :1950 Flat : 13 ## 1st Qu.:5.000 1st Qu.:1954 1st Qu.:1967 Gable :1141 ## Median :5.000 Median :1973 Median :1994 Gambrel: 11 ## Mean :5.575 Mean :1971 Mean :1985 Hip : 286 ## 3rd Qu.:6.000 3rd Qu.:2000 3rd Qu.:2004 Mansard: 7 ## Max. :9.000 Max. :2010 Max. :2010 Shed : 2 ## ## RoofMatl Exterior1st Exterior2nd MasVnrType MasVnrArea ## CompShg:1434 VinylSd:515 VinylSd:504 BrkCmn : 15 Min. : 0.0 ## Tar&Grv: 11 HdBoard:222 MetalSd:214 BrkFace:445 1st Qu.: 0.0 ## WdShngl: 6 MetalSd:220 HdBoard:207 None :864 Median : 0.0 ## WdShake: 5 Wd Sdng:206 Wd Sdng:197 Stone :128 Mean : 103.7 ## ClyTile: 1 Plywood:108 Plywood:142 NA's : 8 3rd Qu.: 166.0 ## Membran: 1 CemntBd: 61 CmentBd: 60 Max. :1600.0 ## (Other): 2 (Other):128 (Other):136 NA's :8 ## ExterQual ExterCond Foundation BsmtQual BsmtCond BsmtExposure ## Ex: 52 Ex: 3 BrkTil:146 Ex :121 Fa : 45 Av :221 ## Fa: 14 Fa: 28 CBlock:634 Fa : 35 Gd : 65 Gd :134 ## Gd:488 Gd: 146 PConc :647 Gd :618 Po : 2 Mn :114 ## TA:906 Po: 1 Slab : 24 TA :649 TA :1311 No :953 ## TA:1282 Stone : 6 NA's: 37 NA's: 37 NA's: 38 ## Wood : 3 ## ## BsmtFinType1 BsmtFinSF1 BsmtFinType2 BsmtFinSF2 ## ALQ :220 Min. : 0.0 ALQ : 19 Min. : 0.00 ## BLQ :148 1st Qu.: 0.0 BLQ : 33 1st Qu.: 0.00 ## GLQ :418 Median : 383.5 GLQ : 14 Median : 0.00 ## LwQ : 74 Mean : 443.6 LwQ : 46 Mean : 46.55 ## Rec :133 3rd Qu.: 712.2 Rec : 54 3rd Qu.: 0.00 ## Unf :430 Max. :5644.0 Unf :1256 Max. :1474.00 ## NA's: 37 NA's: 38 ## BsmtUnfSF TotalBsmtSF Heating HeatingQC CentralAir ## Min. : 0.0 Min. : 0.0 Floor: 1 Ex:741 N: 95 ## 1st Qu.: 223.0 1st Qu.: 795.8 GasA :1428 Fa: 49 Y:1365 ## Median : 477.5 Median : 991.5 GasW : 18 Gd:241 ## Mean : 567.2 Mean :1057.4 Grav : 7 Po: 1 ## 3rd Qu.: 808.0 3rd Qu.:1298.2 OthW : 2 TA:428 ## Max. :2336.0 Max. :6110.0 Wall : 4 ## ## Electrical X1stFlrSF X2ndFlrSF LowQualFinSF ## FuseA: 94 Min. : 334 Min. : 0 Min. : 0.000 ## FuseF: 27 1st Qu.: 882 1st Qu.: 0 1st Qu.: 0.000 ## FuseP: 3 Median :1087 Median : 0 Median : 0.000 ## Mix : 1 Mean :1163 Mean : 347 Mean : 5.845 ## SBrkr:1334 3rd Qu.:1391 3rd Qu.: 728 3rd Qu.: 0.000 ## NA's : 1 Max. :4692 Max. :2065 Max. :572.000 ## ## GrLivArea BsmtFullBath BsmtHalfBath FullBath ## Min. : 334 Min. :0.0000 Min. :0.00000 Min. :0.000 ## 1st Qu.:1130 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:1.000 ## Median :1464 Median :0.0000 Median :0.00000 Median :2.000 ## Mean :1515 Mean :0.4253 Mean :0.05753 Mean :1.565 ## 3rd Qu.:1777 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.:2.000 ## Max. :5642 Max. :3.0000 Max. :2.00000 Max. :3.000 ## ## HalfBath BedroomAbvGr KitchenAbvGr KitchenQual ## Min. :0.0000 Min. :0.000 Min. :0.000 Ex:100 ## 1st Qu.:0.0000 1st Qu.:2.000 1st Qu.:1.000 Fa: 39 ## Median :0.0000 Median :3.000 Median :1.000 Gd:586 ## Mean :0.3829 Mean :2.866 Mean :1.047 TA:735 ## 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:1.000 ## Max. :2.0000 Max. :8.000 Max. :3.000 ## ## TotRmsAbvGrd Functional Fireplaces FireplaceQu GarageType ## Min. : 2.000 Maj1: 14 Min. :0.000 Ex : 24 2Types : 6 ## 1st Qu.: 5.000 Maj2: 5 1st Qu.:0.000 Fa : 33 Attchd :870 ## Median : 6.000 Min1: 31 Median :1.000 Gd :380 Basment: 19 ## Mean : 6.518 Min2: 34 Mean :0.613 Po : 20 BuiltIn: 88 ## 3rd Qu.: 7.000 Mod : 15 3rd Qu.:1.000 TA :313 CarPort: 9 ## Max. :14.000 Sev : 1 Max. :3.000 NA's:690 Detchd :387 ## Typ :1360 NA's : 81 ## GarageYrBlt GarageFinish GarageCars GarageArea GarageQual ## Min. :1900 Fin :352 Min. :0.000 Min. : 0.0 Ex : 3 ## 1st Qu.:1961 RFn :422 1st Qu.:1.000 1st Qu.: 334.5 Fa : 48 ## Median :1980 Unf :605 Median :2.000 Median : 480.0 Gd : 14 ## Mean :1979 NA's: 81 Mean :1.767 Mean : 473.0 Po : 3 ## 3rd Qu.:2002 3rd Qu.:2.000 3rd Qu.: 576.0 TA :1311 ## Max. :2010 Max. :4.000 Max. :1418.0 NA's: 81 ## NA's :81 ## GarageCond PavedDrive WoodDeckSF OpenPorchSF EnclosedPorch ## Ex : 2 N: 90 Min. : 0.00 Min. : 0.00 Min. : 0.00 ## Fa : 35 P: 30 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 ## Gd : 9 Y:1340 Median : 0.00 Median : 25.00 Median : 0.00 ## Po : 7 Mean : 94.24 Mean : 46.66 Mean : 21.95 ## TA :1326 3rd Qu.:168.00 3rd Qu.: 68.00 3rd Qu.: 0.00 ## NA's: 81 Max. :857.00 Max. :547.00 Max. :552.00 ## ## X3SsnPorch ScreenPorch PoolArea PoolQC ## Min. : 0.00 Min. : 0.00 Min. : 0.000 Ex : 2 ## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000 Fa : 2 ## Median : 0.00 Median : 0.00 Median : 0.000 Gd : 3 ## Mean : 3.41 Mean : 15.06 Mean : 2.759 NA's:1453 ## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.000 ## Max. :508.00 Max. :480.00 Max. :738.000 ## ## Fence MiscFeature MiscVal MoSold ## GdPrv: 59 Gar2: 2 Min. : 0.00 Min. : 1.000 ## GdWo : 54 Othr: 2 1st Qu.: 0.00 1st Qu.: 5.000 ## MnPrv: 157 Shed: 49 Median : 0.00 Median : 6.000 ## MnWw : 11 TenC: 1 Mean : 43.49 Mean : 6.322 ## NA's :1179 NA's:1406 3rd Qu.: 0.00 3rd Qu.: 8.000 ## Max. :15500.00 Max. :12.000 ## ## YrSold SaleType SaleCondition SalePrice ## Min. :2006 WD :1267 Abnorml: 101 Min. : 34900 ## 1st Qu.:2007 New : 122 AdjLand: 4 1st Qu.:129975 ## Median :2008 COD : 43 Alloca : 12 Median :163000 ## Mean :2008 ConLD : 9 Family : 20 Mean :180921 ## 3rd Qu.:2009 ConLI : 5 Normal :1198 3rd Qu.:214000 ## Max. :2010 ConLw : 5 Partial: 125 Max. :755000 ## (Other): 9 The training dataset has a mix of numeric, factor and boolean variables. There are a total of 1460 observations comprising of 80 independent variables and 1 dependent variable i.e. Sale Price. (num.records<-nrow(train)) ## [1] 1460 # Check which columns of the dataframe have missing values sapply(X = train, FUN = function(x) sum(is.na(x))) ## Id MSSubClass MSZoning LotFrontage LotArea ## 0 0 0 259 0 ## Street Alley LotShape LandContour Utilities ## 0 1369 0 0 0 ## LotConfig LandSlope Neighborhood Condition1 Condition2 ## 0 0 0 0 0 ## BldgType HouseStyle OverallQual OverallCond YearBuilt ## 0 0 0 0 0 ## YearRemodAdd RoofStyle RoofMatl Exterior1st Exterior2nd ## 0 0 0 0 0 ## MasVnrType MasVnrArea ExterQual ExterCond Foundation ## 8 8 0 0 0 ## BsmtQual BsmtCond BsmtExposure BsmtFinType1 BsmtFinSF1 ## 37 37 38 37 0 ## BsmtFinType2 BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating ## 38 0 0 0 0 ## HeatingQC CentralAir Electrical X1stFlrSF X2ndFlrSF ## 0 0 1 0 0 ## LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath ## 0 0 0 0 0 ## HalfBath BedroomAbvGr KitchenAbvGr KitchenQual TotRmsAbvGrd ## 0 0 0 0 0 ## Functional Fireplaces FireplaceQu GarageType GarageYrBlt ## 0 0 690 81 81 ## GarageFinish GarageCars GarageArea GarageQual GarageCond ## 81 0 0 81 81 ## PavedDrive WoodDeckSF OpenPorchSF EnclosedPorch X3SsnPorch ## 0 0 0 0 0 ## ScreenPorch PoolArea PoolQC Fence MiscFeature ## 0 0 1453 1179 1406 ## MiscVal MoSold YrSold SaleType SaleCondition ## 0 0 0 0 0 ## SalePrice ## 0 Rather than try to impute the missing data records, for now I\u2019ll avoid using the variables with missing values such as LotFrontage, Alley, BsmtCond etc. in the linear model. The response (or dependent) variable is the SalePrice. I\u2019ll check its summary statistics. fivenum(train$SalePrice, na.rm = TRUE)\n## [1] 34900 129950 163000 214000 755000\nsummary(train$SalePrice) ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 34900 129975 163000 180921 214000 755000 The variable shows a fairly wide range. The mean is higher than the median indicating some right skew. # Graph the sale price options(scipen = 4) ggplot(train, aes(x = SalePrice)) + geom_histogram(fill=\"green\", binwidth = 5000) + scale_x_continuous(breaks = seq(0, 1000000, by = 100000)) As expected, the graph shows that the sale price is skewed to the right. Obviously the sale price cannot be negative and there will always be some really high-value transactions. The histogram of the sale price shows a few outliers above$700,000.\n\n# Fixing some column names that got corrupted during data loading\nnames(train)[names(train)=='X1stFlrSF']<-'FirstFlrSF'\nnames(train)[names(train)=='X2ndFlrSF']<-'SecondFlrSF'\nnames(train)[names(train)=='1stFlrSF']<-'FirstFlrSF'\nnames(train)[names(train)=='2ndFlrSF']<-'SecondFlrSF'\nnames(train)\n## [1] \"Id\" \"MSSubClass\" \"MSZoning\" \"LotFrontage\"\n## [5] \"LotArea\" \"Street\" \"Alley\" \"LotShape\"\n## [9] \"LandContour\" \"Utilities\" \"LotConfig\" \"LandSlope\"\n## [13] \"Neighborhood\" \"Condition1\" \"Condition2\" \"BldgType\"\n## [17] \"HouseStyle\" \"OverallQual\" \"OverallCond\" \"YearBuilt\"\n## [21] \"YearRemodAdd\" \"RoofStyle\" \"RoofMatl\" \"Exterior1st\"\n## [25] \"Exterior2nd\" \"MasVnrType\" \"MasVnrArea\" \"ExterQual\"\n## [29] \"ExterCond\" \"Foundation\" \"BsmtQual\" \"BsmtCond\"\n## [33] \"BsmtExposure\" \"BsmtFinType1\" \"BsmtFinSF1\" \"BsmtFinType2\"\n## [37] \"BsmtFinSF2\" \"BsmtUnfSF\" \"TotalBsmtSF\" \"Heating\"\n## [41] \"HeatingQC\" \"CentralAir\" \"Electrical\" \"FirstFlrSF\"\n## [45] \"SecondFlrSF\" \"LowQualFinSF\" \"GrLivArea\" \"BsmtFullBath\"\n## [49] \"BsmtHalfBath\" \"FullBath\" \"HalfBath\" \"BedroomAbvGr\"\n## [53] \"KitchenAbvGr\" \"KitchenQual\" \"TotRmsAbvGrd\" \"Functional\"\n## [57] \"Fireplaces\" \"FireplaceQu\" \"GarageType\" \"GarageYrBlt\"\n## [61] \"GarageFinish\" \"GarageCars\" \"GarageArea\" \"GarageQual\"\n## [65] \"GarageCond\" \"PavedDrive\" \"WoodDeckSF\" \"OpenPorchSF\"\n## [69] \"EnclosedPorch\" \"X3SsnPorch\" \"ScreenPorch\" \"PoolArea\"\n## [73] \"PoolQC\" \"Fence\" \"MiscFeature\" \"MiscVal\"\n## [77] \"MoSold\" \"YrSold\" \"SaleType\" \"SaleCondition\"\n## [81] \"SalePrice\"\n# Calculating a derived variable called Age and adding it to the training dataset\nCurrYear<-as.integer(format(Sys.Date(),\"%Y\"))\ntrain$Age<-CurrYear-train$YearBuilt\n#head(train)\n\nSince location plays an important role in Sale Price, I calculate the average sale price per neighborhood and arrange it from highest to lowest. Based on this, it can be seen that the North Ridge neighborhood has the highest average sale price.\n\n# Group by neighorhood and calculate average sale price\ntrain%>%group_by(Neighborhood)%>%summarise(avg.price=mean(SalePrice))%>%arrange(desc(avg.price))\n## # A tibble: 25 x 2\n## Neighborhood avg.price\n## <fct> <dbl>\n## 1 NoRidge 335295.\n## 2 NridgHt 316271.\n## 3 StoneBr 310499\n## 4 Timber 242247.\n## 5 Veenker 238773.\n## 6 Somerst 225380.\n## 7 ClearCr 212565.\n## 8 Crawfor 210625.\n## 9 CollgCr 197966.\n## 10 Blmngtn 194871.\n## # ... with 15 more rows\n\nI calculate the box plot of the sale price per neighborhood. This shows the spread of the sale price per neighborhood and the number of outliers.\n\nggplot(train, aes(x=reorder(Neighborhood, SalePrice, FUN=median), y=SalePrice) ) + geom_boxplot() + coord_flip()\n\nThe above confirms that the median sale price is the highest in the North Ridge Heights neighborhood, followed by North Ridge, which is the reverse when considering the mean sale price in these top 2 neighborhoods by sale price.\n\n# Initial selection of predictor variables\ncolumns<-c('SalePrice', 'LotArea', 'MSSubClass', 'Neighborhood', 'BldgType', 'FirstFlrSF', 'SecondFlrSF', 'GrLivArea', 'SaleCondition', 'OverallQual', 'OverallCond', 'CentralAir', 'TotRmsAbvGrd', 'Utilities','TotalBsmtSF', 'Age')\n\n# Initial selection of numeric predictor variables\nnum_columns<-c('SalePrice','LotArea', 'FirstFlrSF', 'SecondFlrSF', 'GrLivArea', 'TotalBsmtSF', 'Age')\n\n# Taking a subset of columns to work with\nsub.train<-subset(train, select=columns)\ndim(sub.train)\n## [1] 1460 16\nsmall.train<-train[,num_columns]\ndim(small.train)\n## [1] 1460 7\ntypeof(small.train)\n## [1] \"list\"\nnames(sub.train)\n## [1] \"SalePrice\" \"LotArea\" \"MSSubClass\" \"Neighborhood\"\n## [5] \"BldgType\" \"FirstFlrSF\" \"SecondFlrSF\" \"GrLivArea\"\n## [9] \"SaleCondition\" \"OverallQual\" \"OverallCond\" \"CentralAir\"\n## [13] \"TotRmsAbvGrd\" \"Utilities\" \"TotalBsmtSF\" \"Age\"\n# Calculate correlations between the predictor variables as well between predictor variable and response variable\n\n#pairs(small.train, gap=0.5) #pairs.panels(small.train, method = \"pearson\")\n# Examine correlations between the different numeric columns selected\n(corr_data <- rcorr(as.matrix(small.train))) \n## SalePrice LotArea FirstFlrSF SecondFlrSF GrLivArea TotalBsmtSF\n## SalePrice 1.00 0.26 0.61 0.32 0.71 0.61\n## LotArea 0.26 1.00 0.30 0.05 0.26 0.26\n## FirstFlrSF 0.61 0.30 1.00 -0.20 0.57 0.82\n## SecondFlrSF 0.32 0.05 -0.20 1.00 0.69 -0.17\n## GrLivArea 0.71 0.26 0.57 0.69 1.00 0.45\n## TotalBsmtSF 0.61 0.26 0.82 -0.17 0.45 1.00\n## Age -0.52 -0.01 -0.28 -0.01 -0.20 -0.39\n## Age\n## SalePrice -0.52\n## LotArea -0.01\n## FirstFlrSF -0.28\n## SecondFlrSF -0.01\n## GrLivArea -0.20\n## TotalBsmtSF -0.39\n## Age 1.00\n##\n## n= 1460\n##\n##\n## P\n## SalePrice LotArea FirstFlrSF SecondFlrSF GrLivArea TotalBsmtSF\n## SalePrice 0.0000 0.0000 0.0000 0.0000 0.0000\n## LotArea 0.0000 0.0000 0.0514 0.0000 0.0000\n## FirstFlrSF 0.0000 0.0000 0.0000 0.0000 0.0000\n## SecondFlrSF 0.0000 0.0514 0.0000 0.0000 0.0000\n## GrLivArea 0.0000 0.0000 0.0000 0.0000 0.0000\n## TotalBsmtSF 0.0000 0.0000 0.0000 0.0000 0.0000\n## Age 0.0000 0.5870 0.0000 0.6939 0.0000 0.0000\n## Age\n## SalePrice 0.0000\n## LotArea 0.5870\n## FirstFlrSF 0.0000\n## SecondFlrSF 0.6939\n## GrLivArea 0.0000\n## TotalBsmtSF 0.0000\n## Age\n\nThe above shows a high positive correlation between the sale price and the size of the house (as indicated by Ground floor area, 1st floor area, 2nd floor area) and a high negative correlation between the sale price and the age of the house. Both of these relations make intuitive sense.\n\nThe numeric data above can also be examined visually using the following graph:\n\n# plot the correlation matrix\n\ncorrplot(cor(small.train),type = \"upper\") \n\nThe legend on the right indicates the nature of the correlation and the sixe of the circle indicates the strength of the correlation.\n\n# Create scatterplots of variables with high correlation with the Sale Price\nggplot(small.train, aes(GrLivArea, SalePrice) ) + geom_point()\n\nThese 2 variables depict a positive, linear relationship with the exception of some outliers.\n\n# Select 3 quantitative predictor variables\nq_cols<-c('SalePrice','LotArea', 'GrLivArea')\n# Taking a subset of columns to work with\nq.vars<-train[,q_cols]\ndim(q.vars)\n## [1] 1460 3\n# Plot the 3 selected numeric variables\nplot(q.vars)\n\n# Calculate correlation between these 3 variables\n(q.cor = cor(q.vars))\n## SalePrice LotArea GrLivArea\n## SalePrice 1.0000000 0.2638434 0.7086245\n## LotArea 0.2638434 1.0000000 0.2631162\n## GrLivArea 0.7086245 0.2631162 1.0000000\n# Check significance of the sample correlations, using Pearson's test\n(q.cor1 = cor.test(q.vars$SalePrice,q.vars$GrLivArea,method=\"pearson\",conf.level = 0.80))\n##\n## Pearson's product-moment correlation\n##\n## data: q.vars$SalePrice and q.vars$GrLivArea\n## t = 38.348, df = 1458, p-value < 2.2e-16\n## alternative hypothesis: true correlation is not equal to 0\n## 80 percent confidence interval:\n## 0.6915087 0.7249450\n## sample estimates:\n## cor\n## 0.7086245\n(q.cor1 = cor.test(q.vars$SalePrice,q.vars$LotArea,method=\"pearson\",conf.level = 0.80))\n##\n## Pearson's product-moment correlation\n##\n## data: q.vars$SalePrice and q.vars$LotArea\n## t = 10.445, df = 1458, p-value < 2.2e-16\n## alternative hypothesis: true correlation is not equal to 0\n## 80 percent confidence interval:\n## 0.2323391 0.2947946\n## sample estimates:\n## cor\n## 0.2638434\n(q.cor1 = cor.test(q.vars$LotArea,q.vars$GrLivArea,method=\"pearson\",conf.level = 0.80))\n##\n## Pearson's product-moment correlation\n##\n## data: q.vars$LotArea and q.vars$GrLivArea\n## t = 10.414, df = 1458, p-value < 2.2e-16\n## alternative hypothesis: true correlation is not equal to 0\n## 80 percent confidence interval:\n## 0.2315997 0.2940809\n## sample estimates:\n## cor\n## 0.2631162\n\nBased on the above results (tiny p-value), the null hypothesis that the pair-wise correlation between each pair of these variables is 0 can be rejected. The 80% confidence interval around the correlation parameter for each pair-wise correlation is shown above.\n\nIn statistics, Family-wise Error Rate (FWER) is the probability of making one or more false discoveries, or Type I errors when performing multiple hypotheses tests. Family is a set of related hypotheses that need to be jointly accurate.\n\nIn this case, it means that we consider a random correlation to be a significant correlation based on the sample stats i.e.\u00a0a true null is considered significant i.e.\u00a0a false positive. When we extend the analysis to a family i.e.\u00a0multiple pairs of variables, the degree of error gets compounded. This probability of \u201cfalse positives\u201d or at least one Type 1 error can be estimated as follows:\n\nFWER = 1 - 0.95^n (where alpha = 0.05) where n represents the number of pair-wise correlations (number of multiple hypotheses)\n\nalpha<-0.05\nn<-3 # for 3 pairs of variables\n(fwer<-1-(1-alpha)^n)\n## [1] 0.142625\n\nSo the probability of a false positive here is about 14%, given 3 variables. I would be worried about familywise error. There are multiple corrections which can be considered in this case.\n\n### Linear Algebra and Correlation. Invert your correlation matrix from above. (This is known as the precision matrix and contains variance inflation factors on the diagonal.) Multiply the correlation matrix by the precision matrix, and then multiply the precision matrix by the correlation matrix. Conduct LU decomposition on the matrix.\n\n# Calculate the inverse of the correlation matrix from above\nround(prec.matrix<-solve(q.cor),3)\n## SalePrice LotArea GrLivArea\n## SalePrice 2.035 -0.169 -1.397\n## LotArea -0.169 1.088 -0.166\n## GrLivArea -1.397 -0.166 2.034\n# Can also be done using a different function\nround(precision_matrix<-inv(q.cor),3)\n## SalePrice LotArea GrLivArea\n## SalePrice 2.035 -0.169 -1.397\n## LotArea -0.169 1.088 -0.166\n## GrLivArea -1.397 -0.166 2.034\n# Multiply the correlation matrix by the precision matrix (Right-multiplication)\nround(q.cor %*% prec.matrix, 3)\n## SalePrice LotArea GrLivArea\n## SalePrice 1 0 0\n## LotArea 0 1 0\n## GrLivArea 0 0 1\n#Multiply precision matrix by correlation matrix (Left-multiplication)\nround(prec.matrix %*% q.cor, 3)\n## SalePrice LotArea GrLivArea\n## SalePrice 1 0 0\n## LotArea 0 1 0\n## GrLivArea 0 0 1\n\nAs expected, both the matrix multiplications result in the identity matrix.\n\n# Conduct the LU decomposition\n(lu<-lu.decomposition(q.cor))\n## $L ## [,1] [,2] [,3] ## [1,] 1.0000000 0.00000000 0 ## [2,] 0.2638434 1.00000000 0 ## [3,] 0.7086245 0.08184802 1 ## ##$U\n## [,1] [,2] [,3]\n## [1,] 1 0.2638434 0.70862448\n## [2,] 0 0.9303867 0.07615031\n## [3,] 0 0.0000000 0.49161860\n# Same result via a different function\n(lu1<-lu(q.cor))\n## $L ## SalePrice LotArea GrLivArea ## SalePrice 1.0000000 0.00000000 0 ## LotArea 0.2638434 1.00000000 0 ## GrLivArea 0.7086245 0.08184802 1 ## ##$U\n## SalePrice LotArea GrLivArea\n## SalePrice 1 0.2638434 0.70862448\n## LotArea 0 0.9303867 0.07615031\n## GrLivArea 0 0.0000000 0.49161860\n# Assign the Upper and Lower diagonal matrices\nL<-lu$L U<-lu$U\nlu1$L%*%lu1$U\n## SalePrice LotArea GrLivArea\n## SalePrice 1.0000000 0.2638434 0.7086245\n## LotArea 0.2638434 1.0000000 0.2631162\n## GrLivArea 0.7086245 0.2631162 1.0000000\n# Verify if L*U gives the original correlation matrix\n(L%*%U)==q.cor\n## SalePrice LotArea GrLivArea\n## SalePrice TRUE TRUE TRUE\n## LotArea TRUE TRUE TRUE\n## GrLivArea TRUE TRUE TRUE\n\nIt does return the original correlation matrix.\n\n### Calculus-Based Probability & Statistics. Many times, it makes sense to fit a closed form distribution to data. Select a variable in the Kaggle.com training dataset that is skewed to the right, shift it so that the minimum value is absolutely above zero if necessary. Then load the MASS package and run fitdistr to fit an exponential probability density function. (See https:\/\/stat.ethz.ch\/R-manual\/R-devel\/library\/MASS\/html\/fitdistr.html ). Find the optimal value of \uf06c for this distribution, and then take 1000 samples from this exponential distribution using this value (e.g., rexp(1000, \uf06c)). Plot a histogram and compare it with a histogram of your original variable. Using the exponential pdf, find the 5th and 95th percentiles using the cumulative distribution function (CDF). Also generate a 95% confidence interval from the empirical data, assuming normality. Finally, provide the empirical 5th percentile and 95th percentile of the data. Discuss.\n\n# Select a right-skewed variable\n#dens<-density(small.train$TotalBsmtSF) #hist(small.train$TotalBsmtSF, breaks = 30)\n#plot(dens, type=\"l\", col=\"green\", xlab=\"TotalBasmtSF\", main=\"Basement Area\",lwd=2)\n#+geom_text(aes(x=mean.val+600,label=paste0(\"Mean\\n\",mean.val),y=1.9))\nmean.val<-round(mean(small.train$TotalBsmtSF),0) median.val<-round(median(small.train$TotalBsmtSF),0)\nggplot(small.train,aes(TotalBsmtSF))+geom_histogram(aes(y=..density..), fill=\"lightblue\", bins=30)+ geom_density(color=\"red\", alpha=0.8, size=0.8)+geom_vline(xintercept=mean.val, size=0.5, color=\"red\")+ geom_vline(xintercept=median.val, size=0.5, color=\"blue\")\n\n# Fit the selected variable to the exponential distribution\nfit.var<-fitdistr(small.train$TotalBsmtSF, densfun=\"exponential\") # Check estimated lambda (lambda<-fit.var$estimate)\n## rate\n## 0.0009456896\n\nThe estimated lambda for the fitted exponential distribution is about 0.000945\n\n# Take 1000 samples of the exponential distribution fitted above\nset.seed(42)\nexp.sample<-rexp(1000,lambda)\n\n# Plot histogram\nggplot(as.data.frame(exp.sample),aes(exp.sample))+geom_histogram(binwidth=200)\n\n# Find 5th and 95th percentiles of the exponential distribution\n(pct5<-qexp(0.05,rate=lambda))\n## [1] 54.23904\n(pct95<-qexp(0.95,rate=lambda))\n## [1] 3167.776\n# Calculate 5% and 95% quantiles from emperical data\n(emp.quantiles<-quantile(small.train$TotalBsmtSF, c(0.05, 0.95))) ## 5% 95% ## 519.3 1753.0 Based on the lambda parameter of the fitted exponential distribution, the quantiles are too widely dispersed as compared to the actual data. So the exponential distribution does not seem to be a good candidate for modelling this variable. # Generate a 95% confidence interval from the empirical data, assuming normality (ci(small.train$TotalBsmtSF, confidence=0.95))\n## Warning in ci.numeric(small.train$TotalBsmtSF, confidence = 0.95): No class ## or unkown class. Using default calcuation. ## Estimate CI lower CI upper Std. Error ## 1057.42945 1034.90755 1079.95135 11.48144 (mu<-mean(small.train$TotalBsmtSF))\n## [1] 1057.429\n(sd<-sd(small.train$TotalBsmtSF)) ## [1] 438.7053 (lower<-mu-1.96*sd\/sqrt(num.records)) ## [1] 1034.926 (upper<-mu+1.96*sd\/sqrt(num.records)) ## [1] 1079.933 Assuming normality, the 95% confidence interval based on the estimated mean and standard distribution for this variable is 1034.92 and 1079.93. This range is much tighter than what is observed in the the actual sample data. So even the normal distribution is not a good candidate for modelling this variable. This should be expected from the fact that this variable is right-skewed, and therefore the mean is not the best measure of centrality. ### Modeling. Build some type of multiple regression model and submit your model to the competition board. Provide your complete model summary and results with analysis. Report your Kaggle.com user name and score. # Fit a multiple regression model using a selected set of independent variables model1=lm(SalePrice~LotArea + MSSubClass + OverallQual + OverallCond + TotalBsmtSF + FirstFlrSF + SecondFlrSF + Age, data=sub.train) #model2=lm(SalePrice~LotArea + MSSubClass + OverallQual + OverallCond + TotalBsmtSF + Age, data=sub.train) #model3=lm(SalePrice~GrLivArea + CentralAir + TotRmsAbvGrd + Utilities + FirstFlrSF + SecondFlrSF + + TotalBsmtSF + Age, data=sub.train) # Check the model output summary(model1) ## ## Call: ## lm(formula = SalePrice ~ LotArea + MSSubClass + OverallQual + ## OverallCond + TotalBsmtSF + FirstFlrSF + SecondFlrSF + Age, ## data = sub.train) ## ## Residuals: ## Min 1Q Median 3Q Max ## -505757 -18493 -2362 14200 275355 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -71794.5437 8136.1941 -8.824 < 2e-16 *** ## LotArea 0.5906 0.1053 5.610 2.41e-08 *** ## MSSubClass -145.3752 25.3150 -5.743 1.13e-08 *** ## OverallQual 21978.3193 1142.9454 19.230 < 2e-16 *** ## OverallCond 6015.9364 979.0506 6.145 1.03e-09 *** ## TotalBsmtSF 17.0363 4.2185 4.038 5.66e-05 *** ## FirstFlrSF 65.7950 4.6490 14.153 < 2e-16 *** ## SecondFlrSF 55.1523 2.7777 19.855 < 2e-16 *** ## Age -543.0638 44.6907 -12.152 < 2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 37480 on 1451 degrees of freedom ## Multiple R-squared: 0.7786, Adjusted R-squared: 0.7774 ## F-statistic: 637.9 on 8 and 1451 DF, p-value: < 2.2e-16 The adjusted R-squared value is 0.7775, indicating that this model (using this selected set of predictor variables) explains about 78% of the variability in the Sale Price. # Plot the model output - fitted values versus the residuals plot(fitted(model1), resid(model1), xlab = \"Sale Price\", ylab = \"Residuals\", main = \"Residuals of Sale Price\") abline(h = 0) # Create a Quantile-Quantile Plot qqnorm(model1$residuals)\nqqline(model1$residuals) The above plots show the residuals are not evenly distributed. At higher values of sale price, the variance in the residuals increases a lot. This indicates that there is scope for improving the model by feature engineering, as well as iterating through different combinations of predictor variables to mitigate collinearity, and select only the most useful set of independent variables. # Load the test dataset test<-read.csv(\"C:\/Jagdish\/MastersPrograms\/CUNY\/DS605 Computational Mathematics\/Final Project\/test.csv\") #sub.test<-subset(test, select=columns) #dim(sub.test) # Calculating a derived variable called Age and adding it to the test dataset CurrYear<-as.integer(format(Sys.Date(),\"%Y\")) test$Age<-CurrYear-test$YearBuilt # Fixing some column names that got corrupted during data loading names(test)[names(test)=='X1stFlrSF']<-'FirstFlrSF' names(test)[names(test)=='X2ndFlrSF']<-'SecondFlrSF' names(test)[names(test)=='1stFlrSF']<-'FirstFlrSF' names(test)[names(test)=='2ndFlrSF']<-'SecondFlrSF' names(test) ## [1] \"Id\" \"MSSubClass\" \"MSZoning\" \"LotFrontage\" ## [5] \"LotArea\" \"Street\" \"Alley\" \"LotShape\" ## [9] \"LandContour\" \"Utilities\" \"LotConfig\" \"LandSlope\" ## [13] \"Neighborhood\" \"Condition1\" \"Condition2\" \"BldgType\" ## [17] \"HouseStyle\" \"OverallQual\" \"OverallCond\" \"YearBuilt\" ## [21] \"YearRemodAdd\" \"RoofStyle\" \"RoofMatl\" \"Exterior1st\" ## [25] \"Exterior2nd\" \"MasVnrType\" \"MasVnrArea\" \"ExterQual\" ## [29] \"ExterCond\" \"Foundation\" \"BsmtQual\" \"BsmtCond\" ## [33] \"BsmtExposure\" \"BsmtFinType1\" \"BsmtFinSF1\" \"BsmtFinType2\" ## [37] \"BsmtFinSF2\" \"BsmtUnfSF\" \"TotalBsmtSF\" \"Heating\" ## [41] \"HeatingQC\" \"CentralAir\" \"Electrical\" \"FirstFlrSF\" ## [45] \"SecondFlrSF\" \"LowQualFinSF\" \"GrLivArea\" \"BsmtFullBath\" ## [49] \"BsmtHalfBath\" \"FullBath\" \"HalfBath\" \"BedroomAbvGr\" ## [53] \"KitchenAbvGr\" \"KitchenQual\" \"TotRmsAbvGrd\" \"Functional\" ## [57] \"Fireplaces\" \"FireplaceQu\" \"GarageType\" \"GarageYrBlt\" ## [61] \"GarageFinish\" \"GarageCars\" \"GarageArea\" \"GarageQual\" ## [65] \"GarageCond\" \"PavedDrive\" \"WoodDeckSF\" \"OpenPorchSF\" ## [69] \"EnclosedPorch\" \"X3SsnPorch\" \"ScreenPorch\" \"PoolArea\" ## [73] \"PoolQC\" \"Fence\" \"MiscFeature\" \"MiscVal\" ## [77] \"MoSold\" \"YrSold\" \"SaleType\" \"SaleCondition\" ## [81] \"Age\" # Predict the response variable for the test data test.pred<-round(predict(model1, test),0) # Create a data frame with just the Id and the predicted sale price test.predicted.price<-data.frame(cbind(Id=test$Id,SalePrice=test.pred))\n# Replace NA values with mean of predicted sale price\n\n#nrow(test.predicted.price)\n#test.predicted.price<-test.predicted.price%>%drop_na()\n#nrow(test.predicted.price)\n#test.predicted.price%>%filter(is.na(SalePrice))\n\navg.price<-round(mean(test.predicted.price$SalePrice,na.rm=TRUE),0) test.predicted.price$SalePrice[is.na(test.predicted.price\\$SalePrice)]<-avg.price\ntest.predicted.price%>%filter(is.na(SalePrice))\n## [1] Id SalePrice\n## <0 rows> (or 0-length row.names)\n# Inspect the summary of the predicted sale price for the test dataset\nsummary(test.predicted.price)\n## Id SalePrice\n## Min. :1461 Min. :-21345\n## 1st Qu.:1826 1st Qu.:129878\n## Median :2190 Median :170661\n## Mean :2190 Mean :178212\n## 3rd Qu.:2554 3rd Qu.:222637\n## Max. :2919 Max. :613874\n\nClearly, there need to be improvements made to the model, since it is estimating a negative sale price in some cases.\n\n# Write the predicted values to a csv file for upload to kaggle\n\nwrite.csv(test.predicted.price, file=\"C:\/Jagdish\/MastersPrograms\/CUNY\/DS605 Computational Mathematics\/Final Project\/test_predictions.csv\",row.names=FALSE)","date":"2022-01-16 11:02:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 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\": 0.42755043506622314, \"perplexity\": 4898.274564325217}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"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-2022-05\/segments\/1642320299852.23\/warc\/CC-MAIN-20220116093137-20220116123137-00505.warc.gz\"}"} | null | null |
London Irish Rifles
The London Irish Rifles (LIR) was a volunteer rifle regiment of the British Army with a distinguished history, and now forms 'D' (London Irish Rifles) Company of the London Regiment and is part of the Army Reserve.
Crest of the London Irish Rifles
1920−Present Day
One company
London Regiment
Duke of York's Headquarters (1912−2000)
Flodden Road, Camberwell (2000−Present)
Motto(s)
Quis separabit? "Who shall separate us?"
"Garryowen"
St Patrick's Day (17 Mar)
Loos (25 Sep)
Honorary Colonel
Major-General Sir Sebastian John Lechmere Roberts KCVO OBE
Saffron (pipers kilts)
St Patrick's Blue Hackle worn by Officers, Warrant Officers and Pipers. Dark Green Hackle worn by all other ranks.
1859-1914Edit
18th Middlesex Rifle Volunteers (London Irish), c1895
The London Irish Rifles was originally formed in 1859 during the Victorian Volunteer Movement and named 28th Middlesex (London Irish) Rifle Volunteer Corps.[1] During the Second Boer War, the battalion sent eight officers and 208 private soldiers for active service. Captain EG Concannon won the Distinguished Service Order (DSO). In recognition of their service, the London Irish was granted their first battle honour, "South Africa, 1900-1902".[2]
In 1908, the London Irish was transferred to the Territorial Force and renamed the 18th (County of London) Battalion, the London Regiment (London Irish Rifles).[1]
First World WarEdit
The 1st battalion was mobilised in August 1914, at the start of the First World War at the Duke of York's Headquarters.[3] It landed at Le Havre as part of the 5th London Brigade in the 2nd London Division.[3] The 2nd battalion landed in France in June 1916 in the 180th Brigade in the 60th (2/2nd London) Division.[3] The 2nd battalion served on the Salonika front from December 1916 to June 1917 and then join the Egyptian Expeditionary Force for the advance to Jericho.[4]
At the Battle of Loos, the 1st Battalion LIR particularly distinguished itself. While storming across No-Man's Land to capture the enemy trenches, Rifleman Frank Edwards, the Captain of the football team, kicked a football along in front of the troops as they approached the German lines.[5] Some 1,016 London Irishmen were killed during the conflict.[4]
Inter-warEdit
Cap badge variations between WW1 (Left) and WW2 (Right)
After the cessation of hostilities, the LIR was reduced to cadre strength, before being disbanded in May 1919 at Felixstowe. In February 1920, the 18th (County of London) Battalion of the London Regiment (London Irish Rifles) was reconstituted as a component of the 47th (2nd London) Infantry Division of the new Territorial Army, and in 1923, the designation of the Regiment was shortened to 18th London Regiment (London Irish Rifles).[1]
In 1937, when the London Regiment was disbanded, the unit became known as London Irish Rifles, the Royal Ulster Rifles.[1] After the 47th Division was also disbanded, the London Irish transferred to the 169th (3rd London) Infantry Brigade, part of 56th (1st London) Infantry Division.[6]
Second World WarEdit
In April 1939, the establishment of the Territorial Army (TA), the British Army's part-time reserve, was doubled in size and the 2nd Battalion, London Irish Rifles was reformed, initially as a component unit of the 4th London Infantry Brigade, part of the 2nd London Infantry Division which was a 2nd Line duplicate of the 1st Line 1st London Infantry Division.[7]
The Pipe Band of the London Irish Rifles on parade with their Irish Wolfhound mascot, near Royal Tunbridge Wells, Kent, 31 December 1940.
The 70th (Young Soldiers) Battalion, a Young Soldiers unit of the London Irish Rifles, was also formed, early in 1940, and set up for young men volunteering who were between the ages of eighteen and nineteen and a half. The objective of the battalion was to train the soldiers to the highest standard of drill, skill-at-arms, discipline and turnout in preparation for the time when they would, in theory, be fit to take their place within the 1st and 2nd Battalions. The 70th (Young Soldiers) Battalion ceased to exist in January 1943, when all such units were disbanded.[8]
A company of the 1st Battalion was involved in the Battle of Graveney Marsh, in September 1940 the last ground combat between a foreign invading force and British troops that happened on British mainland soil.[9][10]
The 1st Battalion, London Irish Rifles formed part of the 1st London Infantry Brigade, itself part of the 1st London Division. In November 1940 the battalion transferred to the 2nd London Brigade, which was soon renumbered as the 168th (London) Infantry Brigade, due to the division's redesignation as the 56th (London) Infantry Division. From the outbreak of the Second World War in September 1939 until late July 1942, the battalion was in training, mainly in southeast England. The battalion left England in August 1942 to serve in the Middle East. In April 1943 the battalion, together with the rest of the 168th Brigade, was temporarily transferred to the 50th (Northumbrian) Infantry Division and fought in the Allied invasion of Sicily, codenamed Operation Husky, in July/August. The battalion, as part of the 168th Brigade, returned to the 56th Division in Italy in October, and took part in major actions during the Italian Campaign at Fosso Bottacetto south of Catania, Monte Camino, Monte Damiano, the Garagliano crossing during the first Battle of Monte Cassino and Aprilia (Anzio), and at the Gothic Line, and, transferring back to the 167th Brigade, the battalion played a leading role in the final Allied offensive in Northern Italy during April 1945.[11] In the month that they spent fighting in the Anzio beachhead, the 1st Battalion's casualties totalled 600 officers and other ranks killed, wounded and missing. Some 700 men of the London Irish Rifles were killed in action during the Second World War.[11]
A casualty is brought back across the River Reno during operations by 'C' Company of the 1st Battalion, London Irish Rifles to establish a bridgehead across the river, 6 April 1945.
The 2nd Battalion formed part of the 38th (Irish) Brigade, initially as part of 6th Armoured Division and later within the 78th Battleaxe Division, a division with an excellent reputation, and was in front line service from November 1942 to May 1945 throughout Tunisia and Italy including taking part in major actions at Bou Arada, Heidous, Centuripe, Termoli, Sangro River, the Liri Valley, Trasimeno, Monte Spaduro and at the Argenta Gap. The battalion garrisoned parts of Austria in the immediate post war period. During the final offensive in Italy the battalion was commanded by Lieutenant Colonel H. E. N. Bredin.[12]
Infantrymen of the 2nd Battalion, London Irish Rifles move forward through barbed wire defences on their way to attack a German strongpoint on the southern bank of the River Senio, Italy, 22 March 1945.
Post warEdit
After the war, the battalion re-formed as a battalion of the Royal Ulster Rifles. In 1967, with the disbanding of the London Regiment, the three Irish Regular Infantry Regiments combined to form The Royal Irish Rangers, and the London Irish Rifles became D Company (London Irish Rifles), 4th Battalion The Royal Irish Rangers, remaining so until the re-formation of The London Regiment in 1993.[1]
Since 1993 and the incorporation of the London Irish Rifles as a company of the London Regiment, soldiers from the London Irish Rifles have served in Bosnia, Kosovo, Iraq, Afghanistan and Cyprus. During Operation Telic, the company contributed to the formation of Cambrai Company (Operation Telic 3) and Messines Company (Operation Telic 4), both of which were commanded by officers of the London Irish Rifles. Soldiers from the company also deployed to Afghanistan with Somme Company in 2007 (Operation Herrick 7), Amiens Company in 2010 (Operation Herrick 12) and Arras Company in 2011 (Operation Herrick 13).[13]
The London Irish Rifles moved from their historic home, Duke of York's Headquarters, Chelsea to Flodden Road, Camberwell in 2000.[14][15]
Battle honoursEdit
The regiment's battle honours were as follows:[1]
Second Boer War: South Africa 1900-02
First World War: Festubert 1915, Loos, Somme 1916 '18, Flers-Courcelette, Morval, Messines 1917, Ypres 1917, Langemarck 1917, Cambrai 1917, St. Quentin, Bapaume 1918, Ancre 1918, Albert 1918, Pursuit to Mons, France and Flanders 1915-18, Doiran 1917, Macedonia 1916-17, Gaza, El Mughar, Nebi Samwil, Jerusalem, Jericho, Jordan, Palestine 1917-18
Second World War: Bou Arada, El Hadjeba, Stuka Farm, Heidous, North Africa 1942-43, Lentini, Simeto Bridgehead, Adrano, Centuripe, Salso Crossing, Simeto Crossing, Malleto, Pursuit to Messina, Sicily 1943, Termoli, Trigno, Sangro, Fossacesia, Teano, Monte Camino, Calabritto, Carigliano Crossing, Damiano, Anzio, Carroceto, Cassino II, Casa Sinagogga, Liri Valley, Trasimene Line, Sanfatucchio, Coriano, Croce, Senio Floodbank, Rimini Line, Ceriano Ridge, Monte Spaduro, Monte Grande, Valli di Commacchio, Argenta Gap, Italy 1943-45
Irish regiment
Irish Guards
Royal Irish Regiment
Mike Hoare
^ a b c d e f "London Irish Rifles". Regiments.org. Archived from the original on 10 January 2006. Retrieved 28 May 2017.
^ "Boer War/Pre First World War". London Irish Rifles Association. Retrieved 23 November 2017.
^ a b c "The London Regiment". The Long, Long Trail. Retrieved 27 May 2017.
^ a b "The First World War". London Irish Rifles Association. Retrieved 23 November 2017.
^ "Frank Edwards: Footballer of Loos". World war One: Playing the Game. Retrieved 10 January 2017.
^ "The London Division 1937-1938" (PDF). British Military History. Retrieved 30 April 2016.
^ Joslen, p. 235
^ "70th (Young Soldiers) Battalion". National Archives. Retrieved 28 May 2017.
^ "Kent battle between German bomber crew and British soldiers marked after 70 years". The Daily Telegraph. 20 August 2010. Retrieved 20 August 2010.
^ Green, Ron; Mark Harrison (30 September 2009). "Forgotten frontline exhibition tells how Luftwaffe fought with soldiers on Kent marshes". KentOnline.
^ a b "The Second World War". London Irish Rifles Association. Retrieved 23 November 2017.
^ Major General 'Bala' Bredin, Obituary, The Times, 9 March 2005.
^ "London Parade for returning UK troops". The Daily Telegraph. 15 October 2007. Retrieved 30 April 2016.
^ "D Company". London Irish Rifles Association. Retrieved 23 November 2017.
^ "D Company (London Irish Rifles)". Ministry of Defence. Retrieved 23 November 2017.
SourcesEdit
Joslen, Lt-Col H.F. (2003). Orders of Battle, United Kingdom and Colonial Formations and Units in the Second World War, 1939–1945. Uckfield: Naval & Military. ISBN 1-84342-474-6.
Ford, Ken (2003) [1999]. Battleaxe Division. Stroud, UK: Sutton Publishing. p. 273 pages. ISBN 0-7509-3199-X.
Doherty, Richard (1994) [1993]. Clear The Way! History of the 38th (Irish) Brigade. Dublin, Ireland: Irish Academic Press. p. 336 pages. ISBN 0-7165-2542-9.
All My Brothers By Edmund O'Sullivan. Contains an eyewitness account of serving in the 2nd Battalion of the London Irish Rifles from October 1939 until March 1946.
The History of the London Irish Rifles during the Second World War.
Irish Brigade The Story of the 38th (Irish) Brigade in the 2nd World War Contains the roll of honour of all those in the 1st and 2nd Battalions of the London Irish Rifles who died during the Second World War. The site also contains The London Irish Rifles at War A History of the two Battalions of the London Irish Rifles during the Second World War, the War Diaries of both the 1st and 2nd Battalion of the London Irish Rifles from 1942 to 1945, and the detailed citations of men of the London Irish Rifles who gained honours and awards.
D (London Irish) Company - The London Regiment
London Irish Rifles Association
London Irish Rifles Museum
Retrieved from "https://en.wikipedia.org/w/index.php?title=London_Irish_Rifles&oldid=884984871" | {
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{"url":"http:\/\/arkadiusz-jadczyk.eu\/blog\/category\/elliptic-functions\/","text":"### Attitude matrix and quaternion path for m>1\n\n[latexpage]\nI noticed that somehow I did not finish with the case $m>1.$ So today, without further ado, I am posting the algorithm.\nWe have the body with $I_11\/I_2$, where $d$ is, as always, the ratio of the doubled kinetic energy to angular momentum squared.\nThen we define\n\n\\begin{eqnarray}\nA_1&=&\\sqrt{\\frac{I_1(dI_3-1)}{I_3-I_1}},\\\\\nA_2&=&\\sqrt{\\frac{I_2 (1-dI_1)}{I_2-I_1}},\\\\\nA_3&=&\\sqrt{\\frac{I_3 (1-dI_1)}{I_3-I_1}},\\\\\nB&=&\\sqrt{\\frac{(dI_3-1)(I_2-I_1)}{I_1I_2I_3}},\\\\\n\\mu&=&\\frac{1}{m}=\\frac{(1-dI_1)(I_3-I_2)}{(dI_3-1)(I_2-I_1)}.\n\\end{eqnarray}\n\\begin{eqnarray}\nL_1(t)&=&A_1\\,\\dn(Bt,\\mu),\\\\\nL_2(t)&=&A_2\\,\\sn(Bt,\\mu),\\\\\nL_3(t)&=&A_3\\,\\cn(Bt,\\mu).\n\\end{eqnarray}\n\n\\alpha=\\frac{I_3-I_1}{\\sqrt{\\frac{I_1(dI_3-1)(I_2-I_1)I_3}{I_2}}},\n\n\\nu=\\frac{I_3-dI_1I_3}{I_1-dI_1I_3}.\n\n\\psi(t)=\\frac{t}I_3-\\arctan\\left((A_2\/A_1)\\mathrm{sd}(Bt,\\mu) \\right)+\\alpha \\Pi(\\nu,\\am(Bt,\\mu),\\mu),\\\n\nQ_1(t)=\\begin{bmatrix}1-\\frac{L_1(t)^2}{1+L_3(t)}&-\\frac{L_1(t)L_2(t)}{1+L_3(t)}&-L_1(t)\\\\\n-\\frac{L_1(t)L_2(t)}{1+L_3(t)}&1-\\frac{L_2(t)^2}{1+L_3(t)}&-L_2(t)\\\\L_1(t)&L_2(t)&L_3(t)\\end{bmatrix}.\n\nQ_2(t)=\\begin{bmatrix}\\cos\\psi(t)&-\\sin\\psi(t)&0\\\\\\sin\\psi(t)&\\cos\\psi(t)&0\\\\0&0&1\n\\end{bmatrix}.\n\nQ(t)=Q_2(t)Q_1(t).\n\n\\begin{eqnarray}\nq_0(t)&=&\\sqrt{\\frac{1+L_3(t)}{2}}\\cos\\frac{\\psi(t)}{2},\\\\\nq_1(t)&=&\\frac{1}{\\sqrt{2(1+L_3(t))}}\\left(L_2(t)\\cos\\frac{\\psi(t)}{2}+L_1(t)\\sin\\frac{\\psi(t)}{2}\\right),\\\\\nq_2(t)&=&\\frac{1}{\\sqrt{2(1+L_3(t))}}\\left(L_2(t)\\sin\\frac{\\psi(t)}{2}-L_1(t)\\cos\\frac{\\psi(t)}{2}\\right),\\\\\nq_3(t)&=&\\sqrt{\\frac{1+L_3(t)}{2}}\\,\\sin\\frac{\\psi(t)}{2},\\\\\nq(t)&=&(q_0(t),q_1(t),q_2(t),q_3(t))=q_0(t)+\\mathbf{i}\\,q_1(t)+\\mathbf{j}\\,q_1(t)+\\mathbf{k}\\,q_3(t).\n\\end{eqnarray}\n\nI use the above formulas to draw a stereographic projection of one particular path. So, I take $I_1=1,I_2=2,I_3=3,d=0.5000001$, and do the parametric plot of the curve $\\mathbf{r}(t)$ in $\\mathbf{R}^3,$\nwith\n$\\mathbf{r}(t)=\\left(\\frac{q_1(t)}{1-q_0(t)},\\frac{q_2(t)}{1-q_0(t)},\\frac{q_3(t)}{1-q_0(t)}\\right).$\nI show below two plots. One with $t\\in(-1000,1000),$ and one with $t\\in(-10000,10000).$ For this selected value of $d,$ the time between consecutive flips, given by the formula\n$$\\tau =4\\mathrm{EllipticK}(\\mu)\/B= 116.472.$$\nSo, for $t\\in(-10000,10000)$ we have somewhat less than 200 flips, and the lines are getting rather densely packed in certain regions.\nNotice that is just one geodesic line, geometrically speaking the straightest possible line in the geometry determined by the inertial properties of the body.\n\nIt is this \u201cgeometry\u201dthat will become the main subject of the future notes.\n\nHow can such a line be \u201cstraight\u201d? Well, it is\u2026.\n\n### Attitude matrix for m<1\n\nThe last post was about The final answer for the Universe in which m>1. Yet, as I see it today, it was neither complete nor final. It was a very bad approximation. It may be also that our universe is also a very bad approximation to the one that has been intended. But that is another story. I think I will return to this problem in my blogging, but now I will concentrate on the algorithm for the rotation matrix. At the same time I will make a comment how the algorithm from the last post, for the quaternions, should be improved. The fact is that I was making wrong assumptions in my mind. Making wrong assumptions, without being conscious of the fact that one is making such assumptions, that is very dangerous. Lot of bad things happens around us for this reason\u2026.\n\nSo, here is the code:\n[latexpage]\n\nThe case $m<1.$ The solution $\\mathbf{L}(t)$ of the Euler's equations has two trajectories. For one with $L_3(t)>0$ we take\n\\begin{eqnarray}\nA_1&=&\\sqrt{\\frac{I_1 (d I_3-1)}{I_3-I_1}},\\\\\nA_2&=&\\sqrt{\\frac{I_2 (d I_3-1)}{I_3-I_2}},\\\\\nA_3&=&\\sqrt{\\frac{I_3 (1-d I_1)}{I_3-I_1}},\\\\\n\\end{eqnarray}\nwhile for the other one, with $L_3(t)<0$ we take \\begin{eqnarray} A_1&=&-\\sqrt{\\frac{I_1 (d I_3-1)}{I_3-I_1}},\\\\ A_2&=&\\sqrt{\\frac{I_2 (d I_3-1)}{I_3-I_2}},\\\\ A_3&=&-\\sqrt{\\frac{I_3 (1-d I_1)}{I_3-I_1}}.\\\\ \\end{eqnarray} Let \\begin{eqnarray} B&=&\\sqrt{\\frac{(1-d I_1) (I_3-I_2)}{I_1 I_2 I_3}},\\\\ m&=&\\frac{(d I_3-1) (I_2-I_1)}{(1-d I_1) (I_3-I_2)}. \\end{eqnarray} The solution $\\mathbf{L}(t)$ of the Euler's equations is given by \\begin{eqnarray} L_1(t)&=&A_1\\, \\cn (Bt,m),\\\\ L_2(t)&=&A_2\\, \\sn (Bt,m),\\\\ L_3(t)&=&A_3\\, \\dn (Bt,m), \\end{eqnarray} With constants $\\alpha$ and $\\nu$ defined as $$\\alpha=\\frac{I_3-I_1}{\\sqrt{\\frac{I_1(1-d I_1)(I_3-I_2)I_3}{I_2}}},$$ $$\\nu=\\frac{I_1-dI_1I_3}{I_3-dI_1I_3}$$ we set the phase variable $\\psi(t)$ as $$\\psi(t)=\\frac{t}I_1+\\arctan\\left((A_2\/A_3)\\mathrm{sd}(Bt,m) \\right)-\\alpha \\Pi(\\nu,\\am(Bt,m),m),$\/extract_tex] where the Jacobi function \\mathrm{sd} is defined as \\mathrm{sd}(u,m)=\\sn(u,m)\/\\dn(u,m). Let Q_1(t) =\\begin{bmatrix} L_1(t)& L_2(t)& L_3(t)\\\\-L_2(t)& 1 - \\frac{L_2(t)^2}{1 + L_1(t)}& -\\frac{L_2(t) L_3(t)}{1 + L_1(t)}\\\\ -L_3(t)& -\\frac{L_2(t) L_3(t)}{1 + L_1(t)}& 1 - \\frac{L_3(t)^2}{1 + L_1(t)},\\end{bmatrix} $$Q_2(t)=\\begin{bmatrix} 1 & 0 & 0 \\\\ 0 & \\cos \\psi (t) & -\\sin \\psi (t) \\\\ 0 & \\sin \\psi (t) & \\cos \\psi (t) \\\\ \\end{bmatrix}.$$ Then the attitude matrix Q(t) is given by $$Q(t)=Q_2(t)Q_1(t).$$ If you compare this with the formulas I gave yesterday, you will find the following important difference: now I am playing with signs in the constants A_1,A_3 rather than with the signs in formulas for L_1(t),L_3(t). It took me whole day to realize that this way is a better way. I was not realizing before that there is one sign in the formula for \\psi(t) that depends on the trajectory we are taking. The constant A_2\/A_3 does this job now. In a couple of days I will also change the formulas in the quaternionic algorithm to make them universal as well. Now, I check the modified example3. The modified initial data in init_example3.dat file are as follows: 1.0000000000D0 10.0000000000D0 -0.544332842491675D0 0.729131780907662D0 -0.414811526666455D0 1.000000000000000D0 0.000000000000000D0 0.000000000000000D0 0.000000000000000D0 1.000000000000000D0 0.000000000000000D0 0.000000000000000D0 0.000000000000000D0 1.000000000000000D0 1.000000000000000D0 1.012686988782515D0 3.306237422473038D0 5 They are the same as in the quaternionic case discussed yesterday. The initial attitude matrix is the identity matrix. We get the same t_0. I use Mathematica to calculate the transposed final Q Transpose[Inverse[Q[t0]].Q[t0 + 10.0]] {{0.0656754, 0.550118, -0.832501}, {0.995487, 0.0211483, 0.0925082}, {0.0684964, -0.834819, -0.546246}} We compare it with the Fortran output from 903 code: 0.0656754297 0.55011776 -0.832500564 0.995487311 0.0211482921 0.0925081752 0.0684963551 -0.834819262 -0.546246326 And it seems that our code is doing the same job as the Fortran code from the giants! Yet, as I said at the beginning, it took me the whole days to figure it out why for some initial data I was in agreement, but for another initial data there was a disagreement. There is one little plus of the code above. The coefficient in front of \\arctan is fixed, and equal 1.! Zanna and Celledoni in their paper and in their code have complicated formulas for this coefficient. It would take some work to verify that their complicated formula simplifies to 1. I hope I am right here\u2026. ### The final answer for the Universe in which m<1 This is not an independent post or note or whatever. It is a continuation. In fact it is the continuation of Approaching the ultimate answer for m<1. We have approached enough. We are ready. There was a moment\u2019s expectant pause while panels slowly came to life on the front of the console. Lights flashed on and off experimentally and settled down into a businesslike pattern. A soft low hum came from the communication channel. \u201cGood morning,\u201d said Deep Thought at last. \u201cEr \u2026 good morning, O Deep Thought,\u201d said Loonquawl nervously, \u201cdo you have \u2026 er, that is \u2026\u201d \u201cAn answer for you?\u201d interrupted Deep Thought majestically. \u201cYes. I have.\u201d The two men shivered with expectancy. Their waiting had not been in vain. \u201cThere really is one?\u201d breathed Phouchg. \u201cThere really is one,\u201d confirmed Deep Thought. Douglas Adams, The Hitchhiker\u2019s Guide to the Galaxy [latexpage] We did not get to the answer yesterday, but today is the day. We will be using the formulas from the last post. Here they are again, repeated for your convenience: The case m<1. \\begin{eqnarray} A_1&=&\\sqrt{\\frac{I_1 (d I_3-1)}{I_3-I_1}},\\\\ A_2&=&\\sqrt{\\frac{I_2 (d I_3-1)}{I_3-I_2}},\\\\ A_3&=&\\sqrt{\\frac{I_3 (1-d I_1)}{I_3-I_1}},\\\\ B&=&\\sqrt{\\frac{(1-d I_1) (I_3-I_2)}{I_1 I_2 I_3}},\\\\ m&=&\\frac{(d I_3-1) (I_2-I_1)}{(1-d I_1) (I_3-I_2)}. \\end{eqnarray} The solution \\mathbf{L}(t) of the Euler's equations has two trajectories: one with L_3(t)>0 is given by \\begin{eqnarray} L_1(t)&=&A_1\\, \\cn (Bt,m),\\\\ L_2(t)&=&A_2\\, \\sn (Bt,m),\\\\ L_3(t)&=&A_3\\, \\dn (Bt,m), \\end{eqnarray} while the other one, with L_3(t)<0 is given by \\begin{eqnarray} L_1(t)&=&-\\,A_1\\, \\cn (Bt,m),\\\\ L_2(t)&=&A_2\\, \\sn (Bt,m),\\\\ L_3(t)&=&-\\,A_3\\, \\dn (Bt,m).\\label{eq:3} \\end{eqnarray} With constants \\alpha and \\nu defined as $$\\alpha=\\frac{I_3-I_1}{\\sqrt{\\frac{I_1(1-d I_1)(I_3-I_2)I_3}{I_2}}},$$ $$\\nu=\\frac{I_1-dI_1I_3}{I_3-dI_1I_3}$$ we set the phase variable \\psi(t) as $$\\psi(t)=\\frac{t}I_1-\\arctan\\left((A_2\/A_3)\\mathrm{sd}(Bt,m) \\right)-\\alpha \\Pi(\\nu,\\am(Bt,m),m),\\$$ where the Jacobi function \\mathrm{sd} is defined as \\mathrm{sd}(u,m)=\\sn(u,m)\/\\dn(u,m). Then the quaternionic attitude solution is given by q(t)=W(t)+\\mathbf{i}X(t)+\\mathbf{j}Y(t)+\\mathbf{k}Z(t), with \\begin{eqnarray} W(t)&=&\\cos \\frac{\\psi(t)}{2}\\sqrt{\\frac{1+L_1(t)}{2}},\\\\ X(t)&=&\\sin \\frac{\\psi(t)}{2}\\sqrt{\\frac{1+L_1(t)}{2}},\\\\ Y(t)&=&\\frac{L_3(t)\\cos \\frac{\\psi(t)}{2}+L_2(t)\\sin \\frac{\\psi(t)}{2}}{\\sqrt{2(1+L_1(t))}},\\\\ Z(t)&=&\\frac{-L_2(t)\\cos \\frac{\\psi(t)}{2}+L_3(t)\\sin \\frac{\\psi(t)}{2}}{\\sqrt{2(1+L_1(t))}}\\label{eq:5} \\end{eqnarray} We consider Example Four with \\begin{eqnarray} I_1&=&1.0,\\\\ I_2&=&1.012686988782515,\\\\ I_3&=&3.306237422473038 \\end{eqnarray} \\begin{eqnarray} m_1(0)&=&-0.544332842491675,\\\\ m_2(0)&=&0.729131780907662,\\\\ m_3(0)&=&-0.414811526666455. \\end{eqnarray} m_3(0) is negative, the therefore we take option as in Eq. \\ref{eq:3}). We calculate t_0 that reproduces the initial angular momenta. The method is known from the previous posts: $$am=\\arctan(-m_1(0)\/A_1,m_2(0)\/A_2)=0.925158,$$ $$t_0=\\mathrm{EllipticF}(am,m)=3.17243.$$ So we have t_0. At t=t_0 our angular momentum is the same as angular momentum in example 4 at t=0. We calculate q_0=q(t_0) from Eq'(\\ref{eq:5}) \\[q_0=W(t_0)+X(t_0)\\,\\mathbf{i}+Y(t_0)\\,\\mathbf{j}+Z(t_0)\\,\\mathbf{k},$\n\\begin{eqnarray}\nW(t_0)&=&0.435964,\\\\\nX(t_0)&=&0.194343,\\\\\nY(t_0)&=&-0.0858987,\\\\\nZ(t_0)&=-&0.874521\n\\end{eqnarray}\nthus\n$$q_0=0.435964+0.194343\\,\\mathbf{i}-0.0858987\\,\\mathbf{j}-0.874521\\,\\mathbf{k}.$$\nWe verify that we have indeed a unit quaternion:\n$||q_0||^2=W(t_0)^2+X(t_0)^2+Y(t_0)^2+Z(t_0)^2=1.0.$\nThus the inverse quaternion is the same as conjugated one:\n$q_0^{-1}=0.435964-0.194343\\,\\mathbf{i}+0.0858987\\,\\mathbf{j}+0.874521\\,\\mathbf{k}.$\nIn the Example 4 the initial quaternion, at $t=0$ is $1$. Therefore in order for our solution to reproduce the initial data of the example we set\n$$\\tilde{q}(t)=q_0^{-1}\\,q(t+t_0).$$\nThe final time in Example 4 is $t=10.$ Therefore we calculate\n$$\\tilde{q}(10)=q_0^{-1}q(10+t_0),$$\nwhere the multiplication is the quaternion multiplication.\nCalculated with Mathematica the answer is\n\\begin{eqnarray}\nW&=&=-0.36762,\\\\\nX&=&-0.630629,\\\\\nY&=&-0.612723,\\\\\nZ&=&0.302874.\n\\end{eqnarray}\nThe result from the Fortran code in the file out_example4.dat is\n\n-0.3676198430772359\n-0.6306293413288832\n-0.6127232632258010\n0.3028737154869889\n\nIt seems that therefore that we have obtained the ultimate answer. At least for quaternions. We need to get it also for rotation matrices. So the saga will continue.","date":"2018-02-24 22:02:09","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\": 15, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8467816710472107, \"perplexity\": 2047.9363221665099}, \"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-2018-09\/segments\/1518891815951.96\/warc\/CC-MAIN-20180224211727-20180224231727-00642.warc.gz\"}"} | null | null |
\section{Introduction}
Although current astrophysical observations provide precise information on the geometry of the universe \cite{Komatsu:2010fb}, its topology remains a mystery. We don't even know whether the universe is compact or infinite. Nevertheless, lower bounds can be put on its size for each compact topology (see, \cite{Glen} and references therein).
Amongst the possible topologies for the universe those with some or all spatial dimensions compactified are especially interesting, since then Casimir energies provide an additional contribution to the energy density. This may lead to an interesting vacuum structure for the standard model coupled to gravity which is insensitive to quantum gravity effects \cite{ArkaniHamed:2007gg, AFW, FW}. The simplest flat topology with all dimensions compactified is a three-torus, and that is the topology we will concentrate on throughout this paper.
The scenario of our universe having a three-torus topology was investigated by many authors (see, \cite{Linde} and references therein). Probably one of the most appealing features of such a model is that the creation of a three-torus universe is much more likely to occur than that of an infinite flat or closed universe \cite{Zeldov,Linde}. In addition, it has also been shown that a three-torus topology can provide convenient initial conditions for inflation \cite{Zeldov}.
Here we consider gravitational particle creation in an expanding toroidal universe. The particle production formalism was developed in \cite{Parker1,Parker2,Parker3} and investigated in great detail in later works (see, \cite{Zeldovich,Starob,Grib} and references therein). Since then, it has been thoroughly studied in the case of a FRW cosmology, including its implications for dark matter creation around the inflationary epoch \cite{Chung}. However, particle production in a toroidal universe hasn't been extensively studied (see, \cite{Berger} for some work on the subject).
In this paper we provide a detailed numerical calculation of the particle production in a three-torus universe. We start with introducing the relevant formalism. We then discuss the evolution of the size and energy density of the universe from the Planck time to the present time. Next, we derive analytical formulae for the particle number and energy density at early and late times. We then find full numerical solutions and confirm that they agree with the analytical approximations in the appropriate regions. The particle production through the nonzero modes is somewhat similar as in the closed universe case discussed in \cite{Starob}. However, the three-torus particle creation includes an additional contribution from the zero mode, which strongly depends on the choice of initial conditions.
\section{Three-torus metric}
We start with the following spacetime interval,
\begin{eqnarray}
ds^2 = - d t^2 + t_{i j} d y^i d y^j\,,
\end{eqnarray}
where $t_{i j}$ is the metric on the three-torus with $i, j = 1, 2, 3$, and the compact coordinates are $y^i \in [0, 2\pi)$.
The $3\times3$ matrix with components $t_{ij}$ is positive definite and has a determinant equal to the volume modulus $a^3$. A suitable parametrization is given by,
\begin{eqnarray}\label{torus1}
t_{i j} = \frac{a^2}{(\rho_3 \tau_2)^{2/3}}\left(
\begin{array}{ccc}
1 & \tau_1 & \rho_1 \\
\tau_1 & \tau_1^2+\tau_2^2 & \rho_1\tau_1 + \rho_2\tau_2 \\
\rho_1 & \rho_1\tau_1+ \rho_2\tau_2 & \rho_1^2+\rho_2^2+\rho_3^2 \\
\end{array}
\right) ,
\end{eqnarray}
where $(\tau_1, \tau_2, \rho_1, \rho_2, \rho_3)$ are the shape moduli. We assume that all the parameters in (\ref{torus1}) are independent of the spatial coordinates. Furthermore, we seek stable solutions to Einstein's equations for which the shape parameters are also constant in time. It was shown in \cite{FW} that this is only possible for,
\begin{eqnarray}
\label{shape}
(\tau_1, \tau_2, \rho_1, \rho_2, \rho_3)= \left(\frac{1}{2}, \frac{\sqrt{3}}{2}, \frac{1}{2}, \frac{\sqrt{3}}{6}, \frac{\sqrt{6}}{3}\right),
\end{eqnarray}
which arises from the symmetries of the Casimir energies. For a three-torus universe characterized by the parameters (\ref{shape}) only the evolution of the volume modulus is nontrivial. The corresponding metric takes the form,
\begin{eqnarray}\label{torus}
t_{i j} = \frac{a^2}{\sqrt[3]{4}}\left(
\begin{array}{ccc}
2 & 1 & 1 \\
1 & 2 & 1 \\
1 & 1 & 2 \\
\end{array}
\right) ,
\end{eqnarray}
and this is the metric we will adopt in our further analysis.
\section{Particle production}
We first derive general formulae for the gravitational particle production rate in a three-torus universe.
Let us consider a complex scalar field $\Psi=\Psi(x)$ of mass $m$ with the Lagrangian density given by,
\begin{eqnarray}
\mathcal{L} = \sqrt{-g} \left[g^{\mu \nu}\partial_{\mu} \Psi \,\partial_\nu \Psi^* - \left(m^2+\frac{R}{6}\right) |\Psi|^2\right]\ ,
\end{eqnarray}
where $R$ is the Ricci scalar,
\begin{eqnarray}
R = \frac{6}{a^2} \left(a\,\ddot{a}+\dot{a}^2\right)\ .
\end{eqnarray}
The dot denotes the derivative with respect to time $t$ and the factor $\xi=1/6$ was chosen to have conformal invariance in the limit $m\rightarrow0$.
We note, however, that the results in this paper are not very sensitive to this choice and would be similar, for example, in the case of a minimally coupled scalar field (for which $\xi=0$).
The stress-energy tensor is given by,
\begin{eqnarray}\label{tensor}
T_{\mu\nu} &=& \partial_{\mu} \Psi \,\partial_\nu \Psi^* + \partial_{\nu} \Psi \,\partial_\mu \Psi^* - g_{\mu\nu}\frac{\mathcal{L}}{\sqrt{-g}}\nonumber\\
& & -\, \frac{1}{3}\left(R_{\mu\nu} + \nabla_\mu \nabla_\nu - g_{\mu\nu}\nabla_\gamma \nabla^\gamma \right) |\Psi|^2\ .
\end{eqnarray}
The equation of motion for the field $\Psi$ is,
\begin{eqnarray}\label{eq}
\ddot\Psi + 3 \frac{\dot{a}}{a}\dot\Psi - \nabla^2\Psi + \left(m^2+\frac{\ddot{a}}{a}+\frac{\dot{a}^2}{a^2}\right)\Psi = 0\ ,
\end{eqnarray}
where $\nabla^2$ is the Laplacian on the three-torus.
We write the solutions of equation (\ref{eq}) as,
\begin{eqnarray}
\Psi_\lambda(x) = u_\lambda(t) \,\phi_\lambda(\vec{y})\ ,
\end{eqnarray}
with $\lambda = (\lambda_1, \lambda_2, \lambda_3)$.
In our case,
\begin{eqnarray}\label{nabla}
\nabla^2\phi_\lambda = - \frac{\tilde{t}_{i j}}{a^2} \lambda_i \lambda_j \phi_\lambda,
\end{eqnarray}
where,
\begin{eqnarray}
\tilde{t}_{ij} \equiv t_{ij}/a^2\ ,
\end{eqnarray}
and there is an implicit sum over the repeated indices $i, j = 1, 2, 3$, with $\lambda_i = 0, \pm1, \pm2, ...$. The formula for $\phi_\lambda$
is given by,
\begin{eqnarray}
\phi_\lambda = C\, e^{i \,\tilde{t}_{k l} \lambda_k y^l}\ .
\end{eqnarray}
Note that for $\lambda = (0, 0, 0)$ we have $\phi_0 = \rm const$, which corresponds to the zero mode.
Equation (\ref{eq}) takes the form,
\begin{eqnarray}\label{eq2}
\ddot u_\lambda + 3 \frac{\dot{a}}{a}\dot u_\lambda + \left(\frac{\omega_\lambda^2}{a^2}+\frac{\ddot{a}}{a}+\frac{\dot{a}^2}{a^2}\right) u_\lambda = 0\ ,
\end{eqnarray}
where,
\begin{eqnarray}\label{omega}
\omega_\lambda^2 &=& (m a)^2 + \tilde{t}_{i j} \lambda_i \lambda_j\ .
\end{eqnarray}
We can now quantize the field introducing standard canonical equal-time commutation relations for the field and its generalized momentum. Those relations are satisfied if we write the field $\Psi$ as,
\begin{eqnarray}
\hspace{-2mm}\hat{\Psi} = \frac{1}{(2\pi a)^{\sfrac{3}{2}}} \sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty \left[\phi_\lambda \,u^*_\lambda \,\hat{a}_\lambda + \phi^*_\lambda \,u_\lambda \,\hat{b}_\lambda^\dagger\right],
\end{eqnarray}
where $\hat{a}^\dagger_\lambda$ and $\hat{a}_\lambda$ are the creation and annihilation operators of a particle in the state $\lambda = (\lambda_1, \lambda_2, \lambda_3)$, and $\hat{b}^\dagger_\lambda$ and $\hat{b}_\lambda$ are those for antiparticles, all obeying the usual commutation relations.
Adopting such a convention, the Hamiltonian can be written as \cite{Starob},
\begin{eqnarray}\label{ham}
\hspace{-10mm}\hat{H} &=& \hspace{-3mm} \sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty \omega_\lambda \bigg[A_\lambda\left(\hat{a}_\lambda \,\hat{a}_\lambda^{\dagger} + \hat{b}_{\bar{\lambda}}^{\dagger} \,\hat{b}_{\bar{\lambda}}\right)\nonumber\\
& & \hspace{22mm} +\, B_\lambda\, \hat{a}_\lambda^{\dagger} \,\hat{b}_{\bar{\lambda}}^{\dagger} + B^*_\lambda\, \hat{a}_{\lambda}\, \hat{b}_{\bar{\lambda}} \bigg],
\end{eqnarray}
with,
\vspace{-3mm}
\begin{eqnarray}\label{omega2}
A_\lambda &=& \frac{a^2 |\dot{u}_\lambda|^2}{2\,\omega_\lambda}+\frac{1}{2}\omega_\lambda |u_\lambda|^2\ ,\nonumber\\
B_\lambda &=& \frac{a^2 \dot{u}_\lambda^2}{2\,\omega_\lambda}+\frac{1}{2}\omega_\lambda u_\lambda^2\ ,
\end{eqnarray}
and ${\bar{\lambda}}$ defined through $\phi_{\bar{\lambda}} = \phi_{\lambda}^*$.
In general, the Hamiltonian (\ref{ham}) is non-diagonal. The requirement of it being diagonal at some initial time $t_0$ imposes the following conditions,
\begin{eqnarray}
u_\lambda(t_0) = \frac{1}{\sqrt{\omega_\lambda(t_0)}}\ , \ \ \ \dot{u}_\lambda(t_0) = i \,\frac{\sqrt{\omega_\lambda(t_0)}}{a(t_0)}\ .
\end{eqnarray}
Now, we can diagonalize the Hamiltonian through the following Bogoliubov transformation,
\begin{eqnarray}
\hat{a}_\lambda &=& \alpha^*_\lambda(t)\, \hat{a}_\lambda'(t) + \beta_\lambda(t) \,\hat{b}_{\bar{\lambda}}'^{\dagger}(t) \ ,\nonumber\\
\hat{b}_\lambda &=& \alpha^*_\lambda(t) \,\hat{b}_\lambda'(t) + \beta_\lambda(t) \,\hat{a}_{\bar{\lambda}}'^{\dagger}(t) \ ,
\end{eqnarray}
where $|\alpha_\lambda|^2 - |\beta_\lambda|^2 = 1$.
It can be shown \cite{Starob}, from the requirement that there be no non-diagonal terms $\hat{a}_\lambda'^{\dagger} \hat{b}_\lambda'^{\dagger}$ or $\hat{a}_\lambda' \hat{b}_\lambda'$, that the equations for $\alpha_\lambda(t)$ and $\beta_\lambda(t)$ are,
\begin{eqnarray}
\dot{\beta}_\lambda &=& \frac{\dot{\omega}_\lambda}{2\,\omega_\lambda} \,\alpha_\lambda \exp\left(-2 i \int_{t_0}^t \frac{\omega_\lambda(t')}{a(t')} dt'\right)\ , \label{coupled}\\
\dot{\alpha}_\lambda &=& \frac{\dot{\omega}_\lambda}{2\,\omega_\lambda}\, \beta_\lambda \exp\left(2 i \int_{t_0}^t \frac{\omega_\lambda(t')}{a(t')} dt'\right)\ ,\label{coupled2}
\end{eqnarray}
with the initial conditions $\beta_\lambda(t_0)=0$ and $\alpha_\lambda(t_0)=1$.
The function $u_\lambda$ is expressed in terms of $\alpha_\lambda$ and $\beta_\lambda$ as \cite{Starob},
\begin{eqnarray}
\hspace{-10mm} u_\lambda &=& \frac{1}{\sqrt{\omega_\lambda}} \bigg[\alpha^*_\lambda\exp\left(i \int_{t_0}^t \frac{\omega_\lambda(t')}{a(t')} dt'\right)\nonumber\\
& & \hspace{15mm}+\, \beta_\lambda\exp\left(-i \int_{t_0}^t \frac{\omega_\lambda(t')}{a(t')} dt'\right)\bigg]\ .
\end{eqnarray}
\begin{table*}[t]
\begin{center}
\begin{tabular}[t]{|c|c|c|c|c|c|}
\hline
\multicolumn{1}{|c|}{} & \multicolumn{5}{|c|}{epoch} \\ \cline{2-6}
& \,\,\,pre-inflationary era\,\, & \,\,\,inflation \,\, & \,\,\,radiation era\,\, & \ \ \,\,matter era\, \ \ & dark energy era\\
\hline\hline
& $\approx 5\cdot 10^{-44} \ \rm s$ &\, $\approx 5\cdot10^{-36} \ \rm s $ \,&\, $\approx 10^{-33} \ \rm s $ \,& \, $\approx 7\cdot10^4 \ \rm years$ \, & $\approx 10^{10} \ \rm years$\\
\ \raisebox{1.8ex}[0pt]{$t_{\rm init}$} \ & $\simeq 8\cdot 10^{-20} \ \rm GeV^{-1}$ & $\simeq 7\cdot10^{-12} \ \rm GeV^{-1}$ & $\simeq 10^{-9} \ \rm GeV^{-1}$ & $\simeq 3\cdot 10^{36} \ \rm GeV^{-1}$ & $\simeq 5\cdot 10^{41} \ \rm GeV^{-1}$\\ \hline
\ \ & \, $\approx 5\cdot10^{-36} \ \rm s $ \,& \, $\approx 10^{-33} \ \rm s $ \,& \, $\approx 7\cdot10^4 \ \rm years$ \,& $\approx 10^{10} \ \rm years$ & $\approx 1.37\cdot10^{10} \ \rm years$\\
\ \raisebox{1.8ex}[0pt]{$t_{\rm final}$} \ & \, $\simeq 7\cdot10^{-12} \ \rm GeV^{-1}$ \, & \, $\simeq 10^{-9} \ \rm GeV^{-1}$ \, & \, $\simeq 3\cdot 10^{36} \ \rm GeV^{-1}$ \, & \, $\simeq 5\times 10^{41} \ \rm GeV^{-1}$ \, & $\simeq 7\cdot 10^{41} \ \rm GeV^{-1}$\\ \hline
\ \ & \, & &\, \,& \, \, & \\
\ \ & \raisebox{1.8ex}[0pt]{$a_{p0} \sqrt{t}$} & \raisebox{1.8ex}[0pt]{$a_{i0}\exp\left[\sqrt{\rho_{\rm tot}/(3M_p^2)} \,t\right]$}&\ \raisebox{1.8ex}[0pt]{$a_{r0} \sqrt{t}$} \,& \, \raisebox{1.8ex}[0pt]{$a_{m0} t^{\sfrac{2}{3}}$} \, & \raisebox{1.8ex}[0pt]{$a_{d0}\exp\left[\sqrt{\rho_{\rm tot}/(3M_p^2)} \,t\right]$}\\
\ \raisebox{3.5ex}[0pt]{$a(t)$} \ & \,\raisebox{1.2ex}[0pt]{$a_{p0} \simeq 4\cdot10^{-10} \frac{1}{\sqrt{\rm GeV}}$} & \raisebox{1.2ex}[0pt]{$a_{i 0} \simeq 10^{-15} \ \rm GeV^{-1}$} & \, \raisebox{1.2ex}[0pt]{$a_{r0} \simeq 6\cdot10^{20} \frac{1}{\sqrt{\rm GeV}}$} & \, \raisebox{1.2ex}[0pt]{$a_{m 0} \simeq 6\cdot10^{14} \frac{1}{\sqrt[3]{\rm GeV}}$} & \raisebox{1.2ex}[0pt]{$a_{d 0} \simeq 2\cdot 10^{42} \ \rm GeV^{-1}$} \\ \hline
\ \ & $\approx 2\cdot 10^{-35} \ \rm m$ & $\approx 2\cdot 10^{-31} \ \rm m$ & $\approx 4 \ \rm m$ & \, $\approx 2\cdot 10^{23} \ \rm m$ \, & $\approx 8\cdot10^{26} \ \rm m$\\
\ \raisebox{1.8ex}[0pt]{$a(t_{\rm init})$} \ & $\simeq 10^{-19} \ \rm GeV^{-1}$& $ \simeq 10^{-15} \ \rm GeV^{-1}$ & $\simeq 2\cdot 10^{16} \ \rm GeV^{-1}$ & \, $\simeq 10^{39}\ \rm GeV^{-1}$ \, & $\simeq 4 \cdot 10^{42} \ \rm GeV^{-1}$\\ \hline
\ \ & $\approx 2\cdot 10^{-31} \ \rm m$ & \, $\approx 4 \ \rm m$ \,& \,$\approx 2\cdot 10^{23} \ \rm m$ \,& \, $\approx 8\cdot 10^{26} \ \rm m$ & $\approx 10^{27} \ \rm m$ \\
\ \raisebox{1.8ex}[0pt]{$a(t_{\rm final})$} \ & $ \simeq 10^{-15} \ \rm GeV^{-1}$ & \, $\simeq 2\cdot 10^{16} \ \rm GeV^{-1}$ \, & \, $\simeq 10^{39}\ \rm GeV^{-1}$ \, & \, $\simeq4\cdot 10^{42} \ \rm GeV^{-1}$ \, & $\simeq 5 \cdot 10^{42} \ \rm GeV^{-1}$\\ \hline
\ \ & \, \,& \, \,& \, \,& \, \, & \\
\ \raisebox{1.7ex}[0pt]{$\rho_{\rm tot}(t)$} \ & \, \raisebox{1.7ex}[0pt]{$3 M_p^2 / (4 t^2)$} \, & \, \raisebox{1.7ex}[0pt]{$\rm const$} \, & \, \raisebox{1.7ex}[0pt]{$3 M_p^2 / (4 t^2)$} \, & \, \raisebox{1.7ex}[0pt]{$4 M_p^2 / (3 t^2)$} \, & \raisebox{1.7ex}[0pt]{$ \rm const$} \\ \hline
& & & & & \\
\raisebox{1.7ex}[0pt]{$\rho_{\rm tot}(t_{\rm init})$} & \raisebox{1.7ex}[0pt]{$\approx 7\cdot 10^{74} \ {\rm GeV^4}$} & \raisebox{1.7ex}[0pt]{$\approx 9\cdot10^{58} \ \rm GeV^4$} & \raisebox{1.7ex}[0pt]{$\approx 4\cdot 10^{54} \ \rm GeV^4$} & \raisebox{1.7ex}[0pt]{$\approx 8\cdot 10^{-37} \ \rm GeV^4$} & \raisebox{1.7ex}[0pt]{$\approx 3\cdot10^{-47} \ \rm GeV^4$}\\ \hline
& & $\approx 9\cdot10^{58} \ \rm GeV^4$ & & & \\
$\rho_{\rm tot}(t_{\rm final})$ & $\approx 9\cdot10^{58}\ \rm GeV^4$ & after reheating: & \, $\approx 5\cdot 10^{-37} \ \rm GeV^4$ \, & \, $\approx 3\cdot10^{-47} \ \rm GeV^4$ \, & $\approx 3\cdot10^{-47} \ \rm GeV^4$\\
& & $\approx 4\cdot 10^{54} \ \rm GeV^4$ & & & \\ \hline
\end{tabular}
\end{center}
\vspace{0mm}
\caption{\footnotesize{Estimated timeline for the evolution of a three-torus universe from the Planck time until the present time $t_{\rm univ} \approx 13.7 \ \rm billion \ years$, including the size of the universe and total energy density during different epochs, assuming a pre-inflationary expansion $a(t)=a_{p0}\sqrt{t}\,$ and the current size of the universe $a(t_{\rm univ}) \approx 10 \, R_H$.}}
\end{table*}
\hspace{-1mm}Relations (\ref{coupled}) and (\ref{coupled2}) can be combined into one second order differential equation for $\beta_\lambda(t)$,
\begin{eqnarray}\label{Bog}
\ddot{\beta}_\lambda + \left(\frac{\dot{\omega}_\lambda}{\omega_\lambda} - \frac{\ddot{\omega}_\lambda}{\dot{\omega}_\lambda} +\frac{2 i \omega_\lambda}{a}\right)\dot{\beta}_\lambda - \frac{\dot{\omega}_\lambda^2}{4\,\omega_\lambda^2}\beta_\lambda = 0\ ,
\end{eqnarray}
with the initial conditions,
\begin{eqnarray}\label{initiial}
\beta_\lambda(t_0) = 0\ , \ \ \ \dot{\beta}_\lambda(t_0) = \frac{\dot{\omega}_\lambda(t_0)}{2\,\omega_\lambda(t_0)}\ .
\end{eqnarray}
The normal ordered Hamiltonian now takes the diagonal form,
\begin{eqnarray}\label{ham2}
\hat{H} &=& \hspace{-3mm}\sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty \omega_\lambda \left(\hat{a}_\lambda'^{\dagger} \,\hat{a}_\lambda' + \hat{b}_{\lambda}'^{\dagger} \,\hat{b}_{\lambda}'\right),
\end{eqnarray}
and the physical vacuum depends on time through,
\begin{eqnarray}
\hat{a}_\lambda'(t) |0(t)\rangle = \hat{b}_\lambda'(t) |0(t)\rangle = 0\ .
\end{eqnarray}
It is now straightforward to arrive at the formula for the number density of particle pairs created after time $t$,
\begin{eqnarray}\label{number}
n(t) = \frac{1}{(2\pi a)^3} \sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty |\beta_{\lambda}|^2\ .
\end{eqnarray}
The energy density and pressure of the created particles are calculated from the vacuum expectation values of the appropriate components of the stress-energy tensor (\ref{tensor}). After normal ordering the result is (compare with \cite{Starob}),
\begin{eqnarray}\label{density}
\rho(t) &=& \frac{1}{4\pi^3 a^4} \sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty \omega_\lambda |\beta_{\lambda}|^2\ ,\\
p_{ii}(t) &=& \frac{\sqrt[3]{2}}{12\pi^3 a^4} \sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty \omega_\lambda \nonumber\\ \label{density2}
& & \times \left[|\beta_{\lambda}|^2-\frac{m^2 a^2}{2\,\omega_\lambda}\left(|u_\lambda|^2 - \frac{1}{\omega_\lambda}\right)\right],\\
p_{ij}(t) &=& \frac{p_{ii}(t)}{2} \hspace{4mm} {\rm for} \hspace{4mm} i\ne j\ , \label{density3}
\end{eqnarray}
where $i, j = 1, 2, 3$.
Note that the pressure is not isotropic in our case. It would be isotropic only for the simplest choice of the three-torus metric ${\rm diag}(a^2, a^2, a^2)$.
\section{Evolution of the three-torus universe}
In order to calculate the particle production rate, we first have to know how $a(t)$ evolved in time. Our case is different from the usual FRW cosmology, in which $a(t)$ is the scale factor and can be rescaled by an arbitrary number. For a three-torus universe $a(t)$ has a physical meaning -- it describes the size of the universe at a given time $t$. Recent analyzes (see, \cite{Aneesh} and references therein) set a lower bound on its present value of $a(t_{\rm univ}) \gtrsim 6 R_H$, where $R_H$ is the Hubble radius today. Let's therefore assume that the current size of the three-torus universe is,
\begin{eqnarray}
a(t_{\rm univ}) = 10\, R_H \approx 10^{27} \ \rm m \ .
\end{eqnarray}
Table I shows the estimated timeline, the size of the universe and the total energy density during different epochs in the evolution of the universe.
For each epoch the total energy density is uniquely determined by the expansion rate through the Friedmann equation,
\begin{eqnarray}
\left(\frac{\dot{a}}{a}\right)^2 = \frac{\rho_{\rm tot}}{3 M_p^2}\ ,
\end{eqnarray}
where the reduced Planck mass $M_p \simeq 2.4 \cdot 10^{18} \ \rm GeV$.
Using the formulae for $a(t)$ for different epochs, we can evolve $a(t_{\rm univ})$ back in time and find its value at any particular instance in the past.
Observational data suggest that we currently live in a dark energy dominated universe, where the energy density is roughly constant and the expansion is exponential. It was preceded (at $t \lesssim 10 \ {\rm billion \ years}$) by a matter dominated era with the size of the universe increasing like $t^{2/3}$. Before the matter era (at $t \lesssim 70000 \ {\rm years}$), radiation was driving the expansion like $\sqrt{t}$. It is believed that before the radiation epoch there was a brief period of inflation ($10^{-35} \ {\rm s} \lesssim t\lesssim 10^{-33} \ {\rm s}$), an exponential expansion resulting from a constant energy density. The inflationary energy density in table I was estimated adopting $72$ e-folds of inflation and assuming that it ended at $t \approx 10^{-33} \ {\rm s}$.
The expansion rate in the pre-inflationary era is unknown. However, in the case of a three-torus universe it might have a natural explanation. As mentioned in the introduction, a compact topology results in the appearance of Casimir energies of existing fields. The full formulae for the Casimir energies in a three-torus universe for an arbitrary set of shape moduli was derived in \cite{FW}. For a real scalar field with mass $m \ll 10^{15} \ {\rm GeV}$ the Casimir energy density before inflation for our choice of metric is,
\begin{eqnarray}\label{CE0}
\lefteqn{ \ \rho_{\rm Cas}(a) \ =\ -\frac{2}{(2\pi)^4}\frac{1}{a^4}\, \Bigg\{ \ \frac{\sqrt{3}}{2^{2/3}}\frac{\pi}{12}+\frac{2^{1/3}}{3^{3/2}}\,\frac{\zeta(3)}{\pi}+ 2^{1/3}\frac{\pi^2}{360} }\nonumber\\
& & \hspace{-2mm}\!\!+\,\frac{2^{11/6}}{3^{3/4}}\!\!\!\sum_{n_2, n_3=1}^\infty \left(\frac{n_3}{n_2}\right)^{3/2}\cos\left(\pi\,n_2\,n_3\right)
\,K_{3/2}\!\left(\sqrt{3}\,\pi \,n_2 \,n_3\right)\nonumber\\
& & \!\!\!\!\!\!+\!\!\!\!\!\sum_{n_2, n_3 = -\infty}^\infty\!\!\!\!\!\!\!'\ \ \ \sum_{n_1=1}^\infty \cos\!\Big[\tfrac{2}{3}\pi n_1 (n_2\! +\!n_3)\Big]\sqrt{\tfrac{2^{5/3}}{3}(n_2^2\!-\!n_2 n_3\! +\!n_3^2)}\nonumber\\
& & \ \ \, \times \, \frac{1}{n_1}\,K_1\!\left(\tfrac{4\sqrt{2}}{3}\pi n_1\sqrt{(n_2^2-n_2 n_3 +n_3^2)}\right)\Bigg\}\ ,
\end{eqnarray}
which can be written as,
\begin{eqnarray}\label{Cas}
\rho_{\rm Cas}(a) = -\frac{\kappa}{a^4}\ ,
\end{eqnarray}
where $\kappa\simeq 5 \times 10^{-3}$. In a general case, this formula includes also a factor corresponding to the number of degrees of freedom for a given field and an additional minus sign for fermions. Interestingly, the Casimir energies at $a \ll 1/m$ satisfy the same equation of state as radiation, i.e.,
\begin{eqnarray}
p_{\rm Cas}(a(t)) = \frac{1}{3}\, \rho_{\rm Cas}(a(t))\ .
\end{eqnarray}
Therefore, if there were more fermionic degrees of freedom ($n_f$) than bosonic ($n_b$) and Casimir energies dominated the total energy density before inflation, the universe would expand according to $a(t) = a_{0} \sqrt{t}$, with the total energy density given by,
\begin{eqnarray}
\rho^{\rm tot}_{\rm Cas}(a) = \frac{(n_f-n_b)\kappa}{a^4}\ .
\end{eqnarray}
Surprisingly, if we choose in our case $(n_f-n_b)\approx 20$, we obtain the total Casimir energy density at the time when inflation started,
\begin{eqnarray}\label{condition2}
\rho^{\rm tot}_{\rm Cas}(a(t_{\rm inf})) \approx \rho_{\rm tot}(t_{\rm inf})\ ,
\end{eqnarray}
where $a(t_{\rm inf})$ is the universe size at the beginning of inflation and $\rho_{\rm tot}(t_{\rm inf})$ is the total energy density of the universe during inflation,
both of which where estimated before independently of the Casimir energies through the evolution back in time. Of course, the required value of $(n_f-n_b)$ which satisfies condition (\ref{condition2}) strongly depends on the inflationary parameters.
\begin{figure}[t]
\centerline{\scalebox{1.45}{\includegraphics{figure_1.pdf}}}
\caption{\footnotesize{Size of the three-torus universe as a function of time, assuming $a(t_{\rm univ}) = 10\, R_H$.}}
\end{figure}
\begin{figure}[t]
\centerline{\scalebox{1.45}{\includegraphics{figure_2.pdf}}}
\caption{\footnotesize{Total energy density in the three-torus universe as a function of time.}}
\end{figure}
Another interesting observation concerning the three-torus topology is that assuming the current size of the universe $a(t_{\rm univ}) \approx 10\,R_H$ and a pre-inflationary expansion $a(t) = a_{p0} \sqrt{t}$, the evolution back in time yields the size at Planck time $a(t_p) \approx l_p$, where $l_p$ is the Planck length.
Note that an evolution from the Planck size at Planck time to ten Hubble radii at present time wouldn't be possible if we assumed a universe with a closed topology, since then the curvature term contribution would entirely dominate the total energy density during the early stages of the universe evolution.
The plot of the size of the universe $a(t)$ corresponding to the values from table I is given in figure 1. A similar plot for the total energy density is shown in figure 2.
We note that a similar calculation to the one presented in this paper can be done assuming a different pre-inflationary expansion.
Knowing the shape of $a(t)$, we can now numerically solve equation (\ref{Bog}) for the Bogoliubov coefficients and then use formulae (\ref{number}) and (\ref{density}) to calculate the number density and energy density for the gravitationally created pairs of scalar particles of mass $m$. Our results can be easily generalized for other types of particles by adopting the appropriate form of the stress-energy tensor. We will perform the calculation for three different masses: $m_1=10^{9} \ \rm GeV$, $m_2=10^3 \ \rm GeV$, and $m_3=10^{-3} \ \rm GeV$, without the zero mode first, and then computing its contribution as well. In our calculation we will be using natural units, i.e.,
\begin{eqnarray}
2\cdot10^{-16}\ \rm m \ \approx \ 1 \ {\rm GeV^{-1}} \ \approx \ 7\cdot 10^{-25}\ \rm s\ .
\end{eqnarray}
We will also assume that there is no back-reaction of the created particles on the background evolution.
\section{Analytical results for nonzero modes}
In order to fully understand the numerical solutions it is very helpful to derive their analytical behavior in two regions: $t \ll 1/m$ and $t \gg 1/m$. In contrast to \cite{Zeldovich,Starob}, we choose not to specify the initial conditions at the singularity, but at the Planck time, since the physics at earlier times is unknown,
\begin{eqnarray}\label{init}
\beta_\lambda(t_p) = 0\ , \ \ \ \dot{\beta}_\lambda(t_p) = \frac{\dot{\omega}_\lambda(t_p)}{2\,\omega_\lambda(t_p)}\ .
\end{eqnarray}
However, we note that for the nonzero modes the solutions are insensitive to the value of $t_0$ at which we impose those conditions, as long as we look at the region $t \gg t_0$.
Let us first consider the case $m t \ll 1$ and focus only on the pre-inflationary epoch, for which we adopted $a(t) = a_{p0} \sqrt{t}$.
With the additional assumption $m a \ll 1$ the largest contribution to the sum (\ref{number}) comes from terms with small $\lambda_i$. Thus, we can assume $\lambda_i t \ll a$, in which case the solution to equation (\ref{Bog}) is given by,
\begin{eqnarray}\label{nn}
\beta_{\lambda}(t) \approx \frac{\sqrt{\omega_\lambda}}{2 (\tilde{t}_{ij} \lambda_i \lambda_j)^{\sfrac{1}{4}}}- \frac{(\tilde{t}_{ij} \lambda_i \lambda_j)^{\sfrac{1}{4}}}{2\,\sqrt{\omega_\lambda}}\ .
\end{eqnarray}
After plugging (\ref{nn}) into (\ref{number}), the particle number density is,
\begin{eqnarray}\label{nden}
\hspace{-10mm}n(t) &\approx& \frac{1}{(2\pi a)^3} \sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty\!\!\!\!\!\!\!\!\!\!' \ \ \ \ \frac{\left[\omega_\lambda - (\tilde{t}_{ij}\lambda_i\lambda_j)^{\sfrac{1}{2}}\right]^2}{4\, \omega_\lambda (\tilde{t}_{ij}\lambda_i\lambda_j)^{\sfrac{1}{2}}}\nonumber\\
&\approx & \frac{m^4 a}{128 \pi^3} \sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty\!\!\!\!\!\!\!\!\!\!' \ \ \ \ \ \ \frac{1}{(\tilde{t}_{ij}\lambda_i\lambda_j)^{2}}
\ \simeq \ \frac{m^4 a}{250}\ ,
\end{eqnarray}
where the prime excludes the zero mode.
The calculation of the energy density and pressure in the region $m t \ll 1$ cannot be performed with the same assumption $\lambda_i t \ll a$, as now terms with large $\lambda_i$ contribute significantly. However, for $m a \ll 1$ we have $|\beta_\lambda| \ll 1$ and $\alpha_\lambda \approx 1$. With equation (\ref{coupled}) we can approximate $\beta_\lambda(t)$ by,
\begin{eqnarray}
\beta_\lambda &\approx& \frac{m^2}{2 \,\tilde{t}_{ij}\lambda_i\lambda_j}\int_0^t a(t') \,\dot{a}(t') \nonumber\\
& & \hspace{10mm}\times \exp\left(-2 i \frac{(\tilde{t}_{ij}\lambda_i\lambda_j)^{\sfrac{1}{2}}}{a(t')}\, t'\right) dt'\ .
\end{eqnarray}
Using this result to rewrite (\ref{density}), we arrive at the energy density for the created particles during the pre-inflationary era,
\begin{eqnarray}\label{rrho}
\rho(t) &\approx& \frac{m^4 a_{p0}^4}{64 \pi^3 a^4} \sum_{\lambda_1, \lambda_2, \lambda_3 = -\infty}^\infty\!\!\!\!\!\!\!' \ \ \ \ \frac{1}{(\tilde{t}_{ij}\lambda_i\lambda_j)^{\sfrac{3}{2}}}
\int_0^t dt_1 \int_0^t d t_2 \nonumber\\
& & \times\exp\left[-2 i (\tilde{t}_{ij}\lambda_i\lambda_j)^{\sfrac{1}{2}}\frac{1}{a_{p0}}\left(\sqrt{t_1}-\sqrt{t_2}\right)\right]\ .
\end{eqnarray}
The biggest contribution in equation (\ref{rrho}) comes from summing the terms with large $\lambda_i$. It turns out that we can approximate our three-torus by a three-sphere of radius $\sqrt[6]{2}\, a$, for which it is possible to perform the sum over $\lambda$'s. Equation (\ref{rrho}) takes the form,
\begin{eqnarray}\label{rrho2}
\hspace{5mm}\rho(t) &\approx& \frac{m^4 a_{p0}^4}{64 \sqrt[3]{2}\,\pi^3 a^4} \int_0^t dt_1 \int_0^t d t_2\nonumber\\
& & \times \sum_{\lambda = 1}^\infty\frac{1}{\lambda}
\exp\left[-2 i \frac{\lambda}{a_{p0}}\left(\sqrt{t_1}-\sqrt{t_2}\right)\right]\nonumber\\
& \hspace{-25mm}= & \hspace{-14mm} \frac{m^4 a_{p0}^4}{64 \sqrt[3]{2}\,\pi^3 a^4} \! \int_0^t \!\!\!dt_1 \!\!\int_0^t \!\!\! d t_2\log\!\!\left[\frac{1}{1\!- \exp\left[\frac{2 i}{a_{p0}}\!\left(\sqrt{t_1}\!-\!\sqrt{t_2}\right)\right]}\right].\nonumber\\
\end{eqnarray}
The double-integral above is real and positive. The resulting energy density for $m t \ll 1$ is essentially constant in time.
Using a similar approximation one can derive the formula for the pressure,
\begin{eqnarray}
p_{ij}(t) &\approx& \tilde{t}_{ij}\frac{\rho(t)}{3} - \tilde{t}_{ij}\frac{m^4 a_{p0}^2}{96 \pi^3 a^2} \Bigg\{ \frac{m^2 a_{p0}^2}{4} \int_0^t dt_1 \int_0^t d t_2\nonumber\\
& & \hspace{5mm}\times \,{\rm Li}_3\left(\exp\left[\frac{2 i}{a_{p0}}\left(\sqrt{t_1}-\sqrt{t_2}\right)\right]\right)\nonumber\\
& &\hspace{-16mm} - \, 2 \,{\rm Re}\int_0^t d t_1 \log\left[1- \exp\left(\frac{2 i}{a_{p0}}\left(\sqrt{t_1}-\sqrt{t}\right)\right)\right]
\Bigg\}.
\end{eqnarray}
A numerical check shows that for $m t \ll 1$ the pressure for the created particles is also almost constant and satisfies the ``quasi-vacuum-like'' equation of state, \begin{eqnarray}
p_{ij}(t) \approx -\,\tilde{t}_{ij}\,\rho(t)\ .
\end{eqnarray}
We will not go into the details of calculating the particle number or energy density in a three-torus universe for $m t \gg 1$, since this case is analogous to that of an infinite flat or closed universe, which was explored in detail in \cite{Starob}. Briefly summarizing, for $m t \gg 1$ all Bogoliubov coefficients $\beta_\lambda$ are roughly constant and particle creation doesn't occur. For a universe expanding according to $a(t)=a_0 t^q$, where $0<q\leq 2/3$, the number density and the energy density of the created particles behave in the following way,
\begin{eqnarray}\label{largen}
n(t) &\sim& \frac{m^{3-3q}}{t^{3q}} \sim \frac{1}{a^3}\ , \label{largen2}\\
\rho(t) &\sim& \frac{m^{4-3q}}{t^{3q}} \sim \frac{1}{a^3}\ ,
\end{eqnarray}
while the pressure \ $p_{ij}(t) \ll \rho(t)$.
\section{Numerical results for nonzero modes}
Having an analytical understanding of how the functions $n(t)$ and $\rho(t)$ behave for $m t \ll 1$ and $m t \gg 1$, in this section we discuss the full numerical solutions.
\begin{figure}[t]
\centerline{\scalebox{1.5}{\includegraphics{figure_3.pdf}}}
\caption{\footnotesize{Number density of the created particles for $m_1=10^9 \ \rm GeV$ (blue solid line). The green dashed line corresponds to the $m t \ll 1$ and $m a \ll 1$ approximation given by equation (\ref{nden}) and the orange dot-dashed line corresponds to the $m t \gg 1$ approximation given by equation (\ref{largen}).}}
\end{figure}
\begin{figure}[t]
\centerline{\scalebox{1.5}{\includegraphics{figure_4.pdf}}}
\caption{\footnotesize{Energy density of the created particles for $m_1=10^9 \ \rm GeV$ (blue solid line). The green dashed line corresponds to the constant density for $m t \ll 1$ given by equation (\ref{rrho2}) and the orange dot-dashed line corresponds to the $m t \gg 1$ approximation given by equation (\ref{largen}). For comparison, the total energy density of the universe is plotted in solid red.}}
\end{figure}
We first solve numerically equation (\ref{Bog}) and find $\beta_\lambda(t)$ for different sets of $\lambda_i$'s, with $\omega_\lambda(t)$ defined through equation (\ref{omega}). The initial conditions are chosen according to (\ref{init}). We then plug the calculated $\beta_\lambda(t)$ to equations (\ref{number}) and (\ref{density}), and in this way obtain the particle number and energy density.
Figure 3 shows the plot of the particle number density (in blue) corresponding to a mass of the created particles of $m_1=10^9 \ \rm GeV$. The green dashed line increasing like $\sqrt{t}$ is the $m t \ll 1$ and $m a \ll 1$ approximation given by equation (\ref{nden}). Since the particle mass is large, this approximation breaks down relatively quickly and the number density starts slowly decreasing. During the inflationary epoch, it falls down rapidly by many orders of magnitude. Particles of mass $10^9 \ \rm GeV$ are no longer produced after inflation. This is confirmed by fitting the line falling off like $t^{-3/2}$ (orange dot-dashed line) corresponding to the relation (\ref{largen2}).
\begin{figure}[t]
\centerline{\scalebox{1.5}{\includegraphics{figure_5.pdf}}}
\caption{\footnotesize{Same as figure 3, but for $m_2=10^3 \ \rm GeV$.}}
\end{figure}
\begin{figure}[t]
\centerline{\scalebox{1.5}{\includegraphics{figure_6.pdf}}}
\caption{\footnotesize{Same as figure 4, but for $m_2=10^3 \ \rm GeV$.}}
\end{figure}
Figure 4 shows the time evolution of the energy density for the created particles of mass $m_1=10^9 \ \rm GeV$. The energy density is nearly constant for $m t \ll 1$ and its value agrees with that from equation (\ref{rrho2}), represented by the green dashed line. The subsequent behavior of the energy density is similar as in the number density case -- following a mild decrease there is a rapid fall during inflation, after which the density continues to decrease like $t^{-3/2}$ (orange dot-dashed line), since particle creation no longer takes place. Note that the density of the created particles is small compared to the total energy density in the universe (denoted in figure 2 by the red solid line) at any given time.
Figures 5--8 show the number density and energy density for the created particles with masses $m_2=10^3 \ \rm GeV$ (figures 5, 6) and $m_3=10^{-3} \ \rm GeV$ (figures 7, 8). There are two qualitative differences compared to the previous plots. Because the particles are lighter, the conditions $m t \ll 1$ and $m a \ll 1$ hold also for later times and the plots match the approximations (\ref{nden}) and (\ref{rrho2}) (green dashed line) all the way until the inflation epoch. Secondly, particle creation continues after inflation and stops only at $t\approx 1/m$, which is confirmed by fitting the line (orange dot-dashed) going like $t^{-3/2}$.
\begin{figure}[h]
\centerline{\scalebox{1.5}{\includegraphics{figure_7.pdf}}}
\caption{\footnotesize{Same as figure 3, but for $m_3=10^{-3} \ \rm GeV$.}}
\end{figure}
\begin{figure}[h]
\centerline{\scalebox{1.5}{\includegraphics{figure_8.pdf}}}
\caption{\footnotesize{Same as figure 4, but for $m_3=10^{-3} \ \rm GeV$.}}
\end{figure}
We emphasize that although particle creation lasts arbitrarily long for light enough particles, their energy density is still negligible compared to the total energy density. For instance, if we wanted to have particles created today, we would need a particle of mass $m_{\rm light} \ll 10^{-42} \ \rm GeV$. From formula (\ref{rrho2}) the energy density is suppressed approximately by $m^4/a^4$. Taking into account also the huge decrease in energy density of the created particles during inflation, there is no way it can ever compete with the
total energy density of the universe.
\section{Zero mode}
Let us now consider the contribution of the zero mode. In this case all the formulae simplify significantly. Relation (\ref{omega}) becomes,
\begin{eqnarray}
\omega_0(t) = m\, a(t)\ .
\end{eqnarray}
Equation (\ref{Bog}) for the Bogoliubov coefficient reduces to,
\begin{eqnarray}\label{Bog0}
\ddot{\beta}_0 + \left(\frac{\dot{a}}{a} - \frac{\ddot{a}}{\dot{a}} + 2 i m \right)\dot{\beta}_0 - \frac{\dot{a}^2}{4 a^2}\beta_0 = 0\ ,
\end{eqnarray}
with the initial conditions,
\begin{eqnarray}\label{initiial0}
\beta_0(t_0) = 0\ , \ \ \ \dot{\beta}_0(t_0) = \frac{\dot{a}(t_0)}{2\, a(t_0)}\ .
\end{eqnarray}
The equation for $u_0(t)$ is,
\begin{eqnarray}\label{eq20}
\ddot u_0 + 3 \frac{\dot{a}}{a}\dot u_0 + \left(m^2+\frac{\ddot{a}}{a}+\frac{\dot{a}^2}{a^2}\right) u_0 = 0\ ,
\end{eqnarray}
where,
\begin{eqnarray}\label{initiial00}
u_0(t_0) = \frac{1}{\sqrt{m \,a(t_0)}}\ , \ \ \ \dot{u}_0(t_0) = i \,\sqrt{\frac{m}{a(t_0)}}\ .
\end{eqnarray}
Once equations (\ref{Bog0}) and (\ref{eq20}) are solved, the particle number density, energy density and pressure can be calculated using the simple relations,
\begin{eqnarray}\label{number0}
n(t) &=& \frac{|\beta_{0}|^2}{(2\pi a)^3}\ ,\\
\rho(t) &=& \frac{m |\beta_{0}|^2}{4\pi^3 a^3} \ ,\\
p_{ij}(t) &=& \tilde{t}_{ij}\,\frac{m}{12\pi^3 a^3} \left(|\beta_{0}|^2-\frac{1}{2} m a |u_0|^2 +\frac{1}{2}\right).
\end{eqnarray}
It turns out that equation (\ref{Bog0}) with the initial conditions (\ref{initiial0}) can be solved exactly for simple choices of $a(t)$. For instance, in the pre-inflationary era with $a(t) = a_0 \sqrt{t}$, the solution for a particle of mass $m$ takes the form,
\begin{eqnarray}\label{Leg}
& & \hspace{-7mm}\beta_0(t)= \frac{i}{2m} \,t^{\sfrac{1}{4}}\, t_0^{\sfrac{-5}{4}}\, e^{2 i m (t_0- t)}\bigg[U\left(\tfrac{5}{4},\tfrac{3}{2},2 i m t_0\right) \nonumber\\
& & \times \, L_{-5/4}^{1/2}(2 i m t)-\,U\left(\tfrac{5}{4},\tfrac{3}{2},2 i m t\right) L_{-5/4}^{1/2}(2 i m t_0)\bigg]\nonumber\\
& & \times \bigg[4\,
U\left(\tfrac{5}{4},\tfrac{3}{2},2 i m t_0\right) L_{-9/4}^{3/2}(2 i m t_0)\nonumber\\
& &\hspace{6mm} -5 \,U\left(\tfrac{9}{4},\tfrac{5}{2},2 i m
t_0\right) L_{-5/4}^{1/2}(2 i m t_0)\bigg]^{-1},
\end{eqnarray}
where $U(x,y,z)$ is the confluent hypergeometric function of the second kind, and $L^k_n(x)$ is the associated Laguerre polynomial.
In the limit $m t \ll 1$ the dependence of the Bogoliubov coefficients in formula (\ref{Leg}) on $t$ and $t_0$ is $\beta_0 \sim (t/t_0)^{\sfrac{1}{4}}$, which translates to,
\begin{eqnarray}\label{cond}
n(t, t_0) \sim \rho(t, t_0) \sim \frac{1}{t\,\sqrt{t_0}}\ .
\end{eqnarray}
Thus, setting initial conditions at a small enough $t_0$, one can have an arbitrarily large zero mode particle production at any given instance of time. As mentioned earlier, this situation doesn't occur for the nonzero modes, for which $\dot{\beta}_\lambda(t_0)$ is independent of $t_0$ for $m a \ll 1$.
However, since we don't know the physics before the Planck time, choosing $t_0 < t_p$ is not justified.
In the subsequent calculation we assume $t_0 = t_p$, just as in the case of the nonzero modes.
It turns out that also equation (\ref{eq20}) possesses an analytical solution for $a(t)=a_0\sqrt{t}$, given by,
\begin{eqnarray}\label{Leg2}
& &\hspace{-3mm} u_0(t) = \frac{\pi}{4(m a_0 \sqrt{t})^{1/2}} \Bigg\{Y_{1/4}(m t) \bigg[-2 m
t_0 J_{-3/4}(m t_0)\nonumber\\
& &
\hspace{12mm}+\left(1+2 i m
t_0\right) J_{1/4}(m
t_0)\bigg]+J_{1/4}(m t) \nonumber\\
& & \ \ \ \times \bigg[2 m t_0
Y_{-3/4}(m t_0)
-\left(1+2 i m
t_0\right) Y_{1/4}(m t_0)\bigg]\Bigg\}\ ,\nonumber\\
\end{eqnarray}
where $J_\alpha(x)$ is the Bessel function of the first kind and $Y_\alpha(x)$ is the Neumann function.
\begin{figure}[t]
\centerline{\scalebox{1.5}{\includegraphics{figure_9.pdf}}}
\caption{\footnotesize{Number density of the particles created through the zero mode for $m=10^3 \ \rm GeV$ (blue solid line), assuming $t_0=t_p$. The green dashed line corresponds to the $m t \ll 1$ approximation given by equation (\ref{cond}). The orange dot-dashed line denotes the $m t \gg 1$ approximation given by equation (\ref{approx}).}}
\end{figure}
\begin{figure}[t]
\centerline{\scalebox{1.5}{\includegraphics{figure_10.pdf}}}
\caption{\footnotesize{Energy density of the particles created through the zero mode for $m=10^3 \ \rm GeV$ (blue solid line), assuming $t_0=t_p$. The green dashed line corresponds to the $m t \ll 1$ approximation given by equation (\ref{cond}). The orange dot-dashed line corresponds to the $m t \gg 1$ approximation given by equation (\ref{approx}). The red solid line denotes the total energy density of the universe.}}
\end{figure}
Figure 9 shows the number density and figure 10 presents the energy density for particles of mass $m=10^3 \ \rm GeV$ created through the zero mode, assuming a full evolution of $a(t)$ given in table I, with the initial conditions set at $t_0=t_p$. In the region $m t \ll 1$ both the number density and energy density decrease according to (\ref{cond}), which is confirmed by fitting the line (green dashed) going like $1/t$. Because of choosing a small mass of the created particles, the fit matches the plot until the beginning of inflation, during which both the number density and energy density fall rapidly by many orders of magnitude.
The orange dot-dashed line corresponds to,
\begin{eqnarray}\label{approx}
n(t) \sim \rho(t) \sim \frac{1}{t^{\sfrac{3}{2}}} \sim \frac{1}{a^3} \ ,
\end{eqnarray}
i.e., no particle creation. It fits well the plot for $t \gtrsim 1/m$, which implies that for the zero mode particle creation also stops at $t \approx 1/m$. The energy density of the created particles is again small compared to the total energy density in the universe.\footnote{We note, however, that if $\rho(t) \ll M_p^4$ for a range of $t < t_p$ and the equations in this paper are still valid in that region, by assuming a small enough $t_0$ the energy density of the particles created through the zero mode might in general be large enough to compete with ordinary matter and radiation at some instance of time in the evolution of the universe.}
\begin{figure}[t]
\centerline{\scalebox{1.5}{\includegraphics{figure_11.pdf}}}
\caption{\footnotesize{Ratio of the pressure $p_{ii}(t)$ and the energy density $\rho(t)$ of the particles created through the zero mode for $m=10^3 \ \rm GeV$ assuming the initial condition at $t_0=t_p$.}}
\end{figure}
It is interesting to analyze the equation of state for the matter created through the zero mode, as it has significantly different properties than in the nonzero mode case.
Let us for a moment assume that the entire evolution proceeds according to the pre-inflationary expansion $a(t) = a_{p0} \sqrt{t}$. An analysis of formulae (\ref{Leg}) and (\ref{Leg2}) shows that for such a scenario,
\begin{eqnarray}\label{state}
p_{ij}(t) =
\begin{cases}
-\tilde{t}_{ij}\,\frac{1}{3}\rho(t) & \ \ \ \ {\rm for} \ \ \ m t \ll 1\ ,\\
\ \ \tilde{t}_{ij}\,\frac{1}{3}\rho(t) & \ \ \ \ {\rm for} \ \ \ m t \gg 1\label{state2}\ .
\end{cases}
\end{eqnarray}
Since $\tilde{t}_{ii} = \sqrt[3]{2}$ and $\tilde{t}_{ij} = 1/\sqrt[3]{4}$ for $i\ne j$, the created matter would have a ``quasi-accelerating'' equation of state for times $t \lesssim 1/m$. This picture, however, is significantly modified when we take into account inflation.
Figure 11 shows the the ratio $p_{ii}(t)/\rho(t)$ for the zero mode production of particles with mass $m=10^3 \ \rm GeV$ including the full evolution of the three-torus universe from table I. As expected from equation (\ref{state}), for the pre-inflationary epoch it has the form $p_{ii}(t)/\rho(t)=-\sqrt[3]{2}/3$ . However, it doesn't stay like this until $t \approx 1/m$ -- inflation itself changes the equation of state to $p_{ii}(t) = \rho(t) \sqrt[3]{2}/3$, and it remains this way for the rest of the evolution. This behavior seems generic for all masses of the created particles. An interesting fact is that for much shorter inflation times one could end up with an equation of state with $p_{ii}(t)/\rho(t)$ anywhere between $-\sqrt[3]2/3$ and $\sqrt[3]2/3$ at the end of inflation. However, such short inflation periods are not realistic.
\section{Conclusions}
In the present work we calculated the rate for gravitational particle creation in a three-torus universe.
We performed the calculation assuming the metric on the three-torus for which the shape moduli are stable. We adopted the current size of the universe of ten Hubble radii and estimated its full evolution in time. We argued that the Casimir energies might dominate the total energy density before inflation, resulting in the expansion of the universe like in the radiation era.
We then showed that there are two types of contributions to the particle production rate -- one from the nonzero modes on a torus, and the other coming from the zero mode.
The nonzero mode contribution is interesting because at early times it is characterized by a ``quasi-vacuum-like'' equation of state for the produced matter. The particle production itself continues until $t \approx 1/m$, after which it essentially stops. It turns out that the energy density of particles created through the nonzero modes is tiny compared to the total energy density in the universe at all stages of its evolution.
The production through the zero mode is more unique. The corresponding energy density of the created particles is very sensitive to initial conditions.
If we set those at the Planck time, the energy density of the particles is again small with respect to the total energy density of the universe. We showed that although the particles produced through the zero mode have a ``quasi-accelerating'' equation of state before inflation, they are described by a ``quasi-radiative'' equation afterwards.
\subsection*{Acknowledgment}
The author is extremely grateful to Mark Wise for stimulating discussions and helpful comments.
The work was supported in part by the U.S. Department of Energy under contract No. DE-FG02-92ER40701.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,373 |
Q: Including html parts in another html files I'm working on a "plain" HTML-CSS website. It contains several pages. I want some code to be included in all HTML pages. (All have a navbar at the top)
What is the best way to include that part of the code in all files in order to avoid repeating code?
I've tried creating a directory named "partials", there I added a file called header.html and then tried including it in a different file with PHP. like so:
<?php include "./partials/header.html" ?>
This is not working. Please advise me what to do.
Thanks!
A: From what you answer and ask on the reply's under your question I wonder if you are aware Php code only works when run on a server? You can create your own server environment locally using Xampp.
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**_Routledge Revivals_**
Gramsci's Historicism
First published in 1990, this book is a comprehensive study of Gramsci's _Quaderni_ , and gives the reader a penetrating account of the structure of Gramsci's thought. The author draws on many materials and sources, making accessible to the English-speaking reader a wide range of texts otherwise only available in Italian, French, Spanish, and Catalan. His book sheds light on Gramsci's basic philosophical and methodological principles, and will be useful as an introduction to Gramsci for students of political science, sociology, social science, history, and philosophy, as well as to scholars in the field.
'A great merit of Morera's book is that it does focus centrally on Gramsci's epistemology and on his relation to historicism. In doing so it also provides a clear and accessible guide to debates surrounding these questions in Gramsci's work and delivers one of the best available discussions of the various meanings of historicism in Gramsci's writings' – _Ali Rattansi, The Open University_
**Gramsci's Historicism**
A realist interpretation
**Esteve Morera**
First published in 1990
by Routledge
This edition first published in 2011 by Routledge
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
Simultaneously published in the USA and Canada
by Routledge
270 Madison Avenue, New York, NY 10016
_Routledge is an imprint of the Taylor & Francis Group, an informa business_
© 1990 Esteve Morera
All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers.
**Publisher's Note**
The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original copies may be apparent.
**Disclaimer**
The publisher has made every effort to trace copyright holders and welcomes correspondence from those they have been unable to contact.
A Library of Congress record exists under LC Control Number: 89005996
ISBN 13: 978–0–415–61584–6 (hbk)
ISBN 13: 978–0–415–61587–7 (pbk)
**GRAMSCI'S HISTORICISM**
**_A REALIST INTERPRETATION_**
ESTEVE MORERA
First published 1990
by Routledge
11 New Fetter Lane, London, EC4P 4EE
Simultaneously published in the USA and Canada
by Routledge
a division of Routledge, Chapman and Hall, Inc.
29 West 35th Street, New York, NY 10001
© 1990 Esteve Morera
All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers.
_British Library Cataloguing in Publication Data_
Morera, Esteve, 1946–
Gramsci's historicism : a realist interpretation
1. Italy. Marxism. Gramsci, Antonio – critical studies
I. Title
335.4'092'4
_Library of Congress Cataloging–in–Publication Data_
Morera, Esteve, 1946–
Gramsci's historicism : a realist interpretation / Esteve Morera.
p.cm.
Bibliography
Includes index.
1. Gramsci, Antonio, 1891–1937 – Views on history. 2. Marxian historiography. [1. Gramsci, Antonio, 1891–1937. Quaderni del carcere.] I. Title.
HX289.7.G73M67 1989
335.43'092'4 – dc19
89–5996
CIP
ISBN 0–415–03540–6
**CONTENTS**
Acknowledgements
Introduction
HISTORICISM
_Introduction_
_Varieties of historicism_
_Gramsci's historicism: a preliminary analysis_
_Conclusion_
A GENERAL INTERPRETATION OF GRAMSCI'S HISTORICISM
_Introduction_
_Gramsci's critique of sociology: some preliminary remarks_
_Gramsci's historicism_
_Conclusion_
HISTORY AND POLITICS
_Introduction_
_The relation between structure and superstructure_
_Gramsci's dual conception of politics_
_Conclusion_
CONCLUSION
Notes
Bibliography
Name Index
Subject Index
**Acknowledgements**
Special thanks are due to Frank Cunningham and Danny Goldstick. Without their helpful comments on several drafts of this book, the result would have been far less satisfactory. I would also like to thank Winnie Dobbs and Sholem Peliowski for their help and encouragement, as well as Chris Rojek and Claire Watkins of Routledge for their assistance. Finally, for her unwavering support throughout the production of this book, I owe my deepest appreciation to Alina Márquez to whom it is dedicated.
**Introduction**
In an article on the reception of Gramsci in the English-speaking world, Geoff Eley concludes: 'The philosophers have had their say. The historians should now take the stage'. This would be good advice, had Gramsci's philosophy been sufficiently clarified, explained, and evaluated. Although the literature on Gramsci is now quite voluminous, the bulk of interpretations has been devoted to political philosophy, political theory, and political practice. Yet, some of the fundamental philosophical issues that Gramsci broached in the _Prison Notebooks_ have only been dealt with in passing. Perhaps this is not a state of affairs altogether to be decried – Gramsci's philosophy may not be as influential or as profound as that of other Marxist thinkers. It is certainly not without many ambiguities and inconsistencies. If it deserves any serious attention, it is because his philosophical assumptions do preclude some interpretations of his thought in general, and support others. An important aspect of Gramsci's philosophy is its relation to the thought of Croce. Historians, intellectual historians at any rate, need a deeper analysis of Gramsci's philosophy if they are to assess his position in the development of Italian culture in the 1920s and 1930s.
A crucial issue in philosophical analysis of Gramsci's _Prison Notebooks_ is the elucidation of the concept of historicism, a concept that plays a vital role both in Gramsci's own thinking and in that of his interpreters. Unfortunately, and this is the main reason for disregarding Eley's advice, many commentators have simply assumed that the term 'historicism' has a generally clear and unambiguous meaning, and have proceeded to interpret Gramsci's prison writings on the basis of what they thought that meaning was. Thus, a variety of Gramscian historicisms have emerged. For some, historicism is the theory that only knowledge of history is knowledge – real theoretical, philosophical knowledge – and science is only understood as an aspect, a rather mundane one at that, of historical self-consciousness. Closely related to this view, there is the historicism that truth is relative to its historical conditions. For others, historicism is the theory that only history is real, and that nothing exists outside history. For still others, historicism is the rejection of any form of essentialism. Finally, many have thought that, if historicism means anything, it must be that the economy does not determine politics, or does not determine it fully. In short, 'historicism' has become an empty term into which one could put anything one likes as a powerful armour against everything one dislikes (such as materialism, economism, determinism, essentialism, etc.).
For the above reasons, the unspecified meaning of 'historicism' has also led to attributing to Gramsci's thought political theories of different stripes. Emphasis on the political character of history, on the negation of determinism, etc., leads to theories of political intervention which are different from the ones of those who have defended a Leninist Gramsci. However, whether Leninist or Crocean, scientific or humanist, realist or idealist, Gramsci's thought is now seen as one of the first, and one of the greatest, foes of economism, though there is no agreement on what his anti-economism is. In short, the lack of precise and extended analysis of the concept of historicism in the _Prison Notebooks_ has had a chameleon effect: Gramsci's theory has varied with the seasons, to paraphrase the title of Davidson's essay. Of course, most interpretations of the work of past thinkers undergo this process of adaptation to new intellectual fashions. The ambiguities necessarily present in any work, especially if it is a work that breaks new ground, are always open to competing interpretations and appropriations. In Gramsci's case, however, this is far more evident because of the unfinished character of the _Prison Notebooks_. We shall return to this presently.
Colletti has pointed out that there are two vastly different meanings of 'historicism'. There is, first, the historicism of Marx, which concerns 'history or science, that is, _sociology_ , or history of a socio-economic formation, of a _species_ or phenomenon-type, hence of _repeatable_ processes'. Second, there is an idealist historicism 'that today goes by Marx's name', which 'in practice, is reduced to relating a philosophy to the immediate historical milieu that has seen its birth: where the accuracy of historical judgement is identified precisely with the importance of singular and irrepeatable features that characterize that given milieu'.
In general, this idealist historicism finds its roots in Vico, Kant, and Hegel. Two main varieties of this form emerged in the nineteenth century: the German historical school, of Kantian pedigree; and the Hegelian school, whose principal figure is Croce. Both schools, however, can be traced back to Vico. Both emphasize liberty, rather than necessity, and hence, as their modern successors Dray, Scriven, and others do, they emphasize the decisions and values of historical agents. In both cases, philosophy, and in particular some ethical conception of social reality, takes precedence over empirical explanation. Whereas the Marxist form of historicism does not renounce scientific explanation, the second form embraces humanism: it denies the scientific character of historical studies and, in effect, rejects the theory of unity of scientific method. In place of the latter, it proposes a method of interpretation which wholly dispenses with the notion of causal laws. Since this idealist form is the one most often referred to as historicism, and because Croce exerted considerable influence on Gramsci, it will be necessary to explore in some detail both the main claims put forth by historicism and their relation to Gramsci's thought.
Any interpretation of the _Prison Notebooks_ is faced with two difficulties. First, the scope of Gramsci's thought is far too wide for any specialist to assess his contribution. He writes on philosophy, history, politics, and even grammar. Second, the _Prison Notebooks_ consist of 2353 pages of unfinished notes, with no apparent order or overall structure. These notes, most of which are very short, are often cryptic. Many inconsistencies were left, as Gramsci died only two days after being released from prison before he could revise and organize his prison labour into several monographs, as he had intended to do. Although some notebooks are devoted to more or less defined topics, Gramsci's thought tends to range over several interrelated areas. Given, then, both the scope of the notebooks, and their unfinished and inconsistent character, the interpreter is put in the difficult position of evaluating the relevance of many passages whose meaning is obscure and of dealing with topics of which he or she knows little. This is nevertheless necessary because one never knows where a revealing statement will be found. Above all it is of fundamental importance to read the complete text so as to obtain some insight into Gramsci's general outlook, as well as the weight he placed on different topics.
The contradictions present in the _Prison Notebooks_ make it difficult, if not impossible, to give a consistent interpretation that can account for every single relevant statement. This means that any interpretation will have to leave out some statement; that is, if one tries to verify one's own reconstruction of the _Prison Notebooks_ , one will inevitably find statements that falsify that interpretation. The difficulty faced by any commentator, then, will be that of choosing which statements to ignore; that is, one will have to be prepared to defend some view of the 'real Gramsci', as opposed to the mistaken Gramsci. This process, however, can be an arbitrary one. In what follows, an attempt is made to present one such real Gramsci, one that, it is hoped, will not be a totally arbitrary construction.
In view of the difficulties noted above, it is necessary to give some reasons for the choices made in this work. The method chosen to select texts and interpret them is quite a simple one. First, an attempt has been made to analyse Gramsci's use of the term 'historicist' and its cognates. Surprisingly enough, this has not been done by previous commentators. Fortunately, Gramsci gives some useful hints with regard to his intended meanings of 'historicism', meanings that, as we shall see in Chapter One, fall into four distinct, but interrelated, senses.
Second, care must be taken to interpret the meaning of fundamental terms such as 'immanence' and 'transcendence'. These terms have long standing in philosophical writings; Gramsci uses them in his philosophical analysis of historical materialism. Because these terms are laden with philosophical content that is often extraneous to Marxism, there is the possibility of carrying those contents into Gramsci's reconstruction of Marxism, thus giving rise to Husserlian variations, Crocean variations, etc. Again, fortunately, Gramsci provides some interesting hints about language, hints which remind one of Althusser's concept of 'symptomatic reading', and which allow the interpreter to avoid some too easy traps. Gramsci asserts that words are often used in a metaphorical sense, metaphorical because, although the word is the same, the concept is not: 'Often when a new conception of the world follows a preceding one, former language continues to be used, although it is precisely used only in a metaphorical sense'. This is not to be taken to mean that all 'discourse is metaphorical regarding the thing or sensible and material object indicated (or the abstract concept)' but that today's language 'is metaphorical with respect to the meaning and ideological content that words have had in preceding periods of civilization'. He then adds that historical materialism uses the term 'immanence' in a precise sense, a sense that is concealed 'underneath the metaphor' and whose definition is theoretical. Thus 'immanence', Gramsci contends, is not to be taken as expressing a form of pantheism, or in any other metaphysical or traditional sense. Historical materialism 'purifies the metaphysical apparatus of the concept of immanence and brings it to the concrete terrain of history'. As we shall see, the suggestion is that the meaning and function of the concept of immanence is not that of a speculative philosophical concept, but a historiographical one.
Furthermore, idealist philosophers, such as Croce or even Vico, use explanations of concepts such as 'Providence' or 'fortune', concepts that are speculative, but which point to real processes that must be clarified and understood. The methodological principle we must draw from these reflections is that Gramsci uses many of the terms commonly used by speculative philosophers, but he uses them to express different concepts. Identifying these new concepts is a necessary condition for interpreting Gramsci's philosophy. Gramsci's general procedure, one can infer from some of his remarks, is to take those fundamental terms as indications of real problems, to which he intends to give a real solution. At any rate, this is, for instance, his approach to some of Croce's theories, theories that point to real methodological problems, to which Croce only gave verbal, not real, solutions.
Third, Gramsci's uses of 'historicism' will be taken as areas of interpretation. This means that each separate use will be correlated with other relevant material in the _Prison Notebooks_. The result, it is hoped, will be an integrated reconstruction of Gramsci's concept of historicism, one that can serve as the philosophical basis of Gramsci's thought. By filling in the meanings of 'historicism' with the writings on historiography, sociology, and politics, some light will be shed on the structure of Gramsci's thought.
This method will permit us to discard as slips or confusions some of Gramsci's texts. Since the point of departure is Gramsci's own intended meanings of 'historicism', and since these meanings are specified in terms of his own writings on history and politics, the result will be a definition of 'historicism', and with it his most basic philosophical thesis, that is most consistent with the _Prison Notebooks_ as a whole.
In the first chapter of this work, and after a brief description of various forms of historicism, the four main uses of 'historicism' in the _Prison Notebooks_ will be elucidated. The contrast with both the German historical school and Croce will be immediately obvious, for Gramsci not only espouses (not without grave confusions) philosophical realism, but also a conception of historical laws, the necessary forms of transition of social forms, and the denial, described by him as humanism, of the transcendent origin of thought and of history. Because philosophical realism is a theory most often thought to be rejected by Gramsci, it will be necessary to emphasize his arguments in this respect. It is in this area that many of Gramsci's texts will have to be discarded as mere confusions or slips.
In Chapter Two, the four uses of historicism previously elucidated will be given some specific content. Hence, Gramsci's critique of what he calls 'sociology', as well as his writings on history and politics, will provide all the necessary materials. As it happens, his critique of sociology, apart from some general remarks, can be neatly fitted into four areas of theory that correspond to his four senses of historicism. Little will be added on the question of realism. The emphasis will be laid on his theory of the transience of social forms, which will uncover a general, though not always unambiguous, theory of historical necessity and a corresponding theory of historical time which bears some resemblance to that of Fernand Braudel.
The elucidation of Gramsci's notion of historicism brings to the fore a number of other important issues, issues which have already been amply discussed in the literature and to which little will be added in these pages. To the extent that Gramsci's historicism deals with some conception of the law-like process of social transformation, his contribution to the old questions of Marxist theory are prefigured by his general philosophy. In the third and final chapter a brief sketch of his theory of history and politics will be offered. Some of the questions that have focused debate on the Left today, such as the relevance and importance of class-analysis and the primacy of politics, will be reviewed in so far as they are pertinent to the analysis of Gramsci's _Prison Notebooks_. Although in some socialist circles the concept of final determination by the economy, and hence the importance of classes in history, has become a suspect theory, Gramsci continues to think of history within this model. He offers, however, some theory of the relative autonomy of politics, and hence of the possibility of political intervention in forms that are not exclusively class-bound, though they are generally subject to long-term determination by class-structure. For this reason, Gramsci remains a Marxist, though he offers a number of important insights and fruitful suggestions for the study of complex social wholes. Opposed to economism as he is, he is not opposed to a multi-causal conception of history in which classes are determinant in the last instance.
The effort to present a general interpretation of Gramsci's historicism and the consequences of this concept for Gramsci's theory of history and politics does not, and perhaps cannot, result in a reconstruction free from ambiguities. Gramsci's general thought seems clear enough; its details and implications, alas, are often a matter of conjecture. Given the unfinished character of his work, it is not always possible to offer more than sketchy outlines of the general arguments that can be culled from many disparate statements. Often, one has to find possible solutions to the problems of interpretation in the work of historians, political scientists, and sociologists, as well as philosophers. Thus Gramsci's thought will be clarified by translating it into a more modern language provided by the thinkers to whom reference will be made. This exercise in translation, however, must not be taken as an analysis of modern historiography nor as a history of Gramsci's ideas; its purpose is merely that of providing an interpretation of confusing terms and statements in the _Prison Notebooks_. It is, at any rate, useful to familiarize oneself with the language and modes of thinking of historians, for they speak the language closest to Gramsci's idiom.
Gramsci's dislike of philosophical speculation often led him to pose all problems as historical problems. This has sometimes led to the conclusion that even statements' truth-values are a function of their historical conditions. Our interpretation of Gramsci denies this. In so doing, a conclusion must be reached rejecting the view that Gramsci's historicism is absolute, as Croce's was, or that it subsumes every truth under the general category of historical truth, or that, for Gramsci, truth is simply a matter of the historical function of truth-claims. If there is anything absolute about Gramsci's historicism it is his claim that to explain history we need not have recourse to extra-historical entities such as Providence. The activity of human beings, their relations with nature and among themselves are all that is required to explain the process of social transformation. That Gramsci thought as a historian faced with the task of explaining socio-economic formations, from the mode of economic production to the process of the production of knowledge, does not entail that he denied truth-value's independence of history.
_Chapter One_
**Historicism**
Introduction
In the _Prison Notebooks_ , Gramsci claims that Marxism is an 'absolute historicism'. There are several possible interpretations of this claim, for the term 'historicism' has been used in different senses. Often, historicism is associated with epistemological or moral relativism. In general, historicism is thought to be essentially an idealist philosophy. There is no doubt that the origins of historicism are idealist; they are to be found in the works of Vico, Kant, and Hegel. Moreover, most historicists, such as Croce, Dilthey, Rickert, or Windelband, are clearly associated with either Hegelian or neo-Kantian philosophical schools. Thus, taking Gramsci's claim at face-value, as Althusser seems to do, one would be obliged to conclude that Gramsci is either a neo-Rantian or a Hegelian Marxist In general, Gramsci is thought of as a member of the Hegelian Marxist group of thinkers which included Lukács and Korsch. His Marxism, like western Marxism in general, is an attempt at reinterpreting Marxism with the aim of transcending economism, the theoretical positions of the Second International and, above all, of absorbing the lessons of Lenin's contribution as well as the events of the Russian revolution.
The western Marxism that originated out of those experiences seems to have emphasized the subjective element of historical materialism: class consciousness in Lukács, hegemony in Gramsci. As Alex Callinicos has pointed out, Hegelian Marxism, especially that of Lukács, attempted 'to reintroduce the concept of a transcendental subject into Marxism'. Of course, this subject became a class, rather than a pure ego. Nevertheless, the Hegelian interpretation of Marxism, with its emphasis on the concept of the identity of subject and object, proved unable to overcome idealism for it reduced social relations 'to forms of consciousness', at the same time that it gave primacy to ideological struggle in the strategy for overthrowing capitalism. Clearly, Gramsci seems to fit this pattern quite well. His historicism might be interpreted as the doctrine that asserts 'that scientific theories... have not truth-value independent of the circumstances of their formulation'. The transcendental subject, in Gramsci's case, is historicized, but it nevertheless acquires the status of a philosophical category. Seen in this light, Gramsci's theory of hegemony is the equivalent of Lukács' concept of class consciousness. Gramsci's other general claim, namely, that Marxism is an absolute humanism, seems to confirm this interpretation of his thought.
If we take this interpretation of Gramsci as a credible one, then the emphasis commentators place on his philosophy of praxis as the activity of the will to solve historical problems seems justified. In this case, Gramsci's Marxism is rightly construed as the theory of the primacy of political action, and in particular, a theory of the cultural aspects of that action. In short, seen in this light, Gramsci's reconstruction of Marxism is an anti-determinist, perhaps voluntarist, reduction of Marxism to a humanism in which the political action of groups to preserve or to assume hegemonic status takes the form of the activity, both theoretical and practical, of a historicized transcendental subject. His 'historicism', in essence, is no more than the recognition that the transcendental subject is not a fixed, immutable entity, and that, as a consequence, all activity, both practical and theoretical, will reflect the historicity of the subject. One could go further than that, and claim, as Gramsci does at one point, that the object of both practical and theoretical activity is not independent from the subject.
This historicized transcendental subject, however, poses a conundrum, for how are we to understand the process of the historicization of the subject of history? Does the subject have an essence that is itself historical and whose development determines the historical process? If this is the kind of theory of history that Gramsci espoused, how could he have maintained the primacy of the transcendental subject and claim at the same time that 'human nature is the ensemble of the historically determined social relations, which is an ascertainable historical fact'? An analysis of Gramsci's use of the term historicism suggests a very different theory. Gramsci uses 'historicism' in several senses; one can, however, isolate four distinct, but interrelated, uses of this term in the _Prison Notebooks_. It seems that many interpretations of Gramsci emphasize but one such use, that of historicism as humanism. In the following pages I shall attempt to present the groundwork for a new interpretation of Gramsci's historicism. To do this, I shall first give a descriptive account of the roots of historicism and its two main schools, the German historical school on the one hand, and that of Croce on the other. Second, I shall analyse Gramsci's use of the term 'historicism'. This analysis will immediately disclose the vast differences between Gramsci's thought and the philosophy of other historicists.
Varieties of Historicism
Today, due to the great influence of logical positivism on the social sciences, historicism is not a popular theory. Even within western Marxism, historicism seems to be firmly rejected by such influential writers as Althusser. It has been conceived, by both its defenders and its detractors, as an anti-scientistic theory of history. Its origins are to be found in the reaction against both rationalism and empiricism as it developed during the Enlightenment and after. More recently, it has also been opposed to some aspects of positivism, as is well exemplified by Croce's thought as well as that of Collingwood, William Dray, and Michael Scriven. The philosophical seeds of historicism, or rather, of the various currents which are usually referred to as historicism, were sown by Vico and Kant.
In his _Principles for a New Science_ , Vico set out to establish the foundations of a scientific history that would investigate 'the common nature of nations'. The nature of nations, however, was not understood in terms of some immutable elements or final essence that would underlie the variety of existing nations, but in terms of their genesis. 'The nature of things', Vico wrote, 'is none other than their origin in a certain time and in a certain manner'. The method of the new science could not be thought of as a geometry of nations, taken as aggregates of simple natures; rather, this method had to establish the principles for the study of 'nations in their progress, states, decadence, and end'.
The foundation of the genesis and development of nations, Vico contended, was to be found in the human mind. His principles were intended to produce a history of human ideas which in turn would provide the elements for a 'metaphysics of the human mind'. To fulfil this project, Vico proceeded to study myths and legends, which he believed contained real descriptions of the past cast, however, in the language of imagination. Myths are the first form taken by the human mind; they contain 'civil truths, and for this reason they are the history of the first people'. Myths are cast in what Vico called 'imaginative universals', which are precursors of the true universals of philosophy and science. The interpretation of myths would therefore furnish the first materials for the study of 'modifications of our own minds'.
The results of the history of the modification of the mind would in turn furnish the materials for a deeper study. The aim of the new science is to unravel the apparent disorder and to penetrate the amorphous mass of historical detail in order to bring to light 'an ideal eternal history'. Vico's grand design, then, was aimed at understanding history, in particular at understanding the thread of necessity underneath the apparent accidental occurrence of historical events. In a passage that anticipates Adam Smith's concept of the hidden hand, or Hegel's cunning of reason, Vico argues that 'men love mainly their own utility', but Providence uses the self-interest of individuals to preserve human society. The deeper sense of history, the ideal eternal history, is the history of Providence which 'so ordered things human according to this eternal order'. It is appropriate, then, to think of the new science of history as 'a rational civil theology of divine providence'.
The science of history, is, for Vico, superior to any other science, including geometry. The reasons for this claim are to be found in his epistemology. Both in his _Delia Antichissima_ and in his _New Science_ , Vico stresses the identity of _verum_ and _factum_. This identity is based on a distinction between _inlelligere_ (understanding) and thinking, where the former is far superior to the latter. Vico compares _intelligere_ to 'reading perfectly', for in the same way that reading is the gathering of words and the ideas signified by them, 'understanding is the gathering of all the elements of a thing in order to form a perfect idea of the thing'. But gathering the elements of things is the same as making the things, and hence the perfect knowledge of a thing can only be had by he who makes it, or, what is the same, by he who constructs the thing out of its elements. Hence, the truth of things is known by their maker and it is to be found in the making or genesis of them.
For Vico, this means that God alone, as creator, can understand the nature of all things. Human beings must be satisfied with thinking about the world. Thinking is also a gathering of the elements of things, but it is considerably limited. As maker of things, God can understand both the internal and the external elements of things, whereas human beings can only read the external elements and cannot hope to gather the internal ones. For this reason, human beings cannot attain understanding of the nature of the universe, they cannot have a science of nature. Unfortunately, Vico does not give any precise analysis or definition of the external and internal elements of things. However, in the _New Science_ , he claims that understanding of history is possible because man makes history or, more precisely, because the genesis of history, its internal elements, are to be found in the human mind. This allows the historian to penetrate beyond the appearances, the manifold events and accidents of history, and to tap the modifications of the mind that are the inner essence, the creative power which alone explains history. Vico's claim to the scientific character of his historiography is based on this contention that the historian can know the modifications of the mind which are the inner aspects of history. Knowledge of them is clearly superior to knowledge of the external aspects, and since the study of nature cannot ever reach the inner aspects of natural things, historical knowledge is superior to the natural sciences. In this, we can already see the beginning of what was to become a crucial point for a school of historicists, namely, the distinction between _Natuvurissenschaften_ and _Geisteswissenschaften_.
There seems to be an inconsistency in Vico's thought between his claim for human agency in history and the metaphysics of Providence he espouses. Nevertheless, three essential points of his thought played an important role in the development of historicism: first, the distinction between the internal and external elements of things; second, the belief in the ideal nature of history, with the consequent emphasis on cultural and intellectual history; third, the doctrine that the nature of things is to be found in their genesis. Support for the first two theses was drawn from the philosophy of Kant. The distinction between noumena and phenomena, and the analysis of the third antinomy, provided an interpretation of the distinction between the internal and external elements of history that proved essential in the development of German historicism.
On the traditional interpretation, Kant's solution of the third antinomy, the conflict between freedom and causality, relies on his distinction between the intelligible world, or noumena, and the spatio-temporal world, or phenomena. Causality is the category that regulates the temporal succession of events, hence it belongs wholly to the phenomenal world. Freedom, or the causality of freedom as he calls it, is the sphere of spontaneous action, and it is intelligible in this creation. Freedom belongs to the world of noumena. An action, seen from the point of view of its effects in the sensible world, must be 'in conformity with all the laws of empirical causality'. But from the point of its origin, it 'is not to be looked for in the causally connected appearances', for it 'has in its _noumenon_ certain conditions which must be regarded as purely intelligible'.
Kant himself, in his writings on history, considered human action from this double perspective. He considered human actions to be determined by universal laws in so far as they were the appearances of the freedom of the will. History, in so far as it is the narration of these phenomena, seeks to find the laws of human action. However, in so far as the actions themselves are an expression of freedom, the drama of history is time charged with moral significance. This conception of history became the basis of the anti-naturalist doctrine of the separation of the method of the natural sciences from that of the cultural sciences. The historicist's emphasis on the distinction between _Naturwissenschaften_ and _Giestestvissenschaften_ , which Iggers thinks is 'the core of the historicist outlook', is thus the culmination of a process of thought whose essence is the understanding of history as a moral rather than a natural process. The German historical school tended to ignore Kant's dual analysis of history, as both noumena and phenomena, and to emphasize the inner meaning, or the noumena as the essence that historical knowledge was to capture.
Two main features characterize the German historical school: the first is the critical method developed by Ranke; the second is historicism. The critical method, which Ranke taught in his seminars at the University of Berlin, was essentially a canon for rigorous empirical research. The emphasis of this method lay in the careful study of documents, their authentication and criticism, and the interpretation of the findings. Its motto is to be found in the Preface to Ranke's _Histories of the Latin and Germanic Nations_. He wrote that the task of the historian is not to judge the past, but to show how it really was ( _wie es eigentlich gewessen_ ). This aspect of the German historical school has constituted a positive contribution to historiography. At times, however, it has been interpreted as the view that history should dispense with philosophical or theoretical considerations, and focus on the narration of a carefully researched and well established mass of details. The temptation of empiricist narrative was always close to the German historicist.
The second characteristic of the German historical school was historicism. From Humboldt to Dilthey, Rickertand Meinecke, the painstaking accumulation of facts was viewed as a necessary but external aspect of historical writing: it was concerned with the phenomena of history. Interpretation, understanding or hermeneutics was to penetrate the inner core of history. The inner core was, for most historicists, constituted by moral values, often conceived as a metaphysical reality which manifested itself through the drama of individuals, nations, cultures, etc., of the historical process. The narrative would set out the details of this drama, while understanding would fathom the inner meaning of history. In Dilthey's words, the phenomena of history become 'the subject matter of the human studies when we experience human states, give expressions to them and understand these expressions'. The phenomena perceived by the senses, the description of events, are merely the signs of an inner content. This conception of history is clearly connected to both Vico and Kant, although it focuses on moral values rather than Vico's notion of the development of the mind.
Since the real subject-matter of history is the inner meaning, not the phenomena as perceived by the senses or described in documents, historians must develop a proper method for understanding or interpreting this inner meaning, a method that would not be subject to the 'new bondage' of science. Their arguments centred on what they perceived to be the essential difference between natural science and history. Rickert was perhaps the most successful in formulating this difference. Natural science, he argued, is nomological, that is, it is primarily concerned with establishing regularities, patterns, or laws in events. Individual natural events are taken as instances of general concepts, but not as expressions or signs of an inner meaning. Consequently, no value is attached to them. In contrast, the human sciences are ideographical: they must seek to understand the uniqueness, the value or meaning of historical phenomena. Historians, then, must proceed to interpret the evidence culled from documents so as to arrive at an intuitive understanding of the historical past. In short, intuitive understanding 'must recognize some inner content from signs received by the senses'.
But how is this intuitive understanding possible? How can the historian of the present penetrate into the inner reality of the past? The best answer was probably the one provided by Dilthey. He conceived historical reality as the objectification of the mind, such that one could look at historical events as 'a manifestation of the mind in the world of the senses'. Hence, 'what is around us helps us to understand what is distant and past'. For this to be possible, however, the experience we transfer into the events of the past 'must be permanently and universally valid for man'. Historical understanding, then, is seen as the 'rediscovery of the I in the thou'. In short, it is because of the identification between the mind of the present, embodied in the mental structure of the historian, and the mind of the past, objectified in the phenomena of history, that historical understanding is possible.
One of the consequences of this approach is that, in general, historicists deny the existence of historical laws. Because laws, they contend, are regularities concerning types of events, they can only be formulated where events are repeatable. The inner aspects of historical events are not repeatable, hence no laws applying to them can be formulated. The actions of human beings, as opposed to physical events, are not subject to causal laws; they are, if anything, the expression of freedom'. In this vein, Ranke asserted that 'historical writing traces the scenes of freedom'. Necessity is not denied; it is identified with 'that which has already been formed and cannot be overturned again' by Ranke, and with the natural aspects of human life by Dilthey. According to the latter, the historian may use scientific laws to establish facts, that is, to accumulate and describe the external details of human history. In this, as Rickman points out, his argument is not unlike Popper's who argued that because the whole historic process is a unique event, no laws of historical development can be formulated or tested, though other laws, such as those of psychology and biology, can and must be applied to the study of history.
Along with the conception of historical laws, historicists rejected the conception of a constant human nature and, in particular, the rationalist version of this conception. For them, it was history, not some inherently rational human nature, that was to be taken as 'the only guide to an understanding of things human'. Furthermore, they also dismissed natural law theories that played such an important role in the intellectual upheavals of the eighteenth century. As a consequence, historicists rejected any claim to absolute or trans-historical values based on some conception of either human nature or reason. Instead, they stressed the need to understand the value and meaning of historical deeds and to judge them in terms of their own inherent values, rather than from the standpoint of standards external to the context of their origin.
This stress on the inherent value of all historical deeds, coupled with the rejection of absolutist thinking, leads to the conclusion that it is not possible to judge historical epochs or cultures, or to attribute a higher value to any of them. In general, most historicists tended 'to approach ideas and values not in terms of absolute norms of truth or good, but as expressions of a specific age, culture, or people'. The paradox of this view is that while it may be more tolerant than views based on a conception of absolute values, it can also lead to hardly defensible extremes. For instance, Meinecke held that 'nothing can be immoral which comes from the innermost, individual character of a being', and therefore, 'the seeming immorality of the state's egoism for power can be morally justified'.
This view, as many came to recognize, is itself, or easily leads to, moral and epistemological relativism. Some historicists, however, attempted to avoid it with the argument that all individual values are partial manifestations of a metaphysical reality from which they derive their meaning. Thus, the apparent chaos of actual historical phenomena was, for them, the revelation 'of a fundamental and meaningful unity that unfolded itself in history'. The meaning of any specific event is a function of that unity. For Dilthey, 'the category of meaning designates the relationship, inherent in life, of parts of a life to the whole'. This may seem to avoid relativism. However, the emphasis on the experience of individuals and on the ability of the historian to relive this experience in the present may very well bring relativism in through the back door; for there will be as many pasts as historians' experiences of past deeds, with no universal criteria for assessing competing claims. This theory, which Croce was to reformulate in his concept of 'contemporary history' is one of the essential methodological claims of the German historical school, and perhaps also one of its fatal flaws.
The unravelling of the meaning of history, it was hoped, could in turn provide the foundation for a rational politics. This, as Iggers claims, was a reversal of the Enlightenment's views on the relationship between history and political science. Now history was to be the queen of the sciences, as metaphysics had been before. It was both the study of the past as it had really been, and the main source of ideas for the active politician, aloof and engaged at the same time.
Politically, the majority of German historicists were liberal moderates. Most of them were deeply interested in the German question of the nineteenth century, and some participated in political organizations that shaped the unity of Germany. Generally, they disliked Bismark, but in the end most of them were not too opposed to his policies, as they tended to be suspicious of the value of democracy.
It is possibly in the conception of the state that German historicists came closer to Hegel. As Iggers argues 'German historians and political theorists from Wilhelm von Humboldt to Friedrich Meinecke almost a century later were willing to view the state as an ethical institution', consequently they tended to view history as 'the interplay of great powers' and they neglected the social and economic issues as well as the mass organizations whose importance must have been quite evident in the age of industrialization and revolution. Historicism then, showed a double face, for on the one hand it had attempted to establish historiography on a more solid foundation, while on the other it became an ideology. Its dependence on a metaphysics of moral value and its denial of historical laws, as Cruz has argued, made it impossible to periodize history. As a consequence, the capitalist system could no longer be seen as one more period whose end would necessarily come. More specifically, 'historicism provided a theoretical foundation for the established political and social structure of nineteenth century Prussia and Germany'.
In its distrust of sociological generalizations and historical laws, its rejection of both abstract theories and of natural law, German historicists proposed what in reality amounts to an approach for the study of all social phenomena: the historical or genetic approach. As Ortega y Gasset put it in his study of Dilthey, it is because 'human reality is evolutionary and its knowledge must be genetic', that social phenomena must be studied with the historians' methods. However, the historicists' appeal to a metaphysical reality meant that the very substance of the historical process itself, the order of values whose partial manifestations constituted the inner reality of history, was beyond the historian's grasp. This betrayed the historical approach, for ultimately, history had to be subordinated to metaphysics or to ideology. To avoid relativism, German historicists had to appeal to a supra-historical reality, and thus subordinate history to metaphysics, a predicament that denied their aspirations for history as the master science. On the other hand, if they gave up the supra-historical moral world, they easily fell into ethical and epistemological relativism, casting some serious doubt on the validity of their works.
As we saw earlier, Vico's conception of history was also based on a metaphysical reality, namely Providence. The difference, however, was that Vico conceived of Providence in developmental terms. The emphasis on development was in reality more in tune with the historical nature of social reality than the appeal to a supra-historical order of values. This emphasis on process and development was taken up by Hegel who conceived of history as essentially a dialectical process. Although German historicists rejected Hegel's conception of history because it was too determinist for their taste, it can be argued that, in fact, some features of Hegel's view of social reality are historicist.
As we have seen, German historicists viewed values as expressions of an age or culture. In a similar vein, Hegel took all forms of consciousness, including religion and philosophy, to be subject to a dialectical process of development. The _Phenomenology of Spirit_ can be understood as an ambitious attempt to understand the process of history as the dialectical unfolding of forms of consciousness. The process is dialectical in that it is impelled by the limitations and contradictions with which each stage in the process is fraught Thus, in order to understand a philosophical concept it must first be placed in the context of its historical genesis as well as in relation to the totality of concepts. These two notions, the historicity of consciousness and the concept of totality, are central to Hegel's thinking.
Marx can also be said to be a historicist thinker inasmuch as he stresses the historical character of forms of consciousness and social forms, at the same time as that he denies their natural or absolute character. The conservatism inherent in the German historicists is explicitly rejected by Marx. His conception of dialectics is directed against speculative conceptions of a metaphysical essence of history, at the same time as it attempts to theorize the necessarily transitory character of social processes. In the 'Afterword' to the second German edition of _Capital_ , Marx stated his view of a rational dialectical in opposition to the mystified form which glorified the existing form of society. He wrote that his dialectic 'regards every historically developed social form as in fluid movement, and therefore takes into account its transient nature no less than its momentary existence'.
This view has important consequences for the social sciences. Marx often criticized the analysis of social phenomena of other thinkers on the grounds that their methodology was faulty. For instance, in the _Grundrisse_ , Marx advanced some revealing criticisms against Mai thus' theory of overpopulation
His conception is altogether false and childish (1) because he regards _overpopulation_ as being _of the same kind_ in all the different historic phases of economic development; does not understand their specific difference, and hence stupidly reduces these very complicated and varying relations to a single relation, two equations, in which the natural reproduction of humanity appears on the one side, and natural reproduction of edible plants (or means of subsistence) on the other, as two natural series, the former geometric and the latter arithmetic in progression. In this way he transforms the historically distinct relations into an abstract numerical relation, which he has fished purely out of thin air, and which rests neither on natural nor on historical laws.
Marx is rejecting sociological abstractions that relate two series of phenomena without attempting to trace their relationships to the totality of the historical process. This form of sociological abstractions ignores that overpopulation is 'a historically determined relation' and that the same phenomenon, overpopulation, can have very different causes, as well as very different effects, in different historical periods. Looking merely at the two series – geometrical progression of population and arithmetical progression of food – without taking into consideration 'the inherent conditions of population', is simply looking at the phenomena externally. Marx's own wording, by contrasting 'inherent conditions' to Malthus' 'external checks', reminds us of the internal/external distinction made by Vico and by German historicists. The meaning of this contrast, however, could not be more different. Marx does not trace the distinction on the basis of the meaning or value inherent in every social event, but rather on the basis of the network of historical relations and laws that explain concrete historical situations. In Marx's case, the meaning of overpopulation is to be understood in terms of its relations to the whole of a historical period, in terms of its origins and its effects, and its occurring in a given economic structure.
Similar considerations can be found in other works by Marx and Engels. For instance, in a footnote in _Capital_ , Marx argues that Smith and Ricardo give little importance to the form of value, not only 'because their attention is entirely absorbed in the analysis of the magnitude of value' but because of a reason that lies deeper: they fail to understand, fail to take into consideration 'its special historical character', in other words, they treat this (the capitalist) mode of production as one eternally fixed by Nature for every state of society and overlook that which is the _differentia specifica_ of the value form. In short, they are guilty of producing abstract theories, that is, theories that are not grounded on the historically determined structure of a society. The meaning or value, that is its origin and effects, its relations to the whole of the concrete society, is different in different historical epochs. Marx's analysis is an attempt to grasp the concrete, the historically specific, not the sociological abstraction based on the relations between isolated phenomena.
Marx's methodological injunction has as its necessary basis a view of reality which is well summarized by Engels in his overview of Hegel: 'All that exists deserves to perish'. That is, all reality, and social reality in particular, is becoming a process. On these grounds, Engels argued that all successive historical systems are only transitory stages in the endless course of development of human society from the lower to the higher. Furthermore, 'each stage is necessary and therefore justified for the time and conditions to which it owes its origins'. The significant point in Engels' and Marx's view is that the various stages of development, the different social phenomena, are not just viewed as filled with value in themselves, but as being rational (the real is rational) in so far as they accord with historical necessity. Thus, knowledge of society is at its best when it can place the phenomena under study in the line of development that makes it necessary. This means that sociological abstractions such as those given by Malthus have very limited value. Furthermore, the historical knowledge proposed by Marx and Engels rejects the historicist view of the individuality of historical events and hence their ultimate unintelligibility other than in terms of a metaphysical reality that confers value on them. The study of history is not the study of the inner value of social forms, but the study of a natural process; 'natural', that is, in the sense that it does not depend on a transcendent sphere of being. Rejecting transcendence, Marx and Engels proposed a theory of history that would begin with a real premiss, that is, 'the existence of living human individuals'.
The concept of historical laws on which Marx and Engels' historicism depends is essentially different from the positivist concept of law as the regular conjunction of discrete events. For historical materialism, historical laws are founded on the existence of social structures rather than on the regular conjunction of similar events. The latter is a consequence of the former; for this reason their capacity to explain is rather limited. Because Marx takes the view that society is a totality or system regulated by structural relations, he is not committed to the empiricist atomism for which necessity is a function of the constant conjunction of events. For Marx, necessity arises out of the relations that constitute the social system. On this account events are system-dependent; their full description is not possible without reference to the system. Understanding the concrete, then, requires not only knowledge of the specific features of a phenomenon and the circumstances that surround it, but also its function in the set of relations in which the phenomenon occurs. From this point of view, the question of the typicality or uniqueness of events is a false alternative. Marx insists on the need for a clear understanding of the historical specificity of social phenomena, which may have different significance under different historical conditions. This means that historical events are both of a kind and unique at the same time. From an abstract point of view, overpopulation is overpopulation, a phenomenon of a certain type. From Marx's point of view, overpopulation is assessed in terms of its insertion on a network of historical relations. The typicality of an event, then, is not given by its intrinsic properties; rather, it is determined by both its intrinsic properties and its function within a system.
The principle of the transience of all entities implies that mental constructions, forms of consciousness, are also transient. Writing on the categories of political economy, Marx stated that 'the same men who establish their social relations in conformity with their material productivity, produce also principles, ideas and categories in conformity with their social relations'. As the social relations change, so do the forms of consciousness. The implication is that ideas must be analysed in their historical circumstances. They are not, as they are for idealist thinkers, independent of material reality or manifestations of some transcendent order of being, but a necessary aspect of the material process of history.
To summarize, historical materialism is a form of historicism in so far as it asserts the transient character of reality, both material and spiritual. The study of social formations must be founded on a methodology and a conception of laws and causal relations that are appropriate to a process of change. Furthermore, an important aspect of historical materialism is its conception of the relation between material reality and ideas, as well as the concrete manner in which this relation affects the historical process itself. In _The German Ideology_ , Marx and Engels conceptualized this relation as one of reflection: the ideas of an epoch are the reflection of its material reality. However, the theory of reflection can be understood in at least two different ways. First, it can be conceived as an epistemological theory which proposes that reflection is a causal relationship between matter or material processes and ideas. Complementing this theory, the claim is sometimes advanced that all matter is characterized by a property akin to reflection. Second, the theory of reflection can be taken as a historical hypothesis concerning the correspondence between socio-economic formations and forms of consciousness. In this second sense, the hypothesis is a methodological principle for historical investigation, and it can be said to apply to the long-term relationship between structure and superstructure, but not necessarily to short-term fluctuations of the superstructure. Incidentally, Gramsci is mainly concerned with developing this second view, although he often refers to theories as reflections of reality.
We have so far reviewed various forms of historicism that emerged in Germany during the nineteenth century. It was in Italy, however, that a non-Marxist historicism found one of its most able exponents. Benedetto Croce, whose thought exerted considerable influence on Gramsci, endeavoured to elaborate a thoroughly historicist philosophy both in his philosophical work and in his historical work. Croce's thought, like the thought of German historicists, was a reaction against the dominant positivism of the end of the nineteenth century, a positivism that in the words of Rossi was interpreted 'as the naturalist reduction of man and of his world to his biological environmental conditions, and as the negation of the methodological autonomy of historical research'. However, whereas German historicism originated in Kantian philosophy, the absolute historicism of Croce relied on Hegel.
Like the German historicists, Croce at first emphasized the unique character of historical phenomena. This was the reason, he argued in an essay written in 1893, why history could not be a science and should therefore be classified under the general concept of art. However, in developing his system of philosophy, Croce found it necessary to modify his conception of history. The basis for this new conception was laid in his _Logic_. He argued that 'all features of History are reduced to the definition and identification of history with individual judgement'. The judgement is a synthesis of the individual subject and the predicate, which is a universal concept. In other words, the judgement is a synthesis of representation (narrative) and concept (philosophy), or intuition and thought. For this reason, history is more than narration; in so far as it necessarily employs concepts, it is also philosophy. As he put it in his _Theory and History of Historiography_ , the true subject of history is not the individual subject; it is the predicate, the universal. The historical judgement 'determines the universal by individualizing it'. Hence, 'the subject of social and political history is _Culture, Civilization, Progress, Liberty_... that is, a universal'.
Although the starting points of German historicism and Croce's absolute historicism differ, there is nevertheless an important similarity. Both place ideas, rather than real human beings or social relations, at the centre of history. Croce's history of the predicate, brings to mind a passage in Marx's _Critique of Hegel's Philosophy of Right_. Hegel is taken to task for giving the idea 'the status of a subject'. As Marx puts it, 'the important thing is that Hegel at all times makes the Idea the subject and makes the proper and actual subject, like "political sentiment" the predicate'. The universal predicates that, for Croce, constitute the subject of history, are not simply partial manifestations of a transcendent order of values, as they were for the German historicists, but the essence of a dialectic whose development is the historic process. Thus, whereas for Dilthey, for instance, meaning is constituted by the 'relationship... of parts to the whole', in Croce the whole itself is defined by an essential moment, a centre that unifies the dialectical process. The consequence is that history is not seen as the individual development of unique cultures, but as the ordered process of the unfolding of a fundamental universal. As Rossi observes, whereas 'for Meinecke the recognition of individuality implies... the impossibility of reducing history to rationality, for Croce it results in the thesis of the immanent rationality of historical development'.
However, this 'immanent rationality' of the historical process does not mean that causal laws are applicable to history. Croce rejects causality in history just as much as German historicists did. The search for causes, he argues, leads to an infinite regress, which he finds unacceptable. The infinite regress can be stopped in two different ways. (1) By restricting our search to the sphere of proximate causes. This, however, is not satisfactory, for it is not always easy to determine where to stop the search; that is, the chain of causal links must be arbitrarily cut. (2) By seeking a transcendent end of history. This is also unsatisfactory to Croce, for he sees history as being immanently rational.
Croce's theory of the real subject of history coupled with his theory of pseudo-concepts, already entails the negation of historical causation. For Croce, a pseudo-concept is a general concept, whose 'content is furnished by a group of representations, or even by a single one'. As a consequence, the concepts of the natural sciences are not pure concepts: they are pseudo-concepts. Since the real subject of history is the universal pure concepts that are individuated in particular subjects and events, and since these concepts are 'ultrarepresentative', that is, they are not grounded on groups of representations, it is impossible that causation could be applied to what Croce considers to be the real subject of history. Causation belongs to the realm of individual objects, or in theoretical terms, types of objects. Its application is limited to the realm of Croce's pseudo-concepts. Natural science, Croce argues, is a science of phenomena or facts, philosophy is the science of noumena, or values. Hence, science cannot know what Croce calls pure phenomena; but it does not deal with mere facts either. Natural science elaborates 'representative concepts, which are not intuitions or concepts, but spiritual formations of a practical character'.
The pure concept, in contrast to representative concepts, is one that has no basis in existing objects, although it can be exhibited in them. Croce's arguments, at times, come very close to Plato's. Indeed, perhaps the best example he offers is taken from Platonism. A pure triangle, he argues, is not to be found in reality; the concept of a 'triangle' then, is not a representative one, but a pure one. We do find in actual reality forms that approximate that of the triangle, or which exhibit the general shape of the triangle. They are understood as triangles because the pure concept is already in our possession, prior to the observation of such forms. The identification of the historical subject with pure concepts introduces an element that is pre-experiential, although it can be observed at work in the phenomenal world. For Croce it is the pure concept, the philosophical aspect of history, that renders history rational, something more than the haphazard flow of events. Nevertheless, history is not pure knowledge, precisely because in it the pure concept is always embodied in institutions or in human beings who have practical needs and who are often motivated by passion. Real history, then, does not exemplify the pure concept perfectly; it is, rather, a dialectic of the practical and the ideal.
The unifying concept of all human production and experience is, for Croce as it was for Hegel, the concept of spirit. It is a unity which exhibits four distinctions. There are two basic forms of the spirit, the theoretical and the practical. These two forms, or activities, yield the four-fold distinction of reality into the true, the beautiful, the good, and the useful. The unity of these four is what he calls the circle of the spirit, which should not be taken as a dialectical unity, that is, a unity of opposites. In his essay on _What is Living and What is Dead of the Philosophy of Hegel_ , Croce takes Hegel to task for having 'conceived the link between these degrees dialectically'. A dialectical connection is, for example, the relation between true and false, but not that between false and good.
These distinctions are important for the understanding of history, because 'the human mind cannot think of history as a whole without distinguishing it, at the same time, into the history of deeds and the history of knowledge; into the history of practical activity, and the history of aesthetic production, of philosophical thought, and so on'. On an empirical basis, by introducing empirical concepts into its study, history may be divided into the history of the state, of the Church, of society, etc. But Croce stresses that it is a grave mistake to suppose that these pseudo-concepts have a 'constitutive character', an error that results in 'the positivist fixation to reduce history to a science (a natural science, that is)'. Historical pseudo-concepts, or empirical concepts, have only a 'subsidiary character', they are helpful, for instance, to 'divide the mass of facts and to regroup them for the use of memory'. The task of the historian, as opposed to the task of the chronicler, is to go beyond the mass of individual facts and to grasp the dialectic of the pure concepts. In a passage reminiscent of Vico's thought, Croce remarks that the philosopher, considering the spirit _sub specie aeterni_ , will grasp an 'eternal ideal history'.
The basic pure concept that Croce offers as the essence of the historical process, is the concept of liberty. He came to believe that the best definition of history that could be given is that history is 'the story of liberty', as was common with liberal historians of the period. It is as story of liberty that Croce conceived his _History of Europe in the Nineteenth Century_. In this work, Croce traces the struggle of the religion of liberty against other religions: absolute monarchy, radical democracy, communism, and Catholicism. In keeping with his theory of the historical judgement, the subject of his history is not the various parties that took part in the struggle, nor the victors and the vanquished, but liberty itself, liberty as the immanent force of history that, through the secular labour of philosophy, has finally become a permanent acquisition. This history, then, is an account of what he saw as the lessening of the distance 'between heaven and earth, God and the world, the ideal and the real'. The Hegelian shadow in this passage is quite evident, for Hegel, in the _Phenomenology_ , also envisioned the descent of God to earth or the emergence of the 'universal divine man, the community'.
In his _History of Italy_ , however, Croce presents a somewhat different historical dynamics; here, the two main conceptual poles are ethics and politics, or the ethical ideal of the creation of a unified Italy and the practical needs of building a country. These poles become personified in the historic Right and Left, and in the ruthless Sicilian prime minister Crispi and the liberal Giolitti. The theoretical basis of this dialectic is found in an essay entitled 'State and Church in their ideal sense and in their perpetual struggle in history' first published in 1931. In this essay, Croce argues that Ranke's dictum that 'history is always the history of the relations and of the struggle between the Church and State', is profoundly true. The truth in the dictum, however, is not about the institutions that bear the names of Church and state: these are two different forms of the state. It is, Croce argues, the opposition between 'consciousness and political action on the one hand and consciousness and moral action on the other' that constitutes the inner dynamic of history. This conception of 'ethico-political history' is what enables the historian to construct a history of 'full humanity'. It is indeed this conception of history that, for Croce, enables the historian to grasp the significance of the actual events in terms of the struggle to incarnate liberty, a struggle that is often embodied in the form of the antithesis between practical concerns and ideals.
As it has already been mentioned, this theory of history entails the unity of history and philosophy. This is so for several related reasons. First, in so far as the universal concept or the predicate of the historical judgement is the real subject of history, real historical knowledge will be attained by the analysis of pure concepts, i.e., by philosophy. Second, philosophy is itself history for it offers an analysis of the pure concepts whose dialectic is the historical process. Philosophy, then, is self-consciousness of the progress of ethical ideals, and it becomes the spring from which history flows. The identity of philosophy and history thus presents two aspects. Epistemologically, 'history is not possible without the logical element, which is philosophy; philosophy is not possible without the intuitive element, which is history'. Ontologically, the real ground of historical development, the real motor of history, is a dialectic of ethico-political concepts; consciousness of these concepts, as well as their analysis, is philosophy.
In so far as the 'intuitive element' is said to be historical, and furthermore, in so far as scientific concepts have a mere practical significance, natural science itself is subsumed under history. This is one of the most fundamental aspects of Croce's absolute historicism. As Rossi argues, 'this absorption of nature by history, and the consequent affirmation that historical knowledge is the only authentic form of knowledge, was... foreign to the development of contemporary German historicism'. Whereas the German historicists attempted to make a clear cut between the natural sciences and the cultural sciences, thus denying the positivist doctrine of the unity of method, Croce insists that all sciences are unified in history. This is not to be interpreted as a form of the doctrine of the unity of method. Croce is not claiming that the methods of history should be applied to physics or biology. His claim is that natural science does not count as a theoretical activity because its concepts are not pure concepts. Science can attain certainty; truth, however, can only be attained 'with the help of the principle of historical interpretation'. Because 'thought always thinks history', the full comprehension of reality by means of universal concepts, or truth, is made possible by taking scientific activity, and through it nature itself, as part of the spirit. The all-encompassing reality, then, is spirit, and true knowledge is the knowledge of the dialectic of the activity of the spirit. It is, as Rossi argues, Hegel's influence that 'leads Croce to interpret spiritual activity as an all-inclusive process, in whose circle the individual and the universal can coincide'.
A final note on the spirit and its activity. It seems fairly obvious that for Croce the subject of history is not, and cannot be, any individual human being or group of human beings. As he puts it, 'history, in this conception, as it is no longer the work of nature or of an extramundane God, so it is not either the work of the powerless, empirical, and unreal individual, whose work is interrupted at any moment; it is rather the work of that truly real individual that is the eternally individualizing spirit'. In short, it is not real, empirical, active men and women who make history; they, in fact, play out a history prescribed for them by the dialectic of spirit. The spirit is the subject of history, but it is not a transcendent being. It is rather an idealized version of humanity itself, which in practical terms reduces itself to, or incarnates itself in the great intellectuals, the men of vision, who can transform ethico-political ideals into practical institutions. Neither transcendent God or idea, nor empirical humanity, spirit lives in the vision of an elite of intellectuals; it is they, not the masses, who create history.
From the point of view of the writing of history, Croce argues that all history is contemporary history. The historian must be rigorous in his examination of documents. However, a document 'separated from life, is nothing but a thing'. What brings documents to life is the soul of the historian, the problems and interests he brings to the documents. These problems and interests are contemporary ones: they originate in the life of the present. For this reason, all history is contemporary history. In this sense, contemporary history is conceived as 'the crucible of interests by means of which certainty is transformed into truth', that is, the evidence culled from documents, certainty, is given an interpretation, the truth, whose philosophical basis originates in the life of the present. This is perhaps best exemplified in Croce's histories. In the Preface to his _History of Italy_ , Croce claims that it is not written with a purpose. Nevertheless, in reading it, one feels that Croce is attempting to show that Mussolini's attempt to revive a heroic age is a futile attempt, as empty as the exaggerated verbosity and sensualism of D'Annunzio's poetry. Similarly, in his _History of Europe_ , Croce is clearly defending a liberal conception of society, a conception that he sees threatened by both the fascists and the communists.
However, the contemporaneity of history may mean more than this. As Badaloni points out, there is a second sense of the term 'contemporary' to be found in Croce's thought. In this second sense, contemporary refers to the 'integral acceptance of the past as it realizes itself in the eternal present of the spirit'. In this second sense, the task of the historian is seen as one of understanding, not of judging the past. Indeed, history cannot discriminate between good and bad facts, progressive and regressive epochs. All facts and all epochs are productive in their own way, and 'the past does not live except in the present, as force in the present'. This living of the historical past in the present is a consequence of Croce's conception of the dialectic of the spirit as an eternal ideal history, which has been mentioned above. Indeed, the spirit is an eternal present so that its ideal history is not in time. This being so, it is difficult to see how human thought, which always thinks history, could grasp what is essentially beyond history, and how, for that matter, an eternal present could produce the fleeting life-and-death drama of history. Whereas in the first sense the temporal dimension of history is not denied, in this second sense Croce seems to affirm that the past is either non-existent or unimportant, for what really matters is the present life of the spirit.
This conception of history as philosophical truth to the extent that it reveals the pure concept of the spirit originates with Vico, but is not really different from the metaphysics of the German historical school. In both cases, the attempt to historicize all reality finds its limit in an eternal present. The major difference between these two forms of historicism is that Croce, under the influence of Vico and Hegel, paid more attention to the developmental aspects of history. Whereas for Dilthey, meaning was a function of the relation of parts to the whole, in Croce meaning is a function of a dialectic of the ideal and the practical in which liberty grows. In his later work, which is not considered here for it was not known by Gramsci, Croce began to question his former philosophical historicism. As Rossi notes, World War II and fascism made it very difficult for anyone to believe in the rationality of history. This questioning had a two-fold result: first, Croce began to develop a methodological historicism that would eliminate the Hegelian influence; second, he began to look at the human dimension of historical development.
Finally, Croce's historicism is quite evidently anti-democratic. As Kahn points out, Croce's philosophy does not 'escape from the realm of the mental cogitations of an intellectual elite'. Hence, in so far as philosophy is both epistemologically and ontologically primary in the historical process, no importance is accorded by Croce to the activities of masses of people. The ethico-political ideal of liberty, as it is consciously appropriated by philosophers, rather than classes or masses, is for Croce the substance of history as well as the source of its movement. In theory, the idea of liberty, as Croce warns, should not be confused with economic liberalism, for the latter is a proper economic principle, but not a proper ethical principle. The ideal of liberty is not to be confused either with the liberal party, which is a party among parties, without any prerogatives. In reality, however, Croce first supported the fascist movement until the murder of Matteoti in 1925, and then he became the soul and life of the liberal party. He wrote in his diary that the struggle for the liberation of Italy should follow the example of Garibaldi, thus implicitly rejecting the democratic republicanism of Mazzini.
In the broadest outline, the various historicist theories from Vico to Croce, attempted to offer an alternative to empiricist and rationalist approaches to the study of human reality. What they held in common was the need to give historical explanations for social phenomena; however, their conceptions of what constitutes a historical explanation were vastly different. The German historical school accepted a positivist conception of scientific law, but denied that history is governed by causal laws. The interior of history, the real substance of history, is the meaning that derives from a moral metaphysical reality, which is a reality beyond history. This noumenal reality is expressed or signified in the phenomena of the human world; partial knowledge of it is possible only by means of the hermeneutical method or understanding. Croce also rejected the conception of causal law in history, and, like the German historicists, emphasized the ideal meaning of history. The eternal life of the spirit, which only philosophy can grasp, albeit inadequately, is the real substance of history; it manifests itself in dialectical opposition to the practical needs of human beings, a process that is identical with the progress of liberty.
These idealist forms of historicism are characterized by the rejection of the unity of scientific method and by their anti-naturalism. In contrast, Marxism, which also seeks to understand the underlying realities of the historical process, is a realist and materialist theory of history. These underlying realities – the inner aspect of history – are not moral values or pure concepts; they are social structures whose base is to be found in the process of production. Marxism emphasizes the transient nature of all social forms, and seeks to understand specific phenomena on the basis of the social structure in which they occur; it does not deny the applicability of concepts of causality and of law to human phenomena, but it espouses a conception of them that contrasts with the empiricist view.
Because of the emphasis given to the historical explanation of all social phenomena, historicists have often been considered to fall into epistemological and ethical relativism. If values and ideas are functions of the historical conditions in which they emerge, then they change with changes in those conditions, and no possible evaluation of their value or truth in general is possible. However, not all historicists have been willing to accept this conclusion, and they have had to seek some way out of this predicament. It would seem, however, that idealist historicists, in confusing the conditions of knowledge or experience with the conditions of reality, have been unable to distinguish between the conditions under which knowledge or values arise and the justification of such knowledge or values.
Historicism, in its various and often vague senses, constituted Gramsci's intellectual background. We must now turn to his _Prison Notebooks_ , first to analyse his use of the terms 'historicism' and 'historicist', and later, in Chapter Two, to develop a general _interpretation_ of what he meant by this term. The use of the term 'historicism' alone will already suggest a marked contrast between Gramsci, on the one hand, and Croce, Hegel, and the German historical school, on the other.
Gramsci's Historicism: A Preliminary Analysis
The first issue that we must deal with is that of Gramsci's awareness of the development of historicism from Vico to Croce. There is no doubt that he knew Marx as well as Hegel and that he had read Croce extensively, as his frequent references to his work attest In fact, the _Prison Notebooks_ could be characterized as a sustained dialogue with Croce as well as an attempt to purge his own thought of Crocean influences. Croce's ascendancy over Italian culture, Gramsci felt, had to be opposed with an anti-Croce. Gramsci notes two main reasons why it was necessary to 'write a new _Anti-Duhring':_ (1) Croce's historicism was too speculative, not immanentist enough; (2) Croce was too obstinate in his opposition to historical materialism. Such a critique of Croce would be the first step towards the transformation of Italian culture; hence, besides its theoretical interest, the anti-Croce was conceived as having great practical significance.
Gramsci's knowledge of the German historical school was not as extensive, or as deep, as his knowledge of Croce or Marx. Apart from a few references to Weber, whose interpretative sociology is linked to the German historical school, there is only one work related to German historicism used by Gramsci. This is Ernst Bernheim's _Lehrbuch des Historischen Methode und der Geschichts-philosophie_ , first published in Leipzig in 1903. This work became a widely used textbook to teach the critical method of historical research initiated by Ranke. Essentially, it deals in great detail with historical methodology, authentication and critique of sources, and interpretation. Although Gramsci's direct knowledge of German historicism is limited, his indirect knowledge must not be ignored. For Croce's knowledge of German historiography was considerable, and he often wrote about, or commented on, individual German historicists. Thus we can take Gramsci's concern with the problem of the uniqueness of historical events and the possibility of theory, and with the question of the unity of scientific method, as evidence of his indirect knowledge of German historicism.
However, apart from Gramsci's knowledge of German and Italian historicism, the question that really matters is that of the extent of the influence that these theories had on his thought and his interpretation of Marxism. On this point, commentators are not in agreement. On the one hand, the most widespread interpretation of Gramsci maintains that he is a Hegelian Marxist. A variation on this theme is found in Finocchiaro's essay on 'Gramsci's Crocean Marxism' whose 'proof lends support to the Crocean character of Gramsci's thought in general'. On the other hand, a recent interpretation of Gramsci argues that 'what Gramsci calls "absolute historicism" is precisely the radical rejection of any essentialism and of _a priori_ teleology'. On this view, Gramsci would reject the theory that there is an element, such as the social relations of production, that determines all the other social elements; he would also reject the theory that history has any particular direction in, or end to which, it tends. Since Laclau and Mouffe maintain that 'all identity is relational', it would seem that they place Gramsci closer to Dilthey than to Croce.
For Dilthey the 'category of meaning designates the relationship inherent in life, of parts of a life to a whole', the various elements of reality have a unique and equal value. In contrast, for Laclau and Mouffe, the various elements are 'floating signifiers, incapable of being wholly articulated to a discursive (i.e. social) identity', so that the meaning or identity of elements is partially fixed by a 'practice of articulation'; different practices will produce different meanings. Despite what appear to be fundamental differences between Dilthey, or German historicism in general, and Laclau and Mouffe, they seem to agree in one thing: there is no privileged element, no essential feature that would confer identity to the whole by its relationship to the rest of the elements of that whole. The conclusions, both theoretical and practical, of this position are of great importance for social theory, and particularly for Marxism. For if there is not a privileged element, then history cannot be explained by appealing to any one particular element, be it classes, technology, or whatever. This demise of class-centred history, the rejection of class reductionism, has signalled, perhaps more than any other critique of Marxism, what is now widely claimed to be the crisis or even the death of Marxism.
Let us now turn to the analysis of Gramsci's _Prison Notebooks_ in order to define his own brand of historicism. The aim of this analysis is to lay the groundwork for the general thesis that Gramsci attempts to interpret some of the essential theories of Croce in a realist and materialist sense. In this, he did not always succeed, and thus we find in his _Prison Notebooks_ many passages that are still locked into the idealist view. Nevertheless, his historicism makes no sense unless one takes it as a form of dialectical realism. However, this alone does not account for Gramsci's thought His Anti-Croce and with it the Crocean influence accounts for only a portion, albeit an important one, of his re-interpretation of Marxism. Other important elements must also be considered. In what follows, an attempt will be made to clarify some of the fundamental theoretical questions that are linked to Gramsci's historicism.
A cursory analysis of Gramsci's use of the term 'historicism' and related terms, shows that he consciously attempts to define the term in opposition to speculative thought and to abstract rationalism; consciously, because in many instances he associates terms or expressions with the word 'historicism' which show the meaning he intended. This will allow us to identify four areas, as well as four theoretical positions, where the analysis of Gramsci's 'absolute historicism' is to be sought.
Historicism as transience
One of the terms most frequently associated with 'historicism' is 'transience'. In an argument that closely follows Marx, Gramsci states that whereas the pure economists speak of the determined market and its automatism as natural and eternal elements, the critique of political economy begins with the concept of the 'historicity' of the determined market. It is clear that in this passage Gramsci uses 'historicity' as transience, that is, he affirms the temporary character of economic institutions. Even the 'automatism' of the capitalist economic system, that is, the logic of capital or the laws of capitalist production, is said to be afflicted with transience.
Thought, or consciousness in general, is also said to be transient. This is not to be taken as a denial of the value of past philosophical systems: 'their transience is considered from the point of view of the whole historical development of the life-death dialectic; that they deserved to fall is not a moral judgement or one of objective "truth", but a dialectico-historical one'. Ideology, forms of social consciousness, are thus said to be influential within a defined historical time, which is not to deny that they have any value. The transitory character of forms of consciousness affects the philosophy of praxis itself. Gramsci states that it is implicit in Marxism as a whole, and in particular in the doctrine of the passage from the realm of necessity to the realm of freedom, that 'the philosophy of praxis conceives itself historicistically, that is, as a transitory phase of philosophical thought'.
It is important to stress that Gramsci's approach is that of the historian. He is interested in understanding the forms of development of a social whole, including science and philosophy. It is not an attempt at providing an epistemology. Confusion on this point may lead to some form of subjectivist interpretation of Gramsci. Alas, this sort of confusion did sometimes cloud Gramsci's own thinking. Some interpretations of Gramsci's theory take his historicism to be an epistemological theory or at least to contain 'a formidable epistemology'. There are, indeed, some epistemological theses in Gramsci's thought as we shall see presently, but one should not take as a defence of a general epistemological theory about what counts as knowledge or about what can be known, Gramsci's attempts to offer actual historical or political explanations from within a supposed epistemological framework never fully developed, much less defended, by him.
