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These Monty Python Sketches Are So Rare, John Cleese Doesn't Even Remember Them
A new book delves into the comedy troupe's history.
By Jeff Slate
Adrian Besley © Abrams Books, 2017
"I suppose I'll be able to spend the remaining years of my life reading this over and over again, reminding myself of what a wonderful group of people we were and how we changed civilization," Monty Python's Terry Gilliam jokes to Esquire about the new book, Monty Python's Flying Circus: Hidden Treasures, out this week. "Weren't we funny? Weren't we clever?"
Since disbanding for a final time after the troupe's remarkable run of reunion shows at London's O2 Arena in 2014, surviving Pythons Gilliam, John Cleese, Eric Idle, Terry Jones, and Michael Palin, have been remarkably busy. Cleese and Idle have toured the U.S. sporadically as a duo; Idle released the marvelous What About Dick? and collaborated on a U.K. holiday special with the English physicist Brian Cox called The Entire Universe; Cleese released the first volume of his memoirs to much acclaim. Meanwhile, Gilliam and Palin teamed up on Gilliam's long-gestating Don Quixote film and appeared onstage together in London recently at a charity event, reminiscing about their Python days. Terry Jones, who announced last year that he is suffering from health issues related to dementia, directed Simon Pegg and the late Robin Williams in the film Absolutely Anything, which featured the voices of all the surviving Pythons, and collaborated with his son on a film about the lessons to be learned from the 2008 stock market crash, Boom Bust Boom. The entire troupe even appeared together at the 2015 Tribeca Film Festival to celebrate the 40th anniversary of the film Monty Python and the Holy Grail.
John Cleese Explains Donald Trump\'s Appeal
John Cleese Picks the Funniest Python Sketches
But with a loyal following still driving demand for anything Monty Python, the time seemed right to celebrate their groundbreaking television show, Monty Python's Flying Circus. Hidden Treasures, by author Adrian Besley, tells the story of that show