This aspect of Gramsci's historicism is in fact the rejection of all permanent elements in history. History is life and death, it is change. The social is ephemeral. As he puts it, movement 'is the organic mode in which historical reality manifests itself. This implies that the study of social phenomena must always take into account their fleeting nature; or that the study of society is a study of a temporal process. The problem that one needs to address is that of the forms of this temporal process, that is, the shape of transience itself. The second characterization of historicism that Gramsci gives provides us with some clues about the manner in which the historical process takes place.
Historicism as historical necessity
In discussing the adoption of the Spanish constitution of 1812 by the Neapolitans, Gramsci argues that the constitution was 'the exact expression of the historical necessity of Spanish society', and he suggests that the Neapolitan conditions may not have been very different from Spanish ones, and therefore the adoption of that constitution was not due to political mimesis or mental laziness, for it was 'more historicist than it seems'. In this context, it would seem that 'historicist' is equivalent to 'corresponding to historical necessity'. Other texts by Gramsci confirm this interpretation. True historicism, Gramsci writes in a critical note on Croce and Gioberti, cannot be equivalent to an arbitrary act of the will in choosing the elements of the present that will survive in the future. Whatever survives, as well as what may be generated in the dialectical process of history, 'will result from the process itself, it will have a character of historical necessity'. It is only through an adequate conception of historical necessity, which takes into consideration both the material premisses and the cultural level of society, that a 'historicist conception (and not a speculative–abstract one) of "rationality" in history can be attained'.
This meaning of historicism is the ground for the distinction between arbitrary acts or ideologies, and those that correspond to the movement of history. Thus, an ideology that does not 'correspond to the exigencies of a historical period' will 'more or less rapidly be eliminated from historical competition', although, due to special circumstances, it may become popular for some time. This distinction between 'historicist' and 'arbitrary' phenomena results in a distinction between what is historical and what is ahistorical. The distinction itself is entertained by some historians. For instance, Pierre Vilar refers to suicide as 'an ahistorical fact _par excellence_ , because it cannot, even within a society in a very grave crisis, exceed certain limits, take the character of typicality, become the cause'. It is a 'marginal fact' which does not become part of the 'causes-effects of the dialectic of history'. This distinction implies a conception of history in which certain types of phenomena have a fundamental causative, as well as explanatory, character. Historical necessity is, for Gramsci, the complex set of relationships that account for the historical process as a whole, but not necessarily for everything that happens in a society.
This use of 'historicism' as historical necessity contrasts with the anti-naturalist historicisms of both the German historical school and of Croce. First, it asserts that both actions and ideologies depend on some as yet unidentified elements which necessitate them. Second, it is necessity, rather than liberty or values, that defines Gramsci's historicism. Whether historical necessity can be interpreted in terms of causal laws will be discussed in Chapter Two. Also, we must consider whether the grounds on which historical necessity arises commit Gramsci to some form of essentialism such as the one discussed above.
Historicism as realism
Closely connected with the previous definition of 'historicist', Gramsci offers a third use of term. According to this, 'historicist' is synonymous with 'realist'. In a critique of Croce's and Gentile's interpretation of Hegel, Gramsci wonders whether they eliminated 'the most realist, most historicist part' of Hegel's thought, which constitutes the origins of Marxism. Again, on the relation between 'effectual reality' and what 'ought to be' in the thought of Machiavelli, he points out that in the creation of a new form of society, considerations about what ought to be are not founded on 'abstract and formal thought', but on the 'realist and alone historicist interpretation of reality'.
The first passage quoted above can be construed as a distinction between speculative elements in Hegel, emphasized by Croce and Gentile, and the elements based on a sound analysis of historical reality. The second passage points to 'political realism' in the sense that no major change in society is possible when the conditions for such change are not present. In this sense, 'realism' is in fact similar to, if not the same as, respect for what is 'in accordance with historical necessity'. However, there are still doubts as to whether this is to be interpreted as a realism in the philosophical sense. Nevertheless, in rejecting speculative thought in favour of sound historical analysis, and arbitrary actions in favour of those actions whose conditions are supported by historical necessity, Gramsci clearly rejects a conception of historical reality as dependent on a transcendent world as well as the view that the will can arbitrarily impose itself on reality and create a new world. This would indicate that Gramsci subscribes to the view of the stubborn independence of reality from consciousness, as well as to the view that the origin of ideas is to be found in the real historical world, not a supra-historical or a transcendental consciousness.
This interpretation of Gramsci may be surprising to many. It seems to be a widely accepted view that Gramsci was a subjective idealist, an anti-realist. I have already quoted a passage by Gallinicos which supports this view. Similar views are expressed by Gregor McLennan. He is prepared to accept Gramsci's account of the historical conditions of philosophy, but he claims that this 'does not commit us to his notion of _absolute_ historicism, especially when we recall Gramsci's idealist notion that the existence of the external world is dependent upon human cognition'. It must be admitted that one can find some passages in the _Prison Notebooks_ which justify this statement. However, one can also find passages that contradict it. Because this is a crucial philosophical issue, I am going to attempt to settle it now, before we proceed with further analysis of the term 'historicism'.
A clear indication of Gramsci's realism is found in a note devoted to the physics of infinitely small phenomena. He argues that if these phenomena 'cannot be considered as existing independently of the subject that observes them, they are not really "observed but, created'". And he adds that this theory is not only solipsism, but witchcraft. He also states that 'it is difficult to imagine that reality changes objectively with changes in ourselves, and it is difficult not only for common sense but also for scientific thought to accept this'. Given that knowledge is not definitive, 'it is difficult to avoid the thought of something real beyond this knowledge, not in the metaphysical sense of a "noumenon" or an "unknown God" or of "an unknowable", but in the concrete sense of a "relative ignorance" of reality, of something as yet "unknown", but which will be known some day when the "physical" and intellectual instruments of men are more perfect'. Although this passage might be taken to imply the non-realist theory of the identity of knowledge and reality, the previous quotation, as well as his belief that a theory such as the theory of the atomic structure of matter, although not definitive, is 'the reflection of an unchanging reality', suggests that objects of knowledge exist independently of the beliefs (desires, etc.) of knowing subjects and that it is possible for the latter to discover truths about such objects. On this interpretation, the difficulty in imagining that reality changes with us, which would include its changing with changes in our knowledge, could be taken as grudging surrender to realism, perhaps in a moment of weakness, on the grounds that it is difficult to admit the dependence of reality on cognition, however desirable that position may be. On this view, Gramsci's opposition to realism would be a kind of prejudice rather than a well-thought-out disagreement with it.
However, another interpretation of the text is also plausible. On this other view, Gramsci is performing what could be called a _reductio-ad-absurdum_ argument: it is not any contradiction involved in the negation of the independent existence of the external world, but rather the difficulty for both science and common sense to grasp such a world that shows the realist thesis to be true. In other words, cognition itself is contingent upon the independent existence of the external world. This argument, which is merely adumbrated by Gramsci, has recently been made by Bhaskar, who argues that 'it is a condition of the possibility of science... that such objects exist and act, as what may be termed the _intransitive_ objects of scientific inquiry, independently of their identifixation'. Besides this argument, Gramsci refers to Engels' claim that the materiality and objectivity of the world are proven by the history of science and technology, although it is questionable whether he understands such a proof in the same way as Engels.
In effect, Gramsci for the most part does not offer, nor was he too concerned to offer, a justification for realism. The point, however, is that at least some texts suggest a realist position. In those texts Gramsci's thought fulfils two conditions for philosophical realism: (1) the independent existence of the real; (2) the conception of knowledge as reflecting that reality, which involves a correspondence theory of truth. Further evidence for this interpretation is Gramsci's belief that historical materialism is 'the historical methodology most fitting to reality and to truth', which implies that our effort to know must be adequate to something distinct and independent from that knowledge, rather than reality having to fit knowledge. Gramsci thought that the historicist realism of Marxism, as opposed to the speculative ideology of other systems, was decidedly superior. It was the weakness of speculative philosophy which prompted bourgeois intellectuals to appropriate elements of Marxism in order to 'strengthen their conceptions and to curb their overwhelming speculative philosophizing with the historicist realism of the new theory'.
Although the texts analysed above strongly suggest that Gramsci was a realist, other texts, often quoted by commentators, point to a very different Gramsci, a non-realist Gramsci. It is useless to deny that such passages exist; they often appear within the same paragraph in which realist statements are found. The point that I wish to make is that Gramsci's intention was not to deny realism, but dogmatism, and that he was confused or misled by ambiguities in his use of terms such as 'objective'. We shall return to this below. The objection may be raised that there is no way of knowing Gramsci's intention other than by analysing his writings; but since his writings are unfinished and inconsistent, his intentions remain unclear at best. However, in a passage that refers to the genesis of historical materialism, Gramsci asserts that the only element of French materialism that the philosophy of praxis has kept is philosophical realism. Although the accuracy of this statement may be questioned, it is clear that Gramsci approved of realism. In the absence of any denial of this assertion in _Prison Notebooks_ , there is the strong presumption that, in spite of his inability to argue consistently with realism, he believed it to be a sound philosophical position to take.
A number of reasons may account for his confusions and inconsistencies. To begin with, the conditions under which Gramsci wrote his notes were not the most conducive for serious, consistent work. More important, however, Gramsci's inconsistencies may be the result of his attempt to avoid both empiricist materialism and idealism. In this respect, he assumed different positions against one or the other of the views he objected to for polemical reasons. In any case, he did not completely succeed in formulating an independent Marxist view of these problems. We have to interpret Gramsci, then, as undergoing a process of intellectual maturation which was interrupted by death soon after being released from jail, a process that, had it continued, might have resulted in a more consistent and clear argument for realism.
We must now turn to the anti-realist statements in the _Prison Notebooks_. It is important to note that these statements are often polemical, directed against empiricism, and that, for this reason, he often writes as if he were attacking the realist epistemological foundations some attribute to empiricism. One of the main claims made by Gramsci in these criticisms is that the concept of the objectivity of the external world has its origin in religion. Religion, he writes, has always taught that 'nature, the universe was created by God before the creation of men' and so human beings found it already 'defined once and for all'. Gramsci's main concern is not so much with the concept of objectivity itself, or more precisely, with the independent existence of external reality, as with the conservative and dogmatic use of this concept due to its articulation in a religious discourse. For religion, in particular the Catholicism that Gramsci knew, was not only conservative in its political practice, but in theory it posited a world made by a divine will superior to any human will, and hence unchangeable by human beings. In this conception of reality, men and women were reduced to actors playing their roles with no possibility of consciously overcoming oppressive inequalities. In fact, any rebellion against social reality was characterized as ungodly, as sinful, for it was said to be a transgression of divine law.
Gramsci's argument, then, is designed not so much to reject realism, as to understand it critically in order to dislodge it from any extraneous ideologies. To do so, Gramsci may have questioned, as a sort of exercise in methodological doubt, the conception of objectivity that is implied by realism, and may, furthermore, have been confused about his own procedure. That this is so seems to be suggested by his questioning the belief in, but not the fact of the reality of, the external world: 'What is the origin of this "belief and what critical value does it have "objectively"?'. Since in this passage Gramsci is concerned with questioning Bukharin's discussion of the question of the objectivity of the external world in a popular manual, a question that only elicits laughter from the general public, it cannot be taken to constitute a doubt on objectivity. Rather, it doubts its value in the effort to educate a public for whom the question is settled by religion. If anything, then, that question might reinforce, rather than weaken, religious beliefs. This, however, is not a denial of realism.
His attack on objectivity must be seen as a rejection of prevailing forms of culture, of a level of common sense which he feels is an impediment to progress. In fact, he sees that in 'common sense the "realist", materialist elements predominate, that is, the immediate product of crude sensation. This is by no means inconsistent with the religious element, far from it'. At the same time that he rejects this dogmatic and religious conception of reality, it is clear that, as the previous quotation indicates, Gramsci also objected to the empiricism prevalent in that conception of objectivity. The reason for this exercise is to be sought in what Gramsci thought about the unity and independence of Marxism. Following Labriola, Gramsci argued that Marxism is an original philosophy with no need of support from other philosophical systems. For him, orthodoxy is 'the fundamental concept that the philosophy of praxis is self-sufficient and contains in itself all the fundamental elements to construct a total and integral conception of the world'. Hence Gramsci's arguments must be understood as the attempt to sever philosophical questions both from religious ideology and from other philosophical systems, with the intention of developing a coherent and independent philosophy.
An independent philosophy need not deny whatever true theories other philosophical currents may have. But Gramsci thought that Marxism had to be developed systematically, not as an eclectic aggregate of truths. The importance of this is not merely theoretical, but above all practical and didactic. If Marxism had to 'give life to an integral, practical organization of society, that is, to become a total, integral civilization', it had to pose philosophical questions not merely in a way that could be shown to be objectively true, but in a way that could succeed in dislodging people's beliefs from ideologies or philosophical doctrines that were to be rejected. In other words, posing questions, developing theories, and making them assume the character of social forces is an exercise that must begin with the actual culture of the people to be persuaded. Failing to pose the questions in an appropriate manner may result in emphasizing undesirable elements of the old culture, thus subverting the new one. Marxism is not, nor was Gramsci, immune to extraneous influences. What in effect Gramsci argues for is an appropriate treatment of questions for educational purposes. Marxism must reject the commonsense approach to the question of the existence of the external world, even if they reach the same conclusions.
Extraneous influences, Gramsci thought, had resulted in a 'double revision' of Marxism. On the one hand, a number of pure intellectuals, such as Max Adler, had been 'absorbed by and incorporated into some idealist currents'. On the other hand, those thinkers in close contact with the masses had sought to overcome religious transcendence with 'the most crude and banal materialism'. In an attempt to regain the intellectual independence of Marxism, as well as the capacity to present an alternative hegemony, Gramsci embarked on his reinterpretation of Marxism. Hence his interest in the origin of philosophical concepts such as that of objectivity.
Gramsci's use of the word 'objective' is fraught with ambiguity. Because of this, he often produces fallacious arguments concerning the objectivity of the external world. There are at least five meanings of the word 'objective' in the _Prison Notebooks_. (1) 'being in itself; (2) 'permanent being'; (3) 'common to all men'; (4) 'independent of any point of view which is particular'; (5) 'definitively true'. Sense number one involves an ontological concept of 'objective', as meaning that which exists in itself and is, therefore, independent of its being perceived or known. Gramsci's concern with sense number two stems from his views of the transitory nature of social phenomena, to which he opposes the permanent existence (or permanent relative to history) of natural laws. In this sense, 'objective' is used in a similar sense to 'natural'. It is important for Gramsci to distinguish these two forms of existence, as it was for Marx, because he wanted to avoid any reductionism of social to physical phenomena, or any form of biological determinism. Not only was it necessary for him to reject any conception of capitalism as being natural or determined by physical or biological laws, but he was also concerned with some racist overtones of those social theories. It was argued by some Italian sociologists, including socialist ones, that the backwardness of the south was due to the natural inferiority of the southern peasants. Gramsci rejected this sort of explanation, as he did biological theories of crime, pointing out that they ignored the historical conditions for the backwardness in the south. Against the sense of 'objective' as 'permanent' Gramsci sometimes writes of historically objective', by which he means that social conventions are not natural or God-given; they are objective to the extent that they are appropriate for a given society. Senses number three and number four together are synonymous with 'impartial', as opposed to prejudiced by interests that could not be universally accepted. And finally, in sense number five, objectivity is a property of truth, the correspondence with what is real; Gramsci argues that, in fact, what we take as true or objective knowledge is not definitive, it is always subject to revision.
For our own purposes, it may suffice to distinguish two senses of the word 'objective'. 'Objective' can mean: (1) what exists as an object, be it a substance, property, fact, etc., independent of its being perceived or known, or ontological objectivity; (2) the veracity of thought, its correspondence with what exists objectively in sense number one, or epistemological objectivity.
Some of Gramsci's arguments, which provide the basis for Crocean and subjective-idealist interpretations of his thought, are based on ambiguities and confusions in his use of the term 'objective'. For instance, he affirms that reality is known through its relation to men, which, assuming that human beings are the only knowing subjects, is trivially true. Since human beings change through history, so does knowledge – that is, knowledge is an accumulative process, and its objectivity improves with improvements in both intellectual and practical tools. It follows that the objectivity of this knowledge is subject to a historical process. The conclusion Gramsci draws is that there is no reality outside man. In this argument, Gramsci switches from the empirical conditions of the production of objective knowledge ('objective' in our sense two), to the objective conditions of the existence of real objects ('objective' in our sense one).
In the same note, Gramsci asks whether 'an extra-historical and extra-human objectivity' can exist. Although he does not provide an answer at that point, in asking whether anyone could judge such objectivity or whether anyone could assume the 'point of view of the cosmos itself, a point of view that only God could attain, it seems that what Gramsci has in mind is not the formal possibility of objective knowledge of all reality, but rather, whether human beings can ever acquire such knowledge. It would seem that Gramsci thinks of two limitations to that possibility: (1) the vastness of reality and the indefinitely complex interconnections among things make it impossible as a matter of fact to know everything about any non-trivial object of study; (2) the institutional and intellectual conditions of the acquisition of knowledge are not, and may never be, sufficiently adequate for knowledge perfect to its subject matter. His doubt about the possibility of an 'extra-historical and extra-human objectivity' is then a doubt about the possibility of complete and absolute knowledge for human beings: all knowledge, all objectivity in our sense two, is limited or imperfect, it is rooted in the intellectual and practical activities of historical agents and it is conditioned by those activities. Specifically, the instruments of science, both technical and conceptual on which the advance of knowledge depends, are the result of historical development.
This is a thesis about the history of knowledge, not about truth-conditions, though at times it is stated as if it were an epistemo-logical claim. It is in fact an optimistic thesis about progress in science. Gramsci points out that scientific progress was greatly facilitated by the abandonment of Aristotelian and Biblical conceptions. This change in turn was due to the general progress of modern society. The conclusion Gramsci reaches is that science is not independent of the general development of society, and inasmuch as basic philosophical concepts that spawn scientific theories are often linked to general cultural and political development, the objectivity of scientific theories will depend, at least indirectly, on the adequacy of the latter. Nevertheless, Gramsci does not write, as for instance Kuhn does, of incommensurable scientific paradigms; he writes that progress in science is linked to the historical progress of humanity, and that it is measurable in terms of the ability of a new science either to solve the problems posed by the old science or to show that they are false problems. The solutions to new problems, however, cannot be arbitrary constructions: the difference between the empiricism of common sense and science lies in the fact that the former cannot 'establish the real links of cause and effect'.
Gramsci's interest, it would seem, lies in the interrelationship between knowledge and society. At times, however, he made truth a function of that relation, so that truth is what is 'universally subjective' or accepted by all, which is certainly incompatible with realism. But, if that relation is seen as an aspect of the process of production of knowledge, then his analysis is compatible with realism. Admittedly, a number of statements in the _Prison Notebooks_ point to the anti-realist position. Gramsci's thought is directed to this double aspect of science: (a) as a superstructure, that is, as ideas about reality, often tinged with ideology; (b) in its influence on the development of the forces of production. From this perspective, science is conditioned by the needs of the economy as well as the intellectual attitudes of a society. Gramsci's arguments concern mainly the first aspect, namely, the relationship between ideologies and science.
This historicized view of science is based on the premiss that knowledge of nature is conditioned by the relationship between human beings and nature. Although to the scientist, scientific activity may seem to be a purely contemplative exercise, in reality 'science is tied to the needs, life, and activity of man'. The peculiarity of science is that, as a form of consciousness, it is part of the superstructure, although it has a privileged position because its reaction on the structure has 'greater extension and continuity of development'. Because of this influence, in particular because of the development of scientific instruments which are 'closely linked to the general development of production and technology', science can also be conceived as forming part of the structure, together with labour and class.
The disappearance of distorting points of view is dependent on the disappearance of social contradictions, so that one of the conditions for the acquisition of objective knowledge is the unification of the whole human species in a unitary cultural system. For this reason, the acquisition of objective knowledge is seen from a historical perspective as an on – going struggle: 'there is a struggle for objectivity (for the liberation from partial and fallacious ideologies) and this struggle is the same struggle for the cultural unification of the human species'. There are some respects in which humanity is more unified than others. The natural sciences have provided 'the terrain in which such cultural unity has reached the maximum extension'. As a consequence, the experimental sciences have been able to reach a higher level of objectivity than the social sciences. The 'universal subjectivity' of which Gramsci writes is but a condition for objectivity, namely, the condition that knowledge must not be tinged with fallacious ideological elements. The unification of humanity, however, is not a sufficient condition for the highest objectivity; this unification must also include freedom from ideology, from distorting points of view. Because Gramsci thinks that such distortions are at least in part due to the contradictions that rend societies, the condition of cultural unification and that of the disappearance of distorting points of view are thought to form a single historical process.
There is, however, a related interpretation of this theory of objectivity, one that complements the above remarks. In his critique of modern physics quoted above, Gramsci is concerned that the subjectivity exhibited in some formulations of the new physics entails that science will become 'a series of acts of faith in the assertions of single researchers'. Objectivity as 'universal subjectivity' requires that experiments and theories be open to analysis and verification by anyone. Furthermore, scientific progress depends on this open character of scientific theories in so far as new theories correct and expand previous ones.
Besides textual evidence for realism, Gramsci's writings in general assume a realist position. In general, the concepts he uses, such as 'hegemony', 'relations of forces', 'passive revolution', etc., are conceived as theoretical concepts derived from historical reality and reflecting real social entities. For instance, paraphrasing Marx's 1859 Preface to his _Contribution to the Critique of Political Economy_ , Gramsci writes that the first level in the relations of forces is closely connected to the structure and it is 'objective, independent of the will of men, and can be measured with the systems of the exact or physical sciences'. The subject matter of history is social groups conditioned by economic and other circumstances that are the result of past historical development. The mode of explanation offered by Gramsci is always founded on actually existing conditions, tendencies, ideologies, etc. We do not find in the _Prison Notebooks_ concepts such as reason or consciousness, spirit, or, as in Croce, the concept of liberty. He does not write about man in the abstract, or about universal values whose incarnation is human history. Nor does he seek to re-enact the past in some mode of historical experience, as some historicists did. In short, the tone of his historical and political writings suggests that he considers his concepts and his hypotheses as reflecting a reality that exists in itself, or independently of its being thought. This would suggest that Gramsci is not only a realist but a materialist. We shall return to this in Chapter Two.
The concept of 'reason', moreover, one of the fundamental concepts of idealist philosophy, is hardly present in Gramsci's writings. The word 'reason' itself is seldom used, and when it is, it appears mostly in the adjective form 'rational'. By 'rational', Gramsci usually means one of two things: (1) linked to historical necessity, or historicist; (2) adequate to an end, useful or functional. And, at least in one passage, rational is used in both senses. The conclusion that must be reached is that, for Gramsci, the content of reason does not originate in reason itself, be it due to its structure or to its own life or dialect, which would allow it to formulate problems or concepts outside any relation with the material world. It is for this reason that Gramsci praised Croce for asserting 'that the problems that philosophers must solve are not an abstract offspring of previous philosophical thought, but they are posed by the actual historical development'.
In spite of Gramsci's realist intentions and of the preponderance of realist elements, especially in his political and historical writings, it might be argued that his choice of the expression 'philosophy of praxis', as a substitute for 'historical materialism' indicates that he did not approve of philosophical realism. Gentile, in his book on _Marx's Philosophy_ , used the same expression to characterize the theory in which 'subject and object are two purely correlative terms... such that their effective reality is the result of their relation in the organism'. The nature of this relation, Gentile continues, 'is the activity of knowing'. This version of the philosophy of praxis is rejected by Gramsci, who argues that it is the impure act, the material activity of human beings, not Gentile's pure act, which is the concern of historical materialism.
However, two years before the publication of Gentile's monograph on Marx, Antonio Labriola wrote that 'the philosophy of praxis [he wrote 'praxis', not the usual Italian version _'prassi_ '] is the "marrow of historical materialism"'. It seems more likely that Gramsci followed Labriola rather than Gentile. Labriola, although inconsistent or ambiguous in his epistemology, seems to define the philosophy of praxis as the realist process 'from life to thought', and not the other way around. It is this view that Gramsci echoes in his critique of Gentile. In a note devoted to Machiavelli, Gramsci suggests that he was also developing a philosophy of praxis or a neo-humanism 'in so far as he does not admit transcendental or immanent (in the metaphysical sense) elements, but is wholly based on the concrete action of men who work and transform reality for their historical needs'. Since the note deals with such issues as constitutional law and the state, it would seem that, on this occasion at least, Gramsci used 'philosophy of praxis' to characterize theories of history which seek to understand the social process on the basis of the activity of real men and women, and which reject explanatory frameworks that appeal to divine intervention, Providence, or world spirit. We shall return to this in the next section, when we deal with humanism.
Finally, Gramsci used the terms 'Marxism' or 'historical materialism' until some time in 1932. After that date, the expression 'philosophy of praxis' replaces both Marxism and historical materialism. Since the names of Marx and Engels are also replaced by expressions such as 'the founders of the philosophy of praxis' after the same date, it would seem that Gramsci was concerned with hiding the real identity of his theories, rather than with a theoretical issue. Given, then, that his definition of the 'philosophy of praxis' is concerned with the subject matter of history, not with knowledge, and that he replaced both the names of Marx and Engels with expressions that could be easily associated with Gentile, who became Minister of Education under Mussolini, it is plausible that Gramsci's main concern was avoiding the jail censor.
The analysis of Gramsci's arguments seems to yield three different theories. First, a realist theory of knowledge and a realist ontology; second, a theory about the social conditions of the production of knowledge, the effect of those conditions on the knowledge thus acquired, and the function of knowledge in society; third, a non-realist account of objectivity as the consensus of a community, complemented by the subjective-idealist thesis that nothing exists outside history. Since the first and the third theses are incompatible, one must either choose one of them or, alternatively, conclude that Gramsci confusedly held two contradictory basic epistemological theories. Given the fallacies that he commits and the ambiguities that he cannot unravel, the second of these two alternatives is clearly plausible. However this may be, it seems more interesting as well as useful to choose between realism and anti-realism. The anti-realist Gramsci would be a Crocean Gramsci; in that case, 'historicism' would signify a theory of the identity of truth and the historical conditions of truth-claims. The realist Gramsci, on the other hand, would keep those two aspects separate, the first as an epistemological theory, the second as a sociological or historical one. If we take his statement to the effect that the philosophy of praxis retains philosophical realism from French materialism as a kind of basic programmatic statement or statement of intention, it would not be arbitrary to reformulate Gramsci's theory in a realist fashion, and we could discard any anti-realist statements as mistakes or slips that he would have corrected, had he realized that he had committed them.
To conclude, there are good reasons for a reconstruction of Gramsci's _Prison Notebooks_ on the basis of a realist epistemology. First, he uses 'historicism' as signifying a sort of realism. Second, he contends that the philosophy of praxis surpasses French materialism while retaining its philosophical realism as a programmatic statement. Third, he writes that scientific theories change, but they reflect a 'permanent' nature. Fourth, his writings on history and politics provide some evidence for a theory of truth as a reflection of an independent reality. In view of this, one can dismiss his anti-realist statements as confusions. If this is accepted, then we must reach the conclusion that Gramsci's thought was different from Croce's in important respects, for Croce's absolute historicism encompassed truth.
Given the preponderance of statements in support of realism as well as the realist tone of his historical and political analysis, it is, I think, proper to conclude that Gramsci's historicism is indeed a species of realism. If we take into consideration Gramsci's own statement that the true philosophy of thinkers may not be found in their occasional philosophical reflections, but that it is to be sought in their dominant activities, then we must give more weight to Gramsci's historical and political thought, for these were the areas in which he felt more at home. It seems, then, that the evidence of realism found in his writings on politics and history should be given more weight than his philosophical statements. If this is accepted, we must conclude that for Gramsci, historicism means a species of realism. Whatever anti-realist elements we find in his _Prison Notebooks_ , and there certainly are some, can be attributed to the lingering influence of Croce, an influence that Gramsci was trying to leave behind. As both his work and his Anti-Croce were left unfinished we cannot know what direction his thought might have taken. Nevertheless, it is both proper and in keeping with Gramsci's project, to reconstruct the _Prison Notebooks_ on a realist basis.
This conclusion has been half-heartedly accepted by some commentators, although some do not attempt to make their theory consistent with the kind of realism that Gramsci was beginning to develop. Nemeth, for instance, states that 'the philosophy of praxis _does_ ultimately agree with the realist conclusion of common sense'. However, Nemeth, by means of considerable stretching of concepts, links Gramsci's philosophy of praxis to Husserl's transcendentalism. It is true that Gramsci emphasizes the historical conditions of the production of knowledge, including needs and the relations of individuals to nature. Whether this can be called a transcendental condition of knowledge in a Husserlian sense is doubtful. The weakest point in Nemeth's argument, however, is in his conception of 'objectivity'. He argues that 'objectivity itself must be redefined in terms immanent to consciousness – this is the legacy of modern philosophy, especially of Marx'. He then cites Gramsci's arguments on the limits of epistemological objectivity and his rejection of transcendent explanations of history, to conclude that Gramsci's philosophy is a historicized version of Husserl's phenomenology. The real basis of the transcendental conditions of knowledge is, according to Nemeth, the area of 'transcendental needs'. These are not empirical needs, although 'they have a mundane correlate'.
There are two problems with this interpretation. First, Gramsci's rejection of transcendence and his emphasis on immanence have nothing to do with consciousness or with the constitution of objectivity. For Gramsci, transcendence and immanence are historical concepts, not epistemological ones. For instance, he uses the term to differentiate theories of the extra-historical origin of history, which he terms transcendent, from those theories, such as historical materialism, which seek to understand the 'worldliness and earthliness of thought' or the historical origin of statistical generalizations. Thus, Croce's 'speculative historicism' and 'idealist speculation' which are rooted in the theory of an eternal ideal history are said not to be really immanent, although in Nemeth's use of the term, Croce is an immanentist to the extent that all knowledge and truth depend on their place in history. In brief, Gramsci rejects speculative historical philosophy which conceives history as the result of supra-historical deities, values, or laws. His historicist realism, as a guiding principle for historical research, consists in the injunction to explain history on the basis of historical phenomena and historical necessity and that none of this has a transcendent, religious, or speculative meaning.
Second, the concept of transcendental needs is too speculative for Gramsci's taste. Perhaps one of the most valuable qualities of Gramsci's thought is his avoidance of unnecessary conceptual complexity and his efforts to produce concepts that could be given a historical content. That Nemeth is on the wrong track is shown by what he thought was Gramsci's shortcoming, namely, that he 'failed to see how crucial an adequate account of time is for the completeness of the philosophy of praxis and therefore its self-sufficiency'. The _Prison Notebooks_ show that Gramsci was preoccupied with the concept of time. It was not, however, with 'consciousness of time itself or with 'the constitution of objective time', but with historical time or with the rhythms and forms of transience of social phenomena. This is the cornerstone of Gramsci's philosophy of history as will be seen in Chapter Two. Nemeth's interpretation of Gramsci is flawed in that he did not take into consideration Gramsci's writings on history and politics. As I suggested above, it is in these writings that the structure of Gramsci's thought is to be sought, and consequently they are of the utmost importance for interpreting his philosophy.
_Historicism as humanism_
Gramsci's use of 'historicism' as 'humanism' has received a lot of attention; it is generally the use that most commentators stress to the neglect of the other three. This one-sided emphasis on humanism often leads to voluntarist interpretations of Gramsci. In this fourth sense, historicism is a philosophy that 'does not recognize transcendent or immanent elements (in the metaphysical sense) but is completely grounded on the concrete actions of man who works and transforms reality for his historical needs'. It is in this sense that we must interpret Gramsci when he asserts that the philosophy of praxis is an 'absolute historicism' or an 'absolute humanism'.
It is evident that Gramsci's main concern is the rejection of transcendent metaphysics that would account for the historical process, such as is found, for instance, in the German historicists. Against that sort of metaphysics, Gramsci conceives Marxism as 'the absolute worldliness and earthiness of thought, an absolute humanism of history'. From this perspective, Marxism is seen as having a twofold significance, theoretical and practical, for historicism is 'the liberation from any abstract "ideologism", the real conquest of the historical world, the beginning of a new civilization'. At the same time, however, Gramsci also rejects reductionist varieties of materialism which desire to be ultra-materialist, and attempt to explain social phenomena by appealing to the laws of physics. Similarly, he rejects biological determinism, in particular any theory that biological differences among men, such as race, the colour of skin, or the shape of the head, have a causal significance in the historical process.
If we can give a general meaning to Gramsci's humanism, it must be that history is to be understood as a human process, as opposed to a divine, or biological one; as a consequence, social scientists must look for explanatory frameworks in the relations among human beings and between humankind and nature. The definition does not specify how the process is to be understood, or what kinds of explanations are to be framed. As Althusser recognizes, Gramsci's stress on humanism, more than a positive theory about the subject of history, is a negation of idealist theories according to which history is the dialectic of reason, liberty, moral values, etc. Nevertheless, Gramsci's identification of Marxism with absolute historicism or absolute humanism, which in fact appears only twice in the _Prison Notebooks_ has become an object of some interest in the debate between humanist Marxism and structuralist Marxism. In general, Gramsci would seem to support humanist Marxism; in reality, however, the issue is more complex.
Although it is difficult to provide a single definition of humanism that would cover all humanist Marxists, it seems that three main assumptions underlie humanist interpretations of Gramsci's thought: (1) Marxism is not a science; its purpose is not to explain historical phenomena by appealing to general laws, but to transform society. (2) Primacy is given to the ethico-political aspect of society. (3) Emphasis is placed on human liberation from alienation and on the free development of the individual. A humanist interpretation of Gramsci, such as Salamini's, would tend to emphasize Gramsci's guarded rejection of statistical generalizations; it would oppose historicist Marxism to scientific Marxism; and finally, it would conclude that hegemony is the primary element in a social whole. In doing so, Gramsci's historicism is linked to the historicism of the German historical school in its denial of the possibility of scientific history.
Emphasis on humanism brings to the fore the importance of human agency, and hence the will, in historical development; on this interpretation, Gramsci, often said to be a voluntarist, would tend to dismiss the existence of historical or social laws or would, at least, advocate the study of history simply in terms of the organized will of individuals and groups of individuals. Thus, when Gramsci writes that the main problem of historical materialism is to determine how the historical movement originates on the base of the structure, he seems to be making a sharp distinction between history and some underlying structure which would always remain beyond history, beyond human agency.
Some interpretations of Gramsci, notably that of Badaloni, seem to come close to this conclusion. Badaloni seems to interpret Gramsci as posing a distinction between the forces of production, on the one hand, and the relations of production together with the superstructure, on the other. The structural, or as he puts it, the 'logical' elements are conceived as being essentially outside the historical movement. This, of course, is so by the definition of the terms used by Badaloni. The result, however, is that history is seen as a drama whose actors are classes rather than individuals. Hence, Marxism has been split in two; political economy and drama (history). This split has had profound consequences for the development of historical materialism in the west, as is attested by the debates between structuralist Marxists and humanist Marxists. Whereas the former emphasize the determinist character of social relations, from economic to personal ones, the latter tend to emphasize the creative aspects of human praxis, especially at the level of political intervention.
According to Badaloni, Gramsci's historicism contains two essential elements. The first one is defined as 'actualization of utopia'. On this view, the will becomes the fundamental element of history and, as a consequence, the interpretation of history must be based on the concept of the 'ideas-will'. The second element is defined as critical realism, which consists in giving a realist foundation to the revolutionary will. But in describing Gramsci's historicism as a theory of revolution, Badaloni neglects the other aspects of historicism I have outlined above. The result of this narrowing of perspective is an interpretation of Gramsci as merely a theoretician of the superstructures. This is true, however, in so far as Gramsci dealt mostly with supers true tural matters; but it is not true if this is accorded a philosophical significance, that is, if it is asserted, as Bobbio has, that Gramsci carried out a double inversion of Marx's theories, so that the superstructure, rather than the structure, would have the primary role, and more emphasis would be given to civil society than to the state.
Badaloni does not claim that the logical and the historical form two separate realms. In fact, he presents Gramsci's concept of the 'historical bloc' as an articulation of the logical and the historical, affirming that 'the determining element is that of production', but avoiding economic reductionism inasmuch as 'the starting point is now the domination of the economic by the political'. However, this formulation of the question is not very satisfactory, unless it is admitted that the economic is also historical. The problem with Badaloni's interpretation is that he takes the structure, production, or the economy, as the forces of production which is just one step away from speaking of the economy as the realm of technology. Gramsci rejects this view of the economy and he rejects any historiography that is not based on a deeper understanding of both the structure and historical necessity.
From Gramsci's point of view, the distinction between the logical or structural and the historical, or superstructural, is not a real one, but a didactic one. Describing the material forces as the content and ideologies as the form, he argues that 'the material forces would not be historically conceivable without form, and ideologies without material forces would be individual whims'. Clearly, the material forces are to be conceived historically, which means that they must be taken as an integral part of the network of historical necessity. Gramsci, in fact, attempts to formulate a theory of the identity of politics and the economy, an identity that is manifested in the permanent organizations that 'originate in the "permanent and organic" terrain of economic life'. It is from this perspective that Gramsci objects to Croce's view that historical materialism separates the structure from the superstructure and reinstates a form of theological dualism in which the structure becomes a hidden God. Gramsci's answer to Croce is clear: the structure 'is conceived in an ultrarealist manner', and the development of the structure and the superstructure is thought of as being 'intimately connected and necessarily interrelated and reciprocal'. We shall return to the analysis of the relation between structure and superstructure in Chapter Three, where a non-reductionist view of the determining role of the economic structure will be suggested.
Gramsci's humanism, then, must be taken first as a philosophical theory which understands human agency as a necessary condition of historical development and which rejects any explanation which is grounded on such entities as God or Providence, which are not themselves human, or the result of human activity. Hence, history is the development of human societies as well as the development of the relationship between human beings and nature. But it must not be concluded that, for Gramsci, history is the result of the process of transformation of a transcendental human nature. Dilthey, for instance, conceived of the objective world of history as the materialization of the human mind, and Vico viewed history as essentially the development of the human mind. Gramsci, following Marx, argues that human nature is the ensemble of social relations, and hence he asserts the transience of so-called human nature. Human nature is not prior to history, it 'is a historical fact that can be verified, within certain limits, with philological and critical methods'.
Gramsci's emphasis on hegemony or moral intellectual leadership, on the role of intellectuals, and on popular culture would seem to place him in that rather vague category known as humanist Marxism. It cannot be denied that Gramsci's thought largely focused on those issues. Perhaps it was out of personal interest, or because of the perceived need to fill a gap in Marxist theory, that he devoted most of his thought to the process by which the structure is transformed into a superstructure, a process that he sometimes characterized as 'catharsis'. Catharsis is, according to Gramsci, the 'passage from the merely economic moment (or egoistic-passional) to the ethico-political moment'. This is a passage from the objective to the subjective, in which 'the structure is transformed from an external force that crushes man... to a means for freedom, to an instrument to create new ethico-political form'. This passage from necessity to liberty is a process in which the role of human agency is much more obvious than in structural processes, which are often perceived by the historical agents as external or imposed by the past. As Texier observes, in this process the historical movement is here presented as the struggle of implacably opposed classes, and the result of the conflict depends 'on the intelligence and energy of men'.
The question of the 'humanism' of history depends largely on the perspective from which history is viewed. Gramsci chooses to look at the moments of history in which the cathartic passage is realized, and hence, moments in which human agency is more obvious. This, however, must not be construed as a theory of history; it is possibly a theory of revolution. But Gramsci does not ignore that the depths of history are hardly fathomed by a theory of revolution. In the larger view of history, Gramsci is concerned with the process of integration and disintegration of historical blocs, and this, of course, is far more than a merely humanist theory of history, for it must not only understand humanity as it is expressed in folklore, culture, art, etc., but also in the general structures that condition human activity. Thus, Gramsci's analysis presupposes and supplements the results of the analysis of political economy; it does not replace them.
Conclusion
Commentators on Gramsci's _Prison Notebooks_ have generally agreed that historicism is central to his interpretation of Marxism. Some, like Althusser, have rejected both historicism and humanism. Many have shown a positive attitude towards historicism. In general, they have assumed that Gramsci's historicism is a form of humanism and they have proceeded, quite uncritically, to treat Gramsci's thought as a form of humanism. Since, as Salamini observes, Gramsci gives no definition of humanism, commentators have been free to use whatever definition of humanism they deemed appropriate. A link between humanism and an anti-scientific theory of history which stresses the creative role of the will has been the favoured interpretation of Gramsci's _Prison Notebooks_. As we have seen, Badaloni's analysis of Gramsci takes this route, although he is careful enough to speak of realism, that is, the need for the will to conform to the general pattern of historical causation.
A case which clearly exemplifies this interpretation of Gramsci is provided by the work of Leonardo Salamini. He argues that Gramsci's historicism is a rejection of scientific Marxism as well as the rejection of eternal truths. Basic to Salamini's defence of this humanist Marxism is the thesis that 'the admission of the existence of objective reality outside human will is a blatant historical error'. Although his statement is somewhat ambiguous in so far as we do not know whose human will or what reality is concerned, it seems, nevertheless, that if I am not wrong in my interpretation of Gramsci's historicism, this is not a correct analysis of Gramsci.
The emphasis placed on the role of the will in history, activism, and culture, provide the basis for Salamini's definition of humanism as 'an anthropocentric vision' in which
the reduction of knowledge to historical social relations entails the reduction of the _relations of production_ , political and ideological social relations to _historicized_ "human relations", to inter-human, intersubjective relations, to use Althusser's precise characterization of Gramsci's humanist conception.
The relations of production to which everything is reduced, or 'which are considered to be objective socio-economic categories within orthodox Marxism, are subordinated by Gramsci to man, the centre of the cosmos. This vision, however, according to which human beings are the measure of all things, is never seriously contemplated by Gramsci, who was painfully aware of the fact that his existence was not the measure of very much while he was in jail. In fact, Gramsci, perhaps unfairly, chastises Bukharin for his acritical endorsement of a common sense which has remained 'Ptolemaic, anthropomorphic and anthropocentric'.
Salamini, like many other commentators, offers but a few general remarks by way of definition of historicism. They are mostly based on Gramsci's definition of Marxism as an absolute historicism and absolute humanism, thus ignoring the many passages in which Gramsci uses the term 'historicism' in some other sense. The result is that they provide only a vague, uncritical, and often shallow account of what they consider the marrow of Gramsci's thought
This narrow perspective has led to what I consider serious errors of interpretation of Gramsci's thought in general. Perhaps the most important error is to give his studies of culture and politics a theoretical significance that they do not have. The conclusion that Salamini, Bobbio, and others reach, is that Gramsci 'ascribed to superstructural activities a primary role in Marxist Theory'. However, the fact that Gramsci was interested in culture, perhaps because he felt that this was the least developed aspect of Marxist theory or that it was the most urgent task in the development of communism at the time, is not to be construed as a statement about the primacy of culture. One must look at the theoretical framework within which Gramsci sought to analyse culture; and to do this, a fuller and more precise account of his conception of historicism is necessary. The first step towards this end must be an analysis of the main uses of 'historicism' in the _Prison Notebooks_. This enables us to understand the structure of Gramsci's thought and to establish the main lines of contrast between his thought and that of previous historicist thinkers.
A number of preliminary conclusions can be drawn from a comparison of Gramsci's historicism with the other historicist thinkers we have studied. Perhaps the most significant contrast between Gramsci on the one hand and Hegel, the German historical school, and Croce on the other, is Gramsci's rejection of the concept of an ideal, eternal history. This concept, first formulated by Vico, but traceable to St Agustine's idea in _The City of God_ , found various formulations in nineteenth-century German thought and in that of its Italian followers, such as Croce. Their attempt to see in history more than a narrative of discrete events was positive in so far as it was a critique of empiricism. But the speculative method led them to posit such explanatory concepts as transcendent moral values, the Idea, etc. which Gramsci clearly rejected. In this respect, his realism as well as his critique of transcendence, must be seen as the attempt to develop a non-empiricist theory of history which would grasp the totality and complexity of the historical process, from the tendencies of the economic structure to the forms of popular culture that shaped the consciousness of the masses. Of vital importance in this theory was the analysis of the revolutionary process, the moment at which organized masses break the seeming regularity of history to create new forms of civilization. But this analysis must always be understood in the larger context which Gramsci called integral history.
From Gramsci's perspective, the error of speculative theories is not so much their lack of empirical content, for they often contain sound historical observations, but their attempt to explain this real content as a necessary consequence of metaphysical, i.e. transcendent concepts. Gramsci's relation to Croce must be seen as an effort to take advantage of Croce's acute analysis and to put whatever was living in his thought on a sound realist foundation. Gramsci's approach to speculative philosophy is not entirely different from Marx's. Speculative philosophy, Marx wrote of Hegel, 'makes the Idea the subject and makes the proper actual subject... the predicate'. Thus, the predicates become independent of the real subjects, with the consequence that human activity appears 'as the activity and result of something other than man'. In the case of Croce, despite his attempts to eradicate transcendence from his system, historical agents, as we saw, are not real, empirical men and women, but some abstract conception of a universal humanity, a 'truly real individual' which, nevertheless, succeeds in inverting the subject and predicate.
This conception of history is clearly rejected by Gramsci. His use of historicism as realism, his use of the concept of reason, and the conceptual framework he proposes for historical explanation, suggest that for him the actual subject of history is the real, empirical subject, not ideas. From this perspective, his humanism, as a rejection of speculative transcendence, is an echo of Marx's criticism of Hegel. Both Gramsci and Marx are opposed to a theory of history in which the predicate, be it reason or liberty, is transformed into the active subject of history.
In what concerns the concept of historical necessity, speculative theories advanced a conception of ideal necessity, or a logic according to which the course of history is an objectification or manifestation of the dynamic inherent in concepts. It is the 'ideal eternal history' of Vico rather than a material process governed by material necessity. This inversion of terms is well characterized by Colletti as 'the distortion of fact into a metaphysical axiom'. The German historical school, however, differs substantially from both Hegel and Croce in this respect. Their positivist conception of law as invariant relations between events, together with their conception of the uniqueness of historical phenomena, led them to the conclusion that there are not any historical laws. History, for them, is the realm of freedom, not of necessity. As we saw, this implies that the writing of history should be concerned with the inner aspects of history, not with the events themselves, but with the values, reasons, and ideals of historical agents, or with the ethical substance of the state.
Historicists in general have been concerned with the transitory character of social phenomena. Their reflections often broached this theme. The German historical school advanced the thesis that the past was relived by the historian, and that its meaning, recreated in the historian's mind, depended on its relation to a universal moral reality of which each system of values was a partial manifestation. The present as experience of the historian, and with it the system of values which he shared, was of crucial importance for interpreting history. In this sense, the present as experience was dominant. Similarly, Croce's concept of the contemporaneity of history emphasized the present as the focus of the past's meaning, and at times, as the only existing historical reality. Gramsci, in sharp contrast, writes of the transience of all social forms as being subject to a structure of necessity. The meaning or identity of social phenomena does not depend on the timeless life of the spirit, the ideal eternal history, or any transcendent reality, but on its occurrence in a determinate net of relations, the causal link or nexus, as he often refers to it. And this is the greatest difference between what Gramsci calls 'historicism' and those forms of historicism that emphasize the uniqueness of historical phenomena.
Gramsci's historicism, taken both as a commitment to historical necessity and as realism, suggests that historians must look beyond the fleeting drama of events, beyond the empirically visible, to the inner aspects of history, to its 'generative mechanisms', as Bhaskar appropriately designates them. Thus, in Gramsci, historicism is a rejection of a history that is 'externally descriptive, without bringing into relief the necessary and the causal links'. The problem that Gramsci consciously faces is the need for a theory of history even if historical events appear to be unique. Although he seems to be perplexed about the issue of historical necessity and the uniqueness of events, it is obvious that his historicism, as outlined above, requires a theory of material historical necessity which would avoid both positivism, on the one hand, and the idealism of Hegel, Croce, and the German historical school on the other. Although no fully developed theory of historical necessity is found in the _Prison Notebooks_ , there are indications that he had thought a good deal about it.
It will have been observed in my account of Gramsci's historicism, that I have not dealt with the issue of freedom of the will. I have stressed historical necessity, but have so far ignored Gramsci's well-known statements against determinism and fatalism. The main reason for my proceeding in this manner is simply that Gramsci uses 'historicist' as a synonym for historical necessity. However, there is still pending the matter of the agent in historical activity, or in particular, the political agent. In so far as history is viewed as a result of human activity, the question of freedom of the will must be conceived as the possibility of choice within a network of historical necessity. Suffice it to say at this point that Gramsci was primarily interested in the possibility of effective political intervention by organized groups. He was not concerned to address the abstract philosophical question about whether in general causal determinism is compatible with freedom of the will.
In conclusion, Gramsci's use of 'historicism' suggests that his thinking is radically opposed to all previous historicist thinkers except Marx, with whom he shares a number of views. Furthermore, it appears that the four uses outlined above form a coherent foundation for the social sciences. In simple terms, Gramsci's historicism is the view that all social phenomena exist as aspects of a process, and hence the historical method is the only scientific one. But the historical method is not merely a narrative of events. It is rather the study of the transience of social forms according to a network of necessity. These structures of necessity are not simply logical constructions that fit the events, but real forms of social life. Furthermore, they are ultimately the work of real men and women, even when they appear as external chains that crush them. Gramsci, then, can be seen as rejecting both the historicism of Croce and that of the German historical school because they involved a search for a metaphysics of history, and often fell into relativism; he also rejects the poverty of empiricism, its incapacity to search for historical laws, other than statistical generalizations, as well as the lack of historical specificity of rationalist thought.
Gramsci's historicism is not to be taken so much as a concrete theory of history, in the sense that it specifies his thinking on concrete social phenomena; but rather as a foundation for the social sciences in general, in the sense of a set of guiding principles for social research. These are not _a priori_ principles or a transcendental schema. They are based on the observation that social life is human activity conditioned by the structures inherited from the past; in other words, that social life is history. Consequently, full understanding of social phenomena can only be attained if they are studied from a long-term perspective. As Marc Bloch observed,
In the continuum of human societies, the vibration between molecule and molecule spread out over so great a span that understanding of a single moment, no matter what its place in the chain of development, can never be attained merely by contemplation of its immediate predecessor.
As should be obvious now, Gramsci's historicism, in particular his objections to transcendence and his acceptance of immanence, should not be taken as an epistemology, although, as we have seen, it contains a realist one. Nemeth tends to interpret Gramsci's statements on immanence as if they had a Husserlian transcendental significance, where 'objectivity itself must be redefined in terms of immanent to consciousness'. As we have seen, Gramsci stresses that his comments on the function of ideas and their transience is a historical judgement, not a judgement of value or truth. It is easy to distort Gramsci's thought by attributing to some of his statements an epistemological meaning, when they are in fact intended as, or related to, historical explanation and interpretation. They concern the specific process of the origin of social phenomena and of ideas in so far as they are superstructural elements, not the conditions for truth and assessment of empirical claims.
In so far, then, as Gramsci's historicism is intended as a foundation for the study of society, one could say, for a science of history, it is not to be construed as a denial of objectivity in the ontological sense. Although there are lapses into subjectivism in Gramsci's arguments, they are due to the fact that he was not always able to distinguish between 'epistemological' objectivity and 'ontological' objectivity, and that he confused empirical descriptions about the process of producing knowledge with normative theories concerning truth, as well as with ontological objectivity. Serious as these errors are, it is still possible to accept his theory that knowledge is produced under specific historical conditions which have an effect, positive or negative, on its validity, while preserving a realist epistemology and a realist ontology. However flawed Gramsci's arguments are, it seems that some of his commentators, notably Salamini, have not even attempted to see the missing but suggested element in Gramsci's thought, namely, the distinction suggested above. This, of course, results in the construal of an idealist Gramsci. Nor, for that matter, have they realised that Gramsci's writings on science are not about the methods of science, or its philosophical presuppositions. On the only occasion on which Gramsci approaches the philosophy of science, his analysis leaves no doubt about his realist epistemology, as I have shown above.
When Gramsci writes about the concept of matter, it is not to deny the scientific concept of matter, nor its independent existence, for Gramsci clearly accepts that natural phenomena, such as electricity, existed even before they were known. It is to point out that it is not the business of historical materialism to judge the theories of scientists; its business is to understand how a natural phenomenon is 'historically active, not as mere natural force... but as an element of production mastered by man and incorporated into the ensemble of material forces of production'. And to the extent that scientific ideas shape the culture of an age, historical materialism will study them as an element of the superstructure. This clearly means that Gramsci did not attempt to reduce science to the philosophy of praxis, as some have suggested; a move that would make Gramsci hardly distinguishable from Croce. It means that he had an understanding of society as an interrelated whole and that its study must reconstruct all its elements, including science, and their interrelationships in the movement of history.
If for the 'philosophy of praxis "matter" is to be understood neither in the sense that it has come to have in the natural sciences... nor in that of the meanings that it takes in the diverse materialist philosophies', clearly science has a dimension that is beyond the reaches of historical materialism. The 'diverse physical properties' which together 'constitute matter itself are the object of scientific investigation. This distinction may seem trivial; it shows, however, that Gramsci did not deny the independent existence of the material world or its existence outside history. That science itself is always shaped by the needs of human beings certainly is both historically and theoretically significant; it does not entail, however, that matter or nature depend on history or on human will, though it entails that science does so depend.
A careful reading of Gramsci's writings show that his historicism is a far more complex theory, a much richer and also less extravagant one, than some commentators have suggested. I have attempted to bring out a fuller sense of Gramsci's historicism and to point out two main sources of errors of interpretation, namely, to construe as an epistemology what is a theory of history, and to reduce all aspects of Gramsci's historicism to humanism. In Chapter Two, the four senses of 'historicism' will be given a general interpretation, one that takes into consideration Gramsci's _Prison Notebooks_ as a whole. Such an interpretation, it is hoped, will shed some light on the inner structure of Gramsci's thought.
_Chapter Two_
**A General Interpretation of Gramsci's Historicism**
Introduction
In the preceding chapter four main uses of the term 'historicism' in the _Prison Notebooks_ have been identified. However, that analysis alone does not provide a definition of Gramsci's historicism: it is merely an attempt to lay the groundwork for such a definition, as well as to give a warning that historicism is more complex, and probably more interesting that a cursory reading of the _Prison Notebooks_ might suggest This preliminary work of analysis allowed us to detect some errors of interpretation of Gramsci's work which have seriously flawed some commentaries on the _Prison Notebooks_.
We must now attempt to elucidate the meaning of the four senses of historicism so that a general interpretation of Gramsci's thought can be given. Fortunately Gramsci deals with all of them in the _Prison Notebooks_ , which suggests that his often brief, almost causal definitions of 'historicism' were not unthinking slips of the pen, but part of his deeper interest in historiographical and philosophical questions. And this is the reason why, in Chapter One, I used the expression 'the structure of Gramsci's thought' to refer to his brand of historicism. Unfortunately, as is the case with most questions in the _Prison Notebooks_ , Gramsci's treatment of the issues that concern us here is but sketchy. Hence, only the general outline of his historicism can be drawn with any certainty.
Because it seems to be the cornerstone of Gramsci's historicism, I shall emphasize the notion of transience. Little will be added to the analysis of realism and humanism given in Chapter One. The most difficult part by far is that of the concept of historical necessity and related issues, of which only a tentative interpretation can be given at this point. Gramsci's critique of sociology will provide the backbone for this general interpretation of his historicism.
Gramsci's Critique of Sociology: Some Preliminary Remarks
Perhaps the most revealing passages in the _Prison Notebooks_ are those in which Gramsci discusses sociology. In this section I shall discuss those passages, not so much to clarify Gramsci's view of sociology, but so as to shed light on his historicism. It is important to keep in mind that, as Gallino explains, Gramsci's knowledge of sociology derived mainly from Italian sociology, which was dominated by the evolutionist thought of the last quarter of the nineteenth century. Gramsci's objections, it would seem, were addressed not so much to positivism as to a primitive, substantially backward form of positivist sociology. Nevertheless, as we shall see, he managed to address some of his concerns to fundamental tenets of positivism. In addition to this, Gramsci often discusses Michels and Pareto, and he refers to Weber on six occasions; not to be discounted, as Gallino points out, is the influence of Durkheim through the work of Sorel. Nevertheless, sociology is normally associated by Gramsci with the positivist and theoretically underdeveloped forms of evolutionism prevalent in Italy at the time, and it is in this restricted sense that the term will be used in this text In effect, Gramsci uses the term 'sociology' not so much to indicate the discipline as to characterize a specific approach to the social sciences.
A number of social scientists have studied Gramsci's critique of sociology, often giving accounts of that critique that are mutually incompatible. Thus, Salamini, while acknowledging that 'it would seem paradoxical at first glance to search for a basic structure of Marxist sociology in the anti-sociological writings of Gramsci', reaches the conclusion that his 'rejection of bourgeois sociology does not entail a rejection of the possibility of the existence of sociology within a Marxist perspective'. And yet, Razeto and Misuraca, in an excellent account of some aspects of Gramsci's thought, argue that Gramsci rejects all sociology, whatever its philosophical basis may be.
In their reconstruction of Gramsci's critique, Razeto and Misuraca argue that there are two kinds of reasons, theoretical ones and historical ones, why Gramsci rejected sociology, not just the Italian brand of positivist sociology. Theoretically, sociology was a response to Marx, an attempt to supersede Marxism which was closely linked to the need to contain the dissolution of capitalism. Historically, sociology is the specific mode assumed by ideology, and in this, sociology plays the role formerly played by political economy. Whereas the latter was the science of the origins of bourgeois society, the former is the science of the established bourgeoisie which must now contain its dissolution, it 'anomie', and its disfunction, rather than justify its origins.
Razeto and Misuraca argue that sociology also became the official state doctrine of the Soviet Union when it was confronted with the task of reorganizing the economy. The result was that sociology, developed according to a model borrowed from natural science, became a technique: 'sociological efficacy – assumed as the criterion and guarantee of "scientific objectivity" – is the operational efficacy typical of any science. It manifests itself in the "experimental" character that sociology tends to acquire as a technique of adaptation and of social control'.
Sociology has become the theory on which the decision process of the state is based. The institutional framework on which this process takes place is bureaucracy. The two pillars of the modern capitalist state are, according to Razeto and Misuraca, sociology and the bureaucracy. As they write, 'the organic character of the relationship between bureaucracy and sociology in effect constitutes one of the fundamental characters of the organization of contemporary states'. Accordingly, they analyse Gramsci's notes on sociology and on the nature of bureaucracy to find the foundations of Gramsci's social theory, and in particular, of his analysis of the modern state.
The brief outline of the book by Razeto and Misuraca cannot do justice to their analysis of Gramsci's thought. They reveal, however, two aspects of Gramsci's thought that are particularly interesting for us. First, sociology is an attempt not so much to understand society, but to manipulate it bureauceratically so as to preserve its present irrational state. Hence it is an undemocratic and conservative discipline. Second, at least part of the problem with sociology is said to be that it is modelled on the natural sciences; its foundations are external to itself. This seems to entail one of the central theories of German historicism, namely, the radical distinction between the method of the historical sciences and that of the natural sciences, albeit that no specific form of, or grounds for, this distinction is given.
Let us now turn to Gramsci's own critical remarks on sociology. These can be seen to fall into two main categories. The first one contains the general political and theoretical reasons for his rejection of sociology; the second provides a number of more detailed objections which cover the four aspects of historicism previously analysed. I shall begin with the general comments, and I shall incorporate the detailed ones in the interpretation of Gramsci's historicism that will follow.
Gramsci links the rise of sociology to 'the decadence of the concept of political science and political art that took place in the nineteenth century'. This decadence, Gramsci suggests, results in the reduction of politics to 'parliamentary politics' or 'personal cliques'. The assumption on which sociology is based is that 'with constitutions and parliaments an epoch of "natural" "evolution" had begun, that society had found its definitive because rational foundations'. This assumption about the definitive, rational organization of society makes it possible to study society with the methods of the natural sciences. On this basis, sociology can look for regularities, for statistical laws, assuming that no change will transform them. And, in return, it can use its findings to buttress the capitalist system.
Sociology is not the only discipline to assume the naturalness of capitalism; classical political economy was sharply criticized by Marx for doing so. This assumption of the definitiveness of the present state of society entails a view of history as either a series of fumbling attempts undergone by societies to reach their rational forms, or as the development of inner possibilities that culminate in the modern state. According to the first view, the whole of history is irrational, hence it is not really worth studying; according to the second, the origins must already contain the possibilities of all future changes, as the acorn contains the future growth of the oak tree, which raises the ahistorical question of the cause of that essence. Hegel is sometimes thought to have held the second model. In any case, the sociology Gramsci had in mind seemed to make it impossible to understand the possibility of fundamental change. For this reason, Razeto and Misuraca are right in their view that sociology is a modern form of bourgeois ideology. Gramsci's historicism is first of all a rejection of the assumption of the naturalness and rationality of capitalism common to classical political economy and sociology; hence, Gramsci objects to sociology for its anti-historicism as well as for its political conservatism.
The problem that Gramsci had to face on the ideological front, it seems, was that of breaking the circle of sociology and degeneration of politics, which support each other. As a practical question, then, Gramsci's historicism was conceived as the attempt to dethrone both the influence of Croce and that of positivist sociology on Italian culture. At the same time, the degeneration of politics that resulted in the relegation of all political life to the parliamentary game, with the consequent impoverishment of democracy, had to be reversed. A broader understanding of politics was thus necessary; consequently, Gramsci attempted to introduce the notion that all of life is politics. We will later discuss the two senses that politics came to have in the _Prison Notebooks_.
Gramsci's analysis of the relationship between politics and sociology brings to light an important aspect of his thought Some commentators have observed that Gramsci rejects determinist conceptions of history because they result in the passivity of the masses. Gramsci himself might seem to agree with this view, although he is in fact concerned with fatalism and mechanical determinism. This is, in a sense, a strange thesis, for it assumes that a theory of history will have a major impact on the way the masses think and act, which is itself a determinist thesis. This is of course quite questionable, although it must be admitted that a fatalist theory of history might reinforce certain conceptions of common sense.
A closer look at the _Prison Notebooks_ , however, reveals a different aspect of this issue. First, in the passages analysed above, it is quite obvious that it is the degeneration of politics that produces sociology, not the other way around. Second, in his analysis of the various forms of revisionism in Marxist theory, Gramsci notes that vulgar materialism and the fatalist view of history associated with it emerged not only as a result of the primitive corporatism of the masses but also because of their subordinate position. It is the fatalism present in their common sense which is reflected in vulgar materialism; the latter, of course, gives support to the former and in this sense becomes an impediment to active politics. Nevertheless, Gramsci notes that this conception of history has not been totally useless. Recalling Weber's analysis of Calvinist theories of predestination and the development of capitalism, Gramsci argues that the fatalist conception of history played a useful role in given historical conditions. For, 'when one does not have the initiative in the struggle and the struggle itself becomes identified with a series of defeats, mechanical determinism becomes a formidable force of moral resistance, of cohesion, of patient and obstinate per severance'.
Let us now turn to some of the theoretical objections levelled by Gramsci against sociology. According to Gramsci, 'sociology is the attempt to create a historico-political methodology dependent on a philosophical system already elaborated'. The problem with this approach is that the methodology developed does not respond to the problems posed by the subject matter itself; it is designed to solve problems that are alien to it. The point Gramsci makes is that by assuming the positivist doctrine of scientific method, sociology becomes a 'subordinate fragment' to a conception of the world, and hence, one could conclude, its autonomy as well as its scientificity is impaired. Furthermore, because it is dependent upon an extraneous logic, its coherence is not the coherence of a general theory developed on the basis of original research problems, but an imposed coherence, a mechanical coherence.
At the methodological level, then, the problem with sociology is that it uses the methods of the natural sciences, and attempts to structure the study of society according to those methods, without first critically examining whether they could grasp that subject matter adequately. The task of general theory is not that of elaborating concepts and models applicable everywhere, but rather to develop within each discipline the appropriate concepts and models. This would imply that Gramsci rejected the theory of the unity of scientific method. Furthermore, carried to its extreme, Gramsci's position is far more radical than that of the German historicists, for it entails that each individual discipline would have its own method. I shall return to this question later on.
The second point Gramsci makes regarding sociology is that one must not substitute conjectures or, as he puts it, 'hypothetical history' for 'historical history' that is, for the analysis of documents. For instance, the principle of correlation between the organic parts of a body may be useful, but it cannot take the place of the analysis of documents, without which there is no real historiography. Although it may be useful to begin with the assumption that individuals and groups always act coherently and logically, they do not always act thus; hence, there is the risk of arbitrariness if we allow analogies to take the place of the documents. Clearly, Gramsci thinks that sociological generalizations, in so far as they are attempts to import conceptions or methods from the natural sciences, can easily turn into arbitrary or facile conjectures about the development of societies or the behaviour of individuals. In his critique of Bukharin, Gramsci clearly states that Marxist sociology is an 'incentive for facile journalistic improvisations of the pocket-genius'. And he links sociology to the tendency criticized by Engels in his letters to J. Block and H. Starkennburg.
The uncritical appropriation of the methods of the natural sciences results in what Gramsci considers to be the tendency of sociology to construct abstract schemas. The charge of abstraction, of neglecting the concrete facts, is the one most frequently found in the _Prison Notebooks_ , This brings to light one of the basic features of Gramsci's historicism, namely, that knowledge of social phenomena cannot be produced by inductive generalizations based on apparent similarities of events or, in the language of historicism, on external resemblance. For instance, in a note on the work of Michels, Gramsci contends that he has not developed 'any methodology intrinsic to the facts'; his work is flawed by 'the pure descriptive character and external classification of the old positivist sociology'. Gramsci's charge that sociology produces abstract schemas which do not correspond to concrete facts can be restated as the failure of sociology to meet the criterion of adequate description of social facts.
The question of the specification of facts is of crucial importance in determining the character of Gramsci's historicism. For, as we saw in Chapter One, German historicists have maintained that historical facts are unique and hence no laws of history can be discovered. It seems, then, that the issue of the adequate description of facts is connected with the theory of historical necessity. In what follows I shall take the rest of Gramsci's objections to sociology in the context of the specification of the four meanings of 'historicism' previously outlined. With this, the specific character of Gramsci's historicism, as well as its marked contrast with idealist forms of historicism, will become evident In this chapter it will be necessary to reformulate Gramsci's thought, to translate it as it were, in terms of the language used by historians and philosophers who have reflected on similar problems of the methodology and philosophy of history. Because Gramsci at times remained close to the language of Croce, such procedure will allow us to penetrate to what is his thought. Because identity of terms does not mean identity of concepts, certainly not in the case of Gramsci's use of Crocean language, the introduction of the problematic of a number of modern thinkers will help us avoid some easy errors of interpretation.
Gramsci's Historicism
Transience
In its most complete form, the theory of the transience of all social phenomena holds that even the most durable structures change: history, as Pierre Vilar insists 'is the _change of the_ rhythms, the change of structures. And it is the search for an explanation of these changes'. From this standpoint, then, the study of any society must include the study of its origins as well as that of its dissolution. Gallino has observed that, for Gramsci, the first subject of social science is real history, whereas society in general is never the object of study. This does not mean that history is merely a narrative of change without the attempt to discover the structural causes of change. Gramsci in fact often suggests that history cannot be studied merely as a succession of events; for, after all, the study of change is not possible without the adequate description of what changes. Gramsci is concerned with avoiding a conception of society in general; such a conception would lack specificity and would lead to the kind of empty generalizations that he thought were typical of sociology.
Two main issues are related to the transience of social phenomena. On the one hand, we must understand their temporality, the patterns and rhythms of historical time; on the other hand, the reasons for the change, or historical causation must also be explained. Historical time is in itself an important issue, for it gives a sense to the events occurring at a specified epoch. One of the reasons why Gramsci rejects sociological schemas is that they neglect the conditions of time and place or they are conceived as 'abstract universals, outside time and space'. It is clear that two important aspects must not be neglected in specifications of historical events:(1)their geographical setting, which is a complex of natural and social conditions; (2) their historical time. It is the latter that interests us at this point.
The relevance of historical time is two–fold. On the one hand, as we shall see, there seem to be social processes of different duration; they exhibit different tempos. Second, time in history often takes the character of an index which denominates variations in social systems. Thus, one speaks of the Age of the Reformation, the Middle Ages, or the Roman Empire, as descriptive terms for complex social systems. The adequate description of social phenomena requires, Gramsci suggests, both knowledge of their intrinsic properties and the properties of the system in which they occur, inasmuch as the character of such phenomena varies with systemic variations. A case in point is Gramsci's, as well as Marx's definition of 'human nature' as the ensemble of social relations. The freezing and consequent cracking of a car radiator – the example used by Hempel to illustrate his theory of scientific explanation – will not really differ whether the event takes place in the Arctic in 1946, or in the Alps in 1986. But a social event such as a wedding, may have a very different significance whether it takes place in the twelfth century or the twentieth century, whether it occurs in a rural setting or in a modern city. The wedding of Isabel and Ferdinand in 1469 in effect resulted in the creation of the absolute monarchy of a united Spain, whereas a similar event today is almost unthinkable.
Thus, although under a certain description both weddings are events of the same type, a fuller description (one that includes systemic concepts) results in a different evaluation of their significance and their typicality. The question, then is, how far must one go in describing social events? Marx, in the _Grundrisse_ , as I have already noted in Chapter One, chastised Malthus' conception of overpopulation for being 'altogether false and childish because he regards _over population_ as being of the same kind in all the different historical phases of economic development; does not understand their specific differences, and hence stupidly reduces these very complicated and varying relations to a simple relation....' Both Marx and Gramsci concur in their criticism of generalizations that fail to recognize the different significance of similar social phenomena in different historical circumstances.
The political consequences of this theoretical question did not escape Gramsci. Deficiency of description may be the theoretical aspect of the equation of social democracy with fascism, for they are regimes of the same kind, that is, bourgeois regimes. Yet, as Gramsci saw, there is a world of difference between them.
Although Gramsci does not give any well-developed historical examples to buttress his arguments, he certainly has two in mind. First, he refers to the different forms of universal suffrage that prevailed in France according to changes in economic and political relations between Paris and the provinces, that is, between the urban and rural forces. Gramsci suggests that universal suffrage cannot be understood except by relating it to the relations of forces and to the temporary defeats and victories, the goals and the tactics of these forces. The second example refers to what he calls Caesarism. He argues that Gaesarism is the expression of a situation in which the political forces in struggle are in equilibrium, so that neither can dominate the other. It is in such circumstances that Caesarist solutions are usually found. However, the simple formula of two forces, A and B, in equilibrium is too abstract; Caesarism cannot be understood with such sociological generalizations because its concrete significance varies with the historical circumstances in which it emerges. There can be, he argues, progressive and regressive Caesarism, depending on which element prevails in the dialectic of revolution or restoration. As examples of progressive Caesarism, Gramsci mentions Caesar and Napoleon I; he mentions Napoleon III and Bismarck as examples of regressive Caesarism.
The second example may be thought to introduce evaluative elements in the description of social phenomena. This may be thought to be inappropriate in so far as it is often thought that descriptions should be kept separate from valuations. However, there are two sorts of reasons why Gramsci may have proceeded in this manner. First, the philosophy of praxis, as he often described Marxism, is not only interested in understanding the world, but also in changing it. The political activity of those who are engaged in changing the world must be based on both true descriptions and evaluations, for their attitude towards a progressive force must be very different from that towards a regressive force. As a consequence, Marxist theory, in so far as it aspires to the unity of theory and practice, must, from time to time, evaluate the degree of progressiveness of social forces. This does not mean that such value judgments are arbitrary; for the actions of the parties concerned can be seen to promote universal interests or to inhibit them. And this brings us to the second sort of reason; the evaluation of the degree of progressiveness of a ruler or an institution must be based on the results of his or her actions or its consequences. It is the effects of the situation in which Caesarism emerges that will indicate what kind of situation it is. And this is not a question of value, but a description of effects, a causal judgement. Hence, even if we refuse to evaluate a type of Caesarism, its specific character will be known not from some generalization about Caesarism, but about the effects that any one case will have at a given historical period.
This is one of the crucial aspects of Gramsci's historicism. An historical phenomenon is not fully known until its effects can be described. This is in fact a view held by some historians. For instance, Hexter argues that 'History is a becoming, an ongoing, and it is to be understood not only in terms of what comes before but also of what comes after'. For this reason, as more of the effects of an event are known, the history of that event has to be rewritten. In a similar vein, Randall and Haines argue that 'the meaning and significance of the past is continually changing with the occurrence of fresh events'.
This view of the historical process implies that understanding the present is important for understanding the past In Gramsci's words, the present is 'in a sense the best document of the past', because 'every real historical phase leaves traces of itself in the successive phases'. The present, hence, contains the past, but not all the past; only those aspects that were essential, or viable, survive. These considerations led Gramsci to infer the 'research canon' that 'subsequent events shed light on the preceding ones'. Failure to apply this canon, Gramsci maintains, often results in sociological schemas instead of historical explanation. The present, then, offers a principle of selection, a document of the meaning or significance of the past. Surely, many aspects of the past will be discovered, but one must avoid 'the dangers of sentimental antiquarianism', as Christopher Hill puts it; the selection of sources, as well as our understanding of their significance must be directed by the present as document.
Several issues are closely related to this theory of historical events. First, it seems that one of the important aspects of social institutions, such as Caesarism or hegemony, is their function. It is well known that functional explanations require the explanation of an event in terms of its effects, and in some cases, this might involve some form of teleological explanation. Gramsci does not accept teleological explanations. His 'functional explanations' do not involve the thesis that the future consequences of an event cause this event to take place. Yet Gramsci sometimes explains features of society in terms of their consequences. The point is merely that an adequate description of social phenomena requires knowledge of their consequences, for our knowledge of the significance or function of social phenomena depends on the kinds of consequences that follow them. It is in terms of the function of a phenomenon, more that in terms of its inherent properties, that comparisons between phenomena are possible. On this basis, for instance, Gramsci compares the use of Latin in the Middle Ages in Europe to the ideographical writing of Chinese culture, for although the two phenomena are intrinsically heterogeneous, they performed 'the same function: that of transmitting the culture of a ruling class not rooted in the cultural and linguistic reality' of the national masses.
Second, this theory of historical events entails that the present cannot be fully described, and hence not fully known, precisely because we lack knowledge of its eventual consequences. Gramsci argues that the structural phase of a social formation 'can be concretely studied and analysed only after it has completed all its process of development, not during the process itself. Unfortunately, this statement is ambiguous because Gramsci gives no indication of what a structural phase might be; it may indicate a whole era in which a mode of production is dominant, or it may indicate a stage within the life of a mode of production, say state capitalism, as opposed to other stages in the development of capitalism. Nevertheless, the significance of this passage for our purposes seems to be clear, that is, to reiterate, that knowledge of social phenomena requires that we investigate both its antecedents as well as its consequences, at least until its latent forces are spent or, what is the same thing, until its process of development is completed.
As Bhaskar has recently argued, 'the possibilities inherent in a new social development will often become apparent long after the development itself, which is why 'history must be continually rewritten'. The 'historical (transformational) character' of social systems implies that 'social scientific (unlike natural scientific) theory is _necessarily_ incomplete'. The incompleteness of all social theories, including Marxism, is one of the reasons for their historicity. Their limitations are linked to the objective process of social transformation, as well as the subjective process in so far as social theories are also a part of the process. Thus, their historicity can be said to be two-fold; first, as a social system unfolds, knowledge of that system is modified and second, theories also change to reflect the changes in the systems, that is, they are also, and to a certain extent, ideologies. This double historicity of social theories entails that, as we have seen in Chapter One, Gramsci's historicism is not a closed or an absolute one, for the truth of the theory, which depends on its correspondence to reality, is not necessarily the same as its function, or its character as ideology.
This brings us to the third point. Gramsci's language suggests that 'structural phases' undergo processes of change which come to an end; in other words, that the historical process at the structural level is not a continuous one. The breaks in continuity mark the completion of the process, the exhaustion of its possibilities. This is, in part, the sense that Gramsci extracted from the two principles he so often quoted, namely: 'No social order is ever destroyed before all the productive forces for which it is sufficient have been developed.... Mankind thus inevitably sets itself only such tasks as it is able to solve.'
I think that at this point it is evident that the unit of historical research is, for Gramsci, not the event, and that history is not a narrative or a time series of discrete events. This implies that those philosophers of history who set as a basic example of a historical event 'Caesar crossed the Rubicon', or like Hempel, 'the car radiator cracked', are not engaged in studying the same sort of history that Gramsci conceptualizes. Establishing events as well as explaining the proximate causes, themselves prior events, is only the surface of historical research, the first step in the collection of evidence, but not the proper historiographical task of explaining historical phenomena. The kings of phenomena that form the material for historical explanation are, for Gramsci, structural, institutional, and functional phenomena, such as social groups, parties, hegemony, and, above all, social relations. It would appear that Gramsci's conception of what constitutes the subject matter of social theory is similar to that of Bhaskar, who argues that sociology is concerned 'with the persistent _relations_ between individuals (and groups) and with the relations between these relations (and between such relations and nature and the products of such relations)'. By way of analogy we can visualise Gramsci's concept of history as the constant friction of continental plates in their slow, but sometimes earthshaking motion, rather than the collision of two billiard balls. Again, a similar view has been defended by Bhaskar, who argues that 'the objects of experimental activity are not events and their conjunctions, but structures, generative mechanisms and the like'.
Furthermore, Gramsci approaches historical research in a holistic manner, understanding by holism the view 'that in any given society we cannot understand the parts unless we understand their function and roles in relation to each other and in relation to the whole'. This definition of holism, however, needs some qualification. In the first place, Gramsci holds that there are elements in a social whole that are causally primary; he subscribes to the view that the social relations of production are determining in the last instance. This claim will be further elaborated in Chapter Three. In the second place, it is not always obvious that Gramsci espouses holism, nor is his conception of this theory very clear. We cannot enter here into the debates between holism and methodological individualism; we can, however, propose a tentative interpretation of Gramsci's thought on this issue.
Gramsci affirms that, because 'every social aggregate is in fact something more than the sum of its parts... the law that explains social aggregates is not a "physical law"', in physics one does not leave the realm of 'quantity other than as a metaphor'. The difference, then, between physical laws and laws of society is that whereas the former apply to objects whose aggregates are identical to the sum of their parts, the latter belong to wholes in which the sum of the parts result in the passage from quantity to quality. In this transformation, new properties or new laws emerge; these are not reducible to the properties, or the laws, that regulate the behaviour of the component parts outside the system or whole. For instance, the laws of society are not reducible to, or explainable in terms of, the laws of psychology, without remainder.
It must be noted that Gramsci may be wrong about his assessment of physical aggregates; the behaviour of a planet within the planetary system is different from what it would be in the absence of all the other solar bodies. Its actual behaviour is explained by the application of the laws of physics and a so-called rule of composition, such as the parallelogram of forces. This rule of composition, as Brodbeck argues, is not properly a rule; it is but an empirical law of the system. Whether this law of the system is an emergent law, one not reducible to the laws of the component parts, is an open question. In any case, laws of composition are not foreign to physics.
Gramsci is defending two basic theses, theses that can be taken to constitute his definition of holism. First, social wholes do not exist apart from the activity of individuals. One must not hypostatize such wholes, as idealists do when they posit a spirit, or the state, as a being in itself; or as religion does, he suggests, in referring the earthly process of history to a transcendent being. Modern idealists, he continues in a reference to Gentile, posit a state that is superior to individuals. Whereas idealist and religious thinkers hypostatize the whole, and thus tend to neglect the individuals through whose activity it exists, positivist sociology is content with statistical analysis, that is, with the simple addition of parts. The most fertile and original contribution of historical materialism is that it takes quantity and quality as being closely connected.
Second, and this cannot be too strongly asserted, Gramsci seems to think that what differentiates the mere addition of the parts from a social whole is _functional emergence_ not _existential emergence_ , that is, wholes differ from mere aggregates in that the former are subject to laws which cannot be reduced to the laws applying to its individual members separately, and not because of the emergence of a new object. The difference in the behaviour of a whole is a result of its organization, that is, its structural or systemic character. In Gramsci's view, the social relations of production, hegemony, and, when necessary, coercion are the basic structuring principles of a societal whole, principles that account for the behaviour of individuals in accordance with the emergent laws of the whole. (Gramsci does not use the expression 'emergence'; his theory, as indicated above, is couched in terms of the basic principles of dialectics regarding the passage from quantity to quality.)
Gramsci rejects any attempt to reduce social laws, or laws of history, to psychological, biological, or, as he thinks is done by those who deify hypostatized matter, physical ones. If we accept Gellner's argument that methodological individualism is not different from psychologism, then Gramsci rejects methodological individualism. His argument is based on the premiss that values, dispositions, etc., are shaped by hegemonic forces – in Gellner's view, psychologism fails in that 'as a matter of causal fact, our dispositions are not independent of the social context in which they occur'. Incidentally, Gellner also contends that, as a matter of logic, dispositions 'cannot be described without reference to their social context'.
However, in the same note, Gramsci also maintains that the 'something' hypostatized by idealist thinkers, is 'an arbitrary abstraction, not a procedure of analytical distinction practically convenient for pedagogical reasons'. This, it would seem, points to a different kind of holism; one in which the laws of the system are, in principle, reducible to the laws of its component parts, though in practice it is difficult or even unnecessary to effect the reduction. Given, however, Gramsci's rejection of the causal import of statistical generalizations, as we shall see later on, his acceptance of an undefined link between quantity and quality, and his dislike for reductionism, his philosophy of social explanation is closer to holism than to methodological individualism. In short, Gramsci offers a guarded and partial defence of holism. He is anxious to avoid any metaphysical reality above the activities of individual human beings which would in any case be inconsistent with his humanism; at the same time, he suggests that the organizational complexity of social systems gives rise to laws which are systemic and not reducible without remainder to the laws of psychology, biology, or physics.
Given Gramsci's theory of transience, the relations between parts and whole, their structures and functions must be seen not only as they obtain at any given moment, but, above all, in their development through time. This means that, as we have already seen, the process is best known when its development is completed, that is, when we have the evidence of its consequences as well as that of its causes. A methodological consequence of Gramsci's historicism is that the theoretical concepts proper to the study of society must be historical concepts. Proper theoretical concepts cannot be established by any model of society which merely seeks to capture its structure at any given moment; they cannot be conceived as a structural logic that can simply be abstracted from the totality of social phenomena, for the totality of social phenomena is never given in a single time, and hence no snapshot can adequately grasp it. Theoretical concepts, such as class or hegemony, have a temporal dimension which defines them as much as their synchronic characteristics. They are, in short, each of them an abstraction that holds for a series of interrelated phenomena over a period of time, not simply a matter of series of properties in a static whole. This, of course, is not a denial of social theory, nor is it a rejection of the need to abstract from the empirically given. It is rather a conception of theory thought to be suitable for a type of phenomena, namely, social phenomena, which change rapidly.
The emphasis on the difficulty in knowing the social structure of the present is not intended as a rejection of any attempt to understand the present. But it certainly is a warning that any such attempt can only produce knowledge that is at best uncorroborated hypotheses. In this regard, the expected or predicted outcome of the present situation is relevant evidence for understanding this situation. Consequently, if any trends can be identified in the present, they could be used to produce a fuller but tentative description of current phenomena. This, as is easily seen, involves a circle which seems to be theoretically unsolvable. I shall later return to the question of prediction.
In the context of Gramsci's conception of the present as 'document of the past', we must briefly remember Croce's theory of the contemporaneity of history. As we saw, Croce argued that it is the soul of the historian, steeped as it is in the problems of the present, that brings the available documents to life. A second sense of 'contemporary history' also seems to be present in Croce's work; according to this second sense, the past only lives in the present, that is, in the eternal ideal history of the spirit. Gramsci, in contrast, does not deny the actual past existence of events, nor does he claim that they only become alive in the present. Part of the reason for this is that the significance of the past in relation to the present is a causal one, not one of the preservation of life in an atemporal, ahistorical spirit In short, the relation between past and present is seen in two related ways. First, as a relation of cause and consequence; second, as a relation between historical reality and the evidence for it The present contains evidence of what was necessary in the past. Necessity, then, is seen _post-factum:_ we can now identify the necessary features of the past in so far as they produced effects that have survived to the present.
From a methodological point of view, one of the fundamental components of Gramsci's historicism is that the rigorous investigation of social systems is possible only from a long-term perspective, or a historical perspective. This involves two issues: on the one hand, it is necessary to look at the long-term development of social systems; on the other hand, the theoretical concepts used to explain them must be abstracted from the long-term processes of the system, in other words, they must be historical concepts. Note that this does not mean that as conditions change, the concepts and theories will also change. It means, rather, that theoretical concepts must emerge out of the complex abstraction of evidence ranging over a suitably long period of time, not out of a synchronic analysis of a social system.
It is with this theory in mind that we can understand Gramsci's comments on the periodization of the French Revolution. Noting that historians generally do not agree on the date on which the revolution ended, he argues that it 'was only in 1870 – 71... that all the germs originated in 1789 were historically exhausted'. The reason for this is that only at that time was the victorious class able to defeat both the old regime and the new groups that had arisen in that period. This means that the French social structure was finally settled, as later developments would show, and that allowed the researcher to grasp the real character of the French Revolution, to understand the necessary, vital, and lasting features of that episode of French history.
Given this understanding of social phenomena, it is to be expected that Gramsci would provide some reflections on the subject of historical time. Indeed, the first theme of Gramsci's reflection on the two principles by Marx quoted above, is precisely the various kinds of temporal processes to be found in history, their various rhythms, as well as their possible relationships in a more or less integrated whole. It can be said without exaggeration that Gramsci's reflection on the aforementioned principles provided the foundation for his historicism. Gramsci draws two main consequences from them. First, an organic theory of society which rejects the atomist conception of history as a series of discrete events; second, the rudiments of a theory of historical time, or more precisely, of a theory of the various tempos that criss-cross each other in history. It is this second issue that we shall now discuss.
The temporality of history has been the focus of reflection of historians and philosophers. Among others, Vico espoused a theory of the course and recourse of historical stages in a repetitive cycle of the age of Gods, the age of heroes, and the age of men; each age had its own characteristic mental structure. Comte also thought of history as the progress from the age of theology to the scientific or positive age. And of course Marx not only periodized history according to the various modes of production that succeed one another, but, most important, he called attention to short-term cycles, the five-to-seven-year business cycles, that produced crises in capitalist societies.
In the 1920s Kondratieff and Trotsky engaged in a debate on the condition of equilibrium in capitalist societies which was brought about by the studies of the former on what he called long-wave cycles. This type of cycle, lasting forty to sixty years, Kondratieff reasons, is linked to the 'wear and tear, replacement, and increase in those basic capital goods requiring a long period of time and tremendous investments for their production'.
But the study of historical tempos is best associated with the work of Fernand Braudel and other _Annalist_ historians. In 1949 Braudel published his influential work on _La Mediterranée et le Monde Mediterranéen á l'Époque de Philipe II_ , a book also written in jail. In this work, Braudel produced a three-tiered analysis of the Mediterranean world in which each level represented a type of historical duration. The first part of the book, corresponding to the first level, was devoted to the analysis of 'an almost immobile history, that of man in his relationship to the environment'. The second part, correponding to the second level, contained the study of 'social history, that of groups and their groupings' which exhibits a perceptible but very slow rhythm. The third part, corresponding to the third level, focused on the events and individuals, _l_ ' _histoire événementielle_ as Simiand had called it, which is a history of 'brief, rapid, nervous oscillations'. Braudel called these three types of duration geographical time, social time, and individual time respectively.
Braudel returned to this conception of historical time in an essay published in 1958 where he noted that socio-economic history places the concept of cyclical oscillation at the centre of its investigation. Whereas traditional, narrative history focused on the short duration, the drama of events and individuals, this new history looks at the conjunctures, that is, cycles, that may last 20 or even 50 years. He notes, however, that there are processes that last much longer; the concept proposed by Braudel to grasp this ' _longue durée_ ' is that of structure. Structures 'are stable elements for an infinitude of generations', such as for instance, the geographical determinants that put a constant pressure on the relations between humanity and nature. We must not think, however, that geography provides the only long-lasting structures, for, as Braudel notes, 'mental frameworks are also long-term prisons'. As an example of this kind of structure, he mentions the Aristotelian conception of the universe, which dominated astronomy until the age of Gallileo, Descartes, and Newton.
Braudel's project, as indeed the project of the French historical school known as the _Annales_ school, was a far-reaching attempt to enrich historical studies by introducing the theories developed by the social sciences in general. However, he thought that the lack of concern for duration, the emphasis on the immediate, the present, 'with its "volcanic" heat and teeming richness', detracted from their scientificity, for past and present explain each other, shed light on each other. This is, precisely, the essence of Gramsci's critique of sociology, that is, its neglect of the canon of historical research according to which the present state of society is the consequence of the past and, for this reason, is the best document of the past.
The _Annales_ school founded by Marc Bloch and Lucien Fevre in the 1920s, must be seen as part of the reaction against Rankean history and its emphasis on political history and the history of events. Simiand called this _histoire événementielle_. In order to develop a total history on a more solid foundation, he thought, one must begin with 'an attack on what he called the three "idols of the tribe" of historians: the idol of politics, the idol of the individual and the idol of chronology'. In fact, this is an attack on the historicism of the German school. That attack was led by Lamprecht in Germany, J. H. Robinson and Charles Beard in the USA, Simiand himself and, later, the _Annalistes_ in France. The _Annales_ paradigm, as it has been called, has become very influential, even among Marxist historians. Pierre Vilar, for instance, in his work on _La Catalogue dans l'Espagne Moderns_ focused his research on the geographical milieu and the conjunctural process in an effort to provide not only an understanding of modern Catalonia, but also a theory of the nation.
It would seem that the new historiography in its sympathetic approach to geography, economics, sociology, and psychology is incompatible with Gramsci's historicism. However, on a closer look, Gramsci's historicism is not a rejection of social and economic theories in general, but a rejection of synchronic social theories; as we have seen, Braudel also complains of the lack of understanding of time among sociologists. Gramsci, in fact, often refers to economic theory to explain social phenomena; for instance, in his reflections on Italian society, he suggests that the broad role assigned to the state is linked to patterns of investment typical of a society with many investors and few producers. Furthermore, the existence of a parasite group of middle-class investors, or the absence of 'a rational demographic composition', is given as one of the historically evolved conditions for the existence of a fossilized class of intellectuals typical of European traditions and civilization. If demography and investment patterns are relevant to historical analysis, then the conclusion we must reach, at least tentatively, is that Gramsci was not opposed to theoretical generalizations, although he strongly rejected the kinds of abstract generalizations of the sociology he knew. Let us now turn to his reflections on the issue of historical time.
As I have indicated above, it was Marx's two principles which led Gramsci to think about historical time. In a note devoted to the 'crucial problem' of the relationship between structure and superstructure, Gramsci writes that 'one can draw some canons of historical methodology' from Marx's two principles: the first such canon he draws is that 'in the study of a structure, it is necessary to distinguish that which is permanent from that which is occasional'. He redefined this distinction as that between 'organic movements (relatively permanent)' and 'conjunctural movements (... which appear as occasional, immediate, almost accidental)'.
It is the ensemble of forces of production which Gramsci thinks are 'the least variable element in historical development', and because of this they 'can be measured with mathematical exactitude, which can give rise to an experimental science of history, in the precise sense in which one can speak of "experimental" in history'. Organic movements involve the structure of a social system and tend to last decades. Their long duration furnishes evidence that 'incurable contradictions' have matured and that the forces of conservation are attempting to prevent the dissolution of the _status quo_. It seems, then, that Gramsci is affirming or asserting two propositions: first, that relative to the superstructure, the structure is permanent; second, that serious structural crises tend to last longer than other types of crises.
However, not all long-term processes are structural. Gramsci notes, as Braudel did with mental structures, that intellectual attitudes may last hundreds of years, spanning over different modes of production, with little change. Gramsci indicates his intention to embark on a 'double series of researches. One on the Age of Risorgimento and a second one on the preceding history... inasmuch as it has created cultural elements that have had repercussions on the Age of Risorgimento'. As an example of the second type of research, Gramsci reflects on the origin of what he calls the cosmopolitan character of Italian intellectuals, that is, their failure to produce a national intellectual climate as well as a national popular literature. He indicates that the genesis of this intellectual phenomenon is to be found in the passage from the Roman Republic to the Empire. It was, he notes, the transformation of the 'equilibrium of the peninsula in the classical world' that was involved in the creation of the Empire, that resulted in the creation of a 'bureaucratic' centre in Rome and, with it, the de-nationalization of Rome and the peninsula, which became a 'cosmopolitan terrain'.
Apart from the empirical accuracy of Gramsci's analysis, the methodological point he is making, as well as the remarkable similarity with Braudel's analysis, is clear. For the long duration of intellectual attitudes, such as the cosmopolitanization of Italian intellectuals, its persistence through centuries, is to be understood as a structure in the Braudelian sense, and that means that, as we have seen, historical phenomena are not simply discrete events, but long-lasting, slowly changing, relatively permanent determining factors – what Braudel refers to as prisons.
Absent from Gramsci's reflection is any reference to the temporality of geography. In Braudel's work the geographical structures are the slow-changing, long-term phenomena that underlie all social change, and in Vilar's work on Catalonia the regional aspects of nationality are conceived as forming the core of a way of living, of the psychology of a nation. This is not to say that Gramsci did not pay attention to regional differences. Such differences were so obvious in Italy that they had become the object of intense debate and analysis in which Gramsci himself participated. As I mentioned earlier, Gramsci not only rejected sociology for abstracting from time conditions, but also from space. That is, from the geographical conditions of social processes. In his analysis of Italian history, Gramsci took care to distinguish five 'forces' which were defined in terms of human geography, and which he thought of as a general outline for the study of city/country-side relations. These five forces were: (1) the northern urban force; (2) the southern rural force; (3) the northem/central rural force; (4) the rural force of Sicily; (5) the rural force of Sardinia. He then attempted to understand the relations between the different regions on the analogy of a train whose engine would be the northern urban force. The problem of the unity of the Italian state was, in part, the problem of the best arrangement to 'build a "train" that would advance the fastest through history'. Nevertheless, Gramsci did not fully and explicitly develop his geographical insights, nor did he incorporate them into the analysis of transience he drew from Marx's statements.
The organic crises that Gramsci so carefully distinguished from conjunctural ones, seem to correspond to the exhaustion of the possibilities inherent in a social system. I do not think that the conception of crises that last for decades could be compared to Kondratieff's long wave, simply because Gramsci seems to be concerned with the deep contradictions whose maturation signals the end of a social system, not with the forces of equilibrium within the capitalist mode of production.
Conjunctures are defined by Gramsci 'as the ensemble of circumstances which determine the market in a given phase', and the process of ever new combinations of such circumstances 'as the economic cycle'. In another note, he defines them as 'the complex of the immediate and transitory characteristics of the economic situation'. And he adds that the economic situation is to be understood as the 'more fundamental and permanent characters'. Conjunctural crises, one can conclude, are the temporary crises linked to the business cycle, which in general do not appear to be catastrophic.
So far, we have taken Gramsci's definition of organic and conjunctural movements as being structural. Yet Gramsci's analysis of a situation in terms of relations of forces suggests that a situation also involves the superstructures. In effect, the distinction between conjunctural and organic movements can also be conceptualized from the point of view of politics. In political terms, Gramsci links the study of conjectures to 'immediate politics', or to short-term tactics, one could say, to the solution of day-to-day problems. The study of the situation, on the other hand, is tied to long-term strategy, to fundamental historical problems. Hence, conjunctural problems, although 'certainly dependent' on organic movements, have little historical significance; they give rise to petty political critique, they involve small leading groups and personalities. In contrast, 'organic phenomena give rise to socio-historical critique, which involves the great groupings, beyond the immediately responsible individuals and beyond the leading personnel'.
The distinction between structures and conjunctures, Gramsci maintains, is to be applied to all situations, not only to regressive ones or to crises. In general, it seems that Gramsci attempts to put what he calls the 'situation' as the unit of historical and political analysis. The Argentine sociologist Portantiero has clearly grasped the theoretical significance of Gramsci's analysis of situation. Suggesting that Gramsci should be called the "theoretician of conjunctures", (in Gramsci's terms the modern use of 'conjuncture' is _his_ 'situation') he argues that the situation is 'the concurrence of specific temporalities which results in the "event"'. And he adds that Gramsci's historicism should be taken to mean that the relations of forces in each of the various levels 'express the rhythm of their own, irreducible histories'. Structure, conjuncture, event: these are the elements of the situation, each with its specific rhythm, its temporality, and all linked together in a dialectical unity, a unity of contradictory forces.
It must be noted that Gramsci proposed his theory of historical duration as a principle for historical research. The significance of the principle is not to be taken as a hypostatization of time, time as a creative subject of specific rhythms. If Gramsci thought that that principle had great theoretical and practical significance, it is not because he gave particular attention to time in the abstract, but because he thought that temporal distinctions pointed to a crucial issue, namely, historical causation. He observed that a frequent error in historico-political analysis is that of not finding 'the right relation between that which is organic and that which is occasional: thus one manages to put forward as immediately operative causes that instead are mediately operative, or to assert that the immediate causes are the only effective ones'. These two errors lie at the core of economism and ideologism: 'in one case the mechanical causes are overestimated; in the other the voluntaristic and individual element is exaggerated'. The task of historical and political analysis is to find the right 'dialectical nexus between the two orders of movement', a task that, Gramsci acknowledges, is not easy.
As Fontana, a Spanish historian, has observed with respect to Gramsci's interpretation of Marxism, historical materialism proposes a concept of determinism which refers to 'the "organic" variations that profoundly affect the structure and have important consequences for class-struggle, but not to the immediate, and conjunctural economic reasons of the struggle among groups, which fall in the sphere of traditional political history'. This of course implies that, although the economic structure, that is, the relations among classes, constitute the stage or the backbone of the historical process, not all social phenomena are immediately related to it. The economic structure, the long-term process of class relations, determines the general shape of the landscape of history as well as its fundamental changes, just as the continental plates determine the geography of the earth; but above it, the details of the landscape are autonomous in many ways. The conclusion that one can reach is, in Fontana's words, that it is only with regard to organic changes that 'Marx's assertion according to which men take consciousness of the conflicts that appear in the economic structure in the terrain of ideologies' make sense.
Unfortunately, Gramsci's theory of a situation and its various orders of movement was merely a sketch, not a well developed theory. The situation is the conjunction of structural and superstructural processes, each with its own dynamic, its own temporality. This implies that each process is autonomous to a certain degree, for otherwise the causal links between them would not allow for differences in their rhythms. However, as we have seen above, there are political processes that are organic, that is, linked to the long-term or 'strategic' process of change; and there are as well conjunctural political processes, or short-term or 'tactical' ones. There are also, as we have seen in the case of the cosmopolitanism of Italian intellectuals, superstructural elements of very long duration. One could suggest that other phenomena, for instance patriarchy, could be understood as long-term elements that play a causal role in the specific character of social wholes. In spite of these interesting insights, Gramsci does not give any precise theory of the relationship between these various elements, nor does he suggest how the interdependence on the one hand, and the partial autonomy of the various processes, on the other, could be conceptualized. Thus, as is often the case in the _Prison Notebooks_ , we find a suggestive sketch of how one might approach a historical problem, but little else. This is not to say that the sketch in itself is without value, for it is certainly rich in possibilities.
Perhaps what is most interesting in it is Gramsci's cautious attitude; what is in reality a basic historical problem could hardly be solved by conceptual means alone. If anything, Gramsci wanted to avoid what he thought was one of the basic theoretical errors of economism, namely, to take as a historical cause what is a canon of research and interpretation. This theoretical error, or perhaps it was a mental attitude, transformed 'the methodological principles developed by Marx and Engels into mere verbal, almost liturgical formulae, which are not used as analytical instruments to reach conclusions, but are merely enunciated as if they were an explanation'. Today, Gramsci's caution should be taken as the rejection of the pursuit of pure theory without the support of historical documents; that is, it ought to be seen as a rejection of what E. P. Thompson called the kangaroo factor: 'gigantic bounds through the conceptual elements, with the most gracious curvatures of thought', and little contact with the ground of historical reality, the documents to which Gramsci often referred.
The construction and analysis of situations is a fruitful, if difficult, approach to solving historiographical problems. In a sense, Braudel, Vilar, and many other modern historians, have attempted to develop our understanding of the articulation of structures, conjunctures, and events in the contradictory unity of a social formation. What is remarkable is that Gramsci's historicism as a conception of the transience of social phenomena, should transcend the narrative tradition in history and should begin to think in terms that today seem very modern.
I have suggested above that there are some similarities between Gramsci's and Braudel's thought. These similarities, however, should not be exaggerated, nor should they lead to the conclusion that Gramsci was a precursor of Braudel. My intention in this comparison was primarily to put in relief Gramsci's search for an integral history. In so doing, I neglected some aspects of Gramsci's thought that do not seem to match with Braudel's project. As Aymard has observed, 'the Risorgimento is the centre' of Gramsci's analysis, whereas the French Revolution was never the centre of historical research of the _Annales_ school'. The reason for this is that Gramsci's interest was primarily political, and this marks the great difference between Gramsci and those who followed Simiand in deposing the idol of politics. However, Gramsci's historiography was not political in the old sense of the historicists, as we shall see later on.
Gramsci's view of historicism as the theory of transience contains two related points. First, the principle that historical phenomena must be both described and explained not only by their antecedents but also by their consequences; second, that the unity of historical analysis is the situation, that is, the concurrence of processes of different duration. Both aspects point to the importance of an adequate understanding of historical time. Historical subjects must be studied both diachronically and sychronically; that is, both the sequence of causal links, and the interrelationships between elements at any given point in time are essential for historical understanding. Since Gramsci's analysis, as he explicitly stated, concerns the question of historical causality, I shall now turn to the second aspect of historicism, namely, historical necessity.
Historical necessity
The issue of historical necessity is probably the most crucial one for understanding the contrast between Gramsci's historicism and other forms of historicism, for it is closely linked to the fundamental themes of the nature of historical facts and unity of scientific method.
Salamini has suggested that 'all laws of necessity, causality and objectivity... disappear when the masses become politically and culturally autonomous'. This would indicate that only subaltern classes are subject to laws, whereas ruling classes are free from them. If this were so, the cyclic crises of capitalism would only affect the masses, not the capitalists. In reality, however, such crises become the focus of conjunctural political and economic efforts to minimize losses. In other words, historical forces exist which exert considerable pressure on, or which restrict the freedom of, both leading and subaltern classcs.
It may seem that Gramsci's critique of sociology is above all a rejection of the conception of laws in history. There are a number of passages in the _Prison Notebooks_ which seem to argue that the organized will of the masses replaces laws in history. In his critique of sociology, to which we must now return, Gramsci argues that statistical generalizations, or laws of great numbers, are applicable to historical and political reality 'only in so far as the great masses of population remain passive'. And he adds that political activity precisely aims at changing the behaviour of the masses. So far, Salamini's interpretation agrees with Gramsci's text However, Gramsci develops his argument in a way that is as surprising as it is interesting. For he adds that, although a planned economy is 'destined to break up statistical laws mechanically understood, that is, produced by the fortuitous encounter of an infinite number of arbitrary individual acts', it nevertheless 'must be based on statistics'. And one must suppose that statistical analysis would be used to ascertain generalizations of the very sort Gramsci denounces. Indeed, Gramsci thinks that in any social system there always is a 'conformism', a collective human being, and that a hegemonic struggle in so far as it is a struggle between two forms of civilization, is also a struggle between two kinds of conformism. Each society engenders its own automatism, a conformism, as each economic structure gives rise to its _'homo oeconomicus'_.
The point that Gramsci makes against statistical generalizations is not that they cease to exist when the masses become active; it is rather, that the activity of the masses breaks up existing, oppressive, forms of automatism and substitutes a freely accepted conformism. It is not the existence of laws of great numbers, but their mechanical nature, that is, the fact that they are spontaneously accepted as natural, that Gramsci denounces. As he put it, the result of the activity of the masses is that 'human awareness replaces naturalistic spontaneity'. What underlies Gramsci's argument is his theory of human nature as a historical fact, that is, as the ensemble of social relations. The _homo oeconomicus_ is not a fixed entity, a natural essence with definite dispositions that allow for statistical generalizations.
In short, Gramsci believes that statistical generalizations have practical application, that is, they obtain within certain limits, but they are not historical laws. A prime reason why they are not historical laws is that they neglect change, and therefore they are of limited theoretical value. Politically, the assumption that these laws are 'essential laws, operating with inevitability, is not only a scientific error, but becomes a political one in action; it favours mental laziness and shallowness in programming'.
A second objection raised by Gramsci against statistical generalizations is that they merely state a fact, but have no causal significance. He writes that 'usually they are no more than a duplicate of the observed fact itself. A fact, or a series of facts, is described by means of a mechanical process of generalization, a relation of similarity is derived from it and it is given the name of law, which is then assumed to have a causal function. Gramsci's objection is mainly to the lack of causal significance of these so-called laws. The conclusion we can draw is that Gramsci does not object to either laws or the concept of causality, but to empirical descriptions which are misrepresented as being causal laws.
Gramsci's rejection of statistical generalizations is not surprising, for it is implied by his ontology. Since events are, as it were, only the surface of the social process – the external aspect of history – they are not the most significant aspects of history. They need to be explained, generalizations themselves need to be explained; for a statistical generalization is after all no more than a kind of description. Gramsci's ontology, as we saw, is based on a holistic understanding of the object of study, and it emphasizes structures and functions rather than discrete events. The distinction between the external and internal aspects of history that had been used by historicists since Vico, is used by Gramsci to oppose what he calls 'external description' to analysis of the 'causal nexus'. This distinction raises the issue of the 'right balance between the deductive method and the inductive method', which is the problem of determinate descriptions, or historical descriptions, that is, descriptions that take their subject matter as a specific historical subject, not as an abstract one devoid of temporal references. Induction alone cannot solve the problem of constructing hypotheses, for one must first have a criterion for choosing the relevant facts or the relevant relations among them, and this 'presupposes a "concept" that allows one to distinguish the facts'. As we saw earlier, this is precisely the problem of adequate description.
One must not think that Gramsci is following Croce in rejecting empirical concepts as 'pseudo-concepts', nor does Gramsci either explicitly assert or implicitly assume in his thinking, that the subject of history is the pure concept, or the predicate. Gramsci's critique of empiricism is not really different from Marx's; they both argue that the external aspects of history, the appearances, must be explained by the internal ones, the essence. The internal aspects are, for Gramsci, a 'causal nexus' and, as I have indicated before, social structures such as class-relations, and functions, such as hegemony, play an important role in shaping that causal nexus. The subject matter of history, then, is not the immediate events, although these are also considered and explained, nor is it the predicate, such as Croce's liberty. The subject matter of history is the complex interaction of sub-processes which is the ever-changing situation.
It is interesting to note that, as the expression 'causal nexus' suggests, Gramsci did not reject the concept of historical causality. In fact, he even asserts that the value of common sense is that it is not 'led astray by pseudo-scientific, or pseudo-profound, metaphysical puzzles and quibbles'; it not only 'employs the principle of causality', but identifies 'the exact cause'. What Gramsci rejects is the attribution of single causes to social phenomena. For example, he questions the view that the 'technical instrument is the unique and supreme _cause_ of economic development'.
Historical causality, then, must be analysed in terms of what Gramsci calls the situation: it involves the concurrence of sub-processes, each with its own rhythm, its own duration, resulting in an event or a change in the overall pattern. A feature of this form of causality is the reciprocal action of concurring processes. Gramsci notes how sometimes a phenomenon is both cause and effect of another phenomenon. Such a form of causality cannot, of course, obtain between two momentary discrete events; but it is quite conceivable in the case of long-term structures, where there is a relation of mutual dependence as well as antagonism between the various structural elements, such that any change in either of them affects the overall structure and hence the terms of the relation themselves (in such wholes, the existence and properties of the terms are not independent of the relation in which they arise).
The specific manner in which historical causality manifests itself is not a question that can be determined _a priori_. From Gramsci's point of view, it is an empirical problem, one that requires the most thorough and careful analysis of existing documents. The attempt to give a detailed analysis of causality is, then, a metaphysical enterprise, one that can only fail. Gramsci's scant notes on causality, must be taken as indicating a principle for historical research.
One can distinguish two general types of causality: (a) linear causality, that is, causality which, whether simple or complex, relates a series of successive events or changes; (b) structural causality, or what Gramsci at one point calls dialectical causality and Marx and Engels' reflection, which relates different sub-processes within a whole, that is, it involves the relation between structures and superstructures. In this second sense, the fundamental problem to be resolved is that of the relationship between economic structure and ideology. This distinction is, however, no more than an analytical distinction. In reality, the two forms of causality are not clearly distinguishable, for both account for changes, which are generally temporal processes. The significance of this distinction, which is only hinted at by Gramsci, is that it underlies Gramsci's case in analysing both the linear development of social systems, as well as their social depth, that is, their structure. Gramsci's historicism is not merely an assertion about the importance of historical understanding; it is also the claim that mere narration of events without social theory is scientifically inadequate.
The concept of dialectical causality emerges in a note where Gramsci discusses Corce's theory of the four distinct moments of the spirit and poses the question of the autonomy of politics. 'Given the autonomy of polities', Gramsci asks, 'what dialectical relationship exists between it and other historical manifestations?' Returning to the same issue at a later date (the first note is written in the period 1930–2, the second one in 1932–5), Gramsci writes that Croce's theory of distinct moments is a 'purely verbal solution to a real methodological requirement'. He notes that a dialectic of distinct moments is a contradiction in terms, because dialectics is a relation that obtains between opposites, not between distinct moments.
The question is unresolved by Gramsci, or so it appears. In fact, the problem of the distinction between different temporal processes, and the theory of distinct realms of Crocean origin are the same problem, the 'same methodological requirement' expressed in different terms. There is, however, one suggestion that Gramsci makes with respect to the concept of dialectical causation. He writes that the 'priority of the politico-economic fact, that is, the structure' is 'the point of reference and the point of dialectical, not mechanical, causation of the superstructure'. The expression 'dialectical causality' is dropped in the second version of the note, as also is his reference to the primacy of the politico-economic fact. Nevertheless, the problem is an important one, and much of what Gramsci writes is in some way an attempt at defining and solving this problem. Again, as he often does, Gramsci warns that this is not merely a formal problem. Referring to Croce's conception of the unity of the spirit and to a relationship of implication between distinct moments, he asks rhetorically whether this problem can have a speculative solution or only a historical one. It is obvious from Gramsci's insistence on the historical treatment of problems that he thought that the only adequate answer is a historical one, that is, one drawn from documentary evidence: a real, not speculative, solution.
Gramsci's sparse remarks on a theory of causality do not allow for a full reconstruction of any such theory he may have held. Although on occasion he refers to necessary and sufficient conditions, he does not offer any analysis of causation in these terms. One can conclude, at most, that Gramsci thought that a complex concept of causality was of some importance for the study of history, provided that one avoided a simplistic model of linear causality. Such a form of causality leads, he argues, to the question of the first cause, the prime mover. More effective for understanding history is to unravel the causal nexus, the productive or effective aspects of the situation, without necessarily attributing temporal primacy to any of them. To illustrate with an example the kind of analysis Gramsci may have had in mind, a summary of Bloch's account of the relationship between types of plough and the shape of the fields in feudal France will be useful.
Bloch notes that the wheeled plough requires more space to turn, and, to reduce this problem, the fields tended to be shaped in thin, long strips, which affected the social organization of villages. However, Bloch warns, the temptation 'to trace the whole chain of causation back to a single technological innovation' is to be resisted, for there are many other factors involved in this phenomenon. Noting that wheeled ploughs required long fields, but not narrow ones, Bloch argues that peasant mentality and hence social custom, was responsible for the thinness of the fields, for in this way each individual's land was dispersed in the village land; this allowed for equal participation in the different qualities of land, as well as equal chances of avoiding any disasters that might hit upon a restricted area. Furthermore, communal habits of cultivation were a necessary condition for the adoption of the wheeled plough.
It is the temptation to trace the 'whole development back' to a single cause, which Gramsci also wants to avoid. For in a process as complex as history, the 'single cause' is itself often dependent on some of the other contemporary conditions of the process, just as communal habits of cultivation were necessary for the adoption of the wheeled plough as well as the modifications in land tenure and organization of work that ensued.
The question that we must now turn to is that of historical laws. For if statistical laws have no causal significance, and if causality is a viable concept in historical research, what kind of historical laws would be causally significant and acceptable to Gramsci? Gramsci's critique of statistical generalizations points to both a theory of causality and a theory of causal laws. Gramsci uses the expression 'laws of history' in several contexts, which leave no doubt that he thought that some forms of law acted in social processes. Thus he writes that intellectuals must link dialectically the passion of the masses to the laws of history. This points to a view that what is felt is ultimately a result of one's relation to objective social circumstances, and presumably, knowledge of the latter is indispensable not only for self-awareness but also for political organization and action. In this context, the intellectual has the difficult task of politicizing the feelings of the masses, that is, of channelling the energy contained in those feelings to the right target.
Gramsci also argues that Fordism is the result 'of the immanent necessity' of reaching a planned economy. This would indicate that there are tendencies in the structure of the capitalist mode of production which lead to a planned economy; the outcome of these tendencies, however, depends on the response of the organized forces, an outcome that, depending on which forces prevail, may either be Fordism or even a corporatist state, such as fascism, or a socialist one. There are other instances in which Gramsci seems to depend on some notion of law, or at least, the law-like behaviour of social wholes. An example of these is Gramsci's tendency to engage in comparing aspects of different historical epochs, as he does when he writes that a better understanding of Italian intellectuals might be gained from a study of European Jewish intellectuals.
More important for our purposes are his notes on the stages of development of classes, which seem to have general application, independent of concrete historical circumstances. This form of abstraction, Anderson believes, led Gramsci to commit serious errors. Whatever the consequences which might stem from misinterpreting the assumed similarities between the compared phenomena, the point is that Gramsci implicitly accepted the concept of regularity in historical development. Further evidence of this hypothesis is furnished by Gramsci's statement to the effect that any new hegemonic group is faced by the task of creating a new moral and intellectual order, and by his belief that any newly formed state must go through a primitive, corporatist stage. Finally, Gramsci thought that 'a general principle of political science and art' could be drawn from the fact that in the course of history 'almost always similar situations arise'. It might seem that, after all, Gramsci engaged in some form of sociological abstraction such as the ones he so thoroughly rejected. It must be noticed, however, that Gramsci compares situations, not single events, which is consistent with his critique of positivist sociology as outlined above. The conclusion we can draw from these remarks is that Gramsci did not maintain that there are no laws in history. His negative comments on this respect are directed against simplistic sociological generalizations which, he felt, had no causal significance, were based on a faulty anthropology, and were merely descriptive, not explanatory.
It seems that in the light of what we have seen so far, the first condition that causal laws would have to meet is that they should not be conjunctions of events, such as that whenever A occurs, then B occurs. Events in Gramsci's ontology of history have little causal and explanatory value. It is social relations and the specific manner in which they structure social wholes that are causally primary. Implicit in the _Prison Notebooks_ , we can conclude, is a distinction between patterns of events and causal laws, a distinction which Bhaskar has also noted. These laws would clearly differ from the laws of great numbers which are merely the 'fortuitous encounter of an infinite number of individual free acts'. Nevertheless Gramsci often speaks of individuals, such as Cavour, Mazzini, Croce, etc., in his historical and political analysis. Events themselves – uprisings etc., – are also discussed on occasion. Furthermore, he discusses group activities as examples of the free choice which takes place according to certain lines which are 'identical for a great mass of individuals or single wills'. It would appear, then, that Gramsci is concerned with showing that all historical laws are reducible to patterns of events, a proposition that casts doubt on the holistic interpretation of his thought advanced above. If this were so, however, historical laws would be reducible to statistical generalizations, generalizations that Gramsci believes have no causal import Gramsci does not analyse this question in full; he suggests, however, that the patterns of events are not the cause but rather the effect, or manifestation of a deeper causal mechanism.
An individualist explanation would consist in isolating the dispositions of individuals which account for their decisions and actions. The coincidence of decisions and actions which result in a more or less unified social whole has usually been attributed to a common human nature. Theories of the possessive nature of human beings, referred to as a 'possessive individualism' by C. B. Macpherson, have often been adduced to explain the smooth functioning of the market as well as the form of the state most suited to social life. We find such theories in Machiavelli, who writes of the avaricious nature of man, as well as in Vico, Adam Smith, and others.
Gramsci, in the passage quoted above, also gives credit to the dispositions of individuals, to their wills. The difference is that whereas for the individualist the psychological explanation is ultimate, for Gramsci those dispositions are not uniquely determined by psychological laws. As suggested earlier, dispositions are themselves conditioned by social relations, hegemony, etc. At times, Gramsci's position on this issue is quite extreme. In a letter to his wife, where he discusses the progress of their son Delio, he goes so far as to assert that 'man is completely a historical formation, brought about through coercion (not exclusively understood in the sense of brute force and of external violence)', and condemns as metaphysical the theory that newborns already contain as potentiality or in a latent state their whole future development. In the _Prison Notebooks_ , however, he limits the historicity of human nature to some common element that can be described by statistical generalizations and is determined by social relations.
Historical laws would need to meet another criterion to be acceptable to Gramsci: they must not exist in an absolute or eternal way; they are not determined by extra-historical causes; such as Providence or biology, and they are not unchangeable. Gramsci writes that historical laws must be understood in a historicist manner, that is, they exist to the extent that a climate exists which is 'organically alive and connected' in its development. Although this classification of the sense of 'historicist' is obscure, one can surmise that Gramsci is thinking of the general conditions of existence of a historical bloc. The laws of history are in some sense emergent upon the activity of real empirical men and women and, above all, they depend on, among other things, the social relations that structure society. Such laws, then, are not independent of what human beings do, though they at the same time determine their activity, or at least, the general conditions under which they act. The constitution of a new historical bloc, which is equivalent to the constitution of new social relations, and hence of the emergence of new laws, is a process of transformation which begins in the old historical bloc, and one whose outcome depends on the structure of the old bloc and on the political organization of groups and classes determined by the old social relations.
Historicist laws, one can conclude, are neither 'metaphysical laws of determinism' nor 'general laws of causality'; they are the result of the historical process in which social relations constitute 'relatively "permanent" forces... which act with a certain regularity and automatism'. Long-term structures, rather than mere unstructured conjunctions of events, produce the automatism, or the 'generative mechanism', as Bhaskar calls it, which is said to be a tendential law. At one stroke, Gramsci rejected both the positivist conception of law and the speculative one, the former for its empiricism, the latter for its failure to oppose empiricism with a realist and truly immanent notion of history.
Let us now look at the more detailed notes which Gramsci devoted to the concept of historical laws. The sources of his reflections are Ricardo's conception of tendential laws on the one hand, and Marx's theory of the tendency of the rate of profit to fall on the other. Gramsci argues that the ground for a Marxist concept of tendential law is to be found in Ricardo's concept of the 'determined market' or 'determined relations of social forces in a determined structure of the productive apparatus'. The existence of a determined market reveals that 'certain decisive and permanent forces have emerged historically, forces whose operation presents itself with a certain "automatism" which allows a measure of "predictability"'. Once constituted, the relatively permanent forces are automatic because of 'their relative independence from individual will and arbitrary government intervention'.
The concept of automatism, or structural determination of tendential laws, is founded on the conception of the long-term historical processes described earlier. However, the long duration is not in itself sufficient to distinguish the core of the historical process, for there are other processes, as we have seen, that can last centuries. Gramsci speaks of relations of production and permanent forces as the basis for the emergence of tendential laws, their long duration being but a sign of their vitality and importance. Obviously, natural processes exhibit the longest rhythm; apart from them, however, Gramsci notes that the least variable element in historical development is the ensemble of forces of production, which permits accurate measurement and allows the possibility of an 'experimental science of history'. This is, Gramsci believes, the starting point for a Marxist theory of historical laws, a theory that must be carefully distinguished from statistical generalizations, which may be very useful for some practical purposes but hardly deserve to be taken as laws of historical facts.
To distinguish generalizations of the kind he called statistical laws, and historical laws proper, Gramsci refers to the concept of 'determined abstraction'. A determined abstraction is not one that compares a manifold of individuals, but one that generalizes on the basis of 'determined historical categories'. For example, a Marxist conception of the _homo oeconomicus_ is a determined abstraction because it does not take as a basis for comparison and generalization the biological or natural human being; instead, it takes human nature as historically concrete, or dated, not abstractly universal. Gramsci has little else to say about abstraction, but he seems to be struggling towards a theory of concepts not dissimilar in some respects from Marx's own exposition in the Introduction to the _Grundrisse_. The determined abstraction is Marx's concrete concept in that it is 'the unity of the diverse' rather than a mere abstraction of similarities among a group of individual facts. The diversity of individual characters is, from the point of view of relevant historical concepts, or from the point of view of their function in the social system, a similarity. Hence, determined abstractions must be based on structural conceptions of the social whole, that is, on the complex of relations that confer a specific character on the individual elements or facts.
It is in this context that we must interpret Gramsci's assertion that 'the theory of history and politics is possible for although the facts are always individual and changeable in the flux of historical movement, the concepts can be theorized'. The theoretical concepts of history, such as class, hegemony, etc., are the product of 'determined abstractions', they are what Marx called concrete concepts, concrete because they are 'the concentration of many determinations: and are the result of a "process of concentration"'. German historicists, as we saw, emphasize the uniqueness of historical events, which entails the impossibility of applying the conception of scientific laws to historical research. Gramsci, in distinguishing different temporal dimensions and the different processes that underlie the occurrence of events, is able to avert the theoretical impoverishment that threatens narrative history, thus he is able to provide a more rigorous approach to the study of society. This approach would in fact be what is now called social history, or what Gramsci called integral history. According to Kosellek, one of the basic characteristics of modern social history is precisely the concept that events and structures 'seem to have within the historical movement different temporal dimensions which should be studied separately by historical science'. Although 'events and structures are interlocked with one another', they cannot be reduced to one another. Events in themselves are unique, and therefore difficult to forecast, while structures offer the possibility of predicting the general 'condition of possible events'.
Tendential laws are obtained by isolating a 'certain number of elements, and hence neglecting counteracting forces'. Gramsci offers the law of the fall of the rate of profit as an example. The term 'tendential', he notes, has a historical, and not merely methodological, meaning; it indicates that the social process is a dialectical one, that is, a process characterized by fundamental contradictions. Because of this, events are not uniquely determined by any given causal law, but rather by the conjunction of different and often opposed tendencies.
Absent from Gramsci's thought, at least in any formalized fashion, is a conception of the overall pattern of historical development from its beginnings to his own present. There are two reasons why this is so. First, any such overall pattern, if presented as an inevitable law of progress, could not have been accepted by Gramsci; he would have deemed it too speculative. In this regard, he indicates in a causal remark, that one ought not to think of slavery as a mechanically inevitable stage of historical progress. Second, Gramsci sought to understand the case of the development of Italy since the middle of the seventeenth century. He was concerned with the conditions that led Italy to a fascist solution, hence with the weakness of the state forged by the Risorgimento. And, above all, he was concerned with the political solution to Italy's problems or with the possibility of a fully democratic, socialist state. This means that, although from a methodological standpoint he posed questions of universal interest, with regard to substantive research, he was not focusing on the whole of history. As a consequence, he did not theorize any over-reaching laws of history, laws that, either as teleological tendencies necessitating a number of necessary stages, or tendencies that result from some property of society, inevitably impel history through a series of epochs. He did, as outlined above, suggest that the laws of one epoch are tied to those of the next, but no general hypothesis about history as a whole is advanced in the _Prison Notebooks_. It is perhaps no great exaggeration to assert, as Gallino does, that Gramsci held 'a completely modern concept of law', although, as with most of his reflections, he only provided some general remarks about this concept.
Razeto and Misuraca have argued that there are two types of practical situations in history: (a) a situation where the masses are passive, and (b) one in which the masses emerge from passivity through political action. Thus, whereas in the first situation history appears as the fortuitous encounter of individual free acts, in the second situation human self-consciousness replaces the natural spontaneity of the first. Consequently, tendential laws govern the first type of situation, while self-awareness governs the second one. This is, in general outline, the same argument advanced by Salamini. According to this theory, history would be regulated by the rhythm of the succession of passivity and self-awareness, for, as Razeto and Misuraca admit, one form of automatism gives rise to a new one. The moments of self-awareness would thus punctuate the long-term cadences of passivity.
Gramsci, however, writes of the dichotomy between self-awareness and passivity only in relation to statistical generalizations, not with regard to historical laws. In fact, he argues that historical laws are not in opposition to group liberty, although they are in contrast with individual free will. This suggests that, with respect to macro-determinism, that is, with the general operation of historical laws, Gramsci is a compatibilist, but with regard to macro-determinism, or with individual choice and action, he espouses incompatibilism. It must be emphasized that Gramsci's arguments on determinism concern history, not individual action, hence they offer little evidence on his view on freedom and determinism. This is a problem that does not seem to concern him at all. The laws of history, in so far as they apply to what he calls the 'common part' of individual men and women, determine the general social process, but not all the actions of individuals participating in this process. The will and the initiative of individuals, Gramsci maintains, must not be discarded. However, he does not offer any theories as to whether this will and this initiative are, or are not, themselves determined by other factors or laws.
Furthermore, Gramsci's critique of economism, which he suggests is the theory that the economy uniquely determines all the other social processes, is mainly a rejection of mono-causal theories of history. This, however, does not entail indeterminism at the macro-level, for it would not be inconsistent for Gramsci to argue that the choices of individuals are determined by the conjunction of historical laws and other laws, such a psychological and biological ones. Since Gramsci does not discuss this issue, it is difficult to advance any hypothesis about his beliefs in the matter. What is clear, however, is that for Gramsci social groups are most free when they act according to the laws of history. If his language often suggests incompatibilism, it is because he is concerned with what he calls metaphysical or fatalist accounts of determinism. These, in effect, affirm that nothing one does can make any difference. Both libertarian indeterminists and compatibilists would agree on rejecting this claim.
Gramsci is primarily interested in clarifying an empirical connection, rather than a conceptual one, between metaphysical theories of determinism and dogmatism. He is concerned with situations in which a leader '"enlightened by reason" who has found the natural and infallible laws of historical evolution' disregards the actual possibilities inherent in reality. In this case, the belief in metaphysical determinism or fatalism becomes 'the only and dazzling intellectual motor' which may stimulate the emergence of autocratic rule. As an example of this phenomenon, Gramsci refers to the thought of intellectuals such as Spirito and Volpicelli. They believe, he argues, that they are the guardians of a veritable truth 'while others... understand nothing'. Why they, and not others, possess the truth is never explained by them, Gramsci continues, but there is a 'hint of the means by which these two believe that the truth will have to be disseminated and become self-consciousness: it is the police (remember Gentile's speech at Palermo in '24)'.
Historical laws are manifested through what Gramsci calls the 'homogeneous part' of individual wills. This homogeneous part is the automatism of the ensemble of social relations which, Gramsci seems to suggest, acts as a rule of behaviour, so that whatever the individual actors may do, the limits of their choices are governed by the rule. The automatism is proposed by the structure of a society, and hence it is independent of the will of individuals. Its operation must be manifested in countless acts, repeated many times over, such as selling labour-power, or buying commodities in the market, etc. It must be noted that this manifestation or appearance of the structures and their tendential laws as rules of behaviour, established norms, etc., constitutes the basis for Gramsci's theory of the identity of politics and economics, and it highlights the importance of hegemonic institutions. We have, then, at the level of individual behaviour, rules which are more or less known and which have the character of conformism; they are the repetitive nature of the 'homogeneous part' of individual initiative. Sociological generalizations of these events, acts, etc., are found to be inadequate because they are mere descriptions which do not disclose the 'inner aspect', that is, the structures, such as social relations, and the resultant tendencies, such as the law of the fall of the rate of profit, which account for their existence.
The actors are more or less aware of the rules, even if it is only at the low level of recognizing their existence in their own practice. Becoming conscious of their origin, of their historicity and hence of the possibility of changing the underlying structures, is the process of the formation of organized social groups, a process analysed by Gramsci in terms of the concepts of situation and the relations of forces within each situation.
Given this, one can conclude that consciousness of the structures and of their automatism does not descend upon the masses from time to time; it is rather a process that is coterminous with the historical process itself, so that as the structural elements develop so does the consciousness of the masses. Gramsci's theory of hegemony, of popular culture, and of intellectuals is the attempt to understand this complex, contradictory process. Historical necessity does not act behind, or beside, the actors themselves. True, structures are relatively independent of their will; but it is also true that, as Gramsci writes, 'historical necessity exists when there is an efficient and effective _premiss_ , consciousness of which in men's minds has become operative, proposing concrete goals to the collective consciousness'. This does not preclude the possibility of error, nor does it entail that society is transparent, so that full knowledge of it is readily acquired. As we saw, objectivity is a struggle, a process of deepening one's knowledge of reality, not an immediately given clear and distinct image of the world.
Linked to the problem of historical laws is the issue of prediction in history. On the one hand, Gramsci writes that if prediction in history is not possible, then 'irrationality cannot but dominate and any organization of men is anti-history'. On the other hand, Gramsci rejects a theory of history based on a superficial imitation of the natural sciences which seek to predict by means of law-like regularities. As Bhaskar has pointed out, prediction in history is not possible because of the very complexity of social processes which are open (that is, one cannot isolate a number of variables as is the case in controlled experiments). The tendential laws of which Gramsci writes are obtained by means of what he calls determined abstractions. In reality the various contradictory forces that constitute social reality allow for little predictability of events. Furthermore, simple, discrete events, or individual acts, are in a sense unique, which makes them unpredictable in general. Structures, on the other hand, due to their duration and inherent tendencies, offer some possibility of prediction. Gramsci writes that to predict is to see the past and the present as movement, that is, it is 'to identify accurately the fundamental and permanent elements of the process'. The permanent elements, in Gramsci's terms, are the structures; and since the structures form a contradictory whole, what can be predicted is 'the struggle, but not its concrete moments, which cannot but be the result of contrasting forces in continuous movement, not reducible to fixed quantities for in them quantity becomes quality'.
Prediction, however, is not simply a 'scientific act of knowledge'; it is in reality 'the abstract expression of the effort made, the practical mode of creating a collective will'. These statements are sufficiently ambiguous and obscure to permit differing interpretations; the one advanced here does claim to exclude other possibilities. It does claim, however, that, given Gramsci's historicism, it makes sense. Economic forecasts, such as those elaborated by bank economists, government departments, industries, etc., are based on a general assumption which can be said to be eminently practical or to involve a definite socio-political practice. They are based on the assumption that the general structure of society will not change, however much consumer preferences, investment patterns, etc., may change. The practical character of this assumption lies in the fact that the institutions within which such forecasts are made, such as banks, government offices, and the like, are actively engaged in preserving the structure of society, so that the truth of their forecast is guaranteed, in part, by their involvement in securing the continuance of the present social system. Thus, although individual economists may think that they are engaged in a pure 'scientific act of knowing', the basic assumption they make is not only theoretical; it is a practical stance.
Similarly, one could say that forecasting a future with a different socio-economic structure, when it is not done idly or as a pastime, involves a practical stance, namely, that of guaranteeing or preparing the ground for the new socio-economic structure.
As Gramsci writes, in this case one '"foresees" to the extent that one acts, to the extent that one applies a voluntary effort and hence contributes concretely to create the result "foreseen"'. It is important to notice that Gramsci does not claim that one creates the result out of one's prediction by means of a pure act of the will; he writes of contributing towards an end, which must be understood as the process of becoming conscious of the possibilities inherent in the structure and acting so as to bring them to realization. This suggests, as Texier has observed, that historical necessity and creativity or liberty are not in opposition; they form a unity. The failure to understand this unity leads to the opposition between empty, arbitrary, and individual freedom, on the one hand, and mechanical determinism, on the other.
It might be objected that not all predictions made by those who want to change the social system contain, as an assumption, this practical stance. For instance, in order to overthrow the present state of society at some future date, it is necessary to anticipate, that is, to predict as far as possible its state at that date; this would not imply that those who make such predictions are determined to preserve the present _status quo_. Nevertheless, theirs is a practical stance. Gramsci's theory may not be clear enough, or it may not be satisfactory in many respects; there is no need, however, to interpret it as a voluntarist conception of history, a conception according to which willing is a sufficient condition for the realization of desired goals.
Gramsci's conception of historical laws, causality, and prediction set him apart from both Croce and the German historicists, who in general argued against the notions of historical laws, causality, and prediction, and for whom the inner aspect of history was spiritual, generally identified with freedom and not historical necessity as it is for Gramsci. The issue that still remains to be solved is that of the unity of scientific method. As we have seen, Gramsci suggests that each science has its own method, which would indicate that rather than two general methods, one for the sciences of nature and one for the social sciences, there would be as many different methods as scientific disciplines. If this is true, Gramsci's historicism could easily lead to epistemological anarchism with no general rules for seeking and ascertaining truth. A close reading of the _Prison Notebooks_ , however, produces a more satisfactory approach to this problem, although it does not resolve it completely.
To begin with, when Gramsci writes of method he has far more in mind than the logic of explanation which Hempel and others offer as the only scientific method. There are in the _Prison Notebooks_ a number of principles or criteria said to be methodological, which leave little doubt that, for Gramsci, method is more than logic or a procedure, as it involves concepts and principles that can be considered constitutive of the subject matter itself, that is, ontological principles. A few examples will suffice to clarify this issue.
The distinction between domination and intellectual and moral leadership is presented by Gramsci as a 'methodological criterion on which our study must be based'. He also refers to the principles that 'an independent intellectual class does not exist, but any social group has its own order of intellectuals', as a 'criterion of historico-political research' which appears to be methodologically consistent. Finally, he puts forth as a methodological criterion the principle that 'the historical unity of the leading classes takes place in the state, and their history is essentially the history of states and of groups of states'. From these instances it can be concluded that at least some methodological principles are suggestions for classifying documentary evidence as well as for relating different types of phenomena. In other words, some methodological principles suggest appropriate concepts about what exists as well as explanatory schemas about the causal or other links between the objects thus conceptualized. By calling these principles methodological, Gramsci seems to suggest that they are to be regarded as tentative, always liable to be found inappropriate, and hence that they must never be uncritically superimposed on reality.
Given the broad meaning of 'methodological', it is not so odd that Gramsci should call for a distinct method for each discipline. For if we were to take a concept from physics, for instance gravitation, and attempt to apply it to sociology, it would be difficult to see what it could actually mean in the case of societies. At most, it would be a metaphor for the processes that keep societies unified; but it would not be of great service in describing and explaining that process. On the other hand, concepts such as mode of production or hegemony seem to be of far greater service and are methodologically far more appropriate for explaining social reality. This is not to deny completely that a scientific theory can suggest hypotheses for fields of research other than its own. In this regard Gramsci points out that Cuvier's principle 'of correlation among single organic parts of a body' seems to be useful in the study of society, but it must be understood, he adds, that 'for past history, the principle of correlation (or that of analogy) cannot take the place of the document'.
It has already been noted that Gramsci thinks that the economic structure of society can be the object of an experimental science in so far as it is the more permanent, as well as exactly measurable, element in a social whole. There is no clarification, however, of what 'experimental science' might concretely mean when applied to history. It is clear, however, that, as Marx pointed out, it cannot really mean experimental, for no experiments are possible in social science; instead 'the force of abstraction' must replace experiments, that is, the method cannot be really experimental, it must rely on what Gramsci called 'determined abstraction'.
It is with these considerations in mind that one must read Gramsci's statements that 'there is not a science _par excellence_ , there is not a method _par excellence_ , a "method in itself", or that it is an error to think that a method that has been successful in one type of research will be useful in another field; or that each science develops its own method. There is nothing very strange in these statements, for they do not imply that there is a rationality for physics and another rationality for biology, and so on. For, in reality, Gramsci claims that, despite the differences among the sciences, differences that stem from the distinct characteristics of their subject matter, 'there are general criteria which can be said to constitute the critical consciousness of any scientist'. One such general principle that Gramsci thinks is part of any distinct method, 'consists in its being "adequate to the end"'. To which he adds that 'the most generic and universal methodology is none other than formal or mathematical logic'. Since social phenomena are dialectical, the conclusion we can reach is that for Gramsci formal logic and dialectics are not incompatible. The main point is, however, that there are universal methodological criteria.
We have already seen that the concepts of causality, law, and necessity is not rejected by Gramsci, provided these basic scientific concepts are properly applied to the complexities of social processes. These general concepts are elements of the most general scientific methodology, which, together with formal logic, belong to the 'collection of abstract instruments of thought that have been discovered, purified, and refined through the history of philosophy and culture'. What Gramsci objects to is the uncritical application of these general methodological concepts to any subject matter without due regard to the actual constitution of that subject matter.
Some implications of Gramsci's position need to be stressed. Clearly, he argues for a historiography that explains phenomena in terms of the 'causal nexus'. Since this expression arises in the context of explaining why a hegemonic principle in opposition to another is capable of overcoming this opposition, Gramsci implies that the relations between the various levels in a social whole are causal, not merely isomorphic. This sets him apart from Kantian models of society. A transcendental Kantian social science would be one in which a set of transcendental categories would structure all social phenomena, as they would be manifestations of the human mind. An empirical variation of this conception would substitute the structure of the brain, or some such concept, for the transcendental categories. In both cases, the same set of structures would be manifested in myths, economic relations, etc. As Runciman has pointed out, both Lévi-Strauss and Dilthey can be said to be Kantian despite some differences in some areas of their thought. The conclusion that can be drawn from this is that, despite Gramsci's use of the terms structure and function, he cannot be said to be a structuralist. For him, isomorphic relations, like statistical generalizations, are facts that need explanation. The 'meaning' that originates in the relationship between the parts and whole in Dilthey, and to a certain extent in discourse theory, involves, for Gramsci, as it does for Marx, the underlying causal nexus. In order to study them, Gramsci proposed the concept of situation, which is a concept of the causal interrelationship between temporal processes of different durations.
The Kantian approach to the study of society assumes the existence of a fixed human nature, either as a set of transcendental categories of thought and action, or as a set of characteristics of the brain. This means that the ultimate explanation for society and for history remains outside history. Gramsci, rightly or wrongly, insists on producing historical explanations. Their foundation is his conception of human nature as the ensemble of social relations, and his conception of history in general as an interchange between nature, socialized as forces of production, and human beings. In this interchange nothing is fixed: nature is never taken as a whole in itself, but as a means to reproduce life, hence as socialized or historicized nature. Human beings are also socio-historical products. Although the biological determinants of human nature cannot be dismissed, they merely provide the general problem of survival, or general constraints to action. The solution, the real intercourse of humanity and nature, is a historical process. For this reason, a combination of transcendental or biological structures can never completely account for history and for society.
We must then conclude that Gramsci's historicism is not a denial of the concepts of historical causality and laws, but merely an attempt to produce a conception of them that is suited to the complexities of the historical process and that takes account of the open character of that process. Furthermore, he seeks to give explanations for social phenomena that avoid reference to ahistorical entities, be they metaphysical laws, transcendental categories, or empirical constructions about the nature of the brain. Ultimately, historicism means precisely this: that all explanations of social phenomena should be based on strictly historical, or what he sometimes calls immanent, causes.
Realism
A few brief comments will suffice to complement previous arguments regarding Gramsci's realism. Again, Gramsci's critique of sociology will be the starting point for an elucidation of the kind of realism that seems to be most consistent with his theories.
In a few instances, Gramsci's objections to what he called sociology can be seen to stem from his realism, and thus they furnish further evidence for my interpretation of his historicism. He writes that Michels' classification of political parties is based on generic and external characters. He adds, significantly, that the sociological types developed by Michels 'do not correspond to the concrete fact'. Taking into consideration what I have suggested above about Gramsci's use of the distinction interior/exterior in history, it can be concluded that not only must sociological concepts correspond to concrete facts, but they cannot remain descriptive of superficial characteristics. Concepts, of course, are not true or false; nevertheless, their meaning must be related to the facts, it must be an adequate 'reproduction of the concrete by way of thought', to use Marx's expression in the _Grundrisse_.
It is fashionable to espouse theories of meaning that disregard, or even call into question the external reference of language. For these theories, meaning is constituted within a system of intra-linguistic references, in what can be thought to be variants of Wittgenstein's language games. Apart from the undeniable merits of such theories, especially with respect to the interpretation of literary texts, the fact that for them language tends to be a myth or a metaphor with nothing beyond itself makes them inadequate for scientific theories that claim to appropriate the real in thought. For some of these theories of language, one system of signs may be as appropriate as another with respect to the object, because the object is linguistically constituted. In Gramsci's terms, however, scientific concepts must ultimately be defensible in terms of an extra-discursive reality. This entails a rejection of what S.James has called _'holism of form_ ', which is 'the view that each term owes its meaning to its relations with the others, so that they are all more or less closely interdefined, and a change in the meaning of one will have repercussions for the rest'.
That the internal relations of a language are important is not denied; nor does Gramsci reject the view that language is often laden with metaphors, myths, images that together constitute part of common sense, the mentality of a society which often fogs the reference-relation of scientific as well as everyday concepts. These images can be very powerful; Gramsci was certainly aware of the philosophy, or general conception of the world, contained in language itself. There are, furthermore, conditions of knowledge that also diminish the adequacy of scientific concepts. Nevertheless, such concepts are discovered, refined, and purified through the history of culture; they are the object of the 'struggle for objectivity', which means that they must not only be made internally consistent, or intra-linguistically adequate and meaningful, but also adequate for describing what is not discursive. Gramsci's historicism, as we saw in Chapter One, emphasized the social process of scientific discovery and the social function of science, without denying either the independent existence of reality or the correspondence theory of truth. The same theory can be applied to language. Hence, to assert that meaning, that language, is a historical production, does not entail a denial of the external reference of language.
Although Gramsci devotes notebook No. 29 to the study of grammar, he does not discuss the question of meaning. There is today a vast literature on meaning and reference which would challenge Gramsci's scant remarks on the issue. Nevertheless, his theory of meaning, simple as it may be, is in keeping with his realist historicism. This interpretation of Gramsci's historicism avoids the danger of relativism; for, to use Bhaskar's elaboration of the problem, in respecting 'a distinction between the sense and the reference of propositions, while insisting that all speech acts are made in historical time', we accept the 'correct thesis of the _epistemic relativity'_ , while denying 'the incorrect thesis of _judgemental relativism_ '. And this is precisely the sense of Gramsci's historicism: it calls for the referential adequacy of concepts, for a correspondence theory of truth, while he admits that language and knowledge are historical products. It must be stressed that Gramsci's historicism, despite his assertion to the contrary, is not an absolute historicism, but an open one.
This open character of Gramsci's historicism has already been observed by Melchiorre who, interested in the possibility of a dialogue between Marxism and Christianity, argues that absolute or pure historicism cannot guarantee adequate understanding of history, and that Gramsci's historicism finds its 'dynamism precisely where it ceases to be absolute'. For Melchiorre, however, the understanding of history ultimately comes from a transcendent 'idea-limit', which is absolute and superior to temporal multiplicity. The idea which illuminates the historical process is an ethical principle, socialism. In Melchiorre's model, then, history is explained by a limit which may never be completely obtained, but which draws the historical process forward. Moral, as well as teleological transcendence marks, for Melchiorre, the limits of Gramsci's historicism. It does not appear plausible that Gramsci would accept this interpretation. Nevertheless, its merit rests on the question it poses regarding the intelligibility or, more precisely, the value of knowledge in a pure historicist conception. This question runs deep in the _Prison Notebooks'_ , it hardly ever comes to the surface but it seems to guide Gramsci's thought at crucial junctures.
Closely connected to realism and meaning is the question of values. As we saw in Chapter One, both the German historical school and Croce placed values at the core of the historical process. Their conception of values, however, raises the questions both about the origins and objectivity of value. German historians thought that they could avoid relativism by positing an extra-historical world of values, a transcendent sphere of reality which Gramsci rejects. We must face the possibility, then, that even if Gramsci does not maintain general judgmental relativism, he may still espouse moral relativism. In fact, it is plausible that his rejection of transcendent moral values may lead to a conventionalist view of ethical systems and with it to the view that all ethical systems are equally valid. For our purposes it will suffice to outline the main lines of argument that can be drawn from the _Prison Notebooks_.
The first point that Gramsci makes in defence of historicism is that relativism affects other moral theories as well. As an example, Gramsci points out that Kant's categorical imperative is not free from relativism. For, while the principle may be formally universal, it will differ in its application from culture to culture, depending on what is believed to be natural or universal. Kant's principle thus 'does not surpass a given climate, with all its moral superstitions and its barbaric customs'. It seems, then, Gramsci adds, that the right question to ask is not about the changeability of moral beliefs, but about their capacity to last, that is, their character as organic or long-term phenomena. Although he does not explicitly make the connection at this point, it is evident that the rationality or justification of a moral system is to be conceived in terms of its links to the structural elements of a society. The point Gramsci is trying to make is that in real terms, that is, in terms of the historical record, ethical systems change, that they change with ideas about the nature of human beings, which in turn are an expression of the ensemble of social relations. Morality, in short, changes with the changes in social relations and, as a consequence, any principle, such as Kant's categorical imperative, that claims to be universal will always be limited in practice by the existing moral climate. Because of this, Gramsci adds, Kant's formula 'can be regarded as a truism, since it is difficult to find any one who does not act in the belief that, in the conditions in which he finds himself, everyone else would act in the same way'.
This, although perhaps not completely satisfactory as a critique of Kant, points to a conception of ethics that underlies Gramsci's thought. It seems that in the same way that the use of electrical energy must be preceded by the discovery and the understanding of this form of energy as well as by the infrastructure necessary for its exploitation, an ethical principle must first emerge in the consciousness of men and women before it can be effective in any manner. The difference is that whereas electricity is independent of history, ethics is not, for it contains the basic rules for communal life, and as these rules depend on the existence of such life, their type depends on the kind of community that has evolved in the course of history. This, of course, is first of all a rejection of the view that there are absolute moral values in the sense that there is a moral substance or a God that dictates rules of behaviour. It does not rule out, however, that there may be ethical principles whose long duration is coterminous with the existence of communities, and which can be thought to be necessary conditions for the existence of communities. Whether these rules can be apprehended _a priori_ , as Kant argues, or historically is another question, one that Gramsci does not approach; nevertheless, Gramsci's preference for the historical approach would clearly indicate that such rules are known through historical experience.
Could one argue, however, that strict equality and democracy are good moral norms of universal value? It would seem that if these principles are good today they should be equally good at any time, anywhere. In an abstract sense, this may be so. But in an abstract sense also, electrical energy is good anywhere, anytime, assuming of course that it is good. However, without the technical knowledge and the socio-economic structure that the production and use of electricity requires, it would be of no use to a feudal society. In fact, it is inconceivable to think of a feudal society, just as it existed historically, with an electrical plant. Similarly, strict equality and democracy would have been useless principles in a type of society where the ensemble of social relations had not opened up, so to speak, the real possibility of equality and democracy.
I think that these considerations help to understand Gramsci's thinking on ethics, as well as his insistence that a sound base for a Marxist theory of ethics is to be found in Marx's principle that no society sets itself problems for whose solutions the conditions do not yet exist. The emergence of ethical principles is thus linked to the existence of problems whose solutions require new forms of communal life. With the existence of the conditions, the solution _'becomes_ "duty", and the "will" _becomes_ free'.
The origin of ethical principles lies, according to this theory, in the ensemble of social relations. The long-term process that accounts for the development of contradictions, as well as for consciousness of these contradictions, constitutes the causal ground for the emergence of new ethical principles, consciousness of which first develops within a group whose expansion tends to universalize the new ethical principles. As we saw earlier, historical necessity becomes effective when there is consciousness of the material conditions that are, so to speak, the backbone of such necessity. Similarly, the consciousness of the existence of the conditions for the solution of social problems imposes a new duty. From this point on, a historical process takes place which can be defined as a struggle of hegemonies, or, as we saw earlier, the struggle between different forms of conformism. It is at this level that consciousness and ethical principles become effective historical forces for change. A full analysis of this process is not necessary at this juncture. The point we are pursuing concerns the historical character of Gramsci's ethical theory. Without communal life, values would not exist. The existence of moral values is a feature of societies; they are not embedded in the fabric of nature. They are not, however, dependent on the will of individuals. It is social relations which produce principles of right action. For Gramsci, morals originate in material life. In this respect, his theory of ethics is consistent with his theory of the origin of philosophical problems, according to which it is history, not philosophy itself, which produces philosophical problems.
With this theory the question of the relative value of different ethical systems becomes meaningless. Aside from the difficulty of comparing value-systems without assuming a standard set of values, which of course casts doubt on the validity of the comparison, value systems can be adequate only to the social system of which they are a part. Comparing values is thus transformed into the task of comparing social systems, for rules of conduct are dependent upon the development of the material forces of production. At this level of complexity, however, there is an element that permits a more or less exact measure and comparison, and that is the development of material forces of production and the well-being of individuals. The explanation of the existence of societies with different moral values is hence the problem of elucidating their 'historical necessity', or the objectivity of their rules of communal behaviour. Although Gramsci does not explicitly assert it, it is nevertheless suggested that moral rules are adequate or right to the extent that they further the well-being of all human beings. This would indicate that Gramsci espouses a consequentialist theory of ethics which would be most consistent with the denial of the existence of any spiritual, divine, or metaphysical moral order.
Finally, on the question of the objectivity of moral values, Gramsci maintains that values are objective to the extent that they 'correspond to historical necessity'; consciousness of moral principles, however, is not universal or objective to the extent that a contradictory ensemble of social relations results in contradictory forms of consciousness. The unification of humanity is a necessary condition for the universal acceptance of objective moral principles.
A presupposition of Gramsci's consequentialism is that moral principles must apply universally. Put in other terms, Gramsci accepts some unspecified principle of the equality of all men and women. However, his thought is directed to the 'empirical origin' of the principle of equality. He argues that, at the level of common sense, the saying 'we are all born naked', expresses what biology maintains about the '"natural", that is, psycho-physical equality of all the individual elements of the human race'. Similarly, the philosophical principle that we are all endowed with the faculty of reason, expresses the basic principle of equality. This 'empirical origin', however, does not provide a sufficient explanation, the kind that Gramsci would consider a historical one, of the origin of this principle, nor does it provide a justification for it, for, as Gramsci concedes, 'the environment does not justify but only "explains" the behaviour of individuals'. Gramsci does not advance any hypothesis either as historical explanation or as justification of equality. In the end, and as a complement to his consequentialism, Gramsci seems to espouse some form of deontological theory about the dignity of all human beings, and hence their moral equality. This is perhaps the sense of his apparent approval of the democratic character of both materialist and idealist philosophies; the former because they emphasize biological equality, the latter because they refer to reason as a common faculty of all individuals.
Gramsci's theory of ethics, as well as his remarks on consciousness generally, strongly suggest that he did not hold any theory of a transcendent sphere of being. All that exists, he maintains, is either natural or historical. Furthermore, in spite of his slips into forms of idealism in which nature would exist as part of human history and not independently of it, Gramsci's realism in general asserts the existence of the object of knowledge independent of the knowing subject, as well as the existence of nature independent of human history. This is, at any rate, the sense of his assertions that 'the various physical properties (chemical, mechanical, etc.) of matter' constitute matter itself and that 'as an abstract natural force, electricity existed even before it was reduced to a productive force', as well as other statements already cited. It is true that he claims that the subject matter of historical materialism is not nature, or ideas, in the abstract, but as they exert an influence on the historical process. This is a historical judgement, not an epistemological one.
Ben ton has defined as 'materialist' a theory of knowledge that fulfils the following conditions:
1. it recognises the reality of the object of knowledge, independent of the 'knowing subject', the process of production of the knowledge, and the knowledge itself;
2. adequacy to the object of knowledge is the ultimate standard by which the cognitive status of thought is to be assessed;
3. it recognises the existence of 'thought', 'ideas', 'knowledge' as realities in their own right;
4. it theorises those realities as not _sui generis_ but as the result of underlying causal mechanisms.
If this is supplemented with the condition that nothing exists except nature and society, so that, as with Gramsci, no transcendent sphere of being, such as spirit, Providence, etc., is admitted, we can conclude that Gramsci's theory is a materialist one. For the distinction between ontological objectivity and epistemological objectivity allows Gramsci to avoid judgemental relativism while maintaining epistemic relativity. This enables him to apprehend the historicity of knowledge, the social process of the production of consciousness in general, including ethics, while accepting the independent reality of the object of knowledge. This satisfies criterion number one.
In his theory of scientific concepts, as well as his acceptance of the correspondence theory of truth, Gramsci's theory meets criterion number two.
The recognition of the effectiveness of consciousness of historical necessity, his effort to understand the function of superstructures, as well as his theory of the different durations of structures, mentalities, etc., entail the fulfilment of criterion number three.
Finally, inasmuch as the ensemble of social relations, or history itself, poses the problems philosophy must solve, and, furthermore, because ethical principles originate in material life, it can be concluded that Gramsci's theory of consciousness in general, and of knowledge in particular, meets criterion number four.
It is important to stress that Gramsci's historicism is not only realist, for Hegel's philosophy is also realist, but also materialist, for he disowns any theory of consciousness or reason as an uncaused entity. It is in communal life, in the attempt to solve social problems, that consciousness is born. This does not signify that consciousness is a mere epiphenomenon, or that it is nothing but material life. It has its function and its effectiveness within the limits of historical necessity.
The conclusion that we must reach is that Gramsci's philosophy is a historicist realism. What remains to be done now is to explain the qualification 'historicist'. We have already seen, in the previous discussion of transience, the importance of the passage of time for a correct understanding of social phenomena; the reason, simply put, is that the character of social phenomena is revealed by their consequences as well as their antecedents or their intrinsic features. The problem for a realist conception of scientific concepts and theories is to determine the relations and objects to which they will refer and which they will explain. Gramsci's historicist realism is the first step towards a solution to these problems. Put succinctly, the object to which a concept refers, such as 'class', is not to be taken as an unchangeable object existing in itself at any point in time; rather, that object is a history, and the concept is an attempt to capture the underlying reality of a cluster of phenomena, forms of behaviour, etc., over a period of time. In short, historiographical concepts denote processes rather than things. To paraphrase E. P. Thompson's _The Making of the English Working Class_ , historiographical concepts refer to entities in the making rather than to fully constituted things. Historicism is, then, not a denial of the external reference of concepts, nor a rejection of the correspondence theory of truth; it is, rather, an adaptation of these theories to historical objects, that is, objects whose full identity is revealed not through their intrinsic characteristics at any point in time, but through their development in a temporal process. Gramsci's conception of historical time can now be seen as serving two purposes: first, it draws our attention to the different temporal scopes to which concepts and theories will apply, and hence it suggests a theory about the nature of historical concepts and of historical explanation; second, it seeks to establish a general theory of historical causality, that is, of the generative mechanisms of different duration whose coincidence produces historical effects. These are the main conceptual tools advanced by Gramsci for a concrete analysis of concrete situations.
Humanism
The foregoing account of Gramsci's historicism may appear to call in question his definition of historicism as humanism. In particular, the emphasis on the long-term approach to the study of society, of structures, functions, etc., may be thought to deny any humanist thesis about the nature and dynamic force of history; for it seems to give more importance to the conditions under which decisions and actions take place than to the elements of freedom and human creation that are central to a humanist approach. On the other hand, Gramsci's conception of historical necessity requires both the existence of a set of objective conditions and consciousness of them, as well as of the existing possibilities for action. In other words, Gramsci does not deny either the determining effect of structural conditions nor the decisive role of politics, that is, organized action.
Gramsci is neither a structuralist nor a humanist; for he does not write of individuals as carriers of structures or of history as a process without a subject; nor does he, on the other hand, think of history as a process of individual wills forging the emergence of greater happiness, or less alienation, or more freedom. The importance of organized will, as Gramsci refers to political organizations, stems not merely from the obvious fact that human will has a function in history, but from the view that history is the result of a confrontation of organized wills, or conformisms, rather than the result of a unified general will. It seems, then, that the problem with the sociology Gramsci refers to is that it lacks a dialectical approach to society, that is, it lacks any understanding of the complex process of struggle of hegemonic forces.
Gramsci's humanism, then, can best be described as the view that 'history is a continuous struggle of individuals and of groups to change society'. It is this basic principle that seems to guarantee the earthliness and worldliness that characterize his humanism, for it understands history as an earthly process, not merely a moral one. Gramsci's humanism is little more than the recognition that it is not Providence, nor a cosmic or metaphysical law of evolution that can produce, and explain, history. Historical necessity emerges from given structures, but these would not exist unless human beings were practically engaged in transforming the world. Little else can be said, except that Gramsci does not affirm anywhere that the struggle to transform society is without conditions. For the very word used, namely struggle, as well as the contradictions in the struggles, groups or forces, but also individuals, suppose an array of objective conditions which Gramsci sometimes refers to as 'the situation'. Among those contradictions, there are those responsible for the definition of the forces, which is itself the result of the historical process.
One can thus conclude that Gramsci's humanism is a warning against two kinds of excess. First, it is a warning against speculative thought which seeks to explain history by appealing to some deity, or Providence, or otherwise unearthly entity. The ethical and cultural values associated with these entities are not _sui generis_ , they do not originate or exist on their own; they are predicates of human existence, that is, they describe real men and women, their actions, organizations, and institutions. In this context we should remember that Gramsci's Anti-Croce is the denial that the predicate, be it liberty, equality, or whatever, is the subject of history.
Second, it is a warning against the abuse of theoretical categories, for in dealing with history ultimately we are dealing with human material, and that means that we are not only dealing with the ways in which real men and women are conditioned to act according to structural determinants, but also how they react upon such conditions, and how they experience the process. Whether history is a process with or without a subject is the wrong question to ask for it is hardly conducive to a deeper understanding of history. The danger that the abuse of theory poses is that of taking theoretical categories as speculative philosophers tend to take their concepts; in both cases real empirical women and men play their assigned roles in a drama that happens to them. This, Gramsci suggests, forgets that the social sciences are political, that is, they are engaged in predicting the future because they have a practical stake in that future. Prediction in history, as we saw, is a practical act, for it requires the active participation of the social scientist in bringing about the predicted outcome. It is here that the basis for the unity of theory and practice is to be found. As Badaloni has observed, absolute historicism signifies 'a total reappropriation by the masses of science separated from politics' which ceases to be a technique of domination, as sociology is thought to be by Gramsci. Science and politics, theory and practice, reappropriated by the masses in the struggle to change society, in the attempt, that is, to organize an effective collective will which will materialize the possibilities inherent in the present.
Ultimately, then, Gramsci's historicism does not cease to conceive historiography as basically political. As we saw earlier, the idols of politics, individuals, and narrative dominated earlier historicist thinking. With the new historiography, in particular the _Annales_ school, politics ceased to hold a prominent place in historiography. However, while attempting to develop a deep understanding of history as a whole, Gramsci did not dethrone politics. For him, the focus of historical investigation is politics in a broad sense, because it is concerned with unearthing the long-term process that explains the present as well as the possibilities of the future. But whereas for the old historicism, politics meant the actions of kings, politicians, etc., for Gramsci politics becomes synonymous with the organized attempt to change society. We witness, then, a change from the emphasis on politics in the traditional sense, stressing the subject matter of history, to politics, in the broad sense, as the interest that guides the committed intellectual. In this attempt, the future will provide the best basis for understanding the present; but it is a future whose reality depends on the historicity, on the realism and the rationality, of our actions in the present.
A word of caution is, however, necessary especially because Gramsci is not very clear on the role of intentionality in history. As Sánchez Vázquez has pointed out, substituting the teleology of human intentionality for that of Providence does not provide an adequate foundation for understanding history. For the outcome of history must either be thought to coincide with the intentions of human beings, which the historical record shows mostly not to be the case, or there must be an _a priori_ goal that underlies all their actions, which would contradict Gramsci's emphasis on the historicity of human nature, and hence, the historicity of intentions as well as his denial of any transcendent mind or will.
Although Gramsci's humanism at its worst seems to imply that historical phenomena occur as intended, one must not forget that his conception of history as struggle among opposing forces implies that the result of the clash of wills may not coincide with the intentions or desires of any individual or group. Furthermore, the rationality of action does not depend on a presumed content of reason or a dialectic of consciousness, for Gramsci precisely stresses the dependence of consciousness on material conditions and defines rationality as historical necessity.
In conclusion, Gramsci's definition of historicism as humanism is designed to accomplish two tasks: first, it emphasizes the subjective element in historical necessity, understood as organized politics; second, it underscores the practical significance of knowledge about society. Thus, while emphasizing an integral historiography, Gramsci does not allow us to neglect the importance of politics. The primacy of politics means in effect that the study of society has a practical significance, for the correct identification of the trends of the present is a necessary condition for changing the world. Politics is not the sole subject of historiography; it is the light that illuminates the historian's work.
Conclusion
We can now draw some general conclusions about the nature of Gramsci's historicism. First, Gramsci's historicism is not a theory about the relative, because historical, character of all truths or values. In so far as it is a theory of knowledge, it seeks to understand the origin as well as the function of ideas in the historical process. This is done by considering all human activity as forming a single process, so that the distinctions between ideal activities and material ones, or between subjective and objective processes, superstructures and structures, is an analytic one, not an organic one. In other words, although we can separate these various activities in thought, and furthermore, we can discover inherent properties and tendencies in each, they not only coexist but cannot exist separately.
The consequence of this conception of historical reality and of the origin and function of ideas is that, as Rodriguez-Aguilera has pointed out, 'history has a totalizing character'. This character of Gramsci's historicism can be, and has been, interpreted to mean that all truth is exclusively dependent on the historical conditions of its production. Furthermore, in so far as for Gramsci the historical process is centred on the class struggle, truth can be seen as a function of historically progressive classes. This has been interpreted in a Husserlian fashion by Nemeth, for whom reality is a class-centred construction; Salamini has deduced the subjective idealist proposition that nothing exists outside history. In short, Gramsci's statement that Marxism is an absolute historicism has been immediately thought to mean some form of Crocean historicism, only that the hegemony of a class takes the place of the concept of liberty or the great intellectuals.
Our analysis of Gramsci's notes points to a different interpretation. On this interpretation, we avoid equating absolute historicism with Croce's philosophy, as it is demanded by Gramsci's own statement that Marxism is an absolute historicism, that is, one of a kind, not necessarily Croce's. As we have seen, Gramsci uses 'historicism' in four senses, which have been identified with reference to transience, historical necessity, realism, and humanism. These form the basis of several interrelated theses, central to which is Gramsci's conception of transience.
The central thesis of Gramsci's historicism is that social phenomena are processes whose identification and appropriate description is adequate only when their consequences are known. Hence, the scientific study of social phenomena requires the long-term view or historical method. Different types of phenomena tend to develop at different rhythms, and in constructing a complex situation, that is, the convergence of various temporal processes, care must be taken to assign to each of them its proper causal significance.
The types of relations or structures that have a long-term life or relative permanence provide the basis for historical laws. However, these laws cannot be reduced to regularities that hold between types of events; such regularities are in reality the effect of causal mechanisms, which Gramsci generally, but not exclusively, identifies with social relations of production. In short, for Gramsci historical laws are not descriptions of regularities; rather, they identify the generative mechanisms of different durations that together account for the historical process. Historical necessity is the concurrence of both objective and subjective premisses that result in a given event or phenomenon. Furthermore, historical laws are tendencies that can be identified by isolating certain aspects of the social process. In reality, history is an open process where a number of contradictory tendencies produce events that are not always predictable, though the general conditions of the process are rational, that is, predictable.
Perhaps the most controversial aspect of Gramsci's historicism is his realism. One must admit that there are many passages in the _Prison Notebooks_ which can be clearly characterized as subjective idealist. Nevertheless, other passages point to philosophical realism and, on balance, they seem to predominate in Gramsci's thought. Also, the tone of his historical and political writings and his conception of reason are more consistent with realism than with idealism. On this basis it is clear that Gramsci is a realist; after all, he uses the term 'historicist' as synonymous with 'realist' in a number of passages. Given this conclusion, it is evident that those commentators who propose a phenomenological or an idealist subjectivist interpretation of the _Prison Notebooks_ must have misinterpreted some aspect of Gramsci's work.
In the view of some of his interpreters, Gramsci's absolute historicism cannot but mean that all truth is a function of its historical origin and function; hence, historicism and the correspondence theory of truth are incompatible. This apparent difficulty can be solved by drawing a distinction between ontological objectivity and epistemological objectivity, a distinction, I admit, not explicitly formulated by Gramsci but certainly necessitated by the historicism he seeks to develop. Gramsci's historicism thus claims that all knowledge is a historical production and fulfils a social function; furthermore, there are limits to our capacity to discover truth, some of them due to the historicity of knowledge. Thus, full epistemological objectivity may never be achieved; in this sense, knowledge is relative to the conditions of its production. However, this limitation of epistemological objectivity and its consequent epistemic relativism do not entail the denial of ontological objectivity, or judgmental relativism. There is, then, the need for a standard of truth that is independent of the historicity of knowledge, and this is provided by the correspondence theory of truth, as well as by the referential meaning of concepts in what concerns the theory of language.
The theory of the transience of social objects has, however, an important effect on the application of the correspondence theory of truth. Because the objects that social science studies are only completely known when their consequences are exhausted, the reference of a theory or a concept cannot always be given in a slice of time. At least some social concepts and theories have as a reference a temporal process. For this reason Gramsci often refers to fundamental historiographical concepts and theories as methodological principles. Thus, they have a double function: on the one hand they serve as guides to the historian in collecting and ordering data, and framing explanations and revealing patterns; on the other hand, they are intended as referring to already existing phenomena. It must be reiterated that their reference ranges over a temporal manifold of events.
It seems obvious then that Gramsci's absolute historicism is not so absolute or, at least, it is not absolute in the Crocean sense, for the very intelligibility and value of knowledge depend on the possibility of a standard of truth which is not subject to historicity. Gramsci's historicism is absolute not in the sense of holding that all truth is relative to its historical conditions and function, but in the sense of holding that to explain history no extra-historical entities, other than geographical conditions, are necessary. In this sense, Gramsci's absolute historicism is a critique of Croce as well as of the German historical school, for they had to refer to an eternal ideal history, an ever-present metaphysical reality, in order to explain the historical process. Gramsci's criticism is simply that their historicism was not absolute in that it appealed to extra-historical forces and entities. Also, Gramsci's absolute historicism is a rejection of certain forms of naturalism, prevalent among some Italian positivist sociologists, for whom such phenomena as the backwardness of the Italian south were accounted for by appealing to the natural inferiority of southern people. Hence, Gramsci rejects not only metaphysical entities but also psychologism and any form of biological or physical reductionism as a basis for explaining historical development. The explanation of history, as of social phenomena in general, must have recourse only to historical phenomena, as presented in the available evidence: this is the sense of 'absolute' in Gramsci's historicism, as well as the sense of 'immanentism' found in the _Prison Notebooks_.
It is this sense of 'absolute' that gives us a clue to the meaning of 'humanism' in Gramsci's thought. In the few passages where Gramsci characterizes Marxism as absolute historicism or absolute humanism, it is clear that the intended sense is related to the earthliness and worldliness of thought. If 'humanism' means anything, then, it must mean the view that social phenomena exist because human beings engage in certain activities which result in the establishment of definite relations with nature and among themselves. To explain history one must not have recourse to anything other than those activities, those relations, and their consequences. These consequences do assume a character of their own, such as long-term structures, forms of oppression, etc., which condition the activities of human beings. This does not deny Gramsci's position, for he is simply stating that these developments are not due to divine disposition, world spirit, the kingdom of ends, or any other non-human agency.
There is a second aspect to Gramsci's humanism which is linked to the unity of theory and practice, and this is the position that all human activity has a political significance, that is, it is related to efforts to organize communal life. In this sense of 'humanism', Gramsci advances the thesis that politics is primary inasmuch as the production and reproduction of life, culture, etc., affects the well-being of communities and individuals. He expresses this view by affirming that all of life is politics. Whereas the previous theories define the basic epistemological, ontological, and methodological character of historicism, the last one defines the focus of the interest in the knowledge of history. This interest, stated simply, lies in the fact that knowing the development of a society is an important condition for changing it. And this points to Gramsci's theory of politics, which will be discussed next.
To summarize, central to Gramsci's historicism is the thesis that the long-term view is the only appropriate one for the study of society. Since social phenomena are characterized as processes, that is, as undergoing systemic change, an accurate description of any element in the system depends upon its consequences. Hence, the concepts and theories of the social scientist must refer not to single events or synchronic structural elements, but to definitive temporal processes. From this follows the importance of distinguishing the various kinds of temporality and of giving to each of them an adequate causal weight. Furthermore, the explanation of historical phenomena must not refer to extra-historical entities: all laws and entities are constituted in the intercourse of human beings with their environment and with themselves. Finally, achieving knowledge of the development of society is not simply an exercise in achieving pure knowledge for its own sake; it is an exercise directed at changing society for the better according to its inherent possibilities. Knowledge has a political significance.
_Chapter Three_
**History and Politics**
Introduction
Gramsci's historicism provides a most useful foundation for historical research and political action. In contrast with the historicism of the German school or that of Croce, Gramsci's theory of history does not restrict the sense of the social process to an inner meaning of the actions of men and women which translates into the understanding of history as an ethical drama. Gramsci recognizes the importance of each facet of historical development at the same time as he seeks to provide a general understanding of the relative weight of each one. In so doing, he does not generally impose a given schema on historical data; he seeks to understand the process from a materialist standpoint, without denying the complexity of social processes or the intricacy of the causal nexus that explains historical change.
It is within this framework of historical explanation that we must seek to understand the role of politics in human existence. In what follows, an attempt will be made to elucidate the essential features of Gramsci's conception of society and his general theory of politics. Although they do not follow deductively from his historicism, they are nevertheless connected with it, at least to the extent that his historicism disallows certain interpretations. We shall not develop in any great detail Gramsci's thought on these topics, which has in any case received a great deal of attention. It will suffice to outline, as if it were a matter of developing a research programme, the main lines of argument that are suggested by, or are more compatible with, Gramsci's historicism.
In attempting to define the most general aspects of Gramsci's theory of history and politics, a number of basic problems must be dealt with. We must first consider the nature of the relationship between structure and superstructure; second, the nature of civil society and the role of hegemony; third, the state as both the coercive apparatus of a class and, in its larger sense, as an educational institution. As we shall see, Gramsci maintains a dual conception of politics, one that can be said to be Aristotelian, the other classical Marxist. This dual conception is clearly evidenced in his conception of hegemony and the state. It is not clear, however, from reading the _Prison Notebooks_ whether these two conceptions are compatible.
The Relation between Structure and Superstructure
Some conflicting interpretations
Gramsci's theory of the relation between structure and superstructure has been the subject of some controversy, notably between Bobbio and Texier. It is certainly a crucial issue for those who seek to link Gramsci to Marx and Lenin or to show that, in some sense he is an incipient post-Marxist. The various interpretations given to his thought fall into two main classes; those who establish a topographical model and therefore a synchronic relation between structure and superstructure, and those who propose a temporal model and hence a diachronic analysis of that relation. Furthermore, some commentators stress the primacy of the structure, whereas others that of the superstructure, and yet others place the greatest importance on the unifying link.
In an essay first published in 1968, Norberto Bobbio argues that in Gramsci, as in Marx 'civil society... represents the active and positive moment of historical movement'. However, because Gramsci's use of the term 'civil society' differs in crucial respects from Marx's, Bobbio concludes that for Gramsci the superstructure is the primary moment in the 'reciprocal relation' between structure and superstructure. Furthermore, in the distinction between hegemony and domination, or between civil society and state, which is a distinction within the superstructure, the moment of hegemony, or the private institutions of civil society, 'is always the positive moment', whereas the state is the negative or subordinate one. In short, according to Bobbio, Gramsci asserts that a reciprocal relation exists between two contemporary factors, structure and superstructure, and that the second one in general, and its ethico-political aspect in particular, is the primary and dominant element in a social system.
Bobbio's interpretation has been challenged by Jacques Texier, who cites many passages from the _Prison Notebooks_ which suggest a classical Marxist theory of the relation between structure and superstructure. Texier points out that Bobbio's account would mean that Gramsci's historicism 'would go no further than the historicism of Croce'. Texier, in agreement with Bobbio, notes that 'in Gramsci civil society is not the infrastructure', as it is for Marx. The difference, however, consists merely in the use of a term, it does not have any theoretical significance. For if we look at the concepts of civil society and hegemony as elements in a historical bloc and if, furthermore, we conceive of the relation between structure and superstructure as a process, then we must reach the conclusion that the content of civil society is economic, as 'all superstruetural activities have a class character'. Civil society, Texier argues, represents 'the complex of practical and ideological social relations... which is established and grows up on the base of determined relations of production'. In short, Texier affirms that a determining relation exists between two parallel kinds of phenomena, structural and superstructural ones, which undergo a process of change and in which the structural ones, understood as the social relations of production, are primary or dominant.
A distinct third position is that taken by Portelli in a pertinent book titled _Gramsci et le Bloc Historique_. He asserts that 'the study of the relation between structure and superstructure is the essential aspect in the notion of historical bloc'. But, he continues, 'Gramsci never conceived this study in the form of the primacy of one element of the bloc over the other'. It is futile, then, to attempt to argue for the primacy of any one of the elements; what is essential in 'the relations structure/superstructure is the link that realizes their unity'. And he notes that the organic link between the social structure or classes, which depend on the relations of production, and the ideological and political superstructures, is provided by intellectuals. Thus, 'to pose the question of intellectuals is to pose the question of the historical bloc'.
There is an aspect of Portelli's account which is attractive, namely, the emphasis on the unifying link in a historical bloc. However, Portelli's position is not quite clear, for in his analysis, classes and ideological superstructures appear to be reduced to two separate realms which are brought together by the efforts of a mass of intellectuals. His position is ambiguous because he clearly recognizes the class determination of the superstructures, while at the same time he affirms that the intellectuals are the unifying link in a historical bloc. However, the most serious weakness in Portelli's reconstruction of the concept of historical bloc is that despite his recognition that the 'static study must be completed by a dynamic one', he does not provide a full analysis of the dialectic of the integration and disintegration of historical blocs. It is precisely this dialectic that helps us understand the process of unity which explains the structure as well as causal relations between structures and superstructures.
A salient feature of both Texier and Portelli is their emphasis on the study of the relations between structure and superstructure as a process. This implies that the relation of reflection between structure and superstructure is not an immediate one, but one that develops and that as a consequence has a temporal aspect. The diachronic view of the relation between structure and superstructure has been defended by Nardone, Misuraca, and Salamini. In general, they argue that structure and superstructure constitute two poles of a temporal process, so that the structure represents the past, while the superstructure signifies the future.
In his book _Il_ _Pensiero di Gramsci_ , Nardone argues that a schema of temporal development of the relation structure/superstructure provides a more adequate explanation and that it is in fact coherent with Gramsci's thought as a whole. In Nardone's account, 'the social group is the principal subject of political becoming'. Its function as the subject of history exhibits two forms, first as the 'historical agent insofar as it is identical with the economic base' and second as a political group whose full development is materialized in the party. The temporal process of the relation between structure and superstructure is precisely the 'passage from the economy to polities', or from an economic past to the foundation of a state. In its final stage as a state, a social group unifies and leads all the social forces of a bloc and hence realizes its hegemony. The temporal perspective of the relation between structure and superstructure does not imply that 'the two terms have the same value'. Nardone understands the dialectic structure/superstructure as that between quantity and quality, where the moment of quality, the superstructure, is the 'condition for the appearance of the structure at the same time that it indicates its final destination'.
Salamini, greatly influenced by Nardone's book, has developed a similar interpretation. For him, the relation between structure and superstructure is that between necessity and freedom and the nature of this relation is that of a passage from the first to the second, a passage that corresponds to the 'general direction of history'. He argues that 'Gramsci ascribed to superstructural activities a primary role', which is not a deviation from classical Marxism but rather the return 'to its idealist beginnings'. Like Nardone, he claims that the superstructure is 'the condition for the appearance of the structure', that is, freedom is the condition for the emergence of necessity as well as the overcoming of necessity.
Both Nardone's and Salamini's interpretations of Grarnsci are in fact a modified version of Croce's dialectic of church and state, the ideal and the practical. The dialectic of history is thus removed from the clash of classes to the confrontation between necessity, as exhibited by the objective economic order, and liberty as incarnated in the organized will of the party. Since the passage from necessity, or structure, to freedom, or superstructure, is a temporal process, it is difficult to make sense of the assertion that the superstructure is the condition for the emergence of the structure. Unless, of course, one assumes the view that the ideal-eternal history of liberty spawns, as so many steps towards its full realization, negative moments of structural constraint; or unless one is prepared to accept teleological causation. Both these views, however, are contrary to Gramsci's historicism; specifically, they violate the absolute historicism according to which we are not to seek extra-historical or transcendent explanations for what is an earthly process.
A somewhat different interpretation of the diachronic view of the relation between structure and superstructure is that presented by Misuraca in a short paper on the Gramscian reconstruction of the concepts of 'structure' and 'superstructure'. Misuraca adduces textual evidence from the _Prison Notebooks_ to the effect that by structure Gramsci means 'the ensemble of real historical conditions insofar as they are factually active'. In this sense, structure is the past, and it comprises both the material conditions and the ideological and cultural conditions. However, not all conditions, that is, not all the past without distinction forms part of the structure; the ideological and cultural conditions are considered structure to the extent that they 'are effectively operational in a given situation'. The superstructure, in turn, consists in 'the initiatives which concretely realize this new history, this new structure'.
This interpretation of Gramsci's thought seeks to displace the problem of the relation between socio-economic structure and political and cultural institutions to the problem of the emergence of a new historical bloc out of the disintegration of the old one. However, Misuraca's interpretation must still deal with the problem of the specific link that unites the economic moment and the political and cultural moment within the present historical bloc. This brings the debate back to its beginning. There is, however, some textual justification for Misuraca's position on the use of 'structure' in Gramsci. As we have seen, it is not altogether unjustifiable to take this term in Braudel's sense of long-term processes which include both economic and intellectual elements. Nevertheless, this is merely a linguistic question, one that does not touch on the fundamental problem of the relation between economic structure and political and cultural phenomena.
The diactronic model neglects the simple fact that, regardless of how the terms are defined, there is at any time some sort of relation between two co-existing types of phenomena, what classical Marxism defines as 'structure' and 'superstructure'. In contrast, the synchronic model tends to disregard the character of becoming of a social system and the manner in which this character affects the relations among various kinds of phenomena. It would seem that the difficulties involved in interpreting Gramsci's thought on this issue stem from the fact that he attempts to explain different sorts of phenomena that involve the relation between structural and superstructural elements. On the one hand, Gramsci defines the concept of historical bloc in terms of the general relation between structure and superstructure; on the other hand, he is concerned with the study of the development of a class from its beginning as an economic class to its final hegemonic moment, as a state.
In the analysis of the relation of political forces from the level of the structural determination of classes to the development of a new state, Sassoon has argued, the various levels described by Gramsci 'are separate only in a methodological sense since they are aspects of a single phenomenon at a single moment of time'. And in a footnote she adds that Gramsci's use of the expression 'a subsequent moment' must be taken in a 'schematic sense', not in a temporal one. However, it seems that it is precisely the development of political forces which is most amenable to some form of diachronic analysis, albeit one that takes place in a historical bloc, that is, within a given set of structural and superstructural conditions. It seems that, despite Sassoon's belief that diachronic and synchronic analysis are incompatible, they are both necessary for a full understanding of a historical bloc, for we need to know both the relation that exists between any elements at any point in time as well as their process of transformation during a historical period. Gramsci's analysis of situations is precisely this, namely, the investigation of how temporal processes of different durations intertwine at any given moment in time, so that their long-term causal process and their contemporary relations can be clearly understood. Although Gramsci is primarily concerned with the function of political intervention in social change he does not reject the thesis of the primacy of the structure in the last instance.
Gramsci's analysis
The concept of 'historical bloc'
There are two kinds of texts which offer the solution to the relation between structure and superstructure: first, texts specific to this relation itself, generally contained within Gramsci's discussion of the concept of 'historical bloc'; second, the very important text on the moments of a political situation already mentioned above.
Gramsci gives different formulations of the concept of 'historical bloc', which are not necessarily different in content. In one of his first attempts he argues that 'if men take cognizance of their task in the terrain of the superstructures, this means that between structure and superstructure there is a necessary and vital link, such as is the case in the human body between the skin and the skeleton'. And later, returning to the theme of the role of popular beliefs, he adds that 'the material forces are the content and the ideology the form', a distinction that is 'merely didactic because material forces without form would not be historically conceivable and without material forces ideologies would be individual whims'. The first conclusion that we can draw is that Gramsci conceived of ideas on the one hand and the material forces on the other as two inseparable aspects of one single reality. Moreover, their unity is not just a mere coexistence but it is a function of a necessary link: the 'complex and discordant ensemble of the superstructures are the reflection of the ensemble of the relations of production'. There is, furthermore, a 'necessary reciprocity between structure and superstructure (a reciprocity which is precisely the real dialectical process)'.
The theme of the unity of structure and superstructure as that of the form and content of the historical process appears elsewhere in the _Prison Notebooks_. It forms the basis for Gramsci's critique of Croce's conception of ethico-political history, which he regards to be too speculative. Ethico-political history, Gramsci writes, cannot discard the concept of historical bloc for the social organism 'cannot be conceived without its "material" or practical content'. To write ethico-political history without taking into account the material forces is equivalent to classifying animal species by the colour of their feathers or their skin and not on the basis of their anatomy. Finally, he makes the point that 'it is necessary to demonstrate that form and content are identical, but it is necessary to do so every time in the concrete, individually, otherwise one engages in philosophical speculation, and not history'. The identity of structure and superstructure, or form and content, is thus taken as a methodological principle, that is, as a general hypothesis for gathering and controlling evidence and for generating particular theories about the link between structure and superstructure in given societies. The general methodological character is not a denial of the reality of the link; it is, rather, the denial that a single formula can take the place of research, or that philosophical speculation from general concepts can produce sound knowledge of empirical reality. These are concerns that, as we have seen in Chapter Two, were clearly in Gramsci's mind, as they were in Engels' thought.
So far little has been said about the content of the terms 'structure' and 'superstructure'. Gramsci uses them in the general sense that they have acquired in historical materialism. One peculiarity of most of Gramsci's texts, however, is that he uses the plural 'superstructures', but the singular 'structure', as if a single structure were reflected in several superstructures. The reason for this is to be found in his partial acceptance of Croce's concept of the distinctions in the circle of the spirit. Gramsci argues that Croce produced a 'merely verbal solution' to what is a real methodological problem, for 'it is true that not only oppositions exist, but also distinct moments'. The solution to this problem can only be a historical one based on the concept of historical bloc, which is defined as the 'unity between nature and spirit (structure and superstructure), unity of contraries and of distinct moments'. The superstructure is thus conceived as a unity of distincts, of several levels such as civil society and political society. It is precisely the unity of these levels that constitutes the main field of research in the _Prison Notebooks_.
The structure, however, is also said to be a unity of distinct elements in so far as one can distinguish various elements in it, such as technology, labour, and classes. This is an area of social theory to which Gramsci devotes few pages. A probable reason for this is that he believed that political economy had already been substantially developed, whereas political theory had not received as much attention. The need to develop this theory had clearly been felt by Lenin and now by Gramsci because they were both engaged in the task of establishing political organizations to contest the existing form of the state.
In short, Gramsci proposes the concept of a historical bloc as the necessary unity of several levels. The structure is conceived first as the terrain of the interchange between humanity and nature, an interchange that constitutes the process of production. In this process we can distinguish the technological elements, the labour process, and the classes that result from the organization of this process. For Gramsci, the element of class is the link between the structure and the superstructure, in so far as the latter contains the forms of organization that guarantee the development of the structure in its present form. It is because of this fundamental link that the concept of class plays a fundamental role in Gramsci's theory of history. The superstructure, too, is divided into several levels, notably the private institutions of civil society and the state. There are, moreover, processes of long duration, such as is the case with the cosmopolitan character of Italian intellectuals, which are not directly linked to the structure of the present historical bloc, though they continue to play an important role in the determination of its character.
Historical examples
A brief look at Gramsci's notes on Americanism and Fordism will provide further evidence for this account. We cannot expect, however, a full analysis of political economy; his notes take much for granted, but regardless of the empirical accuracy of his particular thesis, they show the intended use, relevance, and importance of the structure in Gramsci's thought. These notes can be construed as the attempt to understand the restructuring of the state that took place in the USA after the First World War. At the same time, they are a reflection on the Italian situation in which the fascist regime was faced with a similar task. For these reasons, these notes are important for the analysis of the modern state, hegemony, and passive revolution. Most interpretations of these notes are concerned with Gramsci's specific analysis of the emergence of the new form of the state, as well as with the historical accuracy of that analysis. Nevertheless, as Sassoon suggests, in the notes on Americanism and Fordism Gramsci 'indicates the extremely complex nature of the relationship between structure and superstructure, at the same time insisting on the multitude of essential features of any political phenomenon'. In a similar vein, Buci-Glucksmann argues that 'the American model poses new questions for the concept of hegemony, both as a topical political theme and as an occasion for deeper theoretical reflection on the relation of base and superstructure'.
In an unfinished note written in 1934, Gramsci provided a list of the problems he thought were important to discuss under the 'general and somewhat conventional heading of "Americanism and Fordism"'. However one must first consider the 'fundamental fact' that their solution is 'necessarily formulated and attempted within the contradictory conditions of modern society'. From the start, then, we must consider the contradictory nature of a social bloc; in other words, the starting point is never the unity and homogeneity of a social system, rather its heterogeneity. The problem to consider then is the functioning unity of such a system and how it is achieved. In general terms, Gramsci defines Americanism and Fordism as the result 'of the immanent necessity to achieve the organization of a planned economy'. The various problems associated with this necessary change signal the passage 'from the old economic individualism to a planned economy'. The problems emerge because of the resistance to this change, resistance that comes not only from the subaltern classes but also from the allies of the dominant ones.
The list of some of the most important problems associated with Americanism includes the following issues:
1) substitution of a new mechanism of accumulation and distribution of finance capital immediately founded on industrial production for the present plutocratic class; 2) the sexual question; 3) the question of whether Americanism can constitute a historical 'epoch'...; 4) the question of the 'rationalization' of European demographic composition; 5) the question of whether this development must have its starting point within the industrial and productive world or whether it can come from the outside...; 6) the question of the so-called 'high wages' paid by the Fordized and rationalized industry; 7) Fordism as the extreme point of the process of successive attempts by industry to overcome the tendential law of the fall of the rate of profit; 8) psychoanalysis... as expression of the increased moral coercion exercised by the state and social apparatus on single individuals and the morbid crisis that such coercion determines; 9) Rotary Club and Free Masonry...
The note is left unfinished, but it provides a good deal of evidence both of the scope of problems that Gramsci includes under a single phenomenon, as well as the care he takes to relate structural and superstructural phenomena.
Part of Gramsci's analysis deals with the differences between the American and the European and, more specifically, the Italian case. These differences stem from the different demographic conditions found in the two continents. It is important to note that they are differences in the class structure of the countries he contrasts. He argues that in Europe, and specifically in Italy, there is a large parasitic class of individuals without an essential function in the productive world, whereas this stratum of 'producers of savings', does not exist in the USA. The existence of that parasitic class depends on a number of conditions, some of which are related to forms of land-ownership; in particular to the existence of absentee owners who draw their wealth from sharecroppers, rents, etc. Others derive their income from the state, through pensions of various types. What is common to all of them is that they consume and save, but they are not active in economic production. The existence of this class is linked to European culture, and to the strong resistance offered to the modernization of production in Italy. The suggestion is that modernization in Italy must be different from the American case, and that the fascist state may constitute the attempt to accomplish the same end.
At the structural level, then, Gramsci makes some distinctions. First, there is an economic fact, the tendency of the rate of profit to fall, which prompts the capitalist class to introduce changes. This is done at the individual level, as he notes, with the view to obtain and 'maintain a position of superiority over the competition'. Ford's initiatives in developing more efficient work methods, in organizing transportation and distribution of the commodities produced in his enterprises is an instance of such an effort. The element of technique, in this case, work methods, is a second distinction within the structure. Furthermore, beyond the attempt of individual industries to overcome the fall of the rate of profit, the economic power of the class, which is the third element, must be restructured, so that a more effective accumulation and distribution of finance capital may be achieved. To a certain extent, the restructuring of the state, whether through the New Deal policies in the USA or through fascism in Italy, was the result of immanent needs of the economy. There are, therefore, two sets of problems which must be solved, namely, those that will increase productivity and those that will secure a universal solution to the problem of the fall of the rate of profit. The individual solution is that which is attempted from the point of view of the self-interest of individual capitalists. The universal solution to the problem is a hegemonic one, one that must ultimately involve the state. These two solutions are not in contradiction even if a true hegemonic solution will necessitate that concessions be made in order to attract the consent of possible allies. Gramsci's analysis of Americanism and Fordism is in fact an analysis of the emerging hegemony in the USA.
Gramsci notes that the rationalization of production was accomplished in two ways: by means of force, such as the destruction of trade unions, and by means of consent, such as social benefits, high wages, and ideological and political propaganda. High wages were necessary to select and keep well-trained workers. The new methods of work required a stable working force, which meant that traditional puritanism had to be articulated in a new social ethics that emphasized monogamy, and, of course, prohibition. Also, the workers had to be educated so that the 'trained gorilla' in the assembly line, bored with meaningless work, could resist the temptation to entertain 'non-conformist thoughts'. This process is, in short, the attempt to create a new type of worker who will be well adapted, both physically and psychologically, to the new conditions of production. The reason, then, for the ideology of high wages, and, one must add, the puritanism that was expected to produce well-adjusted individuals, 'is a phenomenon derived from an objective necessity of modern industry... and not a primary one'. Nevertheless, Gramsci argues, this does not diminish the importance of the influence that ideology in itself had on the development of the new state.
The foregoing analysis, while shedding light on important aspects of American society, does not provide an exhaustive view of that society. Among the items in the list of problems that Gramsci thinks are of some importance, the sexual question cannot be fully explained within the framework of analysis presented above. Gramsci in fact provides some interesting suggestions on how this question should be treated, hints that, while scant and little developed, provide evidence for his originality; furthermore, they show that, while he regarded the economic structure as the motor of history, he did not reduce all problems to economic ones.
Gramsci affirms that 'the "economic" function of reproduction is not only tied to the productive economic world, but it is also an internal one'. In the second draft of this note, he writes that the economic function of reproduction 'is not only a general fact that is of interest to the entire society... but it is also a "molecular" fact, internal to the smaller economic aggregates such as the family'. The exact meaning of these two passages is not clear, though it is reasonably safe to assert that Gramsci thinks of the sexual question as being simultaneously part of the economic structure at the same time that it is independent of it. It is a general economic question to the extent that the reproduction of the population, and hence of the labour force, depends on it; furthermore, sexual morality inherited from the past, such as is linked with puritanism in the American case, can be adapted to new emerging conditions with the end of forging a new attitude towards work. It is independent of the economic structure to the extent that it is an 'ethico-civil' question.
Gramsci considers the issue of the 'formation of a new feminine personality' to be 'the most important ethico-civil question tied to the sexual question'. This question, however, cannot be solved by the party or by any group of legislators. It can only be solved, he writes, 'when women have attained independence _vis-á-vis_ men' and have developed 'a new conception of themselves and of their role in sexual relations'. Any attempt to legislate on sexual questions before this new feminine self-image is achieved, he warns, must proceed with great caution, for 'the sexual question will be rich with morbid characteristics'.
One can conclude that any social reform is faced with problems that, although they are set within a specific class framework, both in their long history and in their scope, transcend socio-economic relations. It is in the attempt to include these problems in his study of historical blocs that Gramsci develops the concept of hegemony. The hegemony of a group depends not only on its ability to organize consensus on problems related to the economic structure, but also on those problems of an extra-economic nature, or of mixed nature as Gramsci regards the sexual question, that, whether they emerge under new circumstances or whether their origin is in the very distant past, are faced by society. As Gramsci writes, 'any innovative historical movement is mature to the extent that the elderly, the young and women can participate in it'. It would seem, then, that those who have lately sought to develop a socialist theory of democracy have been on the right track in examining Gramsci's conception of hegemony as a fundamental concept upon which to ground such a theory.
The various texts discussed above indicate that Gramsci quite clearly thought of 'the objective necessity of modern industry' as being primary. This objective necessity originates in the need to overcome the tendency of the rate of profit to fall, and it requires structural changes as well as superstructural ones. Hence the economic thrust, the necessity of the structure, must be supplemented by superstructural elements, such as education, legislation, etc. However, some of the characteristics and the concomitant problems of these superstructural questions, notably patriarchy, are not caused by the economic structure, though they must be made to conform to it or at least not to impede its automatism. It seems, then, that one cannot affirm the unqualified primacy of the economic element without begging some questions. In the study of any given situation, one may conclude, it is always difficult to ascertain that the economy is dominant or primary in any absolute sense, though it certainly sets the general conditions of existence of any society. In Gramsci's analysis of Americanism, the economy poses problems whose solutions are structural and superstructural at once. The problems themselves often depend on the relations of forces, that is, on the relative strength and organization of the fundamental classes. To provide a solution to this question we must turn to Gramsci's analysis of the relations of forces. Before that, however, a brief look at his analysis of the Italian Risorgimento will provide further evidence for his theory.
Pizzorno has argued that Gramsci's thesis on the Risorgimento, in particular that of the effect of the failure on the part of the Moderates to carry out an agrarian reform, 'cannot be considered a historiographical thesis' because a 'historiographical problem is always the problem of the _identification_ of historical subjects and the _attribution_ of historical actions to one or another subject'. In short, because Gramsci is concerned with the types of effects that follow from types of actions, his is a theoretical analysis, not a historical one. It is true that, just as his analysis of Americanism and Fordism is an attempt to deepen his understanding of the modern state and of fascism, his analysis of the Risorgimento is an attempt to understand the origins of the bourgeois state in Italy; in both cases, a crucial aspect of the analysis is the contrast that he draws between two different situations, and the conditions he identifies as responsible for the different solutions to similar problems. In the case of the Risorgimento, he contrasts the Italian case with the French Revolution so as to understand the reason for the weakness of the Italian State.
In Gramsci, history and theory are not two separate disciplines; they are not conceived as a discipline of precise empirical research and a theory of society, a narrative of facts and sociology which formulates some general laws. Gramsci's historicism, to the extent that it is a theory of historiography, is the demand for a history with depth, and hence, a history that understands any situation in terms of the confluence of structures of different durations. Furthermore, it is premissed on the possibility of identifying general tendencies, or historical laws, and networks of necessity which allows him to compare different social processes. Comparative history, it was argued earlier, is premissed on the conception that history is not simply the narration of unique events.
For these reasons, Gramsci's argument on the lack of an agrarian reform is not mere speculation on what might have been, but rather experimental historiography to the extent that this is possible in history. It is the stability of the structure that permits such experiments even if only in the form of abstractions, as Marx argued in _Capital_. This is, after all, what Gramsci probably means when he writes that Ricardo's hypothetical method has a philosophical importance for Marxism. The importance of this is that, in his historical reflections, especially in his analysis of the Risorgimento, Gramsci had to start from the secure foundation of the structure, for he thinks that it is the most adequate for an 'experimental science of history'. The existence of social groups with a productive function, or the existence of groups without such functions who consumed surplus-value but did not produce any, is, for him, of crucial importance. There are, of course, other elements of importance; but the structural ones are the cornerstone of his _experiments_ , of his application of theoretical considerations about the generative mechanism of historical processes and about the degree of 'automatism' or necessity of these processes.
The first note fully devoted to the Risorgimento is titled 'Political direction of a class before and after its journey to power'. He later rewrote this note, giving it a new title: 'The problem of political leadership in the formation and development of the nation and the modern state in Italy'. In both cases, however, the problem is set out in the following way:
The whole problem of the connection among the various political currents of the Risorgimento, that is, of their reciprocal relations and their relations with homogeneous or subordinate social groups that exist in the various historical sections (or sectors) of the national territory, can be reduced to this fundamental factual datum: the moderates represented a relatively homogeneous social group... whereas the so called Party of Action was not specifically based on any historical class.
In the first draft of this note, Gramsci employs the expression 'relatively homogeneous class' instead of 'relatively homogeneous social group'.
The terms in which Gramsci seeks to analyse the problems of the Risorgimento are clear. For although the problem is conceived in terms of political connections, the fundamental fact is the relationship of representation between political parties and classes. There is, furthermore, the regional problem, which cannot be defined merely in terms of geographical location, but rather as the emergence of different social blocs within the geographical boundaries of the emerging Italian state. These social blocs are defined in terms of class structure, as well as culture. The general theoretical position that Gramsci seeks to develop is that the relationship between north and south is similar in some respects to that of urban centre and countryside. There is, however, an important difference; this relation is not a normal organic one, but one 'between two vast territories of very different civil and cultural traditions' which give rise to conflict of nationalities. This conflict has a very precise significance for, as Buci-Glucksmann argues, the backwardness of the south is considered by Gramsci as 'the condition for the capitalist development of the north'.
As the analysis proceeds, Gramsci's conceptual framework becomes more complex. Nevertheless, both the structural and the regional elements continue to provide the backbone of his analysis. Posing the problem in terms of the unification of a class in the state, he seeks to analyse the political process by means of which the Italian northern-bourgeoisie managed to accomplish the integration of a heterogeneous population as well as that of the various regions. We see then, in Gramsci's thinking, the progress from the problem of relations among political groups to the problem of the integration of a new historical bloc. The task that the Moderate party faced was that of unifying the five main forces so as to build a forward moving train. These forces were: (1) the northern urban force, which was the locomotive, (2) the northern-central rural force, (3) rural/south, (4) rural Sicily, (5) rural Sardinia.
It seems clear, then, that whatever the historical accuracy of his specific theses may be, Gramsci sought to study the Risorgimento as a problem similar to that of the French Revolution, a problem that was essentially a political process. The elements of this process, which were social forces, would eventually determine the outcome of the process, i.e., the specific type of the new Italian state. Again, the analysis is complex, and there is no suggestion that either the structure or the superstructure are primary in any immediate sense. Furthermore, the unification of Italy, which is seen as the unification of the bourgeoisie in a new state, is presented as a task, a task which, he writes, presented problems that the Moderates were able to solve with great skill. Nevertheless, the basic historical subjects were social forces; it is to this concept of the relations of forces that we must now turn.
Analysis of the relations of forces
It is in a note on the relationship between structure and superstructure that Gramsci broaches as 'another aspect of this same problem', the question of the relations of forces. In the relations of forces three moments or degrees are to be distinguished. First, 'a relation of social forces closely connected to the structure', this is said to be an objective relation, or 'naturalist datum' that 'can be measured with the system of mathematical or exact sciences'. Second, the relation of political forces, which is the 'degree of homogeneity and of self-consciousness attained by the various social groupings'. Third, there is the relation of military forces, which is often the decisive one. The second moment, or that of political relations, is itself divided into three moments, 'which correspond to the different degrees of political consciousness, such as have hitherto been manifested in history'. These moments are, in brief, the economic-corporative, where there is consciousness of the unity of the professional group, but not of the class; the moment where 'consciousness of the solidarity of interests among all the members of the social grouping is attained' but this is still limited to the economic sphere; and lastly, there is the moment where consciousness of the narrow corporative interest is transcended. This last phase, Gramsci writes 'marks the clear passage from the pure structure to the complex superstructures'.
These three moments of political forces represent the process from the origins of the individual consciousness of narrow economic interests to the hegemonic moment, where a universal solution is possible. The solution, however, is limited by the form of the state which is still the organ to 'create favorable conditions for the maximum expansion' of a group, though this expansion and development 'are conceived and presented as the motor force of a universal expansion of a development of all "national" energies'. This is the hegemonic moment, the moment where concessions can be made in order to obtain the consent of allied groups, where moral and intellectual reform organize that consent. In real history, Gramsci contends, these three moments of the relations of political forces 'imply each other reciprocally, horizontally and vertically so to speak; that is, according to socio-economic activity (horizontally) and according to territory (vertically), combining and dispersing in different ways'.
This analysis presents several problems. First, as we noted earlier, it is possible to interpret these various moments as existing at the same time, thus forming a complex set of relations whose morphology would constitute the object of the science of politics; or, they could be conceived as a temporal process. Second, the idea that the three moments imply each other, but that they can form diverse combinations or even split up, is intriguing, but not very clear. We must now attempt to clarify these issues.
To begin with, it seems to make perfect sense to interpret Gramsci's analysis as a temporal process. He himself speaks of 'reaching' degrees of consciousness, and he refers to the second moment as a 'successive moment'. It would seem that Gramsci is writing on the process in which a class is formed in the economic world and becomes conscious of its position and of the possibility to found a new state. In real history, this process is often a long one; one fraught with problems, setbacks, etc. This genetic approach is fully consistent with Gramsci's general principle that social problems should be studied historically. Furthermore, this analysis offers a conception of the theory of reflection as well as an interpretation of Engels' view that the economy is determining in the last instance. For in the genetic conception of the development of forces, the existence of classes as structured in the world of production is the temporally prior and necessary condition for the development of the second moment, that is, for the development of political forces, and the hegemonic solution of the problems that confront them.
These tasks are those of securing the expansion of the dominant class or of securing an acceptable rate of profit. The solutions to this problem, however, are not and cannot be simply economic. The lack of homogeneity, the very existence of conflicts of various kinds, and of class struggle, necessitate solutions at the political level, at the level of hegemony and the state. In this case, the reflection of the structure in the superstructure is a process, essentially a political process, in which the activity of the various historical subjects, classes, determine the specific structure of the state. This means that the political institutions and the moral and intellectual elements that predominate in a social system are not immediately or mechanically determined by the economy. In other words, there is no iron law of history that produces concrete political and ideological forms out of the changes in the structure. Rather, the political and ideological forms are responses to the historical problems within the limits of the class structure, and thus ultimately, of the economy. In this interpretation politics and culture are characterized by a certain degree of autonomy which allows for significant intervention in these fields. Most importantly, however, the specific solutions to historical problems depend upon a great variety of factors. In the case of the crisis of the 1920s and 1930s, demographic conditions, cultural traditions, etc., determine the final solution to similar problems, solutions that are in themselves as different as the New Deal or the fascist Italian state.
This view is consistent with Gramsci's conception of historical necessity. Since laws are tendencies abstracted from empirical reality, their effects on an open system cannot have a unilineal and inevitable character. It is because of this that, as Femia points out, 'although men are rooted in an economic reality that circumscribes their free initiative, this objective world of fact is not passively registered, human intervention is decisive'. Such intervention is necessary because the existing structural tendencies may not be realized. For, as Gramsci points out, 'at certain moments the automatic thrust due to the economic factor is slowed down, obstructed, or even momentarily broken down by traditional ideological elements', in which case 'appropriate political initiative is always necessary to free the economic thrust from the shackles of established politics'. Historical necessity, as we concluded earlier, is not solely a function of the structure or of an objective premiss, but also a function of the degree of consciousness and organization of the existing forces.
Since the development of class consciousness, or of an alternative hegemony, is not an automatic development or immediate reflection of the structure, the mechanisms by which this development can take place are of foremost importance. Hence, Gramsci's analysis of the development of parties, of intellectuals, and the role of culture in general is of crucial importance. In this respect, Gramsci can be said to develop Lenin's political theory, in so far as the latter clearly saw the importance of political intervention, and implicitly the falseness of any mechanistic theory of the relation between the structure and the superstructure.
The genetic approach is also consistent with Gramsci's theory of historical time, for it allows one to trace the lines of development of the forces whose relations constitute the fundamental problem in a situation. It is important to stress that the note in which Gramsci presented his analysis of situations and relations of forces begins with his distinction between structures and conjunctures. This approach, then, when fully developed, would lead the historian to uncover the 'molecular' processes which repeated _ad infinitum_ , become the 'homogeneous part' in the activity of individuals. That is, they become structures, but also rules of behaviour; customs as well as ethical norms.
In short, the genetic interpretation of Gramsci's analysis of situations is consistent with his historicism. It provides a general sketch for the theory of the reflection of the structure in the superstructure, and affirms the temporal primacy of the structure, so that a given type of structure becomes an empirically necessary prior condition for the foundation of a historical bloc. The theory of reflection and the determination of the economy in the last instance are interpreted as methodological principles in the sense elucidated in Chapter Two. As such, they are taken as controlling hypotheses, but also as real historical processes whose specific character must be confirmed by documented evidence.
If this is so, then it is possible to interpret Gramsci's assertion that the three moments of political forces imply each other, in the sense that the lower level, that is, the level of economic-corporate interests, is an empirically necessary temporal pre-condition for the others, inasmuch as it is closely linked to the structure. The existence of the other two levels are sufficient evidence for the existence of the structural ones, for they would not exist unless adequate structures did. In this manner, the appearance, for instance, of a working class party is sufficient evidence of the existence of the working class, and the latter must exist before its corresponding cultural and political elements emerge. At any point in time, however, a class may exist but not its corresponding superstructural elements. The various combinations and dispersions of the various elements constitute the process of the development of a class from its subaltern position to its hegemonic one.
However adequate the above view may be, there are good reasons for construing the relation between the three moments of political forces as a synchronic one. Two main reasons can be given in its support. First, a situation has been defined as the conjunction of several processes, and hence it is but a slice of time in the historical process. Second, the emphasis on the relations of forces suggests that Gramsci is attempting to unravel the general structuring of a social whole at a given time in order to assess the possibilities inherent in it as well as the appropriate form of political intervention most conducive to their realization.
Given this approach, it is clear that the various social forces are not necessarily whole classes, for there can be sectors of classes that are more developed than others, that is, sectors that have reached a higher level of consciousness and organization. The analysis of a specific situation, in this case, must first identify the various social groups, as well as their objective class base, their degree of development and, of course, the possibilities of political intervention. The analysis in this case is not simply founded on the existence of classes, but rather on the existence of groups, which are defined mainly in terms of both their class belonging and their degree of consciousness and organization. In this sense, Sassoon would be right in that the three levels coexist. Furthermore, since the problem now is to assess the relative strength of the various forces, as well as their interrelationships, and since, furthermore, the structural determinants, as we have seen, may either be actualized or obstructed by superstructural elements, there is no good reason for asserting that any of the levels is necessarily primary or dominant. This would be fully consistent with Portelli's view that the essential problem for Gramsci is the relation between structure and superstructure and not the primacy of any one of these elements.
This approach is appealing in so far as it recognizes the complexity and uneven development of situations and it stresses the discordant combinations and dispersions of political and ideological forms. Its primary interest can be said to be political, in that it seeks to gain a firm understanding of the present so as to develop the appropriate strategy for political action. Two weaknesses, however, seem to be present in this approach. First, there is Gramsci's insistence on solving theoretical problems historically, and this can only mean genetically. Second, and this is perhaps only an aspect of the first problem, Gramsci's theory of transience indicates that the consequences of a phenomenon may only come to full fruition in a rather long period of time. As a consequence, it is always necessary to look at the past for a better understanding not only of the present situation but also of future possibilities, for, in general, the consequences of past phenomena, of past situations, may not yet have been fully realized. Hence, even if the interest of our knowledge is political intervention in the present, we cannot neglect the general tendencies that have been formed in the past.
But the most important point that can be made in order to appreciate fully Gramsci's theory is that there is no need for presenting the two approaches as exclusive alternatives, for Gramsci did not think in these terms. In fact, both approaches are but abstractions which are untenable in isolation. For the problem in understanding history, and hence, the problem of the knowledge that is necessary for political action, entails that we must unravel the origin and development of classes, that is, the long-term structural process, as well as the various processes of 'combination and dispersion' that form, at any given time, the structuring of a situation. These are not two problems in reality; they become so only by theoretical fiat. The point that Gramsci seems to be attempting to make is that the concept of class only makes sense in the long term, that is, the reference of 'class' is to a long-term process. This view of class is close to that espoused by E. P. Thompson, who defines it as 'a _historical_ category: that is, it is derived from the observation of the social process over time'. At the more empirical or immediate level, we can distinguish social groups with different degrees of homogeneity, consciousness, and organization. Today, these would include social movements such as those devoted to specific causes like the ecology, peace, women, etc.
As I stated earlier, the structure of society, understood as the class structure, is temporally primary. This means that the economic formation of classes, that is, of groups within the production function, is temporally prior to their various forms of development. Also, the concept of class is theoretically primary in that it is designed to make sense of long-term historical processes. However, given any situation, the empirical groups may or may not act in class ways; they may have reached different degrees of consciousness and thus constitute different levels in the structuring of the relations of forces. If the concept of class has any validity, a class can only be fully evaluated by taking into consideration the behaviour of its members, and of the various groups it may give rise to, over a complete historical period. This full validation of the concept, however, does not imply that before the end of the historical period, we cannot use the concept with a high degree of accuracy. There is, after all, considerable historical evidence, as we find in the work of E. P. Thompson, Vilar, and others, to validate the use of this concept. Gramsci's historicism constitutes an important effort to specify the concept of class, to justify it historically, and to indicate both its uses and its limits.
In this synthesis of the diachronic and the synchronic approach, Gramsci's assertion that the various moments of the relation of political forces imply each other contains, in a nutshell, his theory of historical necessity discussed earlier. The structure is not only the empirically necessary prior condition for the existence of the corresponding superstructure in the development of a class, but, in the larger context of a historical bloc, structures and superstructures affect each other. This is the sense of the dual analysis of causality implied by some of Gramsci's reflections, that is, linear causality and structural causality, which underlies the concept of historical necessity as the concurrence of objective and subjective processes of different duration.
Gramsci's analysis, in all its complexity, seems to be a viable alternative to economistic theories in which class consciousness is said to be immediately determined by the structure. The distinction between the long-term class conditions of historical development, on the one hand, and the various relations of forces at any given time, on the other, is translated in political action as the distinction between stragetic goals and conjunctural or tactical political intervention as it is possible at any given time.
The analysis of situations, Gramsci believes, can be understood as 'an elementary exposition of political science and art, understood as a set of practical canons of research and of observations particularly useful to arouse an interest in effectual reality and elicit more vigorous and rigorous political institutions'. And he adds that empirical observations must be centred on the relations of forces, including international forces. Along with this, he states that the correct meaning of strategy and tactics must be developed. In the same vein, Gramsci distinguishes 'great politics' which is the activity directed to found new states, the 'struggle to destroy, defend, preserve determined social-economic organic structures', from 'minor politics' or the partial or daily questions that arise within an established structure.
In these Gramscian texts the intention of the author is clear, even if their formulation is not always well developed. Taken together with the analysis of situations, they stress the need to distinguish the long-term processes, the making of classes to use E. P. Thompson's expression, from the various combinations of social forces which, in their daily encounters, present the problems of minor politics. The latter offer the field for immediate empirical observations; the former suggest the generative mechanisms that produce a general direction to history; that is, they provide the meaning of historical events. The dominant classes, Gramsci observes, often attempt to exclude the issues of great politics from the internal life of the state; this is, however, great politics: it is their attempt to defend and preserve the existing socio-economic structure.
Having made the distinction between the long-term class process and the various social forces that result in different combinations, that is, a distinction between the structural generative mechanism on the one hand, and the various structurings of immediate and empirically observable political formations on the other, we can arrive at some formulation of the general problem of the primacy of the structure. In fact, Gramsci himself provides a succinct formulation:
A class is formed on the base of its function in the productive world: the development and the struggle for power and for the preservation of power create the superstructures which determine the formation of a 'special material structure' for their own diffusion, etc Logically and even chrono logically there is: social structure – superstructure – material structure of the superstructure.
By the 'material structure of the superstructure', Gramsci means the necessary means for the existence of superstructures, such as the printing press. Nevertheless, the character of those superstructures which depend on material structure for their existence and propagation, is not determined by these material conditions but by the social structure. The importance of this fact is crucial, for instance, in the study of the media. It does not deny the importance of the type of technology used, but it certainly denies that the medium is the message.
The important point that Gramsci makes in the text quoted above is that both logically and chronologically the social structure precedes the other elements. And this is precisely the position we have developed so far. As we have seen, the structure has a temporal primacy, in so far as it is a prior necessary condition for the development of the superstructure; and it also has theoretical primacy in so far as it is thought of as a generative mechanism that, as Femia asserts with respect to the productive forces, explains _'the basic trajectory of human history'_ although it does not explain the _'specific course of any given society'_ in so far as that may 'vary in accordance with the dynamics of its own individual situation'. The dynamics of any individual situation, that is, the relations of forces in that situation depend, as we have seen, on a number of factors, such as geographical, demographic, and cultural conditions and, in particular, on the existence of strata of intellectuals and the development of alternative hegemonies which contribute to the unification of social groups and classes.
In the general process of history, however, the distinction between structure and superstructure, or between material forces and ideology, is merely a didactic one, for one cannot exist without the other. The logical and chronological primacy of the structure must then be seen in terms of the development of a class from its origin in the world of production to the founding of a new hegemony and a new state. This is what some commentators, as we have seen, refer to as the passage from necessity to liberty, and hence, they see the relation between the structure and the superstructure as holding between tradition and the future. Nevertheless, this is not the social process as a whole; there are other classes with their own superstructures which undergo transformations of their own and whose political initiatives react upon those of the emerging class. In the analysis of situations, Gramsci sketches the most general elements for the study of both the development of a new state and the relations that exist between the given structure, the various classes, and the superstructures. For this, both the diachronic and the synchronic approaches are necessary.
Finally, Gramsci feels that the crucial problem in historical materialism is that of the manner in which the historical movement emerges from the structures. As I suggested earlier, this must not be taken to signify a distinction between two different objects, such as logic and history. Rather, given Gramsci's historicism, it implies two temporal orders; the relatively permanent order of structural phenomena, and the faster tempo, hence the expression 'historical movement', of the group formations of social forces. Historical necessity is constructed as the superimposition, or rather, the concurrence of the various orders, rather than the single effect of the logical or structural order. As Fontana has noted, Gramsci's theory is far from a linear theory, limited to a schematic analysis of global facts; he does not assume that social classes are homogeneous by definition. Indeed, he is aware of the uneven development of classes, of the contradictory evolution of classes and of class consciousness. It is the recognition of this fact that led Gramsci to forge a theory of the historical bloc as the conjunction of different processes, of partial and often contradictory superstructures, of groups that have a common origin in the social structure but which have developed in different ways.
Although Gramsci focuses most of his analysis on the development of intellectuals, popular culture and, in general, hegemonic systems, his reflections on historical situations point to a global conception of historical investigation, what he called integral history. Fontana points out that 'a global study should begin with the examination of structural transformations... proceed then to the examination of the ways in which these changes in the structure of production... affect the various classes... to examine... how the relations of production already analysed bring about a configuration of ideologies and political programmes'. Above all, however, Gramsci's theory should not be taken as a fully structured schema that can be readily applied to any society or any situation. For, as he writes, 'reality is rich in the most strange combinations and it is the theoretician who must find confirmation for his theories in this oddity. He must translate the elements of historical life into theoretical language; and it is not, vice versa, reality that must present itself according to abstract schemas'.
Gramsci's Dual Conception of Politics
Roger Simon argues that in Lenin politics was primary only in revolutionary periods whereas for Gramsci, politics is always primary. Furthermore, he argues that Gramsci avoids economism and class reductionism inasmuch as his concept of hegemony is 'based on the recognition that popular democratic struggles, and the parliamentary institutions which they have helped to shape, do not have a necessary class character'. As we have seen above, the formation of social forces which are not directly linked to class-structure is the terrain of political intervention, but, as Simon also recognizes, it is also the 'terrain for political struggle between the two major classes – the working class and the capitalist class'. The problem for the socialist movement, he suggests, is 'to find the way to link these popular democratic struggles with its socialist objectives', a problem which consists in forging an alternative hegemony.
There is in this interpretation of Gramsci the suggestion that he holds two views of politics: (a) a classical Marxist view, in which the state is an instrument of the dominant class; and (b) an Aristotelian view of politics as the science of the good life. The emphasis on hegemony as moral and intellectual leadership implies, Simon argues, that politics embraces 'a much wider field of human activity than the struggle for state power'. This double conception of politics renders the expression 'primacy of politics' somewhat ambiguous; for it may indeed be primary in the Aristotelian version, but not primary in the Marxist sense. This ambiguity permeates much of Gramsci's writings and gives rise to radically different interpretations of his thought, ranging from those that emphasize the Leninist and orthodox views of politics as class politics, to those who believe Gramsci is a post-Marxist who has no use for the concept of class, or who, like Laclau and Mouffe, think that Gramsci was unable to realize fully and develop the implications of his concept of hegemony.
From our general interpretation of Gramsci's historicism and of his theory of the relationship between structure and superstructure, it would seem that the ambiguity exists only if one does not realize that the two meanings of politics function within different theoretical orders, orders that are specified in Gramsci's theory of historical time. However, this is a general solution which follows from Gramsci's historicist position. In order to understand the role of this dual conception of politics we shall now turn to the concepts of civil society, hegemony, and the state.
Civil society and hegemony
It is in the attempt to understand the process of unification of the Italian state that Gramsci first defines the concept of hegemony. He writes that 'the historico-political criterion on which one's research must be founded is the following: that a class is dominant in two ways, that is, it is "leading" and "dominant". It leads the allied classes and dominates the oppressed ones'. Later, he defines this 'methodological criterion' and substitutes 'supremacy of a class', for 'a class is dominant', so as to distinguish more precisely between domination and consent. Two aspects of this concept must be immediately clarified, one with respect to the context in which the concept appears; the other pertains to the double function it plays in Gramsci's theory.
First the concept of hegemony is presented in the context of the analysis of the politics of the Risorgimento. The suggestion is that hegemony is a permanent element in society, that is, that no society exists without a certain degree of hegemony, however slight that degree may be. That Gramsci thought so can be confirmed by reference to his statement that public opinion, which 'is closely connected with political hegemony inasmuch as it is 'the point of contact between "civil society" and "political society'", has always existed. Furthermore, to the rhetorical question whether there has ever been a state without hegemony, he answers that 'there is a struggle between two hegemonies, always'. Later, returning to the same idea, he writes that there has always been 'struggle between two hegemonic principles'.
Although it is true that, as Sassoon points out, 'Gramsci develops the concept of hegemony in his attempt to analyse the state in a specific historical period', it is not valid to infer, as she seems to do in her book on _Gramsci's Politics_ , that it 'arises from the development of modern society'. Furthermore, in the text on public opinion cited above, Gramsci seems to suggest that civil society is also a permanent feature of society. This being so, one must conclude that the difference between modern capitalist societies and other societies is not the existence of civil society and hegemony in the former, and their absence in the latter; rather, the difference is in the degree of development of the institutions of civil society and hegemony. Gramsci often thinks of dialectics as, among other things, the passage from quantity to quality. Perhaps this is applicable to the development of the modern state; the proliferation of the private institutions of civil society, and the corresponding growth of the dependence of hegemony on these private organizations, results in a qualitative change. This qualitative change, in turn, demands new strategies for political activity.
The text that is probably most often quoted from the _Prison Notebooks_ is the one in which Gramsci identifies the main difference between Eastern and Western European states. He writes that, in contrast to the West, in the East 'the state was everything, civil society was primordial and gelatinous'. In fact, he does not affirm that either hegemony or civil society were non-existent in the East; he argued, and in that the leadership of the Russian Social Democratic Party agreed, that the private institutions of civil society were as yet inchoate. In a note on Italian politics after 1870, Gramsci argues that, in Italy, there was a clear separation between state and civil society, and that because _'civil society_ was something amorphous and chaotic' it was possible for the state to dominate it. At the same time, however, Gramsci contends that one of the functions of the modern state is to adapt civil society to the economic structure. Thus, whereas private institutions can be formed independently of the power of the state, their potential for real opposition, whether it is progressive or regressive, must be continually checked by the state. In so far as the institutions of civil society are not well developed, they are easily controlled and dominated by the state. As Gramsci writes of post-1870 Italy, the state could easily 'overcome the conflicts that, from time to time, would emerge sporadically, in a localized fashion, without national nexus or simultaneity'.
Once civil society has developed, that is, once there is some national unity and hence simultaneous action at the national level is possible, then the state must change its relation to private institutions, for it can no longer dominate them and overcome conflicts in an easy way. The potential for conflict must be transformed into organized consensus; conflict must be contained within the limits of permissible opposition. That is, the role of the state as force diminishes, while the importance of its ethico-political character of hegemony grows. It is in terms of the relation between civil society and state, and the various degrees of the relation force/con sent, that the development of the modern state is analysed. Crucial in this analysis is the degree of development of civil society, and hence, the approach that the state must take to secure its continued hold on possible conflicts.
The second point that must be made with regard to the concept of hegemony is that, as has been well noted by commentators, it serves a double purpose: it is a concept for historical interpretation and also a concept for the art of politics. Gramsci introduces this principle as a 'politico-historical criterion for research' and, in the second draft of the same note, he refers to it as a 'methodological criterion'. Furthermore, Gramsci states that 'the most important observation' with respect to the analysis of situations is that they 'cannot and must not be ends in themselves (unless one is simply writing a chapter on past history), but they acquire significance only if they serve to justify a practical activity, an initiative of the will'. It is this double function of theoretical concepts that sets the foundation for the unity of theory and praxis. If the assertion that politics is primary has any concrete sense, it must be sought in Gramsci's statement that the significance of historical analysis is given by its justification of political action. Political intervention, then, is the goal of Gramsci the historian. This is, of course, based on the belief that knowledge of the past, if expressed in the right conceptual framework, can help make the decisions of the present, for there are patterns or tendencies in history. This has already been discussed earlier; the point, however, bears repetition: the theory of the unity of theory and praxis is firmly founded on the belief in the regularity of some historical processes, as well as on the belief that the potentialities inherent in the past may only be fully developed in the future. This is one of the senses that Gramsci draws from the two principles from Marx that he often cites.
This double function of concepts is not limited to the concept of hegemony. Other concepts, such as that of 'passive revolution', are also used in this dual form. It is the analysis of this last concept that leads Davis to the conclusion that Gramsci's political and historical methods are inseparable. Apart from the significance of this for the philosophy of praxis, it must be stressed that politics is, for Gramsci, a historical science. This means that it is not a purely normative theory of power, state, etc., which seeks merely to justify a given form of society on some moral or practical grounds, but one that seeks to intervene so as to realize some inherent possibilities. Pure normative theories, Gramsci would argue, are already forms of intervention.
The concept of hegemony is the item in the _Prison Notebooks_ that has received by far the most attention. It is, in a way, central to Gramsci's theory, for it unifies his various studies on the intellectuals, popular culture, folklore, and the state. Hegemony, Gramsci writes, 'signifies a determined system of moral life'. It is also defined as 'government with permanently organized consent'. In a more general sense, Gramsci also speaks of 'intellectual and moral leadership'. And in a letter to Tania Schucht he defines it as the moment of 'consensus, of cultural leadership' and contrasts it to 'the moment of force, of constraint, of legislative and state or police intervention'. Gramsci is not the first political thinker to analyse politics in terms of the dichotomy between coercion and consensus. In the _Prince_ , Machiavelli wonders whether it is better to be loved or feared and his response is that a ruler should be both loved and feared but 'because it is difficult to reconcile them, it is much more secure to be feared than loved, when one cannot have both'. Modern liberal political theory is also concerned with such alternatives to coercion so as to minimize conflict. Thinkers such as Dahl argue that in a situation of conflict, such as is wont to arise in human society, there are only three solutions: coercion, deadlock and peaceful adjustment. The latter, of course is favoured, but is conceived in terms of a multi-party, liberal democracy in which the electorate is to have the ultimate power of political decision. Gramsci often cites Machiavelli's double perspective and the image of the centaur with two heads. However, the concept of consensus in Gramsci, as Buci-Glucksmann suggests, is more complex than it is for those who emphasize the acceptability of a social system as a condition for its reproduction.
It is perhaps important to stress that the dichotomy between hegemony and dominion, or consensus and coercion, is not simply meant to describe some of the conditions under which the actions of individuals take place. The meaning of consensus in Gramsci's theory of hegemony must be found not in the apparent willingness of an individual to engage in certain activities, but rather in the conditions for that willingness to be present. For, as Gramsci puts it, hegemony is not the result of the sum of individual acts of consent, but rather, the organization of a collective will. To create a new hegemony means to organize the will of individuals so that in their free actions they nevertheless choose within permissible limits, limits that are set by the interests of a ruling class. Femia has emphasized the 'psychological state, involving some kind of acceptance... of the socio-political order or of certain vital aspects of that order' as the core of the meaning of consensus. In his view, Gramsci's concept is thus purely descriptive, excluding 'the moral and prescriptive connotations' which are often attached to it. This view, helpful as it is in understanding the individual's response to the socio-political order, must be complemented by the analysis of the structural basis of consent. Gramsci's analysis of the moments of the relation of forces is relevant and highly signifficant to this issue, because it is the basic interests that originate at the lowest level of the development of the relations of forces that provide the foundation for spontaneous consensus. Further development of that consensus is coterminous with the development of a political consciousness, a process which does not occur spontaneously, but which is subject to ever higher degrees of organization and control. It is this aspect of the organization of a universal consensus that is the core of Gramsci's concept of hegemony.
As we saw earlier, Gramsci analyses the activity of individuals into two elements: a common element, which is related to the structural basis of society; and an element of differentiation between individuals, which of course is undetermined by historical laws. The reproduction of a social system is contingent on the character of habit, and of 'norm' or 'nature', that the constant element acquires. This constant element, such as is expressed in theories of human nature or on the assumption of the naturalness of _homo oeconomicus_ , originates in the actions of individuals in a given economic system and is defended, justified, and made acceptable by the work of intellectuals. Hegemony, then, is not spontaneous, but 'organized consensus'. But that, one must immediately point out, is not to be taken as simply a theory of false consciousness which is somehow made to prevail with the uninformed masses. For Gramsci, the emergence of a new hegemony is a genuine act of historical creation in which a class, showing that it is capable of solving all the problems of the moment, can forge a higher moral and intellectual system. As Buci-Glucksmann argues 'Hegemony is not force... it is not imposed: it is conquered through a specific and intellectual and moral dimension'.
The analysis of hegemony requires the concept of the historical bloc, that is, the unity of structure and superstructure, for it is only in terms of the development of the relations of forces within a historical bloc that a given hegemonic system can be understood and assessed. The development of a hegemony is contingent on the development of a political group which is able to go beyond its class's immediate economic-corporative interests. In order to do this, the class or most progressive section of the class, as for instance the Jacobins during the French Revolution, must be able to make concessions to other groups, so that they will become allies rather than enemies. In his notes on 'Americanism and Fordism', Gramsci speaks of high salaries as an attempt to win the consent of the workers; but as we have seen above, other questions must also be solved, questions that transcend the narrow economic interest of classes, or ethico-civil questions. In his analysis of the Risorgimento, Gramsci points out the failure to carry out an agrarian reform which would have created a wider consensual basis for the emerging Italian state.
Of course, solving some of the problems of potential allies is but one step in the development of a hegemonic system. As important, if not more so, is intellectual and moral reform, the creation of a new conception of the world with its consequent ethics which must show itself to be both viable and superior to the prevailing one. Nevertheless, the possibility of the triumph of one hegemony over another does not derive from its logical character, namely its superior intellectual qualities. Gramsci points out that the reasons for the triumph of a hegemony over another is to be sought in the 'causal and necessary nexus'. In other words, the reasons for the triumph of one hegemony are to be found in the specific relations of forces that characterize a given situation, and this requires a careful study of the various temporal processes, the different causal elements and their scope, that result in any given event. Gramsci also contends that when a social group is progressive, the other groups are spontaneously attracted by it. The 'spontaneous consensus given by the great masses of the population to the direction impressed in social life by the fundamental dominant group' is said to 'originate "historically" from the prestige... derived by the dominant group from its position and from its function in the world of production'.
Gramsci's insistence on the historicity of hegemony and on the historical, rather than intellectual, reasons for the triumph of one hegemonic system over another are of the utmost importance for a clear understanding of this crucial concept. As we have seen, Gramsci's historicism is, among other things, the rejection of all transcendentalism, as well as a rejection of the view that reason contains in itself a set of ideas, or ethical norms, whose development provides the basis for the dialectic of history. For Gramsci, thought derives from being, philosophical problems are presented by history. The conclusion we must reach is that hegemonic principles, or hegemonic systems, are not ethical-cultural ideologies which pre-exist historical development and one-sidedly determine the movement of history. On the contrary, hegemonic principles originate in the social and economic organization of life. What presents itself as spontaneous consensus to efforts of a group to organize society is not related to the discovery of some principle of reason that finally makes itself noticeable, but rather to the discovery that the new organization of socio-economic life offers the possibilities of greater individual as well as group development and satisfaction. The prestige that a group derives from its position and its function in the world of production is the result of the perception that the group can solve the problems facing a society. The problems facing a society are both economic and ethico-political. For this reason, Gramsci contends that hegemony 'cannot but be also economic, cannot but have its foundation in the decisive function that the leading group exercises in the decisive nucleus of economic activity'.
Hegemony, then, is not merely an ethico-political phenomenon. It is, rather, the ethico-political aspect of the historical bloc. Admittedly the problems that a social group faces are not merely economic problems. They are also problems of the development of culture, of education. Above all, in our times, they are the problems of the various social movements whose connection to the economic base is not direct, if there is one at all. In general, the problem faced by the ruling class _vis-à-vis_ these groups is one of leading society in general towards genuine equality in the areas of gender, race, etc., as well as the problems of peace and ecological rationality. The significance of this is that some social groupings with no necessary class identity have entered into political activity; these groups may be formed by members who objectively belong to different classes. This, it has been argued, is a serious problem which traditional Marxist class-reductionism cannot solve.
Hegemony and Gramsci's essentialism
The attempt to extract a non-economistic and non-class-reductionist theory of politics has been undertaken by several recent interpreters of Gramsci, among whom Laclau and Mouffe, under the influence of Derrida, have presented the most elaborate theory. In her several essays on Gramsci's concept of hegemony, Mouffe has argued that for Gramsci 'the struggle for hegemony is a struggle _within_ ideology and not, as with Althusser, a struggle _between_ ideologies'. The significance of this point is that ideological elements in themselves do not have a class identity, so that 'the class character of an element will be the result of its articulation to a determined hegemonic principle'. The aim of cultural struggle, according to this interpretation, is that of appropriating ideological elements and organizing them according to a new hegemonic principle. The class that succeeds in this task will become hegemonic; success does not result from its imposing a 'class ideology on other social groups', but rather from its ability 'to articulate to its hegemonic principle the majority of the important ideological elements of a given society'.
Evidence for this reading of Gramsci's concept of hegemony is found in two notes. First, Gramsci argues that:
What matters is the criticism to which such an ideological complex is subjected by the first representatives of the new historical phase. This criticism makes possible a process of differentiation and change in the relative weight that the elements of the old ideologies used to possess. What was previously secondary and subordinate, or even incidental, is now taken to be primary – becomes the nucleus of a new ideological and theoretical complex. The old collective will dissolves into its contradictory elements since the subordinate ones develop socially'.
Second, as ideology is the 'terrain of an incessant struggle between two hegemonic principles', the question of the disarticulation of the old ideological elements and their articulation by a new hegemonic principle is proposed by Gramsci in the following way:
How then must this determinate historical consciousness be formed autonomously? How must the elements be chosen and combined for such an autonomous consciousness? Will each 'imposed' element be rejected a priori? It will be rejected a priori, but not itself; that is, it will be necessary to give it a new form which is appropriate to the given group.
Mouffe then concludes that
for Gramsci it is not a question of making a clean sweep of bourgeois ideology with all the elements which constitute it, but that there are within it some elements which must be appropriated by the working class provided they are transformed and given a new form.
Given that Gramsci never defines the term 'hegemonic principle' with any precision, Mouffe suggests that 'it involves a system of values the realization of which depends on the central role played by the fundamental class at the level of the relations of production'. It is through this basic system of values that the 'ideological elements acquire their class character which is not intrinsic to them'.
This is a valuable attempt to develop a radical theory of politics able to deal both with those political movements which bear no connection to classes and those which do. In her interpretation, Mouffe still accepts the class identity of the articulating hegemonic principle. However, lately she has become more critical of this remnant of essentialism in Gramsci's thought. Laclau and Mouffe in their book _Hegemony and Socialist Strategy_ argue that, for Gramsci, 'an organic ideology... is formed... through the articulation of elements which, considered in themselves, do not have any necessary class belonging'. They reject the 'naturalist fallacy' because of its consequence 'that hegemony must always correspond to a fundamental economic class'. Moreover, Laclau, in another essay, argues that the limitations of Gramsci's approach lie precisely in his view that 'only the fundamental classes of society can be hegemonic subjects'. It would seem that Laclau and Mouffe argue that Gramsci's theories can be formulated in a non-essentialist discourse, but that his thought is still based on, and limited by, essentialist assumptions. In short, they point to what they regard as a deep contradiction in the _Prison Notebooks_ between what is in effect the old Marxist essentialist discourse, on the one hand, and the new non-essentialist discourse they approve and seek to develop.
There are, however, some other fundamental differences between Gramsci's historicism and discourse theory (these are already quite visible in the two essays by Mouffe discussed earlier) whose full consequences only begin to appear in Laclau's and Mouffe's latest book. These fundamental differences arise out of radically different philosophical positions. The fundamental philosophical thesis that characterizes discourse theory is the rejection of what Althusser refers to as the Hegelian conception of expressive totality. This is, in effect, a form of essentialism in which a single historical element produces, or is reflected, in all the others. The first consequence of this is class-reductionism, in so far as classes are thought to be the subjects of history. To replace this conception of history, the advocates of discourse theory propose a conception of the intrinsic neutrality of all social elements. This, of course, is based on a theory according to which the meaning of a term is a function of its place in the discourse, not of a possible reference to something n ondiscursive. This emphasis on the intra-discursive constitution of all meaning is, in effect, equivalent to a kind of reduction, in the sense of Husserl's _epoche_.
As we saw, Gramsci denies that all meaning is relational: a function of the relations between terms in a discourse. Although Laclau and Mouffe do not deny that there are, in some sense, real objects in the world, independent of consciousness, they nevertheless affirm that they are constituted as objects only within a discursive practice. Hence, they sever the reference relation as if the object itself were devoid of importance. Perhaps this is a modified version of the conception of historical experience that was held by Croce as well as by Collingwood and some of the German historicists; in the present case it is a discursive practice, rather than the re-enactment of the past or the contemporaneity of history, which confers identity on social phenomena.
The significance of this lies in the attempt to provide a model for an adequate analysis of modern social movements. In their theory, discourse theorists such as Laclau and Mouffe espouse a concept of politics that is based on the non-fixedness of all elements and of human nature, so that any particular social configuration is to be explained in terms of whatever hegemonic principle succeeds at the time. Because all identity is conceived as relational and since the principle of articulation, that is, the principle that links to some unity the various elements of a social system, is hegemony, the meaning or identity of social elements depends on a practice of articulation. This is defined as a 'practice establishing a relation among elements such that their identity is modified as a result of the articulatory practice'. The identity of social elements depends on the hegemonic principle that brings them together as a more or less, but never completely, unified or closed system.
Needless to say, Gramsci does not draw an analogy between society and language, an analogy that presents some difficulty inasmuch as it is not clear at all that non-referential meaning relations are similar to social relations. However, the point is not whether Gramsci was consciously thinking along these lines, but whether his concept of hegemony necessitates this form of discourse to develop its meaning fully. We have already seen Gramsci's conception of the meaning or identity of social phenomena. He rejects both the idealist historicist version of the inner meaning of historical events, and the positivist theory of mere external description of types of events. Instead, he proposes a conception of historical events in terms of the causal nexus, or the network of temporal processes which together become historical necessity. The meaning of a social phenomenon is not merely a function of its own intrinsic characteristics, nor simply a matter of the hegemonic practice that articulates it. It is, rather, its position in a system of generative mechanisms, some of which are dependent on hegemonic articulation, some of which are not. That is why Gramsci insists that to understand the victory of a hegemonic principle one must look beyond the character of that hegemony, for not to do so would be to engage in mere external description. The meaning, or the content of identity of hegemony, is to be found in the causal nexus. And this seems to be a far more complex and richer analysis of hegemony than the one proposed by discourse theorists.
Whatever their merits, however, their discourse is radically different from Gramsci's. The contradiction they claim undermines Gramsci's thought is in reality not an inconsistency. Gramsci's theory is a form of essentialism, for it does not deny the primacy of classes as the long-term causal mechanism of the historical process. His essentialism, however, is not the one rejected by Laclau and Mouffe, for it does not deny either the relative autonomy of politics and culture, or the importance of distinct groupings that emerge in civil society. Whereas discourse theory stresses the importance of the empirically evident groupings that exist and seeks to provide a model to understand their dynamics, Gramsci attempts to understand both the 'combinations and dispersions' of social elements as well as the deeper, long-term causal process determined by class-structures.
The groups that are formed in the terrain of civil society advance claims on the state, or even attempt to change the state according to the problems that emerge from their position in the social system or from some other area of concern. Gramsci's theory, however, is not an ethical one. Despite his stress on the concept of hegemony, it is an explanatory one, a historical one; the main question is not about the moral worth of any kind of action or hegemonic principle, but about the generative mechanisms of history. On this question, Gramsci's position is clear. The full specification of a historical bloc demands that both economic and extra-economic factors be taken into consideration and that their causal weight be assessed carefully. As a matter of historical hypothesis, Gramsci claims that the class structure of a social bloc is the strongest causal determinant in the long run.
Perhaps it is true that in the present, the working class has not been as politically active as it was after the Russian Revolution, and that, in general, its practice is reformist. And so the banner of political intervention is carried by other groups which have no class identity. The question, however, is whether this is sufficient reason to change the philosophical basis of socialist theory. A positive answer to this question reveals the most relativist form of historicism, a form to which Gramsci certainly did not adhere. Of course, there may be good reasons for altering specific empirical hypotheses. The question that must be asked is rather whether the present theoretical crisis, if one exists, is a conjunctural one or a permanent one. Gramsci's historicism suggests that the answer to this question must be sought in the long-term development of the socio-economic structure.
As we saw earlier, the growing complexity of civil society represents a problem for the dominant groups. For conflict can arise out of the various institutions of civil society, conflict that, admittedly, may not have a necessary class character. It is under these circumstances that hegemony becomes a decisive force, for it is the means by which the supremacy of the dominant class is preserved. Hegemony serves the function of unifying civil society so that it remains adequate for the existing socio-economic structure. The decisive function of hegemony is, then, that of unifying the heterogeneous and dispersed wills of individuals, of transforming them into a homogeneous, coherent whole. It is because of this decisive function of hegemony which stems from the growing complexity of civil society, that hegemony has acquired its vital strategic role. And this means that socialist forces must be able to show both their willingness and their ability to solve the problems facing society today.
Hegemony, power and the state
The view of hegemony as both the universal solution to the problems of a society, which includes all the liberation movements, and as the class-based foundation of a new state, points to Gramsci's dual conception of politics. When Gramsci affirms that all of life is politics, he endorses a view that politics is the activity of organizing a society so that the best possible life for everyone is secured. In this sense, the concern for equality and democracy is paramount. This is mainly an ethical concern, one whose central value is perhaps a deontological emphasis on the equal dignity of all human beings. It is, perhaps, no different from Marx's desire to construct a society where each receives according to his or her needs and each gives according to his or her abilities. However, the ethical universality of this conception of politics is limited in various ways. First, ethical principles must be discovered; this depends on the growth and development of societies. Second, class-structure limits the scope of politics; accordingly the rules of the good life are not intended to secure universal equality but, rather, to promote a certain inequality. Hence, politics is linked to coercion, to power understood as the supremacy of one class over the other, or of one group over another.
In this sense of coercion, politics is concerned, as Gramsci writes of the state, with adapting 'civil society to the economic structure'. And this is not possible simply by persuasion and propaganda. To expect that civil society adapt to a new structure, that is, 'that the old _homo oeconomicus_ disappear without being buried with all the honors it deserves is a form of economic rhetoric, a new form of vacuous and inconclusive economic moralism'. In short, ethico-political or hegemonic methods are not sufficient for effecting structural changes. The possibility for developing a social organization truly conducive to the good life does not depend on the higher moral and intellectual features of a counter-hegemony alone; it cannot be materialized by moral means alone. Gramsci is far from espousing a liberal theory of politics. The ethical, or Aristotelian, conception of politics is concerned with the possibilities of a truly human organization of society. In reality, however, the obstacles to the realization of human dignity make us think about the real historical processes which give rise to possibilities within power structures or class structures which, in the long run, set the limits of any conscious intervention designed to change society.
It is in this realist conception of politics that Gramsci espouses a theory of the identity of politics and economics. The origin of this identity is found in Marx's _Capital_ , where he argues that the exploitation of the working-class by capital, defined in economic terms as the appropriation of surplus-value, develops 'into a coercive relation'. Whereas surplus value is an economic category, coercion is a political one; it is in effect a relation of power between two classes. In its restricted sense, Gramsci's conception of politics is based on this identity of politics and economics, an identity that, it is suggested, imprints a form of behaviour, a homogeneous element in the otherwise differentiated mode of behaviour of individuals. In short, the permanent structures of a society become 'spontaneous' or 'natural' forms of behaviour, feelings, etc. for great masses of people. The role of hegemony in this situation is that of making homogeneous the dispersed will of individuals, of creating the conditions under which the structural coercion is freely accepted as a mode of living.
In this case, hegemony finds its source, its original principle, in coercion, or more precisely, in the exploitation first of labour but also of other identifiable groups. This social relation of production is transformed into a political one. However, politics, for Gramsci, is not reduced to this power relation. Although it constitutes the essential aspect of any hegemonic system, an aspect that cannot change without transforming society as a whole, it is possible and necessary to make concessions, as Gramsci puts it, to 'the groups over which hegemony is exercised', that is, the ruling group can make 'sacrifices of an economic-corporate order; but there also is no doubt that such sacrifices and such a compromise cannot touch that which is essential, for though hegemony is ethico-political, it cannot but also be economic, it cannot but have its foundation on the decisive function exercised by the leading groups in the decisive nucleus of economic activity'. As we saw earlier, the high salaries paid by Ford industries was an attempt to win the consent of workers to the new work methods. Perhaps a better example is to be found in recent attempts to introduce equal pay legislation in Ontario. Apart from the narrow scope of this law, its meaning lies in the fact that it can make economic-corporate concessions to a group, without giving up any of the essential conditions of capitalism. In this sense, the Liberal government is exercising the hegemony of the dominant classes, making concessions which will be costly in economic terms, but which will control the conflicts that emerge in the private institutions of civil society.
In hegemonic struggles, then, the two conceptions of politics are synthesized. For civil society, as we saw earlier, gives rise to conflicts which are not linked to class-structure, and whose solution is, from an ethical point of view, as important as class conflicts. However, the solution to these problems can only be a partial one, as it must take place within the limits of the existing class-structure. For a fuller solution to be possible, it must be articulated to a new hegemonic class, as Mouffe suggests, a class that can present itself as being able to solve all the problems facing a society, that is, it is mature enough to include in its programme the interests and concerns of non-class groups, such as women, children, the elderly, etc.
The growing complexity of civil society, with the need for the dominant class to control any conflicts that may arise in the sphere of private organizations, has resulted in a new relationship between state and civil society. Under these circumstances, the function of the state has been expanded, involving, as Buci-Glucksmann points out, 'an incorporation of hegemony and its apparatus into the state'. This is what Gramsci calls the integral concept of the state, which is defined as the unity of dictatorship and hegemony, as 'political society and civil society, that is, hegemony armoured with coercion'.
There are two kinds of circumstances that lie at the source of the expansion of state functions. First, as has been mentioned, there is the growth of civil society. Gramsci points out that with the colonial expansion of European countries and the increasing complexity of the internal and external relations of the state the 'formula of civil hegemony' replaces that of permanent revolution. Among the changes he thinks are significant, he lists the emergence of political parties and trade unions, as well as other associations; and he suggests that proliferation of important urban centres also contributed to this development.
Second, there are economic reasons for the expansion of the state. As we have seen, the reorganization of the state in the 1930s, in the contrasting variations of the New Deal in the USA and the corporate state in Italy, were prompted by economic factors. But, as de Giovanni has observed, 'a central knot in the morphological transformations of polities' lies in 'the shift of great human masses to a _direct_ relationship with the state'. This shift, Gramsci argues, originates in the desire of' the mass of savers to break off any direct connection with the _ensemble_ of private capitalism'. The mass of savers, however, do 'not refuse their confidence to the state: they want to take part in economic activity, but through the state, which can guarantee a modest but sure return on investment'.
In its extended role, then, the state includes civil society, but it does not cease to be political society, that is, the expression of class power. This conception of the expansion of the state seems to obliterate what may be a useful distinction between the ethical or consensual aspects of social life and the coercive aspects that are part of the state power as it controls the judicial system, the bureaucracy, and the army. However, the intervention of the state in education and other social services, as well as its interest in containing the growing demands from the voluntary associations of civil society, force the state to be more interventionist, to participate more directly not only in preserving law and order, but in organizing civil society. What Gramsci suggests is that the ruling group, through the agency of the state, must take a direct interest in civil society in order to control it and to steer its possible conflict along permissible channels. Because the state represents the 'historical unity of the ruling classes', it must intervene both by means of force and by hegemonic means wherever this unity might be compromised.
The distinction between civil society and political society is thus somewhat blurred because 'in actual reality civil society and state become identified'. There is, however, a deeper reason why the state's function expands as much as it does; this is that the state in its historical meaning is not identical with the government or with any institutional framework. For, as Simon rightly points out, in Gramsci's theory 'power is conceived as a relation', a relation that permeates all social activity. What Gramsci suggests, in Simon's words, 'is that the social relationships of civil society are relations of power just as much (though in a different way) as are the coercive relations of the state'. The expansion of the state is then to be conceived as the historical process in which the fundamental relation that structures the relations of production penetrates more and more aspects of social life, so that, as Gramsci points out, the modern state, as opposed to the medieval state, 'substitutes for the mechanical bloc of social groups their subordination to the active hegemony of the leading and dominant group; hence it abolishes some autonomies, which, however, re-emerge in other forms, as parties, unions, cultural associations'.
The historical meaning of the state, then, lies in the social relations, or power relations that exist between classes, although not all the problems that arise out of civil society are related to class-struggle. Nevertheless, the power relations must be made to prevail in all areas of social life. The state, in short, must educate; it must adapt 'civil society to the economic structures'. In the words of Bonomi, the optimum condition for the members of the ruling class is one in which they 'govern with the "spontaneous consent" of the adverse classes, and can give a "universal character" to their goods and their interests'. The more they can do so without resorting to force, making concessions within the necessary limits, the more viable, secure, and strong the state will remain.
It is in this expanded conception of the state that Gramsci's analysis of the superstructures is synthesized. Although one can distinguish several levels of the superstructures, and hence distinguish civil from political society, their unity is guaranteed by the fundamental social relations that originate in the world of production. Civil society is often the source of problems, some of which have no class identity. The continued power and prestige of the leading groups depends on their response to these problems. The hegemony of a class depends on its ability to present the solutions to social problems as universal, coherent, and viable. It is in this theory of the superstructures, and in particular, of the role of the state in preserving and expanding the unity of the ruling classes, that Gramsci's thought differs from that of Marx. Luporini has argued that Marx maintained that the working of the internal mechanism of the mode of production was sufficient for the reproduction of class domination. The question that arises is, 'why does the political state not only exist but gets improved?' Though Marx did not completely disregard the importance of politics, as Luporini thinks he did, he did not, and could not, anticipate the expansion of the state's functions, its changing relationship to what Gramsci calls civil society. Gramsci's theory attempts to adapt Marx's thought to the new situation. In so doing, he kept the foundational role of social relations of production, and attempted to provide a conceptual framework for the analysis of both class and non-class conflicts that threaten the hegemony of the ruling group. In his analysis of the state and politics in general, Gramsci did not, as Marx seems to do, emphasize the logic of capital or derive, as some have attempted to do, the forms of the state from the necessary forms of development of capital. It is in this respect that Gramsci's historicism most differs from Marx's thought, for Gramsci's historicism is not the attempt to derive politics from the socio-economic structure, though it does not disregard the fundamental determining role of the economy in the last instance. In the attempt to understand the complexity of the historical bloc, to fathom both its long-term phenomena and its conjunctural ones, its economic determinates as well as its ethico-civil ones, Gramsci is much more sensitive to the open character of the historical process, much more capable of understanding the role of both class and non-class politics in history. This being said, however, it is also true that, for Gramsci, no historical explanation and no political movement can dispense with the stable and long-term, though often invisible, determination of the socio-economic structure.
Finally, whatever concrete strategies may be drawn from Gramsci's _Prison Notebooks_ , they must take account of the complex analysis of politics that Gramsci proposed. It is not only in the changing relations between civil society and state, but also in the relation between structure and superstructure, that the basic strategic principles must be sought.
Conclusion
The foregoing discussion is no more than an attempt to provide a general framework for the analysis of Gramsci's theory of history and politics. It is not, then, a full interpretation of his thought; the main purpose is to point to the kind of interpretation that seems to be the most consistent with his historicism.
Gramsci's historicism, it must be stressed, does not commit him to a theory of the ethical meaning of the inner aspects of history. This means that it does not commit him to a theory of the causal or generative primacy of politics. In so far as Gramsci makes the distinction between the exterior and interior of history, it is primarily a distinction between description and explanation. Gramsci's concern with the interior of history is to find the causal nexus, the generative mechanisms whose concurrence produces social phenomena. The explanation of social phenomena must take into consideration two levels of explanation; on the one hand, the processes of development that result in the phenomena, their history, must be carefully analysed; on the other hand, the structure of the social systems at any given point in time must also be known. Needless to say, a correct appreciation of the relative temporality of each aspect of a social system is necessary for an accurate analysis of the causal nexus.
This model of explanation is advanced as a probable solution to the problem of the relationship between structure and superstructure, that is, the problem of the reflection of the structure in the superstructure. Given the existence of non-class groups which have entered the political arena, it is not possible to claim that all political activity and all ideas are reflections of the structure. Yet, in some sense, Marxism claims that, in the last instance, the structure determines historical movement. It is the relationship between structure and historical movement, as Gramsci contended, that constitutes the most important problem of historical materialism.
According to Gramsci, society is structured in three main levels. First, the class-structure of society; second, the voluntary associations of civil society; third, the state or political society. Whereas the objective existence of classes as well as the relations between them is determined by the structure, their development as political agents is subject to mechanisms that do not bear a direct relationship to the structure. Furthermore, other non-class groups and movements make this political development far more complex. In the conditions of modern capitalism, then, the state is related not only to the world of economic production, but also to civil society. Indeed, the relationship between civil society and state has become so complex and important that it often masks the other relation between state and structure. Those who claim that Gramsci holds a theory of the primacy of politics are not too far from ignoring, or even dismissing, the state-structure relation. But this is based on a mere external description of Gramsci's _Prison Notebooks_.
The empirical or descriptive reading of Gramsci's prison work, will certainly conclude that Gramsci gave primacy to the superstructures, and in particular to hegemony, for this is the problem that occupied most of Gramsci's attention. This reading, however, fails to give an account of Gramsci's theoretical assumptions. In part, as I have tried to illustrate, this is due to the scant attention given to Gramsci's uses of 'historicism', which has led to an unwarranted Crocean interpretation of his thought.
It is undeniable that, for Gramsci, the class structure of society plays a fundamental role in the determination of history. But the concept of class is a historical one, which means that its reference ranges over a whole period of history. In empirical terms, the groups that emerge in civil society and the individual who objectively belongs to the class, may or may not behave in class ways. The long-term process, however, is mainly determined by the class structure of the historical bloc. This does not deny that interests other than class interests arise in any society. But in the terrain of political activity, these interests are satisfied in ways and by means that are designed to preserve the power of the ruling classes, to add to their prestige by convincing the masses that they are capable of solving the problems of the day. The struggle for hegemony, then, is presented as taking place on two fronts: on the economic front, as the struggle to eliminate classes; on the ethico-political front, as the struggle to create a truly democratic world. A truly progressive force is one that can offer solutions to both kinds of problems, solutions that are not merely dreamt up as necessary concessions, but that are evolved on the basis of equal participation by those directly affected by them.
Gramsci's claim is that the modern state has been expanded to allow the ruling classes to intervene effectively in civil society. This means that the historical meaning of the state as a power relation between classes, expands to allow for the state's exercising its supremacy by other than coercive means, that is, by presenting its _Weltanschauung_ and its ethics as universally valid. In so doing, the state fulfils the role of educator.
Gramsci's theory, one must conclude, is a form of essentialism, but not the one so often criticized by structuralists and discourse theorists. For according to the latter, essentialism is a form of historical determinism in which the essence, the economic structure, determines all other social phenomena. In their language, the essence determines the meaning or identity of all social elements. In Gramsci's theory, the essence, class-structure, determines the general direction of historical movement; but the causal-nexus that determines every event, every change, every social element, consists in the concurrence of processes which are characterized by their own particular dynamism. In this regard, his analysis of situations and of the relations of forces offers a theoretical model for understanding how historical movement emerges out of the structure. Historical necessity, then, is not merely constituted by the structure, but by the structure plus the organized actions of groups that emerge on the basis of their position in the social world.
It has been noted that Gramsci holds two conceptions of politics. The most general one, which I have called Aristotelian, is best exemplified by his identification of life with politics; it is the theory of the good life. The other one is a classical Marxist one; it is the theory of class power as exerted by the state. What Gramsci seems to suggest is that the hegemony of a class is composed of two kinds of elements. There is, first of all, a set of basic principles that is closely related to its class interests, and which is expressed under capitalism in theories of the _homo oeconomicus_ , i.e. economic individualism, property, etc. Second, there are elements that, in so far as they can be accommodated within the scope of the first ones, allow for a higher form of civilization. For instance, as long as the claims of the women's movement can be accommodated within economic individualism, property and contract laws, etc., they may be satisfiable. In a class state, then, the ethical conception of the good life is second to the principles of class power.
To transcend class structures, then, is to establish the possibility of the good life. And this is, Gramsci writes, 'the end of the state and of law as they become useless, as they exhaust their task and are absorbed by civil society'. And it is here that Gramsci's conception of democracy finds its deeper meaning; democracy is not conceived, as is the liberal model, in terms of the relations of power and in terms of elections, but in terms of the collective decision-making of all parts of society, in a society without classes, without any power relations.
**Conclusion**
In his reconstruction of historical materialism, Gramsci often used terms that had important theoretical functions in the philosophy of Benedetto Croce. 'Absolute historicism', 'transcendence', 'immanence', are all terms that played important roles in Croce's thought. Furthermore, Gramsci also espoused a theory of the identity of philosophy and history, a theory that, in Croce's system, acquires a fundamental meaning: history is the history of universal or pure concepts, in particular, it is the story of liberty. Thus, when Gramsci argues that 'split from the theory of history and politics, philosophy cannot be but metaphysics' and that the 'great conquest of modern thought... is the historicization of philosophy and its identification with history', he seems to be arguing for a position that is very close to that of Croce. The similarity in the language used by both thinkers, however, should not lead us to believe that there is a similarity of content as well.
Croce's conception of the unity of history and philosophy is a re-translation of historical materialism into speculative language, of the 'progressive acquisitions of the philosophy of praxis', such as is developed in the 'Theses on Feuerbach' and in Engels' _Feuerbach and the End of Classical German Philosophy._ What is then, for Gramsci, the unity of history and philosophy? The historicity of philosophy in its largest sense, he writes, consists in its having 'become the conception of reality of a social mass (with a corresponding ethics)'. It is in this sense of a conception of the world with practical implications, that the philosophy of our epoch forms a bloc with the history of the same epoch. The reasons for the diffusion of a philosophy, however, are not to be found merely in the intellectual and logical character of the philosophy itself. As he argues in the case of hegemonic principles, this expansive character must be justified historically: its 'necessary and causal nexus' must be explained. Whereas for Croce the problems of philosophy emerge out of the dialectic of ethical ideals and practical requirements, for Gramsci they emerge out of the depths of material life, they arise in the terrain of social relations.
It is obvious that by 'philosophy' Gramsci does not mean the thought of professional philosophers. Philosophy, for him, is synonymous with the ideas of an epoch: 'The philosophy of an epoch is not the philosophy of one or other philosophers', it is a combination of the thought of intellectuals, groups, and popular masses which 'become the norm of collective action'. In short, philosophy and politics form a unity. This implies that, as Cloutier has argued, one must 'envisage philosophical work in terms of philosophical hegemony, or, more precisely, within the Gramscian programme of a "cultural and moral revolution"'. Whereas for Groce the work of the philosopher is concerned with contemplating the eternal life of spirit, and the philosopher, as Gramsci suggests with respect to Croce himself, becomes a lay Pope, for Gramsci the task of the philosopher is that of disseminating hegemonic principles or participating in the political process of social transformation.
Gramsci does not deny the truth value of philosophical theories or of knowledge in general. He is concerned, however, with the analysis of the social function of knowledge. He investigates the role of science, philosophy, etc., as ideologies, that is, as superstructural elements that shape the way men and women view natural and social reality and respond to social change. The point Gramsci develops is that the social function of knowledge need not coincide with its truth-value. A thoroughgoing study of a social system must bring to light the complex interrelationships that exist between all its elements; the study of the relation between science and society is but an aspect of that study.
This conception of historicized philosophy does not deny the other philosophy, that is, the basic logical, ontological, and epistemological conceptual frameworks with which professional philosophers deal most of the time. This type of philosophy, as we have seen in the preceding pages, is not totally foreign to Gramsci, nor is he silent on some of its fundamental problems. The attempt to define Gramsci's concept of historicism has brought out the general outline of Gramsci's philosophy, a concept that he himself often defined with reference to philosophical concepts, in particular, with reference to the concept of 'realism'. We can now establish the fundamental theses that together define Gramsci's 'absolute historicism'. Some of these theses pertain to philosophical realism, others to an ontology of social systems, still others to the general methodological principles for a science of society. Together, they amount to a general approach to the study of society.
The basic epistemological thesis espoused by Gramsci is philosophical realism. He asserts that reality exists independently of its being known or perceived. He also asserts that reality can be known, although its vastness and complexity make it impossible as a matter of fact to know it completely. Although this knowledge may have a social function that does not coincide with its truth, it can nevertheless be objectively true. In addition, Gramsci espouses the correspondence theory of truth. Furthermore, he maintains (a) that ideas reflect reality, or that being is prior to consciousness, and (b) that there are no transcendent beings, such as Providence, Spirit, Reason, etc., so that only nature, and men and women in social systems exist. The first thesis of Gramsci's historicism, then, constitutes a materialist theory of knowledge.
Gramsci's ontology of social systems is contained in six basic theses. First, social relations, rather than the decisions of great men, or single events, are the basic facts to be established, basic because they provide the real causal mechanism for social transformation. Second, social systems are not static; they are involved in transformational processes, so that even the laws of social systems are subject to change. Third, social systems are composed of several sub-processes of different temporal rhythms; their conjunction at any given time constitutes a situation. Fourth, historical events are not uniquely determined by any single law, but by the coincidence of several law-like processes of different duration. Fifth, social systems are determined by diachronic laws of the succession of various situations, and by synchronic laws determining the connections among the several component parts of the system. Although Gramsci does not develop this thesis enough for us to be able to assess it, he suggests that the two types of causality that rule succession and contemporaneity respectively are not independent of each other. In general, the theory of the reflection of the structure in the superstructure is construed as a complex process of development. Sixth, although society and the state do not exist otherwise than as the activities of, and relations between, individuals, the laws that rule their social existence are emergent upon those activities and relations, that is, they cannot be reduced without remainder to the dispositions of the individuals of the system. Gramsci defines this emergence as the dialectical transformation of quantity into quality.
A salient point of Gramsci's social ontology is his rejection of any form of reductionism to psychological, biological, or physical laws. He maintains that the explanation of social phenomena must rely on appropriate concepts obtained by means of a complex procedure of abstraction, what he calls 'determined abstraction'. In this procedure, the long-term transformations of a system yield the best evidence for constructing the appropriate conceptual and theoretical frameworks. Thus, although Gramsci does not fully reject the conception of methodological criteria general to all disciplines, he nevertheless defends the substantive autonomy of history from psychology, biology, or physics.
From a methodological point of view, the basic thesis of Gramsci's historicism is that, because society is a transformational process, the long-term perspective, or diachronic approach, is the most adequate for studying social phenomena. This is not intended as rejecting all sociology, as he often appears to do. It is, rather, a denial of the scientific character of merely synchronic studies of society. His efforts at explaining social phenomena in terms of underlying causal mechanisms, his theory of tendential laws of history, and in general his conceptual framework are part of his effort to integrate history and social theory. In this respect, Marx, as well as the _Annales_ school among others, have developed similar views of an integrated scientific history. The emphasis on the long-term view and the realist theory of scientific concepts and theories suggests a second methodological principle. Some historical concepts are complex abstractions from a multitude of events, forms of behaviour, etc., over long periods of time. The reference of the relevant concepts and theories is not to a thing in a slice of time; it is to a process whose visible features are due to underlying transformational processes, and explained by means of long-term concepts and theories.
The long-term view is crucial for the study of social systems. It alone makes it possible to understand the structure of a social whole. Full description of societies, Gramsci maintains, is only possible when all their inherent possibilities are exhausted. This implies that, without the benefit of knowledge of the future states of a social whole, one can only describe and know its present state imperfectly. The long-term view, then, is essential for both describing and explaining social phenomena. This view, which many historians accept, entails that, as more of the effects of an event come to light, our understanding of its meaning will change, and its history will have to be rewritten. However, this does not commit Gramsci to the Crocean view that all history is contemporary history, nor to a conception of historical experience such as that espoused by some historicist thinkers. In Gramsci's view, the present is the consequence of the past and as such it contains the vital aspects of the past; the structure of the present constitutes the best evidence of what was historically necessary in the past.
The specificity of Gramsci's historicism is contained in his theory of historical time. His conception of laws as relatively permanent structures, the suggested temporal scope of concepts and theories, his emphasis on the long-term perspective, all point to the crucial importance of the rhythms of change of social phenomena. The different tempos of the various social sub-processes are an indication of various underlying causal mechanisms, whose relative weight must be carefully assessed for an adequate understanding of historical facts. The coincidence of the various sub-processes, their mutual relations, and their potential development constitute what Gramsci calls the situation. It is the situation, and in particular, the array of social forces that are engaged in struggle for hegemony, that constitutes the unit of analysis of history.
The contrast between Gramsci's historicism and that of Croce or the German historical school is quite evident. First, Gramsci does not reject the conception of laws in history, though he rejects any simplistic application of the concepts of natural science to history. Second, the subject-matter of history is not, as it was for the various forms of idealist historicism, values or meanings, liberty, or the decisions of great men; for Gramsci, the subject-matter of history is the complex and contradictory relations and struggles that are formed on the basis of social relations of production. It is, hence, the economic order, as well as politics, culture, and morality. Although Gramsci's own research focused mainly on cultural and political issues, on what he generally defined as hegemony, the inner aspect of history was not constituted simply by values or meaning, but rather by a set of historically specific causal mechanisms. Thus, whereas the historical experience to which historicists in general referred was the empathetic re-enactment of the past in the mind of the historian, Gramsci's concept of historical experience is a question of the knowledge of the past as it is carefully documented and as it informs the practice, above all the political practice, of the present. As a consequence, whereas for the idealist historicists in general the values and problems of the present gave a meaning to historical experience and, through it, the past; for Gramsci the social reality of the present is evidence for the elements of the past that corresponded to historical necessity at the same time that it contains the necessary conditions for the future. Knowledge of them is of great political significance.
Gramsci's _Prison Notebooks_ are mostly concerned with political, cultural, and historical issues. His comments on philosophical issues are not negligible, but they are often inconsistent. They are also easily misunderstood, as he used a language that suggested Croce's influence, and because he often had recourse to the arguments of idealist philosophers in his critique of positivism and vulgar materialism. Although his philosophy offers some interesting suggestions for the study of social phenomena, his most important work, it is generally agreed, relates to political theory. Among the most important theoretical issues that he discussed is the relation between structure and superstructure as well as the role of politics in social change.
Gramsci's focus on cultural and political studies should not be taken as an assertion of the primacy of politics, or the primacy of the superstructures. His analysis of historical subjects, such as the Risorgimento, or Americanism and Fordism, points to an interpretation that is much closer to the classical Marxist theory of the determining role of the structure. Gramsci's conception of historical laws, and of the varying temporal dimensions of different structural and superstructural processes, allows him to assert that the structure is primary in the long run, while the superstructural elements undergo changes that are not immediately determined by the structure. Because Gramsci holds a multi-causal conception of historical necessity, he can argue that the effects of the structure manifest themselves over the life of social systems, but do not uniquely determine the superstructures. There are, furthermore, long-term phenomena that do not originate directly in the socio-economic structure but which have considerable importance in the development of the historical bloc. Nevertheless, in terms of temporal succession, the various superstructural orders either originate in the social relations of production, without which no society would be conceivable, or they are inherited from the past and adapted to the class structure of the present. Gramsci engages in a dual analysis of the relation between the structure and the superstructure. First, he studies the passage from the structure to the superstructure as a temporal process, hence he focuses on the forms of political and cultural activity that originate from a given social structure. Second, he develops a conceptual framework for the study of the complex set of relations that exists among the various forces that vie for social control at any point in time, as well as between structural elements and superstructural ones. These forces are generally considered to be grounded on socio-economic classes, though they also include groups with other interests, such as women, children, and the elderly. Thus, the full specification of a historical situation must include these various elements and care must be taken to assess their respective causal weight in a realist manner.
The concept of hegemony can be studied from the point of view of class developing from a mere economic existence to its hegemonic function through the state. It can also be studied as an aspect of the domination of a class over other groups in a social system. Both kinds of analysis, diachronic and synchronic, are fundamental to Gramsci's approach to social theory. Whereas the first kind emphasizes the transformational character of the system, its process of integration and disintegration, the second attempts to show the systemic character of historical blocs. The two forms of analysis, however, cannot be taken as two mutually independent methods for the study of two different aspects of society, such as the methods of a history and a sociology. Gramsci's conception of integral history, his attempt to integrate history and a social theory, demand that the two methods be integrated. The basis for this integration is to be found in his theory of causality, and in particular his suggested, but never explicitly developed, theory of the mutual interdependence of diachronic and synchronic causality.
It has been noted that Gramsci's concept of hegemony points to a dual conception of politics. First, there is the classical Marxist conception, in which the state, hegemony, etc., are said to serve a function of domination of one class over others. Second, in its Aristotelian conception, Gramsci's expanded ideas of politics can be defined as the science of the good life. In this second conception, which is an ethical one, the problems facing a historical bloc are not merely, or not all of them, class-related problems. Nevertheless, the solutions to the problems are framed within the forms of domination prevalent in the system; that is, the long-term determination of the structure limits their possible solutions. A complete solution to all problems of this kind, Gramsci suggests, is possible only when all forms of domination disappear. The unification of humankind, as a necessary condition for objective knowledge, is seen as the process that can lead to a rational social order, an order in which the state, as coercion, has been absorbed by civil society, or by consensual decision-making.
There is a dual conception of the state in the _Prison Notebooks_. The state is conceived first as the relations of power, rather than the institutions that exercise such power, between dominant and subaltern classes. In its second, or integral, definition, the state is conceived as both hegemony and force. In this expanded role, the state must intervene in civil society, educating, making concessions, and in general controlling the conflicts that arise in the terrain of civil society. In this role, the state must ensure that civil society remains within the permissible bounds imposed by the economic structure of society. This dual conception of the state must not be construed as a Crocean liberal idea of the ethico-political state. In Gramsci's view, the supremacy of a class, and power in general, is manifested through both domination, or force, and hegemony, or ethico-political leadership. In this respect, Gramsci's analysis of culture represents the effort to understand the subtle ways in which power is manifested, or alternatively, the ways in which a new conception of the world begins to emerge in popular culture. For this reason, he paid more attention to the function of culture than to its actual content, though this is not to say that Gramsci disregarded the latter or that he thought one could be understood without the other.
Today, the proliferation of social movements seems to have cast some doubt on the validity of some of the central theses of historical materialism, in particular the thesis of the economic determination of historical change. Because of this, radical social theorists have attempted to develop Gramsci's insights on the hegemonic functions of the state from a non-class-reductionist perspective. In so doing, however, most of these interpreters of the _Prison Notebooks_ have based their reading of Gramsci on assumptions about his historicism that a close reading of his work does not bear out. From Gramsci's perspective, the various groupings that originate in the terrain represent conflicts that the state must solve within the limits of the present social structure. The various forms that these groups take, the degree of consciousness that they reach, he suggests, must not be thought to challenge the Marxist concept of class structure. Whereas the former are the most empirically evident forms of struggle, the latter contains the mechanism of social transformation, a mechanism that, like Braudel's prisons, exerts its influence over long periods of time, in an often imperceptible fashion. To assert this, however, is not to deny the importance of the new social movements, or the urgency and well-foundedness of their demands.
Gramsci's theory of politics is not a denial of the primacy of economics. It is a denial that the structures are the only determining elements of a social system and that the superstructures are epiphenomena devoid of any causal import. This theory, hence, does not deny some form of essentialism, though it certainly rejects simplistic conceptions. The same reservations Gramsci had against economism, namely, that it neglects to evaluate the different causal weight of different social sub-processes, can also be addressed to those theories which deny any form of essentialism. The latter, in so far as they cannot point to any general causal mechanism of social wholes, must be limited to describing particular situations. Although in each case they may be capable of establishing the causal importance of the various elements, their findings cannot be generalized.
In conclusion, Gramsci's historicism is not an idealist, anti-scientific theory of society. Though he emphasizes the historical character of knowledge, he does so only in terms of its function in the organization and transformation of societies, not in terms of its truth value. Gramsci's political theory is his most important and lasting contribution to Marxist thought; his historicism, however, is an interesting attempt to reconstruct historical materialism that cannot be lightly dismissed.
**Notes**
Introduction
. G. Eley (1984) 'Reading Gramsci in English: observations on the reception of Antonio Gramsci in the English–speaking world 1957–82', _European History Quarterly_ , 14 (October), 470.
. L. Golletti (1976) _Il Marxismo e Hegel_ vol. 1: _Su i 'Quaderni Filosofici_ ' di _Lenin_ (Bari: Laterza & Figli), 121.
. A. Gramsci (1975) _Quaderni del Carcere_ , 4 vols. ed. V. Gerratana (Turin: Einaudi Editore), 2: 1438.
. ibid., 2: 1427.
. ibid., 2: 1438.
. ibid., 2: 1438–9.
. ibid., 2: 1480.
. ibid., 2: 1316.
Chapter One
. Gramsci, _Quaderni_ , 2:1437; 3:1826.
. A. Callinicos (1983) _Marxism and Philosophy_ (Oxford: Oxford University Press), 77.
. ibid., 78.
. ibid., 73. See also p. 151.
. Gramsci, _Quaderni_ , 2:1437; 3:1826–7.
. ibid., 2:1416.
. ibid., 3:1599.
. L. Althusser and E. Balibar (1970) _Reading Capital_ , trans. B. Brewster (London: NLB) 119–40.
. G. Vico (1976) _Principj di Scienza Nuova_ , 3 vols, ed. F. Nicolini (Turin: Eindaudi Editori), 1:71.
. ibid., 1:76.
. ibid., 1:95.
. ibid., 1:124.
. ibid., 1:87.
. ibid., 1:89.
. ibid., 1:125.
. ibid.
. ibid., 1:127.
. ibid., 1:15.
. ibid., 1:4.
. ibid., 1:125.
. G. Vico (1972) _Opere_ , vol. 1: _Delia Antichissima Sapienza degli Italiani Rivelata delle Origine delta Lingua Latina_ , ed. R. Parenti (Naples: Casa Editrice Fulvio Rossi), 237.
. ibid.
. Vico, _Principj_ 1:115.
. I. Kant (1929) _Critique of Pure Reason_ , trans. N. K. Smith (London: Macmillan), 467.
. ibid., 471.
. ibid., 470.
. ibid., 471.
. I. Kant (1963) _On History_ , ed. L. W. Beck (Indianapolis: Bobbs-Merrill Co.), 11.
. G. G. Iggers (1983) _The German Conception of History. The National Tradition of Historical Thought from Herder to the Present_ (Middletown: Wesleyan University Press), 4–5.
. W. Dilthey (1976) _Selected Writings_ , trans. and ed. H. P. Rickman (Cambridge: Cambridge University Press), 94.
. ibid., 159.
. ibid., 248.
. ibid., 191.
. ibid., 203.
. ibid., 208.
. L. von Ranke (1973) _The Theory and Practice of History_ , ed. G. G. Iggers and K. von Moltke (Indianapolis: Bobbs-Merrill Co.), 57.
. ibid., 57–8.
. Dilthey, _Selected Writings_ , 166.
. H. P. Rickman (1961) 'General Introduction' to _Meaning in History;_ by W. Dilthey (London: G. Allen & Unwin), 37.
. K. Popper (1961) _The Poverty of Historidsm_ (London: Routledge & Kegan Paul), 108–9.
. Iggers, _The German Conception of History_ , 5.
. ibid., 8.
. ibid., 127.
. F. Meinecke, _Werke_ , vol. 5: _Weltbügertum und Nationalstaat_ , 83, cited by Iggers, _The German Conception of History_ , 9.
. Iggers, _The German Conception of History_ , 127.
. Dilthey, _Selected Writings_ , 255.
. Iggers, _The German Conception of History_ , 6.
. ibid., 16.
. ibid., 12.
. M. Cruz (1981) _El Historicismo. Ciencia Social y Filosofia_ (Barcelona: Montesinos Editor), 59.
. Iggers, _The German Conception of History_ , 17.
. J. Ortega y Gasset (1965) _Kant. Hegel. Dilthey_. (Madrid: Revista de Occidente), 149.
. K. Marx (n.d., 1967, 1971) _Capital_ , 3 vols, ed. F. Engels (Moscow: Progress Publishers), 1:29.
. K. Marx (1976) _Grundrisse. Foundations of the Critique of Political Economy_ , trans. M. Nicolaus (New York: Vintage Books), 605–6.
. ibid., 606.
. Marx, _Capital_ , 1:85, n.l.
. F. Engels (1946) _Ludwig Feuerbach and the End of Classical German Philosophy_ (Moscow: Progress Publishers), 37.
. K. Marx and F. Engels (1976) _The German Ideology_ (Moscow: Progress Publishers), 37.
. K. Marx (1973) _The Poverty of Philosophy_ (Moscow: Progress Publishers), 95.
. P. Rossi (1957) 'Benedetto Croce e lo storicismo assoluto', _Il Mulino_ 6 (May), 327.
. B. Croce (1909) _Logica come Scienza del Concetto Puro_ (Bari: Laterza & Figli), 195.
. B. Croce (1920) _Teoria e Storia della Storiografia_ 2nd edn. (Bari: Laterza & Figli), 49–50.
. K. Marx (1970) _Critique of Hegel's 'Philosophy of Right'_ , trans. J. O'Malley (Cambridge: Cambridge University Press), 8.
. ibid., 11.
. Dilthey, _Selected Writings_ , 235.
. Rossi 'Croce e lo storicismo assoluto', 322–3.
. Croce, _Logica_ , 17.
. ibid., 229.
. ibid., 52.
. B. Croce (1907) _Ciò che è Vivo e Ciò che è Morto della Filosofia di Hegel_ (Bari: Laterza & Figli), 93.
. ibid., 89–90.
. Croce, _Logica_ , 209.
. ibid., 210.
. ibid., 211.
. Croce, _Ciò_ _che è Vivo_ , 91.
. B. Croce (1930) 'Antistoricismo', _La Critica_ 27, 407.
. It must be noted that by 'religion' Croce meant 'a conception of reality and a corresponding ethics', B. Croce (1932) _Storia de Europa nel Secolo Decimonono_ (Bari: Laterza & Figli), 23.
. ibid., 13.
. G. W. F. Hegel (1977) _Phenomenology of Spirit_ , trans. A. V. Miller (Oxford: Oxford University Press), 478.
. B. Croce (1967) _Etica e Politica_ (Bari: Laterza & Figli), 284.
. ibid., 285.
. ibid., 288–9.
. Croce, _Logica_ , 215.
. Rossi, 'Croce e lo Storicismo assoluto', 324.
. B. Croce (1963) _Ultimi Saggi_ (Bari: Laterza & Figli), 369–70.
. Croce, _Teoria e Storia_ , 118.
. Rossi, 'Croce el o storicismo assoluto', 323.
. Croce, _Teoria e Storia_ , 87.
. ibid., 12.
. ibid., 4.
. N. Badaloni (1975) _Marxismo come Storicismo_ (Milan: Giangiacomo Feltrinelli), 135.
. B. Croce (1928) _Storia d'Italia del 1871 al 1915_ , 2nd edn. (Bari: Laterza & Figli), vii.
. Badaloni, _Marxismo come Storicismo_ , 135.
. Croce, _Teoria e Storia_ , 78.
. Croce, _Ciò che è Vivo_ , 91.
. Rossi, 'Croce e lo storicismo assoluto', 351.
. ibid., 353–4.
. B. L. Kahn (1985) 'Antonio Gramsci's reformulation of Benedetto Croce's speculative idealism', _Idealistic Studies_ 15 (January), 33.
. Croce, _Etica e Politico_ , 264.
. ibid., 235.
. B. Croce (1950) _Croce, the King, and the Allies. Extracts from a Diary by Benedetto Croce, July 1944-June 1945_ , trans. S. Sprigge (London: George Allen & Unwin), 30.
. Gramsci, _Quaderni_ , 2:1088, 1225, 1477.
. ibid., 2:1234.
. ibid., 2:1433.
. ibid., 2:826.
. M. Finocchiaro (1979) 'Gramsci's Crocean Marxism', _Telos_ 4l, 32.
. E. Laclau and C. Mouffe (1985) _Hegemony and Socialist Strategy_ , trans. W. Moore (London: Verso), 90, n. 19.
. ibid., 113.
. Dilthey, _Selected Writings_ , 235.
. Laclau and Mouffe, _Hegemony_ , 113.
. Gramsci, _Quaderni_ , 2:1018, 1478.
. ibid., 2: 1079. In the same passage Gramsci adds a parenthetical note linking his analysis to Engels' interpretation of Hegel's statement to the effect that the real is rational.
. ibid., 2:1487, 1489.
. T. Nemeth (1981) _Gramsci's Philosophy_ , (Brighton: Harvester Press; Atlantic City, N.J.: Humanities Press), 5.
. _Quaderni_ , 2: 1139.
. ibid., 2:838–9.
. ibid., 2:1325–6. See also 2:958.
. ibid., 2:1480.
. ibid., 2:1393.
. P. Vilar (1982) _Une Histoire en Construction. Approche Marxiste et Problematiques Conjoncturelles_ (Paris: Editions du Seuil), 328.
. Gramsci, _Quaderni_ , 1:504; 2:1317.
. ibid., 2:990, see also 3:1578.
. G. McLennan (1981) _Marxism and the Methodologies of History_ (London: Verson and NLB), 23.
. Gramsci, _Quaderni_ , 2:1048, 1454.
. ibid., 2:1454.
. ibid., 2:1290–1.
. ibid., 2:1445.
. R. Bhaskar (1979) _The Possibility of Naturalism. A Philosophical Critique of the Contemporary Human Sciences_ (Atlantic Highlands: Humanities Press), 13.
. Gramsci, _Quaderni_ , 2:1415.
. ibid., 2:1467.
. ibid., 1:332.
. ibid., 3:1855.
. ibid., 2:1250.
. ibid., 2:1412.
. ibid., 2:1411–12.
. ibid., 2:1397; see also 2:1456.
. ibid., 1:435; 2:1434.
. ibid.
. ibid., 2:1456.
. ibid., 3:1854–5.
. ibid., 1:466–7.
. ibid., 1:47; 3:2022.
. ibid., 2:1033.
. ibid., 2:1416.
. ibid., 2:1415.
. ibid., 2:1421.
. ibid.
. ibid., 2:1423.
. ibid., 1:467, 2:1456.
. ibid., 2:1456.
. ibid., 2:1457.
. ibid., 2:1421.
. ibid., 2:977.
. ibid., 2:1416.
. ibid., 2:1452.
. K. Marx (1970) _A Contribution to the Critique of Political Economy_ ; trans. M. Dobb (Moscow: Progress Publishers), 21.
. Gramsci, _Quaderni_ , 3:1583.
. ibid., 2: 958, 1246, 1479.
. ibid., 1:817, 3:1656, 1727, 1766, 2259.
. ibid., 3:1724–5.
. ibid., 2:1225.
. G. Gentile (1974) _La Fibsofia di Marx_ , ed. V. A. Bellezza (Florence: Sansoni), 76–7.
. Gramsci, _Quaderni_ , 1:455, 2:1492.
. A. Labriola (1973) _Scritti Filosofici e Politici_ , vol. 2: _Discorrendo di_ _Socialismo e di Fihsofia_ , ed. F. Sbarberi (Turin: Einaudi Editore), 702.
. Gramsci, _Quaderni_ , 1:657.
. ibid., 2:1493.
. Nemeth, _Gramsci's Philosophy_ , 78.
. ibid., 7.
. ibid., 140–1.
. Gramsci, _Quaderni_ , 2:1437.
. ibid., 2:1478–9.
. ibid., 2:1088, 1225, 1477; see also 1:657, and A. Gramsci (1965) _Lettere del Carcere_ , 5th edn. ed. S. Caprioglio and E. Fubini (Turin: Einaudi Editore), 619.
. Nemeth, _Gramsci's Philosophy_ , 136.
. Gramsci, _Quaderni_ , 1:657.
. ibid., 3:1826–7.
. ibid., 2:1437.
. ibid., 3:1864.
. ibid., 2:1444–5; see also 1442.
. ibid., 2:884–5.
. Althusser and Balibar, _Reading Capital_ , 127.
. L. Salamini (1974) 'Gramsci and Marxist sociology of knowledge: an analysis of hegemony–ideology–knowledge', _Sociological Quarterly_ 15 (Summer), 371.
. Gramsci, _Quaderni_ , 2:869, 1422.
. N. Badolini (1975) _Il Marxismo di Gramsci_ (Turin: Einaudi Editor), 156.
. N. Badolini (1975) 'L'Historicisme de Gramsci face au Marxisme contemporain', _Les Temps Modemes_ 30 (February), 1021.
. ibid., 2:1022.
. ibid., 1024.
. N. Bobbio (1979) 'Gramsci and the conception of civil society', in _Gramsci and Marxist Theory_ , ed. C. Mouffe (London: Routledge & Kegan Paul), 33, 35.
. Badaloni, _Il Marxismo di Gramsci_ , 143.
. ibid., 142.
. Gramsci, _Quaderni_ , 2:869.
. ibid., 2:1022.
. ibid., 2:854, 1300.
. ibid., 1:431; 2:1032, 1284: 3:1599, 1874–5.
. ibid., 3:1599.
. ibid., 2:1244.
. J. Texier (1973) 'Gramsci: nécessité et créativité historique', _La Nouvelle Critique_ , 69, 63.
. Salamini, 'Gramsci and Marxist sociology of knowledge', 373.
. L. Salamini (1981) _The Sociology of Political Praxis_ (London: Routledge & Kegan Paul), 38; see also pp. 54, 160, and 162.
. Salamini, 'Gramsci and Marxist sociology of knowledge', 373.
. ibid.
. Gramsci, _Quaderni_ , 2:1397.
. Salamini, _The Sociology of Political Praxis_ , 12.
. Marx, _Critique of Hegel's 'Philosophy of Right'_ , 11.
. ibid., 23.
. ibid., 39.
. See above, 25 and n. 62.
. L. Colletti, _Il_ _Marxismo e Hegel_ , vol. 1: _Su i 'Quaderni Filosofici' di Lenin_ , 115.
. Bhaskar, _The Possibility of Naturalism_ , 12.
. Gramsci, _Quaderni_ , 2:1236.
. ibid., 2:1433.
. ibid., 2:1246.
. M. Bloch (1966;) _French Rural History. An Essay on its Basic Characteristics_ , trans. J. Sondheimer (Berkeley and Los Angeles: University of California Press), 248.
. Nemeth, _Gramsci's Philosophy_ , 7.
. Gramsci, _Quaderni_ 2:1079.
. ibid., 2:1443–4.
. ibid., 2:1443.
. Salamini, _The Sociology of Political Praxis_ , 171. A similar view is expressed in: A. Pizzorno (1970) 'Sul metodo di Gramsci: dalla storiografia alla scienza politica', in _Gramsci e la Cultura Contemporanea. Atti del Convegno Internazionale tenuto a Cagliari il 23–27 Aprile 1967_ , 2 vols, ed. P. Rossi (Roma: Editori Riuniti-Instituto Gramsci), 2:126.
. Gramsci, _Quaderni_ 2:1442.
. ibid., 2:1457.
Chapter Two
. L. Gallino (1970) Gramsci e le scienze sociali', in _Gramsci e la Cultura Contemporanea. Atti del Convegno Internazionale tenuto a Cagliari il 23–27 Aprile 1967_ 2 Vols, ed. P. Rossi (Rome: Editori Riuniti-Istituto Gramsci), 2:91–2.
. Salamini, _The Sociology of Political Praxis_ , 55–6.
. L. Razeto Migliaro and P. Misuraca (1978) _Sociologia e Marxismo nella Critica di Gramsci_ (Bari: De Donato Editore), 40.
. ibid., 21.
. ibid., 20.
. ibid., 20–1.
. ibid., 46.
. ibid., 101.
. Gramsci, _Quaderni_ , 3:1765.
. ibid., 2:886, 977; 3:1766.
. Salamini, _The Sociology of Potitical Praxis_ , 53.
. Gramsci, _Quaderni_ , 2:1388–89; 3:1612.
. ibid., 2:1386–7.
. ibid., 2:1387–8.
. ibid., 2:1394.
. ibid., 2:1388.
. ibid., 1:434–35; 2:1432.
. ibid., 2:738.
. ibid., 3:1687.
. ibid., 2:856, 142. Gramsci refers to Engel's letters to J. Block of 21–22 September 1890, and to H. Starkenburg of 25 January, 1894. See K. Marx and F. Engels (1965) _Selected Correspondence_ , 2nd edn. ed. S. Ryazanskaya (Moscow: Progress Publishers), 417–19, 466–8.
. Gramsci, _Quaderni_ , 1:118, 119, 134, 235, 432; 2:865, 1194, 1197; 3:1619, 1621.
. ibid., 1:238.
. P. Vilar, _Une Histoire en Construction_ , 355.
. Gallino, 'Gramsci e le scienze sociali', 84.
. Gramsci, _Quaderni_ , 1:118; 3:1647.
. ibid., 2:1046, 1402.
. K. Hempel (1942) 'The function of general laws in history' _, Journal of Philosophy_ 39 (January), 36.
. Marx, _Grundrisse_ , 605.
. Gramsci, _Quaderni_ , 1:118–9; 3:1647–8.
. ibid., 2:1194–5, 1197; 3:1619.
. J. H. Hexter (1961) _Reappraisals in History. New Views on History and Society in Early Modern Europe_ (New York: Harper Torchbooks), 11—12.
. J. H. Randall, Jr., and G. Haines IV (1946) 'Controlling assumptions in the practice of American historians', in _Theory and Practice in Historical Study: A Report of the Committee on Historiography_ (New York: Social Science Research Council), 18.
. Gramsci, _Quaderni_ , 2:873. See also 1:310, 319; 2:865, 1169; 3:1980.
. ibid., 2:1169; 3:1980
. ibid., 2:865.
. C. Hill (1969) _Reformation to Industrial Revolution_ (Harmondsworth: Penguin), 20.
. Randall and Haines, 'Controlling assumptions', 18.
. Gramsci, _Quaderni_ , 1:558.
. L. Rosiello (1982) 'Linguistica e Marxismo nel pensiero di Antonio Gramsci', _Historiographia Linguistica_ , 9, 445.
. Gramsci, _Quaderni_ , 2:872.
. Bhaskar, _The Possibility of Naturalism_ , 62.
. K. Marx, _A Contribution to the Critique of Political Economy_ , 21. References to these statements are found in Gramsci, _Quaderni_ 1:455; 2:855; 3:1579, 1774.
. Bhaskar, _The Possibility of Naturalism_ , 36.
. ibid., 12.
. E. P. Thompson (1978) 'Eighteenth-century English society: class struggle without class?' _Social History_ 3 (May), 133.
. Gramsci, _Quaderni_ , 1:451; 2:1446–7.
. M. Brodbeck (1966) 'Methodological individualisms: definition and reduction', in _Philosophical Analysis and History_ , ed. W. H. Dray (New York: Harper and Row), 321.
. Gramsci, _Quaderni_ , 1:451; 2:1447.
. M. Mandelbaum (1951) 'A note on emergence', in _Freedom and Reason_ , ed. S. W. Baron, Nagel and K. S. Pinson (Glencoe, Illinois: The Free Press), 175–6.
. Gramsci, _Quaderni_ , 1:47; 3:2022.
. ibid., 1:451; 2:1447.
. E. Gellner (1959) 'Holism _versus_ individualism in history and sociology', in _Theories of History_ , ed. P. Gardiner (Glencoe, Illinois: The Free Press), 501.
. Gramsci, _Quaderni_ , 1:451; 2:1447.
. Gramsci, _Quaderni_ , 2:872.
. ibid.
. ibid., 3:1992.
. ibid., 1:456; 3:1581–2.
. N. Kondratieff (1984) _The Long Wave Cycle_ , trans. G. Daniels (New York: Richardson Snyder), 93.
. F. Braudel (1969) _Écrits sur l'Historie_ (Paris: Flammarion), 11–13.
. ibid., 50.
. ibid., 51–2.
. ibid., 58–9.
. P. Burke (1980) _Sociology and History_ (London: George Allen & Unwin), 25.
. T. Stoianovich (1976) _French Historical Method. The Annales Paradigm_ (Ithaca: Cornell University Press).
. Gramsci, _Quaderni_ , 2:1100–1; 3:2176.
. ibid., 3:2141. See also 1:70–1.
. ibid., 1:455.
. ibid., 3:1579.
. ibid., 1:444; see also 2:1443.
. ibid., 1:455; 3:1579–80.
. ibid., 3:1959–60.
. ibid., 1:38; 3:2042.
. ibid., 3:1774.
. ibid., 2:797.
. ibid.
. ibid., 3:1579–80.
. J. C. Portantiero (1979) 'Gramsci y el análisis de coyuntura (algunas notas)', _Revista Mexicana de Sociología_ 41 (Jan.–Mar.), 59.
. ibid., 60–1.
. Gramsci, _Quaderni_ , 3:1580; 1:456.
. J. Fontana i Lázaro (1967) 'Gramsci i la ciencia històrica', _Nous Horitzons_ 12, 40.
. Gramsci, _Quaderni_ , 3:1583; 1:457.
. Fontana 'Gramsci i la Ciencia Històrica', 40.
. E. P. Thompson (1978) _The Poverty of Theory and Other Essays_ (New York and London: Monthly Review Press), 124.
. M. Aymard (1978) 'Impact of the _Annales_ school in Mediterranean countries', _Review_ 1 (Winter–Spring), 62–3.
. Salamini, _The Sociology of Political Praxis_ , 79.
. Gramsci, _Quaderni_ , 2:856–7, 1429–30.
. ibid., 2:1430.
. ibid., 2:862; 3:1565–6.
. ibid., 2:862.
. ibid., 2:1253.
. ibid., 2:1430.
. ibid., 2:1429–30.
. ibid., 1:442; 2:1433.
. ibid., 2:1433.
. ibid., 2:1236.
. ibid., 2:1284.
. ibid., 3:1926.
. ibid., 2:1334.
. ibid., 3:1755.
. ibid., 1:440.
. ibid., 1:503.
. ibid.
. ibid., 2:1.
. ibid., 1:503; 2:1316.
. ibid., 1:503.
. ibid., 2:1316.
. ibid., 1:445; 2:1445.
. Bloch, _French Rural History_ 54–5.
. Gramsci, _Quaderni_ 1:452, 2:1505.
. ibid., 3:2139.
. ibid., 1:384–85.
. P. Anderson 'The Antinomies of Antonio Gramsci', _New Left Review_ 100, 20.
. Gramsci, _Quaderni_ , 2:1508–9.
. ibid., 2:1053.
. ibid., 3:1767.
. Bhaskar, _The Possibility of Naturalism_ , 12.
. Gramsci, _Quaderni_ , 2:1430.
. ibid., 2:1246.
. C. B. Macpherson(1962) _The Political Theory of Possessive Individualism. Hobbes to Locke_ (Oxford: Oxford University Press), 3.
. Gramsci, _Lettere del Carcere_ , 313–14.
. Gramsci, _Quaderni_ , 2:1018, 1478.
. ibid., 2:1248.
. ibid., 2:1018, 1479.
. ibid., 2:1477.
. ibid., 1:444.
. ibid., 2:1019, 1479.
. Marx, _Grundrisse_ , 101.
. Gramsci, _Quaderni_ , 2:1433. See also 1:435.
. Marx, _Grundrisse_ , 101.
. Gramsci, _Quaderni_ , 2:1235.
. R. Kosellek (1982) 'Concepts of historical time and social history', in _Philosophy of History and Contemporary Historiography_ , D. Carr _et al_. eds (Ottawa: University of Ottawa Press), 121.
. ibid., 122.
. Gramsci, _Quaderni_ , 2:1279.
. ibid., 2:1061.
. Gallino, 'Gramsci e le scienze sociali', 86–7.
. Razeto and Misuraca, _Sociologia e Marxismo_ , 60.
. ibid., 68.
. Gramsci, _Quaderni_ , 2:1245.
. ibid., 3:1765–6.
. ibid., 3:1650.
. ibid., 2:755.
. ibid., 2:1246.
. ibid., 2:1479; see also 2:1089.
. ibid., 3:1557.
. ibid., 2:1059, 1403.
. Bhaskar, _The Possibility of Naturalism_ , 27.
. Gramsci, _Quaderni_ , 3:1810.
. ibid., 2:1403.
. ibid., 2:1403–4; see also 2:1059.
. Texier, 'Gramsci, nécessité et créativité historique', 65.
. Gramsci, _Quaderni_ , 2:826.
. ibid., 3:2010.
. ibid., 3:2012.
. ibid., 3:2287–8.
. ibid., 3:1687.
. ibid., 1:444; see also 2:1443.
. Marx, _Capital_ , 1:19.
. Gramsci, _Quaderni_ , 2:826.
. ibid., 2:1404.
. ibid., 2:826.
. ibid.
. W.J. Runciman (1973) 'What is Structuralism?' in _The Philosophy of Social Explanation_ , ed. A. Ryan (Oxford: Oxford University Press), 199–200.
. Gramsci, _Quaderni_ , 1:234, 235.
. Marx, _Grundrisse_ , 101.
. S. James (1984) _The Content of Social Explanation_ , (Cambridge: Cambridge University Press), 3.
. Gramsci, _Quaderni_ , 2:1375.
. Bhaskar, _The Possibility of Naturalism_ , 73–4.
. V. Melchiore (1966) 'Sullo storicismo di Gramsci', _Humanitas_ 21 (June), 586.
. ibid., 590.
. Gramsci, _Quaderni_ , 2:1035; 3:1877.
. ibid., 2:1484.
. ibid., 2:750.
. ibid., 2:855.
. ibid., 2:1273.
. ibid., 3:1875–6.
. ibid., 3:1875.
. ibid., 2:887.
. ibid., 3:1878.
. ibid., 2:1280–1.
. ibid., 1:443–4; 2:1442–3.
. T. Benton (1977) _The Philosophical Foundations of the Three Sociologies_ (London: Routledge & Kegan Paul), 171.
. Gramsci, _Quaderni_ , 2:1035; 3:1878.
. ibid., 2:1437.
. ibid., 2:1018,1478.
. Badaloni, _Il Marxismo di Gramsci_ , 133.
. A. Sánchez Vázquez _et al_. (1975) _Estructuralismo y Marxismo_ (Barcelona: Ediciones Grijalbo, S.A.), 43–4.
. Gramsci, _Quaderni_ , 2:869.
. C. Rodriguez-Aguilera guezAguilerade Prat (1983) 'Gramsci i la història d'Italia', _L'Avenç_ , 56, 58.
Chapter Three
. N. Bobbio (1979) 'Gramsci and the conception of civil society', in _Gramsci and Marxist Theory_ , ed. C. Mouffe (London: Routledge & Kegan Paul), 31.
. ibid., 33.
. ibid., 35.
. J. Texier (1979) 'Gramsci, theoretician of the superstructures. On the Concept of Civil Society', in _Gramsci and Marxist Theory_ , ed. C. Mouffe, 49.
. ibid., 67.
. ibid., 52.
. ibid., 71.
. H. Portelli (1972) _Gramsci et le Bloc Historique_ (Paris: Presses Universitaires de France), 10.
. ibid., 97.
. ibid., 11.
. G. Nardone (1971) _Il_ _Pensiero di Gramsci_ (Bari: De Donato Editore), 41.
. ibid., 42.
. ibid., 39.
. ibid., 42.
. ibid., 41.
. ibid., 332.
. Salamini, _The Sociology of Political Praxis_ , 146.
. ibid., 12. See also 119, 146.
. ibid., 119.
. ibid., 146.
. P. Misuraca (1977) "Sulla ricostruzione Gramsciana dei concetti di struttura e superstruttura", _Ressegne Italiana di Sociologia_ 18 (July-Sept.), 440.
. ibid., 444.
. A. S. Sassoon (1980) _Gramsci's Politics_ (London: Groom Helm), 184.
. ibid., 241, n.6.
. ibid., 139.
. Gramsci, _Quaderni_ , 1:437.
. ibid., 2:869.
. ibid., 2:1051.
. ibid., 2:1052.
. ibid., 2:1091.
. ibid., 2:1316.
. ibid., 3:1569; see also 2:977.
. ibid.
. Sassoon, _Gramsci's Politics_ , 216.
. C. Buci–Glucksmann (1980) _Gramsci and the State_ , trans. D. Fernbach (London: Lawrence and Wishart), 77.
. Gramsci, _Quaderni_ , 3:2139.
. ibid.
. ibid., 3:2139–40.
. ibid., 3:2143.
. ibid., 3:2145.
. ibid., 2:1281–2.
. ibid., 3:2145–6.
. ibid., 3:2165.
. ibid., 3:2171.
. ibid., 3:2172.
. ibid., 1:73.
. ibid., 3:2148.
. ibid., 3:2149.
. ibid. See also 1:73.
. ibid., 3:2149–50. See also 1:73.
. ibid., 2:903.
. For a comprehensive and useful treatment of this issue see: F. Cunningham (1987) _Democratic Theory and Socialism_ (Cambridge: Cambridge University Press).
. A. Pizzorno (1970) 'Sul metodo di Gramsci: della storiografia alla scienza politica', in _Gramsci e la Cultura Contemporanea_ , ed. P. Rossi, 114.
. Gramsci, _Quaderni_ , 2:1019, 1479; see also 2:1247.
. ibid., 1:444.
. ibid., 1:40.
. ibid., 3:2010.
. ibid.
. ibid., 1:40.
. ibid., 3:2037; see also 1:35.
. Buci-Glucksmann, _Gramsci and the State_ , 26.
. Gramsci, _Quaderni_ , 3:2042, 1:38.
. ibid., 3:2011.
. ibid., 1:457; 3:1582–3.
. ibid., 1:457; 3:1583.
. ibid., 1:458; 3:1585.
. ibid., 1:457; 3:1583.
. ibid.
. ibid., 1:458; 3:1584.
. ibid., 1:458; 3:1584–5.
. Femia, _Gramsci's Political Thought_ , 117.
. Gramsci, _Quaderni_ , 2:872.
. ibid., 2:1120, 3:1612.
. ibid., 2:1058.
. ibid., 2:1246.
. E. P. Thompson, 'Eighteenth-century English society: class struggle without classes?, 147.
. Gramsci, _Quaderni_ , 3:1561.
. ibid., 3:1561–2.
. ibid., 3:1563–4.
. ibid., 3:1564.
. ibid., 1:433–4.
. ibid., 1:433.
. Femia, _Gramsci's Political Thought_ , 116.
. Gramsci, _Quaderni_ , 2:869.
. ibid., 2:869, 1422.
. Fontana, 'Gramsci i la ciencia històdrica', 41.
. ibid., 42.
. Gramsci, _Quaderni_ , 1:332. Cited by Fontana, 'Gramsci i la ciencia històrica', 42.
. R. Simon (1982) _Gramsci's Political Thought. An Introduction_ (London: Lawrence and Wishart), 15.
. ibid., 18.
. ibid., 91.
. Laclau and Mouffe, _Hegemony and Socialist Strategy_ , 69.
. Gramsci, _Quaderni_ , 1:41.
. ibid., 3:2010.
. ibid., 2:914.
. ibid., 2:1084.
. ibid., 2:1236.
. A. S. Sassoon (1982) 'Hegemony, war of position and political intervention', in _Approaches to Gramsci_ , ed. A. S. Sassoon (London: Writers and Readers Publishing Cooperative Society), 95.
. Sassoon, _Gramsci 's Politics_ , 113.
. Gramsci, _Quaderni_ , 2:866.
. ibid., 1:117; 3:2057.
. ibid., 3:1254.
. ibid., 3:2057; see also 1:117–8.
. ibid., 1:41.
. ibid., 3:2010.
. ibid., 3:1588.
. J. A. Davis (1979) 'Introduction: Antonio Gramsci and Italy's passive revolution', in _Gramsci and Italy's Passive Revolution_ , ed. J. A. Davis (London: Croom Helm), 14.
. Gramsci, _Quaderni_ , 2:1084.
. ibid., 1:58; 3:1636.
. ibid., 3:2010.
. Gramsci, _Lettere del Carcere_ , 616.
. N. Machiavelli (1976) _Il_ _Principe e Altre Opere Politiche_ (Milano: Garzanti Editore), 65.
. R. A. Dahl (1963) _Modern Political Analysis_ (Engelwood Cliffs, NJ: Prentice Hall Inc.), 73.
. C. Buci-Glucksmann (1982), 'Hegemony and consent: a political strategy', in _Approaches to Gramsci_ , ed. A. S. Sassoon, 118.
. Femia, _Gramsci's Political Thought_ , 37.
. Buci-Glucksmann, 'Hegemony and consent: a political strategy', 120.
. Gramsci, _Quaderni_ , 1:461; 3:1591.
. ibid., 3:2145, 2171–2.
. ibid., 1:42; 3:2012.
. ibid., 2:1236.
. ibid., 1:42; 3:2012.
. ibid., 2:1519.
. ibid., 2:1273.
. ibid., 3:1591; also 1:123.
. C. Mouffe (1981) 'Hegemony and the integral state in Gramsci: towards a new concept of polities', in _Silver Linings. Some Strategies for the Eighties_ , ed. G. Bridges and R. Brunt (London: Lawrence and Wishart), 175.
. ibid., 173.
. Gramsci, _Quaderni_ , 2:1058, cited in Mouffe, 'Hegemony and the integral state in Gramsci', 174.
. ibid., 2:1236, cited in Mouffe, 'Hegemony and the integral state in Gramsci', 173.
. ibid., 3:1875, cited in Mouffe, 'Hegemony and the integral state in Gramsci', 175.
. Mouffe, 'Hegemony and the integral state in Gramsci', 175.
. C. Mouffe (1979) 'Hegemony and ideology in Gramsci', in _Gramsci and Marxist Theory_ , ed. C. Mouffe, 193.
. Laclau and Mouffe, _Hegemony and Socialist Strategy_ , 68.
. ibid., 69.
. E. Laclau (1984), 'Transformations of advanced industrial societies and the theory of the subject', in _Rethinking Ideology: a Marxist Debate_ , ed. S. Hanninen and L. Paldan (Berlin: Argument Verlag), 42.
. Althusser and Balibar, _Reading Capital_ , 17.
. Laclau and Mouffe, _Hegemony and Socialist Strategy_ , 113.
. ibid., 105.
. Gramsci, _Quaderni_ , 2:1236.
. ibid., 2:1254.
. Marx, _Capital_ , 1:293.
. Gramsci, _Quaderni_ , 3:1591; see also 1:461.
. Buci-Glucksmann, _Gramsci and the State_ , 70.
. Gramsci, _Quaderni_ , 2:810–11.
. ibid., 2:763–4.
. ibid., 2:1566.
. B. de Giovanni (1979) 'Lenin and Gramsci: state, politics, and party', in _Gramsci and Marxist Theory_ , ed. C. Mouffe, 273–4.
. Gramsci, _Quaderni_ , 3:2175.
. ibid., 1:372; 3:2287.
. ibid., 3:1590.
. G. Bonomi (1975) 'La Théorie Gramscienne de l'état', _Les Temps Modernes_ 30 (Feb.), 977. He cites Gramsci, _Quaderni_ , 2:2020, in which Gramsci notes that in 'common speech the name of state is given to state life and that it is vulgarly understood as the whole of the state'.
. Simon, _Gramsci's Political Thoughts_ , 73.
. ibid., 72.
. Gramsci, _Quaderni_ , 3:2287. See also 1:303.
. ibid., 1:56; 3:1565, 2314.
. ibid., 3:1254.
. Bonomi, 'La Théorie Gramscienne de l'état', 989.
. C. Luporini (1979) 'La Politique et l'étatique: une our deux critiques?' in _Marx et sa Critique de la Politique_ , E. Balibar _et al_. (Paris: Francois Maspero), 9.
. Gramsci, _Quaderni_ , 2:937.
Conclusion
. Gramsci, _Quaderni_ 2:1426.
. ibid., 2:1271.
. ibid., 2:1272.
. ibid., 2:1255.
. ibid., 2:1236.
. ibid., 2:1255.
. ibid., 2:1241.
. Y. Cloutier (1983) 'Gramsci et la question de l'idéologie', _Philosophiques_ 10 (Oct.), 253.
. Gramsci, _Quaderni_ , 2:1327.
. ibid., 2:1303.
**Bibliography**
Works by Gramsci
In Italian
Gramsci, A. (1954) _L_ ' _Ordine Nuovo_ ( _1919–1920_ ), Turin: Einaudi Editore.
Gramsci, A. (1958) _Scritti Giovanili_ ( _1914–1918_ ), Turin: Einaudi Editore.
Gramsci, A. (1960) _Soto la Mole_ ( _1916–1920_ ), Turin: Einaudi Editore.
Gramsci, A. (1965) _Lettere dal Carcere_ , ed. S. Caprioglio and E. Fubini, Turin: Einaudi Editore.
Gramsci, A. (1966) _Socialism e Fascismo. L'Ordine Nuovo_ ( _1921–1922_ ), Turin: Einaudi Editore.
Gramsci, A. (1971) _La Costruzione del Partito Comunista_ ( _1923–1926_ ), Turin: Einaudi Editore.
Gramsci, A. (1975) _Quademi del Carcere_ , 4 vols, ed. V. Gerratana, Turin: Einaudi Editore.
English Translations
Gramsci, A. (1957) _The Modem Prince and Other Writings_ , trans. L. Marks, New York: International Publishers.
Gramsci, A. (1971) _Selections from the Prison Notebooks_ , ed. and trans. G. Hoare and G. Nowell-Smith, New York: International Publishers.
Gramsci, A. (1973) _Letters from Prison_ , trans. L. Lawner, New York: Harber & Row.
Gramsci, A. (1975) _History, Philosophy and Culture in the Young Gramsci_ , ed. P. Cavalcanti and P. Piccone, St. Louis: Telos Press.
Gramsci, A. (1977) 'Notes on Journalism', _Telos_ 32, 139–151.
Gramsci, A. (1977) _Selections from Political Writings, 1910–1920_ , ed. J. Mathews and Q. Hoare, New York: International Publishers.
Gramsci, A. (1978) _Selections from Political Writings, 1921–1926_ , trans, and ed. Q. Hoare, New York: International Publishers.
Gramsci, A. (1979) 'Science and scientific ideologies', _Telos_ 41, 151–155.
Gramsci, A. (1984) 'Notes on language', _Telos_ 59, 127–150.
Gramsci, A. (1985) _Selections from Cultural Writings_ , ed. D. Forgus and G. Nowell-Smith, London: Lawrence and Wishart.
Marzani, C. (1957) _The Open Marxism of Antonio Gramsci_ , New York: Cameron Associations.
Bibliographies
Biondi, M. (1977) _Guida Bibliografica a Gramsci_ , Cesena: Libreria Adamo Bettini.
Cozens, P. (1977) _Twenty Years of Antonio Gramsci: A Bibliography of Gramsci and Gramsci Studies Published in English, 1957–1977_ , London: Lawrence and Wishart.
Fubini, E. (1970) 'Bibliografia Gramsciana', in _Gramsci e la Cultura Contemporanea. Atti del Convegno Internazionale tenuto a Cagliari ii 23–2 7 Aprile_ 1967, ed. P. Rossi, 477–544, Rome: Editori Riuniti-Istituto Gramsci.
Fubini, E. (1977) 'Bibliografia Gramsciana, 1968–1977', in _Politico e Storia in Gramsci. Atti del Convegno Internazionale di Studi Gramsciani. Firenze, 9–11 Dicembre, 1977_ ed. F. Ferri, 649–733, Rome: Editori Riuniti-Instituto Gramsci.
Kaye, H. J. (1981) 'Antonio Gramsci: an annotated bibilography of studies in English', _Politics and Society_ 10, 335–353.
Works on Gramsci
Adamson, W. (1978) 'Beyond "Reform or Revolution": notes on political education in Gramsci, Habermas, and Arendt', _Theory and Society_ 4 (November), 429–460.
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Adamson, W. (1980) 'Gramsci's interpretation of Fascism', _Journal of the History of Ideas_ 41 (October-December), 615–633.
Adamson, W. (1980) _Hegemony and Revolution. A Study of Antonio Gramsci's Political and Cultural Theory_ , Berkeley: University of California Press.
Adamson, W. (1987) 'Gramsci and the politics of civil society', _Praxis International_ 7 (October 1987-January 1988), 320–339.
Adler, F. (1977) 'Factory councils, Gramsci and the industrialists', _Telos_ , 31, 67–90.
Agazzi, E. _et al_. (1979) _Gramsci un Ereditá Contrastata. La Nuova Sinistra Rilegge Gramsci_ , Milan: Edizioni Ottaviano.
Albers, D. (1980) 'Gramsci ja-Bauernein?' _Das Argument_ 22 (March-April), 221–224.
Albers, D. (1983) _Versuch Über Otto Bauer und Antonio Gramsci: Zur Politischen Theorie des Marxismus_ , Berlin: Argument-Verlang.
Amendola, G. (1978) _Antonio Gramsci nella Vita Culturale e Politica Italiana_ , Naples: Guida Editori.
Amodio, L. (1986) 'Rosa Luxemburg e Gramsci. Continuita e differnze', _Il_ _Politico_ 51 (March), 183–194.
Anderson, P. (1968) 'Introduction to Antonio Gramsci, 1919–1921', _New_ _Left Review_ , 51, 22–27.
Anderson, P. (1976) 'The Antinomies of Antonio Gramsci', _New Left Review_ , 100, 5–78.
Arnold, D. (1984) 'Gramsci and peasant subalternity in India', _Journal of Peasant Studies_ 11 (July), 155–177.
Asaro Mazzola, G. (1980) _Gramsci fuori dal Mito_ , Rome: A. Armando.
Asor Rosa, A. (1978) 'Gramsci and Italian cultural history', _Praxis_ , 41, 107–113.
Auciello, N. (1974) _Socialismo ed Egemonia in Gramsci e Togliatti_ , Ban: De Donato.
Badaloni, N. (1970) '11 fondamento teorico dello storicismo Gramsciano', in _Gramsci e la Cultura Contemporanea. Atti del Convegno Intemazionale tenuto a Cagliari il 23–27 Aprile 1967_ , ed. P. Rossi, Rome: Editori Riuniti-Istituto Gramsci, vol. 2, 73–80.
Badaloni, N. (1974) 'Gramsci et le problème de la revolution', _Dialectiques_ 4–5, 103–125.
Badaloni, N. (1975) 'L'Historicisme de Gramsci face au Marxisme contemporain', _Les Temps Modernes_ 30 (February), 1019–1047.
Badaloni, N. (1975) _Il Marxismo di Gramsci_ , Turin: Einaudi Editori.
Badaloni, N. (1979) 'Gramsci and the problem of the revolution', in _Gramsci and Marxist Theory_ , ed. C. Mouffe, London: Routledge & Kegan Paul, 80–109.
Badaloni, N. _et al_ (1977) _Attualita di Gramsci. L'Egemonia, lo Stato, la Cultura, il Metodo, il Partito_ , Milan, Il Saggiatore.
Badia, G. (1970) 'Gramsci et Rosa Luxemburg', _La Nouvelle Critique_ 30, 71–73.
Baldan, A. (1977) 'Gramsci as an historian of the 1930s', _Telos_ 31, 100–111.
Baldan, A. (1978) _Gramsci come Storico. Studio sulle Fonti dei 'Quademi del Carcere'_ , Bari: Dedalo Libri.
Bates, T. R. (1974) 'Antonio Gramsci and the Soviet experiment in Italy', _Societas_ 4 (Winter), 39–54.
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Benney. M. (1983) 'Gramsci on law, morality, and power', _International Journal of the Sociology of Law_ 11 (May), 191–208.
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Boggs, G. (1972) 'Gramsci's "Prison Notebooks'", _Socialist Revolution_ 2 (September-October), 79–118.
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Entwistle, H., (1978) 'Antonio Gramsci and the school as hegemonic', _Educational Theory_ 28 (Winter), 23–33.
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**Name Index**
Althusser, L. , , , , ,
Anderson, P.
Aristotle , ,
Aymard, M.
Badaloni, N. , , , ,
Bernheim, E.
Bhaskar, R. , , , , , , ,
Beard, C.
Benton, T.
Bloch, M. , ,
Block, J.
Bobbio, N. , , ,
Brodbeck, M.
Braudel, F. , , , , , , , ,
Buci-Glucksmann, C. , , , ,
Bukharin, N. ,
Callinicos, A. ,
Cavour, C.
Colletti, L. ,
Collingwood, R. G. ,
Comte, A.
Croce, B. , , , , , , , –, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
Cruz, M.
Cuvier, G.
Dahl, R.A
Davidson, A.
Davis, J. A.
Derrida, J.
Descartes, R.
Dilthey, W. , , , , , , , ,
de Giovanni, B.
Dray, W. ,
Durkheim, E.
Eley, G.
Engels, F. , , , , , , , , , ,
Femia, J. , ,
Fevre, L.
Finocchiaro, M.
Fontana, J. , , ,
Gallileo, G.
Gallino, L. , ,
Garibaldi, G.
Gellner, E.
Gentile, G. , , , , ,
Haines, G.
Hegel, G. W. F. , , , , , , , , , , , , , , , , , , , , ,
Hempel, C. G. ,
HexterJ. H.
Hill, C.
Humbolt, W. von ,
Husserl, E. ,
Iggers, G. G. ,
James, S.
Kahn, B. L.
Kant, I. , , , , , , ,
Kondratieff, N.
Korsch, K.
Koselleck, R.
Kuhn, T.
Labriola, A. ,
Laclau, E. , , , , , ,
Lamprecht, K.
Lenin, V. I. , , , ,
Levy-Straus, C.
Lukács, G.
Luporini, C.
Machiavelli, N. , , ,
McLennan, G.
Macpherson, C B.
Marx, K. , –, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
Matteoti, G.
Mazzini, J. ,
Meinecke, F. , , ,
Melchiorre, V.
Michels. R. , ,
Misuraca, R. , , , , , ,
Mouffe, C. , , , , , , ,
Nardone, G. ,
Nemeth, T. , ,
Newton, I.
Ortega y Gasset, J.
Pareto, W.
Pizzomo, A.
Popper, K.
Portantiero, J. C.
Portelli, H. , ,
Randall, J. H.
Ranke, L. von , , ,
Razeto Migliaro, L. , , ,
Ricardo, D. , ,
Rickert, H. ,
Robinson, J. H.
Rodríguez-Aguilera de Prat, C.
Rossi, P. , , ,
Runciman, W. D.
Salamini, L. , , , , , , ,
Sánchez Vázquez, A.
Sassoon, A. S. , , ,
Scucht. T.
Scriven, M. ,
Simiand, F.
Simon, R. , ,
Smith, A. , ,
Spirito, U.
Starkenburg, H.
Texier, J. , , , ,
Thompson, E. P. , , ,
Trotsky, L.
Vico, G. , , , –, , , , , , , , , , , ,
Vilar, P. , , , , ,
Volpicelli, A.
Weber, M. ,
Windelband, W.
Wittgenstein, L.
**Subject Index**
Americanism and Fordism , –, ,
_Annales_ school –, , ,
categorical imperative
causation , , , , , , , , , , , , , , , , , , , , , –, , , , , , , , , , , , , , –, , , , ,
civil society –, , , –, , , , –, –, , ,
class , , , , , , , , , , , , , , –, , , , –, , , –, –, , , , , –, –
class reductionism , , , ,
class-struggle , , ,
coercion , –, , , , , , _see also_ domination
common sense , , , , , , , , , ,
concepts , , , , , , , , , , , , , , , , –, , , –, , –, , , –, , –
conjunctures , , –, , , ,
consciousness , , , , , , , , , , , , , , , , –, , , –, , , , , –, , , , , , ,
consensus , , , , –, , ,
corporatism , , –, , , –,
culture , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
democracy , , , , , ,
demography ,
description , , , , , , , , –, , , , , ,
descriptive adequacy , , , , ,
determinism , , , , , , , –, ,
discourse theory , –,
domination , , , , , , , , , , , , _see also_ coercion
economism , , , , , ,
economy , , , , , , , , , , , , , , , –, –, , , , , , , , , , , , –, –, –, , , –, , , –, , , , , ; identity of politics and – ,
emergence: existential –; functional –; _see also_ laws
empiricism , , , , , , , , , ,
epistemological anarchism
epistemology , , , , , , , , , , , , , , , , , ,
essentialism , , –,
ethics –, , , , , –, , –, , , , _see also_ morality
events, , , , , , , , , , , , , , , , , , , , , –, , , , , , , –, , , , , , , , –, , , ,
experience , , , , , , , , ,
fascism , , , , , ,
fatalism , ,
feminism ,
forces; hegemonic – , ; of production , , , , , , , , , ; relations of , , , , , , –, –, , ; social – , , , , , –,
freedom , , , , , , , –, , , , _see also_ liberty
function , , , , , , , , , ,
geography , , , , ,
hegemony , , , , , , , , , , –, , , , –, –, , , –, , , ,
hermeneutics , ,
historical bloc , , –, –, , , –, , , , , ,
historical laws _see_ laws
historical materialism , , –, , , , , , , , , , , , , , , , _see also_ Marxism, philosophy of praxis
historical necessity –, , , , , , , –, , , –, –, , , –, , –, –, –, , , ,
Historicism , , , , , , , , , , , , , , , , , , , , , ; absolute-25, , , , , , , , , , , , –, , ; Croce's – –, ; German Historicism , –, , , , , , , , , , , , , , , , , , , , , , , , , , , ; Gramsci's – , , , , , , , , , , , , , , , , , , , , , , , –, –; – as historical necessity – –, –, ; – as humanism –, , –, , – as realism , –, , , , , –, , , – as transience –, , –, ; Hegel's – –; Marxist – –, –
historiography , , , , , , , , , , , ,
history , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , –, , , , , , , , , , , , , , , –, , –, –, , , , , , , , , , ; contemporaneity of – , , , , , ; cultural – ; different from science ; – as a material process ; – as a moral process , , , , , , , , , ; – as a natural process , ; – as a science , , , , , , ; – as an ideal process , , , , , ; eternal ideal – , –, , , , , , ; explanation in – , , , , , , , , ; identity of philosophy and – , , , , ; intellectual – ; integral history , , , ; intentionality in – –; interior/exterior aspects of- , , –, , , , , , , , , , , ; laws in – _see_ laws; meaning in – , , , , , , , , , , , , , , , ; narrative – , , , , , , , ; theory of – , , , , , , , , , , , , ,
holism –, , ,
human agency , , , , , , , , , , , , , , , , , , , , , –, , 131, ,
human nature , , , , , –, , , , ,
humanism , , –, , , , , –,
idealism , , , , , , , , , , , , , , , , , , , , , , , ,
ideology , , , , , , , , , , , , , , , , , , –, , , , , –
immanence , , , , , , , , , , , , , , , ,
incompatibilism –
intellectuals , , , , , , , , , , , , –, , , , , ,
interior/exterior _see_ history
interpretation , , , , , , , , _see also_ intuitive understanding and hermeneutics
intuitive understanding , _see also_ hermeneutics and interpretation
knowledge , , , , , , , , , , –, , , –, , , , , , , , , , , , –, , , , , , ,
language –, –, , , ,
laws: emergent – , , –, ; historical – , , , , , , , , , , , –, –, –, –, , , ; tendential – , , , , , , , , ,
libertarianism
liberty –, , , , , , , , , , , , , , _see also_ freedom
Marxism , , , , –, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , _see also_ historical materialism and philosophy of praxis
materialism , , , , , , , –
matter –, , , , , –
metaphysics , , , , , , , , , , , , , , , , , –, , , , , , ,
method , , , , , , , , , , , , , , , , , –, , , , , , , , , , , , , , , –, , , , , , , –, , , , ,
moral and intellectual: leadership , , , ; reform ,
morals , , , , , , , , , –, , , , , ,
nation , , , ,
nature , , , , , , , , , , , , , , , ,
_Naturwissenschaften/Geisteswissenschaften_ ,
New Deal , ,
Noumena , , ,
objectivity , , , , , , , , , , , , , , , , , , –; epistemological , , , ; ontological – , , ,
ontology , , , , , ,
philosophy , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , –, , –
philosophy of praxis , , , , –, , , , , , ,
politics , , , , , , , , , , , , , , , , , , , , , , , –, , , , , –, , ; identity of economy and – ,
political society , , –,
positivism , , , , , , , , , , , , , ,
power , , , , , , –, –
prediction –, –
providence , , , , , , , ,
quantity/quality , , ,
realism , , –, , , –, , , , ,
reason , , , ,
relativism , , , , , , , –, , ; epistemic – , , ; judgemental – , , ,
reproduction –
revolution , , , , , ; French – , , , , ; passive – , , ; Russian – ,
Risorgimento , , , –, , ,
sexual question , –
science: natural , , , , , , , –, –, , , , , , , , , ; social , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
situation , , , –, , , , , , , , , , , , , –, , ,
social movements , , , , , , , , , , ,
social relations , , , , , , , , , , , , –, , , , , , , , , , , , ,
sociology , , , , , , –, , , –, , , , , , , , , , , , , ,
speculative thought , , , , , , , , ,
spirit , , , , , , , , ,
state , , , , , , , , , , , , , –, , , , , , –, , –, –,
statistical generalizations , , –, , , , , ,
structuralism , , , , ,
structure , , , , , , , , , , , , , , , , –, –, , , , , , , , , , , , , , , , , , , , , , –, , , , , –, , –, –, , –
superstructure , , , , , , , , , , –, , , , , , –, , , , , –, –, –
Teleology , , , , ,
theory and practice , –, , ,
time , –, –, , , , , , , , , , , , , , , , ,
transcendence , , , , , , , , , , , , , , , , , ,
transience , –, , , , , –, , , ,
truth , , , , , , , , , , , , , , , , , , , , , –, , , –, , ,
Uniqueness of historical events , , , , , , , , , –,
voluntarism , ,
Will, the , , , , , , , , , , , , , –, , , , , , , , –, , –, , , ,
| {
"redpajama_set_name": "RedPajamaBook"
} | 3,635 |
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Please contact Jason Stiffler with any questions. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,357 |
import buildRoutes from 'ember-engines/routes';
export default buildRoutes(function() {
// Define your engine's route map here
this.route('index', { path: '/' });
this.route('cluster-setting');
this.route('project-setting');
this.route('node-detail', { path: '/:node_id' })
});
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,503 |
{"url":"http:\/\/mathoverflow.net\/questions\/124434\/concentration-of-sum-of-pairwise-squared-euclidean-distances-of-random-vectors","text":"# Concentration of sum of pairwise squared Euclidean distances of random vectors\n\nLet $X_1, \\ldots, X_n$ be independent random vectors in $B(0, D) \\subset R^d$ ($\\ell_2$ ball of radius $D$ centered at the origin). I am trying to find the concentration of the following quantity around its expectations: $$f(X_1, \\ldots, X_n) = \\frac{1}{n^2} \\sum_{1 \\leq i,j \\leq n} \\|X_i - X_j \\|_2^2$$ Using McDiarmid's inequality, I can show that $$\\Pr(|f(X_1,\\ldots,X_n) - \\mathbb{E} f(X_1,\\ldots,X_n)| \\geq \\epsilon) \\leq 2 \\exp\\left(- \\frac{2n\\epsilon^2}{16D^4}\\right).$$ This tells me that with high probability, $\\epsilon \\sim O(1\/\\sqrt{n})$.\n\nUsually sum of $n$ independent random variables concentrate with the similar dependence on $n$ (that is, $O(1\/\\sqrt{n})$) unless I use Berstein's inequality. And it is believed that in some sense, among functions of independent random variables, sums are the least concentrated.\n\nIn my situation, the function is a sum of $n^2$ non-independent random variables (if you think of $Z_{ij} = \\| X_i - X_j \\|_2^2$ as a random variable). So I believe that the concentration should be better than $O(1\/\\sqrt{n})$.\n\nDoes anybody have any idea of how such a guarantee can be achieved? Or can anybody show that the $O(1\/\\sqrt{n})$ is the best I can hope for?\n\n-\nI think you should expect to get something like $O(1\/n)$. I think the random variables behave essentially as if they were independent, so that you're summing $n^2$ random variables of variance $\\Theta(1)$ (assuming $d$ and $D$ are fixed), and dividing by $n^2$. The variance should be $\\Theta(1\/n^2)$, so the standard deviation should be something like $1\/n$. \u2013\u00a0 Anthony Quas Mar 13 '13 at 18:44\nNotice that this is a (multivariate) $U$-statistic. I would start by searching with those terms. Have you already looked at the case $d = 1$? \u2013\u00a0 cardinal Mar 14 '13 at 0:56\nAre your $X_i$ uniformly distributed in the ball? If so, you may be able to do better using logarithmic Sobolev inequalities (but I haven't thought through the normalizations to be sure). \u2013\u00a0 Mark Meckes Mar 14 '13 at 14:56\n@cardinal Thanks for the pointer to U-statistic. The function is basically a V-statistic (in this case, it is same as the U-statistic barring a normalization factor). The results for the concentration of U-statistics (and V-statistics) generally show that $\\epsilon \\sim O(1\/\\sqrt{n})$ but can be improved to $O(1\/n)$ at best with Berstein style results. It appears that I might not be able to do better than $\\epsilon \\sim O(1\/n)$. \u2013\u00a0 PRam Mar 18 '13 at 17:04\nSuppose your points were instead on the surface the ball, say by projecting them outwards. This is much the same question for large d. However now the distances are pairwise uncorrelated, so var(f) is O(1\/n^2). Have you computed correlations between distances and hence the variance in your case? \u2013\u00a0 guest Apr 1 at 8:52\n\nYou're right, you can get a better concentration inequality with $\\epsilon \\sim O(1\/n)$ considering that's a sum of $n^2$ dependent random variables. You first need to use decoupling for $U$-statistics that relates the dependent setting to the independent one as it is shown in [1]. In your case, you can show that there exist a constant $C$ such that\n\n$P\\left(\\left| \\frac{1}{n^2} \\sum_{1 \\leq i \\ne j \\leq n} \\|X_i - X_j \\|_2^2 - \\mathbb{E}f\\right| \\ge t\\right) \\le \\\\ \\qquad \\qquad C P\\left(C\\left|\\frac{1}{n^2} \\sum_{1 \\leq i \\ne j \\leq n} \\|X_i^{(1)} - X_j^{(2)} \\|_2^2 - \\mathbb{E}f\\right| \\ge t\\right) ,$\n\nwhere $X_i^{(1)}, X_i^{(2)}$ are independent copies of $X_i$. Then you can apply the McDiarmid inequality on the sum of $n(n-1)$ independent terms and get an inequality achieving the rate $O(1\/n)$. Moreover, as your U-statistic is symmetric you can reverse this inequality to get a lower bound and convince you that you can't do better.\n\n[1] de la Pe\u00f1a, V. H., & Montgomery-Smith, S. J. (1995). Decoupling inequalities for the tail probabilities of multivariate U-statistics. The Annals of Probability, 806-816. Avialable : http:\/\/arxiv.org\/pdf\/math\/9309211v2.pdf\n\n-\n\nI wanted to comment but don't have enough reputation yet. With regards to showing the optimality of the $O(1\/\\sqrt{n})$ rate, can you try the following strategy? Fix $d = 1$ and $D = 1$. Let $X_1, \\ldots, X_n$ be iid Rademacher random variables (i.e taking values $1$ and $-1$ each with probability $1\/2$). Then the random variable $f(X_1, \\ldots, X_n)$ simplifies to $2 n^2 - 2 \\sum_{1 \\leq i, j \\leq n} X_i X_j$, and we equivalently care about the concentration properties of $\\sum_{1 \\leq i, j \\leq n} X_i X_j$. This is just the simplest possible Rademacher chaos of order two.\n\nNow, you might try looking for lower bounds on the probability that the 2nd order Rademacher chaos is outside some radius $t$ of its expectation. Upper bounds are known, for instance in http:\/\/projecteuclid.org\/download\/pdf_1\/euclid.aop\/1055425791 and the references in that paper to earlier results by Talagrand and by Ledoux. Perhaps they've also shown optimality of the rates, which would be sufficient for your purposes. I don't think the linked paper shows rate optimality, but try the Talagrand or Ledoux papers.\n\n-\n\nWouldn't it suffice simply to calculate the dispersion of $f$? You can calculate it easily: each term is equal to $\\langle X_i-X_j, X_i-X_j \\rangle$, so it's quite easy to work with them, there are no square roots or other nasties. And to calculate the dispersion you need only individual dispersions (easy), and covariances (not too difficult, too). (Perhaps, you'll find it easier to use linearity first, so you have the sum of the terms of the types $\\langle X_i, X_i \\rangle$ and $\\langle X_i, X_j \\rangle$, this will simplify the further calculations.)\n\nEither the dispersion decreases quicker than $1\/n$, and then you are done by Chebyshev inequality. Or it does not, and then no hope for quicker than $O(1\/\\sqrt{n})$ decrease.\n\nMy personal opinion here is that the decrease is indeed $O(1\/\\sqrt{n})$. For the following reason: the number you evaluate is some kind of a variance, evaluated for your sample $X_1,\\dots,X_n$. I would be surprised if there existed a method more efficient than the standard $\\hat{\\sigma}_n^2$, that has a variance of $\\sim 1\/n$. In fact, my intuition tells me that your $f$ is proportional to $\\hat{\\sigma}_n^2$ (or to the sum of its diagonal elements in the $d$-dimensional case).\n\n-","date":"2014-12-19 07:18:19","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\": 0.9006018042564392, \"perplexity\": 192.61323257781865}, \"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-2014-52\/segments\/1418802768285.15\/warc\/CC-MAIN-20141217075248-00061-ip-10-231-17-201.ec2.internal.warc.gz\"}"} | null | null |
On June 27, 2014, the U.S. Department of Justice (DOJ) intervened in a False Claims Act (FCA) suit in the Southern District of New York alleging that defendants Continuum Health Partners, Inc. (Continuum) and several Mount Sinai-related hospitals that were formerly part of Continuum's network, failed to return more than $1 million worth of Medicaid overpayments to the government within the 60-day period required by the Affordable Care Act (ACA). The DOJ's complaint specifically alleges that the defendants "knowingly concealed and knowingly and improperly avoided or decreased an obligation to pay or transmit money or property to the [g]overnment" in violation of the FCA.
The case began after Continuum improperly billed Medicaid starting in 2009, on behalf of its hospitals, for services rendered to patients covered by a Medicaid managed care plan, Healthfirst (also named as a defendant). The overpayments arose due to Healthfirst's inclusion of coding on remittance advices to Continuum's hospitals that incorrectly indicated that additional payments from secondary payors, including Medicaid, were available. The Healthfirst payments should have constituted full reimbursement to the hospitals (meaning Medicaid would not provide any additional reimbursement), but a software glitch in the generation of Healthfirst's remittance advices erroneously indicated that the hospitals could seek additional reimbursement from secondary payors, including Medicaid. After the New York State Comptroller's office identified overpayments on a few of Continuum's hospitals' Medicaid secondary payor claims, Continuum ordered an internal investigation in which Robert Kane, a former Continuum employee and the whistleblower in this suit, uncovered more than 900 improperly billed claims between the various defendants totaling more than $1 million in overpayments.
According to the complaint, Continuum began repaying the overpayments "in small batches of affected claims." However, the key issue in the case is not that the defendants did not return the more than $1 million in overpayments — in fact, they did eventually pay the full amount back. But the complaint alleges that Continuum did not repay the final 300 claims for which they were overpaid until they received a civil investigative demand (similar to an administrative subpoena) concerning the overpayment. Thus, the thrust of the complaint by the DOJ is that Continuum "fraudulently delayed" the repayments. According to the ACA, an overpayment must be reported and repaid within 60 days after it is identified. The DOJ's position is that the overpayments were identified in February 2011 when Mr. Kane notified Continuum executives of the widespread problem; yet, Continuum did not fully repay the government until March 2013. The complaint also alleges that Healthfirst caused Continuum to submit the erroneous claim to Medicaid due to the glitch in its system that generated the remittance advices.
The case was originally brought by Kane as a whistleblower on behalf of the government. The Department of Justice and State of New York filed the Complaint in Intervention on June 27, 2014, indicating their intent to take over prosecution of the lawsuit from Kane. In the Complaint, the government requests the maximum penalty under the FCA — $11,000 for every improper overpayment plus treble damages — which could result in an almost $30 million fine for the defendants. The suit is one of the first of its kind in applying the new provisions under the ACA and makes it clear that the government plans to strictly enforce not only the repayment rules under the FCA, but also the 60-day rule under the ACA.
Click here for a full text of the Government's Complaint-In-Intervention.
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,128 |
\section{Introduction}
The nuclear fusion, known as the nuclear reaction between the light nuclei, gives out a few MeVs energy due to the mass difference between the initial and final nuclei.
Thus, it is considered to be an important way to obtain nuclear power from nature.
However, in order to make the nuclear fusion happen within the nuclear distance (a few fms), the coulomb barrier
between two nuclei has to be overcome which requires a high temperature or pressure. And by far, no design of nuclear fusion has produced more fusion energy than the input electrical power.
The $\mu$ catalyzed fusion ($\mu$CF) has been studied as a reliable low energy nuclear fusion for a long history \cite{Jackson1957,Zelddovich1960,Vesman,kamimura1988,kamimura1993,Kami2022,Kami1989}. Among all of the $\mu$CF studies, the dt$\mu$ system is considered to be a possible resource of fusion which happens in a deuterium and
tritium (D-T) mixture.
The idea of $\mu$CF originates from the fact that the $\mu$ mass (105.66 MeV) is almost 207 times of the electron mass (0.55 MeV). Then, the radius of the $\mu^-$ atom is nearly 1/207 times smaller than the normal atom. Considering a molecular consisting of the deuteron, triton and $\mu$, the distance between two nuclei should be much smaller than a normal D$_2$ or T$_2$ molecular.
The first key process of dt$\mu$ $\mu$CF is the formation of the t$\mu$ atom. When the $\mu$s go into the D-T mixture, they will immediately ($\sim 10^{-11} \mathrm{~s}$) replace the electrons inside the deuterium and tritium to formate the d$\mu$ and t$\mu$ due to a much larger binding energy with the deuteron and triton. More importantly, since the mass of the triton is heavier than the deuteron, the binding energy of t$\mu$ is larger than the d$\mu$. Thus, the muon inside d$\mu$ will be taken by the triton to form t$\mu$, which is known as the so-called muon transfer reaction \cite{Hiyama2003GEM}.
Then, the t$\mu$ atom, which is electrically neutral, enters into a D$_2$ molecule and is captured by a deuteron to form a dt$\mu$ molecule.
It should be noted that the formation of the dt$\mu$ molecular happens via the Vesman mechanism \cite{Vesman} in ${\rm t} \mu(2 s)-{\rm D}_{2}$ scattering,
$\mathrm{t}\mu(2 \mathrm{~s})+\mathrm{D}_{2} \rightarrow[(\mathrm{dt} \mu) \mathrm{dee}]$.
If the energy of the dt$\mu$ molecular with respect to the t$\mu$-d threshold is less than the
dissociation energy of ${\rm D}_{2} \simeq 4.56$ eV, the released energy during the formation of the dt$\mu$ can be absorbed by the electrons in the D$_2$ which make it transfer into the excited states without breaking the whole D$_2$ molecular. In Refs. \cite{Vesman,dtmform1982}, they gave the muon molecular's formation rate of
$10^8$ s$^{-1}$ which is almost 200 times larger than the muon decay rate.
Finally, in the dt$\mu$ molecule, fusion reaction ${\rm d}+{\rm t} \rightarrow \alpha+{\rm n}+17.6$ MeV takes place immediately $\left(\sim 10^{-12}
\mathrm{~s}\right)$ due to the small distance between deuteron and triton \cite{Kami2022,Kami1989}. After that, the $\mu$ becomes free again and continues to catalyze the fusion reaction until its life time is exhausted.
Unfortunately, with a small probability $(\sim 1\%)$ \cite{alphastick1986,Zelddovich1960}, $\mu$ is captured by the generated $\alpha$ particle from the fusion reaction and exhausts its lifetime in the atom, although there is a probability of that the muon could be recaptured by the D$_2$ or T$_2$ during the time sticking with the $\alpha$ particle.
This sticking behavior of the $\mu$ causes a major reduction of the fusion times for each muon.
In order to produce one $\mu$, the input energy is estimated to be $\sim 5$ \rm{GeV} \cite{1980Petrov}. If $N_{f}$ is the number of fusions catalyzed by one muon, since one d-t fusion generates 17.6 MeV, we easily judge that $N_{f}\sim 280$ is necessary to reach the scientific break-even. Experiments performed so far show that $N_{f}$ increases almost linearly with the density of the $\mathrm{D}_{2} / \mathrm{T}_{2}$ mixture, reaching $N_{f} \sim 150$ at the density of liquid hydrogen. However, the fusion number comes to a limitation if we can't solve the alpha sticking problem.
In terms of the alpha sticking issue, we consider a muonic lithium hydride (LiH) molecular as the fusion reaction stage instead of the dt$\mu$.
When a muonic LiH or LiH$^+$ is formed, the fusion reaction $^7{\rm Li}+{\rm p}\rightarrow2\alpha+17.35$ MeV could happen.
According to Ref. \cite{Jackson1957}, the alpha sticking probability strongly depends on the velocity of the outgoing alpha particle.
In the nuclear fusion reaction $^7{\rm Li}+{\rm p}\rightarrow2\alpha$, the outgoing alpha particle carries more momentum than the one in the d+t$\rightarrow\alpha$+n. In this case, it may be more difficult for the alpha particle to capture the muon than in the D-T mixture.
Besides, since the $^7$Li$^{3+}$ has three plus electric charge and the muon may have a large probability to be recaptured by the $^7$Li$^{3+}$ with the muon transfer reaction after the fast moving He$-\mu$ is slowed down.
In this work, we investigate the alpha sticking probability after the fusion reaction happens in the muonic LiH and LiH$^+$.
First, we study the bound system of the Lip$\mu_4$ and Lip$\mu_3^+$.
In order to solve the few body Schr$\ddot{\rm o}$dinger equation, we apply the Gaussian expansion method (GEM), which is a reliable variational method and is used in nuclear and atomic physics \cite{Hiyama2003GEM,35hiyama1997ptp}.
The strict five body or six body Li+p+$\mu$s systems are difficult to solve with GEM, however, due to
the extremely large number of Gaussian basis which goes beyond our temporary supercomputer's power.
Then, we take an approximation.
As we know, the first ionization energy of the Li is 5.39 eV while the second and third
ionization energy are 75.64 eV and 122.45 eV, respectively.
Thus, we give a vague picture of the bound Lip$\mu_4$ and Lip$\mu_3$ molecular by approximately treat the Li$\mu_2$ as a whole part.
The bound system of muonic LiH and LiH$^+$ are discussed in the next section.
Second, in section \uppercase\expandafter{\romannumeral3}, we calculate the alpha sticking probability in muonic LiH$^+$
after the fusion reaction.
After that, we give a summary in the final section.
\section{Bound state of muonic LiH and LiH$^+$}
As we mentioned in the first section, we treat the muonic LiH as a four body Li$\mu_2$-p-$\mu$-$\mu$ system and the
muonic LiH$^+$ as a three body system. Then, the four body hamiltonian is written as:
\begin{equation}
H=T+\frac{e^{2}}{r_{1}}+\frac{e^{2}}{r_{2}}-\frac{e^{2}}{r_{3}}-\frac{e^{2}}{r_{5}},
\end{equation}
where $T$ is the kinetic energy and $r_1~r_5$ are the relative coordinates in Fig. \ref{fig:jaco}.
Then, in order to solve this equation, we apply the Gaussian expansion method and the trivial wave function is constructed with a
sum of 8 Jacobian coordinates channels, shown in Fig. \ref{fig:jaco} and the whole Li$\mu_2$ part is named as the Li in short.
The total wave function of the munic LiH with angular momentum J and its z-component is written as follows:
\begin{equation}\label{eq1}
\begin{aligned}
\Phi_{JM}({\rm LiH})&=\sum_{c=1}^{8} \sum_{ n \ell N L v \lambda \Lambda I S} C^c_{ n \ell N L v \lambda \Lambda I S}
\mathcal{A}[[[\psi_{n \ell}(\mathbf{r_c}) \\
& \otimes \phi_{N L}(\mathbf{R_c})]_{\Lambda}\otimes \varphi_{\nu \lambda}(\rho_c)]_{I}
[\chi^{\mu_1}_{1/2}\chi^{\mu_2}_{1/2}]_{S}]_{JM}
\end{aligned}
\end{equation}
where the $C^c_{n \ell N L v \lambda \Lambda I S}$ are the parameters and $\mathcal{A}$ is the antisymmetric operator between the two muons.
$\chi^{\mu}_{1/2}$ is the spin wave function of the muon. In this work, we omit the spin of the all nuclei we mention.
The basis functions have the Gaussian radial shape multiplied by spherical harmonics.
\begin{equation}
\psi_{i \ell}(\mathbf{r})=r^{\ell} e^{-\alpha_{i} r^{2}} Y_{\ell m}(\hat{\mathbf{r}}),
\end{equation}
and similarly for $\phi(\mathbf{R})$ and $\chi(\rho)$.
The Gaussian range parameters are taken to lie in a geometrical progression.
The parameters C are then obtained with applying Eq. \ref{eq1} into the Rayleigh-Ritz variational method.
As for the three body Li$\mu_2$-p-$\mu$ system, its wave function can be written as:
\begin{equation}\label{eq1-1}
\begin{aligned}
\Phi_{JM}({\rm LiH^+})=\sum_{c=1,3} \sum_{ n \ell N L} C^c_{ n \ell N L}
[\psi_{n \ell}(\mathbf{r_c})\otimes\phi_{N L}(\mathbf{R_c})]_{JM}
\end{aligned}
\end{equation}
where c=1 and 3 are the similar ones in Fig. \ref{fig:jaco} with taking $\rho_1$ and $\rho_3$ out.
Here we omit the spin of the single $\mu$.
\begin{figure}[htbp]
\setlength{\abovecaptionskip}{0.cm}
\setlength{\belowcaptionskip}{-0.cm}
\centering
\includegraphics[width=0.45\textwidth]{Lipmm-jaco.eps}
\caption{
Jacobian coordinates of four body Li$\mu_2$-p-$\mu$-$\mu$ system. Here Li stands for the Li$\mu_2$ in short.
}
\label{fig:jaco}
\end{figure}
It should be noted that we calculate the binding energy of the muonic LiH with respect to the Li$\mu$-p$\mu$ threshold, which is $-2763.1$ eV for Li$\mu_2$-$\mu$ and $-2528.9$ eV for p-$\mu$. And the binding energy for muonic LiH$^+$ is calculated with respect to the Li$\mu_2$-$\mu$.
Here, the binding energy between the Li$\mu_2$ and $\mu$ shows one major short come of our approximation.
As shown in Table.\ref{tab:level1}, the whole four body calculation of Li$\mu_3$ gives the first ionization energy with 861.4 eV while it gives 2763.1 eV when we treat the Li$\mu_2$ as a whole.
It is reasonable since the electrons inside Li has a 1S$_2$2S$_1$ structure.
For comparison, we calculate the ionization energy of Lithium atom and muonic Lithium atom, which are shown in Table. \ref{tab:level1}.
The first, second and third ionization energy of Lithium atom are close to the experimental values. As for the muonic Lithium atom,
the 2763.1 eV, which is calculated within two body Li$^+$-$\mu$ system, certainly gives the energy in the 1S orbit, which is not far from the 4 times of the first ionization energy of Li$\mu_3$, 861.5 eV.
The way we treat the four body Li$\mu\mu\mu$ calculation is
given in the next section.
\begin{table}[tbh]
\begin{center}
\caption{The ionization energy of Lithium atom and muon Lithium atom. The experimental values of Lithium atom
are taken from Ref. \cite{ionization}. The units are in eV.}
\begin{tabular}{p{2.0cm}p{2.0cm}p{2.5cm}p{2.0cm}}
\hline
& Li($e_3$) & Li($\mu_3$) & Exp. \cite{ionization}\\
\hline
First & 5.36 & 861.50 &5.392 \\
Second & 75.64 & 15369.00 &75.640 \\
Third & 122.44 & 24916.50 &122.454 \\
Total & 203.44 & 41146.99 &203.486 \\
\hline
\end{tabular}
\label{tab:level1}
\end{center}
\end{table}
Once we treat the Li$\mu_2$ as a whole part, the structures of muonic LiH and LiH$^+$ may be similar as the dt$\mu_2$ and dt$\mu$, respectively.
Since they are all composed of two heavy and positive charged particles and two (one) light and negative charged particles.
This also reminds of the D$_2$ and H$_2$ molecular where the two hydrogen atoms are bound with the covalent bond and the two electrons are shared by the two protons.
In Table. \ref{tab:level}, we show the binding energy of the Lip$\mu_4$, Lip$\mu_3$, dt$\mu_2$ and st$\mu$. And we only show the ground states' energy (J=0).
The calculated binding energy of muonic LiH is 478.5 eV with respect to the Li$\mu_3$-p$\mu$ threshold and the binding energy of muonic LiH$^+$ is 207.1 eV.
Together with this, the binding energies of the ground state of dt$\mu_2$ and dt$\mu$ are also shown and all three states have the same angular momentum as J=0.
The binding energy for the dt$\mu$ is 319.1 eV with respect to the t$\mu$-d threshold.
And the binding energy for the doubly $\mu$ dt$\mu_2$ molecular is
536.8 eV, with respect to the t$\mu$-d$\mu$ threshold. This also agrees with the one calculated in Ref. \cite{kamimura2001}.
\begin{table}[tbh]
\begin{center}
\caption{Binding energies of the ground state of the Lip$\mu_4$, Lip$\mu_3$, dt$|mu_2$ and dt$\mu$.
Here d, t and Li represent the deuteron ($^2$H), triton ($^3$H) and $^7$Li nucleus, respectively.
$\Psi(0)$ is the wave function with the relative distance between two nuclei being equal to 0.
The $a_\mu$ represents the $\mu$ atomic unit which is equal to $\hbar^2/e^2m_\mu$.}
\begin{tabular}{p{2.8cm}p{2.8cm}p{2.8cm}}
\hline
Molecular & $E_{00}$ (eV) & $\Psi(0)$ ($a_{\mu}^{-3/2}$) \\
\hline
Lip$\mu_4$ & 478.5 & 0.016 \\
Lip$\mu_3$ & 207.1 & 0.003 \\
dt$\mu_2$ & 536.8 & 0.021 \\
dt$\mu$ & 319.1 & 0.003 \\
\hline
\end{tabular}
\label{tab:level}
\end{center}
\end{table}
It is reasonable to assume that the wave functions between the two nuclei in muonic LiH and dt$\mu_2$ are more compact than ones in the dt$\mu$
and muonic LiH$^+$. In the third column of table \ref{tab:level}, we show $\Psi(0)$ of these four systems which $\Psi(0)$
is defined as follows:
\begin{equation}
\Psi(0)=\int dR_1d\rho_1 \Psi(r_1=0,R_1,\rho_1).
\end{equation}
The $\Psi(0)$ in Lip$\mu_4$ and dt$\mu_2$ is larger than the ones in dt$\mu$ and muonic LiH$^+$.
Moreover, we calculate the density
distribution $\rho(r)$ of these four systems which is defined as:
\begin{equation}
\rho(r)=\int d\hat{r}dRd\rho \Psi(r,R,\rho).
\end{equation}
In Fig. \ref{fig:density}, the density distributions as a relative distance between Li$\mu_2$ and the proton in muonic LiH and LiH$^+$ are shown in the red solid and dash-dotted line. And the ones between deuteron and triton in dt$\mu_2$ and dt$\mu$ are shown in the black dashed and dash-dotted line. The density distribution and the $\Psi(0)$ of muonic LiH are similar as the ones in dt$\mu_2$. And similar behavior
exists between the muonic LiH$^+$ and dt$\mu$.
It is obvious that the major part of the wave function is located around 1 to 3 $a_\mu$ which is approximately around 100 to 500 fm. This allows a much more significant wave function around the 1 to 10 fm than the normal molecular.
In terms of the exact nuclear fusion rate, we plan to discuss it in our future work.
\begin{figure}[htbp]
\setlength{\abovecaptionskip}{0.cm}
\setlength{\belowcaptionskip}{-0.cm}
\centering
\includegraphics[width=0.45\textwidth]{Lipmm-den2.eps}
\caption{
Density distributions $\rho(r)$ as a function of the relative distance between Li and proton (black) and between deuteron and triton (red).
The black solid and dash-dotted line represent the density distribution of the Lip$\mu_3$ and Lip$\mu_4$, respectively.
The red solid and dash-dotted line represent the density distribution of the dt$\mu\mu$ and dt$\mu$, respectively.
$a_\mu$ represents the $\mu$ atomic unit which is equal to $\hbar^2/e^2m_\mu$.}
\label{fig:density}
\end{figure}
\section{$\alpha$ sticking probability}
In this section, we calculate the $\alpha$ sticking probability after the nuclear fusion reaction happens in the muonic LiH$^+$.
As we mentioned in the first section, our computer resource can't afford a full five body A$\mu\mu\mu\mu$ calculations.
In this case, we only calculate the sticking probability in the muonic LiH$^+$ and
solve a four body A$\mu\mu\mu$ system.
According to Ref. \cite{Zelddovich1960}, when the nuclear fusion happens, the nucleus $^7$Li and proton becomes close enough. Then,
the whole system can be regard as a core nucleus with the mass equal to Li+p and the positive charge 4.
At this moment, the wave function of
one single $\mu$ is given with solving the four body A$\mu_4$ system, where A$^{4+}$ is a combination of the $^7$Li and the proton.
When the fusion reaction:
\begin{equation}
^7\rm{Li}+\rm{p}\rightarrow2\alpha,\; Q=17.35\;\rm{MeV}
\end{equation}
happens, the two $\alpha$ particles receive a recoil energy E and spread with a velocity v. Thus, when the $\mu$ is captured by the
fast-moving $\alpha$ particle to its ground state, its final state is
\begin{equation}
\phi_f(\bf{r})=e^{ip\cdot \bf{r}/\hbar}(\frac{8}{\pi a_\mu^3})^{1/2}e^{2r/a_\mu}.
\end{equation}
Here $p=m_\mu v$ and $r$ is the relative distance between the $\mu$ and the $\alpha$ particle.
Since the function $e^{ip\cdot \bf{r}/\hbar}$ oscillates strongly, the major contribution comes from the short-range part of $r$ ($r\leq\hbar/p$).
And the wave function at $r=0$ is propagational to $1/n^3$. One the other hand, the item $r^l$ in the excited states ($l\neq0$) should strongly reduce the integration than the $r^0$. Thus, the probability of being captured to the excited state of He-$\mu$ is much smaller than being captured to the ground state. Therefore, in this work, we only study the alpha sticking probability of $\mu$ being captured to the ground state of He$-\mu$.
The sticking probability S is given as:
\begin{equation}\label{eqa1}
S=\left|\int d\bf{r}^3\phi_f(\bf{r})\varphi_\mu(r)\right|^2
\end{equation}
where $\varphi_\mu(\bf{r})$ is the wave function of the ground state of $\mu$ particle in the A$\mu_4$.
In order to solve this equation, we write the oscillation part $e^{ip\cdot \bf{r}/\hbar}$ as:
\begin{equation}\label{eqa2}
e^{i\rm{p}\cdot \bf{r}/\hbar}=4\pi\sum_{\lambda=0}^{\infty}\sum_{\beta=-\lambda}^{\lambda}
(-i)^\lambda j_\lambda(-|r||p|/\hbar)Y^*_{\lambda\beta}(\hat{\bf{p}})Y_{\lambda\beta}(\hat{\bf{r}})
\end{equation}
where j$_\lambda(x)$ is the spherical Bessel function.
Thus, the integration over the $\bf{r}$ leads to a nonzero value only when $\lambda$=$\beta$=0.
Then, Eq. \ref{eqa1} turns to
\begin{equation}\label{eqa3}
S=4\pi\int_{0}^{\infty}\varphi_\mu(r)(\frac{8}{\pi a_\mu^3})^{1/2}e^{2r/a_\mu}\frac{sin(pr/\hbar)}{p\hbar}rdr.
\end{equation}
Besides, the relation between the p and the recoil energy E is
\begin{equation}\label{eqa4}
p=\sqrt{2EM_\mu^2/M_\alpha}.
\end{equation}
where M$_\mu$ and M$_\alpha$ are the mass of the $\mu$ and $\alpha$ particle, respectively.
In order to obtain the wave function of the $\mu$, we need to solve the four body A$\mu_4$ system. Here we use the Gaussian
expansion method and the wave function is written as
\begin{equation}
\begin{aligned}
\Phi_{JM}&=\sum_{c=1}^{4} \sum_{n \ell N L v \lambda \Lambda I s S} C^c_{n \ell N L v \lambda \Lambda I s S}
\mathcal{A}[[[\psi_{n \ell}(\mathbf{r_c}) \\
& \otimes \phi_{N L}(\mathbf{R_c})]_{\Lambda}\otimes \chi_{\nu \lambda}(\rho_c)]_{I}
[[\chi^{\mu_1}_{1/2}\chi^{\mu_2}_{1/2}]_{s}\chi^{\mu_3}_{1/2}]_S]_{JM}.
\end{aligned}
\end{equation}
where c$=1\sim4$ is the channels of the Jacobian coordinates in Fig.\ref{fig:jaco2} and $\mathcal{A}$ is the antisymmetric operator between the three $\mu$s.
In Fig. \ref{fig:jaco2}, the A represents the heavy nuclei which is $^7$Li$+$p.
\begin{figure}[htbp]
\setlength{\abovecaptionskip}{0.cm}
\setlength{\belowcaptionskip}{-0.cm}
\centering
\includegraphics[width=0.45\textwidth]{Am3.eps}
\caption{
Jacobian coordinates of four body A-$\mu$-$\mu$-$\mu$ system.
}
\label{fig:jaco2}
\end{figure}
Accordingly, the wave function of one single $\mu$ is defined as
\begin{equation}
\varphi_\mu(r)=\left|\int d\hat{r_1}dR_1d\rho_1 \Phi(r,R,\rho)\right|^{1/2}
\end{equation}
And as mentioned in the former section,
the same mode space and method are used in
calculating the ionization energies of Lithium atom and muonic Lithium atom with simply replacing A with Li$^{3+}$.
We then calculate the alpha stick probability of the following two nuclear reactions:
\begin{equation}
\begin{aligned}
^7\rm{Li}+\rm{p}\rightarrow& 2^4\rm{He},\quad E=8.67\;\rm{MeV}.\\
d+t \rightarrow& ^4\rm{He}+n,\quad E=3.5\;\rm{MeV}.
\end{aligned}
\end{equation}
where E is the recoil energy of the $\alpha$ particle.
It should be noted that in the dt$\mu$, the wave function of the $\mu$ when the dt fusion happens can be regarded as the wave function of
the Helium atom \cite{Zelddovich1960}.
Shown in Table. \ref{tab:stick}, the $\alpha$ sticking probabilities of these two reactions are calculated to be 0.0098 and 0.0021, respectively for dt$\mu$ and Lip$\mu_3$.
As we can see, the sticking probability is almost five times smaller than the one in the dt$\mu$. As we mentioned in the introduction section,
the sticking probability have a strong dependence of fourth power of the velocity of the outgoing $\alpha$ particle \cite{Zelddovich1960}.
Thus, it is reasonable to have a much smaller sticking probability in LiH since the recoil energy in the fusion reaction is much larger than the one in dt$\mu$.
\begin{table}[tbh]
\begin{center}
\caption{Alpha sticking probability of dt$\mu$ and LiH$\mu_4$.}
\begin{tabular}{p{3cm}p{3cm}}
\hline
system & probability \\
\hline
dt$\mu$ & 0.0098 \\
Lip$\mu_3$ & 0.0021 \\
\hline
\end{tabular}
\label{tab:stick}
\end{center}
\end{table}
\section{Summary}
In order to give a possible solution to the $\alpha$ sticking issue in the normal dt$\mu$ $\mu$CF,
we put forward the muonic LiH and LiH$^+$ as the stage of the $\mu$CF.
The goal fusion reaction is $^7{\rm Li}+{\rm p}\rightarrow2\alpha+17.35$ MeV.
We calculate the ground state energies and the wave functions of the muonic LiH and LiH$^+$ based on a four body
Li$\mu_2+{\rm p}+\mu+\mu$ and three body Li$\mu_2+{\rm p}+\mu$ model.
To make the calculation practicable, we treat the Li$\mu_2$ as one whole part due to the large binding
energy of the two $\mu$s and the Li$^{3+}$.
We find that the dynamical behaviors between $^7$Li and proton in muonic LiH and LiH$^+$ are similar as the ones in dt$\mu_2$ and dt$\mu$, respectively.
Thus, the nuclear reaction in the muonic LiH and LiH$^+$ might happen immediately when the muonic LiH or LiH$^+$ is formed.
It should be noted that another nuclear reaction $^7{\rm Li}+{\rm p}\rightarrow ^7{\rm Be}+n$ could happen in muonic LiH.
And the detailed investigation concerning the fusion channels and rates in muonic LiH will be our next work.
Then, we calculate the $\alpha$ sticking probability after the fusion reaction.
We find that the sticking probability of the $\mu$ being captured to the ground state of He$\mu$ in the muonic LiH$^+$ is almost five times smaller than the one in the dt$\mu$.
However, it may not ease the current circumstance of the $\mu$CF concerning the $\alpha$ sticking issue as we explained in the first section.
We give further discussions as follows.
On the one hand, in the muonic LiH or LiH$^+$, it requires four or three $\mu$s
and two $\alpha$ particles are generated after the fusion.
Therefore, the total improvement of to the whole $\mu$CF cycle in muonic LiH or LiH$^+$ could be marginal.
On the other hand, if the He$-\mu$ is slowed down in
the LiH system, the $\mu$ particle could be recaptured by the Li$^{3+}$ with the $\mu$ transfer reaction.
The similar reaction also happens in d$\mu$-t$\mu$ transfer reaction \cite{Hiyama2003GEM}.
This calculation of the $\mu$ transfer reaction between the He$\mu$ and Li$\mu$ is our next work.
We have to admit that one major impediment of our conjecture is that the formation of the muonic LiH or LiH$^+$.
Since LiH$^{4+}$ has four positive charge, it has to capture at least three $\mu$s which we think is very difficult in the actual design.
But we hope modern experimental technology can help solve this problem.
\begin{acknowledgments}
This work is supported by the Strategic Priority Research Program of Chinese Academy of Sciences under the Grant NO. XDB34030301, the National Natural Science Foundation of China under the Grant NOs. 12005266, 12075288, 11735003, 11961141012 and Guangdong Major Project of
Basic and Applied Basic Research No. 2020B0301030008. It is also
supported by the Youth Innovation Promotion Association CAS.
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,556 |
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"redpajama_set_name": "RedPajamaC4"
} | 7,173 |
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InitialMembershipListener (Hazelcast Root 3.4.2 API)
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com.hazelcast.core</FONT>
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Interface InitialMembershipListener</H2>
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<DT><B>All Superinterfaces:</B> <DD><A HREF="http://download.oracle.com/javase/1.6.0/docs/api/java/util/EventListener.html?is-external=true" title="class or interface in java.util">EventListener</A>, <A HREF="../../../com/hazelcast/core/MembershipListener.html" title="interface in com.hazelcast.core">MembershipListener</A></DD>
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<DT><PRE>public interface <B>InitialMembershipListener</B><DT>extends <A HREF="../../../com/hazelcast/core/MembershipListener.html" title="interface in com.hazelcast.core">MembershipListener</A></DL>
</PRE>
<P>
The InitializingMembershipListener is a <A HREF="../../../com/hazelcast/core/MembershipListener.html" title="interface in com.hazelcast.core"><CODE>MembershipListener</CODE></A> that first receives a
<A HREF="../../../com/hazelcast/core/InitialMembershipEvent.html" title="class in com.hazelcast.core"><CODE>InitialMembershipEvent</CODE></A> when it is registered so it immediately knows which members are available. After
that event has been received, it will receive the normal MembershipEvents.
When the InitializingMembershipListener already is registered on a <A HREF="../../../com/hazelcast/core/Cluster.html" title="interface in com.hazelcast.core"><CODE>Cluster</CODE></A> and is registered again on the same
Cluster instance, it will not receive an additional MembershipInitializeEvent. This is a once only event.
<P>
<P>
<DL>
<DT><B>Author:</B></DT>
<DD>Peter Veentjer.</DD>
<DT><B>See Also:</B><DD><A HREF="../../../com/hazelcast/core/Cluster.html#addMembershipListener(com.hazelcast.core.MembershipListener)"><CODE>Cluster.addMembershipListener(MembershipListener)</CODE></A>,
<A HREF="../../../com/hazelcast/core/MembershipEvent.html#getMembers()"><CODE>MembershipEvent.getMembers()</CODE></A></DL>
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<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../com/hazelcast/core/InitialMembershipListener.html#init(com.hazelcast.core.InitialMembershipEvent)">init</A></B>(<A HREF="../../../com/hazelcast/core/InitialMembershipEvent.html" title="class in com.hazelcast.core">InitialMembershipEvent</A> event)</CODE>
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<TD><CODE><A HREF="../../../com/hazelcast/core/MembershipListener.html#memberAdded(com.hazelcast.core.MembershipEvent)">memberAdded</A>, <A HREF="../../../com/hazelcast/core/MembershipListener.html#memberAttributeChanged(com.hazelcast.core.MemberAttributeEvent)">memberAttributeChanged</A>, <A HREF="../../../com/hazelcast/core/MembershipListener.html#memberRemoved(com.hazelcast.core.MembershipEvent)">memberRemoved</A></CODE></TD>
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<A NAME="init(com.hazelcast.core.InitialMembershipEvent)"><!-- --></A><H3>
init</H3>
<PRE>
void <B>init</B>(<A HREF="../../../com/hazelcast/core/InitialMembershipEvent.html" title="class in com.hazelcast.core">InitialMembershipEvent</A> event)</PRE>
<DL>
<DD>Called when this listener is registered.
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>event</CODE> - the MembershipInitializeEvent received when the listener is registered</DL>
</DD>
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"redpajama_set_name": "RedPajamaGithub"
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The Patchwork Girl (a.k.a. Scraps) is a character from the fantasy Oz Book series by L. Frank Baum. She first appeared in The Patchwork Girl of Oz.
History
Scraps is a living rag doll made of patchwork, button eyes, brown yarn hair, a felt tongue, and pearl teeth. She was originally brought to life by a Munchkin magician named Dr. Pipt by means of his Powder of Life formula to be a servant for his wife Margolotte. Ojo overloaded her with magic brains in the process of bringing her to life, and as she happily jumped around she accidentally spilled the Liquid of Petrifaction on Mrs. Pipt and Ojo's uncle, consequently turning them to stone. Much of their first adventure is gathering the ingredients to find a counterspell.
She later became the companion of the Scarecrow who found her quite beautiful.
She had major roles in such Oz books as The Gnome King of Oz and The Wonder City of Oz, and was the title character in A Runaway in Oz.
The Patchwork Girl was likely influenced by the character of Topsy in Uncle Tom's Cabin, and she may have influenced the character of Raggedy Ann.
Scraps in other media
Despite her popularity, to the point that her image was used in at least two advertisements for student desks, she has appeared in only five film productions, two of which were made for television. When Baum produced a film version of the title story, he was not able to find a woman of athleticism suitable to play the role, and therefore cast the male French acrobat Pierre Couderc. She was portrayed by Doreen Tracy on the 4th Anniversary episode of Disneyland.
Patchwork Girl appears in Return to Oz. She is seen in the background at Princess Ozma's coronation.
On The Oz Kids, she was voiced by Lori Alan and had numerous infant patchwork kids. She also appeared in Walter Murch's Return to Oz as an unbilled extra. Thundertoad Animation's comparatively primitive CGI version from 2005 featured Cyndi Hotopp in the title role.
There were at least two versions of the above-mentioned advertisement, a classroom poster issued by American Seating Company. They were not bootlegs and were authorized by the publishers. They include the statement "These quaint characters are quoted from the famous Oz books and were created by L. Frank Baum. Used by permission of Reilly and Lee Company, the publishers." However this appears in very fine print and is easy to miss, especially on a small photo or reproduction of the poster. An earlier version of the poster is printed mostly in green and orange, a later version has more colors. A picture of a girl sitting at a desk in the lower right corner is also different in these two versions.
Scraps stood alongside her friends when they rallied against a "new" Witch trying to obliterate the entirety of Oz in the comic book The Oz/Wonderland Chronicles.
The Patchwork Girl also appeared in a leading role in the unaired television pilot Lost in Oz. In this version, her name is Serena and it is implied that she was once human. After her best friend became the new Wicked Witch of the West, she was literally ripped apart, but later repaired by an unknown person. The Witch also killed her family, and for this she has sworn vengeance against her former friend. Physically, she is very different from her book counterpart. She is extremely athletic, and looks like a pale human with dark hair. However, after her outfit is damaged, it is revealed that she is made of fabric underneath. The actress also portrayed the best friend of the heroine, Alex, at the beginning of the episode, a nod to the 1939 film in which Dorothy's comrades were portrayed by her friends.
In Emerald City Confidential, she owns a general store located next to Petra's office. She is also part of Frogman's smuggling ring.
In Talking With..., the second monologue is about a housewife who dresses up as Scraps to escape her mundane life.
Patchwork Girl is a supporting character in Dorothy and the Wizard of Oz, voiced by Jessica DiCicco. Just like the books, Scarecrow found her quite beautiful.
References
Oz (franchise) characters
Fictional dolls and dummies
Literary characters introduced in 1913
Female characters in literature
Rag dolls
Teenage characters in literature
Sentient toys in fiction | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,564 |
SOUTHERN African countries could realise savings 40 times what they would otherwise spend if they were to test and treat all mineworkers in the gold and platinum group metal industries for tuberculosis (TB), according to the preliminary findings of a World Bank study released on Tuesday.
From the director of the EXPOSED series, Undermined explores the river of TB flowing out from the mines, and why a vaccine is critical to the global fight against this disease.
Mining companies owe R1.5 billion to workers who developed occupational illnesses like silicosis while on the job, according to Health Minister Dr Aaron Motsoaledi.
Johannesburg - More than 40 advocates have gathered in the Johannesburg High Court today to hear class certification arguments lodged by gold miners against gold giants.
20 October, 2015 -- Gold Fields Limited on Monday opposed the certification of a class of mineworkers who have tuberculosis saying there is no evidence to prove that exposure to silica dust underground causes the disease. | {
"redpajama_set_name": "RedPajamaC4"
} | 683 |
\section{Introduction}
The Big Data industry is estimated to be worth more than hundreds of billions of dollars and still growing~\cite{bigdata,bigdata2}. Along with the Big Data phenomenon, many systems emerge to fulfill the tasks of collecting, processing and analyzing the huge amount of data, e.g., Hadoop~\cite{hadoop} and Spark~\cite{spark}. To support the variety of Big Data use cases, many Big Data related systems are designed and developed with a large number configuration parameters (or knobs)~\cite{knobs}. For example, Hadoop~\cite{hadoop} has more than 180 knobs, while the database system MySQL~\cite{mysql} has more than 450 knobs. These tunable configuration parameters control nearly all aspects of system runtime behaviors~\cite{ituned}.
On the one hand, these configuration parameters are highly correlated with the system performance~\cite{tuneSpark,tuneHadoop,tuneMysql}. Take MySQL for instance. Changing the configuration setting can result in more than \textbf{11 times} performance gain for MySQL ($\S$\ref{sec:11times}). On the other hand, the large number of configuration parameters lead to an ever-increasing complexity of configuration issues that overwhelm users, developers and administrators. As multiple systems can be involved in a task of Big Data management, tuning multiple systems' configuration parameters that intrinsically interact in an application has surpassed the abilities of humans~\cite{asilomar}.
\begin{figure*}
\centering
\subfigure[MySQL: \textbf{uniform read}]{
\label{fig:mysql}
\includegraphics[width=0.3\textwidth,height=90pt]{mysql.eps}}
\subfigure[Tomcat: \textbf{default JVM settings}]{
\label{fig:tomcat}
\includegraphics[width=0.35\textwidth,height=90pt]{tomcatSurf.eps}}
\subfigure[Spark: \textbf{standalone}]{
\label{fig:spark}
\includegraphics[width=0.28\textwidth,height=90pt]{sparkKmeansStandalone.eps}}
\subfigure[MySQL: \textbf{zipfian read-write}]{
\label{fig:mysqlZipf}
\includegraphics[width=0.31\textwidth,height=90pt]{mysqlZipf.eps}}
\subfigure[Tomcat: \textbf{tuned JVM settings}]{
\label{fig:tomcatJvm}
\includegraphics[width=0.35\textwidth,height=90pt]{tomcatJvm.eps}}
\subfigure[Spark: \textbf{cluster}]{
\label{fig:sparkcluster}
\includegraphics[width=0.29\textwidth,height=90pt]{sparkKmeansCluster.eps}}
\caption{\underline{Diverging} performance surfaces of \emph{MySQL}, \emph{Tomcat} and \emph{Spark} under different \underline{workloads} and \underline{deployments}.}
\label{fig:perfFunc}
\end{figure*}
Automatic configuration tuning (ACT) can help users tune the large number of configuration parameters towards a better overall performance. ACT involves solving the performance optimization problem in the high-dimensional space of configuration parameters. Previous attempts to automate configuration tuning have used search-based~\cite{rrs,smarthillclimbing}, model-based~\cite{starfish,ituned} or control-based~\cite{RLweb,virtualConfig} methods. Some of these methods assume manually constructed models~\cite{starfish} or the existence of system simulators~\cite{rrs,paraTuning,resSurf}. These assumptions are feasible for a specific system with a limited number of parameters~\cite{eurosysConf, RLweb}. Some methods assume the existence of a large sample set~\cite{aloja}. Many have not considered the influence of workloads on tuning~\cite{ottertune}, and hardly any related work considers the deployment environment as a factor that affects configuration tuning.
Now, the problem of automatic configuration tuning is facing three new challenges not studied before ($\S$\ref{sec:challenges}). These challenges come from the large number of configuration parameters, the dynamicity and complexity of the performance model, and the expensive sample collection process. The unprecedentedly large number of configuration parameters have complicated the performance model of a system. Worse still, the complex performance model is also related to factors like workloads and deployment environments; hence, a system must be tuned in a deployment environment similar or the same as the real system deployment. This fact makes the collection of samples very expensive.
Automatic configuration tuning with scalability guarantees (ACTS) is in need to address these challenges. In this work, we motivate the study of the ACTS problem: automatically tuning the system configuration parameters while addressing the above challenges by guaranteeing five scalability requirements ($\S$\ref{sec:problem}). The five scalability requirements involve the scalability regarding SUT (system under tune), workload, deployment environment, parameter set, and sample set size.
Despite the difficulty of the ACTS problem, we propose a preliminarily feasible solution ($\S$\ref{sec:solution}). This solution has a flexible system architecture different from previously proposed architectures. This flexible architecture can adapt to different SUTs, workloads and deployment environments. It also allows the easy integration of scalable sampling methods and scalable optimization algorithms to solve the ACTS problem. We have implemented the solution to demonstrate the benefits of ACTS.
Solving the ACTS problem can lead to great benefits for users ($\S$\ref{sec:benefits}), including but not limited to facilitating the system usage, improving the system performance, increasing the system utilization, saving labor costs, fairer benchmarking results, identifying system bottlenecks, etc. As only sporadic efforts are found to study the problem of automatic configuration tuning, our goal here is mainly to motivate the study of the ACTS problem, as well as demonstrating the feasibility and the great benefits of solving ACTS
\section{New Challenges of ACT}%
\label{sec:challenges}%
The problem of automatic configuration tuning (ACT) is becoming more challenging. On the one hand, ACT involves an optimization problem which is previously known to be difficult to solve. On the other hand, new challenges are emerging, thanks to Big Data
\subsection{A Large Number of Knobs}\vspace{3pt}
\textbf{The number of configuration parameters is now tens, hundreds or more}. Previously, the number of variables is multiple in the optimization problem of configuration tuning~\cite{rrs,paraTuning,resSurf}. As Big Data systems are targeting a wide range of use cases, they can provide tens or hundreds of configuration parameters~\cite{knobs} for users in various use cases and with various deployment environments. Moreover, co-deployed systems might need to be tuned together for one use case such that the number of parameters to tune can further increase. For example, the tuning guides for Hadoop suggest tuning the configuration parameters of both the Hadoop (with more than a hundred knobs) and the JVM (Java Virtual Machine, with tens of knobs)~\cite{hadoopJvm1,hadoopJvm2}. Thus, the performance optimization problem of configuration tuning must be solved in a high-dimensional space that rarely occurs in previous optimization problems' settings.\vspace{3pt}
\textbf{The number of parameters can hardly be reduced in configuration tuning}. The impacts of configuration parameters on a system's performance are intrinsic and complicated. Sometimes, a configuration parameter can have impacts unfound even by system developers~\cite{ituned}. Besides, configuration parameters are non-stochastic variables. Hence, the dimension reduction methods commonly used in machine learning cannot be applied to reduce the number of configuration parameters, e.g., factor analysis~\cite{fa} or principal component analysis~\cite{pca}. Even though the more impacting knobs can be tuned first~\cite{ottertune}, the less impacting knobs cannot be neglected in tuning, because it is likely that the combined impact of all the less impacting knobs exceeds that of the more impacting knobs.
\subsection{Dynamicity and Complexity}
We have carried out \textbf{thousands of experiments} to study the dynamicity and complexity of performance models. The performance model of an SUT is highly dynamic and complex, because it is related to not only the SUTs, but also the varying workloads and deployment environments. The impacts of the deployment environment can come from the hardware and the software~\cite{configInteracts1,configInteracts2}. Such impacts make it infeasible to decompose the SUT and the deployment environment into subcomponents for tuning. These facts also make it very difficult for human beings to manually construct models or simulators for general systems.\vspace{3pt}
\textbf{Different SUTs have different performance models}. Take the widely used database system MySQL~\cite{mysql}, Web server system Tomcat~\cite{tomcat} and big data processing system Spark~\cite{spark} for example. We plot in Figure~\ref{fig:mysql}, \ref{fig:tomcat} and \ref{fig:spark} their performance functions projected in low-dimensional spaces respectively. For MySQL, the projection is two lines, while Tomcat's is a irregularly bumpy surface. Spark's is a relatively smooth surface, which can be depicted as smooth lines when projected to a 2-D space.\vspace{3pt}
\textbf{Different workloads also lead to different performance models}. For the same deployment of MySQL, we apply the different workloads of uniform read and zipfian read-write. The differed workloads result in the diverging plots in Figure~\ref{fig:mysql} and \ref{fig:mysqlZipf}. For the uniform read workload, the \emph{query\_cache\_type} is the configuration parameter dominating the system performance. But for the zipfian read-write workload, the value of \emph{query\_cache\_type} has no such dominant influence. The impacts of configuration parameters are workload related.\vspace{3pt}
\textbf{The hardware of the deployment environment influences the performance model}. A system can be deployed on a single server or a server cluster. The system deployed on a single server generally behaves differently from that deployed in a cluster. To demonstrate the hardware impact from the deployment environment, we deploy Spark in the standalone mode and the cluster mode. Applying the same workload, we get two differed performance functions as plotted in Figure~\ref{fig:spark} and \ref{fig:sparkcluster}. As compared to the smooth performance function of the standalone mode, that of the cluster mode rises up sharply at some points, e.g., when the value of \emph{executor.cores} equals to four.\vspace{3pt}
\textbf{The co-deployed software also has intrinsic impacts on the SUT's performance}. For Big Data applications, multiple systems might need to be deployed together to accomplish one task. For example, we might need to deploy the Hadoop file system for using Spark; and, running Java-based systems requires the running of JVM (Java Virtual Machine). Co-deployed software systems can interact with and influence each other, as they might share hardware resources like CPU cycles, memory and network bandwidth. For instance, Figure~\ref{fig:tomcatJvm} differs from Figure~\ref{fig:tomcat} only in that we change the JVM setting \emph{TargetSurvivorRatio} when generating Figure~\ref{fig:tomcatJvm}. Although the performance surface remains as bumpy, the maximum performance is achieved at different areas.\vspace{-3pt}
\subsection{Costly Sample Collection}
\textbf{Only a limited number of samples can be collected for tuning}. Because of the impacts from the deployment environment and the workload, the performance-configuration samples can only be generated in tests that apply the workload on the deployed system. Thus, collecting a large set of tuning samples is too expensive to be practical. As performance models or simulators can hardly be constructed due to complexity, no arbitrary number of samples can be generated for configuration tuning. It is not practical at all to collect thousands of samples as required by existing solutions to configuration tuning~\cite{paraTuning}. Rather, users might expect a solution exploiting only hundreds or tens of samples, considering that Big Data workloads generally take time to run~\cite{cloudsuite,bigbench}. In sum, configuration tuning must restrain the overhead of sample collection
\section{The New Problem: ACTS}\vspace{3pt}%
\label{sec:problem}%
The new challenges in fact call for solutions to a new problem. The new problem is the problem of \emph{automatic configuration tuning with scalability guarantees (ACTS)}. The ACTS problem is to find, within a given \textbf{resource limit}, a \textbf{configuration setting} that can optimize the performance of a given \textbf{SUT}'s \textbf{deployment} under a specific \textbf{workload}.\vspace{6pt}
Resource limit can be represented as the time or the number of tests allowed for tuning. Different measures for resource can be transformed into and represented by each other. For convenience, we consider in this paper the resource limit as the number of allowed tests, which is equal to the number of samples to be collected.
The solution to the ACTS problem must guarantee scalability with regard to \textbf{resource limit}, \textbf{configuration parameter set}, \textbf{SUT}, \textbf{deployment environment} and \textbf{workload}. When the resource limit is relaxed, the solution to ACTS is expected to output a configuration setting with a better performance. The solution must also be able to find new best configuration settings when new configuration parameter sets, SUTs, deployment environments and workloads are provided. It must adapt to the changes of these factors. Besides, the integration of evolved SUTs, deployment environments and workloads must be facilitated.\vspace{3pt}
The problem of ACTS and the scalability requirements invalidate the assumptions of related works on automatic configuration tuning. First, preconstructing models or simulators~\cite{starfish} has surpassed the capabilities of humans due to the large number of configuration parameters in the overall system, as well as due to the complicated interactions between the SUT, the workload and the deployment environment. Second, the sample collection becomes very expensive as the tuning samples can only be collected for a specific deployment of system, instead of being reused across deployments~\cite{ottertune}. The costs of sample collection must be taken into account in configuration tuning, rather than assuming a large sample set~\cite{paraTuning}. Third, assuming strong conditions for tuning is impractical as the performance model of an SUT is correlated with the varying workloads, hardware settings, co-deployed software, and the set of configuration parameters.
\section{A Preliminary ACTS Solution}%
\label{sec:solution}%
Although the ACTS problem is difficult, we demonstrate that it is solvable by presenting a preliminary ACTS solution in this section.
\subsection{Design Rationale}%
\label{sec:design}
To solve the ACTS problem, we must allow the tuning system to collect samples directly from the SUT in the target deployment environment and under the real workload. The sample collection process requires changing the configuration settings of the SUT, which must be restarted to allow the new configuration setting to take effect. Therefore, the tuning system must be able to control the SUT and run the workload. To fulfill this purpose, we design the architecture of the tuning system with the components of system manipulator and workload generator. To avoid the interference with the real applications on tuning, the design of this architecture takes advantage of the staging environment that commonly exists and that is the same as the actual deployment environment. The resulting architecture is plotted in Figure~\ref{fig:act4gen}. Section~\ref{sec:arch} presents a brief overview of the architecture and the interactions between system components.
While the problem about how to collect samples with scalability guarantees is solved by the flexible architecture, the problem about which samples to collect remains to be addressed. Due to the large number of configuration parameters and their wide ranges, it is impossible to try every possible combinations. In fact, only a very limited number of configuration settings can be tested and sampled, because of the resource limit in the ACTS problem. Here, there exists a subproblem of sampling.
The subproblem of sampling must handle all types of parameters, including boolean, enumeration and numerics. The resulted samples must have a wide coverage of the solution space. To guarantee scalability, the sampling method must also guarantee better coverage of the whole solution space if more samples are allowed by the users. Thus, the sampling method must produce sample sets satisfying the following three conditions: (1) the set has a wide coverage over the high-dimensional space of configuration parameters; (2) the set is small enough to meet the resource limit and reduce test costs; and, (3) the set can be scaled to have a wider coverage, if the resource limit is expanded. We propose to use the LHS (Latin Hypercube Sampling)~\cite{lhs} method to solve the sampling subproblem, as it meets all the three conditions (detailed in $\S$\ref{sec:lhsrrs}).
There also exists the second subproblem, which is to maximize the performance metric based on the given number of samples. It is required that the output configuration setting must improve the system performance than a given configuration setting, which can be the default one or one manually tuned by users. To optimize the output of a function/system, two general methods exist, i.e., model-based and search-based. Whichever method is used, the optimization must satisfy the following conditions: (1) it can find an answer even with a limited set of samples; (2) it can find a better answer if a larger set of samples is provided; and, (3) it will not be stuck in local sub-optimal areas and has the possibility to find the global optimum, given enough resources. As model-based methods generally require a large sample set, we consider search-based methods. Thus, we propose to use, along with LHS, the recursive random search (RRS) algorithm~\cite{rrs} that satisfies all the three conditions (detailed in $\S$\ref{sec:lhsrrs}).
\subsection{A Flexible Architecture}%
\label{sec:arch}
The flexible architecture is depicted in Figure~\ref{fig:act4gen}. It mainly consists of three components, i.e., a tuner, a system manipulator, and a workload generator. Abiding by the ACTS problem definition, the tuner accepts the resource limit (typically the number of allowed tests) from the user. It extracts the configuration parameter set and their ranges from the SUT. The tuner allows different sampling and optimization methods to be used, because the SUT, the deployment environment and the workload are decoupled from the tuning process by the other two components. The workload generator allows the easy integration of various workloads for tuning, thus satisfying the workload scalability. The system manipulator can easily integrate with different SUTs in different deployment environments.
Existing ACT solutions cannot solve the ACTS problem partially because their architecture designs are based on assumptions violating the scalability requirements. We can group the architectures of ACT solutions into three categories, i.e., the simulation-based architecture~\cite{paraTuning}, the large-sample-set-based architecture~\cite{aloja} and the deployment-irrelevant architecture~\cite{ottertune} that reuses samples collected from different system deployments. These architectures are illustrated in Figure~\ref{fig:otherArchs}. Explained in Section~\ref{sec:challenges}, the new challenges invalidate the assumptions that underlie these architectures.
Compared to the architectures in Figure~\ref{fig:otherArchs}, three major differences exist for the flexible architecture. First, the SUT, workload and deployment scalability is considered in the design of the workload generator and the system manipulator, with the tuner controlling these two components. Second, the tuner has not reused samples collected from other system deployments. As explained in Section~\ref{sec:challenges}, performance models are deployment-related, thus samples for other deployments cannot be reused.
Third, the tuning tests are run in a staging environment, instead of real systems or simulators. The staging environment is a mirror of the production environment, having the same actual deployment settings (e.g. hardware, clustering, software, etc.)~\cite{stagingBig,stagingWp,stagingIbm}. Using live data, it is mainly for a final test of the system before production~\cite{stagingAzure,stagingDltj}. And, implementing the real application workload in the workload generator is possible for the system in the staging environment, e.g., by log replay~\cite{replayVM,replayMr,replayCloud}. Our architecture exploits the staging environment such that samples can be collected without affecting applications on the real system deployment
\begin{figure}[!t]
\centering
\includegraphics[width=0.5\textwidth]{ACT4Gen.eps
\caption{Architecture: automatic configuration tuning for general systems. (Best view in color)}\vspace{-12pt}
\label{fig:act4gen}
\end{figure}
\begin{figure*}[!b]
\centering
\includegraphics[width=\textwidth]{otherArchs.eps}
\caption{Common assumptions and architectures for configuration tuning in related works. (Best view in color)}
\label{fig:otherArchs}
\end{figure*}
\subsection{Subproblem Solutions: LHS + RRS}%
\label{sec:lhsrrs}
Following the analysis for solving the two subproblems ($\S$~\ref{sec:design}), we adopt the LHS (Latin Hypercube Sampling)~\cite{lhs} method and the recursive random search (RRS) algorithm~\cite{rrs}.
LHS is a classic method for experimental design. Assuming that we need to collect $m$ samples. LHS divides the range of each parameter into $m$ intervals. It combines one interval of each parameter to form a subspace, in which LHS randomly chooses a sample. Repeating this process for $m$ times, $m$ samples get chosen. It is required that every interval of each parameter is used exactly once in the process.
LHS is a scalable sampling method. First, it has a wide coverage over the high-dimensional space because it considers every interval of each parameter. Second, it can sample by setting $m$ equal to the sample set constraint. Third, if $m$ is increased, it can be scaled to have a wider coverage, because the sampling process of LHS is based on $m$.
The RRS algorithm has the exploitation and exploration structure commonly seen in search-based algorithms. In the exploration stage, RRS searches in a sample set that is taken from the whole parameter space and finds a promising sample that has the best performance. Then, it starts an exploitation stage by searching around the promising sample in the local parameter subspace. The exploitation stage is for locally searching the best point. When no improvement is made in the exploitation stage, RRS reenters the exploration stage to search globally to avoid local suboptimal results.
RRS algorithm is a scalable optimization algorithm. First, with the sample set size constraint, we can actually tune the optimization problem into one for finding a configuration setting \textbf{better} than a known setting. As a search-based method, RRS works for a sample set of any size. Second, RRS will find a better answer if a larger set of samples is provided, as it can search locally around the best sample. Third, RRS will not be stuck in local sub-optimal areas, because it has the exploration stage.
\section{How ACTS Benefits Users}%
\label{sec:benefits}
We have implemented LHS and RRS with the flexible ACTS architecture, as well as trying other sampling and optimization algorithms. We apply the ACTS implementation to MySQL and Tomcat to demonstrate how ACTS can benefit users.
ACTS can bring about the benefits of manual configuration tuning by improving system performance and increasing system utilization. Besides, due to its objectivity, ACTS also brings about the extra benefits such as enabling fairer system comparisons and identifying system bottlenecks
\subsection{Improving System Performance:\\{\it 11 Times Better}
\label{sec:11times}
Configuration tuning can improve the system performance, thus manual configuration tuning before using a system is in fact a common practice. General rules of "best practices" can be found on the Web for many popular systems, but they do not always provide the best results in many cases. Besides, some rules are difficult for common users to follow. As a result, although manual configuration tuning can improve system performance, users cannot always tune a system to the system's best potential.
ACTS only changes the configuration settings of a system, but the possible performance gain can be as much as \textbf{11 times}. In the example of MySQL, the best configuration setting suggested by ACTS can reach a throughput of 118184 ops/sec, while that for the default setting is only 9815 ops/sec. In comparison, many systems implementing new designs can only improve the system performance by \emph{a limited percentage or multiple times.} That is, an easy change of the configuration settings can benefit the user much more than laboriously implementing new designs. Moreover, as many workloads are repetitive and recurring~\cite{repeatWork2,repeatWork1}, this performance gain can actually be highly significant to users
\begin{table}[b]
\centering
\small
\renewcommand\arraystretch{1.1}
\caption{ACTS improving performances of a fully-utilized Tomcat server.}\vspace{-3pt}
\label{tbl:tomcatOnArm}%
\begin{tabular}{lllc}
\toprule[1pt]
{ \textbf{Metrics}} & { \textbf{Default}} & { \textbf{BestConfig}} & \textbf{\small Improvement}\\
\midrule[0.8pt]
Txns/seconds& 978 & 1018 & $\mathbf{4.07\%\uparrow}$\\
\midrule[0.2pt]
Hits/seconds& 3235 & 3620 & $\mathbf{11.91\%\uparrow}$\\
\midrule[0.2pt]
Passed Txns& 3184598& 3381644& $\mathbf{6.19\%\uparrow}$\\
\midrule[0.2pt]
Failed Txns& 165& 144& $\mathbf{12.73\%\downarrow}$\\
\midrule[0.2pt]
Errors& 37& 34& $\mathbf{8.11\%\downarrow}$\\
\bottomrule[1pt]
\end{tabular}
\end{table}
\subsection{Improving System Utilization:\\{\it Eliminating 1 from every 26}}\vspace{2pt}
ACTS can also improve system utilization by reducing the demands of virtual machines. Nowadays, it is common that many systems are deployed on the virtual machines in the cloud. Improving the throughputs of a single virtual machine can in turn reducing the number of virtual machines in need.
In a use case of Tomcat, we apply ACTS to Tomcat servers deployed on virtual machines, which run on physical machines equipped with ARM CPUs. Each virtual machine is configured to run with 8 cores, among which four are assigned to process the network communications. Under the default configuration setting, the utilizations of the four cores serving network communications are fully loaded, while the utilizations of the other four processing cores are about 80\%. By automatic configuration tuning, a better configuration setting is found to improve the performance of the deployment by 4\%, while the CPU utilizations remain the same. The performance results of the tuned and the default configuration settings are presented in Table~\ref{tbl:tomcatOnArm}. We can observe improvements on every performance metric by the tuned configuration setting. With this improvement on throughput, we can eliminate 1 virtual machine from every 26 virtual machines, if the tuned configuration setting is used instead.\vspace{1.5pt}
\subsection{Saving Labor Costs:\\{\it Machine-Days vs. Man-Months}}\vspace{1.5pt}
Configuration tuning is highly time-consuming and laborious. It requires the users: 1) to find the heuristics for tuning; 2) to manually change the system configuration settings and run workload tests; and, 3) to iteratively go through the second step many times till a satisfactory performance is obtained. Sometimes, the heuristics in the first step might misguide the users, as some heuristics are correct for one workload but not others; then, the latter two steps are in vain.
In our experience with MySQL tuning, it has once taken five junior employees about half a year to find an appropriate configuration setting for a cloud application workload. We have also exploited our ACTS system to tune the same system deployment. A better performance is achieved within two days. Automatic configuration tuning not only saves labor costs, but also shortens the tuning time from months to days. Even if system experts might tune a system much better and faster than common users, they are very expensive to hire~\cite{expensive}. In comparison, automatic configuration tuning almost involves no labor costs
\subsection{Fairer Benchmarking and Comparison of Systems}\vspace{1.5pt}
Benchmarking is a well-established method for comparing the performance of various hardware or software systems~\cite{greybenchmark,berkeleyview}, e.g., running SPEC for hardware comparison~\cite{spec} or TPC benchmarks for database systems~\cite{tpc}.To enable an \emph{apples-to-apples} comparison between systems, it is required that the only changed factor on benchmarking is the system under test. Besides, to get a good benchmarking result, the system under test must be well tuned~\cite{fairbenchmarking,tuneb4benchmark}. Configuration tuning is part of the performance tuning process. However, the performance tuning process is highly subjective and depends heavily on the tuning experts.
ACTS enables an objective tuning process and enables fairer starting points for benchmarking. As demonstrated by the MySQL case, a simple change of parameters can lead to more than 11 times performance improvement. As many new system designs can only improve system performances by some percentage or multiple times, it is more relevant that any improvement on system be tested on an optimized system state. Without a proper configuration tuning process, the benchmarking results can be highly suspicious or misguiding. As previous configuration tuning is usually manual work, there is no way to define how a system is in a state ready for benchmarking. To tap the performance potential of a system, system users need help in configuration tuning.\vspace{1.5pt}
\subsection{Identifying System Bottlenecks}\vspace{1.5pt}
In the use case of Big Data, it is common that multiple systems are deployed simultaneously for an application. For example, we might need to deploy the Hadoop file system for using Spark, or run a workload balancing system to distribute requests to the backend database system. Among the co-deployed systems, we might need to find out which system is the bottleneck in order to improve the overall performance.
ACTS can help identify system bottlenecks by (1) tuning the subsystem to its best performance; and, (2) combine systems to tune for the best performance. Take the database system for example. Database is usually deployed along with a front-end caching and load balancing system. Once we have tuned a database system by itself and improved the performance by 63\%. Then, we apply the same workload to the tuned database system through a front-end caching and load balancing system. Even after a long time tuning, we found that the performance remaind at the untuned level for the database system co-deployed with the front-end system. By such, we located the bottleneck to be the front-end caching and load balancing system. Without automatic configuration tuning, we would not be able to make sure whether the reason is configuration setting or systems themselves.
Furthermore, by automatically tuning each system or the system combination to its best performance, we can also identify the bottleneck to be a specific system, if the system has the worst performance among all systems and system combinations; or, if the system combination has the worst performance, the bottleneck is the specific system combination. When a combination of systems has the worst performance, it indicates that the member systems are having interactions affecting the overall performance. This bottleneck identification can help users decide whether to improve the design of a specific system or to reduce the influences between systems.\vspace{3pt}
\section{Conclusion}
In this paper, we comprehensively investigate the challenges and analyze the characteristics of the ACTS problem. The solution to the ACTS problem must guarantee scalability with regard to resource limit, configuration parameter set, SUT, deployment environment and workload. We propose and implement a preliminary ACTS solution. This solution features a flexible architecture, which enables the easy integration of various SUTs, deployment environments and workloads, as well as scalable sampling methods and optimization algorithms. The scalable sampling method and optimization algorithm adopted in the preliminary solution are LHS and RRS respectively. Based on the initial experimental results, we demonstrate that ACTS can benefit users in facilitating the system usage, improving the system performance, increasing the system utilization, saving labor costs, fairer benchmarking results, system bottleneck identification, etc.
Systems are becoming more complex nowadays. We believe that ACTS will become more beneficial or even indispensable to users. As a result, we believe that future systems should be equipped with automatic configuration tuning. We have only proposed a preliminary solution to the ACTS problem to demonstrate that ACTS is solvable. Great research opportunities exist in devising better solutions to ACTS and equipping systems with ACTS.\vspace{6pt}
\section*{Acknowledgments}
We would like to thank our shepherd, Cheng Li, and the anonymous reviewers for their constructive comments and inputs to improve our paper. This work is in part supported by the National Natural Science Foundation of China (Grant No. 61303054), the State Key Development Program for Basic Research of China (Grant No. 2014CB340402) and gifts from Huawei
\balance
\bibliographystyle{ACM-Reference-Format}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,213 |
/*! ***********************************************************************
License: MIT Licence
Description:
Storage capacities, allow to manage many storage to get quick access
to everything
cookie : Cookie functionnality, manipulate cookie with a simplified
interface
temporary : Use the "most powerfull" system in the whole list of
temporary store available
************************************************************************ */
/**
* Storage capacities, allow to manage many storage to get quick
* access to everything.
*
* @constructor
*/
a.storage = {
/**
* Debug on console the get item action.
*
* @private
*
* @param {String} element The element (like cookie,
* localStorage, ...)
* @param {String} key The key to debug
* @param {Mixed} value The value to dump
*/
debugGet: function(element, key, value) {
if(key !== '_support_t') {
a.console.storm('log', 'a.storage.type.' + element + '.get',
'Get the element ```' + key + '``` with value ```' + value+
'```', 3);
}
},
/**
* Debug on console the get item error action.
*
* @private
*
* @param {String} element The element (like cookie,
* localStorage, ...)
* @param {String} key The key to debug
*/
printError: function(element, key) {
if(key !== '_support_t') {
a.console.storm('log', 'a.storage.type.' + element + '.get',
'Unable to find the key ```' + key + '``` in store...', 3);
}
},
/**
* Debug on console the set item action.
*
* @private
*
* @param {String} element The element (like cookie,
* localStorage, ...)
* @param {String} key The key to debug
* @param {Mixed} value The value to dump
*/
debugSet: function(element, key, value) {
if(key !== '_support_t') {
a.console.storm('log', 'a.storage.type.' + element + '.set',
'Add the element key ```' + key + '``` with value ```' +
value + '```', 3);
}
},
/**
* Debug on console the remove item action.
*
* @private
*
* @param {String} element The element (like cookie,
* localStorage, ...)
* @param {String} key The key to debug
*/
debugRemove: function(element, key) {
if(key !== '_support_t') {
a.console.storm('log', 'a.storage.type.' + element + '.remove',
'Remove the element ```' + key + '```', 3);
}
},
// Access to individual storage
type: {}
};
/*
------------------------------
COOKIE
------------------------------
*/
/**
* Cookie functionnality, manipulate cookie with a simplified interface.
*
* @constructor
*/
a.storage.type.cookie = {
/**
* @property support
* @type Boolean
* @default false
*/
support: false,
/**
* @property engine
* @type String
* @default cookie
* @final
*/
engine: 'cookie',
/**
* Test the engine support.
*
* @return {Boolean} True, the engine pass the test,
* false, something went wrong
*/
test: function() {
// Cookie
// Testing the current
var test = '_support_t';
this.set(test, 'o');
// Test system is working
if(this.get(test) == 'o') {
this.remove(test);
return true;
}
return false;
},
/**
* Set a new cookie, or delete a cookie using a too old expires.
*
* @param {String} name The key to use
* @param {Mixed} value The value to store
* @param {Integer} days Number of days before expires
*/
set: function(name, value, days) {
var expires = '';
a.storage.debugSet('cookie', name, value);
if(days) {
var date = new Date();
date.setTime(date.getTime()+(days*24*60*60*1000));
expires = '; expires=' + date.toGMTString();
}
var cookieSet = name + '=' + escape(a.parser.json.stringify(value));
cookieSet += expires + '; path=/';
document.cookie = cookieSet;
},
/**
* Get the stored cookie, return null if something went wrong.
*
* @param {String} name The cookie name stored
* @return {Mixed | Null} Any data stored inside cookie
*/
get: function(name) {
if (document.cookie.length > 0) {
var start = document.cookie.indexOf(name + '=');
if (start != -1) {
start = start + name.length + 1;
var end = document.cookie.indexOf(';', start);
if (end == -1) {
end = document.cookie.length;
}
var result = a.parser.json.parse(
unescape(document.cookie.substring(start, end)));
a.storage.debugGet('cookie', name, result);
return result;
}
}
a.storage.printError('cookie', name);
return null;
},
/**
* Remove a previously stored cookie.
*
* @param {String} name The cookie name to delete
*/
remove: function(name) {
a.storage.debugRemove('cookie', name);
this.set(name, '', -1);
}
};
/**
* Cookie functionnality, manipulate cookie with a simplified interface.
*
* @constructor
*/
a.storage.cookie = a.storage.type.cookie;
/*
------------------------------
LOCAL STORAGE
------------------------------
*/
/**
* LocalStorage HTML5 support.
*
* @constructor
*/
a.storage.type.localStorage = {
/**
* @property support
* @type Boolean
* @default false
*/
support: false,
/**
* @property engine
* @type String
* @default localStorage
* @final
*/
engine: 'localStorage',
/**
* Test the engine support.
*
* @return {Boolean} True, the engine pass the test,
* false, something went wrong
*/
test: function() {
var obj = a.storage.type.localStorage,
idTest = '_support_t';
// Test support (if you use localStorageShim
// this should work for most of browsers (including old IE) !)
if('localStorage' in window && window.localStorage !== null) {
// localStorage may have no space left, making everything crash
try {
// Testing database work or not
window.localStorage.setItem(idTest, 'o');
// Test system is working
if(window.localStorage.getItem(idTest) === 'o') {
window.localStorage.removeItem(idTest);
return true;
}
} catch(e) {
return false;
}
}
return false;
},
/**
* Get the stored key.
*
* @param {String} key The key to retrieve
* @return {Mixed | Null} The value in case of success,
* null if not found
*/
get: function(key) {
if(this.support) {
var item = window.localStorage.getItem(key);
if(a.isNone(item)) {
a.storage.printError(this.engine, key);
return null;
}
var value = a.parser.json.parse(item);
a.storage.debugGet(this.engine, key, value);
return value;
}
return null;
},
/**
* Store a new key/value pair.
*
* @param {String} key The key to set
* @param {Mixed} value The data to add
*/
set: function(key, value) {
if(this.support) {
a.storage.debugSet(this.engine, key, value);
window.localStorage.setItem(key, a.parser.json.stringify(value));
}
},
/**
* Remove a given key from store.
*
* @param {String} key The key to remove
*/
remove: function(key) {
if(this.support) {
a.storage.debugRemove(this.engine, key);
window.localStorage.removeItem(key);
}
}
};
/*
------------------------------
GLOBAL STORAGE
------------------------------
*/
/**
* globalStorage HTML5 support (old).
*
* @constructor
*/
a.storage.type.globalStorage = {
/**
* @property support
* @type Boolean
* @default false
*/
support: false,
/**
* @property engine
* @type String
* @default globalStorage
* @final
*/
engine: 'globalStorage',
/**
* Test the engine support.
*
* @return {Boolean} True, the engine pass the test,
* false, something went wrong
*/
test: function() {
var idTest = '_support_t',
hostname = window.location.hostname;
if(!a.isNone(window.globalStorage)) {
// In case of space not left, we can have crash
try {
window.globalStorage[hostname].setItem(idTest, 'o');
// Test system is working
if(window.globalStorage[hostname].getItem(idTest) == 'o') {
window.globalStorage[hostname].removeItem(idTest);
return true;
}
} catch(e) {
return false;
}
}
return false;
},
/**
* Get the stored key.
*
* @param {String} key The key to retrieve
* @return {Mixed | Null} The value in case of success,
* null if not found
*/
get: function(key) {
if(this.support) {
var item = window.globalStorage[hostname].getItem(key),
value = null;
// On some system, item will be an object with
// "value" and "secure" property
if(a.isTrueObject(item) && !a.isNone(item.value)) {
value = a.parser.json.parse(item.value);
a.storage.debugGet(this.engine, key, value);
return value;
} else if(!a.isNone(item)) {
value = a.parser.json.parse(item);
a.storage.debugGet(this.engine, key, value);
return value;
} else {
a.storage.printError(this.engine, key);
return null;
}
}
return null;
},
/**
* Store a new key/value pair.
*
* @param {String} key The key to set
* @param {Mixed} value The data to add
*/
set: function(key, value) {
if(this.support) {
a.storage.debugSet(this.engine, key, value);
window.globalStorage[hostname].setItem(key,
a.parser.json.stringify(value));
}
},
/**
* Remove a given key from store.
*
* @param {String} key The key to remove
*/
remove: function(key) {
if(this.support) {
a.storage.debugRemove(this.engine, key);
window.globalStorage[hostname].removeItem(key);
}
}
};
/*
------------------------------
MEMORY STORE
------------------------------
*/
/**
* memory object (so if page close, everything is lost).
*
* @constructor
*/
a.storage.type.memory = {
/**
* @property _store
* @private
* @type a.mem
*/
_store: a.mem.getInstance('app.storage'),
/**
* @property support
* @type Boolean
* @default true
*/
support: true,
/**
* @property engine
* @type String
* @default memory
* @final
*/
engine: 'memory',
/**
* Test the engine support.
*
* @return {Boolean} True, the engine pass the test,
* false, something went wrong
*/
test: function() {
return true;
},
/**
* Get the stored key.
*
* @param {String} key The key to retrieve
* @return {Mixed | Null} The value in case of success,
* null if not found
*/
get: function() {
return this._store.get.apply(this._store, arguments);
},
/**
* Store a new key/value pair.
*
* @param {String} key The key to set
* @param {Mixed} value The data to add
*/
set: function() {
return this._store.set.apply(this._store, arguments);
},
/**
* Remove a given key from store.
*
* @param {String} key The key to remove
*/
remove: function() {
return this._store.remove.apply(this._store, arguments);
}
};
/**
* Memory store functionnality, manipulate memory storage class with a
* simplified interface.
*
* @constructor
*/
a.storage.memory = a.storage.type.memory;
/*
------------------------------
SESSION STORAGE
------------------------------
*/
/**
* sessionStorage HTML5 support.
*
* @constructor
*/
a.storage.type.sessionStorage = {
/**
* @property support
* @type Boolean
* @default false
*/
support: false,
/**
* @property engine
* @type String
* @default sessionStorage
* @final
*/
engine: 'sessionStorage',
/**
* Test the engine support.
*
* @return {Boolean} True, the engine pass the test,
* false, something went wrong
*/
test: function() {
var idTest = '_support_t',
ss = 'sessionStorage';
// Test support
if(ss in window && !a.isNone(window[ss])) {
try {
// Testing database work or not
window.sessionStorage.setItem(idTest, 'o');
// Test system is working
if(window.sessionStorage.getItem(idTest) == 'o') {
window.sessionStorage.removeItem(idTest);
return true;
}
} catch(e) {
return false;
}
}
return false;
},
/**
* Get the stored key.
*
* @param {String} key The key to retrieve
* @return {Mixed | Null} The value in case of success,
* null if not found
*/
get: function(key) {
if(this.support) {
var item = window.sessionStorage.getItem(key);
if(a.isNone(item)) {
a.storage.printError(this.engine, key);
return null;
}
var value = a.parser.json.parse(item);
a.storage.debugGet(this.engine, key, value);
return value;
}
return null;
},
/**
* Store a new key/value pair.
*
* @param {String} key The key to set
* @param {Mixed} value The data to add
*/
set: function(key, value) {
if(this.support) {
a.storage.debugSet(this.engine, key, value);
window.sessionStorage.setItem(key, a.parser.json.stringify(value));
}
},
/**
* Remove a given key from store.
*
* @param {String} key The key to remove
*/
remove: function(key) {
if(this.support) {
a.storage.debugRemove(this.engine, key);
window.sessionStorage.removeItem(key);
}
}
};
/*
------------------------------
USER DATA (Internet Explorer)
------------------------------
*/
/**
* userData IE support (old).
*
* @constructor
*/
a.storage.type.userData = {
/**
* @property support
* @type Boolean
* @default false
*/
support: false,
/**
* @property engine
* @type String
* @default userData
* @final
*/
engine: 'userData',
/**
* Test the engine support.
*
* @return {Boolean} True, the engine pass the test,
* false, something went wrong
*/
test: function() {
var idTest = '_support_t',
uid = 'a_storage',
dbName = 'aUserDataStorage';
// Store for internet explorer
// Test support
if(document.all) {
// On some IE, db.load and db.save may be disabled
// (binary behavior disable)...
try {
// Creating userData storage
document.write(
'<input type="hidden" id="' + uid +
'" style="display:none;behavior:url(\'#default#userData\')" />'
);
var db = document.getElementById(uid);
db.load(dbName);
// Testing work before setting as default
db.setAttribute(idTest, 'o');
db.save(dbName);
// Test system is working
if(db.getAttribute(idTest) == 'o') {
// Deleting test
db.removeAttribute(idTest);
db.save(dbName);
return true;
}
} catch(e) {
return false;
}
}
return false;
},
/**
* Get the stored key.
*
* @param {String} key The key to retrieve
* @return {Mixed | Null} The value in case of success,
* null if not found
*/
get: function(key) {
if(support) {
var value = a.parser.json.parse(db.getAttribute(key));
if(a.isNone(value)) {
a.storage.printError(this.engine, key);
return null;
}
a.storage.debugGet(this.engine, key, value);
return value;
}
return null;
},
/**
* Store a new key/value pair.
*
* @param {String} key The key to set
* @param {Mixed} value The data to add
*/
set: function(key, value) {
if(support) {
a.storage.debugSet(this.engine, key, value);
db.setAttribute(key, a.parser.json.stringify(value));
db.save(dbName);
}
},
/**
* Remove a given key from store.
*
* @param {String} key The key to remove
*/
remove: function(key) {
if(support) {
a.storage.debugRemove(this.engine, key);
db.removeAttribute(key);
db.save(dbName);
}
}
};
/*
------------------------------
FLASH
------------------------------
*/
/**
* flash external storage.
*
* @constructor
*/
a.storage.type.flash = new function() {
var support = false,
ready = false,
id = 'flashstorage';
/**
* Start flash and check availability.
*
* @private
* @async
*
* @param {Function | Null} callback The callback function to call
* after loading
*/
function includeFlash(callback) {
if(support === false && ready === false) {
// Append to root an object for recieving flash
var root = document.createElement('div');
root.id = 'flashstoragecontent';
document.body.appendChild(root);
var data = {
id : id,
rootId : root.id,
flashvars : {},
params : {
wmode: 'transparent',
menu: 'false',
scale: 'noScale',
allowFullscreen: 'true',
allowScriptAccess: 'always'
}
};
// Loading file
a.loader.flash(a.url + 'vendor/storage/flash/localStorage.swf',
function(e) {
ready = true;
var el = document.getElementById(data.id);
if(el.testData() === true) {
support = true;
el.setDatabase('a_flashStorage');
}
if(support === true && a.isFunction(callback)) {
callback(support);
}
}, null, data);
} else if(support === true && a.isFunction(callback)) {
callback(support);
}
}
/**
* Get the support state of flash.
* Note: it may arrive little bit after using start function...
*
* @return {Boolean} True if support is active,
* false in other cases
*/
this.support = function() {return support;};
/**
* Get the ready state of flash object.
*
* @return {Boolean} True if it's ready,
* false in other cases
*/
this.ready = function() {return ready;};
/**
* @property engine
* @type String
* @default flash
* @final
*/
this.engine = 'flash';
/**
* Start (include and prepare) flash object
* Note: automatically done by system you don't need to...
*
* @async
*
* @param {Function} callback The function to call
* in case of success
*/
this.start = function(callback) {
includeFlash(callback);
};
/**
* Get the stored key.
*
* @param {String} key The key to retrieve
* @return {Mixed | Null} The value in case of success,
* null if not found
*/
this.get = function(key) {
this.start();
if(support === true) {
var item = document.getElementById(id).getData(key);
if(a.isNone(item)) {
a.storage.printError(this.engine, key);
return null;
}
a.storage.debugGet(this.engine, key, item);
return item;
}
return null;
};
/**
* Store a new key/value pair.
*
* @param {String} key The key to set
* @param {Mixed} value The data to add
*/
this.set = function(key, value) {
this.start();
if(support === true) {
a.storage.debugSet(this.engine, key, value);
document.getElementById(id).setData(key, value);
}
};
/**
* Remove a given key from store.
*
* @param {String} key The key to remove
*/
this.remove = function(key) {
this.start();
if(support === true) {
a.storage.debugRemove(this.engine, key);
return document.getElementById(id).removeData(key);
}
};
};
/*
------------------------------
SILVERLIGHT
------------------------------
*/
/**
* silverlight external storage.
*
* @constructor
*/
a.storage.type.silverlight = new function() {
var support = false,
ready = false,
id = 'silverlightstorage';
/**
* Start silverlight and check availability.
*
* @private
* @async
*
* @param {Function | Null} callback The callback function to
* call after loading
*/
function includeSilverlight(callback) {
if(support === false && ready === false) {
// Append to root an object for recieving flash
var root = document.createElement('div');
root.id = '_silverlightstorage';
document.body.appendChild(root);
var data = {
id : id,
rootId : root.id,
params : [{
name : 'minRuntimeVersion',
value : '2.0.31005.0'
},{
name : 'autoUpgrade',
value : 'true'
}]
};
// Loading file
a.loader.silverlight(a.url +
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this.engine = 'javafx';
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this.start = function(callback) {
includeJavaFX(callback);
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javafxstorage.localStorage.loadData(key);
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(function() {
var engines = [a.storage.type.cookie, a.storage.type.localStorage,
a.storage.type.globalStorage, a.storage.type.sessionStorage,
a.storage.type.userData];
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engines[i].support = engines[i].test();
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a.message.dispatch('a.storage.temporary.change',
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return a.storage.type[temp];
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// Memory store should be always OK, so this should never arrive
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a.storage.external.support = type.support;
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a.storage.external.get = type.get;
a.storage.external.set = type.set;
a.storage.external.remove = type.remove;
if(a.isFunction(callback)) {
callback();
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return {
/**
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var silvt = a.storage.type.silverlight,
flash = a.storage.type.flash,
javax = a.storage.type.javafx,
source= 'a.storage.external',
cs = 'Choosing the storage ';
// Loading silverlight
silvt.start(function(svtSupport) {
if(svtSupport) {
a.console.storm('info', source, cs + 'silverlight', 3);
startCallback(silvt, callback);
} else {
// Loading flash
flash.start(function(flashSupport) {
if(flashSupport) {
a.console.storm('info', source, cs + 'flash', 3);
startCallback(flash, callback);
} else {
javax.start(function(javaxSupport) {
if(javaxSupport) {
a.console.storm('info', source, cs +
'javafx', 3);
startCallback(javax, callback);
} else {
a.console.storm('info', source, cs +
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a.storage.persistent = (function() {
'use strict';
var store = ['localStorage', 'globalStorage', 'userData', 'cookie'];
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{"url":"https:\/\/blender.stackexchange.com\/questions\/95860\/view-selected-numpad-and-zooming-out-with-a-single-shortcut","text":"# View Selected (Numpad .) and zooming out with a single shortcut\n\nEvery time I use View Selected (Numpad .), the view zooms in too much in the object I want to center in my view, so I always need to zoom out to have a proper sight of it.\n\nThis can be tested easily with the cube in the default scene of blender.\n\nI wonder if it is possible to write a script that handles this (Numpad . + Zoom Out with just one shorcut).\n\n\u2022 I do not know python, but I think I could get by with a little help. Any suggestions or leads about the API commands that will be needed, would be appreciated. \u2013\u00a040detectives Dec 4 '17 at 21:43\n\u2022 While not an answer you can try to use Shift+B instead and draw a rectangle of the area you'd like to be as new center. \u2013\u00a0Mr Zak Dec 5 '17 at 1:23","date":"2019-09-15 06:15:26","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\": 0.2946217656135559, \"perplexity\": 786.8516307219026}, \"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-2019-39\/segments\/1568514570740.10\/warc\/CC-MAIN-20190915052433-20190915074433-00117.warc.gz\"}"} | null | null |
\section{Introduction}
Given the current paradigm of active galactic nuclei (AGNs), the observed
huge luminosities of AGNs are powered by gravitational accretion onto
a supermassive black hole (e.g., Rees 1984; Blandford 1990; Antonucci 1993;
Peterson 1997). The central engines are considered to be surrounded by dusty
tori whose typical inner radii are on the order of $\sim$ 1 pc (e.g.,
Antonucci, Miller 1985; Pier, Krolik 1992, 1993). Therefore, in order to
understand AGNs, it is very important to investigate the spatial structures
of the inner $\sim$ 1 pc regions in which a supermassive black hole, an
accretion disk, warm absorbers, and broad emission-line regions (BLRs) reside.
The innermost constituent is the accretion disk; its typical radius is $\sim$
(10 --- 100) $R_{\rm S} \sim (10^{-4}$ --- $10^{-3})M_{8}$ pc where
$R_{\rm S}$ is the Schwarzschild radius of a black hole and $M_{8}$ is the
black-hole mass in units of $10^{8} M_{\sun}$. The existence of accretion
disks in AGNs has been demonstrated by the recent X-ray spectroscopy,
collected using {\it ASCA} (Tanaka et al. 1994). The {\it ASCA} X-ray spectra
of type-1 AGNs show the presence of very broad Fe K$\alpha$ emission, whose
line profile can be fitted well by some accretion-disk models (Tanaka et al.
1995; Fabian et al. 1995; Mushotzky et al. 1995; Iwasawa et al. 1996; Nandra
et al. 1997; Reynolds 1997). An ionized accretion disk has also been detected
by the recent radio continuum mapping in the archetypical, nearby Seyfert
galaxy NGC 1068 (Gallimore et al. 1997).
Another inner constituent is broad-line regions (BLRs), because their typical
radii are of on the order of 0.01 pc (e.g., Peterson 1993). One of the most
important questions related to the BLRs is how emission-line clouds are
distributed around AGNs. Although there is still no definite consensus
concerning the dynamical and spatial structure of BLRs, there are three
alternative models: 1) the disk model (Shields 1979; see also Osterbrock
1989), 2) the high-velocity streamer model (Zheng et al. 1991), and 3) a pair
of conical regions in which photoionized clouds are orbiting randomly with
Keplerian motion (Wanders et al. 1995; Wanders, Peterson 1996, 1997; Goad,
Wanders 1996). In particular, a recent detailed analysis of the reverberation
mapping has strongly suggested that the BLRs of the type-1 Seyfert galaxy
NGC 5548 has the third type of geometry (Wanders et al. 1995). It is,
however, still not known which model is the most popular one.
Since recent observations have shown that the BLRs are dominated by
rotational motion, rather than the radial motion (e.g., Peterson 1993;
Wanders et al. 1995), it is interesting to examine whether or not the
rotational axis of the BLR is nearly the same as that of the accretion disk.
If the disk model for BLRs would be correct, the BLRs may be coplanar with
respect to the accretion disk. In fact, double-peaked BLRs have sometimes
been considered to arise from accretion disks, themselves [e.g., P\'erez
et al. (1988); Livio, Xu (1997) and references therein; see also, however,
Gaskell (1996)]. Motivated by this, we investigate the relationship between
the inclination angle of the accretion disk and the width of BLR
statistically using published data.
\section{Data}
Nandra et al. (1997) presented a systematic analysis of the {\it ASCA} X-ray
spectra of 18 type-1 Seyfert galaxies. They fitted the Fe K$\alpha$ emission
profiles and derived the most probable inclination angles for the following
three models: Model A, the Schwarzschild model with reflection; Model B, the
Schwarzschild model with the emissivity law for $q = 2.5$ (see below); and
Model C, the Kerr model with reflection, where the Schwarzschild and Kerr
models refer to those proposed by Fabian et al. (1989) and Laor (1991),
respectively. In their model-fitting procedures, there are five parameters:
1) the inner radius of the disk ($R_{\rm i}$), the outer radius
($R_{\rm o}$), the inclination of the axis of rotation with respect to the
line of sight ($i_{\rm AD}$), the rest energy of Fe K$\alpha$ line
($E_{\rm K\alpha}$), and the line normalization ($I_{\rm K\alpha}$). They
adopted $R_{\rm i} = 3 R_{\rm S}$, $R_{\rm o} = 500 R_{\rm S}$, and
$E_{\rm K\alpha} = 6.4$ keV for Models A and B, while $R_{\rm i} =
0.615 R_{\rm S}$ and $R_{\rm o} = 200 R_{\rm S}$ for Model C. In addition to
the above parameters, the line emissivity is also another parameter, which
is usually parameterized by a power law as a function of the radius;
i.e., $R^{-q}$. Model B is the case for {\it q} = 2.5, which is an
averaged value for the case of free line emissivity [see table 4 and
figure 6 in Nandra et al. (1997)]. The inclination angles for the three
models are summarized in table 1. Note that some Seyfert nuclei were observed
by {\it ASCA} more than once (e.g., NGC 4151). In these cases, we tabulated
the estimated inclination angles for all of the observations.
We have compiled the line widths of both H$\alpha$ and H$\beta$ emission,
FWZI (full width at zero intensity), for the above 18 Seyfert galaxies based
on the literature. Since it is known that the BLR emission generally shows
time variations (e.g., Peterson 1993), it would be desirable to obtain the
data of both BLR and Fe K$\alpha$ emission simultaneously. However, all of the
BLR data were taken far before the X-ray observations. In order to minimize
any possible effect of time variations, we compiled more than-one
measurements for each galaxy as much as possible, and then used the averaged
value in a later analysis. For some Seyferts, FWHMs (full width at half
maxima) of the emission lines are only available in the literature. In these
cases, we estimated FWZIs using a relation FWZI = $2\sqrt3$ FWHM (Wandel, Yahil
1985). The compiled data are summarized in table 2.
\section{Results}
In figure. 1, we compare sin $i_{\rm AD}$ with FWZI(H$\alpha$)/
$L^{1/4}_{\rm X}$ ({\it left column}) and with FWZI(H$\beta$)/
$L^{1/4}_{\rm X}$ ({\it right column}) for the three accretion-disk
models A, B, and C, where $L_{\rm X}$ is the X-ray (2 --- 10 keV) luminosity.
In these comparisons, we used both FWZI(H$\alpha$)/$L^{1/4}_{\rm X}$ and
FWZI(H$\beta$)/$L^{1/4}_{\rm X}$, instead of their raw FWZI values.
The reason for this is that the velocity width of BLRs depends on the
central mass, even if the inner radius of the BLRs would be the same among
the Seyferts, while the inclination angle of an accretion disk has no
dependence on the black-hole mass. If the Eddington ratios are not very
different among the Seyferts (i.e., the mass-to-luminosity ratios are nearly
the same among the Seyferts), we expect the relationship FWZI $\propto
L^{1/4}$, which is analogous to the so-called Faber-Jackson relation
(Faber, Jackson 1976). We adopted the X-ray luminosities given by Nandra
et al. (1997).
Figure 1 shows that {\it all of the correlations are negative}. As shown in
table 3, the correlation coefficients suggest that the negative correlations
are not significant statistically. Therefore, our modest conclusion may be
that there is a slight correlation between $\sin i_{\rm AD}$ with
FWZI(H$\alpha$)/$L^{1/4}_{\rm X}$, suggesting a random orientation between
the BLRs and the accretion disks. However, it is quite unlikely that the
large errors in the estimate of $i_{\rm AD}$ cause any accidental negative
correlations for all of the cases shown in figure 1. Therefore, we may
conclude that there is a tendency of a negative correlation between
$\sin i_{\rm AD}$ With FWZI(H$\alpha$)/$L^{1/4}_{\rm X}$. More interestingly,
we mention that there is no hint of a positive correlation between them.
\section{Discussion}
The most important result in this study is that there is no obvious
{\it positive} correlation between $\sin i_{\rm AD}$ with FWZI(H$\alpha$)/
$L^{1/4}_{\rm X}$. This suggests that {\it the BLRs are not coplanar with
respect to accretian disks}.
Some Seyfert nuclei in our sample show double-peaked BLRs (DBLRs). It has
sometimes been considered that such DBLRs may arise from an accretion disk,
itself (e.g., P\'erez et al. 1988). The DBLR emission profiles of the four
Seyfert nuclei in our sample (NGC 3227, NGC 3783, NGC 5548, and 3C 120) were
studied by Rokaki et al. (1992) using a standard geometrically-thin accretion-
disk model; also, the inclination angles of the DBLRs ($i_{\rm BLR}$) were
derived. We compare these inclination angles with those of the accretion
disks in figure 2. This comparison also suggests a negative correlation
between $i_{\rm AD}$ and $i_{\rm BLR}$, being consistent with our result.
This strengthens our suggestion that the BLRs are not coplanar with respect
to the accretion disks in the Seyfert nuclei studied here.
Let us consider what kind of geometrical configuration can explain the
non-coplanar property. The negative correlation means that the normalized
velocity width increases with decreasing inclination angle; i.e., {\it Seyfert
nuclei with a more face-on accretion disk tend to have larger BLR velocity
widths}. There may be three alternative ideas to explain this property. One
is the bipolar streamer model (e.g., Zheng et al. 1990). If we observe the
accretion disk from a face-on view, the velocity width would be widest because
the bipolar wind flows along our line of sight. However, this model has an
intrinsic difficulty, as claimed by Livio and Xu (1996), because the emitting
region on the receding flow (jet) is obscured from view by the accretion disk;
the standard, optically thick accretion disk is opaque up to $\sim$ 1 pc, and,
thus, the BLR component behind the disk cannot be seen, because the typical
radial distance of BLRs from the central engine is on the order of 0.01 pc
(e.g., Peterson 1993). The second idea is that BLRs are located in nearly the
same plane as that of an accretion disk, but are orbiting with poloar orbits.
If a two-sided jet is ejected with a highly inclined angle with respect to
the {\it global} accretion disk, we can explain the negative correlation.
Such a jet model is briefly described by Norman and Miley (1984). This idea
is consistent with the recent reverberation mapping result for the BLRs of
NGC 5548 because the most likely geometry of the BLRs of this galaxy is a
pair of conical regions in which photoionized clouds are orbiting randomly
with Keplerian motion (Wanders et al. 1995; Wanders, Peterson 1996, 1997; see
also Goad, Wanders 1996). This model may also have the same obscuration
problem as that for the above streamer model. However, if the BLR clouds are
moving at randomly oriented orbits (Wanders et al. 1995), there may be no
obscuration problem. The third idea is that BLRs arise from outer parts of
a warped accretion disk. The disk model for BLR is the standard idea (Shields
1977; see also for a review Osterbrock 1989). It has been recently shown
that accreting gas clouds probed by water-vapor maser emission at 22 GHz
show evidence of significant warping (Miyoshi et al. 1995; Begelman,
Bland-Hawthorn 1997). The warping of accretion disks can be driven by the
effect of the radiation-pressure force (Pringle 1996, 1997). For typical AGN,
the warping may occur at {\it r} $>$ 0.01 pc (Pringle 1997), which is at a
similar distance as BLRs. Therefore, the warped-disk model can explain the
observed negative correlation reasonably well. This model is schematically
shown in figure 3. Since the degree of warping and the viewing angle are
different from AGN to AGN, the negative correlation between $i_{\rm AD}$
and $i_{\rm BLR}$ may be blurred as obtained in our analysis, although
the poor correlation may be also due to the large errors in the estimate of
$i_{\rm AD}$.
\acknowledgements
We would like to thank Kazushi Iwasawa, Toru Yamada, and Youichi Ohyama for
their useful discussion and comments. We would also like to thank the
anonymous referee for his/her very useful comments and suggestions. TM was
supported by the Grant-in-Aid for JSPS Fellows by the Ministry of Education,
Science, Sports and Culture. This work was supported in part by the Ministry
of Education, Science, Sports and Culture (No. 07044054).
\clearpage
| {
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Ариэль Рамирес (; 4 сентября 1921, Санта-Фе, Аргентина — 18 февраля 2010, Монте Гранде, Буэнос-Айрес, Аргентина) — аргентинский композитор, исследователь народной музыки и традиционных ритмов Южной Америки. Автор музыкального произведения, получившего всемирную популярность как мелодия «Жаворонок» в исполнении оркестра Поля Мориа.
Биография
Родился в Санта-Фе. Отец по профессии был учителем.
В 1950—1954 годах обучался в Мадриде, Риме и Вене. После возвращения в Аргентину собрал около четырёхсот народных и популярных песен и основал Compañía de Folklore Ariel Ramírez.
Одна из самых известных композиций Рамиреса — «Креольская месса» () для тенора, смешанного хора, перкуссии, фортепиано и народных инструментов — полностью основана на традиционных ритмах (chacarera, carnavalito, estilo pampeano). «Креольская месса» записывалась с такими известными певцами, как Мерседес Соса (1999) и Хосе Каррерас (1990).
Рамирес является автором знаменитой мелодии, известной как «Жаворонок» () в исполнении оркестра Поля Мориа, которая использовалась в заставке советской телепрограммы «В мире животных». В оригинале это отрывок из кантаты для хора «Наше Рождество» () на слова Феликса Луны (1964) и называется «Паломничество» (), и он до сих пор очень популярен в испаноязычном мире. Услышав песню в исполнении аргентинской певицы Мерседес Сосы, французский шансонье Жиль Дрё (Gilles Dreu) попросил поэта-песенника Пьера Деланоэ сделать адаптацию, и тот использовал созвучие первых слов оригинала A la huella () и французского слова Alouette. Эта версия стала эстрадным шлягером 1968 года, а после аранжировки оркестром Поля Мориа — всемирно известной эстрадно-симфонической композицией.
Музыкальные произведения Рамиреса исполнялись такими мировыми звёздами, как Пласидо Доминго, Хосе Каррерас, Монсерат Кабалье.
В 1970—1978 и в 1993—2004 годах — председатель Союза композиторов Аргентины. Автор более 300 произведений, включая песню Мерседес Сосы «Аргентинские женщины» () и «Южноамериканскую кантату» (; 1972, либретто Феликса Луны).
Умер 18 февраля 2010 в возрасте 88 лет от пневмонии в госпитале города Монте-Гранде. Похоронен 21 февраля на кладбище Ла-Чакарита.
Произведения
La tristecita, Samba, 1945
Agua y sol del Paraná
Misa Criolla, Chormesse, 1964
Navidad Nuestra, 1964
Navidad en Verano, 1964
Los caudillos, Kantate, 1965
Mujeres argentinas, Kantate, 1969
Cantata sudamericana, Kantate, 1972
Tríptico mocoví, 1980
La hermanita perdida, 1980
Misa por la paz y la justicia (по текстам Иоанна Павла II), 1980
Alfonsina y el mar
Ссылки
https://www.youtube.com/watch?v=Mu8uuqxv_98 La Peregrinación [Mercedes Sosa] (по-испански)
https://www.youtube.com/watch?v=qAkA0ixDkSQ Жиль Дрё — Alouette (по-французски)
https://web.archive.org/web/20160307132836/http://nephelemusic.ru/forum/viewtopic.php?f=32&t=4777
http://www.vz.ru/news/2010/2/19/377320.html
Примечания | {
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{"url":"https:\/\/www.acmicpc.net\/problem\/27798","text":"\uc2dc\uac04 \uc81c\ud55c\uba54\ubaa8\ub9ac \uc81c\ud55c\uc81c\ucd9c\uc815\ub2f5\ub9de\ud78c \uc0ac\ub78c\uc815\ub2f5 \ube44\uc728\n20 \ucd08 (\ucd94\uac00 \uc2dc\uac04 \uc5c6\uc74c) 1024 MB666100.000%\n\n\ubb38\uc81c\n\ntl;dr: Given a string of digits S, insert a minimum number of opening and closing parentheses into it such that the resulting string is balanced and each digit d is inside exactly d pairs of matching parentheses.\n\nLet the nesting of two parentheses within a string be the substring that occurs strictly between them. An opening parenthesis and a closing parenthesis that is further to its right are said to match if their nesting is empty, or if every parenthesis in their nesting matches with another parenthesis in their nesting. The nesting depth of a position p is the number of pairs of matching parentheses m such that p is included in the nesting of m.\n\nFor example, in the following strings, all digits match their nesting depth: 0((2)1), (((3))1(2)), ((((4)))), ((2))((2))(1). The first three strings have minimum length among those that have the same digits in the same order, but the last one does not since ((22)1) also has the digits 221 and is shorter.\n\nGiven a string of digits S, find another string S', comprised of parentheses and digits, such that:\n\n\u2022 all parentheses in S' match some other parenthesis,\n\u2022 removing any and all parentheses from S' results in S,\n\u2022 each digit in S' is equal to its nesting depth, and\n\u2022 S' is of minimum length.\n\n\uc785\ub825\n\nThe first line of the input gives the number of test cases, T. T lines follow. Each line represents a test case and contains only the string S.\n\n\ucd9c\ub825\n\nFor each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the string S' defined above.\n\n\uc81c\ud55c\n\n\u2022 1 \u2264 T \u2264 100.\n\u2022 1 \u2264 length of S \u2264 100.\n\nTest Set 1 (5\uc810)\n\n\u2022 Each character in S is either 0 or 1.\n\nTest Set 2 (11\uc810)\n\n\u2022 Each character in S is a decimal digit between 0 and 9, inclusive.\n\n\uc608\uc81c \uc785\ub825 1\n\n4\n0000\n101\n111000\n1\n\n\n\uc608\uc81c \ucd9c\ub825 1\n\nCase #1: 0000\nCase #2: (1)0(1)\nCase #3: (111)000\nCase #4: (1)\n\n\n\ud78c\ud2b8\n\nThe strings ()0000(), (1)0(((()))1) and (1)(11)000 are not valid solutions to Sample Cases #1, #2 and #3, respectively, only because they are not of minimum length. In addition, 1)( and )(1 are not valid solutions to Sample Case #4 because they contain unmatched parentheses and the nesting depth is 0 at the position where there is a 1.\n\nYou can create sample inputs that are valid only for Test Set 2 by removing the parentheses from the example strings mentioned in the problem statement.\n\n\ucc44\uc810 \ubc0f \uae30\ud0c0 \uc815\ubcf4\n\n\u2022 \uc608\uc81c\ub294 \ucc44\uc810\ud558\uc9c0 \uc54a\ub294\ub2e4.","date":"2023-03-27 20:38:32","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\": 0.3567020893096924, \"perplexity\": 1749.472430907459}, \"config\": {\"markdown_headings\": false, \"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\/1679296948684.19\/warc\/CC-MAIN-20230327185741-20230327215741-00242.warc.gz\"}"} | null | null |
Spreading Acts of Kindness in PH
Sustainability Community kindness Consumer
Globe Telecom is calling on various organizations and volunteers to join its nationwide volunteer program slated to launch this month to promote sharing an act of kindness among Filipinos and collectively contribute to social development.
Globe Chief Sustainability Officer Yoly Crisanto said, "We are reaching out to individuals, communities and companies to help create a "Globe of Good" thru the program."
"Studies have shown that company volunteerism is a great tool for employee engagement. Over 90% of employees who volunteer are happier with their employers while majority of those who are proud of their company's contributions to society are engaged at work. Our program aspires to bring families, friends, and co-workers to form a unique culture of kindness," she added.
Globe partnered with Future Maker iVolunteer Philippines to provide the volunteer sign-up platform through any device with internet access. Individuals can sign up or register for FREE provided groups are formed comprised of two to four volunteers to join the activities.
Companies with no existing volunteer programs will find it easy to look for various opportunities to match the needs of its employees. On the other hand, companies with existing volunteer programs may also register to get their volunteer hours counted for a chance to win exciting prizes.
"Everyone has an opportunity to volunteer. We encourage our fellow Filipinos especially our customers to share their time, talent or treasure for a good cause," Crisanto said. Individuals and groups who wish to volunteer can visit facebook.com/GlobeBridgeCom.
In 2017, the Philippines ranked 7th in the world out of 139 countries with the highest number of people volunteering their time based on the Charities Aid Foundation World Giving Index. The report said 25 million Filipinos volunteered in 2016.
Globe, DepEd Join Hands in Fight against Child Abuse & Threats against Child Safety Jan 24, 2023 | 09:00 AM
Globe Urges Filipinos To Continue Supporting Local Businesses As It Wraps Up Purposeful Holiday Celebration Jan 17, 2023 | 11:00 AM | {
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pwd est une commande UNIX. Son nom signifie en anglais « print working directory ». Elle permet d'afficher le chemin d'accès vers le répertoire où se situe l'utilisateur qui a entré la commande.
Si un utilisateur se trouve dans le répertoire "/home/utilisateur" la commande pwd lui retournera : "/home/utilisateur" (Voir les exemples d'utilisation)
Exemple d'utilisation
$> pwd
/home/root
$> cd ..
$> pwd
/home
$> PS1='$PWD> ' # Inclusion de pwd dans les prompts
/home> cd root
/home/root>
Liens externes
Introduction à pwd
La page man de pwd
pwd.c Code source de la version UNIX de pwd
Commande Unix | {
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Das Haus Mauerstraße 9 ist ein Bauwerk in Darmstadt.
Geschichte und Beschreibung
Das Wohnhaus Mauerstraße 9 wurde um das Jahr 1843 erbaut.
Stilistisch gehört das Gebäude zum Biedermeier.
Bauherr war der Darmstädter Zimmermeister Georg Friedrich Mahr.
Der unprätentiöse biedermeierliche Landhaustyp stammt aus den Anfängen der Martinsviertelbebauung.
Das ehemals freistehende Wohnhaus besitzt zweieinhalb Geschosse.
Das große Anwesen wurde zu einem späteren Zeitpunkt vom Bauherrn selbst mit weiteren Miethäusern überbaut.
Der achsensymmetrische kubische Baukörper mit einem weit vorgezogenen Dach wird durch eine sparsame Ornamentik gekennzeichnet.
Die rechteckigen Sprossenfenster sitzen in scharfkantig begrenzten Wandflächen.
Das Obergeschoss ist durch ein einfaches Überdachungsmotiv ausgezeichnet.
Alle Fenster – außer dem Halbrundfenster im Giebel – besitzen gusseiserne Brüstungsgitter.
Die ursprünglich den ländlichen Charakter unterstreichenden Fensterläden – die dieser schlichten Gestaltung gleichzeitig als Schmuckform dienten – fehlen heute zum größten Teil.
Im Hof erhalten geblieben ist eines von ehemals zwei reich gearbeiteten Gartenhäuschen mit einem Fachwerk aus den 1860er-Jahren.
Die Gefache sind kunstvoll ausgemauert, das Giebelfeld und die Traufbretter sind mit gesägter Ornamentik verziert.
Denkmalschutz
Das Wohnhaus ist ein typisches Beispiel für die Architektur der Biedermeierzeit in Darmstadt.
Aus architektonischen, baukünstlerischen und stadtgeschichtlichen Gründen steht das Bauwerk unter Denkmalschutz.
Literatur
Günter Fries et al.: Stadt Darmstadt. (= Denkmaltopographie Bundesrepublik Deutschland, Kulturdenkmäler in Hessen.) Vieweg Verlag, Braunschweig 1994, ISBN 3-528-06249-5, S. 253.
Mauerstrasse 09
Erbaut in den 1840er Jahren
Bauwerk aus Stein
Biedermeier
Wohngebäude in Darmstadt | {
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\section{Introduction}
Let $(X,x)$ be a normal complex surface singularity. Fix a local embedding of $(X,x)$
in $({\mathbb{C}}^N, 0)$. Then a small sphere $S^{2N-1}_{\epsilon} \subset {\mathbb{C}}^N$ centered at
the origin intersects $X$ transversely, and the complex hyperplane distribution
$\xi_{can}$ on $M=X\cap S^{2N-1}_{\epsilon}$ induced by the complex structure on $X$
is called the \emph{canonical} contact structure. For sufficiently small radius
$\epsilon$, the contact manifold is independent of $\epsilon$ and the embedding, up
to isomorphism. The $3$-manifold $M$ is called the link of the singularity, and $(M,
\xi_{can})$ is called the \emph{contact boundary} of $(X,x)$.
A contact manifold $(Y, \xi)$ is said to be \emph{Milnor fillable} if it is isomorphic
to the contact boundary $(M, \xi_{can})$ of some isolated complex surface singularity
$(X, x)$. In addition, we say that a closed and oriented $3$-manifold $Y$ is Milnor
fillable if it carries a contact structure $\xi$ so that $(Y,\xi)$ is Milnor fillable.
It is known that a closed and oriented $3$-manifold is Milnor fillable if and only if
it can be obtained by plumbing according to a weighted graph with negative definite
intersection matrix (cf. \cite{mum} and \cite{gr}). Moreover any $3$-manifold has at
most one Milnor fillable contact structure up to \textit{isomorphism} (cf.
\cite{cnp}). Note that Milnor fillable contact structures are Stein fillable (see
\cite{bd}) and hence tight \cite{eg}. Here we prove that every Milnor fillable
contact structure is in fact universally tight, i.e., the pullback to the universal
cover is tight. We would like to point out that universal tightness of a contact
structure is not implied by any other type of fillability.
In \cite{etn}, Etnyre settled a question of Eliashberg and Thurston \cite{elit} by
proving that every contact structure on a closed oriented $3$-manifold is obtained by
a deformation of a foliation and raised two other related questions:
\vskip.12in
(Question $4$ in \cite{etn}) \emph{Is every
universally tight contact structure on a closed $3$-manifold with infinite
fundamental group the deformation of a Reebless foliation?}
\vskip.12in
(Question $5$ in \cite{etn}) \emph{Is every
universally tight contact structure on an atoroidal closed $3$-manifold with infinite
fundamental group the deformation of a taut foliation?}
\vskip.12in
In this note we answer both questions negatively as a consequence of our main result, although one does not necessarily need our main result to find counterexamples. As a matter of fact, one can drive the same consequence by the existence of (small) Seifert fibered $L$-spaces carrying transverse contact structures which are known to be universally tight (see Remark~\ref{ibne}).
The assumption on the fundamental group is necessary since every foliation on a closed $3$-manifold with finite fundamental group has a Reeb component (and hence is not taut) by a theorem of Novikov. Moreover Ghiggini \cite{gh} gave examples of toroidal $3$-manifolds which carry universally tight contact structures that are not weakly fillable (and therefore can not be perturbations of taut foliations by \cite{elit}).
We contrast our result with the result of Honda, Kazez and Mati\'{c} in \cite{HKM}, where
they show that for a sutured manifold with annular sutures, the existence
of a (universally) tight contact structure is equivalent to the existence of a taut
foliation.
We assume that all the $3$-manifolds are compact and oriented, all the contact
structures are co-oriented and positive and all the surface singularities are isolated
and normal.
\section{Milnor fillable implies universally tight}
A {\em graph manifold} is a 3-manifold $M(\Gamma)$ obtained by plumbing circle bundles
according to a connected weighted plumbing graph $\Gamma$. More precisely, let $A_1,
\ldots, A_r$ denote vertices of a connected graph $\Gamma$. Each vertex is decorated
with a pair $(g_i, e_i)$ of integral weights, where $g_i \geq 0$. Here the $i$th
vertex represents an oriented circle bundle of Euler number $e_i$ over a closed
Riemann surface of genus $g_i$. Then $M(\Gamma)$ is the $3$-manifold obtained by
plumbing these circle bundles according to $\Gamma$. This means that if there is an edge
connecting two vertices in $\Gamma$, then one glues the circle bundles corresponding to these vertices as follows.
First one removes a neighborhood of a circle fibre on each circle bundle which is given by the preimage of a disk on the base.
The resulting boundary torus on each circle bundle can be identified with $S^1 \times S^1$ using the natural trivialization of the circle fibration
over the disk that is removed. Now one glues these bundles together using the diffeomorphism that exchanges the two circle
factors on the boundary tori.
A \emph{horizontal} open book in
$M(\Gamma)$ is an open book whose binding consists of some fibers in the circle
bundles and whose (open) pages are transverse to the fibers. We also require that the
orientation induced on the binding by the pages coincides with the orientation of the
fibers induced by the fibration.
In this paper, we will consider horizontal open books on graph manifolds coming from
isolated normal complex singularities. Given an analytic function $f\colon (X,x)
\rightarrow ({\mathbb{C}} , 0)$ vanishing at $x$, with an isolated singularity at $x$, the
open book decomposition $\mathcal{OB}_f$ of the boundary $M$ of $(X,x)$ with binding $L=M \cap
f^{-1} (0)$ and projection $ \pi=\frac{f}{|f|}\colon M \setminus L \to S^1 \subset
{\mathbb{C}}$ is called the \emph{Milnor open book} induced by $f$.
\begin{theorem} \label{unit} A Milnor fillable contact structure is universally tight.
\end{theorem}
\begin{proof} Given a Milnor fillable contact $3$-manifold $(Y, \xi)$. By definition
$(Y, \xi)$ is isomorphic to the link $(M, \xi_{can})$ of some surface singularity.
Hence it suffices to show that $(M, \xi_{can})$ is universally tight. It is known that
$M$ is an irreducible graph manifold $M(\Gamma)$ where $\Gamma$ is a negative definite
plumbing graph \cite{neumann}. Moreover, such a manifold is characterized by the
property that there exists a unique minimal set $\mathcal{T} $ (possibly empty) consisting of pairwise disjoint \emph{incompressible} tori in $M$
such that each component of $M - \mathcal{T}$ is an orientable Seifert fibered manifold
with an orientable base \cite{neumann}. In terms of the plumbing description
$\mathcal{T}$ is a subset of the tori that are used to glue the circle bundles in the
definition of $M(\Gamma)$. The set $\mathcal{T}$ is minimal if in plumbing of two circle bundles the homotopy class of circle fiber in one boundary torus is not identified with the homotopy class of the fiber in the other boundary torus.
Recall that an arbitrary Milnor open book $\mathcal{OB}$ on $M$ has the following essential features \cite{cnp}: It is compatible with
the canonical contact structure $\xi_{can}$, horizontal when restricted to each
Seifert fibered piece in $M - \mathcal{T}$ which means that the Seifert fibres
intersect the pages of the open book transversely, and the binding of the open book consists of some number (which we can take to be non-zero) of regular fibres of the Seifert fibration in each Seifert fibred piece.
In the rest of the proof, we will construct a universally tight contact structure $\xi$ on $M$ which is compatible with the Milnor open book $\mathcal{OB}$. This implies that
the canonical contact structure $\xi_{can}$ is isotopic to $\xi$ (since they are both compatible with $\mathcal{OB}$) and thus we conclude that $\xi_{can}$ on the singularity link $M$ is universally tight.
Let $V_i$ denote a Seifert fibered $3$-manifold with boundary, which is a component of $M - N(\mathcal{T})$, where $N(\mathcal{T})$ denotes a regular neighborhood of $\mathcal{T}$. Consider the $3$-manifold $V_i^\prime$ obtained by removing a regular neighborhood of the binding of $\mathcal{OB}$ from $V_i$. Note that $V_i^\prime$ is also a Seifert fibered manifold since the binding consists of regular fibers of the Seifert fibration on $V_i$. Then the restriction of a page of $\mathcal{OB}$ to $V_i^\prime$ is a connected horizontal surface (see the proof of Proposition $4.6$ in \cite{cnp}) which we denote by $\Sigma_i^\prime$. It follows that $V_i^\prime$ is a surface bundle over $S^1$ whose fibers are precisely the restriction of the pages of $\mathcal{OB}$ to $V_i^\prime$, since $\Sigma_i^\prime$ does not separate $V_i^\prime$. Note that $\Sigma_i^\prime$ is a branched cover
of the base of the Seifert fibration on $V_i^\prime$ and the monodromy $\phi_i$ of this surface bundle
is a periodic self-diffeomorphism of $\Sigma_i^\prime$ of some order $n_i$ (cf. Section $1.2$ in \cite{H}).
Now we construct, as in Section $2$ in \cite{gh}, a contact structure $\xi_i^\prime$
on $V_i^\prime$ which is ``compatible'' with the surface fibration $V_i^\prime \to
S^1$. Here compatibility means that the Reeb vector field of the contact form is
transverse to the fibers, keeping in mind that a fiber of this fibration is cut out
from a page of the open book $\mathcal{OB}$. Let $\beta_i$ denote a $1$-form on
$\Sigma_i^\prime$ such that $d\beta_i$ is a volume form on $\Sigma_i^\prime$ and
$\beta_i|_{\partial \Sigma_i^\prime}$ is a volume form on $\partial \Sigma_i^\prime$.
Then the $1$-form $$ \beta_i^\prime = \frac{1}{n_i} \displaystyle\sum_{k=0}^{n_i -1}
(\phi_i^k)^* \beta_i ,$$ which also satisfies the above conditions, is a $\phi_i$
invariant $1$-form on $\Sigma_i^\prime$. Let $t$ denote the coordinate on $S^1$. It
follows that for every real number $\epsilon > 0$, the kernel of the $1$-form $dt +
\epsilon \beta_i^\prime$ is a contact structure on $V_i^\prime$ which is compatible
with the fibers. Note that the characteristic foliation on every torus in $\partial
V_i^\prime$ is linear with a slope arbitrarily close to the slope of the foliation
induced by the pages when $\epsilon \to 0$. Here we point out that, for fixed
$\epsilon > 0$, different choices of $\beta_i$ give isotopic contact structures by
Gray's theorem, while the choice of $\epsilon$ will not play any role in our
construction as long as it is sufficiently small. Therefore, we will fix a sufficiently
small $\epsilon$ and denote the isotopy type of this contact structure by
$\xi_i^\prime$. Moreover the Reeb vector field $R_i$ is tangent to the circle fibers
in the Seifert fibration and hence transverse to the fibers of the surface bundle
$V_i^\prime \to S^1$.
Furthermore, we observe that $\xi_i^\prime$ is transverse to the Seifert fibration on
$V_i^\prime$ and can be extended over to $V_i$ along the neighborhood of the binding
so that it remains transverse to the Seifert fibration. Now we claim that the resulting
contact structure $\xi_i$ on $V_i$ is universally tight. This essentially follows from
an argument in Proposition $4.4$ in \cite{mas} where the universal tightness of
transverse contact structures on closed Seifert fibered 3-manifolds is proven (see
also Corollary 2.2 in \cite{lm}). The
difference in our case is that $V_i$ may have toroidal boundary. Nevertheless, the argument
in \cite{mas} still applies. Namely, any contact structure which is transverse to the
fibers of a Seifert manifold (possibly with boundary or non-compact) is
universally tight. Consider first the universal cover of the base of the Seifert
fibration. This can be either $S^2$ or $\mathbb{R}^2$. If it is $S^2$, then the $V_i$
cannot have any boundary, as we arranged that if there is a boundary to $V_i$, it
should be incompressible. Therefore, in that case $\mathcal{T}=\emptyset$ and $M$ is
closed Seifert fibred space with base $S^2$ with a contact structure transverse to the
fibres of the Seifert fibration. The universal cover of $M$ is now obtained by
unwrapping the fibre direction. Hence it is either $S^3$ or $S^2\times \mathbb{R}$
depending on whether $\pi_1(M)$ is finite or infinite. However, it cannot be
$S^2\times \mathbb{R}$ as $M$ is irreducible. In particular, when
$\mathcal{T}=\emptyset$, it
follows that $M$ is either a small Seifert fibered or a lens space and its universal cover is $S^3$. The
contact structure and the Seifert fibration lifts to a transverse contact structure on
$S^3$. It follows that this is the standard tight contact structure on $S^3$ (for
example, see \cite{mas}). Next, suppose that the base of the Seifert fibration on
$V_i$ has universal cover homeomorphic to $\mathbb{R}^2$. We then lift the Seifert
fibration and the contact structure to get a contact structure on $\mathbb{R}^2 \times
S^1$, such that the contact structure is transverse to the $S^1$ factor. Next, we
unwrap the $S^1$ direction to get a contact structure on $\mathbb{R}^2 \times \mathbb{R}$ such
that the contact structure is transverse to the $\mathbb{R}$ factor and invariant under
integral translations in this direction. It follows that this latter contact structure
is the standard tight contact structure on $\mathbb{R}^3$ (see \cite{gir} Section
2.B.c).
Let $V_1, \ldots, V_n$ denote the Seifert fibered manifolds in the decomposition of $M
- N(\mathcal{T})$. Our goal is to glue together $\xi_i$'s on $V_i$'s to get a
universally tight contact structure $\xi$ on $M$ which is \emph{compatible} with
$\mathcal{OB}$. We should point out that if one ignores the compatibility with $\mathcal{OB}$, then
$\xi_i$'s can be glued along the incompressible pre-Lagrangian tori on $\partial
V_i$'s to yield a universally tight contact structure on $M$, by Colin's gluing
theorem \cite{col}. This was already described in Theorem $1.4$ in \cite{col2},
although the contact structures on Seifert fibered pieces were obtained by perturbing Gabai's taut foliations \cite{g}.
By construction, the contact structure $\xi_i$ on $V_i$ is compatible with the restriction of $\mathcal{OB}$ to $V_i$.
We first modify $\xi_i$ near each component of $\partial V_i$ to put it in a certain
standard form. To this end, let $N(T_{ij})$ denote the normal neighborhood of a torus
$T_{ij} \in \mathcal{T}$ along which plumbing is performed between $V_i$ and $V_j$.
Recall that the plumbing was perfomed by trivializing the boundary of the circle
bundles hence identifying them with $T^2=S^1 \times S^1$ and then exchanging the two circle factors.
We can extend these trivialization in a neighborhood of $T_{ij}$, by picking sections
$s_i$ near $T_{ij}$ which extends the section used for the plumbing. Let $r_i$ denote
the fibre direction of the Seifert fibration on $V_i$. Then, we can identify the
boundary of $N(T_{ij})$ in $V_i$ with $T^2$ so that the basis $(r_i,s_i)$ is sent to
the standard basis $\{ \partial_x , \partial_y \} $ of $T^2$. Hence, we can identify $N(T_{ij}) = T^2 \times
[a_i,b_i] \cup_{\rho_{ij}} - T^2\times [a_j,b_j]$ where $\rho_{ij}: T^2 \times \{b_i\}
\to - T^2 \times \{ b_j \} $ is the gluing map used in plumbing sending $(r_i,s_i) \to (s_j,r_j)$.
Let $\mathcal{F}_i$ denote the foliation by circles with a certain rational slope
$m_i/m_j$ on $T^2\times \{a_i\}$ induced by the pages of $\mathcal{OB}$. This means that the
page intersects $T^2 \times \{a_i \}$ at a linear curve tangent to $m_j r_i + m_i s_i$
, we also scale $m_i$ and $m_j$ so that we have $\beta'_i(m_j r_i + m_i s_i)=1$ (The
latter can be arranged as by construction $\beta'_i$ restricts to a volume form on the
boundary of the pages of the open book when restricted to $V_i$). The pages extend
into $T^2 \times [a_i,b_i]$ linearly, as they intersect each $T^2 \times \{c\}$
transversely with slope $m_i/m_j$, thus we obtain the foliation $\mathcal{F}_i \times
[a_i,b_i]$. Similarly, $\mathcal{F}_j$ denote the foliation by circles given by the
intersection of the pages of $\mathcal{OB}$ with $T^2 \times \{a_j\}$ which necessarily has
rational slope $m_j/m_i$ so that the gluing map $\rho_{ij}$ glues the pages in each
piece together to form $\mathcal{OB}$.
For later convenience, in our identification $N(T_{ij}) = T^2 \times [a_i,b_i]
\cup_{\rho_{ij}} - T^2\times [a_j,b_j]$, we will choose $-\frac{\pi}{2} < a_i < b_i <
\frac{\pi}{2}$ so that $- \cot a_i = m_i/ (m_j - \epsilon) $ is the slope of the
characteristic foliation of the contact structure $\xi_i$ on $T^2\times \{a_i\}$ and
$b_i$ so that $-\cot b_i = m_i /m_j$ is the slope of the pages of $\mathcal{OB}$. By our
construction, the characteristic foliation is the integral of the vector field
$-\epsilon r_i + (m_jr_i+m_i s_i)$ and we can choose $\epsilon$ as small as we need,
so that the slope of the characteristic foliation is arbitrarily close to the slope of
the pages. In particular, we can arrange that $b_i \in (a_i, a_i + \frac{\pi}{2})$.
We now need to glue together the contact forms that we constructed on $V_i$ by extending them to $N(T_{ij})$. For our purposes, we need to pay special attention to compatibility with $\mathcal{OB}$ on $N(T_{ij})$.
Consider the contact form $\alpha_i= \cos t dx + \sin t dy$ on $T^2 \times [a_i,
b_i]$. By \cite{ch} Lemma $9.1$ we can isotope $\xi_i$ on $V_i$ near the boundary so
that it is defined by a contact form that glue to $\alpha_i$ (note that the slopes of
the characteristic foliations on $T^2 \times \{ a_i \}$ induced by $\xi_i$ and
$\alpha_i$ agree). Moreover, after this isotopy the Reeb vector field of $\xi_i$ still
remains transverse to the pages of $\mathcal{OB}$ on $V_i$. Furthermore, the Reeb vector field
of $\alpha_i$, has slope $\tan a_i$ hence it is perpendicular to the slope $- \cot
a_i$ at $T^2 \times \{ a_i \}$ which we know to be arbitrarily close the slope of the
foliation $\mathcal{F}_i \times \{a_i\} $ induced by the page of $\mathcal{OB}$. Since the
slope of the Reeb vector field changes by strictly less than $\pi /2$ as we go from
$a_i$ to $b_i$, the Reeb vector field still remains transverse to $\mathcal{F}_i
\times [a_i,b_i]$. Therefore, the form $\alpha_i$ is compatible with $\mathcal{OB}$ in $T^2
\times [a_i, b_i]$. Finally, to finish the construction of the contact structure
$\xi$ on $M$, we observe that the gluing map $\rho_{ij}$ sends $\alpha_i$ to
$\alpha_j$, since we arranged that the slope of $\alpha_i$ and the slope of the
characteristic foliation induced by the page are the same at $T^2 \times \{b_i \}$.
We constructed a contact structure $\xi$ which is compatible with a Milnor open book (hence is isomorphic to $\xi_{can}$) such that $\xi$ is isotopic to $\xi_i$ on $V_i$, a universally tight contact structure, furthermore for each incompressible torus $T \in \mathcal{T}$, the characteristic foliation of $\xi$ is a linear foliation (with slope $m_i / m_j$). Therefore, we are in a position to apply the gluing result of Colin \cite{col} which states that universally tight contact structures can be glued along pre-Lagrangian tori to a universally tight contact structure. This shows that $\xi_{can}$ is a universally tight contact structure. \end{proof}
\begin{remark} The above construction shows that when the fibres of each Seifert
fibered piece is not contractible, then $\xi_{can}$ is {\em hypertight}, that is, it
can be defined by a contact form whose associated Reeb vector field has no
contractible orbits. Thus, for example when $\mathcal{T} \neq \emptyset$, $\xi_{can}$
is hypertight. Note that hypertight contact structures are tight \cite{hof} and any finite cover of
a hypertight contact manifold is hypertight \cite{gh}.
These results together with the fact that graph manifolds have residually finite
fundamental groups give another proof of universally tightness (avoiding Colin's
gluing result). Since $M$ is irreducible, its universal cover is diffeomorphic to
either $S^3$ or $\mathbb{R}^3$ depending on whether $\pi_1(M)$ is finite or infinite.
The universal cover is $S^3$ if and only if $M$ is atoroidal, then $M$ is either a small
Seifert fibered space or a lens space and these have no hypertight contact structures.
Therefore, $M$ is hypertight if and only if $\pi_1(M)$ is infinite (or equivalently
its universal cover is $\mathbb{R}^3$).
\end{remark}
\begin{remark}
It is known that any finite cover of a singularity link is a singularity link.
Therefore, another approach to prove Theorem \ref{unit} would be to show that a finite
cover of a Milnor fillable contact structure is Milnor fillable. It is not clear to
the authors of this paper whether this is indeed true. Note that there exist finite
covers of Stein fillable contact structures which are not tight (in particular, not Stein
fillable) \cite{gompf}.
\end{remark}
\begin{remark} Since any Milnor fillable contact $3$-manifold $(Y,\xi)$ is Stein
fillable (see \cite{bd}) , it follows from Theorem 1.5 in \cite{OS} that the
contact invariant $c(\xi) \in \widehat{HF}(-Y)/(\pm 1)$ is non-trivial. Therefore, by
\cite{GHV}, the Giroux torsion of $Y$ is zero. In particular, the incompressible
tori in $\mathcal{T}$ have zero torsion. This was predicted in \cite{nem} and was
raised as a question there.
\end{remark}
\section{Universally tight but no taut}
A rational homology sphere is called an $L$-space if $\operatorname{rk} \widehat{HF}(Y) = |H_1(Y; {\mathbb{Z}})|$. Lens spaces are basic examples of $L$-spaces which explains the name. A characterization of $L$-spaces among Seifert fibered $3$-manifolds is given by
\begin{theorem}\label{hom} \cite{ls} A rational homology sphere which is Seifert fibered over $S^2$ is an $L$-space if and only if it does not carry a taut foliation.
\end{theorem}
A huge class of examples of $L$-spaces come from complex surface singularities. Recall
that an isolated normal surface singularity $(X,x)$ is rational (cf. \cite{a}) if the geometric
genus $p_g := \text{dim}_\mathbb{C} H^1(\tilde{X} , \mathcal{O}_{\tilde{X}})$ is
equal to zero, where $\tilde{X} \to X$ is a resolution of the singular point $x\in X$. This definition does not depend on the resolution.
\begin{theorem}\label{rat} \cite{nem} The link of a rational surface singularity is an $L$-space.
\end{theorem}
\begin{corollary}\label{main}
If $Y$ is the link of a rational surface singularity which is Seifert fibered over $S^2$, then $Y$ carries a universally tight contact structure that can not be obtained by a deformation of a taut foliation.
\end{corollary}
\begin{proof}
The link of a rational surface singularity is an $L$-space by Theorem~\ref{rat} and hence it does not carry any taut foliations by Theorem~\ref{hom}. Moreover, Theorem~\ref{unit} implies that the canonical contact structure on this link is universally tight. \end{proof}
\begin{remark} \label{ibne}
Note that Seifert fibered $3$-manifolds as above carry transverse contact structures (by Theorem
$1.3$ in \cite{lm}) and such contact structures are known to be universally tight (cf. Corollary $2.2$ in \cite{lm} and also Proposition $4.4$ in \cite{mas}).
\end{remark}
\begin{corollary}\label{app} There exist infinitely many atoroidal $3$-manifolds with
infinite fundamental groups which carry universally tight contact structures that are
not deformations of taut (or Reebless) foliations.
\end{corollary}
\begin{proof}
It is known (cf. \cite{dim}) that the link of a complex surface singularity has finite
fundamental group if and only if it is a quotient singularity. Thus the link of a
rational but not quotient surface singularity has an infinite fundamental group. Note
that the links of a quotient surface singularities (all small Seifert fibered
$3$-manifolds) are explicitly listed in \cite{bho} via their dual resolution graphs.
It is easy to see that there are many infinite families of small Seifert fibered
$3$-manifolds which are links of rational but not quotient surface singularities. This
finishes the proof using Corollary~\ref{main} since all small Seifert fibered
$3$-manifolds are known to be atoroidal. Note that on an atoroidal $3$-manifold, a Reebless foliation is taut.
\end{proof}
Consequently,
Corollary~\ref{app} answers Questions 4 and 5 of Etnyre \cite{etn} negatively. For the sake of
completeness we give an infinite family of counterexamples. The small Seifert fibered
$3$-manifold $$Y_p= Y(-2; \frac{1}{3}, \frac{2}{3}, \frac{p}{p+1})$$ can be described by the surgery
diagram depicted in Figure~\ref{seif}, where $p$ is a positive integer.
Note that $Y_p$ is the link of a complex surface singularity whose dual resolution graph is given in Figure~\ref{yprat}.
\begin{figure}[ht]
\relabelbox \small {\epsfxsize=2.5in
\centerline{\epsfbox{seif.eps}}}
\relabel{p}{$-3$}
\relabel{q}{$-\frac{3}{2}$}
\relabel{r}{$-\frac{p+1}{p}$}
\relabel{s}{$-2$}
\endrelabelbox
\caption{Rational surgery diagram for $Y_p$ } \label{seif}
\end{figure}
\begin{figure}[ht]
\relabelbox \small {\epsfxsize=2.5in
\centerline{\epsfbox{yprat.eps}}}
\relabel{a}{$-2$}
\relabel{b}{$-2$}
\relabel{c}{$-2$}
\relabel{d}{$-3$}
\relabel{e}{$-2$} \relabel{f}{$-2$} \relabel{g}{$-2$}
\relabel{r}{$p$ vertices}
\endrelabelbox
\caption{Dual resolution graph} \label{yprat}
\end{figure}
Let $(X,x)$ be a germ of a complex surface singularity. Fix a resolution
$\pi\colon \tilde X\to X$ and denote the irreducible
components of the exceptional divisor $E=\pi^{-1}(x)$ by
$\bigcup_{i=1}^n E_i$. The {\em fundamental cycle} of $E$ is
by definition the componentwise smallest nonzero effective divisor $Z=\sum z_i E_i$
satisfying $Z\cdot E_i\leq 0$ for all $1 \leq i \leq n$. It turns out that the singularity $(X,x)$
is rational if each irreducible component $E_i$ of the
exceptional divisor $E$ is isomorphic to ${\mathbb{C}} P^1$ and
$$ Z\cdot Z+\sum_{i=1}^n z_i(-E_i^2-2)= -2, $$
where $Z=\sum z_iE_i$ is the fundamental cycle of $E$.
Enumerate the vertices in the dual resolution graph for $Y_p$ from left to right along the
top row with the bottom vertex coming last (see Figure~\ref{yprat}). It is then easy to check (cf. \cite{bo})
that the coefficients $(z_1, z_2, \ldots, z_n)$ of the corresponding fundamental cycle
is given by $(1,2,3,3,\ldots,3,3,2,1,1)$. It follows that $Y_p$ is
the link of a rational surface singularity and hence it is an
L-space. We conclude that the
canonical contact structure $\xi_{can} $ on $Y_p$ is universally tight but it can not
be obtained by perturbing a taut foliation. Moreover, if $p \geq 2$, then $Y_p$ is not a quotient singularity
\cite{bho} and thus its fundamental group is infinite.
\vskip.12in \noindent {\bf {Acknowledgement}}: We would like to thank Tolga Etg\"u for helpful
conversations, Patrick Massot for his comments on a draft of this paper and the Mathematical Sciences Research Institute for its hospitality during the \textit{Symplectic and Contact Geometry and Topology} program 2009/2010. B.O. was partially supported by the BIDEP-2219 research grant of the Scientific and Technological
Research Council of Turkey and the Marie Curie International Outgoing Fellowship 236639.
\bibliographystyle{amsplain}
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\providecommand{\MRhref}[2]{%
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| {
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# Biology as Ideology
**The Doctrine of DNA**
**R. C. Lewontin**
Copyright © 1991 R. C. Lewontin
and the Canandian Broadcasting Corporation
All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
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This edition published in 2010 by
House of Anansi Press Inc.
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Toronto, ON, M5V 2K4
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Fax 416-363-1017
www.anansi.ca
_LIBRARY AND ARCHIVES CANADA CATALOGUING IN PUBLICATION_
Lewontin, Richard C., 1929-
Biology as ideology
(CBC Massey lectures series; 1990)
Includes bibliographical references.
eISBN 978-0-88784-847-6
1. Biology—Philosophy. 2. Biology—Social aspects.
I. Title. II. Series; CBC Massey Lectures series: 1990.
QH331.L48 1991 574'.01 C91-095327-9
Cover design: Bill Douglas
Cover photograph: Ann Cutting/Photonica
_We acknowledge for their financial support of our publishing program the Canada Council for the Arts, the Ontario Arts Council, and the Government of Canada through the Canada Book Fund._
## **Preface**
For a large part of the history of Western culture, the chief sources of popular consciousness about society were tradition and the Christian Church. Even social revolutionaries like the ideologues of the American Revolution appealed to divine providence for a justification of their politics. In the present century, however, Western society has become more secular and more rationalist, and the chief sources for social theory have become the professional intellectuals, the scientists, economists, political theorists, and philosophers who work largely in universities. These intellectuals are aware of the power they have to mold public consciousness, and they constantly seek ways in which they can publicize their ideas. The common pathway is to become a minor celebrity, known for some all-encompassing and usually rather simplistic "discovery" about the secret of human social and psychic existence. It's all sex or money or genes. A simple and dramatic theory that explains everything makes good press, good radio, good TV, and best-selling books. Anyone with academic authority, a halfway decent writing style, and a simple and powerful idea has easy entry to the public consciousness.
On the other hand, if one's message is that things are complicated, uncertain, and messy, that no simple rule or force will explain the past and predict the future of human existence, there are rather fewer ways to get that message across. Measured claims about the complexity of life and our ignorance of its determinants are not show biz.
Fortunately, there is a tradition, of which the Massey Lectures are an important part, of providing a public forum for a more complex and less showy world view. So, I was both flattered and delighted to be invited to give the 1990 Massey Lectures on the CBC and to turn the lectures into this book. That invitation has provided an opportunity to struggle against the view that science consists of simple objective truths and that if only we will listen to biologists we will know everything worth knowing about human existence.
The rhetoric, and especially the written rhetoric, of science is very different from ordinary forms of communication, so it was especially difficult to create a set of radio lectures that would be accessible to listeners in general. There was then the further difficulty of delivering those lectures in a lively manner to an unseen radio audience. To the extent that I have succeeded in these tasks, I owe it to the critical judgment of Jill Eisen of the CBC, who made me do it over again until it was right. Without her work and encouragement, the lectures would have been a total failure.
In turning the lectures into this book, I have resisted the temptation to lapse back into the formal rhetoric of written intellectual production, and instead have kept the radio lectures pretty much as they were. Inevitably that leads to some discursiveness and lack of clarity. I am tremendously indebted to Shaun Oakey for editing the text with a touch that was both light and unerring. He made great improvements.
Finally, I am indebted to Rachel Nasca for her production of several versions of the lectures and text from tapes and illegible scrawls. Nothing would have been produced without her.
R.C. LEWONTIN
_Cambridge, Massachusetts
16 July 1991_
## **_A Reasonable Skepticism_**
**_S_** cience is a social institution about which there is a great deal of misunderstanding, even among those who are part of it. We think that science is an institution, a set of methods, a set of people, a great body of knowledge that we call scientific, is somehow apart from the forces that rule our everyday lives and that govern the structure of our society. We think science is objective. Science has brought us all kinds of good things. It has tremendously increased the production of food. It has increased our life expectancy from a mere 45 years at the beginning of the last century to over 70 in rich places like North America. It has put people on the moon and made it possible to sit at home and watch the world go by.
At the same time, science, like other productive activities, like the state, the family, sport, is a social institution completely integrated into and influenced by the structure of all our other social institutions. The problems that science deals with, the ideas that it uses in investigating those problems, even the so-called scientific results that come out of scientific investigation, are all deeply influenced by predispositions that derive from the society in which we live. Scientists do not begin life as scientists, after all, but as social beings immersed in a family, a state, a productive structure, and they view nature through a lens that has been molded by their social experience.
Above that personal level of perception, science is molded by society because it is a human productive activity that takes time and money, and so is guided by and directed by those forces in the world that have control over money and time. Science uses commodities and is part of the process of commodity production. Science uses money. People earn their living by science, and as a consequence the dominant social and economic forces in society determine to a large extent what science does and how it does it. More than that, those forces have the power to appropriate from science ideas that are particularly suited to the maintenance and continued prosperity of the social structures of which they are a part. So other social institutions have an input into science both in what is done and how it is thought about, and they take from science concepts and ideas that then support their institutions and make them seem legitimate and natural. It is this dual process—on the one hand, of the social influence and control of what scientists do and say, and, on the other hand, the use of what scientists do and say to further support the institutions of society—that is meant when we speak of science as ideology.
Science serves two functions. First, it provides us with new ways of manipulating the material world by producing a set of techniques, practices, and inventions by which new things are produced and by which the quality of our lives is changed. These are the aspects of science to which scientists appeal when they try to get money from governments or when they appear on the front pages of newspapers in their public relations efforts to maintain their prosperity. We read repeatedly about how "science has discovered" something, but more often than not those announcements are hedged with qualifiers. Biologists discover "evidence for" genes that "may one day" lead to "a possible" cure for cancer. While their over-optimistic reports breed a certain cynicism, it is nevertheless true that scientists do actually change the way we confront the material world.
The second function of science, which is sometimes independent and sometimes closely related to the first, is the function of explanation. Even if scientists are not actually changing the material mode of our existence, they are constantly explaining why things are the way they are. It is often said that these theories about the world must be produced in order, ultimately, to change the world through practice. After all, how can we cure cancer unless we understand what causes cancer? How can we increase food production unless we understand the laws of genetics and plant and animal nutrition?
Yet it is remarkable how much important practical science has been quite independent of theory. In Chapter 3, I will consider one of the most famous examples of scientific agricultural change: the introduction of hybrid corn all over the world. Hybrid corn is said to be one of the great triumphs of modern genetics in action, helping to feed people and increase their well-being. Yet the development of hybrid corn and, indeed, almost all plant and animal breeding as it is actually practiced has been carried out in a way that is completely independent of any scientific theory. Indeed, a great deal of plant and animal breeding has been done in a way indistinguishable from the methods of past centuries before anyone had ever heard of genetics.
The same is true for our attempts to cope with killers like cancer and heart disease. Most cures for cancer involve either removing the growing tumor or destroying it with powerful radiation or chemicals. Virtually none of this progress in cancer therapy has occurred because of a deep understanding of the elementary processes of cell growth and development, although nearly all cancer research, above the purely clinical level, is devoted precisely to understanding the most intimate details of cell biology. Medicine remains, despite all the talk of scientific medicine, essentially an empirical process in which one does what works.
Also in Chapter 3, I will consider the relationship between scientific biology and changes in life expectancy. It is not at all clear that a correct understanding of how the world works is basic to a successful manipulation of the world. But explanations of how the world really works serve another purpose, one in which there has been a remarkable success, irrespective of the practical truth of scientific claims. The purpose is that of _legitimation._
Regardless of one's political view, everyone must agree that we live in a world in which psychic and material welfare is very unevenly distributed. There are rich people and poor people, sick people and healthy people, people who have control over the conditions of their own lives, work, and time (like professors who are invited to give lectures on the radio and turn them into books) and those who have their tasks assigned to them, who are overseen, who have little or no control over any psychic or material aspect of their lives. There are rich countries and poor countries. Some races dominate others. Men and women have very unequal social and material power.
Some kind of inequality of status, wealth, health, and power have been characteristic of every known society. That means that in every known society there has been some form of struggle between those who have and those who have not, between those with social power and those deprived of it. The uprising of Blacks in America in the 1960s and 1970s, in which there was vast destruction of property and a radical redistribution of consumer goods, and the armed struggle of Mohawks in Canada to prevent the encroachment of commercial and state power on their lands, are only the most recent events in a long history of violent confrontations between those with status, wealth, and power and those without. Repeated peasant uprisings in Europe in the sixteenth and seventeenth centuries resulted in the whole-sale destruction of crops and buildings and the loss of hundreds of thousands of lives. The deeds of peasant rebels like Pugachev and Stenka Razin live in song and story. In the United States just after independence from Britain, the farmers of western Massachusetts, led by Daniel Shays and still in possession of their muskets, occupied the general courts to prevent bankers from obtaining judgments to confiscate farmers' property for debt. The bankers in Boston succeeded in getting Continental troops to put down this rebellion, but all at the cost of considerable social upheaval. It is obviously in the interest of those who have power in society to prevent such violent and destructive conflicts, even if, with the police power of the state, they are sure to win.
As such struggles occur, institutions are created whose function is to forestall violent struggle by convincing people that the society in which they live is just and fair, or if not just and fair then inevitable, and that it is quite useless to resort to violence. These are the institutions of social legitimation. They are just as much a part of social struggle as the rick-burnings and machinery destruction of the Captain Swing riots in Britain in the nineteenth century. But they use very different weapons — ideological weapons. The battleground is in people's heads, and if the battle is won on that ground then the peace and tranquillity of society are guaranteed.
For almost the entire history of European society since the empire of Charlemagne, the chief institution of social legitimation was the Christian Church. It was by the grace of God that each person had an appointed place in society. Kings ruled _Dei gratia_. Occasionally divine grace could be conferred on a commoner who was ennobled, and grace could be removed. Grace was removed from King Charles I, as Cromwell noted, and the proof was Charles's severed head. Even the most revolutionary of religious leaders pressed the claims of legitimacy for the sake of order. Martin Luther enjoined his flock to obey their lords, and in his famous sermon on marriage he asserted that justice was made for the sake of peace and not peace for the sake of justice. Peace is the ultimate social good, and justice is important only if it subserves peace.
For an institution to explain the world so as to make the world legitimate, it must possess several features. First, the institution as a whole must appear to derive from sources outside of ordinary human social struggle. It must not seem to be the creation of political, economic, or social forces, but to descend into society from a supra-human source. Second, the ideas, pronouncements, rules, and results of the institution's activity must have a validity and a transcendent truth that goes beyond any possibility of human compromise or human error. Its explanations and pronouncements must seem to be true in an absolute sense and to derive somehow from an absolute source. They must be true for all time and all place. And finally, the institution must have a certain mystical and veiled quality so that its innermost operation is not completely transparent to everyone. It must have an esoteric language, which needs to be explained to the ordinary person by those who are especially knowledgeable and who can intervene between everyday life and mysterious sources of understanding and knowledge.
The Christian Church or indeed any revealed religion fits these requirements perfectly, and so religion has been an ideal institution for legitimating society. If only people with special grace, whether they be priests, pastors, or ordinary citizens, are in direct contact with the divine inspiration through revelations, then we must depend upon them completely for an understanding of what has been divinely decreed.
But this description also fits science and has made it possible for science to replace religion as the chief legitimating force in modem society. Science claims a method that is objective and nonpolitical, true for all time. Scientists truly believe that except for the unwanted intrusions of ignorant politicians, science is above the social fray. Theodosius Dobzhansky, a famous scientist who was a refugee from the Bolshevik Revolution and who detested the Bolsheviks, devoted a great deal of energy to pointing out the serious scientific errors that were being made in the Soviet Union in biology and genetics as a consequence of the unorthodox biological doctrines of T.D. Lysenko. It was pointed out to him that, given his own political convictions, he should not carry on that campaign against Lysenko. After all, he believed that sooner or later a global conflict would occur with the United States and the Soviet Union on opposite sides, and he also believed that Lysenko's false scientific doctrines were severely weakening Soviet agricultural production. Why did he then not simply remain quiet about Lysenko's errors so that the Soviet Union would be weakened and compromised in the conflict that was to come? His answer was that his obligation to speak the truth about science was superior to all other obligations and that a scientist must never allow a political consideration to prevent him from saying what he believes to be true.
Not only the methods and institutions of science are said to be above ordinary human relations but, of course, the product of science is claimed to be a kind of universal truth. The secrets of nature are unlocked. Once the truth about nature is revealed, one must accept the facts of life. When science speaks, let no dog bark. Finally, science speaks in mysterious words. No one except an expert can understand what scientists say and do, and we require the mediation of special people — science journalists, for example, or professors who speak on the radio — to explain the mysteries of nature because otherwise there is nothing but indecipherable formulas. Nor can one scientist always understand the formulas of another. Once, when Sir Solly Zuckerman, the famous English zoologist, was asked what he did when he read a scientific paper and came across mathematical formulas, he said, "I hum them."
Despite its claims to be above society, science, like the Church before it, is a supremely social institution, reflecting and reinforcing the dominant values and views of society at each historical epoch. Sometimes the source in social experience of a scientific theory and the way in which that scientific theory is a direct translation of social experience are completely evident, even at a detailed level. The most famous case is Darwin's theory of evolution by natural selection. No scientist doubts that the organisms on earth today have evolved over billions of years from organisms that were very unlike them and that nearly all types of organisms have long since gone extinct. Moreover, we know this to be a natural process resulting from the differential survivorship of different forms. In this sense, we all accept Darwinism as true.
But Darwin's explanation for that evolution is another matter. He claimed that there was a universal struggle for existence because more organisms were born than could survive and reproduce, and that in the course of that struggle for existence, those organisms who were more efficient, better designed, cleverer, and generally better built for the struggle would leave more offspring than the inferior kinds. As a consequence of this victory in the struggle for existence, evolutionary change occurred.
Yet Darwin himself was conscious of the source of his ideas about the struggle for existence. He claimed that the idea for evolution by natural selection occurred to him after reading the famous "Essay on Population" by Thomas Malthus, a late-eighteenth-century parson and economist. The essay was an argument against the old English Poor Law, which Malthus thought too liberal, and in favor of a much stricter control of the poor so they would not breed and create social unrest. In fact, Darwin's whole theory of evolution by natural selection bears an uncanny resemblance to the political economic theory of early capitalism as developed by the Scottish economists. Darwin had some knowledge of the economic survival of the fittest because he earned his living from investment in shares he followed daily in the newspapers. What Darwin did was take early-nineteenth-century _political_ economy and expand it to include all of _natural_ economy. Moreover, he developed a theory of sexual selection in evolution (about which more will be said in Chapter 4), in which the chief force is the competition among males to be more appealing to discriminating females. This theory was meant to explain why male animals often display bright colors or complex mating dances. It is not clear that Darwin was conscious of how similar his view of sexual selection was to the standard Victorian view of the relationship between middle-class males and females. In reading Darwin's theory, one can see the proper young lady seated on her sofa while the swain on his knees before her begs for her hand, having already told her father how many hundreds a year he has in income.
Most of the ideological influence from society that permeates science is a great deal more subtle. It comes in the form of basic assumptions of which scientists themselves are usually not aware yet which have profound effect on the forms of explanations and which, in turn, serve to reinforce the social attitudes that gave rise to those assumptions in the first place. One of the assumptions is the relation of individual to collectivity, the famous problem of part and whole. Before the eighteenth century, European society placed little or no emphasis on the importance of the individual. Rather, the activity of people was determined for the most part by the social class into which they were born, and individuals confronted each other as representatives of their social group. In a dispute, for example, between a priest and a merchant over a commercial matter, the priest would make his case in an ecclesiastical court and the merchant in the court of his own lord rather than both being subject to the same judgment. Individuals were seen not as the causes of social arrangements but as their consequence.
Moreover, people were not free to move in the economic hierarchy. Peasants and lords alike had mutual obligations and were bound to each other by those obligations. There was no freely moving competitive labor force where each person had the power to sell his or her labor power in a labor market. These relations made it quite impossible to develop the kind of productive capitalism that marks our own era, in which freedom for individuals to move from place to place, from task to task, from status to status, to confront each other sometimes as tenants, sometimes as producers and sometimes as consumers, is an absolute necessity. For example, serfdom had to be abolished in Russia in the middle of the nineteenth century because there was a shortage of factory labor and serfs were legally prohibited from being sent to factories. Sometimes, in fact, serf owners illegally shipped their peasants into factories, and serfs petitioned the czar for relief.
The developing science of the Middle Ages and Renaissance was characterized by seeing all of nature as a kind of indissoluble whole. Living and dead could be transformed one into the other, provided one knew the mystical formula. Nature could not be understood by taking it into pieces because by doing so one destroyed what was essential to it. Alexander Pope said it was "like following life through creatures you dissect. /You lose it in the moment you detect." Just as social organization was seen as an indissoluble whole, so was nature.
With the change in social organization that was wrought by developing industrial capitalism, a whole new view of society has arisen, one in which the individual is primary and independent, a kind of autonomous social atom that can move from place to place and role to role. Society is now thought to be the consequence, not the cause, of individual properties. It is individuals who make society. Modern economics is grounded in the theory of consumer preference. Individual autonomous firms compete with each other and replace each other. Individuals have power over their own bodies and labor power, in what MacPherson called "possessive individualism." This atomized society is matched by a new view of nature, the reductionist view. Now it is believed that the whole is to be understood _only_ by taking it into pieces, that the individual bits and pieces, the atoms, molecules, cells, and genes, are the causes of the properties of the whole objects and must be separately studied if we are to understand complex nature. Darwin's theory of evolution was a theory of the differential reproductive rate of individuals, and all of the phenomena of evolution were to be understood at this individual causal level. All of modern biology and, indeed, all of modern science takes as its informing metaphor the clock mechanism described by René Descartes in Part V of his _Discourses._ Descartes, being religious, excluded the human soul from the _bête machine,_ but that very soon became included as well to make the _homme machine_ of the present view. Modern science sees the world, both living and dead, as a large and complicated system of gears and levers.
A second feature of the transformation of scientific views has been the clear distinction between causes and effects. Things are supposed to be either one or the other. Again, in Darwin's view, organisms were acted upon by the environment; they were the passive objects and the external world was the active subject. This alienation of the organism from its outside world means that the outside world has its own laws that are independent of the organisms and so cannot be changed by those organisms. Organisms find the world as it is, and they must either adapt or die. "Nature — love it or leave it." It is the natural analog of the old saw that you can't fight city hall. As I shall show in Chapter 5, this is an impoverished and incorrect view of the actual relationship between organisms and the world they occupy, a world that living organisms by and large _create_ by their own living activities.
So, the ideology of modern science, including modern biology, makes the atom or individual the causal source of all the properties of larger collections. It prescribes a way of studying the world, which is to cut it up into the individual bits that cause it and to study the properties of these isolated bits. It breaks the world down into independent autonomous domains, the internal and the external. Causes are either internal or external, and there is no mutual dependency between them.
For biology, this world view has resulted in a particular picture of organisms and their total life activity. Living beings are seen as being determined by internal factors, the genes. Our genes and the DNA molecules that make them up are the modern form of grace, and in this view we will understand what we are when we know what our genes are made of. The world outside us poses certain problems, which we do not create but only experience as objects. The problems are to find a mate, to find food, to win out in competition over others, to acquire a large part of the world resources as our own, and if we have the right kinds of genes we will be able to solve the problems and leave more offspring. So in this view, it is really our genes that are propagating themselves through us. We are only their instruments, their temporary vehicles through which the self-replicating molecules that make us up either succeed or fail to spread through the world. In the words of Richard Dawkins, one of the leading proponents of this biological view, we are "lumbering robots" whose genes "created us body and mind."
Just as at one level genes determine individuals, so at another level it is individuals who determine collectivities. If we want to understand why an ant colony has a particular division of tasks or a flock of birds flies in a particular way, we need only look at the individual ants and individual birds, because the behavior of the group is a consequence of the behaviors of the individual organisms; that behavior is in turn determined by genes. For human beings that means that the structure of our society is nothing but a result of the collection of individual behaviors. If our country goes to war, we are told it is because we feel aggressive as individuals. If we live in a competitive entrepreneurial society, it is because, in this view, each one of us, as an individual, has a drive to be competitive and entrepreneurial.
Genes make individuals and individuals make society, and so genes make society. If one society is different from another, that is because the genes of the individuals in one society are different from those in another. Different races are thought to be genetically different in how aggressive or creative or musical they are. Indeed, culture as a whole is seen as made up of little bits and pieces of cultural bric-a-brac, what some sociobiologists call _culturgens._ In this view, aculture is a sack of bits and pieces such as aesthetic preferences, mating preferences, work and leisure preferences. Dump out the sack and culture will be displayed before you. Thus, the hierarchy is complete. Genes make individuals, individuals have particular preferences and behaviors, the collection of preferences and behaviors makes a culture, and so genes make culture. That is why molecular biologists urge us to spend as much money as necessary to discover the sequence of the DNA of a human being. They say that when we know the sequence of the molecule that makes up all our genes, we will know what it is to be human. When we know what our DNA looks like, we will know why some of us are rich and some poor, some healthy and some sick, some powerful and some weak. We will alsp know why some societies are powerful and rich and others are weak and poor, why one nation, one sex, one race dominates another. Indeed, we will know why there is such a thing as a science of biology, which itself is one of the bits and pieces of culture lying at the bottom of the sack.
We have become so used to the atomistic machine view of the world that originated with Descartes that we have forgotten that it is a metaphor. We no longer think, as Descartes did, that the world is _like_ a clock. We think it _is_ a clock. We cannot imagine an alternative view unless it be one that goes back to a prescientific era. For those who are dissatisfied with the modern world and dislike the artifacts of science, the pollution, the noise, the industrial world, the overmechanized medical care that seems not to make us feel better much of the time — for people who want to go back to nature and the good old ways, the response has been to return to a description of the world as an indissoluble whole that we murder to dissect. For them, there is no use in trying to break anything down into parts because we inevitably lose the essence, and the best we can do is treat the world holistically.
But this holistic world view is untenable. It is simply another form of mysticism and does not make it possible to manipulate the world for our own benefit. An obscurantist holism has been tried and it has failed. The world is not one huge organism that regulates itself to some good end as the believers in the Gaia hypothesis believe. While in some theoretical sense "the trembling of a flower is felt on the farthest star," in practice my gardening has no effect on the orbit of Neptune because the force of gravitation is extremely weak and falls off very rapidly with distance. So there is clearly truth in the belief that the world can be broken up into independent parts. But that is not a universal direction for the study of all nature. A lot of nature, as we shall see, cannot be broken up into independent parts to be studied in isolation, and it is pure ideology to suppose that it can.
The problem is to construct a third view, one that sees the entire world neither as an indissoluble whole nor with the equally incorrect, but currently dominant, view that at every level the world is made up of bits and pieces that can be isolated and that have properties that can be studied in isolation. Both ideologies, one that mirrors the premodern feudal social world, and the other that mirrors the modern competitive individualist entrepreneurial one, prevent us from seeing the full richness of interaction in nature. In the end, they prevent a rich understanding of nature and prevent us from solving the problems to which science is supposed to apply itself.
In the ensuing chapters, we will look in some detail at particular manifestations of the modern scientific ideology and the false paths down which it has led us. We will consider how biological determinism has been used to explain and justify inequalities within and between societies and to claim that those inequalities can never be changed. We will see how a theory of human nature has been developed using Darwin's theory of evolution by natural selection to claim that social organization is also unchangeable because it is natural. We will see how problems of health and disease have been located within the individual so that the individual becomes a problem for society to cope with rather than society becoming a problem for the individual. And we will see how simple economic relationships masquerading as facts of nature can drive the entire direction of biological research and technology.
While these examples are meant to disillusion the reader about the objectivity and vision of transcendent truth claimed by scientists, they are not intended to be antiscientific or to suggest that we should give up science in favor of, say, astrology or thinking beautiful thoughts. Rather, they are meant to acquaint the reader with the truth about science as a social activity and to promote a reasonable skepticism about the sweeping claims that modern science makes to an understanding of human existence. There is a difference between skepticism and cynicism, for the former can lead to action and the latter only to passivity. So these pages have a political end, too, which is to encourage the readers not to leave science to the experts, not to be mystified by it, but to demand a sophisticated scientific understanding in which everyone can share.
## **_All in the Genes?_**
**_O_** ur society was born, at least politically, in revolutions of the seventeenth century in Britain and the eighteenth century in France and America. Those revolutions swept out an old order characterized by aristocratic privilege and a relative fixity of persons in the society. The bourgeois revolutions in England, France, and America claimed that this old society and its ideology were illegitimate, and the ideologues of those revolutions produced and legitimized an ideology of liberty and equality. Diderot and the Encyclopedists and Tom Paine were the theorists of a society of "liberté, égalité, fraternité," of all men created equal. The writers of the Declaration of Independence asserted that political truths were "self-evident; that all men are created equal; that they are endowed by their creator with certain unalienable rights; that among these are life, liberty, and the pursuit of happiness" (by which, of course, they meant the pursuit of money). They meant literally all _men,_ because women were not given the right to vote in the United States until 1920; Canada enfranchised women a little sooner, in 1918—but not in provincial elections in Quebec until 1940. And of course they didn't mean _all_ men, because slavery continued in the French dominions and in the Caribbean until the middle of the nineteenth century. Blacks were defined by the United States Constitution as only three-fifths of a person, and for most of the history of English parliamentary democracy, a man had to have money to vote.
To make a revolution, you need slogans that appeal to the great mass of people, and you could hardly get people to shed blood under a banner that read "Equality for some." So the ideology and the slogans outstrip the reality. For if we look at the society that has been created by those revolutions, we see a great deal of inequality of wealth and power among individuals, between sexes, between races, between nations. Yet we have heard over and over again in school and had it drummed into us by every organ of communication that we live in a society of free equals. The contradiction between the claimed equality of our society and the observation that great inequalities exist has been, for North Americans at least, the major social agony of the last 200 years. It has motivated an extraordinary amount of our political history. How are we to resolve the contradiction of immense inequalities in a society that claims to be founded on equality?
There are two possibilities. We might say that it was all a fake, a set of slogans meant to replace a regime of aristocrats with a regime of wealth and privilege of a different sort, that inequality in our society is structural and an integral aspect of the whole of our political and social life. To say that, however, would be deeply subversive, because it would call for yet another revolution if we wanted to make good on our hopes for liberty and equality for all. It is not a popular idea among teachers, newspaper editors, college professors, successful politicians, indeed anyone who has the power to help form public consciousness.
The alternative, which has been the one taken since the beginning of the nineteenth century, has been to put a new gloss on the notion of equality. Rather than equality of _result,_ what has been meant is equality of _opportunity._ In this view of equality, life is a foot race. In the bad old days of the _ancien régime,_ the aristocrats got to start at the finish line whereas all the rest of us had to start at the beginning, so the aristocrats won. In the new society, the race is fair: everyone is to begin at the starting line and everyone has an equal opportunity to finish first. Of course, some people are faster runners than others, and so some get the rewards and others don't. This is the view that the old society was characterized by _artificial_ barriers to equality, whereas the new society allows a natural sorting process to decide who is to get the status, wealth, and power and who is not.
Such a view does not threaten the status quo, but on the contrary supports it by telling those who are without power that their position is the inevitable outcome of their own innate deficiencies and that, therefore, nothing can be done about it. A remarkably explicit recent statement of this assertion is the one by Richard Herrnstein, a psychologist from Harvard, who is one of the most outspoken modern ideologues of natural inequality. He wrote,
the privileged classes of the past were probably not much superior biologically to the downtrodden which is why revolution had a fair chance of success. By removing artificial barriers between classes society has encouraged the creation of biological barriers. When people can take their natural level in society, the upper classes will, by definition, have greater capacity than the lower.
We are not told precisely what principle of biology guarantees that biologically inferior persons cannot seize power from biologically superior ones, but it is not logic that is at issue here. Such statements as Herrnstein's are meant to convince us that although we may not live in the best of all _conceivable_ worlds, we live in the best of all _possible_ worlds. The social entropy has been maximized so that we have as much equality as possible because the structure is essentially one of equality, and whatever inequalities are left over are not structural but based on innate differences between individuals. In the nineteenth century this was also the view, and education was seen as the lubricant that would guarantee that the race of life was run smoothly. Lester Frank Ward, a giant of nineteenth-century sociology, wrote, "Universal education is the power which is destined to overthrow every species of hierarchy. It is destined to remove all artificial inequality and leave the natural inequalities to find their true level. The true value of a newborn infant lies in its naked capacity for acquiring the ability to do."
This was echoed 60 years later by Arthur Jensen at the University of California, who wrote about the inequality of intelligence of Blacks and whites: "We have to face it, the assortment of persons into occupational roles simply is not fair in any absolute sense. The best we can hope for is that true merit given equality of opportunity acts as a basis for the natural assorting process."
Simply to assert that the race of life is fair and that different people have different intrinsic abilities to run it is not enough to explain the observations of inequality. Children seem, by and large, to acquire the social status of their parents. About 60 percent of the children of "blue collar" workers remain "blue collar," while about 70 percent of "white collar" workers' children are "white collar." But these figures vastly overestimate the amount of social mobility. Most people who have passed from "blue collar" to "white collar" jobs have passed from factory production-line jobs to office production-line jobs or have become sales clerks, less well paid, less secure, doing work just as numbing of the soul and body as the factory work done by their parents. The children of gas station attendants usually borrow money, and the children of oil magnates usually lend it. The chance that Nelson Rockefeller would have wound up pumping gas was pretty close to zero.
If we live in a meritocracy, in which each person can rise to the status allowed by his or her innate capacities, how do we explain this passage of social power from parent to offspring? Are we really just back in an old aristocratic situation? The naturalistic explanation is to say that not only do we differ in our innate capacities but that these innate capacities are themselves transmitted from generation to generation biologically. That is to say, they are in our genes. The original social and economic notion of inheritance has been turned into biological inheritance.
But even the claim that the intrinsic ability to win success is inherited in the genes is not sufficient to justify an unequal society. After all, we might assert that there ought not to be any particular relationship between what one can accomplish and what social and psychic rewards are given. We might give the same material and psychic rewards to house painters and picture painters, to surgeons and to barbers, to professors who give lectures, and to the janitors who come in and clean up the classroom afterward. We might create a society on whose banners are inscribed, "From each according to his ability, to each according to his need."
To meet this objection to an unequal society there has been developed a biological theory of human nature that says that while the differences between us are in our genes, there are certain inborn similarities among us all. These similarities of human nature guarantee that differences in ability will be converted into differences in status, that society is naturally hierarchical, and that a society of equal reward and status is biologically impossible. We might pass laws requiring such equality, but the moment the vigilance of the state was relaxed we would return to "doing what comes naturally."
These three ideas—that we differ in fundamental abilities because of innate differences, that those innate differences are biologically inherited, and that human nature guarantees the formation of a hierarchical society—when taken together, form what we can call the _ideology of biological determinism._
The idea that blood will tell was not invented by biologists. It is a dominant theme of nineteenth-century literature, and one can hardly appreciate the most praised and popular writers of the last century without seeing how a theory of innate difference informed their work. Think of Dickens's _Oliver Twist._ When Oliver first meets young Jack Dawkins, the Artful Dodger, on the road to London, a remarkable contrast in body and spirit is established. The Dodger is described as "a snub-nosed, flat-browed, common-faced boy ... with rather bow-legs, and little, sharp, ugly eyes," and his English was not the best. What can we expect from a 10-year-old street urchin with no family, no education, and only the lowest criminals of London for companions? Oliver's speech, however, is perfect (he knows when to use the subjunctive) and his manner is genteel. He is described as a pale, thin child, but with a good sturdy spirit in his breast. Yet Oliver was raised from birth in the most degrading of nineteenth-century British institutions, the parish workhouse, an orphan with no education and little to eat. He is described as having spent the first nine years of his life rolling about on the floor all day "without the inconvenience of too much food or too much clothing." Where amid the oakum-pickings did Oliver garner that sensitivity of soul and perfection of English grammar? _Oliver Twist_ is a mystery novel, and that is its mystery. The answer is that although his food was gruel, his blood was upper-middle-class. His mother was the daughter of a naval officer. His father's family was well off and socially ambitious.
A similar theme is central to George Eliot's Daniel Deronda. We first meet Daniel, the young stepson of an English baronet, wasting his time in a fashionable gambling spa. When he becomes a bit older, he suddenly has mysterious longings for things Hebrew. He falls in love with a Jewish woman, studies the Talmud, and converts. The reader will not be surprised to learn that he is the son of a Jewish actress whom he has never seen but whose blood tells. Nor is this a madness only of the Anglo-Saxons. The Rougon-Macquart novels of Émile Zola were deliberately written as a kind of experimental literature to illustrate the discoveries of nineteenth-century anthropology. In the preface, Zola tells us that "heredity has its laws just like gravitation." The Rougon-Macquarts are a family descended from the two lovers of one woman, one of whom was a solid, industrious peasant, while the other was a wastrel and degenerate. From the dependable peasant descend solid, honest stock, while from the degenerate ancestor descend a long line of social misfits and criminals including the famous Nana, who was a nymphomaniac from early childhood, and her mother, Gervaise, the laundress, who despite beginning a solid entrepreneurial life, lapses into her natural indolence. When Gervaise's husband, Copeau, the father of Nana, was admitted to hospital with the D.T.s, the first question the physician asked him was, "Did your father drink?" The public consciousness of the period both in Europe and North America was permeated with the notion that intrinsic differences in temperament and merit will finally dominate any mere effect of education and environment.
The fictional Rougon-Macquarts are seen again in the equally fictional but supposedly real family of Kallikaks, who graced virtually every textbook of American psychology until the Second World War. The Kallikaks were supposed to be two halves of a family descended from two women of contrasting nature and a common father. This piece of academic fiction was meant to convince malleable young minds that criminality, laziness, alcoholism, and incest were inborn and inherited.
Nor were supposedly innate differences restricted to individual variation. Nations and races were said to be characterized by innate temperamental and intellectual differences. These claims were made not by racists, demagogues, and fascist know-nothings but by the leaders of the American academic, psychological, and sociological establishments. In 1923, Carl Brigham, who was later secretary of the College Entrance Examination Board, produced a study of intelligence under the direction of R.M. Yerkes, professor of psychology at Harvard and the president of the American Psychological Association. The study asserted: "We must assume that we are measuring inborn intelligence. We must face the possibility of racial admixture here in America that is infinitely worse than that faced by any European country for we are incorporating the Negro into our racial stock. The decline of the American intelligence will be more rapid... owing to the presence here of the Negro."
Yet another president of the American Psychological Association said that whenever there has been mixed breeding with the Negro, there has been deterioration of civilizations. Louis Agassiz, one of the most famous zoologists of the nineteenth century, reported that the skull sutures of Negro babies closed earlier than the sutures of white babies, so their brains were entrapped, and it would be dangerous to teach them too much. Perhaps the most extraordinary of claims was that of Henry Fairfield Osborne, president of the American Museum of Natural History and one of America's most eminent and prestigious paleontologists, who worked out the sequence of evolution of the horse. He wrote,
The northern races invaded the countries to the south, not only as conquerors but as contributors of strong moral and intellectual elements to a more or less decadent civilization. Through the Nordic tide which flowed into Italy came the ancestors of Raphael, Leonardo, Galileo, Titiano; also, according to Günther, of Giotto, Botticelli, Petrarca, and Tasso. Columbus, from his portraits and from busts, _whether authentic or not,_ was clearly of Nordic ancestry. [emphasis added]
Whether authentic or not, indeed! Over and over again, leading intellectuals have assured their audiences that modern science shows that there are inborn racial and individual differences in ability. Nor have modern biologists taken a different view. Except for a brief interruption around the time of the Second World War, when the crimes of Nazism made claims of innate inferiority extremely unpopular, biological determinism has been the main-stream commitment of biologists. Yet these claims are made without a shred of evidence and in contradiction to every principle of biology and genetics.
To realize the error of these claims, we need to understand what is involved in the development of an organism. First, we are not determined by our genes, although surely we are influenced by them. Development depends not only on the materials that have been inherited from parents—that is, the genes and other materials in the sperm and egg—but also on the particular temperature, humidity, nutrition, smells, sights, and sounds (including what we call education) that impinge on the developing organism. Even if I knew the complete molecular specification of every gene in an organism, I could not predict what that organism would be. Of course, the difference between lions and lambs is almost entirely a consequence of the difference in genes between them. But variations among individuals within species are a unique consequence of both genes and the developmental environment in a constant interaction. Moreover, curiously enough, even if I knew the genes of a developing organism and the complete sequence of its environments, I could not specify the organism.
There is yet another factor at work. If we count the number of bristles under the wing of a fruitfly, for example, we find that there is a different number on the left side than on the right. Some have more bristles on the left, some more on the right; there is no average difference. So, there is a kind of fluctuating asymmetry. An individual fruitfly, however, has the same genes on its left side as on its right. Moreover, the tiny size of a developing fruitfly and the place it develops guarantee that both left and right sides have had the same humidity, the same oxygen, the same temperature. The differences between left and right side are caused neither by genetic nor by environmental differences but by random variation in growth and division of cells during development: _developmental noise._
This chance element in development is an important source of variation. Indeed, in the case of the fruitfly bristles, there is as much variation consequent on developmental noise as there is from genetic and environmental variation. We do not know in human beings, for example, how much of the difference between us is a consequence of the random differences in the growth of neurons during our embryonic life and early childhood. It is our common prejudice that even if one had practiced the violin from a very early age, one would not be able to play as well as Menuhin, and we think of him as having special neuronal connections. But that is not the same as saying that those neuronal connections were coded in his genes. There may be large random differences in the growth of our central nervous systems. It is a fundamental principle of developmental genetics that every organism is the outcome of a unique interaction between genes and environmental sequences modulated by the random chances of cell growth and division, and that all these together finally produce an organism. Moreover, an organism changes throughout its entire life. Human beings change their size, not only growing larger as children, but as they grow old, growing smaller as their joints and bones shrink.
A more sophisticated version of genetic determinism agrees that organisms are a consequence of both environmental and genetic influences but describes differences between individuals as differences in _capacity._ This is the empty bucket metaphor. We each begin life as an empty bucket of a different size. If the environment provides only a little water, then all these buckets will have the same amount in them. But if an abundance is provided from the environment, then the small buckets will overflow and the large ones will hold more. In this view, if every person were allowed to develop to his or her genetic capacity, there would indeed be major differences in ability and performance, and these would be fair and natural.
But there is no more biology in the metaphor of innate capacity than there is in the notion of fixed genetic effects. The unique interaction between organism and environment cannot be described by differences in capacity. It is true that if two genetically different organisms developed in exactly the same environment, they would be different, but that difference cannot be described as different capacities because the genetical type that was superior in one environment may be inferior in a second developmental environment. For example, strains of rats can be selected for better or poorer ability to find their way through a maze, and these strains of rats pass on their differential ability to run the maze to their offspring, so they are certainly genetically different in this respect. But if exactly the same strains of rats are given a different task, or if the conditions of learning are changed, the bright rats turn out to be dull and the dull rats turn out to be bright. There is no general genetic superiority of one rat strain over another in finding its way through a problem.
A more subtle and mystifying approach to biological determinism rejects both the genetic fixity of the first view and the capacity metaphor of the second and is, instead, statistical. Essentially, it states the problem as one of partitioning the effects of environment and genes so that we can say that, perhaps, 80 percent of the difference among individuals is caused by their genes and 20 percent by their environment. Of course, these differences must be on a population level rather than an individual level. It would make no sense at all to say that of someone's height of five feet eleven and a half inches, five feet two were a result of her genes and the other nine and a half inches were put there by the food she ate. The statistical view considers the proportion of _variation_ among individuals rather than partitioning a particular individual measurement. The statistical approach tries to assign some proportion of all of the variation among individuals or groups to variation among their genes, and a second proportion that results from variation among their environments.
The implication is that if most of the variation in, say, intelligence among individuals is a consequence of variation among their genes, then manipulating the environment will not make much difference. It is often said, for example, that 80 percent of the variation among individual children in their I.Q. performance is caused by variation in their genes and only 20 percent by variation in their environments. The result is that the greatest possible amelioration of environment could not eliminate more than 20 percent of differences among individuals, and the 80 percent would still be there because it is a consequence of genetic variation. This is a completely fallacious although plausible-sounding argument. There is no connection whatsoever between the variation that can be ascribed to genetic differences as opposed to environmental differences and whether a change in environment will affect performance and by how much. We should remember that any very ordinary arithmetic student in primary school in Canada can correctly add a column of figures vastly more quickly than the most intelligent Ancient Roman mathematician, who had to struggle with cumbersome X's, V's, and I's. That same ordinary student can multiply two five-digit numbers with a $10 hand-held calculator more quickly and accurately than a professor of mathematics could have a century ago.
A change in environment, in this case of cultural environment, can change abilities by many orders of magnitude. Moreover, the differences between individuals are abolished by cultural and mechanical inventions. Differences that can be ascribed to genetic differences and that appear in one environment may disappear completely in another. Although there may be biologically based average differences in physique and strength between a random group of men and random group of women (and these are less than usually supposed), these differences rapidly become irrelevant and disappear from practical view in a world of electrically driven hoists, power steering, and electronic controls. So the proportion of variation in a population as a consequence of variation in genes is not a fixed property but one that varies from environment to environment. That is, how much difference among us is a consequence of genetic differences between us depends, curiously enough, on environment.
Conversely, how much difference there is between us that is a consequence of environmental variation in our life histories depends on our genes. We know from experiments that organisms that have some particular genes are very sensitive to environmental variation while other individuals with different genes are insensitive to environmental variation. Environmental variation and genetic variation are not independent causal pathways. Genes affect how sensitive one is to environment, and environment affects how relevant one's genetic differences may be. The interaction between them is indissoluble, and we can separate genetic and environmental effects statistically only in a particular population of organisms at a particular moment with a particular set of specified environments. When an environment changes, all bets are off.
The contrast between genetic and environmental, between nature and nurture, is not a contrast between fixed and changeable. It is a fallacy of biological determinism to say that if differences are in the genes, no change can occur. We know this to be true from medical evidence alone. There are many so-called inborn errors of metabolism in which a defective gene results, in normal circumstances, in a defective physiology. An example is Wilson's disease, a genetic defect that prevents its sufferers from detoxifying the copper that we all consume in minute quantities in our ordinary food. The copper builds up in the body and eventually causes nervous degeneration and finally death, some time in adolescence or early adulthood. Nothing could be more perfectly described as a genetic disorder. Yet people with this defective gene can lead a perfectly normal life and have a normal development by taking a pill that helps them get rid of the copper, and they are then indistinguishable from anyone else.
It is sometimes said that examples of changing the conditions of performance, such as the invention of Arabic numerals, or the calculator, or providing a pill, are beside the point because we are interested in some sort of basic unaided, naked ability. But there are no measures of "unaided" ability, nor are we really interested in them. There are some people who can remember long columns of figures and others who are good at adding and multiplying large numbers in their heads. So why do we give written I.Q. tests, which, after all, are simply giving the crutch of paper and pencil to people who do not have the "unaided" ability to do mental arithmetic? Indeed, why do we allow people taking mental tests to wear eyeglasses, if we are interested in culturally unmodified "naked" abilities? The answer is that we have no interest in arbitrarily defined abilities, but are concerned with differences in the ability to carry out _socially constructed_ tasks that are relevant to the structure of our actual social lives.
Aside from the conceptual difficulties of trying to ascribe separate effects to genes and environment, there are severe experimental difficulties in detecting the influence of genes, especially when we deal with human beings. How do we decide whether genes influence differences in some trait? In all organisms the process is the same. We compare individuals who are differently related to one another, and if more closely related individuals are more similar than are more distantly related ones, we ascribe some power to the genes. But herein lies the deep difficulty of human genetics. Unlike experimental animals, people who are more closely related to each other not only share more genes in common but they also share environment in common because of the family and class structure of human societies. The observation that children resemble their parents in some trait does not distinguish between similarity that comes from genetic similarity and similarity that arises from environmental resemblance. The resemblance of parents and children is the observation to be explained. It is not evidence for genes. For example, the two social traits that have the highest resemblance between parents and children in North America are religious sect and political party. Yet even the most ardent biological determinist would not seriously argue that there is a gene for Episcopalianism or voting Social Credit.
The problem is to distinguish genetic similarity from environmental similarity. It is for this reason that so much emphasis has been put on twin studies in human genetics. The idea is that if twins are more similar than ordinary sibs or if twins raised in completely isolated families are still similar, then this surely must be evidence for genes. In particular, there has been a fascination with a study of identical twins raised apart. If identical twins—that is, twins sharing all the same genes—are similar even though raised apart, then their traits must be strongly genetically influenced. Much of the claim for the high heritability of I.Q., for example, comes from studies of identical twins raised apart.
Only three such studies have been published. The first and largest set of studies was reported by Sir Cyril Burt. This was the only study that claimed no similarity between the family circumstances of the families that raised separated twins. It also claimed a heritability of 80 percent for I.Q. performance. However, careful investigation by Oliver Gillie of the _Times_ of London and Professor Leon Kamin at Princeton revealed that Burt had simply made up the numbers and made up the twins. He even made up the collaborators whose names appeared with his in the publications. We need consider these claims no further. They represent one of the great scandals of modern psychology and biology.
When we look at the other studies, which actually give family details of the separated twins, we realize that we live in a real world and not in a Gilbert and Sullivan operetta. The reason that twins are separated at birth may be that their mother has died in childbirth, so that one twin is raised by an aunt and another by a best friend or grandmother. Sometimes the parents cannot afford to keep both children so they give one to a relative. In fact, the studied twins were not raised apart at all. They were raised by members of the same extended family, in the same small village. They went to school together. They played together. Other adoption studies of human I.Q. that are said to demonstrate the effect of genes have their own experimental difficulties, including the failure to match children by age, extremely small samples, and biased selection of cases for study. There is a strong effort on the part of parents of many twins to make them as similar as possible. They are given names beginning with the same letter and are dressed alike. International twin conventions give prizes for the most similar twins. One twin study advertised in the newspapers and offered a free trip to Chicago for identical twins, thus attracting those who were the most similar. As a consequence of such biases, there is at present simply no convincing measure of the rple of genes in influencing human behavioral variation.
One of the major biological ideological weapons used to convince people that their position in society is fixed and unchangeable and, indeed, fair is the constant confusion between inherited and unchangeable. This confusion is nowhere more manifest than in the very studies of adoptions that are meant to measure biological similarities. In human populations, one carries out an adoption study like that of separation of identical twins to try to break the connection between resemblance that comes from genetic sources and resemblance that comes from the sources of family similarity. If adopted children resemble their biological parents more closely than they resemble their adopting parents, then the geneticists quite correctly regard this as evidence for the influence of genes. When one looks at all the studies of adoption in order to study the genetic influence on intelligence, there are two constant results.
First, adopted children do resemble their biological parents in the sense that the higher the I.Q. score of the biological parent, the higher the I.Q. score of the child who was adopted. So, biological parents are having some influence on the I.Q. of their children even though those children are adopted early, and putting aside the possibility of prenatal nutritional differences or extremely early stimulation, it would be reasonable to say that genes have some influence on I.Q. scores. We can only speculate about the source of genetic influence. There is a premium on speed in I.Q. testing, and genes might have some influence on reaction times or general speed of central nervous processes.
The second feature of adoption studies is that the I.Q. test scores of the children are about 20 points higher than those of their biological parents. It is still the case that the biological parents with the higher I.Q. scores have children with higher scores, but the children as a group have moved well ahead of their biological parents. In fact, the average I.Q. scores of these adopted children are about equal to the average I.Q. of the adopting parents, who always do much better on I.Q. tests than the biological parents. What is at stake here is the difference between _correlation_ and _identity._ Two variables are positively correlated if higher values of one are matched with higher values of the other. The ordered set of numbers 100, 101, 102, and 103 is perfectly correlated with the set of 120, 121, 122, and 123 because each increase in one set is perfectly matched by an increase in the other. Yet the two sets of numbers are clearly not identical, differing as they do by 20 units on the average. So the I.Q. of parents may be excellent predictors of the I.Q.s of their children in the sense that higher values for parents are matched with higher values for offspring, but the _average_ I.Q. value of their children may be much greater. For the geneticist, it is the _correlation_ that indicates the role of genes; the heritability predicts nothing about changes in the group average from generation to generation. The adoption studies are a revelation of the meaning of I.Q. tests and of the social reality of adoption.
First, what do I.Q. tests actually measure? They are a combination of numerical, vocabulary, educational, and attitudinal questions. They ask such things as "Who was Wilkins McCawber?", "What is the meaning of 'sudiferous'?", "What should a girl do if a boy hits her?" (Hitting him back is _not_ the right answer!) And how do we know that someone who does well on such a test is _intelligent_? Because, in fact, the tests were originally standardized to pick out precisely those children in a class whom the teacher had already labeled intelligent. That is, I.Q. tests are instruments for giving an apparently objective and "scientific" gloss to the social prejudices of educational institutions.
Second, people who decide on an early adoption for their children are usually working-class or unemployed people who do not share in the education and culture of the middle class. People who adopt children, on the other hand, are usually middle-class and have an appropriate education and cultural experience for the content and intent of I.Q. tests. So adopting parents have, as a group, much higher I.Q. performances than the parents who have chosen adoption for their children. The educational and family environment in which these children are then raised has the expected result of raising all their I.Q.s even though there is evidence for some genetic influence from their biological parents.
These results of adoption studies illustrate perfectly why we cannot answer a question about how much something can be changed by answering a different question, namely, are there genes influencing the trait? If we wanted seriously to ask the question posed by Arthur Jensen in his famous article "How much can we boost I.Q. and scholastic achievement?", the only way we could answer would be to try to boost I.Q. and scholastic achievement. We do not answer it by asking, as Jensen did, whether there is a genetic influence on I.Q., because to be genetic is not to be unchangeable.
Biological determinists claim that there are not only differences in ability among individuals but that these individual differences explain racial differences in social power and success. It is hard to know how one would get evidence about Black-white differences that did not totally confound genetic and environmental variation. Inter-racial adoptions, for example, are uncommon, especially of white children adopted by Black foster parents. Occasional evidence does appear, however.
In Dr. Bernardo's homes in Britain, where children are taken as orphans soon after birth, a study was done of intelligence testing of children of Black and white ancestry. Several tests were given at various ages, and small differences were found in the I.Q. performance between these groups, but these were not statistically significant. If nothing more was said about it, most of the readers would assume that the small differences showed whites were better than Blacks. But in fact the reverse was true. The differences were not statistically significant, but where there were any differences, they were in favor of Blacks. There is not an iota of evidence of any kind that the differences in status, wealth, and power between races in North America have anything to do with the genes, except, of course, for the socially mediated effects of the genes for skin color. Indeed, there is in general a great deal less difference genetically between races than one might suppose from the superficial cues we all use in distinguishing races. Skin color, hair form, and nose shape are certainly influenced by genes, but we do not know how many such genes there are, or how they work. On the other hand, when we look at genes we do know something about, genes that influence our blood type, for example, or genes for the various enzyme molecules essential to our physiology, we find that although there is a tremendous amount of variation from individual to individual, there is remarkably little variation on the average between major human groups. In fact, about 85 percent of all identified human genetic variation is between any two individuals from the same ethnic group. Another 8 percent of all the variation is between ethnic groups within a race—say, between Spaniards, Irish, Italians, and Britons—and only 7 percent of all human genetic variation lies on the average between major human races like those of Africa, Asia, Europe, and Oceania.
So we have no reason _a priori_ to think that there would be any genetic differentiation between racial groups in characteristics such as behavior, temperament, and intelligence. Nor is there an iota of evidence that social classes differ in any way in their genes except insofar as ethnic origin or race may be used as a form of economic discrimination. The nonsense propagated by ideologues of biological determinism that the lower classes are biologically inferior to the upper classes, that all the good things in European culture come from the Nordic groups, is precisely nonsense. It is meant to legitimate the structures of inequality in our society by putting a biological gloss on them and by propagating the continual confusion between what may be influenced by genes and what may be changed by social and environmental alterations.
The vulgar error that confuses heritability and fixity has been, over the years, the most powerful single weapon that biological ideologues have had in legitimating a society of inequality. Since as biologists they must know better, one is entitled to at least a suspicion that the beneficiaries of a system of inequality are not to be regarded as objective experts.
## **_Causes and Their Effects_**
**_M_** odern biology is characterized by a number of ideological prejudices that shape the form of its explanations and the way its researches are carried out. One of those major prejudices is concerned with the nature of causes. Generally one looks for _the_ cause of an effect, or even if there are a number of causes allowed, one supposes that there is a major cause and the others are only subsidiary. And in any case, these causes are separated from each other, studied independently, and manipulated and interfered with in an independent way. Moreover, these causes are usually seen to be at an individual level, the individual gene or the defective organ or an individual human being who is the focus of internal biological causes and external causes from an autonomous nature.
This view of causes is nowhere more evident than in our theories of health and disease. Any textbook of medicine will tell us that the cause of tuberculosis is the tubercle bacillus, which gives us the disease when it infects us. Modern scientific medicine tells us that the reason we no longer die of infectious diseases is that scientific medicine, with its antibiotics, chemical agents, and high-technology methods of caring for the sick, has defeated the insidious bacterium.
What is the cause of cancer? The cause is the unrestricted growth of cells. That runaway growth, in turn, is a consequence of the failure of certain genes to regulate cell division. So we get cancer because our genes are not doing their business. It used to be that people thought that viruses were a major cause of cancer, and a great deal of money and time has been spent looking for the viral causes of cancer in humans without success. Biology has moved on from the time when viruses were all the rage to a time when genes are much more trendy.
Alternatively, there are environmental insult theories of the causes of cancer. Cancers are caused, we are told, by asbestos or by PVC or by a host of natural chemicals over which we have no control, and although they are present in very low concentrations, we are exposed to them over our whole lives. So, just as we will avoid dying from tuberculosis by dealing with the bug that causes it, so we will avoid dying from cancer by getting rid of particularly nasty chemicals in the environment. It is certainly true that one cannot get tuberculosis without a tubercle bacillus, and the evidence is quite compelling that one cannot get the cancer mesothelioma without having ingested asbestos or related compounds. But that is not the same as saying that _the_ cause of tuberculosis is _the_ tubercle bacillus and _the_ cause of mesothelioma is asbestos. What are the consequences for our health of thinking in this way? Suppose we note that tuberculosis was a disease extremely common in the sweatshops and miserable factories of the nineteenth century, whereas tuberculosis rates were much lower among country people and in the upper classes. Then we might be justified in claiming that _the_ cause of tuberculosis is unregulated industrial capitalism, and if we did away with that system of social organization, we would not need to worry about the tubercle bacillus. When we look at the history of health and disease in modern Europe, that explanation makes at least as good sense as blaming the poor bacterium.
What is the evidence for the benefits of modern scientific medicine? Certainly we live a great deal longer than our ancestors. In 1890, the years of life expected for a white child at birth in North America were only 45, whereas now the expected life span is 75 years, but that is not because modern medicine has prolonged the life of elderly and sick people. A very large fraction of the change in the average life expectancy is a tremendous reduction in infant mortality. Before the turn of the century and especially earlier in the nineteenth century, there was a considerable chance that a child never got to be a year old—in 1860, the infant mortality rate in the U.S. was 13 percent—, so the average life expectancy for the population as a whole was reduced considerably by this early death. The gravestones of people who died in the middle of the nineteenth century indicate a remarkable number of deaths at an old age. In fact, scientific medicine has done little to add years for people who have already reached their maturity. In the last 50 years, only about four months have been added to the expected life span of a person who is already 60 years old.
As we all know, in modern Europe women live longer than men, but they used not to. Before the turn of the century, women died sooner than men did, and a common explanation offered by scientific medicine is that a leading cause of death in women in the days before modern medicine was childbirth fever. According to this view, modern antiseptic medicine and hospital practice has been a major life saver for younger women during their childbearing years. But a look at the statistics reveals that child-birth fever was a minor cause of death during the nineteenth century, even of women of childbearing age, and was certainly not the cause of the excess mortality of women. Nearly all that excess mortality was a consequence of tuberculosis, and when tuberculosis ceased to be a major killer, women ceased to have a shorter life span than did men. A leading cause of mortality in young children was scalds and burns, especially among young girls because, of course, girls spent a great deal of time in very dangerous conditions, around open kitchen fires. Their young brothers spent a good deal of time outside the household, in workshops, admittedly not in the most favorable of working conditions, but somewhat less dangerous than the family hearth.
We return, then, to tuberculosis and the other infectious diseases that were such killers in the nineteenth century and the early part of the twentieth. An examination of the causes of death, first systematically recorded in the 1830s in Britain and a bit later in North America, show that most people did, indeed, die of infectious disease and in particular of respiratory diseases. They died of tuberculosis, of diphtheria, of bronchitis, of pneumonia, and particularly among children they died of measles and the perennial killer, smallpox. As the nineteenth century progressed, the death rate from all these diseases decreased continuously. Smallpox was dealt with by a medical advance, but one that could hardly be claimed by modern scientific medicine, since smallpox vaccine was discovered in the eighteenth century and already was quite widely used by the early part of the nineteenth. The death rates from the major killers like bronchitis, pneumonia, and tuberculosis fell rather regularly during the nineteenth century, with no obvious cause. There was no observable effect on the death rate after the germ theory of disease was announced in 1876 by Robert Koch. The death rate from these infectious diseases simply continued to decline as if Koch had never lived. By the time chemical therapy was introduced for tuberculosis in the earlier part of this century, more than 90 percent of the decrease in the death rate from that disease had already occurred.
One of the most revealing cases is measles. At present, Canadian and American children do not often get measles because they are vaccinated against it, but a generation ago every schoolchild had measles, yet death from measles was extremely rare. In the nineteenth century, measles was the major killer of young children, and in many African countries today it remains the highest cause of death among children. Measles is a disease that everyone used to contract, for which there is no known cure or medical treatment, and which simply stopped being fatal to children in advanced countries.
The progressive reductions in the death rate were not a consequence, for example, of modern sanitation, because the diseases that were the major killers in the nineteenth century were respiratory and not waterborne. It is unclear whether simple crowding had much to do with the process, since some parts of our cities are quite as crowded as they were in the 1850s. As far as we can tell, the decrease in death rates from the infectious killers of the nineteenth century is a consequence of the general improvement in nutrition and is related to an increase in the real wage. In countries like Brazil today, infant mortality rises and falls with decreases and increases in the minimum wage. The immense betterment of nutrition also explains the drop in the higher rate of tuberculosis among women than among men. In the nineteenth century, and even long into the twentieth in Britain, working men were far better nourished than home-bound women. Often if meat could be afforded for the table in an urban working-class family in Britain, it was saved for the man. So there have been complex social changes, resulting in increases in the real earnings of the great mass of people, reflected in part in their far better nutrition, that really lie at the basis of our increased longevity and our decreased death rate from infectious disease. Although one may say that the tubercle bacillus causes tuberculosis, we are much closer to the truth when we say that it was the conditions of unregulated nineteenth-century competitive capitalism, unmodulated by the demands of labor unions and the state, that was the cause of tuberculosis. But social causes are not in the ambit of biological science, so medical students continue to be taught that the cause of tuberculosis is a bacillus.
In the past 20 years, precisely because of the decline in infectious disease as an important cause of ill health, other single causes have been raised as the culprits in disease. It is undoubtedly true that pollutants and industrial wastes are the immediate physiological causes of cancers, miners' black lung, textile workers' brown lung, and a host of other disorders. Moreover, it is undoubtedly true that there are trace amounts of cancer-causing substances even in the best of our food and water unpolluted by pesticides and herbicides that make farm workers sick. But to say that pesticides cause the death of farm workers or that cotton fibers cause brown lung in textile workers is to make a fetish out of inanimate objects. We must distinguish between _agents_ and _causes._ Asbestos fibers and pesticides are the agents of disease and disability, but it is illusory to suppose that if we eliminate these particular irritants that the diseases will go away, for other similar irritants will take their place. So long as efficiency, the maximization of profit from production, or the filling of centrally planned norms of production without reference to the means remain the motivating forces of productive enterprises the world over, so long as people are trapped by economic need or state regulation into production and consumption of certain things, then one pollutant will replace another. Regulatory agencies or central planning departments will calculate cost and benefit ratios where human misery is costed out at a dollar value. Asbestos and cotton lint fibers are not the causes of cancer. They are the agents of social causes, of social formations that determine the nature of our productive and consumptive lives, and in the end it is only through changes in those social forces that we can get to the root of problems of health. The transfer of causal power from social relations into inanimate agents that then seem to have a power and life of their own is one of the major mystifications of science and its ideologies.
Just as pollution is the most modern and up-to-date version of the external hostile forces of the physical world that are said to confront us, so simple internal forces, the genes, are now held responsible not only for human health in its normal medical sense but for a variety of social problems, among them alcoholism, criminality, drug addiction, and mental disorders. We are assured that if we could only find those genes that underlie alcoholism or the genes that have gone awry when we get cancer, then our problems will be over. The current manifestation of that belief in the importance of our inheritance in determining health and disease is the human genome sequencing project, a multibillion-dollar program of American and European biologists that is meant to take the place of space programs as the current great consumer of public money in the interest of conquering nature.
We know a great deal about what genes are made of and how they work at the most basic level. A gene is a long sequence of elements called nucleotides, of which there are only four kinds, identified by the letters A, T, C, and G. Every gene is a long string, of sometimes thousands or even tens of thousands of these A's, T's, C's, and G's, in a particular order: AATCCGGCATT and so on. This long sequence serves two functions. First, part of it specifies, like a code, exactly what the constitution of the protein molecules of our body will be. These proteins comprise the structural elements of which our bodies are made, the materials of our cells and tissues, and also the enzymes and hormones that make our metabolism possible. Corresponding to a particular sequence of A's, T's, C's, and G's, there will be produced by the machinery of the body a long molecule, a protein made up of simple elements, the amino acids. Each gene specifies the molecular makeup of a different protein. The particular sequence of amino acids that constitutes a particular protein is determined by the sequence of the nucleotides in the gene. If one or more nucleotides in the gene are changed, a different amino acid may be specified in the protein, which then may not be able to carry on its physiological function as well as before. In some cases, when a different nucleotide is substituted in a gene, less or even none at all of a particular protein may be manufactured because the machinery of the cell has a hard time recognizing the code.
Second, other parts of the gene, also sequences of nucleotides, form part of the machinery that turns off and turns on the production of proteins. In this way, although the same genes are in every part of the body during every part of the life of an organism, proteins corresponding to some genes will be produced at some times and in some parts of the body whereas they will not be produced at other times and in other parts of the body. The turning off and on of the production of the body's constituents is itself sensitive to external conditions. For example, if the sugar lactose is provided to the coliform bacterium, the presence of the sugar will signal the bacterial machinery to start making a protein that will break down the lactose and use it as a source of energy. The signal to start translating the gene code into protein is, in fact, detected by part of the gene itself. So, nucleotide sequences determine what kind of proteins organisms will make, and they are also part of the signaling machinery that controls the manufacturing of those proteins in response to external conditions. The signaling system is a mechanism by which environment interacts with genes in creating organisms.
Genes have yet a further function, which is to serve as a pattern for the manufacture of further copies of themselves. When cells divide and sperm and egg cells are produced, every new cell has a complete set of genes that are more or less identical to the genes in the old cells. These newly manufactured genes are copied directly from the gene molecules that previously existed. Since no chemical copying process is perfect, mistakes are made, so-called mutations, but these happen about one in a million copies as a rule.
The description I have just given of genes as determining the particular proteins that an organism can manufacture, as being part of the signaling system that responds to the environment in turning on and off the manufacture of protein, and as being the model for the manufacture of more of themselves, differs in a subtle way from the usual description of these relations. It is usually said that genes _make_ proteins and that genes are _self-replicating._ But genes can _make_ nothing. A protein is made by a complex system of chemical production involving other proteins, using the particular sequence of nucleotides in a gene to determine the exact formula for the protein being manufactured. Sometimes the gene is said to be the "blueprint" for a protein or the source of "information" for determining a protein. As such, it is seen as more important than the mere manufacturing machinery. Yet proteins cannot be manufactured without _both_ the gene and the rest of the machinery. Neither is more important. Isolating the gene as the "master molecule" is another unconscious ideological commitment, one that places brains above brawn, mental work as superior to mere physical work, information as higher than action.
Nor are genes self-replicating. They cannot make themselves any more than they can make a protein. Genes are made by a complex machinery of proteins that uses the genes as models for more genes. When we refer to genes as self-replicating, we endow them with a mysterious, autonomous power that seems to place them above the more ordinary materials of the body. Yet if anything in the world can be said to be self-replicating, it is not the gene, but the entire organism as a complex system.
The human genome sequencing project is an ambitious plan to write down the complex nucleotide sequence of A's, T's, C's, and G's for all the genes of human beings. With current technology, this is an immensely ambitious project that might take 30 years and occupy tens or even hundreds of billions of dollars. Of course, there is always the promise that more efficient technology will become available to reduce the magnitude of the job. But why would one like to know the complete sequence of A's, T's, C's, and G's that make up all the human genes?
The claim is that if we had a reference sequence from a so-called normal individual and we compared bits and pieces of the sequence from a person with some disorder, then we could locate the genetic defect that causes the disease. We could then translate the genetic code of the altered person into an altered protein to see what is wrong with the protein, and this might tell us how to treat the disease. So, if diseases are caused by altered defective genes and if we know what a normal gene looks like in its finest molecular detail, we then would know what to do about fixing the abnormal physiology. We would know what proteins have gone awry in cancer and could somehow or another invent ways to fix them. We might find particular altered proteins or missing proteins in schizophrenics or in manic-depressives or in alcoholics or in drug-dependent people, and with an appropriate medication relieve them of these terrible disabilities. Moreover, by comparing all the human genes in their molecular detail with the genes of, say, a chimpanzee or a gorilla, we would know why we are different from chimpanzees. That is, we would know what it is to be human.
What is wrong with this vision? The first error it makes is in talking about the human gene sequence as if all human beings were alike. In fact, there is an immense amount of variation from normal individual to normal individual in the amino acid sequence of their proteins because a given protein may have a variety of amino acid compositions without impairing its function. Each of us carries two genes for each protein, one that we got from our mother and one from our father. On the average, the amino acid sequence specified by our maternally inherited and paternally inherited genes differ in about one every 12 genes. In addition, because of the nature of the genetic code, many changes occur at the level of DNA that are not reflected in proteins themselves. That is, there are many different DNA sequences that correspond to the same protein. We do not have good estimates for humans at the moment, but if humans are anything like experimental animals, about one in every 500 nucleotides will differ in DNA taken from any two individuals chosen at random. Since there are roughly 3 billion nucleotides in human genes, any two human beings will differ on the average in about 600,000 nucleotides. And an average gene that is, say, 3,000 nucleotides long will differ between any two normal individuals by about 20 nucleotides. Who's genome, then, is going to provide the sequence for the catalog for the normal person?
Moreover, every normal person carries a large number of defective genes in single dose inherited from one parent that are covered up by a normal copy that they received from their other parent. So any piece of DNA that is sequenced will have a certain number of unknown defective genes entered into the catalog. When the DNA from a person with a disease is compared to the DNA from the standard normal sequence, it would be impossible to decide which if any of the multiple differences between the two DNAs is responsible for the disease. It would be necessary to look at a large population of normal and diseased people to see if one could find some common difference between them, but even this may not happen if the disease in question has a multiple genetic cause so that different people have the same disease for different reasons, even if all those reasons are a consequence of genetic changes. We already know this to be the case for one human disease called thalassemia. Thalassemia is a blood disorder in which less than the normal amount of hemoglobin is made, a disorder many Asians and Mediterranean Europeans suffer. The deficiency is a consequence of defects in the gene that codes for the hemoglobin protein. It turns out there are at least 17 different defects in different parts of the hemoglobin gene, all of which result in a reduction in the amount of hemoglobin produced. We would look in vain for a particular nucleotide that differed between thalassemia and normal people. In the case of thalassemia, extensive population studies have revealed the correct story, but the possession of a standard normal sequence of the entire human genome was of no help here, nor would it be in any other case.
The second problem of the human genome sequencing project is that it also claims that in knowing the molecular configuration of our genes, we know everything that is worth knowing about us. It regards the gene as determining the individual, and the individual as determining society. It isolates an alteration in a so-called cancer gene as _the_ cause of cancer, whereas that alteration in the gene may in turn have been caused by ingesting a pollutant, which in turn was produced by an industrial process, which in turn was the inevitable consequence of investing money at 6 percent. Once again, the impoverished notion of causation that characterizes modern biological ideology, a notion that confuses agents with causes, drives us in particular directions to find solutions for our problems.
Why, then, do so many powerful, famous, successful, and extremely intelligent scientists want to sequence the human genome? The answer is, in part, that they are so completely devoted to the ideology of simple unitary causes that they believe in the efficacy of the research and do not ask themselves more complicated questions. But in part the answer is a rather crass one. The participation in and the control of a multibillion-dollar, 30- or 50-year research project that will involve the everyday work of thousands of technicians and lower-level scientists is an extraordinarily appealing prospect for an ambitious biologist. Great careers will be made. Nobel Prizes will be given. Honorary degrees will be offered. Important professorships and huge laboratory facilities will be put at the disposal of those who control this project and who succeed in producing thousands of computer discs of human genome sequence. The realization that there are fairly straightforward economic and status rewards awaiting those who take part in the project has given rise to a powerful opposition to the project from within biology itself, from others who are doing a different kind of science and see their own careers and their own research threatened by the diversion of money, energy, and public consciousness. Some farsighted biologists have cautioned against the terrible public disillusionment that will follow the completion of the human genome sequencing project. The public will discover that despite the inflated claims of molecular biologists, people are still dying of cancer, of heart disease, of stroke, that institutions are still filled with schizophrenics and manic-depressives, that the war against drugs has not been won. The fear among many scientists is that by promising too much, science will destroy its public image and people will become cynical as, for example, they became cynical about the war on cancer, not to speak of the war on poverty.
Research scientists are involved in this struggle not only in their role as academics. Among molecular biologists who are professors in universities, a large proportion are also principal scientists or principal stockholders in biotechnology companies. Technology is a major industry and a major source of hoped-for profit for venture capital. The human genome sequencing project, to the extent that it creates new technologies at public expense, will provide very powerful tools to biotechnology companies for carrying out their production of commodities for sale on the market. Moreover, the success of the project will give greater faith in the power of biotechnology to produce useful products.
Nor are biotechnologies the only producers of commodities that stand to gain immensely from the human genome sequencing project. The project will consume vast quantities of chemical and mechanical commodities. There are commercial machines that manufacture DNA from small amounts of sample material. There are machines that automatically sequence DNA. These machines require the input of a variety of chemical materials all of which are sold at an immense profit by the companies that manufacture the machines. The human genome sequencing project is big business. The billions of dollars that are to be spent on it will go in no insignificant fraction into the annual dividends of productive enterprises.
We see in the genome sequencing project an aspect of biological science that is not often spoken of and is perhaps the most mystified of all. What are said to be fundamental discoveries about the nature of life often mask simple commercial relations that provide a powerful impetus for the direction and subject of research. The best documented example that we have of purely commercial interest driving what is said to be a fundamental discovery about nature is in agriculture. It is commonly said that the invention of hybrid corn has resulted in immense increases in the productivity of agriculture and the consequent feeding of hundreds of millions of people at low cost and with great efficiency. Whereas in the 1920s an average acre sown with maize in the cornbelt of North America might have yielded 35 bushels per acre, today it can yield 125 bushels. This is widely regarded as one of the greatest triumphs of basic genetics as applied to human welfare. But the truth is more interesting.
Hybrid corn is produced by crossing two true-breeding inbred varieties and planting the seed from that cross. These true-breeding inbred varieties are created by a long process of self-pollination to make each variety completely uniform genetically. A seed company will spend a certain number of years self-pollinating lines of corn until it gets uniform lines, and it will then sell to the farmer the seed that comes from crossing two of these lines. The inbred homogeneous lines themselves give rather poor yields, whereas the hybrid is superior in productivity both to the inbred lines and to the original open-pollinated population of corn from which the inbreds came. It is not the case that a cross between any two inbred homogeneous lines of corn will produce a hybrid with high yield. It is necessary to search among many such homogeneous inbred lines to find pairs that will do the trick.
The hybrid cross between the inbred lines has another quality, which is not much spoken about, a quality with a unique commercial value. If a farmer has a high-yielding variety of some crop, one that is resistant to disease and produces high commercial output as compared to the cost of inputs, his normal way of carrying on his business would be to save some of the seed of this high-yielding variety and plant it next year to again achieve high yields. Once the farmer acquired the seed of this wonderful variety, he would no longer have to pay again to reacquire it, because plants, like other organisms, reproduce themselves. But this self-reproduction presents a serious problem to someone who wants to make money by developing new varieties of organisms. For how will he make a profit if the moment he has sold the seed, its further production is in the hands of the person who bought it? He will get to sell it one time only, and then it will be distributed everywhere for nothing.
This is the problem of copy protection that also exists for computer software programs. The developer of computer software will be unwilling to devote time, energy, and money to developing a new program if the first purchasers can copy it and pass it around to their friends for virtually nothing. That has always been the problem of plant and animal breeding. Plant breeders and seed producers could never make much money because farmers, having bought the seed or the animal variety, would produce future generations themselves. Of course, seeds produced on the farm may contain a certain amount of weed seed and not be produced under the best conditions for germination so, in fact, farmers will occasionally go back to the seed producer for a new stock. In France, for example, the average wheat farmer goes back once every six years to replenish the supply of wheat seed.
Hybrid corn is different. Because it is the cross between two self-propagating homogeneous lines, one cannot plant the seed of hybrid corn and get new hybrid corn. Hybrids are not true-breeding. The seeds that are borne on a hybrid plant are not themselves hybrids but form a population of plants of varying degrees of hybridity, a mixture of homogeneous and heterogeneous varieties. A farmer who saved seed from his hybrid corn and planted it the next year would lose at least 30 bushels per acre in the next crop. To maintain high yields, it is necessary for the farmer to go back every year and buy the seed again. So, the hybrid seed corn producer has found a method of copy protection. Moreover, the producer of the hybrid seed can charge the farmer a price for the hybrid seed that is equivalent to the amount the farmer would have lost—that is, the market value of 30 bushels per acre—had he not returned to the seed company for more hybrid seed. The invention of hybrid corn was, in fact, a deliberate use of the principles of genetics to create a copy-protected product. We have that on the best authority possible, the inventors of hybrid corn themselves, Shull and East, who wrote that hybrids are
something that might easily be taken up by the seedsmen; in fact, it is the first time in agricultural history that a seedsman is enabled to gain the full benefit from a desirable origination of his own or something that he has purchased ... The man who originates a new plant which may be of incalculable benefit to the whole country gets nothing—not even fame— for his pains and the plant can be propagated by anyone ... The utilization of the first generation hybrids enables the originator to keep the parental types and give out only the crossed seeds, which are less valuable for continued propagation.
The realization that the hybrid method could guarantee to the inventor immense profits has resulted in the introduction of the hybrid method into all of agriculture. Chickens, tomatoes, swine, indeed, nearly every commercial plant or animal where it is possible to introduce the method has seen the growth of hybrids at the expense of older varietal forms. Major seed companies, like the Pioneer Hybrid Seed Company, have invested millions of dollars in attempting to produce hybrid wheat that would then capture an immense untapped market. So far, they have not succeeded, because the cost of production of the hybrid seed is excessive.
The Pioneer Hybrid Seed Company itself is the consequence of the activities of a single important political and scientific figure, Henry A. Wallace. Wallace's father was appointed secretary of agriculture of the United States by President Warren Harding in 1920. The elder Wallace sent Henry on a tour of agricultural experiment stations. On his return, Henry advised his father to appoint as head of plant breeding a man who was devoted to hybrids. In the meanwhile, Henry was himself experimenting with hybrids, and in 1924 he sold his first hybrid seed com at a profit of about $740 an acre. In 1926, he founded the Pioneer Hybrid Seed Company, and when, in 1932, he was appointed secretary of agriculture by President Franklin Roosevelt, pressure for the introduction of hybrid corn in the United States, and subsequently in Canada, became irresistible.
If hybrids really are a superior method for agricultural production, then their commercial usefulness to the seed company is a side issue. The question is whether other methods of plant breeding might have worked as well or better without providing property-rights protection for the seed companies. The answer to that question depends on some issues in basic genetics that were undecided in the early history of hybrid corn, and until 30 years ago, one might have argued that the basic biology of corn production is such that only hybrids would provide the added yield. However, we have known the truth of the matter for the last 30 years. The fundamental experiments have been done and no plant breeder disagrees with them. The nature of the genes responsible for influencing corn yield is such that the alternative method of simple direct selection of high-yielding plants in each generation and the propagation of seed from those selected plants would work. By the method of selection, plant breeders could, in fact, produce varieties of corn that yield quite as much as modern hybrids. The problem is that no commercial plant breeder will undertake such investigation and development because there is no money in it.
One of the most interesting features of this story is the role of agricultural experiment stations like the state agricultural experiment stations in the United States or the Canadian Department of Agriculture. These institutions might be expected to develop alternative methods since they are not concerned with profit and are working at public expense. Yet the U.S. Department of Agriculture and the Canadian Department of Agriculture are among the strongest proponents of the hybrid method. A purely commercial interest has so successfully clothed itself in the claims of pure science that those claims are now taught as scientific gospel in university schools of agriculture. Successive generations of agricultural research workers, even those who work in public institutions, believe that hybrids are intrinsically superior even though the experimental results that contradict this have been published in well-known journals for more than 30 years. Once again, what appears to us in the mystical guise of pure science and objective knowledge about nature turns out, underneath, to be political, economic, and social ideology.
## **_A Story in Textbooks_**
**_T_** he claim that all of human existence is controlled by our DNA is a popular one. It has the effect of legitimizing the structures of society in which we live, because it does not stop with the assertion that the differences in temperament, ability, and physical and mental health between us are coded in our genes. It also claims that the political structures of society — the competitive, entrepreneurial, hierarchical society in which we live and which differentially rewards different temperaments, different cognitive abilities, and different mental attitudes — is also determined by our DNA, and that it is, therefore, unchangeable. For after all, even if we were biologically different from one another, that in itself would not guarantee that society would have given different power and status to people who are different. That is, to make the ideology of biological determinism complete, we have to have a theory of unchangeable human nature, a human nature that is coded in our genes.
Every political philosophy has to begin with a theory of human nature. Surely, if we cannot say what it is to be truly human, we cannot argue for one or another form of social organization. Social revolutionaries, especially, must have a notion of what it is to be truly human because the call for revolution is the call for the spilling of blood and a wholesale reorganization of the world. One cannot call for a violent overthrow of what is, without claiming that what will be is more in accord with the true nature of human existence. So, even Karl Marx, whose view of society was an historical one, nevertheless believed that there was a true human nature and that human beings realize themselves in their essence by a planned social manipulation of nature for human welfare.
The problem for political philosophers has always been to try to justify their particular view of human nature. Before the seventeenth century, the appeal was made to divine wisdom. God had made people in a certain way Indeed, they were made in God's image, although a rather blurred one, and moreover, human beings were basically sinful from the time of Adam and Eve's Fall. But modern secular technological society cannot draw its political claims from divine justification. From the seventeenth century onward, political philosophers have tried to create a picture of human nature based on some sort of appeal to a naturalistic view of the world. Thomas Hobbes in his _Leviathan,_ which argued for the necessity of the king, built a picture of human nature from the simplest axioms about the nature of human beings as organisms. To Hobbes, human beings, like other animals, were self-enlarging, self-aggrandizing objects that simply had to grow and occupy the world. But the world was a place of finite resources, and so it necessarily would happen that human beings would come into conflict over those resources as they expanded and the result would be what he called "the war of all against all." The conclusion for Hobbes was that one needed a king to prevent this war from destroying everything.
The claims that organisms, especially human beings, grow without bound and that the world in which they grow is finite and limited are the two basic claims that have given rise to the modern biological theory of human nature. They resurfaced in the Reverend Malthus's treatise on population, in his famous law that organisms grow geometrically in numbers while the resources for their subsistence grow only arithmetically, and so again a struggle for existence must occur. As we all know, Darwin took over this notion of nature to build his theory of natural selection. Since all organisms are engaged in a struggle for existence, those that are better suited by their shape and form, by their physiology, and by their behavior to leave more offspring in that struggle will do so, and the consequence will be that their kind will take over the earth. The Darwinian view is that whatever human nature may be, it, like everything else about humans, who are after all living organisms, has evolved by natural selection. Therefore, what we truly are is the result of two billions years of evolution from the earliest rudimentary organisms to us.
As evolutionary theory has developed over the last one hundred years and become technologically and scientifically sophisticated, as vague notions of inheritance have become converted into a very precise theory of the structure and function of DNA, so the evolutionary view of human nature has developed a modern, scientific-sounding apparatus that makes it seem every bit as unchallengeable as the theories of divine providence seemed in an earlier age. What has happened in effect is that Thomas Hobbes's war of all against all has been converted into a struggle between DNA molecules for supremacy and dominance over the structures of human life.
The most modern form of naturalistic human nature ideology is called sociobiology. It emerged onto the public scene about 15 years ago and has since become the ruling justifying theory for the permanence of society as we know it. It is an evolutionary and a genetic theory that uses the entire theoretical apparatus of modern evolutionary biology, including a great deal of abstruse mathematics, which is then translated for the inexpert reader in coffee-table books with beguiling pictures and in magazine articles and newspaper accounts. Sociobiology is the latest and most mystified attempt to convince people that human life is pretty much what is has to be and perhaps even ought to be.
The sociobiological theory of human nature is built in three steps. The first is a description of what human nature is like. One looks around at human beings and tries to build a fairly complete description of the features that are said to be common to all human beings in all societies in all places in all times.
The second step is to claim that those characteristics that appear to be universal in humans are, in fact, coded in our genes, that is, in our DNA. There are genes for religiosity, genes for entrepreneurship, genes for whatever characteristics are said to be built into the human psyche and human social organization.
These two claims — that there is a universal human nature and that it is coded in the genes and is unchangeable — would be sufficient as a biological theory of human nature in a purely descriptive sense. That is what we are; take it or leave it. But sociobiological theory, being built on evolutionary theory, goes one step further, as it must to fulfill its program. It must explain, and in some sense justify, how we come to have these particular genes rather than some other genes that might have given us quite a different human nature.
The theory thus goes on to the third step, the claim that natural selection, through the differential survival and reproduction of different kinds of organisms, has led inevitably to the particular genetic characteristics of individual human beings, characteristics that are responsible for the form of society. This claim strengthens the argument of legitimacy because it goes beyond mere description to assert that the human nature described is inevitable, given the universal law of the struggle for existence and the survival of the fittest. In this sense, the sociobiological theory of human nature puts on a mantle of universality and of utter fixity. After all, if 3 billion years of evolution have made us what we are, do we really think that a hundred days of revolution will change us?
Sociobiologists take the first step, the claimed correct description of what is universal in all human beings, more or less as every human nature theorist has done it, by looking around to see what people in their society are like and to some extent by telling their own life stories. Having looked inward at themselves and outward at modern capitalist society for a description of human nature, they then extend it a bit further by looking into the anthropological record in order to assure us that those very same elements that they find in twentieth-century North America and Britain are also, in one form or another, displayed by the Stone Age people of New Guinea. For some reason, they do not look much at the historical record of European society, of which they seem to be quite ignorant, but perhaps they feel that if New Guinea highlanders and Scottish highlanders show the same characteristics today, then there cannot have been much change in 1,500 years of recorded history.
And what are these human universals that sociobiologists find? One can hardly do better than look at the most influential, and in some sense, founding document of sociobiological theory, E.O. Wilson's _Sociobiology: The New Synthesis_. Professor Wilson tells us, for example, that human beings are indoctrinable. He says, "Human beings are absurdly easy to indoctrinate. They seek it." They are characterized by blind faith: "Man would rather believe than know." That statement is, we must note, found in what is called a scientific work, used as a textbook in courses all over the world, filled with the mathematics of modern population biology, crammed with observations and facts about the behavior of all kinds of animals, based on what _Time_ magazine has called the "iron laws of nature." But surely, "man would rather believe than know" is more in the line of barroom wisdom, the sort of remark one makes to one's friend at the local after work following a particularly frustrating attempt to persuade the person in the next office that he ought to do things in a different way. Among other aspects of human nature are said to be a universal spite and family chauvinism. We are told that "human beings are keenly aware of their own blood lines and the intelligence to plot intrigue." Xenophobia, the fear of strangers, is part of our universal equipment. "Part of man's problem is that his intergroup responses are still crude and primitive and inadequate for the extending territorial relationship that civilization has thrust upon him." One of the results of this, we are told, is that "the most distinctive human qualities have emerged during the phase of social evolution that occurred through intertribal warfare and through genocide." And then there is the relationship between the sexes. Male dominance and superiority is part of human nature. Wilson writes that "among general social traits in human beings are aggressive dominance systems with males dominant over females." The list is not complete. Nor is this simply the idiosyncratic view of one influential sociobiologist. The claims that human warfare, sexual dominance, love of private property, and hate of strangers are human universals are found over and over in the writings of sociobiologists, whether they be biologists, economists, psychologists, or political scientists.
But to make such claims, one must be quite blind even to the history of European society. Take, for example, the claim of a universal xenophobia. In fact, the attitudes of people toward foreign cultures and other countries have varied tremendously from social class to social class and time to time. Could the aristocracy of Russia in the nineteenth century, which thought all things Slavic to be inferior, which spoke French by preference, which looked to Germany for its military and technological resources, be described as xenophobic? Educated and upper classes in particular have often looked to other cultures for the highest and the best. English-speaking scientists on occasion are interviewed by Italian radio and television, and the answers given to the producer's questions are translated into Italian, which the listeners hear in a voice-over after a few moments of the scientist's English. When the producers are asked why they do not get an Italian scientist to do the program, they say that Italians simply do not believe any claims about science that are made in Italian and that they have to hear it in English if they are to believe it is true.
Nothing better reveals the narrow ahistorical claims of sociobiological description than the standard discussion of the economy of scarcity and unequal distribution. So, Professor Wilson writes that "the members of human societies sometimes cooperate closely in insectan fashion, but more frequently they compete for the limited resources allocated to their role sector. The best and the most entrepreneurial of the role actors usually gain a disproportionate share of the rewards while the least successful are displaced to other less desirable positions." But this description completely ignores the immense amount of sharing of resources that occurs among a whole variety of modern hunting and gathering societies like Eskimos, and it completely distorts the history even of Europe. The concept of entrepreneurship does not work for, say, the thirteenth century in the Île-de-France, an agrarian feudal society in which land could not be bought and sold, in which labor could not be hired and fired, and in which the so-called market mechanism was a rudimentary form of exchange of a few goods. Of course, sociobiologists recognize that there are exceptions to these generalizations, but their claim is that those exceptions are temporary and unnatural, and that they will not persist in the absence of constant force and threat. So, societies may indeed, like blue-clad regimented Chinese, cooperate in so-called insectan fashion. But this can be managed only by constant supervision and force. The moment one relaxes one's vigil, people will revert to their natural ways. It is rather as if we could make a law saying that everyone would have to walk on their knees, which would be physically possible but terribly painful. The moment we relaxed our vigil, everyone would stand upright again.
At the surface of this theory of human nature is the obvious ideological commitment to modern entrepreneurial competitive hierarchical society. Yet underneath is a deeper ideology, and that is the priority of the individual over the collective. Despite the name _sociobiology_ , we are dealing with a theory not of social causation but of individual causation. The characteristics of society are seen as caused by the individual properties that its members have, and those properties, as we shall see, are said to derive from the members' genes. If human societies engage in war, that is because each individual in the society is aggressive. If men as a group dominate women or whites Blacks, it is because each man as an individual is desirous of dominating each woman and each white person has feelings of personal hostility set off by the sight of Black skin. The structures of society simply reflect these individual predispositions. Society is nothing but the collection of individuals in it, just as culture is seen as nothing but the collection of disarticulated bits and pieces, individual preferences and habits.
Such a view completely confuses, partly by linguistic confusion, very different phenomena. It is obviously not the case that Britain and Germany made war on each other in 1914 because individual Britons and individual Germans felt aggressive. If that were the case, we would not need conscription. Englishmen, Canadians, and Americans killed Germans and vice versa because the state put them in a position that made it inevitable they did so. A refusal to be conscripted meant a jail term and the refusal to obey orders in the field meant death. Great machines of propaganda, martial music, and stories of atrocities are manufactured by the state to convince its citizens that their lives and the chastity of their daughters are at risk in the face of the threat of barbarians. The confusion between individual aggression and national aggression is a confusion between the rush of hormones that may be felt if someone is slapped in the face and a national political agenda to control natural resources, lines of commerce, prices of agricultural goods, and the availability of labor forces that are the origins of warfare. It is important to realize that one does not have to have a particular view of the content of human nature to make this error of individuals causing society. Prince Kropotkin, a famous anarchist, also claimed that there was a universal human nature but one that would create cooperativeness and would be anti-hierarchical if only it were allowed free play. But his theory was no less a theory of the dominance of the individual as the source of the social.
Having described a universal set of human social institutions that are said to be the consequence of individual natures, socio-biological theory then goes on to claim that those individual properties are coded in our genes. There are said to be genes for entrepreneurship, for male dominance, for aggressivity, so conflict between the sexes and parents and offspring is said to be genetically programmed. What is the evidence that these claimed human universals are in fact in the genes? Often, it is simply asserted that because they are universal they must be genetic. A classic example is the discussion of sexual dominance. Professor Wilson has written in _The New York Times,_ "In hunter-gatherer societies, men hunt and women stay at home. This strong bias persists in most agricultural and industrial societies [apparently, he has not yet caught up with women in the workforce], and on that ground alone appears to have a genetic origin." This argument confuses the observation with its explanation. If the circularity is not obvious, we might consider the claim that since 99 percent of Finns are Lutherans, they must have a gene for it.
_A_ second evidence offered for the genetic determination of human universal traits is the claim that other animals show the same traits and, therefore, we must have a genetic continuity with them. Ants are described as making "slaves" and having "queens." But the slavery of ants knows nothing of the auction block, of the buying and selling, of the essentially commodity nature of the slave relations of human society. Indeed, ant slaves are almost always of other species, and ant slavery has a great deal more in common with the domestication of animals. Nor do ants have "queens". The force-fed egg factory encased in a special chamber in the middle of an ant colony that is called a queen has no resemblance to the life of either Elizabeth I or Elizabeth II or of their different political roles in society. Nor are the words "slave" and "queen" simply convenient labels. Ant "slavery" and ant "royalty" are claimed to have important causal continuity with their human counterparts. They are said to be products of the same forces of natural selection.
This confusion between qualities of animals and qualities of human society is an example of the problem of _homology_ and _analogy._ By homologous traits, biologists mean those properties of organisms that are shared by different species because they have a common biological origin and some common biological genetic ancestry, and they derive from common features of anatomy and development. Even though they look very different and are used for very different purposes, the bones of a human arm and of a bat's wing are homologous because they are anatomically derived from the same structures and influenced by the same genes. On the other hand, a bat's wing and an insect's wing are only analogous. That is, they look superficially alike and they seem to serve the same function, but they have no origin in common at the genetic or morphological level. But analogy is in the eye of the observer. How do we decide that slavery in ants and ant queens are like human slavery and like human royal families? How do we decide that the coyness we see in people is the same as the behavior in animals called coyness? What happens is that human categories are laid on animals by analogy, partly as a matter of convenience of language, and then these traits are "discovered" in animals and laid back on humans as if they had a common origin. There is in fact not a shred of evidence that the anatomical, physiological, and genetic basis of what is called aggression in rats has anything in common with the German invasion of Poland in 1938.
The third kind of evidence that is presented for a genetic basis of human social behavior is the report of heritability of human traits. Such characteristics as introversion and extroversion, personal tempo, psychomotor and sports activities, eroticism, dominance, depression, and even conservatism and liberalism are said to be heritable. But the evidence for the heritability of these traits is totally absent. We must remember that genetics is a study of similarity and difference between relatives. We judge things to be heritable if close relatives are more alike than distant relatives or unrelated persons. But the problem in human genetics in particular is that similarity between relatives arises not only for biological reasons but for cultural reasons as well, since members of the same family share the same environment. This has always been the problem of human genetics whether we are talking about traits of personality or anatomy. Most reports of the heritability of personality traits are simple observations that parents and children resemble each other in some respect. The highest similarity between parents and offspring for social traits in North America is for political party and religious sect, yet no serious person believes genes determine these attributes. The observation of similarity of parents and offspring is not evidence of their biological similarity. There is a confusion between the observation and the possible causes. The fact is, not a single study of personality traits in human populations successfully disentangles similarity because of shared family experience and similarity because of genes. So, in fact, we know nothing about the heritability of human temperamental and intellectual traits that are supposed to be the basis for social organization.
There is a deeper problem. To carry out a heritability study, even a correct one, we require differences between individuals. If everyone is identical in some respect, that is, if everybody has exactly the same genes for some characteristic, then there is no way to investigate its heritability, because genetic investigations require contrasts between individuals. Sociobiological theory claims that all human beings share genes for aggression, for xenophobia, for male dominance, and so on. But if we all share these genes, if evolution has made us all alike in this human nature, then in principle there would be no way to investigate the heritability of the traits. On the other hand, if there is genetic variation among human beings in these respects, then on what basis do we declare that one or another manifestation is universal human nature? If it is genetically determined human nature that we are aggressive and like to go to war, then we must suppose that A.J. Mustie, the famous pacifist, lacked this gene and was, therefore, in some sense less than human. If, on the other hand, he possessed the gene but was a pacifist, the genes seem somewhat less than all-powerful in determining behavior. Why are we not all like A.J. Mustie? There are deep contradictions in simultaneously asserting that we are all genetically alike in certain respects, that our genes are all-powerful in determining our behavior, and at the same time observing that people differ.
Finally, there is an extraordinary biological naivete and ignorance of the principles of developmental biology involved in assertions that genes make us behave in particular ways in particular circumstances. DNA functions in several ways in influencing the development of organisms.
First, the exact sequence of the amino acids in our proteins is coded in our genes, but no one would suggest that the amino acid sequence for a particular protein in itself can make us liberal or conservative. Second, genes influence when in the course of development and in which part of the body particular proteins are to be produced, and this in turn influences cell division and cell growth. So it might be claimed that there is a fixed pattern of neurons in our central nervous system, influenced by the turning on and turning off of genes during development, that makes us warlike or pacifist. However, this would require a theory of the development of the central nervous system that makes no allowances for developmental accidents and little or no role for the creation of mental structures by experience. Yet even the rudimentary social organization of ants, with their structure of work and interindividual relations that is so simple compared with ours, is very flexible with respect to information for the external world. Ant colonies change their collective social behavior over time and depending on how long the colony has occupied a given territory. It takes an enormous set of assumptions to suppose that the human central nervous system, with thousands of times more nervous connections than in an ant, has completely stereotyped and fixed genetic responses to circumstance. The incredible variety of human social circumstances would require an amount of DNA that we simply do not possess. There is enough human DNA to make about 250,000 genes. But that would be insufficient to determine the incredible complexity of human social organization if it were coded in detail by specific neuronal connections. Once we admit that only the most general outlines of social behavior could be genetically coded, then we must allow immense flexibility depending on particular circumstances.
The final step in the sociobiological argument is to say that the genes we possess for universal human nature have been established in us through evolution by natural selection. That is, once upon a time human beings varied genetically in the degree to which they were aggressive, xenophobic, indoctrinable, male dominant, and so on, but those individuals who were most aggressive or most male dominant left more offspring, so the genes that were eventually left in us as a species were the ones that now determine those traits. The argument of natural selection seems a fairly simple and straightforward one for some kinds of traits. For example, it is argued, the more aggressive of our ancestors would leave more offspring because they would swoop down on the less aggressive and eliminate them. The more entrepreneurial would have appropriated more resources in short supply and starved out the wimps. In each of these cases, it is easy to make up a plausible story that would explain the superior reproductive abilities of one type over another.
There are, however, some traits that are said to be universal and that do not lend themselves so easily to this story of individual reproductive advantage. An example, and one that is discussed a great deal by sociobiologists, is altruistic behavior. Why should we be cooperative under some circumstances, and why should we sometimes give up what appear to be immediate advantages for the benefit of others? To explain altruism, socio-biologists advance the theory of kin selection. Natural selection for a trait does not require that individuals possessing it leave more offspring but only that the genes coding the trait be represented in larger numbers in future generations.
There are two ways to increase the representation of one's genes in future generations. One is to leave more offspring. The other is to arrange that even if one does not leave more offspring, one's relatives do so, since close relatives share genes. So, a person could sacrifice his reproduction completely, provided his brothers and sisters left many more children. Thus, his kind of genes would increase indirectly through his relatives and, in this indirect way, he would leave more offspring. An example of this phenomenon is the occurrence of "helpers at the nest" in birds, in which it is said that nonreproductive birds help out their close relatives, who are then able to raise more than the ordinary number of offspring and in the end more family genes are left. To make kin selection work, a sufficient number of excess offspring must be left by relatives. For example, if an individual gives up its own reproduction, its brothers and sisters must have twice as many offspring as ordinarily, but one can at least tell a story that might make this plausible.
We are then left with those traits that do not even benefit relatives differentially, for example, a general altruism toward all members of the species. Why are we good to strangers? For this phenomenon, the sociobiologist provides the theory of "reciprocal altruism". The argument is that even if we are unrelated, if I do you a favor that costs me something, you will remember that favor and reciprocate in the future, and by this indirect path I will succeed in advancing my own reproduction. An example often given is that of the drowning person. You see someone drowning and jump in to save that person even at the risk of your own life. In the future, when you are drowning, the person whose life you have saved will remember, and save you in gratitude. By this indirect path you will increase your own probability of survival and reproduction over the long run. The problem with this story is, of course, that the last person in the world you want to depend on to save you when you are drowning is someone whom you had to save in the past, since he or she is not likely to be a strong swimmer.
The real difficulty with the process of explanation that allows direct advantage, or kin selection, or reciprocal altruism when one or the other is useful in the explanation, is that a story can be invented that will explain the natural selective advantage of any trait imaginable. When we combine individual selective advantage with the possibility of kin selection and reciprocal altruism, it is hard to imagine any human trait for which a plausible scenario for its selective advantage could not be invented. The real problem is to find out whether any of these stories is _true._ One must distinguish between plausible stories, things that _might_ be true, and true stories, things that actually have happened. How do we know that human altruism arose because of kin selection or reciprocal altruistic selection? At the very minimum, we might ask whether there is any evidence that such selective processes are going on at the present, but in fact no one has ever measured in any human population the actual reproductive advantage or disadvantage of any human behavior. All of the sociobiological explanations of the evolution of human behavior are like Rudyard Kipling's _Just So_ stories of how the camel got his hump and how the elephant got his trunk. They are just stories. Science has been turned into a game.
The entire process of sociobiological reasoning is illustrated by two cases, one meant only fancifully by sociobiologists as a teaching exercise, and one they take seriously. The fanciful one concerns the problem of why children hate spinach and adults like it. It is contained in a high-school textbook written by socio-biologists in order to train children in adaptive thinking. The first step is the description of a human universal. All children hate spinach. To see the universal truth of this assertion, it is only necessary to look around and ask our friends. Moreover, when we look around we find that adults eat spinach. How has this happened? We imagine that there is a gene that causes children to hate spinach but allows adults to like it. Note that there is no evidence for such an unlikely gene. It is simply postulated. Spinach contains a substance, oxalic acid, that interferes with the absorption of calcium, which young children need for their growing bones. So any child in the past who had the wrong gene and ate spinach would have had defective growth, suffered from rickets, and might not have left many offspring. (Although it is far from clear that crooked legs interfere with reproduction and longevity.) On the other hand, adults' bones have stopped growing, calcium is not so important to them, and they are free to take advantage of the nutrients in spinach, so there is no selection against their liking it. As a consequence, it is part of genetically determined human nature that children hate spinach but adults like it. We have a completely articulated story of a claimed universal fact of human nature. We should not let the silliness of this case distract from its essential features. It is meant to teach students all the elements of a naturalistic argument about human nature. It makes a generalized observation by looking around. It postulates genes without any evidence, and then it tells a plausible or perhaps not so plausible story.
Let us see how this is applied to a serious case and one widely discussed by sociobiologists: the existence in human societies of homosexuality. Homosexuality is claimed to be a biological problem because, after all, since homosexuals leave no offspring, the genes for homosexuality should have long ago disappeared. Why have they not? First, the sociobiologist makes the assumption that homosexuals leave fewer offspring. This implies a description of human sexual behavior in which the world is divided between heterosexuals and homosexuals, one class that leaves offspring and the other that does not. This description, however, does not correspond to our knowledge of human sexuality. In fact, the world is not divided between two classes. On the contrary, there is continuum of sexuality from persons who have never engaged in anything but heterosexual behavior, through those who have a somewhat wider range of experiences, through those who are regularly bisexual to those who are totally homosexual. According to a number of surveys, about half of all males in North America have had at least one homosexual contact. Moreover, this range of behaviors has varied historically by social class. There was widespread bisexuality among the upper classes in Classical Rome and Greece and, indeed, what were the usual homosexual practices in these societies were different from present practices. Moreover, there is, curiously enough, not an iota of evidence about the relative reproductive rates of people with different sexual histories. Obviously those who engage _exclusively_ in homosexual behavior have, until the recent advent of artificial insemination, left no offspring. But nothing is known about the reproductive rates of those who are totally heterosexual as opposed to those who have a broad range of sexual experience. So, for example, we do not know whether a person who is heterosexual in 40 percent of his or her encounters and homosexual in 60 percent has fewer or more children than a person who is totally heterosexual. Indeed, we could make an argument that bisexuality is a manifestation of greater general libido, and it might turn out that bisexual people leave more offspring. We simply do not know the answer.
Second, there is absolutely no evidence that there are any genetic differences between individuals of different sexual preferences. If it were true that homosexuals left no offspring, there would be a certain problem in studying the heritability of homosexual behavior. In fact, there are no studies of the heritability of sexual preference, so the claims for genetic predisposition to different forms of sexuality are pure fancy.
Finally, there is the problem of an evolutionary story. The one told by sociobiologists is that of helpers at the nest. Homosexuals in the past, it is argued, did not themselves leave any offspring but helped their heterosexual brothers and sisters to raise more children by sharing resources with them, and this compensation was sufficient to keep the genes for homosexuality in the population. It must be remembered that the nonreproductive homosexuals must help their brothers and sisters so well that those relatives have twice as many offspring as usual if kin selection is to work. But there is no evidence for helpers at the nest in human societies. If our remote prehistoric ancestors were anything like modern hunting and gathering people, a general sharing of resources would be a common phenomenon not only within the family but within entire villages so that the "nest" included nonrelatives. But we know nothing about the relative number of offspring left at present by people who have homosexual brothers and sisters, for no one has ever measured family size in relation to this question.
Thus, the entire discussion of the evolutionary basis of human sexual preference is a made-up story, from beginning to end. Yet it is a story that appears in textbooks, in courses in high schools and universities, and in popular books and journals. It bears the legitimacy given to it by famous professors and by national and international media. It has the authority of science. In an important sense, it _is_ science because science consists not simply of a collection of true facts about the world, but is the body of assertions and theories about the world made by people who are called scientists. It consists, in large part, of what scientists say about the world whatever the true state of the world might be.
Science is more than an institution devoted to the manipulation of the physical world. It also has a function in the formation of consciousness about the political and social world. Science in that sense is part of the general process of education, and the assertions of scientists are the basis for a great deal of the enterprise of forming consciousness. Education in general, and scientific education in particular, is meant not only to make us competent to manipulate the world but also to form our social attitudes. No one saw this more clearly, and was more honest about it, than one of the most conservative political figures in American history, Daniel Webster, who wrote that "education is a wise and liberal form of police by which property and life and the peace of society are secured."
## **_Science as Social Action_**
**_T_** he previous pages have all been concerned with a particular ideological bias of modern biology. That bias is that everything that we are, our sickness and health, our poverty and wealth, and the very structure of the society we live in are ultimately encoded in our DNA. We are, in Richard Dawkins's metaphor, lumbering robots created by our DNA, body and mind. But the view that we are totally at the mercy of internal forces present within ourselves from birth is part of a deep ideological commitment that goes under the name of _reductionism._ By reductionism we mean the belief that the world is broken up into tiny bits and pieces, each of which has its own properties and which combine together to make larger things. The individual makes society, for example, and society is nothing but the manifestation of the properties of individual human beings. Individual internal properties are the causes and the properties of the social whole are the effects of those causes. This individualistic view of the biological world is simply a reflection of the ideologies of the bourgeois revolutions of the eighteenth century that placed the individual at the center of everything.
Such a view about causes and effects and the autonomy of individual bits and pieces not only results in a belief that internal forces beyond our control govern what we are as individuals. It also posits an external world with its own bits and pieces, its own laws, which we as individuals confront but do not influence. Just as the genes are totally inside of us, so the environment is totally outside of us, and we as actors are at the mercy of both these internal and external worlds. This gives rise to the false dichotomy of nature and nurture. Against those who say that our ability to solve problems, our intelligence, is determined by our genes, there exists a contrary party that claims that our intelligence is determined by our environment. And so the struggle goes on between those who believe in the primacy of nature and those who believe in the primacy of nurture.
The separation between nature and nurture, between the organism and the environment, goes back to Charles Darwin, who finally brought biology into the modern mechanistic world view. Before Darwin, it was the general view that what was outside and what was inside were part of the same whole system and one could influence the other. The most famous theory of evolution before Darwin was that of Jean Baptiste Lamarck, who believed in the inheritance of acquired characteristics. Changes occurred in the environment that caused changes in the body or behavior of organisms, and it was believed that the changes induced by the environment would enter into the hereditary structure of the organisms and would be passed on to the next generation. In this view, nothing separates what is outside from what is inside because external alterations would enter into the organism and be perpetuated in future generations.
Darwin completely rejected this world view and replaced it with one in which organisms and environment were totally separated. The external world had its own laws, its own mechanisms of operation. Organisms confronted these and experienced them and either successfully adapted to them or failed. The rule of life, according to Darwin, is "adapt or die." Those organisms whose properties enabled them to cope with the problems set by the external world would survive and leave offspring, and the others would fail to do so. The species would change, not because the environment directly caused physical and body changes in organisms, but because those organisms smart enough to be able to handle the problems thrown at them by nature would leave more offspring, who would resemble them. The deep point of Darwinism was the separation between the forces of the environment that create the problems and the internal forces of the organism that throw up solutions to problems more or less at random, the correct solutions being preserved. The external and internal forces of the world behave independently. The only connection between them is a passive one. The organisms who happen to be lucky enough to find a match between what is going on inside themselves and what was going on outside themselves survive.
Darwin's view was essential to our successful unraveling of evolution. Lamarck was simply wrong about the way the environment influences heredity, and Darwin's alienation of the organism from the environment was an essential first step in a correct description of the way the forces of nature act on each other. The problem is that it was only a _first_ step, and we have become frozen there. Modern biology has become completely committed to the view that organisms are nothing but the battle grounds between the outside forces and the inside forces. Organisms are the passive consequences of external and internal activities beyond their control. This view has important political reverberations. It implies that the world is outside our control, that we must take it as we find it and do the best we can to make our way through the mine field of life using whatever equipment our genes have provided to us to get to the other side in one piece.
What is so extraordinary about the view of an external environment set for us by nature, and essentially unchangeable except in the sense that we might ruin it and destroy the delicate balance that nature has created in our absence, is that it is completely in contradiction to what we know about organisms and environment. When we free ourselves of the ideological bias of atomism and reductionism and look squarely at the actual relations between organisms and the world around them, we find a much richer set of relations, relations that have very different consequences for social and political action than are usually supposed, for example, by the environmental movement.
First, there is no "environment" in some independent and abstract sense. Just as there is no organism without an environment, there is no environment without an organism. Organisms do not experience environments. They create them. They construct their own environments out of the bits and pieces of the physical and biological world and they do so by their own activities. Are the stones and the grass in my garden part of the environment of a bird? The grass is certainly part of the environment of a phoebe that gathers dry grass to make a nest. But the stone around which the grass is growing means nothing to the phoebe. On the other hand, the stone is part of the environment of a thrush that may come along with a garden snail and break the shell of the snail against the stone. Neither the grass nor the stone are part of the environment of a woodpecker that is living in a hole in a tree. That is, bits and pieces of the world outside of these organisms are made relevant to them by their own life activities. If grass is used to make a nest, then grass is part of the environment. If stones are used to break snails on, then stones are part of the environment.
There is an infinity of ways in which parts of the world can be assembled to make an environment, and we can know what the environment of an organism is only by consulting the organism. Not only do we consult the organism, but when we describe the environment we describe it in terms of the organism's behavior and life activities. If you are in any doubt of this, you might try asking a professional ecologist to describe the environment of some bird. He or she will say something like the following. "Well, the bird builds its nest three feet off the ground in hardwoods. It eats insects part of the year but then may switch to seeds and nuts when insects are no longer available. It flies south in the winter and comes back north in the summer, and when it is foraging for its food it tends to stay in the higher branches and at their outer tips," and so on. Every word uttered by the ecologist in describing the environment of a bird will be a description of the life activities of the bird. That process of description reflects the fact that the ecologist has learned what the environment of the bird is by watching birds.
A practical demonstration of the difficulty of describing an environment without having seen an organism that determined and defined it is the case of the Mars Lander. When the United States decided to send a landing module to Mars, biologists wanted to know if there was any life there. So the problem was to design a machine to detect life on Mars. There were several interesting suggestions. One was to send a kind of microscope with a long sticky tongue that would unroll on the planet's surface and then roll back up and put whatever dust it found under the microscope. If there was anything that looked like a living organism, we would see it in the images sent back to Earth. One might call this the morphological definition of life. If it looks right and it wiggles, then it is alive.
What appears to be a more sophisticated approach was taken. Instead of asking whether things on Mars look alive, it was decided to ask whether they have the metabolism of living things. So the Mars Lander contained what was essentially a long hose attached to a vacuum cleaner inside of which was a container of radioactive growth medium. When the Lander got to Mars, it would suck up some dust into the medium and if there were any living organisms in the dust, they would break down the medium as bacteria do on Earth, radioactive carbon dioxide would be produced, and a detector in the machine would signal the presence of this gas. And that is exactly what happened. When the Mars Lander sucked up the dust, radioactive carbon dioxide was produced in a pattern that had everyone convinced that there was life on Mars fermenting the medium. But then suddenly the process shut down and there was no further fermentation. This was not what living organisms were supposed to do, and the consequence was scientific confusion. After a debate among those concerned with the experiment, it was decided that there was no life on Mars. Instead, it was postulated that there was a kind of chemical reaction on finely divided clay particles catalyzed by the particles, which were not ordinarily seen on Earth. Later, this reaction was successfully mimicked in the laboratory, so everybody has now agreed that they decided correctly and that there is no life on Mars.
The problem with this experiment arises precisely from the fact that organisms define their own environment. How can we know whether there is life on Mars? We present Martian life with an environment and see whether it can live in it. But how can we know what the environment of Martian life is unless we have seen Martian organisms? All that the experiment of the Mars Lander showed was that there is no Earth-like bacterial life on Mars. We may know the temperature, the gas content of the atmosphere, the humidity, and something about the soil on Mars, but we do not know what a Martian environment is like because the environment does not consist of temperature, gas, moisture, and soil. It consists of an organized set of relationships among bits and pieces of the world, which organization has been created by living Martian organisms themselves.
We must replace the adaptationist view of life with a constructionist one. It is not that organisms find environments and either adapt themselves to the environments or die. They actually _construct_ their environment out of bits and pieces. In this sense, the environment of organisms is coded in their DNA and we find ourselves in a kind of reverse Lamarckian position. Whereas Lamarck supposed that changes in the external world would cause changes in the internal structures, we see that the reverse is true. An organism's genes, to the extent that they influence what that organism does in its behavior, physiology, and morphology, are at the same time helping to construct an environment. So, if genes change in evolution, the environment of the organism will change too.
Consider the immediate environment of a human being. If one takes motion pictures of a person, using schlieren optics that detect differences in the refractive index of the air, one can see that a layer of warm, moist air completely surrounds each one of us and is slowly rising from our legs and bodies and going off the top of our heads. In fact, every living organism including trees has this boundary layer of warm air that is created by the organism's metabolism. The result is that we are encapsulated in a little atmosphere created by our own metabolic activities. One consequence is what is called the wind-chill factor. The reason that it gets much colder when the wind blows across us is because the wind is blowing away the boundary layer and our skins are then exposed to a different set of temperatures and humidities. Consider a mosquito feeding on the surface of the human body. That mosquito is completely immersed in the boundary layer that we have constructed. It is living in a warm, moist world. Yet one of the most common evolutionary changes for all organisms is a change in size, and over and over again organisms have evolved to be larger. If the mosquito species begins to evolve to a larger size, it may in fact find itself with its back in the "stratosphere" and only up to its knees in the warm, moist boundary layer while it is feeding. The consequence will be that the mosquito's evolution has put it into an entirely different world. Moreover, as human beings early in their evolution lost hair and the distribution of sweat glands over their bodies changed, the thickness of the boundary layer changed and so changed the micro-world that they carry with them, making it rather less hospitable for fleas, mosquitoes, and other parasites that live on hairy animals. The first rule of the real relation between organisms and environment is that environments do not exist in the absence of organisms but are constructed by them out of bits and pieces of the external world.
The second rule is that the environment of organisms is constantly being remade during the life of those living beings. When plants send down roots, they change the physical nature of the soil, breaking it up and aerating it. They exude organic molecules, humic acids, that change the soil's chemical nature as well. They make it possible for various beneficial fungi to live together with them and penetrate their root systems. They change the height of the water table by removing water. They alter the humidity in their immediate neighborhood, and the upper leaves of a plant change the amount of light that is available to the lower leaves. When the Canadian Department of Agriculture takes weather records for agricultural purposes, they do not set up a weather station in an open field or on the roof of a building. They take measurements of temperature and humidity at various levels above the ground in a field of growing plants because the plants are constantly changing the physical conditions that are relevant to agriculture. Moles burrow in the soil. Earthworms through their castings completely change the local topology. Beavers have had at least as important an effect on the landscape in North America as humans did until the beginning of the last century. Every breath you take removes oxygen and adds carbon dioxide to the world.
Mort Sahl once said, "Remember, no matter how cruel and nasty and evil you may be, every time you take a breath you make a flower happy."
Every living organism is in a constant process of changing the world in which it lives by taking up materials and putting out others. Every act of consumption is also an act of production. And every act of production is an act of consumption. When we consume food, we produce not only gases but solid waste products that are in turn the materials for consumption of some other organism.
A consequence of the universality of environmental change induced by the life activity of organisms is that every organism is both producing and destroying the conditions of its existence. There is a great deal of talk about how we as human beings are destroying the environment. But we are not unique in the fact that our life processes are recreating the world in a way that is in part hostile to the continuation of our own lives. Every bacterium uses up food material and excretes waste products that are toxic to it. Organisms ruin the world not only for their own lives but for their children as well.
The entire vegetational landscape of New England is a consequence of that process. The primeval forest in New England consisted of a mixture of hardwoods, pines and hemlocks. As agriculture spread at the end of the eighteenth and through the nineteenth century, all these forests were cut down and replaced by farms. Then, just before and after the Civil War, there were wholesale migrations out of the rocky soils of New England, where one could barely plant a crop, to the deep and productive soils of the Middle West. As a result, farms were abandoned and plants started to infiltrate these old fields. The first thing that came in was a variety of weeds and herbs. These were replaced later by white pines. White pines can form an almost pure stand in an old field and many such pure white pine stands could be seen in New England earlier in this century. However, they do not last. The pines make a dense shade that is inhospitable to the growth of their own seedlings, and so they cannot replace each other. As the pines die or if, as in New England, they are cut wholesale, what comes in are hardwoods, whose seedlings have been waiting around for a little opening. The white pines disappear forever with the exception of an occasional old tree, and a composition similar to the prehistoric virgin forest appears. This old-field white pine to hardwood succession is a consequence of the conditions of light and soil being changed by the pine trees in such a way that their own offspring cannot succeed them. The generation gap is not simply a human phenomenon.
So, we must put away the notion that out there there is a constant and fixed world that human beings alone are disturbing and destroying. We are certainly changing it, as all organisms do, and we certainly have a power that other organisms do not have, both to change the world extremely rapidly and, by willful activity, to change the world in various ways that we may think beneficial. Nevertheless, we cannot live without changing the environment. That is the second law of the relationship between organism and environment.
Third, organisms determine the statistical nature of the environment at least as far as it has an influence on themselves. Organisms are capable of averaging over time and buffering out the fluctuations in physical factors. An important example is the way animals and plants store sunlight. Even though the conditions for growth and good nutrition do not exist all year around in a temperate zone, it is not only farmers who make hay while the sun shines. Potatoes are the storage organs of potato plants and acorns form the storage for oak trees. Other organisms, in turn, use these storage devices for their own storage. Squirrels store away acorns for use in the winter and human beings store away potatoes. As human beings, we have even a further level of averaging: money. Money is the way in which, through futures contracts, fluctuations in the availability of natural products are ironed out for the market, and savings banks are where we put money for a rainy day. So organisms do not, in fact, perceive at a physiological level much of the fluctuation that goes on in the external world.
Conversely, organisms have techniques of reacting to the rates of change of the external world rather than the actual levels of resources. Water fleas are sometimes sexual and sometimes asexual. They change from nonsexual reproduction to sexual reproduction when a drastic change occurs in the environment, say, the change in the amount of oxygen in the water in which they live or a change in its temperature or a change in food availability. They do not alter from nonsexual to sexual when the temperature is high or when it is low but when it changes rapidly in either direction. They are detectors of change pure and simple. Our visual system is also a sensitive detector of change. Our central nervous system, by complex processing of images, enables us to see differences in intensity of light across edges in a way that is superior to what physical and electronic devices can do. We accomplish this by magnifying differences across small distances. Thus, we have greater visual acuity than optical scanning machinery. The third rule of organism and environment, then, is that fluctuations in the world matter only as organisms transform them.
Finally, organisms actually change the basic physical nature of signals that come to them from the external world. As the temperature in a room rises, my liver detects that change, not as a rise in temperature, but as a change in the concentration of sugar in my blood and the concentration of certain hormones. What begins as a change in the rate of a vibration of air molecules—a change in temperature—becomes converted inside the body into a change in the concentration of certain chemical substances. The nature of that conversion is a consequence of the action of genes, which have a strong influence on anatomy and physiology. When I am out in the desert doing my field work and I hear and see a rattlesnake, those rarefactions of the air that impinge on my eardrums and those photons of light that come into my eye are changed by my central nervous system into a chemical signal and suddenly my adrenaline starts to flow. But these vibrations and photons would be changed to a very different chemical signal in the body of another snake that is receiving exactly the same sights and sounds, especially if it were a snake of the opposite sex. This difference in transformation of one signal into another is coded in the difference between human genes and the genes of a snake. The last rule of the relation between organism and environment is that the very physical nature of the environment as it is relevant to organisms is determined by the organisms themselves.
It may be objected that such an interactive picture of organism and environment is all very well but it ignores some obvious aspects of the external world over which organisms have no control. A human being may have _discovered_ the law of gravitation, but he certainly did not _pass_ it. You cannot fight gravity. But that, in fact, is not true. A bacterium living in liquid does not feel gravity because it is so small and its buoyant properties free it from what is essentially a very weak force. But the size of a bacterium is a consequence of its genes, and so it is the genetic difference between us and bacteria that determines whether the force of gravitation is relevant to us.
On the other hand, bacteria feel a universal physical force that we do not, the force of Brownian motion. Precisely because bacteria are so small, they are battered from one side to the other by the motion of molecules in the liquid in which they are suspended. We, fortunately, are not constantly reeling from one side of the room to the other under the influence of that bombardment because we are so large. All forces of nature depend for their influence on size, distance, and time duration. How large an organism is, how rapidly it alters its state and position, how far it is from other organisms of different sizes and kinds are all deeply influenced by the organisms' genes. So, in a very important sense, the physical forces of the world, insofar as they are relevant to living beings, are encoded in those beings' genes. Just as we cannot talk about living organisms as just products of their genes but must recognize that the genes interact with the environment in producing the organism in its development and activity, so reciprocally we cannot make the mistake of saying that organisms confront an autonomous external world. The environment influences organisms only through interaction with their genes. The internal and the external are inextricably bound up with each other.
The facts of the relationship between organism and environment have important consequences for current political and social movements. There is a widespread perception that in many ways the world is becoming a rather less pleasant and more threatening place to live in, and there is a good possibility that it may grow catastrophically unpleasant in the not too distant future. It may get a lot warmer. A good deal more ultraviolet light may strike us than now does. The world does not smell very good. There are all sorts of noxious substances that are the agents of illness and even death, and we recognize all these changes as the consequence of human activity. It is entirely correct that human beings should want to make a world in which they can live happy, healthful, and reasonably long lives. But we cannot do that under the banner of "Save the Environment," because this slogan assumes that there is _an_ environment that has been created by nature and that we in our foolishness are destroying. It assumes, too, that there is such a thing as the balance of nature, that everything is in a balance and harmony that is being destroyed only by the foolishness and greed of human beings.
There is nothing in our knowledge of the world to suggest there is any particular balance or harmony. The physical and biological worlds since the beginning of the earth have been in a constant state of flux and change, much of which has been far more drastic than anyone can now conceive. Indeed, much of what we conceive of as the environment has been the creation of living organisms. The atmosphere that we all breathe and that we hope we can continue to breathe is about 18 percent oxygen and a fraction of a percent of carbon dioxide. But that atmosphere was not on earth before living organisms. Most of the oxygen was bound up in chemicals. Oxygen is a very unstable compound and does not exist stably in free form. There was, however, a high concentration of free carbon dioxide. The carbon dioxide was removed from the atmosphere and deposited in limestone and chalk by the action of algae and bacteria during the early history of the earth and in oil and coal by plants somewhat later. The oxygen, which was not present at all, was put into the atmosphere by the activity of plants, and then animals evolved in a world made for them by the earlier organisms. Only 60,000 years ago, Canada was completely under ice, as was the middle of the United States. _The_ environment has never existed and there has never been balance or harmony. Fully 99.999 percent of all species that have ever existed are already extinct, and in the end all will become extinct. Indeed, life is about half over. Our estimates are that the first living organisms appeared on earth in the order of 3 to 4 billion years ago, and we know from stellar evolution that our sun will expand and burn up the earth in another 3 to 4 billion years, putting an end to everything.
So any rational environmental movement must abandon the romantic and totally unfounded ideological commitment to a harmonious and balanced world in which the environment is preserved and turn its attention to the real question, which is, how do people want to live and how are they to arrange that they live that way? Human beings do have a unique property not shared by other organisms. It is not the destructive property but the property that they can plan the changes that will occur in the world. They cannot stop the world from changing, but they may be able with appropriate social organization to divert those changes in a more beneficial direction, and so, perhaps, even postpone their own extinction for a few hundred thousand years.
Is it within the biological capability of human beings to reorganize their futures? This question brings us back to the issue of human nature and its biological determination. If sociobiologists are right, then human beings have limitations coded in their genes that make them individually entrepreneurial, selfish, aggressive, xenophobic, family oriented, driven toward dominance, self-interested in a way that precludes any real possibility for a radical reorganization of society. You cannot fight human nature. On the other hand, if Kropotkin was right that human beings are biologically impelled toward cooperation and have been artificially held away from it historically, then such a reorganization might be possible. So it would seem that we would need to know the truth about individual human biological limitations. After all, we cannot transcend the limitations that are part of our biological nature. Perhaps we really had better sequence the entire human DNA because that is a first step, although an insufficient one, to learn what human limitations may be. In his book _Sociobiology,_ Professor Wilson says,
If the decision is taken to mold cultures to fit the requirements of the ecological steady state, some behaviors can be altered experientially without emotional damage or loss in creativity. Others cannot ... We do not know how many of the most valued qualities are linked genetically to the more obsolete destructive ones. Cooperativeness towards group mates might be coupled with aggressivity towards strangers, creativeness with the desire to own and dominate. If the planned society, the creation of which seems inevitable in the coming century, were deliberately to steer its members past those stresses and conflicts that once gave the destructive phenotypes their Darwinian edge, the other phenotypes might dwindle with them. In this, the ultimate genetic sense, social control would rob man of his humanity.
It appears, then, that we need to know the genetic linkages between the various aspects of an individual's behavior, because if we do not, we may ruin the world altogether in our blundering attempts to make it better.
The demand for biological information and the implied assumption that society needs to be guided, in the end, by a technocratic elite who understand genetics totally confounds the properties and limitations of individuals with the properties and limitations of the social institutions that they create. It is the ultimate political manifestation of the belief that individual autonomous units determine the properties of the collectivities in which they assemble.
But when we look around at society, we see that the opposite is true. If we have to characterize social organization and its consequences, it is that social organization does not reflect the limitations of individual biological beings but is their _negation._ No individual human being can fly by flapping his or her arms and legs. That is indeed a biological limitation having to do with our size and the size of our appendages. Nor could human beings fly if a very large number of them assembled in one place and all flapped their arms and legs simultaneously. Yet I did fly to Toronto last year, and the ability to fly was a consequence of social action. Airplanes and airports are products of educational institutions, scientific discoveries, the organization of money, the production of petroleum and its refining, metallurgy, the training of pilots, the actions of government in creating air traffic control systems, all of which are social products. These social products have come together to make it possible for us as individuals to fly.
It is important to note that although flight is a social product, it is not society that flies. Society cannot fly. Individuals fly. But they fly as a consequence of social organization.
Sherlock Holmes once explained to Dr. Watson that he did not know whether the sun went around the earth or the earth went around the sun because it made no difference whatsoever to his affairs. He analogized the mind to a kind of attic in which one could put just a certain amount of lumber, and every new fact added had to displace an old one. There is indeed a limit to what any human being can remember if by "remember" we mean the number of things that one can pull out of one's head. No historian of health and disease can remember all the bills of mortality, all the demographic statistics since the nineteenth century. Yet historians do remember those facts because they can look them up in books, and books are a social product, as are the libraries that hold them. So social activity makes it possible for us to remember what no human being could remember as an isolated entity.
Individual biological limitations understood from viewing individuals as isolated entities in a vacuum are not individual limitations for individuals embedded in society. It is not that the whole is more than the sum of its parts. It is that the properties of the parts cannot be understood except in their context in the whole. Parts do not have individual properties in some isolated sense, but only in the context in which they are found. The theory of human nature that searches for that nature in the products of genes in individuals and the limitations of individuals caused by those genes, or in the properties of an external world that are fixed and that cannot be altered except in a destructive way misses the whole point.
It is indeed the case that human social and political organization is a reflection of our biological being, for, after all, we are material biological objects developing under the influence of the interaction of our genes with the external world. It is certainly not the case that our biology is irrelevant to social organization. The question is, what part of our biology is relevant? If one were to choose a simple biological property of human beings that was of supreme importance, it would be our size. The fact that we are somewhere between five and six feet tall has made all of human life possible as we know it. Gulliver's Lilliputians, who were said to be six inches tall, could not, in fact, have had the civilization that he ascribed to them because six-inch-tall human beings, no matter how they were shaped and formed, could not have created the rudiments of a technological civilization. For example, they could not have smelted iron. They could not have mined minerals, because a six-inch-tall being could not get sufficient kinetic energy from swinging a tiny pickax to break rocks. That is why when babies fall they do not hurt themselves. Nor could the Lilliputians have controlled fire, because the tiny twigs that they could bring to a fire would burn up instantly. Nor is it likely that they could have thought about mining or have been able to speak, because their brains would be physically too small. It probably takes a central nervous system of a certain size to have enough connections and enough complexity of topology for speech. Ants may be terribly strong and terribly clever for their size, but their size alone guarantees that they will never write books about people.
The most important fact about human genes is that they help to make us as big as we are and to have a central nervous system with as many connections as it has. However, there are not enough genes to determine the detailed shape and structure of that nervous system nor of the consciousness that is an aspect of that structure. Yet it is consciousness that creates our environment, its history and the direction of its future. This then provides us with a correct understanding of the relation between our genes and the shape of our lives.
Our DNA is a powerful influence on our anatomies and physiologies. In particular, it makes possible the complex brain that characterizes human beings. But having made that brain possible, the genes have made possible human nature, a social nature whose limitations and possible shapes we do not know except insofar as we know what human consciousness has already made possible. In Simone de Beauvoir's clever but deep apothegm, a human being is _"l'être dont l'être est de n'être pas,"_ the being whose essence is in not having an essence.
History far transcends any narrow limitations that are claimed for either the power of genes or the power of the environment to circumscribe us. Like the House of Lords that destroyed its own power to limit the political development of Britain in the successive Reform Acts to which it assented, so the genes, in making possible the development of human consciousness, have surrendered their power both to determine the individual and its environment. They have been replaced by an entirely new level of causation, that of social interaction with its own laws and its own nature that can be understood and explored only through that unique form of experience, social action.
## **Notes**
### 1/ A REASONABLE SKEPTICISM
. C.B. MacPherson, _The Political Theory of Possessive Individualism_ (New York: Oxford University Press, 1962).
### 2/ ALL IN THE GENES?
. R.J. Herrnstein, _I.Q. in the Meritocracy_ (Boston: Altantic-Little, Brown, 1973), 221.
. L.F. Ward, "Education" (manuscript, Special Collection Division, Brown University, Providence, RI, 1873).
. A.R. Jensen, "How much can we boost I.Q. and scholastic achievement?", _Harvard Educational Review_ 39 (1969): 15.
. C.C. Brigham, _A Study of American Intelligence_ (Princeton: Princeton University Press, 1923), 209-210.
. H.L. Garrett, _Breeding Down_ (Richmond, VA: Patrick Henry Press, no date).
. H.F. Osborne, letter, _New York Times,_ 8 April 1924, 18.
. R.C. Lewontin, S. Rose, and L.J. Kamin, _Not in Our Genes_ (New York: Pantheon, 1984), 101-106.
. L.J. Kamin, _The Science and Politics of I.Q._ (Potomac, MD: Erlbaum, 1974).
. Ibid.
. Jensen, _op cit._
. B. Tizard. "IQ and Race," _Nature_ 247 (1974): 316.
. R.C. Lewontin, _Human Diversity_ (San Francisco: Scientific American Books, 1982).
### 3/ CAUSES AND THEIR EFFECTS
. E.M. East and D.F. Jones, _Inbreeding and Outbreeding_ (Philadelphia: Lippincott, 1919).
### 4/ A STORY IN TEXTBOOKS
. E.O. Wilson, _Sociobiology: The New Synthesis_ (Cambridge, MA: Harvard University Press, 1975).
. Ibid., 562.
. Ibid., 561.
. Ibid., 119.
. Ibid., 556.
. Ibid., 575.
. Ibid., 552.
. Ibid., 554.
. P. A. Kropotkin, _Mutual Aid_ (1901), Chapter 1.
. E.O. Wilson, "Human decency is animal," _New York Times Magazine,_ 12 October 1975, 38-50.
. _Exploring Human Nature_ (Cambridge, MA: Education Development Center, 1973).
### 5/ SCIENCE AS SOCIAL ACTION
. E.O. Wilson, _Sociobiology,_ 575.
## **About the Author**
R. C. Lewontin was born and raised in New York City. In 1951 he earned a bachelor's degree in biology at Harvard University, followed by a master's degree in mathematical statistics, and a doctorate in zoology at Columbia University. Lewontin went on to teach at North Carolina State University, the University of Rochester, and the University of Chicago. A leading geneticist, he is well known for his work in population and experimental genetics, his interest in new technology, and his critiques concerning aspects of neo-Darwinism. Lewontin is the author of many books including _The Genetic Basis of Evolutionary Change, It Ain't Necessarily So_ , and _The Triple Helix_ , and co-author of _Not in Our Genes_ (with Steven Rose and Leon J. Kamin), _The Dialectical Biologist_ , and _Biology Under the Influence_ (with Richard Levins). Lewontin is also a frequent contributor to the _New York Review of Books_. He is Alexander Agassiz Research Professor at the Museum of Comparative Zoology at Harvard University.
## **The Massey Lectures Series**
The Massey Lectures are co-sponsored by CBC Radio, House of Anansi Press, and Massey College in the University of Toronto. The series was created in honour of the Right Honourable Vincent Massey, former Governor General of Canada, and was inaugurated in 1961 to provide a forum on radio where major contemporary thinkers could address important issues of our time.
This book comprises the 1990 Massey Lectures, "Biology as Ideology: The Doctrine of DNA," broadcast in November 1990 as part of CBC Radio's _Ideas_ series. The producer of the series was Jill Eisen; the executive producer was Bernie Lucht.
## The CBC Massey Lectures Series List
_The Wayfinders_
Wade Davis
ISBN 978-0-88784-842-1
eISBN 978-0-88784-969-5
_Payback_
Margaret Atwood
ISBN 978-0-88784-810-0
eISBN 978-0-88784-872-8
_More Lost Massey Lectures_
Bernie Lucht, ed.
ISBN 978-0-88784-801-8
eISBN 978-0-88784-866-7
_The City of Words_
Alberto Manguel
ISBN 978-0-88784-763-9
eISBN 978-0-88784-849-0
_The Lost Massey Lectures_
Bernie Lucht, ed.
ISBN 978-0-88784-217-7
eISBN 978-0-88784-864-3
_The Ethical Imagination_
Margaret Somerville
ISBN 978-0-88784-747-9
eISBN 978-0-88784-883-4
_Race Against Time_ Stephen Lewis
ISBN 978-0-88784-753-0
eISBN 978-0-88784-875-9
_A Short History of Progress_
Ronald Wright
ISBN 978-0-88784-706-6
eISBN 978-0-88784-843-8
_The Truth About Stories_
Thomas King
ISBN 978-0-88784-696-0
eISBN 978-0-88784-895-7
_Beyond Fate_
Margaret Visser
ISBN 978-0-88784-679-3
eISBN 978-0-88784-846-9
_The Cult of Efficiency_
Janice Gross Stein
ISBN 978-0-88784-678-6
eISBN 978-0-88784-880-3
_The Rights Revolution_
Michael Ignatieff
ISBN 978-0-88784-762-2
eISBN 978-0-88784-892-6
_The Triumph of Narrative_
Robert Fulford
ISBN 978-0-88784-645-8
eISBN 978-0-88784-894-0
_Becoming Human_
Jean Vanier
ISBN 978-0-88784-809-4
eISBN 978-0-88784-845-2
_The Elsewhere Community_
Hugh Kenner
ISBN 978-0-88784-607-6
eISBN 978-0-88784-882-7
_The Unconscious Civilization_
John Ralston Saul
ISBN 978-0-88784-731-8
eISBN 978-0-88784-896-4
_On the Eve of the Millennium_
Conor Cruise O'Brien
ISBN 978-0-88784-559-8
eISBN 978-0-88784-870-4
_Democracy on Trial_
Jean Bethke Elshtain
ISBN 978-0-88784-545-1
eISBN 978-0-88784-854-4
_Twenty-First Century Capitalism_
Robert Heilbroner
ISBN 978-0-88784-534-5
eISBN 978-0-88784-897-1
_The Malaise of Modernity_
Charles Taylor
ISBN 978-0-88784-520-8
eISBN 978-0-88784-886-5
_Biology as Ideology_
R. C. Lewontin
ISBN 978-0-88784-518-5
eISBN 978-0-88784-847-6
_The Real World of Technology_
Ursula Franklin
ISBN 978-0-88784-636-6
eISBN 978-0-88784-891-9
_Necessary Illusions_
Noam Chomsky
ISBN 978-0-88784-574-1
eISBN 978-0-88784-868-1
_Compassion and Solidarity_
Gregory Baum
ISBN 978-0-88784-532-1
eISBN 978-0-88784-851-3
_Prisons We Choose to Live Inside_
Doris Lessing
ISBN 978-0-88784-521-5
eISBN 978-0-88784-874-2
_Latin America_
Carlos Fuentes
ISBN 978-0-88784-665-6
eISBN 978-0-88784-862-9
_Nostalgia for the Absolute_
George Steiner
ISBN 978-0-88784-594-9
eISBN 978-0-88784-869-8
_Designing Freedom_
Stafford Beer
ISBN 978-0-88784-547-5
eISBN 978-0-88784-855-1
_The Politics of the Family_
R. D. Laing
ISBN 978-0-88784-546-8
eISBN 978-0-88784-889-6
_The Real World of Democracy_
C. B. Macpherson
ISBN 978-0-88784-530-7
eISBN 978-0-88784-890-2
_The Educated Imagination_
Northrop Frye
ISBN 978-0-88784-598-7
eISBN 978-0-88784-881-0
Available in fine bookstores and at www.anansi.ca
## **About the publisher**
House of Anansi Press was founded in 1967 with a mandate to publish Canadian-authored books, a mandate that continues to this day even as the list has branched out to include internationally acclaimed thinkers and writers. The press immediately gained attention for significant titles by notable writers such as Margaret Atwood, Michael Ondaatje, George Grant, and Northrop Frye. Since then, Anansi's commitment to finding, publishing and promoting challenging, excellent writing has won it tremendous acclaim and solid staying power. Today Anansi is Canada's pre-eminent independent press, and home to nationally and internationally bestselling and acclaimed authors such as Gil Adamson, Margaret Atwood, Ken Babstock, Peter Behrens, Rawi Hage, Misha Glenny, Jim Harrison, A. L. Kennedy, Pasha Malla, Lisa Moore, A. F. Moritz, Eric Siblin, Karen Solie, and Ronald Wright. Anansi is also proud to publish the award-winning nonfiction series The CBC Massey Lectures. In 2007 and 2009 Anansi was honoured by the Canadian Booksellers Association as "Publisher of the Year."
| {
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Q: Gmail API endpoint "https://accounts.google.com/o/oauth2/v2/auth" does not return authorization code The "https://accounts.google.com/o/oauth2/v2/auth" endpoint is used to initiate the authorization code flow for authenticating and obtaining a token through the provided authorization code
When this endpoint is called, it redirects the user to the gmail authorization login page, where the user can enter their credentials and consent to the requested permissions. After successful authentication, page will be redirected the user back to the redirect URI specified in the initial request, along with an authorization code in the query string. But in our case, sometimes we do not receive "code" along with redirect URI in the query string.
Could you please let us know what could be causing the issue here?
It is a random issue, sometimes we do not receive "code" along with redirect URI in the query string.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 655 |
{"url":"http:\/\/accessmedicine.mhmedical.com\/content.aspx?bookid=331§ionid=40726841","text":"Chapter 103\n\nAnemias associated with normocytic and normochromic red cells and an inappropriately low reticulocyte response (reticulocyte index <2\u20132.5) are hypoproliferative anemias. This category includes early iron deficiency (before hypochromic microcytic red cells develop), acute and chronic inflammation (including many malignancies), renal disease, hypometabolic states such as protein malnutrition and endocrine deficiencies, and anemias from marrow damage.\n\nMarrow damage states are discussed in Chap. 107.\n\nHypoproliferative anemias are the most common anemias, and anemia associated with chronic inflammation is the most common of these. The anemia of inflammation, similar to iron deficiency, is related in part to abnormal iron metabolism. The anemias associated with renal disease, inflammation, cancer, and hypometabolic states are characterized by an abnormal erythropoietin response to the anemia.\n\nIron is a critical element in the function of all cells, although the amount of iron required by individual tissues varies during development. At the same time, the body must protect itself from free iron, which is highly toxic in that it participates in chemical reactions that generate free radicals such as singlet O2 or OH. Consequently, elaborate mechanisms have evolved that allow iron to be made available for physiologic functions while at the same time conserving this element and handling it in such a way that toxicity is avoided.\n\nThe major role of iron in mammals is to carry O2 as part of hemoglobin. O2 is also bound by myoglobin in muscle. Iron is a critical element in iron-containing enzymes, including the cytochrome system in mitochondria. Iron distribution in the body is shown in Table 103-1. Without iron, cells lose their capacity for electron transport and energy metabolism. In erythroid cells, hemoglobin synthesis is impaired, resulting in anemia and reduced O2 delivery to tissue.\n\nTable 103-1 Body Iron Distribution\n\n### The Iron Cycle in Humans\n\nFigure 103-1 outlines the major pathways of internal iron exchange in humans. Iron absorbed from the diet or released from stores circulates in the plasma bound to transferrin, the iron transport protein. Transferrin is a bilobed glycoprotein with two iron binding sites. Transferrin that carries iron exists in two forms\u2014monoferric (one iron atom) or diferric (two iron atoms). The turnover (half-clearance time) of transferrin-bound iron is very rapid\u2014typically 60\u201390 min. Because almost all of the iron transported by transferrin is delivered to the erythroid marrow, the clearance time of transferrin-bound iron from the circulation is affected most by the plasma iron level and the erythroid marrow activity. When erythropoiesis is markedly stimulated, the pool of erythroid cells requiring iron increases and the clearance time of iron from the circulation decreases. The half-clearance time ...\n\nSign in to your MyAccess Account while you are actively authenticated on this website via your institution (you will be able to tell by looking in the top right corner of any page \u2013 if you see your institution\u2019s name, you are authenticated). You will then be able to access your institute\u2019s content\/subscription for 90 days from any location, after which you must repeat this process for continued access.\n\nOk\n\n## Subscription Options\n\n### AccessMedicine Full Site: One-Year Subscription\n\nConnect to the full suite of AccessMedicine content and resources including more than 250 examination and procedural videos, patient safety modules, an extensive drug database, Q&A, Case Files, and more.","date":"2014-10-30 18:57:08","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\": 0.17548784613609314, \"perplexity\": 8030.479496800283}, \"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-2014-42\/segments\/1414637898751.26\/warc\/CC-MAIN-20141030025818-00176-ip-10-16-133-185.ec2.internal.warc.gz\"}"} | null | null |
The new monitor has its ups and downs (I think I've fixed the driver conflict), but one of the ups is definitely the automatic portrait mode. I just turn the screen 90°, and the screen magically reorients itself. Really, I have no idea how it is done. It must be magic.
In this mode, the monitor seems very tall indeed, and things don't fall off the bottom nearly as quickly. This is glorious when writing, since pages are never as wide as they are tall, and words flow naturally from top to bottom, with a decent line length.
There's a quirk of portrait mode, though, that I just discovered tonight. When the screen loads a new Web page, it normally rewrites lines from top to bottom. Your eyes do not notice this; the refresh is scanning too quickly. But in portrait mode, the refresh happens from right to left, against the grain of your eye's movement across the page. You can see the refesh, just barely, and the page load makes a tiny flicker as you turn the pages of the Internet.
I love this — even the direction is just like a book. Flip. Flip. Riffle — fffffffp.
The Internet sure has a lot of pages.
Like a book -- that's so cool!
It's one of those little things that amuses me way more than seems reasonable.
I like it when tech does something subtle, rather than the flashy stuff. | {
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\section{Introduction.}
High T$_c$ superconductivity of the cuprates, it is generally agreed
upon, emerges out of an unconventional normal state. The most remarkable
signatures of its strange metal behavior are the pseudogap in the density of
states and the associated to it remnant Bogoliubov modes. Both show up in a
wide temperature regime above T$_c$ in the single-particle excitations, observed
in angle resolved photoemission spectroscopy (ARPES) \cite{expPG}. Novel
scanning tunneling microscopy are now able to measure the spatial distribution
of quasi-particle excitations on the atomic length scale \cite{Kohsaka-2007,Gomes-2007,McElroy-2003,Valla-2006,Kohsaka-2008} and
find intrinsic
textured electronic structures, ranging over a wide regime from low doped
to optimally doped and beyond. The spatial patterns of the single-particle spectral properties indicate an inter-relation between the low frequency Bogoliubov
modes and their high frequency counterparts, representing localized glassy
structures. In this work we show how this feature can be related to a scenario in
which itinerant fermionic charge carriers scatter in and out of bosonic tightly
bound pairs of them in which they are momentarily trapped on nano-size
deformable molecular clusters. The single-particle excitations thus appear as superpositions of itinerant and localized entities.
\begin{figure}[t]
\begin{center}
\includegraphics*[width=3in,angle=0]{fig1_jrTD09PRB.eps}
\caption{(Color online) An idealized picture of the local structure of the CuO$_2$ planes,
compatible with the STM results \cite{Kohsaka-2007,Gomes-2007,McElroy-2003,Valla-2006,Kohsaka-2008}.
It is composed of (i)
Cu$_4$O$_{12}$ domains acting as localizing pairing centers with directionally oriented
Cu-O-Cu molecular bonds, having central bridging O's (grey circles) which can be displaced out of the
CuO$_2$ plane and (ii) Cu$_4$O$_4$ square plaquettes housing the delocalized charge carriers.
Small red circles denote Cu cations and the larger blue ones the O anions not directly involved
in displacements.}
\label{fig1}
\end{center}
\end{figure}
Ever since the discovery of the high T$_c$ cuprates, experimental evidence for
their very unusual lattice properties has become increasingly evident. Apart
from their well established strongly correlated nature, these compounds
are metastable single phase materials \cite{Sleight-1991}. Their metastability
arises from frozen-in structural misfits, involving an incompatibility
between the Cu-O distances of square planar [Cu-O$_4$] configurations in the
CuO$_2$ planes and of cation-ligand distances in the adjacent layers.
Metastable compounds have been known for a long time for their intrinsic
local diamagnetic fluctuations \cite{Vandenberg-1977}, capable of inducing a
strong pairing component in the many-body ground state wave function.
The interest in synthesizing materials with such properties was to bypass the
stringent conditions on the upper limit of T$_c$, imposed by phonon mediated
BCS superconductivity \cite{Anderson-1966}.
On a microscopic level, the metastability in the cuprates arises from
fluctuating [Cu-O-Cu] molecular bonds in the CuO$_2$ planes \cite{Kohsaka-2007,Gomes-2007}. Their deformable ligand
environments \cite{Cuk-2004,Lee-2006} act as potential pairing centers \cite{McElroy-2003} induced in the undoped systems upon hole doping. These nano
size domains exhibit an atomic structure \cite{Valla-2006}, which
locally breaks translational as well as rotational symmetry \cite{Kohsaka-2008}.
Two degenerate spatially orthogonally oriented [Cu-O-Cu] bonds cause the
CuO$_2$ plane structure to segregate into a patchwork of orientationally disordered
domains, separated by a lattice of essentially undeformable molecular
clusters. Ultimately, this forms an effective bipartite lattice
structure \cite{Kohsaka-2007,Kohsaka-2008} of the CuO$_2$ planes. The
charge transfer between the pairing centers and the molecular clusters on
the lattice surrounding them leads to resonant pairing on that latter. It
is controlled by an interplay between localization of the charge
carriers in form of bound pairs on the pairing centers and their delocalization
on the lattice which spatially separates them. On a macroscopic level,
those materials exhibit an overall homogeneous crystal structure
in a coarse grained sense \cite{Balatsky-2006}. But occasionally, such as in
La$_{2-x}$Ba$_{x}$CuO$_4$ for x=1/8, the local lattice deformations of the
pairing centers lock together in a charge ordered phase and thereby impeach superconductivity to occur\cite{Valla-2006}.
\section{THE SCENARIO}
The "formal chemical" Cu valence - not to be confused with its ionic charge -
in the d-hole doped CuO$_2$ planes lies between Cu$^{II}$ and Cu$^{III}$. For
an isolated undoped CuO$_2$ plane this would correspond to stereochemical
[Cu$^{II}$-O] distances of 1.94 $\AA$ in the [Cu-O$_4$] basic blocks. The misfits
between the atomic structure of the CuO$_2$ planes and those of the adjacent
layers, which furnish the dopant holes, push the bridging oxygen of the
[Cu-O-Cu] bonds out of the CuO$_2$ plane, making them buckled. By doing so,
they can accommodate the stereochemically assigned inter-atomic distance of
those bonds.
The scenario for the doped cuprates, which we want to advocate in this work, is
that the static displacements of the bridging oxygens, which characterize the
undoped and low doped insulating phase, become dynamic. The fluctuation of
the bridging oxygens of the [Cu-O-Cu] bonds, in and out of the planes, tends
to diminish the plane buckling which characterizes the undoped material.
This tendency gets more and more pronounced as the doping is increased, driven
by the increased covalency of the CuO$_2$ basal plane building
blocks. It however shows a marked slowing down of this behavior as one passes
through optimal doping\cite{Roehler-2004}. On a microscopic level, this implies
fluctuations between kinked [Cu$^{II}$ - O - Cu$^{II}$] molecular
bonds (characteristic for the undoped systems) and straightened out ones
[Cu$^{III}$ - O - Cu$^{III}$], with an ideal stereochemical [Cu$^{III}$-O] distances
of 1.84 $\AA$. In this process two electrons get momentarily captured in the
local dynamically deformable structure of the CuO$_2$ planes. It results in
locally correlated charge-deformation fluctuations which break up the
over-all homogeneous structure of the cuprates into a checker-board
structure, as scanning tunneling microscopy (STM) results (Figs. 4 and 5 in
Ref. 6) have shown. The net difference in length between the
two different molecular bonds on such charge-deformation fluctuating
checker-board pairing domains can be reduced (i) because of the dynamical
nature of these pairing fluctuations and (ii) because it involves
cooperatively several of such [Cu-O-Cu] bonds.
The likelihood of a segregation of a homogeneous lattice structure into
polaronic domains, embedded in a non-polaronic matrix, such as advocated
in the present scenario, had been speculated upon for a long time. For the case
of intermediate electron-lattice coupling and the adiabatic to anti-adiabatic
cross-over regime, individual itinerant charge carriers are known to fluctuate
in and out of localized polaronic states \cite{Polaronworks}. Unfortunately,
the present state of art of the theory of many-polaronic systems can still
not handle situations other than for homogeneous or globally symmetry broken
solutions. Nevertheless indications for resonant pairing in such systems
exist, where the single-particle spectral function has both coherent
delocalized contributions and localized ones in form of localized polarons, respectively bipolarons. This has been discussed in the framework of dynamical
mean field theory, numerical renormalization group and Monte Carlo
studies \cite{DMFT-polarons}.
Given the complexity of the inter-related charge-deformation dynamics in
such systems, it appeared judicious to introduce a phenomenological
Boson-Fermion model (BFM), to capture the salient features of such intrinsically
locally dynamically unstable systems with a tendency to segregate into
subsystems of localized and itinerant charge carriers. This idea was
originally proposed by one of us (JR) in the early eighties in an attempt
to describe the abrupt cross-over between a weak coupling adiabatic
electron-phonon mediated BCS superconductor and an insulating state,
respectively superconducting phase, of bipolarons in the strong coupling
anti-adiabatic regime. The essential features of this conjectured BFM was to
introduce an effective local boson-fermion exchange coupling between
polaronically bound pairs and itinerant charge carriers. This picture
has been substantiated subsequently by small cluster calculations for
electrons strongly coupled to localized lattice vibrational
modes \cite{Ranninger-2006-2008}. It permits to relate the effective
boson-fermion exchange coupling back to the parameters, characterizing
the electron-lattice coupled system, ie., local phonon frequency and
electron-phonon coupling.
In order to cast into a tractable model the physics of dynamically fluctuating
[Cu-O-Cu] bonds, which trigger local double charge fluctuations, we present
in Fig. 1 an idealized structure for such a local checker-board bipartite
lattice structure, which comes very close to the actually observed structure.
The corresponding checker-board pairing centers consist of Cu$_4$O$_{12}$
domains (three nearest neighbor Cu-Cu distances across) on which charge
carriers pair up, driven by polaronic effects. The lattice deformations
of adjacent Cu$_4$O$_{12}$ domains are assumed to be uncorrelated in order
to prevent the system to undergo a global lattice instability. The
orientational randomness of the [Cu-O-Cu] unidirectional bonds, together with
the quadratic Cu$_4$O$_4$ plaquettes (see Fig.1), which separate those
polaronic Cu$_4$O$_{12}$ domains, justifies that. Ultimately, this results
in the picture of an overall bipartite lattice structure for the CuO$_2$ planes
with a periodicity of four nearest neighbor Cu-Cu distances. d-holes on the
non-polaronic Cu$_4$O$_4$ plaquettes in the cuprates are known to behave
as delocalized, though strongly correlated, entities subject to
d$_{x^2 - y^2}$ - wave pairing correlations \cite{Hirsch-1988,Altman-2002}.
In the present study we shall concentrate on the purely lattice driven
pairing aspects in the cuprates, caused by their intrinsic metastabilities. We
hence neglect here any Hubbard type correlations leading to hole pairing and
treat the Cu$_4$O$_4$ square plaquettes as effective lattice sites on which
the charge carriers behave as itinerant uncorrelated quasi-particles.
When they hop on and off the Cu$_4$O$_{12}$ pairing centers,
they interact with their local dynamical deformations. The resulting local
physics for resonant pairing for such a set-up and its manifestations in the
electronic and phononic spectral properties have been studied in some detail
by exact diagonalization studies \cite{Ranninger-2006-2008}.
Indications for resonant pairing in the cuprates, driven by local dynamical
lattice fluctuations can be found in quite a variety of experimental studies:
the longitudinal optical (LO) Cu-O bond stretching mode of about 60 meV appears
strongly coupled to charge carriers
near the {\it hotspot} anti-nodal points in the Brillouin zone (BZ) $[q_x,q_y]=
[\pm \pi/2,0],[0, \pm \pi/2]$ \cite{Cuk-2004,Lee-2006}. Their pairing results
in the pseudogap feature, setting in when reducing the temperature T to below
a certain, strongly doping dependent, T$^*$. Upon entering the superconducting
doping regime, coming from the insulating parent compound, this LO mode
splits into two modes, separated by $\simeq$ 10 meV \cite{Reznik-2006}.
This indicates a crystal lattice symmetry breaking, linked to dynamical
charge inhomogeneities which are absent in the underdoped and overdoped insulating phases. Pressure \cite{Haefliger-2006},
isotope substitution studies \cite{Rubio-Temprano-2000} and atomic resolution
$d^2I/d V^2$-spectroscopy \cite{Lee-2006} show concomitant anticorrelated modulations
of the pseudo-gap size and the frequency of this LO buckling mode. Correlated
charge-deformation fluctuations, related to a resonant pairing superconducting phase show up in
the onset of a macroscopic superfluid state of the charge carriers together with
changes in the local lattice dynamics which acquires phase correlated macroscopic features.
They are seen in Rutherford back scattering experiments \cite{Sharma-1996}, an abrupt
decrease in the kinetic energy of local vibrational modes \cite{Mook-1990}, a similar abrupt
increase of a low energy electronic background, seen in near IR excited Raman
scattering \cite{Ruani-1997} and an increase in intensity of certain Raman active
phonon modes \cite{Misochko-1999}, indicative of changes in the scattering mechanism
involving the charge carriers and local lattice modes.
\section{THE MODEL}
Superconductivity in the cuprates is destroyed, exclusively, by phase
fluctuations of a bosonic order parameter \cite{Emery-Kivelson-1995,Franz-1998},
with the finite amplitude of it, being already established well above T$_c$.
It reflects the local nature of the Cooper-pairs, whose signature is (i) a $T_c$ scaling with the zero temperature density of superfluid carriers \cite{Uemura-1989} and (ii) the XY character of the transition \cite{Salamon-1993}. Going into the normal state, above T$_c$, the propagating
Cooperons become diffusive and the superconducting gap changes into a pseudogap
in a continuous fashion \cite{Devillard-2000}. The observed Nernst \cite{Wang-2006}, transient Meissner effect \cite{Corson-1999} and the proximity induced
pseudogap \cite{Yuli-2009} bare this out. The gap in the single-particle
spectrum and the diffusively propagating strongly bound Cooper pairs testify
the competition between amplitude and phase fluctuations of the order parameter
in form of an anti-correlated T$_c$ versus T$^*$ variation upon changing
the hole doping \cite{Tesanovic-2008,Huefner-2008}. The insulating, not
antiferromagnetically ordered glassy state, at low temperature and low doping
can be envisaged as a Mott correlation driven state of phase
uncorrelated singlet-{\it bonding pairs}. With increased doping, this
insulating state changes into a superconducting phase correlated state of such
{\it bonding pairs} \cite{Cuoco-2006,Stauber-2007}.
{\it Bonding pairs} are defined by local linear superpositions of bound pairs
and pairs of itinerant charge carriers. To what extent such an insulating state could result from a Cooper-pair Wigner crystallization, has been investigated \cite{Tesanovic-2004,Pereg-Barnea-2006}.
The features which characterize the normal and superconducting phase of the cuprates
necessitate to treat amplitude and phase fluctuations on an equal footing. This had
originally also been the objective in conjecturing the BFM and to project out coexisting
effective bosonic and fermionic charge excitations for systems which are at the frontier
between amplitude
fluctuation driven BCS superconductors and a phase fluctuation driven superfuidity of tightly
bound real-space pairs. The BFM is designed to treat a \underline{single component} system,
where at any given moment a certain percentage of the charge carriers is locally paired and
thus results in a finite bosonic amplitude. This is achieved by imposing a common chemical
potential (determined by the bosonic energy level) for the fermionic and bosonic charge carriers.
A charge exchange term, linking the fermionic and bosonic subsystem, then controls the
inter-related dynamics between amplitude and phase fluctuations. It drives the system either
to an insulating or superfluid state with corresponding superconducting, respectively
insulating, gaps being centered at the chemical potential. The opening of such gaps
does not depend on any particular set of Fermi wavevectors and hence is unrelated to any
global translational symmetry breaking.
The degree of anisotropy of pairing and of the charge carrier dispersion
in the CuO$_2$ planes monitors the relative importance of localization
versus delocalization in different regions of the Brillouin zone. Near the
anti-nodal points, strong pairing results from strong intra-{\it bonding pair} correlations between bound pairs on the pairing centers
and their itinerant counterparts in their immediate vicinity \cite{Ranninger-2006-2008}. It leads to their partial localization, which
shows up in form of a pseudogap in the single-particle spectral properties
and destroys the Fermi surface. As one moves toward the nodal points,
$[k_x,k_y] = [\pm \pi/2,\pm \pi/2]$, along the socalled Fermi arc in the
Brillouin zone (corresponding to the Fermi surface in the non-interacting
system), those intra-{\it bonding pair} phase correlations are weakened. The
degree of localization then reduces and with it, the size of the pseudogap.
At the same time, inter-{\it bonding pair} phase correlations between
neighboring pairing domains come into play and with it, superconducting phase
locking. At low energies, this leads to Bogoliubov like modes, which emerge out
of localized phase uncorrelated {\it bonding pairs}. We derive below these
properties on the basis of the BFM, adapted to the specific anisotropic
features of the cuprates.
Transposing our picture of the cuprate molecular structure (Fig. 1) onto the
BFM (see also Figs. 3 and 4 in Ref.~\cite{Ranninger-2010}) implies the
following: We introduce effective lattice sites, which are
composed of two components: One which represents the pairing centers
(the Cu$_4$O$_{12}$ domains) and describes selftrapped bosonic pairs of charge
carriers. The other one which describes the itinerant charge carriers on the
four-site ring, constituted of the Cu$_4$O$_4$ plaquettes, taking into account
that each such plaquette is shared by four neighboring pairing centers. For
the undoped half-filled band situation, with one electron per Cu site, we thus
have four itinerant electrons on the ring, belonging to a specific pairing
center and four electrons being localized in form of two
Cu$^{II}$-O-Cu$^{II}$ bonds on the pairing centers. Deviating from the
undoped limit upon doping n$_h$ holes per Cu ion into the systems, reduces the
concentration of Cu$^{II}$-O-Cu$^{II}$ bonds in the trapping centers by
n$_B$ $\simeq$ $\frac{1}{2}$ n$_h$ . This opens up the phase space for
itinerant electrons from the four-site ring to hop on off those trapping
centers. Such a resonant scattering process converts a small
number n$_B$ of those itinerant charge carriers
into bosonic bound pairs. Following the experimental results of the strong
changes in local lattice properties with hole doping, we assume that hole
doping monitors exclusively the concentration of the Cu$^{II}$-O-Cu$^{II}$
bonds and that hence the total number of itinerant electrons and induced pairs
of them will remain roughly the same as it was in the undoped case, i.e.,
n$_{tot}$ = n$_F$ + 2n$_B$ = 1.
The d-wave paring symmetry of those systems imposes an analogous d-wave symmetry
for the exchange interaction between (i) pairs
of itinerant charge carriers $c^{(\dagger)}_{{\bf k}\sigma}$, corresponding
to the "plaquette site" states and (ii) polaronicaly bound pairs of them
$b_{\bf q}^{(\dagger)}$, corresponding to the "pairing center site" states.
The Hamiltonian describing such a scenario is then given by
\begin{eqnarray}
H_{BFM} &=& H^0_{BFM} + H^{exch}_{BFM} \\
H^0_{BFM} &=& \sum_{{\bf k}\sigma}(\varepsilon_{\bf k} -\mu)c_{{\bf k}\sigma}^{\dagger}
c_{{\bf k}\sigma}+\sum_{\bf q}
(E_{\bf q}-2\mu) b_{\bf q}^{\dagger} b_{\bf q}.\qquad\\
H^{exch}_{BFM}&=&(1/\sqrt{N})\sum_{{\bf k},{\bf q}}(g_{{\bf k},{\bf q}}b_{\bf q}\dag
c_{{\bf q-k},\downarrow}c_{{\bf k},\uparrow}+H.c.),
\label{H_exch}
\end{eqnarray}
The anisotropy, which characterizes the electronic structure of cuprates, is contained
in the standard expression for the bare charge carrier dispersion given by
$\varepsilon_{\bf k} = -2t[cos k_x + cos k_y] + 4t'cos k_x cos k_y$ of the
CuO$_2$ planes with $t'/t=0.4$ and the bare d-wave exchange coupling
$g_{{\bf k},{\bf q}} = g[cos k_x - cos k_y]$. Given the polaronic origin of the
localized pairs of tightly bound charge carriers, we assume them as dispersionless
bosonic excitations with $E_{\bf q}=2\Delta$.
The charge exchange term $H^{exch}_{BFM}$ controls the transfer of electrons
(holes) between real and momentum space \cite{Hanaguri-2008} and monitors the
interplay between the delocalizing and the localizing effect. Depending on the strength of
the exchange coupling $g_{{\bf k},{\bf q}}$, it results in a
competition between local intra-{\it bonding pair} correlations, favoring insulating features,
and spatial inter-{\it bonding pair} correlations, favoring superconducting phase locking \cite{Cuoco-2006}. The
fermionic particles thereby acquire contributions coming from the bosonic particles and the
bosonic particles having features derived from their fermionic constituents. As we shall see
below, the physically meaningful fermions in such a system are superpositions of fermions and
bosonic bound fermion pairs, accompanied by fermion holes. This boson-fermion duality, which
characterizes the electronic state of the cuprates, results from
the "duplicituous"\cite{Hanaguri-2008} nature of their charge carriers, which
supports simultaneously superconducting correlations
in momentum space (fermionic Bogoliubov excitations) and real space correlations resulting
in the pseudogap (derived from localized bosonic bound fermion pairs). This apparent "schizophrenic"
behavior \cite{Goss-Levi-2007} of the quasi-particles can be traced back to their different energy
scales characterizing their excitations. Large excitation energies (above the Fermi energy)
characterize their localized selftrapped nature and small excitation energies (below the Fermi energy) their
quasi-coherently propagating Cooper pair nature.
In order to obtain the spectroscopic features of effective fermionic and bosonic excitations we
have to reformulate this interacting Boson-Fermion mixture in terms of two effective
commuting Hamiltonians, one describing purely fermionic excitations and one purely
bosonic ones. The boson-fermion interaction thereby is absorbed into inter-dependent
coupling constants by renormalizing $g_{{\bf k},{\bf q}}$ down to zero via a
flow-equation renormalization approach \cite{Wegner-1994}. At every step of this procedure the
renormalized Hamiltonian is projected onto the basic structure given by $H^0_{BFM}$ plus a
renormalization generated fermion-fermion interactions term\cite{Domanski-2001}
\begin{eqnarray}
H^{F-F}_{BFM} = {1 \over N} \sum_{{\bf p},{\bf k},{\bf q}} U^{F-F}_{{\bf p},{\bf k},{\bf q}}
c^{\dagger}_{{\bf p} \uparrow}c^{\dagger}_{{\bf k} \downarrow}c_{{\bf q} \downarrow}
c_{{\bf p}+{\bf k}-{\bf q} \uparrow}.
\end{eqnarray}
This is achieved by transforming the Hamiltonian in infinitesimal steps,
controlled by a flow parameter $\ell$ in tems of repeated unitary transformations
$H(\ell)=e^{S(\ell)}He^{-S(\ell)}$, resulting in differential equations
$\partial_\ell H(\ell)=[\eta(\ell),H(\ell)]$ with
$\eta(\ell) \equiv (\partial_\ell e^{S(\ell)}/\partial_\ell)e^{-S(\ell)}$, determining the flow of the parameters of our system. In its canonical form \cite{Wegner-1994}, $\eta(\ell)=[H^0(\ell),H(\ell)]$ presents an
anti-Hermitean generator. For details of the ensuing coupled non-linear differential
equations for the various $\ell$ dependent parameters $\varepsilon_{\bf k}(\ell),
E_{\bf q}(\ell), U^{F-F}_{{\bf p},{\bf k},{\bf q}}(\ell), g_{{\bf k},{\bf q}}(\ell), \mu(\ell)$
we refer the reader to our previous work \cite{Domanski-2001,Domanski-2003a}. The parameters,
characterizing $H^0$ and $H^{exch}$, evolve as the flow parameter $\ell$ increases.
The renormalization procedure starts with $\ell=0$, for which they are given by the bare values
$\varepsilon_{\bf k}, E_{\bf q} = 2\Delta, g_{{\bf k},{\bf q}}$ together with
$U^{F-F}_{{\bf p},{\bf k},{\bf q}} \equiv 0$. The chemical potential
$\mu(\ell)$ is chosen at each step of the renormalization flow such as to fix a
given total number of fermions and bosons. The flow of these parameters converges for
$\ell \rightarrow \infty$ and results in two uncoupled systems: one for the effective fermionic
excitations and one for the effective bosonic ones with a fix point Fermion dispersion
$\varepsilon^*_{\bf k} = \varepsilon_{\bf k}(\ell \rightarrow \infty)$.
For isotropic exchange coupling and fermion dispersion this problem had been studied
previously \cite{Domanski-2001,Domanski-2003a,Stauber-2007}, predicting
the pseudogap \cite{Ranninger-1995} and damped Bogoliubov modes \cite{Domanski-2003a}
in angle resolved photoemission spectra. Both have since been verified
experimentally \cite{expPG}.
\section{The Boson-Fermion duality.}
The anisotropy of the electronic structure of cuprates tracks a change-over
from self-trapped (localized) fermions, in form of diffusively propagating bosonic pairs,
into itinerant propagating (delocalized) fermions upon going from the anti-nodal to the nodal point
on an arc in the Brillouin zone, determined by $\varepsilon^*_{{\bf k}_F}(\phi) = \mu$.
To illustrate that, we evaluate the single-particle spectral function for wave vectors
${\bf k}=|{\bf k}|[sin \phi,cos \phi]$, orthogonally intersecting this arc at various
${\bf k}_F(\phi)$, where the motion of the charge carriers is essentially one dimensional. $\phi$
denotes the angle of those ${\bf k}$-vectors with respect to the line $[\pi,\pi]- [\pi,0]$, (see Fig.3).
In order to relate our study to a nearly half filled band situation,
characterizing the doped cuprates, we choose $\Delta \simeq 0.75$ (in units of
a nominal fermionic band width of 8t), with the bosonic level lying just barely
below the center of the itinerant fermion band such as to reproduce the typical
shape of the CuO$_2$ planar Fermi surface. Our choice of the
boson-fermion exchange coupling strength g = 0.1, yields a typical
onset temperature T$^* = 0.016$ for the pseudogap of roughly a hundred
degrees K. For a characteristic temperature of the pseudogap phase
($T= 0.007 < T^*$), it implies a concentration of itinerant fermionic charge carriers $n_F = \sum_{{\bf k}\sigma}\langle c^{\dagger}_{{\bf k}\sigma}c_{{\bf k}\sigma}\rangle = 0.88$ and that of self-trapped ones bound into fermion pairs,
$n_B = \sum_{\bf q} \langle b^{\dagger}_{\bf q} b_{\bf q}\rangle = 0.075$.
This corresponds to a hole doping $n_h=0.12$, with a total number of carriers
of $n_{tot} = n_F + 2n_B =1.03$. Hole doping redistributes the relative
occupation of fermions and bosons which ultimately leads to a shrinking of the
arcs (see section V). The charge carriers around the nodal point are primarily
given by delocalized fermionic one-particle states, while at the hotspot
anti-nodal points they are localized bosonic bound fermion pairs. Yet, as we shall see below, they will become itinerant and
eventually condense as the temperature is decreased. The reason for that is that
the bare exchange coupling $g_{{\bf k},{\bf q}}$ is equal to zero at the nodal
point ($\phi = \pi/4$) and increases as one moves to the anti-nodal points
($\phi = 0, \pi/2$), where it reaches its maximal value, equal to g. As a consequence, $\varepsilon^*_{\bf k}$ remains essentially unrenormalized for
${\bf k}$ vectors crossing the arc near the nodal point. Upon approaching the
anti-nodal point, on the contrary, $\varepsilon^*_{\bf k}$ acquires a
sharp S-like inflexion at ${\bf k}_F(\phi)$, which leads to the the appearance
of the pseudogap in the single-particle density of states.
Our prime objective in the present study is to disentangle the contributions to
the single-particle spectral function coming from the itinerant and from
the localized features. The latter arise from single-particles being
momentarily trapped in form of localized pairs. The effective fermionic and
bosonic excitations are obtained in a renormalization procedure similar
to that of the Hamiltonian, but this time by applying it to the fermion and
boson operators themselves \cite{Domanski-2003a,Domanski-2004}. The evaluation
of the single-particle spectral function
\begin{eqnarray}
A^F({\bf k}, \omega) &=& -{1 \over \pi} Im \int_0^{\beta} d \tau G^F({\bf k},\tau)
e^{(\omega +0^+)\tau} \qquad\qquad \nonumber \\
G_F({\bf k},\tau) &=& \langle \langle c_{{\bf k} \uparrow}(\tau);
c^{\dagger}_{{\bf k}\downarrow}\rangle\rangle_H
\end{eqnarray}
in a correspondingly renormalized manner is achieved by applying the unitary
transformation $e^{S(\ell)}$ to the Green's function itself. It results in
\begin{eqnarray}
\langle \langle c_{{\bf k} \sigma}(\tau);c^{\dagger}_{{\bf k}\sigma}(0)\rangle\rangle_H=
\qquad\qquad\qquad\qquad\qquad\qquad\quad\nonumber &\\
\langle \langle e^{S(l)}e^{\tau H(\ell)}c_{{\bf k} \sigma}e^{-\tau H(\ell)}e^{-S(l)};e^{S(l)}
c^{\dagger}_{{\bf k}\sigma}e^{-S(l)}\rangle\rangle_{H(\ell)} = \nonumber & \\
\langle \langle e^{S(\infty)}e^{\tau H^*}c_{{\bf k} \sigma}e^{-\tau H^*}
e^{-S(\infty)};e^{S(\infty)} c^{\dagger}_{{\bf k}\sigma}e^{-S(\infty)}\rangle\rangle_{H^*}, &
\end{eqnarray}
where the trace has to be carried out over the fully renormalized fixed point Hamiltonian $H^*$.
Neglecting the residual interaction $U^{F-F}_{{\bf p},{\bf k},{\bf q}}$ between the fermions
and restricting ourselves to the pseudogap phase without any long range phase locking, we obtain
the following renormalized fermion operators \cite{Domanski-2004}:
\begin{eqnarray}
{c^{\dagger}_{-{\bf k},-\sigma}(\ell) \brack c_{{\bf k},\sigma}(\ell)} &=&
u^F_{\bf k}(\ell) {c^{\dagger}_{-{\bf k},-\sigma} \brack c_{{\bf k},\sigma}} \nonumber \\
&&\mp \frac{1}{\sqrt N}\sum_{\bf q}v^F_{{\bf k},{\bf q}}(\ell){b^{\dagger}_{\bf q}
c_{{\bf q+k}, \sigma} \brack b_{\bf q} c^{\dagger}_{{\bf q-k}, -\sigma}},
\end{eqnarray}
with $\ell$ dependent parameters $u^F_{\bf k}(\ell), v^F_{\bf k}(\ell)$ determined by the
flow equations. The single-particle fermionic spectral function resulting from such a procedure
\begin{eqnarray}
A^F({\bf k},\omega) = |u^F_{\bf k}(\infty)|^{2} \delta \left( \omega\!+\!\mu\!-\!\varepsilon^*_{\bf k}
\right) \qquad \nonumber \\
+ \frac{1}{N} \sum_{{\bf q}\neq{\bf 0}} \left( n_{\bf q}^{B} + n_{{\bf q}-{\bf k}\downarrow}^{F}
\right) |v^F_{{\bf k},{\bf q}}(\infty) |^{2} \delta ( \omega\!-\!\mu \!+\! \varepsilon^*_{{\bf q}
\!-\!{\bf k}} \!-\!E^*_{\bf q}), \label{spectral}
\end{eqnarray}
is illustrated in Fig. 2 for T = 0.007 ($< T^*=0.016$), which lies in the pseudogap phase.
We choose a ${\bf k}$ traversing the arc in the Brillouin zone at ${\bf k}_F(\phi)$,
in a characteristic region around $\phi = \phi_c=15^o$,
where the T independent gap for $\phi \leq \phi_c$ changes over into a T dependent gap in the
single-particle density of states for values of $\phi \geq \phi_c$ (see Fig 3). $\phi_c$
signals the separation between localized and delocalized, respectively bosonic and fermionic, features
in the Brillouin zone.
For ${\bf k}$ vectors below ${\bf k}_F(\phi)$, $A^F({\bf k},\omega)$ exhibits
(i) low energy ($\leq \mu$) delocalized single-particle excitations (the first
term in eq. 8), which follow essentially the dispersion
$\varepsilon^*_{\bf k} \simeq \varepsilon_{\bf k}$ and (ii) a high energy
($\geq \mu$) broadened upper Bogoliubov like branch. For $k \rightarrow 0$
that latter merges into the time reversed spectrum $-\varepsilon_{\bf k}$.
For wave vectors ${\bf k}$ above ${\bf k}_F(\phi)$,
$A^F({\bf k},\omega)$ shows simultaneously two features:
(i) low frequency diffusively propagating Bogoliubov modes and (ii) high frequency
single-particle excitations with a dispersion given by
$\varepsilon^*_{\bf k} \simeq \varepsilon_{\bf k}$ and moving in a cloud of
bosonic two-particle excitations in form of bonding and antibonding states,
seen by the wings on either side of the coherent part (the first term in Equ. 8)
of those excitations. These low and high frequency excitations for a given
wave-vector characterize the low and high frequency response of one and the
same phenomenon, with the latter testing the internal degrees of
freedom of the collective diffusively propagating Bogoliubov like modes.
These internal degrees of freedom are images of localized bonding and
anti-bonding states, such as given by the Green's function in the
atomic limit ($t, t' = 0$) \cite{Domanski-1998,Domanski-2003c},
$G^F_{at}(i \omega_n)=1/[G^F_{at}(i \omega_n)^{-1} - \Sigma^F_{at}(i \omega_n)]$
with the selfenergy
\begin{eqnarray}
\Sigma^F_{at}(i \omega_n) = {(1-Z) \; g^{2} \;(i \omega_n + \mu) \over
[(i \omega_n + \mu)(i \omega_n - 2 \Delta + \mu) - Zg^2]},
\end{eqnarray}
\begin{figure}[t]
\begin{center}
\includegraphics*[width=8.5cm,angle=0]{fig2_jrTD09PRB.eps}
\caption{(Color online) $A({\bf k},\omega)$ at $T= 0.007$ ($< T^* = 0.016$) as a function
of $|{\bf k}|$ (in units of the inverse lattice vector) near ${\bf k}_F$ (red line),
corresponding to $\phi = 15^o$, orthogonally crossing the Fermi arc. The spectral weight of
the coherent and incoherent contributions are indicated by blue, respectively yellow bars.}
\label{fig2}
\end{center}
\end{figure}
\begin{figure}[b]
\begin{center}
\includegraphics*[width=8.5cm,angle=0]{fig3_jrTD09PRB.eps}
\caption{(Color online) Variation of the pseudogap for different k vectors,
orthogonally crossing the arc, given by angles $\phi$.}
\label{fig3}
\end{center}
\end{figure}
which differs qualitatively from any BCS like structure of Cooperons, because taking into
account their intrinsic single-particle localized internal degrees of freedom.
$Z \simeq 2/[3+ \cosh (g/k_{B}T)]$ (for our choice of parameters) denotes the
spectral weight of non-bonding delocalized charge carriers, described by
$G_0^F(i \omega_n)= 1/(i \omega_n - \mu)$.
The pseudogap in the density of states,
$\rho(\omega) = (1/N) \sum_{{\bf k}}A^F({\bf k}, \omega)$, which opens up at
some $T = T^*$ at ${\bf k}_F(\phi)$ has a size $\Delta_{pg}(\phi)$. It
is determined by the distance between the peaks either side of
$\varepsilon^*_{{\bf k}_F(\phi)}$, when upon lowering T the deviation from
the bare density of state,
$\rho^0(\omega) = (1/N) \sum_{\bf k}\delta(\omega - \varepsilon_{\bf k})$ becomes
noticeable. We take as a criterion a reduction to $90 \%$ of $\rho^0(\omega=0)$.
The sharp peak in $A^F({\bf k}_F, \omega)$ in Fig. 2, arising from the coherent
part of this spectrum, is a consequence of having neglected the residual
fermion-fermion interaction $U^{F-F}_{{\bf p},{\bf k},{\bf q}}$, eq. 4. The effect
of this interaction is to broaden this delta function like peak, as we know
from previous studies using different approaches \cite{Ranninger-1996,Robin-1998}.
To describe this effect within the present flow equation approach, requires a
fully self-consistent treatment of the diagonal part of the renormalized
fermions given by
$\sum_{{\bf k}\sigma}(\varepsilon^*_{\bf k}-\mu)c^{\dagger}_{{\bf k}\sigma}c_{{\bf k}\sigma}$ and the residual fermion-fermion interaction $H^{F-F}_{BFM}$ -
an issue, which will be treated in some future study.
The appearance of the pseudogap is associated with a reduction of the spectral
weight of this coherent contribution (given by the height of the blue bars in
Fig. 2). We illustrate in Fig. 3 the variation of $\Delta_{pg}(\phi)$ for
different T. Close to the anti-nodal point - the localized and bosonic
dominated regime - it is relatively T independent. But approaching the nodal
point, it abruptly drops to zero, even though $g_{{\bf k},{\bf q}}$ is still
finite. Although reminiscent of BCS like superconducting correlations (without
any pseudogap) for $60^o \geq \phi \geq 30^o$, the momentum dependence of
the gap in the superconducting phase is T dependent. This, clearly is a not a BCS
mean-field type behavior \cite{Lee-2007}. The reason behind the change-over from an
essentially T independent gap for $\phi \leq \phi_c$ and a T dependent gap
for $\phi \geq \phi_c$ is the following: As $\phi$ decreases, the size of
the pseudogap increases and at the same time its
position in the Brillouin zone at some ${\bf k}_F(\phi)$ diminishes
until it reaches the bottom of $\varepsilon^*_{\bf k}$.
(see Fig. 2 in Ref. 37). At this point, itinerant fermionic charge
carriers disappear in that part for the Brillouin zone, having been converted
into bosonic fermion pairs. The accumulation of such bosonic charge carriers near
the anti-nodal point is a direct consequence of the anisotropic boson-femion
exchange coupling and d-wave pairing in those cuprates. Since the excitation
energies (size of the pseudogap) characterizing such entities are determined
by purely local effects, they are relatively temperature as well as doping
independent for $\phi \leq \phi_c$. Doping dependent however is the
value $\phi=\phi_c$ of the cross-over to itinerant charge carriers, as confirmed
in ARPES experiments \cite{Lee-2007}.
In order to visualize the accumulation of bosonic charge cariers near the
anti-nodal points let us investigate how the fermionic charge carriers in
the various regions near the arc in the Brillouin zone get converted into
diffusively propagating bound pairs of them. To do that we evaluate the
renormalized Bose spectral function,
\begin{eqnarray}
A^{B}({\bf q},\omega) &=& - \frac{1}{\pi} \; \mbox{Im} \; \int_0^{\beta} d\tau
G^{B}({\bf q},\tau)e^{(\omega +i0^+)\tau} \nonumber \\
G^{B}({\bf q},\tau) &=& \langle \langle b_{\bf q} (\tau) ;
b_{\bf q}^{\dagger} \rangle \rangle_H ,
\end{eqnarray}
for which we had previously derived the corresponding renormalization flow
equations \cite{Domanski-2004}. It results in renormalized boson operators
\begin{eqnarray}
b_{\bf q}(\ell)= u^B_{\bf q}(\ell) b_{\bf q} +
\frac{1}{\sqrt{N}} \sum_{\bf k} v^B_{{\bf q},{\bf k}}(\ell)
c_{{\bf k}\downarrow} c_{{\bf q}-{\bf k}\uparrow},
\label{b_Ansatz}
\end{eqnarray}
with $b_{\bf q}^{\dagger}(\ell)= (b_{\bf q}(\ell))^{\dagger}$, which ultimately leads to the renormalized Boson spectral function given by
\begin{eqnarray}
A^{B}({\bf q},\omega) = | u^B_{\bf q}(\infty)|^{2}
\delta \left( \omega - E^*_{\bf q} \right)\nonumber \qquad \\
+ \frac{1}{N} \sum_{\bf k} f_{{\bf k},{\bf q}-{\bf k}}
| v^B_{{\bf q},{\bf k}} (\infty) |^{2}
\delta \left( \omega - \varepsilon^*_{\bf k}
- \varepsilon^*_{{\bf q}-{\bf k}} \right).
\end{eqnarray}
\begin{figure}[b]
\begin{center}
\includegraphics*[width=8.5cm,angle=0]{fig4_jrTD09PRB.eps}
\caption{(Color online) Variation of the number of paired fermions
as a function of wavevectors ${\bf q}$ along different directions in the Brillouin
zone given by the angle $\theta$. The variation of the total number of such pairs
is illustrated in the inset.}
\label{fig4}
\end{center}
\end{figure}
\begin{figure}[b]
\begin{center}
\includegraphics*[width=3.5in,angle=0]{fig5_jrTD09PRB.eps}
\caption{(Color online) Variation of the renormalized single-particle
dispersion for wave-vectors $\bf k$ orthogonally crossing the arcs along
different directions in the Brillouin zone, characterized by the angle $\phi=arcsin(k_x/|{\bf k})|$.
The reduction in the value of $|{\bf k}_F(\phi)|$ upon
approaching the anti-nodal regime indicates an emptying out of the fermionic
single-particle excitations in favor of an increase in their paired states.}
\label{fig5}
\end{center}
\end{figure}
The corresponding number of such bosonic charge carriers is given by
$n^B(q_x,q_y) = \int d \omega A^{B}({\bf q},\omega) [exp(\omega/k_BT) -1]^{-1}$. We
plot it for a series of ${\bf q}$ vectors in Fig. 4 for T=0.007, which sample the anisotropy of the CuO$_2$ electronic structure, where $\theta$ indicates the azimuthal angle in this plane. Notice that along the nodal direction the number of bosons is independent on $|{\bf q}|$, because of the absence of any boson-fermion
coupling. As one approaches the direction linking the center of the zone with the anti-nodal points, the
exchange coupling steadily increases and consequently the intrinsically localized bosons acquire
itinerancy and gather in a region of long wavelength. Those bosons have internal structure of two
fermions with opposite momenta centered around ${\bf k}_F(\phi)$. In the inset of Fig. 4 we illustrate the
total number of such bosons along the various ${\bf q}$ vectors and notice the relative increase, respectively
decrease compared to their average value $0.075$, depending on whether we are sampling the nodal or the
anti-nodal directions. The accumulation of fermions getting converted into fermion pairs
in certain parts of the Brillouin zone, close the anti-nodal points, has its counter part in the
diminishing density of single-particle fermionic
excitations in the same regions. We illustrate that in Fig. 5, where we plot the variation of the coherent
part of the single-particle dispersion, given by $\varepsilon^*_{\bf k}$ around ${\bf k}_F(\phi)$. We
notice that with diminishing $\phi$, approaching the anti-nodal points, the corresponding value of
${\bf k}_F(\phi)$ diminishes. This announces a shrinking of the Fermi sea, causing an emptying out of
single-particle states and
consequently an increase of bound fermion pairs. This feature had previously been observed in connection
with the transition between the superconducting state of phase correlated bonding pairs and the insulating
state of such phase uncorrelated bonding pairs \cite{Stauber-2007}.
\section{Summary and Outlook}
Our scenario for the cuprate superconductivity is based on resonant pairing,
induced by local dynamical lattice instabilities upon hole doping. It makes use
of the fact that such systems are prone to a segregation of globally
homogeneous crystal structures into small nano-size pairing domains. This
breaks locally the translational as well as rotational symmetry by randomly
orienting uni-directional Cu-O-Cu molecular bonds in different directions. As
a result, the fermionic charge carriers acquire single-particle spectral features
which comprise simultaneously: (i) quasi localized states, where they are
momentarily trapped in form of bound pairs in polaronic charge fluctuating
local domains and (ii) delocalized states on a sublattice in which those
polaronic domains are embedded.
Due to the d-wave pairing, which in our case is encoded in
the anisotropic Boson-Fermion exchange coupling $g_{{\bf k},{\bf q}}$, the
spectral properties of the single-particle excitations exhibit a pseudogap
with the following features: As we move on a constant energy line in the
Brillouin zone, corresponding to the chemical potential (where such an arc
determines the Fermi surface, whenever it exists), $|g_{{\bf k},{\bf q}}|$
diminishes as we go from the anti-nodal ($\phi \simeq 0$) to the nodal region
($\phi \simeq \pi/4$). Concomitantly the size of the pseudogap,
$\Delta_{pg}$, decreases. For $0 < \phi <\phi_c$, with $\phi_c \simeq 15^o$ for
our choice of parameters, it remains relatively unaffected by changes
in temperature T. On the contrary, for $\phi_c < \phi < \pi/4$, $\Delta_{pg}$
becomes strongly T dependent. For low T, it tends to zero gradually as
one approaches $\phi = \pi/4$. With increasing T, it tends to zero at
increasingly larger values of $\phi$, (see Fig.3), as observed
experimentally \cite{Kohsaka-2008}. This suggest that:
(i) the pseudogap in a finite region ($0 < \phi < \phi_c$) around the
anti-nodal point is controlled by predominately local pairing
(via intra-{\it bonding-pair} correlations), which is independent on doping
and largely unaffected by superconducting phase fluctuations.
(ii) the pseudogap in a finite region ($\phi_c < \phi < \pi/4$) around
the nodal point is controlled by both, local intra-{\it bonding-pair} as well
as non-local superconducting inter-{\it bonding-pair} correlations, which
are sensitive to phase fluctuations and cause the dependence of $\Delta_{pg}$ on
T as well as on doping.
The diffusively propagating low energy Bogoliubov like excitations around
${\bf k}_F$, which trace out the pseudogap, are a hallmark of the
single-particle spectral features of such resonant pairing systems and which
exist even near the anti-nodal points. In contrast to a BCS scenario, here,
their appearence above T$_c$ does not require a phase coherence of
the bosonic bound fermion pairs. Such Bogoliubov like modes
nucleate from local intra-{\it bonding-pair} correlations
between pairs of itinerant fermions and localized fermion
pairs \cite{Domanski-1998,Domanski-2003c} on local molecular clusters,
such as discussed here. They are a signature of a prevailing glassy Bose
metallic behavior prone to transit into a superconducting state of phase
correlated such bosonic intra-{\it bonding-pairs}. The momentum dependence of
those two-particle excitations, shows a strong tendency
toward condensation (see Fig. 4), which tracks the anisotropic behavior of the gap.
Provided the Boson-Fermion exchange coupling is not too big, such bosonic
pairs forming near the anti-nodal points, will dominate the
superconductivity, against a widespread opinion that they should be localized
there. For sufficiently large g, they of course will be localized. This is a topic which
will require further investigations, dealing with the superconductor to insulator
(Bose glass) transition with reduced hole doping.
The internal structure of those diffusively propagating Cooperons, consisting
of selftrapped fermions, is manifest in
their single-particle excitations above the chemical potential. It reflects
their atomic localized nature, where two-particle localized bonding and
anti-bonding satellites trail the dispersion of their delocalized coherent
contributions \cite{Domanski-1998,Domanski-2003c}. The low energy diffusive
collective Bogoliubov excitations and the high energy single-particle
excitations are two different manifestations of the same entity.
Whether there is a sharp border line for the onset of the high energy
localized features in the Brillouin zone, as suggested by a socalled
doping independent "extinction line" \cite{Kohsaka-2008,Hanaguri-2008},
will have to be checked in future for the present scenario.
Let us conclude this study with some remarks on the kind of doping
mechanism we can envisage in the cuprate high T$_c$ compounds. For low hole
doping it can be understood in terms of a doped Mott insulator and
an antiferromagnetic ground state, transiting into a spin singlet liquid
glassy state with increased doping. For the remaining doping regime,
approaching the optimal and overdoped regions, it remains largely an open problem
to be resolved. Experimentally one finds a singular universal optimal
doping rate n$_h^{opt} = 0.16$ holes/Cu atom, where T$_c$ reaches its
maximum together with a maximal volume fraction of the Meissner effect and
a Hall number becoming sharply peaked \cite{Balakirev-2003}. In scenarios,
like the present one, based on inter-related amplitude and
phase fluctuations, optimal doping also characterizes the
region where the energies of the superconducting phase stiffness and that of the
pairing coincide \cite{Emery-Kivelson-1995}. These doping dependent
electronic features are accompanied by a reduction of the buckling of the
CuO$_2$ planes \cite{Roehler-2004}, which characterizes the low doped
insulating phase. Pressure tuned electronic transitions, testing electronic
and lattice features at the same time \cite{Cuk-2008}, point to a critical
pressure which can be identified with the critical doping rate n$_h^{opt}$.
The universal value of $n_h^{opt}$=0.16, occures for any optimally doped system,
whatever the chemical structure of the doping blocks might be. This suggests
that, upon approaching optimal doping, the electronic and lattice degrees of
freedom must get strongly locked together \cite{Roehler-2009} and by doing
so increase the stability of these intrinsically metastable materials. And
indeed, upon trying to force extra holes into such systems by overdoping
$n_h > n_h^{opt}$, they segregate into different crystalline
phases \cite{Martovitski-2007}, with superconducting components composed
of underdoped and optimally doped regions. Understanding the doping
dependence of the cuprates thus becomes tantamount to understanding the
structural stability of those system. It necessarily must involve correlated
macroscopic features \cite{Sharma-1996,Mook-1990} of charge and lattice
deformations, such that precisely at optimal doping they optimally and
constructively interfere with each other.
Transposing these experimental facts on the scenario discussed in this paper,
the fluctuating local domains in the CuO$_2$ planes get increasingly
coherently locked together as hole doping increases. This results in a
decrease of spatial phase fluctuations of the bosonic resonantly bound fermion
pairs driven by locally fluctuating lattice structures, while at the same time
their conjugate amplitude fluctuations increase. As a consequence T$_c$
increases and T$^*$ decreases. Previous studies \cite{Ranninger-2003,Cuoco-2004}
on the interplay between amplitude and phase fluctuations bare that out.
According to the presently available experimental facts (Ref. 13,34,35,53-55),
the chemical doping mechanism, which imposes itself in the cuprates (following
our scenario), converts part of the itinerant electrons into polaronically driven resonating pairs, predominantly in certain regions of the Brillouin zone (see Fig. 4) near the anti-nodal points. It manifests itself in
the opening of a pseudogap, which nucleates at the socalled hot-spots, where
the local Boson-Fermion exchange coupling g is maximal. The
self-regulating redistribution of itinerant charge carriers and bosonic bound
pairs of them on the arcs in the Brillouin zone, is an intrinsic rather
than an extrinsic \cite{Perrali-2000} feature of the scenario presented here.
It originates from strong electron-lattice coupling, in a system with a
highly anisotropic electronic dispersion and coupling to local lattice
modes, evidenced in the anisotropic isotope dependent pseudogap and responsible
for the local symmetry breaking of those systems. Given this experimental
situation, we conjecture that hole doping primarily will replace the
buckled Cu$^{II}$-O-Cu$^{II}$ bonds by unbuckled Cu$^{III}$-O-Cu$^{III}$ ones,
whose density n$_B$ will be roughly given by $\frac{1}{2}$n$_h$, n$_h$ denoting
the concentration of chemically doped holes. Doping a single hole into the
basic cluster of
our segregated CuO$_2$ planes means a doping rate of 1/8= 0.125 per Cu ion.
This is very close to the critical doping rate, which changes the insulating
glassy phase into the superconducting one. Doping a hole into the trapping
centers breaks a Cu$^{II}$-O-Cu$^{II}$ bond. Since this is not compatible with
the basic square planar CuO$_4$ structure in the CuO$_2$ planes, doping will
trigger a charge transfer between the trapping centers and the surrounding
four-site rings, either by transferring an electron from the ring to the trapping
center and re-establish the stable square planar Cu$^{II}$-O-Cu$^{II}$ bond, or
by transferring an electron from that hole doped bond into the ring and leave behind
a stable square planar Cu$^{III}$-O-Cu$^{III}$ bond.
Both of these processes act together to ensure the overall crystalline
stability in systems with intrinsic local dynamically correlated
charge-lattice fluctuations and thus result in
resonant pairing of the itinerant electrons on the ring. The
end-effect of this is a transfer of a fraction n$_F^h$ of the electrons
on the ring into the pairing centers, where they form pairs on a finite time
scale with a concentration n$_B$ = $\frac{1}{2}$n$_F^h$. This simultaneously
implies a shrinking of the Fermi surface. n$_{tot}$ = n$_F$ + 2n$_B$ in this doping
procedure remains unaltered i.e., equal to unity as it is in the undoped case.
The effect of hole doping is hence to change the relative concentration of itinerant electrons with respect to the concentration of partly bound pairs of them.
A multitude of different experimental results discussed here have been shown
to be compatible with the resonant pairing scenario. Qualitatively different
from any BCS pairing scenario, here the itinerant delocalized Bogoliubov
excitations coexist with localized single-particle ones which
are selftrapped inside of them. Concerning the origin of this resonant
pairing in the cuprates, which could be electronic \cite{Altman-2002}, as
well as polaronic, the recently observed breakdown of their homogeneous
crystal structures into translational/rotational symmetry broken local
clusters \cite{Kohsaka-2008}, gives us confidence that dynamical lattice
deformations should play a determinant role in the superconducting state
of high T$_c$ compounds.
\section{Acknowledgement}
We thank Juergen Roehler for constructive remarks concerning this work and its
presentation.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,115 |
Inspiration: in honor of the first day of BreyerFest.
Model: from my adopted herd [Surprise!].
Technical bits: Taken on auto. I tried to shoot on aperture priority [Recommitment, pages 54-55] for a shallow depth of field. The results made me want to heave the camera. The theory was that I pick the aperture and then the camera picks the rest of the settings. Result, wide aperture equaled way too much light. Sigh. Perhaps photography is not my thing. Perhaps I shouldn't have tried after a lesson when I'm so stupid tired that a nap doesn't make a dent.
And maybe it is the camera. The little digital ones can only do so much – tho more than i once thought possible. You take some good pictures!
My sister and I used to collect Breyers when we were kids 40 years ago. We still have them of course. We have both those models. Breyers got us started into horses–we owe a lot to them!
I like the big nose and the little horse. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,484 |
\section{Introduction}
\label{sec:intro}
Given a simple undirected graph $G=(V,E)$, (see \citet{DW00}), on $n$ vertices, an $f$-factor of $G$ is a spanning subgraph $H$ such that $d_H(v)=f(v)$ for every $v$ in $V$. The problem of deciding whether a given graph $G$ has an $f$-factor is a well studied problem over many years by \citet{An85,tutte1952factors,cornuejols1988general, liu2008toughness} and \citet{PM07}. \citet{WT54} has shown the problem to be polynomial time reducible to perfect matching. Since perfect matching is polynomial time solvable it follows that testing for an $f$-factor is polynomial time solvable, and we refer to this algorithm as the {\em Tutte's $f$-factor algorithm}.
We consider the problem of finding a connected subgraph which is an $f$-factor.
For the case where $f(v) = 2$ for every $v$ in $V$, a connected $f$-factor is a Hamiltonian cycle. It is well known that the Hamiltonian cycle problem is NP-Complete. In fact, \citet{CC90} have shown that for each constant $d$, when $f(v)=d$ for every $v$, the connected $f$-factor problem is NP-Complete. We refer this connected regular spanning subgraph as a connected $d$-factor. Further, recently \citet{BN13} showed that for every $0<\epsilon<1$, for $f(v) \geq n^{1-\epsilon}$ the connected $f$-factor problem is NP-Complete.
For the case when $f(v) \geq \ceil {\frac{n}{2}} -1$, \citet{BN13} have also shown a simple test for the existence of a connected $f$-factor.
We observe that when $f(v)\geq \ceil{n/2}$ for every $v$ in $V$, any $f$-factor of a given graph $G$ is connected and has diameter at most 2. From the work by \citet{BN13} when $f(v)=\ceil{n/2}-1$, if the input graph has a $f$-factor with two components and {\em also} a connected $f$-factor, then there exists a connected $f$-factor of diameter 3. Similarly, for the case where $f(v) \geq \frac{n}{c}$ for each $v$ in $V$ and a constant $c$, the diameter of a connected $f$-factor is upper bounded by $3c-1$. This is because if we consider a diametric path $u_1,u_2,\cdots,u_{3c}$, the sets $N(u_i)$ and $N(u_{i+j})$ have to be disjoint for each $j \geq 3$. Further, each such set $|N(u_i)| \geq \frac{n}{c}$ and it is impossible to have such $c$ pairwise disjoint vertex sets. Thus for $f(v) \geq \frac{n}{c}$ for each $v$ in $V$, there seems to be a concrete correspondence between the diameter of connected $f$-factors and the value $c$. We use this correspondence to come up with a polynomial time algorithm for $c=2.5$. It may be possible to extend the idea to solve the problem for any constant $c$.
\noindent
{\bf Our Work.}
We present a diameter based characterization of graphs having connected $f$-factors where $f(v) \geq\ceil{\frac{n}{2.5}}$ for every $v$ in $V$. For each such $f$, we refer to the connected $f$-factor problem as $\textsf{Con-$f$-F}$. Our main result which we prove in Section \ref{sec:method} is as follows:
\begin{Theorem}
Let $G$ be an instance of \textsf{Con-$f$-F}. If each connected $f$-factor of $G$ has diameter at most 2, then every $f$-factor of $G$ is connected.
\label{mainthm}
\end{Theorem}
\noindent
We use the above characterization to show that $\textsf{Con-$f$-F}$ can be solved in polynomial time using the following two main graph theoretic results.
\begin{enumerate}
\item If an instance $G$ of $\textsf{Con-$f$-F}$ has a connected $f$-factor and also an $f$-factor $H$ with two components , then $G$ has a connected $f$-factor $G'$ of diameter at least 3.
\item Given two vertices $u,v$ in $V(G)$, the problem of computing an $f$-factor in which distance between $u$ and $v$ is 3, reduces to perfect matching. This result can be seen as a generalization of the Tutte's reduction of the $f$-factor problem to the graph perfect matching problem.
\end{enumerate}
\noindent
{\bf Preliminaries and Notations}\\
Throughout this paper, $f$ is a function $f:V \rightarrow \mathbb{N}$ such that for each $v$ in $V$, $f(v) \geq \ceil{\frac{n}{2.5}}$ where $n=|V|$. Consequently, we have the following fact.
\begin{Fact}
Let $G_f$ be an $f$-factor of $G$. Then the number of components in $G_f$ is at most 2.
\end{Fact}
\noindent
Unless otherwise mentioned, $G$ always represents the input graph.
We also assume that the number of vertices in $G$, denoted by $n$, is at least 12 (the cause for this will be clear from the analysis).
We use the following standard definitions and notations from \citet{DW00}: degree $d_G(v)$ of a vertex $v$ in a graph $G$, minimum degree $\delta(G)$, and the open neighborhood, $N(v)$ of a vertex $v$. We leave out the subscript $G$ when the graph in question is clear from the context. Further, the concepts of bridge or cut-edge, the edge-cut $[X,V \setminus X]$ created by a vertex partition $\{X, V \setminus X\}, X \subseteq V$, a tour, the diameter $diam G$, a circuit, and the subgraph of G induced by $S \subseteq V$, denoted by $G[S]$, are all standard. For a set $S \subseteq V$, $\displaystyle N(S) = \bigcup_{v \in S} N(v) \setminus S$ is the open neighbourhood of $S$.
Let $\{X,V \setminus X\}$ be a partition of $V$. We say $E' \subseteq E(G)$ is \textit{incident on} $\{X,V \setminus X\}$ if $E' \cap [X, V \setminus X] \neq \emptyset$. Further, we say $E' \subseteq E(G)$ \textit{covers} $\{X,V \setminus X\}$ if, $E'$ is incident on $\{X, V \setminus X\}$, and
there exists $S \in \{X,V \setminus X\}$ such that $\forall v \in S$, $v$ is incident on some edge $e \in E'$.\\
\noindent
{\bf Equitably Colored Graphs and Alternating Circuits} were introduced by \citet{DP83}. Let $G$ be a edge colored graph in which each edge is colored either red or blue. $G$ is said to be equitably colored if for every vertex $v \in V(G)$, the number of red edges incident on $v$ is equal to the number of blue edges incident on $v$. An eulerian closed trail $v_1,v_2, \ldots, v_{2t},v_1$ (a sequence of vertices) is said to be an alternating circuit if the edges $\{v_1,v_2\}, \{v_2,v_3\}, \ldots, \{v_{2t},v_1\}$ are coloured alternatingly red and blue. In other words, an alternating-circuit is a circuit that is equitably colored. A minimal alternating circuit $T$ is an alternating circuit such that no proper subset of edges of $T$ forms an alternating circuit.
\noindent
Let $G'$ be a spanning subgraph of an edge colored graph $G$. An alternating circuit $T$ in $G$ is defined to be a \textit{switch on} $G'$ if the set of red edges in $T$ is a subset of $E(G')$ and the set of the blue edges of $T$ is disjoint from $E(G')$. If $T$ is a switch on $G'$, the operation Switching($G'$,$T$) is a graph obtained by removing from $G'$ all the red edges in $T$ and adding all the blue edges in $T$ to $G'$.
\section{On the Diameter of Connected $f$-factors}
\label{sec:method}
\noindent
In this section we present our diameter based characterization for graphs which have a connected $f$-factor.
The following two facts are simple graph theoretic facts and the proofs are straightforward.
\begin{Fact}
Let $G$ be an undirected graph such that the minimum degree $\delta(G) \geq \frac{n}{2}$, then the diameter of $G$ is at most 2.
\label{diameter2}
\end{Fact}
\begin{comment}
\begin{proof}
Consider an arbitrary vertex $v_r$ in $G$. There are at least $\frac{n}{2}$ neighbors for $v_r$. The number of vertices in $V \setminus(\{v_r\} \cup N(v_r))$ is strictly less than $\frac{n}{2}$. Hence each of those vertices in $V(G) \setminus(\{v_r\} \cup N(v_r))$ are adjacent to some vertex in $N(v_r)$ and hence the proof.
\end{proof}
\end{comment}
\begin{Fact}
Let $G$ be a graph in which each edge is assigned a color from the set $\{red,blue\}$. $G$ is a set of vertex disjoint alternating-circuits if and only if $d_R(v)=d_{B}(v)$ for all $v$ in $G'$. \label{rblemma}
\end{Fact}
\begin{comment}
\begin{proof}
\textit{Necessity:}Passage of the circuit through each vertex uses one red and one blue edge incident on that vertex, and the first red(blue) edge is paired with the last blue(red) edge.
\textit{Sufficiency:}Consider Hierholzer's algorithm for finding Eulerian circuit in $G'$. We run Hierholzer's algorithm in a restricted way to get an alternating $RB$-alternating-circuit. Start with an arbitrary vertex $u$ of positive degree. Start the trail from $u$ through a red(blue) edge. Whenever the trail enters a vertex through a red edge, there exists an extra blue edge incident on $v$ through which we make the tour to leave the vertex and vice versa. Once the trail passes through a vertex $v$, both its $deg_{red}(v)$ and $deg_{blue}(v)$ get reduced exactly by one. For $u$, there will be an extra blue(red) edge through which the tour can complete the circuit. As this procedure does not violate the underlying Hierholzer's algorithm, the procedure ends up in an $RB$-alternating-circuit that is $Eulerian$.
\end{proof}
\end{comment}
\begin{Lemma}
Let $T$ be a minimal alternating-circuit. For each vertex $v$, both $d_{R}(v)= d_{B}(v) \leq 2$.
\label{rbminimalitythm}
\end{Lemma}
\begin{proof}
The proof is by contradiction. Let $v$ be a vertex in $T$ which has at least 3 incident red edges. We show the existence of an alternating circuit $T'$ whose edges are a proper subset of the edges of $T$ as follows: Consider the sequence of edges obtained from $T$ by starting at the first occurence of $v$ in $T$, and returning to $v$ for the {\em the second time}. Let $e_1, e_2, e_3, e_4$ be the edges incident on $v$ in the sequence, in the same order in which they were present in the sequence. $e_2$ and $e_3$ are consecutive in the sequence and are of different colors. If $e_1$ and $e_2$ are of different colors, then the sequence of edges from $e_1$ to $e_2$ is an alternating circuit, thus contradicting the minimality of $T$. If $e_1$ and $e_2$ are of the same color, and if $e_3$ and $e_4$ are of the same color, all the edges in the sequence form an alternating circuit, and is proper subset of the edges in $T$. The proper containment follows because at least one red edge incident of $v$ is not present in this sequence. This contradicts the minimality of $T$. If $e_3$ and $e_4$ are of different colors, then the sequence of edges from $e_3$ to $e_4$ is an alternating circuit, again contradicting the minimality of $T$. Hence the lemma.
\end{proof}
\begin{Lemma}
\label{cutincidencelemma}
Let $G$ be a graph of diameter 2 and let $\{X,V \setminus X\}$ be a partition of $V(G)$. There exists a set of edges $E' \subseteq [X,V\setminus X]$ that covers $\{X, V \setminus X\}$.
\end{Lemma}
\begin{proof}
We obtain a contradiction to the fact that the graph has diameter 3 by assuming that the lemma is false.
Let $v_1 \in X, v_2 \in V\setminus X$ such that $N(v_1) \subseteq X$ and $N(v_2) \subseteq V \setminus X$.
Then the shortest path between $v_1$ and $v_2$ is of length at least 3, and this contradicts the premise $diam ~G = 2$. Hence the claim in the lemma is true.
\end{proof}
\noindent
In the following, given an $f$-factor of $G'$ of $G$ we consider the coloring of $G$ in which $E(G')$ is colored red, and $E(G) \setminus E(G')$ is colored blue. The alternating circuits we consider are with respect to this coloring.
\begin{Lemma}
Let $G$ be a graph with at least 12 vertices.
Let $X$ and $V \setminus X$ be two components of an $f$-factor $G'$ of $G$. Let $T$ be a minimal alternating-circuit which is a switch on $G'$ and is incident on $\{X, V \setminus X\}$.
Then Switching($G'$,$T$) is a connected $f$-factor of $G$.
\label{minauglemma}
\end{Lemma}
\begin{proof}
Since $X$ and $V \setminus X$ have at least $\ceil{\frac{n}{2.5}}+1$ vertices, it follows that both $X$ and $V \setminus X$ are of size at most $\lfloor{\frac{1.5n}{2.5}}\rfloor-1$. Let $G''$ denote the graph Switching($G'$,$T$). Without loss of generality, let us consider $X$.
We know that the minimum degree in $G'[X]$ is at least $\ceil{\frac{n}{2.5}}$. Since $T$ is a minimal alternating circuit, from Lemma \ref{rbminimalitythm}, it follows that the degree of each vertex in $G''[X]$ is at least $\ceil{\frac{n}{2.5}}-2$. Further, the number of vertices in $X$ is at most $\lfloor{\frac{1.5n}{2.5}}\rfloor-1$. For $n\geq 12$, $\lfloor{\frac{1.5n}{2.5}}\rfloor-1< 2 \times (\ceil{\frac{n}{2.5}}-2)$. In other words the minimum degree in $G''[X]$ is more than half the number of vertices in $X$. Consequently, by Fact \ref{diameter2}, $G''[X]$ is of diameter at most 2. Similarly, $G''[V \setminus X]$ is of diameter at most 2. Further, since $T$ is incident on $\{X,V \setminus X\}$, there is an edge with one end point in $X$ and the other in $V \setminus X$. Therefore $G''$ is connected.
\end{proof}
\noindent
The next lemma plays a critical role in the polynomial time computability of \textsf{Con-$f$-F}. It implies that if Tutte's $f$-factor algorithm returns a solution with 2 components and if the graph has a connected $f$-factor, then there is one of diameter at least 3.
\begin{Lemma}
Let $G'$ be an $f$-factor of $G$ with two components $\{X, V\setminus X\}$.
If $G$ has a connected $f$-factor, then there exists a minimal alternating-circuit $T$ incident on $\{X, V \setminus X\}$ and is a switch on $G'$. Further, Switching($G'$,$T$) is an $f$-factor of diameter at least 3.
\label{switchinglemma}
\end{Lemma}
\begin{proof}
We prove by contradiction on the diameter of the $f$-factor computed by the switching operation. Let $H$ be a connected $f$-factor of $G$. Color the edges in $G'$ with color red and those in $H$ with color blue. By Fact \ref{rblemma}, each component in $E(G')\bigtriangleup E(H)$
is an alternating-circuit. Since $H$ is connected, there exists a minimal alternating-circuit $T$ in $E(G')\bigtriangleup E(H)$, which is a switch on $G'$ and is incident on $\{X,V\setminus X\}$. From Lemma \ref{minauglemma} it follows that Switching($G'$,$T$), denoted by $G''$, is a connected $f$-factor. Our proof analyzes two cases on the structure of such a $T$:\\
{\bf Case 1: There exists a $T$ with exactly four edges:}In this case we prove that $G''$ is of diameter at least 3. Let $u \in X$ and $v \in V \setminus X$ be vertices not in $V(T)$. Clearly, these are at a distance of atleast 3 in $G''$. \\
{\bf Case 2: Every $T$ is of length more than 4:} Let us assume that $G''$ is of diameter at most 2. Consider an edge $(u_1,u_2)$ in $E(G'')$ such that $u_1 \in X$ and $u_2 \in V \setminus X$. Now, the number of vertices
in $N_{G'}(\{u_1,u_2\})$ is at least $\ceil{\frac{2n}{2.5}}$, since $G'$ is an $f$-factor. Therefore the number of vertices in $V \setminus N_{G'}[\{u_1,u_2\}]$ is at most $\lfloor \frac{n}{5} \rfloor-2$. Since we have assumed that $G''$ is of diameter at most 2, from Lemma \ref{cutincidencelemma} we know that one of the two sets from $\{X, V \setminus X\}$ has the property that each vertex in the set is incident on an edge in $[X, V \setminus X] \cap E(T)$. Without loss of generality, let $X$ be this set and let $E' = [X, V \setminus X] \cap E(T)$. Therefore, each vertex in $N_{G'}(u_1)$ is incident on an edge in $[X,V \setminus X] \cap E(T)$. Further, each edge incident on a vertex in $N_{G'}(u_1)$ is not incident on a vertex in $N_{G'}(u_2)$- the reason for this is that the existence of such an edge will result in an alternating circuit consisting of 4 edges, and we are in the case where such an alternating circuit does not exist. Therefore, the number of blue edges in $E'$ incident on vertices in $(V \setminus X) \setminus N_{G'}(u_2)$ is at least $\ceil{{\frac{n}{2.5}}}$. Since $T$ is a minimal alternating circuit, $u_2$ has at most one more blue edge incident on it other than $\{u_1,u_2\}$. Therefore, it follows that the number of edges of $E'$ incident on vertices in $(V \setminus X) \setminus N_{G'}[u_2]$ is at least $\ceil{{\frac{n}{2.5}}}-1$. On the other hand, since $u_1$ and $u_2$ are in different components in $G'$, $|(V \setminus X) \setminus N_{G'}[u_2]| \leq |V \setminus N_{G'}[\{u_1,u_2\}]|$. Since $|V \setminus N_{G'}[\{u_1,u_2\}]| \leq \lfloor \frac{n}{5} \rfloor-2$, it follows that $|(V \setminus X) \setminus N_{G'}[u_2]| \leq\lfloor \frac{n}{5} \rfloor-2$.
Since $T$ is a minimal alternating-circuit, by Lemma \ref{rbminimalitythm} the blue degree at each vertex is at most 2.
Therefore, the number of edges in $E'$ incident on the vertex set $(V \setminus X) \setminus N_{G'}[u_2]$ is at most twice the size of the set. Thus the number of edges in $E'$ incident on $(V \setminus X) \setminus N_{G'}[u_2]$ is at most $\lfloor \frac{n}{2.5} \rfloor -4$.
We have derived a contradictory set of inequalities involving the number of edges in $E'$ incident on $(V \setminus X) \setminus N_{G'}[u_2]$.
Therefore our assumption on the diameter of $G''$ being at most 2 is wrong. Hence the lemma.
\end{proof}
\noindent
We now complete the proof of Theorem \ref{mainthm}.\\
\textit{\textbf{Proof of Theorem \ref{mainthm}:}}
\begin{proof}
If $G$ has an $f$-factor $G'$ with two components and also has a connected $f$-factor, then, from Lemma \ref{switchinglemma}, there exists a minimal alternating-circuit $T$ such that $G''$=Switching($G'$,$T$) is a connected $f$-factor of diameter at least 3. Consequently, it follows that if all
connected $f$-factors of $G$ are of diameter at most 2, then all $f$-factors of $G$ are connected. Hence the theorem.
\end{proof}
\noindent
In the next section, we use this characterization to design a polynomial time algorithm for $\textsf{Con-$f$-F}$.
\begin{comment}
The algorithm explained in this paper is based on the following lemma.
\begin{lemma}
Let $G(V,E) \in$ \textsf{Con-$f$-F}. If all connected $f$-factors of $G$ are of diameter less than or equal to 2, then all $f$-factors of $G$ are connected.
\label{mainlemma}
\end{lemma}
\end{comment}
\section{Polynomial time Algorithm for the Connected $f$-factor Problem}
We start by presenting the Algorithm $A_f$ for the connected $f$-factor problem as follows:
\begin{enumerate}
\item Run Tutte's $f$-factor algorithm with $G$ and $f$ as input.
\item {\bf If} the algorithm fails to return an $f$-factor, then exit after reporting Failure.
\item {\bf Else} If it returns a connected $f$-factor, then output it and exit.
\item {\bf Else} Let $G'$ be the output $f$-factor, with two components $\{X, V \setminus X\}$.
\begin{enumerate}
\item For each $u \in X$ and $v \in V \setminus X$, and each induced path $P_{uv}$ of 3 edges \\
{\tt/* Lemma \ref{diameterlemma} shows that one of these choices is correct. */}
\begin{enumerate}
\item Test for an $f$-factor of $G$ containing $P_{uv}$ as a shortest path between $u$ and $v$. \\
{\tt /* Using subroutine Distance-Constrained-Factor */}
\item If an $f$-factor is found, output it and exit. \\
{\tt /* Theorem \ref{3diafact} shows that it is a connected $f$-factor */}
\end{enumerate}
\item Exit reporting failure.
\end{enumerate}
\end{enumerate}
We start with the following lemma that is crucial to prove the correctness of the iteration in Step 4.a and then present a variant of Tutte's reduction to deal with Distance Constrainted $f$-factors.
\begin{Lemma}
Let $G$ be a graph with at least 12 vertices, and let $G'$ be an $f$-factor of $G$ with two components $\{X, V\setminus X\}$. If $G$ has a connected $f$-factor $G''$=Switching($G'$,$T$) for a minimal alternating-circuit $T$, then
for each pair of vertices $u,v$ at a distance at least 3 in $G''$, exactly one of $u$ and $v$ is in $X$.
\label{diameterlemma}
\end{Lemma}
\begin{proof}
Since $G'$ is an $f$-factor, it follows that $|X| < \frac{3n}{5}$ and $ |V \setminus X| < \frac{3n}{5}$. Since $f(v) \geq \frac{n}{2.5}, v \in V$, it follows from Fact \ref{diameter2} that the diameter of $G'[X]$ and $G'[V \setminus X]$ is at most 2.
Further by Lemma \ref{rbminimalitythm}, we know that the minimum vertex degree in $G''[X]$ and $G''[V \setminus X]$ is at least $\frac{n}{2.5}-2$- since $G''=$Switching($G'$,$T$) where $T$ is a minimal alternating-circuit. Since $n \geq 12$, $\frac{n}{2.5}-2 > \frac{1}{2} \times \frac{2n}{5}$.
For $n \geq 12$, in $G''$, the minimum degree in $G''[X]$ is at least $\frac{|X|}{2}$ and the minimum degree in $G''[V \setminus X]$ is at least $\frac{|V \setminus X|}{2}$. Therefore, by Fact \ref{diameter2}, $G''[X]$ and $G''[V \setminus X]$ are subgraphs of diameter at most 2. Therefore, any two vertices $u$ and $v$ which are at distance at least 3 cannot both be in $X$ or $V \setminus X$. Hence the lemma.
\end{proof}
\begin{algorithm}[H]
\label{Algo2}
\SetKwInOut{Input}{Input}\SetKwInOut{Output}{Output}
\Input{$G(V,E)$,$f$,$u$,$v$}\Output{$H$ an undirected graph}
Remove edge $\{u,v\}$ from $G$ if exists.\\
{\tt /* Tutte's Reduction from $f$-factor to Perfect Matching */}\\
For each vertex $x$ in $V(G)$, Let $e(x) = d_G(x) - f(x)$; \\
Construct graph $H$ as follows:\\
For each $x$ in $V(G)$, add a biclique $K_{\{e(x),d(x)\}}$, having sets $A(x)$ of size $d(x)$ and $B(x)$ of size $e(x)$.\\
For each edge $(q,w)$ in $E(G)$, add an edge involving one vertex of $A(q)$ and one vertex of $A(w)$, and for each $\upsilon \in V$, each vertex of $A(\upsilon)$ participates in one such edge. \\
{\tt /* Enforcing the distance of more than 2 between $u$ and $v$*/ }\\
Let $S=\{l| (u,l) \text{ and } (l,v) \in E(G)\}$. //{\tt the $f$-factor should avoid each path $P_{uv}$ of length two}\\
For each $l \in S$ steps 10 and 11:\\
\hspace*{0.5cm}Let $\{x,y\} \subseteq A(l)$ such that $x$ is adjacent to a vertex in $A(u)$
and $y$ is adjacent to a vertex in $A(v)$ in $H$.\\
\hspace*{0.5cm}Let $z \in B(l)$. Remove edge set $\{\{z,w\}|w \in A(l)\setminus \{x,y\}\}$ from $H$.\\
\caption{Redn-PM($G$,$f$,$u$,$v$)-
Reduction from $f$-factor with Distance Constraints to Perfect Matching}
\end{algorithm}
\noindent
The routine {\bf Distance-Constrained-Factor($G$,$f$,$u$,$v$)} performs the following steps to compute an $f$-factor $G'$ in which the distance between $u$ and $v$ is at least 3.
\begin{enumerate}
\item Generate an instance of perfect matching $H$ using the reduction Redn-PM($G$,$f$,$u$,$v$) as shown in Algorithm 1.
\item If $H$ does not have a perfect matching report failure to find an $f$-factor in which distance between $u$ and $v$ is at least 3 and exit.
\item Let $M$ be a perfect matching in $H$. Compute the $f$-factor $G'$ from $M$ and $H$ using the $f$-factor computation in Tutte's reduction.
\end{enumerate}
We state the following theorem without proof about the reduction described in Algorithm 1.
The proof has been left out as it is exactly on the lines of Tutte's proof as presented in the book by \citet{DW00} (page 141).
\begin{Theorem}
\label{tutteredn}
Let $G(V,E)$ be an undirected graph, function $f:V \rightarrow \mathbb{N} \cup \{0\}$ and vertices $u,v \in V$. $G$ has an $f$-factor in which the distance between $u$ and $v$ is at least 3 if and only if $H$ output by Redn-PM($G$,$f$,$u$,$v$) has a perfect matching.
\end{Theorem}
\noindent
\begin{Theorem}
Let $G\in$ \textsf{Con-$f$-F}. Then algorithm $A_f$ outputs a connected $f$-factor of $G$ in polynomial time.
\label{3diafact}
\end{Theorem}
\begin{proof}
If $G$ does not have a connected $f$-factor, then the algorithm reports this correctly.
If all the $f$-factors are connected $f$-factors, then the algorithm is correct, as the first step is the Tutte's $f$-factor algorithm, and it will find a connected $f$-factor. On the other hand if there is an $f$-factor with two components and $G$ has a connected $f$-factor, then we know from Lemma \ref{switchinglemma} that there exists a connected $f$-factor $G''$ = Switching($G'$, $T$) of diameter at least 3, where $T$ is a minimal alternating-circuit. Further, from Lemma \ref{diameterlemma} we know that any pair of vertices $u,v$ such that distance in $G''$ is 3 are not both in the same component.
The algorithm $A_f$ enumerates each such candidate path $P$ of length 3 for each pair of vertices, one from $X$ and the other from $V \setminus X$, and, using Distance-Constrained-Factor, checks for an $f$-factor of $G$ containing $P$ as a shortest path between $u$ and $v$. To check for an $f$-factor of $G$ containing $P$ as a shortest path, we reduce the $f$ value of $u$ and $v$ by 1, the values of $a$ and $b$ by 2, remove the edges which are among the vertices of $P$ in $G$, and invoke Distance-Constrained-Factor. If for a path $P=\{u,a,b,v\}$ of length 3 between two vertices $u$ and $v$, an $f$-factor is found by Distance-Constrained-Factor, then we claim that this $f$-factor is indeed a connected $f$-factor in $G$. The proof is by contradiction - Let us assume that the graph is not connected. Let $Y$ be the component that contains $u$ and $v$ and the path $P$. Since $P$ is a shortest $u$-$v$ path in the output factor, it follows that $N(v) \cap N(u) = \emptyset$. Therefore, the number of vertices in the component $Y$ is at least $\frac{2n}{2.5}+2$.
The number of vertices $V \setminus Y$ is at most $n - \frac{2n}{2.5}-2= \frac{n}{5}-2$. However, this is a contradiction to the fact that in an $f$-factor, each component has at least $\frac{n}{2.5}+1$ vertices. Therefore, the $f$-factor found by the algorithm is indeed a connected $f$-factor and consequently, the algorithm is correct.
Given $G'$, there are at most $n^4$ such paths to enumerate, and Distance-Constrained-Factor is basically a polynomial time perfect matching computation due to Theorem \ref{tutteredn}. Therefore, $A_f$ runs in polynomial time and decides whether $G$ has a connected $f$-factor.
\end{proof}
\begin{comment}
In this section, we explain the algorithm for solving \textsf{Con-$f$-F}. The algorithm uses a subroutine $FindFactor(G',f')$, which uses Tutte's algorithm \citet{WT54} for finding $f'$-factor in the graph $G'$. Without loss of generality, we assume that the input graph $G$ is a "yes" instance of \textsf{Con-$f$-F}. Now, either there exists connected $f$-factors of diameter $\geq 3$ or all those connected $f$-factors are of diameter $<3$.
We give an algorithm that comes up with a connected $f$-factor of $G$, if one of diameter $\geq 3$ exists. If all connected $f$-factors of diameter $<3$, then by theorem \ref{mainthm} any $f$-factor of $G$ will be a connected $f$-factor. This in turn imply that we can use subroutine $FindFactor(G,f)$ as such to get the required solution.
Consider the case where the given graph $G$ has a connected $f$-factor $G_f$ of diameter $\geq 3$. Clearly, because of the substructure property of the shortest paths, there exists a pair of vertices $v_1$ and $v_4$ such that the shortest path $P_{v_1v_4}$ between $v_1$ and $v_4$ in $G_f$ is of length exactly 3. The idea is to consider all possible candidates for $v_1$ and $v_4$, check for existence of a $f$-factor $G_f$ of $G$ that does not contain any paths of length less than 3 between $v_1$ and $v_4$ but contain some path of length equal to 3. Further we argue that if such a $f$-factor exists, it will always be connected.
To start with, we define a reduction procedure $R$ that takes a graph $G$ and a set of edges $I \subseteq E(G)$ as input and generates a graph $G'$. The reduction procedure $R$ does the following for each edge $e(x,y) \in I$(figure \ref{reduction1}).
\begin{itemize}
\item Initialize $G'$ with $G$.
\item Replace the edge $e=(x,y)$ with a gadget $g_e$, constructed by removing an edge $(u,v)$ from a complete graph on $d+1$ vertices(for some constant $d>1$).
\item Add edges $(x,u)$ and $(v,y)$ to $G'$.
\item For each vertex $v' \in g_e$, define $f'(v')=d$.
\end{itemize}
\begin{figure}
\begin{center}
\includegraphics[scale=0.6]{reduction1.eps}
\label{reduction1}
\caption{The reduction procedure $R$}
\end{center}
\end{figure}
Further, for all vertices in $V(G)$, we define $f'(v)=f(v)$.
\begin{lemma}
Given $G(V,E)$ and $I$, $G$ has a $f$-factor $G_f$ with $I \subseteq E(G_f)$ if and only if $G'$ has a $f'$-factor.
\label{reductionlemma}
\end{lemma}
\begin{proof}
It is easy to observe that each $e$ in $I$ will have both its end vertices connected to an associated $g_e$ in any $f'$-factor of $G'$. Once we have a $f'$-factor $G'_{f'}$ of $G'$, replace the set of edges $E(g_e) \cup \{(x,g_e(u),(g_e(v),y)\}$ with the corresponding edge $e=(x,y)$. This modification of $G'_{f'}$ does not alter the degrees of any of those vertices in $V(G)$ and hence gives a $f$-factor $G_f$ of $G$. Similarly if there exists $f$-factor $G_f$ of $G$ containing all those edges in $I$, then applying the reduction procedure $R$ over the pair $(G_f,I)$ clearly gives a $f'$-factor of $G'$. \rule{7pt}{7pt}
\end{proof}
Note that if $|I| \leq c$ for some constant $c$, then $R$ is a polynomial time procedure.
We define an operation, $Modified$-$Bipartite$-$Expansion(G,v_1,v_4)$ which operates almost in the same way as the \textit{graph transformation}\citet{DW00} in Tutte's algorithm. A set of special vertices $S$, is uniquely identified by a pair of vertices $v_1$ and $v_4$. Special vertices are all those vertices in $V(G) \setminus \{v_1,v_4\}$, that are adjacent to both $v_1$ and $v_4$. In other words, all those shortest paths between $v_1$ and $v_4$ of length $<3$ goes through some vertex in $S$(the pair $v_1$ and $v_4$ is such that $G$ don't have the edge $(v_1,v_4)$). We formally define the operation as follows.
\\
\\
Modified-Bipartite-Expansion$(G,v_1,v_4)$
\begin{enumerate}
\item
{Identify the set of special vertices $S$.}
\item
For each vertex $v \in S$, do the following:
\begin{enumerate}
\item Replace $v$ with a bipartite graph $H_{\{deg(v)-f(v),deg(v)\}}$, having bipartite sets $A(v)$ of size $deg(v)$ and $B(v)$ of size $deg(v)-f(v)$.
\item For each edge $(v,w) \in E(G)$, add an edge joining one vertex of $A(v)$ to $w$.
\item There exists $\{r_1,r_4\} \in A(v)$ such that $r_1$ is adjacent to $v_1$ and $r_4$ is adjacent to $v_4$.
\item Select a vertex $r \in B(v)$. For each vertex $l_b\in B(l) \setminus \{r\}$ and for each $l_a \in A(l)$, add all edges of the form $(l_b,l_a)$.
\item In addition, add edges $(r,r_1)$ and $(r,r_4)$.
\item Return the new graph $H$.
\end{enumerate}
\end{enumerate}
Consider the graph $H$ obtained by applying $Modified$-$Bipartite$-$Extension$ over $G$ as above. We make the following claim.
\label{clm:lbe}
\begin{Claim}
Any perfect matching in $H$ can not have both the edges $(v_1,r_1)$ and $(v_4,r_4)$ coexisting in it.
\end{Claim}
It is easy to observe that any perfect matching in $H$ should have either the edge $(r,r_1)$ or the edge $(r,r_4)$, but not both. In addition, it is quite possible that one of the vertices in the set $\{r_1,r_4\}$ may get matched to $r$ and the other to some other vertex in $B(v)$. So it may be the case that both the edges $(v_1,r_1)$ and $(v_4,r_4)$ are not present in a perfect matching of $H$.
We come up with the following algorithm $A_f$ which takes $G$ as input and produces a $f$-factor of diameter $\geq 3$, if one exists.
\begin{algorithm}[htpb]
\SetKwInOut{Input}{input}\SetKwInOut{Output}{output}
\Input{$G(V,E)$}
\Output{$G_f$}
Initialize $G'$ with $G$;\\
Enumerate all candidates for the pair $\{v_1,v_4\}$;\\
Enumerate all paths $P_{v_1v_4}=\{(v_1,v_2),(v_2,v_3),(v_3,v_4)\}$ of length 3 in $G$;\\
For each path $P_{v_1v_4}$, do the following:\\
\textbf{begin:}\\
\hspace{1cm}Set $I=E(P_{v_1v_4})$;\\
\hspace{1cm}Invoke reduction procedure $R(G,I)$ to get graph $G_P$;\\
\hspace{1cm}Define function $f'$ using $f$ and constant $d$ used in $R$;\\
\hspace{1cm}Remove edges $E(G_P) \cap \{(v_1,v_4),(v_2,v_4),(v_3,v_1)\}$ from $G_P$ to get $G'_P$;\\
\hspace{1cm}Compute the set of special vertices $S$ in $G'_P$ with respect to the set \phantom{\hspace{1cm}}$\{v_1,v_4\}$;\\
\hspace{1cm}Compute $G''_P=$Modified-Bipartite-Expansion$(G'_P,v_1,v_4)$;\\
\hspace{1cm}For $v \in S$, for each $v' \in A(v) \cup B(v)$, define $f'(v')=1$. Do the same for \phantom{\hspace{1cm}}every $v \in S$ ;\\
\hspace{1cm}Invoke $FindFactor(G''_P,f')$;\\
\hspace{1cm}If $FindFactor(G''_P,f')$ fails, exit;\\
\hspace{1cm}If we get a $f'$-factor of $G''_P$, use lemma \ref{reductionlemma} to construct $f'$-factor of $G'_P$;\\
\hspace{1cm}Otherwise go \textit{next iteration};\\
\hspace{1cm}In the $f'$-factor of $G'_P$, contract the set of vertices $A(v) \cup B(v)$ \phantom{\hspace{1cm}}corresponding to each $v \in S$ to single vertex $v$, to get $f$-factor of $G_p$ and \phantom{\hspace{1cm}}exit loop;\\
\textbf{end:}\\
Set $G_f=f$-factor of $G_P$ and return;\\
\label{Algo1}
\caption{Algorithm for finding $f$-factor of diameter $\geq 3$}
\end{algorithm}
\begin{lemma}
If $G$ has a $f$-factor of diameter $\geq 3$, then algorithm $A_f$ finds that in polynomial time.
\label{3diafact}
\end{lemma}
\begin{proof}
Without lose of generality we assume that $G$ has a connected $f$-factor of diameter $\geq 3$. By substructure property of shortest paths, such an $f$-factor contains a pair of vertices $v_1$ and $v_4$ such that there exists a path $P_{v_1v_4}$ of length exactly equal to 3. We use $G_3$ to denote any of those connected $f$-factors in which the shortest path between $v_1$ and $v_4$ is of length exactly equal to 3. Observe that $P_{v_1v_4}$ is a subgraph of $G$. There exists an iteration of \textit{step 4} in which algorithm $A_f$ enumerates one of the shortest paths $P_{v_1v_4}$ between $v_1$ and $v_4$ in $G_3$. From \textit{steps 7,8} and lemma \ref{reductionlemma}, any $f'$-factor $G'_{p}$ computed in \textit{step 15} contains the path $P_{v_1v_4}$ as a subgraph.
Since $G_3$ does not contain any of the edges shortcutting the vertices in $P_{v_1v_4}$, \textit{step 9} does not remove any of those edges in $G_3$. Hence any $f$-factor of $G_p$ will have a path of length 3 as in any valid $G_3$.
Consider any special vertex $l \in S$ computed in \textit{step 10}. From \textit{steps 11,12} and claim \ref{clm:lbe}, there does not exists a vertex $l \in S$ such that the edges $\{(v_1,l),(l,v_4)\}$ coexists in an $f$-factor of $G_p$ computed by the end of \textit{step 15}. Thus, any $f$-factor computed by $A_f$ is a valid $G_3$. \rule{7pt}{7pt}
\end{proof}
\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.8]{path_figure.eps}
\caption{Algorithm $A_f$ ensures that the distance between $v_1$ and $v_4$ in $G_f$ is exactly 3}
\end{center}
\end{figure}
\begin{lemma}
$G_3$ will always be a connected $f$-factor.
\label{3diaconn}
\end{lemma}
\begin{proof}
Assume that $G_3$ is not connected. Then $G_3$ will have exactly two components, as each component in $G_3$ should contain at least $\ceil{\frac{n}{2.5}}+1$ vertices. Consider the largest component $C$ in $G_3$. $C$ will contains at most $n-(\ceil{\frac{n}{2.5}}+1)$ vertices. As $|C|<2 \times mindegree(C)$, from fact \ref{diameter2} each component will have diameter 2 contradicting the existence of shortest path $P_{v_1v_4}$. \rule{7pt}{7pt}
\end{proof}
\begin{theorem}
If $G$ has a connected $f$-factor of diameter $\geq 3$, algorithm $A_f$ finds it in polynomial time.
\end{theorem}
\begin{proof}
The proof is straight forward from lemmas \ref{3diafact} and \ref{3diaconn}. \rule{7pt}{7pt}
\end{proof}
The number of $P_3$s in $G$ is at most $\binom{n}{2} \times (n-2)$. The reduction procedure $R$ increases the size of the graph only by a polynomial factor which together implies that $A_f$ is a polynomial time procedure.
\end{comment}
\begin{comment}
\section{Finding the Optimum Connected-$f$-factor}
In this section, we consider the optimization version(maximization/minimization) of $\textsf{Con-$f$-F}$ problem. We show that the techniques used to solve $\textsf{Con-$f$-F}$ can be used as such to solve both maximum weighted and minimum weighted connected $f$-factor problems. We observe that Tutte's reduction transforms the optimum weighted $f$-factor problem to the optimum weighted perfect matching problem which can be solves using \textit{blossom} algorithm by Edmonds\citet{EJ65,JE65}.
As before, we assume that the input graph $G$ is in \textsf{Con-$f$-F}. If there exists an optimum connected $f$-factor and if it is of diameter $\geq 3$, then iterating the algorithm $A_f$ over all paths of length 3 and selecting the one of optimum cost will give the required solution. Otherwise there are two possibilities. Either there exists an optimum $f$-factor of $G$ that is disconnected, or all optimum $f$-factors of $G$ are connected and are of diameter 2. If all those optimum $f$-factors are connected, then using $FindFactor()$ as such gives us the required solution.
\begin{lemma}
If $G$ does not have an optimum connected $f$-factor of diameter $\geq 3$, then $G$ does not have a disconnected $f$-factor.
\end{lemma}
\begin{proof}
We argue by contradiction. Let there be an optimum $f$-factor $G_f$ of $G$ that has more than one component. Let $G_{cf}$ be one of the optimum connected $f$-factors of diameter 2. Consider the set $Switch=E(G_f) \ominus E(G_{cf})$. Color the edges in the set $E(G_f) \cap Switch$ as red and those in the set $E_{cf} \cap Switch$ with color blue. Then by Fact \ref{rblemma}, there exists an alternating-circuit $T$ such that $G_{cf}=Switching(G_f,T)$. Of course $T$ has at least one blue edge across the components of $G_f$. Consider any minimal alternating-circuit $T_{min}$ such that $E(T_{min}) \subseteq E(T)$ and $T_{min}$ has at least one blue edge across the components of $G_f$. As with any other minimal alternating-circuits of $T$, cost of $T_{min}$ should be $\geq 0$ as otherwise will contradict optimality of $G_{f}$. This in turn implies cost of $Switching(G_f,T_{min}) \leq$ Cost of $Switching(G_f,T)$. By lemma \ref{switching lemma} this contradicts the assumption that there does not exists an optimum
connected $f$-factor of diameter $\geq 3$. \rule{7pt}{7pt}
\end{proof}
\begin{comment}
\begin{theorem}
Given a graph $G$ and a $d \geq \ceil{\frac{n}{2.5}}$, if $G$ has all its connected $f$-factors are of diameter $<3$, then $G$ don't have a disconnected $f$-factor.
\label{dia2thm}
\end{theorem}
\begin{proof}
Assume that there exists a disconnected $f$-factor $G_f$ of $G$. Then there exists a partitioning $P=\{P_1,P_2\}$ of the vertex set induced by the components of $G'_f$. Consider an arbitrary connected $f$-factors $G_{cf}$ of $G$. By lemma \ref{minauglemma} there exists a $G_{cf}$ that can be obtained by augmenting $G_f$ with a minimal $RB$-alternating-circuit $T$. We further partition the vertices in $V(G)$ in to levels as follows.
\begin{enumerate}
\item Consider an edge across the partition in $T$. Define both its end vertices to be \textit{level 1} vertices. We use $u_1$ to denote the \textit{level 1} vertex in $P_1$ and $u_2$ defined in the same way.
\item \textit{level 2} vertices are all those that are neighbors of \textit{level 1} vertices.
\item Assign all the remaining vertices to the class of \textit{level 3} vertices.
\end{enumerate}
\begin{claim}
There does not exists an edge across the partition in $G$ that has both its end vertices in \textit{level 2}. In addition, there exists at most 1 edge across the partition that join a \textit{level 1} vertex to a \textit{level 2} vertex in $G$.
\label{crossedgclaim}
\end{claim}
If any one of the statements in claim \ref{crossedgclaim} gets violated, then we have an edge switch pair that can be augmented to $G'_f$ to get a connected solution of diameter 3 and hence contradiction.
Note that the total number of \textit{level 2} vertices is at least $\ceil{\frac{2n}{2.5}}$ and hence the number of \textit{level 3} vertices is at most $\lfloor \frac{n}{5} \rfloor-2$. From lemma \ref{cutincidencelemma}, we define $P_1$ to be the partition that has all its vertices incident on some edge across the partition.
\begin{figure}[htpb]
\begin{center}
\includegraphics[scale=0.55]{node_levelization.eps}
\caption{Levelizing vertices in $G_f$}
\end{center}
\end{figure}
There exists a red edge connecting a \textit{level 1} vertex to a \textit{level 2} vertex in $P_1$. Let $(u_1,v_1)$ be this edge. Similarly there exists a red edge $(u_2,v_2)$ in $P_2$. Since the shortest paths $u_1 \sim v_2$ and $u_2 \sim v_1$ are of length at most 2, there exists edges across partitions that connects vertices in \textit{level 1} to vertices in lower levels of opposite partition.
Now there are two possibilities.
\begin{enumerate}
\item $u_2$ is connected to a \textit{level 2} vertex in $P_1$.
\item $u_2$ is connected to a \textit{level 3} vertex in $P_1$.
\end{enumerate}
$T$ will have at least $\ceil{{\frac{n}{2.5}}}$ $blue$ edges joining \textit{level 2} vertices of $P_1$ to either \textit{level 1} vertex or \textit{level 3} vertices in $P_2$. Now since $T$ is minimal, by theorem \ref{rbminimalitythm} the maximum number of blue edges that can be incident on some vertex in \textit{level 3} of $P_2$ is at most twice the total number of \textit{level 3} vertices in $P_2$. This implies there can be at most $\lfloor \frac{n}{2.5} \rfloor -4$ blue edges incident on \textit{level 3} vertices in $P_2$. In addition the number of blue edges joining \textit{level 1} vertex in $P_2$ to a \textit{level 2} vertex in $P_1$ is at most 1. Thus we have a contradiction on the number of blue edges across the partition incident on \textit{level 2} vertices in $P_1$. \rule{7pt}{7pt}
\end{proof}
\begin{comment}
to be proved..
If there are two factors connected and disconnected then there exists a Switching that takes one to the other
\end{comment}
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\section{Introduction and summary}
The purpose of this paper is to determine precisely which constraints the presence of the
kappa-symmetry of the Green-Schwarz (GS) superstring places on the target space (super) geometry. In an influential 1985 paper \cite{Witten:1985nt} Witten showed that the equations of motion of 10d super Yang-Mills theory can be expressed as integrability along light-like lines
and showed that this condition is closely connected to kappa-symmetry of the superparticle
in the super Yang-Mills background.
He also suggested that there should be a similar connection between the kappa-symmetry of the
GS superstring and the supergravity equations of motion.
Shortly thereafter, the type II GS superstring action in a general supergravity background was written down in \cite{Grisaru:1985fv} and it was shown that the standard on-shell
superspace constraints of type IIB supergravity \cite{Howe:1983sra} are sufficient for the string to be kappa-symmetric. It was conjectured that these constraints are also necessary for the kappa-symmetry.
In \cite{Shapiro:1986yy} it was found that for the type I superstring the kappa-symmetry implies the basic (i.e. dimension 0 and --$\ha$) superspace constraints on the torsion and 3-form $H=dB$ superfields\footnote}\def \la{\label{There is also a constraint for the Yang-Mills sector which we will ignore here.
In our notation $a,b,...=0,1,2,...,9$ are bosonic tangent space indices, and $\alpha,\beta,...=1,...,16$ are 10d Majorana-Weyl spinor indices.}
\begin{equation}
T_{\alpha\beta}{}^a=-i\gamma^a_{\alpha\beta}\,,\qquad \qquad H_{\alpha\beta\gamma}=0\,,\qquad\qquad H_{a\alpha\beta}=-i(\gamma_a)_{\alpha\beta}\,.
\label{1.1}
\end{equation}
Ref.\cite{Shapiro:1986yy} also argued that these constraints are enough to make the target space geometry a solution of type I supergravity.\footnote}\def \la{\label{More recently \cite{Berkovits:2001ue} it was shown that (classical) BRST invariance of the pure spinor superstring \cite{Berkovits:2000fe} (which may be viewed as an
analog of kappa-symmetry in this formulation) implies the basic
type I and type II constraints. It was argued
that these constraints are enough to put the corresponding supergravity background completely on-shell (see, however, note added in section \ref{sec:conclusion}).
}
While in the 11d case the condition of kappa-symmetry of the supermembrane action \cite{Bergshoeff:1987cm}
leads to a constraint on the torsion which implies that the background should satisfy the standard 11d supergravity equations of motion \cite{Howe:1997he},
here we will find (in disagreement with the earlier conjectures/claims)
that this is not so in the 10d superstring case:
the 10d
supergravity equations are sufficient but not necessary for kappa-symmetry.
In the case of the type I GS superstring where the kappa-symmetry implies the basic constraints (\ref{1.1}),
we shall show, by solving completely the Bianchi identities for the torsion and the 3-form,
that these constraints actually lead to a weaker set of equations than those of type I supergravity. These equations are similar to the
conditions for 1-loop scale invariance of the GS sigma model \cite{Arutyunov:2015mqj},
which are, in general, weaker than the Weyl invariance
conditions required to define a consistent superstring theory.
This is not totally surprising as the condition of classical kappa-symmetry does not take into account the dilaton term $\int d^2 \xi \sqrt g R^{(2)} \phi(x)$ required to make the quantum
2d stress tensor traceless (see \cite{ca} and discussion in
\cite{Arutyunov:2015mqj}).\footnote}\def \la{\label{Some discussions of one-loop
quantum corrections in GS sigma model (in the heterotic string case) appeared in \cite{het}.}
Indeed, the problem in 10d compared to the 11d case is the presence of the dilaton. The dimension $\ha$ component of the torsion is expressed in terms of a spinor (``dilatino") superfield $\chi_\alpha$. If one requires that $\chi_\alpha$ is expressed in terms of a scalar superfield $\phi$ (the dilaton) as
\begin{equation}\la{1.2}
\chi_\alpha=\nabla_\alpha\phi
\end{equation}
then the Bianchi identities for the torsion imply
the standard type I supergravity equations \cite{Nilsson:1981bn}.
However, if this extra assumption \rf{1.2} (not required for kappa-symmetry)
is dropped,
the basic constraints \rf{1.1} imply only the equations for a
``partially off-shell" generalization of the type I supergravity equations.
The solution of the constraints and Bianchi identities then depends on an
arbitrary vector $X_a$ (that replaces the dilaton gradient)\footnote}\def \la{\label{As $X_a$ is subject to a
constraint on its divergence we get 8 additional bosonic fields compared to
the standard type I theory. These are matched by an extra 8
fermionic components present due to the fact that the dilatino $\chi$ is now off-shell
whereas in the standard type I supergravity it satisfies a Dirac equation.}
and the bosonic equations of motion take the form (here
fermionic fields are set to zero)
\begin{align}
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over R_{ab}+2\nabla_{(a}X_{b)} -\frac14H_{acd}H_b{}^{cd}=&0\,,\la{1.3}\\
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \nabla^cH_{abc}-2X^cH_{abc} -4\nabla_{[a}X_{b]}=&0\,,\la{1.4}\\
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \nabla^aX_a-2X^aX_a+\frac{1}{12}H^{abc}H_{abc}=&0\,.\la{1.5}
\end{align}
If one restricts to the special case of $X_a=\del_a\phi$,
these equations reduce to the standard type I supergravity equations of motion
(or string effective equations in the NS-NS sector).
The generalized equations \rf{1.3},\rf{1.4}
coincide with the 1-loop scale invariance conditions of a bosonic sigma model $L=(G-B)_{mn} \del_+ x^m \del_- x^n$ provided the reparametrization and $B$-field gauge freedom vectors
are chosen to be equal.\footnote}\def \la{\label{In the notation of
\cite{Arutyunov:2015mqj} this means $Y_a=X_a$.
This identification is a consequence of the underlying supersymmetry of the
equations leading to \rf{1.3}--\rf{1.5}. It should come out automatically if the scale invariance of the GS string is studied in the manifestly supersymmetric (superspace) form.}
The conclusion is that the condition of classical kappa-symmetry is essentially
equivalent to the one-loop scale invariance condition for the type I GS sigma model.
Only the stronger condition of 2d Weyl invariance (eqs. \rf{1.3}--\rf{1.5} with
$X_a =\del_a \phi$)
is equivalent to the standard type I supergravity equations of motion.
Performing a similar analysis in the case of the type IIB GS superstring we will find that the
kappa-symmetry implies the direct generalization
of the basic constraints \rf{1.1} on the torsion and 3-form\footnote}\def \la{\label{Here $i,j,k=1,2$ label the two MW spinors of type IIB superspace and $(\sigma^r)_{ij}$ ($r=1,2,3$) are Pauli matrices. The gamma-matrices $\gamma^a_{\alpha\beta}$ and $\gamma_a^{\alpha\beta}$ are $16\times16$ symmetric `Weyl blocks' of 10d Dirac matrices satisfying
$\gamma^a_{\alpha\beta}(\gamma^b)^{\beta\gamma}+\gamma^b_{\alpha\beta}(\gamma^a)^{\beta\gamma}=2\eta^{ab}\delta_\alpha^\gamma\,,$
see \cite{Wulff:2013kga} for more details on our notation.}
\begin{equation}
T_{\alpha i\, \beta j }{}^a=-i\delta_{ij}
\gamma^a_{\alpha\beta}\,,\qquad \qquad H_{\alpha i\, \beta j\, \gamma k}=0\,,\qquad\qquad H_{a\, \alpha i\, \beta j }=-i \sigma^3_{ij} (\gamma_a)_{\alpha\beta}\,.
\label{1.6}
\end{equation}
When the Bianchi identities are solved we will conclude that these constraints
lead again not to the type IIB supergravity equations but to a weaker set of generalized type IIB
equations involving, instead of the dilaton scalar, two vectors ${\rm X}_a$ and $K_a$.
The corresponding bosonic equations may be written as (here as in \rf{1.2}--\rf{1.5} the fermionic
component fields are set to zero)
\begin{align}
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over R_{ab}+2\nabla_{(a} X_{b)}-\frac14H_{acd}H_b{}^{cd}+\frac{1}{128}\mathrm{Tr}(\mathcal S\gamma_a\mathcal S\gamma_b)=0\,, \la{17}\\
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \nabla^cH_{abc}-2{ X}^cH_{abc}-4\nabla_{[a}X_{b]} -\frac{1}{64}\mathrm{Tr}(\mathcal S\gamma_a\mathcal S\gamma_b\sigma^3)=0\,, \la{18}\\
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \nabla^a X_a-2{ X}^a X_a +\frac{1}{12}H^{abc}H_{abc}-\frac{1}{256}\mathrm{Tr}(\mathcal S\gamma^a\mathcal S\gamma_a)=0\,, \la{19}\\
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \gamma^a\nabla_a\mathcal S
-\gamma^a\mathcal S\,\mathrm ({\rm X}_a - \sigma^3 K_a)
+\big(\frac18 \gamma^a\sigma^3\mathcal S\gamma^{bc}\,
+\frac{1}{24}\gamma^{abc}\sigma^3\mathcal S\,\big)H_{abc}
=0\,. \la{20}
\end{align}
They generalize the type I equations \rf{1.3}--\rf{1.5} to the presence of
the analog of the RR field strength bispinor $\mathcal S = (\mathcal S^{\alpha i\, \beta j})$ (which includes the factor of $e^\phi}\def \del {\partial$ in the standard type IIB case
\cite{Tseytlin:1996hs,Wulff:2013kga})
\begin{equation}\la{200}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\mathcal S=-i\sigma^2\gamma^a\mathcal F_a-\frac{1}{3!}\sigma^1\gamma^{abc}\mathcal F_{abc}-\frac{1}{2\cdot 5!}i\sigma^2\gamma^{abcde}\mathcal F_{abcde}\,.
\end{equation}
Combining \rf{17} and \rf{19} we get the following
generalized ``central charge" equation
\begin{equation}\la{233}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\bar \beta ^X\equiv R-\frac{1}{12}H_{abc}H^{abc}+4\nabla^a X_a-4{ X}^a X_a=0\,.
\end{equation}
As was shown in \cite{Arutyunov:2015mqj}, the relation $\del_a \bar \beta ^X=0$
follows, in fact, from eqs.\rf{17},\rf{18},\rf{20} so that the ``dilaton equation" \rf{19}
is not indepedent.
In the above equations \rf{17}--\rf{233}
\begin{align}
X_a \equiv {\rm X}_a + K_a \ , \la{21}\end{align}
and the vectors ${\rm X}_a$ and $K_a$ are subject to
\begin{align}
& \nabla_{(a}K_{b)}=0 \la{222} \ , \qquad \qquad {\mathrm X}^aK_a=0 \ , \\
&\qquad 2\nabla_{[a}\mathrm X_{b]}+K^cH_{abc}=0 \,.\la{22}
\end{align}
Thus $K_a$ satisfies the Killing vector equation, while eq.\rf{22}
expresses the fact that the 3-form $H$ is isometric, i.e. the two-form potential $B$
transforms by a gauge transformation under the isometry generated by $K_a$,
$\mathcal L_K B=d(i_K B -{\rm X})$, where $\mathcal L_K=i_K\, d+d\, i_K$ is the Lie derivative. It follows from \rf{222},\rf{22} that not only the three-form $H$ but also the one-form ${\rm X}$ respect the isometry, i.e.
\begin{equation} \la{225}
\mathcal L_K H=0 \ , \qquad \qquad \mathcal L_K {\rm X}=0 \ . \end {equation}
Furthermore, it follows from the ``Bianchi" part of the $\cal S$ equation \rf{414}
that the ``RR'' forms in \rf{200} also respect the isometry
\begin{equation}\la{223}
\mathcal L_K {\cal F}_{2n+1} = 0 \ , \ \ \ \ \ \ \ \ \ \ \ \ \ n=0,1,2 \ . \end {equation}
Thus the whole bosonic background $(G,H,\mathcal F)$ is $K$-isometric. This statement can, in fact, be generalized to superspace as we will show in section \ref{sec:lifting}.
Assuming that the $B$-field may be chosen (by a gauge transformation)
to be isometric, eq. \rf{22}
may be explicitly solved as \cite{Arutyunov:2015mqj} (here $m,n$ are 10d coordinate indices)
\begin{equation} \la{2334} {\rm X}_m = \del_m \phi}\def \del {\partial - B_{mn} K^n \ , \ \ \ \ \ \ {\rm i.e.} \ \ \ \ \ \
X_m = \del_m \phi}\def \del {\partial + (G_{mn} - B_{mn}) K^n
\ , \end {equation}
where $\phi}\def \del {\partial$ is an arbitary scalar that should also satisfy the isometry condition
$K^m \del_m \phi}\def \del {\partial=0$ according to \rf{222}.
We conclude that the generalized system of equations \rf{17}--\rf{20}
involves the standard fields of type II supergravity (including the dilaton $\phi$)
plus an extra Killing vector $K_a$.\footnote}\def \la{\label{Note that
if the metric admits several Killing vectors, choosing them as $K$ one by one will lead to different
solutions of the generalized equations (e.g., different RR backgrounds).}
Eqs. \rf{222} and \rf{22} always admit the following special solution
\begin{equation} K_a=0 \ , \ \ \qquad \ \ \ \ \ X_a ={\rm X}_a =\del_a \phi \ . \la{23}\end {equation}
In that case the generalized system \rf{17}--\rf{20}
reduces to the bosonic sector of the standard type IIB supergravity equations
with $\phi}\def \del {\partial$ being the dilaton.\footnote}\def \la{\label{See, e.g., appendix A in \cite{Borsato:2016zcf} where the same RR bispinor notation for RR fields is used.}
In particular, eq.\rf{20} contains both the dynamical equations and the Bianchi identities for the RR field strenghts $F_p = e^{-\phi}\def \del {\partial}{ \cal F}_p= d C_{p-1} +...$ in \rf{200}.
The above generalized type IIB equations have of course
a straightforward analog in type IIA case -- following from kappa-symmetry condition of type IIA GS string.
Let us also note that there is a natural generalization of the notion of a supersymmetric solution
to the generalized type IIB supergravity equations, namely, the one for which the
component fermionic fields as well as their supersymmetry variations vanish, i.e. $\chi_{\alpha i}|_{\theta=0}=\psi_{ab}^{\alpha i}|_{\theta=0}=0$ and $\epsilon^{\alpha i}\nabla_{\alpha i}\chi_{\beta j}|_{\theta=0}=\epsilon^{\alpha i}\nabla_{\alpha i}\psi_{ab}^{\beta j}|_{\theta=0}=0$. The latter two equations give the generalization of the dilatino and the (integrability\footnote{The Killing spinor equation itself takes the form (cf. \rf{410})
$
(\nabla_a+\frac18H_{abc}\,\gamma^{bc}\sigma^3+\frac18\mathcal S\gamma_a)\epsilon=0\,.
$
From the GS sigma model perspective this condition follows from the requirement of a residual global
supersymmetry of the action describing a superstring moving in a non-trivial bosonic background.
}
of the) gravitino conditions respectively. Using \rf{eq:nabla-chi-IIB} and \rf{eq:nabla-psi-IIB} they take the form
\begin{align}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \big[
(\mathrm X_a+\sigma^3K_a)\gamma^a
+\frac{1}{12}H_{abc}\,\sigma^3\gamma^{abc}
+\frac{1}{8}\gamma_a\mathcal S\gamma^a
\big]\epsilon=\,0\,,
\\
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \big[
R_{ab}{}^{cd}\gamma_{cd}
+\frac12H_{ace}H_{bd}{}^e\,\gamma^{cd}
-\nabla_{[a}H_{b]cd}\,\sigma^3\gamma^{cd}
-\nabla_{[a}\mathcal S\gamma_{b]}\qquad&
\nonumber\\
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \qquad -\frac{1}{8}(\mathcal S\sigma^3\gamma_{[a}\gamma^{cd}-\gamma^{cd}\sigma^3\mathcal S\gamma_{[a})H_{b]cd}
-\frac{1}{8}\mathcal S\gamma_{[a}\mathcal S\gamma_{b]}
\big]\epsilon
=\,0\,.
\end{align}
These differ from the standard type IIB supersymmetry conditions only by the replacements $\nabla_a\phi\rightarrow\mathrm X_a+\sigma^3K_a$ and $e^{\phi}F\rightarrow\mathcal F$ inside the RR bispinor $\mathcal S$. It would be interesting to find solutions to these equations with $K_a\neq0$.
The generalized equations \rf{17}--\rf{22} are precisely the ones identified in
\cite{Arutyunov:2015mqj} as being satisfied by the target space background
of the so-called $\eta$-deformation \cite{Klimcik:2008eq,Delduc:2013qra,Arutyunov:2015qva}
of the $AdS_5\times S^5$ superstring model.\footnote}\def \la{\label{The relation to the notation in \cite{Arutyunov:2015mqj} is
${\rm X}_a=Z_a$ and $K_a=I_a$.
As in \cite{Arutyunov:2015mqj}, we find that while the NS-NS subset of equations
depends on ${\rm X}_a$ and $K_a$ only through their sum $X_a$ in \rf{21}, the two vectors enter separately
in the RR equations \rf{20}. While in the NS-NS sector one does not need the orthogonality condition ${\rm X}_a K^a=0$, this condition was, in fact, imposed in \cite{Arutyunov:2015mqj}
once the RR fields were included (see eq. (5.37) there).}
The resulting picture is thus in perfect agreement
with the fact that the $\eta$-model is kappa-symmetric \cite{Delduc:2013qra}
but the corresponding background does not satisfy the type
IIB equations \cite{Arutyunov:2015qva}.\footnote{This assumes that the action and kappa-symmetry transformations of the $\eta$-model are the same as those of the Green-Schwarz string. This can
be shown to be the case and is also true for the $\lambda$-model of \cite{Hollowood:2014qma}
upon integrating out the superalgebra-valued 2d gauge field.}
Further examples of solutions of the generalized type IIB equations \rf{17}--\rf{22}
should be provided by some other $\eta$-models \cite{Kyono:2016jqy,HS}, as was
indeed shown in \cite{HS} for the models based on Jordanian R-matrices.
The solution \rf{23} is the only possible one if the metric does not admit Killing vectors, i.e.
kappa-symmetric GS sigma models with non-isometric metric must correspond to
standard type IIB solutions. An example is provided by the $\lambda$-deformed model
which has kappa-symmetric action \cite{Hollowood:2014qma} with the corresponding metric \cite{st}
not admitting any Killing vectors: as was explicitly demonstarted in \cite{Borsato:2016zcf}
in the $AdS_2\times S^2\times T^6$ case the corresponding $\lambda$-deformed
background solves the standard type IIB equations.
It was argued in \cite{Arutyunov:2015mqj} that the above generalized type IIB
equations
imply the scale-invariance conditions for the GS sigma model.
In particular, the
2nd-derivative scale-invariance conditions for the ``RR" fields
follow immediately upon ``squaring" of the Dirac equation for $\mathcal S$ in \rf{20}.\footnote}\def \la{\label{In general, the equations \rf{17}--\rf{20} are thus somewhat stronger than the scale invariance conditions,
but still not sufficient to imply the Weyl invariance unless $K_a=0$.}
Thus non-trivial solutions of the generalized equations with $K_a\not=0$ should represent UV finite
but not Weyl-invariant GS sigma models so
their string theory interpretation is a priori unclear.
As follows from the analysis in \cite{Arutyunov:2015mqj}, starting with
a type IIA supergravity solution
with all the fields being isometric apart from a linear term in the dilaton \cite{ht2},
and performing the standard
T-duality transformation on all the fields except the dilaton (i.e. on
the GS sigma model on a flat 2d background)\footnote}\def \la{\label{In general, T-duality of GS sigma model on a flat 2d background should preserve its kappa-symmetry
\cite{Kulik:2000nr} and should be expected
not take one out of
the class of solutions of the generalized equations.}
then the resulting background should
solve precisely the generalized equations \rf{17}--\rf{22} with $K_a$ and ${\rm X}_a$ determined by the original dilaton and the metric.\footnote}\def \la{\label{In particular, the resulting
$K_a$ is then proportional to the derivative of the dilaton along the non-isometric direction
\cite{Arutyunov:2015mqj}.}
The converse should also be true \cite{Arutyunov:2015mqj}
given a non-trivial solution of the generalized type IIB equations \rf{17}--\rf{22} with a
non-null Killing vector $K_a$,
its $(G,B,\mathcal F)$ fields should be related by
a T-duality transformation to the fields of the corresponding type IIA supergravity solution with the
dilaton containing a linear isometry-breaking term.
Thus each solution of the generalized type II system \rf{17}--\rf{22} can be
associated with a particular solution of the standard type II supergravity equations.
This observation may
help understanding if it is possible to relate a solution of the generalized type II equations
with a consistent string theory.
We shall start in section 2 with a derivation of the type I and type IIB constraints \rf{1.1} and \rf{1.6}
on the superspace torsion and 3-form $H$ that follow from the condition of kappa-symmetry for the GS superstring in a non-trivial background.
The solution of the Bianchi identities supplemented by these basic constraints
leads, as will be described
in section 3,
to the generalized equations of motion \rf{1.3}--\rf{1.5} and \rf{17}--\rf{22}.
In section 4 we shall present a superspace formulation of the equations on $K_a$ and ${\rm X}_a$
and invariance conditions and superspace Bianchi identities for the ``RR" form fields.
Some concluding remarks will be made in section 5.
Details of the solution of the superspace Bianchi identities will be provided in an Appendix.
\section{Constraints from kappa-symmetry}\label{sec:kappa}
The classical GS superstring action in an arbitrary super-background
is (in the Nambu-Goto form) \cite{Grisaru:1985fv}
\begin{equation}
S=\int d^2\xi\,\sqrt{-G}-\int_\Sigma\,B\,,\qquad \qquad G=\det{G_{IJ}}\,, \la{2.1}
\end{equation}
where $\xi^I$ ($I,J=0,1$) are worldsheet coordinates, $G_{IJ}$ is the induced metric
\begin{equation} \la{2.2}
G_{IJ}=E_I{}^aE_J{}^b\eta_{ab}\,,\qquad E_I{}^A=\partial_Iz^ME_M{}^A (z)\,,\qquad z^M=(x^m,\,\theta^\mu)\,,
\end{equation}
while $B$ is the pull-back of a superspace two-form. This action is required to be invariant under the following kappa-symmetry transformations of the coordinates $z^M$
\begin{equation} \la{2.3}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\delta_\kappa z^ME_M{}^a=0\,,\qquad\delta_\kappa z^ME_M{}^{\alpha i}=\frac12(1+\Gamma)^{\alpha i}{}_{\beta j}\kappa^{\beta j}\,,\qquad\Gamma=\frac{1}{2\sqrt{-G}}\varepsilon^{IJ}E_I{}^aE_J{}^b\gamma_{ab}\sigma^3\,,
\end{equation}
where we have written the expressions appropriate to type IIB superspace. In the type IIA case the Pauli matrix $\sigma^3$ is replaced by $\Gamma_{11}$ while in the type I case one is to keep only the $i=1$ component.
The operator $\Gamma$ is traceless and satisfies the projector condition
$\Gamma^2=1$ so
this symmetry removes half of the fermionic components.\footnote}\def \la{\label{The origin of
kappa-symmetry is best understood via embedding a worldvolume superspace in a target superspace. This so-called superembedding formalism is reviewed in \cite{Sorokin:1999jx}.}
The requirement that the string action be invariant under the above transformations imposes constraints on the background. We will now determine what these basic constraints are and in the next section we will work out all their consequences. Varying the action we find
\begin{equation} \la{2.4}
\delta_\kappa S=-\int d^2\xi\,\delta_\kappa z^ME_M{}^{\alpha i}
\left[
\sqrt{-G}\, G^{IJ}E_I{}^aE_J{}^CT_{C\alpha i}{}^b\eta_{ab}
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over +\frac12\varepsilon^{IJ}E_I{}^CE_J{}^B H_{BC\alpha i}
\right]\,,
\end{equation}
where $T^A=dE^A+E^B\wedge\Omega_B{}^A$ is torsion and
$H=dB$. Note that the term involving the super-connection $\Omega_B{}^A$
does not contribute to \rf{2.4}
due to it being valued in $SO(1,9)$ (i.e.
$\Omega_{\alpha i}{}^b=0$ and $\Omega^{ab}=\Omega^{[ab]}$), it is nevertheless convenient to write the kappa-symmetry conditions covariantly in terms of $T^A$ rather than $dE^A$. Since the (pulled-back) supervielbeins are assumed to be independent fields and since the projector $\Gamma$ only involves the bosonic supervielbeins,
eq. \rf{2.4} implies the following conditions
\begin{align} \la{2.5}
&\qquad \qquad \qquad H_{\beta j\gamma k\alpha i}(1+\Gamma)^{\alpha i}{}_{\delta l}
=0\,,
\\ \ &\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \qquad
E_I{}^a
\left[
\sqrt{-G}\, G^{IJ}T_{\alpha i\beta j a}
-\varepsilon^{IJ}H_{a\alpha i\beta j}
\right](1+\Gamma)^{\alpha i}{}_{\gamma k}
=0\,,
\label{2.6}
\\ &\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \la{2.7}
E_I{}^aE_J{}^b\left[
\sqrt{-G}\,G^{IJ}T_{\alpha iab}
+\frac12\varepsilon^{IJ} H_{\alpha iab}
\right](1+\Gamma)^{\alpha i}{}_{\beta j}
=0\,.
\end{align}
The third condition turns out to be implied by the first two, see eq. (\ref{eq:dim-half-IIB}) in the next section.
Since the two terms in \rf{2.5} come with different powers of the induced metric, and since the components of $H$ cannot depend on the induced metric if $H$ is to have a target space interpretation, the this equation implies the vanishing of the dimension --$\ha$ component of the 3-form $H$
\begin{equation}\la{2.8}
H_{\alpha i\beta j\gamma k}=0\,.
\end{equation}
To solve the second condition \rf{2.6} for the dimension 0 torsion and 3-form components we parametrize these as
\begin{align}
T_{\alpha i\beta j}{}^a=
s^1_{ij}\gamma^b_{\alpha\beta}t_b{}^a
+s^2_{ij}\gamma^{bcdef}_{\alpha\beta}t_{bcdef}{}^a
+\varepsilon_{ij}\gamma^{bcd}_{\alpha\beta}t_{bcd}{}^a\,, \la{2.9}
\\
H_{a\alpha i\beta j}=
s^3_{ij}\gamma^b_{\alpha\beta}h_{ba}
+s^4_{ij}\gamma^{bcdef}_{\alpha\beta}h_{bcdefa}
+\varepsilon_{ij}\gamma^{bcd}_{\alpha\beta}h_{bcda}\,,\la{2.10}
\end{align}
where $s^{p}_{ij}$ are constant symmetric matrices and $t$ and $h$ are tensor superfields.
Tracing (\ref{2.6}) with $\gamma^{a}$ and multiplying with $G_{JK}$ we find the condition
\begin{align}
& \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
s^1_{ij}\sqrt{-G}E_K{}^bt_{ab}
-(s^3\sigma^3)_{ij}\frac{(\varepsilon G)^L{}_K\varepsilon^{IJ}}{\sqrt{-G}}E_L{}^cE_I{}^bE_{Ja}h_{bc}
-3\sigma^1_{ij}\frac{(\varepsilon G)^L{}_K\varepsilon^{IJ}}{\sqrt{-G}}E_L{}^dE_I{}^bE_J{}^ch_{abcd}
\nonumber\\
&{}
-s^3_{ij}\varepsilon^{IJ}G_{JK}E_I{}^bh_{ab}
+(s^1\sigma^3)_{ij}\varepsilon^{IJ}E_K{}^cE_I{}^bE_{Ja}t_{bc}
+3\sigma^1_{ij}\varepsilon^{IJ}E_K{}^dE_I{}^bE_J{}^ct_{abcd}
=0\,.
\label{2.6-1}
\end{align}
The first three terms and last three terms here have to cancel independently since they come with different powers of the bosonic supervielbeins. The requirement that the last three terms cancel gives
\begin{equation}\la{2.12}
\varepsilon^{IJ}E_I{}^bE_J{}^cE_K{}^d
\left(
s^3_{ij}h_{ab}\eta_{cd}
+(s^1\sigma^3)_{ij}\eta_{ab}t_{cd}
-3\sigma^1_{ij}t_{abcd}
\right)
=0\,,
\end{equation}
implying that\footnote}\def \la{\label{Note that the part anti-symmetric in $[bcd]$ vanishes trivially due to the fact that the world-sheet indices $I,J,K$ only take two values.}
\begin{equation}\la{2.13}
s^3_{ij}h_{a[b}\eta_{c]d}
+(s^1\sigma^3)_{ij}(\eta_{a[b}t_{c]d}-\eta_{a[b}t_{cd]})
-3\sigma^1_{ij}(t_{abcd}-t_{a[bcd]})
=0\,.
\end{equation}
After a little bit of algebra the solution is found to be
\begin{equation}\la{2.14}
s^3=s^1\sigma^3\,,\qquad t_{ab}=-h_{ab}=-i\eta_{ab}\,,\qquad t_{abcd}=t_{[abcd]}\,,
\end{equation}
where we have used the freedom to rescale the fermionic supervielbeins to normalize $t_{ab}$. The same freedom allows us to set $s^1_{ij}=\delta_{ij}$. The vanishing of the first three terms in (\ref{2.6-1}) then gives also
\begin{equation}
h_{abcd}=h_{[abcd]}\,.\la{2.15}
\end{equation}
Tracing (\ref{2.6}) with $\gamma^{abc}$ and $\gamma^{abcdef}$ and using the above conditions we find also that the components of $t$ and $h$ fields with more than two indices must vanish.
We conclude therefore that the
kappa-symmetry of the type IIB GS string action implies, in addition to \rf{2.8},
the standard dimension 0 superspace constraints
\begin{equation}\la{2.16}
T_{\alpha i\beta j}{}^a=-i\delta_{ij}\gamma^a_{\alpha\beta}\,,\qquad\qquad
H_{a\alpha i\beta j}=-i\sigma^3_{ij}(\gamma_a)_{\alpha\beta}\,.
\end{equation}
The type IIA cases can be analysed similarly.
The constraints in the type I
case \rf{1.1} are obtained by keeping only the $i=j=1$ components in
the type IIB ones.
The next step is to determine the consequences of these constraints by solving the superspace Bianchi identities for the torsion and the 3-form $H$. This will lead us to the generalized supergravity equations described in the Introduction.
\section{Generalized equations
from Bianchi identities and constraints}\label{sec:solution}
Our aim will be to find the most general solution to the 10d superspace Bianchi identities for the torsion and 3-form consistent with the dimension $-\ha$ \rf{2.8}
and dimension 0 \rf{2.16} constraints
following from kappa-symmetry of the GS string.
We will consider the type I and type IIB cases in parallel
and present the summary of the results while details will be provided in the Appendix.
Let us first recall the basic superspace conventions we will need.
The torsion satisfies the Bianchi identity\footnote{Our conventions are such that $d$ acts from the right and the components of forms are defined as
\noindent
$\omega^{(n)}=\frac{1}{n!}E^{A_n}\wedge\cdots\wedge E^{A_1}\omega_{A_1\cdots A_n}$.}
\begin{equation}\nabla T^A=E^B\wedge R_B{}^A\,, \qquad \qquad
T^A=\nabla E^A\equiv dE^A+E^B\wedge\Omega_B{}^A\,,\label{3.1}
\end{equation}
where $R_B{}^A$ is the curvature superfield 2-form
\begin{equation} \la{31}
R_B{}^A=d\Omega_B{}^A+\Omega_B{}^C\wedge\Omega_C{}^A
\ , \qquad \qquad \nabla R_B{}^A=0 \ .
\end {equation}
As follows from the fact that the
structure group is $SO(1,9)$, the non-zero components of the curvature
are $R_a{}^b$ and
\begin{equation}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\mbox{\bf Type I:}\quad R_\alpha{}^\beta=-\frac14R^{ab}(\gamma_{ab})^\beta{}_\alpha\,,\qquad\qquad
\mbox{\bf Type IIB:}\quad R_{\alpha i}{}^{\beta j}=-\frac14R^{ab}\delta_{ij}(\gamma_{cd})^\beta{}_\alpha\,.
\label{eq:T0}
\end{equation}
In components, the torsion and curvature Bianchi identities in \rf{3.1} and \rf{31} take the form
\begin{align}
&\nabla_{[A}T_{BC]}{}^D+T_{[AB}{}^ET_{|E|C]}{}^D=R_{[ABC]}{}^D\,, \label{eq:torsion-bianchi}\\
&\nabla_{[A}R_{BC]D}{}^E+T_{[AB}{}^FR_{|F|C]D}{}^E=0\,.
\label{eq:curvature-bianchi}
\end{align}
A useful fact is that the curvature Bianchi identities are a consequence of the torsion Bianchi identities.\footnote{The proof goes as follows \cite{Dragon:1978nf}. Taking the covariant derivative of (\ref{3.1}) gives $E^B\wedge\nabla R_B{}^A=0$ and using the fact that the indices belong to the structure group
$SO(1,9)$ this implies $E^b\wedge\nabla R_b{}^a=0$ and $(\gamma_{ab}E)^{\alpha i}\wedge\nabla R^{ab}=0$. Analyzing the components of these equations it is not hard to see that they imply the curvature Bianchi identity $\nabla R_B{}^A=0$.} This means that we only need to solve the torsion Bianchi identities.
We also have to solve the Bianchi identity for the 3-form $dH=0$, or, in components,
\begin{equation}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla_{[A}H_{BCD]}+\frac32T_{[AB}{}^EH_{|E|CD]}=0\,.
\label{eq:H-bianchi}
\end{equation}
There is some freedom in how one presents
the constraints. We will write them in essentially the same form as the type II constraints of \cite{Wulff:2013kga}, which is particularly simple, rather than, for example, in the form of the type I constraints used in \cite{Nilsson:1981bn}. The details of the solution to the Bianchi identities are given in Appendix
\footnote}\def \la{\label{In Appendix we analyze also a more general case when in the type I case
one imposes only the torsion constraint in \rf{1.1}.}
We shall discuss the consequences of the Bianchi identities and constraints
in order of increasing dimension of the component superfields.
\noindent
{\bf Dimension --$\ha$}:
As we have seen above, kappa-symmetry of the string implies the vanishing of the dimension --$\ha$ component \rf{2.8} of the 3-form, i.e.
\begin{equation}\la{3.7}
\mbox{\bf Type I:}\qquad H_{\alpha\beta\gamma}=0\qquad\qquad\qquad
\mbox{\bf Type IIB:}\qquad H_{\alpha i\beta j\gamma k}=0\,.
\end{equation}
\noindent
{\bf Dimension 0}:
Kappa-symmetry of the string also requires the standard dimension 0 torsion and 3-form constraints \rf{2.16}
\begin{align}
&\la{3.8} \mbox{\bf Type I:}\qquad \quad T_{\alpha\beta}{}^a=-i\gamma^a_{\alpha\beta}\,,\qquad\quad H_{a\alpha\beta}=-i(\gamma_a)_{\alpha\beta}\ ,
\\
&\la{3.9} \mbox{\bf Type IIB:}\qquad T_{\alpha i\beta j}{}^a=-i\delta_{ij}\gamma^a_{\alpha\beta}\,,\quad H_{a\alpha i\beta j}=-i\sigma^3_{ij}(\gamma_a)_{\alpha\beta}\,.
\end{align}
These are consistent with the dimension 0 Bianchi identity and the vanishing of the dimension --$\ha$ component of $H$.
\noindent
{\bf Dimension $\ha$}:
Let us start with the type I case. For the torsion we shall require that
\begin{equation}\la{3.10}
T_{\alpha[bc]}=0\ ,
\end{equation}
which just serves to fix the corresponding component of the spin connection, $\Omega_\alpha{}^{bc}$. By redefining the frame fields we can also arrange that\footnote{Taking
$E'=E+ i u E^b\gamma_cT_b{}^c+i v E^b\gamma_bT_c{}^c$ gives $T'_{(bc)}=T_{(bc)}-u\gamma_{(c}\gamma_dT_{b)}{}^d-v \eta_{bc}T_a{}^a$. This implies $\gamma^bT'_{(bc)}=(1-6u)\gamma^bT_{(bc)}+(\ha u -v)\gamma_cT_b{}^b$ which vanishes for a suitable choice of the constants $u,v$.
}
\begin{equation}
(\gamma^b)^{\alpha\beta}T_{\beta bc}=0\,.
\end{equation}
The torsion Bianchi identity we have to solve reads
\begin{equation}
T_{(\alpha\beta}{}^\delta\gamma^d_{\gamma)\delta}-\gamma^e_{(\alpha\beta}T_{\gamma)e}{}^d=0\,,
\end{equation}
where we used the form of the dimension 0 torsion component.
With some work one can show that this, together with the Bianchi identity for the three-form, finally
implies
\begin{equation}\la{3.14}
\mbox{\bf Type I:}\qquad H_{\alpha bc}=0\,, \qquad
T_{\alpha b}{}^c=0\,,\qquad T_{\alpha\beta}{}^\gamma=2\delta^\gamma_{(\alpha}\chi_{\beta)}-\gamma_{\alpha\beta}^a(\gamma_a\chi)^\gamma\,,
\end{equation}
where $\chi_\alpha$ is some MW spinor superfield.
For the type IIB case a similar analysis gives the following conditions
\begin{align}
\label{eq:dim-half-IIB} \mbox{\bf Type IIB:}\quad
&T_{\alpha ib}{}^c=0\,,\qquad
H_{\alpha i bc}=0\,,
\\
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over T_{\alpha i\beta j}{}^{\gamma k}=
\delta^{\gamma k}_{(\alpha i}\chi_{\beta j)}
+(\sigma^3\delta)^{\gamma k}_{(\alpha i}(\sigma^3\chi)_{\beta j)}
-\frac12\delta_{ij}\gamma_{\alpha\beta}^a(\gamma_a\chi)^{\gamma k}
-\frac12\sigma^3_{ij}\gamma_{\alpha\beta}^a(\gamma_a\sigma^3\chi)^{\gamma k}\,,
\nonumber
\end{align}
where $\chi_{\alpha i}$ are some two MW spinor superfields.
\noindent
{\bf Dimension 1}:
We shall impose the standard requirement
\begin{equation}
T_{ab}{}^c=0\ ,
\end{equation}
which fixes the remaining components $\Omega_c{}^{ab}$ of the spin connection. The type I torsion Bianchi identities we need to solve are then
\begin{equation}
-2iT_{c(\alpha}{}^\gamma\gamma^d_{\beta)\gamma}=R_{\alpha\beta c}{}^d
\ , \qquad \qquad
\nabla_{(\alpha}T_{\beta\gamma)}{}^\delta
+T_{(\alpha\beta}{}^\epsilon T_{\gamma)\epsilon}{}^\delta
-i\gamma^a_{(\alpha\beta}T_{|a|\gamma)}{}^\delta
=R_{(\alpha\beta\gamma)}{}^\delta\,.
\end {equation}
The Bianchi identity for the 3-form imposes the condition
\begin{equation}
T_{\alpha\beta}{}^eH_{cde}
+2T_{c(\alpha}{}^\gamma H_{\beta)\gamma d}
-2T_{d(\alpha}{}^\gamma H_{\beta)\gamma c}
=0\,.
\end{equation}
After some algebra one obtains the solution as
\begin{equation}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
T_{a\alpha}{}^\delta=
\frac18(\gamma^{bc})_\alpha{}^\delta H_{abc}
\,,\qquad\qquad
R_{\alpha\beta}{}^{cd}=\frac{i}{2}(\gamma_b)_{\alpha\beta}H^{bcd}
\,.
\end{equation}
In addition, one finds that the derivative of the spinor superfield $\chi$ in \rf{3.14} should be given by
\begin{equation}\mbox{\bf Type I:}\qquad \qquad\qquad
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla_\alpha\chi_\beta=\chi_\alpha\chi_\beta+\frac{i}{2}\gamma_{\alpha\beta}^aX_a-\frac{i}{24}\gamma^{abc}_{\alpha\beta}H_{abc}\,,
\label{eq:nablachi}
\end{equation}
where $X_a$ is some vector superfield.\footnote}\def \la{\label{While as superfields $\chi_\alpha$ and
$X_a$ are of course related, their first components will be independent fields entering the
generalized equations. We will use same notation for superfields and their lowest components, with the interpretation being hopefully clear from the context.}
In the type IIB case we find, by a similar analysis,
\begin{align}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \mbox{\bf Type IIB:}\qquad
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over T_{a\alpha i}{}^{\delta j}=
\frac18(\gamma^{bc}\sigma^3)_{\alpha i}{}^{\delta j} H_{abc}
+\frac18(\gamma_a\mathcal S)_{\alpha i}{}^{\delta j}\,,\\ &
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over R_{\alpha i\beta j}{}^{cd}=\frac{i}{2}(\gamma_b\sigma^3)_{\alpha i\beta j}H^{bcd}-\frac{i}{4}(\gamma^{[c}\mathcal S\gamma^{d]})_{\alpha i\beta j}\,,
\label{eq:T1-IIB}
\\
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over\nabla_{\alpha i}\chi_{\beta j}=
\frac12\chi_{\alpha i}\chi_{\beta j}
+\frac12(\sigma^3\chi)_{\alpha i}(\sigma^3\chi)_{\beta j}
+\frac{i}{2}\gamma_{\alpha\beta}^a (\delta_{ij}\mathrm X_a + \sigma^3_{ij} K_a)
\nonumber\\
&{}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \qquad \qquad \qquad \qquad
-\frac{i}{24}\sigma^3_{ij}\gamma^{abc}_{\alpha\beta}H_{abc}
-\frac{i}{16}(\gamma_a\mathcal S\gamma^a)_{\alpha i\beta j}\,,
\label{eq:nabla-chi-IIB}
\end{align}
where $\mathrm X_a$ and $K_a$ are some vector superfields.
$\mathcal S= (\mathcal S^{\alpha i, \beta j})$ is an anti-symmetric $32\times32$ matrix which is off-diagonal in $i,j$ and can therefore be represented as
\begin{equation}\la{324}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\mathcal S=-i\sigma^2\gamma^a\mathcal F'_a-\frac{1}{3!}\sigma^1\gamma^{abc}\mathcal F'_{abc}-\frac{1}{2\cdot 5!}i\sigma^2\gamma^{abcde}\mathcal F'_{abcde}\,,
\end{equation}
for some $p$-form superfields $\mathcal F'_p$.\footnote}\def \la{\label{The reason for the primes on ${\cal F}_p$ will become clear in the next section
(the lowest components of
$\mathcal F'_p $ and $\mathcal F_p $ will differ only by bilinear fermionic terms).}
\noindent
{\bf Dimension $3\ov 2$}:
The type I torsion Bianchi identities to solve at dimension $3\ov 2$ are
\begin{align}
&-i\gamma^d_{\alpha\beta}T_{bc}{}^\beta=2R_{\alpha[bc]}{}^d
\ , \\
&\nabla_aT_{\beta\gamma}{}^\delta
-2\nabla_{(\beta}T_{|a|\gamma)}{}^\delta
+2T_{a(\beta}{}^\epsilon T_{\gamma)\epsilon}{}^\delta
-T_{\beta\gamma}{}^\epsilon T_{a\epsilon}{}^\delta
-i\gamma^e_{\beta\gamma}T_{ea}{}^\delta
=2R_{a(\beta\gamma)}{}^\delta\,. \la{326}
\end{align}
The first one is easily solved for the curvature as
\begin{equation}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
R_{\alpha bcd}=\frac{i}{2}(\gamma_b\psi_{cd})_\alpha-i(\gamma_{[c}\psi_{d]b})_\alpha\,,
\end{equation}
where $T_{ab}{}^\beta=\psi_{ab}^\beta$ is
the gravitino field strength. Using this in \rf{326}
one finds after a bit of algebra that the solution is
\begin{equation}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\mbox{\bf Type I:}\qquad
\nabla_\alpha H_{abc}
=
3i(\gamma_{[a}\psi_{bc]})_\alpha
\,,\qquad\qquad
i(\gamma^b\psi_{ab})_\alpha
=
2\nabla_a\chi_\alpha
+\frac14(\gamma^{bc}\chi)_\alpha H_{abc}\,.
\label{eq:gammatracepsi}
\end{equation}
This solves the Bianchi identities but we must also remember the consistency conditions which follow from the equation for $\nabla_\alpha\chi_\beta$ in (\ref{eq:nablachi}). Taking another spinor derivative of this equation and symmetrizing we find an expression for the spinor derivative of $ X_a$
\begin{align}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla_\alpha X_a
=&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\frac12(\gamma^b\gamma_a\nabla_b\chi)_\alpha
+(\gamma_a\gamma^b\chi)_\alpha X_b
+\frac{1}{48}(\gamma_a\gamma^{bcd}\chi)_\alpha H_{bcd}
+\frac{1}{8}(\gamma^{bc}\chi)_\alpha H_{abc}\,.
\label{329}
\end{align}
A similar analysis in the type IIB case gives the following superfield relations
\begin{align}
\mbox{\bf Type IIB:}\quad
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over i(\gamma^b\psi_{ab})_{\alpha i}=2\nabla_a\chi_{\alpha i}+\frac14(\gamma^{bc}\sigma^3\chi)_{\alpha i}H_{abc}\,,\quad
\nabla_{\alpha i}H_{abc}=3i(\gamma_{[a}\sigma^3\psi_{bc]})_{\alpha i}\,,\quad
\label{eq:gravitino-eom}
\\
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over R_{\alpha ibcd}=\frac{i}{2}(\gamma_b\psi_{cd})_{\alpha i}-i(\gamma_{[c}\psi_{d]b})_{\alpha i}\,,
\\ \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla_{\alpha i}\mathcal S^{\beta1\gamma2}
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over =&
\mathcal S^{\beta1\gamma2}\chi_{\alpha i} \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
-2\delta_{\alpha i}^{[\beta1}(\mathcal S\chi)^{\gamma2]}
+2(\gamma^a\mathcal S)_{\alpha i}{}^{[\beta1}(\gamma_a\chi)^{\gamma2]}
+4i(\gamma^{ab})^{[\beta1}{}_{\alpha i}\psi_{ab}^{\gamma2]}\,,
\\
\nabla_{\alpha i}\mathrm X_a
=&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla_a\chi_{\alpha i}
-\frac14(\gamma_a\gamma^b\nabla_b\chi)_{\alpha i}
+\frac12(\gamma_a\gamma^b
({\rm X}_b + \sigma^3K_b) \chi\big)_{\alpha i}
\nonumber\\
&{}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \qquad +\frac18(\gamma^{bc}\sigma^3\chi)_{\alpha i} H_{abc}
+\frac{1}{96}(\gamma_a\gamma^{bcd}\sigma^3\chi)_{\alpha i}H_{bcd}
+\frac{1}{16}(\gamma_a\mathcal S\chi)_{\alpha i} \ ,
\label{329-IIB}
\\
\nabla_{\alpha i}K_a
=&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
-\frac14(\gamma_a\gamma^b\sigma^3\nabla_b\chi)_{\alpha i}
+\frac12\big(\gamma_a\gamma^b\sigma^3({\rm X}_b + \sigma^3K_b) \chi\big)_{\alpha i}
\nonumber\\
&{}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over\qquad
+\frac{1}{96}(\gamma_a\gamma^{bcd}\chi)_{\alpha i}H_{bcd}
-\frac{1}{16}(\gamma_a\sigma^3\mathcal S\chi)_{\alpha i}\,.
\label{eq:nabla-K-IIB}
\end{align}
\noindent
{\bf Dimension 2}:
In the type I case the torsion Bianchi identities read
\begin{equation}
R_{[abc]}{}^d=0
\ , \qquad
\nabla_\alpha T_{bc}{}^\beta
+2\nabla_{[b}T_{c]\alpha}{}^\beta
+2T_{[b|\alpha|}{}^\gamma T_{c]\gamma}{}^\beta
+T_{bc}{}^\gamma T_{\gamma\alpha}{}^\beta
=R_{bc\alpha}{}^\beta\,.
\end{equation}
They determine the spinor derivative of the gravitino field strength superfield
\begin{equation}\la{336}
\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla_\alpha\psi_{ab}^\beta
=
\frac18(\gamma^{cd})^\beta{}_\alpha\big(2\nabla_{[a}H_{b]cd}+H_{eca}H^e{}_{bd}-2R_{abcd}\big)
-\delta^\beta_\alpha\psi_{ab}\chi
-\psi_{ab}^\beta\chi_\alpha
+(\gamma^c\psi_{ab})_\alpha(\gamma_c\chi)^\beta\,.
\end{equation}
We are finally ready
to derive the equations of motion for the bosonic superfields.
Contracting \rf{336} with $\gamma^a$ and using (\ref{eq:gammatracepsi}) gives the equations
\begin{align} & \mbox{\bf Type I:}\qquad
\nabla_{[a}H_{bcd]}=0\,,\qquad \qquad R_{a[bcd]}=0\,,
\label{eq:H-R-bianchi} \\ &\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla^cH_{abc}-4\nabla_{[a}X_{b]}-2X^cH_{abc}-4\psi_{ab}\chi=0\,,\qquad
R_{ab}+2\nabla_{(a}X_{b)}-\frac14H_{acd}H_b{}^{cd}=0\,,
\label{eq:einstein-eq-I}
\end{align}
where $R_{ab}=R_{ac}{}^c{}_b$.
Evaluating $\nabla_{(\alpha}\nabla_{\beta)}X_a$ and
using (\ref{329}) we find also
\begin{equation}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla^aX_a-2X^aX_a+\frac{1}{12}H^{abc}H_{abc}+2i\chi\gamma^a\nabla_a\chi-\frac{i}{12}\chi\gamma^{abc}\chi\,H_{abc}=0\,.
\label{eq:div-X-I}
\end{equation}
The lowest components of these superfield equations
give us the generalized type I equations \rf{1.3}--\rf{1.5} discussed
in the Introduction (where fermionic components were set to zero).
In the type IIB case one finds the fermionic equation
(\ref{eq:nabla-psi-IIB}) together with the following equations for the bosonic superfields\footnote}\def \la{\label{Here the covariant derivatives (e.g. in \rf{eq:dh-etc})
contain fermionic terms so, e.g., $K_m=0, \ {\rm X}_m = \del_m \phi$ is always a solution even for non-zero fermionic fields.}
\begin{align}
&
\mbox{\bf Type IIB:}\qquad
R_{a[bcd]}=0\,,\qquad\nabla_{[a}H_{bcd]}=0\,,\la{eq:dH}\\
&
\qquad
2\nabla_{[a}\mathrm X_{b]}+K^cH_{abc}+\psi_{ab}\chi=0\,,\qquad\nabla_{(a}K_{b)}=0\,,
\label{eq:dh-etc}
\\
&\qquad \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over K^a\mathrm X_a-\frac{i}{4}\chi\gamma^a\sigma^3\nabla_a\chi+\frac{i}{96}\chi\gamma^{abc}\chi\,H_{abc}=0\,,
\label{eq:div-K}
\\
&\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \qquad R_{ab}+2\nabla_{(a}\mathrm X_{b)}-\frac14H_{ade}H_b{}^{de}+\frac{1}{128}\mathrm{Tr}(\mathcal S\gamma_a\mathcal S\gamma_b)=0\,,
\label{eq:einstein-eq-IIB}
\\
&\qquad \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \nabla^cH_{abc}-2{\mathrm X}^cH_{abc}-4\nabla_{[a}K_{b]} -\frac{1}{64}\mathrm{Tr}(\mathcal S\gamma_a\mathcal S\gamma_b\sigma^3)-2\psi_{ab}\sigma^3\chi=0\,,
\label{eq:div-H}
\\
&\qquad \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \nabla^a\mathrm X_a-2{\mathrm X}^a\mathrm X_a-2K^aK_a+\frac{1}{12}H^{abc}H_{abc}\nonumber\\
& \qquad\qquad \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over -\frac{1}{256}\mathrm{Tr}(\mathcal S\gamma^a\mathcal S\gamma_a)+i\chi\gamma^a\nabla_a\chi-\frac{i}{24}\chi\gamma^{abc}\sigma^3\chi\,H_{abc}=0\,,
\label{eq:div-X-IIB}
\\
&\qquad \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
(\gamma^a\nabla_a\mathcal S)_{\alpha i}{}^{\beta j}
-\big(\gamma^a ({\rm X}_a + \sigma^3 K_a) \mathcal S\big)_{\alpha i}{}^{\beta j}
+\big[\frac18(\gamma^a\sigma^3\mathcal S\gamma^{bc})_{\alpha i}{}^{\beta j}
+\frac{1}{24}(\gamma^{abc}\sigma^3\mathcal S)_{\alpha i}{}^{\beta j}\big]H_{abc}
\nonumber\\
&{}\qquad
+i\chi_{\alpha i}(\mathcal S\chi)^{\beta j}
-i(\sigma^3\chi)_{\alpha i}(\sigma^3\mathcal S\chi)^{\beta j}
+2(\gamma^{cd}\chi)_{\alpha i}\psi_{cd}^{\beta j}
-2(\gamma^{cd}\sigma^3\chi)_{\alpha i}(\sigma^3\psi_{cd})^{\beta j}
=0\,.
\label{eq:RR-eom}
\end{align}
These are the generalized type IIB equations implied by the kappa-symmetry of the GS string (generalizing \rf{17}--\rf{20} where fermions were set to zero).
One can show that they
reduce to the standard type IIB supergravity equations in the special case of $K_a=0$.
\section{Lifting the Killing vector and IIB form fields to superspace}\label{sec:lifting}
The generalized type IIB equations in the previous section can be formulated in a geometrical way in superspace by lifting the Killing vector field $K_a$ and the
form fields $\mathcal F_p$ to superspace vector field and superspace forms.
We begin with the one-form with 10d coordinate components ${\rm X}_m$
and lift it to a one-form ${\rm X}=dz^M{\rm X}_M$ in superspace. We must then constrain the extra spinor
component not to introduce extra degrees of freedom. This is done by
imposing the constraint
\begin{equation}\la{4.1}
\mathrm X_{\alpha i}=\chi_{\alpha i}\,.
\end{equation}
The equation for $\nabla_{[a}\mathrm X_{b]}$ in (\ref{eq:dh-etc})
as well as the equation (\ref{329-IIB})
for $\nabla_{\alpha i}\mathrm X_a$ and the equation for $\nabla_{(\alpha i}\chi_{\beta j)}$ in (\ref{eq:nabla-chi-IIB}) are then all summarized by the ``superspace Bianchi identity"
\begin{equation}
d\mathrm X+i_KH=0\qquad\Leftrightarrow\qquad\mathcal L_KB=d(i_KB-\mathrm X)\,,
\label{eq:X-bianchi}
\end{equation}
or, in components,
\begin{equation}\la{4.3}
2\nabla_{[A}\mathrm X_{B]}+T_{AB}{}^C\mathrm X_C=-K^CH_{ABC}\,.
\end{equation}
This equation says that $B$ transforms by a gauge transformation under the superisometries generated by $K^A=(K^a,\Xi^{\alpha i})$, where the Killing spinor superfield $\Xi^{\alpha i}$ is set to be
\begin{equation}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \la{4.4}
\Xi
=
\frac{i}{4}
\big(\gamma^a\nabla_a
-2\gamma^a\,\mathrm X_a
-2\gamma^a\sigma^3\,K_a
-\frac{1}{24}\gamma^{abc}\sigma^3\,H_{abc}
-\frac{1}{4}\mathcal S
\big)\sigma^3\chi\,.
\end{equation}
This definition together with (\ref{eq:div-K}) implies that
\begin{equation}
i_K\mathrm X=0\,.
\label{eq:KX}
\end{equation}
Using (\ref{eq:X-bianchi}) we then conclude that (super)isometries generated by $K$ leave $\mathrm X$ invariant (the rotation matrix $L_A{}^B$ is defined below)
\begin{equation}
\mathcal L_K\mathrm X=0\,,
\ \ \ \qquad {\rm i.e.} \ \ \ \ \qquad
K^C\nabla_C\mathrm X_A+L_A{}^B\mathrm X_B+i_K\Omega_A{}^B\mathrm X_B=0\,.
\end{equation}
Indeed, the superspace vector field $K^A$ satisfies the superspace Killing equation (see, for example, \cite{Wulff:2015mwa})
\begin{equation}\la{48}
E^BL_B{}^A=\mathcal L_KE^A=\nabla K^A+i_KT^A-E^Bi_K\Omega_B{}^A\,.
\end{equation}
This equation expresses the fact that
under the superisometry generated by the vector superfield $K^A$
the frame $E^A$ transforms by a local Lorentz transformation with the parameter $L_B{}^A=(L_b{}^a,\frac14L_{ab}(\gamma^{ab})_{\beta j}{}^{\alpha i})$ .
The component form of \rf{48} is
\begin{equation}\la{49}
\nabla_BK^A+K^CT_{CB}{}^A=L_B{}^A+i_K\Omega_B{}^A\,.
\end{equation}
Taking the parameter of the local Lorentz transformation to be
\begin{equation}
L_{ab}
=
\nabla_{[a}K_{b]}
-i_K\Omega_{ab}
\,,
\end{equation}
one gets, from the $(ab)$ component of \rf{49},
the standard Killing vector equation $\nabla_{(a}K_{b)}=0$. The $(a\beta j)$-component gives the equation (\ref{eq:nabla-K-IIB}) for $\nabla_{\alpha i}K_a$. The $(\alpha i\beta j)$ component implies the equation
(\ref{eq:RR-eom}) for $\mathcal S$ (except for the $\gamma^{abcd}$ part),
and also the equation of motion (\ref{eq:div-H}) for $B$,
the equation (\ref{eq:div-X-IIB}) for the divergence of $\mathrm X_a$,
as well as the constraint (\ref{eq:div-K})
on $K^a\mathrm X_a$. To show this requires using the equation for the spinor derivative of the bosonic fields and the gravitino equation of motion. Finally, the $(\alpha ib)$ component of \rf{49} is the superspace Killing spinor equation
\begin{equation}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over \la{410}
\nabla_b\Xi^{\alpha i}
+\frac18(\gamma^{cd}\sigma^3\Xi)^{\alpha i}\,H_{bcd}
+\frac18(\mathcal S\gamma_b\Xi)^{\alpha i}
-K^c\psi_{bc}{}^{\alpha i}
=0\,,
\end{equation}
and its lowest component is the usual Killing spinor equation.\footnote}\def \la{\label{This equation \rf{410} is not independent and arises by taking a spinor derivative of the $(\alpha i\beta j)$ component of \rf{49}, symmetrizing and using
the other equations given above.}
Finally, we can also lift to superspace the form fields appearing in the bispinor
$\mathcal S$ in \rf{324}
setting there
\begin{equation}
\mathcal F'_{a_1\cdots a_n}=\mathcal F_{a_1\cdots a_n}+i\chi^1\gamma_{a_1\cdots a_n}\chi^2\,.
\end{equation}
This works almost identically the same as for the standard type IIB supergravity
theory
where $\mathcal F_p$ are the RR field strengths multiplied by $e^\phi$ \cite{Wulff:2013kga}. Imposing the following constraints on their dimension 0 and dimension
$\ha$ components
\begin{align}
&\qquad \mathcal F_{\alpha i\beta jc}=i\sigma^1_{ij}(\gamma_c)_{\alpha\beta}\,,\qquad\qquad
\mathcal F_{\alpha i\beta jcde}=-\sigma^2_{ij}(\gamma_{cde})_{\alpha\beta}
\ , \\
&\mathcal F_{\alpha i}=-i(\sigma^2\chi)_{\alpha i}\,,\qquad
\mathcal F_{\alpha ibc}=-(\sigma^1\gamma_{bc}\chi)_{\alpha i}\,,\qquad
\mathcal F_{\alpha ibcde}=-i(\sigma^2\gamma_{bcde}\chi)_{\alpha i}\,,
\end{align}
one can show that they satisfy the following ``generalized Bianchi identities"
(same as in \cite{Arutyunov:2015mqj} for 10d components)\footnote}\def \la{\label{The $n=-1$ case corresponds to the condition $i_K \, \mathcal F_1=0$ \cite{Arutyunov:2015mqj}.}
\begin{equation}
d\mathcal F_{2n+1}+\mathrm X\wedge\mathcal F_{2n+1}-H\wedge\mathcal F_{2n-1}-i_K\mathcal F_{2n+3}=0\ , \qquad n=-1,0,1,2\,,\la{414}
\end{equation}
or, in components,
\begin{align}\textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
\nabla_{[A_1}\mathcal F_{A_2\cdots A_{2n+2}]}
+\frac{2n+1}{2}T_{[A_1A_2}{}^B\mathcal F_{|B|A_3\cdots A_{2n+2}]}
-\mathrm X_{[A_1}\mathcal F_{A_2\cdots A_{2n+2}]}\nonumber
&\\ \textstyle} \def \ha {{\te {1\ov2}}} \def \ov {\over
+\frac{(2n+1)2n}{3!}H_{[A_1A_2A_3}\mathcal F_{A_4\cdots A_{2n+2}]}
-\frac{1}{2n+2}K^B\mathcal F_{BA_1\cdots A_{2n+2}}
\,&=0\,.
\end{align}
It is easy to check, using (\ref{eq:X-bianchi}) and (\ref{eq:KX}), that as a consequence of these generalized Bianchi identities the forms $\mathcal F_p$ are also invariant under the (super)isometries generated by $K$, i.e.
\begin{equation}
\mathcal L_K\mathcal F_{2n+1}=0\,, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n=0,1,2\,. \la{416}
\end{equation}
\section{Concluding remarks}\label{sec:conclusion}
In this paper we have found the equations imposed on the target space (super) geometry by the requirement that the classical Green-Schwarz superstring should
be kappa-symmetric. The bosonic part of these equations are exactly the same as suggested earlier in \cite{Arutyunov:2015mqj}.
The resulting generalization of the standard 10d supergravity
equations is automatically supersymmetric as it was
obtained from a superspace construction.
There is also a straightforward generalization of the notion of a supersymmetric solution of the generalized equations.
We have performed the detailed analysis for the type I and type IIB cases but the corresponding generalized type IIA equations can be written down almost immediately using the results of \cite{Wulff:2013kga}.
One open question (raised already in \cite{Arutyunov:2015mqj}) is whether these equations \rf{17}--\rf{20} can be derived from an action and should thus satisfy certain integrability conditions.
Another is about possible uplift of the generalized type IIA equations to 11 dimensions
and a relation to a (partially off-shell?) generalization of 11d supergravity.
Non-trivial solutions of the type II generalized equations
describe backgrounds symmetric with respect to the vector $K_a$. Applying T-duality
one then gets a type II supergravity solution with a dilaton containing a linear non-isometric term
\cite{ht2,Arutyunov:2015mqj}.
It would be interesting to extend the discussion in \cite{Arutyunov:2015mqj}
to determine how more general T-dualities act on these equations.
Applying T-duality to the GS sigma model \cite{Kulik:2000nr}
should transform the background fields in a way consistent with kappa-symmetry
and should thus map one solution of the generalized equations to another.
To investigate the properties of the corresponding sigma models
one may consider the component expansion of the type II GS
superstring action in these more general backgrounds.
This expansion takes the same form as in the standard type II supergravity backgrounds
\cite{Wulff:2013kga}
provided one replaces the dilaton-modified RR field strengths $ e^\phi F_p$ by $\mathcal F_p$ and the dilaton gradient term $\frac{i}{2}\delta_{ij}\gamma^a\partial_a\phi$ in the quartic fermion terms (appearing in the matrix $T$ in \cite{Wulff:2013kga})
by $\frac{i}{2}\gamma^a(\delta_{ij}\mathrm X_a+\sigma^3_{ij}K_a)$.
\vspace{.5cm}
\noindent
{\bf Note added:} After this paper appeared in arXiv we were informed of an earlier work on the pure spinor superstring that also observed that classical BRST invariance, the analog of kappa symmetry in that formulation, is not enough to restrict the background to be a supergravity solution \cite{Mikhailov:2012id}. The relation with the condition $\chi_{\alpha i}=\nabla_{\alpha i}\phi$ and the fact that the generalized backgrounds (referred to there as ``non-physical'') are connected with global symmetries were commented on in section 7.3 of \cite{Mikhailov:2014qka}.
\section*{{Acknowledgments}}
We acknowledge R. Borsato, B. Hoare and C. Hull for useful discussions.
We are grateful to R. Borsato, B. Hoare and R. Roiban for helpful comments on the draft.
AAT would like to thank R. Roiban for important
discussions on the relation between $\kappa$-symmetry and supergravity constraints.
LW is grateful to P. Howe for important clarifying discussions.
We also thank A. Mikhailov for pointing out references \cite{Mikhailov:2012id,Mikhailov:2014qka} to us.
This work was supported by the ERC Advanced grant No.290456.
The work of AAT was also supported by the
STFC Consolidated grant ST/L00044X/1 and
by the Russian Science Foundation grant 14-42-00047.
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TARCOPOL Sp. z o.o., with its registered office in Starachowice, was established in 1991 as a Polish-Danish limited company. Its initial capital was put up by the Danish TARCO VEJ A/S road and bridge construction company. In 2006, TARCO was bought out by Munck Gruppen A/S, another Danish road and bridge company.
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From the very beginning, the company's management, heavily involved in its development, always pursue the goal of maintaining close, constant cooperation with research entities and technical universities in order to access current know-how and the latest achievements in science and technology. A specialist branch of TPM Consulting, separate from the main business structure, offers services in bridge design, evaluation and inspection, assessments and quality control of engineering and industrial bridges.
After many years of business activity, the name TARCOPOL is widely recognisable in the transport infrastructure market as an experienced and reliable contractor for dedicated bridge works. This is reflected in the company's references, which come from companies and road authorities all over Poland. The dynamic development of the company has also been acknowledged with a prestigious Gazela Biznesu ('Business Gazelle') award in the 2009, 2012 and 2013 edition of the rankings.
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In Bangladesh, a bat-borne virus is poised to become the next pandemic. Is an ecological intervention the answer?
Steven Bedard
This story originally appeared in bioGraphic, an online magazine about nature and sustainability powered by the California Academy of Sciences.
The young man shifts nervously in the front seat of the van as it turns down increasingly narrow roads, then alleyways, and eventually dirt tracks. His broad grin and swagger have faded since he first volunteered to lead us to the home of a local gachhi , a collector and seller of date palm sap. Leaning out the open window, he asks for directions from three men standing over the parts of a disassembled engine scattered on a dusty concrete floor, then from a man butchering chickens on a wood block out front of a roadside stand.
An Indian flying fox (Pteropus medius) peers out of the leaves of a date palm tree (Phoenix dactylifera) in India's West Bengal, just across the border with Bangladesh. Photograph by Dhritiman Mukherjee.
Whether our guide's waning confidence is due to the fact that he doesn't know the area as well as he first let on, or because revealing a local secret to a vanload of outsiders might be frowned upon isn't clear. But after casting a few wary glances over his shoulder, he resigns himself to continuing our quest.
The gachhi we're searching for is not just any sap collector. He's rumored to make and sell tari , a fermented brew that's popular among men in this part of northern Bangladesh—especially bus drivers, truckers, and day laborers—but one that's prohibited for two reasons. In this predominantly Muslim nation tucked under the crook of India's east arm, consumption of alcoholic beverages is forbidden (except by foreigners), so tari has always been technically off-limits. But now, even fresh date palm sap is banned because of its connection to an emerging infectious disease that is threatening to become the next global epidemic.
In 2005, scientists drew a link between this nearly universally loved local delicacy and Nipah virus encephalitis, a disease that has killed nearly 75 percent of those who have contracted it since 2001, when Bangladesh's first outbreak occurred. Scientists' understanding of the link between the sap—fermented or otherwise—and Nipah infection grew stronger as subsequent outbreaks mounted. But it wasn't until 2011, in the wake of a particularly deadly winter, that the Bangladesh government declared a ban on the sale of date palm sap, an act akin to the U.S. government prohibiting the sale of apple cider.
Of course, banning a substance that's loved by so many and enforcing such an order are two different things, particularly when the risks of consuming that substance are poorly understood. Which is precisely why this team of public health investigators from an organization funded in part by the U.S. Centers for Disease Control and Prevention (CDC) has come here to the village of Mohonpur, near Bangladesh's northeast border.
The team's lead, Hossain M. S. Sazzad, a physician who also holds a Master's degree in health economics, leans forward and addresses the young man in the front seat in a calm, measured tone. He explains that he and his colleagues are not here to enforce the ban. They're health workers, he says, and only wish to talk and learn.
When the track narrows to a width the van can no longer squeeze through, the team sets off on foot. We follow a path that cuts between thatch- and tin-roofed homes, past goat pens, and along spindly fences lined with reeds that have had dung hand-molded along their lengths and been left to dry in the sun—fuel for another day. Dogs bark, and women and children wrapped in brightly colored cloths come to observe the spectacle of city folk traipsing through their village. Eventually, the team turns down a narrower side path leading to a dwelling that several villagers have pointed them toward. The whereabouts of the local gachhi , it turns out, is not a particularly well-kept secret.
They find the sap collector behind his house hacking at a stack of thick, green bamboo cuttings piled on the ground. While his greeting is less hospitable than is customary in Bangladesh, he seems more perplexed than annoyed by the unannounced visit.
As if amiably chatting with a farmer about the weather and his crop, Sazzad asks the man about his daily activities, his health, his method of sap collection, if he's heard about Nipah virus, if he ever observes bats near the trees he taps.
Standing a pace or two away from the group, the old man, his white hair and beard glinting in the dappled sunlight, says that he's been climbing and tapping date palms on this land since before the country's 1971 War of Independence. He's now 85. As evidenced by more than a dozen clay pots lying on the ground behind him, he admits that he still collects sap daily during the winter, but now only for personal consumption, and claims he doesn't ferment it to make tari .
This man says he has been tapping date palm trees near his home for more than 50 years, since before Bangladesh's 1971 War of Independence. Photograph by A.M. Ahad.
A few moments later, though, the man asks if anyone in the group wants to purchase sap from the haul he collected the night before. When they decline, his scant interest in the conversation vanishes entirely. He turns, gathers up his tools—a handful of clay pots, a long, curved knife he uses to carve away the bark of date palms, and a rope that will loop around his waist and the trunks of the trees as he climbs them—and sets off to make his afternoon rounds.
This brief exchange feels anticlimactic to me, especially after our long search for the source of a potentially fatal outbreak. Sazzad and the others don't seem fazed, though. In a way, it's emblematic of the inconclusive and unfinished nature of the work they do—and its importance. Yes, the gachhi will continue collecting, and likely selling, date palm sap. But now they know exactly where he lives, and that this is an area they will need to keep an eye on.
While the man is not the villain I may have envisioned when we were searching for him—just an old man looking to make a few extra Taka by tapping the local trees—these health workers, and health officials around the world, know that the next outbreak could begin with him, or someone just like him. And although Nipah virus has killed fewer than 400 people since it was first identified 20 years ago, they also know that the pathogen's persistence in the environment, its ability to change quickly, and its potential, under the right set of conditions, to spread like wildfire could enable the next outbreak, or the one after that, to become a pandemic. Many experts think that the right set of conditions might already be in place here and across a vast swath of western Bangladesh known as the "Nipah Belt."
As we make our way back through the village, I can't help retracing the steps I took to get here. It's just a few kilometers and a very plausible route from this tiny village to a city center and onto a crowded bus through one of the most densely populated countries in the world, then on to the country's capital of nearly 9 million, and possibly onto an international flight bound for another metropolis. It took me two days to travel that route in the other direction—well within the virus's incubation period.
Nipah virus encephalitis is one of eight diseases that the World Health Organization (WHO) has identified as epidemic threats in need of prioritization. The list includes Ebola, SARS, Zika, and an as-yet unknown affliction referred to as "Disease X." All eight have been prioritized because of their inherent epidemic potential, and also the fact that there are currently insufficient measures in place to prevent them.
While the WHO's "priority pathogens" vary in terms of their geographic distribution and the havoc they inflict on the human body, they have a couple of things in common that enhance their epidemic potential. First, they're all viruses (or likely to be in the case of Disease X). Second, they're all zoonotic, which means that they all reside in another animal, but are capable of jumping, or spilling over, into humans. These characteristics are important, because viruses reproduce very quickly, which amplifies their potential to change into more pathogenic forms. And a reservoir host acts like a bunker, a safe haven between outbreaks, in which the pathogen can regroup and potentially undergo a change, a random mutation that will better prepare it for the next spillover opportunity.
Nipah virus's safe haven is the fruit bat, or more accurately, several species of bat in the genus Pteropus . Fruit bats, also known as flying foxes, are small- to medium-sized herbivorous mammals that roost in trees by day and take to the wing by night in search of nectar, pollen, and fruit. According to Emily Gurley, an epidemiologist at Johns Hopkins Bloomberg School of Public Health who has been studying Nipah in Bangladesh since 2004, most bats in the genus Pteropus carry antibodies for Nipah or other closely related henipaviruses. That means the bats have at least been exposed to the pathogen, and many harbor live viruses in their tissues.
Gurley and other scientists think that fruit bats have carried Nipah virus for a very long time. "The bats have always had it," she says. Not only that, she suspects that the virus began spilling over into humans hundreds of years ago, if not more. Until recently, though, there were likely fewer opportunities to do so. There was also no diagnostic test for the virus, and so, like trees falling in the forest with no one to hear, when spillover events did occur, they went unnoticed.
After its early, unheralded debuts, Nipah virus found its big opportunity in 1998 in the tiny Malaysian village of Sungai Nipah from which the virus acquired its name. The factors that led to that first big spillover event are unfortunately all too familiar in the histories of zoonotic pathogens, currently responsible for 75 percent of all emerging infectious diseases. As the number of humans on the planet has exploded toward and then beyond 7 billion, we've increasingly pushed into and degraded natural ecosystems, causing many organisms to go extinct, and putting ourselves into close contact with those that remain. The lifeforms we now cohabitate with include both the animals and plants we can see, and the microbes they harbor, which we can't.
According to Kevin Olival, an ecologist and evolutionary biologist for the non-profit organization EcoHealth Alliance, it was this type of ecological shift that led to Malaysia's 1998 outbreak. Olival, who has studied routes of transmission from bats to humans all over the world, says that "contact between these animals and people has probably always happened to some degree because we both eat fruit—so there's always been some overlap." But, he says, industrialized agriculture near forest edges over the past several decades has dramatically altered that interface, intensifying contact between bats and humans.
In the mid- to late-90s, pig farming was booming in Malaysia. Farmers cleared forest to make way for more and larger operations. This not only put the farms in closer proximity to the wildness of the rainforest, it reduced the number of fruit and nectar trees available to bats. Drought and fires in Indonesia in preceding years also contributed to food shortages and caused bats to migrate greater distances in search of flowering and fruiting trees. Many of them found what they were looking for around Malaysian pig farms, which were often lined with mango trees. The bats, at least some of which carried Nipah, feasted on the cultivated fruit. And if a bat-nibbled mango dropped into a sty from the tree above, a pig had a chance of picking up the virus along with a tasty snack.
Infected pigs suffered acute respiratory distress, like a horrible case of the flu. The vast majority of animals on stricken farms became infected, and 20 percent of those that fell ill died. Farm workers who handled sick and dying pigs fared even worse. After an incubation period of several days to more than a week, many workers who were exposed developed encephalitis, an often-deadly inflammation of the brain.
Encephalitis is common in Nipah sufferers. But in 1998, no one had ever heard of Nipah virus, and it wasn't clear how people were getting sick in the first place. Doctors initially suspected an outbreak of Japanese encephalitis, a mosquito-borne disease. Eventually, though, when the infections were linked to direct contact with pigs, they realized they had something different on their hands. Identification of the virus in the cerebrospinal fluid of an outbreak victim confirmed that the pathogen was not only new to science, it was of a type known to be carried by mammals, not mosquitoes.
With this telling but incomplete knowledge in hand, the Malaysian government took a bold step. It ordered the slaughter of more than a million pigs in the hope of preventing a national or global health crisis. Like amputating a limb to stop a rampant infection, the move crippled the country's booming pork industry in a matter of weeks. But it also stopped the Nipah outbreak in its tracks. By May 1999, the nightmare was over. Unfortunately, this would not be the last the world had seen of Nipah virus.
The pathogen reemerged in two separate outbreaks in 2001, one in Siliguri, India and another in Meherpur, Bangladesh. Although the infectious agent was confirmed to be Nipah virus, there were some alarming differences in these new outbreaks. First, neither India nor Bangladesh had large-scale pig farming operations, so there was no obvious intermediate host. More troublingly, the new outbreaks, though significantly smaller than Malaysia's, had much higher fatality rates—about 70 percent. What's more, a number of cases in Siliguri resulted from caregivers being infected by patients. The virus had jumped from person to person.
Although Nipah was at the heart of each case, the virus was clearly behaving differently from place to place, outbreak to outbreak. And that pattern, or lack thereof, has continued over the past 17 years. Bangladesh has seen at least one new Nipah outbreak nearly every year since 2001. India has documented several more as well, including one this past summer that killed 17 of the 19 people who were infected.
What this variation and regular recurrence means is that health workers like Sazzad and Gurley never quite know what to expect from their moving target. "In Bangladesh, we have documented closing in on a hundred different spillover events," says Gurley. "So, that's a hundred different opportunities for a more transmissible strain to be introduced into people. And that's scary."
A lone figure in a long silk shirt and tupi hat pedals silently down a road of damp, red clay packed hard by ages of foot and wheeled traffic. He rides past a great egret probing the surface of a flooded rice field, and between towering fig trees and houses still quiet under a blanket of cook-stove smoke and pre-dawn mist.
In the morning stillness, it's hard to believe that the chaotic crush of Rangpur City is just a short, harrowing 5-kilometer drive from here. There, pushcarts and auto rickshaws and lumbering trucks filled with bricks will soon begin jockeying for position in front of merchant stalls, some peddling mobile phones, others cooking biryani and flatbread over open fires. Here, the chaotic competition is of a different kind—ecological, otherworldly.
Above our heads, hundreds of fruit bats are coming home to roost. Their translucent wings stretch wide as they maneuver between careening bodies and twisted tree limbs before braking hard, grasping with outstretched feet, and awkwardly hanging themselves upside down for the day. As disorderly as the bats' morning approach may seem, the real scrum begins when they land. Someone's always too close, or hanging in a prime patch of sun or shade. Often the only way to regain one's rightful place in the roost is with a warning screech or a swift nip or wingslap.
Fortunately for these bats, the antagonism remains within the colony. This group of Indian flying foxes ( Pteropus medius ) has been lucky enough to take up residence in an enormous sacred fig tree ( Ficus religiosa ), which sits at the center of a local Hindu temple. Though the fig's twisted trunk brings to mind the menacing trees from The Wizard of Oz , the temple's low, deteriorating walls demarcate a peaceful place in which the tree and its many inhabitants can live out their existence free from harassment.
While the temple offers an extra level of protection, people in Bangladesh are generally resigned to living among bats. "They're everywhere," says Gurley. "There's hardly any village, among the hundreds we've visited, that doesn't have a bat roost."
Driven by a lack of primary forest and reliable food resources across much of their native range, the bats likewise seem resigned to living near people. Just like their relatives in Malaysia, bats in this region frequently take advantage of cultivated crops such as mangoes and figs to make up for the native fruit and nectar missing from their diets. Many have also developed a taste for date palm sap.
In 2004, when Gurley first began studying Nipah in earnest, she and her team of investigators quickly zeroed in on that bat-sap connection. They asked Nipah survivors and loved ones of the deceased about direct contact with bats, about tree climbing, about living near bat roosts and eating fruit that had fallen from trees. They also asked about consumption of date palm sap. Of all the activities the team explored, sap drinking was one of the most consistent among those who had fallen ill.
The clearest evidence of sap contamination, though, came in 2010 when researchers set up infrared cameras trained on the collection pots that gachhis had hung on date palm trees. The results of this study couldn't have been more telling. Over 20 nights of observation, the cameras captured 132 visits from fruit bats on 14 separate nights. Bats could be seen lapping up the sweet sap oozing from the sections of tree trunk where the gachhis had shaved the bark away. In some instances, the images captured bats in the act of relieving themselves directly above the collection pots. The contamination was unintentional, of course, but the possible route of transmission was undeniable.
Among mammals, bats rank number one in terms of their role in spreading zoonotic diseases. Scientists have linked them to at least a dozen human afflictions, including four of the eight diseases the WHO has prioritized. Exactly what makes bats such good hosts for disease-causing agents—or if in fact they are particularly suited to carrying and transmitting disease—has been poorly understood for decades. But new research suggests that the answers may have something to do with flight.
While a number of mammals can glide, bats are the only members of the group capable of sustained flight. This feat requires a huge amount of energy—a 16-fold increase in metabolic rate, according to Raina Plowright, a veterinarian and professor of epidemiology at Montana State University. That high sustained output would typically be associated with oxidative damage to cells, she says, but somehow bats have developed mechanisms to prevent or repair the damage.
Bats are also long-lived compared to similar-sized mammals. As a general rule, the more you weigh, the longer you live. But bats are complete outliers in that respect, Plowright says. For example, the oldest known bat, which lived 41 years, weighed less than 8 grams. This suggests that bats have a way to combat the cell damage that typically leads to senescence. "We think that somehow this ability to not have oxidative damage and the ability to repair DNA and not go into senescence are tied up," she says, "and perhaps even tied up with their ability to host viruses."
Because bats typically live in large colonies and roost in close proximity to one another, microbes are easily passed among members of the group. While virus numbers are typically kept in check by each bat's immune system, when an animal is stressed, its defenses can become compromised. Much as a cold might make us cough and sneeze, a bat's weakened immune system can cause the animal to shed viruses into its surroundings through saliva, urine, and feces.
According to Plowright and Gurley, bats tend to shed viruses in pulses, high concentrations of the pathogens excreted by a colony into the environment over a short period of time. These pulses seem to coincide with Nipah outbreaks, but what stresses the bats in the first place is unknown. Plowright suspects an ecological cause, possibly related to food. "We don't know much about their response to the environment and nutrition," she says. "Maybe we see high rates of excretion in winter because there's less food available. We just don't know."
Those unknowns are of course what flash through my mind on this winter morning as I stand there gawking up at hundreds of bats that have just returned from a night of foraging. I glance down at the backpack I carelessly dropped into the perpetually damp soil at the base of the tree when I first arrived. Now I can't help wondering: How much virus does it take to get sick? How much am I breathing in now? Unfortunately, not even the experts have the answers to these questions.
Two weeks from now, when I'm back in the U.S. and most likely safely outside the virus's incubation period, I'll quiz Gurley about my activities that morning—and the mist that I may or may not have felt as I stood under the roost. Choosing her words carefully, she'll explain that bats do tend to urinate more frequently in the morning. "So, they leave the roost at night to feed, right? And when they come back, that's typically when they urinate so… yeah, I probably wouldn't do that again…."
In January of 2010, Sazzad found himself in the midst of one the most uncomfortable moments of his career. Sitting in an isolation room at the Faridpur Medical College Hospital, wearing gloves and an N95 surgical mask designed to prevent the spread of airborne viruses, the soft-spoken, then-33-year-old doctor was interviewing a patient who suffered from fever, dizziness, and shortness of breath. The man's nephew had died from Nipah virus encephalitis about a week earlier, as had three other people from the same village. By the time the patient arrived at the hospital in Faridpur, he was so disoriented that his responses to Sazzad's questions were mostly nonsensical. In 2010, knowledge was limited about how Nipah manifests in the human body or how it spreads. Still, Sazzad knew more than enough to be cautious.
According to Johns Hopkins University epidemiologist Emily Gurley, Bangladesh medical facilities have very little to offer patients like this young man in the Faridpur Medical College Hospital, so often people who fall ill don't bother to seek treatment. That can make tracking diseases like Nipah a huge challenge. Photograph by A.M. Ahad.
But it was stuffy in the isolation room, and Sazzad, who was coming down with a cold and was feeling pretty lousy himself, felt like he was suffocating behind his mask. Twice during the stifling, hour-long interview, the urge for fresh air became so overpowering that he slipped the back of a pen under the edge of his mask to create a small gap. Just a quick breath, he thought.
The next morning, Sazzad learned that the patient had died, and a diagnosis was confirmed. Nipah virus had been raging through the man's body during the interview. When the young doctor started coughing that night, a concerned colleague called Sazzad's advisor Stephen Luby, a professor of medicine at Stanford University who at the time was stationed at the CDC office in Bangladesh, to ask what to do. They all told themselves it was just a cold, but Sazzad couldn't stop thinking about those two breaths. Or about his wife and one-year-old son at home. Eventually, a blood test put their anxieties to rest. But all these years later, when he tells me the story as we tour a hospital ward just two floors above that isolation room, he still visibly shudders.
A member of a Nipah-focused team of doctors and scientists based at the International Centre for Diarrhoeal Disease Research, Bangladesh (ICDDR,B), Sazzad is one of about 20 staffers charged with investigating and following up on suspected Nipah outbreaks across the country—all on an annual budget of $150,000 per year. That's no small task in a nation that's roughly the size of the state of Illinois and packed with a population that's more than half that of the entire U.S.
Interviews with sap collectors, potential Nipah victims, and past outbreak survivors are a key part of the team's efforts to understand the disease and its transmission. Despite having conducted more than a hundred of these high-stakes conversations, Sazzad still sometimes feels nervous. "When you are just inside an outbreak," he explains, "when you don't know the whole picture of who's transmitting to whom, you feel very unsafe, because you don't know if you have been exposed or not. You could be part of the chain."
Despite the risks, Sazzad and his colleagues persist, because they know the next conversation they have or observation they make may mean the difference between life and death for someone—or many. They also know their front-lines work is leading to a much clearer picture of the way the virus works, providing the basic information necessary to help stop a future epidemic.
The symptoms of the disease are now well documented, although they vary considerably from patient to patient and strain to strain. While some infected humans are completely asymptomatic, most initially develop symptoms including fever, headaches, vomiting, and sore throat. Some develop acute respiratory infections in the early stages of the disease; others never do. After a few days to a couple of weeks, many patients start to exhibit more serious signs of encephalitis—dizziness, drowsiness, altered consciousness, and other neurological changes. Within another day or two, the disease often progresses to coma, then death.
Transmissibility is also highly variable. While the world has yet to see a strain of Nipah virus that is especially proficient at jumping from human to human, many past spillover strains have managed to make that leap, traveling in fluids spewed from a mouth or nose, or through urine or blood. "Immunological studies have shown that the primary route of human transmission is through saliva," says Sazzad, "but we still don't know if a fraction of cases are caused by airborne transmission. Is there any additional route of transmission? We don't know."
So far, most documented person-to-person transmission has been from patient to family caregiver. Even in hospitals, patients are more likely to receive direct care from a family member than a doctor or nurse, partly because of staffing levels at the hospitals and partly because of cultural taboos around physical contact with strangers.
As Sazzad and I walk the concrete halls of the Faridpur Medical College Hospital, I recall a pre-trip conversation with Gurley, who told me that one of the biggest challenges her team faces in their infection-control work in Bangladesh is that family members, and in many cases even the health workers, caring for Nipah patients "don't understand contagion and how diseases are being transmitted." Mothers hand-feed food to sick children, then finish the leftovers themselves. Daughters use the long folds of their skirts to wipe mucus from a dying parent's face, then use the same skirt to wipe their own tears moments later.
Now that I'm here, it has become abundantly clear that it's not only possible for person-to-person transmission to happen inside hospital walls—it's likely.
Each day during the winter, Bangladesh's gachhis climb date palm trees, carve away a layer of bark and collect the thin, sweet sap that oozes form the tree. Photograph by A.M. Ahad.
According to Gurley, who led the Surveillance and Outbreak Investigation Unit and directed the Programme on Emerging Infections at ICDDR,B from 2003 to 2015, it's not a matter of if there will be another pandemic on our crowded and degraded planet, it's a question of when, and which disease it will be—Ebola, Disease X, Nipah? She's spent the past 15 years, first at ICDDR,B and now at Johns Hopkins, doing everything in her power to make sure it's not Nipah.
After my trip, having seen everything she's up against, I comment that I'm amazed by her ability to stay motivated in the face of such monumental challenges.
She laughs. "I think the word you're looking for is 'stubborn,' right?"
Her persistence is unquestionably derived, in part, from her self-described love of big, hairy problems. "I guess I run under the assumption that if there's a good reason to do something, then there's gotta be a way to figure it out," she admits. But she reminds me that she has reasons to be optimistic about the progress they're making.
While there's never enough money to go around, and while Gurley and Sazzad both lament the fact that sexy projects like vaccine development are much easier to secure support for than things like hospital infrastructure and disease surveillance, total funding for Nipah research and response is at an all-time high. Most of the other diseases on the WHO watch list still attract far more attention than Nipah, but at least, says Gurley, "it's on the radar."
Additionally, thanks to intensive surveillance efforts over the past 15 years, Gurley says we now know more about how to stop Nipah than we do many other emerging infectious diseases. "We know how to prevent transmission of Nipah from wildlife to people," she points out. "Can we do that for Ebola? No. And it's because we haven't spent the same time with other diseases monitoring every single case and looking into it."
But knowing what needs to change and convincing people to make those changes are two very different matters.
Once Gurley's team determined that bat-contaminated date palm sap was the culprit in most, if not all, Nipah outbreaks, they launched an educational campaign urging people to stop drinking raw sap. But since they knew most people would continue to risk drinking the delicacy, they also started looking into possible "safe sap" options.
Researchers at Bangladesh's ICDDR,B found that bamboo skirts, locally called bana, were effective at keeping bats—and Nipah virus—out of date palm sap. Convicing gachhis to apply the skirts and people to demand only "safe sap" that has been protected by the skirts, however, is another matter. Photograph by Rebeca Sultana.
For decades, some gachhis have wrapped their sap collection pots in protective shields that resemble bamboo placemats. They've done so not because they were worried about disease transmission, but because they wanted to keep bats and birds from drinking and dirtying their hard-earned sap. Most gachhis rarely took this precaution, presumably because scaling towering date palm trees is hard enough without lugging extra equipment up the trunk. But when field studies proved that the skirts reliably kept bats out of the sap, Gurley's team began campaigning to make that practice the norm.
They visited dozens of gachhis in many dozens of villages to pitch them on the benefits of safeguarding their sap collection pots with bamboo skirts. They produced posters and aired docudrama PSAs with soap-opera-style storylines warning people of the dangers of drinking unprotected sap. They hired locally trained anthropologists to help them frame their messaging in the best possible way. And their efforts have helped, a bit. But, says Gurley, "getting people to change what they do when it's culturally ingrained is really hard. Really, really hard. I mean, people still smoke cigarettes. People still start smoking cigarettes!" In Bangladesh, gachhis still collect sap all across the Nipah Belt, most often without bamboo skirts. And in each of those villages, people still consume unsafe sap.
Behavior change is also a major factor in the team's efforts to prevent person-to-person transmission. Installing portable hand-washing stations, or even running water, in hospitals, for instance, will only help control infection to the extent that health workers can convince people to start washing their hands. The same is true for ongoing efforts to develop faster diagnostic tests that would allow for earlier diagnosis and reduced transmission opportunities—those tests will only matter if health workers can convince more people to seek treatment. "A hospital in Bangladesh, it's a really unpleasant place," says Gurley. "If you're in the context of an outbreak, and everybody who's gone to the hospital has died, why would you go?"
One key to incentivizing hospital visitation, says Gurley, is the development of therapeutic drugs that could at least treat, if not cure, the disease. "Realistically, medical facilities currently have very little to offer people with Nipah. They can provide some basic supportive care, but most of these people are going to die," she says. If better treatment options were available, more patients might be motivated to seek medical care, which would improve both surveillance efforts and the potential for better infection control.
As a member of WHO's Nipah Virus Taskforce, Gurley is currently advising on efforts to develop both therapeutic drugs and vaccines. The latter now has the benefit of a $25 million grant from the Coalition for Epidemic Preparedness Innovations (CEPI) for the development of a candidate vaccine, which is projected to be ready for human trials within the next five years.
When asked if a vaccine is likely to solve the Nipah problem, Gurley is quick and decisive with her response. "A vaccine itself is never going to be the only answer. The only disease we've ever eradicated with a vaccine is smallpox." It would certainly help, especially to be able to inoculate the health workers, like Sazzad and his medical technicians, who regularly come into contact with or treat Nipah patients. But, she says, infection control and surveillance are always going to be important, as are diagnostics and therapeutics. "All these issues are linked together. In some ways that's daunting, and in another way, it can give us some optimism that if we make progress in just one area, it will reinforce all the others."
Undoubtedly, the progress that's been made over the past two decades in understanding Nipah virus and implementing infection control interventions has saved countless lives. Still, though, the potential for a catastrophic outbreak looms large.
In 1994, Hendra virus—a deadly, bat-borne disease that is closely related to Nipah—jumped from bats to domesticated horses for the first time (at least as far as anyone knew). Endemic to Australia, the virus has since killed more than a hundred horses and has made the leap from livestock to humans on seven occasions. As the outbreaks began to mount, Raina Plowright returned to her native Australia to study the dynamics of Hendra virus transmission. Since her path to infectious disease research included a degree in veterinary medicine, and a Master's in epidemiology, she was quite possibly the perfect person to take on this challenge for her PhD.
Hundreds of fruit bats lift off over Queensland, Australia. Photography by Raina Plowright.
After assembling a diverse team of collaborators, including veterinarians, range managers, behavioral ecologists, and virologists, Plowright set out to identify the factors that had regularly, but so far unpredictably, led to Hendra spillover. As the research progressed, she observed that each of her colleagues viewed the virus through the lens of their particular specialty, and most seemed to view the piece they studied as the most important one—the factor ultimately responsible for spillover.
To gain a more complete view of Hendra transmission, Plowright forced herself to step back a pace or two. Suddenly she began to see the virus's route from bat to human as a series of barriers through which the pathogen must pass to move from reservoir host to recipient. The concept that Plowright sketched that evening before it could once again fade from view was a stack of widely spaced layers. Like slices of Swiss cheese, each layer was pockmarked with holes that represented potential routes the virus might exploit to move on to the next step.
The arrangement of the layers in Plowright's mind was anything but arbitrary; it was hierarchical. In other words, if a virus was unable to circumvent any one barrier, spillover would be impossible—and none of the other barriers in the chain would matter, regardless of how porous they might be. The uppermost layer in Plowright's model, for example, represented the distribution of a reservoir host population, specifically its proximity to people or domestic animals. No matter how transmissible or virulent a virus might be, if a reservoir host had no contact with a recipient, spillover couldn't happen.
The many layers that Plowright sketched that evening illustrated why spillover isn't inevitable; it's actually quite difficult, and rare. Not only does a virus need to find a route through each barrier, but those Swiss cheese holes need to be aligned with one another in space and time. The virus can only get through if it has a straight shot. "It's kind of a no-brainer," Plowright says now. "Of course that's how it works."
Still, the more she looked at her sketch, the more she felt like she was onto something important. She could see how various changes in the environment, or the virus's genetic makeup, or the recipient host's immune response could influence the size and position of those holes, making it easier or more difficult for spillover to occur. The framework was not only an intuitive way to think about zoonotic disease, Plowright thought, it might also help researchers pinpoint the most effective ways to close off those routes of transmission and prevent spillover from happening in the first place.
Historically, our battles against infectious diseases have largely been waged at the level of the recipient host—the person who has fallen ill or who might become infected in the future. That's the level that medical care, drug therapies, and vaccines target. Plowright is quick to acknowledge the critical role that medical and public health workers play in disease prevention. "But," she says, "we think we could probably prevent spillover at the top, at the level of the reservoir host… rather than at the lowest level of recipient-host susceptibility."
For the past 25 years, one of Plowright's collaborators, a bat ecologist named Peggy Eby, has documented the rapid decline of native forests in eastern Australia, and the dramatic shifts in bat populations that have followed. Plowright suspects that this ecological degradation has been a major cause of the increased incidence of Hendra virus outbreaks. "Something has switched in the system," she says. "Bats are now staying closer to their food sources because the habitats that provided high-energy nectar in the winter are mostly gone." That switch has put Australia's bats in closer contact with people and domestic animals as the bats supplement their diets with cultivated fruits and ornamental flowers.
Although there are surely many environmental factors involved in Hendra transmission, the timing and location of several recent outbreaks has led Plowright to key in on one in particular: food. "For some reason, it's the winter after nutritional stress events that seems to be the worst for Hendra spillover."
Another observation that supports the connection between food availability and Hendra outbreaks also hints at a potential ecological intervention—one that could reduce viral shedding and pull bats back out of cities and into more natural habitats. Eby observed that when spotted gum trees flower, an event that occurs every few years, the bats empty out of cities to take advantage of this rich food source. Now the scientists are exploring ways to mimic this effect by encouraging agencies and organizations working on reforestation projects to incorporate winter-flowering trees into their replanting efforts. Plowright imagines that a similar type of intervention might also be possible in Bangladesh, encouraging bats to rely more on natural sources of food.
Such speculation will soon be put to the test as Plowright, Gurley, and more than 20 other collaborators begin an ambitious $10 million research project that will span eastern Australia and Bangladesh's Nipah Belt, as well as Ghana and Madagascar, where closely related bat-borne viruses are also found. The aim of this research, funded by the Defense Advanced Research Projects Agency (DARPA), is to understand the ecology of Hendra, Nipah, and other henipaviruses, how they're sustained within bat populations, and why they're excreted. The hope is that this information will help scientists, doctors, and public health workers identify bottlenecks in the spillover process, where applying relatively little effort and expenditure could have a significant impact on reducing a virus's epidemic potential.
With research teams going into the field this month, just as Bangladesh's Nipah season gets underway, it's impossible not to view this work as a race against the clock—albeit one with significantly better odds of success with a new influx of funding.
Back under the sacred fig tree, as I watch the light and color drain from the sky, it strikes me that this is an appropriate place to begin my journey back home. Among all the experiences I've had in this fascinating, beautiful, and troubled country, this is perhaps the most bewildering and overpowering. With the roots of the local Hindu's venerated tree under my feet, I hear the Muslim call to prayer burst from a loudspeaker in the unseen distance. High above, the bats stir, their urge to feed now undeniable.
As a crowd of villagers gathers, I'm struck by the amalgam of nature and people and tradition and modernity all gathered together in this one tiny plot. This, I think, is why Nipah's epidemic potential is so great—potentially. The old gachhi 's unprotected collection pots hang from date palm trees just 4 kilometers away as the bat flies. There, a new strain of Nipah virus could jump to a little girl or an entire village tomorrow morning, or next week. Days later, a doctor—or a journalist—who has visited those villagers in their homes and hospital wards could board a plane bound for Hong Kong. And this is just one of countless ways that a small spillover event could metastasize into a pandemic.
I shudder to think of the possibilities as I make my way back to the van with Sazzad and the others. Just before we climb in, several dozen bats drop from their perches, open their wings, and head off into the remaining orange light above the horizon. In this moment, it's hard to imagine the bats going anywhere other than the many sap collection pots nearby. But maybe someday, if an ecological intervention takes root, a future flight path will carry these reservoirs toward native fruits and flowers instead.
As the bats dissolve into the darkness, Sazzad and several of the others bid them adieu. " Ḍināra samaẏa," they say in unison. "Dinner time."
Steven Bedard is bioGraphic's Editor-in-Chief. A former field biologist who spent the early 90s chasing spotted owls and northern goshawks through the woods, he now writes and produces media about the work of scientists, instead of actually doing the scientific research—it's way easier. Having written about archaeology, engineering, and astrophysics, he's found a much happier place covering the living world for bioGraphic. Follow him on Twitter @steventbedard. | {
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José Nemesio García Naranjo (Lampazos de Naranjo, Nuevo León, 8 de marzo de 1883 - Ciudad de México, 21 de diciembre de 1962) fue un abogado, periodista, escritor, historiador, político, catedrático y académico mexicano.
Formación
Nació en Lampazos de Naranjo, Nuevo León, el 8 de marzo de 1883, siendo hijo de Nemesio García y García, alcalde de Lampazos, y de Juana Naranjo Pérez; por parte de su madre estuvo emparentado con el general Francisco Naranjo y con el hijo de éste, el Ing. Francisco Naranjo García. Por reveses políticos su familia se trasladó al Encinal, Texas, donde Nemesio aprendió inglés, concluyó la primaria en el Instituto Felipe Naranjo en su natal Lampazos; cursó la secundaria y la preparatoria en el Colegio Civil de la ciudad de Monterrey. El 4 de enero de 1903 se trasladó a la Ciudad de México para ingresar a la Escuela Nacional de Jurisprudencia. Ahí publicó algunos artículos en el Diario del Hogar contra Bernardo Reyes.
En enero de 1905, gracias a la influencia de su amigo, el abogado porfirista Rosendo Pineda, obtuvo una plaza de subteniente en la Marina de Guerra, que alternó con sus estudios de derecho. Al año siguiente ganó un premio literario en unos juegos florales otorgado por el Liceo Altamirano, a un poema de diez sonetos para celebrar el Tercer Centenario de la aparición de la primera parte de El Quijote, lo que lo dio a conocer como poeta. Al finalizar el año dimitió de la Armada y consiguió una beca para asistir a la cátedra de historia, que Genaro García impartía en el Museo Nacional de Historia. Esto, aunado a su desempeño como bibliotecario en la Academia Nacional de Bellas Artes, le permitió enriquecer su cultura.
En 1908 se trasladó a Madrid y a Toledo; retornó al país ese mismo año para impartir la cátedra de Historia de México en la Escuela Nacional Preparatoria, y en el Heroico Colegio Militar impartió la materia de Historia Universal. Obtuvo el título de abogado el 24 de abril de 1909. Ese mismo año fue miembro fundador del Ateneo de la Juventud, publicó algunos de sus poemas en la Revista Moderna de México.
Matrimonio e hijos
Nemesio García Naranjo contrajo matrimonio con la escritora Angelina Natalia Elizondo Cisneros (27 de julio de 1888 - 12 de enero de 1971), originaria también de Lampazos, el 14 de enero de 1912. La pareja procreó cinco hijos:
Nemesio García Naranjo y Elizondo (1914 - 25 de enero de 1990), casado con María del Carmen Álvarez.
Luis Constantino García Naranjo y Elizondo (1919 - 27 de septiembre de 1993), casado con Mercedes González Quiroz.
Angelina García Naranjo y Elizondo (1913 - 13 de agosto de 1963) casada con Manuel Olea Nájera
Leonor García Naranjo y Elizondo (1916 - ¿?), casada con Francisco Plancarte y Haro.
Arturo García Naranjo y Elizondo (3 de febrero de 1918 - ¿?)
Inicios en la política
El régimen de Porfirio Díaz requería de jóvenes talentosos, y por ello Rosendo Pineda creó una Comisión de Propaganda para las siguientes elecciones presidenciales. Con José María Lozano quedó al frente de esa comisión, a propuesta del director de la Escuela Nacional Preparatoria, Genaro García. En El Debate García Naranjo editó las primicias de su labor periodística, que lo absorbió por más de 60 años.
En 1910 fue elegido diputado de la XXV Legislatura y participó activamente en las festividades del Centenario de la Independencia de México. Al finalizar el periodo del último congreso porfirista emprendió su campaña para reelegirse como diputado, representando al Partido Liberal de Nuevo León. Triunfó, al igual que sus compañeros José María Lozano, Francisco M. de Olaguíbel y Aquiles Elorduy. Todos ellos, junto con Querido Moheno que luego se incorporó al grupo, constituyeron el famoso Cuadrilátero en la XXVI Legislatura federal, conjunto parlamentario opositor al presidente Francisco I. Madero.
Fundó el periódico La Tribuna con el auspicio del licenciado Eduardo Tamariz; en él publicó sus artículos más candentes contra el gobierno maderista. Como resultado de sus posiciones políticas, en varias ocasiones afrontó graves peligros; incluso, estuvo a punto de batirse a muerte con el gran poeta peruano, simpatizante de la Revolución Mexicana, José Santos Chocano.
Gobierno de Victoriano Huerta
Cuando Victoriano Huerta se consolidó en la presidencia y decidió renovar su gabinete, en octubre de 1913 García Naranjo fue nombrado ministro de Instrucción Pública. Al militarizarse las secretarías pasó a ser miembro del Ejército con el grado de general de brigada. Durante su gestión —y de acuerdo con los ideales ateneístas— inició la renovación del método de enseñanza de la Escuela Nacional Preparatoria que hasta entonces se había basado en el positivismo de Augusto Comte por un plan de estudios que seguía la escuela filosófica de Henri Bergson y Émile Boutroux.
Primer destierro (1914 - 1923)
Al triunfo del movimiento constitucionalista, en julio de 1914, salió desterrado a Nueva York. De allí, junto con Rubén Valenti, el 28 de diciembre se embarcó a Guatemala. Ante la escisión revolucionaria entre convencionistas y constitucionalistas, no dio margen a que lo incluyeran en bando alguno y en marzo de 1915 navegó rumbo a Nueva Orleans; ahí permaneció algunos días con Querido Moheno y después partió a Laredo, Texas donde residían su padre y hermanos.
Para entonces Monterrey había sido tomada por los villistas, en tanto que Nuevo Laredo, Piedras Negras y Matamoros eran dominio de los carrancistas; con ello se frustró toda posibilidad de que su esposa e hijos se reunieran con él. Posteriormente se trasladó a San Antonio, Texas. Rechazó la oferta que le hiciera Victoriano Huerta para emprender una rebelión armada y reconquistar el gobierno de México.
En agosto de 1915 editó La Revista Mexicana, que apareció el 25 de enero de 1920 en San Antonio. Más tarde, a invitación del periodista nuevoleonés Ignacio E. Lozano, participó en el diario La Prensa. En 1920 se le sometió a un proceso judicial en Laredo, Texas, acusado de violar las leyes de neutralidad y de estar envuelto en acciones conspiratorias; de este último cargo quedó absuelto, y por el primero pagó una multa de 500 dólares. Luego del incidente, el director del semanario Omega de la Ciudad de México le pidió copia de sus artículos para publicarlos.
Regreso a México
En 1923, tras nueve años de exilio, regresó al país por Lampazos y Monterrey. Alternó sus labores de jurista con trabajos para El Universal, entre 1924 y 1925. En este lapso ingresó en la Academia Mexicana de la Lengua y fue nombrado miembro correspondiente el 22 de julio de 1925, y miembro de número el 6 de julio de 1938, tomó posesión de la silla XI el 17 de enero de 1940.
En abril de 1926 asistió a una convención de periodistas representando a Excélsior de México, La Prensa de San Antonio, Texas, y El País de La Habana, Cuba.
Segundo destierro (1926 - 1934) y regreso a México
En la capital estadounidense, García Naranjo recibió la noticia de que por orden de las autoridades mexicanas no podía regresar a México, con lo cual comenzó su segundo destierro. Viajó con frecuencia y residió en distintos lugares: dos años en Nueva York, seis meses en Madrid, año y medio en París, dos años más en Nueva York, dos en Venezuela y el último en California.
Como resultado de su actuación en la asamblea de periodistas, el jefe de la delegación venezolana, Alejandro Fernández García, propuso que se le impusiera la condecoración del Busto del Libertador, para premiar el discurso que pronunció en Washington en homenaje a Simón Bolívar.
En marzo de 1928 se trasladó a Madrid como abogado consejero de la Pantepec Oil Company, después a Roma y luego se estableció en París. De 1929 a 1934 estuvo en Nueva York y en Caracas, Venezuela. En este último año volvió a México y se dedicó al periodismo.
En 1947, por invitación del gobierno español, participó en la conmemoración del Cuarto centenario del deceso de Hernán Cortés. Escribió poesía, teatro y novela. Fue miembro de la Academia Mexicana de Jurisprudencia y Legislación, y de la Academia Mexicana de la Historia desde su fundación; recibió el grado de Doctor Honoris Causa por la Universidad de Guadalajara.
Nemesio García Naranjo murió en la Ciudad de México, a las 5:45 de la tarde del 21 de diciembre de 1962 a consecuencia de un mal hepático. Fue sepultado en el Panteón Francés de San Joaquín.
Periodismo
García Naranjo colaboró en los siguientes periódicos y publicaciones:
En México
Impacto y Todo, de la Ciudad de México.
Diálogo de Yucatán.
El Porvenir, de Monterrey.
El Siglo, de Torreón.
El Informador de Guadalajara.
El Dictamen de Veracruz.
El Mundo de Tampico.
El Heraldo de San Luis Potosí.
El Diario de Nuevo Laredo.
El Diario de Ciudad Victoria.
El Heraldo de Chihuahua.
La Voz de Michoacán.
El Sol de Puebla.
El Sol del Centro de Aguascalientes.
Amanecer de Querétaro.
Y en todos los de la cadena García Valseca.
En el extranjero
La Prensa de San Antonio.
La Opinión de Los Ángeles.
La Nación de Buenos Aires.
El Diario de la Marina de Cuba.
El Nuevo Diario de Caracas.
Otras contribuciones
García Naranjo fue el autor del lamento generalmente atribuido a Porfirio:
"¡Pobre México, tan lejos de Dios y tan cerca de Estados Unidos!"
Obras publicadas
La histórica Sor Juana Inés de la Cruz (1907)
Discursos, prólogo de Querido Moheno (1923)
El aroma viril (1925)
Venezuela y su gobernante (1927)
El quinto evangelio (1929)
Porfirio Díaz (1930)
Simón Bolívar (1931)
Mi madre, mi señora, mi maestra (1937)
El vendedor de muñecas (obra teatral, 1937)
Estrellita (1938)
Alma norteña (1939)
La matanza de las flores
En los nidos de antaño, (1951)
Bajo el signo de Hidalgo (1953)
Una industria en marcha (1955)
El milagro de los franciscanos (1956)
El romance de Angelina, (1958)
Memorias de García Naranjo (1956 - 1963), integradas por diez volúmenes:
Panoramas de la adolescencia vistos desde la vejez, prólogo de Ernesto Zertuche.
El Colegio Civil de Nuevo León, prólogo de Fernando Gómez.
La vieja Escuela de Jurisprudencia, prólogo de Eduardo Pallares.
Dos bohemios en París, prólogo de José Castellot.
El crepúsculo porfirista, prólogo de Alberto María Carreño.
Elevación y caída de don Francisco I. Madero, prólogo de Aquiles Elorduy.
Mis andanzas con el general Victoriano Huerta
Nueve años de destierro, prólogo de Nemesio García Naranjo y Elizondo.
Mi segundo destierro, prólogo de Angelina García Naranjo y Elizondo.
La repatriación definitiva
Referencias
Enlaces externos
GARCÍA NARANJO, Nemesio. Escritores del cine mexicano.
Texto completo de sus Memorias
Nemesio García Naranjo. Academia Mexicana de la Lengua.
Fundadores de la Revista Siempre!.
Nacidos en Lampazos de Naranjo
Escritores de Nuevo León
Escritores en español del siglo XX
Guionistas de cine de México
Poetas de Nuevo León
Abogados de Nuevo León
Historiadores de México
Dramaturgos de México
Novelistas de México
Maestros de México
Diputados de la XXV Legislatura de México
Diputados de la XXVI Legislatura de México
Periodistas de Nuevo León
Miembros de la Academia Mexicana de la Lengua
Miembros de la Academia Mexicana de la Historia
Miembros de la Academia Mexicana de Jurisprudencia y Legislación
Secretarios de Educación Pública (México)
Miembros del Ateneo de la Juventud Mexicana
Masones de México
Alumnado de la Escuela Nacional de Jurisprudencia
Doctores honoris causa de la Universidad de Guadalajara
Fallecidos en Ciudad de México | {
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Frédéric Berthet, né le à Neuilly-sur-Seine et mort le à Paris, est un écrivain français.
Formation
Ancien élève de l'École normale supérieure, rue d'Ulm (1974-1977), Frédéric Berthet est pensionnaire de la Bibliothèque nationale de France où il a notamment travaillé sur le fonds Barrès.
Parcours littéraire
Frédéric Berthet fut notamment attaché culturel à New York de 1984 à 1987. Pierre Bayard, l'un de ses camarades de la rue d'Ulm et ami, dit de lui :
Cinq livres ont été publiés de son vivant, en l'espace de dix années. Simple journée d'été, que l'auteur définit lui-même comme une « suite » de nouvelles, au sens musical du terme, paraît chez Denoël dans la collection L'Infini, en . Fait notable, cette première publication ne comporte aucune mention de genre ou de format littéraire. Daimler s'en va, nouvelle incursion sur le « territoire romanesque », toujours selon ses propres termes, est publié dans la même collection, désormais chez Gallimard, en . Le livre, salué notamment dans Le Monde par Bertrand Poirot-Delpech, qui lui consacre l'intégralité de son feuilleton, connaît un large succès critique. Dès lors, et bien que le titre de ce roman invite à la réflexion comme le dernier mot de son récit au silence, chacun des livres de Frédéric Berthet est attendu avec curiosité.
En janvier 1993 paraissent simultanément Felicidad, second recueil de nouvelles (le bandeau de la collection L'Infini précise : « Nouvelles du front »), et Paris-Berry (celui de la collection Blanche : « Contre-attaque »), bref récit tout aussi inclassable que les précédents, mais qui suscite dans la presse une vague d'interrogations, sinon d'indignations : un rien désinvolte, cette irruption dans la collection mythique de Gallimard est-elle une provocation ?
Dernier livre publié, Le Retour de Bouvard et Pécuchet, et peut-être faut-il percevoir dans ce titre une relation de cause à effet, paraît aux éditions du Rocher en .
L'œuvre littéraire de Frédéric Berthet, cependant, commence dès l'année 1970. Il a 16 ans. Au fil de ces trente-trois années, son activité littéraire s'exerça sous de multiples formes : essais, conférences, communications, entretiens, traductions, articles et chroniques de presse... Leur lecture révèle aujourd'hui que chacune de ces manifestations participe d'une même actualité de pensée : la réalisation d'un « programme » formulé dès 1970 et resté en suspens au lendemain de sa disparition.
Frédéric Berthet vivait depuis 1993 à Chambon-sur-Voueize, mais meurt dans son appartement de la rue Tournefort, dans le .
Œuvre
Une (1970-2003) est actuellement en cours de préparation.
Publications de son vivant
Simple journée d'été (nouvelles), Denoël, coll. L'Infini, 1986 ; rééd. Denoël, coll. Romans français, 2006.
Daimler s'en va (roman), Gallimard, coll. L'Infini, 1988 (prix Roger-Nimier 1989) ; rééd. La Table Ronde, coll. « La petite vermillon », 2011, 2018.
Felicidad (nouvelles), Gallimard, coll. L'Infini, 1993 (Prix de la nouvelle de l'Académie Française 1993) ; rééd. La Table Ronde, coll. « La petite vermillon », 2013.
Paris-Berry (récit), Gallimard, coll. Blanche, 1993 ; rééd. La Table Ronde, coll. « La petite vermillon », 2013
Le Retour de Bouvard & Pécuchet, Le Rocher, 1996 ; rééd. Belfond, « Domaine Français - Remake », 2014.
Éditions posthumes
Journal de Trêve (Journal littéraire 1979-1982), suivi de Lettre à Saul Bellow, Gallimard, coll. L'Infini, 2006
Correspondances 1973-2003 (choix de lettres), La Table Ronde, coll. Vermillon, 2011
En revues
Rouge, Blanc, Noir & Or (nouvelle), La Nouvelle Revue française , Gallimard, 2007
The Book of Truce (extraits du Journal de Trêve, trad. Linda Coverdale), The Reading Room , New York : Great Marsh Press, 2007
La Petite en enfer (nouvelle), Décapage , La Table Ronde, 2008
En paix (chronique de presse), Décapage , La Table Ronde, 2011
Ce qu'ils appelaient désespoir (nouvelle), L'Infini , Gallimard, 2012
Time-Lapse (extraits de Préparatifs de roman 1976-1979), La Revue Singulière, 2013
Notes et références
Liens externes
Écrivain français du XXe siècle
Nouvelliste français du XXe siècle
Romancier français du XXe siècle
Auteur français de journal intime
Épistolier français
Épistolier du XXe siècle
Élève de l'École normale supérieure
Lauréat du prix Roger-Nimier
Naissance en août 1954
Naissance à Neuilly-sur-Seine
Naissance dans le département de la Seine
Décès en décembre 2003
Décès dans le 5e arrondissement de Paris
Décès à 49 ans | {
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01/06/2018 3:16 PM IST | Updated 02/06/2018 3:02 AM IST
13 Breakfast Items With More Sugar Than A Doughnut
By Kristen Aiken, HuffPost US
If you think a doughnut is one of the most sugar-laden breakfast choices you could make, you'd be wrong.
This isn't to say a doughnut is ever a nutritious choice. While delicious, it's filled with empty calories and provides you with virtually none of the vitamins and nutrients that will keep you alive, whereas something like a banana is a good source of potassium, dietary fiber, vitamin C and vitamin B-6.
But, shockingly, a banana has more sugar than a doughnut.
Now, don't stop eating bananas just yet. Sugars from fresh fruits and milk aren't as warned against as "free sugars," a term that refers to added sugar, as well as sugars naturally present in honey, syrups, fruit juices and fruit juice concentrates.
But it's important to be aware of how much sugar you're eating. The World Health Organization recommends that only 5 percent of daily caloric intake come from free sugar, and 13 percent of calories in the typical American diet consist of it.
"Many Americans eat about five times the amount of sugar they should consume," Natasa Janicic-Kahric, an associate professor of medicine at Georgetown University Hospital, told The Washington Post.
Besides contributing to weight gain, sugar ― whether natural or added ― has a host of negative effects on our bodies: It creates a vicious cycle of intense cravings, impairs memory and learning skills, may cause or contribute to depression and anxiety, and is a risk factor for age-related cognitive decline and dementia.
So let's take a look at how much sugar is in 13 common breakfast items that, while often more nutritious than a doughnut, contain more sugar than a glazed treat from Dunkin' Donuts, which contains 260 calories and 12 grams of sugar.
(To be fair, not all doughnuts are created equal: An apple fritter from Dunkin', for instance, has 420 calories and 24 grams of sugar.)
Here's the rundown:
Dunkin' Donuts Glazed Donut: 260 calories, 12g sugar
Dunkin' Donuts Hot Coffee with Cream and Sugar, Extra Large: 320 calories, 44g sugar
Starbucks Chai Latte with 2% Milk, Tall: 240 calories, 32g sugar
Kellogg's Raisin Bran: 190 calories, 18g sugar
Silk Vanilla Almond Milk (80): 80 calories, 13g sugar
Noosa Blueberry Yogurt: 280 calories, 31g sugar
Nature Valley Cranberry Almond Protein Granola: 210 calories, 14g sugar
Panera Cinnamon Crunch Bagel: 380 calories, 32g sugar
Liquiteria Mean Green Acai Bowl: 620 calories, 54g sugar
Jamba Juice Aloha Pineapple Smoothie, Small: 310 calories, 67g sugar
Banana: 105 calories, 14g sugar
Panera Blueberry Muffin with Fresh Blueberries: 460 calories, 40g sugar
Tropicana Original Orange Juice: 110 calories, 22g sugar
Mott's 100% Original Apple Juice: 120 calories, 28g sugar
Now don't go and replace all your healthy breakfast options with doughnuts, but keep these numbers in mind if you're trying to keep track of your sugar intake. A doughnut every once in a while isn't the worst thing in the world.
This story has been updated to include more details about the WHO's recommendations for sugar intake.
Kristen Aiken .
MORE: calories diet Doughnuts food lifestyle sugar | {
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The Alaska Chapter of the Association of Fundraising Professionals (AFP, AK Chapter) is Alaska's only professional organization for fundraisers. We offer our members professional development opportunities and the chance to network and connect with colleagues, engage in creative thinking, and achieve great results for Alaska's nonprofit sector.
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Copyright 2019 AFP AK Chapter. All rights reserved. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,333 |
{"url":"https:\/\/eguruchela.com\/math\/calculator\/geometric-progression","text":"# Geometric progression Calculator\n\nCalculate geometric sequence of a series of numbers for given values.\nThe geometric progression is also known as a geometric series. It is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio (common difference) of the sequence. The geometric progression of n terms, we mean a finite sequence in the form as follows :\na, ar, ar2, ar3, . . . . arn-1\nWhere (a) is the first term of GP and real number (r) is common difference.\nGeometic Sequence Calculator\n Enter nth term (n) : Enter first term (a) : Enter common difference (r) : Geometric Progression :","date":"2021-05-08 04:41:11","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\": 0.8694872856140137, \"perplexity\": 662.923136052396}, \"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-2021-21\/segments\/1620243988837.67\/warc\/CC-MAIN-20210508031423-20210508061423-00604.warc.gz\"}"} | null | null |
\section{Introduction}
Response teams sent to areas stricken by disaster work in highly dynamic and unstructured environments; every second counts when lives are in danger. Robots have been deployed in these humanitarian assistance and disaster relief (HA/DR) efforts~\citep{murphy2014disaster}, but a number of gaps still need to be addressed to further improve the reliability of these fielded autonomous assets. We focus specifically on the importance of quickly learning and adapting navigational behavior for unmanned ground vehicles (UGVs).
Many high level tasks performed by UGVs under dynamic and unstructured scenarios require autonomous navigation. Advances in visual perception~\citep{simonyan2015very,szegedy2015going,krizhevsky2012imagenet} make it possible to provide fine-grained semantic segmentations~\citep{badrinarayanan2015segnet,long2015fully} of an environment that an UGV can use to make navigation decisions. This includes determining the traversability of terrain~\citep{shneier2008learning,papadakis2013terrain,roncancio2014traversability}. However, in the wake of a disaster, many expected contextual cues for navigation will be unavailable, unreliable, or misleading. For example, visual appearance and traversability of roads may have changed due to being covered in mud or sand after a hurricane. Thus, previously learned behavior may not be relevant and could be dangerous for the UGV to execute. To operate successfully in these scenarios, an UGV will need to be adapted quickly and with minimal human supervision to minimize impact on personnel and equipment.
\begin{figure*}
\centering
\includegraphics[width=0.85\linewidth]{overview-cameraready-new.png}
\caption{Overview of the off-line training process and on-line path planning of our system that learns to assign cost values to regions in an urban environment.}
\label{fig:overview}
\end{figure*}
In addition to the perceptual and control challenges of adapting to support operation in an environment recovering from a disaster, an UGV might be called upon to perform unforeseen and unexpected roles in the field. The dynamic and unpredictable nature of a disaster scenario precludes preparing for every possible role. Therefore, the ability to rapidly train UGVs to perform novel tasks in the field increases their utility to first responders.
Early robot navigation efforts focused on finding minimum distance collision-free paths to a goal. Further developments began considering safety because navigating optimally with zero margin to obstacles often results in collision in the real world. In scenarios where robots interact with people, certain additional conventional behaviors for navigation are expected which are not obvious from a traversability or safety standpoint, e.g., vehicles should drive on the right (or left) side of the road. For this particular example, semantics can be recognized as relating to the boundary between two adjacent concepts such as where the edge of the road and grass meet.
In the case of path planning for vehicles, the optimal path is not always the collision-free path of shortest distance. This is especially true in the case of larger vehicles or in situations where robots and humans must interact. Additionally, there may be cultural or right-of-way considerations such as the desire to not trespass into private property where it can be avoided. Programmatically encoding each of these desiderata into the autonomy software for an UGV may be infeasible or imprecise. Learning desired navigation behaviors from human examples is a viable approach in these cases.
In our prior work, we have demonstrated approaches to reduce the time and effort required to assign labels to visual data and adapt visual classifiers to novel environments~\citep{Wigness16IROS,wigness2017unsupervised}. This paper describes the combination of these techniques with a method for learning robot control parameters through inverse optimal control (IOC). Our IOC solution uses the theory of maximum entropy to learn a reward function given environment features extracted from visual perception, and minimal ``optimal'' trajectory examples collected by a human driving the robot in the environment. We deploy the learned behavior on a robot and test at multiple navigation sites in a real-world environment. Figure~\ref{fig:overview} is an overview of the off-line reward function learning, and its use in on-line navigation. Lastly, we demonstrate the ability to learn new behaviors quickly in the field.
This article is an extension of our earlier conference paper~\citep{wigness2018robot}. In addition to a more thorough discussion of our approach, the main contributions of this extension include 1) additional field experiments for three learned behaviors, 2) the introduction of non-terrain feature maps for learning, and 3) an on-line human-in-the-loop capability.
\section{Related work}
Research in terrain traversability has been performed to provide details of an environment that mobile robots can use to make navigation decisions. \cite{papadakis2013terrain} provides a survey of work done in terrain traversability analysis. Most commonly, traversability analysis is treated as a binary classification problem, e.g., traversable versus non-traversable, for path planning~\citep{shneier2008learning,suger2015traversability,milella2015self}. Instances of multi-class terrain analysis have taken a supervised classification approach. Talukder et al. assume three terrain classes are known \textit{a priori} and train using Expectation Maximization to classify terrain for dynamic control of UGVs~\citep{talukder2002autonomous}. For multi-class problems, a continuous value relating to the cost of traversal for different terrains can also be assigned. These values have been assumed to be known~\citep{roncancio2014traversability} or can be learned~\citep{silver2008high}. Although it is likely that human operators demonstrating optimal trajectories are internally considering traversal feasibility for the platform, learning behaviors is more complex than a binary traversability problem.
Self-supervised learning or learning from experience has been performed by maintaining traversal history and evaluating bumper collisions~\citep{shneier2008learning, Lookingbill07IJCV} for navigation tasks. This does not require any human intervention, but is only reliable in situations when collisions are minimal and present no risk to the robot. Imitation learning has been leveraged by collecting expert annotation of desirable traversal routes from aerial imagery~\citep{silver2008high}, and having humans teleoperate a mobile robot to collect desirable traversal examples~\citep{suger2015traversability}. The problem of learning from demonstrations has been addressed for situations requiring replication of behavior. Solutions based on inferring the agent's underlying reward structure have the advantage of being more succinct than the policy-based approaches and are therefore preferable as generalization becomes important~\citep{abbeel-icml-04,ziebart-AAAI-08,kitani-eccv-2012}.
Most similar to our work is that of \cite{silver2008high}, who use maximum margin planning~\citep{ratliff-icml-06} to learn costs given desirable trajectory examples. However, this method performs poorly with imperfect behavior observations or when the feature space cannot perfectly describe the observed behavior. Our work addresses this limitation by replacing maximum margin planning with an approach based on the principle of maximum entropy~\citep{ziebart-AAAI-08}. Additionally, while \cite{silver2008high} uses overhead imagery which presents coarse-grained details of the terrain type, our work uses a visual classifier at ground level that can differentiate many types of terrain. Similarly, operation at ground level provides a limited view of the environment and unlike the case of aerial imagery, our example trajectories do not have long range knowledge of ``optimal'' paths in the environment.
A potential limitation of the maximum entropy approach used in our work is the use of a linear reward function, which may lack the representational power for some behaviors. \cite{levine-nips-11} developed GPIRL, which applies Gaussian Process Regression to learn nonlinear reward functions. Similarly, \cite{choi2013bayesian} proposed a Bayesian nonparametric approach to find a limited set of nonlinear rewards by learning a set of composites of logical conjunctions of atomic features. \cite{wulfmeier2016watch} describe an approach to learn cost maps from a large number of human driving demonstrations using maximum entropy deep inverse reinforcement learning with Fully Convolutional Neural Networks to represent the reward function. Although these approaches outperform the original maximum entropy framework~\citep{ziebart-AAAI-08}, they require a larger number of examples to learn a reward function. The nature of our application requires an approach that can adapt to situations involving smaller sets of training examples.
\section{Inverse optimal control methodology}
The approach we have developed for learning perception and control for robot navigation from human demonstration leverages many components from our prior work which is detailed in~\cite{Gregory16FSR,Wigness16IROS}. In this section, we focus on the key components specifically developed for this work. These components include a methodology for learning reward functions from human examples, and how to build occupancy feature maps from data taken from the robot's onboard sensors.
\subsection{Reward function learning}
In this work we generate motion models from examples and use them to plan paths for a robot that replicate the behavior demonstrated. Work in optimal control theory has produced algorithms that can learn motion models based on the observation of trajectories demonstrated by people (or other agents) as they move~\citep{kitani-eccv-2012,ziebart-iros-09}. These motion models capture the preferences of movers as they react to certain features in the environment. These preferences are encoded using a reward function, which describes how much a person favors taking a certain path over others.
The problem of recovering this reward function can be solved using Inverse Optimal Control, which is also called Inverse Reinforcement Learning (IRL)~\citep{abbeel-icml-04}. In our work, we apply a specific solution to IRL based on the principle of maximum entropy that was originally proposed by \cite{ziebart-AAAI-08}. The advantage of this approach is that it resolves the ambiguity in choosing a distribution over decisions when finding a reward function. It selects the distribution that does not exhibit any additional preferences beyond matching feature expectations. In other words, it selects distributions based on what is known from the observations, without making any assumptions about what is not known. Moreover, the maximum entropy approach is well suited to the nature of our application, which focuses on the ability to quickly train for different behaviors in the field. By being no more committed to any particular path except the ones which have been demonstrated, it is possible to find reward functions without requiring a large number of examples.
The following sections provide a description of the elements of IRL that are more relevant to our work.
\subsubsection{Preliminaries}
The decisions made by a moving agent are modeled using a Markov Decision Process (MDP). An MDP is a tuple $\left( S,A,\left\lbrace P_{ss'}^{a}\right\rbrace,R,\gamma \right)$ where $S$ is a set of \textit{states}; $A$ is a set of \textit{actions}; $\left\lbrace P_{ss'}^{a}\right\rbrace$ is a set of \textit{transition probabilities}, where $P_{ss'}^{a}$ represents the probability of transitioning from state $s\in S$ to state $s'\in S$ after taking action $a\in A$; $R(s,a):S\times A\rightarrow \Re$ is the \textit{reward} function, which represents how much the agent is recompensed by taking an action $a$ when it is in a given state $s$ (though this work only considers reward functions that are independent of an action); and $\gamma \in [0,1)$ is a \textit{discount factor} that represents how much a reward in the future is worth compared to receiving the same reward now.
The behavior of an agent under this MDP is defined by a \textit{policy} $\pi : S \rightarrow A$, where the function $\pi (s)$ determines the action an agent should take in state $s$. Similarly, $\zeta$ is a \textit{path} taken by an agent under this MDP, and is a sequence of state and action tuples $\zeta = [(s_{1},a_{1}),(s_{2},a_{2}),\ldots]$. The probability of traversing a path is denoted $P(\zeta)$. Likewise, the reward function for taking a given path is
\begin{equation} \label{eq:path_reward}
R(\zeta)=\sum_{(s_{i},a_{i})\in \zeta} R(s_{i}).
\end{equation}
We also define a set of \textit{features} that represent the particular attributes of each state. Let $\phi: S\rightarrow \Re^D$, where $D$ indicates the dimensionality of the feature space. The feature vector representing state $s$ is $\phi (s)$. Additionally, the \textit{feature counts} of a path $\zeta$ is defined as
\begin{equation} \label{eq:feature_counts}
\phi_{\zeta}=\sum_{(s_{i},a_{i})\in \zeta} \phi (s_{i}).
\end{equation}
\subsubsection{Training a predictive model}
We now focus on the problem of learning a reward function (or \textit{training stage}) from a set of observations. The derivation presented in this section was reported by \cite{ziebart-AAAI-08} and is included here for a more complete description of our work. It is assumed that the observations were made from an agent behaving optimally, i.e. acting according to the optimal policy $\pi^*$. The reward function is defined as a linear combination of the features, i.e. $R=\theta^{T} \boldsymbol{\phi}(s)$. In this stage, we obtain the vector of weights $\theta$ of the optimal reward function. Per the maximum entropy distribution, paths that result in higher total reward should be exponentially more likely to be chosen. This concept is expressed as
\begin{equation} \label{eq:dist_over_paths}
P(\zeta )= \frac{1}{Z(\theta)}\mathrm{exp}(R(\zeta ) ),
\end{equation}
where $Z(\theta)$ is the partition function. Assuming that transitioning randomness has little effect on behavior and the partition function is constant, a tractable approximation to Eq. (\ref{eq:dist_over_paths}) is given by:
\begin{equation} \label{eq:apx_dist_over_paths}
P(\zeta \mid \theta) \approx \frac{\mathrm{exp}(\theta^{T}\boldsymbol{\phi}_{\zeta})}{Z(\theta)} \prod_{(s_{t},a_{t}),(s_{t+1},a_{t+1}) \in \zeta}P_{s_{t}s_{t+1}}^{a_t}
\end{equation}
This provides a stochastic policy, where an action is selected with a probability weighted by the sum of all probabilities of the paths taken that start with that action, as expressed by
\begin{equation} \label{eq:stochastic_policy}
P(a \mid \theta) \propto \sum_{\zeta:a\in \zeta_{t=0}}P(\zeta \mid \theta).
\end{equation}
To find $\theta$ we maximize the log-likelihood of the distribution over paths (Eq. (\ref{eq:apx_dist_over_paths})). This is a convex optimization problem, where the optimal vector $\theta^*$ is given by
\begin{equation} \label{optimal_theta}
\theta^{*}=\operatornamewithlimits{argmax}_{\theta}L(\theta)=\operatornamewithlimits{argmax}_{\theta}\sum_{i=1}^{N}\log P(\zeta_{i} \mid \theta),
\end{equation}
where $N$ is the number of training examples.
To solve this optimization problem \cite{ziebart-AAAI-08} express the gradient as the difference between empirical feature counts and the learner's expected feature counts, which in turn can be expressed in terms of expected state visitation frequencies $D_s$:
\begin{equation} \label{eq:gradient}
\nabla L(\theta)=\hat{\phi}_{obs} - \sum_{i=1}^{N}P(\zeta \mid \theta)\phi_{\zeta} = \hat{\phi}_{obs}-\sum_{s\in S}D_{s}\phi(s)
\end{equation}
$D_s$ represents the probability of being in a given state $s$. It can be efficiently computed using dynamic programming. The transition probabilities can be approximated by the observed trajectories. \citeauthor{ziebart-AAAI-08} describe in detail the algorithm for the calculation of expected state frequencies.
\subsubsection{Trajectory generation}
After finding the reward function, the distribution over trajectories (Eq. (\ref{eq:apx_dist_over_paths})) is used to predict a trajectory and fed to the planner. We apply the methodology described in~\cite{ziebart-iros-09} to generate a path. However, since our planner requires only one goal, we don't reason about all possible destinations, though the smoothing procedure is still used to generate the destination prior distribution.
\subsection{Environment features} \label{sec:features}
Environment features are encoded as binary occupancy grid maps, where a grid cell in a feature map denotes the presence/absence of the feature it is modeling. Most of the feature types used in this work are modeled from sensor data, including obstacle features from LiDAR, and $m$ terrain classes identified in the environment via semantic segmentation. However, any feature that can be encoded as a binary occupancy grid could be used for learning. In Section~\ref{sec:landmine}, we discuss scenarios where \textit{a priori} information about the environment is encoded to model potentially dangerous traversal regions.
Figure~\ref{fig:feature grid_examples} provides an example of three binary occupancy grid maps that encode the features \textit{obstacle}, \textit{grass}, and \textit{road}. The individual maps for each feature type can be seen in the top of the figure, where black denotes the presence of the feature and white denotes its absence. The color coded combination of these occupancy maps is provide in the bottom of the figure with a demonstrated trajectory overlaid in red. Specific details on how these feature grids are produced is provided in the remainder of this section.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{occ-grids.png}
\caption{(Top) Example binary occupancy grids for three feature types; obstacle collected by LiDAR and grass and road collected via semantic segmentation. (Bottom) An illustration of the obstacle grids overlaid one another with the corresponding demonstrated trajectory seen in red that was driven with respect to these environment features.}
\label{fig:feature grid_examples}
\end{figure}
Each binary occupancy grid feature map is output from a SLAM system based on the \emph{OmniMapper} described in~\cite{Trevor14ICRA}. Briefly, our SLAM system maintains a pose-graph along the robot's trajectory. Edges in this graph consist of measurements between consecutive robot poses in the form of odometry and 3D Generalized Iterative Closest Point (G-ICP)~\citep{Segal2009RSS}, in addition to loop-closure measurements through ICP when the robot revisits a previously explored location. The pose graph solution also incorporates measurements from GPS as in~\cite{Rogers14ACC}, allowing for long-term error correction in the absence of loop closures, and a global frame-of-reference to enable navigation to previously surveyed waypoints.
Keyframes are collected along the robot's trajectory to store relevant sensor data for building binary occupancy feature grid maps. The obstacle feature map is produced from a Velodyne HDL-32E LiDAR, which is also used for G-ICP in consecutive keyframes and loop-closures. Keyframes are also created to establish the pose of the robot's cameras at each image taken to perform semantic segmentation, which is used to generate terrain feature maps. If the robot's trajectory is corrected through a loop closure or GPS measurement, keyframe poses are updated, resulting in newly rendered corrected binary occupancy feature maps.
Semantic segmentation output at each camera keyframe is projected into the grid feature map by finding a bounding box of grid cells that project into the image. This is done by finding intersections between a flat ground plane and the extents of the image. Corner points of each candidate cell are projected into the image, and all pixels within the resulting quad are ``voted" into the occupancy grid based on their classification label. The label with the most votes sets that cell in the corresponding feature map; the cells in the terrain feature maps are entirely disjoint. This technique allows a cell to be updated by all images which observe it, and closer observations are naturally weighted higher due to the larger number of pixels in those images. Keyframes for laser data are limited to occur at no less than $50cm$ of distance traveled from the last keyframe to balance map quality with processing load. Visual keyframes are added at the frame rate of the visual semantic segmentation algorithm.
\begin{figure*}
\centering
\includegraphics[width=\linewidth]{classified_images_both.png}
\caption{Visual classification output by (Left) the HIM and (Right) the FCNN during on-line navigation. These frames are projected into the ground plane to generate binary occupancy grids for terrain feature types.}
\label{fig:classified_imgs}
\end{figure*}
Two different semantic segmentation algorithms are used throughout the experimental evaluation. Initial experiments (Sections~\ref{sec:roadgrass} and~\ref{sec:covert}) use the semantic segmentation output from a trained Hierarchical Inference Machine (HIM)~\citep{munoz13thesis}. The HIM trains a hierarchy of regressors to predict per pixel label output, and works well with a comparatively smaller set of training data compared to deep learners~\citep{simonyan2015very,szegedy2015going,krizhevsky2012imagenet,badrinarayanan2015segnet,long2015fully,zhou2014learning}. Efficient label collection techniques~\citep{Wigness16IROS,wigness2017unsupervised} are used to reduce human labeling intervention for classifier re-training and adaptation. The left portion of Figure~\ref{fig:classified_imgs} shows the label set and a selection of frames classified by the HIM in the real-world testing environment B.
The HIM is limited to processing speeds around $0.5 Hz$ for visual frames with resolution 344x275. Although this proves to be sufficient for real-time operation, deep learning techniques that perform inference on GPUs are able to provide significantly more visual perception information. For this reason, an implementation of a Fully Convolutional Neural Network (FCNN)~\citep{long2015fully}
is trained using the Caffe framework~\citep{jia2014caffe}. This model is run on a Jetson TX2 (used in experiments from Sections~\ref{sec:landmine} and~\ref{sec:online}) to produce semantic segmentation inference at a rate of around $2 Hz$. The right portion Figure~\ref{fig:classified_imgs} shows the label set and frames classified by the FCNN in environment B. Qualitatively, the accuracy of both techniques is similar, yet the improved processing speed of the FCNN provides more visual information to project into terrain feature maps, giving denser information during training and on-line operation.
In addition to the raw grid feature maps, several Gaussian blurred versions of these maps are used as additional features to encode the distance to the nearest cell of the classes. Figure~\ref{fig:sample_blurred_feat} shows an example obstacle map and a corresponding blurred feature map. The blurring effect extends the degree to which a cell represents the feature based on the values of cells within a specified radius. Cells closer to positive values, i.e., presence of the feature, in the grid map are weighted more heavily. Typically, for each feature we use a conventional grid map and at least one blurred map. Specific details regarding the feature set used in each experiment are provided in Section~\ref{sec:init}.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{sample_blurred_feature.png}
\caption{A sample obstacle feature map (left) and its corresponding blurred feature map with a radius of 5 cells (right).}
\label{fig:sample_blurred_feat}
\end{figure}
\section{Experiment setup}
\subsection{Outdoor environments}
Two urban environments are used to train and test our traversability cost learning with inverse optimal control. Environment A consists of a paved road intersection in an otherwise grassy wooded area, and is used as a training site to learn the first traversal behavior (discussed in Section~\ref{sec:roadgrass}). Environment B is a training facility meant to resemble a village in the developing world, with many small structures and gravel and dirt roads. Environment B is our primary testing environment, and is also used to collect data and train new behaviors in the field.
\subsection{Human demonstrated trajectory collection}
Trajectory exemplars are collected using a Clearpath Husky, as seen in Figure~\ref{fig:husky}. This platform is also used to deploy the learned behavior during testing. The robot is teleoperated by a human from an initial starting point $i$ to a predefined goal destination $g$ with some human defined optimality. This optimality is defined based on the behavior that the operator would like the robot to learn. Section~\ref{sec:experiments} discusses and evaluates three learned behaviors, 1) traversal near a road edge, 2) covert traversal, and 3) traversal modification given intel relating to potentially dangerous areas.
\begin{figure}
\centering
\includegraphics[width=0.6\columnwidth]{husky_callout.jpg}
\caption{The Husky robot with relevant sensor and components labeled.}
\label{fig:husky}
\end{figure}
Multiple demonstrated trajectories are collected for each behavior that is learned. Our training framework is capable of processing training exemplars with various feature map resolutions. This provides the added benefit of collecting demonstrations of varying trajectory length, and in different regions of the environment. Mapping and visual perception is run on-line during the trajectory demonstration to produce the binary feature maps for the relevant area of the environment.
\subsection{Training details} \label{sec:init}
The number of blurred maps and associated radii can be selected on a per-behavior basis. That is, some behaviors could be trained with many blurred feature maps with larger radii when feature information at larger distances is needed. The initial experiments for the edge of road traversal and covert traversal behaviors (discussed in Sections~\ref{sec:roadgrass} and~\ref{sec:covert}) were each performed with a feature set hand selected for the behavior. In addition to both behaviors learning a feature weight for obstacle, road, and grass features, a constant or bias feature is added to the feature weight vector. The blurred map radii used for each environment feature map for these behaviors is defined in Table~\ref{table:blur_info}.
However, in scenarios where a robot may need to rapidly switch between learned behaviors during on-line operation, it is ideal to have a standardized feature set, where each behavior is differentiated only by the values of its weight vector, $\theta$. Experiments discussed in Sections~\ref{sec:landmine} and~\ref{sec:online} all use learned reward functions based on a standardized feature set, which are summarized in the last two rows of Table~\ref{table:blur_info}.
When training without any prior initial weights, weights in $\theta$ are randomly initialized to values in the range of $[-5,5]$. The three experiments described in Section~\ref{sec:experiments} learn the behaviors from scratch with this random initialization. A previous set of weights can also be loaded to initialize $\theta$, which is the strategy used in our on-line experiments in Section~\ref{sec:online}. Each time the human interrupts the robot to provide a new trajectory demonstration, the weights currently being used for live operation are used to initialize $\theta$, and re-training is used to update these weights given the new demonstration.
\begin{table}
\footnotesize\sf\centering
\caption{Overview of the radii used to generate blurred feature maps for the environment features. A dash indicates that the environment feature was not used for the specified behavior.}
\label{table:blur_info}
\begin{tabular}{c|c|c|c|c}
\toprule
& \multicolumn{4}{c}{Blurred Map Radii} \\
Behavior & obstacle & road & grass & avoidance \\
\midrule
Edge of Road & 4 & 3, 6 & 3, 6, 9 & -- \\
Covert & 5, 10 & 5, 10 & 5, 10 & -- \\
ZOD Avoidance & 1, 2, 3, 4 & 1, 2, 3, 4 & 1, 2, 3, 4 & 1, 2, 3, 4 \\
On-line & 1, 2, 3, 4 & 1, 2, 3, 4 & 1, 2, 3, 4 & 1, 2, 3, 4 \\
\bottomrule
\end{tabular}
\end{table}
\subsection{Live operation experiment trials} \label{sec:trials}
In each navigation experiment, the robot must traverse from its initial location, $i$, to a waypoint goal, $g$, given GPS coordinate information. Selected $(i,g)$ pairs used in our experiments require on the range of 60 to 250 meters of traversal. For each experiment, a \textbf{ground truth (GT)} trajectory is collected according to $\pi^*$. Additionally, we run a \textbf{baseline} planner based on the search-based planning library (SBPL)~\citep{Cohen10ICRA} for comparison during each experiment. This planner generates a kinematically achievable global plan by searching combinations of motion primitives. This global plan minimizes traversal cost to the goal, and considers unknown grid cells to be of relatively high costs. This planner uses an unthresholded version of the obstacle feature map which additionally contains intermediate values for obstacles of varying laser ``opacity". This is accumulated in a negative log-odds grid based on the evidence of laser scans being interrupted by an obstacle in this cell against the evidence of which laser scans have passed through this cell. This planner does not make use of visual terrain features for planning. Finally, the \textbf{IOC} planner, when given a goal location, generates an output reward map. The reward map is then searched for an optimal reward trajectory which reaches the goal. This trajectory is passed to the navigation system of the robot which executes a kinematically feasible approximation of this trajectory.
Unless otherwise noted, four trials are run at each experiment site. Specifically, trial 1 captures trajectories of ground truth from $(i,g)$, IOC from $(g,i)$, and baseline from $(i,g)$. Trial 2 begins where trial 1 left off, i.e., from $g$, thus ground truth from $(g,i)$, IOC from $(i,g)$, and baseline from $(g,i)$. Trials 3 and 4 swap planner ordering to ground truth, baseline and IOC. By defining these four trials we are able to facilitate faster experimentation while collecting multiple trajectories for each technique in both directions of waypoint pairs. Further, this setup allows us to assume that coarse information about terrain and obstacles in the environment are known so the IOC and baseline planners have a larger field of view for navigation. By beginning each trial with a ground truth trajectory, this information can be populated in the map prior to the other planner execution. In future work this information could be obtained by teaming with an aerial vehicle that passes through the environment prior to the UGV, and providing an initial terrain classification from aerial imagery.
The trajectories for each trial are collected by recording the GPS measurements using the robot's onboard sensor as it moves between the two waypoints. Due to some GPS measurement drift\endnote[1]{We observed a GPS measurement bias of 2 or 3 meters at times due to signal blockage, resulting in minor abnormalities when the robot's position is plotted against a geo-referenced image.}, each trajectory starting point is re-aligned to the known surveyed waypoint start location. Trajectories for the third behavior experiment discussed in Section~\ref{sec:landmine} are collected using a Leico Viva TS16. The use of the total station allows us to eliminate the GPS drift issue for a more accurate trajectory comparison. The total station tracking prism is mounted on the middle of the right edge of the UGV main body, and tracked for each trajectory during an experiment trial.
\subsection{Evaluation metrics}
Performance is measured by comparing a navigation trajectory, i.e., baseline or IOC, with a ground truth trajectory produced by human teleoperation. Trajectories are compared using the modified Hausdorff distance (MHD)~\citep{dubuisson1994modified,shao2010modified},
\begin{equation}
h(A,B) = \frac{1}{|A|} \sum_{a_i \in A} (\min_{b_j \in B} d(a_i,b_j)),
\end{equation}
where $B$ is the ground truth trajectory, $A$ is the trajectory to be compared, and function $d$ measures the distance between two points along these trajectories. This metric compares the geometry of trajectories, with lower MHD indicating higher similarity.
We present the mean and median MHD for the set of trials in each experiment, and the MHD for the best trial in each experiment. Each point along the trajectory is represented by its UTM coordinates, measuring distance in meters. The best mean MHD score is highlighted in bold during experimental analysis throughout this paper.
\section{Learned behaviors} \label{sec:experiments}
\subsection{Edge of road traversal} \label{sec:roadgrass}
For the first learned behavior, the optimal navigation policy ($\pi^*$) should maintain close proximity to grass but only traverse road terrain. This optimal behavior requires learning more than how to simply assign costs to distinct terrain types. Context of the environment with respect to the robot's task must also be considered. This behavior is chosen because it represents a traversal pattern that allows a mobile robot to adhere to common vehicular practice, i.e., driving on the road, but keeps the smaller platform away from potentially larger vehicles that may also be occupying the road.
\begin{figure*}
\centering
\includegraphics[width=.7\linewidth]{reward_function.png}
\caption{Sample reward map obtained from demonstrated behavior. This figure illustrates the case of a robot that tends to drive on the road while staying close to the grass. As seen in the magnified insert (bottom left corner), this preference is indicated by a slight bump in the reward function.}
\label{fig:learned_reward_map}
\end{figure*}
\paragraph{\textbf{Environment A}} The training for this behavior is performed in environment A. Six exemplar trajectories are collected between the waypoint pair $(A,C)$ (referenced in Figure~\ref{fig:aerial_envA2}). Figure~\ref{fig:learned_reward_map} visually depicts the rewards learned for the features after training from trajectory examples and visual features collected in environment A. The individual feature maps are shown in the top left of the image, and an overlay of these feature maps are presented as a heat map on the right. Areas in the map that correspond to road have the highest reward seen in red, whereas obstacles have the lowest traversal reward seen in dark blue, and grass falls between these two features. The bottom left of the image is a magnified 3-D illustration of the map, which shows that not all areas of road terrain are represented by the same reward value. As demonstrated by the human trajectory exemplars, a higher reward can be seen on the edge of the road alongside the grass. This is visually indicated by the bump (outlined in blue) in the reward values on the map.
As a preliminary test, the learned costs for this behavior are deployed on the robot for on-line operation in environment A. Testing is performed in the same area as the training trajectories were demonstrated, but the navigation task is extended to be roughly twice the distance as that represented in the training trajectories. Seven testing trials are performed between the waypoint pair $(A,B)$ in environment A. Table~\ref{tab:envA-test} compares the MHD of the baseline and IOC planners at this testing sites with respect to the ground truth.
\begin{table}
\footnotesize\sf\centering
\caption{Comparison of the modified Hausdorff distance for the baseline and IOC planners with respect to ground truth trajectories near the original training site in environment A.}
\label{tab:envA-test}
\begin{tabular}{c|c|c|c|c|c|c}
\toprule
& \multicolumn{3}{c|}{Baseline} & \multicolumn{3}{c}{IOC} \\
Test Site & Mean & Median & Best & Mean & Median & Best \\
\midrule
(A,B) & 4.114 & 3.488 & 1.447 & \textbf{3.036} & 2.827 & 1.376 \\
\bottomrule
\end{tabular}
\end{table}
Across the seven trials our learned IOC planner produces a navigation trajectory that more closely resembles the optimal traversal behavior as defined by the collected GT trajectories. Although this initial test is performed in the same environment, test experiments were performed roughly two months after the collection of training data. This shows that the learned behavior is able to generalize to small changes in environment that naturally occur over time. Figure~\ref{fig:aerial_envA2} illustrates the trajectories from two of the testing trials to qualitatively show the closer trajectory aligned of the IOC planner to the ground truth than that of the baseline planner.
\paragraph{\textbf{Environment B}}
To better show the generalization of the learned feature costs, we extensively test the learned behavior through a series of navigation experiments in environment B. Figure~\ref{fig:aerial_envB} is an aerial map of this environment, and depicts the test site waypoints and trajectories observed during evaluation. Each of the nine $(i,g)$ waypoint pairs are selected such that the shortest straight line trajectory between the waypoints does not follow $\pi^*$ used to collect training trajectories. The set of testing sites are diverse with respect to traversal distance, buildings, road width, and goal waypoint visibility.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{b507_ioc_traj_ijrr.jpg}
\caption{Aerial view of environment A and the trajectories driven by the robot during two trials of the preliminary experimental evaluation of the learned behavior that focuses on maintaining close proximity to the edge of the road while navigating.}
\label{fig:aerial_envA2}
\end{figure}
\begin{figure*}
\centering
\includegraphics[width=0.85\linewidth]{overview_of_trajectories.jpg}
\caption{Aerial view of environment waypoints and the trajectories driven by the robot during experimental evaluation of the learned behavior that focuses on maintaining close proximity to the edge of the road while navigating.}
\label{fig:aerial_envB}
\end{figure*}
Table~\ref{table:envB-results} compares the MHD of the baseline and IOC planners at these nine testing sites with respect to the ground truth. The MHD results indicate that overall the IOC planner generates trajectories more similar to the ground truth than the baseline planner. This indicates that the IOC framework in fact learned $\pi^*$ well, and plans according to this policy even with training examples from a different domain.
A qualitative comparison of the trajectories output by the IOC and baseline planners allows us to visually see the learned behavior. The left image in Figure~\ref{fig:qualitative} show trajectories from one trial of the $(M,N)$ testing site. The trajectory overlays on the map show the close alignment of IOC and ground truth, whereas the baseline trajectory is much further away.
However, Table~\ref{table:envB-results} also shows the baseline planner has a better median and best MHD than IOC at testing site $(B,I)$. The right image in Figure~\ref{fig:qualitative} shows an experiment trial from this site where the IOC trajectory actually deviates from the road, causing an increased MHD. We hypothesize that the poorer results at this testing site are caused by a less prevalent grass feature and narrower roadway than other testing sites.
\begin{table}
\footnotesize\sf\centering
\caption{Comparison of the modified Hausdorff distance for the baseline and IOC planners with respect to collected ground truth trajectories in environment B. *one trial and **two trial experiments.}
\label{table:envB-results}
\begin{tabular}{c|c|c|c|c|c|c}
\toprule
& \multicolumn{3}{c|}{Baseline} & \multicolumn{3}{c}{IOC} \\
Test site & Mean & Median & Best & Mean & Median & Best \\
\midrule
(D,E) & 5.908 & 5.636 & 4.122 & \textbf{3.648} & 3.460 & 3.233 \\ \hline
(B,I) & \textbf{3.222} & 3.698 & 1.713 & 4.174 & 3.597 & 2.263 \\ \hline
(A,J) & 4.242 & 3.786 & 3.530 & \textbf{3.626} & 3.836 & 1.025 \\ \hline
(F,G) & 2.641 & 2.413 & 1.871 & \textbf{1.738} & 1.844 & 1.018 \\ \hline
(Q,R) & 2.443 & 2.470 & 1.341 & \textbf{2.003} & 1.988 & 0.723 \\ \hline
(L,M) & 2.913 & 3.169 & 1.178 & \textbf{1.748} & 1.373 & 1.344 \\ \hline
(P,Q)** & 1.496 & 1.496 & 1.246 & \textbf{1.130} & 1.130 & 1.086 \\ \hline
(L,O)* & -- & -- & 3.604 & -- & -- & \textbf{1.993} \\ \hline
(M,N)* & -- & -- & 4.682 & -- & -- & \textbf{2.164} \\
\bottomrule
\end{tabular}
\end{table}
We note that although in this image the IOC trajectory appears to pass through the buildings as it deviates from the road, this was not observed in the live experiments. Our UGV uses a Garmin GPS 18x single frequency (L1) receiver for global positioning. GPS signals are typically broadcast with $< 0.715m$ range error\endnote[2]{\url{www.gps.gov/systems/gps/performance/accuracy}}, but the GPS receiver solution can be corrupted by signal blockage (i.e. buildings, trees) and atmospheric conditions. In practice, we observed up to 2 or 3 meters of bias in some locations near buildings when the robot's position is plotted against a geo-referenced image. By subtracting this offset from the surveyed waypoint, this bias is removed from our evaluated trajectories. In the future, we intend to switch to a Hemisphere GNSS positioning system\endnote[3]{\url{https://hemispheregnss.com/Products/Products/Position/r330e284a2-gnss-receiver-760}} which incorporates the L2 signal, in addition to the other global positioning satellite constellations and multiple land-based corrections.
\begin{figure*}
\centering
\includegraphics[width=\linewidth]{run_details_roadgrass_combined.jpg}
\caption{Detailed views of two test runs. (Left) Test site $(M,N)$ which depicts a typical example of how the IOC planner closely mimics the GT trajectory while the baseline planner opts for paths far from obstacles. (Right) An example run from test site $(B,I)$ with poor performance from the IOC planner, where the grass feature was not found adjacent to the road, causing the robot to deviate off the expected path.}
\label{fig:qualitative}
\end{figure*}
\subsection{Covert traversal} \label{sec:covert}
One major benefit of the maximum entropy IOC learning approach is that reward functions can be learned with a relatively small number of training examples. This was demonstrated in the previous behavior with the use of only six demonstrated trajectories. This provides a way to quickly adapt a current behavior or learn a completely new behavior with minimal interruption in the robot's mission efforts. Our second experiment demonstrates the speed in which an alternative behavior can be learned and deployed with our IOC learning.
More specifically, this second experiment was performed end-to-end over the course of the last few hours of our field experimentation. This includes the collection of new training data, re-training of the reward function, and deployment of this behavior on the robot for live operation. The second learned behavior is described as ``covert" traversal. During this behavior, the robot should traverse in such a fashion that it is not openly acknowledged or visible. In this case, buildings, objects or other structures could be used as cover. We collect four new training demonstrations that keep the robot close to building edges and out of more visible, open areas such as roadways. Training data is collected from an area in environment B disjoint from any of the test waypoint locations. Using these new training examples, feature weights are re-learned and the robot is deployed to waypoint site $(P,Q)$ for testing.
Table~\ref{table:newwights-results} shows the MHD results for the baseline and IOC planners for the covert traversal experiments. As in the previous experiments, ground truth is collected prior to running the IOC and baseline planners. Results show that the IOC planner performs more similarly to the ground truth than the baseline, suggesting the covert behavior has been learned well. Figure~\ref{fig:run_p_q_covert} also illustrates the trajectories of the trials for this experiment, showing qualitatively, the similarity between the ground truth and IOC.
\begin{table}
\footnotesize\sf\centering
\caption{Comparison of the modified Hausdorff distance for the baseline and IOC planners with respect to ground truth trajectories depicting covert traversal behavior.}
\label{table:newwights-results}
\begin{tabular}{c|c|c|c|c|c|c}
\toprule
& \multicolumn{3}{c|}{Baseline} & \multicolumn{3}{c}{IOC} \\
Test Site & Mean & Median & Best & Mean & Median & Best \\
\midrule
(P,Q) & 5.201 & 4.457 & 3.422 & \textbf{1.415} & 1.362 & 1.160 \\
\bottomrule
\end{tabular}
\end{table}
The MHD results also indicate that covert behavior is significantly different than a normal traversal behavior depicted by the baseline planner. In the first traversal behavior experiments, the IOC planner achieves only a 0.366 mean performance improvement over the baseline at waypoint site ($P,Q)$ (seen in Table~\ref{table:envB-results}). The performance gap jumps to 3.786 at the same site during the covert behavior experiment. This emphasizes the importance of learning behavior relevant to the current mission requirements or state of the dynamic environment, as normal behavior could deviate strongly from what is necessary to successfully complete tasks.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{run_detail_p_q_covert.jpg}
\caption{Experiment trajectories$^1$ from P to Q using the new ``covert" training.}
\label{fig:run_p_q_covert}
\end{figure}
\subsection{Dangerous zone avoidance traversal} \label{sec:landmine}
Previous experiments focused on learning traversal behaviors related to environment features identifiable from LiDAR and camera sensor data. This perception information grounds the behavior learning to the context of physical objects and terrains in the environment. However, for certain applications, optimal task performance may require additional information beyond perception. For example, it may be desirable for a robot to stay within a specific communication radius. Conversely, there may be areas in an environment believed to present potential danger to a robot. Given known locations of communication nodes/dangerous zones, this information can be encoded as a binary occupancy grid indicating if grid cells are within the desired communication/dangerous range or not.
\begin{figure*}
\centering
\includegraphics[width=.8\linewidth]{b507_ioc_traj_ijrr_lejeune.jpg}
\caption{Aerial view of environment waypoints and the trajectories driven by the robot during experimental evaluation of the learned behavior that focuses on avoiding traversal through zones of danger but otherwise maintaining close proximity to the edge of the road while navigating.}
\label{fig:landmine_map}
\end{figure*}
Our third behavior experiment focuses on a scenario that requires a traversal behavior that learns from perception derived feature maps in addition to features that are provided as \textit{a priori} intel. The optimal robot behavior for this task should maintain close proximity to the road edge (as in the experiment from Section~\ref{sec:roadgrass}), but should deviate when a potential zone of danger (ZOD) is encountered. Specifically, this scenario is designed to emulate a robot operating in an environment that may contain explosive devices. The \textit{a priori} information about the potential location of these devices and their expected blast radius is encoded as an \textit{avoidance} binary occupancy feature map.
Training and testing of this behavior was performed in environment B. Figure~\ref{fig:landmine_map} shows an aerial view of the environment with all testing trajectories, testing waypoint sites, and zones of danger used in this experiment. Each ZOD marker in the map indicates the center of a circular zone of danger. Table~\ref{table:landmine_radius} indicates the specific radius in meters $(m)$ that defines each ZOD. The location and radius of ZODs are defined specifically to cover large portions of the road, including areas near road edges to test edge of road traversal deviation when a dangerous zone is encountered.
\begin{table}
\sf\centering
\caption{Radius associated with each zone of danger (ZOD).}
\label{table:landmine_radius}
\begin{tabular}{c|c}
\toprule
radius ($m$) & ZODs \\
\midrule
2 & 2, 3, 4 \\
2.5 & 5 \\
3 & 6, 7, 8, 9 \\
\bottomrule
\end{tabular}
\end{table}
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{landmine_training_map.png}
\caption{Illustration of a training demonstration example and the corresponding reward map learned by our approach for the traversal behavior that avoids dangerous regions. (Left) An overlay of color coded feature maps, obstacle (black), road (gold), grass (green), and avoidance (red), with the exemplar trajectory shown in blue. (Right) The learned reward map for this exemplar is illustrated as a heat map, where hot colors indicate high reward. Notice that the location of the dangerous area (illustrated as red circles in the left image) is learned to be a low reward traversal region as indicated by the cooler colors in this area.}
\label{fig:landmine_reward_maps}
\end{figure}
12 training demonstrations were collected in the environment near waypoint Q, some of which were west of the testing waypoint site $(Q,U)$ (seen in Figure~\ref{fig:landmine_map}). Figure~\ref{fig:landmine_reward_maps} depicts one demonstrated trajectory exemplar and its corresponding reward map found during training. On the left is a color coded overlay of the feature maps used for this behavior including, obstacle (black), road (gold), grass (green), and avoidance (red). The demonstrated trajectory through this environment with these features is depicted by the blue line. The trajectory illustrates the desired behavior of traversing near the edge of the road until an avoidance region impacts this trajectory, forcing the traversal route to deviate around the ZOD into the grass before continuing along the edge of the road once the dangerous region has been passed.
The right image in Figure~\ref{fig:landmine_reward_maps} is the reward map found for this training example. The reward map is illustrated as a heat map, where red indicates the highest reward and blue the lowest. The demonstrated trajectory is also overlaid on the heat map to qualitatively show the rewards corresponding to this learned behavior. Notice that the reward map assigns a very low cost to the avoidance feature region, with higher rewards seen in all cells around this circular region. Further, although this particular demonstration deviated around the avoidance region by going ``below" this region, the reward function has learned that it is also reasonable to deviate over the ``top" of this region to mimic the optimal behavior.
This experiment represents a much more complex behavior than those demonstrated previously. For this scenario, there are really two underlying behaviors, i.e., traversing near the road edge and avoiding dangerous regions, that must be de-conflicted to perform the navigation task optimally. For this reason, we found that using more training exemplars than the previous behaviors provided better performance.
Evaluation of this behavior is performed at three waypoint sites in environment B. Table~\ref{table:landmine-mhd} compares the MHD scores for this behavior using our IOC planner and the baseline planner discussed previously. As seen the previous behaviors, the learned IOC reward function results in trajectories that closely resemble the ground truth trajectories that demonstrate the optimal behavior. This is seen in all cases (mean, median, and best of the trials), as IOC has a lower MHD than that of the baseline planner. We note that comparing the MHD of the IOC and baseline planners is not provided to show a ``superior" performance by the IOC for this behavior. Because the baseline planner is operating given only obstacle information, of course it will plan and have the robot traverse through the dangerous zones. Instead, the comparison is made to more fully indicate that the IOC planner is indeed learning the demonstrated behavior.
\begin{table}
\footnotesize\sf\centering
\caption{Comparison of the modified Hausdorff distance for the baseline and IOC planners with respect to ground truth trajectories depicting traversal behavior that avoids dangerous regions. **two trial experiment}
\label{table:landmine-mhd}
\begin{tabular}{c|c|c|c|c|c|c}
\toprule
& \multicolumn{3}{c|}{Baseline} & \multicolumn{3}{c}{IOC} \\
Test Site & Mean & Median & Best & Mean & Median & Best \\
\midrule
(Q,U) & 1.703 & 1.703 & 1.320 & \textbf{1.682} & 1.666 & 1.381 \\
(B,V)** & 1.047 & 1.047 & 0.904 & \textbf{0.775} & 0.775 & 0.720 \\
(C,V) & 1.263 & 1.251 & 1.127 & \textbf{1.100} & 1.204 & 0.677 \\
\bottomrule
\end{tabular}
\end{table}
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{b507_ioc_traj_ijrr_lejeune_main_street2.jpg}
\includegraphics[width=\columnwidth]{b507_ioc_traj_ijrr_lejeune_marketplace2.jpg}
\caption{Qualitative illustrations of trajectories produced from human demonstration (GT), and the IOC and baseline planners during one trial of the dangerous zone avoidance traversal behavior experiments. (Top) Trial from test site $(C,V)$ with five ZODs to avoid. (Bottom) Trial from test site $(Q,U)$ with three ZODs to avoid.}
\label{fig:landmine_trials}
\end{figure}
Figure~\ref{fig:landmine_trials} provides a qualitative comparison of trajectories from one trial at test site $(C,V)$ (top image), and one trial from test site $(Q,U)$ (bottom image). As expected, because the baseline planner has no knowledge of dangerous zones in the environment it traverses down the road, and enters the radius of ZOD5. However, the IOC planner has learned through the demonstrations that the radius of the dangerous zones should be avoided. While, the IOC trajectory does not deviate around the ZODs in strictly the same manner as the GT trajectory, the general behavior is still exemplified well. Part of the trajectory mismatch seen between IOC and GT in this trial run comes from the fact that the two trajectories are collected in different directions, i.e., GT from $(V,C)$ followed by IOC from $(C,V$) (as outlined in Section~\ref{sec:trials}. Because IOC begins at location $C$ it chooses to go around the ``top" side of ZOD8, but as IOC traverses closer to $V$ the trajectory more closely resembles the GT by deviating ``below" all other ZODs and also maintaining close proximity to the road edge.
Similar qualitative observations can be made about the trial run from $(Q,U)$ in the bottom image of Figure~\ref{fig:landmine_trials}. The IOC and GT trajectories at times take different deviations around a ZOD, but both trajectories do avoid the dangerous zone. This trial highlights that not only is the IOC planner avoiding the dangerous zones, but also maintains close proximity to the road edge in areas without ZODs. This is apparent when comparing the IOC trajectory to that of the baseline, which remains relatively centered in the road as it plans between the waypoints. Notice again that this causes the baseline trajectory to traverse extremely close to ZOD2 and ZOD4.
\section{On-line human demonstration and training} \label{sec:online}
In difficult or changing terrain, the ability to leverage corrective teleoperation provided by a human teammate could be used to enable on-line adaptation. Once a human teammate determines that the UGV is not exhibiting the desired behavior due to the presence of unexpected cues or changing environment conditions, they can pick up a joystick and demonstrate a desired trajectory. An on-line adaptive learning system can then record this trajectory segment together with the observed environmental features, and update its models appropriately while in the field and then resume operation.
To enable this capability, we made several modifications to the existing learning from demonstration system. In the typical experimental setup, the left trigger on an XBox 360 joystick is depressed to override autonomous control with teleoperation. This type of teleoperation is used to maneuver to prepare for an experimental trial run or for platform safety. We have added a module which detects when this teleoperation trigger is depressed in addition to the right trigger. Depressing both triggers is used to indicate that a human teammate is providing a trajectory demonstration, and the trajectory is recorded until the triggers are released.
Once the human teammate has finished providing the new demonstrated training trajectory and autonomous control is restored to the UGV, the trajectory along with all feature maps (discussed in Section~\ref{sec:features}) are provided to an on-line training module. The on-line training module behaves similarly to the off-line procedure used in the previous experiments except that the weight vector $\theta$ is initialized with the current weights deployed on the UGV, and optimization is limited to 30 seconds to provide a quick on-line update to improve the platform navigation behavior. The on-line retraining procedure currently uses all previous training examples together with any new demonstrated trajectories and features. Once the optimization procedure converges or the allotted time elapses, the new weights are sent to update the control module. If the desired behavior is still not exhibited fully by the platform, the human teammate can interrupt UGV operation at any time to provide additional examples; in our experience a new behavior can be learned in as little as four examples.
An initial set of experiments were performed to determine the effectiveness of the on-line procedure. Figures~\ref{fig:online-roadedge} and~\ref{fig:online-landmine} illustrate several sequential steps of the on-line learning process for the scenario outlined in the rest of this section. These images show layers of information within the map used for navigation. The generated LiDAR obstacles are colored as grey/black regions. The visual perception terrain maps for road and grass are colored as pink and green, respectively. The reward heat map\endnote[4]{The illustration of reward heat maps show a visualization artifact that resembles lightning originating from the robot's position. This effect is a result of using the Manhattan distance to calculate the blurred features and the destination prior distribution.} is overlaid in most of these images, indicating the path planned by the robot given its current set of feature weights. Dangerous zones are visualized as circular grey/black regions. Finally, demonstrated trajectories are drawn in blue. These visualizations are provided to show progression of learning that takes place with the on-line module.
For this scenario, the UGV is assumed to start with no traversal behavior knowledge, i.e., no demonstrated training trajectories exist and thus, feature weights are randomly initialized (as outlined in Section~\ref{sec:init}). To begin, the human teammate determines that the UGV should behave in such a way that its traversal pattern follows the edge of the road (just as in the experiments from Section~\ref{sec:roadgrass}). As the robot has no understanding of this behavior the human teammate must provide some demonstration.
\begin{figure*}
\centering
\begin{subfigure}[b]{\textwidth}
\centering
\includegraphics[width=0.45\textwidth]{first_three_training_trajectories.png}
\includegraphics[width=0.43\textwidth]{first_test_with_three_training_examples.png}
\caption{(Left) Three initial training trajectories are collected that demonstrate edge of road traversal. (Right) Testing results when running this behavior after these three demonstrations.}
\label{fig:road_tr_phase1}
\end{subfigure}
\begin{subfigure}{\textwidth}
\centering
\includegraphics[width=0.45\textwidth]{fourth_training_trajectory.png}
\includegraphics[width=0.425\textwidth]{second_test_with_four_training_examples.png}
\caption{(Left) Collection of one initial training trajectory to improve the learned behavior of edge of road traversal. (Right) Testing results when running this behavior after the four demonstrations.}
\label{fig:road_tr_phase2}
\end{subfigure}
\caption{On-line demonstration interaction and testing operation of our IOC approach for the edge of road traversal behavior.}
\label{fig:online-roadedge}
\end{figure*}
The human teammate depresses the trigger buttons, and provides three demonstrations of this behavior, which are labeled as $\left(1,2,3\right)$ in the left image of Figure~\ref{fig:road_tr_phase1}. The weight function is then automatically re-learned with these new examples onboard the UGV. The human teammate then asks the UGV to autonomously traverse to a specified location, but it exhibited unexpected behavior by driving into grass regions. This can be seen in the right image of Figure~\ref{fig:road_tr_phase1}, where the hot part of the heat map is completely ``above" the road terrain (shown in pink) and instead overlays the grass regions. To improve this behavior, a fourth training example was provided by the human teammate, as shown in the left of Figure~\ref{fig:road_tr_phase2}. The weights were updated onboard the UGV, and in a subsequent autonomous command the desired behavior of following the edge of the road was exhibited correctly, as seen in the right of Figure~\ref{fig:road_tr_phase2}, where the hot part of the heat map resides along the edge of the road terrain.
We then assume within this scenario that the environment and information about the safety of the environment changes. From the previous demonstrations, the robot is currently operating under the traversal behavior that maintains close proximity to the road edge, but now enters a section of the environment filled with areas that are dangerous to traverse. Absent any relevant training examples for this situation, the robot will plan autonomous trajectories that pass directly through these dangerous regions. This can be seen in the left of Figure~\ref{fig:landmine_tr_phase1}, where the dangerous zone is the dark circular region that the planned path crosses. The intel on these environment changes is provided to the robot as an additional feature, i.e., the avoidance feature map, and the human teammate seizes control of the UGV to provide two training examples, labeled as $\left(5,6\right)$ in the right image of Figure~\ref{fig:landmine_tr_phase1}, that exemplify how the robot should update its behavior in the presence of this new feature.
These new training examples were incorporated into the learned model, and the weights were updated to reflect the cost of driving in the dangerous zones. Given this new training, the robot is assigned goals to test the updated behavior. Figure~\ref{fig:landmine_tr_phase2} shows two planned trajectories, and corresponding reward heat maps where the robot plans around these dangerous zones. The performance of avoiding these dangerous areas allows the human teammate to carry out other tasks relevant to the mission, while the robot autonomously and safely maneuvers to carry out its other higher level tasks.
\begin{figure*}
\centering
\begin{subfigure}[b]{\textwidth}
\centering
\includegraphics[width=0.475\textwidth]{third_test_landmine_no_lm_training.png}
\includegraphics[width=0.415\textwidth]{lm_training_trajectories.png}
\caption{(Left) Testing results when running the behavior in an environment that now includes dangerous regions (shown as dark circles). Since the previous demonstrations were not based on this information, the planned path traverses straight through the dangerous region. (Right) Collection of two demonstrations that exhibit the behavior to traverse around these regions when present, otherwise maintaining close proximity to the road edge as demonstrated previously.}
\label{fig:landmine_tr_phase1}
\end{subfigure}
\begin{subfigure}{\textwidth}
\centering
\includegraphics[width=0.475\textwidth]{test_lm_avoid1.png}
\includegraphics[width=0.425\textwidth]{test_lm_avoid2.png}
\caption{Two examples of testing results after the human demonstrations of traversing around the dangerous zones.}
\label{fig:landmine_tr_phase2}
\end{subfigure}
\caption{On-line demonstration interaction and testing operation when the robot is in a situation where it needs to change behaviors from edge of road traversal to now include dangerous region avoidance as well.}
\label{fig:online-landmine}
\end{figure*}
This initial on-line experiment demonstrates the potential of our inverse optimal control methodology. With only a few demonstrated trajectories and limited training time, our system was able to learn feature weights that allowed the UGV to mimic the desired traversal behavior. This allows a robot to be deployed and updated in the field with minimal human interactivity. This is ideal for environments or missions that have the possibility to change rapidly during operation.
\section{Conclusions}
Several concerns need to be addressed when training UGVs to work alongside human teammates in unstructured environments, e.g., HA/DR or military operation. First, prior training may not be available or inadequate due to the chaotic nature of a scenario. This inadequacy can come in the form of visual appearance cues being altered so terrain cannot be evaluated correctly, as well as traversal cost changes i.e. dirt becomes mud which is harder to traverse. Secondly, the roles and activities envisioned by robot programmers might not encompass all of those which are needed in a dynamic and fast-evolving unstructured environment. An adaptable system will be able to contribute to the operation in more ways than a fixed one. By minimizing the effort needed to retrain or train a new behavior, a system will also reduce demands on personnel who are busy with other tasks.
This paper described an approach to building such a system which learns from human demonstration to acquire new skills with limited supervision in the field. The trained system was extensively evaluated in a real-world environment demonstrating three learned behaviors: 1) driving along the edge of the road, 2) covert traversal, and 3) avoidance of dangerous zones. The approach was shown to learn these behaviors with the use of feature maps built from visual perception input and \textit{a priori} intel. Further, the system was modified to allow human interruption to provide additional trajectory demonstrations and re-training updates during on-line operation. Currently, the types of skills learned are limited to navigational behaviors. However, with additional effort this approach should be applicable to other task domains. Future work will be to develop an end-to-end system that directly couples the visual classifier and IOC reward function without intermediate human-guided semantics. In this system, unsupervised clustering will replace visual classifier training, requiring only supervision in the form of example driving trajectories.
\theendnotes
| {
"redpajama_set_name": "RedPajamaArXiv"
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"redpajama_set_name": "RedPajamaC4"
} | 6,125 |
// Copyright (c) Christof Senn. All rights reserved. See license.txt in the project root for license information.
namespace Aqua.Tests.TypeSystem.TypeResolver
{
using Aqua.TypeSystem;
using Shouldly;
using System;
using Xunit;
public class When_resolving_different_anonymous_types_with_same_name_and_same_properties
{
private readonly Type type1;
private readonly Type type2;
private readonly TypeInfo typeInfo1;
private readonly TypeInfo typeInfo2;
private readonly Type resolvedType1;
private readonly Type resolvedType2;
public When_resolving_different_anonymous_types_with_same_name_and_same_properties()
{
type1 = TestObjects1.Helper.GetAnonymousType0<int, string>();
type2 = TestObjects2.Helper.GetAnonymousType0<int, string>();
typeInfo1 = new TypeInfo(type1);
typeInfo2 = new TypeInfo(type2);
var typeResolver = new TypeResolver();
resolvedType1 = typeResolver.ResolveType(typeInfo1);
resolvedType2 = typeResolver.ResolveType(typeInfo2);
}
[Fact]
public void Type_infos_should_not_be_equal()
{
typeInfo1.ShouldNotBe(typeInfo2);
}
[Fact]
public void Resolved_types_should_be_equal()
{
resolvedType1.ShouldBe(resolvedType2);
}
[Fact]
public void Resolved_type1_should_be_equal_to_original_type1()
{
resolvedType1.ShouldBe(type1);
}
[Fact]
public void Resolved_type2_should_not_be_equal_to_original_type2()
{
resolvedType2.ShouldNotBe(type2);
}
[Fact]
public void Resolved_type2_should_be_equal_to_original_type1()
{
resolvedType2.ShouldBe(type1);
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,773 |
Sergei Michailowitsch Ljapunow (, wiss. Transliteration Sergej Michajlovič Ljapunov; * in Jaroslawl, Zentralrussland; † 8. November 1924 in Paris) war ein russischer Komponist und Pianist.
Leben
Ljapunow erhielt seinen ersten Klavierunterricht von seiner Mutter. Nach dem Tod seines Vaters Michail Wassiljewitsch Ljapunow zog seine Mutter im Jahre 1870 mit ihm und seinem älteren Bruder, dem späteren Mathematiker Alexander Ljapunow, nach Nischni Nowgorod. Dort nahm er seit 1874 an Kursen der Russischen Musikgesellschaft teil. Vier Jahre später begann er, am Moskauer Konservatorium Klavier (u. a. bei Karl Klindworth), Kontrapunkt und Komposition (bei Sergei Tanejew) zu studieren. Nachdem er 1883 seine Studien abgeschlossen hatte, zog er zwei Jahre später nach Sankt Petersburg, wo er Kontakt zum "mächtigen Häuflein" schloss. 1894–1902 leitete Ljapunow mit Mili Balakirew die Hofsängerkapelle. Er wurde 1905 Lehrer an der von Balakirew gegründeten Musik-Freischule und leitete sie 1908–1910. Ab 1910 war er Professor für Klavier, ab 1917 auch für Komposition am Sankt Petersburger Konservatorium. Er beendete 1918 seine Lehrtätigkeit und wirkte eine Zeitlang an der Kaiserlichen Kunstakademie in Petersburg. Im Jahre 1923 emigrierte er aus der neugegründeten Sowjetunion nach Paris, wo er noch eine Musikschule gründete. Er starb kurz vor seinem 65. Geburtstag.
Stil
Ljapunow wurde von zwei Komponisten geprägt, von Franz Liszt und von seinem Mentor Mili Balakirew. Von ersterem übernahm er v. a. den brillanten, virtuosen Klaviersatz und die Art und Weise der pianistischen Verarbeitung von Themen. Auch seine Gattungswahl war stark von Liszt geprägt (vgl. z. B. sein Opus 11). Von Balakirew übernahm er das Interesse an russischen Volksliedthemen und Orientalismen wie Melodien aus dem Kaukasus. Außerdem vollendete er einige von Balakirews unfertig hinterlassenen Werken. Ljapunows Schaffen stellt eine Synthese aus romantischem Virtuosentum und der nationalrussischen Bewegung her. Als hochgeachteter Pianist verfügte er über ein ungewöhnlich vielseitiges Repertoire. Im Frühjahr 1910 nahm er vier eigene Klavierstücke für das Reproduktionsklavier Welte-Mignon auf. Auch als Pädagoge war Ljapunow eine wichtige Persönlichkeit in der russischen Musikgeschichte. Dass sein Schaffen heute eher unbeachtet ist, entspricht seiner Einschätzung als Epigone.
Werke
Orchester
Symphonie Nr. 1 h-Moll op. 12 (1887)
Symphonie Nr. 2 b-Moll op. 66 (1917)
Klavierkonzert Nr. 1 es-Moll op. 4 (1890)
Klavierkonzert Nr. 2 E-Dur op. 38 (1909)
Rhapsodie auf ukrainische Themen für Klavier und Orchester op. 28 (1908)
Violinkonzert d-Moll op. 61 (1915, rev. 1921)
Vokalmusik
"Abendlied", Kantate op. 68 für Tenor, Chor und Orchester (1920)
Lieder
Volksliedbearbeitungen
Klavier- und Kammermusik
Sonate f-Moll op. 27 (1906–08)
Sonatine Des-Dur op. 65 (1917)
12 Etudes d'exécution transcendante op. 11 (1897–1905)
8 Mazurken (1898–1909)
3 Valses-impromptus (Nr. 1 D-Dur op. 23, 1905, Nr. 2 Ges-Dur op. 29, 1908, Nr. 3 E-Dur op. 70, 1919)
Préludes
zahlreiche weitere Klavierstücke
Sextett b-Moll op. 63 für Klavier und Streicher (1915, rev. 1921)
Weblinks
Werkverzeichnis
Einzelnachweise
Komponist (Romantik)
Komponist klassischer Musik (20. Jahrhundert)
Komponist (Russland)
Klassischer Pianist
Hochschullehrer (Sankt Petersburger Konservatorium)
Person (Jaroslawl)
Russischer Emigrant
Russe
Geboren 1859
Gestorben 1924
Mann
Absolvent des Moskauer Konservatoriums | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,891 |
Zwarcie krtaniowe – w fonetyce określenie bezdźwięcznej zwartej spółgłoski krtaniowej. Dźwięk powstaje poprzez zwarcie i rozwarcie strun głosowych (więzadła głosowe) w krtani. Zwarcie utworzone przez struny głosowe zatrzymuje przepływ strumienia wydychanego powietrza. Powietrze jest jednak dalej "tłoczone" przez płuca, więc jego ciśnienie poniżej strun głosowych wzrasta. Po rozwarciu strun głosowych, sprężone powietrze uwalnia się gwałtownie, czemu towarzyszy plozja, tj. charakterystyczny "wybuchowy" dźwięk. W trakcie zwarcia struny głosowe nie mogą drgać, dlatego spółgłoska ta nie ma dźwięcznego odpowiednika.
W alfabecie fonetycznym IPA zwarcie krtaniowe jest oznaczane symbolem [].
W wielu językach głoska ta nie ma statusu fonemu i pojawia się w nagłosie przed samogłoską, stąd bywa nazywana wstępnym zwarciem krtaniowym. Taka sytuacja występuje w języku polskim, w którym na początku wyrazów przed samogłoską słychać wstępne zwarcie krtaniowe, zwłaszcza gdy wyrazy takie wymawiane są dobitnie (np. wyraźnie zaprzeczenie wyrażone poprzez nie-e, właśnie między pierwszym a drugim e występuje zwarcie krtaniowe), w izolacji lub po pauzie, np. w wyrazach on, ale. Rzadziej wymawiane jest w środku wyrazu, najczęściej na początku morfemu po innej samogłosce, np. u-iścić, za-awansowany, prze-intelektualizowany (granicę morfemów oznaczona dywizem, w wymowie ze zwarciem słychać jakby krótką pauzę). Wprowadzanie zwarcia w innych pozycjach między samogłoskami w wyrazach obcego pochodzenia np. boa, teatr itp. uznawane jest za niepoprawne.
Podobna sytuacja występuje w języku niemieckim, gdzie zwarcie krtaniowe wymawia się przed samogłoską akcentowaną w nagłosie morfemu (jest to tzw. Knacklaut).
W niektórych dialektach języka angielskiego zwarcie krtaniowe zastępuje inne spółgłoski zwarte, np. fonem /t/ w cockneyu i Estuary English. Inne przykłady języków używających fonemicznego zwarcia krtaniowego to arabski, hebrajski, maltański, czeczeński, inguski, hawajski, samoański, tahitański, klallam czy nahuatl.
Przykłady
w języku angielskim (RP oraz GA): button [] "przycisk"
w języku arabskim: ﺫﺌﺐ [] "wilk"
w języku czeczeńskim: кхоъ / qo' [] "trzy"
w języku hawajskim: Hawaiʻi [] "Hawaje"
w języku maltańskim: qattus [] "kot"
w języku niemieckim: Beamter [] "urzędnik"
w języku pirahã: baíxi [] "rodzic"
w języku na'vi: Na'vi "lud"
w języku nawaho: ła' [ɬaʔ] "trochę"
Zobacz też
hamza
saltillo
stød
Przypisy
Spółgłoski płucne | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,111 |
{"url":"https:\/\/www.physicsforums.com\/threads\/help-with-taylor-series-maclaurin-series-question.751141\/","text":"# Help with Taylor Series\/Maclaurin Series Question\n\n1. Apr 28, 2014\n\n### student93\n\n1. The problem statement, all variables and given\/known data\n\nProblem is attached in this post.\n\n2. Relevant equations\n\nProblem is attached in this post.\n\n3. The attempt at a solution\n\nI've tried using Maclaurin Series for e^x, and get the term -x^10\/5!, however f(0) = 0 which is not the correct answer. Also taking 10 derivatives seems too burdensome of a task etc. Is there any other method to solve this problem?\n\n#### Attached Files:\n\n\u2022 ###### Screen shot 2014-04-28 at 8.17.30 PM.png\nFile size:\n6.2 KB\nViews:\n103\n2. Apr 28, 2014\n\n### SammyS\n\nStaff Emeritus\n\n$\\displaystyle f^{(10)}(x) = \\frac{d^{10}}{dx^{10}}f(x)\\ .$\n\nIt's not $\\displaystyle \\left(f(x)\\right)^{10}$\n\n3. Apr 28, 2014\n\n### student93\n\nI don't understand what you mean?\n\n4. Apr 28, 2014\n\n### SammyS\n\nStaff Emeritus\nIt's the tenth derivative ... evaluated at x = 0 .\n\n5. Apr 28, 2014\n\n### student93\n\nI know that, but solving for 10 derivatives seems like an impractical way to solve this problem. Is there any other method to solve this problem?\n\n6. Apr 28, 2014\n\n### SammyS\n\nStaff Emeritus\nSolving for 10 derivatives is not really that difficult -- using the MacLaurin Series.\n\nWhat is the 10th derivative of x6, for example?\n\n7. Apr 28, 2014\n\n### student93\n\n10th derivative of x^6 =0, I've tried Maclaurin, and got my 10th powered term as -x^10\/5!, but f(0)=0 and the answer is -10!\/5!\n\n8. Apr 28, 2014\n\n### SammyS\n\nStaff Emeritus\nWhat is the 10th derivative of x10 ?\n\n9. Apr 28, 2014\n\n### student93\n\n3,628,800\n\n10. Apr 28, 2014\n\n### SammyS\n\nStaff Emeritus\nYes, that's 10! . Right.\n\nEven if x = 0.\n\n11. Apr 28, 2014\n\n### student93\n\nSo do I take the derivative of -x^10\/5!?\n\n12. Apr 28, 2014\n\n### SammyS\n\nStaff Emeritus\nWhat is the MacLaurin series for $e^{-x^2} \\ ?$\n\nThe 10th derivative of of the first 5 terms, those with power, 0, 2, 4, 6, 8, are all zero, right?\n\n...\n\n13. Apr 28, 2014\n\n### student93\n\nYes:\n\n1 - x^2 +x^4\/2! - x^6\/3! +x^8\/4! - x^10\/5! ...... etc.\n\n14. Apr 28, 2014\n\n### SammyS\n\nStaff Emeritus\n$1 - x^2 +x^4\/2! - x^6\/3! +x^8\/4! - x^{10}\/5!+x^{12}\/6! \\dots$\n\nThe 10th derivative of that ... evaluated at x = 0 ?\n\n15. Apr 28, 2014\n\n### student93\n\nI understand it now, thanks for the help. (Since the f^(10)(0)\/10! = -1\/5! etc.)\n\n16. Apr 28, 2014\n\n### SammyS\n\nStaff Emeritus\nGood.\n\nThat notation is a bit strange.\n\nIf $f(x) = 1 - x^2 +x^4\/2! - x^6\/3! +x^8\/4! - x^{10}\/5!+x^{12}\/6!\\ \\dots$\n\nthen the 10th derivative is:\n\n$f^{(10)}(x) = - 10!\/5!+(12!\/2)x^{2}\/6!\\ \\dots$\n\nThen $f^{(10)}(0) = - 10!\/5!+(12!\/2)0^{2}\/6!\\ \\dots =- 10!\/5!$","date":"2017-08-23 05:05:09","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\": 0.5795037150382996, \"perplexity\": 6026.438489208937}, \"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-2017-34\/segments\/1502886117519.92\/warc\/CC-MAIN-20170823035753-20170823055753-00676.warc.gz\"}"} | null | null |
class CreateItems < ActiveRecord::Migration[5.0]
def change
create_table :items do |t|
t.string :title
t.string :photo
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,925 |
We may have room to grow in the rankings, but don't write Dallas-Fort Worth off as a leader in sustainable building practices. Industry experts say the region is underrated.
Here's how North Texas builders, designers, and cities are pushing green practices forward.
A year ago, Dallas-Fort Worth might not have come to mind when ranking the most sustainable regions, but progressive city codes, innovative developers and designers, and large corporate companies are changing that.
The word "green" as a moniker for sustainability and environmentally conscious real estate typically elicits thoughts of coastal cities such as San Francisco or Boston. But don't write DFW off just yet.
Architects, developers, and thought leaders within the sustainability community say the region is underrated. While the Dallas-Fort Worth region may have room to grow in the rankings of the nation's greenest cities — those that use the most renewable energy, offer the best public transit, or have an environmental impact at the center of many public policies — it's just getting started.
"In some areas, we're ahead of a lot of the country," U.S. Green Building Council-Texas Chapter Executive Director Jonathan Kraatz says, citing public policies in the region's largest cities. Dallas was one of the first major cities to champion and pass comprehensive standards for sustainable building practices in 2008.
The Fort Worth Better Buildings Challenge, sponsored by the U.S. Department of Energy, aims to decrease energy consumption by one-fifth by 2020. Many other local cities have adopted incentive-based programs to encourage developers to pursue third-party certifications, such as the USGBC's Leadership in Energy and Environmental Design (LEED) designations.
And it's working. Dallas-Fort Worth has 149,146,781 square feet of a LEED-certified real estate, according to the USGBC, accounting for 682 commercial projects.
This summer, Site Selection magazine named Dallas-Fort Worth-Arlington as No. 8 on its list of the Top 10 Metros in its 2018 Sustainability Rankings. And, a recent Abodo study ranked Dallas-Fort Worth-Arlington as the ninth highest metro area for LEED-certified real estate by square footage.
LEED, first launched as a pilot in 1998, is a credit-based certification that has many versions to account for project types (i.e. residential or commercial) and types of certification (i.e. building design and construction or operations and maintenance).
"Our concern is the built environment, and many pieces go into that—energy use, materials, indoor air quality, water use," Kraatz says. "We're looking at having a built environment that is better for the planet and the people on it, but it's also a profitable venture for those operating it. If those things don't balance out, none will survive." Approaching the latter—profitability—often resonates more with Dallas-Fort Worth decision makers.
"Dallas is a very business-oriented city and … our cities are going to have to become more regenerative to continue to attract and retain corporate clients," HKS Principal and COO Kirk Teske says.
When considering how DFW stacks up to other metros, Teske says demand for "green" projects is still relatively low, but rethinking how designers approach conversations about sustainability can have a positive response. When designers or developers can prove to building owners, lenders, or investors that, say, lowering energy or water usage positively impacts the bottom line, they're more likely to pursue environmentally conscious practices.
Dallas Innovates, Every Day: Sign up to keep your eye on what's new and next in Dallas-Fort Worth, every day.
Finding the right words to use, and finding the things the client can be most passionate about can make a difference says 5G Studio Collaborative Associate Principal Christine Robbins-Elrod. Depending on who you're talking to, "sustainability" may be a controversial word, "but resiliency — [such as] preparedness for extreme weather events — is something we all want," she says.
Buildings are capable of significantly impacting energy consumption when it comes to factors such as production, operation, and maintenance. Sustainable construction incorporates environmentally efficient elements that contribute positively to the future of the area, such as lowering greenhouse gas emissions.
Successful sustainable construction meets economic and social needs while remaining ecologically conscious—but that doesn't necessarily mean it's LEED certified.
Some industry experts in DFW say that LEED doesn't have as much appeal as it did a decade ago. Kyle Whitesell, executive vice president of Arlington-based Bob Moore Construction, says it's mainly large corporations that take the LEED route, while smaller clients steer towards meeting baseline state environmental codes. Sustainability Manager at CxL Building Services Jolene Young, who works with numerous construction companies in the DFW area, agreed.
"The biggest trend we've seen is that city, county, and state environmental code regulations have been catching up to LEED certification standards the last few years," Whitesell says.
While DFW is on its way to a more sustainable future, major steps need to be taken that go beyond the fundamentals — a challenge that will require tapping into renewable solutions, according to Corgan Design Director Chuck Armstrong.
Beyond the environmental impact, sustainability can offer a competitive advantage for companies. As recruiting and retaining top-notch talent becomes ever more important, businesses are increasingly looking to differentiate themselves and their office space. Sustainability and wellness can help employers do that, experts say. Employee wellness — a close cousin of sustainability — has emerged as a key differentiator.
Businesses that offer sit-stand desks, access to walking trails or fitness amenities, and natural daylight in workspaces, have a leg up on ones that don't.
And as the wellness field gains traction, more and more academic research emerges proving that employees are more productive and healthier in wellness-minded work environments, thereby saving employers on turnover and health-care costs.
He's being asked by more and more local and national clients about certifications beyond LEED, such as Living Future Institute's (ILFI) Zero Energy Building (ZEB) Certification or Delos' Well Building Standard. "If CEOs would understand this — it has a bigger impact on the bottom line," Gorthy says.
In Dallas-Fort Worth, both sustainability and wellness are poised to gain traction for two reasons. First, the region is densifying and becoming more urban. "Sustainability standards often come into play because of transit or density. Texas has always had more land available. But as [Dallas-Fort Worth] has gotten denser in the last five or 10 years, now is the time people are thinking about these strategies," Gorthy says.
The Bush Presidential Center at Southern Methodist University in Dallas achieved Platinum certification by the U.S. Green Building Council—the first presidential library to achieve that status. According to its website, the center features green roofing systems that reduce heating and cooling demands, solar panels for producing electricity and hot water, building materials that were sourced from the North Texas region to lower transportation impacts, and a rainwater recycling system that provides 50 percent of the irrigation needs of the native Texas landscaping.
Second, corporate office users relocating from elsewhere are setting the pace for the region. Larger, corporate companies — generally build-to-suit office users—are an easy sell for sustainability and wellness measures. As users relocate to the region, they bring along their desires for less environmental impact and increased wellness for employees. HKS's Teske, DPR's Gorthy, and 5G's Robbins-Elrod agreed that pursuing sustainability or wellness goals — spanning commercial office, data centers, hospitality, and more — is still largely client driven.
In many instances, Texas energy codes have outpaced LEED standards, HKS's Teske says. "It's time to move beyond sustainability and toward a more regenerative mind thinking," he says. And as more and more projects serve as a litmus test for proving a slew of positive impacts—increased returns, lower energy bills, and operating expenses, more efficient employees, stronger recruitment and retention—more developers will pursue third-party certifications.
Though it may take a few more pioneering projects spanning varying asset classes from multitenant offices to retail stores in order to reach a critical mass of environmentally conscious development.
Associate Editor Alex Edwards contributed to this report.
A version of this article appeared in the Dallas-Fort Worth Real Estate Review, Summer 2018.
It's nice to see green building innovation get some attention in DFW – I recommend that you also spotlight WELL Buildings, which are the next frontier, focusing on human movement and well-being within the buildings. Our solar-powered coworking space in the Cedars is pursuing LEED Platinum and WELL Building certification, bringing green building and cutting edge sustainability to the DFW startup ecosystem! | {
"redpajama_set_name": "RedPajamaC4"
} | 3,204 |
{"url":"https:\/\/eslprep.com\/how-many-fyfsjzy\/dab9ec-formal-charge-calculator","text":"# formal charge calculator\n\nThe formal charge of an atom in a molecule is the hypotheticalcharge the atom would have if we could redistribute the electrons in the bonds evenly between the atoms. The formal charge of an atom can be determined by the following formula: $FC = V - (N + \\frac{B}{2})$ H C= = o H The formal charge on carbon is o anbrecano1 is waiting for your help. Who is free talk with me A beaker contains a mixture of ammonium chloride, ink and iron fillings. One Nitrogen atom = 1 x -3 (nitrogen's charge) = -3 Three hydrogen atoms = 3 x +1 (hydrogen's charge) = 3 -3 + 3 = 0 (net charge of NH_3) If you refer to a periodic table you'll see columns. With over 200+ pages of content (and growing), we hope that you dive deep into the realms of chemistry and understand how the structure and composition of matter explain our world. For calculating the formal charge of an atom in any compound, you need to know what is the bonding structure of the compound. To assist with this problem, chemists often calculate the formal charge of each atom. plz mark as brainliest . Calculate the formal charge on each atom in the following structure. Lone Pairs = lone electrons sitting on the atom. Examples Of Formal Charge. Home\u00a0 | \u00a0Contact\u00a0 | \u00a0About\u00a0 | \u00a0Amazon Disclaimer\u00a0 | \u00a0Terms and Conditions\u00a0 | \u00a0Privacy Policy\u00a0 | \u00a0Legal Disclaimer\u00a0 |\u00a0 Sitemap. See this post of the nitrate resonance structures. It is actually spread out through the other atoms and is not only on the one atom. Net charge is the sum of all formal charges of the atoms in a molecule. Formal Charge= Valence Electrons - 0.5Bonding Electrons - Nonbonding Electrons. To calculate formal charge on an atom, we use the formula: Formal Charge = Valence Electrons - Non-Bonding Electrons - {eq}\\frac {1} {2} {\/eq} Bonding Electrons. Formal charge is the charge of an atom in a molecule. The formal charge on each O- atom of O3 molecule is given as,The Lewis structure of O3 may be drawn as:The atoms have been numbered as 1, 2 and 3. Thus, we calculate formal charge as follows: formal charge=# valence shell electrons (free at\u2026 Show transcribed image text The following equation is used to calculate the formal charge of an atom. The formal charge of an atom is the difference between the number of valence electrons in the free atom adnd the number of electrons assigned to that atom in lewis structure; Formal charge = V.E of free atom - VE assigned in lewis structure. Formal charge calculation: Significance of formal charge: Formal charge of CO molecule in the Lewis structure . It can be obtained through: )on central O-atom numbered. eval(ez_write_tag([[728,90],'calculator_academy-medrectangle-3','ezslot_8',169,'0','0'])); The following equation is used to calculate the formal charge of an atom. Oxygen (O) is in group 16, so that means it has 6 valence electrons. These hydrogens are all zero. The formal charge is the electric charge an atom would have if all the electrons were shared equally. The term \u201cformal\u201d means that this charge is not necessarily on the presented atom because in some cases, it is also prevalent on other atoms present in the molecule. Formal charge is calculated using the equation: FC = e V - e N - e B \/2 FC = V \u2013 ( LP +.5 * BE) Where FC is the formal charge Identifying a formal charge involves: The formal charge on an atom can be calculated using the following mathematical equation. In chemistry, a formal charge (FC) is the charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity. A number of bonding electrons: 2 for H, 6 for C, [Formal charge]H = 1 \u2013 (1\/2) \u00d7 2 \u2013 0 = 0 \u21d2 This applies to each hydrogen. calculate the formal charge of an atom in an organic molecule or ion. Formal Charge = (Valence electrons) - (Nonbonding valence electrons) - (Bonding electrons \/ 2) For HCl, if we want to find the formal charge on the H, we know that first, hydrogen has 1 valence electron, and in the covalent bond it forms with Cl, it has 0 \u2018nonbonding valence electrons\u2019 because the 1 \u2026 Formal charge assumes any shared electrons are equally shared between the two bonded atoms. formal charge = 4 - 0 - 8\/2 = 0 . Formal charge varies when you look at resonance structure. The formal charge of carbon is 0. A number of bonding electrons: 2 for H, 8 for C, A number of non-bonding electrons: 0 for both H and C. [Formal charge]H = 1 \u2013 (1\/2) \u00d7 2 \u2013 0 = 0 \u21d2 This applies to each hydrogen. The sum of all the formal charges should equal the total charge \u2026 Formal charge of FC is the difference between the number of valence electrons of each atom and the number of electrons the atom is associated with. Formula for formal charge : The Lewis-dot structure are shown below. Formal charge of ammonium cation ( NH4+ ) molecule in the Lewis structure . I would love to hear what you have to think. - [Voiceover] In this video we'll assign formal charge to nitrogen, and just to remind you of the definition for formal charge, formal charge is equal to the number of valance electrons in the free atom minus the number of valence electrons in the bonded atom. When determining the best Lewis structure (or predominant resonance structure) for a molecule, the structure is chosen such that the formal charge on each of the atoms is as close to zero \u2026 Formal charge is calculated using the valence, lone pair, and bound electrons of the atom to it\u2019s surrounding molecule. Formal Charge and Resonance NAME: Formal charge is an accounting procedure. To view this video please enable JavaScript, and consider upgrading to a Count all of its lone pair electrons, and half of its bonding electrons. This is because it has five valence electrons but it owns six \u2013 two lone pairs and one electron from each bond: How to Identify and Calculate the Formal Charge. calculation of formal charge Definition Formal charge is defined as the charge that is present on the atom in a molecule. The structure is in brackets with a superscript minus after the right bracket. Formal charge (F.C. For example, the nitrogen below has a formal charge of negative one. How to calculate formal charge Once we add all the formal charges for the atoms in the Lewis structure, we should get a value equal to the actual charge of the molecule or ion. Drawing the Lewis structure of the molecule reveals that it can be sketched out in three different ways. A number of bonding electrons: 2 for H, 6 for C. A number of non-bonding electrons: 0 for both H and C. [Formal charge]H = 1 \u2013 (1\/2) \u00d7 2 \u2013 0 = 0 \u21d2 This applies to each hydrogen. To calculate formal charge of an atom, use the equation below. It is calculated by assigning electrons to individual atoms in a molecule according to different rules. CH 3+, methyl cation. The nonbonding electrons, on the other hand, are the unshared electrons and these are shown as dots. Save my name, email, and website in this browser for the next time I comment. The elements in hydrogen's column have a +1 charge. The formula of formal charge, F C = V \u2212 N \u2212 2 B where V the number of valence electrons of the neutral atom in isolation (in its ground state); N is the number of non-bonding valence electrons on this atom in the molecule, and B is the total number of electrons shared in bonds with other atoms in the molecule. The formal charge is the electrical charge of an individual atom that is contained within a larger molecule. It helps to estimate the electric charge distribution within a molecule. on end O-atom numbered 3.Hence, we represent O3 along with the formal charges as follows: Another way of saying this is that formal charge results when we take the number of valence electrons of a neutral atom, subtract the nonbonding electrons, and then subtract the number of bonds connected to that atom in the Lewis structure. Formal Charge Formula. Formal charge of O3 molecule in the Lewis structure . Comments: Counting electrons to calculate formal charges is different from counting electrons for octets. arusoni456 arusoni456 Answer: It should be -1,-1,0 . Now we have to calculate the formal charges of each oxygen atom. An atom can have the following charges: positive, negative, or neutral, depending on the electron distribution. This is often useful for understanding or predicting reactivity. FOR Example: In SO2 It allows chemists to determine the location of charge in a molecule as well as compare how good a Lewis structure might be. There are 4 dots around oxygen, so that means it has 4 nonbonding electrons. Lewis structures also show how atoms in the molecule are bonded. Let\u2019s look at an example of formal charge calculation: Carbon dioxide, CO2, is a neutral molecule that possesses 16 electrons in its valence shell. Now that we know the formal charge formula, we can move onto an example and understand how to calculate formal charge \u2026 Definition: The charges placed on different atoms in the Lewis structure of a molecule is called formal charge. Solution for 5. If it is a neutral molecule, then the sum of all the formal charges must equal zero. One dot is equal to one nonbonding electron. Formal charge (F.C.) Calculate the formal charge on each element in the Lewis structure. Formal Charge = [# valence electrons on neutral atom] \u2013 [ (# lone electron pairs) + (\u00bd # bonding electrons)] Valence electrons = corresponds to the group number of the periodic table (for representative elements). supports HTML5 video, Calculator Academy\u00a9 - All Rights Reserved 2020, how to calculate formal charge from lewis structure, calculate the formal charge of each oxygen atom of ozone molecule, how to calculate formal charge of an atom, determine the formal charge of nitrogen in this structure, how to find the formal charge of a lewis structure, determine the formal charges on the highlighted atoms, how to find the formal charge of an atom in a lewis structure, calculate the formal charge on each atom in o3, how to find formal charges on lewis structures, how to find formal charge from lewis structure, how to find the formal charge of a compound, how to calculate the formal charge of an atom, calculate the formal charges of the atoms in co, calculating formal charge from lewis structure, what is formal charge and how is it calculated. - To assign formal charge, you take the number of valence electrons in the free atom, or the number of valence electrons the atom is supposed to have, and from that, you subtract the number of valence electrons in the bonded atom, or the number of valence electrons the atom actually has in the drawing. Net charge is the charge of the molecule. Take the valence number of the atom and subtract the number of bonds and the number of non-bonding electrons. What is formal charge ? Calculate the formal charge of N atom in the following ions compounds: a) NH4* b) CH2N2 Identifying formal charges helps you keep track of the electrons. To find formal charges in a Lewis structure, for each atom, you should count how many electrons it \"owns\". There is NCO, with double bonds between all atoms and two lone pairs at the N atom and the O atom. The formal charge is the charge on the atom in the molecule. Add your answer and earn points. We half the value of bonding electrons because the bond exists between two electrons. These hydrogens are all zero. If you have any questions or would like to share your reviews on the How to calculate formal charge, then comment down below. One line corresponds to two electrons. New questions in Chemistry. Explanation: hope you like it . The valence electrons are the electrons in the outermost shell of the atom. [Formal charge]C = 4 \u2013 (1\/2) \u00d7 6 \u2013 0 = 4 \u2013 3 \u2013 0 = +1. [Formal charge]C = 4 \u2013 (1\/2) \u00d7 6 \u2013 0 = 4 \u2013 3 \u2013 0 = +1, A number of non-bonding electrons: 0 for H, 2 for C, [Formal charge]C = 4 \u2013 (1\/2) \u00d7 6 \u2013 2 = 4 \u2013 3 \u2013 2 = -1. These hydrogens are all zero. identify and recognize the bonding patterns for atoms of carbon, hydrogen, oxygen, nitrogen and the halogens that have a formal charge of zero. Formal charge is a technique to identify which resonance structure is the more correct structure. The most correct Lewis structure will be the structure where the formal charges are evenly distributed throughout the molecule. Enter the total number of valence electrons, lone pairs of electrons, and total number of bound electrons to calculate the formal charge. Formal Charge = Group Number \u2212 (number of nonbonding electrons + number of bonds) Personally I would suggest you use logic rather than memorizing an equation that you can easily forget. web browser that Here is the formula: Formal Charge = [V \u2013 N \u2013 (B\/2)] In this formula, V stands for the number of valence electrons of that atom (these are the electrons that revolve in the outermost orbit of the atom), N stands for the number of non-bonded electrons, and B stands for the number of electrons that are a p\u2026 Formal charge (F.C.) Oxygen (O) is in group 16, so that means it has 6 valence electrons. Step 2: Calculate the Formal Charge of Oxygen on the Left. ot all atoms within a neutral molecule need be neutral. The difference between the atom's number of valence electrons and the number it owns is the formal charge. ChemistryScore is an online resource created for anyone interested in learning chemistry online. They can be drawn as lines (bonds) or dots (electrons). 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\section{Introduction}
In the past few years, gamma-ray observations revealed the possibility of dark matter annihilation in our galaxy. Several groups claim that the excess GeV gamma rays emitted from our Galactic center can be best explained by dark matter annihilation through $b\bar{b}$ channel \cite{Daylan,Abazajian,Calore,Calore2}. The rest mass of dark matter and the required annihilation cross section are $m=30-50$ GeV and $<\sigma v>=(1.4-7.5)\times 10^{-26}$ cm$^3$ s$^{-1}$ respectively \cite{Daylan,Abazajian,Calore2}. However, recent studies of the Milky Way dwarf spheroidal satellite galaxies (MW dSphs) challenge the above claim. The constrained annihilation cross sections lie below the canonical thermal relic cross section ($<\sigma v> \approx 2.2\times 10^{-26}$ cm$^3$ s$^{-1}$) for dark matter of mass $\le 100$ GeV annihilating via quark and $\tau$-lepton channels \cite{Steigman,Ackermann}. As a result, only a very small parameter space remains possible for the dark matter interpretation of the GeV gamma-ray excess. Therefore, it is very important for us to search another independent observation to verify the claim.
Besides gamma-ray observations, radio observation is another way to test the dark matter annihilation model. It is commonly believed that many high-energy electron-positron pairs are produced from dark matter annihilation. These high-energy electrons and positrons would emit strong synchrotron radiation when there is a strong magnetic field. In fact, radio observations can give a stringent constraint on annihilating dark matter. For example, using the radio observational data obtained in \cite{Davies} (at 408 MHz from the inner 4 arcsecond cone around Sgr A*) can give a very strong constraint on the dark matter annihilation cross section \cite{Regis,Bertone}. For $m=40$ GeV, the annihilation cross section of the $b\bar{b}$ channel is $<\sigma v> \le 10^{-27}$ cm$^3$ s$^{-1}$ \cite{Bertone,Cholis}. However, the analyses of the data from this very small region have large uncertainties, including the uncertainties of the magnetic field strength and the complicated process of the electron and positron diffusion near the Milky Way center. Moreover, as pointed out in \cite{Cholis}, the effect of inverse Compton scattering might significantly affect the constraints obtained. Some other radio observations also provide good constraints on annihilating dark matter \cite{Borriello,Hooper,Storm,Laha,Wechakama}. However, due to the observational limitations and uncertainties, these constraints are generally less stringent.
Besides our Galaxy, M31 is also a good candidate because it is a nearby and well-studied galaxy. Recent radio observations of M31 constrain the dark matter mass $m \ge 100$ GeV and $m \ge 55$ GeV annihilating via $b\bar{b}$ and $\tau^+\tau^-$ channels respectively for $<\sigma v>=3 \times 10^{-26}$ cm$^3$ s$^{-1}$ \cite{Egorov}. However, since the central magnetic field and the dark matter density are poorly constrained for that small observed region ($\approx 1$ kpc), the results have large uncertainties. In this article, we revisit the constraints on annihilating dark matter by using the radio data from \cite{Giebubel}, which originate from a larger region ($\approx 17.5$ kpc) of M31. Also, we model the dark matter density profile of M31 by using the latest data from M31 rotation curve. We mainly focus on six different standard model annihilation channels ($e^+e^-, \mu^+\mu^-, \tau^+\tau^-, u\bar{u}, b\bar{b}$ and $W^+W^-$).
\section{Radio observations of M31}
The group in \cite{Giebubel} uses the Westerbork Synthesis Radio Telescope (WSRT) to observe M31 in the frequency range $\nu=310-376$ MHz. After analyzing the radio data, a uniformly weighted average of the final total power image is obtained for a region of 17.4 kpc. The total flux density $F=(4 \pi D^2)^{-1}dW/d\nu$ integrated over the radius interval $R=0-17.4$ kpc is $F=10.6 \pm 0.7$ Jy, where $D$ is the distance of M31. It is equivalent to the total energy flux $S=\nu F \le 4 \times 10^{-14}$ erg cm$^{-2}$ s$^{-1}$ (2$\sigma$ upper limit). If we assume that all the radio radiation originates from the synchrotron radiation of the electron and positron pairs produced by dark matter annihilation, the above upper limit of the total energy flux can be used to constrain the cross section of dark matter annihilation (no spectral index has to be assumed). From the analyses in \cite{Egorov}, synchrotron radiation dominates the cooling rate of the electron and positron pairs. Therefore, we neglect the effect of the inverse Compton scattering. Also, the cooling processes by other mechanisms such as bremsstrahlung, ionization, scattering, advection loss and re-acceleration are negligible. These processes just contribute 1\% of the total cooling rate. Furthermore, the diffusion time scale of the electron and positron pairs is much longer than the cooling time scale. For a 1 GeV electron, the diffusion and cooling time scales are $t_D \sim R^2/D_0 \sim 10^{17}$ s and $t_c \sim 1/b \sim 10^{16}$ s respectively \cite{Colafrancesco}, where $D_0 \sim 10^{28}$ cm$^2$ s$^{-1}$ is the diffusion coefficient of M31 \cite{Berkhuijsen} and $b \sim 10^{16}$ s$^{-1}$ is the cooling rate. Therefore, the diffusion term can be neglected and the injected spectrum of the electron and positron pairs is proportional to the source spectrum \cite{Storm}.
Since the diffusion process is not important and the radio emissivity is mainly determined by the peak radio frequency (monochromatic approximation), the total synchrotron radiation energy flux of the electron and positron pairs produced by dark matter annihilation is given by \cite{Bertone,Profumo}:
\begin{equation}
S \approx \frac{1}{4 \pi D^2} \left[ \frac{9 \sqrt{3}<\sigma v>}{2m^2} \int_0^R 4 \pi r^2 \rho_{DM}^2EY(E)dr \right],
\end{equation}
where $D=785 \pm 25$ kpc \cite{Egorov}, $\rho_{DM}$ is the dark matter density profile of M31, $E=0.43(\nu/{\rm GHz})^{1/2}(B/{\rm mG})^{-1/2}$ GeV, and $Y(E)=\int_E^m(dN_e/dE')dE'$. Here, $B$ is the magnetic field strength in M31 and $dN_e/dE'$ is the electron or positron spectrum of dark matter annihilation. The electron or positron spectrum for each annihilation channel can be obtained in \cite{Cirelli}. The magnetic field strength in M31 is quite uniform for $r=6-14$ kpc, which is about $4.6-5.2$ $\mu$G \cite{Fletcher}. For the outer region, the magnetic field is about 4 $\mu$G with a weak radial dependence \cite{Granados}. In the following analysis, we follow \cite{Giebubel} to use $B=5 \pm 1$ $\mu$G for M31. Therefore, the peak energy used in Eq.~(1) is $E=3.1-4.2$ GeV. Since the magnetic field is much stronger near the center of M31, the larger value of $B$ would give a smaller value of $E$ and a larger value of $Y(E)$. However, it is not easy to determine the magnetic field strength profile precisely near the M31 center. Studies in \cite{Egorov,Giebubel2} point out that the magnetic field structure of the central region in M31 is very complicated. The magnetic field strength can vary from 10 $\mu$G to 50 $\mu$G in different regions \cite{Egorov,Giebubel2}. In fact, the dependence of the magnetic strength in Eq.~(1) is quite weak. A factor of 10 larger in $B$ would just give less than a few percent larger in $S$. Therefore, we use a constant profile of $B=5 \pm 1$ $\mu$B to model the magnetic field strength of M31. This would underestimate the total radio flux $S$ calculated by Eq.~(1). Nevertheless, the underestimated value of $B$ can give a conservative lower limit of $S$ for dark matter annihilation.
For the dark matter density profile, recent analysis of the M31 rotation curve gives a robust set of parameters with small errors. Sofue (2015) \cite{Sofue} shows that the NFW profile \cite{Navarro} is likely to be a realistic approximation to model the dark matter density profile of M31:
\begin{equation}
\rho_{DM}=\frac{\rho_sr_s^3}{r(r_s+r)^2},
\end{equation}
where $\rho_s=(2.23 \pm 0.24) \times 10^{-3}M_{\odot}$ pc$^{-3}$ and $r_s=34.6 \pm 2.1$ kpc \cite{Sofue}. Besides the NFW profile, we also examine two other popular profiles, the Burkert profile $\rho_{DM}=\rho_sr_s^3[(r_s+r)(r_s^2+r^2)]^{-1}$ and the Einasto profile $\rho_{DM}=\rho_s\exp\{-17.668[(r/r_s)^{1/6}-1] \}$ \cite{Tamm}. The corresponding parameters for the Burkert profile and the Einasto profile are $(\rho_s,r_s)=(3.68 \pm 0.40 \times 10^{-2}M_{\odot}~{\rm pc}^{-3},9.06 \pm 0.53~{\rm kpc})$ and $(\rho_s,r_s)=(8.12 \pm 0.16 \times 10^{-6}M_{\odot}~{\rm pc}^{-3},178\pm 18~{\rm kpc})$ respectively \cite{Tamm}.
By putting the above different density profiles into Eq.~(1) and using the lower limits of $\rho_s$ and $r_s$ and the upper limit of $D$, we can get an analytic expression for the lower limit of $S$:
\begin{equation}
S \ge S_0 \left( \frac{<\sigma v>}{2.2 \times 10^{-26}~\rm cm^3~s^{-1}} \right) \left(\frac{m}{\rm GeV}\right)^{-2} \left( \frac{E}{\rm GeV} \right)Y(E),
\end{equation}
where $S_0=1.34 \times 10^{-10}$ erg cm$^{-2}$ s$^{-1}$ for the NFW profile, $S_0=1.12 \times 10^{-10}$ erg cm$^{-2}$ s$^{-1}$ for the Burkert profile and $S_0=2.89 \times 10^{-10}$ erg cm$^{-2}$ s$^{-1}$ for the Einasto profile. By using the $Y(E)$ values shown in Fig.~1 and assuming the canonical thermal relic annihilation cross section, we can get the lower limit of $S$ for different annihilation channels and different density profiles (see Figs.~2-4). For the most popular $b\bar{b}$ annihilation channel, the lower bound of $m$ is 120 GeV for the NFW profile. This is a bit tighter than the constraint obtained in the gamma-ray observations of the MW dSphs ($m \ge 100$ GeV) \cite{Ackermann} and the previous radio observation of M31 ($m \ge 90$ GeV for the $b\bar{b}$ channel with $<\sigma v>=2.2 \times 10^{-26}$ cm$^3$ s$^{-1}$) \cite{Egorov}. If we use the Burkert profile, the lower limits would be smaller by about 10-20\%. Although the Burkert profile is not a robust profile for large galaxy such as M31, we still consider these lower limits the most conservative limits of our analyses. In table 1, we summarize the conservative lower limits of the dark matter mass for $<\sigma v>=2.2 \times 10^{-26}$ cm$^3$ s$^{-1}$.
\begin{table}
\caption{Lower limits of the dark matter mass for different dark matter density profiles. Here, we assume $<\sigma v>=2.2 \times 10^{-26}$ cm$^3$ s$^{-1}$.}
\label{table1}
\begin{tabular}{@{}lccc}
\hline
& NFW & Burkert & Einasto \\
\hline
$e^+e^-$ & 190 GeV & 170 GeV & 270 GeV \\
$\mu^+\mu^-$ & 100 GeV & 90 GeV & 140 GeV \\
$\tau^+\tau^-$ & 90 GeV & 80 GeV & 140 GeV \\
$u\bar{u}$ & 110 GeV & 90 GeV & 230 GeV \\
$b\bar{b}$ & 120 GeV & 90 GeV & 250 GeV \\
$W^+W^-$ & 90 GeV & 90 GeV & 200 GeV \\
\hline
\end{tabular}
\end{table}
If we assume that the annihilation cross section is a free parameter, we can compare our results with the constraints obtained in the recent gamma-ray observations of the MW dSphs \cite{Ackermann} and the Milky Way center \cite{Calore2,Abazajian2}. In Fig.~5, our upper limits are 1-2 orders of magnitude tighter than the 95\% C.L. upper limits obtained in the MW dSphs for the $e^+e^-$ and $\mu^+\mu^-$ channels for $m=10-1000$ GeV. It is because a large amount of high-energy electron-positron pairs is produced in these two channels. The predicted synchrotron radiation signals are very large and hence the constraints are more stringent. For the other channels, our results are generally tighter when $m$ is smaller than $\sim 100$ GeV (except the $u\bar{u}$ channel). In Fig.~6, we compare our results with the recent empirical fits of the Galactic GeV excess obtained in \cite{Calore2,Abazajian2}. We can see that our constraints rule out the best models of dark matter interpretation of the GeV excess for the $b\bar{b}$, $\mu^+\mu^-$ and $\tau^+\tau^-$ channels (by at least 2$\sigma$). Nevertheless, the parameters of the $u\bar{u}$ channel can still satisfy our constraints marginally. Since the studies in \cite{Ackermann,Calore2} assume the NFW profile to calculate the limits, we also use the NFW dark matter profile to do the analysis.
If we allow mixed annihilations, Calore et al. (2015) \cite{Calore2} predict that the ratio $b\bar{b}:c\bar{c}:\tau^+\tau^-=0.87:0.08:0.05$ ($bc\tau$ model) would be the best to account for the Milky Way GeV gamma-ray excess. A good fit can also be obtained if the annihilation products are $\mu^+\mu^-$ and $\tau^+\tau^-$ ($\mu\tau$ model) for $m \sim 50$ GeV with the branching ratio of $\mu^+\mu^-$ $\ge 0.6$ \cite{Calore2}. If we assume $m=50$ GeV, our results rule out the $bc\tau$ model and $\mu\tau$ model by the 1$\sigma$ and 2$\sigma$ radio upper limit respectively. Therefore, based on our analyses, our new constraints do not favor the dark matter interpretation of the Milky Way GeV gamma-ray excess. Our results support the conclusion drawn from the Fermi-LAT gamma-ray observations of the MW dSphs \cite{Ackermann}.
\begin{figure}
\vskip 10mm
\includegraphics[width=82mm]{y.eps}
\caption{The graph of $Y(E)$ versus $m$ for the six annihilation channels. Here, we use $E=3.5$ GeV.}
\vskip 10mm
\end{figure}
\begin{figure}
\vskip 10mm
\includegraphics[width=82mm]{S.eps}
\caption{The minimum values of $S$ for $<\sigma v>=2.2 \times 10^{-26}$ cm$^3$ s$^{-1}$ with the NFW density profile. The dashed line is the 2$\sigma$ upper limit of the radio observations \cite{Giebubel}.}
\vskip 10mm
\end{figure}
\begin{figure}
\vskip 10mm
\includegraphics[width=82mm]{S_b.eps}
\caption{The minimum values of $S$ for $<\sigma v>=2.2 \times 10^{-26}$ cm$^3$ s$^{-1}$ with the Burkert density profile. The dashed line is the 2$\sigma$ upper limit of the radio observations \cite{Giebubel}.}
\vskip 10mm
\end{figure}
\begin{figure}
\vskip 10mm
\includegraphics[width=82mm]{S_e.eps}
\caption{The minimum values of $S$ for $<\sigma v>=2.2 \times 10^{-26}$ cm$^3$ s$^{-1}$ with the Einasto density profile. The dashed line is the 2$\sigma$ upper limit of the radio observations \cite{Giebubel}.}
\vskip 10mm
\end{figure}
\begin{figure}
\vskip 10mm
\includegraphics[width=82mm]{radio_dwarf.eps}
\caption{The upper limits of the annihilation cross sections for the six annihilation channels (assumed NFW profile) (black: our results; red: gamma-ray observations of Milky Way dwarf spheroidal satellite galaxies \cite{Ackermann}.)}
\vskip 10mm
\end{figure}
\begin{figure}
\vskip 10mm
\includegraphics[width=82mm]{sigma.eps}
\caption{The upper limits of the annihilation cross sections for the six annihilation channels (assumed NFW profile). The data points with 1$\sigma$ error bars are the results obtained in \cite{Calore2,Abazajian2} for the dark matter interpretation of the GeV excess. The dotted line is the canonical thermal relic cross section.}
\vskip 10mm
\end{figure}
\section{Discussion}
In this article, we revisit the radio constraints of annihilating dark matter by using the M31 radio data in \cite{Giebubel}. Our results generally give more stringent constraints on annihilation cross sections for the six standard model annihilation channels. Here, the uncertainties of the parameters involved in the analyses, such as the scale density $\rho_s$, the scale radius $r_s$, magnetic field strength $B$ and the observed radio flux $S$, are relatively small compared with previous studies. Since the magnetic field strength is greater in the center of M31, the radio flux emitted by the electron-positron pairs produced from dark matter annihilation should be larger. Therefore, our assumption of the constant magnetic field strength gives a conservative lower limits of the radio emission. We find that all of the conservative lower limits are larger than the 2$\sigma$ upper limits of the observed flux for $m \ge 80$ GeV if we assume a canonical thermal relic cross section. It is consistent with the results obtained by gamma-ray observations of the MW dSphs \cite{Ackermann}. Therefore, our result provides an independent support of the recent analysis that most of the standard $10-100$ GeV dark matter annihilation models should be ruled out.
If we release the annihilation cross section to be a free parameter, we also obtain constraints of the annihilation cross sections for the six channels. Generally speaking, our constraints are more stringent than that obtained in \cite{Ackermann}, especially for the $e^+e^-$ channel, $\mu^+\mu^-$ channel, $\tau^+\tau^-$ channel for $m \le 140$ GeV, $b\bar{b}$ channel for $m \approx 40-60$ GeV and $W^+W^-$ for $m \le 300$ GeV. These constraints are useful to examine the most popular dark matter interpretation of the GeV excess \cite{Calore2,Abazajian2}, such as the $b\bar{b}$ and $\tau^+\tau^-$ channels. Based on our analyses, most of the models are ruled out except the $u\bar{u}$ model. Our analyses also show that the $bc\tau$ mixed annihilation model and the $\mu\tau$ mixed annihilation model exceed the 1$\sigma$ and 2$\sigma$ upper limit of the radio flux respectively. If we can get some better radio data of M31 or precisely determine the magnetic field profile in the future, more stringent constraints can be obtained.
\section{acknowledgements}
This work is partially supported by a grant from the Education University of Hong Kong (Project No.:RG57/2015-2016R).
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,297 |
\section{Introduction}
In recent years, developments in the field of ultracold atomic gases have considerably enlarged the possibilities for exploring the physics of strongly correlated systems~\cite{bloch_cold_atoms_optical_lattices_review}. For instance, the study of quantum phase transitions, a subject of continuous theoretical interest, has been strongly stimulated by the experimental observation of the superfluid to Mott insulator transition using optical lattices~\cite{greiner_transition_superfluid_mott}. Indeed, ultracold atom systems offer us an unprecedented
control over the system parameters, which can allow us to ultimately understand the physics of
very hard problems such as the phase diagram of the Hubbard model
in two-dimensions~\cite{ho_attractive_hubbard}.
A particularly interesting and fertile arena is the study of disordered ultra-cold atoms. Random potentials can be introduced in a controlled way by laser beams generating speckle patterns~\cite{lye_speckle_disorder,%
clement_speckle_transport,fort_speckle_expansion,schulte_anderson_localization,chen_phase_coherence,white_disordered_bosons_optical_lattice}, or by loading in an optical lattice a mixture of two kinds of atoms, one heavy and one light. When the heavy atoms
become randomly localized in the lattice, they will act as impurities for the lighter atoms~\cite{gavish_disorder_impurities}. Another available technique is to superimpose two optical lattices with incommensurate periodicities, thus generating a quasi-periodic potential~\cite{fallani_bichromatic_shaking}. The quasi-periodic lattices as well as the speckle patterns have been recently used in the experimental efforts to observe the effects of Anderson localization in dilute Bose gases expanding in highly elongated traps~\cite{aspect_anderson_localization_BEC,roati_anderson_localization_BEC}.
Since Anderson localization is a single-particle effect, the next logical step is to study the interplay of disorder and interactions in strongly interacting ultra-cold atomic systems~\cite{orso_BEC-BCS_crossover,roux_quasiperiodic_phase_diagram,deng_phase_diagram_bichromatic,roscilde_one_dimensional_superlattices}.
The latter may be accessible by tuning interparticle interactions using Feshbach resonances~\cite{roati_feshbach_resonances}, or by loading the atoms in sufficiently deep optical lattices\cite{white_disordered_bosons_optical_lattice} and/or
strongly confining them to low-dimensions in tight traps~\cite{bloch_cold_atoms_optical_lattices_review}.
In the context of the efforts described above, one of the experimental challenges is to observe in ultra-cold gases clear signatures of the theoretically-predicted transition from a superfluid to the Bose-glass phase~\cite{giamarchi_anderson_localization_1D,fisher_bose_glass,delande_compression}. A pioneering step in this direction was recently taken by the Florence group by using lattice modulation spectroscopy~\cite{fallani_bichromatic_shaking}. This technique consists in heating an ultra-cold gas loaded in a optical lattice by periodically modulating the depth of the lattice~\cite{stoeferle_shaking_fast_tunnability,iucci_shake_bosons_theory,kollath_bosons_shaking_dmrg}. When perturbed in this way, the gas is driven out of equilibrium and absorbs energy. When the perturbation is switched off, and after re-thermalization, the broadening of the momentum distribution around zero momentum is taken as a measure of the energy absorbed by the system during the lattice modulation~\cite{stoeferle_shaking_fast_tunnability}. On the theory side, for non-disordered lattices, the calculation of the energy absorption rate due to the lattice modulation was first performed analytically within linear response theory by some of the present authors~\cite{iucci_shake_bosons_theory}.
These results were confirmed and extended beyond linear response using time-dependent density-matrix renormalization group methods, both for the case of bosons~\cite{kollath_bosons_shaking_dmrg} and fermions~\cite{kollath_shake_fermions_DMRG}. More recently, for disordered optical lattices, the energy absorption rate has been numerically calculated using full diagonalization in small systems~\cite{hild_shaking_bichromatic,hild_quasimomentum_absorption_superlattice}. Other methods
that have also been discussed in the literature for detecting signatures of the effect of disorder (or quasi-periodicity)
on interacting boson systems in one dimension focus on the momentum distribution~\cite{egger_disorder,deng_phase_diagram_bichromatic}
in disordered systems as well as quasi-periodic systems or the expansion dynamics in quasi-periodic
systems~\cite{roux_quasiperiodic_phase_diagram}.
Let us consider a one dimensional disordered Bose gas described by the following Hamiltonian:
\begin{align}\label{Hbh}
H &=-J\sum_{j}(b_{j+1}^{\dag }b_{j}^{\phantom{\dagger}}+\text{h.c.}) +\frac{U}{2}\sum_{j}n_{j}(n_{j}-1) \nonumber\\
& +\sum_{j}( \epsilon _{j}
+ V^\textrm{ho}_j ) n_{j},
\end{align}
where $b_j$ denotes the boson annihilation operator at sites $j$, $n_{j}=b_{j}^{\dag }b_{j}^{\phantom{\dagger}}$ being the local density.
Here $J$ and $U$ are the usual parameters of the Bose-Hubbard model corresponding to the tunneling rate and the onsite repulsion $(U>0)$. The last term in the rhs of Eq.~(\ref{Hbh}) accounts for the presence of both the harmonic trap, $V^\textrm{ho}_j$, and the disorder potential $\epsilon_j$.
The distribution of the on-site energies $\epsilon_j$ in Eq.~(\ref{Hbh}) depends on the specific choice of the random (or pseudo-random) potential. In this work we extensively compare two cases:
\begin{eqnarray}\label{sources}
&a)& \;\epsilon_j \;\textrm{uniformly distributed in}\;\; [-\Delta ,\Delta ] \\
&b)& \;\epsilon_j = \Delta \cos(2\pi j \sigma),\;\;\;\; \textrm{$\sigma$ irrational},
\end{eqnarray}
where $\Delta$ measures the strength of the disorder.
From the experimental point of view, speckle patterns and lattice containing heavy atom
impurities can be modeled by case a) whereas
quasi-periodic potentials obtained by superimposing two
optical potentials with incommensurate periodicities $d_1/d_2=\sigma$ are described
by case b).
In this work we assume that the hopping amplitude $J$ in Eq.~(\ref{Hbh}) is modulated periodically
in time according to $J(t)=J+\delta J\cos \omega t$, where $\omega$ is the modulation frequency.
We calculate the energy absorption rate within linear response theory, which is valid for weak lattice modulations $\delta J \ll J$.
We shall restrict ourselves to the strongly repulsive regime of Eq.~(\ref{Hbh}), where the on-site repulsion is large compared to both the hopping amplitude and the disorder strength ($U \gg J,\Delta$).
We first discuss systems in the thermodynamic limit by setting $V^\textrm{ho}_j =0$. Effects of the harmonic trapping
potential will be discussed later, in Sect.\ref{sec:sec5}. We also set $\hbar=1$ to simplify the notation.
In the thermodynamic limit both the number $N$ of bosons and the length $M$ of the chain diverge. The ratio $\nu=N/M$ is instead finite and corresponds to the \emph{filling} factor, i.e. the average number of bosons per lattice site.
We must distinguish between two physically different situations.
For \textsl{incommensurate fillings} $\nu<1$, the system has gapless excitations. Thus, a good approximation to
the absorption rate at frequencies $\omega \ll U$ can be obtained by formally taking $U\to +\infty$ and
mapping the resulting hard-core bosons to
non-interacting fermions using a Jordan-Wigner transformation (see \emph{e.g.}
Ref.~\cite{Cazalilla_tonks_gases}). The resulting single particle problem can be easily solved
for a given choice of $\epsilon_i$ and $V^\textrm{ho}$ and the energy absorption obtained.
On the other hand, for \textsl{unit filling} ($\nu=1$) the ground state is a Mott insulator with a gap. In this case,
the elementary excitations are particles and holes~\cite{iucci_shake_bosons_theory}
and in a homogeneous system the absorption can only occur at frequencies $\omega \sim U$.
In the absence of disorder, the response of the system to the lattice modulation has been computed using degenerate perturbation theory within the subspace of particle and hole excitations~\cite{iucci_shake_bosons_theory}.
The same methods can be generalized to deal with disordered case, as shown below.
The resulting general picture of the energy absorption is depicted in Fig.~\ref{fig:sketch}.
The low frequency $0<\omega<W$, where $W \sim \textrm{max}(4J,2\Delta)$ is the effective bandwidth, is only present for incommensurate fillings, $\nu<1$.
A second distribution is centered at frequency $\omega= U$ and comes from particle-hole excitations
generating doubly occupied sites. The width of this absorption line is also given by $W$.
\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.98\columnwidth]{sketch}
\end{center}
\caption{
Sketch of the full absorption spectrum at incommensurate filling. Here $W \sim \textrm{max}(4J,2\Delta)$ is the effective bandwidth. The peak at $\omega\sim U$ stems from particle-hole excitations, whereas the low frequency absorption appears as a consequence of the formation of a Bose-glass at incommensurate filling.}
\label{fig:sketch}
\end{figure}
The paper is organized as follows. In Section~\ref{sec:sec2}, we present the general formalism
needed to calculate the absorption rate for incommensurate and unit filling. In Section~\ref{sec:sec3} and Section~\ref{sec:sec4}, we present our analytical and numerical results obtained for the random and the quasi-periodic potential, respectively. In Section~\ref{sec:sec5}, we discuss the effects of a trapping potential. Finally in Section~\ref{sec:sec6} we provide our conclusions. A derivation of the general formula [see Eq.~(\ref{asy_weak})] for the absorption rate valid for weak disorder is given in the Appendix~\ref{sec:sec7}).
\section{Energy Absorption: Linear Response Theory}\label{sec:sec2}
For weak perturbations, corresponding to $\delta J \ll J$, the energy absorption rate $\dot{E}_{\omega}$ can be calculated using linear response theory. The general formula has been first derived in Ref.\cite{iucci_shake_bosons_theory}
and in the presence of disorder it takes the form
\begin{equation}
\dot{E}_{\omega }=\frac{1}{2}\delta J_{0}^{2}\,\omega \: \overline{\mathrm{\Im}\left[ -\chi _{K}(\omega )\right] }, \label{def}
\end{equation}
where $\chi_{K}(\omega )$ is the Fourier transform of the \emph{retarded} correlation function $\chi _{K}(t)=-i\Theta (t)\langle [ K(t),K(0)] \rangle$ of the hopping operator $K=-\sum_{j}(b_{j+1}^{\dag }b_{j}^{\phantom{\dagger}}+\text{h.c.})$, being $\Theta(t)$ the step function. In Eq.~(\ref{def}) the bar means average over different disorder (Sect.~\ref{sec:sec4})
or quasi-periodic (Sect.~\ref{sec:sec3}) realizations.
In general, the calculation of the correlation function in Eq.~(\ref{def}) is a complicated many-body problem.
However, in the limit of strong repulsion where $U \gg J,\Delta$, calculations are considerably simplified by the
fact that we can accurately restrict ourselves to work within a subspace of the total Hilbert space, whose detailed
structure depends on the filling. In the case of an \emph{incommensurate} filling (\emph{i.e.} $\nu <1$) this subspace
can be described in terms of non-interacting fermion states (that is, Slater determinants). For commensurate
filling (\emph{i.e.} \emph{unit} filling, $\nu =1$) we can restrict ourselves to the subspace with one particle and one
hole excitation, as described below.
\subsection*{Incommensurate filling}
For filling $\nu<1$ and large on-site repulsion $J,\Delta \ll U $, we take the hard core limit $U\rightarrow +\infty$.
Bosons are then mapped onto \emph{non interacting} spinless fermions via the Jordan-Wigner transformation:
%
\begin{equation} \label{Jordan}
c_{j} = \exp\left[ i\pi\sum_{k=1}^{j-1}n_{j}\right] b_{j},
\end{equation}
where $c_j$ satisfy fermionic commutation relations $\{c_j^{\phantom{\dagger}},c_j^{\phantom{\dagger}}\}=0$ and $\{c_j^{\phantom{\dagger}},c_j^{\dag}\}=1$. Under the above transformation, the Hamiltonian (\ref{Hbh}) is mapped onto the single particle Hamiltonian:
\begin{equation} \label{h0}
H^\prime=-J\sum_j (c_{j+1}^{\dag}c_{j}^{\phantom{\dagger}}+\text{h.c.}) + \sum_j\epsilon_{j}^{\phantom{\dagger}} \: c_{j}^{\dag}c_{j}^{\phantom{\dagger}},
\end{equation}
where the on-site repulsion $U$ has disappeared and the hopping operator $K$ in Eq.~(\ref{def}) is now given by
$K^\prime=-\sum_{j}(c_{j+1}^{\dag }c_{j}^{\phantom{\dagger}}+\text{h.c.})$. Notice that the mapping of observables that are non local in space
is far less trivial, an example is the momentum distribution studied in Ref.~\cite{egger_disorder} for disordered hard-core bosons in one dimension.
After some algebra, the absorbtion rate~(\ref{def}) becomes
%
\begin{equation} \label{formula}
\dot{E}_{\omega}=\,\frac{\delta J_{0}^{2}\pi\omega}{2}\sum_{\alpha,\beta }\overline{\mathcal{K}_{\alpha\beta}\left[f(\varepsilon_{\alpha})-f(\varepsilon _{\beta})\right] \delta(\omega+\varepsilon_\alpha-\varepsilon_\beta)},
\end{equation}
where the matrix $\mathcal{K}$ is defined as:
\begin{equation} \label{K}
\mathcal{K}_{\alpha\beta}=|\sum_{j}\left[ \psi_{\alpha}(j+1)\psi_{\beta}(j)+\psi_{\alpha}(j)\psi_{\beta}(j+1)\right]|^{2}.
\end{equation}
In the previous expressions $\varepsilon_\alpha$ and $\psi_\alpha(j)$ are the eigenvalues and eigenfunctions of $H^\prime$, respectively. In Eq.~(\ref{formula}) $f(\varepsilon)=(\exp[(\varepsilon-\mu)/T]+1)^{-1}$ is the Fermi-Dirac distribution function at a temperature $T$ and chemical potential $\mu$. The latter is fixed by the normalization condition $\nu=\sum_\alpha f(\varepsilon_\alpha)$. At zero temperature the only relevant processes in Eq.~(\ref{formula}) correspond to transitions from an occupied level (with energy $\varepsilon_\alpha < \mu(T = 0)$) to an unoccupied level ($\varepsilon_\beta > \mu(T = 0)$). In particular, for unit filling the absorption (\ref{formula}) vanishes, consistently with the fact
that a Mott insulator can only absorb at much higher frequencies $\omega \sim U$.
In the absence of disorder [\emph{i.e.} for $\epsilon_i=0$ in Eq.~(\ref{h0})], the
hopping modulation commutes with the Hamiltonian $H'$ and therefore
the absorption rate vanishes to all orders, even beyond
linear response. In the above expression, this is reflected in
that, for $\epsilon_i = 0$, the eigenstates of $H'$ become plane waves, $\psi_k(j) \propto e^{i k j}$, with energy
dispersion $\varepsilon_k=-2J \cos k$ ($k$ being the lattice momentum). Thus the matrix (\ref{K}) is diagonal, \emph{i.e.} $\mathcal{K}_{kk^{\prime}}=4\delta_{k,k^{\prime}}\cos^2 k$, which, together with the factor $f(\varepsilon_{k})-f(\varepsilon_{k^{\prime}})$ in Eq.~(\ref{formula}) makes $\dot{E}_{\omega}$ vanish.
At weak disorder (\emph{i.e.} $J\gg \Delta$), the absorption rate (\ref{formula})
can be evaluated using perturbation theory (the details can be found in the Appendix), which
yields:
\begin{equation}\label{asy_weak}
\dot{E}_{\omega}=\,\frac{\delta J_{0}^{2}\pi\omega}{2M} \sum_{k,k^\prime } \frac{\overline{|V_{k-k^\prime}|^2} }{J^2}
\left[f(\varepsilon_k)-f(\varepsilon _{k^\prime})\right] \delta(\omega + \varepsilon_k - \varepsilon _{k^\prime} ),
\end{equation}
where $V_{k}=\frac{1}{\sqrt{M}}\sum_{j=0}^{M-1} e^{i k j}\epsilon_j$
is the Fourier transform of the disorder potential. Equation (\ref{asy_weak}) shows that
the perturbation expansion in disorder is well defined provided the Fourier transform, $V_{k}$, is finite.
Let us finally consider the so-called atomic limit, which corresponds to $J\ll \Delta$ (yet $\Delta \ll U$). In this
limit, tunneling can be neglected and the eigenstates are given by
$\psi_m(j)=\delta_{jm}$. From Eq.~(\ref{K}) we find $\mathcal{K}_{j j^{\prime}}=1$ if $j$ and $j^{\prime}$
are nearest neighbor and zero otherwise. The absorption rate, Eq.~(\ref{formula}), thus reduces to
\begin{equation} \label{asy_strong}
\dot{E}_{\omega}=\,\frac{\delta J_{0}^{2}\pi\omega}{2}\sum_{r=\pm 1}\sum_{j=0}^{L-1}\overline{\left[f(\varepsilon_j)-f(\varepsilon _{j+r})\right] \delta(\omega+\varepsilon_j-\varepsilon_{j+r})}.
\end{equation}
In Sect.~\ref{sec:sec31} we shall explicitly compare the results obtained using exact numerical diagonalization with the
above results obtained both in the limit of weak (\ref{asy_weak}) and strong (\ref{asy_strong}) disorder.
Finally, it is important to emphasize that Eq.~(\ref{formula}) does not account for
particle-hole excitations which are relevant at much higher frequencies, $\omega \sim U$.
These excitations become particularly important at unit filling ($\nu=1$),
when the strongly repulsive Bose gas becomes a Mott insulator and
the absorption at low frequency $\omega \ll U$ predicted by Eq.~(\ref{formula}) vanishes because there are
no empty sites (\emph{i.e.} holes) in the ground state. The contribution to the absorption
from particle-hole excitations at unit filling will be discussed next.
\subsection*{Unit filling}
We next turn our attention to the \emph{commensurate} case with $\nu=1$. For large enough $U/J$ and $U/\Delta$, the system becomes a bosonic Mott insulator. In Ref.~\onlinecite{iucci_shake_bosons_theory}, it was shown that for clean systems the absorption rate is zero at low frequencies and exhibits a narrow peak of width $\sim J$ centered about $\omega=U$. In this section, we consider the modifications of such peak due to a disorder or quasi-periodic potential, $\epsilon_i$.
In order to obtain the energy absorption rate within linear response, we first use
the spectral decomposition of the correlation function $\chi_K(\omega)$ in terms of the exact
eigenstates of the unperturbed Hamiltonian. This yields the following expression for the energy
absorption:
\begin{equation} \label{Mott1}
\dot E_\omega=\delta J^2 \omega \frac{\pi}{2} \sum_{n} \overline{\left\vert\left\langle \Psi_n \right\vert K \left\vert \Psi_{0}\right\rangle\right\vert ^{2}\delta\left( \omega+E_{0}-E_{n}\right)},
\end{equation}
where $\vert \Psi_n \rangle$ are the eigenstates of the original Hamiltonian (\ref{Hbh}) with energies $E_n$, and
$\left\vert \Psi_{0}\right\rangle =\left\vert 1, 1,\ldots,1 \right \rangle$ is the ground state in the Fock representation
corresponding to one boson per lattice site.
The low energy states are particle-hole excitations
$\left\vert \phi\left( m,j \right) \right\rangle = \frac{1}{\sqrt{2}}b_{m}^{\dagger}b_{m+j}\left\vert \Psi_{0}\right\rangle$
corresponding to double occupation at site $m$ and an empty site $m+j$. These excitations are all degenerate with energy $U$ in the absence of tunneling and (\emph{i.e.} for $\Delta=J=0$).
For finite values of $\Delta$ and $J$, the eigenstates $\Psi_n$ can be calculated using degenerate perturbation theory by writing $\left\vert \Psi_n \right\rangle=\sum_{m,j} f_{m,j} \left\vert \phi\left(
m, j \right)\right\rangle$, where the coefficients satisfy:
\begin{equation}\label{diag}
\sum_{m^\prime,j^\prime}\left\langle \phi\left( m, j \right) \right\vert H
\left\vert \phi\left(
m^{\prime},j^{\prime}\right) \right\rangle f_{m^\prime,j^\prime}=E f_{m,j}.
\end{equation}
The above matrix element and the energy absoption can be computed by
taking into account that $\langle \phi\left( m, j \right) \vert K \vert \Psi_{0}
\rangle= -\sqrt{2}\delta_{j,\pm 1}$, within the subspace containing just one particle
and one hole. Hence, the matrix elements in Eq.~(\ref{Mott1}) correspond to $\left\langle
\Psi_n \right\vert K \left\vert \Psi_{0}\right\rangle =- \sum_{m,r=\pm 1} \sqrt{2}
f_{m,r} $.
Again, let us note that, in the `atomic limit' where the tunneling can be neglected, Eq.~(\ref{Mott1})
simplifies considerably. Localized particle-hole excitations become the
exact eigenstates $\vert \Psi_n \rangle = \left\vert \phi\left( m,j \right) \right\rangle$ with energy $E_0+U+\varepsilon_m-\varepsilon_{m+j}$, where $E_0=\sum_{i=1}^{M} \varepsilon_i$ is the energy of the ground state for a given realization of $\epsilon_{i}$. The absorption rate (\ref{Mott1}) then takes the form:
\begin{equation}\label{atomic_Mott}
\dot{E}_{\omega}=\, \delta J_{0}^{2}\pi\omega\sum_{r=\pm 1}\sum_{m=1}^{M}\overline{ \delta(\omega-U+\varepsilon_m-\varepsilon_{m+r})},
\end{equation}
which can be readly evaluated numerically once the disorder potential is known.
\section{Results for a disorder potential}\label{sec:random}\label{sec:sec3}
In this section we assume that the on-site energy $\epsilon_i$ in Eq.~(\ref{Hbh}) are random numbers uniformly distributed within the interval $[-\Delta,\Delta]$. The absorption rate (\ref{def}) can thus be conveniently recast
as:
\begin{equation}\label{defF}
\dot{E}_\omega=M\delta J_0^2 F,
\end{equation}
where $F$ is a dimensionless function that can be numerically evaluated. The results
for incommensurate and commensurate cases are described below.
\subsection*{Incommensurate filling}\label{sec:sec31}
As stated above, the absorption rate is calculated numerically at zero temperature starting from Eqs. (\ref{formula}) and (\ref{K}). In Fig.~\ref{fig:fill} we plot the frequency dependence of the response function $F$ for \emph{different} fillings and increasing values of disorder $\Delta=0.1 J$ (upper panel), $\Delta= J$ (central panel) and $\Delta=5 J$ (lower panel). Since, in the fermionic representation, the Hamiltonian of Eq.~(\ref{h0}) is particle-hole symmetric, the absorption rate in Eq.~(\ref{formula}) is unchanged under the transformation $\nu\rightarrow 1-\nu $, so we restrict our discussion to fillings $\nu \leqslant 1/2$.
\begin{figure}[tb]
\begin{center}
\subfigure{\includegraphics[width=3.0in]{hc_L500_D4000_Delta0_1}}
\subfigure{\includegraphics[width=3.0in]{hc_L500_D4000_Delta1_0}}
\subfigure{\includegraphics[width=3.0in]{hc_L500_D4000_Delta5_0}}
\end{center}
\caption{Energy absorption rate of hardcore bosons in a \emph{random} potential: the response function $F$ [see Eq~(\ref{defF})] is plotted versus modulation frequency for different filling factors and increasing values of disorder strength: $\Delta=0.1J$ (top panel), $\Delta=J$ and $\Delta=5J$.
Calculations are done on a ring of $M=500$ lattice sites yielding negligeable finite size effects. The number of disorder realizations used was $N_r=500$. }
\label{fig:fill}
\end{figure}
A noticeable feature of Fig.~\ref{fig:fill} is that the response at high frequencies is \emph{independent} of the filling factor. In this limit, the relevant processes contributing to the absorption mainly involve transitions from states far below the Fermi level (\emph{i.e.} $(\varepsilon_{\alpha} \ll \mu)$ into empty states far above it (\emph{i.e.} $(\epsilon_\beta \gg \mu)$). As a result, the Fermi-Dirac distributions in Eq.~(\ref{formula}) become irrelevant, and thus any dependence on the value chemical potential $\mu$ disappears.
\begin{figure}[tb
\begin{center}
\includegraphics[width=0.98\columnwidth]{infineweak}
\end{center}
\caption{
Comparison between numerics [symbols] and analytics [Eq.~(\ref{asy_weak}), solid line] for weak disorder. Here $\Delta/J=0.01$ and we consider two filling factors $\nu=0.3$ and $\nu=0.5$. The length of the chain is $M=2000$ and the number of disorder realizations is $N_r=2000$.
The inset is a zoom of the low frequency regime, where the absorption rate is quadratic in frequency as given by Eq.~(\ref{IF})}.
\label{fig:pt}
\end{figure}
However, at low frequencies, the absorption rate vanishes {\it quadratically} with
frequency for any strength $\Delta$ of the disorder. To understand this, let us expand
in Eq.~(\ref{formula} the distribuntion functions, $f(\varepsilon_{\alpha})-f(\varepsilon _{\beta})\simeq (\varepsilon_{\alpha}-\varepsilon _{\beta}) \: \partial_{\varepsilon} f(\varepsilon_{\alpha})$.
Taking into account that, at zero temperature,
$\partial_{\varepsilon} f(\varepsilon) =-\delta(\mu-\varepsilon)$, we find that $F \simeq C \omega^2$, where
the constant
\begin{equation}
\label{square}
C =\frac{\pi}{2} \sum_{\alpha \neq \beta} \overline{\mathcal{K
}_{\alpha \beta} \delta(\mu-\varepsilon_\alpha)\delta(\mu-\varepsilon_\beta)}
\end{equation}
can be evaluated numerically. From Eq.~(\ref{square}) it can be seen that the constant $C$ is non zero provided there are non-vanishing matrix elements $\mathcal{K}_{\alpha \beta}$ connecting two states $\alpha$ and $\beta$ at the Fermi level, $\varepsilon_{\alpha}=\varepsilon _{\beta}=\mu$.
In the limit of weak disorder corresponding to $\Delta \ll J$, the absorption can be evaluated using Eq.~(\ref{asy_weak}), where $\overline{|V_k|^2}=\Delta^2/3M$, as follows from the expression for the Fourier
transform of the disorder potential, $V_{k}$. Going to the thermodynamic limit and introducing the density of
states $\rho(\varepsilon)=(2\pi J \sqrt{1-\varepsilon^2/4 J^2})^{-1}$, we find:
\begin{equation} \label{weak2}
F =\frac{ \omega \Delta^2}{24 \pi J^4} \int_{a}^{b} \frac{d\epsilon}{\sqrt{1-\epsilon^2/4J^2}\sqrt{1-(\epsilon+\omega)^2/4J^2}},
\end{equation}
where $a=\text{max}(-2J,\mu-\omega)$ and $b=\text{min}(\mu,2J-\omega)$. Here the chemical potential $\mu$ is related to the filling factor by $\mu = -2J \cos \pi \nu$. By expanding Eq.~(\ref{weak2}) at low frequencies,
we again obtain that the quadratic behavior discussed above:
\begin{equation} \label{IF}
F =\frac{\Delta^2 \pi}{6 J^2}\rho(\mu)^2 \: \omega^2 =\frac{\Delta^2}{24 \pi J^4}\frac{\omega^2}{\sin^2(\pi \nu)},
\end{equation}
It should be noticed that the right hand-side of Eq.~(\ref{IF}) diverges in the limit of vanishing lattice filling $\nu \rightarrow 0$ because the density of states $\rho(\varepsilon)$ has a van Hove singularity at zero energy
in one dimension. Thus the low filling limit, the quadratic behavior of Eq.~(\ref{IF}) is only recovered at
increasingly low frequencies, as shown in Fig.~\ref {fig:fill}(upper panel).
In Fig.~\ref{fig:pt} we show a comparison, in the limit of weak disorder ($\Delta=0.01J$), of the numerical results (open symbols) obtained using exact diagonalization with the analytical expression of Eq.~(\ref{weak2}) (continuous lines). The agreement is indeed very good over the entire frequency range. In the inset it is demonstrated that numerical results are consistent with the quadratic behavior of Eq.~(\ref{IF}), expected at low frequencies.
On the other hand, in the opposite limit of strong disorder, $\Delta \gg J$, the tunneling can be neglected. In this limit, the absorption rate can be evaluated directly from Eq.~(\ref{asy_strong}). Taking into account that the on-site energies $\epsilon_j$ at different sites are completely uncorrelated, we find
\begin{equation}\label{mia}
F=\pi \omega \int_{-\Delta}^{\overline \mu} d\epsilon \overline{\rho}(\epsilon) \int_{\overline \mu}^{\Delta} d\epsilon^\prime \overline{\rho}(\epsilon^\prime) \delta(\omega + \epsilon-\epsilon^\prime),
\end{equation}
where $\overline \mu$ and $\overline{\rho}$ are the \emph{disorder-averaged} chemical potential and density of states, respectively. In the random potential the latter is constant and given by $\overline{\rho}(\epsilon)=1/2\Delta$, and therefore $\overline{\mu}=(2\nu-1)\Delta$. Using Eq.~(\ref{mia}), the following low-frequency behavior is
obtained:
\begin{equation}
\label{stro}
F= \frac{\pi}{4\Delta^2}\omega \left[\text{min}(\overline\mu,\Delta-\omega)-\text{max}(-\Delta,\overline\mu-\omega)\right].
\end{equation}
This behavior is exhibited by the numerics, as shown in Fig.~\ref {fig:fill} (lower panel, see also discussion
further below). Furthermore, in the low frequency limit Eq.~(\ref{stro}) we again recover the quadratic behavior
described above on general grounds:
\begin{equation} \label{IFstrongD}
F=\frac{\pi}{4 \Delta^2}\omega^2.
\end{equation}
Notice however that the proportionality constant is now independent of the filling factor.
In Fig.~(\ref{fig:atomic}) a more detailed comparison of the numerics with the analytical result of Eq.~(\ref{stro}) for the limit of strong disorder is shown. In the inset, we also compare our numerical results with the quadratic behavior (\ref{IFstrongD}) expected at low frequency. In both cases the agreement is remarkably good.
\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.98\columnwidth]{infine}
\end{center}
\caption{
Comparison between numerics [symbols] and analytics [solid line, Eq.\ref{stro})] for \emph{strong} disorder. The value of the disorder is $\Delta/J=100$ and the filling factors are $\nu=0.3$ and $\nu=0.5$. The length of the chain is $M=2000$ and the number of disorder realizations is $N_r=2000$. In the inset we compare our numerics with the quadratic expansion (\ref{IFstrongD}) expected at low frequency. In both cases the agreement is quite good.}
\label{fig:atomic}
\end{figure}
\subsection*{Unit filling}
The absorption rate for $\nu=1$ is calculated numerically starting from Eqs (\ref{Mott1}) and (\ref{diag}). The result is shown in Fig.~\ref{fig:Mott} as a function of frequency for different values of
the disorder strength $\Delta$ and $J=0.01U$.
In the absence of disorder $(\Delta=0)$ the absorption rate can be evaluated analytically
and the dimensionless function $F$ in Eq.~(\ref{defF}) is given by \cite{iucci_shake_bosons_theory}:
\begin{equation}\label{zero_dis}
F=\frac{2\omega}{3J} \left| \sin \left[ \cos^{-1}\: \left(\frac{\omega-U}{6J}\right)\right] \right|,\;\;\;\mbox {for}\, \, |\omega-U|<6J,
\end{equation}
and vanishes otherwise. The dashed line in Fig.~\ref{fig:Mott} corresponds to our numerical result for $\Delta = 0$ which fully agrees with the above formula.
\begin{figure}[t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{MottBOXfinal}
\end{center}
\caption{Energy absorption rate in the Mott insulator phase for hardcore bosons in a random potential: the response function $F$ (see Eq.~(\ref{defF})) is plotted versus modulation frequency for fixed $J=0.01U$ and increasing values of the disorder strength $\Delta/U=0 \textrm{(dashed line)},0.03,0.06, 1$. The length
of the chain is $M=60$ and the number of disorder realizations is $N_r=200$. A broadening of the absorption peak is observed for increasing disorder.}
\label{fig:Mott}
\end{figure}
As the strength of disorder is increased, we see
from Fig.~\ref{fig:Mott} that the absorption spectrum becomes broader and progressively develops
a triangle-like shape as the limit $J\ll \Delta$ is approached. This behavior can be obtained analytically
starting from Eq.~(\ref{atomic_Mott}). In the $J\ll \Delta$ limit, since the on-site energies at different lattice
sites are uncorrelated, we obtain:
\begin{equation} \label{MottD}
F \simeq \frac{\pi \omega}{2 \Delta^2} \int_{-\Delta}^\Delta d\epsilon \int_{-\Delta}^\Delta d\epsilon^\prime \delta(\omega-U+\epsilon-\epsilon^\prime),
\end{equation}
where $\overline{\rho}(\epsilon)=1/2\Delta$ is the disorder-averaged density of states in the atomic limit
introduced above. Upon integration, Eq.~(\ref{MottD}) yields
\begin{equation} \label{stroD}
F \simeq \frac{\pi \omega}{2\Delta^2}(2\Delta-|\omega-U|),
\end{equation}
showing that the lineshape of the absorption rate in the atomic limit is approximately triangular and vanishes at
$|\omega-U|=2\Delta$ for $J\ll \Delta$.
\section{Quasi-periodic potential}\label{sec:sec4}
In this section we assume that the external potential in Eq. (\ref{Hbh}) is $\epsilon_j = \Delta \cos(2\pi j \sigma)$~\cite{roux_quasiperiodic_phase_diagram,deng_phase_diagram_bichromatic,roscilde_one_dimensional_superlattices}, being $\sigma$ an irrational number. This quasi-periodic potential distribution is realized experimentally by superimposing two different periodic potentials with incommensurate lattice periods~\cite{fallani_bichromatic_shaking}. Differently from the disorder potential considered in the previous section, where all states are localized (in the thermodynamic limit) for an arbitrarily small amount of disorder, in the quasi-periodic case there is a phase transition~\cite{sokoloff_review_harper_equation} at $\Delta_c=2J$: for $\Delta<2J$ all states are \emph{extended} while for $\Delta>2J$ all states are \emph{exponentially} localized.
As described below, we find that the absorption spectra of bosons in the quasi-periodic potential are remarkably different from the spectra described in Sect.~\ref{sec:sec3} for the bosons moving on a disorder potential.
\subsection*{Incommensurate filling}
For lattice fillings $\nu<1$ (\emph{i.e.} less than a boson per site), we calculate the absorption rate numerically
starting from Eqs (\ref{formula}) and (\ref{K}). We restrict to zero temperature and fix $\sigma=0.77145245$ which is relevant to the experiments carried out by the Florence group.
\begin{figure}[tb]
\begin{center}
\includegraphics[width=2.8in]{glassQPD=01}
\includegraphics[width=2.8in]{glassQPD=1}
\includegraphics[width=2.8in]{glassQPD=10}
\caption{Energy absorption rate of hardcore bosons in a \emph{quasi periodic} potential with $\sigma=0.77145245$: the response function $F$ [see Eq.~(\ref{defF})]
is plotted versus modulation frequency for different filling factors and increasing values of disorder strength:
$\Delta=0.1J$ (top panel), $\Delta=J$ and $\Delta=10J$.
Calculations are done on a ring of $M=1200$ lattice sites yielding almost negligeable finite size effects. The number of disorder realization is $N_r=500$. }
\label{fig:hc_quasi_disorder}
\end{center}
\end{figure}
In Fig.~\ref{fig:hc_quasi_disorder} we plot the frequency dependence of the response function (\ref{defF})
for increasing values of the disorder strength $\Delta$. Compared to Fig.~\ref {fig:fill}, we see that the absorption spectra in quasi-periodic potential exhibit a much richer structure.
Interestingly, the response function becomes very large (and actually diverges) when $\omega$ matches special values. Moreover, for a given filling factor, the absorption rate is non-zero only within a certain range of frequencies.
These features can again be understood in the limits of weak and at strong disorder, where results can be obtained analytically. In the limit $\Delta \ll J$, the absorption rate can be calculated starting from
Eq.~(\ref{asy_weak}) and taking the thermodynamic limit. This yields ($\varepsilon_{k} = -2J \cos k$):
\begin{equation}\label{weakTrue}
F=\frac{\pi \omega} {2} \int \frac{dk}{2\pi}\frac{dk^\prime}{2\pi} \frac{|V(k-k^\prime)|^2}{J^2}
\delta(\omega+\varepsilon_{k} +\varepsilon_{k^{\prime}}),
\end{equation}
where the integration over momenta is restricted to $[0,2\pi]$.
Using that the (modulus square of the) Fourier transform of the disorder potential
is $|V(k)|^2=\lim_{M \rightarrow \infty} |V_M(k)|^2 $, where
\begin{equation}\label{help}
|V_{M}(k)|^2= \frac{\Delta^2}{4M}\left | \frac{e^{i (k+k_0) M}-1}{e^{i (k+k_0)}-1} +
\frac{e^{i (k-k_0) M}-1}{e^{i (k-k_0)}-1} \right |^2,
\end{equation}
and $k_0=2 \pi \sigma$, for $M \to \infty$, the right hand-side of Eq.~(\ref{help}) becomes
a series of delta functions:
\begin{equation}\label{diracdelta}
|V(k)|^2=\frac{\pi \Delta^2}{2} \sum_{n=-\infty}^{+\infty}\left[\delta(k+k_0 +2\pi n)+\delta(k-k_0 +2\pi n)\right].
\end{equation}
Putting Eq.~(\ref{diracdelta}) this result into Eq.~(\ref{weakTrue}) we obtain:
\begin{eqnarray}
F&=&\frac{\omega\pi \Delta^2}{4J^2} \int_0^{2\pi} \frac{dk}{2\pi} \delta (\omega -\varepsilon_{k}+ \varepsilon_{k+k_0}) \nonumber \\ && \Theta(\mu+\varepsilon_{k}) \Theta(\omega-\varepsilon_{k+k_0}).\label{ciao}
\end{eqnarray}
The integral in Eq.~(\ref{ciao}) can be evaluated using the identity $a \sin k + b \cos k= c \cos(k+\gamma)$, where
$c=\sqrt{a^2+b^2}$ and $\tan \gamma=-a/b$. Since $a=\sin k_0$ and $b=1-\cos k_0$ we obtain $c=2\sin (k_0/2)$
and $\tan \gamma=-1/\tan(k_0/2)$. The zeroes of the $\delta$-function in Eq.~(\ref{ciao})
occur at $k=k_\pm=-\gamma\pm \arccos(\omega/2 J c)$. Hence, we obtain:
\begin{equation}\label{risweak}
F=\frac{\Delta^2}{4J^2}\frac{\omega/2}{\sqrt{(2 J c)^2-\omega^2}} \sum_{r=\pm} \Theta(-\xi_r) \Theta(\omega+\xi_r),
\end{equation}
where $\xi_r=- \epsilon_{k_r} - \mu = 2J \cos k_r -\mu$. Eq.~(\ref{risweak}) shows that the absorption is finite only in a range of frequencies
given by the conditions $\xi_r<0$ and $\xi_r+\omega>0$, where $\xi_r$ itself depens on $\omega$ through the
$\omega$ dependence of $k_r$. Moreover, the response diverges for $\omega=2 J c$, provided this frequency value is allowed for a given filling factor. Since $c=2\sin \pi \sigma=1.31576$, the divergence occurs at $\omega=2.6315J$, as
found numerically and shown in Fig.~\ref{fig:hc_quasi_disorder} (upper panel).
For a potential strength comparable to the tuneling rate, \emph{i.e.} $\Delta \sim J$, the absorption spectrum develops very sharp peaks as shown in the central panel of Fig.~\ref{fig:hc_quasi_disorder}. These peaks gradually disappear as
$\Delta$ increases and becomes much larger than $J$. In this regime, however, the energy absorption spectrum becomes indeed rather similar to the case of weak quasi-periodic potential, as can seen by comparing the upper and lower panels of Fig.~\ref{fig:hc_quasi_disorder}. This peculiar effect can be explained analytically starting from Eq.~(\ref{asy_strong}) which applies in the atomic limit. Introducing the variable $y=2 \pi \sigma n$, in the thermodynamic limit, we obtain:
\begin{eqnarray}
F=\omega\pi \int_0^{2\pi} \frac{dy}{2\pi} \delta (\omega + \Delta \cos y-\Delta \cos (y+2\pi\sigma)) \nonumber \\
\Theta(\mu-\Delta \cos y) \Theta(\omega+\Delta \cos y-\mu) \label{interqp}
\end{eqnarray}
The integral in Eq.~(\ref{interqp}) becomes the integral in Eq.~(\ref{ciao}) after a change of variable $k=y+\pi$. We thus obtain:
\begin{equation}\label{ris}
F=\frac{\omega/2}{\sqrt{(\Delta c)^2-\omega^2}} \sum_{r=\pm} \Theta(\mu+\Delta \cos k_r) \Theta(\omega-\Delta \cos k_r-\mu),
\end{equation}
showing that the behavior of the absorption rate at strong quasi-periodic potential can be obtained from Eq.~(\ref{risweak}) by simply replacing $2J$ with $\Delta$.
\subsection*{Unit filling}
\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.98\columnwidth]{insiemeQP}
\caption{Energy absorption in the Mott insulator phase for bosons in a \emph{quasi-periodic} potential with $\sigma=0.77145245$: the response function $F$ [see Eq.~(\ref{defF})] is plotted versus modulation frequency for fixed $J=0.01U$ and increasing disorder strength $\Delta/U=0 \textrm{(dashed line)}, 0.03, 0.06, 1$. Here convergence is achieved for system size $L=70$. As disorder increases, the response function broadens and changes convexity, as predicted by Eq.~(\ref{asQP}).}
\label{fig:Mott_quasi_disorder}
\end{center}
\end{figure}
We have obtained the absorption spectrum at unit filling numerically using Eq.~(\ref{Mott1}) and Eq.~(\ref{diag}),
for the same value of $\sigma=0.77145245$. The result is plotted in Fig.~\ref{fig:Mott_quasi_disorder} for fixed $J/U=0.01$ and increasing values of the quasi-periodic potential strength, $\Delta$. The dashed line corresponds to the clean case, $\Delta=0$, where the absorption rate is given by Eq.~(\ref{zero_dis}).
We see that the shape of the absorption spectrum changes considerably as $\Delta$ increases.
For sufficiently weak quasi-periodic potential, $\Delta \lesssim 3J$,
the spectrum does not become broad, but instead satellite peaks appear on the sides of the central absorption
feature. For stronger quasi-periodic potentials, the central peak disappears and the spectrum develops a two hump structure. To understand these features, let us again focus on the `atomic limit' where the absorption rate can be obtained analitically using Eq.~(\ref{atomic_Mott}). Introducing the variable $y=2 \pi \sigma n$ and passing to the continuum limit, we obtain the result:
\begin{equation}\label{intermediate}
F=2\omega\pi \int_0^{2\pi} \frac{dy}{2\pi} \delta (\omega-U + \Delta \cos y-\Delta \cos (y+2\pi\sigma)).
\end{equation}
The integral (\ref{intermediate}) can be readily evaluated using the identity $a \sin y + b \cos y= c \cos(y+\gamma)$, where $\tan \gamma=-a/b$ and $c=\sqrt{a^2+b^2}$. From Eq.~(\ref{intermediate}) we have that $c=2 \sin \pi \sigma$ and therefore,
\begin{equation}\label{asQP}
F=\frac{2\omega}{\sqrt{(\Delta c)^2-(\omega-U)^2}},
\end{equation}
showing that the absorption rate diverges at the the egde where $|\omega-U|=\Delta c$. This means that the shape of the absorption spectrum changes completely going from weak to strong quasi-periodic potential, as obtained numerically and shown in Fig.~\ref{fig:Mott_quasi_disorder}. Finally, upon comparing Eq.~(\ref{stroD}) and Eq.~(\ref{asQP}) we see that in a
quasi-periodic potential the absorption spectrum is (at least in the atomic limit) narrower because $c <2$.
\section{Effects of a parabolic trap}\label{sec:sec5}
In this section we discuss the effects of a harmonic trapping potential $V (z)=m\omega_\textrm{ho}^2 z^2/2$
on the absorption spectrum. Here $m$ is the atom mass and $\omega_\textrm{ho}$ is the trapping frequency.
In this case $V^\text{ho}_j$ in Eq.~(\ref{Hbh}) is non-zero and given by
$V_j^\textrm{ho}=\alpha^\textrm{ho}(j-M/2)^2$, where $\alpha^\textrm{ho}=m\omega_\textrm{ho}^2 d^2/2$, $d$ being the lattice period.
We have repeated the calculations of the absorption spectrum including $V^\text{ho}_j$ and the result is shown in
Fig~\ref{fig:trap}. For a system of hard-core bosons in the absence of disorder or quasi-periodic potential, the trap favors the formation of a Mott insulator in the center surrounded by a superfluid region at the trap edges. This gives rise to a finite absorption
at low frequency (see inset in the upper panel), which is related to the creation of excitations at the edge of the trap. By contrast, in a uniform system of hard-core bosons, as we have described in Sect.~\ref{sec:sec2} the energy absorption vanishes to all orders because the hopping operator $K$ commutes with the Hamiltonian.
Let us next consider the effect of a small amount of disorder or a weak quasi-periodic potential. Clearly the Mott insulator at the center of the trap
cannot absorb energy at low frequency, so the only contribution comes from the outer shell, where the filling factor is less than unity.
In particular the low frequency peak arising from edge excitations fragments in multiple peaks with little spectral weight compared to the
response from the bulk discussed in Sections ~\ref{sec:random} and ~\ref{sec:sec4}.
We also see in Fig.~\ref{fig:trap} that the behavior of the absorption spectrum at frequencies close to the bandwidth crucially depends on whether the applied potential is truly random or quasi-periodic.
Whereas the disordered case exhibits a smooth behavior in the absorption up to the bandwidth $4J$ where it falls to zero, the quasi-periodic one shows a sharp peak located at the bandwidth $4Jc$ which resembles the divergence found in the corresponding homogeneous case. Note that the position of this peak is almost independent on the number of atoms in the tube and therefore, the peak should be visible in a realistic experimental situation where an average over a multiple tube setup with variable filling is performed. The same conclusion applies to the system with strong disorder or quasi-periodic potential as can be observed in the lower panel in Fig.~\ref{fig:trap}. For $\Delta\sim J$ (Fig.~\ref{fig:trap}, middle panel) the peak structure in the quasi-periodic case is more complex, and thus the averaging procedure will produce some rounding off of the peaks. Still, the absorption can be considerably larger than in the disordered case and this difference should be clearly visible.
\begin{figure}
\begin{center}
\includegraphics[width=0.98\columnwidth]{trap}
\caption{Energy absorption rate of disordered and quasi-disordered hardcore bosons in a parabolic trap. The response function $F$ is plotted versus modulation frequency for different fillings. Upper panel: $\Delta=0.1J$, middle panel: $\Delta=J$, lower panel: $\Delta=10J$. The system size is $M=500$, the number of disorder realizations is $N_r=4000$ and $\alpha^\text{ho}=2.88\times 10^{-4}J$. The inset in the upper panel shows the low frequency absorption in the absence of disorder, which is finite for trapped gases. As $\Delta$ increases, this sharp peak fragments out and is no longer visible on the scale of the bulk contribution. }
\label{fig:trap}
\end{center}
\end{figure}
\section{Conclusions}\label{sec:sec6}
In conclusion we have investigated the energy absorbed by a disordered strongly interacting Bose gas in the presence of periodically modulated optical lattices.
For filling factor less than one, the absorption rate has been calculated exactly in the hard-core limit via the Bose-Fermi mapping. For commensurate filling, corresponding to one boson per lattice site, the gas is a Mott insulator and can only absorbs energy at much higher frequency (of the order of the repulsive interaction $U$). The disorder induced broadening of the absorption spectrum has been calculated by restricting to the subspace of particle-hole excitations.
We have performed extensive calculations comparing two different sources of disorder: a random potential, which is relevant for current experiments based on speckle patterns, and a quasiperiodic potential, which is obtained by superimposing two optical lattices with incommensurate periods. Our results indicate that the response of the gas to the lattice modulation significantly depends on the chosen source of randomness.
This work was partly supported by ANR grant 08-BLAN-0165-01 and by the Swiss National Fund under MaNEP and Division II. AI gratefully acknowledges financial support from CONICET and UNLP. During the initial stage of this project, GO was also supported by the Marie Curie Fellowship under contract n. EDUG-038970. MAC was supported by MEC (Spain) Grant No. FIS2007-066711-C02-02 and CSIC (Spain) through Grant No. PIE 200760/007.
\section{Appendix}\label{sec:sec7}
In this Appendix we shall derive the asymptotic formula (\ref{asy_weak}) based on perturbation theory for weak disorder.
For clarity, we rewrite the general expression (\ref{formula})
\begin{equation}\label{app1}
\dot{E}_{\omega}=\,\frac{\delta J_{0}^{2}\pi\omega}{2} \sum_{k,k^\prime } \mathcal K_{k k^\prime}
\left[f(\varepsilon_k)-f(\varepsilon _{k^\prime})\right] \delta(\omega + \varepsilon_k - \varepsilon _{k^\prime} )
\end{equation}
using new indices $k$ and $k^\prime$. Moreover we find convenient to introduce the matrix elements
\begin{equation}\label{app2}
A_{k k^\prime}=\sum_{j}\left[ \psi_{k}^*(j+1)\psi_{k^\prime}(j)+\psi_{k}^*(j)\psi_{k \prime}(j+1)\right]
\end{equation}
so that $\mathcal{K}_{k,k^\prime}=|A_{k,k^\prime}|^2$.
In the absence of disorder $\Delta=0$, the eigenstates are plane waves $\psi_k^0(n)=e^{i k n}/\sqrt{L}$
with energy $\epsilon_k^0=-2J \cos k$. Therefore from Eq.~(\ref{app2}) we find
\begin{equation}\label{A0}
A^0_{k k^\prime}=2\delta_{k k^\prime} \cos k,
\end{equation}
showing that the matrix $A$ is \emph{diagonal} in momentum space. Since the matrix $\mathcal{K}_{kk^{\prime}}^0=4\delta_{k,k^{\prime}}\cos^2 k$
is also diagonal, the absorption rate (\ref{formula}) \emph{vanishes}.
For $\Delta \ll J$, we formally expand the rhs of Eq.~(\ref{app2}) in powers of the disorder strength $A_{k,k^\prime}=A^0_{k k^\prime}+A^1_{k k^\prime}+A^2_{k k^\prime}+O(\Delta^3)$, so the matrix $\mathcal K$ takes the form
\begin{align}
\mathcal K_{k,k^\prime} =&\mathcal{K}_{kk^{\prime}}^0+A^0_{k k^\prime} (A^1_{k k^\prime}+A^1_{k^\prime k}+A^2_{k k^\prime}+A^2_{k^\prime k})\label{expa}\\
& +|A^1_{k k^\prime}|^2+ \textrm{O}(\Delta^3) .\label{expa1}
\end{align}
Taking Eq.~(\ref{A0}) into account, we see that the only \emph{non-diagonal} term appearing in the expansion (\ref{expa1})
is $|A^1_{k k^\prime}|^2$, which is second order in $\Delta$.
This term can be readily evaluated
from Eq.~(\ref{app2}) by applying first order perturbation theory for the eigenstates
\begin{equation}
\psi_k=\psi_k^0+\sum_{q \neq k} \frac{\langle \psi_q^0|V|\psi_k^0\rangle}{\epsilon_k^0-\epsilon_q^0}\psi_q^0.
\end{equation}
After a simple algebra we obtain
\begin{equation}\label{app3}
A^1_{k k^\prime}=\frac{\langle \psi_k^0|V|\psi^0_{k^\prime}\rangle }{\epsilon_k^0-\epsilon_{k^\prime}^0} 2(\cos k -\cos k^\prime),
\end{equation}
which is valid up to linear order in $\Delta$.
Finally, by using the dispersion relation $\varepsilon_k^0=-2J \cos k$, Eq.~(\ref{app3}) further simplifies yielding
\begin{equation}\label{ultima}
A^1_{k k^\prime}=\frac{\langle \psi_k^0|V|\psi^0_{k^\prime}\rangle}{J}.
\end{equation}
Substituting Eq.~(\ref{ultima}) into Eq.~(\ref{app1})
and replacing the eigenstates by their zero order values $\epsilon_k=\epsilon_k^0$,
we recover the asymptotic formula (\ref{asy_weak}).
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,030 |
In March this year Google announced to all Google Analytics users the option to use Universal Analytics. This offers a new way for businesses to understand the changing, multi-device customer journey through the conversion path, as a typical consumer today uses multiple devices to access the web and interact in many ways with a business. This is likely to become the default system for Google Analytics, so websites have the option to try this for themselves now.
Improving the speed of a website by reducing client-side demands.
The aim is to change the way that data is collected and organised in the rapidly evolving online world of multiple platforms. Multiple platforms are not just limited to desktop, tablet, phone, but also game consoles, the point of purchase (POP), the shopping trolley, ski lift, billboard and so on.
Many of the benefits promised by Google's UA hinge on two updates to the platform. Firstly, the ability to get data into UA from any source, and secondly, the shift from tracking visits to tracking visitors. The future of data does indeed seem to be blurring the lines between online and offline, and with these new tools, the hope is to make more sense of it all and to paint a better picture for the brand, the client, or any user's understanding of the data and trends. Through an understanding of this data, business and individuals can better understand how visitors interact with their business online.
UA is an exciting development that holds significant promise for solving some difficult issues such as multi-device measurement and online/offline integration. Currently, the technology is still new, so more experimentation is needed in order to test UA's promises in real-world environments. However, new Analytics accounts have the option to use this code, or existing accounts are gradually getting the option to upgrade as UA is being rolled out by Google.
If you would like more details about how the use of Google's Universal Analytics can help your business, contact us now. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,813 |
Q: Two html forms on one page; Can only select second form fields with tab I have a a page with two forms on it. I can only click inside the input boxes of one form. For the other form, I can select the input boxes but only if I use tab. Is there anyway I can fix this? The site is http://login.peakperformancecct.com/. Just for reference, here is my code:
<div class="login">
<h1>Email Login</h1>
<form name="emaillogin" id="loginform" action="http://www.nspirelab.com:2095/login" method="POST">
<p>
<label for="user">Email Address<br />
<input class="input" id="user" name="user" type="text" value="" size="20" /></label>
</p>
<p>
<label for="pass">Password<br />
<input id="pass" name="pass" class="input" type="password" size="20" /></label>
</p>
<p class="submit">
<input type="submit" class="button-primary" value="Log In" />
</p>
</form>
</div>
<div class="login">
<h1>Site Login</h1>
<form name="sitelogin" id="loginform" action="http://peakperformancecct.com/wp-login.php" method="post">
<p>
<label for="user">Username<br />
<input class="input" type="text" name="log" id="log" value="" size="20" /></label>
</p>
<p>
<label for="pass">Password<br />
<input class="input" type="password" name="pwd" id="pwd" size="20" /></label>
</p>
<p class="submit">
<input type="submit" name="submit" value="Log In" class="button-primary" />
</p>
</form>
</div>
A: Validate, validate, validate.
Your labels in the second form are for the inputs in the first form.
Clicking on the label sends the focus to the input with which it is associated
(Since the inputs are inside the labels, so you can't click on the input without clicking on the label too).
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,263 |
Nonprofit Bike Shop: Can I Do That?
Yesterday, AL.com reported that Marcus Fetch, a former nomadic traveler was opening Redemptive Cycles, a nonprofit bike shop. The article explains, "The [shop's] nonprofit status allows the business to serve a charitable function, rebuilding, fixing and reselling used bikes at the cheapest price possible."
How is it possible that a retail store, which provides goods and services in the selling and repair of bicycles, can be a nonprofit organization? It seems so… commercial.
Beginning with the End in Mind: Legal Entity Selection for Social Ventures
It can be daunting to decide whether to organize a new venture as a nonprofit, tax-exempt organization or as a for-profit, business entity. Sometime an organization could be organized and operated both in a manner that qualifies for tax-exemption under Internal Revenue Code Section 501 or as a taxable business entity. Toss in a number of recently developed "hybrid" legal entities like the L3C and the social benefit corporation, and it is easy to quickly become misguided and/or confused in the options. Founders should thus heed Stephen Covey's wisdom and begin with the end in mind. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 311 |
package simple.obj;
import javafx.geometry.Point2D;
public abstract class AbstractViewableObject implements IViewableObject{
private SimpleBoundingBox myBoundingBox;
private String myPath;
public AbstractViewableObject(Point2D point, double width, double height, String path){
myBoundingBox = new SimpleBoundingBox(point, width, height);
myPath = path;
}
@Override
public SimpleBoundingBox getBoundingBox(){
return myBoundingBox;
}
@Override
public String getPath(){
return myPath;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,851 |
{"url":"https:\/\/www.nature.com\/articles\/s41396-021-00933-x?error=cookies_not_supported&code=3da6893c-42b6-4cae-bf06-1c72a21754a9","text":"## Introduction\n\nBacterial lipids are the key constituent segregating cellular components from the external environment. Bacterial lipids are highly diverse yet there is currently little understanding of the benefits that this diversity provides [1]. Glycerophospholipids are by far the best studied lipids in bacteria and a key branch point for glycerophospholipid biosynthesis is phosphatidic acid (PA), from which a variety of lipids, including phosphatidylglycerol (PG), phosphatidylethanolamine (PE), phosphatidylcholine (PC), diacylglycerol (DAG), and triacylglycerol (TAG), can be made through either the cytidine diphosphate (CDP)-diacylglycerol (DAG) pathway or the Kennedy pathway [2]. PA biosynthesis in bacteria is carried out by a membrane-attached acyltransferase PlsC, the founding member of the large lysophosphatidic acid acyltransferase (LPAAT) family [3, 4].\n\nAside from phospholipids, the study of bacterial lipid diversity is currently hampered by a lack of knowledge of both the chemical structures of many of these lipids and the identity of genes involved in their synthesis. These have severely hindered our understanding of lipid diversity and their physiological function in bacteria. Once the chemical structure of a lipid is known, analytical strategies can then be devised to detect the lipid in both the natural environment and cell cultures [5]. This can also help to direct studies into the biosynthesis of the lipid, knowledge of which can provide a clearer idea of the likely distribution of the lipid amongst various bacterial classes. A group of poorly studied bacterial lipids are the aminolipids, of which only ornithine lipids have been detected in diverse cultured bacteria since the 1960s [6]. However, it was not until the genes involved in its biosynthesis were elucidated that it became clear how widespread the capacity to produce ornithine lipid really was [7, 8]. Similarly, Sebastian et al. [9] found several uncharacterized aminolipids in marine heterotrophic bacteria one of which was recently determined as a glutamine-containing aminolipid, often found in the marine roseobacter group [10]. Both ornithine and glutamine lipids play a key role in the adaptation of cosmopolitan marine bacteria (e.g., the marine SAR11 clade and the roseobacter group) to oligotrophic environments [9,10,11].\n\nIn this study, we report the characterization and chemical structure of a novel sulfur-containing aminolipid using high resolution-accurate mass spectrometry from the marine roseobacter group. This newly identified lipid represents a novel class of sulfur-containing lipids with an aminosulfonate head group. Furthermore, we describe a novel acyltransferase enzyme (SalA), part of the LPAAT family, that is responsible for the biosynthesis of this sulfonolipid. This sulfonolipid appears widespread within the roseobacter group that are key players in marine biogeochemical cycles and important for biofilm formation. Furthermore, the salA gene is abundant and actively transcribed in marine surface microbial assemblages.\n\n## Materials and methods\n\n### Bacterial strains and cultivation\n\nAll marine bacteria used in this study were cultivated using either marine broth medium (BD Difco\u2122 2216), \u00bdYTSS medium containing yeast extract (2\u2009g\/L), tryptone (1.25\u2009g\/L), and sea salts (20\u2009g\/L,\u00a0Sigma-Aldrich) or a defined marine ammonium mineral salts (MAMS) medium [10]. The MAMS medium contained 30\u2009g\/L NaCl, 10\u2009mM glucose, 1\u2009mM K2HPO4, 0.75\u20137.5\u2009mM NH4Cl, 10\u2009mM HEPES buffer (pH 7.6), 1.36\u2009mM CaCl2, 0.98\u2009mM MgSO4, 7.2\u2009\u00b5M FeCl2, 84\u2009\u00b5M Na2MoO4, 370\u2009nM ZnCl2, 510\u2009nM MnCl2, 97\u2009nM H3BO3, 1.1\u2009\u00b5M CoCl2, 12\u2009nM CuCl2, 100\u2009nM NiCl2, 30\u2009nM thiamine, 160\u2009nM nicotinic acid, 97\u2009nM pyridoxine, 73\u2009nM aminobenzoic acid, 53\u2009nM riboflavin, 84\u2009nM pantothenate, 4.1\u2009nM biotin, 1.5\u2009nM cyanocobalamin, and 11\u2009nM folic acid. All cultures were grown at 30\u2009\u00b0C aerobically in a shaker (150 r.p.m) unless stated otherwise.\n\n### Intact polar lipid analysis\n\nLipid extraction from bacterial cultures was carried out using the modified Folch extraction protocol as described previously [10, 12]. Briefly 1\u2009mL culture of OD540\u2009~\u20091.0 was collected by centrifugation. Total lipids were then extracted using methanol-chloroform, dried under nitrogen gas and the pellet re-suspended in 1\u2009mL solvent (95% (v\/v) liquid chromatography-mass spectrometry (LC-MS) grade acetonitrile and 5% 10\u2009mM ammonium acetate pH 9.2 in water). These lipids were then analysed by LC-MS using a Dionex 3400RS HPLC with a HILIC BEH amide XP column (2.5\u2009\u00b5m, 3.0 \u00d7 150\u2009mm, Waters) coupled with an amaZon SL ion trap MS (Bruker) via electrospray ionization (ESI) in both positive (+ve) and negative (\u2212ve) ionization mode. Samples were run on a 15\u2009min gradient from 95% (v\/v) acetonitrile\/5% (w\/v) ammonium acetate (in water, 10\u2009mM, pH 9.2) to 70% (v\/v) acetonitrile\/30% (w\/v) ammonium acetate (in water, 10\u2009mM, pH 9.2), followed by 5\u2009min of isocratic run 70% acetonitrile\/30% ammonium acetate with 10\u2009min equilibration between samples. The flow rate was maintained at 150\u2009\u03bcL\u2009min\u20131 and the column temperature at 30\u2009\u00b0C. The injection volume was 5\u2009\u03bcL for each run; the ionization was done in both positive and negative mode. Drying conditions were the same for both modes (8\u2009L\u2009min\u20131 drying gas at 300\u2009\u00b0C and nebulizing gas pressure of 15\u2009psi). The end cap voltage was 4500\u2009V in positive mode and 3500\u2009V in negative mode, both with 500\u2009V offset. Data analysis was carried out using the Bruker Compass software package. Unless stated otherwise, base peak chromatographs were presented with m\/z range from 400 to 1000.\n\nHigh resolution MS identification and fragmentation was carried out using either a quadrupole-time-of-flight MS (Q-TOF, Waters Synapt G2-Si) or an Orbitrap Fusion (Thermo Fisher Scientific) by direct infusion and collision induced dissociation (CID). For the Orbitrap Fusion, the resolution was set at 120\u2009K with CID for MSn. A TriVersa Nanomate nanospray source (Advion, NY) was used and the flow rate was at 300\u2009nL\u2009min\u22121. The voltage was set at 1.4\u2009kV and the gas pressure was 0.3\u2009psi. Sheath and sweep gas were set to zero and the cone voltage was 2100\u2009V and the mass range was from 50 to 1000\u2009Da. MS data were analyzed using Xcalibur (Thermo Fisher Scientific). For Q-TOF, samples were injected through a Universal NanoFlow Sprayer (Waters) by direct infusion at 200\u2013300\u2009nL\u2009min\u22121 and the cone voltage was 30\u2009V in negative mode ESI. Mass range was set from 50 to 1000\u2009Da and data analyses ware carried out in MassLynx (Waters). The most abundant peak in the negative ion spectrum corresponding to the SAL lipid (m\/z 656.6) was selected for MSn fragmentation. Spectra were obtained in profile mode and smoothed using a moving mean. Background correction using a linear baseline was applied with a 40% noise cut-off. For accurate mass determination, the centroid of each peak was used. The peak corresponding to\u00a0C17H33COO (m\/z 281.2480, an 18:1 fatty acid carboxylate anion) was used as a lock mass. Calculation of candidate elemental formulae from the accurate mass considered formulae containing C0\u2013100, H0-100, N0-100, S0-4, and P0-1. A conservative mass error of 100 ppm was assumed.\n\n### Marker-exchange mutagenesis\n\nMarker-exchange mutagenesis was carried out as described previously using a suicide vector pK18mobsacB [10]. Briefly, DNA fragments corresponding to an upstream element and a downstream element that flank the target gene were amplified by PCR using high-fidelity Phusion DNA polymerase. A Gm-resistance cassette was amplified from plasmid p34S-Gm [10, 13]. These fragments, together with the linearized pK18mobsacB vector were then assembled through Gibson cloning and transformed into competent Escherichia coli DH5\u03b1 cells. The engineered suicide vector was then extracted from E. coli DH5\u03b1 and transformed into the conjugation donor strain E. coli S17.1 \u03bbpir before conjugating into Ruegeria pomeroyi DSS-3 as described previously [10]. Transconjugants were then selected on defined MAMS medium containing gentamycin (Gm, 10\u2009\u03bcg\u2009mL\u22121). All mutants were confirmed by PCR using the confirmation primers (Supplementary Table\u00a01) and subsequent Sanger sequencing.\n\n### Transposon library of Phaeobacter inhibens DSM 17395\n\nA library of 5500 transposon mutants of Phaeobacter inhibens DSM 17395, which was established at the DSMZ, served as a basis to identify genes involved in the biosynthesis of the novel SAL lipid. Transposon mutagenesis was performed\u00a0with\u00a0the EZ-Tn5<R6K\u03b3ori\/Kan-2> Tnp Transposome kit (Epicentre, Illumina, CA, USA) and the insertion site of all mutants was determined via arbitrary PCR [14]. Transposon mutants were streaked out three times to eliminate attached wild type cells. The absence of wild type cells and the presence of the 65\u2009kb plasmid were validated as described previously [14,15,16]. The transposon integration site of each mutant was also confirmed via sequencing of the amplification PCR product, and stable maintenance of all three extrachromosomal elements was validated via diagnostic PCR [17].\n\nThe transposon mutant #1036 of P. inhibens DSM 17395 (PGA1_c01210) unable to produce the SAL lipid was complemented using the salA homolog of Ruegeria pomeroyi DSS-3 (locus tag SPO0716) and P. inhibens DSM 17395 (locus tag PGA1_c01210). Complementation was carried out by PCR amplification of the salA homologs together with a constitutive promoter (~250\u2009bp upstream of the aacC1 gene from plasmid p34S-GM [13]), which was then cloned into the broad host range vector pBBR1MCS and transformed into the salA mutant of P. inhibens DSM 17395 by conjugation as described previously [9, 10]. The complemented mutants were cultivated using marine broth medium and cells were harvested for lipidomics analysis as described above.\n\n### Biofilm assays\n\nTo grow biofilms of Phaeobacter inhibens DSM 17395 and the salA mutant, post-exponential grown bacterial cells were washed and diluted in fresh marine broth medium and inoculated at an OD590 nm of 0.2 into 24-well plates (Corning Incorporated Costar\u00ae, New York, NY, USA) containing a sterilized glass coverslip into each well. At each time point (3, 24, and 48\u2009h), biofilms were washed to remove non-adherent bacteria and fixed using formalin 3.5% (v\/v) for 20\u2009min. Bacteria were stained using DAPI (5\u2009\u03bcg\u2022\u2009mL\u22121, Sigma-Aldrich, Darmstadt, Germany) and coverslips were mounted with a drop of Mowiol antifade before observation using confocal laser scanning microscopy (CLSM) (Zeiss LSM 880, G\u00f6ttingen, Germany). The biovolume and the average thickness of the biofilms were determined using COMSTAT software developed in MATLAB R2017a (MathWorks, Natick, MA, United States) as described previously [18, 19]. To test for statistically significant differences between the wild-type strain and the salA mutant, a t-test was performed using SPSS 13.0 (IBM, Armonk, NY, USA).\n\nA crystal violet biofilm assay was also performed which was adapted from Guillonneau et al. [18]. Bacterial biofilms were developed in 96-well microtiter plates (Greiner Bio-One, Kremsm\u00fcnster, Austria) with bacteria in the post-exponential growth phase using marine broth medium. Cells were diluted to a final OD590 nm\u2009=\u20090.1 into each well (n\u2009=\u20094 for both the wild type and the salA mutant) and grown in static conditions at 30\u2009\u00b0C. At each time point (3, 24, 48, and 72\u2009h) samples were washed three times with fresh marine broth medium and dried for 30\u2009min at 50\u2009\u00b0C. Biofilms were then stained for 15\u2009min with 200\u2009\u03bcL crystal violet 0.01% (w\/v), rinsed three times with phosphate-buffered saline and dried for 10\u2009min. Biofilm quantification was performed by releasing the stain from the biofilm using absolute ethanol for 10\u2009min at 30\u2009\u00b0C with gentle shaking. The absorbance of the crystal violet in solution was measured at 595\u2009nm. The final absorbance of each sample was calculated by subtracting the blank (i.e., marine broth medium only treated with crystal violet, n\u2009=\u20094).\n\n### Bioinformatics analysis\n\nPhylogenetic analysis of 16S rRNA genes from Rhodobacteraceae was carried out using the full length 16S rRNA gene retrieved from the Integrated Microbial Genomes (IMG) database (https:\/\/img.jgi.doe.gov\/). Sequence alignment of 16S rRNA genes and LPAAT genes (also retrieved from IMG) were performed using Muscle and phylogenetic analyses were performed with MEGA7.0 [20] with 500 bootstrap replicates. Sequence alignment was visualized using JalView [21].\n\nTo search for SalA homologs in the Tara metagenome\/metatranscriptomics datasets, we used the Ocean Gene Atlas (OGA) database OM_RGCv2_metaG (metagenomics) and OM-RGCv2_metaT (metatranscriptomics) with e-value cut-off of e\u221240 [22]. Abundance was normalized as a percentage of the median mapped read abundance of genes\/transcripts of ten prokaryotic single-copy marker genes [23]. Taxonomic distribution of homologs was displayed using Krona in the OGA interface.\n\nThe genomes of the marine roseobacters used in this study were downloaded from the NCBI database. These comprised nine strains that were found to produce SAL and two strains (Stappia stellulata DSM 5886 and Dinoroseobacter shibae DFL12) that did not. In order to identify genes potentially involved in SAL synthesis, each gene from the 11 genomes was assigned to an orthologous group using the eggNOG mapper [24]. This program conducts a BLAST search of each sequence against the eggNOG database [25] of orthologous genes, with the query sequence being annotated with the same orthologous group as the best BLAST hit. Orthologous groups that were present in the genomes of all SAL-producing strains but absent from the genomes of S. stellulata and D. shibae were considered to be potentially involved in SAL synthesis.\n\nAbundance data of SalA homologs from four depths derived from the Tara metagenomics\/metatranscriptomics datasets were tested for normal distribution using a Shapiro\u2013Wilks test. Significant differences between depths was tested for using a Kruskal\u2013Wallis test followed by a post-hoc Dunn\u2019s test using Holm\u2019s correction for multiple comparisons. All statistical analysis was performed in RStudio (version 1.3) using R (version 4.02).\n\n### In silico homology modeling and docking studies for SalA\n\nA SalA homology model was generated using the Phyre2 protein folding prediction server [26], and the lyso-SAL lipid was drawn in MarvinSketch (v19.10.0, 2019, ChemAxon for Mac) and exported as a Mol SDF format file. The homology model was built using the structure of the lysophosphatidic acid acyltransferase PlsC (PDB code 5KYM [4]). The SalA protein model was then imported into Flare (v3.0, Cresset) for docking the lyso-SAL substrate and energy minimized with 2000 iterations with a cut off of 0.200\u2009kcal\/mol\/A. The lyso lipid was imported as a ligand and energy minimized in Flare before being docked into the active site and the best scoring pose selected.\n\n## Results\n\n### A new sulfur-containing aminolipid is found in Ruegeria pomeroyi DSS-3\n\nDuring LC-MS analysis of lipid extracts from Ruegeria pomeroyi DSS-3 grown on \u00bd YTSS medium, two prominent peaks eluting around 3.5\u2009min were found in both negative and positive ionization mode (Fig.\u00a01). The most prominent ions in the two peaks had m\/z values of 656.6 and 672.7 in the negative ionization mode, respectively. Other major lipids identified in this bacterium include two phospholipids, PG and PE and two aminolipids, ornithine lipid (OL) and glutamine lipid (QL) [10].\n\nTo elucidate the structure of the new lipids eluted at 3.5\u2009min, the most intense species, at 656.4882\u2009m\/z, was selected for high resolution MS\/MS analysis on a quadrupole-time of flight (Q-TOF) mass spectrometer (Fig.\u00a02). At low collision energy (40\u2009eV) the major species formed corresponded to a neutral loss of 282 mass units. This is consistent with the neutral loss of an 18:1 fatty acid. A second peak at m\/z 281.2480 is likely the carboxylate anion of an 18:1 fatty acid. Further fragmentation, at higher collision energies (up to 90\u2009eV), yielded a major ion at m\/z 237.2159. This ion likely corresponds to a 16:0 fatty acid present as a ketene, which would be consistent with the fragmentation scheme proposed for ornithine lipids and glutamine lipids [27]. These results therefore suggest a lipid class with a similar fatty acyl backbone structure to the aminolipids, such as ornithine and glutamine lipid [10]. The glutamine lipid (QL, [M+H]+ m\/z 719.7) and ornithine lipid (OL, [M+H]+ m\/z 705.7) was eluted at 9.5 and 12.5\u2009min, respectively (Fig.\u00a01). The formation of these novel lipids at ~3.5\u20134\u2009min is not affected in the olsA or glsB mutants of R. pomeroyi DSS-3 (Supplementary Fig.\u00a0S1). The olsA and glsB genes in R. pomeroyi DSS-3 were essential for the production of the nitrogen-containing ornithine\/glutamine lipids [10].\n\nProminent peaks at 80 and 81\u2009m\/z, respectively, were apparent in the fragmentation spectrum obtained at 90\u2009eV collision energy (Fig.\u00a02c). The accurate masses of these ions were 79.9568 and 80.9643. Of the candidate formulae within 100 ppm of the measured mass, $${\\mathrm{SO}}_3^ -$$ and $${\\mathrm{HSO}}_3^ -$$ appear most plausible, with mass errors of 0.182 ppm and 4.194 ppm, respectively. A smaller peak doublet at m\/z 63.9611 and 64.9692 was also present in the 90\u2009eV spectrum. These masses are unambiguously assigned to $${\\mathrm{SO}}_2^ -$$ (mass error 12.506 ppm) and $${\\mathrm{HSO}}_2^ -$$ (mass error 8.08 ppm). Taken together, these results demonstrate the presence of a sulfonate group in the lipid. An ion at 136.0045\u2009m\/z corresponded to the deprotonated head group. The mass determined here is larger than that of deprotonated taurine (m\/z 124). Since the head group includes a sulfonate ($${\\mathrm{SO}}_3^ -$$) group, the plausible formula most closely corresponding to the accurate mass is C3H6NSO3 (Table\u00a01). This is consistent with the structure being aminopropane sulfonic acid, although the position of the amino group cannot be unequivocally determined by mass spectrometry (Fig.\u00a02). The proposed fragmentation scheme is presented in Fig.\u00a03.\n\nTo further confirm the presence of an amino-group in the hydrophilic head of this SAL, we cultivated Ruegeria pomeroyi DSS-3 in a chemically defined marine ammonium mineral salts (MAMS) medium using 15N-ammonium as the sole nitrogen source. Indeed, the 15N-labeled SAL was readily observed in the lipid extract resulting in a shift of m\/z from 656.4951 to 657.4903 (Supplementary Fig.\u00a0S2a), whereas the non-nitrogen containing lipids, such as PG were not labeled by 15N as expected (Supplementary Fig.\u00a0S2b). The incorporation of the 15N isotope into the head group of SAL was confirmed by MSn (Supplementary Fig.\u00a0S2c, d). We also performed the same MSn analysis on the m\/z 672.4875 species as well as the 15N-labeled m\/z 673.4852 species. Loss of 282 at MS2 (672.4875\u2192390.2317; 673.4852\u2192391.2285) suggests the R2 fatty acid was C18:1. Therefore, the data suggest that the lipid species eluted immediately after the m\/z 656.6 species is likely a hydroxylated SAL, and the proposed fragmentation scheme is presented in Supplementary Fig.\u00a0S3.\n\n### The sulfur-containing aminolipid is found in a range of marine roseobacters\n\nTo investigate the presence of SAL amongst roseobacters we selected 16 strains, in addition to R. pomeroyi DSS-3, to obtain a wide coverage of the roseobacter group including the model roseobacter bacterium Phaeobacter inhibens DSM 17395 (Fig.\u00a04). The selected strains included Stappia stellulata, which recent phylogenetic studies indicate is not a member of the Rhodobacteraceae [28], which served as an outgroup. These strains were each grown in marine broth overnight, before cells were harvested for lipid analysis. SAL was detected in all the strains tested apart from S. stellulata and Dinoroseobacter shibae (Fig.\u00a04a). The separation of these two strains from the remaining roseobacter sequences is in line with previous results showing D. shibae branching deeply within the Rhodobacteraceae phylogeny [29].\n\n### Comparative genomics to determine genes involved in SAL biosynthesis\n\nWe then conducted a comparative genomics investigation into the roseobacter strains whose lipid profiles had been analysed. We reasoned that synthesis of the SAL would require an N-acyltransferase activity to acylate aminopropane sulfonic acid, analogous to that mediated by OlsB and GlsB in the synthesis of ornithine and glutamine lipid [8, 10]. We investigated predicted N-acyltransferases that were present in all the strains that produced SAL in marine broth (the \u201cproducers\u201d), while being absent from the strains that did not produce SAL (the \u201cnon-producers\u201d). We assigned all the genomic sequences from the nine genome-sequenced producer strains and two non-producer strains to orthologous groups (OGs) using the eggNOG-mapper software [24], which provides a consistent pipeline for sequence annotation and OG assignment by comparison to the eggNOG database [24]. We identified a group of 1417 \u201ccore\u201d genes which were present in the genomes of all SAL producer strains of which 1060 were also present in the two non-producers (Fig.\u00a04b). Thirty-seven candidate genes are present in all SAL producer strains but not in the genomes of the non-producers (Fig.\u00a04b), two of which (OG accession numbers 08UX5 and 05CDD) were annotated as being potential acyltransferases (Table\u00a02). We therefore generated mutants in these two genes in the two model bacteria, R. pomeroyi DSS-3 and P. inhibens DSM 17395 and screened for the loss of SAL production. The 08UX5 mutant (locus SPO2471) of R. pomeroyi DSS-3 still produced SAL to the same level as the wild type (data not shown), suggesting that this gene is unlikely involved in SAL formation. However, in the 05CDD mutant of P. inhibens DSM 17395 (locus tag PGA1_c01210), SAL formation is completely abolished, suggesting that this gene is indeed responsible for SAL biosynthesis (Fig.\u00a04c). This gene is named salA hereafter. Indeed, when the mutant was complemented with either salA from R. pomeroyi DSS-3 (SPO0716) or P. inhibens DSM 17395 (PGA1_c01210), SAL production was restored (Fig.\u00a04d).\n\nSalA is a putative O-acetyltransferase-like protein with a recognized LPAAT (lysophosphatidic acid acyltransferase) domain. Amongst bacterial LPAAT-domain containing proteins, the best characterized examples are PlsC and OlsA, encoding enzymes responsible for the final step in the biosynthesis of the anionic phospholipid phosphatidic acid (PA) and the ornithine\/glutamine-containing aminolipid, respectively [3, 10, 30]. The structure of PlsC has recently been solved, showing an in silico docked LPA lipid together with the fatty acid in an acyl carrier protein (ACP, [4]). Multiple sequence alignments of SalA, PlsC, and OlsA shows the presence of two conserved sequence motifs (Fig.\u00a05), representing the catalytic center (HX4\/5D) and the substrate co-ordination center (FP[E\/S]G[T\/V]), respectively. Notably, both PlsC and OlsA have the conserved HX4D motif whereas SalA has the HX5D motif. Interestingly, the reported key Lys105 in PlsC, thought to be responsible for electrostatic interactions via its amide nitrogen backbone to the negatively-charged oxygen of the ACP-fatty acid intermediate, was replaced with Arg135 in SalA. The LPA phosphate head group is thought to be coordinated by Arg159 in PlsC. However, the sequence alignment shows a Val189 in SalA. In order to further investigate the implications of the sequence alignment, we obtained a homology model of SalA. The model shows the catalytic HX5D motif to be structurally comparable to that of PlsC despite the additional residue, with the His109 and Asp115 adjacent to each other, analogous to that in PlsC (Supplementary Fig.\u00a0S4). In silico docking of a lyso-SAL lipid molecule into the model demonstrated a possible pose for the lyso-lipid hydroxy group adjacent to His109 (Supplementary Fig.\u00a0S4), with the Arg135 suggested to coordinate the sulfonate head group. The conformationally flexible alkyl chain group was able to adopt many configurations, but the polar head group was docked consistently in the same region. Overall, the data suggests a diversification in function of LPAAT family enzymes during evolution, with SalA representing a novel member of this group. The presence of this unique motif of HX5D in SalA allowed us to determine the distribution of SAL-biosynthesis in environmental metagenomes and metatranscriptomes (see below).\n\n### SAL production in Phaeobacter inhibens DSM 17395 is involved in biofilm formation\n\nWe next investigated the role of SAL lipids in the physiology of roseobacters. The loss of SAL lipids had no clear role in the growth of the bacterium. Both wild type and the salA mutant of Phaeobacter inhibens DSM 17395 had comparable growth rates and reached similar final cell density in marine broth medium (Supplementary Fig.\u00a0S5a). An important change of lifestyle for roseobacters is the switch from planktonic growth to biofilm formation, which triggers a particle-associated life strategy that is ecologically relevant for their survival in the natural environment [31]. It has been shown previously that many roseobacters including Phaeobacter inhibens DSM 17935 are able to form a biofilm, and a 65\u2009kb plasmid in this bacterium was important for biofilm formation [15, 16]. Interestingly, we observed that the salA mutant has a significantly reduced ability to form biofilms when in contact with solid surfaces, such as glass (Fig.\u00a06) and plastics (Supplementary Fig.\u00a0S5b). Both the bioviolume on the glass surface as well as the thickness of the biofilm are significantly reduced in the salA mutant strain in the early phase of biofilm formation (3\u2009h), and the latter stage (24 and 48\u2009h) of biofilm maturation (Fig.\u00a06). The 65\u2009kb biofilm plasmid was confirmed to be present in the salA mutant (Supplementary Fig.\u00a0S5c). Thus, the significant reduced ability of the salA mutant in biofilm formation suggests that this lipid may play a key role in roseobacters in their natural environment.\n\n### Distribution of the new acetyltransferase SalA in the Tara Ocean metagenomes and metatranscriptomes\n\nTo better understand the distribution of SAL in environmental microbial assemblages, we searched the Tara Ocean metagenomes and metatranscriptomics datasets using SalA (locus tag, SPO0716 of R. pomeroyi DSS-3) as the query. We experimentally determined the e value cut-off to be e\u201340 at which value it selectively retrieves LPAAT homologs belonging to SalA but not OlsA or PlsC. The environmental SalA homologs obtained from the Tara Oceans metagenome and metatranscriptomics dataset were aligned, and the key sequence motifs were manually examined. In particular, the HX5D motif is strictly conserved in all SalA sequences retrieved from the Tara Oceans datasets providing strong support, that these environmental sequences are of the SalA but not PlsC nor OlsA clade. On average, between 2\u20134% of microbial cells are estimated to have the potential for SAL biosynthesis; this is comparable to that of the olsA gene but somewhat lower than the plcP\u00a0gene in the same dataset, suggesting SAL biosynthesis is less prevalant than the PlcP-mediated lipid remodeling pathway [9, 10]. This is likely due to the fact that SALs are primarily found in marine roseobacters but not in other dominant marine Alphaproteobacteria, such as the abundant bacterium Pelagibacter ubique of the SAR11 clade which are capable of PlcP-mediated lipid remodeling [9, 11]. Indeed, the majority (>85%) of the SalA sequences from the Tara Oceans dataset were classified as members of the Rhodobacteraceae in both Tara Oceans metagenomes and metatranscriptomes (Fig.\u00a07), and a thorough search of 120-genome sequenced Rhodobacteraceae confirmed the wide occurrence of salA in all ten clades of the roseobacters (Supplementary Fig.\u00a0S6 [32]).\n\n## Discussion\n\nHere, we identify a novel aminolipid containing an aminopropane sulfonic acid head group that is widespread amongst marine roseobacters. The presence of a sulfonate group means this SAL lipid also falls into the broad category of sulfonolipids. The most abundant, and arguably one of the best studied lipids of this type, is sulfoquinovosyl diacylglycerol (SQDG), which is present in the membranes of most oxygenic phototrophs [33] as well as some heterotrophic bacteria [34]. SQDG likely plays a structural role in photosynthetic membranes, since crystal structures of photosystem proteins show specific binding of this lipid [35].\n\nOther sulfolipids appear to elicit potent responses when certain organisms are exposed to them. Thus, a sulfolipid produced by zooplankton from a number of copepod species was found to induce toxin production in the dinoflagellate Alexandrium minutum [36], likely as a defense against predation. Conversely, a sulfonolipid produced by the Bacteroidetes bacterium Algoriphagus machipongonensis induced the development of multicellularity in a choanoflagellate [37]. Both examples suggest that sulfolipids are used by the sensing organism as a marker for the presence of another organism with which it interacts (either as a predator or as a symbiont). The fact that sulfolipids appear to be relatively rare across the tree of life likely makes them well suited to mediate such chemical interactions, where a high degree of specificity is required. Lipids similar to those produced by A. machipongonensis have been described in a number of Bacteroidetes, particularly amongst Cytophaga [38,39,40]. They tend to be localized to the outer membrane, and seem to play a role in the gliding motility of these organisms [41, 42]. The sulfonolipids from Bacteroidetes differ from those that we describe here in roseobacters in that they are composed of a base, termed capnine, similar to the sphingoid bases of sphingolipids, which may be N-acylated to form the full sulfonolipid [38]. In this way they are similar structurally to sphingolipids, whereas the SALs of the roseobacter group are more similar to aminolipids such as ornithine lipid and glutamine lipid (Fig.\u00a05). Whether the SAL lipid plays a role in interspecies interactions requires further work. However, we already observed that this lipid is involved in biofilm formation in Phaeobacter inhibens DMS17395 (Fig.\u00a06), suggesting that formation of this SAL lipid may play an important role in the adaptation of marine roseobacters to a biofilm lifestyle.\n\nA survey of the distribution of SAL among isolates from the roseobacters indicated that the ability to produce this lipid is widely distributed within the group. One strain, D. shibae, taxonomically the most basal of the strains examined, lacked any SAL under the conditions assessed, as did the outgroup strain Stappia stellulata. The absence of SAL in these strains suggests they lack the capacity to produce this lipid as the other roseobacters examined seem to produce SAL constitutively. However, it is possible that these strains have the capacity to produce SAL, but only do so under certain conditions. This pattern is observed for ornithine lipid, which is produced constitutively in some bacteria, such as R. pomeroyi DSS-3 [10], but in others is only produced as a response to P-depletion [11, 43]. Indeed, a close salA homolog was found in the genome of D. shibae (Dshi_0206), but it is absent in S. stellulata.\n\nAlthough we have identified the LPAAT enzyme, SalA, involved in the last step of synthesis of this new sulfur-containing aminolipid, the key steps and genes involved in the synthesis of the lyso-SAL lipid remain to be determined. It is likely that SAL synthesis occurs in a manner analogous to that of ornithine and glutamine lipids. As such, 3-hydroxy fatty acids would be required as a substrate for the first step in SAL synthesis [44]. Such a hypothesis suggests that the aminopropane sulfonic acid moiety is also directly produced by the marine roseobacters since no exogenous supply was provided. The presence of 3-aminopropane sulfonic acid (a.k.a. homotaurine) has been documented in some red algae [45, 46] and unicellular green algae (prasinophytes such as Ostreococcus and Micromonas, [47]) but, to the best or our knowledge, never previously in bacteria. However, a hydroxylated form of 2-aminopropane sulfonic acid, cysteinolic acid, has been found in a variety of marine phytoplankton and heterotrophic bacteria, including Ruegeria pomeroyi DSS-3 although its biosynthetic pathway remains to be established [47]. Nevertheless, it is tempting to speculate that 2-aminopropane sulfonic acid is likely the hydrophilic head of the new SAL observed in these marine roseobacters, and this certainly warrants further investigation.\n\nTo sum up, this study describes a new class of lipid, which are an important component of the membranes of a number of marine Rhodobacteraceae. Comparative genomics of SAL-producing strains has identified a novel acyltransferase (SalA), which is involved in the production of this lipid. salA is widely distributed in marine microbial assemblages in the Oceans and actively expressed in Tara Oceans metatranscriptomes, and its functional role in addition to biofilm formation in these marine bacteria certainly warrants further investigation.","date":"2022-12-03 10:37:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5929983854293823, \"perplexity\": 9705.912306802846}, \"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\/1669446710926.23\/warc\/CC-MAIN-20221203075717-20221203105717-00334.warc.gz\"}"} | null | null |
{"url":"http:\/\/physics.stackexchange.com\/tags\/entanglement\/new","text":"# Tag Info\n\n0\n\nHere are my two cents on this. In quantum mechanics, one, two,...many particles are described by a state function. The state function is gives a probability distribution that includes all the possible measurable values of the one,two...many particles. Let us take two for simplicity and because here is where confusion arises. Because of conservation of ...\n\n1\n\nIn case your box was classical, it'd output either vertically polarized A and horizontally polarized B or vise-versa, a 45 degree polarizer placed in front of both would allow both to pass half of the time, and block them half of the time - but the pass\\block statistics would not be correlated, while in the entangled case, if A passed, B will be blocked, and ...\n\n5\n\nWhat you are proposing is called a local hidden variable theory. Bell's theorem proves that any such local hidden variable theory is inconsistent with behavior predicted by quantum mechanics. Bell test experiments have been performed, which show that the predictions made by quantum mechanics are correct, in ways that cannot be explained by a local hidden ...\n\n1\n\nMy understanding is that the Aspect experiment shows that your understanding is wrong. http:\/\/en.wikipedia.org\/wiki\/Aspect_experiment\n\n0\n\nSeeing your last question, why would you even consider this scenario with entangled photons? Seems like the same question can be perfectly asked with one single photon. But anyway, ignoring the possible optical issues in the scenario, like the exact color of the film you use, or what Nanite has commented about, either way you will not see a superposition of ...\n\n0\n\nMathematically you have a superposition of two Eigenstates and you use it because you don't know all parameters of the source. And yes, you use a probabilistic source, otherwise you will not do any experiment with it. Using your special source you get always the next result: Measuring one of the photons you know immediately the Eigenstates of the twisted ...\n\n1\n\nThere exists a precise way of calculating the entanglement entropy in a conformal field theory via the Ryu-Takayanagi (RT) prescription in the context of the AdS\/CFT correspondence. The RT prescription says that the entanglement entropy of a sub-system $A$ in the CFT$_{d+1}$ that lives on the boundary of AdS$_{d+2}$ is given by the minimal area surface ...\n\n1\n\nAll different QKD protocols are well covered in most Quantum Information textbooks, e.g. Quantum Information by Jaeger. Trying to give a complete, understandable coverage of the matter is impossible in a post like this, so I'll just give you an overview: In the E91 scheme, entangled photon pairs are used between Alice & Bob, and unlike the single-photon ...\n\n2\n\nThe answer is definitely yes. The ground states (and low-lying eigenstates) of many-body systems are generically entangled. Examples include the ground states of local quantum field theories (which describe the fundamental particles and forces of nature) and ground states of fermionic lattice models (which describe much of the solid matter we see around us). ...\n\n1\n\nIn short, entanglement is perfectly normal. I am sure that entanglement is ubiquitous in, say, atoms with more than one incomplete subshell, as well as in some kind of organic molecules, but I am not a quantum chemistry expert and can\u2019t provide an easy-to-realize example. Generally, any decay process produce particle states that are entangled in some way ...\n\n6\n\nThe morally correct answer is that the measurement of one spin in the EPR-entangled pair eliminates the entanglement as it picks a particular factorized basis vector for the measured spin, and the total wave function therefore has to factorize to $\\psi_\\text{just measured}\\otimes \\psi_{\\rm something}$. If you parameterize the multi-fermion states in terms ...\n\nTop 50 recent answers are included","date":"2014-09-03 02:39:11","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\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7284241914749146, \"perplexity\": 518.1608188691373}, \"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-2014-35\/segments\/1409535924131.19\/warc\/CC-MAIN-20140901014524-00310-ip-10-180-136-8.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
NGC~2264~C is a nearby \citep[distance=738~pc][]{Kamezaki2014} cluster forming region. Many millimeter and submillimeter sources have so far been identified in this region \citep{Ward-Thompson2000,Peretto2006,Peretto2007}. \citet{Maury2009} found eleven outflow lobes in the NGC~2264~C region by an extensive mapping observation of CO. Recently, \citet{Ana2016} found the SiO emission with narrow line width in the periphery of NGC~2264~C, and suggested that it reveals a remnant of past star formation activities. In such a complex structure of this region, NGC~2264~CMM3 is known to be the most massive core \citep[40~M$_{\odot}$:][]{Peretto2006} located almost at its geometrical center. According to the theoretical model, CMM3 is predicted to evolve into a main sequence star with a mass of $8M_{\odot}$ \citep{Maury2009}. The protostar of CMM3 is deeply embedded in an envelope, and hence{\rm ,} no mid-infrared source is identified even in the 24~$\mu$m band of \textit{Spitzer}. A definitive evidence of star formation in CMM3 was first found by \citet{Saruwatari2011}, who identified a compact bipolar outflow with a dynamical age of 140--2000~year by the CO and CH$_3$OH observations with the Submillimeter Array (SMA). \citet{Cunningham2016} also identified the bipolar outflows in the CO, H$_2$CO, SO, and SiO lines. Judging from the non-detection of mid-infrared sources and the association of dynamically young outflows, \citet{Saruwatari2011} suggested that CMM3 is a candidate of a high mass protostar in the early evolutionary phase.
Toward CMM3, a chemical composition has been studied by a spectral line survey observation with single dish telescopes in the 4~mm, 3~mm, and 0.8~mm bands \citep{Watanabe2015}. In their survey, carbon-chain molecules such as C$_4$H, HC$_5$N, and C$_3$S are found to be relatively abundant in CMM3 compared with the representative high-mass star forming region Orion~KL, while complex organic molecules are deficient. This result suggests chemical youth of the CMM3 envelope.
Recently, we carried out a spectral line survey toward CMM3 at a high angular resolution with ALMA in the 0.8~mm band. Here we report the results on the continuum emission and the distributions of the emission of complex organic molecules.
\section{Observation and Reduction}
The observations were carried out with ALMA on 19 July 2014 and 20 May 2015, where the numbers of the 12~m antenna used in those observations were 31 and 39, respectively. Minimum and maximum baseline lengths were 14~m and 649~m on the ground, respectively. Twelve spectral windows were employed to cover the frequency ranges of 336.0--347.3~GHz and 348.0--359.3~GHz at a frequency resolution of 0.98~MHz. The phase-center coordinate is ($\alpha_{\rm J2000}$, $\delta_{\rm J2000}$) = (6:41:12.3, +9:29:8.0). The quasars J0510+1800 and J0725-0054 were observed for the bandpass calibration in the 2014 and 2015 sessions, respectively. The quasars J0643+0857 and J0700+1709 were observed for the amplitude and phase gain calibrations in the 2014 and 2015 sessions, respectively. The absolute flux was calibrated by using the quasar J0750+125. The uncertainty of the absolute flux calibration is 10~\% according to ALMA Cycle 2 Technical Handbook (Lundgren~2013). In these observations, any structure extended over $\sim 13''$ or larger is subject to the resolving-out effect, judging from the minimum baseline length of 14~m.
Data reduction was carried out with the Common Astronomy Software Applications package (CASA; Version 4.5.3). A continuum image was obtained by averaging line-free channels of all the spectral windows. Self-calibration was performed by using the continuum data, and then the solutions were applied to both the continuum and spectral line data. After the self-calibration procedures, the data were imaged and CLEANed by using the Briggs weighting with the robustness parameter of 0.5. The resulting synthesized beam and the root-mean-square (rms) noise of the continuum image are $0.37'' \times 0.30''$ (P.A.$=-30.7^{\circ}$) and 0.35~mJy~beam$^{-1}$, respectively. The signal-to-noise ratio in the continuum image was improved from 190 to 723 by applying the self-calibration procedure. The synthesized beam and the rms noise of spectral images range from 0.28$''$ to 0.49$''$ and from 4.2~mJy~beam$^{-1}$ to 7.0~mJy~beam$^{-1}$ at the frequency resolution of 0.98~MHz, respectively, depending on the frequency.
\section{Results}
\subsection{Detection of a Potential Binary System in the CMM3}
Figure~\ref{fig01}a shows the 0.8~mm continuum image of NGC~2264~CMM3 observed with ALMA. The beam size of $0.37'' \times 0.30''$ (P.A.$=-30.7^{\circ}$) corresponds to a linear scale of $\sim270$~au at the distance of 738~pc. CMM~3 is well resolved into the two continuum peaks CMM3A and CMM3B with comparable flux densities of 431.8~mJy and 313.0~mJy, respectively (Table~\ref{tab01}). The angular separation between the two peaks is $\sim 0.9''$, which corresponds to $\sim660$~au. The line of sight velocities of molecules associated with CMM3A ($\sim 7.4$~km~s$^{-1}$) are similar to those of CMM3B ($\sim 7.8$~km~s$^{-1}$). Therefore, the two protostars are most likely gravitationally bound to each other. In the previous studies, CMM3 has been recognized as a single source because of insufficient angular resolutions \citep[e.g.][]{Peretto2007, Sakai2007, Saruwatari2011,Cunningham2016}. It should be noted that the potential binary components, CMM3A and CMM3B, are surrounded by an extended envelope. The continuum emission shows asymmetric elongation toward the south-eastern and northern directions from CMM3B and slightly toward the north-western direction from CMM3A. This emission would likely trace the circumbinary envelope.
In addition to the two bright continuum peaks, six compact continuum sources (CMM3C, CMM3D, CMM3E, CMM3F, CMM3G, and CMM3H) are detected around CMM3A/B, as shown in Figure~\ref{fig01}a. Here, we have identified local intensity peaks detected with more than $10\sigma$ as the continuum peaks (Table~\ref{tab01}). CMM3C, CMM3D, and CMM3E are point sources, because the FWHM evaluated by the 2D-Gaussian fitting is similar to the synthesized beam of the observation. In the near-infrared images (Figures~\ref{fig01}c--f), faint sources seem to be associated with CMM3C, CMM3D, and CMM3E. Therefore, these three continuum sources would be low-mass Class I or Class II protostars. On the other hand, CMM3F is marginally resolved, and is associated with no infrared source. It may represent a low-mass protostellar/prestellar source. For CMM3G and CMM3H, no parameter was derived by the 2D Gaussinan fitting, because the fitting did not converge. Note that these two peaks are close to the outflow lobe B1 reported by \citet{Saruwatari2011}.
\subsection{Chemical Difference between CMM3A and CMM3B}
Although CMM3A and CMM3B have comparable flux densities in the 0.8~mm continuum emission, their spectral patterns are found to be much different from each other. Figures~\ref{fig02}a and \ref{fig02}b show the spectra of CMM3A and CMM3B, respectively, in the frequency range from 338.3~GHz to 338.8~GHz. The spectrum of CMM3A shows many emission lines of CH$_3$OH and SO$_2$, and those of complex organic molecules such as HCOOCH$_3$, CH$_3$CH$_2$OH, and c-C$_2$H$_4$O even in this narrow frequency range. The full spectra (336.0--347.3~GHz and 348.0--359.3~GHz) and line lists of this spectral line survey will be available in a forthcoming paper (Watanabe~et~al. in prep). In the previous observation with the single-dish telescope ASTE in the 0.8~mm band (Figure~\ref{fig02}c), the lines of these complex organic molecules were not seen at all except for CH$_3$OH in this frequency range \citep{Watanabe2015}, although HCOOCH$_3$ and CH$_3$OCH$_3$ have been weakly detected in the 3~mm band \citep{Sakai2007,Watanabe2015}. This means that the hot core was not traced by the single-dish telescope observation even in the sub-mm band, since its contribution is heavily diluted. The single-dish spectrum is dominated by the contribution from the surrounding envelope. For example, only 4~\% of flux density of the CH$_3$OH ($13_1 - 13_0\,{\rm A}^{-+}$) line observed with ASTE is calculated to come from CMM3A and CMM3B. The high angular resolution observation with ALMA allows us to detect the hot core associated with CMM3A for the first time.
Figures~\ref{fig03}a, b and c show integrated intensity maps of CH$_3$OCH$_3$, HCOOCH$_3$, and CH$_3$OH, respectively. These transition lines are selected as examples to demonstrate the distributions of complex organic molecules and that of CH$_3$OH with the very high upper-state energy (451~K), because they seem to be less contaminated from other molecular lines. As expected from their spectra (Figure~\ref{fig02}a,b), the complex organic molecules and the very high excitation CH$_3$OH are associated only with CMM3A. Furthermore, they are concentrated in a compact region ($<300$~au) around the continuum peak. High excitation lines ($E_{\rm u}>100$~K) of complex organic molecules are detected, and hence, a hot core is thought to have already been formed in CMM3A. The existence of the hot core is indeed supported by the high rotation temperature ($385 \pm 58$~K) of CH$_3$OH estimated by using the rotation diagram method under the assumption of optically thin conditions and local thermodynamic equilibrium (LTE) (Figure~\ref{fig04}). The uncertainty of the derived rotation temperature is relatively large because of the non-LTE effects, optical depths of lines, blending with the other lines, and the resolving-out effect for low-excitation lines. Nevertheless, the high temperature condition is evident.
In contrast to the richness of emission lines in CMM2A, only CH$_3$OH is detected marginally in CMM3B. Although the HCOOCH$_3$ may marginally be detected, it could be blended with the CH$_3$OH line. Since no complex organic molecules are definitively detected (Figure~\ref{fig03}a, b), a hot core has not yet been formed in CMM3B.
We here evaluate column densities of CH$_3$OH, CH$_3$OCH$_3$, and HCOOCH$_3$, and their fractional abundances relative to H$_2$. The column densities are derived under the LTE approximation with the rotation temperatures of 100~K and 300~K. Because CH$_3$OCH$_3$ and HCOOCH$_3$ are not definitively detected in CMM3B, their column densities cannot be determined for CMM3B. In order to compare the chemical compositions between CMM3A and CMM3B on the same basis, we derived the column densities by using the same transitions. As mentioned above, the rotation temperature evaluated from the rotation diagram of CH$_3$OH (Figure~\ref{fig04}) suffers from various systematic uncertainties. Therefore, we employ the rotation temperatures of 100~K and 300~K for both CMM3A and CMM3B. We use a few transitions without contamination from other molecular lines as listed in the captions of Table~\ref{tab02}, and evaluate the column densities by taking the averages of the results from the transition lines. The results are summarized in Table~\ref{tab02}.
The column densities of H$_2$ ($N_{\rm H_2}$) are calculated from the continuum peak flux of the 0.8~mm band by using the formula used by \citet{Imai2016} with the dust temperatures of 100~K and 300~K. Here, we adopt the mass absorption coefficient of the dust of $\kappa_{\nu}=0.0182$~cm$^2$g$^{-1}$ derived by \citet{Jorgensen2016}, which is an interpolated value of the numerical simulation \citep{Ossenkopf1994}. The gas-to-dust mass ratio is assumed to be 100.
The derived H$_2$ column densities and fractional abundances of molecule relative to H$_2$ are summarized in Table~\ref{tab02}. The fractional abundances of CH$_3$OH and CH$_3$OCH$_3$ are found to be higher in CMM3A than those in CMM3B by factor of 5, while the upper limit of HCOOCH$_3$ is not stringent. This chemical difference will be discussed in the latter section.
The HCOOCH$_3$/CH$_3$OH and CH$_3$OCH$_3$/CH$_3$OH ratios in CMM3A are roughly comparable to or even higher than the averaged values in the low-mass and high-mass protostars \citep{Taquet2015}. Therefore, CMM3A possesses analogous chemical compositions of complex organic molecules to other protostars.
\subsection{Outflows}
Figures~\ref{fig05}a and c show the 0th and the 1st moment maps of HCN, respectively. We find a prominent bipolar outflow blowing from CMM3A toward northern and southern directions, which are blue-shifted and red-shifted, respectively (Figure~\ref{fig05}c). The blue-shifted and red-shifted outflows can also be seen in the channel maps of HCN (Figure~\ref{fig06}). This bipolar outflow system corresponds to that found by \citet{Saruwatari2011} in the CO($J=2-1$) line with SMA. Their B1 and R1 lobes are seen in Figure~\ref{fig05}, while B2 and R2 lobes are out of the field of view in the present ALMA observation. As seen in the expanded figure of the 0th HCN moment map (Figure~\ref{fig05}b), this bipolar outflows system is launched from CMM3A. It is also visible in other molecular lines including CO~($J=3-2$), CS~($J=7-6$), SO~($N_J=8_7-7_6$), and CH$_3$OH~(e.g., $13_1-13_0, {\rm A^{-+}}$) (Figure~\ref{fig07}a-d).
It should be noted that the continuum peak CMM3G is close to the B1 lobe (Figure~\ref{fig02}). This indicates that the blue-shifted outflow is interacting with a dense material traced by the continuum emission (CMM3G) and the B1 lobe is induced by the shocks caused by the interaction. Moreover, we find that the outflow is elongated toward the northwest direction from the B1 lobe (Figure~\ref{fig05}a). This elongation can be seen from 3.3~km~s$^{-1}$ to -16.6~km~s$^{-1}$ in the channel maps (Figure~\ref{fig06}). Therefore, the direction of outflow may be changed by the dynamical interaction with the dense clump of CMM3G.
In addition to the prominent bipolar outflow, we find another bipolar outflow system along the northeast to southwest direction (Figures~\ref{fig05}a). The second outflow is also seen from 16.5~km~s$^{-1}$ to -5.0~km~s$^{-1}$ in the channel maps of HCN (Figure~\ref{fig06}). This outflow system is well-collimated, and is also visible in other molecular lines including CO, CS, SO, and CH$_3$OH (Figure~\ref{fig07} e-h). The velocity-integrated emission from the second outflow is much fainter than that from the prominent outflow, because the velocity range of the second outflow is narrower ($\sim 20$~km~s$^{-1}$ than that of the prominent outflow ($\sim 70$~km~s$^{-1}$). Moreover, a part of the second outflow is strongly affected by the resolving-out effect at the system velocity (8.2~km~s$^{-1}$ and 6.6~km~s$^{-1}$ in Figure~\ref{fig06}). The southwestern lobe of this outflow can be seen in the CH$_3$OH ($5_0 - 4_0$ A$^{+}$) line in Figure~4a of \citet{Saruwatari2011}. This collimated outflow system seems to be launched from CMM3B, since the outflow axis just passes through the peak of CMM3B (Figure~\ref{fig05}b). The velocity field map (Figure~\ref{fig05}c) shows small velocity gradient along the bipolar outflow axis. This result indicates that the outflow blows almost in parallel to the plane of sky. The detection of this outflow provides us with a strong evidence of the presence of a protostar in CMM3B. Its well collimated feature suggests that the outflow system would most likely be in the early phase \citep{Arce2006}.
\section{Discussion}
In this study, we have found that CMM3 is a potential binary protostellar source. More importantly, the binary components, CMM3A and CMM3B, show different spectral appearance in spite of their comparable continuum intensities. It is interesting to note that a similar feature has recently been reported for the young low-mass binary source NGC~1333~IRAS4A \citep{Ana2017}. We here discuss possible origins of the difference in CMM3.
The first possibility is the difference of the physical evolutionary stage between the two sources. Considering the prominent outflow feature and the association of the hot core, CMM3A seems to harbor young high-mass (or intermediate-mass) protostar. In contrast, deficient molecular emission in CMM3B might originate from its youth. Namely, the protostar may be so young that the hot core would not have been developed yet or would be still tiny around the protostar. In this case, most of organic molecules are still frozen out on dust grains, and their gas phase abundances are expected to be low. This possibility is supported by the well collimated outflow from CMM3B, which is usually interpreted as a sign of a young dynamical age \citep{Arce2006}. The envelope mass is derived based on the formula given by \citet{Ward-Thompson2000}. For CMM3A, it is evaluated to be 18~M$_{\odot}$ and 5.7~M$_{\odot}$, assuming the dust temperature of 100~K and 300~K, respectively. For CMM3B, it is 13~M$_{\odot}$ and 4.1~M$_{\odot}$, respectively. Thus, the envelope mass of CMM3B could be higher than CMM3A, if the dust temperature is lower in CMM3B because of its youth.
The second possibility is the dust opacity effect. The dust emission at 0.8~mm is not always optically thin at a scale of a few tens of au. If the dust opacity is so high that the emission of various molecules originated from the innermost part of the dust emitting region is heavily absorbed by the dust, the molecular emission could be very weak. This may be the situation for CMM3B. Since the dust temperature of CMM3A is expected to be higher than that of CMM3B, the dust opacity would be lower in CMM3A, and this effect is less significant. As mentioned before, it is most likely that the outflow from CMM3B is almost on the plane of sky. In this case, the disk/envelope system of CMM3B is almost edge-on, which could make the dust opacity high.
The third possibility is the difference of masses of the protostars between CMM3A and CMM3B. If CMM3B is less massive than CMM3A, a size of the hot region where complex organic molecules can be sublimated is very small due to low luminosity. Since the hot region is smaller in CMM3B than CMM3A, the dust temperature is also expected to be lower in CMM3B than CMM3A. Therefore, a larger envelope gas would still be remaining in CMM3B, as discussed in the first possibility.
Apparently, these three possibilities are interrelated to one another. The scenario of a less massive protostar for CMM3B is related to the evolutionary scenario, because the protostar evolution would strongly depend on its mass. It is also related to the dust opacity scenario, because a young protostar is deeply embedded in the parent cloud. In order to disentangle these three possibilities, we need to define the spectral energy distributions for the two sources. Then, we can derive the disk/envelope mass accurately, and estimate the evolutionary stage of the protostar reasonably. High angular resolution observations resolving CMM3A and CMM3B at various wavelength from cm wave to sub-mm wave are awaited.
\acknowledgments
We thank the anonymous reviewer for helpful comments and suggestions to improve this paper. This paper makes use of the ALMA data set ADS/JAO.ALMA\#2013.1.01192.S. ALMA is a partnership of the ESO (representing its member states), the NSF (USA) and NINS (Japan), together with the NRC (Canada) and the NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by the ESO, the AUI/NRAO and the NAOJ. The authors are grateful to the ALMA staff for their excellent support. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center, funded by the National Aeronautics and Space Administration and the National Science Foundation. This research has made use of the NASA/ IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This study is supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (No. 25108005 and 16K17657).
{\it Facilities:} \facility{ALMA}.
| {
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Ivermectin for cats - Dosage and uses!
Ivermectin is an common antiparasitic drug for cats, dogs and other animals. Currently, however, the are other products which have been proven safer for cats. If you are wondering, is ivermectin safe for cats? You've come to the right place.
Here at AnimalWised we aim to discuss everything you need to know about Ivermectin for cats, including its recommended dosage, uses and side effects. Keep reading for more.
Ivermectin for cats: what is it?
Ivermectin is a macrocyclic lactone that has been used since the 1980s for cows, sheep, goats or horses. Its antiparasitic activity is the reason why this treatment was extended to pet care, treating animals like dogs and cats. Ivermectin functions by paralyzing and, consequently, killing the parasites. It is marketed in various formats such as ivermectin paste, pipettes and oral administration.
Ivermectin administration on the skin, however, can cause alopecia and peeling. Selamectin or moxidectin are other widely used lactones commonly used in pipettes. These are both recommended alternatives to ivermectin for cats.
Home remedies for intestinal parasites in cats.
The application of ivermectin is capable of eliminating nematodes and mites in cats. Ivermectin for cats can be used as an internal dewormer against round worms. This is in addition to functioning as treatment for diseases caused by mites, both inside the ears and on the skin. Ivermectin is often used, for example, to treat or deter mange caused by ear mites in cats. Its application for the treatment of infestations by external parasites (fleas and ticks) is controversial, therefore we recommend the use of other antiparasitics that eliminate and prevent these re-infestations.
In addition, we must highlight the common use of ivermectin in the prevention and treatment of heartworm in cats, a parasite capable of occupying the heart, lungs and veins directed to the liver. This worm accesses the organism in immature forms, transmitted through the bite of an infected mosquito. Due to the importance of the organs that it affects, it is a parasitic of potentially fatal severity.
The use of ivermectin in animals suspected of suffering from filariasis, should be applied following strict veterinary control. A dose able to kill microfilariae rapidly can also trigger severe anaphylactic shock in an animal, thus this needs to be avoided.
For more, we recommend reading our article about mites on cats.
Administration and frequency of an ivermectin dose for cats will vary predominantly on what is being treated. Therefore, it is important that before treating a cat with ivermectin,you should consult a veterinarian.
Ivermectin will affect different animals differently and this needs to be taken into consideration. Keep reading to find out more about the possible side effects of ivermectin for cats.
Tremors and exaggerated wide movements.
Paralysis in the hind legs.
If, after your cat has been administered ivermectin you notice any of the above symptoms, you should visit your veterinarian IMMEDIATELY. There is no antidote against ivermectin, treatment is based on an establishment of fluid therapy and appropriate drugs. Recovery may take several weeks.
For more, we recommend taking a look at our article where we discuss poisoning in cats.
Lastly, before administering ivermectin for kittens, you should consult a veterinarian. An overdose of ivermectin in kittens is incredibly dangerous, in the same way that you shouldn't offer this antiparasitic drugs to cats who are allergic to it. Special precautions should also be taken when treating pregnant and/or lactating cats.
If you want to read similar articles to Ivermectin For Cats - DOSAGE, we recommend you visit our Medicine category. | {
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Hrabstwo Spokane (ang. Spokane County) – hrabstwo w stanie Waszyngton w Stanach Zjednoczonych. Hrabstwo zajmuje powierzchnię 1763,64 mil² (4567,81 km²). Według szacunków United States Census Bureau w roku 2009 miało 468 684 mieszkańców. Siedzibą hrabstwa jest Spokane.
Hrabstwo powstało w 1858.
Miasta
Airway Heights
Cheney
Deer Park
Fairfield
Latah
Liberty Lake
Medical Lake
Millwood
Rockford
Spangle
Spokane
Spokane Valley
Waverly
CDP
Country Homes
Fairwood
Four Lakes
Green Bluff
Mead
Otis Orchards-East Farms
Town and Country
Przypisy
Bibliografia
Hrabstwo Spokane w stanie Waszyngton – podstawowe dane statystyczne United States Census Bureau
Spokane
Spokane | {
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It's a Fact is the first solo album by jazz musician Jeff Lorber.
Track listing
Personnel
Jeff Lorber – keyboards, Steinway grand piano, Fender Rhodes, Rhodes EK-10, clavinet, Oberheim OB-X, Prophet-10, Minimoog, Moog Modular System, Moog Liberation, Linn LM-1, string arrangements (1)
Marlon McClain – guitar solo (5, 8)
Pat Kelly – guitar solo (7)
Nathan East – electric bass
John Robinson – drums (1)
Paulinho da Costa – percussion
Kenny Gorelick – soprano saxophone, tenor saxophone, flute, sax solos
Tom Browne – trumpet (2, 5), flugelhorn (2, 5)
George Del Barrio – horn and string arrangements (4, 6)
Pete Christlieb – horn conductor (4, 6)
Lynn Davis – backing vocals
Sylvia St. James – backing vocals, lead vocals (6)
Arnold McCuller – lead vocals (2, 6)
Greg Walker – lead vocals (2)
Production
Jeff Lorber – producer
Chris Brunt – associate producer, recording, mixing
Dennis Hansen – assistant engineer
Ken Perry – mastering at Capitol Mastering (Hollywood, California).
Ria Lewerke-Shapiro – art direction
Sue Reilly – design
Aaron Rapoport – photography
Jeffrey Ross Music – management
Charts
References
External links
Jeff Lorber-It's A Fact at Discogs
1982 albums
Jeff Lorber albums
Arista Records albums | {
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} | 9,853 |
Name | Type | Description | Notes
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**registrationId** | **string** | | [optional] [default to null]
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\section{Introduction}
The kinetics of vortex production in superconductors and
superfluids is one of the intriguing problems of condensed
matter physics. It is interesting not only in the field
of solid state physics but represents as well a very good
model to study topological phase transitions in cosmology and
other branches of physics \cite{zurek1}. In
the last few decades different scenarios for vortex production
in superconductors and superfluids were proposed. The most common
way to produce vortices is to increase the superfluid velocity in
order to reduce the energy barrier between homogeneous flow and
flow with vortices. This mechanism is observed in rotating
$^{3}\text{He}$ where vortex nucleation and critical velocities
are measured \cite{parts}. In 2D homogeneous superconducting films,
increasing the current leads to dynamics which are similar
to the phase slip (PS) transition in 1D \cite{ludac}. The order
parameter (OP) reaches zero along a straight line across the film
and the phase displays a $2\pi$ jump along this line. This PS
line solution \cite{Weber09} corresponds to the
deterministic and most ordered PS kinetics in 2D. The
inhomogeneity caused by current contacts leads to a qualitatively
similar picture. The OP is strongly suppressed along a straight
line across the film but it reaches zero only at two points on
this line. This pair of vortices is called kinematic vortex-antivortex
(VaV) pair \cite{andronov93}. It spreads quickly in
opposite directions along this line propagating the $2\pi$ jump of
the phase. Therefore PS occurs without formation of well defined
VaV pairs \cite{berdiyorov}.
A different scenario of vortex production was proposed by
Kibble\cite{kibble1} and Zurek\cite{zurek2} (KZ). When the sample
is quickly quenched through the critical temperature $T_c$, the
nucleation of the low temperature phase starts in different places
with uncorrelated phases of OP. Then, domains grow and start to
overlap leading to the formation of vortices. This mechanism is a
promising way to test cosmological theories in condensed matter
physics \cite{Ruutu96-98, Maniv03}. This dynamics is stochastic and
sensitive to small variations of initial conditions. On the
other hand the dependence of the vortex density on the quench time
and their spatial correlation are universal. Later, in Refs.
\cite{kibblevolovik,kopninthuneberg}, it was proposed that the
quench occurs not only due to fast temperature change but also due
to the temperature front propagation. Aranson \textit{et al.}
considered the case of a temperature quench in the presence of
external current \cite{aranson}. The new phase with zero current
grows after the quench. Therefore on the border of the quenched
region, the superfluid velocity has tangential discontinuity,
leading to vortex formation, similarly to the classical
hydrodynamic Kelvin-Helmholtz (KH) instability \cite{fridman}
which is also known in superfluids \cite{Blaauwgeers02,volovikKH}.
Moreover, the KH instability suppresses the development of KZ
vortices \cite{aranson}. In this paper, kinematic VaV, KZ and KH
vortices are distinguished by their production mechanism although they
are topologically equivalent.
To demonstrate how deterministic type of dynamics becomes
stochastic, we model a superconducting film rolled on a cylinder
in an external time dependent magnetic field parallel to the
cylinder axis (Fig.1). Depending on the applied magnetic
field and the dimensions of the ring, we follow the evolution
from the deterministic PS line dynamics to the stochastic behavior
described by the KZ mechanism. In the proposed model, topological
defects are generated by the intrinsic quench induced by the
external field. The evolution towards
stochastic behavior is strongly influenced by the KH instability
which develops in the presence of inhomogeneities. To model the
inhomogeneity of the film we assume that there is a thin stripe
of superconductor along the film with a different coherence length.
\begin{figure}
\includegraphics[width = 40mm]{fig1.eps}
\caption{Geometry of the system : a 2D cylinder with an applied
magnetic field $\mathbf{H}$.}
\end{figure}
The thickness of the film $d$ is small $d\ll \xi\
\ll \lambda_{\text{eff}}$. Here $\xi$ is the coherence length and
$\lambda_{\text{eff}}$ is the Pearl penetration depth. Therefore
we can neglect all corrections to the external magnetic field
$\mathbf{H}$ caused by the current in the film. The radius of the
film is $R > \xi$.
The time dependent Ginzburg-Landau (TDGL) equation in
dimensionless units has the form:
\begin{equation}
u(\frac{\partial\psi}{\partial t}+i\Phi \psi) =
b(z)(\psi-\psi|\psi|^{2})-(i\nabla+\mathbf{a})^{2}\psi
+\eta.\label{tdgl1}
\end{equation}
Here $\psi$ is the dimensionless complex OP, the spacial
coordinate ${\mathbf r}$ is measured in units of $\xi$ and time
is measured in units of phase relaxation time
$\tau_{\theta}=\frac{4\pi\lambda_{\text{eff}}\sigma_{n} }
{c^{2}}$, $\lambda_{\text{eff}}=\frac{\lambda^{2}}{d}$, $\lambda$
is the bulk penetration depth, $\sigma_{n}$ is the normal state
conductivity, and $c$ is the speed of light. The parameter
$u=\frac{\tau_{\psi}}{\tau_{\theta}}$ is a material dependent
parameter, where $\tau_{\psi}$ is the relaxation time of the
amplitude of the OP. According to the microscopic theory, $u$ is
ranging from $5$ to $12$ but we assume $0<u<\infty$. The vector
potential $\mathbf{a}$ is measured in units of
$\frac{\phi_{0}}{2\pi\xi}$ where $\phi_{0}$ is the flux quantum.
The function $b(z)$ models the $z$ dependence of the coherence
length $\xi(z)$. As shown in Fig.1, we chose
$\xi(z)=\xi/\sqrt{b(z)}$ and
$b(z)=1-b^{2}\vartheta(z-w/4)\vartheta(3w/4-z)$. Here $w$ is the
width of the film in units of $\xi$, $b$ parameterizes the level
of inhomogeneity of the film and $\vartheta(x)$ is the Heaviside
step function. Here we use periodic boundary conditions and the
boundary condition with vacuum \cite{degennes} at $z=0$
and $z=w$. The equation for the electrostatic potential $\Phi$,
measured in units of $\frac{\phi_{0}}{2\pi c\tau_{\theta}}$,where
$e$ is the electronic charge and $\hbar$ is the Planck constant,
reads:
\begin{equation}
\nabla^{2}\Phi=-\nabla\Bigl[
{{i}\over{2}}(\psi^{*}\nabla\psi-\psi\nabla\psi^{*})
+\mathbf{a}|\psi|^{2}\Bigr].\label{tdgl2}
\end{equation}
To model the process of vortex formation we assume that at time
$t<0$ external magnetic field is absent.
At $t=0$ the field suddenly appears and stays constant for $t>0$
i.e. tangential component of the vector potential is
$a\vartheta(t)$. We thus study the kinetics of the vortex
generation as a function of $a$ with different values of $u$.
Let us first consider the stability of the solution in the uniform
case. We linearize the TDGL Eqs.(\ref{tdgl1},\ref{tdgl2}) in small
fluctuations of OP $f(\mathbf{r},t)=\psi(\mathbf{r},t)-\psi_{0}$
and search for a solution in the form
$f(\mathbf{r},t)=\sum_{\mathbf{k}}C_{\mathbf{k}}
\exp{(i\mathbf{kr}+\lambda_{\mathbf{k}} t)}$. It is clear that the
transverse $k_{z}$ component always contributes to the stability
of the initial state. Therefore, the condition
$\lambda_{\mathbf{k}}>0$ is the same as in 1D \cite{ludac}:
$\frac{\phi}{\phi_0}
> > \frac{R}{\xi\sqrt{3}}$, where $\phi$ is the magnetic flux
through the ring at $t>0$. This condition provides a rough
estimate for the number of the expected PS events $N\sim
\frac{\phi}{\phi_0}$. It defines the first critical value of the
external field $a_{c1}=1/\sqrt{3}$. Therefore, in the low field
limit $a_{c1}\leq a \leq 1$, the dynamics will be similar to the 1D
case with very weak $z$-dependence. Well defined vortices may
appear in this region of the field if the film is inhomogeneous as
shown in Fig.1. The situation is different when the field
$a$ increases further. Dropping $k_{z}=0$, the
eigenvalues are:
\begin{eqnarray}
\lambda^{(1,2)}_{\mathbf{k}}=-\psi_{0}^{2}/2+(1
-2\psi_0^2-a^2-k^2)/u \nonumber \\ \pm \sqrt{(16\psi_0^2
a^2+\psi_0^4(u-2)^2+16k^2a^2)/4u^2} \label{decay}
\end{eqnarray}
$\lambda_{\mathbf{k}=0}=\frac{1-2
\psi_0^2-a^2}{u}-\frac{\psi_{0}^2}{2} - \sqrt{(16\psi_0^2
a^2+\psi_0^4(u-2)^2)/4u2}$ describes the decay rate of the
uniform solution. On the other hand for finite $k$,
$\lambda_{\mathbf{k}}$ is positive and characterizes the growth of
the corresponding Fourier components $C_{\mathbf{k}}$. The fastest
growth is found for $k=\frac{1}{4a} \sqrt{-16u\psi_0^2a^2-
\psi_0^4(u-2)^2+16a^4}$ and the rate is
determined by
$\lambda_{\text{max}}=\frac{1}{16ua^2}(8(u-4)\psi_0^2a^2
+16a^2+\psi_0^4(u-2)^2)$. The qualitative
difference in kinetics takes place when the decay rate of the
uniform solution becomes faster then the growth of the new phase.
This effect is similar to the quench through $T_{c}$ in the KZ
mechanism \cite{zurek1,kibble1}. We find that at
$a>a_{c2}=\sqrt{2}$, the OP is suppressed to zero and the growth
of the phase with finite $k$ is accompanied by the rapid
development of vortices. The density of vortices may be estimated
using Zurek arguments where the quench time should be replaced by
$\tau_{Q}=(a^{2}-1)^{-1}$ leading to $n\propto \tau_{Q}^{-1/2}$
\cite{zurek3}.
We simulate Eqs.(\ref{tdgl1},\ref{tdgl2}) using the fourth order
Runge-Kutta method. The spatial derivatives are evaluated using
a finite difference scheme of
second order or using a fast fourier transform algorithm depending
on the boundary conditions. The choice of the algorithm is made to
optimize the convergence and the calculation times. The
calculations are performed for the vector potential $0<a<5$ and
for the total flux $\phi$ through the ring ranging from $0$ to $50
\phi_0$.
\begin{figure*}
{\includegraphics[width=175mm]{fig2.eps}}
\caption{(Color online) Total number of vortices $v$ in the system
and the sample average
value $|\rho|$ of the OP as a function of time for
$\phi/\phi_0=20$ and $a=0.6$ (a), $a=0.8$(b) and $a=1.8$ (c).
The insets represent snapshots the amplitude of OP at
$t=700$ (a) and $t=105$ (b). For the quenched case (c),
the snapshot displays the local vorticity at $t=20$. }
\end{figure*}
We investigate the flux penetration into the homogeneous ring for
two different boundary conditions. In the case of periodic
boundary conditions we identify different regimes in accordance
with Eq.(\ref{decay}). In the small field limit $a<a_{c1}$ the
ring is in a stable state and the penetration of the magnetic flux
into the ring can only be induced by a very strong noise $\eta$ in
Eq.(\ref{tdgl1}). When $a_{c1}<a<a_{c2}$, in agreement with the
stability analysis, the PS kinetics depends on the external
magnetic field. When $\frac{\phi}{\phi_0}<10$ the kinetics is
similar to the 1D case. The transition is characterized by one or
more lines in the $z$-direction where the OP decreases to zero
(the PS line case \cite{andronov93}). These lines may appear
simultaneously or consecutively in time, depending on $u$
\cite{ludac}. As expected, the number of PS events is determined
by the ratio $\frac{\phi}{\phi_0}$. These PS lines represent the
limiting case of kinematic VaV pairs travelling with infinite
velocity.
When the flux is increased ($\frac{\phi}{\phi_0}>10$), the
kinematic vortices become clearly distinguishable. In Fig.2(a), we
present the time evolution of the average value of the OP together
with the time dependence of the number of vortices in the
sample. The kinetics is characterized by series of consecutive PS
events well separated in time (Fig.2(a)). As it was noticed
\cite{vodo07}, few VaV pairs may propagate along the same line at
the same time. PS events are produced by kinematic VaV pairs
propagating along the same line where the amplitude of OP is
reduced. Kinematic vortices can propagate in the same direction,
one after another or in opposite direction leading to annihilation
of VaV pairs and accelerating the dynamics. Contrary to
\cite{berdiyorov}, kinematic VaV pairs are formed without any
inhomogeneity in the film. At higher fluxes kinematic VaV pairs
are randomly created on the line like in the case of a "1D
quench". In the $x$ direction, the dynamics remains very ordered
with values of the standard deviation of the position of the
vortices $\sqrt{\bar{\delta x^{2}}}$ approaching $0.5\xi$.
\begin{figure*}
{\includegraphics[width=175mm]{fig3.eps}}
\caption{(Color online) Total number of vortices $v$ in the system and
the sample average value $|\rho|$ of the OP as a function
of time for $a1=0.4$, $\phi/\phi_0=5$ and $b=4$ (a); $\phi/\phi_0=20$
and $b=2.25$ (b); $\phi/\phi_0=50$ and $b=12.25$ (c). The insets
represent snapshots of the amplitude of the OP at $t=120$ (a) ;
$t=790$ and $t=830$ (b). For the quasi quenched case (c), the snapshot
displays the local vorticity at $t=112$. }
\end{figure*}
With the further increase of $a$ the number of PS lines increases
and the kinetics becomes more stochastic because of the
interaction of different PS lines. As a result, straight lines are
replaced by vortex rivers which become broader and have finite
curvature (Fig.2(b)). The vortex rivers are comparable to the vortex self-organization
discussed in \cite{Aranson96} under different boundary conditions.
Along one vortex river, few vortex-antivortex pairs are
propagated. The kinetics is determined by the motion of these
pairs along the rivers and finally by their annihilation.
Importantly, the sample average of OP never reaches zero,
contrarily to the case of the large field $a>a_{c2}$. The total
number of vortices in the beginning of the process is larger than
$\frac{\phi}{\phi_0}$ (Fig.2(b)) which is also an indication of
the growing importance of chaotic behavior in the dynamics. The
values of $\sqrt{\bar{\delta x^{2}}}$ are also strongly enhanced,
reaching $2\pi R/3$. The velocity of vortices along the rivers
becomes smaller which is seen from the time dependence of the
vortex number (Fig.2(d)). Nevertheless the velocity is still high
compared to the case when the OP has recovered to its equilibrium
value. The last regime $a>a_{c2}$ is presented in Fig.2(c). Here
the quench condition is satisfied and the OP decreases uniformly
until it reaches zero (Fig. 2(c)). As a result, the new phase
starts to grow uncorrelated and the vortices are created
randomly. The number of vortices is substantially larger than
$\frac{\phi}{\phi_0}$. Most of these vortices recombine rapidly.
The remaining vortices move slowly through the sample propagating
the $2\pi$ phase jump. The random dispersion of these vortices is
a fingerprint of the KZ mechanism. Indeed, $\sqrt{\bar{\delta
x^{2}}}$ reaches now $2\pi R/2$, which means that vortex
distribution is completely random. Another characteristic of the
KZ scenario is that the vortices are created while the order
parameter is very close to zero and not during the fast growth
like in the previous cases as one can see by comparing Fig. 2(a)
and (b) with Fig. 2(c). It is important to notice that the total
net vorticity is strictly equal to zero at any time in the case of
periodic boundary condition in the z direction.
For vacuum boundary conditions \cite{degennes} the
kinetics is very similar. When $a_{c1}<a<a_{c2}$ and
$\frac{\phi}{\phi_0}<10$ one or more lines with reduced OP are
formed. The difference is that the PS lines here have finite
curvature, because they start to grow from the edges of the film
and finally connect each other. Further increase of the flux,
keeping $a$ constant leads to the formation of flux rivers. The
most important difference is that not all "rivers" necessarily
connect two edges of the film. As a result some of them ended in
the middle of the film, leading to the relatively small vorticity.
These remaining vortices and antivortices propagate slowly to the
edges of the film and kinetic is determined by the slow vortex
motion. The dynamics when $a>a_{c2}$ is governed by KZ mechanism,
as in the previous case but the total net vorticity may be finite.
In the case of an inhomogeneous superconductor, the effective
coherence length is now $z$-dependent $\xi(z) = \xi/\sqrt{b(z)}$.
Therefore only the middle part of the ring may be unstable while
the other parts of the film remain in the metastable state. The
introduction of $z$-dependence of the parameters in
Eq.(\ref{tdgl1}) is designed to enhance the transverse vortex
dynamics and allows to demonstrate different mechanisms of vortex
formation. As expected, the PS dynamics starts first in the region
with stronger current and is characterized by $a$ and
$\frac{\phi}{\phi_0}$.
In the region $a_{c1}<a<a_{c2}$ and small flux
$\frac{\phi}{\phi_0}<10$ the initial stage of the kinetics is
similar to kinetics in the homogeneous film. The VaV pairs are not
well defined. However, when kinematic VaV pairs approach the low
current regions, they become well defined and are slowing down
(fig.3(a)). Therefore vortices are stabilized near the line where
the tangential velocity has discontinuity. These vortices
represent another case of KH instability in superconductors. This
instability leads to the formation of well defined vortices and
governs the kinetics of the PS. To the best of our knowledge this
is the only instability which allows vortex production in the low
flux limit.
When the flux through the ring is large $\frac{\phi}{\phi_0}>10$,
the initial fast dynamics is similar to the dynamics in the
homogeneous case until vortices reach the low current regions.
Then they become slow and well defined. As it is seen in
Fig.3(b), the vortices propagate one after another to the film
edge, demonstrating the vortex-vortex attraction even in the case
when the OP has already recovered.
The further increase of $a>a_{c2}$ leads to the quench in the
middle part of the film (Fig.1). During the quench many KZ vortices
are created. Most of them are annihilated on a very short
time scale. The rest reaches the line separating the region with
different currents. The vortices almost stop near this line. The
further dynamics is determined by the diffusion of these vortices
to the film edges. When $a$ is large enough, the KH vortices
become well defined before the recovery of the OP in the middle
part of the film and therefore the inhomogeneity suppresses the KZ
mechanism in agreement with Ref.\cite{aranson}, making kinetics
less stochastic.
Experimentally, observing such dynamics of vortices might
be a real challenge because the short characteristic times does
not allow the use of instruments with sufficient space resolution.
However, recent works \cite{Maniv03, Silhanek10} showed that
freezing the dynamics can characterize both KZ and vortex river
scenarios. Another idea is to use time resolved femtosecond
optical spectroscopy as proposed in the Ref.\cite{yusupov}.
As it is shown in the Refs.\cite{ludac,suppl} the role of
heating is not important for the proposed
geometry of the film.
We have considered the kinetics of the flux penetration to the 2D
ring. We found out that for small values of the external field $a$,
the kinetics is
deterministic and essentially 1D. Increasing the flux $\phi$ creates
kinematic vortices and even leads to a 1D quench along the PS line
which is a first step towards stochastic behavior (see Ref.\cite{suppl}). Further
increase of $a$ leads to the formation of vortex rivers, and
ultimately to the quench of the sample leading to the stochastic dynamics of KZ vortices.
The dynamics in the inhomogeneous film demonstrates that the VaV pairs are the
topological analog of the PS mechanism in 2D but this analogy is
not as straightforward as is often believed. Finally,
our calculations for a partially quenched film indicate that KH
vortices at the interface are strongly predominant.
\section{Phase diagram of the different dynamics}
We observe different dynamics in the homogeneous case, depending on the value of the magnetic vector potential $a$ and the number of flux quanta $\phi/\phi_0$ penetrating the cylinder. In order to plot a phase diagram and display the different types of dynamics, we needed to choose between multiple criteria. We found out that the stochasticity is a good approach to this problem and chose the standard deviation of the $x$ coordinate of vortices to define regions where the dynamics are comparable. The normalized standard deviation $\frac{\sqrt{\bar{\delta x^{2}}}}{\pi R}$ is shown in Fig.1 (R is the radius of the cylinder). The different regions where the standard deviation is similar are separated by lines of constant standard derivation.
\begin{itemize}
\item Part $1$ of the phase diagram corresponds to the phase slip (PS) line solution. No vortices are present and we define there $\frac{\sqrt{\bar{\delta x^{2}}}}{\pi R}=0$ because the dynamics is very ordered.
\item Part $2$ ($0<\frac{\sqrt{\bar{\delta x^{2}}}}{\pi R}\leq 0.23$) corresponds to kinematic vortices traveling on a single line.
\item Part $3$ ($0.23<\frac{\sqrt{\bar{\delta x^{2}}}}{\pi R}<0.48$) is assigned to multiple vortex rivers : stochasticity is increased by the the increasing number of rivers.
\item Part $4$ ($0.55<\frac{\sqrt{\bar{\delta x^{2}}}}{\pi R}$) corresponds to Kibble-Zurek (KZ) type dynamics which displays the highest possible stochasticity.
\item Part 5 ($0.48<\frac{\sqrt{\bar{\delta x^{2}}}}{\pi R}\leq 0.55$) represents the region where the standard deviation fails to clearly distinguish between KZ and vortex rivers. In this region, the area with low $a$ corresponds to vortex rivers and should belong to the part 3. Indeed, when the flux is increased at low $a$, the number of vortex river increases and the vortices often travel from one river to the other : their position becomes stochastic. On the opposite, at low flux, the area with high $a$ should belong to part 4.
\end{itemize}
\begin{figure}
\includegraphics[width = 70mm]{fig1a.eps}
\caption{(Color online) Phase diagram of the possible evolution drawn from the normalized standard deviation $\frac{\sqrt{\bar{\delta x^{2}}}}{\pi R}$ of the $x$ coordinate of the vortices. We chose to define $\frac{\sqrt{\bar{\delta x^{2}}}}{\pi R}=0$ when no vortices are present (Part 1). Part 1 corresponds to the PS line, part 2 the kinematic vortices, part 3 to vortex rivers and part 4 to KZ type dynamics. The part 5 represents a region where the standard deviation is not sufficient to distinguish between the dynamics. The standard deviation is plotted as a function of the vector potential $a$ and of the number of flux quanta (a) for $u=10$. $a_{c1}$ is the critical value under which dynamics are very improbable and $a_{c2}$ is the critical value over which we calculated KZ dynamics would occur. }
\end{figure}
\section{Heating}
The estimate of the heating of the cylinder may be done using Ohm's law. We consider that a part of the cylinder of area $\pi \xi^2$ for the vortex or $2\pi R \xi$ for the PS line, behaves like a normal conductor of conductivity $\sigma_n$ until its annihilation and sustains a current $J_s$ (in cgs units). The energy dissipated per unit of volume is, as in \cite{ludac}:
\begin{equation}
E=\frac{J_s^2}{\sigma_n}\tau_{\theta}=\frac{\left [\phi_0 a (1-a^2) \right ]^2}{16\pi^3 \xi^2\lambda_{\text{eff}}^2}.
\end{equation}
This energy is less than a quarter of the condensation energy $\frac{H_{c_2}^2}{16\pi\kappa^2}$. In the case of PS lines and kinematic vortices, when dynamics are fast and the areas behaving as normal conductors are small, the heat will be dissipated along the sample and through the contacts. It will not impact the dynamics. However, in the case of multiple vortex rivers or in the quenched KZ scenario, the total heating will be much larger but can be tackled by modern experimental techniques. Indeed, modern cooling methods are fast enough \cite{Maniv03}.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 582 |
The Battle of Santa Clara, nicknamed the "Battle of the Mustard Stalks", was a skirmish during the Mexican–American War, fought on January 2, 1847, 2½ miles west of Mission Santa Clara de Asís in California. It was the only engagement of its type in Northern California during the war.
Background
Californios were angry at United States immigrants settling on their ranchos. Six men of the U.S. sloop Warren, who had gone ashore to buy cattle from Mexicans for food, were taken hostage by a group under Francisco Sánchez. One of the hostages was Lieutenant Washington Allon Bartlett, the alcalde of Yerba Buena (soon to be renamed San Francisco). Captains Joseph Aram and Charles Maria Weber, commanding U.S. volunteers at Santa Clara and San Jose respectively, were sent to free them. Sánchez had command of 200 men, so U.S. marines and artillery under Captain Marston were dispatched as reinforcement. James F. Reed, acting lieutenant of the San Jose volunteer contingent, was in the area to muster a rescue party for his family, members of the Donner Party snowbound in the high Sierras. The war made volunteers hard for him to find.
Battle
The Americans were in a mustard field in a dry creek when the Mexicans opened fire. Once the Americans reached open ground the fighting turned their way. An armistice was agreed after two hours, by which time four Mexicans were killed, with four Mexicans and two Americans injured. Tinkham writes, "The women stood on the housetops at Santa Clara and anxiously watched the battle. After the battle the regulars marched into the pueblo and were given a rousing reception and a dinner."
Aftermath
The putative site of the "Armistice Oak" is marked beside El Camino Real near Lawrence Expressway. The Mexicans retreated to the Santa Cruz Mountains. On January 8, the Marines having arrived, Sánchez surrendered. The Americans did agree to respect the Californios' property.
See also
Battles of the Mexican–American War
References
External links
Historical Marker Database:
The Battle of Santa Clara; January 2-7, 1847
Armistice Oak Tree Site
Santa Clara
History of Santa Clara County, California
History of Santa Clara, California
1847 in the Mexican-American War
January 1847 events | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,682 |
\section{Introduction}
\cite{Amendola1999}
\chapter{Introduction}
\section{Motivation}
It is a truth universally acknowledged that any enlightened human being in
possession of a healthy curiosity must be in want of an understanding of the
world around him. In the past few decades, two mysterious phenomena have
emerged in cosmology that challenge our understanding of the Universe in the
post provoking way: dark matter and dark energy. The ``stuff'' that we
observe, that makes up the galaxies and stars, the protons and the neutrons,
the planets and the moons, the plants and the animals and even ourselves,
everything we ever knew and all of what we thought there ever was, makes up
only a meager 4\% of the cosmos. At first glance, this presents a huge
problem for cosmology. But in the grand picture, it might be an opportunity
for all of physics to make progress. Now, for the first time in history,
cosmology is inspiring particle physics via dark matter for the hunt of a
new particle, bringing physics to a full circle. At the same time, dark
energy is causing embarrassment in the quantum field theory department by
deviating from the predicted value by 120 orders of magnitude.
Closing all gaps in our knowledge about the Universe on a large scale is
therefore necessary in order to understand physics and our world as a whole.
Experiments are the physicist's way of unlocking the Universe's secrets, but
they are incredibly limited in the field of cosmology. The studied object is
unique and cannot be manipulated, only be observer through large telescopes
either on the ground or in space. There is no shortage of theories that
could explain some of the issues that are troubling cosmologists these days,
but they all look very similar and it is hard to tell them apart by looking
at the sky. Subtle clues need to be picked up to succeed, and for this we
need better and better surveys. To shed light onto the dark Universe,
several missions are being planned, designed, or are already in progress.
In the design stage in particular, it is interesting to see what kind of
results one can expect depending on the experiment's specifications.
A lot of dark energy models are degenerate in the sense that some of their
predictions match or are indistinguishable by reasonable efforts. The
most popular ones predict critical values for some parameters, so unless we
are provided with a method that allows for infinite precision in our
measurements, we will never know, for instance, whether the Universe is flat
or has a tiny, but non-zero curvature that is too small to be detectable, or
whether dark energy is really a cosmological constant or is time-dependent
in an unnoticeable way. We hope to break at least some of the degeneracies
by investigating how growth of structure in the matter distribution evolved
throughout the history of the Universe.
Information about how the matter used to be distributed is naturally
obtained by analyzing far away objects, since the finite speed of light
allows us to look as far into the past as the Universe has been transparent.
But the nature of dark matter is hindering us from getting a full picture of
the matter distribution, because only 20\% of all matter interacts
electromagnetically. The only sensible way to detect all of matter is via
its influence on the geometry of space-time itself. Distortions of
background galaxies will reveal perturbations in the fabric of the cosmos
through which their light has passed, unbiased in regard of matter that
happens to be luminous or not. In particular, the signal coming from the
so-called weak lensing effect is sensitive to the evolution of both dark
energy and growth related parameters. To make the most out of this
phenomenon, we ``slice up'' the Universe into shells in redshift space and
study the correlation of these redshift bins, a technique which has been
dubbed \textit{weak lensing tomography}.\footnote{Tomos ($\tau\acute o\mu o
\varsigma$): Greek for slice, piece.}
\section{Objective}
By assuming the validity of Einstein's general relativity, all observations
are biased towards the standard model and the growth of structure might not
have been measured correctly. Instead, we want to allow for the possibility
of modified gravity. Our goal is to investigate how future weak lensing
surveys like {\sc Euclid} can constrain the expansion rate $H(z)$ and the
growth function $G(z)$ without assuming a particular model parameterizing
those two quantities. We first select a suitable number of redshift bins in
which we divide a given galaxy distribution function. Starting from a
fiducial model with a list of cosmological parameters that take on
particular values determined by Wilkinson Microwave Anisotropy Probe
(WMAP)\footnote{A probe of the cosmic microwave background radiation, see\\
\url{http://map.gsfc.nasa.gov}.}, we then take the values of $H$ and $G$ in
each bin as a constant, treat them as additional cosmological parameters,
and rebuild these two functions as linear interpolations between supporting
points in the redshift bins.
Using these new functions, we calculate the weak lensing power spectrum in
each bin as well as their cross-correlation spectra based on the non-linear
matter power spectrum, which we take from fitting formulae found by other
groups. The weak lensing power spectrum is then used in the powerful Fisher
matrix formalism, which allows us to estimate the uncertainty of all
cosmological parameters, including the values of $H$ and $G$ at the chosen
redshifts. With these forecast error bars, we can compare competing theories
of modified gravity to our simulated results of next generation weak lensing
surveys.
\section{Symbols and notation}
We use units where the speed of light equals unity. Vectors are lower case
and printed in bold (e.g. $\vec x$), while matrices are upper case and
printed sans serifs (e.g. $\mat F$). The metric has signature $-$+++.
Derivatives are sometimes written using the comma convention: $\partial
\phi/\partial x^i = \phi_{,i}$. The logarithm to base ten is denoted by
$\lg$, and the logarithm to base $e$ by $\ln$. The Fourier transform of a
function $f(x)$ is written with a tilde: $\tilde f(k)$. Due to the
one-to-one correspondence of the redshift and the scale factor, $a=1/(1+z)$,
we may denote the dependence on either one of those quantities
interchangeably, for instance it is obvious that $H(a) = H(1/(1+z))$, so we
might as well consider $H(a)$ as a function of $z$ and write $H(z)$.
Sometimes, the value of redshift dependent quantities like $\Omega_m(z)$
as of today is given as just $\Omega_m$, for instance. A list of commonly
used symbols follows.
\begin{longtable}{lp{11cm}}
$a$ & Scale factor\\
$\chi$ & Complex ellipticity\\
$C_{ij}$ & Covariance matrix\\
$\delta_{ij}$ & Kronecker delta\\
$\delta_\mathrm{D}$ & Dirac delta function\\
$\delta_m(z)$ & Matter density contrast\\
$\Delta_z$ & Photometric redshift error\\
$E(z)$ & Dimensionless Hubble parameter, $E(z)=H(z)/H_0$\\
$F_{ij}$ & Fisher matrix\\
$f(z)$ & Growth rate\\
$G$ & Newton's gravitational constant\\
$G(z)$ & Growth function\\
$\gamma$ & Growth index\\
$\gamma_\mathrm{int}$ & Intrinsic galaxy ellipticity\\
$\gamma_i$ & Shear, $i=1,2$\\
$\gamma_\mathrm{ppn}$ & Parameterized post-Newtonian parameter\\
$h_i,g_i$ & Values of the logarithm of $H(z),G(z)$ at redshift $z_i$, $i=1,\dots,\mathcal N$\\
$H_0$ & Hubble constant\\
$h$ & Dimensionless Hubble constant, $h=H_0 / 100 \unit{km/s/Mpc}$\\
$J_{ij}$ & Jacobian matrix\\
$k$ & Wave number\\
$\kappa$ & Convergence\\
$\ell$ & Multipole\\
$\mathcal L$ & Likelihood, Lagrangian\\
$n(z)$ & Galaxy distribution function\\
$n_i(z)$ & Galaxy distribution function for the $i$-th redshift bin\\
$n_i$ & Average galaxy density in the $i$-th redshift bin\\
$n_s$ & Scalar perturbation spectral index\\
$n_\vartheta$ & Angular galaxy density\\
$\mathcal N$ & Number of redshift bins\\
$\omega_x$& Reduced fractional density for component $x$: $\omega_x=\Omega_x h^2$\\
$\Omega_x(a)$ & Fractional density for component $x$ as a function of the
scale factor or redshift ($x=m,b,c$ for matter, baryons, cold dark matter)\\
$\Omega_m$ & Fractional matter density today\\
$P_m(k)$ & Matter power spectrum\\
$P(\ell)$ & Convergence power spectrum\\
$p$ & Pressure\\
$P(A|B)$ & Probability of $A$ given $B$\\
$\Phi,\Psi$ & Scalar gravitational potentials\\
$r(z)$ & Comoving distance\\
$\rho$ & Density\\
$\sigma_8$ & Fluctuation amplitude at $8\unit{Mpc}/h$\\
$\sigma(x)$ & Uncertainty of the quantity $x$\\
$\tau$ & Reionization optical depth\\
$t$ & Cosmic time\\
$\vec \theta$ & Vector in parameter space; angular position\\
$w$ & Equation-of-state ratio\\
$W(z)$ & Window function\\
$z$ & Redshift\\
$z_m$ & Median redshift\\
$z_i,\hat z_i$ & Endpoint, center of the $i$-th redshift bin\\
\end{longtable}
\chapter{Theoretical preliminaries}
This section outlines the basic theory behind dark energy by giving a brief
historical introduction. Furthermore, the basics of weak lensing and the
Fisher information matrix formalism are explained, as well as the concept of
power spectra, an immensely important tool not only in the remainder of this
thesis, but in all of modern cosmology. A much more detailed treatment of
the topics presented in this section can be found in many excellent standard
text books, such as~\citet{Carroll2003} for the derivation of cosmology from
general relativity,~\citet{Weinberg2008} and~\citet{Amendola2010} (hereafter
referred to as A\&T) for an up to date reference to modern cosmology, dark
energy and useful statistical tools, \citet{Peebles1980} also for the
statistics and~\citet{Bartelmann2001} for a comprehensive treatment of weak
gravitational lensing.
\section{Dark energy: A historical summary}
A short while after Albert Einstein derived his famous field equations he
proposed the idea of inserting a cosmological constant originally in order
to allow for a non-expanding Universe, because he felt that a world that
was spatially closed and static was the only logical
possibility \citep{Einstein1917}. This view was the general consensus at the
time, considering that all visible stars seemed static and other galaxies
had not been discovered yet. From the first and
second Friedmann equations
\begin{align}
\left( \frac{\dot a}{a} \right)^2 & = \frac{8\pi G}{3}\rho
-\frac{k}{a^2} \label{eq:2-friedmann1}\,,\\
\frac{\ddot a}{\dot a} & = -\frac{4\pi G}{3}(\rho+3p)\,,
\label{eq:2-friedmann2}
\end{align}
we can easily see, that for a static solution with $\ddot a=\dot a=0$, we
need a component in the Universe that bears a negative pressure
\begin{equation}
p = -\frac{1}{3}\rho
\label{eq:2-pressure}
\end{equation}
with an overall positive spatial curvature that is finely tuned to
\begin{equation}
\frac{k}{a^2} = \frac{8\pi G}{3}\rho.
\label{}
\end{equation}
At this point, we mention that it is often useful to plug the time
derivative of eq.~(\ref{eq:2-friedmann1}) into eq.~(\ref{eq:2-friedmann2})
to arrive at the continuity equation
\begin{equation}
\dot \rho = -2\frac{\dot a}{a}(\rho+p)\,.
\label{eq:2-conti}
\end{equation}
It can be shown that for dust, i.e. non-relativistic baryonic or
dark matter, the pressure vanishes and for radiation or ultra-relativistic
matter the pressure is one third of the energy density. This means that
ordinary forms of energy cannot produce the desired result. Einstein
recognized that we the Lagrangian in the Hilbert-Action can be changed to
\begin{equation}
S = \frac{1}{16\pi G}\int \mathrm d^4 x \sqrt{-g}(R-2\Lambda)
\end{equation}
by introucing a constant $\Lambda$.
We can interpret this term as a form of energy density $\rho_\Lambda =
\Lambda/8\pi G$ that does not
depend on the scale factor, which leads to $p=-\rho$ according to
eq.~(\ref{eq:2-conti}).
Thus $\rho$ in eqs.~(\ref{eq:2-friedmann1})
and (\ref{eq:2-friedmann2}) can be replaced by $\rho_m+\rho_\Lambda$.
Then a Universe in which $\rho_m=2\rho_\Lambda$ or $\Lambda=4\pi G \rho_m$
satisfies \eq{eq:2-pressure}.
However, Einstein's conservative view of the world did not live up to
experimental facts. Only a short time later, after Edwin Hubble's
revolutionary discovery of apparently receding galaxies in 1923, Einstein
readily discarded the idea of a static Universe. Because an expanding
Universe does not necessarily need a cosmological constant (see
fig.~\ref{fig:evolscalfac}), the introduction of the cosmological constant
was considered a mistake for decades after that \citep{Peebles2003}.
It was not until the early 1960s, when $\Lambda$ had to be revived to
explain a new measurement of $H_0$ by Allen Sandage that was more accurate
than the original one by Hubble by one order of magnitude. After a proper
recalibration of the distance measure, he found $H_0\approx75
\unit{km/s/Mpc}$, causing an incompatibility of what was then concluded
to be the age of the Universe ($7.42 \unit{Gyr}$) with that of the age of
the oldest known star in the Milky Way, which was at the time estimated to
be greater than $15 \unit{Gyr}$ \citep{Sandage1961}. Even though the numbers
were slightly off according to our current knowledge, Sandage was on the
right track and immediately suggested that a cosmological constant could
easily resolve this issue. This was the first hint that the Universe was not
only expanding, but expanding in an accelerated manner.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=9cm]{graphics/evolscalfac}
\includegraphics[width=9cm]{graphics/evolscalfac-exotic}
\end{center}
\caption{Solutions of the Friedmann equation demonstrating the evolution of
the Universe. We have set the Hubble constant $H_0$ to unity for
convenience, which implies that $t=-1$
corresponds to the Hubble time $-13.9\unit{Gyr}$. All curves pass $t=0$
(today) with $a(0)=\dot a(0)=1$. \textit{Top panel}: From the top: The
expansion history and future for our Universe with $(\Omega_m =
0.3,\Omega_\Lambda=0.7)$, an open matter-only Universe $(0.3,0)$ and the
Einstein--de Sitter model $(1, 0)$. \textit{Bottom panel}: Some more exotic
solutions: A pure cosmological constant $(0,1)$, the Milne model $(0,0)$ and
a closed Universe $(6,0)$.}
\label{fig:evolscalfac}
\end{figure}
Several decades later, the highest authority in physics---the
experiment---put an end to all speculations. In the late 1990s
\citet{Riess1998} observed ten supernovae of type Ia that they used as
standard candles to infer their luminosity distance as a function of
redshift and found that they were on average 10\%--15\% farther away than
one would expected in an open, mass dominated Universe. They were able to
rule out the $\Omega_\Lambda=0$ case at the $9\sigma$ confidence level,
leading the way for precision cosmology. Almost simultaneously, an
independent measurement by \citet{Perlmutter1998} confirmed their findings
by analyzing 42 high--redshift supernovae of type Ia. Thus, the notion that
the expansion of the Universe was accelerating was confirmed. Our failure to
understand the nature of this accelerated expansion is reflected in the name
for this phenomenon: \textit{dark energy}. It is important to stress that
the underlying
physical cause of the acceleration does not have to be a new form of energy,
it might as well be a new form of physics that mimics the effects of a
cosmological constant, which is often misunderstood even by physicists
unfamiliar with cosmology. Whether we are faced with a ``physical darkness
or dark physics'', to say it with the words of \citet{Huterer2007}, is the
whole crux of the matter. Evidence independent of the distance-luminosity
relation for type 1a supernovae which supports the idea of acceleration
has steadily increased since the findings of Riess and Perlmutter. For
instance, the late integrated Sachs-Wolfe effect \citep{Scranton2003}, or
the cosmic microwave background radiation \citep{Komatsu2011} and a dark
energy
component is part of today's standard model of the Universe. But does this
mean that cosmology as a science is done?
On the contrary. Even though the so called flat $\Lambda$CDM model (cold
dark matter with a cosmological constant) with only six free parameters
($\omega_m$,$\omega_b$,$\Omega_\Lambda$,$n_s$,$\sigma_8$,$\tau$)
\footnote{The exact meaning of those parameters will be explained in
section~\ref{survey}.} agrees remarkably well with all observations, most
physicists are still not satisfied with it for a number of reasons. First of
all, the value of the cosmological constant is incredibly small. When we
express $\Lambda$ in natural units, i.e. where the Planck length $l_P =
\sqrt{\hbar G} =1$, we get $\Lambda = 3.5 \times 10^{-122}$. Even worse,
when we interpret the cosmological constant simply as the vacuum energy
predicted from quantum field theory, the value diverges. Because it is
widely believed that new physics are needed at the Planck scale where
neither quantum effects nor gravity are negligible, namely a
theory of quantum gravity \citep{Carroll1992}, one can renormalize the
integral over all modes of a scalar, massive field (e.g. a spinless boson)
with zero point energy $\hbar \omega/2$ by introducing a cutoff at Planck
length. This generates a finite value, but one that is still 120 orders of
magnitude too large, making it arguably the worst prediction in the history
of physics. Finding a mechanism that would cause fields to cancel out each
other's contributions to the vacuum energy density would be a challenge, but
a mechanism that leaves a tiny, positive value seems completely out of reach
for now. The most promising resolution might lie in super symmetry,
super gravity or super string theory. This is commonly referred to as the
\textit{cosmological constant problem} \citep{Weinberg1989}.
The second problem is the \textit{coincidence problem}, which describes the
curious fact that we live exactly in a comparably short era in which matter
surrenders its dominance to dark energy. This can be visualized if we
consider the time dependence of the dimensionless dark energy
density\footnote{Radiation energy scales as $a^{-4}$ and was only relevant
at very early stages of the Universe, which is why we shall not consider it
here.}:
\begin{equation}
\Omega_\Lambda(a)=\frac{\rho_\Lambda}{\rho_\mathrm{crit}(a)}=
\frac{\rho_\Lambda}{\rho_m(a)+\rho_\Lambda}=
\frac{1}{\frac{\rho_m(a_0)}{\rho_\Lambda}a^{-3}+1} \approx
\frac1{\frac37a^{-3}+1},
\end{equation}
because $\rho_m$ scales as $a^{-3}$ while $\rho_\Lambda$ stays constant,
when $a_0$ is the scale factor today, usually normalized to unity.
Plotting this with its derivative on a logarithmic scale (see
fig.~\ref{fig:coinc}) shows the coincidence.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=9cm]{graphics/coinc}
\end{center}
\caption{Visualization of the coincidence problem. Shown here is the
dimensionless dark energy density $\Omega_\Lambda(a)$ in dependence of the
scale factor $a$ and its derivative on a logarithmic scale. Highlighted with
dashed lines are the times of big bang nucleosynthesis (BBN) at
$a\approx10^{-10}$, recombination at $a\approx 1/1000$ and today at $a=1$.
Dark energy started to dominate right when structures emerged in the
Universe.}
\label{fig:coinc}
\end{figure}
Until now, there is no satisfactory solution to these problems. String
theorists argue that we might live in one of $10^{500}$ realizations of the
Universe, corresponding to the number of false vacua that are allowed by
string theory \citep{Douglas2003}. This approach comes down to an anthropic
argument, stating that it is no surprise that the cosmological constant has
the value that it has, since any other value might be realized in a
different Universe, but would not lead to the growth of structure required
for sentient life that can ponder the value of natural constants
\citep{Susskind2005}. This argument is controversial amongst physicists. As
one of the leading cosmologists Paul Steinhard puts it in a \textsc{Nature}
article \citep{Brumfiel2007}: ``Anthropics and randomness don't explain
anything.''
Alternative theories include the postulation of Quintessence, a new kind of
energy in the form of a scalar field with tracker solutions mimicking a
cosmological constant \citep{Zlatev1999}, or a modification of Einstein's
theory of general relativity, where, in the most popular case, the Ricci
scalar in general relativity is replaced as the Lagrangian by some function
$f(R)$ \citep{Felice2010}. Unfortunately, current observational constraints
are insufficient when it comes to discriminating between competing theories.
\section{Weak lensing}
When light passes through a gravitational potential, its trajectory is bent
in a way described by general relativity. This process, dubbed ``lensing'',
can alter the shape, size and brightness of the original image. We usually
distinguish between strong, weak and micro lensing. The mechanism of micro
lensing relies on small objects of low magnitude being the lens, such as
brown or white dwarfs, neutron stars, planets and so on, that transit a
bright source and temporarily increase the source's brightness on time
scales of several seconds to several years \citep{Paczynski1996}. The other
two cases are static on those time scales, since more massive lenses like
galaxies or clusters are involved, which means that the distances involved
are several orders of magnitude larger. Strong lensing occurs when multiple
images of the same galaxy from behind a super massive object can be
observed, as seen in the bottom left corner of the left panel in
fig.~\ref{fig:2-lensing}.
\begin{figure}[htbp]
\begin{center}
\includegraphics{graphics/lensing}
\end{center}
\caption{\textit{Left panel}: Simulation of a gravitational lens with a
case of strong lensing in the lower left corner at an average redshift of
one. \textit{Right panel}: Enhancement of the upper right section of the
left panel, depicting
lensing in the weak regime. The contours are ellipses derived from the
quadrupole moment of each galaxy image. The two bars in the upper right
corner show the average shear, where the lower one represents the expected
shear and the upper one the actual shear. The deviation stems from shot
noise due to the intrinsic ellipticity and random orientation of the
galaxies. Taken from \citet{Mellier1998}.}
\label{fig:2-lensing}
\end{figure}
While strong and micro lensing are relatively rare, weak lensing is an
effect that can be observed over large areas of the sky (see upper right
corner of the right panel in fig.~\ref{fig:2-lensing}). Its power lies in
statistical analysis, since weakly lensed objects are only slightly
distorted and impossible to detect individually. Only the average distortion
field reveals the cosmological information that we are looking for. As it
turns out, weak lensing changes the ellipticity of galaxies (in a first
order approximation), but the intrinsic ellipticity always dominates the
shape. We need to gather large enough samples and then
subtract the noise, which is relatively simple if the magnitude and
direction of the intrinsic ellipticity is uncorrelated to the signal. This
is unfortunately not entirely the case due to tidal effects
(\textit{intrinsic alignment}), and this is only one of the many challenges
that weak lensing harbors. The most obvious one is illustrated in
fig.~\ref{fig:cosmicshear}. Others include photometric redshift errors,
calibration errors and uncertainties in power spectrum theory. A lot of
these systematic errors can be accounted for by introducing several
nuisance parameters~\citep{Bernstein2009}. The trade-off is that a high
number of nuisance parameters diminish the merit of the Fisher matrix
formalism, as there are degeneracies to be expected, so we will only account
for photometric redshift error and the intrinsic ellipticity in this thesis.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\textwidth]{graphics/cosmicshear}
\end{center}
\vspace{-.5cm}
\small\hspace{1cm}a)\hfill b)\hfill c)\hfill d)\hfill e)\hspace{1cm}
\caption{A schematic illustration of the process of weak lensing detection,
demonstrating its difficulty.
a) The original source galaxy. b) Weak lensing distorts the shape and adds a
shear to the image. c) The image is convolved by the telescopes point spread
function and, in
case of ground based surveys, the atmosphere. d) The effect of the finite
resolution of the detector. e) Additional noise is applied to the image. The
challenge now is to infer b) from e). (Image of M31 by courtesy of Robert
Gendler.)}
\label{fig:cosmicshear}
\end{figure}
An expression describing the shear can be obtained by perturbing the
Friedmann-Lema\^itre-Robertson-Walker
metric in the Newtonian gauge
\begin{equation}
\,\mathrm d s^2 = -(1+2\Psi)\,\mathrm d t^2 + a^2(t)(1+2\Phi)(\,\mathrm d x_1^2 + \,\mathrm d x_2^2 + \,\mathrm d
x_3^2)\,,
\label{eq:2-newt-gauge}
\end{equation}
where $\Psi$ and $\Phi$ are scalar gravitational potentials. We can then
solve the geodesic equation for a light ray
\begin{equation}
\frac{\,\mathrm d k^\mu}{\,\mathrm d \lambda}+ \Gamma_{\alpha\beta}^\mu k^\alpha k^\beta =
0\,,
\end{equation}
which can be rewritten in our case as
\begin{equation}
\frac{\,\mathrm d^2}{\,\mathrm d r^2}(r\theta_i) = \Phi_{,i}-\Psi_{,i}\,.
\end{equation}
Thus, we obtain the lensing equation
\begin{equation}
\theta_i = \theta_{0i} + \int_0^r \,\mathrm d r'\left(1-\frac{
r'}{r}\right) \phi_{,i}(r' \theta_{01}, r' \theta_{02},r')
\end{equation}
with the lensing potential $\psi = \Phi-\Psi$. Here $r$ is the radial
comoving coordinate, $\theta_i=x_i/r$ is the angle of the light ray with
respect to the $r$-axis, and $(x_1,x_2)$ are displacement coordinates
perpendicular to the $r$-axis.
\begin{figure}[htbp]
\begin{center}
\scalebox{.75}{\input{graphics/lensing-description}}
\end{center}
\caption{Description of the lensing configuration. Note that comoving
distances cannot be added trivially, i.e. $r_s \neq r_l+r_{ls}$.}
\label{fig:2-descrip}
\end{figure}
The distortion of a source image at distance $r_s$ to first order is a
linear transformation described by the symmetric matrix
\begin{equation}
A_{ij}\equiv \frac{\partial \theta_{si}}{\partial \theta_{0j}} =
\delta_{ij} + D_{ij}
\label{}
\end{equation}
with
\begin{equation}
D_{ij}(r_s) = \int_0^{r_s}\,\mathrm d r' \left( 1-\frac{ r'}{r_s}
\right) r' \psi_{,ij} = \left( \begin{array}{cc}-\kappa_\mathrm{wl}
-\gamma_1 &
-\gamma_2\\ -\gamma_2 & -\kappa_\mathrm{wl}+\gamma_1\end{array}\right)\,.
\end{equation}
Here we introduced the convergence
\begin{equation}
\kappa_\mathrm{wl} = -\frac{1}{2}\int_0^{r_s}\,\mathrm d r' \left(
1-\frac{ r'}{r_s}\right) r'(\psi_{,11}+\psi_{,22})\,,
\label{eq:2-conv}
\end{equation}
which is a measure for the magnification of the image, and the shear
\begin{align}
\gamma_1& = -\frac{1}{2}\int_0^{r_s}\,\mathrm d r' \left(
1-\frac{ r'}{r_s}\right) r'(\psi_{,11}-\psi_{,22})\,,\\
\gamma_2& = -\int_0^{r_s}\,\mathrm d r'\left( 1-\frac{r'}{r_s}
\right) r' \psi_{,12}\,,
\end{align}
which describes the distortion. These quantities will become important when
we want to describe the cosmic shear by statistical means, in particular its
power spectrum.
We can measure the ellipticity of real astronomical images by computing
their quadrupole moment, which is defined as
\begin{equation}
q_{ij} = \int I(\vec \theta)\theta_i\theta_j\,\mathrm d^2\theta \,,
\end{equation}
where $I(\vec\theta)$ is the luminous intensity of the galaxy image with its
center at $\vec \theta =0$. The complex ellipticity is then given by
\begin{equation}
\chi\equiv\frac{q_{11}-q_{22}+2iq_{12}}{q_{11}+q_{22}}\,.
\end{equation}
It is straight forward to show that according to this definition the complex
ellipticity for an ellipse with semiaxes $a$ and $b$, rotated by an angle
$\phi$, is
\begin{equation}
\chi = \frac{a^2-b^2}{a^2+b^2}e^{2i\phi}\,.
\end{equation}
To first order, a weak lens distorts a spherical object into an ellipse with
a simple relation between the shear and the complex ellipticity, namely
\begin{equation}
\chi = 2(\gamma_1 + i\gamma_2)\,.
\end{equation}
We can use this to compute the power spectra $P_{\gamma_i}(\ell)$, which
describe the auto-correlation of the shear field at the multipole $\ell$,
the adjoint variable to $\theta$. It can be
shown that the convergence power spectrum $P$ is related to the matter power
spectrum and can be written to first order
as a linear combination $P = P_E = c_1P_{\gamma_1}+c_2P_{\gamma_2}$. Another
linear combination, $P_B = c_1P_{\gamma_1}-c_2P_{\gamma_2}$, must vanish.
These are usually referred to as the electric and magnetic part of the
shear field. Thus, the convergence power spectrum contains all the
information while the magnetic part provides a good check for systematics.
But, as mentioned before, not all galaxies appear circular even if their
intrinsic shape was a perfectly circular disc and there was no gravitational
lensing distorting our view of the sky, as they are randomly oriented and
thus, viewed from the side, look like ellipses.
This intrinsic ellipticity, denoted by $\gamma_\mathrm{int}$, can be
reflected in a noise term that is added to the power spectrum, if we assume
that the noise is uncorrelated to the weak lensing signal\footnote{As
mentioned before, because of tidal effects this is not necessarily the
case.}:
\begin{equation}
P = P_\mathrm{signal} + \gamma_\mathrm{int}^2 n^{-1}\,,
\end{equation}
where $n$ is the average galaxy density (A\&T, ch. 14.4).
The shear field is a vector field of dimension two. To access the full power
of weak lensing, we must also include the third dimension, which can be done
by considering the redshift of each source galaxy. Weak lensing works
linearly, so we can add up the transformation matrices of all galaxies and
find for the full transformation matrix
\begin{equation}
\mathcal D_{ij} = \int_0^\infty \,\mathrm d r' n(r') D_{ij}(r')\,,
\label{eq:2-trans}
\end{equation}
where $n(r)\,\mathrm d r$ is the number of galaxies in a shell with width $\,\mathrm d r$
and the galaxy distribution function $n(r)$ is normalized to unity. Making
use of the fact that for any real, integrable functions $f(x)$ and $g(x,y)$
the identity
\begin{equation}
\int_0^\infty \,\mathrm d x f(x) \int_0^x \,\mathrm d y g(x,y) = \int_0^\infty \,\mathrm d y
\int_y^\infty \,\mathrm d x f(x) g(x,y)
\end{equation}
holds, we can rewrite eq.~(\ref{eq:2-trans}) to get
\begin{equation}
\mathcal D_{ij} = \int_0^\infty \,\mathrm d r w(r) \psi_{,ij}\,.
\end{equation}
Here we abbreviated the weight function as
\begin{equation}
w(r) \equiv \int_r^\infty\,\mathrm d r'\left( 1-\frac{r}{r'} \right)r n(r')\,.
\end{equation}
Thus, the total convergence field from eq.~(\ref{eq:2-conv}) now reads
\begin{equation}
\kappa_\mathrm{wl} = -\frac{1}{2}\int_0^\infty \,\mathrm d r w(r)
\left(\psi_{,11}+\psi_{,22}\right)\,.
\label{eq:2-totconv}
\end{equation}
By grouping all observed
galaxies into redshift bins, we are able to extract more information out of
the given data by calculating the power spectrum in each each redshift bin
as well as their cross correlation. This is called \textit{power spectrum
tomography}~\citep{Hu1999}. We shall cover this in more detail in
section~\ref{sec:tomography}.
\section{Power spectra}
Almost every book and every lecture on modern cosmology begins with the
cosmological principle: the assumption that the Universe is, simply put,
homogeneous and isotropic. Now obviously the average density, say,
$100\unit{m}$ below the University Square in Heidelberg is quite different
than the average density $100\unit{m}$ above, and it is still quite
different at the midpoint between the Sun and Alpha Centauri -- we
say that the Universe has \textit{structure}. But if we look at the Universe
at sufficiently large scales of $\gtrsim 1\unit{Gpc}$, the overall success
of the standard model confirms our initial assumption~\citep{Komatsu2011}.
While there are research groups who investigate the possibility of genuine
large scale inhomogeneities~\citep{Barausse2005,Kolb2005}, we remain
confident that there is good reason to believe that the cosmological
principle applies to the Universe as a whole.
The matter distribution in tour Universe consists mostly of structures at
different scales, which can be roughly classified as voids,
super clusters, clusters, groups, galaxies, solar systems, stars, planets,
moons, asteroids and so on. This ``lumpiness'' is inherently random, but
like all randomness it can be characterized by an underlying set of well
defined rules by using statistics. The matter distribution in our Universe
is one sample drawn from an imaginary ensemble of Universes with an
according probability distribution function (PDF), and we are now facing the
challenge of determining that PDF.
We require our models to make precise predictions regarding the structure of
matter. Naturally, no model will be able to predict the distance between the
Milky Way and Andromeda for instance, but it should be able to predict how
likely it is for two objects of that size to have the separation that they
have. To quantify and measure the statistics of the irregularities in the
matter distribution in the cosmos, we define the \textit{two-point
correlation function} $\xi$ as the average of the relative excess number of
pairs found at a given distance. That is, if $n_i,\, i\in\{1,2\},$ denotes
the number of point-like objects (nucleons, or galaxies, or galaxy clusters)
found in some volume element $\,\mathrm d V_i$ at position $\vec r_i$ with a sample
average $\langle n_i\rangle=n_0 \,\mathrm d V_i$, we can write the average number of
pairs found in $\,\mathrm d V_1$ and $\,\mathrm d V_2$ as
\begin{equation}
\langle n_1 n_2 \rangle = n_0^2 \,\mathrm d V_1 \,\mathrm d V_2 [1+\xi(\vec r_1,\vec r_2)],
\label{eq:2-pairs}
\end{equation}
where $n_0=N/V$ is the mean number density. If the matter distribution was
truly random, then any two volume elements would be uncorrelated, which
means that $\xi$ would vanish and the average number of pairs would simply
be the product of the average amount of objects in each volume element. If
$\xi$ is positive (negative), then we say those two volume elements are
correlated (anti-correlated).
Assuming a statistically homogeneous Universe, $\xi$ can only depend on the
difference vector $\vec r_{12} = \vec r_2-\vec r_1$. Further assuming
statistical isotropy allows $\xi$ to only depend on the distance $r$ between
$\vec r_1$ and $\vec r_2$. Hence, we denote the two-point correlation
function as $\xi(r)$. Solving eq.~(\ref{eq:2-pairs}) leads to
\begin{equation}
\xi(|\vec r_2-\vec r_1|) = \frac{\langle n_1n_2\rangle}{n_0^2 \,\mathrm d V_1 \,\mathrm d
V_2} - 1 = \langle \delta_m(\vec r_1) \delta_m(\vec r_2) \rangle,
\label{eq:2-corr}
\end{equation}
which can be easily checked by plugging in the definition of the density
contrast
\begin{equation}
\delta_m\left( \vec r_i \right) = \frac{n_i - \langle n_i \rangle}{\langle
n_i \rangle}.
\label{eq:2-contrast}
\end{equation}
Thus, the correlation function is often written as the average over all
possible positions
\begin{equation}
\xi(|\vec r|) =
\frac{1}{V}\int_V \delta_m(\vec x)\delta_m(\vec x+\vec r) \,\mathrm d^3 x.
\label{eq:2-corr2}
\end{equation}
Another important tool that will later prove to be invaluable is the
\textit{power spectrum}, which is in a cosmological context the square of
the Fourier transform of a perturbation variable (up to some normalization
constant). For instance, the matter
power spectrum is defined as
\begin{equation}
P_m(\vec k) \equiv V \tilde \delta_m(\vec k) \tilde \delta_m^*(\vec k)=
\frac{1}{V}\left|\int \delta_m(\vec x)
e^{-i\vec k\cdot\vec x} \,\mathrm d^3x\right|^2.
\label{}
\end{equation}
Rewriting the norm yields
\begin{equation}
P_m(\vec k) = \frac{1}{V}\int\delta_m(\vec x)\delta_m(\vec y) e^{-i\vec k
\cdot (\vec x - \vec y)}\,\mathrm d^3x\,\mathrm d^3y
\end{equation}
or, if we substitute $\vec r = \vec x-\vec y$
\begin{equation}
P_m(\vec k) = \frac{1}{V} \int \delta_m(\vec x)\delta_m(\vec x - \vec r)
e^{-i\vec k \vec r} \,\mathrm d^3x \,\mathrm d^3r
= \int \xi(r)e^{-i\vec k \vec r} \,\mathrm d^3r\,,
\end{equation}
where we used eq.~(\ref{eq:2-corr2}) in the last step. Hence the power
spectrum is the Fourier transform of the two-point correlation
function.\footnote{This is the Wiener-Khinchin Theorem.}
The power spectrum is amongst the cosmologist's favorite tool to describe
our Universe in a meaningful way. It is often applied for instance to the
matter distribution, the anisotropies of the cosmic microwave background
radiation or the shear field of weak lensing.
The convergence power spectrum describing the cosmic shear of galaxy images
can be expressed in terms of the matter power spectrum. Since the matter
distribution is 3-dimensional, but the convergence is a function of the
2-dimensional sky, we need Limber's theorem to relate those two. It states
that the power spectrum for a projection
\begin{equation}
F(\theta_x,\theta_y) = \int_0^{\infty} w(r) f(\theta_x r,\theta_y r, r) \,\mathrm d
r\,,
\end{equation}
where $w(r)$ is a weight function (normalized to unity), turns out to be
\begin{equation}
P(q) = \int_0^\infty \,\mathrm d r \frac{w(r)^2}{r^2}p\left( \frac{q}{r} \right)\,,
\label{}
\end{equation}
where $p(k)$ is the power spectrum of $f$. This theorem is directly
applicable to the total convergence field in eq.~(\ref{eq:2-totconv}), so
that its power spectrum becomes
\begin{align}
P_{\kappa_\mathrm{wl}}(q) &= \frac{1}{4}\int_0^\infty \,\mathrm d
r\frac{w(r)^2}{r^2} P_{\Sigma_i \psi_{,ii}}\left( \frac{q}{r} \right)\\
&= \frac{1}{4}\int_0^\infty \,\mathrm d z \frac{W(z)^2}{H(z)}P_{\Sigma_i
\psi_{,ii}}\left( \frac{q}{r} \right)
\end{align}
with
\begin{equation}
W(z) \equiv \frac{w(r(z))}{r(z)}
\end{equation}
being the window function. All we need to know now is the power spectrum of
$\psi_{,ij}$, which is simply
\begin{equation}
P_{\psi_{,ij}} = k_i^2 k_j^2 |\tilde\psi|^2
\end{equation}
because the Fourier transform of $\psi_{,ij}$ is $-k_ik_j\tilde \psi$. Then
we can plug in the Poisson equation in Fourier space, which is
\begin{equation}
k^2\tilde\psi = 3a^2H(a)^2\Omega(a) \delta_m(a)
\end{equation}
(in the absence of anisotropic stress, i.e. $\psi=2\Phi$) to obtain
\begin{equation}
P_{\Sigma_i \psi_{,ii}}(k) = k^4\tilde\psi = 9 H(a)^4 \Omega_m^2/(1+z)^4
P_m(k)\,.
\end{equation}
Putting it all together, and replacing $q$ with the multipole $\ell/\pi$,
finally yields the power spectrum for the convergence,
\begin{equation}
P(\ell) = \frac{9H_0^3}{4}\int_0^\infty
\frac{W(z)^2E(z)^3\Omega_m(z)^2}{(1+z)^4}P_m\left(
\frac{\ell}{\pi r(z)}\right)\,\mathrm d z\,.
\label{eq:2-convps}
\end{equation}
More details can be found in A\&T (ch. 4.11, 14.4) or \citet{Hu2004}.
In fig.~\ref{fig:2-ps} we can see the matter power spectrum derived
from linear perturbation theory as well as non-linear corrections.
Fig.~\ref{fig:2-ps} shows the convergence power spectrum, derived from
the linear and non-linear matter power spectrum according to
eq.~(\ref{eq:2-convps}).
\begin{figure}[htpb]
\begin{center}
\includegraphics[width=9cm]{graphics/matter-ps}
\includegraphics[width=9cm]{graphics/convps}
\end{center}
\caption{\textit{Top panel:} Comparison between a matter power spectrum
with (purple) and without (blue) non-linear corrections in arbitrary units.
The fitting formulae were taken from \citet{Eisenstein1999} and
\citet{Smith2003}.
Non-linear corrections become important only at wave numbers
$k>0.1\unit{Mpc}^{-1}$. Note that $k$ is not in units of $h\unit{Mpc}^{-1}$
in this case. \textit{Bottom panel:} Comparison between a convergence
power spectrum from eq.~(\ref{eq:2-convps}) based on the linear and
non-linear matter power spectrum (no redshift binning).} \label{fig:2-ps}
\end{figure}
\section{Fisher matrix formalism}
The last tool we will need is the powerful theory of Bayesian statistics.
In physics we define a theory by a set of parameters encapsulated in the
vector $\vec \theta$. The ultimate goal is to deduce the value of
$\vec\theta$ by performing a series of experiments that yield the data $\vec
x$. If we were given the values of $\vec \theta$, we could calculate the
probability density function $f(\vec x, \vec \theta)$ and thus predict the
probability $P$ of getting a realization of the data $\vec x$ given the
theory $\vec \theta$, which is usually denoted by $P(\vec x|\vec \theta)$.
But since we rarely are given the exact theory, all we can do is draw
samples $\vec x_i$ of an unknown PDF by conducting experiments in order to
estimate the parameters $\vec\theta$. In a {\textit{frequentist}} approach,
we would take those parameters as the true ones that maximize the so-called
\textit{likelihood function}
\begin{equation}
\mathcal L(\vec \theta,\vec x_i) \equiv \prod\limits_i f(\vec x_i,\vec
\theta)\,, \label{eq:2-pdf}
\end{equation}
which is nothing but the joined PDF, with $\vec \theta$ now being
interpreted as a variable and $\vec x$ as a fixed parameter. But in
cosmology, we often have prior knowledge about the parameters from other
observations or theories that we would like to account for. For this, we
need Bayes' theorem:
\begin{equation}
P(\vec \theta| \vec x,I) = \frac{ P(\vec \theta|I) P(\vec x|\vec
\theta,I)}{P(\vec x|I)}\,.
\label{eq:2-bayes}
\end{equation}
In this \textit{Bayesian} approach, we turn the situation around so that we
are asking the question: \textit{What is the probability of the theory,
given the observed data?} Note that we included the background information
$I$ in every term even though it is hardly relevant to the derivation. It is
to remind ourselves that we always assume some sort of prior knowledge, even
when we do not realize it. For instance, we might implicitly assume that
the Copernican principle holds true, or that the Universe is described by
the Einstein field equations.
Here the prior knowledge (or just \textit{prior}) is given by $P(\vec
\theta|I)$, and $P(\vec x|I)$ is the marginal probability of the data $\vec
x$ which acts as a normalization factor, requiring that $\int \mathcal
L(\vec \theta,\vec x_i)\,\mathrm d^n \theta = 1$.
$P(\vec x|\vec \theta,I)$ is identical to the likelihood, which is given
by the model. This could be for instance a Gaussian PDF
\begin{equation}
\prod\limits_{i=1}^n\frac{1}{\sigma_i \sqrt{2\pi}} \exp\left( -
\frac{(\hat{x}_i - x_i(\vec \theta))^2}{2\sigma_i^2} \right)\,.
\label{eq:2-gauss}
\end{equation}
The left hand side of
eq.~(\ref{eq:2-bayes}) is then called the
\textit{posterior}~\citep[p. 42]{Hobson2009a}. We now have all the
ingredients to calculate the posterior probability of the parameters given
the data. This quantity is important for computing the so-called evidence,
which is defined by the integral over the numerator in
eq.~(\ref{eq:2-bayes})
and needed for model selection.
Unfortunately, the likelihood is often not a simple Gaussian. Finding the
values of $\vec \theta$ that maximize the PDF given by
eq.~(\ref{eq:2-bayes}) can be computationally demanding, since a (na\"ive)
algorithm for finding the extremum scales exponentially with the number of
dimensions of the parameter space. This will becomes a problem when
considering 30 parameters as we will later in this thesis. It is not unusual
for Bayesian statistics to suffer from the ``curse of
dimensionality''\citep{Bellman2003}. One way to overcome this curse is by
using Markov chain Monte Carlo methods. In the case of
a likelihood that is not a multivariate Gaussian, we can simply assume that
it can at least be approximated by one. This is not an unreasonable
assumption, since the logarithm of the likelihood can always be Taylor
expanded up to the second order around its maximum, denoted by $\hat{\vec
\theta}$:
\begin{equation}
\ln\mathcal L(\vec \theta) \approx \ln \mathcal L(\hat{\vec\theta}) +
\frac{1}{2}\sum\limits_{i,j} \left.\frac{\partial^2 \ln \mathcal L(\vec
\theta)}{\partial\theta_i \partial\theta_j}\right|_{\vec
\theta=\hat{\vec\theta}}(\theta_i-\hat\theta_i)(\theta_j-\hat\theta_j)\,.
\label{}
\end{equation}
No first order terms appear since they vanish in a maximum by definition.
It is now quite useful to define the \textit{Fisher matrix} as the negative
of the Hessian of the likelihood,
\begin{equation}
F_{ij} \equiv -\left.
\frac{\partial^2\ln\mathcal L(\vec
\theta)}{\partial\theta_i\partial\theta_j}\right|_{\vec
\theta=\hat{\vec\theta}}\,.\label{eq:2-fm}
\end{equation}
This definition is not very useful when we need to find the
maximum of a multi-dimensional function and then compute the derivatives
numerically
anyway, since many expensive evaluations is what we wanted to avoid in the
first place. However, since this thesis deals with constraints by
\textit{future} surveys, using
some fiducial model which we already know the expected outcome of and thus
the peaks of the likelihood. This is the reason why the Fisher matrix is a
perfect tool in assessing the merit of future cosmological surveys.
Let us consider a survey in which we measure some set of observables $\vec
x$ (along with their respective standard errors $\vec \sigma$)
whose theoretical values $\hat{\vec x}(\vec \theta)$ depend on our model.
These observables could be the same quantity at different redshifts, i.e.
$x_i = x(z_i)$, or different quantities all together, e.g. $\vec
x=(z_\mathrm{CMB},c_s,\Omega_k)$, or a mixture of both. Assuming a Gaussian
PDF we can write down the likelihood as
\begin{equation}
\mathcal L(\vec\theta) \propto \exp\left(-\frac12 \sum\limits_i
\frac{(x_i-\hat{ x_i}(\vec\theta))^2}{\sigma_i^2}\right)\,.
\end{equation}
Using the definition in eq.~(\ref{eq:2-fm}) we get for the Fisher matrix
\begin{equation}
F_{ij} = - \sum\limits_k \left.\frac{1}{\sigma_k^2}\frac{\partial^2 \hat
x_k(\vec \theta)}{\partial\theta_i\partial\theta_j}\right|_{\vec
\theta=\hat{\vec\theta}} \,.
\end{equation}
\subsection{Calculation rules}
\label{calcrules}
We will not go into a full derivation of the rules, as they can be found
in~A\&T~(ch. 13.3) and are quite straight forward, but rather simply state
them here.
\paragraph{Fixing a parameter.} If we want to know what the Fisher matrix
would be given that we knew one particular parameter $\theta_i$ precisely,
we simply remove the $i$-th row and column of the Fisher matrix.
\paragraph{Marginalizing over a parameter.} If, on the other hand, we want
to disregard a particular parameter $\theta_i$, we remove $i$-th row
and column from the inverse of the Fisher matrix (the so-called
\textit{correlation matrix}) and invert again afterwards. If we are only
interested in exactly one parameter $\theta_i$, then we cross out all other
rows and columns until the correlation matrix only has one entry left. Thus,
we arrive at the important result
\begin{equation}
\sigma(\theta_i)^2= (\mat F^{-1})_{ii}\,.
\end{equation}
This implies that the Fisher matrix must be positive definite, as it must be
as the Hessian in a maximum.
\paragraph{Combination of Fisher matrices.} Including priors in our analysis
is extremely simple in the Fisher matrix formalism, since all we need to do
is add the Fisher matrix:
\begin{equation}
\mat F' = \mat F + \mat F^\mathrm{prior}\,.
\end{equation}
This only holds if both matrices have been calculated with the same
underlying fiducial model, i.e. the maximum likelihood is the same. The only
difficulty lies in ensuring that the parameters of the model belonging to
each matrix are identical and line up properly. If one matrix covers
additional parameters, then the other matrix must be extended with rows and
columns of zeros accordingly.
\paragraph{Parameter transformation.} Often a particular parameterization of
a model is not unique and there exists a transformation of parameters
\begin{equation}
\vec \theta' = \vec\theta'(\vec \theta)\,,
\end{equation}
which might happen when combining Fisher matrices from different sources.
Then the Fisher matrix transforms like a tensor, i.e.
\begin{equation}
\mat F' = \mat J^T \mat F \mat J\,,
\end{equation}
where $\mat J$ is the Jacobian matrix
\begin{equation}
J_{ij} = \frac{\partial \theta_i}{\partial \theta_j'}\,,
\end{equation}
which does not necessarily need to be a square matrix. If it is not,
however, note that the new Fisher matrix will be degenerate and using it
only makes sense when combining it with at least one matrix from a different
source.
\chapter[Constraints by future surveys]{Constraints on cosmological
parameters by future dark energy surveys}
With the knowledge of the observational specifications of future weak
lensing surveys, we can use the Fisher matrix formalism to forecast the
errors that said surveys will place on cosmological parameters. In
particular, we want to expand the list of those parameters with values of
the Hubble parameter and growth function at certain redshifts. An invaluable
resource for this chapter is the book by A\&T (ch. 14)
\section{Power spectrum tomography} \label{sec:tomography}
It has been shown that dividing up the distribution of lensed galaxies into
redshift bins and measuring the convergence power spectrum in each of these
bins as well as their cross-correlation can increase the amount of
information extracted from weak lensing surveys \citep{Hu1999,Huterer2002}.
This means on one hand that we need to have additional redshift information
on the lensed galaxies, but on the other that we are possibly rewarded with
gaining knowledge about the evolution of dark energy parameters. Note that
the purpose of the redshift bins in this thesis is two-fold, and power
spectrum tomography is only one of them. The other is the linear
interpolation of $H(z)$ and $G(z)$, where the centers of the redshift bins
act as supporting points, making our analysis independent of assumptions
about the growth function by any particular model. We choose to divide the
redshift space into $\mathcal N$ bins such that each redshift bin contains
roughly the same amount of galaxies according to the galaxy density function
$n(z)$, i.e.
\begin{equation}
\int_{z_{i-1}}^{z_{i}} n(z)\,\mathrm d z = \frac1\mathcal N
\int_0^{\infty}n(z)\,\mathrm d z
\end{equation}
for each $i$. We infer the values of the $z_i$ via a series
of successive numerical integrations with $z_0=0$ and $z_\mathcal N=3$ (see
fig.~ref{fig:2-zbins}).
A common parametrization of $n(z)$ is
\begin{equation}
n(z) \propto z^\alpha e^{-\left( {z}/{z_p} \right)^\beta},
\end{equation}
with $\alpha=2$ and $\beta=\frac32$. Here $z_p$ is related to the median
redshift $z_m=1.412 z_p$ \citep{Amara2008}.
\begin{figure}[htpb]
\begin{center}
\includegraphics[width=9cm]{graphics/zbins-galaxy-df}
\end{center}
\caption{The area under the curve of the galaxy density function
is the same in each redshift bin for $\mathcal N=5$.}
\label{fig:2-zbins}
\end{figure}
We need a galaxy density function for each bin, and the naïve choice
would be
\begin{equation}
\hat n_i(z) = \left\{
\begin{array}{ll}
n(z) & z_{i-1}<z\leq z_i\,,\\
0 & \mathrm{else.}
\end{array}
\right.
\end{equation}
But to account for redshift measurement uncertainties, we will convolve
$\hat n(z)$ with the probability distribution of the measured redshift
$z_\mathrm{ph}$ given the real value $z$:
\begin{equation}
n_i(z) = \int_0^\infty\,\mathrm d z'
\hat n_i( z') P_i(z_\mathrm{ph}= z'|z) \,.
\end{equation}
Note that the integral vanishes if $ z'$ lies outside the
$i$th bin, so the limits can be adjusted to the according finite values.
This convolution reflects the fact that we cannot assign a galaxy to a
particular bin by measuring the photometric redshift with finite precision.
The probability distribution is here modeled by Gaussian, i.e.
\begin{equation}
P_i(z_\mathrm{ph}|z) = \frac{1}{\sqrt{2\pi}\sigma_i} \exp\left(-\frac{\left(
z_\mathrm{ph}-z \right)^2}{2 \sigma_i^2}\right)
\end{equation}
with $\sigma_i = \Delta_z(1+(z_{i-1}+z_i)/2)$ (see \cite{Ma2006} for
details). Finally, we normalize each function to unity, such that
\begin{equation}
\int_0^\infty n_i(z)\,\mathrm d z = 1\,.
\end{equation}
The resulting functions can be visualized as in fig. \ref{fig:3-ngal}.
\begin{figure}[htpb]
\begin{center}
\includegraphics[width=9cm]{graphics/ngal}
\end{center}
\caption{Normalized galaxy density functions for each bin with $\mathcal N=5$,
convolved with a Gaussian to account for photometric redshift measurement
errors.} \label{fig:3-ngal}
\end{figure}
\section{The matter power spectrum}\label{sec:nonlinear}
Future weak lensing surveys will supply us with the convergence power
spectrum in which the cosmological information we are seeking is imprinted.
However, for now we will have to rely on simulated data. As we will see in
section~\ref{sec:convps}, the convergence power spectrum depends on the
matter power spectrum which can be simulated by a
fitting formula derived by \citet{Eisenstein1999}. Non-linear corrections
need to be accounted for, since we are assuming an angular galaxy density of
$35\unit{arcmin}^{-2}$, which corresponds to a multipole up to a order of
magnitude of
\begin{equation}
\lg\left(\sqrt{35 \unit{arcmin}^{-2}}\right)\approx 4\,.
\label{eq:3-ellmax}
\end{equation}
As we saw in fig.~\ref{fig:2-ps}, non-linear corrections are required for
$\ell\gtrsim10^3$, and for this we need to use the results by
\citet{Smith2003}. Here we will give a brief overview of the essential
results found in the two papers cited above, using our notation and some
simplifications (no massive neutrinos, flat cosmology).
\subsection{Fitting formulas}\label{subsec:fitting}
It should be stressed that the growth function $D(z)$ in Eisenstein's paper
differs from ours by a factor of $a=1/(1+z)$, so $D(z) = a G(z)$. A precise
definition of the growth function will be given in
section.~\ref{sec:growth}. They also define $\Theta_{2.7} \equiv
T_\mathrm{CMB}/2.7\unit{K}$. Only in this section will we differentiate
between the linear and the non-linear power spectrum. Later on, the
expression ``power spectrum'' or $P_m(k)$ will always imply that non-linear
corrections have been applied.
Using the definition of the growth function, the matter power spectrum in
the linear regime can be written as (cf. eq.~(\ref{eq:3-mps2}))
\begin{equation}
P_\mathrm{L}(k) \propto k^{n_s} \frac{G(z)^2}{(1+z)^2} T(z,k)^2\,,
\label{eq:3-mps1}
\end{equation}
where $n_s$ is called the scalar spectral index. The transfer function
$T(k)$ can now be fitted by a series of functions as follows.
\begin{equation}
T(k) = \frac{L B(k)}{L+C q_\mathrm{eff}^2}\,,
\end{equation}
with (we assume that there are no massive neutrinos, in which case $B(k)$
equals unity)
\begin{align}
L &= \ln(e+1.84\beta_c\sqrt{\alpha_\nu} q_\mathrm{eff})\\
C&= 1.44+\frac{325}{1+60.5 q_\mathrm{eff}^{1.11}}
\end{align}
where
\begin{align}
q_\mathrm{eff} &= \frac{k \Theta^2_{2.7}}{\Gamma_\mathrm{eff}
\unit{Mpc}^{-1}}\\
\Gamma_\mathrm{eff} &= \omega_m \left( \sqrt{\alpha_\nu} +
\frac{1-\sqrt{\alpha_\nu}}{1+(0.34ks)^4} \right)\\
\end{align}
and
\begin{multline}
\alpha_\nu = \frac{\omega_c}{\omega_m}\frac{5-2(p_c +
p_m)}{5-4p_m} \left( 1-0.553 \omega_b + 0.126\omega_b^3\right)
(1+y_d)^{p_m-p_c}\\
\times \left\{ 1 + \frac{p_c-p_{cb}}{2}\left[
1+\frac{1}{(3-4p_c)(7-4p_m)} \right](1-y_d)^{-1} \right\}\,.
\end{multline}
Here, we used the abbreviations
\begin{align}
p_x &= \frac{1}{4}(5-\sqrt{1+24\omega_x})\\
y_d & = \frac{1+z_\mathrm{eq}}{1+z_d}
\end{align}
with
\begin{align}
z_\mathrm{eq} &= 2.50 \times 10^4 \omega_m \Theta_{2.7}^{-4}\\
z_d &= 1291 \frac{ \omega_m^{0.251}}{1+0.659\omega_m^{0.828}}
(1+b_1\omega_m^{b_2})\\
b_1 &= 0.313\omega_m^{-0.419}(1+0.607\omega_m^{0.674})\\
b_2 &= 0.238\omega_m^{0.223}\,.
\end{align}
By definition, the power spectrum needs to be normalized such that
\begin{equation}
\sigma_8^2 = \int_0^\infty \frac{\,\mathrm d k}{k} \frac{k^3}{2\pi^2}
P_\mathrm{L}(k)|\tilde W_8(k)|^2\,,
\end{equation}
where $\tilde W_R(k)$ is the Fourier transform of the real-space window
function, in this case a spherical top hat of radius $R$ (in Mpc), i.e.
\begin{align}
W_R(r) &\propto \left\{
\begin{array}{ll}1& \mathrm{if}\:\:r \leq R\\
0 & \mathrm{otherwise}
\end{array}
\right.\\
\tilde W_R(k) &= \frac{3}{(kR)^3}(\sin kR -kR \cos kR)\,.
\end{align}
\subsection{Non-linear corrections}
When applying non-linear corrections, we use the dimensionless power
spectrum, which is defined by
\begin{equation}
\Delta_\mathrm{L}^2(k) = \frac{4\pi k^3}{(2\pi)^3 } P_\mathrm{L}(k) \,,
\end{equation}
and similarly for other indices. It turns out that the non-linear power
spectrum can be decomposed into a quasi-linear term and contributions from
self-correlations
\begin{equation}
\Delta_\mathrm{NL}^2 = \Delta^2_\mathrm{Q}(k) + \Delta^2_\mathrm{H}(k)\,,
\end{equation}
which are given by
\begin{align}
\Delta_\mathrm{Q}^2(k) &= \Delta_\mathrm{L}^2(k)\left(
\frac{(1+\Delta_\mathrm{L}^2(k))^{\beta_n}}
{1+\alpha_n\Delta_\mathrm{L}^2(k)} \right)\exp(-y/4-y^2/8)\\
\Delta_\mathrm{H}^2(k) &= \frac{ {\Delta_\mathrm{H}^2}'(k)}{1+\mu_n
y^{-1}+\nu y^{-2}}\,,
\end{align}
with $y \equiv k/k_\sigma$ and
\begin{equation}
{\Delta^2_\mathrm{H}}'=\frac{a_n y^{3f_1(\Omega_m)}}{1+b_n
y^{f_2(\Omega_m)}+(c_n f_3(\Omega_m)y)^{3-\gamma_n}}\,.
\end{equation}
In these equations, $k_\sigma$ is defined via
\begin{equation}
\sigma(R_\mathrm{G})^2 \equiv \int_\infty^\infty \Delta_\mathrm{L}^2(k)
\exp(-k^2 R_\mathrm{G})^2 \,\mathrm d \ln k
\end{equation}
by
\begin{equation}
\sigma(k_\sigma^{-1}) = 1\,,
\end{equation}
while the effective index is
\begin{equation}
n = -3- \left. \frac{\,\mathrm d \ln \sigma(R)^2}{\,\mathrm d\ln R}\right|_{\sigma=1}
\end{equation}
and the spectral curvature is
\begin{equation}
C = \left.\frac{\,\mathrm d^2\ln\sigma(R)^2}{\,\mathrm d\ln R}\right|_{\sigma=1}\,.
\end{equation}
The best fit yielded the following values for the coefficients:
\begin{align}
\lg a_n &= 1.4861+1.8369n+1.6762n^2+0.7940n^3+0.167n^4-0.6206C\nonumber\\
\lg b_n &= 0.9463+0.9466n+0.3084n^2-0.9400C\\
\lg c_n &= -0.2807+0.6669n+0.3214n^2-0.0793C\\
\alpha_n &= 1.3884+0.3700n-0.1452n^2\\
\beta_n &= 0.8291+0.9854n+0.3401n^2\\
\gamma_n &= 0.8649+0.2989n+0.1631C\\
\lg \mu_n &= -3.5442+0.908n\\
\lg \nu_n &= 0.9589 + 1.2857n\,.
\end{align}
Also, the functions $f_i$ in a flat universe are given by
\begin{align}
f_1(\Omega_m) &= \Omega^{-0.0307}_m\\
f_2(\Omega_m) &= \Omega^{-0.0585}_m\\
f_3(\Omega_m) &= \Omega^{0.0743}_m\,.
\end{align}
\subsection{Parameterized post-Newtonian formalism}
We shall allow another degree of freedom in our equations that stems from
scalar theories in more than four dimensions. The Gauss-Bonnet theorem in
differential geometry connects the Euler characteristic of a two-dimensional
surface with the integral over its curvature. In general relativity, it
gives rise to a term with unique properties: It is the most general term
that, when added to the Einstein-Hilbert action in more than four
dimensions, leaves the field equation a second order differential equation.
In four dimensions, the equation of motion does not change at all under this
generalization, unless we are working in the context of a scalar-tensor
theory, in which the Gauss-Bonnet term couples to the scalar part and
modifies the equation of motion. For our purposes, this will effectively
make Newton's gravitational constant $G$ a variable, denoted by $G_*(\eta)$
(for details, see \cite{Amendola2006} and references therein). This is
called the \textit{parameterized post-Newtonian} (PPN) formalism.
By defining
\begin{equation}
Q \equiv \frac{G_*}{G}\,,
\end{equation}
one can write the Poisson equation in Fourier space as
\begin{equation}
k^2 \phi = -4\pi G a^2 Q \rho_m \Delta_m\,,
\end{equation}
where $\Delta_m$ accounts for comoving density perturbations of matter. If
we admit anisotropic stress, then the two scalar gravitational potentials do
not satisfy $\Psi=-\Phi$, and we parameterize this by
\begin{equation}
\Psi \equiv -(1+\eta(k,a))\Phi\,.
\end{equation}
With weak lensing, only the combination
\begin{equation}
\Sigma \equiv Q(1+\eta/2)
\end{equation}
appears in the convergence power spectrum in a very simple way, where we can
just replace the matter power spectrum $P_m(k)$ by $\Sigma P_m(k)$.
Obviously, in the standard $\Lambda$CDM model, we have $\Sigma=1$, so we
allow it to vary in time and parameterize it as
\begin{equation}
\Sigma(a) =1+\Sigma_0 a\,,
\end{equation}
such that initially it looks like the standard model and then gradually
diverges from there \citep{Amendola2008}. Finally, we add $\Sigma_0$ to our
list of cosmological parameters with a fiducial value of 0.
\section{The Fisher matrix for the convergence power spectrum}
\label{sec:convps}
Building on the methods outlined in chapter 2, we can now compute the weak
lensing Fisher matrix. A full derivation of its expression can be found in
A\&T, ch. 14.4 or \cite{Hu1999}, with the final result being
\begin{equation}
F_{\alpha\beta} = f_\mathrm{sky} \sum_\ell
\frac{(2\ell+1)\Delta\ell}{2}
\sum\limits_{ijkm}\frac{\partial P_{ij}(\ell)}{\partial
\theta_\alpha}C^{-1}_{jk}\frac{\partial P_{km}(\ell)}{\partial
\theta_\beta}C^{-1}_{mi}\,.
\label{eq:3-fm}
\end{equation}
For this we need a multitude of cosmological functions that will be defined
in this section from the bottom up. First of all, note that the sum should
go over all multipoles $\ell$ inside an interval
$\ell_\mathrm{min}..\ell_\mathrm{max}$ that is determined by the fractional
survey size $f_\mathrm{sky}$ and the angular galaxy density $n_\vartheta$.
However, this poses a computational challenge. Hence, we rather sum over
bands with width $\Delta\ell$ while keeping in mind that one multipole
$\ell$ contains $(2\ell+1)$ modes \citep{Hu2004}. The multipole intervals
will be logarithmically spaced and the choice $\lg\Delta\ell$ shall be
justified in section~\ref{sec:lgell}.
$C_{jk}$ is the covariance matrix, given by
\begin{equation}
C_{jk}=P_{jk} + \delta_{jk}\gamma_\mathrm{int}^2 n^{-1}_j\,,
\end{equation}
where $\gamma_\mathrm{int}$ is the shot noise due to the intrinsic
ellipticity and $n_j$ is the number of galaxies per steradians belonging to
the $j$-th bin:
\begin{equation}
n_j = 3600 \left( \frac{180}{\pi} \right)^2
n_\vartheta\int_{0}^\infty n_j(z)\,\mathrm d z,
\label{}
\end{equation}
where $n_\vartheta$ is the galaxy density per $\unit{arcmin}^2$.
The convergence spectrum $P_{ij}$ depends on the matter power spectrum
$P_{m}$ and is given by (now with the PPN parameter)
\begin{equation}
P_{ij}(\ell) = \frac{9}{4}\int_0^\infty
\frac{W_i(z)W_j(z)H^3(z)\Omega_m(z)^2}{(1+z)^4}\Sigma(z) P_{m}\left(
\frac{\ell}{\pi r(z)}\right)\,\mathrm d z\,,
\label{eq:3-convspec}
\end{equation}
which can be slightly simplified, by using
$\Omega_m(z)=\Omega_m\times(1+z)^3/E(z)^2$, to
\begin{equation}
P_{ij}(\ell) = \frac{9H_0^3}{4}\Omega_m^2\int_0^\infty
\frac{W_i(z)W_j(z)(1+z)^2}{E(z)}\Sigma(z) P_{m}\left(
\frac{\ell}{\pi r(z)}\right)\,\mathrm d z\,.
\end{equation}
Here, $H(z)$ denotes the Hubble parameter, which is
given by the first Friedmann equation (\eq{eq:2-friedmann1}) as
\begin{equation}
H(z) = H_0 \sqrt{ \Omega_m(1+z)^3 + (1-\Omega_m)
\exp(f_w(z))}\,,
\label{eq:3-e(z)}
\end{equation}
and $E(z)\equiv H(z)/H_0$ is its dimensionless equivalent. The function
\begin{equation}
f_w(z)=3\int_0^z
\frac{1+w(z)}{1+ z'}\,\mathrm d z'\,.
\end{equation}
describes how the dark energy density scales with the scale factor
and is the solution of the continuity
equation~(\ref{eq:2-conti}).
The equation-of-state ratio $w(z)\equiv \rho/p$ is from
now on assumed to take the common CPL parameterization\footnote{Relevant
literature often uses $w_a$ instead of $w_1$.}
\citep{Chevallier2001,Linder2003}
\begin{equation}
w(z) = w_0 + w_1 \frac{z}{1+z}\,,
\label{eq:3-w(z)}
\end{equation}
in which case the above function can be calculated analytically and takes
the form
\begin{equation}
f_w(z) = 3 \left((w_0+w_1+1) \ln
(z+1)-\frac{w_1 z}{z+1}\right)\,.
\end{equation}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/window}
\end{center}
\caption{The window functions $W_i(z)$ for five redshift bins.}
\label{fig:3-wind}
\end{figure}
One of the most crucial functions being used in this calculation is the
window function
\begin{equation}
W_i(z) = \int_z^\infty \frac{\,\mathrm d z'}{H( z')}\left( 1-\frac{r(z)}{r( z')}
\right) n_i(r( z')),
\label{eq:3-wind}
\end{equation}
where $r(z)$ is the comoving distance at redshift $z$, i.e.
\begin{equation}
r(z) = \int_0^z \frac{\,\mathrm d z'}{H(z')}\,.
\end{equation}
Lastly, we need the matter power spectrum $P_{m}$ to infer the
convergence power spectrum. For this we use the fitting formulae covered in
section~\ref{sec:nonlinear}.
\section{Survey parameters}
\label{survey}
The quality of any weak lensing survey is determined by a set of
parameters that includes the fraction of the sky covered\footnote{Since the
Milky Way is blocking roughly half of our sky for deep surveys, even the
most ambitious missions will have $f_\mathrm{sky}=0.5$.}, the median
redshift, and so on. In table \ref{tab:3-survey} all of the parameters that
are used in our simulation are shown. Weak lensing surveys should aim at
wide and deep field coverage. Since these projects are all still in
development, the exact numbers that will be used in the end may vary, and
some are still undecided.
\begin{table}[htbp]
\centering
\begin{tabular}{ccl}
\hline\hline
Parameter & Value & Comment\tabularnewline
\hline
$f_\mathrm{sky}$ & 0.5 & Fraction of sky surveyed \tabularnewline
$z_m$ & 0.9 & Median redshift\tabularnewline
$\Delta_z$ & 0.05 & Relative photometric redshift error\tabularnewline
$n_\vartheta$& 35 & Galaxy density per $\unit{arcmin}^2$ \tabularnewline
$\gamma_\mathrm{int}$ & 0.22 & Intrinsic shear\tabularnewline
\hline
\end{tabular}
\caption{Shown here are typical values of survey parameters determining the
quality of the experiment, which we will use in our calculation
\citep[cf.][]{Huterer2006}.}
\label{tab:3-survey}
\end{table}
\subsection{Ground based surveys: LSST}
The Large Synoptic Survey Telescope,\footnote{\url{http://www.lsst.org/}}
funded partially privately and by the U.S. Department of Energy, is a wide
field survey telescope working in the visible band, located on the Cerro
Pach\'on in Chile. It is currently in the design and development stage and
is scheduled to be fully operational by 2020 with a lifetime of at least ten
years. It will feature a 3.2 Gigapixel camera and a large aperture with an
8.4m (6.5m effective) primary mirror and cover the entire extra galactic sky
of 20 000 deg$^2$ with a depth up to an apparent magnitude of $r\sim 27.7$
for point sources. Besides weak lensing measurements, the mission will
observe super novae as well as map the Milky Way and small objects in the
solar system (such as asteroids).
This ultra wide and deep survey will provide a good data
source for weak lensing observations.
\subsection{Space based surveys: \texorpdfstring{\sc Euclid}{Euclid},
WFIRST}
{\sc Euclid}\footnote{
\url{http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=42266}} is
a proposed mission from ESA for a satellite orbiting the second Lagrangian
point as part of their cosmic vision program. It is still in the definition
phase and currently competing with PLATO and Solar Orbiter to be one the two
missions that will be approved by ESA in mid 2011. It is foreseen to be
launched in 2017 with a nominal mission lifetime of five years. This survey
might also cover up to 20 000 deg$^2$. The telescope will be a 1.2m Korsch
operating within the visible and infrared wavelengths with the ability of
detecting galaxies in the redshift range $0.5<z<2$ and therefore provide an
excellent probe for dark energy.
The Wide Field Infrared Survey Telescope
(WFIRST\footnote{\url{http://wfirst.gsfc.nasa.gov}}, formerly known as
JDEM-Omega) is another survey investigating dark energy, funded by NASA and
the U.S. Department of Energy and proposed by the Joint Dark Energy Mission.
In addition to weak lensing and baryon acoustic oscillations, WFIRST will
also probe supernovae with high precision. It is still at a very early stage
and has been postponed to launch at an unknown date, possibly not before
2025, due to budgeting and scheduling issues on a seperate project, the
James Webb Space Telescope \citep{Overbye2011}.
\begin{table}[htb]
\centering
\begin{tabular}{rrrrrp{4cm}}
\hline\hline
Survey & $f_\mathrm{sky}$ & $\Delta_z$ & $z_m$ &
$n_\vartheta/\unit{arcmin}^{-2}$ & Reference\\
\hline
LSST & $0.37$ & 0.02 & $0.7$ & $30$ & \cite{Huterer2006,Ivezic2008}\\
{\sc Euclid} & 0.5 & $0.05$& 0.8 & 30-40 & \cite{Euclid2009}\\
WFIRST & $0.25$ & 0.04 & ? & $\geq 30 $ & \cite{Gehrels2010}\\
\hline
\end{tabular}
\caption{Overview of current and planned surveys.}
\label{tab:surveys}
\end{table}
\section{Fiducial model}
In order to apply the Fisher matrix formalism, we need a fiducial
cosmological model which represents the vector in parameter space where the
likelihood has its maximum. We use
the standard model of cosmology, a flat universe with cold dark matter and a
cosmological constant (called $\Lambda$CDM, which makes six parameters). We
additionally consider some extra parameters which are allowed to vary in a
non-standard way, in particular
\begin{equation}
\vec \theta = (\omega_m,\omega_b,\tau,n_s,\Omega_m,
w_0,w_1,\gamma,\Sigma_0 ,\sigma_8)\,, \label{eq:3-params}
\end{equation}
where $\omega_m=\Omega_mh^2$ is the reduced fractional matter density,
and $\omega_b$ is defined analogous for baryons. Their numerical
values according to the WMAP 7-year data~\citep{Komatsu2011} can be seen in
table \ref{tab:wmap7}. The growth index $\gamma$ is taken to be
$6/11\approx0.55$ in the standard model~\citep{Wang1998}.
It should be pointed out that the reionization optical depth $\tau$ is
merely a remnant, and none of the functions in the code in later section
depend on $\tau$; however, it was not removed, however, due to the
possibility of future modifications to the code. The inclusion of functions
that depend on $\tau$ will thus be easier, as long as we remember to cross
out the according row and column in the resulting Fisher matrix.
\begin{table}
\centering
\begin{tabular}{lll}
\hline\hline
Parameter & Fiducial value & Description\\
\hline
$\omega_m$ & $0.1352(36)$ & Reduced matter density today\\
$\omega_b$ & $0.02255(54)$ & Reduced baryon density today\\
$\Omega_m$ & $0.275(11)$ & Matter density today\\
$\tau$ & $0.088(14)$ & Reionization optical depth\\
$n_s$ & $0.968(12)$ & Scalar spectral index\\
$\sigma_8$ & $0.816(24)$ & Fluctuation amplitude at $8\unit{Mpc}/h$\\
\hline
$w_0^\dagger$ & $-1$ & Current equation-of-state ratio\\
$w_1^\dagger$ & $0$ & Higher order equation-of-state ratio\\
$\gamma^\dagger$ & $6/11$ & Growth index\\
$\Sigma_0^\dagger$ & $0$ & Parameterized Post-Newtonian
parameter\\
\hline
\end{tabular}
\caption{Our ten-parameter fiducial model. The second column represents the
WMAP7+BAO+$H_0$ Mean taken from \citet{Komatsu2011}. Quantities with a
dagger are fixed in
the standard flat $\Lambda$CDM model and thus not included here by the WMAP
measurement. Uncertainties in the last two digits are given in parenthesis.
They will be needed in Section~\ref{sec:priors}.}
\label{tab:wmap7}
\end{table}
\comment{
\section{Parametrization via rectangular functions}
The rectangular $\sqcap(x)$ function can be defined in terms of the
Heaviside step function $\Theta(x)$ as
\begin{equation} \sqcap(x) =
\Theta\left(x+\frac12\right)\Theta\left(\frac12-x\right) = \left\{
\begin{array}{ll} 1\quad \mathrm{if}\; |x|\leq\frac12\\ 0\quad \mathrm{else
} \end{array} \right.. \end{equation}
After choosing $\mathcal N+1$ numbers $x_0,x_1,\ldots,x_\mathcal N$ with
$x_i<x_{i+1}$, we can approximate any function $f(x)$ with rectangular
functions so that the function assumes a constant value in the respective
bin:
\begin{equation}
f(x) \approx \sum_{i=1}^\mathcal N \alpha_i \sqcap\left(
\frac{x-(x_{i-1}+x_i)/2}{x_i-x_{i-1}} \right)
\label{}
\end{equation}
where $\alpha_i=f( (x_{i-1}+x_i)/2)$. In case of a cosmological function of
the redshift $z$, this allows us to treat the coefficients $\alpha_i$ as
independent cosmological parameters after choosing some appropiate redshift
bins.
\begin{figure}[htpb]
\begin{center}
\includegraphics[width=9cm]{graphics/rectangular-function}
\end{center}
\caption{A function being approximated by rectangular functions.}
\label{fig:2-rec}
\end{figure}
}
\section{Model-independent parameterization}
\subsection{Expansion rate}\label{sec:3-hubble}
In order to see how observations can constrain the history of the expansion
rate without assuming a particular parameterization of it, we take the
values of the Hubble parameter at a series of redshifts determined in
section~\ref{sec:tomography} using our fiducial model and build a linearly
interpolated function going through these supporting points. For this, we
define
\begin{equation}
h_i = \ln H(\hat z_i),
\end{equation}
where $\hat z_i$ is at the
center of the $i$-th redshift bin. The use of the logarithm is purely for
convenience. The Hubble parameter itself from now on is a linearly
interpolated function through these points. It is evident that the
dependency of the Hubble parameter on the other cosmological quantities
changes from $H(z;\Omega_m,w_0,w_1)$ to $H(z;h_1,\ldots,h_\mathcal N)$. The
consequence of this is that all cosmological functions that depend on
$H(z)$ are now treated as functions of the $h_i$s, resulting in $\mathcal N$
additional parameters being added to the fiducial model.
\subsection{Growth function} \label{sec:growth}
The growth function is defined by
\begin{equation}
G(a) \equiv \frac{\Phi(a)}{\Phi(a_T)}\,,
\label{eq:3-growthfunc}
\end{equation}
where $\Phi$ is the scalar gravitational potential
from~(\ref{eq:2-newt-gauge}) and $a_T$ stands for the transfer epoch, which
typically has a value of $0.03$ (see
for instance A\&T or \citet{Dodelson2003}). Be advised that in relevant
literature the growth function is often defined such that $G(a)$ needs to be
replaced with $aG(a)$ in eq.~(\ref{eq:3-growthfunc}). Also, it is sometimes
referred to as $D$ or $D_1$. The growth function can be identified with the
matter density contrast over the scale factor, i.e.
\begin{equation}
G(a) = \frac{\delta_m(a)}{a\delta_m(0)}\,,
\end{equation}
which is given by
\begin{equation}
\delta_m(a) \equiv \frac{\rho(a) }{\langle \rho\rangle}-1\,.
\end{equation}
A practical quantity in cosmology is the so called growth index $\gamma$,
defined by
\begin{equation}
f(a) \equiv \Omega_m(a)^\gamma\,, \label{eq:3-gammafit}
\end{equation}
where $f$ is the growth rate
\begin{equation}
f(a) \equiv \frac{\,\mathrm d \ln \delta_m(a)}{\,\mathrm d \ln
a}\label{eq:3-growthrate}\,.
\end{equation}
Note that the power law in \eq{eq:3-gammafit} is an empirically found fit
for the growth rate \citep{Wang1998}, which was shown to be accurate to
within 0.2\% of the exact solution \citep{Linder2005}.
After reminding ourselves that
\begin{equation}
\,\mathrm d \ln a = \frac{\,\mathrm d a}{a} = (1+z)\,\mathrm d\left( \frac{1}{1+z} \right) =
-\frac{\,\mathrm d z}{1+z}\,,
\end{equation}
we can eliminate $\delta_m(a)$ and $f$ from eqs.
(\ref{eq:3-growthfunc} - \ref{eq:3-gammafit}) to find
\begin{equation}
G(z) = G_0 \exp\left({-\int_0^z\frac{\Omega_m( z')^\gamma-1}
{1+ z'}\,\mathrm d z'}\right)\,,
\label{eq:3-growth}
\end{equation}
where the matter density is
\begin{equation}
\Omega_m(z) =\frac{\rho_m(z)}{\rho_m(z)+\rho_\Lambda} =
\frac{\Omega_m\times(1+z)^3}{E(z)}\,.
\end{equation}
The only point where the growth function enters the calculation is via the
matter power spectrum, which is given by (see A\&T, p. 75; cf.
eq.~(\ref{eq:3-mps1}))
\begin{equation}
P_m(k,z) = \frac{2\pi^2\delta^2_H}{\Omega_m^2} \left(
\frac{k}{H_0} \right)^{n_s}T(k)^2\frac{G(z)^2}{(1+z)^2} H_0^{-3}.
\label{eq:3-mps2}
\end{equation}
Just as in section \ref{sec:3-hubble} we can now finally define
\begin{equation}
g_i \equiv \ln G(\hat z_i)
\end{equation}
and replace the original growth function with a linear interpolation through
the $\hat z_i$s. The number of parameters in our model thus increases to
$10+2\mathcal N$. Naturally, every function that depends on the matter power
spectrum now also becomes a function of the $g_i$s.
\section{The figure of merit}
In order to have a quantifiable gauge of the information content of the
final result, we define the figure of merit (FOM) for the error bars on the
$h_i$s and $g_i$s, respectively, as
\begin{align}
\mathop{\mathrm{FOM}}(H) \equiv& \sum_{i=1}^\mathcal N \sigma(h_i)^{-2}\,,\\
\mathop{\mathrm{FOM}}(G) \equiv &\sum_{i=1}^\mathcal N \sigma(g_i)^{-2}\,.
\label{eq:3-fom}
\end{align}
It is obvious that the smaller the error bars are, the larger the FOM
becomes. The idea of using this definition is that the FOM should not change
too much if only one error bar is significantly larger than all the other
ones.
While the particular value of the FOM has no deeper meaning, it provides a
convenient tool to easily compare the errors resulting from different sets
of parameters. Note that this definition does not match the
popular definition by the Dark Energy Task Force, which suits a
different purpose \citep{Albrecht2006}.
\section{An implementation in \texorpdfstring{{\sc Mathematica\ }}{Mathematica}}
To do the actual computation, we use {\sc Mathematica\ } 8.0.1.0, which supplies us with
all necessary numerical procedures.
In an attempt to seperate all the parameters that determine the final
outcome of the computation from the rest of the code, they are all defined
at the beginning of the {\sc Mathematica\ } notebook.
We further
calculate a checksum, a digital fingerprint of those parameters via an
injective\footnote{At least for our purposes.} map from the set of all
parameters onto the set of integers, comparable to a hash function. This
will be useful when we store results in a file when changing the parameters
without having to worry about overwriting previous results.
We can roughly differentiate between physical parameters (such as matter
density, baryon density, etc.) and technical
parameters (the limit of a certain integral, step size in an
interpolating function, etc.). For an overview, we refer to
tables~\ref{tab:3-functions}, \ref{tab:3-physical}, and \ref{tab:3-tech}.
\begin{table}[htb]
\centering
\begin{tabular}{ll}
\hline\hline
\multicolumn{2}{c}{Functions}\\
\hline
\verb|logprint[string]| & Prints messages and saves them to a log file\\
\verb|loadfile[filename]| & Uses pre-calculated expressions if applicaple\\
\verb|ngal[[i]][z]| & $n_i(z)$\\
\verb|hub[z,dbins]| & $H(z;h_1,\dots,h_\mathcal N)$\\
\verb|dist[z,dbins]| & $r(z)$\\
\verb|omgen[z,om,w0,w1]| & $\Omega_m(z)$\\
\verb|growthfastgen[z,gbins]| & $G(z;g_1,\dots,g_\mathcal N)$\\
\verb|wind[i,z,om,dbins]| & $W_i(z)$\\
\verb|pk[k,z,...]| & $P_m(k)$ (Linear)\\
\verb|pknl[k,z,...]| & $P_m(k)$ (Non-linear)\\
\verb|clnngen[i,j,ell,...]| & $P_{ij}(\ell)$\\
\verb|dcdp[pi,i,j,ell,ref]| & $\partial P_{ij}/\partial \theta_{pi}$\\
\hline
\end{tabular}
\caption{Functions as used in the {\sc Mathematica\ } notebook.}
\label{tab:3-functions}
\end{table}
\begin{table}[htb]
\centering
\begin{tabular}{llll}
\hline\hline
\multicolumn{4}{c}{Physical parameters}\\
\hline
\verb|omh2| & $\omega_m$ &
\verb|obh2| & $\omega_b$\\
\verb|tau| & $\tau$ &
\verb|ns| & $n_s$\\
\verb|om| & $\Omega_m$ &
\verb|w0| & $w_0$\\
\verb|w1| & $w_1$ &
\verb|gamma| & $\gamma$\\
\verb|gppn| & $\Sigma_0$ &
\verb|s8| & $\sigma_8$\\
\verb|dbins[[i]]| & $h_i$ &
\verb|gbins[[i]]| & $g_i$\\
\hline
\end{tabular}
\caption{Variables referring to physical parameters as used for arguments in
functions in the {\sc Mathematica\ }
notebook. Their fiducial value is stored in a variable that has the string
\textit{ref} attached.}
\label{tab:3-physical}
\end{table}
\begin{table}[htb]
\centering
\begin{tabular}{lrp{9cm}}
\hline\hline
\multicolumn{3}{c}{Technical parameters}\\
\hline
\verb|zlimit|&3& Redshift limit after which we assume $n(z)\approx0$\\
\verb|nbins|&5& Number of redshift bins $\mathcal N$\\
\verb|eps|&0.025& Step size for numerical differentiation\\
\verb|zsigma|&4 & Integration length in units of standard deviations\\
\verb|zsmax|& 4& Maximum redshift for interpolated functions\\
\verb|fitstepz|& 0.2 & Step size for interpolated functions\\
\verb|lellmax|& 4 & Decadic logarithm of upper limit of the multipole\\
\verb|lellmin|& 2 & Decadic logarithm of lower limit of the multipole\\
\verb|lstep|&0.2 & Decadic logarithmic step size of the multipole\\
\verb|piv| & & List of parameters that are not fixed\\
\verb|dir|& & Directory where data is stored\\
\hline
\end{tabular}
\caption{Parameters determining the accuracy of the result and their default
value.}
\label{tab:3-tech}
\end{table}
In the first section of actual computation, we infer the boundaries of the
redshift bins depending only on $\mathcal N$, $\Delta_z$, and the galaxy
distribution function $n(z)$. The definition of the necessary cosmological
functions is straight forward. They often involve the computation of time
intensive numerical integrals, especially the highly used window function.
These functions are interpolated by cubic splines. All functions are
sufficiently ``nice'' (not more than one extremum) so that we do not have to
retreat to more conservative linear splines.
In order to save processing time and memory (especially in sequenced
executions of the notebook) we employ a little trick when computing
expensive functions. To avoid
loss of data after unexpected computer crashes, it makes sense to store not
only the final result, i.e. the Fisher matrix, but also intermediate results
on the hard drive. For this, the function \verb|loadfile| evaluates the
expression given in the second argument only if the file given in the first
argument does not exist, and then stores the result in said file and returns
it. If the file does exist, the expression in it will be loaded and
returned. This is applied to all time sensitive functions. All files are
saved in \verb|dir|, which contains the checksum of all parameters, except
for the window functions $W_i(z)$. Because they only depend on $\Omega_m$,
$\mathcal N$, the $h_i$s and the number of the redshift bin, they are stored in a
sibling directory to save computing time when calculating the Fisher matrix
after only, say, $\Delta\lg\ell$ has changed. The computation of the
interpolating functions of the window functions has also been parallelized
by using the {\sc Mathematica\ } command \verb|ParallelTable|.
Very often we have to interpolate a function depending on several
parameters, such as the window function $W_i(z;\Omega_m, h_1,\dots
h_\mathcal N)$, which generally needs to be evaluated for the derivatives at all
$0<z<3$ for $\Omega_m$, $\Omega_m (1\pm\epsilon)$ and so on. We define the
function such that it is computed only when needed, which can be achieved in
{\sc Mathematica\ } by writing schematically
\begin{verbatim}
fAux[a_] := fAux[a] =
Interpolation[Table[{x,f[x,a]},{x,x0,x1,dx}]];
fFast[x,a] := fAux[a][x];
\end{verbatim}
The \verb|fFast[x,a]| is a fast, interpolated version of \verb|f[x,a]|,
where \verb|x| is the variable and \verb|a| a parameter. The extra \verb|=|
sign in the first line makes {\sc Mathematica\ } look up the cached value if
there is one, preventing it from making an expensive computation more than
once.
What follows is a relatively straight forward implementation of
sections~\ref{sec:nonlinear} and~\ref{sec:convps}. It is important to note,
however, that all the functions that ultimately depend on the growth
function, i.e. all functions that depend on the linear matter power
spectrum, have been overloaded such that they might take \verb|gbins| as an
argument, in which case the power spectrum uses the interpolated growth
function. The reason for this will become apparent in chapter~4.
Most functions have been carefully defined to avoid warnings by {\sc Mathematica\ }
concerning numerical issues like non-converging integrals. Vanishing
integrals are hard to detect with numerical methods, since a sufficiently
sharp, high peak would require an arbitrary large number of sampling points.
Many functions have been tweaked (if possible) to avoid these warnings. Very
often, {\sc Mathematica\ } also tries to simplify an expression before plugging in actual
values, which causes a lot of warnings and can slow down the computation
significantly. To prevent this, we declared certain arguments as
``numerical'' so that {\sc Mathematica\ } plugs in these values immediately. For instance
the comoving distance is defined as
\begin{verbatim}
dist[z_?NumericQ, dbins_] := NIntegrate[1/hub[zx, dbins],
{zx, 0, z}];
\end{verbatim}
This way, {\sc Mathematica\ } will not try to numerically evaluate the integral in a
subsequent definition of a function (which would be futile) before a
specific value for the redshift is given. We found that this significantly
reduces numerical instabilities and improves the overall results.
\chapter{Results}
Before we cover the analysis of the results, it needs to be pointed out that
\textit{ two} Fisher matrices have been calculated. The first Fisher matrix
was computed while using the standard expression in eq.~(\ref{eq:3-growth})
for $G(z)$ and linearly interpolating $H(z)$, and the second Fisher matrix
was computed by linearly interpolating both $H(z)$ and $G(z)$. We will
refer to this as the $H$-\textit{case} and the $G$-\textit{case}
respectively. This introduces a certain degeneracy, since the variables
$h_i$ occur in both the $H$-case and the $G$-case and generally take on
different values. Hence we will denote those variables in the $H$-case as
$\hat h_i$ to avoid confusion, although they will be barely used.
Unless mentioned otherwise, the Fisher matrix has been calculated using the
parameters shown in tab.~\ref{tab:3-tech}, where we cross out the rows and
columns corresponding to $(\tau,w_0,w_1,\gamma,\Sigma_0)$ in the standard
case. The order of our parameters was given in eq.~(\ref{eq:3-params}); here
is a reminder:
\begin{equation}
\vec \theta = (\omega_m,\omega_b,\tau,n_s,\Omega_m,
w_0,w_1,\gamma,\Sigma_0 ,\sigma_8)\,. \label{eq:4-params}
\end{equation}
From the resulting Fisher matrix,
we can easily extract the errors on each cosmological parameter. A typical
example of plotting the error bars on the Hubble parameter and growth
function can be seen in fig. \ref{fig:4-errors}.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/h-errors}
\includegraphics[width=9cm]{graphics/g-errors}
\caption{A typical plot of the error bars on the $h_i$s (top) and $g_i$s
(bottom) for $\mathcal N=5$
with a figure of merit of 7634 and 2865 respectively. The bins are chosen
such that they all contain the same number of galaxies.}
\label{fig:4-errors}
\end{center}
\end{figure}
\section{Consistency checks}
Since we naturally cannot compare our results with observations within the
next decade, we have limited means to make sure that they are meaningful and
error free. One way to check is to see whether the matrix satisfies basic
properties, another is to compute intermediate, partial results and compare
them with the numerical results. A first approach would be to visually
compare the derivative of the convergence power spectrum
in two particular bins with respect to a particular cosmological parameter,
e.g.
\begin{equation}
\frac{\partial P_{12}(\ell)}{\partial g_1}\,,
\end{equation}
with and without interpolated functions. However, this turned out to be
unpractical due to the long runtime of over three days even with the use of
four parallel kernels and reducing the sampling points in the numerical
integration down to 50.
But we can still easily do another check. As the negative of the Hessian of
a function at its maximum, the Fisher matrix needs to be positive definite.
Looking at the eigenvalues of the Fisher matrix, we find in the $H$-case
(descending order)
\begin{multline}
\vec \lambda_H = (1.03\times 10^8,4.87\times 10^6,1.89\times
10^5,7.29\times 10^4,3.34\times 10^4,\\9.11\times
10^3,6.71\times 10^3,6.57\times 10^2, 3.2\times
10^2,1.06\times 10^2,\\4.76\times 10^1,1.67\times
10^1,3.53,1.04\times 10^{-2},1.4\times
10^{-15})\,.
\label{eq:ev1}
\end{multline}
Note that the last eigenvalue is thirteen orders of magnitude smaller than
the next largest eigenvalue. The corresponding normalized eigenvector is,
while neglecting numbers that are smaller than $10^{-13}$,
\begin{equation}
\vec e_{H,15} = (0, 0, -1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)\,.
\end{equation}
This reveals that it points only in the $\tau$-direction in parameter space,
as we can see in eq.~(\ref{eq:4-params}). This degeneracy is expected, since
the
convergence power spectrum does not depend on $\tau$. All other eigenvalues
are positive, so this check is passed.
In the $G$-case, the eigenvalues of the Fisher matrix are
\begin{multline}
\vec \lambda_G = (1.24\times 10^8,5.21\times 10^6,6.63\times
10^5,1.86\times 10^5,8.85\times 10^4,\\4.08\times
10^4,9.26\times 10^3,7.65\times 10^3,2.96\times
10^3,1.\times 10^3,\\5.16\times 10^2,1.4\times
10^2,30.3,7.36,3.56,0.83,\\-1.92\times 10^{-14},5.33\times
10^{-15},-5.31\times 10^{-15},1.07\times
10^{-46})\,.
\label{eq:ev2}
\end{multline}
There are two negative eigenvalues among the last four of them, but as they
are at least thirteen orders of magnitude smaller than the next largest
eigenvalue, they are consistent with zero. Again, analyzing the according
eigenvectors while neglecting values below $10^{-13}$ yields
\begin{align}
\vec e_{G,17} & = (0, 0, 0, 0, 0, 0.085, -0.23, 0.97, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0) \\
\vec e_{G,18} & = (0, 0, 0, 0, 0, 0.98, 0.17, -0.047, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0)\\
\vec e_{G,19} & = (0, 0, 0, 0, 0, -0.15, 0.96, 0.24, 0, 0, 0, 0, 0, 0,
0, 0,0, 0, 0, 0) \\
\vec e_{G,20} & = (0, 0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0)\,.
\end{align}
Comparing again with eq.~(\ref{eq:4-params}) shows that these eigenvectors
lie in the parameter subspace spanned by $\tau$, $w_0$, $w_1$ and $\gamma$,
as we would expect since now the growth function depends on the $g_i$s
instead of the equation-of-state parameters $w_i$ and the growth index
$\gamma$. At this point, the convergence power spectrum does not depend on
any quantity that in turn depends on those parameters, so the Fisher matrix
will be degenerate if we do not cross out the according rows and columns.
Just like in the $H$-case, all remaining eigenvalues are positive.
\section{Improving the figure of merit}
In this section we want to find out how the FOM behaves when we modify
various parameters. This provides us with a way of gauging the
quality of the tomography process, seeing how much information we were able
to extract out of the weak lensing signal.
\subsection{Impact of the number of redshift bins}
Running the {\sc Mathematica\ } notebook for various values of $\mathcal N$ lets us compare
the FOM for different binning.
To get optimal results, we let the number of redshift bins $\mathcal N$ run
between 2
and 20, using the values 2, 3, \dots, 10, 15 and 20. In
fig.~\ref{fig:4-h-hist}, we can clearly see a peak at $\mathcal N=3$ in the
$H$-case with a decreasing trend for higher numbers of redshift bins.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=9cm]{graphics/h-hist}
\end{center}
\caption{Comparing the FOM for various values of $\mathcal N$ in the $H$-case.}
\label{fig:4-h-hist}
\end{figure}
\begin{figure}[htb]
\begin{center}
\includegraphics{graphics/nbins15}
\end{center}
\caption{The galaxy distribution function in 15 redshift bins, which are
overlapping heavily.}
\label{fig:4-nbins15}
\end{figure}
Doing the same in the $G$-case yields a slightly different result,
shown in fig. \ref{fig:4-hg-hist}. Here the FOM for $H$ peaks at $\mathcal N=6$
while the FOM for $G$ peaks at $\mathcal N=3$.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/h-g-hist}
\end{center}
\caption{In the $G$-case, the FOM in dependence of $\mathcal N$ takes a
slightly different shape. Blue represents $\mathop{\mathrm{FOM}}(H)$, green is $\mathop{\mathrm{FOM}}(G)$
and yellow is the sum of both.}
\label{fig:4-hg-hist}
\end{figure}
When examining the galaxy distribution function for each bin (see
fig.~\ref{fig:4-nbins15}) in the case of 15 redshift bins, we can see
that with our assumed photometric redshift error they are ``smeared out''
to the point where it becomes impossible to confidently assign a redshift
bin to a given galaxy.
\subsection{\texorpdfstring{On $\ell_\mathrm{max}$ and $\Delta{\lg
\ell}$}{On ell max and delta lg ell}}
\label{sec:lgell}
It is not obvious how far the sum in eq. (\ref{eq:3-fm}) should go or what
the step size for $\ell$ should be. Estimating a realistic value for the
upper limit $\ell_\mathrm{max}$ has been done in eq.~(\ref{eq:3-ellmax}), but it is
interesting to see how the FOM behaves for larger values.
We therefore try several values for $\ell_\mathrm{max}$ and see whether the FOM
approaches some constant or not. The result can be seen in
fig.~\ref{fig:4-lellmax}.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/lellmax}
\end{center}
\caption{When increasing $\ell_\mathrm{max}$, the upper limit of the sum in
eq.~(\ref{eq:3-fm}), the FOM changes, but increases by less than 15\% beyond
$\ell_\mathrm{max}=10^4$. Shown here is the $H$-case, the $G$-case looks
similar.}
\label{fig:4-lellmax}
\end{figure}
We observe that the FOM only changes slightly for values above 4, as we
would expect due to the finite angular galaxy density.
Doing the same for some values for $\Delta{\lg \ell}$ at a fixed
$\ell_\mathrm{max}=10^4$ yields the numbers
used in fig. \ref{fig:4-lellstep}. We see that essentially all the
information is being extracted at a logarithmic multipole step size of
$0.2$. This figure roughly matches the result of $0.3$ found in
\cite{Bernstein2009}, where it is argued that the broad window function
``smoothes away fine structure'' in the convergence power spectrum, such
that at some point further increasing of the number of multipole bins will
no longer have beneficial effects. On the other hand, it is
interesting to note that the FOM increases almost by an order of magnitude
by going from $\Delta\lg\ell=0.8$ to $0.4$.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/lstep}
\end{center}
\caption{The figure of merit for various values of $\Delta{\lg \ell}$ in the
$H$-case. Going beyond $0.2$ does not change much. The situation is the
same in the $G$-case and thus not shown here.}
\label{fig:4-lellstep}
\end{figure}
\afterpage{\clearpage}
\section{Fixing various parameters}
In order to determine the parameter which the Fisher matrix is most
sensitive, we will fix one additional parameter after another and analyze
the behavior of the FOM. Remember, fixing a parameter within the Fisher
matrix formalism is as easy as crossing out the according row and column of
the Fisher matrix. As we can see in fig.~\ref{fig:fixing}, knowing the
scalar spectral index $n_s$ in the $H$-case as well as possible pays off
the most, as the FOM increases roughly by a factor of three if we know it
exactly.
On the other hand, in the $G$-case, depicted in fig.~\ref{fig:fixing-g}, it
is most beneficial to know $\Omega_m$ (factor of six) to get the highest
increase in $\mathop{\mathrm{FOM}}(H)$, but knowing $\sigma_8$ exactly gives another factor
of two for $\mathop{\mathrm{FOM}}(G)$.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/fixing}
\end{center}
\caption{Various parameters are being fixed successively ($H$-case). Each
bar is labeled with the parameter that has been fixed on top of the previous
one, such that all of them are fixed on the right side of the diagram.
Fixing the scalar spectral index is most beneficial, as the FOM triples in
the best case.}
\label{fig:fixing}
\end{figure}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/fixing-g1}
\includegraphics[width=9cm]{graphics/fixing-g2}
\end{center}
\caption{Various parameters are, again, being fixed successively ($G$-case).
Here, knowledge about $\Omega_m$ and $\sigma_8$ pays off most for $\mathop{\mathrm{FOM}}(H)$
(\textit{top}) and $\mathop{\mathrm{FOM}}(G)$ (\textit{bottom}) respectively.}
\label{fig:fixing-g}
\end{figure}
\section{Uncertainties}
Finally, we can present the uncertainties on the values of $H$ and $G$ at
different redshifts. We use the parameters
$\mathcal N=5$, $\ell_\mathrm{max}=10^4$ and $\Delta{\lg\ell}=0.2$ and find
the results shown in tables~\ref{tab:4-results} and~\ref{tab:4-resultsH}.
These are derived from the full Fisher matrix as seen in tab.~\ref{tab:fm}
(for the $G$-case). As
expected, the constraints in the $G$-case are not as tight as those in the
$H$-case, since we allow the growth function to vary in a more general way.
\begin{table}[htb]
\centering
\begin{tabular}{lccccc}
\hline\hline
&$\sigma(\omega_m)$ & $\sigma(\omega_b)$ & $\sigma(n_s)$ &
$\sigma(\Omega_m)$ & $\sigma(\sigma_8)$\\
\hline
$H$-case & 0.17 & 0.065& 0.049 & 0.012 & 0.011\\
$G$-case & 0.17 & 0.066 & 0.059 & 0.021 & 0.041\\
\hline
\vspace{.5cm}
\end{tabular}
\begin{tabular}{lccccc}
\hline\hline
$i$ & 1 & 2 & 3 & 4 & 5\\ \hline
$\sigma(\hat h_i)$ & 0.038 & 0.015 & 0.033 & 0.026 & 0.053\\
$\sigma(h_i)$ & 0.044 & 0.036 &0.044 &0.049 &0.48\\
$\sigma(g_i)$ & 0.039 & 0.023 & 0.068 & 0.094 & 0.88\\
\hline
\end{tabular}
\caption{Errors on the cosmological parameters as well as $\hat h_i, h_i,
g_i$ while fixing $\tau, w_0, w_1, \Sigma_0, \gamma$ and keeping $\mathcal N=5$,
$\ell_\mathrm{max}=10^4$, $\Delta{\lg\ell}=0.2$.} \label{tab:4-results}
\end{table}
\begin{table}
\centering
\begin{tabular}{ccccccccc}
\hline\hline
$\sigma(\omega_m)$ & $\sigma(\omega_b)$ & $\sigma(n_s)$ &
$\sigma(\Omega_m)$ & $\sigma(w_0)$ & $\sigma(w_1)$ & $\sigma(\gamma)$ &
$\sigma(\Sigma_0)$ &
$\sigma(\sigma_8)$\\ \hline
0.23 & 0.081 & 0.077 & 0.045 & 3.0 & 9.3 & 0.67 & 0.40 & 0.11\\
\hline
\end{tabular}
\caption{Errors on the cosmological parameters while fixing $\tau$,
marginalizing everything else, and keeping $\mathcal N=5$,
$\ell_\mathrm{max}=10^4$, $\Delta{\lg\ell}=0.2$ in the $H$-case.}
\label{tab:4-resultsH}
\end{table}
\begin{table}[p!]
\small
\begin{flushleft}
\begin{tabular}{rrrrrrr}
\hline
$\Omega_mh^2$ & $\Omega_bh^2$ & $n_s$ & $\Omega_m$ & $\sigma_8$ & $h_1$ &\\
\hline\hline
5.89991\text{e}6 & -1.29794\text{e}7 &
3.04031\text{e}6 & 1.77766\text{e}7 &
8.47979\text{e}6 & -3.10712\text{e}6 & \\
-1.29794\text{e}7 & 2.85559\text{e}7 &
-6.68462\text{e}6 & -3.91594\text{e}7 &
-1.86837\text{e}7 & 6.8399\text{e}6 & \\
3.04031\text{e}6 & -6.68462\text{e}6 &
1.57342\text{e}6 & 9.0384\text{e}6 &
4.30423\text{e}6 & -1.59096\text{e}6 & \\
1.77766\text{e}7 & -3.91594\text{e}7 &
9.0384\text{e}6 & 6.56348\text{e}7 &
3.13299\text{e}7 & -1.06167\text{e}7 & \\
8.47979\text{e}6 & -1.86837\text{e}7 &
4.30423\text{e}6 & 3.13299\text{e}7 &
1.50269\text{e}7 & -5.05321\text{e}6 & \\
-3.10712\text{e}6 & 6.8399\text{e}6 &
-1.59096\text{e}6 & -1.06167\text{e}7 &
-5.05321\text{e}6 & 1.99529\text{e}6 & \ldots \\
-1.94576\text{e}6 & 4.28365\text{e}6 &
-9.92991\text{e}5 & -7.29185\text{e}6 &
-3.45161\text{e}6 & 9.6474\text{e}5 & \\
-1.16652\text{e}5 & 2.56784\text{e}5 &
-5.94073\text{e}4 & -4.72584\text{e}5 &
-2.22597\text{e}5 & 4.63944\text{e}4 & \\
4.1346\text{e}6 & -9.11132\text{e}6 &
2.09669\text{e}6 & 1.51661\text{e}7 &
7.2877\text{e}6 & -2.56814\text{e}6 & \\
1.91022\text{e}6 & -4.20561\text{e}6 &
9.75038\text{e}5 & 6.89405\text{e}6 &
3.2877\text{e}6 & -9.21068\text{e}5 & \\
4.52229\text{e}4 & -9.9446\text{e}4 &
2.3215\text{e}4 & 1.77003\text{e}5 &
8.31533\text{e}4 & -1.48989\text{e}4& \\
\hline
\end{tabular}
\end{flushleft}\vfill
\begin{flushright}
\begin{tabular}{rrrrrr}
\hline
&$h_2$ & $h_3$ & $g_1$ & $g_2$ & $g_3$\\
\hline\hline
& -1.94576\text{e}6 & -1.16652\text{e}5 &
4.1346\text{e}6 & 1.91022\text{e}6 &
4.52229\text{e}4 \\
& 4.28365\text{e}6 & 2.56784\text{e}5 &
-9.11132\text{e}6 & -4.20561\text{e}6 &
-9.9446\text{e}4 \\
& -9.92991\text{e}5 & -5.94073\text{e}4 &
2.09669\text{e}6 & 9.75038\text{e}5 &
2.3215\text{e}4 \\
& -7.29185\text{e}6 & -4.72584\text{e}5 &
1.51661\text{e}7 & 6.89405\text{e}6 &
1.77003\text{e}5 \\
& -3.45161\text{e}6 & -2.22597\text{e}5 &
7.2877\text{e}6 & 3.2877\text{e}6 &
8.31533\text{e}4 \\
\ldots & 9.6474\text{e}5 & 4.63944\text{e}4 &
-2.56814\text{e}6 & -9.21068\text{e}5 &
-1.48989\text{e}4 \\
& 1.03799\text{e}6 & 7.90972\text{e}4 &
-1.55933\text{e}6 & -9.6674\text{e}5 &
-3.22527\text{e}4 \\
& 7.90972\text{e}4 & 7.59839\text{e}3 &
-9.07882\text{e}4 & -7.37654\text{e}4 &
-3.24212\text{e}3 \\
& -1.55933\text{e}6 & -9.07882\text{e}4 &
3.61394\text{e}6 & 1.48555\text{e}6 &
3.17958\text{e}4 \\
& -9.6674\text{e}5 & -7.37654\text{e}4 &
1.48555\text{e}6 & 9.18941\text{e}5 &
3.03478\text{e}4 \\
& -3.22527\text{e}4 & -3.24212\text{e}3 &
3.17958\text{e}4 & 3.03478\text{e}4 &
1.4814\text{e}3\\
\hline
\end{tabular}
\end{flushright}
\caption{The full Fisher matrix in the $G$-case for three redshift bins.}
\label{tab:fm}
\end{table}
\section{Including priors} \label{sec:priors}
As mentioned in section~\ref{calcrules}, the magic of Fisher lets us easily
include priors from other experiments. All we need to do is line up the
right rows and columns of two different Fisher matrices and take their sum,
i.e.
\begin{equation}
F_{ij}' = F_{ij} + F_{ij}^\mathrm{prior}.
\label{eq:4-prior}
\end{equation}
We can do this for two measurements of the cosmic microwave background
radiation. The first one is an already completed experiment, namely WMAP,
and the second one a planned mission, {\sc Planck}, both of which use the
same fiducial model as in this thesis.
\subsection{WMAP}
A Gaussian prior, that is a fiducial value $p_i$ with Gaussian error
$\sigma(p_i)$, is represented simply by a Fisher matrix that has
$\sigma(p_i)^{-2}$ as its $i$-th diagonal entry \citep{Albrecht2006}.
Gaussian priors can be obtained from recent observations. We use the data
from the WMAP survey, one of the most precise measurements of cosmological
parameters as of now. The standard deviations can be taken from
table~\ref{tab:wmap7} and---while taking into consideration the order we are
using---the corresponding Fisher matrix thus becomes
\begin{align}
\mat F^\mathrm{WMAP7} = \mathrm{diag}\,&[77160.5, 3.42936\text{e6}, 5102.04,
\nonumber\\
&6944.44, 9291.96, 0, 0, 0, 0, 1736.11, 0, \dots, 0 ]\,.
\end{align}
\subsection{ \texorpdfstring{\sc Planck} {Planck}}
The Fisher matrix $\hat{\mat F}^\mathrm{Planck}$ for the planned {\sc
Planck} mission is shown in table~\ref{tab:fm-planck}.
\begin{table*}[htb]\scriptsize
\begin{flushleft}
\begin{tabular}{lrrrc}
\hline
\hline
& $w_0$ & $w_a$ & $\Omega_\mathrm{DE}$ \\
\hline
$w_0$ & .172276e+06 & .490320e+05 & .674392e+06 &\\
$w_a$ & .490320e+05 & .139551e+05 & .191940e+06&\\
$\Omega_\mathrm{DE}$ & .674392e+06 & .191940e+06 & .263997e+07&\\
$\Omega_k$ & $-$.208974e+07 & $-$.594767e+06 & $-$.818048e+07 & \dots \\
$\omega_m$ & .325219e+07 & .925615e+06 & .127310e+08 &\\
$\omega_b$ & $-$.790504e+07 &$-$.224987e+07&$-$.309450e+08& \\
$n_S$ & $-$.549427e+05 & $-$.156374e+05 & $-$.215078e+06 & \\
\hline
\end{tabular}
\end{flushleft}
\begin{flushright}
\begin{tabular}{crrrr}
\hline
\hline
& $\Omega_k$ & $\omega_m$ & $\omega_b$ & $n_S$ \\
\hline
& $-$.208974e+07 &.325219e+07 & $-$.790504e+07 & $-$.549427e+05 \\
& $-$.594767e+06 &.925615e+06 &$-$.224987e+07 &$-$.156374e+05\\
&$-$.818048e+07 & .127310e+08 &-.309450e+08 &$-$.215078e+06\\
\dots& .253489e+08& $-$.394501e+08 & .958892e+08 & .666335e+06\\
& $-$.394501e+08 &.633564e+08 & $-$.147973e+09 & $-$.501247e+06\\
& .958892e+08 &$-$.147973e+09 &.405079e+09 & .219009e+07\\
& .666335e+06 &$-$.501247e+06 & .219009e+07 & .242767e+06\\
\hline
\end{tabular}
\caption{Fisher matrix $\hat{\mat F}^\mathrm{Planck}$ for ($w_0$, $w_a$,
$\Omega_\mathrm{DE}$, $\Omega_k$, $\omega_m$, $\omega_b$, $n_s$) derived from the
covariance matrix for $(R, l_a, \Omega_b h^2, n_s)$ from {\sc Planck}
\citep{Mukherjee2008}.}
\label{tab:fm-planck}
\end{flushright}
\end{table*}
This matrix needs to be transformed for compatibility with our Fisher
matrix. The parameter transformation is given by
\begin{equation}
\vec \theta'(\vec \theta) =
(\theta_5,\theta_6,\text{const.},\theta_7,1-\theta_3,\theta_1,\theta_2,
\text{const.},\dots,\text{const})\,,
\end{equation}
where $\vec \theta'=(\omega_m,\omega_b,\tau,n_s,\Omega_m, w_0,
w_1,\gamma,\Sigma_0,\sigma_8,h_1,\dots,g_1,\dots)$ is the vector
in parameter space in our formalism, and $\vec
\theta=(w_0,w_a,\Omega_\mathrm{DE},\Omega_k,\omega_m,\omega_b,n_s)$ is the
vector in parameter space in the formalism of \citet{Mukherjee2008}. The
Jacobian matrix thus reads
\begin{equation}
J_{ij}= \left(\frac{\partial \theta'_i}{\partial \theta_j}\right)^T =
\underbrace{\left(
\begin{array}{cccccccccc}
0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & \dots & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & \dots & 0 \\
0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & \dots & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \dots & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \dots & 0 \\
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & \dots & 0 \\
0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & \dots & 0 \\
\end{array}
\right)}_{10+\mathcal N(+\mathcal N)\textrm{ columns}}\,.
\end{equation}
The zeros on the right hand side account for the $\hat h_i$s (or $h_i$s and
$g_i$s), which the original {\sc Planck} Fisher matrix naturally does not
contain. The Fisher matrix with the {\sc Planck} prior for our use is then
\begin{equation}
\mat F^\mathrm{Planck} = \mat J^T \hat{\mat F}^\mathrm{Planck} \mat J.
\end{equation}
\subsection{Summary}
We can now examine how including priors from WMAP, {\sc Planck}, or both
will affect the constraints on $H(z)$ or $G(z)$. For this, we will choose
$\mathcal N=5$ while marginalizing over all other parameters, although $G(z)$ is
fixed when calculating the $\mathop{\mathrm{FOM}}(H)$. The results are summarized in
table~\ref{tab:priors}.
\begin{table}[htb]
\centering
\begin{tabular}{ccccc}
\hline\hline
& WL & WL+WMAP7 & WL+{\sc Planck} & WL+{\sc Planck}+WMAP7 \\
\hline
$\mathop{\mathrm{FOM}}(H)$ & 7636 & 13778 & 25194 & 26096\\
$\mathop{\mathrm{FOM}}(G)$ & 2865 & 5697 & 4350 & 6805\\
\hline
\end{tabular}
\caption{Comparison of the FOM when including different priors for the
$H$-case and the $G$-case, respectively.}
\label{tab:priors}
\end{table}
Naturally, the FOM improves in both cases as we include additional priors.
Unexpectedly, the growth function is more constrained by assuming WMAP
priors compared to {\sc Planck} priors. With {\sc Planck} being one
generation ahead of WMAP, it should be the other way around. But if we take
fig.~\ref{fig:fixing-g} into consideration, it is clear that while fixing
$\Omega_m$ is most important for constraining $G$, fixing $\sigma_8$ also
almost doubles the FOM. Unlike the WMAP prior, the {\sc Planck} prior does
not constrain $\sigma_8$ at all, thus even though {\sc Planck} constrains
$\Omega_m$ much more than WMAP in this parameter configuration, it is not as
important with regard to constraining the growth function. Another
observation we can make is that in either case the FOM does not increase
significantly compared to the next higher value when including the second
prior, i.e. the FOM in the $H$-case, when including WMAP and {\sc Planck},
is almost the same as only including {\sc Planck}. In the $G$-case, the FOM
is almost the same when including both priors as compared to only including
WMAP. This is to be expected, as both experiments probe the cosmic microwave
background radiation, except with different sensitivities. Therefore, no
more cosmological information can be extracted.
\section{Comparison to current constraints}
When we try to compare how weak lensing in this context will constrain the
growth function compared to current constrains, we notice that our
constraints are very poor at high redshifts. \cite{Rapetti2010} measured the
growth index via a combination of X-ray cluster growth data with cluster gas
mass fraction, type 1a supernovae, baryon acoustic oscillations and cosmic
microwave background data, where they found that $\gamma =
0.55^{+0.13}_{-0.10}$. As shown in fig.~\ref{fig:current}, these constraints
are not very tight when applied to the growth function (even when assuming
that $\Omega_m$ is known exactly), but the error bars from the Fisher matrix
analysis hardly seem any better, especially at high redshifts. It is
interesting, though, to have a model independent confirmation of our
observations that is comparable with current constraints.
\begin{figure}[htb]
\begin{center}
\includegraphics{graphics/growth-observ}
\end{center}
\caption{Current constraints on the growth function via the growth index by
using X-ray cluster growth data. Shown is the $1\sigma$ confidence band of
the growth funcion.}
\label{fig:current}
\end{figure}
\section{Possibility of ruling out modified gravity models}
According to the data displayed in fig.~\ref{fig:4-hg-hist}, we get the best
results for the growth function when using three redshift bins, which is why
we shall adopt this number for this and the next section.
Fig.~\ref{fig:growth-best} shows the error bars on $G(z)$ in this case,
along with the growth function as predicted by the Starobinsky model with
$\gamma_\mathrm{Sta}=0.42$ \citep{Fu2010,Starobinsky2007} and the DGP model
with $\gamma_\mathrm{DGP}$ by Dvali, Gabadadze and Porrati
\citep{Gong2008,Dvali2000}. We also see the same diagram with priors from
WMAP and {\sc Planck} included. From the visual, we recognize a slight
disagreement at low redshifts while the error bars at high redshifts are
too large to make any statements about the competing models.
One caveat: The Starobinsky model actually predicts a redshift dependent
growth index. Trying to fit a power law to the growth rate in this case,
i.e. $f=\Omega_m(z)^\gamma_\mathrm{Sta}$ with a constant $\gamma_{Sta}$,
yields a deviation of up to 10\% at intermediate redshifts, which indicates
that the result cited above is biased. A linear expression for the growth
index, $\gamma_\mathrm{Sta}=\gamma_0 + \gamma_1 z$, is more accurate but
fails at high redshifts with $z>0.5$. However, the result, $\gamma_1\approx
-0.24$ indicates a decreasing growth index \citep{Fu2010}. Thus, in the
case of the Starobinsky model the power law does not seem to be a good fit
and the following discussion should be taken with a grain of salt.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/growth-compare}
\includegraphics[width=9cm]{graphics/growth-prior-compare}
\end{center}
\caption{The growth function with error bars for the binning with the
highest FOM. Also shown (from the top): The growth function from
eq.~(\ref{eq:3-growth}) for the DGP model $\gamma_\mathrm{DGP}=11/16\approx
0.69$, the standard model $\gamma=6/11\approx0.55$ and the Starobinsky model
with $\gamma_\mathrm{Sta}=0.42$. \textit{Top panel:} Weak lensing only.
\textit{Bottom panel:} Including priors from WMAP and {\sc Planck}.}
\label{fig:growth-best}
\end{figure}
We now want to attempt to quantify the deviation from these two models.
Assuming the errors on the growth function are Gaussian, we can compute the
likelihood function for the growth index $\gamma$ as
\begin{equation}
\mathcal L(\gamma) = \exp\left( -\frac{1}{2} \sum_{i=1}^{3}
\frac{(G(z_i;\gamma)-g_i)^2}{\sigma(g_i)^2} \right)
\end{equation}
using the error estimates from the Fisher matrix and keeping $\Omega_m$
fixed. The likelihood is plotted in fig.~\ref{fig:likelihood}. Obviously,
the maximum of the likelihood is found at the fiducial value $\gamma=0.55$.
In this case, the likelihood can be approximated by a Gaussian with good
agreement, and we find a standard deviation of $\sigma_0(\gamma)=0.056$ with
weak lensing only and $\sigma_1(\gamma)=0.037$ while including priors from
WMAP and {\sc Planck}. Considering that both the DGP model as well as the
Starobinsky model deviate from the fiducial value by at least
$\Delta\gamma=0.13$, they could both be ruled out at the $2\sigma$
confidence level with weak lensing only and at the $3\sigma$ confidence
level with priors. This does not seem to be entirely conclusive, especially
when we consider the uncertainty in the $\gamma_\mathrm{Sta}$ that we
mentioned earlier. However, we need to keep in mind that these constraints
are model independent.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=9cm]{graphics/likeli}
\includegraphics[width=9cm]{graphics/likeli-prior}
\end{center}
\caption{The likelihood for the growth index with a fitted Gaussian (dashed
line). Indicated are the predicted values for the Starobinsky, DGP and
standard model. \textit{Top panel:} Weak lensing only. The Gaussian has a
standard deviation of $\sigma = 0.056$. \textit{Bottom
panel:} Including priors from WMAP and {\sc Planck}. Here, the standard
deviation is $\sigma = 0.037$.}
\label{fig:likelihood}
\end{figure}
\afterpage{\clearpage}
\section{Problems and outlook}
It is not surprising that the Fisher matrix formalism can only provide a
lower bound on the expected error bars. This bound is called the
Cram\'er-Rao bound, which expresses the fact that the maximum likelihood
estimate constrains the model parameters at best with the value given by the
Fisher matrix \citep{Shao2003}.
We should also keep in mind that when the errors become too large, the
approximation of the likelihood by a Gaussian may lose its validity.
Besides that, we did not take into account several systematic errors that
might present itself while observing the weak lensing signal, like the
aforementioned intrinsic alignment. Other potential error sources include:
shear calibration errors, intrinsic galaxy alignment, and non-Gaussian
statistics, some of which are discussed in \citet{Bernstein2009} and
\citet{Albrecht2009}.
Regarding the source code of the notebook, while it does satisfy all the
requirements for calculating the Fisher matrix, there certainly is still
substantial room for improvement. One desirable feature would be the
abstraction of cosmological parameters, such that they would not have to be
hard coded into the arguments of any function, making it easier to add or
remove parameters later on. In appendix~\ref{coupledquint}, large parts of
the code were reused, but almost all arguments had to be adjusted manually,
a cumbersome and error prone job. Another issue, that the runtime on a
typical machine is of order several hours to a few days with parallelizing
part of the code, which could perhaps be reduced significantly by examining
the step size of interpolated functions more carefully. Many of them (and
especially the window functions, a very central part of the computation)
only have a single extremum and tend to approach zero after that. Limiting
the evaluation of sampling points specifically to regions where the function
takes non-negligible values might speed up the computation drastically.
From a more structural point of view, a more modular setup by using {\sc Mathematica\ }
packages would be desirable to avoid duplicate code fragments, which would
make the program more expandable, robust, and easier to use.
\chapter{Implications for cosmology}
\section{Theoretical interpretation}
\section{On the possibility of ruling out dark energy models}
\chapter{Conclusion}
We presented and developed the formal basis of the theory of dark energy,
weak lensing, and statistics in cosmology (in particular the Fisher matrix
formalism), on which the remainder of this thesis built. Furthermore, we
described the specifics of the methods of weak lensing tomography using
fitting formulas for the matter power spectrum with non-linear corrections
and how it is used to compute the observable, the convergence power
spectrum. It was demonstrated how we avoided assuming an underlying model
for the Hubble parameter and growth function by using linear interpolation
based on a choice of redshift bins. We showed how the convergence power
spectrum is related to the matter power spectrum and how the matter power
spectrum can be separated into the growth function and the transfer
function. We gave the fitting formula for the transfer function and how the
non-linear corrections are applied. Finally, we outlined how to implement
the computation in {\sc Mathematica\ } and what kind of challenges might arise in doing
so.
Then we analyzed the behavior of the Fisher matrix when varying different
parameters and why it makes sense to use their particular values. We showed
how to include priors from other experiments and how it improves the FOM, a
quantity that we defined as a quality measure. We found that a small number
number of redshift bins is sufficient to extract most of the cosmological
information from the weak lensing signal -- five for best constraints of
$H(z)$ and three for $G(z)$. It turned out that the error bars on the growth
function are most sensitive to the fractional matter density $\Omega_m$ and
power spectrum amplitude $\sigma_8$. The results indicated that the
constraints that we can expect are comparable to current constraints from
several probes combined.
According to a likelihood analysis, we conclude that future weak lensing
surveys, using this kind of technique on $H(z)$ and $G(z)$, might be able to
rule out the Starobinsky and DGP model for modified gravity only at a
$2\sigma$ level when used by itself. Together with priors from surveys of
the cosmic microwave background like {\sc Planck}, this might improve to a
$3\sigma$ level instead.
It may not have the kind of certainty that meets the ambitious standards of
physics, but this the price we pay for parameterizing cosmological
quantities this way. As a model independent approach it represents an
important check that is not biased towards a model, supplementary to other
measurements.
Regardless, the next decade promises to be an exciting
one for cosmology and dark energy research as new probes and unprecedented
high precision data will become available from {\sc Euclid} and similar
surveys. Perhaps it is weak lensing what will unravel the mystery that is
dark energy by providing the necessary insights into the evolution of the
growth of structure\dots we can only imagine what the consequences
for physics will be.
\chapter{Weak lensing Fisher matrix for coupled
quintessence}\label{coupledquint}
With quintessence being one of the most popular candidates for dark energy
\citep{Copeland2008}, it is interesting to study the coupling between a
scalar field and matter. A simple case would manifest in the conservation
equations with a coupling constant $C$ such that
\begin{align}
T^{\mu\nu}_{(m);\mu} &= -C T_{(m)} \phi^{;\nu}\\
T^{\mu\nu}_{(\phi);\mu}& = C T_{(\phi)}\phi^{;\nu}\,,
\end{align}
where $T_{(m)}^{\mu\nu}$ and $T_{(\phi)}^{\mu\nu}$ describe the
energy-momentum tensor of matter and the scalar field
respectively (see \cite{Amendola1999,DiPorto2008}). It is convenient to
define a dimensionless coupling constant $\beta$ proportional to $C$, i.e.
\begin{equation}
\beta \equiv \frac{C}{\sqrt{8\pi G}}\,.
\end{equation}
The evolution of the density contrast $\delta(a)$ must then satisfy
\begin{equation}
\delta''(\alpha) + \left( \frac{1}{2} - \frac{\Omega_m'}{2\Omega_m}
\right)\delta'(\alpha) - \frac{3}{2}\Omega_m(1+2\beta^2) \delta(\alpha)=0\,,
\end{equation}
where $\alpha \equiv \ln a$ and $'=\,\mathrm d/\,\mathrm d \ln a$. In an attempt to
approximate the solution $\delta(a)$ and considering that $G(z)=\delta(z)$,
one can try to generalize
the solution of the original equation (with $\beta=0$) phenomenologically as
\begin{equation}
G(z) = \exp\left( -\int_0^z
\Omega_m(z')^\gamma(1+c\beta^2)\frac{\,\mathrm d z'}{1+z} \right)\,.
\end{equation}
\citet{DiPorto2008} found that a well working least square fit to the exact
solution, derived numerically, yields the values
\begin{equation}
\gamma = 0.56\,,\qquad c=2.1\,.
\end{equation}
Provided that we are given the transfer function for this scenario to plug
into eq.~(\ref{eq:3-mps1}), we can skip the fitting procedure for the matter
power spectrum in
section~\ref{subsec:fitting} and proceed directly with the non-linear
corrections and the convergence power spectrum.
Now we can run the code with a slightly modified growth function and a
fiducial model with the parameters
\begin{equation}
(\beta, \sigma, \Omega_c, h,\Omega_b,n_s)=(0.01, 0.2, 0.226, 0.703, 0.0451,
0.966)\,,
\end{equation}
where $\sigma$ is the exponent in the potential for the scalar field, which
we take here to be
\begin{equation}
V(\phi) = V_0 \phi^{-\sigma}\,.
\end{equation}
\begin{table}\small
\centering
\begin{tabular}{cccccc}
\hline\hline
$\beta$&$ \sigma$&$ \Omega_c$&$ h$&$\Omega_b$&$n_s$\\
\hline
6.08293\text{e}5 & $-$1.28992\text{e}5 &
5.48499\text{e}6 & 3.73233\text{e}6 &
3.3104\text{e}6 & 5.02321\text{e}5 \\
$-$1.28992\text{e}5 & 2.80677\text{e}4 &
$-$1.2008\text{e}6 & $-$8.22476\text{e}5 &
$-$7.44588\text{e}5 & $-$1.044\text{e}5 \\
5.48499\text{e}6 & $-$1.2008\text{e}6 &
5.28593\text{e}7 & 3.61948\text{e}7 &
3.27805\text{e}7 & 4.54416\text{e}6 \\
3.73233\text{e}6 & $-$8.22476\text{e}5 &
3.61948\text{e}7 & 2.48333\text{e}7 &
2.26252\text{e}7 & 3.06263\text{e}6 \\
3.3104\text{e}6 & $-$7.44588\text{e}5 &
3.27805\text{e}7 & 2.26252\text{e}7 &
2.1013\text{e}7 & 2.62304\text{e}6 \\
5.02321\text{e}5 & $-$1.044\text{e}5 &
4.54416\text{e}6 & 3.06263\text{e}6 &
2.62304\text{e}6 & 4.55493\text{e}5\\
\hline
\end{tabular}
\caption{The weak lensing Fisher matrix for coupled quintessence with
$\mathcal N=5$, $\ell_\mathrm{max}=10^4$, $\Delta\lg\ell=0.2$. }
\label{tab:cqfm}
\end{table}
Using $\mathcal N=5$, $\ell_\mathrm{max}=10^4$, $\Delta\lg\ell=0.2$, we find
the resulting Fisher to be as in tab.~\ref{tab:cqfm}
We can now show the correlation of all possible parameter pairs by
marginalizing over
all other parameters such that the correlation matrix takes the form
\begin{equation}
\mat C = \left( \begin{array}{cc}
\sigma_1^2 & \rho\sigma_1\sigma_2\\
\rho\sigma_1\sigma_2 & \sigma_2^2
\end{array}\right)\,.
\end{equation}
Then we can plot ellipses whose semiaxes are proportional to the square
root of the eigenvalues of $\mat C$, i.e.
\begin{equation}
a_{1,2}^2 = \frac{1}{2} \left( \sigma_1^2+\sigma_2^2\mp
\sqrt{\sigma_1^4-2\sigma_1^2\sigma_2^2 + 4\rho^2\sigma_1^2\sigma_2^s +
\sigma_2^4} \right)
\end{equation}
with an angle with respect to the coordinate axes of
\begin{equation}
\tan 2\alpha = \frac{2\rho\sigma_1\sigma_2}{\sigma_1^2-\sigma_2^2}\,.
\end{equation}
The semiaxes need to be scaled by a factor of 1.51, 2.49, 3.44 so that the
area of the ellipsis corresponds to the $1\sigma$, $2\sigma$, $3\sigma$
probability content respectively (A\&T, ch. 13.3). The result can be seen in
fig.~\ref{fig:coup-ellipses1} and~\ref{fig:coup-ellipses2}
\citep{Amendola2011}. These plots enable us to judge how different surveys
can complement each other, e.g. we could overlay ellipses derived from CMB
(if we had it available)
data and see how much the confidence regions overlap. Ideally, we would want
to see thin, perpendicular ellipses.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\textwidth]{graphics/wl-ellipses-alt-thesis1}
\end{center}
\caption{Confidence ellipses for dark energy parameters in the coupled
quintessence model. Shown are the ellipses for the 68\%, 95\% and 99\%
confidence level.}
\label{fig:coup-ellipses1}
\end{figure}
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\textwidth]{graphics/wl-ellipses-alt-thesis2}
\end{center}
\caption{Confidence ellipses for dark energy parameters in the coupled
quintessence model (continued).}
\label{fig:coup-ellipses2}
\end{figure}
\chapter*{Acknowledgement}
This thesis represents the culmination of a six year long journey through a
wonderful world full of femtoseconds and Gigayears, strings and galaxies,
harmonic oscillators and harmonic oscillators, Germany and New
Mexico, coffee and beer, and many people who I had the pleasure of meeting
during this journey deserve to be mentioned here.
First of all, words cannot express strongly enough my gratitude towards the
love of my life and best friend Kathleen, who was always there for me and
made great sacrifices to do so.
I also wish to thank my parents for their unconditional support over
numerous years, without which studying physics would have been a lot more
difficult and I would not be anywhere near where I am now. Danke!
Of course I also appreciate that Professor Luca Amendola gave me the
opportunity of having an active part in one of the most exciting research
areas of our time, as well as the Institute for Theoretical Physics for
providing an excellent work environment in their beautiful villa. Thanks to
Professor Matthias Bartelmann for agreeing to be the second referee.
Many friends and roommates that I met in Würzburg, Heidelberg and
Albuquerque---too many to name here without taking the risk of forgetting
someone---that I spent endless hours with socializing deserve to be thanked
as well.
For writing this thesis I heavily relied on a number of outstanding free
software tools, for which I thank the many developers of GNU/Linux, \LaTeX,
Vim, subversion, Gimp, KDE and many more.
This research has made use of NASA's Astrophysics Data System.
\pagestyle{empty}
\cleardoublepage
\begingroup
\selectlanguage{\ngerman}
\thispagestyle{empty}
\chapter*{Erklärung}
Ich versichere, dass ich diese Arbeit selbstständig verfasst habe und keine
anderen als die angegebenen Quellen und Hilfsmittel benutzt habe.\\[2cm]
Heidelberg, den 8. Juni 2011 \hspace{3cm}\dotfill\\
\mbox{}\hfill\textit{(Adrian Vollmer)}\hspace{.8cm}
\endgroup
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,198 |
require 'spec_helper'
require 'virtus'
require 'guid'
require 'rubygems'
class Person
include Virtus
attribute :id, String, :default => Guid.new.to_s
attribute :first_name
attribute :last_name
def full_name
[first_name, last_name].join(' ')
end
def ==(person)
id == person.id
end
end
class PeopleTable < SimpleStore::Disk
def initialize
super(:people)
end
def put(person)
super(person.attributes)
end
def get(id)
Person.new(super(id))
end
end
describe 'using as super class for a table' do
it 'works' do
person = Person.new
person.first_name = 'Kris'
person.last_name = 'Leech'
table = PeopleTable.new
table.put person
table.get(person.id).should == person
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,788 |
Q: How do I specify that "bold" should be "Avenir Heavy" not "Avenir Black"? I need to send HTML-formatted email using the Avenir font (if it's present in the OS). Two of this font's weights are Heavy and Black (the latter being the heaviest weight). I want mail clients to use Avenir Heavy for bold text, but they're using Avenir Black instead.
In my HTML I have a <style type="text/css"> tag with:
body {
font-family: Avenir, Helvetica, Arial, sans-serif;
}
.font_h1 {
font-weight: bold;
}
When I open my HTML file in a desktop browser (Firefox, Chrome, or Safari), it uses Avenir Heavy as the bold font. But when I email it and view it in Mac Outlook 2016 or in iOS 10's Mail client, those display the bold font with Avenir Black, which is a much heavier font. Same thing happens if I specify the font-weight as bolder.
Oddly, if I say:
body {
font-family: Avenir Heavy;
}
then the page is still rendered by desktop browsers with Avenir Medium, with Avenir Heavy used for bold.
I don't think that @font-face is my answer, because I'm not loading a font from a URL.
How can I tell the browser or mail client to specifically use Avenir Heavy as the bold weight?
A: I declare Avenir like this:
@font-face {
font-family: 'Avenir';
font-weight: 300;
font-style: normal;
src: local('Avenir Book'), local('Avenir-300'),
url('../../assets/fonts/Avenir-Book/Avenir-Book.eot') format('embedded-opentype'),
url('../../assets/fonts/Avenir-Book/Avenir-Book.woff') format('woff'),
url('../../assets/fonts/Avenir-Book/Avenir-Book.ttf') format('truetype');
}
@font-face {
font-family: 'Avenir';
font-weight: 500;
font-style: normal;
src: local('Avenir Medium'), local('Avenir-500'),
url('../../assets/fonts/Avenir-Medium/Avenir-Medium.eot') format('embedded-opentype'),
url('../../assets/fonts/Avenir-Medium/Avenir-Medium.woff') format('woff'),
url('../../assets/fonts/Avenir-Medium/Avenir-Medium.ttf') format('truetype');
}
@font-face {
font-family: 'Avenir';
font-weight: 700;
font-style: normal;
src: local('Avenir Heavy'), local('Avenir-700'),
url('../../assets/fonts/Avenir-Heavy/Avenir-Heavy.eot') format('embedded-opentype'),
url('../../assets/fonts/Avenir-Heavy/Avenir-Heavy.woff') format('woff'),
url('../../assets/fonts/Avenir-Heavy/Avenir-Heavy.ttf') format('truetype');
}
@font-face {
font-family: 'Avenir';
font-weight: 900;
font-style: normal;
src: local('Avenir Black'), local('Avenir-900'),
url('../../assets/fonts/Avenir-Black/Avenir-Black.eot') format('embedded-opentype'),
url('../../assets/fonts/Avenir-Black/Avenir-Black.woff') format('woff'),
url('../../assets/fonts/Avenir-Black/Avenir-Black.ttf') format('truetype');
}
And then in CSS:
body {
font-family: Avenir, Helvetica, Arial, sans-serif;
}
h1 {
font-weight: 900; // black
}
h2 {
font-weight: 700; // heavy
}
h3 {
font-weight: 500; // medium
}
...
A: I think you need to explicitly open the font (using a font processing app, such as fontforge) and check which family it belongs to. Then use that family name and you'll be home safe. Also, if you want to be precise about your weights, use numbered values such as
*
*400 for normal
*700 for bold
*900 for black
*etc.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,208 |
import * as R from '../ramda/dist/index';
declare const string: string;
declare const number: number;
// @dts-jest:pass:snap
R.repeat(string);
// @dts-jest:pass:snap
R.repeat(string)(number);
// @dts-jest:pass:snap
R.repeat(string, number);
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,060 |
Kristina Böhlke (* 26. September 1972) ist eine deutsche Politikerin der SPD und war als politische Beamtin vom 24. März 2011 bis zum 14. März 2012 Staatsrätin der Behörde für Wissenschaft und Forschung in Hamburg.
Werdegang
Kristina Böhlke hat Biologie studiert und im Bereich Biotechnologie promoviert. Zusätzlich verfügt sie über einen Master in Management.
Von 2001 bis 2004 war Kristina Böhlke Referentin im Bundesministerium für Bildung und Forschung (BMBF) und dort anschließend bis 2005 Leiterin des Ministerbüros. Bis März 2011 war sie Leiterin des Projektträgers DESY.
In ihrer Zeit als ehrenamtliche Deputierte war sie von 1997 bis 2001 aktiv für die Behörde für Umwelt und Gesundheit und von 2008 bis 2011 für die Behörde für Wissenschaft und Forschung.
In der SPD Hamburg war sie von 2010 bis 2012 Beisitzerin des Landesvorstands.
Weblinks
http://www.hamburg.de/staatsraete/2830944/lebenslauf-boehlke.html
SPD Hamburg
http://www.hamburg.de/pressearchiv-fhh/3332964/2012-03-14-pr-staatsrat.html
Einzelnachweise
Staatsrat (Hamburg)
SPD-Mitglied
Politiker (21. Jahrhundert)
Deutscher
Geboren 1972
Frau
Person (DESY) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,261 |
\section{Introduction}
In the last years great attention has been drawn to the time dependent quantum harmonic oscillator. This problem has been thoroughly studied both from mechanical \cite{Yeon1994, Guasti2003} and electromagnetic \cite{Pedrosa2009, Choi2004} points of view, showing squeezing effects. The approach most used in the tackle of this sort of problems is the use of quantum mechanical invariant operators, in particular the Lewis-Ermakov invariant \cite{Lewis1967}.
In the field of guided propagation of light, the analogous problem is the study of longitudinally inhomogeneous (${\it LI}$) media. An invariant approach was extensively used in \cite{Krivoshlykov1992} and more recently in \cite{MoyaCessa2009} in the study of graded index media but, in both cases, they studied classical problems by means of a quantum-theoretical approach. Quantum propagation problems have been dealt with in homogeneous media, as shown in \cite{Luks2002} and references therein. These studies provided the background of the quantum theory of light propagation showing that the operator which describes correctly the quantum spatial propagation along an arbitrary direction $z$ is the Momentum operator $\hat{\mathcal{M}}$, since the Hamiltonian approach fails for problems like dispersive media, counterpropagation and ${\it LI}$ media as well \cite{Linares2008}. A first approximation to ${\it LI}$ media were carried out by Abram \cite{Abram1987} and Glauber and Lewenstein \cite{Glauber1991}, where single optical discontinuities between homogeneous media were analyzed. In these studies they showed the different physical behaviour the fields experience from the analogous mathematical problem of the time dependent quantum harmonic oscillator, proving that the field quadrature noise does not exhibit real squeezing, in agreement with experiments.
As far as we know, there is not any work dealing with quantum states of light propagating in ${\it LI}$ media in such a way that field quadratures do not exhibit real squeezing. So, our purpose is to give a phenomenological approach to this problem in waveguides. To this end, we will start obtaining the classical solutions which help us to find a reference frame which continuously performs a physical variable change in ${\it LI}$ media and eliminates the virtual squeezing, leading us to a proper propagation generator, a quantum Lewis-Ermakov type Momentum operator $\hat{\mathcal{M}}$. From this operator we will obtain Fock states in the optical-field strength (OFS) representation $\mathcal{E}$ and derive the propagator, proving the lack of squeezing in this representation and the arising of a quantum Gouy's phase. Furthermore, we will present the particular case of propagation of a gaussian quantum state in a cosine-type ${\it LI}$ medium, where will be shown that the net effect of this kind of media on quantum states is the generation of a quantum Guoy's phase dependent on features of both the media and the input quantum state.
\section{Classical analysis of propagation in longitudinally inhomogeneous media}
Our aim is to study the propagation of waveguided modes of quantum light in dispersion-free and non-magnetic media with separable inhomogeneous refractive index in an arbitrary direction of propagation $z$, given by \cite{Sodha1977}:
\begin{equation} \label{index}
n^{2}(x,y,z)= n_{0}^{2}\, f^{2}(x,y) + \Delta n^{2}\, h^{2}(z),
\end{equation}
where the longitudinal $h(z)$ and transversal $f(x,y)$ parts of the index are completely independent and $n_{0}$ and $\Delta n$ are constants. We focus on the separable index problem as it does not show coupling and therefore radiation modes (losses).
From Maxwell equations, it is easy to show that the electric field $\boldsymbol{E}(x,y,z,t)$ obeys the vectorial wave equation \cite{Marcuse1974}:
\begin{equation}\label{VWE}
\mathbf{\nabla}^{2} \boldsymbol{E}_{t}+\mathbf{\nabla}_{t}( \boldsymbol{E}\,\mathbf{\nabla} (\ln n^{2})\,)=\frac{n^{2}}{c^{2}} \frac{\partial^{2} \boldsymbol{E}_{t}}{\partial t^{2}},
\end{equation}
with $\boldsymbol{E}=(E_{x}, E_{y}, E_{z})\equiv(\boldsymbol{E}_{t}, E_{z})$. Let us consider monochromatic guided $1D$ vector modes with frequency $\omega_{\sigma}$ represented by vector field solutions with the following factorable complex amplitudes:
\begin{equation} \label{ModesE}
\boldsymbol{E}_{t}(x,y,z,t)= \sum_{\sigma} q_{\sigma c}(z)\boldsymbol{\xi}_{t\sigma}(x,y)\,e^{-i\omega_{\sigma} t}, \\
\end{equation}
where we have used $\sigma$ for simplicity standing for the modal numbers $\nu$, $\mu$ in each transverse direction, z-dependent complex coefficients $q_{\sigma c}(z)$ fulfilling $\sum_{\sigma}\vert q_{\sigma c}(z) \vert^{2}=1$, and electric normalized transverse complex amplitudes $\boldsymbol{\xi}_{t\sigma} (x,y)$ corresponding to quasi-TE (or quasi-TM) modes fulfilling a {\it quasi}-complete orthonormalization condition \cite{Linares2008}, which belong to the homogeneous part of the refractive index and satisfy:
\begin{equation}\label{TransWaveEq}
\begin{split}
\nabla_{t}^{2} \, \boldsymbol{\xi}_{t\sigma} +& k_{0}^{2} n_{0}^{2} f^2 (x,y) \,\boldsymbol{\xi}_{t\sigma} +\\&\nabla_{t}( \boldsymbol{\xi}_{t\sigma}\,\nabla_{t} (\ln n_{0}^{2} f^2 (x,y)) = \beta_{t \sigma}^{2}\,\boldsymbol{\xi}_{t\sigma},
\end{split}
\end{equation}
with $ \beta_{t}$ the transverse propagation constant. Solutions of this equation give us the invariant transverse modal structure of the field. Applying equations \textcolor{black}{(\ref{index})}, (\ref{ModesE}) and (\ref{TransWaveEq}) into (\ref{VWE}), we obtain:
\begin{equation}\label{WaveEq}
\frac{d^{2}q_{\sigma}}{dz^{2}}+\beta_{\sigma}^{2}(z)\,q_{\sigma}=0,
\end{equation}
\textcolor{black}{where ${q}_{\sigma}=({q}_{\sigma c}+{q}_{\sigma c}^{*})/2$ stands for the real electric field coefficients}, $\beta^{2}_{\sigma}(z) = \beta_{t \sigma}^{2} + k_{0}^{2} \Delta n^{2} h^{2}(z)$ is the local propagation constant of the $\sigma$-mode \textcolor{black}{and where we have used the approximation $E_{z}\ll E_{x}, E_{y}$. It is important to outline that $E_{z}=0$ in the case of TE modes, that is, equation (\ref{WaveEq}) is exact for such modes.} This propagation equation clearly suggests a local spatial harmonic oscillator and therefore it can be directly derived from spatial-type Hamilton equations where the Hamilonian is substituted by the Momentum, since it is the generator of spatial translations \textcolor{black}{\cite{Abram1987,Linares2012},} given by:
\begin{equation} \label{MomentoOH}
\mathcal{M}_{\sigma}= \frac{1}{2} [p_{\sigma}^{2} + \beta_{\sigma}^{2}(z)\,q_{\sigma}^{2}],
\end{equation}
with $p_{\sigma}=q_{\sigma}'$ and prime stands for $z$-derivative. This result is analogous to that obtained in \cite{Pedrosa2009} where time-dependent linear media was studied. The classical Momentum (\ref{MomentoOH}) is equivalent to the Hamiltonian of a time-dependent harmonic oscillator, with $\beta (z)$ playing the role of $\omega(t)$ \cite{Lewis1967}.
Likewise, the solution of equation (\ref{WaveEq}) is easily obtained via the use of the complex electric field ${q}_{\sigma c}$ in the following way:
\begin{equation} \label{qc}
{q}_{\sigma c}(z)=\rho_{\sigma} \,e^{i\theta_{\sigma}} {q}_{\sigma c}(0),
\end{equation}
where $\rho_{\sigma}$ and $\theta_{\sigma}$ are real functions obtained by solving:
\begin{gather} \label{EL}
\frac{d^{2}\rho_{\sigma}}{dz^{2}}+\beta_{\sigma}^{2}(z)\rho_{\sigma}=\frac{\beta_{0 \sigma}}{\rho_{\sigma}^{3}}, \\ \label{ELtheta}
\frac{d\theta_{\sigma}}{dz}=\frac{\beta_{0 \sigma}}{\rho_{\sigma}^{2}},
\end{gather}
with $\beta_{o \sigma} \equiv \beta_{\sigma} (0)$. Equation (\ref{EL}) is an Ermakov-Pinney equation with solutions given by \cite{Pinney1950}:
\begin{gather}\label{rhoz}
\rho_{\sigma}(z)=[(\beta_{o \sigma}\,u_{\sigma}(z))^{2} + v_{\sigma}^{2}(z)]^{1/2},\\ \label{rho0}
\rho_{\sigma}(0)=1, \quad \rho_{\sigma}'(0)=0,
\end{gather}
and where $u_{\sigma}$ and $v_{\sigma}$ are linearly independent functions that satisfy equation (\ref{WaveEq}) and have the following initial conditions and Wronskian:
\begin{gather} \label{cond1}
{u_{\sigma}}(0)={v_{\sigma}'}(0)=0, \\ \label{cond2}
{u_{\sigma}'}(0)={v_{\sigma}}(0)=1, \\ \label{Wronskian}
{{W_{\sigma}}}={u_{\sigma}'}\,{v_{\sigma}}-{v_{\sigma}'}{u_{\sigma}}=1.
\end{gather}
So, the classical wave amplitude changes continously during propagation by a factor $\rho_{\sigma}$, whereas the modal propagation constant is given by $\tilde{\beta_{\sigma}}\equiv\theta'_{\sigma}$ via equation (\ref{ELtheta}) where $\theta_{\sigma}$ represents the total phase accumulated in the propagation.
\section{Quantization in longitudinally inhomogeneous media}
The next step is to quantize the classical Momentum (\ref{MomentoOH}). But before carrying out this step, some considerations have to be taken into account. Direct quantization of the classsical fields $q_{\sigma}$ and $p_{\sigma}$ would lead to a quantized $z$-dependent Momentum analogous to the Hamiltonian for a time-dependent harmonic oscillator and, therefore, following the usual steps, we would have propagation equations leading to quadrature noise squeezing \cite{Yeon1994, Guasti2003, Pedrosa2009, Choi2004}. But in the sudy of propagation in $\it{LI}$ dielectric media, this approach does not provide consistent results. As was pointed out by Abram in his seminal paper about quantization of light in dielectric media \cite{Abram1987}, when quantum states propagating in a dielectric are represented in the basis of free-space photons, they seem to be squeezed, but inside a dielectric there is no experiment that can detect free-space photons. This happens because if we wish to detect photons inside the medium the fields would experiment an effective refractive index equivalent to the squeezing parameter and, therefore, a scale change is necessary. In the same spirit an interesting discussion about quantization in a dielectric was carried out by Glauber and Lewestein in \cite{Glauber1991}. In this study is stressed that the measurement of quantum states of light is based on photoabsorption processes carried out in the basis which diagonalizes the Hamiltonian in every medium. This is so because the photocount distribution is given by a normal ordered correlation product in the local basis, result of the physical property of the photoabsorption process that the energy of the field decreases when a photon is absorbed. But in any other basis this is not true, because of the mixing of absorption and emission operators, and therefore of frequencies, lacking the normal ordering in the correlation product. Thereby the state in these bases can not be measured and the photons are so-called virtual and, accordingly, the squeezing is virtual as well. This statement is closely related with Abram's idea and has to be applied to $\it{LI}$ media as it is the continuous limit of single discontinuities.
Hence, we look for some transformation which takes the classical Momentum (\ref{MomentoOH}) to be a constant of motion suitable to be quantized and simultaneously get rid of the virtual squeezing in a continuous way. Since carrying out the usual approach \cite{Yeon1994, Guasti2003, Pedrosa2009, Choi2004} squeezing proportional to the function $\rho(z)$ would appear, following the idea of a scale change in the discontinuity \cite{Abram1987, Glauber1991} we propose the following generalized canonical transformations from a generating function $G_{2}(q,\tilde{P})= \tilde{P}q/\rho$ and $z$ transformation \cite{Chetouani1989}:
\begin{equation}\label{GCT}
\tilde{Q}_{\sigma}=\frac{q_{\sigma}}{\rho_{\sigma}}, \quad \tilde{P}_{\sigma}= \rho_{\sigma} p_{\sigma}, \quad s_{\sigma}=(\int^{z}_{0} \rho_{\sigma}^{2}(\textsl{z})\, d\textsl{z})^{-1};
\end{equation}
and the next gauge transformations related to the new $s$-frame:
\begin{equation}\label{GCT2}
Q_{\sigma}=\tilde{Q}_{\sigma}, \qquad P_{\sigma}= \tilde{P}_{\sigma} - \frac{\dot{\rho}_{\sigma}}{\rho_{\sigma}} \tilde{Q}_{\sigma},
\end{equation}
with the dot standing for an $s$-derivative. Applying these relations into (\ref{MomentoOH}), we directly obtain the following Momentum:
\begin{equation} \label{MomentoGCT}
\mathcal{M}_{\sigma}(Q,P,s)= \frac{1}{2} [P_{\sigma}^{2}(s) + \beta_{0\sigma}^{2}\,Q_{\sigma}^{2}(s)],
\end{equation}
where we have used the auxiliar equation (\ref{EL}). It is remarkable that these new phase space and longitudinal coordinates ($Q, P, s$) are analogous to the comoving coordinates and the conformal (or arc-parameter) time used in cosmology and, likewise, the canonical momentum transformation (\ref{GCT2}) is related to the Hubble's law \cite{Misner1973}. After these transformations, the continuous change in the value of the harmonic potential appears as constant in the new comoving frame of reference \cite{Takagi1990}. So, in this frame, there are not scale changes differentially and the medium seems to be homogeneous. The generalized canonical transformations eliminate the squeezing at each plane $z$ and none signature of it is obtained. These insights lead us to consider the comoving frame as the physical one and therefore the proper one for quantization. Furthermore, interestingly, if we rewrite this Momentum in the original phase space, we obtain:
\begin{equation} \label{MomentoOHEL}
\mathcal{M}_{\sigma}(q,p,z)= \frac{1}{2} [(\rho_{\sigma}\, p_{\sigma} - q_{\sigma}\, \rho_{\sigma}')^{2}+\beta_{0\sigma}^{2}(q_{\sigma}/\rho_{\sigma})^{2}].
\end{equation}
This is the space-analog of an Ermakov-Lewis invariant \cite{Lewis1967}. So, it can be said that the Momentum (\ref{MomentoGCT}) is a spatial Ermakov-Lewis invariant in a comoving frame and that this invariant is the generator of spatial propagation in this kind of media.
Now, following the principle of quantization of quantum mechanics $(Q_{\sigma}, P_{\sigma})\rightarrow (\hat{Q}_{\sigma}, \hat{P}_{\sigma})$, where $[\hat{Q}_{\sigma},\hat{P}_{\sigma'}]=i\hbar\delta_{\sigma, \sigma'}$, we obtain the Momentum operator:
\begin{equation} \label{QMomento}
\hat{\mathcal{M}}_{\sigma}= \frac{1}{2} [\hat{P}_{\sigma}^{2}(s) + \beta_{0\sigma}^{2}\,\hat{Q}_{\sigma}^{2}(s)].
\end{equation}
In order to obtain the eigenvalues and eigenfunctions of this operator, we define the following annihilation and creation operators:
\begin{gather}\label{dest}
\hat{A}_{\sigma}(s)=\frac{1}{\sqrt{2\hbar\beta_{0\sigma}}}[\beta_{0\sigma}\hat{Q}_{\sigma}+i\hat{P}_{\sigma}], \\ \label{creat}
\hat{A}^{\dag}_{\sigma}(s)=\frac{1}{\sqrt{2\hbar\beta_{0\sigma}}}[\beta_{0\sigma}\hat{Q}_{\sigma}-i\hat{P}_{\sigma}].
\end{gather}
Therefore, equation (\ref{QMomento}) in terms of (\ref{creat}) can be rewritten as:
\begin{equation} \label{QMomento2}
\hat{\mathcal{M}}_{\sigma}= \hbar \beta_{0\sigma}[\hat{A}^{\dag}_{\sigma}\hat{A}_{\sigma}+1/2].
\end{equation}
The eigenstates of this Momentum are the same as those of the Number operator $\hat{N}_{\sigma}=\hat{A}^{\dag}_{\sigma}\hat{A}_{\sigma}$, which fulfills the next eigenvalue equation:
\begin{equation}
\hat{N}_{\sigma} \vert N_{\sigma} \rangle = N_{\sigma} \vert N_{\sigma} \rangle,
\end{equation}
where $N_{\sigma}$ and $\vert N_{\sigma} \rangle$ are eigenvalues and eigenstates for the Number operator, respectively. In terms of quantum-optical units \cite{Loudon1982}, we can redefine the quantum comoving scaled position $\hat{Q}_{\sigma}$ as the OFS operator $\hat{\mathcal{E}}_{\sigma}$, whose eigenstates are those measured in homodyne experiments \cite{Vogel1990, Schleich2001} and central to generalized quantum polarization \cite{Linares2011, Barral2013}, that is $\hat{\mathcal{E}}_{\sigma}=\sqrt{\beta_{0 \sigma }/2\hbar}\, \hat{Q}_{\sigma}$. The eigenstates $\vert N_{\sigma} \rangle$ in the optical field-strength $\mathcal{E}$ basis are given in terms of Hermite-Gauss functions as:
\begin{equation}
\Psi_{N}(\mathcal{E}_{\sigma},0)= \frac{2^{1/4}}{\sqrt{2^{N}\pi^{1/2}\,N!}}\,H_{N}(\sqrt{2}\mathcal{E}_{\sigma})\,e^{-\mathcal{E}^{2}_{\sigma}},
\end{equation}
and their quantum propagation is given by a spatial Schr\"odinger equation:
\begin{equation}\label{Schrodinger}
\hat{\mathcal{M}}_{\sigma} \,\Psi_{N} \equiv \hbar\beta_{0\sigma}\,[-\frac{1}{4}\frac{\partial^{2}}{\partial{\mathcal{E}_{\sigma}}^{2}}+\mathcal{E}^{2}_{\sigma}] \, \Psi_{N} = \hbar\beta_{0\sigma}\,\Psi_{N}.
\end{equation}
The solution of this equation yields the following propagated eigenstates $\vert N_{\sigma} \rangle$:
\begin{equation}\label{Number}
\Psi_{N}(\mathcal{E}_{\sigma}; s)=\frac{2^{1/4} \,e^{ i(N+1/2)\theta_{\sigma}}}{\sqrt{2^{N}\pi^{1/2}\,N!}}\,H_{N}(\sqrt{2}\mathcal{E}_{\sigma})\,e^{-\mathcal{E}^{2}_{\sigma} } ,
\end{equation}
with $\theta_{\sigma}=\beta_{0\sigma} s_{\sigma}$ the total accumulated phase, in the same way as a quantum state propagating in a homogeneous medium, but in this case in a comoving frame, which is the physical one for this kind of problems as shown above. Because of the similarity of this phase with the classical Gouy's phase \cite{Boyd}, we call it spatial quantum Gouy's phase.
\section{Propagation of quantum light in longitudinally inhomogeneous media}
Now, in order to gain insight into the behaviour of the longitudinally inhomogeneous waveguide, we study the spatial propagation of gaussian states, like the coherent and squeezed quantum states of light, in the OFS representation. From the wavefunction (\ref{Number}) and Mehler's formula \cite{Yeon1994}, we easily obtain the propagator of the system for every mode \cite{Linares2012}:
\begin{equation*}
K ( \boldsymbol{\mathcal{E}}, \boldsymbol{\mathcal{E}_{0}}; z, 0 )=(\frac{i}{\pi})^{N/2} \prod_{\sigma}\, (\sin\theta_{\sigma})^{-1/2}
\end{equation*}
\vspace{-0.2cm}
\begin{equation} \label{Propagator2}
e^{-\frac{i}{\sin\theta_{\sigma}} [\cos \theta_{\sigma}\,(\mathcal{E}_{\sigma}^{2} + \mathcal{E}_{0 \sigma}^{2}) - 2 \mathcal{E}_{\sigma} \mathcal{E}_{0 \sigma}] },
\end{equation}
and the wavefunction of any pure state at the end of the medium can be worked out by means of:
\begin{equation} \label{PropWaveFunc}
\Psi(\boldsymbol{\mathcal{E}}; z)= \int K ( \boldsymbol{\mathcal{E}}, \boldsymbol{\mathcal{E}_{0}}; z, 0 )\, \Psi(\boldsymbol{\mathcal{E}_{0}}; 0)\, d\boldsymbol{\mathcal{E}_{0}},
\end{equation}
where $\boldsymbol{\mathcal{E}_{0}}$ and $\boldsymbol{\mathcal{E}}$ stand for the $N$-mode field-strength at the beginning and any point of the $z$-dependent medium, respectively.
\vspace{-0.5cm}
\begin{figure}[h]
\centering
\includegraphics[width=0.51\textwidth]{Figure1.eps}
\vspace {0cm}\,
\hspace{0cm}\caption{\label{F1}\small{Cosine-type effective refractive index $N(z)\equiv\beta(z)/k_{0}$ (solid line, left) and total accumulated classical phase $\theta$ (dash line, right) versus propagation distance $z$, for parameters $N_{t}\equiv\beta_{t}/k_{0}=1.515$, $\Delta n=0.5$ and $\Lambda=k_{0}/50$ $nm^{-1}$ for a wavelength $\lambda=653$ nm.}}
\end {figure}
A single-mode gaussian state $\vert \alpha \rangle$, where $\alpha= \vert \alpha \vert e^{i\phi}$, in the OFS space is given by \cite{Linares2012}:
\begin{equation} \label{CoherentIn}
\Psi(\mathcal{E}_{0}; 0)=(\frac{2}{\pi\,\Delta\mathcal{E}_{0}^{2}})^{1/4} exp\{\frac{-[\mathcal{E}_{0}-\vert \alpha \vert \,\cos\phi ]^2}{\Delta\mathcal{E}_{0}^{2}} \}\,e^{-i\delta_{0}},
\end{equation}
where $\delta_{0}=\sin \phi\, [\vert \alpha \vert^{2} \cos \phi - 2\vert \alpha \vert \mathcal{E}_{0}]$, $\phi=-\omega t$ is the phase associated to the temporal evolution of the state at every plane $z$ and $\Delta\mathcal{E}^{2}_{0}$ is the quantum noise or squeezing factor, with a value of one for a coherent state or different from one for squeezed states. Inserting equations (\ref{Propagator2}) and (\ref{CoherentIn}) in (\ref{PropWaveFunc}), after a long but straightforward calculation, we obtain the wavefunction at any point $z$ of the waveguide:
\begin{equation}\label{SqueezedOutFinal}
\begin{split}
\Psi(\mathcal{E}; z)&=(\frac{2}{\pi\,\Delta\mathcal{E}^{2}})^{1/4} \,e^{ i\Theta/2} e^{-i\delta} \\
&exp\{ \frac{-1}{\Delta\mathcal{E}^{2}} [\mathcal{E}-\vert \alpha \vert\, \cos(\phi+\theta)\, ]^2 \},
\end{split}
\end{equation}
where we have denoted $\theta_{\sigma}\equiv\theta$ and defined $\delta=\sin (\phi+\theta)\, [\vert \alpha \vert^{2} \cos (\phi+\theta) - 2\vert \alpha \vert \mathcal{E}]$ and:
\begin{gather}\label{sq}
\Delta\mathcal{E}=[\frac{\sin^{2}\theta}{\Delta\mathcal{E}_{0}^{2}} + \cos^{2}\theta\,\Delta\mathcal{E}_{0}^{2}]^{1/2}, \\ \label{phasesq}
\Theta=arctan[\frac{\tan\theta}{\Delta\mathcal{E}_{0}^{2}}].
\end{gather}
Therefore, a coherent state keeps its quantum noise constant through propagation, $\Delta\mathcal{E}^{2}=\Delta\mathcal{E}_{0}^{2}=1$, and gets a Gouy's phase equal to the classical accumulated phase given by (\ref{ELtheta}), $\Theta=\theta$, as expected, unlike what we would obtain via the usual approach. On the other hand, an input squeezed state is both amplitude and phase modulated by the inhomogeneous medium, leading to different squeezing oscillations from those corresponding to an homogeneous medium, and with a squeezing factor given by ($\ref{sq}$). It is important to outline that the phase acquired by a squeezed state ($\ref{phasesq}$) is not predicted by the classical theory.
\begin{figure}[h]
\centering
\includegraphics[width=0.46\textwidth]{Figure2.eps}
\vspace {0cm}\,
\hspace{0cm}\caption{\label{F2}\small{Evolution of the quantum noise $\Delta \mathcal{E}^{2}$ in a cosine-type longitudinally inhomogeneous medium for coherent (solid line) and squeezed (dash and dash-dot lines) states of light.}}
\end {figure}
Next, we show a specific example of the effects this kind of medium produce over a single-mode gaussian quantum state like the above introduced. We present a longitudinally inhomogeneous cosine-type medium with $h(z)=\cos(\Lambda z)$ and length $L=2\pi/\Lambda$, as that depicted in Figure 1. The solution of equation (\ref{EL}) is given in terms of linearly independent Mathieu functions $u(z)$ and $v(z)$ \cite{Casperson1985}. Applying these solutions into equations (\ref{ELtheta}) and (\ref{rhoz}), we can obtain numerically the value of $\theta$ and, therefore, the squeezing factor (\ref{sq}) and the Gouy's phase (\ref{phasesq}), which characterize the output quantum state after propagation in this medium. In Figures 2 and 3 we show the behaviour of the Gouy's phase $\Theta$ and the quantum noise $\Delta\mathcal{E}^{2}$, respectively, for three different input quantum states: the solid line stands for the propagation of a coherent state where $\Delta\mathcal{E}_{0}^{2}=1$ and the dash and dash-dot lines for squeezed states with $\Delta\mathcal{E}_{0}^{2}=3/2$ and $\Delta\mathcal{E}_{0}^{2}=1/2$, respectively. As can be checked in Figure 2, the planes where maximum or minimum squeezing of the quantum noise are produced depend on the accumulated phase $\theta$, being different from those corresponding to an homogeneous medium, and the value of the input quantum noise $\Delta\mathcal{E}_{0}^{2}$. Likewise, as was outlined above, the classical equations do not predict the behaviour of states far from the classical, since squeezed and coherent states get different amounts of Guoy's phase $\Theta$, as is sketched in Figure 3. The classical phase $\theta$ is recovered at the planes of maximum and minimum squeezing. {Finally, we stress the interest this phase may have in quantum interferometry, since with an appropriate $\it{LI}$ medium in one arm of an interferometer, quantum interference can be adjusted controlling the strength of the quantum noise in a squeezed input state via equation (\ref{phasesq}).}
\begin{figure}[h]
\centering
\includegraphics[width=0.46\textwidth]{Figure3.eps}
\vspace {0cm}\,
\hspace{0cm}\caption{\label{F3}\small{Evolution of the quantum Gouy's phase $\Theta$ in a cosine-type longitudinally inhomogeneous medium for coherent (solid line) and squeezed (dash and dash-dot lines) states of light.}}
\end {figure}
\section{Summary}
We have studied the propagation of quantum states of light in separable longitudinally inhomogeneous media. We have proposed canonical transformations in a comoving frame and derived the generator of propagation, the classical Momentum, realizing that it is a spatial Lewis-Ermakov invariant. We have quantized it and obtained the propagator in the OFS representation which is physically consistent. Furthermore, we have presented the propagation of a gaussian quantum state of light in a cosine-type refractive index medium and shown the net effect produced by this family of media: a quantum Gouy's phase dependent on the input quantum state with application in quantum interferometry.
\vspace{0.6cm}
\section*{Bibliography}
| {
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} | 9,677 |
A 6066 Hendricks (ideiglenes jelöléssel 1987 SZ3) a Naprendszer kisbolygóövében található aszteroida. Edward L. G. Bowell fedezte fel 1987. szeptember 26-án.
Kapcsolódó szócikkek
Kisbolygók listája (6001–6500)
Jegyzetek
A Naprendszer kisbolygói | {
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Каринтийский плебисцит 10 октября 1920 года был одним из референдумов, проведённых на территории этнически смешанных регионов Восточной Европы с целью определения их территориально-административной принадлежности к тому или иному государству. Завершился передачей всей плебисцитной Каринтии в состав Австрии несмотря на то что в 2 из 4 плебисцитных округах население высказалось за присоединение к будущей Югославии. Несмотря на противоречивые результаты референдума, граница, установленная в результате его проведения, была ещё раз подтверждена двусторонним соглашением между Югославией и Австрией в 1955 году.
Геополитическая ситуация
Фактически данный референдум явился следствием Сен-Жерменского мирного договора 1919 года. В неспокойные 1920-е годы геополитическая обстановка в Европе менялась быстро и непредсказуемо. Если ещё в 1919 году в странах-победителях Первой мировой войны, инициировавших референдум, преобладали антинемецкие настроения, то в 1920-м году Великобритания уже начала опасаться усиления Франции и формирующегося СССР на континенте, а потому приложила все усилия для минимизации этих процессов за счёт укрепления границ немецкого государства на востоке.
Условия проведения
На протяжении 1919—1920 гг. Каринтия подверглась этническому джерримандерингу, в ходе которого небольшая, но политически значимая часть её территории (долина р. Межица с Дравоградом и Езерско) с исключительно словенским населением была передана Королевству сербов, хорватов и словенцев без всякого референдума. Практически полностью словенская Зильская долина также без плебисцита передана Австрии, а Канальская долина, точно также без плебисцита, была уступлена Италии. Эти шаги уменьшили концентрацию словенцев на территориях, на которых должен был состояться плебисцит. Сама плебисцитная территория в свою очередь была подразделена на две зоны: преимущественно словенскую зону А на юге и преимущественно немецкую зону Б на севере. Примечательно, что плебисцит в северной зоне Б должен был состояться только в случае победы сторонников Югославии в зоне А.
Агитация среди населения
Обеим сторонам, австрийской и югославской, разрешалось проводить агитацию в сравнительно непринуждённой обстановке, в отличие от той же Восточной Пруссии, где немецкие власти подавляли пропольскую агитацию. Тем не менее, напряжение сохранялось: проавстрийские агитаторы обрисовывали Королевство сербов, хорватов и словенцев как бедное, хаотичное и экономически нестабильное формирование. В свою очередь, проюгославская сторона взывала к национальным чувствам славянского большинства, подчёркивая уважение к простому образу жизни славянских крестьян и недовольство спекуляцией немецких бюргеров.
Результаты
Анализ результатов голосования показал, что за Австрию голосовали практически все этнические немцы, жители городов, а также 40 % местных словенцев, что и обеспечило победу проавстрийской стороны. За Югославию проголосовало 60 % словенцев. Многие словенцы голосовали за Австрию только потому, что плебисцитная зона А была искусно проведена вплоть до предместий города Целовца (ныне Клагенфурт), но сам город оставался вне её. Такое распределение зон вызвало у словенских крестьян боязнь потерять рынок в Целовце в случае югославской победы. В результате многие словенские крестьяне голосовали за Австрию.
Сравнения
Примечательно, что интерпретация результатов Каринтийского референдума была гораздо более бескомпромиссной, чем аналогичного плебисцита в Восточной Пруссии. Несмотря на то, что Варминско-Мазурский плебисцит показал, что 98 % мазурского населения пожелали остаться в составе Германии, организаторы референдума всё же уступили Польше несколько небольших приграничных деревень, где большинство населения проголосовало за вхождение в состав Польши, даже несмотря на сильное немецкое давление. В Каринтии, где голоса разделились почти поровну по географическому признаку, никаких территориальных уступок югославской стороне сделано не было, даже несмотря на то, что географически жители более половины территории зоны А в Каринтии, пусть и с меньшей плотностью населения, высказалось за вхождение в состав Югославии. В некоторых приграничных с Югославией муниципалитетах вдоль хребта Караванке доля голосов, отданных за Югославию, превышала 90 %. Им также не было позволено присоединиться к последней.
Примечания
Каринтия
История Австрии
Референдумы 1920 года
Референдумы в Австрии | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,155 |
A snowman who finds it dreadfully cold keeps doing things that cause him to melt, while the children who rebuild him each time offer clothing to keep him warm.
"The repetitive, rhyming text reads well. The bright, cartoonlike illustrations are hand drawn and colored in Photoshop, and the small details will reward those who have a close look, particularly at those cardinals. This new take on a popular seasonal theme should find a warm audience during cold months."
The rhyming text keeps the snow show moving along at a brisk, bouncing pace, and the series of problems and solutions creates an entertaining, recognizable pattern. The large digital illustrations are colorful and uncluttered, and they slyly integrate the additional antics of two boisterous cardinals, who cavort along with Sneezy until his happy, Goldilocks-like proclamation, "At last! I feel just right."
Wright's rhyming text is well suited to this whimsical story. Parent storytellers will have fun acting out Sneezy's big sneezes and exhortations, while emergent readers will appreciate the refrains throughout. Gilpin's illustrations are attention-getting and fun, punctuated with the antics of a pair of amusing cardinals. Young readers will ask for this book more than once. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,125 |
package subnet
import (
"time"
log "github.com/coreos/flannel/Godeps/_workspace/src/github.com/golang/glog"
"github.com/coreos/flannel/Godeps/_workspace/src/golang.org/x/net/context"
)
// WatchLeases performs a long term watch of the given network's subnet leases
// and communicates addition/deletion events on receiver channel. It takes care
// of handling "fall-behind" logic where the history window has advanced too far
// and it needs to diff the latest snapshot with its saved state and generate events
func WatchLeases(ctx context.Context, sm Manager, network string, ownLease *Lease, receiver chan []Event) {
lw := &leaseWatcher{
ownLease: ownLease,
}
var cursor interface{}
for {
res, err := sm.WatchLeases(ctx, network, cursor)
if err != nil {
if err == context.Canceled || err == context.DeadlineExceeded {
return
}
log.Errorf("Watch subnets: %v", err)
time.Sleep(time.Second)
continue
}
cursor = res.Cursor
batch := []Event{}
if len(res.Events) > 0 {
batch = lw.update(res.Events)
} else {
batch = lw.reset(res.Snapshot)
}
if batch != nil {
receiver <- batch
}
}
}
type leaseWatcher struct {
ownLease *Lease
leases []Lease
}
func (lw *leaseWatcher) reset(leases []Lease) []Event {
batch := []Event{}
for _, nl := range leases {
if lw.ownLease != nil && nl.Subnet.Equal(lw.ownLease.Subnet) {
continue
}
found := false
for i, ol := range lw.leases {
if ol.Subnet.Equal(nl.Subnet) {
lw.leases = deleteLease(lw.leases, i)
found = true
break
}
}
if !found {
// new lease
batch = append(batch, Event{EventAdded, nl, ""})
}
}
// everything left in sm.leases has been deleted
for _, l := range lw.leases {
batch = append(batch, Event{EventRemoved, l, ""})
}
lw.leases = leases
return batch
}
func (lw *leaseWatcher) update(events []Event) []Event {
batch := []Event{}
for _, e := range events {
if lw.ownLease != nil && e.Lease.Subnet.Equal(lw.ownLease.Subnet) {
continue
}
switch e.Type {
case EventAdded:
batch = append(batch, lw.add(&e.Lease))
case EventRemoved:
batch = append(batch, lw.remove(&e.Lease))
}
}
return batch
}
func (lw *leaseWatcher) add(lease *Lease) Event {
for i, l := range lw.leases {
if l.Subnet.Equal(lease.Subnet) {
lw.leases[i] = *lease
return Event{EventAdded, lw.leases[i], ""}
}
}
lw.leases = append(lw.leases, *lease)
return Event{EventAdded, lw.leases[len(lw.leases)-1], ""}
}
func (lw *leaseWatcher) remove(lease *Lease) Event {
for i, l := range lw.leases {
if l.Subnet.Equal(lease.Subnet) {
lw.leases = deleteLease(lw.leases, i)
return Event{EventRemoved, l, ""}
}
}
log.Errorf("Removed subnet (%s) was not found", lease.Subnet)
return Event{EventRemoved, *lease, ""}
}
func deleteLease(l []Lease, i int) []Lease {
l[i], l = l[len(l)-1], l[:len(l)-1]
return l
}
// WatchNetworks performs a long term watch of flannel networks and communicates
// addition/deletion events on receiver channel. It takes care of handling
// "fall-behind" logic where the history window has advanced too far and it
// needs to diff the latest snapshot with its saved state and generate events
func WatchNetworks(ctx context.Context, sm Manager, receiver chan []Event) {
nw := newNetWatcher()
var cursor interface{}
for {
res, err := sm.WatchNetworks(ctx, cursor)
if err != nil {
if err == context.Canceled || err == context.DeadlineExceeded {
return
}
log.Errorf("Watch networks: %v", err)
time.Sleep(time.Second)
continue
}
cursor = res.Cursor
batch := []Event{}
if len(res.Events) > 0 {
batch = nw.update(res.Events)
} else {
batch = nw.reset(res.Snapshot)
}
if batch != nil {
receiver <- batch
}
}
}
type netWatcher struct {
networks map[string]bool
}
func newNetWatcher() *netWatcher {
return &netWatcher{networks: make(map[string]bool)}
}
func (nw *netWatcher) reset(networks []string) []Event {
batch := []Event{}
newNetworks := make(map[string]bool)
for _, netname := range networks {
if nw.networks[netname] {
delete(nw.networks, netname)
} else {
// new network
batch = append(batch, Event{EventAdded, Lease{}, netname})
}
newNetworks[netname] = true
}
// everything left in sm.networks has been deleted
for netname, _ := range nw.networks {
batch = append(batch, Event{EventRemoved, Lease{}, netname})
}
nw.networks = newNetworks
return batch
}
func (nw *netWatcher) update(events []Event) []Event {
batch := []Event{}
for _, e := range events {
switch e.Type {
case EventAdded:
batch = append(batch, nw.add(e.Network))
case EventRemoved:
batch = append(batch, nw.remove(e.Network))
}
}
return batch
}
func (nw *netWatcher) add(network string) Event {
if _, ok := nw.networks[network]; !ok {
nw.networks[network] = true
}
return Event{EventAdded, Lease{}, network}
}
func (nw *netWatcher) remove(network string) Event {
if _, ok := nw.networks[network]; ok {
delete(nw.networks, network)
} else {
log.Errorf("Removed network (%s) was not found", network)
}
return Event{EventRemoved, Lease{}, network}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,966 |
Giunture o La Giuntura (Indura in dialetto locale, Juncturae in latino) è una frazione del comune di Sant'Apollinare, in provincia di Frosinone. Nei suoi pressi si forma il fiume Garigliano, con la confluenza del Gari nel fiume Liri (giuntura, appunto). La località segna il confine tra i comuni di Cassino e Sant'Apollinare, ma nei pressi della congiunzione vengono toccati anche i comuni di Sant'Ambrogio sul Garigliano (sulla sponda opposta del Liri) e di Rocca d'Evandro (in questo caso al di là del Garigliano e dell'ultimo tratto del Gari).
Storia
Giunture è stato fondato con il nome di Juncturae dai monaci benedettini prima dell'anno 1000, in quanto la zona tra i fiumi Gari e Liri era, come d'altronde è ancora, molto fertile, e situata al termine del tratto di fiume navigabile (provenendo dal Mar Tirreno). Pare che presso tale località vi fosse un porticciolo d'attracco per le navi da trasporto provenienti dal Tirreno ed in particolare per le merci destinate all'Abbazia di Montecassino. Dall'anno 1000 e fino al 1300 circa, l'Università (così erano nominate le località della Terra di San Benedetto) di Juncturae divenne un importante punto di riferimento dell'intero feudo benedettino. Nel 1040 l'Abate di Montecassino Richerio dota l'Infermierato di Montecassino (una sorta di Ospedale dell'epoca) dei beni derivanti da "terre, case, chiese, selve, acque, molini, peschiere. Gli uomini che vi abitavano erano tenuti a servire l'Infirmario e corrispondergli il terratico, il glandatico, i polli e i servizi". Nei documenti benedettini ricorre il nome di Nicola da Iuntura, Magistro costruttore di numerosi edifici in tutta la Terra di San Benedetto durante la prima metà del Duecento.
Nel 1183 papa Lucio III in un documento cita ancora Junturae, confermando il servizio dei suoi abitanti per l'Infermierato. Di Juntura vi sono documenti conservati presso la biblioteca del Monastero di Montecassino nel periodo di tempo dal 1040 fino al 1578. La località è andata spopolandosi dopo le varie scorrerie dei barbari che hanno interessato l'attuale basso Lazio.
Nel 1692 la località era quasi disabitata: il 13 settembre 1692, infatti, papa Innocenzo XII conferisce all'Abate di Montecassino l'incarico di investigare circa la depredazione di beni subiti dalla chiesa di San Martino in Sant'Apollinare, situata presso la congiunzione, e scomunicare gli illeciti detentori.
Dall'anno 1302 fino al 1861 il territorio della località rientrò nel Regno di Napoli e poi nel Regno delle due Sicilie. Diversi anni dopo il territorio della località rimase, negli anni, condiviso tra i comuni di Sant'Angelo in Theodice e Sant'Apollinare (il primo appartenente al Circondario di Sora e al Mandamento di San Germano, l'altro appartenente al Circondario di Gaeta ed al Mandamento di Roccaguglielma - oggi Esperia). Il municipio di Sant'Angelo, con il decreto dell'allora re delle due Sicilie Francesco II dell'11 luglio 1860 (n°36), fu poi soppresso ed annesso al comune di San Germano (oggi Cassino).
Oggi, la porzione della località appartenente al comune di Cassino viene anche chiamata "colle nuovo".
Posizione Geografica
La frazione, raggiungibile principalmente dalla Strada Regionale (già Provinciale) dei Santi, è posta alle propaggini meridionali della Valle del Liri e dà origine alla gola della Valle del Garigliano, tra i Monti Aurunci ed il vulcano spento di Roccamonfina. Risulta quindi essere una zona di confine molto rilevante, in quanto in una manciata di chilometri si possono raggiungere agevolmente tre province (Latina, Caserta e Isernia) e due regioni (Campania e Molise) italiane.
Le coste del Mar Tirreno sono quindi accessibili a circa 30km (Scauri), a 17km è raggiungibile la millenaria Abbazia di Montecassino, mentre con altrettanti km si raggiunge, ad esempio, il Sacrario Militare di Montelungo e le Terme di Suio.
Caserta è la città d'arte più vicina, a meno di 70km, mentre con circa 90 è raggiungibile Napoli e con circa 140 Roma. Tra i centri abitati medio-piccoli, Cassino è situata a 10km circa, Formia e Gaeta a 35 e 40 rispettivamente, Sessa Aurunca a 30, Venafro a 25.
Con circa 90km di strada si raggiunge poi il Parco Nazionale d'Abruzzo, mentre a raggio più breve sono presenti i parchi regionali del Matese, di Roccamonfina e degli Aurunci.
In quanto a servizi pubblici, la fermata bus COTRAL (per Cassino, Scauri, Suio Terme) è posta sulla Strada Regionale dei Santi, mentre gli scali ferroviari più comodi e di rilevanza sono Cassino e Formia-Gaeta, sebbene ve ne siano altri (Fontanarosa-Cervaro) anche più vicini ma più carenti di servizi a lungo raggio. L'Autostrada del Sole è equidistante nelle stazioni di San Vittore e Cassino (circa 7km).
Edifici Pubblici
Nella località era presente una scuola primaria (chiusa a fine anni Settanta), il cui edificio è ancora presente e a partire dagli anni Ottanta è stato diverse volte sfruttato come circolo ricreativo, in occasione anche della costruzione di un campo di bocce nei pressi. Alcune aule sono oggi utilizzate dal comune di Sant'Apollinare come archivio, mentre i restanti locali (ad esempio, i servizi igienici) sono utilizzati durante la locale festa, a fine agosto.
La chiesetta della Madonna di Canneto è stata invece edificata nell'immediato dopoguerra e tuttora utilizzata per la Messa domenicale. Non distante da quest'edificio è in costruzione la nuova chiesa sussidiaria, che andrà a sostituire quella esistente, relativamente piccola ed in condizioni difficili per un restauro integrale.
Economia
L'economia di questa località è legata all'economia del cassinate, con gran parte degli abitanti impiegati nell'industria e nei servizi. Non mancano i lavoratori nel settore agricolo (granturco, orzo, grano, pioppi da cellulosa) ed alla pastorizia (ovini e bovini) con produzione di pregiati formaggi pecorini.
Eventi
Nella località esiste una chiesetta dedicata alla Madonna di Canneto, presso la quale ogni anno, nell'ultima domenica di agosto, si svolge una festa con relativa grande processione. La statua che viene portata durante la festa tra le strade della zona, è una replica lignea della statua della Madonna di Canneto situata a Settefrati.
Frazioni di Sant'Apollinare
Frazioni di Cassino | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,752 |
Peperuda Island (, ) is the mostly ice-free island 592 m long in west-southwest to east-northeast direction and 309 m wide in the Wilhelm Archipelago, Antarctic Peninsula region. Its surface area is 9.51 ha.
The feature is so named because of its shape supposedly resembling a butterfly ('peperuda' in Bulgarian), and in association with other descriptive names of islands in the area.
Location
Peperuda Island is located at , which is 25 m north of Hovgaard Island, 150 m west of Pléneau Island, and 2.33 km south of Lamya Island in the Dannebrog Islands group. British mapping in 2001.
Maps
British Admiralty Nautical Chart 446 Anvers Island to Renaud Island. Scale 1:150000. Admiralty, UK Hydrographic Office, 2001
Brabant Island to Argentine Islands. Scale 1:250000 topographic map. British Antarctic Survey, 2008
Antarctic Digital Database (ADD). Scale 1:250000 topographic map of Antarctica. Scientific Committee on Antarctic Research (SCAR). Since 1993, regularly upgraded and updated
See also
List of Antarctic and subantarctic islands
Notes
References
Peperuda Island. SCAR Composite Gazetteer of Antarctica
Bulgarian Antarctic Gazetteer. Antarctic Place-names Commission. (details in Bulgarian, basic data in English)
External links
Peperuda Island. Adjusted Copernix satellite image
Islands of the Wilhelm Archipelago
Bulgaria and the Antarctic | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,246 |
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android:layout_width="wrap_content"
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android:id="@+id/text"
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android:clickable="false"
android:gravity="center_vertical"
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android:textColor="@color/white"
android:textSize="12.0sp" />
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android:id="@+id/blackIcon1"
android:layout_width="5.0dip"
android:layout_height="5.0dip"
android:layout_marginLeft="@dimen/tag_margin1"
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</RelativeLayout> | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,846 |
Ergebnis gesprochen von "Shawn Compton" in Alle Kategorien
Jugendliche & Heranwachsende
20 Stunden & mehr
1 - 20 von 124 Ergebnissen
Battleship: Leviathan
Battleship Leviathan Series, Book 1
Von: Craig Martelle
Gesprochen von: Shawn Compton
A derelict warship, ancient but still alive. A small team of humans fighting for all humanity. Built for a time when the races were just finding their way to the stars, finding that they could dominate others. The galactic conquests created the arms race and the ancients, the Progenitors had to protect their own. They built a ship to drive the others away.
Serie: Battleship Leviathan, Titel 1
The Guardian of the Dead
An NPC's Path, Book 4
Von: Pavel Kornev, Irene Woodhead - translator
Dying in virtual reality isn't fun, but facing bullets from real-world criminal overlords is really the pits. In such a desperate scenario, their demand to render them a service in VR doesn't sound like such a bad alternative. The problem is, the games played by spook agencies follow much harsher rules. For them, the absence of choice doesn't sound like a good excuse - not if you end up in the grindstones of their undercover schemes.
Serie: An NPC's Path, Titel 4
5 out of 5 stars 10 Bewertungen
I Was Legion
Imperium of Terra, Book 1
Von: Evan Currie
Almost 400 years the Terran Imperium has languished, an Empire in name only. The young colonies exploded out of the Diaspora Era, supplanting the homeworld in importance as they left a broken world in their wake. Earth's people, guided by the Conwin line, have clawed and climbed from the darkness left the night the lights went out. They built and rebuilt the weary and weakened world they inherited, even when it seemed bent on killing them from sheer spite.
Serie: Imperium of Terra Series, Titel 1
House Omega
Marshals of Rhea, Book 1
Von: Gus Harris-Reid
For over 100 cycles, the Marshals of Rhea have defended their strongholds against the wastelands' many dangers, from vicious raiders to mechanical beasts. Anticipation is high as they gather for a major hunting expedition. So when disaster strikes and House Omega is left leaderless, it falls to no-nonsense Head Cook Xanthe to investigate. She's not alone, however, and is aided by an unlikely group of individuals - including a haughty young noblewoman, a world-weary Armorer, a fastidious bodyguard, and a whimsical assassin.
Serie: Marshals of Rhea, Titel 1
The Entrepreneur's Paradox
And How to Overcome the 16 Pitfalls Along the Startup Journey
Von: Curtis Morley
The exact qualities that bring an individual to found a start-up company (their brilliance and expertise) are what prevent them from achieving the success they are looking for - this is the paradox that is entrepreneurship. What starts out as freedom and financial independence turns into grueling hours and added stress and bills. But successful five-time entrepreneur Curtis Morley is here to help. He shares that every entrepreneur is typically doing the same 15 things wrong or just not doing them at all - regardless of industry or business type.
The Dead Rogue
Von: Pavel Kornev, Petr Burov - translator, Irene Woodhead - translator, und andere
A game is only a game if you can quit. This is something I learned the hard way. I just wanted to let off some steam in virtual reality and ended up getting murdered and imprisoned in the body of one of the undead - slow, clumsy, and cursed to die at the hand of other players over and over again. The only way out of this awful predicament was to find the legendary Scroll of Rebirth, but the helpless plague-ridden corpse would need to be turned into a real killing machine. If only people knew what it was like to level up a dead rogue....
sonderbar
Von Albert Am hilfreichsten 09.02.2019
Von: Pavel Kornev, Petr Burov - translator, Irene Woodhead - translator, Neil P. Woodhead - translator
Superpower Interrupted
The Chinese History of the World
Von: Michael Schuman
This global history as the Chinese would write it gives brilliant and unconventional insights for understanding China's role in the world, especially the drive to "Make China Great Again." In this colorful, informative story filled with fascinating characters, epic battles, influential thinkers, and decisive moments, we come to understand how the Chinese view their own history and how its narrative is distinctly different from that of Western civilization.
Flying the SR-71 Blackbird
In the Cockpit on a Secret Operational Mission
Von: Richard H. Graham
The Lockheed SR-71, unofficially known as the Blackbird, was an advanced, long-range, Mach 3 strategic reconnaissance aircraft developed by Lockheed Skunk Works. The aircraft flew so fast and high that not one was ever shot down, even by a missile. SR-71 pilot and instructor Colonel Richard Graham offers a rare cockpit perspective on how regular Air Force pilots and navigators transformed themselves into SR-71 Blackbird crews, turning their unique aviation talents to account in an unprecedented way.
Fall of Houston Series, Book 4
Von: T.L. Payne
Will's homecoming to Calcasieu Parish is anything but welcoming as he comes face to face with the Blanchards, a local crime family who have taken over the town. But long-strained family ties are strengthened when Will's cousins come to the rescue. A new community is formed as residents of Sugar Cove Road band together to protect their loved ones. As one thing leads to another, they become increasingly unable to secure their community against a much more powerful foe than the Blanchards.
Serie: Fall of Houston, Titel 4
Blood Gun Money
How America Arms Gangs and Cartels
Von: Ioan Grillo
Guns from America reach more than 130 countries, and inundate Mexico, with over 200,000 guns every year crossing the border and arming the drug cartels. In this groundbreaking new work of investigative journalism, master of reportage Ioan Grillo delves into the enormous black market for firearms in the Americas. Along the way, Grillo lays bare the many ways that guns slip through the legal cracks and into the hands of criminals, fuelling violence among Mexico's powerful cartels and beyond.
The Fall of Fortresses
The Classic Account of One of the Most Daring and Deadly Air Battles of WWII
Von: Elmer Bendiner
On an August morning in England in 1943, a group of American airmen were told that before the day was out they would deliver the blow that would win the war. Flying the legendary B-17 Flying Fortress, their mission was to destroy the industrial facilities that kept the Nazi war machine in business-Schweinfurt's ball-bearing factories. But a determined and ferocious defense awaited the bomber crews of the USAAF's Mighty Eighth. Somehow, navigator Elmer Bendiner and his crew survived, their faithful B-17, Tondelayo, carrying them home. Hundreds of their young compatriots did not.
Combat Stories from America's Last WWII Veterans, Told Through an M1 Garand
Von: Andrew Biggio
The Rifle is the inspirational story of a 28-year-old US Marine, Andrew Biggio, who returned home from combat in Afghanistan and Iraq, full of questions about the price of war. He found answers from those who survived the costliest war of all - WWII veterans. It began when Biggio bought a 1945 M1 Garand Rifle, the most common rifle used in WWII. When Biggio showed the gun to his neighbor, WWII veteran Corporal Joseph Drago, it unlocked memories Drago had kept unspoken for 50 years.
Von: T. L. Payne
Wounded and weary from their battle at the military base, Will and Isabella want to rest and gather their strength for what lies ahead. But as the military continues to battle foreign insurgents bent on gaining control of Houston, Will and the others must flee the city or risk being pulled back into the fight. Danger awaits them at every turn as they make their way across East Texas. Desperate and dangerous people have flooded the roadways fleeing the fighting ravaging the city. It becomes a constant struggle for survival.
No B.S. Marketing to the Affluent
No Holds Barred, Take No Prisoners, Guide to Getting Really Rich 3rd
Von: Dan S. Kennedy
In this new edition of No B.S. Marketing to the Affluent, millionaire maker Dan S. Kennedy shows you how to re-position your business, practice, or sales career to attract customers or clients for whom price is not a determining factor. Learn how to sell to those who will always be spending as Kennedy shines the spotlight on the practical strategies used by The Ritz-Carlton, Disney, Harrah's Entertainment, Dove, AARP, Dr. Oz, Starbucks, Williams-Sonoma, DeBeers, the health and wellness industry, and many other fascinating and diverse true-life examples.
Deadman's Retinue
Spieldauer: 11 Std. und 4 Min.
Getting stuck in virtual reality isn't fun, but being trapped in an NPC's dead body is really the pits. Still, there might be a way out-provided John can find the Scroll of Rebirth. The problem is, finding it is only half the hassle; knowing how to use it is another bag of worms entirely. Several months of full VR immersion may have turned the cumbersome walking deadman into a swift killing machine, allowing him to earn the patronage of the Lord of Chaos and even acquire his own crypt - but John is still a long way away from reaching the coveted level 100.
An NPC's Path Series, Book 2
Von: Pavel Kornev, Irene Woodhead - translator, Neil P. Woodhead - translator
Instead of enjoying the game, I found myself trapped inside my character's dead body. Now the only way I can save myself is by procuring the Scroll of Rebirth. The problem is my chances of getting it are slim. I'm an undead: an outlaw with no friends, only fickle allies and plenty of enemies. Who are only waiting for their chance to strike. My undead hangman character has to tread a razor's edge, with only the support of his fellow players preventing his imminent plunge into the abyss. But are they who they claim they are?
HBR's 10 Must Reads on AI, Analytics, and the New Machine Age
HBR's 10 Must Reads Series
Von: Harvard Business Review, Michael E. Porter, Thomas H. Davenport, und andere
Gesprochen von: Shawn Compton, Teri Schnaubelt
In this book, you'll learn how: data science, driven by artificial intelligence and machine learning, is yielding unprecedented business insights; blockchain has the potential to restructure the economy; drones and driverless vehicles are becoming essential tools; 3-D printing is making new business models possible; augmented reality is transforming retail and manufacturing; smart speakers are redefining the rules of marketing; and humans and machines are working together to reach new levels of productivity.
Von: Harvard Business Review, Michael E. Porter, Thomas H. Davenport, Paul Daugherty, H. James Wilson
Serie: HBR's 10 Must Reads series, Titel 28
The Deep Learning Revolution
Von: Terrence J. Sejnowski
The deep-learning revolution has brought us driverless cars, the greatly improved Google Translate, fluent conversations with Siri and Alexa, and enormous profits from automated trading on the New York Stock Exchange. Deep-learning networks can play poker better than professional poker players and defeat a world champion at Go. In this book, Terry Sejnowski explains how deep learning went from being an arcane academic field to a disruptive technology in the information economy.
The Pivot
Addressing Global Problems Through Local Action
Von: Steve Hamm
Early in the crisis, a global volunteer collaboration called Pivot Projects was formed to rethink how the world works. Some members are experts in the sciences and the humanities; others are environmental activists or regular people who see themselves as world citizens. In The Pivot, the journalist Steve Hamm - who embedded in the enterprise from the start - explores their efforts and shows how their approach provides a model for achieving systemic change.
The Lost World of the Old Ones
Discoveries in the Ancient Southwest
Von: David Roberts
In this thrilling story of intellectual and archaeological discovery, David Roberts recounts his last 20 years of far-flung exploits in search of spectacular prehistoric ruins and rock art panels known to very few modern travelers. His adventures range across Utah, Arizona, New Mexico, and southwestern Colorado, and illuminate the mysteries of the Ancestral Puebloans and their contemporary neighbors the Mogollon and Fremont, as well as of the more recent Navajo and Comanche.
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\section{Introduction}\label{sec:intro}
Measurements of the angular power spectrum of the cosmic microwave
background (CMB) anisotropies from the WMAP experiment have been used
to constrain the standard cosmological parameters to unprecedented
accuracy \cite{Spergel2003,Spergel2006,wmap5,wmap7}. At the same
time, several anomalies have been observed, one of which is the
missing power above 60 degrees on the sky in the maps where the
galactic plane has been masked
\cite{Spergel2003,wmap123,wmap12345}. This is unexpected not only
because skies with such lack of large-scale power are expected with
the probability of about 0.03\% in the standard Gaussian, isotropic
model \cite{wmap123,wmap12345,Sarkar}, but for two other
reasons. First, the missing power occurs on the largest observable
scales, where a cosmological origin is arguably most likely. Second,
missing correlations are inferred from cut-sky (i.e.\ masked) maps of
the CMB, which makes the results insensitive to assumptions about what
lies behind the cut.
For review of the missing correlations (and other so-called ``large-angle
anomalies'' in the CMB), see \cite{CHSS_review}; for debate on this issue, see
\cite{CHSS_review,Efstathiou2009,Pontzen_Peiris,Aurich_Lustig}; for signatures
of the anomalies in future polarization observations, see \cite{Dvorkin}.
In this paper we study the possibility that the {\it primordial} power
spectrum is suppressed at large scales. This explanation has been
invoked before in order to explain the low power in the multipole
spectrum (e.g.\ \cite{Contaldi}). In the meantime, observations have
made it apparent that the harmonic-space quadrupole and octopole are
only moderately low (e.g.~\cite{O'Dwyer2004,Hinshaw:2006ia}), and it
is really a range of low multipoles that conspire to produce the
vanishing $C(\theta)$. Specifically, as discussed in \cite{wmap12345},
there is a cancellation between the combined contributions of
$C_2$,...,$C_5$ and the contributions of $C_\ell$ with $\ell\geq 6$. It
is this conspiracy that is most disturbing, since it violates the
independence of the $C_\ell$ of different $\ell$ that defines statistical
isotropy.
Note however that it is {\it a priori} not at all clear that
suppression in the large-scale power can explain the WMAP observations
on large scales. While the missing large-angle correlations in the
angular two-point correlation function of the CMB $C(\theta)$ could be
trivially explained by the missing primordial power, a large
suppression would lower the harmonic power spectrum $C_\ell$, inferred
using the maximum-likelihood estimator, too much to be consistent with
observations. [We discuss this in Sections \ref{sec:statistical} and
\ref{sec:constraints} below.]
In this paper we perform a two-pronged analysis. First, we adopt a simple
parametric model for the suppression, and perform a detailed analysis to find
the suppressed power spectrum that improves the fit of the vanilla $\Lambda$CDM\; model
to the angular correlation function measured by WMAP in cut-sky maps, and at
the same time improves the fit to the angular power spectrum inferred from the
maximum-likelihood analysis presented by the WMAP team. Second, we address the
following question: {\it if} the CMB observations are telling us that the
three-dimensional primordial power spectrum is indeed suppressed at large
scales (and our adopted model for the suppression is at work), could this
effect be confirmed in redshift surveys, with observations of suppressed
clustering of galaxies on the largest scales?
It is important to note that we do not concern ourselves with
questions recently discussed in the literature as to whether the
full-sky or the cut-sky measurements are more robust. It could be the
case that one of these measurements, full-sky or cut-sky, is correct
while the other is not due to some type of systematic error; it could
also be that both of these measurements are correct (in which case the
assumption of statistical isotropy is arguably on less firm
footing). We consider these possibilities separately in order to get a
rough idea on what scale the data favor power suppression in either
case. Regardless of which of these possibilities is true, however, our
results regarding the detectability of power suppresion, presented in
Sec.~\ref{sec:future}, are valid.
The paper is organized as follows. In Sec.~\ref{sec:prelim} we do a
preliminary investigation in which we attempt to reconstruct the suppression
of the primordial power spectrum (and, correspondingly, the matter power
spectrum) directly from CMB angular power spectrum measurements (the
$C_{\ell}$). In Sec.~\ref{sec:suppressed}, we take the complementary approach,
parameterizing the suppression and finding how it affects the $C_{\ell}$ and
$C(\theta)$. Sec.~\ref{sec:statistical} quantifies how well a given suppressed
model fits CMB data in both $C_{\ell}$ and
$C(\theta)$. Sec.~\ref{sec:constraints} provides a discussion of the results
that we obtain from this analysis; we find that large-scale suppression of
power can significantly increase the likelihood of the observed CMB at large
scales. Finally, in Sec.~\ref{sec:future}, we discuss the possibility of
detecting suppression in the matter power spectrum with an upcoming
large-volume redshift survey. We conclude in Sec.~\ref{sec:conclusions}.
\section{Suppressed power: preliminary investigations}\label{sec:prelim}
Let us first review the basic way in which the primordial power
spectrum determines fluctuations in the CMB observed today. The CMB
temperature anisotropies are decomposed into spherical harmonics with
coefficients $a_{\ell m}$
\begin{equation}
\frac{\Delta T}{T}(\theta,\phi) = \sum_{\ell=2}^\infty \sum_{m=-\ell}^\ell a_{\ell m} Y_{\ell m}(\theta, \phi),
\label{eqn:SHdecomposition}
\end{equation}
where $T$ is the average temperature of the CMB. The angular power
spectrum, which quantifies the contribution to the variance of the
temperature fluctuations at each $\ell$, is then given by the
coefficients $C_\ell$ where, assuming statistical isotropy,
$\left \langle a_{\ell m} a_{\ell' m'} \right \rangle=C_\ell
\delta_{\ell\ell'}\delta_{mm'}$.
We will also consider the angular two-point correlation function
\begin{equation}
C(\theta)\equiv \left\langle \frac{\Delta T}{T}(\hat n)
\frac{\Delta T}{T}(\hat n')\right\rangle_{\hat n\cdot\hat n'=\cos \theta},
\label{eq:ctheta}
\end{equation}
where we have assumed statistical isotropy, and the expectation is taken over
the ensemble of universes. $C(\theta)$ is related
to the anisotropy power spectrum by
\begin{equation}
C(\theta) = \frac{1}{4\pi}\sum_{\ell=2}^\infty (2\ell +1) C_\ell P_\ell (\cos
\theta).
\label{eq:Ctheta_vs_Cl}
\end{equation}
The angular power spectrum $C_\ell$ is directly related to the primordial
power spectrum of curvature perturbations laid down by inflation. The
$C_{\ell}$ are given in terms of the primordial power spectrum by
\begin{equation}
\frac{\ell (\ell + 1) C_{\ell}}{2 \pi} = \int d(\ln k)
\left \lbrack T_{\ell}(k) \right \rbrack ^2 \Delta_{R}^2 (k),
\label{eqn:ClDelta}
\end{equation}
where $T_{\ell}(k)$ is the transfer function and $\Delta_R^2(k)$ is
the dimensionless curvature power spectrum
\begin{equation}
\Delta_{R}^2 (k) \equiv \frac{k^3 P_{R}(k)}{2 \pi^2},
\label{eqn:Delta2def}
\end{equation}
where $P_R(k)$ is the curvature power spectrum which, at late times
and on subhorizon scales, is related to the matter density power
spectrum $P(k)$ via $P_R(k) \propto k^{-4} P(k)$.
We would like to infer the primordial curvature power spectrum
$\Delta^2_R(k)$ given the angular power spectrum $C_\ell$ measured
from the CMB. There are two approaches we could take to dealing with
Eq.~(\ref{eqn:ClDelta}): the inverse problem (discussed in this
section) and the parametric forward problem of starting with various
power spectra and attempting to fit the $C_\ell$ (discussed in the
next section and pursued in the rest of the paper).
The first option is to directly calculate $\Delta^2_R(k)$ from the
measured angular power spectrum $C_{\ell}$. This inverse problem,
where we know the result of the integration but not the integrand, is
difficult because the primordial power spectrum $\Delta_R^2(k)$ is a
three-dimensional quantity while the CMB angular power spectrum
$C_{\ell}$ is a two-dimensional, projected quantity. When the problem
is discretized, as described below, it becomes clear that the problem
is underdetermined and ill-conditioned, as is typical for inverse
problems: small changes in the observed $C_\ell$ typically lead to
large changes in the inferred $\Delta^2_R(k)$.
Since we are examining the phenomenon of low power on large angles in the CMB,
it is really the $C(\theta)$ data that we wish to be faithful to, so we take
$C(\theta)$ as our starting point rather than $C_{\ell}$. We start from the
pixel-based measurement of the angular correlation function (adopted from
\cite{Sarkar}), which we denote with a tilde, $\tilde C(\theta)$. In order to
smooth out the noise in the measured $\tilde C(\theta)$, and thereby simplify
the inverse problem somewhat, we use a ``smoothed model'' for $\tilde C(\theta)$ that
is designed to agree with $\Lambda$CDM\; at small angular scales while closely matching
the actual WMAP data at larger angular scales. To this end, we take the $\Lambda$CDM\;
$C(\theta)$ and modify it so that it smoothly transitions to zero for $\theta$
above roughly 60 degrees (Figure \ref{fig:ctheta}).
Inverting Eq.~(\ref{eq:Ctheta_vs_Cl}), we can determine the angular
power spectrum coefficients $\tilde{C}_{\ell}$ inferred from our (smoothed) pixel-based estimate $\tilde C(\theta)$
\begin{equation}
\tilde C_{\ell} = 2 \pi \int_{-1}^{1} P_{\ell}(\cos \theta) \tilde C(\theta) d(\cos \theta).
\label{eqn:clctheta}
\end{equation}
We are now in a position to directly address the inverse problem in
Eq.~(\ref{eqn:Delta2def}). We solve this numerically by discretizing the
integral
\begin{eqnarray}
\label{eqn:ClDeltakernel_orig}
\frac{\ell (\ell + 1) \tilde C_{\ell}}{2 \pi} &=& \int d(\ln k)
\left \lbrack T_{\ell}(k) \right \rbrack ^2 \Delta_{R}^2 (k) \\[0.2cm]
& \equiv & \sum_k F_{\ell k} \Delta_R^2(k).
\label{eqn:ClDeltakernel}
\end{eqnarray}
The kernel $F_{\ell k}$ is extracted from CAMB \cite{CAMB}. The basic
strategy here, distilled in diagrammatic form, is to start from
$\tilde C(\theta)$ to find the corresponding $\Delta_R^2(k)$:
\begin{equation}
\tilde C(\theta) \rightarrow \tilde C_{\ell} \rightarrow \Delta_R^2(k).
\label{eqn:flowchart}
\end{equation}
We attempted two different methods of solving this inverse problem,
explained more fully in Appendix \ref{sec:inverse}. Both methods give
similar results, shown with a sample reconstruction in
Fig.~\ref{fig:inverseproblemresult} in the Appendix. While this result
can only be suggestive (given that we used a smoothed model for
$\tilde C(\theta)$ and given that the inverse problem is
ill-conditioned and underdetermined), it does indicate that a
transition to low/zero power on large angular scales in $\tilde
C(\theta)$ can be explained by suppression at low $k$ in the
primordial power spectrum $\Delta_R^2(k)$. If the transition to zero
power in $\tilde C(\theta)$ occurs at about 60 degrees, as it appears
to do in the WMAP cut-sky data, then this corresponds to power
suppression at scales of $k \lesssim 10^{-3.6} {\rm Mpc}^{-1} \approx 3.5
\times 10^{-4} h/{\rm Mpc}$.
\begin{figure}[t]
\begin{center}
\includegraphics[width=.45\textwidth]{fig1.pdf}
\caption{The angular two-point function $C(\theta)$. Measurement from
the W-band WMAP 7-year maps, adopted from \cite{Sarkar}, is shown
here in blue, while our model in which $C(\theta)$ smoothly
transitions to zero at higher $\theta$ is shown in green. This
smoothed model mimics and idealizes the behavior of the measured
$C(\theta)$ at large scales but follows the $\Lambda$CDM\; prediction (red
curve) on smaller scales, below roughly 50 degrees. The dotted line
shows zero correlation for reference.}
\label{fig:ctheta}
\end{center}
\end{figure}
\section{Suppressed primordial large-scale power}\label{sec:suppressed}
The inverse approach from the previous section and the Appendix shows that the
direct inversion of our smoothed $C(\theta)$ leads to a suppression of $P(k)$
at $\log_{10}(k_c/(h/\Mpc)) \lesssim -3.5$, but the inversion is very noisy
and non-robust, as expected. We now change tactics and move to the
alternative approach to Eq.~(\ref{eqn:ClDelta}). Instead of treating this as
an inverse problem, we now parameterize $\Delta_R^2(k)$ and treat this as a
(much more stable) forward problem. We utilize a three-parameter model
parameterizing the suppressed $\Delta_R^2(k)$ with an exponential cutoff:
following \cite{Contaldi} and \cite{Mort_Hu_pklow}, we write
\begin{eqnarray}
\Delta_{R, {\rm sup}}^2(k) &=& \left [1 - \beta e^{-(k/k_c)^{\alpha}}\right ]
A_s (k/k_0)^{n_s - 1} \\[0.2cm]
&\equiv & S(k; k_c, \alpha, \beta) \Delta_{R, {\rm unsup}}^2(k),
\label{eqn:suppressionparameterized}
\end{eqnarray}
where we have implicitly defined the factor $S(k; k_c, \alpha, \beta)\equiv 1
- \beta \exp(-(k/k_c)^{\alpha}) $ by which the power spectrum is
suppressed. The parameter $k_c$ controls the $k$-value of the transition;
$\alpha$ controls the sharpness of the transition; and the extra parameter
$\beta$, which is not found in \cite{Contaldi} or \cite{Mort_Hu_pklow}, allows
the power spectrum to plateau to a value other than zero at low $k$
($S(k)\rightarrow 1 - \beta$ for $k \rightarrow 0$). Note that this
parameterization has enough freedom to mimic the results of the inversion
shown in Fig.\ \ref{fig:inverseproblemresult} almost perfectly.
For a given set of parameters $\{k_c, \alpha, \beta\}$, we have a well-defined
$\Delta_R^2(k)$ and can thus use the numerical kernel $F_{\ell k}$ to find the
corresponding $C_{\ell}$'s, as in Eq.~(\ref{eqn:ClDeltakernel}). We can then
determine which combinations of parameters give $C_{\ell}$'s that fit the
observed WMAP $C_{\ell}$'s, and likewise the observed $C(\theta)$. We are now
moving in a direction opposite the one in Eq.~(\ref{eqn:flowchart}):
\begin{equation}
\Delta_R^2(k) \rightarrow C_{\ell} \rightarrow C(\theta).
\label{eqn:flowchartbackward}
\end{equation}
Plots of the suppression factor $S(k)$ for several sample parameter
values are shown in Figure \ref{fig:skvsk}.
\begin{figure}[t]
\begin{center}
\includegraphics[width=.45\textwidth]{fig2a.pdf}
\includegraphics[width=.45\textwidth]{fig2b.pdf}
\includegraphics[width=.45\textwidth]{fig2c.pdf}
\caption{Illustration of what the suppression factor $S(k)$ looks like for
various combinations of parameters. The default parameters are $\log(k_c)
\equiv \log_{10}(k_c/(h/\Mpc)) = -2.85$, $\alpha = 3.0$,
and $\beta = 1.0$. In each plot, one of these parameters is varied, while
the other two are held fixed at their default values.}
\label{fig:skvsk}
\end{center}
\end{figure}
When varying the suppression parameter $k_c$ (and, optionally, $\alpha$ and
$\beta$), we have {\it not} simultaneously varied other parameters that
describe the primordial power spectrum, such as the dark matter and baryon
densities, spectral index, etc. The reason, in addition to simplicity, is that
none of these other parameters can mimic the large-scale suppression of power,
and therefore, power suppression is not degenerate with other cosmological
parameters. The one possible exception would be primordial nongaussianity of
the local type, which does indeed affect the power spectrum of halos (and,
thus, galaxies) on large scales \cite{Dalal}; however, including this
degeneracy is beyond the scope of this project.
\section{Statistical tests}\label{sec:statistical}
\begin{figure}[t]
\begin{center}
\includegraphics[width=.45\textwidth]{fig3a.pdf}
\includegraphics[width=.45\textwidth]{fig3b.pdf}
\includegraphics[width=.45\textwidth]{fig3c.pdf}
\caption{Effects of the suppression on the angular power spectrum
$C_{\ell}$. The default parameters are again $\log(k_c) \equiv
\log_{10}(k_c/(h/\Mpc)) = -2.85$, $\alpha = 3.0$, and $\beta = 1.0$. In each panel,
one of these parameters is varied, while the other two are held
fixed at their default values. The WMAP measurements are shown as
points with measurement error bars (too small to see in this
plot). Cosmic variance (assuming full-sky measurements) is plotted
as a band around the most heavily suppressed model (green curve) in
each panel.}
\label{fig:clvary}
\end{center}
\end{figure}
\begin{figure}[t]
\begin{center}
\includegraphics[width=.45\textwidth]{fig4a.pdf}
\includegraphics[width=.45\textwidth]{fig4b.pdf}
\includegraphics[width=.45\textwidth]{fig4c.pdf}
\caption{ Effects of the suppression on the real-space two-point correlation
function in the CMB, $C(\theta)$. The default parameters are again
$\log(k_c) \equiv \log_{10}(k_c/(h/\Mpc)) = -2.85$, $\alpha = 3.0$, and $\beta = 1.0$. In
each plot, one of these parameters is varied, while the other two are held
fixed at their default values.}
\label{fig:cthetavary}
\end{center}
\end{figure}
We are interested in how a suppressed primordial power spectrum, as
given in Eq.~(\ref{eqn:suppressionparameterized}), affects both
$C_{\ell}$ and $C(\theta)$. Figures \ref{fig:clvary} and
\ref{fig:cthetavary} show examples of how these quantities vary with
changes in the parameters.
More specifically, we look to quantify whether, and to what extent, a
suppressed primordial power spectrum gives a better fit to
observations of $C_{\ell}$ (typically inferred using
maximum-likelihood-type techniques at large scales) and $C(\theta)$
estimated on cut-sky maps using a pixel-based estimator. We restrict
attention here to varying $k_c$ rather than all three parameters,
since variations in $k_c$ have the greatest effects on the likelihood,
and also since $k_c$ directly controls the scale at which the
suppression occurs.
In the case of $C_{\ell}$, it is relatively straightforward to quantify the
fit between a given suppressed model and the WMAP data. We simply generate a
suppressed model using CAMB and then feed the resulting $C_{\ell}$ spectrum
into the WMAP likelihood code\footnote{Available from
\url{http://lambda.gsfc.nasa.gov/product/map/dr4/likelihood_info.cfm}.} to
obtain a goodness-of-fit criterion. Further details are covered in
Sec. \ref{subsec:cl}.
Quantifying the fit between a suppressed-model $C(\theta)$ and the
WMAP data requires a bit more work. In Sec. \ref{subsec:ctheta}, we
examine the statistic $S_{1/2}$, which gives a measure of correlations
in the CMB above scales of $60\hbox{$^\circ$}$. In analogy to our treatment of
the angular power spectrum, we define a $\chi^2$ statistic to quantify
the goodness of fit between a given suppressed model and the WMAP
data.
\subsection{Angular Power Spectrum $C_{\ell}$}\label{subsec:cl}
To quantify how well the suppressed angular power spectrum $C_{\ell,
{\rm sup}}$ fits the WMAP observations $C_{\ell, {\rm WMAP}}$, we
use the WMAP likelihood code to compute $\chi^2_{C_{\ell},\rm sup}(k_c) = -2
\ln \mathcal{L}_{\rm sup}(k_c)$ from $C_{\ell, {\rm sup}}$. We
likewise compute $\chi^2_{C_{\ell},\rm unsup} = -2 \ln \mathcal{L}_{\rm unsup}$
from the unsuppressed $\Lambda$CDM\; power spectrum $C_{\ell, {\rm unsup}}$,
finding the difference
\begin{equation}
\Delta \chi^2_{C_{\ell}}(k_c) = \chi^2_{C_{\ell},\rm sup}(k_c) - \chi^2_{C_{\ell},\rm unsup}
\label{deltachi2cl}
\end{equation}
as a final quantification of how well the suppressed model fits
$C_{\ell}$ data relative to the unsuppressed $\Lambda$CDM\; model.
A negative $\Delta \chi^2_{C_{\ell}}$ indicates that the suppressed model is a better fit to the
WMAP data than $\Lambda$CDM\;. For models with a large amount of suppression (i.e.,
high $k_c$), the suppressed model affects the $C_\ell$ at increasingly smaller
scales (higher $\ell$), making them inconsistent with the $C_\ell$ measured
from WMAP and thus making the quantity $\Delta \chi^2_{C_{\ell}}$ large and positive.
The results are shown further below in Fig.~\ref{fig:pclps12}, with discussion
in Section \ref{sec:constraints}.
\subsection{Angular Correlation Function $C(\theta)$}\label{subsec:ctheta}
We now study to what extent the power suppression from our model can account
for the low correlations observed above $60\hbox{$^\circ$}$ on the cut-sky WMAP maps
\cite{Spergel2003,wmap123,wmap12345}. The statistic $S_{1/2}$, defined in
\cite{Spergel2003}, quantifies the lack of correlation above 60 degrees
\begin{equation}
S_{1/2} \equiv \int_{-1}^{1/2} \left \lbrack C(\theta) \right \rbrack ^2 d(\cos \theta).
\label{eqn:s12definition}
\end{equation}
It is possible to calculate $S_{1/2}$ directly from the $C_{\ell}$'s:
\begin{equation}
S_{1/2} = {1 \over (4 \pi)^2} \sum_{\ell, \ell'} (2 \ell + 1)(2 \ell' + 1) C_{\ell} I_{\ell, \ell'}(1/2) C_{\ell'}.
\label{eqn:s12fromCl}
\end{equation}
For details of how the quantity $I_{\ell, \ell'}$ is calculated, see Appendix
A of the published version of Ref.~\cite{wmap12345}.
We would like to generate statistical realizations of the angular
power spectrum based on the underlying primordial power spectrum
$\Delta_R^2$. To do that, we first calculate the expected angular
power spectrum $C_{\ell, {\rm original}}$ (using
Eq.~(\ref{eqn:ClDeltakernel_orig})), and then create realizations
using
\begin{equation}
C_{\ell, {\rm realization}} = f C_{\ell, {\rm original}}
\label{eqn:realizations}
\end{equation}
where the multiplicative factor
\begin{equation}
f = \frac{\Gamma(k=(2 \ell+1) f_{\rm sky}/2, \theta=2)}{(2 \ell+1) f_{\rm sky}}:
\label{eqn:f}
\end{equation}
the numerator is drawn from a gamma distribution with scale parameter
$\theta=2$ and shape parameter $k=(2 \ell+1) f_{\rm sky}/2$, and the
denominator ensures that the mean of $f$ is unity. The reason we draw
from a gamma distribution is that this is the appropriate
generalization of a $\chi^2$ distribution when the number of degrees
of freedom is non-integer, as it is above for $f_{\rm sky} \neq 1$;
$\Gamma(k=r/2, \theta=2)$ is identical to a $\chi^2$ distribution for
integer $r$ degrees of freedom. We adopt $f_{\rm sky}=0.75$ for the
remainder of this paper. [Modeling of the noise is unnecessary since
cosmic variance dominates at these large scales.]
\begin{figure}[t]
\begin{center}
\includegraphics[width=.45\textwidth]{fig5a.pdf}
\includegraphics[width=.45\textwidth]{fig5b.pdf}
\caption{The distribution of our realizations of the statistic
$S_{1/2}$ for the unsuppressed (red histograms) and a sample
suppressed (green histograms) model. The suppressed model has
$\log_{10}(k_c/(h/\Mpc)) = -2.85$, $\alpha = 3.0$, and $\beta=1.0$, and has a better
fit than the unsuppressed model by $\Delta \chi^2_{S_{1/2}} = -7.9$. The bottom panel
clearly shows that the distribution of $S_{1/2}$ is lognormal,
whether or not the underlying power spectrum is suppressed.}
\label{fig:s12distribution}
\end{center}
\end{figure}
We examine the resulting distribution of $S_{1/2}$ values by performing
100,000 realizations of the $C_{\ell}$ for $2\leq\ell\leq 50$ (going to higher
values of $\ell$ barely changes the $S_{1/2}$ statistic, since scales above
$60\hbox{$^\circ$}$ are mostly affected by $\ell\lesssim 10$), assuming central values
$C_{\ell, {\rm original}}$ calculated based on the suppressed primordial power
spectrum as in Eq.~(\ref{eqn:ClDeltakernel}), and calculating $S_{1/2}$ for
each set of $C_{\ell, {\rm realization}}$. We find that $S_{1/2}$ is
distributed approximately according to a lognormal distribution, both for
suppressed and unsuppressed models, and regardless of the particular value of
$k_c$. This is illustrated in Fig.~\ref{fig:s12distribution}.
In the sample suppressed model ($\log_{10}(k_c/(h/\Mpc)) = -2.85$) shown in
Fig.~\ref{fig:s12distribution}, the histogram of $S_{1/2}$ peaks at
$1000 (\mu K)^4$, has a mean of $8300 (\mu K)^4$, and a median of
$4300 (\mu K)^4$. The histogram of $\ln(S_{1/2})$ peaks at 8.4,
corresponding to an $S_{1/2}$ of $4400 (\mu K)^4$. These values are
all much lower than the mean value expected in the best-fit $\Lambda$CDM\;
cosmology (about $50,000 (\mu K)^4$), but bigger than the value
measured in WMAP cut-sky maps (about $1000 (\mu K)^4$).
In order to calculate a $\chi^2$ statistic in analogy to the $\Delta \chi^2_{C_{\ell}}$ above, we
first transform the lognormal $S_{1/2}$ distribution to a Gaussian by taking
the natural log of the $S_{1/2}$ values. The result, a nearly perfect
Gaussian, is shown for the unsuppressed and the sample suppressed model in the
lower panel of Fig.~\ref{fig:s12distribution}. We can then calculate the
$\chi^2$ corresponding to the probability of getting a certain value
$S_{1/2}^{\rm obs}$ of $S_{1/2}$
\begin{equation}
\chi^2_{S_{1/2}, {\rm sup}} = \left \lbrack \frac{\ln (S_{1/2}(k_c)) - \ln (S_{1/2}^{\rm obs})}
{\sigma_{\ln(S_{1/2})}} \right \rbrack ^2
\label{eqn:chi2s12}
\end{equation}
where $\ln(S_{1/2}(k_c))$ is the mean over the realizations of $\ln(S_{1/2})$
for the given $k_c$ and $\sigma_{\ln(S_{1/2})}$ is the standard deviation over
all realizations. For the purposes of this paper, we choose $S_{1/2}^{\rm obs}
= 1000\, (\mu$K$)^4$, since this is (roughly) the value of $S_{1/2}$ favored
by the cut-sky WMAP observations \cite{Spergel2003,wmap123,wmap12345,Sarkar}.
We also performed 6,500,000 realizations of the $C_{\ell}$ assuming
central values $C_{\ell, {\rm original}}$ corresponding to the
\textit{unsuppressed} $\Lambda$CDM\; model. From the $S_{1/2}$ values
associated with these realizations, we calculate $\chi^2_{S_{1/2},
{\rm unsup}}$ in exact analogy to Eq.~(\ref{eqn:chi2s12}), and then
compute
\begin{equation}
\Delta \chi^2_{S_{1/2}}(k_c) = \chi^2_{S_{1/2},\rm sup}(k_c) - \chi^2_{S_{1/2},\rm unsup}.
\label{deltachi2s12}
\end{equation}
A combined statistic that takes into account both the measurements of the
angular power spectrum $C_\ell$ and the total angular correlation above $60\hbox{$^\circ$}$
parameterized by the statistic $S_{1/2}$, is then given by\footnote{Since we
are interested in how likely the low value of $S_{1/2} \approx 1000 (\mu
K)^4$ is, given suppression of power, we could have simply calculated
$P(S_{1/2} < 1000)$ -- the probability that $S_{1/2}$ is \textit{as low as}
1000 -- instead of performing the more complicated calculation above to
obtain $P(S_{1/2})$. However, the danger in doing this is that suppression
on small enough scales leads to values of $S_{1/2}$ that are much lower than
1000, and then the probability that $S_{1/2}$ is \textit{as high as} 1000
should become low.
Considering the Gaussian likelihood in $\ln (S_{1/2})$, as we have done,
correctly penalizes values of $S_{1/2}$ that are too low {\it or} too high.
}
\begin{eqnarray}
\mathcal{L}(k_c) &=&
\exp\left (-\frac{\Delta \chi^2_{C_{\ell}}(k_c)}{2}\right )\times
\exp\left (-\frac{\Delta \chi^2_{S_{1/2}}(k_c)}{2}\right )\nonumber \\[0.2cm]
&\equiv & P(C_{\ell}) \times P(S_{1/2}).
\label{eqn:likelihoods}
\end{eqnarray}
Both $P(S_{1/2})$ and $P(C_{\ell})$ are normalized so that their values for the
unsuppressed $\Lambda$CDM\; model are 1. Hence $P(S_{1/2})$ and $P(C_{\ell})$ should be interpreted
as the improvement (relative to fiducial unsuppressed $\Lambda$CDM) in how
well a given suppressed model fits the WMAP data for $C_{\ell}$ and
$S_{1/2}$.
Note that we are not taking the correlation between the
(maximum-likelihood) $C_\ell$ and the (pixel-based) $S_{1/2}$ into
account in our statistic $\mathcal{L}(k_c)$. We define the statistic
in the simplest possible way, by multiplying the individual
likelihoods in $C_\ell$ and $S_{1/2}$. This simple combination is
sufficient, since it favors suppression on scales between the scales
which $P(S_{1/2})$ and $P(C_{\ell})$ independently prefer (this is confirmed in
Fig.~\ref{fig:pclps12}), and thus captures the essence of how these
two quantities jointly favor suppression.
Note that the main results of this paper, presented in Sec.~\ref{sec:future},
do not depend on exactly how we combine the likelihood in the measured
full-sky $C_{\ell}$ and cut-sky $S_{1/2}$; we only use $\mathcal{L}(k_c)$ from
Eq.~(\ref{eqn:likelihoods}) to get a rough idea about the scale at which
suppression is favored by the data if both measurements are taken at face
value. We then proceed in Sec.~\ref{sec:future} to study the detectability of
suppressed power corresponding to a range of values of the suppression scale
$k_c$; these results do not depend on how $P(C_{\ell})$ and $P(S_{1/2})$ are combined.
We are now in a position to determine which values of the suppression scale
$k_c$ improve the joint fit to the angular power spectrum $C_\ell$ and the
cut-sky measurements of the angular correlation function $C(\theta)$ above
$60\hbox{$^\circ$}$ (quantified by the statistic $S_{1/2}$).
\section{Current constraints from the CMB}\label{sec:constraints}
\begin{figure}[t]
\begin{center}
\includegraphics[width=.45\textwidth]{fig6a.pdf}
\includegraphics[width=.45\textwidth]{fig6b.pdf}
\caption{The improvements in $P(S_{1/2})$, $P(C_{\ell})$, and the product thereof
-- all relative to the unsuppressed model -- are plotted as a
function of $k_c$. The top panel shows $P(S_{1/2})$ divided by 10 and
$P(C_{\ell})$ multiplied by 10. The $P(S_{1/2})$ values are based on 100,000
realizations of the $C_{\ell}$'s as described in the text. The
bottom panel shows the same information as the top panel, but puts
it in terms of chi-square goodness-of-fit statistics. The maximum
improvement in $P(S_{1/2}) \times P(C_{\ell})$, relative to the unsuppressed
$\Lambda$CDM\; model, is a factor of 8.7 ($\Delta \chi^2_{S_{1/2}} + \Delta \chi^2_{C_{\ell}} = -4.3$), occurring
at $\log_{10}(k_c/(h/\Mpc)) \approx -3.3$. All calculations were performed assuming
$f_{\rm sky} = 0.75$.}
\label{fig:pclps12}
\end{center}
\end{figure}
The top panel of Fig.~\ref{fig:pclps12} shows $P(S_{1/2})$, $P(C_{\ell})$, and their
product as a function of $k_c$, with $\alpha$ held fixed at 3.0 and $\beta$
held fixed at 1.0. The bottom panel displays the same result using
$\chi^2_{S_{1/2}}$ and $\chi^2_{C_{\ell}}$ on the vertical axis instead of
$P(S_{1/2})$ and $P(C_{\ell})$.
As indicated in Fig.~\ref{fig:pclps12}, introducing suppression in the
primordial power spectrum can increase the likelihood of both the observed
$C_{\ell}$ and the observed $S_{1/2}$, but these two observations favor
suppression at different scales. The likelihood of the $C_{\ell}$ is improved
by at most a factor of
2.2, with the improvement peaking at
$\log_{10}(k_c/(h/\Mpc)) = -3.4$, while greater suppressions can improve the likelihood of the
$S_{1/2}$ data by huge factors of up to 131, peaking around
$\log_{10}(k_c/(h/\Mpc)) = -2.6$ (note the plotting scale of likelihoods in
Fig.~\ref{fig:pclps12}, where individual likelihood curves are divided
or multiplied by 10 for visual clarity). The $C_{\ell}$ measurements
thus favor suppression on very large scales, while the cut-sky
$S_{1/2}$ favor suppression all the way down to relatively small
scales, where suppression is overwhelmingly ruled out by $C_{\ell}$
data. This is another reminder of just how low the pixel-based cut-sky
measurement of $S_{1/2}$ is. It is also a reminder of the fact that
such a low value of $S_{1/2}$ represents a conspiracy of the
low-$\ell$ $C_{\ell}$ values: the WMAP cut-sky data indicate that
$S_{1/2}$ is sufficiently low as to strongly (by factors of over 100
in likelihood) favor suppression of primordial power at scales
corresponding to $k = 10^{-2.6} \approx 0.003\, h/{\rm Mpc}$, even though
the maximum-likelihood $C_{\ell}$ favor suppression only weakly, at
far larger scales, and overwhelmingly reject the possibility of
suppression at the scales favored by the cut-sky $S_{1/2}$. A sky
with such a low $S_{1/2}$ as the WMAP cut sky \textit{ought}
to have $C_{\ell}$'s that are even more suppressed
than the most suppressed model in Fig.~\ref{fig:clvary}. What we see instead
are low-$\ell$ $C_{\ell}$ values that are not so close to zero, but which
instead conspire with one another in just such a manner as to produce an
exceptionally low value of $S_{1/2}$ anyway \cite{wmap12345}.
In any case, we have calculated the product statistic $\mathcal{L}(k_c) = P(S_{1/2})
\times P(C_{\ell})$, or alternatively $\Delta \chi^2_{S_{1/2}} + \Delta \chi^2_{C_{\ell}}$, as a measure of how
well a given suppressed model fits the WMAP data in both $C_{\ell}$
and $C(\theta)$ (the latter via the specific statistic
$S_{1/2}$). Since $C_{\ell}$ and $S_{1/2}$ data favor suppression at
such different scales, there should be a ``sweet spot'' somewhere
between the peak in $P(C_{\ell})$ and the peak in $P(S_{1/2})$, where suppression
is moderately favored by both $C_{\ell}$ and $S_{1/2}$, or heavily
favored by one and still allowed by the other. This is indeed what we
find, as indicated by the red curve in Fig.~\ref{fig:pclps12}. Because
suppression on overly small scales (below $\log_{10}(k_c/(h/\Mpc)) \sim -3.2$) brings
the $C_{\ell}$ data for the suppressed model into severe conflict with
the WMAP $C_{\ell}$'s, the peak of the $\mathcal{L}$ curve occurs
above these scales, even in spite of the huge gains in likelihood that
$P(S_{1/2})$ gives us at much smaller scales, where the gain in $P(S_{1/2})$ is
still substantial and the $C_{\ell}$ data still favor -- or at least
do not heavily disfavor -- suppression. The maximum improvement
possible in $P(S_{1/2}) \times P(C_{\ell})$, relative to the unsuppressed $\Lambda$CDM\;
model, is a factor of 8.7 ($\Delta \chi^2_{S_{1/2}} + \Delta \chi^2_{C_{\ell}} = -4.3$), occurring at
$\log_{10}(k_c/(h/\Mpc)) \approx -3.3$.
The WMAP likelihood code uses a Bayesian (Gibbs sampler) maximum
likelihood method (e.g.\ \cite{Efstathiou2003}) to compute the
fiducial $C_{\ell}$'s at the multipoles $\ell \leq 32$
\cite{Dunkley_wmap5,Larson_wmap7}. We experimented with running the
likelihood code using pseudo-$C_{\ell}$ estimates at low
multipoles\footnote{We did this by turning off the {\tt use\_lowl\_TT}
option in the {\tt test.F90} routine of the WMAP likelihood code,
and also switching off polarization by turning off the {\tt use\_TE}
and {\tt use\_lowl\_pol} options.} and discovered that in this case,
suppression is much \textit{more} heavily favored by the $C_{\ell}$
likelihood than it is in the (presumably more accurate) Gibbs sampler,
or else a similar Maximum Likelihood Estimate (MLE) method. This
result is expected, and holds because the $C_{\ell}$'s that result
from the pseudo-$C_{\ell}$ estimates are lower than those found using
the Gibbs sampler method (see e.g.\ Fig.~15 in \cite{Hinshaw:2006ia}),
and suppression fits them better. In this case we can get $\Delta \chi^2_{C_{\ell}}$ as
low as $-7.6$, corresponding to improvements in $P(C_{\ell})$ by factors of
up to 44 (as opposed to roughly 2 in the best-case scenarios discussed
above).
\section{Future detectability using galaxy surveys}\label{sec:future}
The results of the previous section indicate that suppression of primordial
power on large scales can increase the likelihood of both the observed
$C_{\ell}$ angular power spectrum and the observed cut-sky value of $S_{1/2}$,
provided the suppression ``kicks in'' on appropriate scales. Now we turn to
the question of whether large-scale suppressed power could be detected in the
matter power spectrum as measured by upcoming redshift surveys such as the
Large Synoptic Survey Telescope (LSST; \cite{LSST}). If the zero-correlation
signature of large-angle $C(\theta)$ in the CMB is an authentic effect
indicating a deficit of power on the Universe's largest scales, is it possible
to cross-check and verify this result using large-scale-structure data?
Given suppression of the primordial power spectrum $\Delta_R^2(k)$ as
parameterized in Eq.~(\ref{eqn:suppressionparameterized}), the matter power
spectrum will be suppressed by the same factor as $\Delta_R^2(k)$:
\begin{equation}
P_{\rm sup}(k) = S(k) P_{\rm unsup}(k)
\label{eqn:pksuppressed}
\end{equation}
where $S(k) \equiv S(k; k_c, \alpha, \beta)$ is the same as before. We wish
to determine whether this suppressed matter power spectrum could be
distinguished from the unsuppressed $\Lambda$CDM\; matter power spectrum $P_{\rm
unsup}(k)$ by a large-volume redshift survey.
When measuring the matter power spectrum with a redshift survey, the error
bars in each thin slice in redshift $dz$ and wavenumber $dk$ are given
by the Feldman-Kaiser-Peacock (FKP; \cite{FKP}) formula
\begin{equation}
\sigma_P^2(k,z) = \frac{4 \pi^2 P(k,z)^2}{k^2\, d k\, d V_{\rm eff}}
\label{eqn:errorbars}
\end{equation}
where the effective volume element $dV_{\rm eff}(k,z)$ is related to a
comoving volume element via
\begin{equation}
d V_{\rm eff}(k,z) = \left \lbrack \frac{n(z)P(k,z)}{1+n(z)P(k,z)}
\right \rbrack ^2 dV_{\rm survey}(z).
\label{eqn:Veff}
\end{equation}
The differential survey volume is given in terms of $dz$ via
\begin{equation}
dV_{\rm survey} = \Omega_{\rm survey} \frac{r(z)^2}{H(z)} dz,
\end{equation}
where $r(z)$ is the comoving distance as a function of redshift, $H(z)$ is the
Hubble parameter as a function of redshift, and $\Omega_{\rm survey}$ is the
angular size of the survey in steradians.
The number density of galaxies $n(z)$ can be found from
\begin{equation}
n(z) = m(z) \times \frac{N_{\rm tot}}{\Omega_{\rm survey} \int m(z) [r(z)^2/H(z)] dz}
\label{eqn:nz}
\end{equation}
where the second term on the right-hand side provides a normalization. Here
$N_{\rm tot}$ is the total number of galaxies in the survey and $m(z)$ is the
(unnormalized) number density of galaxies, whose functional form we adopt to
be
\begin{equation}
m(z) = \frac{z^2 e^{-z/z_0}}{2 z_0^3}.
\label{eqn:mz}
\end{equation}
We take $z_0 = 0.35$, corresponding to the density roughly expected in the
imaging portion of the LSST survey \cite{HTBJ}, and assume a 23,000 square
degree redshift survey with $0.5$, $5$ or $50$ spectra per square
arcminute. [Note that the $0.5$ and $5$ gal/arcmin$^2$ cases are realistic,
being targeted by surveys in the near future \cite{BigBoss,Wang_space},
while $50$ gal/arcmin$^2$ corresponds to the more aggressive case where
spectra of most galaxies in the imaging portion of the survey are taken.]
Given a suppressed power spectrum as in Eq.~(\ref{eqn:pksuppressed}),
we can calculate
\begin{eqnarray}
d \chi^2 &\equiv & \frac{\left \lbrack P_{\rm unsup}(k,z) - P_{\rm sup}(k,z)
\right \rbrack ^2}{\sigma_P^2} \\[0.2cm]
& = & \left \lbrack \frac{nP}{1+nP} \right \rbrack ^2
\left \lbrack \frac{\Omega_{\rm survey} k^3}{4 \pi^2 P^2} \right \rbrack
\left \lbrack \frac{r^2}{H} \right \rbrack \nonumber \\[0.2cm]
&&\times \left \lbrack P_{\rm unsup} - P_{\rm sup} \right \rbrack ^2 d(\ln k) dz
\label{eqn:dchi2}
\end{eqnarray}
and then integrate in order to find the $\chi^2$ statistic for how
well the survey can distinguish between the suppressed and
unsuppressed models.
Note that in the above two equations, wherever a $P \equiv P(k,z)$ occurs
without being marked as either suppressed or unsuppressed, this is intended to
indicate that either $P_{\rm sup}$ or $P_{\rm unsup}$ may be used. Whether we
use $P_{\rm sup}$ or $P_{\rm unsup}$ depends entirely on which question we are
trying to answer: If we use suppressed-model error bars, then this $\chi^2
\equiv \chi^2_{\rm sup}$ indicates at what confidence level the survey can
rule out suppression. Meanwhile, if we use unsuppressed-model error bars, then
$\chi^2 \equiv \chi^2_{\rm unsup}$ indicates at what confidence level the
survey can rule out the unsuppressed $\Lambda$CDM\; model. Ruling out $\Lambda$CDM\; is
considerably more ambitious than ruling out suppression, since the error bars
tend to be smaller when they are based on the suppressed model (due to the
fact that $\sigma_P \propto P+1/n$).
\begin{figure}[b]
\begin{center}
\includegraphics[width=.50\textwidth]{fig7.pdf}
\caption{Matter power spectrum $P(k)$ with and without suppression. In
the suppressed model, the parameters are $\log_{10}(k_c/(h/\Mpc)) = -2.85$, $\alpha =
3.0$, and $\beta = 1.0$. The power spectrum is shown at $z=0$ for a
redshift survey with 50 galaxies per square arcminute. The error
bars are based on the suppressed power spectrum, which means that a
sufficiently high $\chi^2$ value here would indicate the possibility
of ruling out suppression. The value of $\chi^2$ turns out to be 57.8,
good enough to rule out suppression at roughly 7.6$\sigma$. (Bins without
vertical error bars contribute nothing to the $\chi^2$ -- in effect,
their error bars are infinite.) Note the log scale on both axes.}
\label{fig:pkvsk}
\end{center}
\end{figure}
\begin{figure}[t]
\begin{center}
\includegraphics[width=.50\textwidth]{fig8.pdf}
\caption{The detectability of suppression as a function of
$k_c$. These results apply to a survey that extends from $z=0$ to
$z=3$ covering 23,000 square degrees of sky. From bottom to top in
each set of lines, we assume 0.5, 5 or 50 (spectroscopic) galaxies
per square arcminute. [Note that the $0.5$ gal/arcmin$^2$ case is
entirely realistic in the near future, corresponding to the number
density of spectra planned by e.g.\ BigBoss \cite{BigBoss}, while
$50$ gal/arcmin$^2$ corresponds to the more aggressive case where
spectra of most galaxies in a large-volume imaging survey are
taken.] Here $\alpha$ is fixed at 3.0 and $\beta$ is fixed at 1.0.}
\label{fig:chisquareresults}
\end{center}
\end{figure}
This is illustrated in Fig.~\ref{fig:pkvsk}. The plot shows the
unsuppressed matter power spectrum, along with the suppressed version
for a particular choice of parameters. The goal of calculating
$\chi^2$ as in Eq.~(\ref{eqn:dchi2}) is to determine whether the
unsuppressed power spectrum can be distinguished from the suppressed
power spectrum for a given set of parameters within the error bars
that would be set by an LSST-like survey. For the case pictured -- in
which the unsuppressed model is taken as true, and the error bars are
calculated based on the suppressed model which is being tested -- it
is possible to rule out suppression with high statistical
significance. The opposite is, however, not true: if the suppressed
model is true, it will be very difficult to rule out the standard
unsuppressed $\Lambda$CDM\; due to its larger errors.
For example, survey measurements that fell along the curve predicted
for the unsuppressed $P(k)$ would, in the case shown in
Fig.~\ref{fig:pkvsk}, fall outside some of the suppressed-model error
bars, and ultimately combine to give a total $\chi^2$ of $57.8$, given
the survey parameters outlined in the next paragraph. Meanwhile,
taking the unsuppressed model as fiducial would allow for the
possibility of survey measurements ruling out $\Lambda$CDM, but the
total $\chi^2$ would shrink to $2.0$ due to the larger error bars.
The final results for the detectability of suppression are shown in
Fig.~\ref{fig:chisquareresults}. Instead of plotting $\chi^2$ we show the
number of sigmas (i.e.\ $\sqrt{\Delta\chi^2}$) at which suppressed and
unsuppressed power spectra can be distinguished assuming one degree of freedom
on the measurements of $P(k)$. The figure shows the results as a function of
$k_c$, holding the parameters $\alpha$ and $\beta$ fixed at 3.0 and 1.0,
respectively, and assuming three different possible values for the number of
galaxies observed per square arcminute ($0.5$, $5$, and $50$) in the
spectroscopic survey. We also examined the results with different values of
$\alpha$ and $\beta$, but changes in these parameters do not greatly affect
the results unless $\beta$ becomes close to zero. The scale
of the suppression as determined by $k_c$ is by far the greatest contributing
factor in determining whether a given suppressed model will be detectable to a
large-volume redshift survey.
Comparison of Fig.~\ref{fig:chisquareresults} with Fig.~\ref{fig:pclps12}
shows that if present data for $C_{\ell}$ and $C(\theta)$ truly point to
suppression of the primordial power spectrum, that suppression is likely on
scales that are too large for foreseeable redshift surveys to either detect or
rule out. The most optimistic scenario shown in
Fig.~\ref{fig:chisquareresults}, in which there are 50 galaxies per square
arcminute in the spectroscopic survey, still cannot (at 3$\sigma$) rule out
suppression if $\log_{10}(k_c/(h/\Mpc)) \lesssim -3.0$,
and cannot rule out $\Lambda$CDM\; unless the Universe actually shows suppression of
the matter power spectrum on much smaller scales, with $\log_{10}(k_c/(h/\Mpc)) \gtrsim -2.7$.
Suppression on scales this small is strongly disfavored by WMAP $C_{\ell}$
observations. Meanwhile, the scales on which WMAP observations tend to favor
suppression ($\log_{10}(k_c/(h/\Mpc)) \sim -3.3$) are nearly inaccessible to galaxy
surveys. This is a reflection of the fact that the CMB probes much larger
scales than even the largest-volume redshift surveys of the near future.
If {\it only} the cut-sky $S_{1/2}$ statistic is taken into account, CMB
observations heavily favor suppression on scales where suppression would be
readily detectable by redshift surveys, at several sigma, for number densities
of galaxies expected in near-future spectroscopic samples.
\section{Conclusions}\label{sec:conclusions}
In this paper we have studied the suppression of primordial power on large
scales as a possible explanation for the CMB observations. Without considering
particular physical models for the suppression, we adopted a more pragmatic
approach and addressed the following question: do the suppressed models
actually improve the likelihood of the observed CMB sky and, if so, can the
upcoming large-volume galaxy redshift surveys be used to confirm this
suppression?
We first motivated our search by attempting to invert the observations of the
angular power spectrum $C_\ell$ in order to reconstruct the three-dimensional
power spectrum $P(k)$. As expected, this procedure is very unreliable and
noisy due to the nature of the inverse problem; nevertheless, we obtained
useful hints for the form of the suppression that we should be considering
(see Fig.~\ref{fig:inverseproblemresult} in the Appendix).
We then proceeded to use a parametric model of the suppression
(Eq.~(\ref{eqn:suppressionparameterized})), with the most important
parameter (and the only one we varied in our analysis) being the
suppression scale $k_c$. We found (see Fig.~\ref{fig:pclps12}) that
the angular power spectrum $C_\ell$, traditionally inferred using
maximum-likelihood-type estimators, prefers a moderate suppression of
power; conversely, the cut-sky pixel-based correlation $C(\theta)$
prefers a stronger suppression. It is also possible that both the
full-sky measurement of $C_\ell$ {\it and} the cut-sky measurement of
$C(\theta)$ are not anomalous, but rather that the underlying
cosmological model is not statistically isotropic. While it is not
clear how to write down the combined likelihood in the full-sky and
cut-sky measurements without assuming statistical isotropy, our simple
choice (Eq.~(\ref{eqn:likelihoods})) prefers the suppression at $\log_{10}(k_c/(h/\Mpc))
\approx -3.3$, and increases the combined likelihood by about a factor
of 8.7, corresponding to $\Delta\chi^2=-4.3$.
Detectability of such a large-scale suppression with future surveys will be
difficult, however, as shown in Fig.~\ref{fig:chisquareresults}. In order to
detect the suppression favored by the CMB angular power spectrum, an LSST-type
survey, with a volume of about 100 Gpc$^3$ and a very large number of galaxy
redshifts measured, will be necessary. Roughly speaking, a statistically
significant ruling-out of the power suppression will require spectra taken of
most galaxies in the imaging portion of the survey; this will require a $\sim
10$-meter ground-based, or a $\sim 1.5$-meter space-based, telescope dedicated
to taking spectra. Alternatively, photometric redshift techniques may someday
become so accurate that our preferred case of ``nearly all galaxies being
spectroscopic'' is validated relatively straightforwardly.
Additionally, we point out that suppressed power will be more easily ruled out
(given that the true power is not suppressed) than vice versa, essentially
because the model being tested has smaller cosmic-variance errors if it has
lower power. Therefore, if indeed we live in the universe with the true power
spectrum of density fluctuations being standard inflationary power-law (i.e.\
unsuppressed), then, for example, a survey covering half the sky with 5 galaxy
redshifts per square arcminute will be able to rule out power suppressions on
scales above roughly 1 Gpc at 3$\sigma$ confidence; suppression extending to
smaller scales is even easier to detect.
Overall, we are optimistic about the prospects of galaxy surveys to
test models of the suppressed large-scale power of primordial
fluctuations. Dark Energy Survey (DES; \cite{des05}), Baryon
Oscillation Spectroscopic Survey (BOSS; \cite{boss}) and, especially,
very-large-volume surveys such as the LSST \cite{LSST}, Joint Dark
Energy Mission (JDEM; \cite{JDEM}), Euclid \cite{Euclid}, and BigBoss
\cite{BigBoss}, will be able to test, at least in part, observations
of CMB experiments on the largest observable scales.
\acknowledgments
We thank Craig Copi, Dominik Schwarz, Glenn Starkman, Roland de Putter,
J\"{o}rg Dietrich, and Andrew Zentner for useful discussions. The authors are
supported by NSF under contract AST-0807564, NASA under contract NNX09AC89G,
and DOE OJI grant under contract DE-FG02-95ER40899.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,224 |
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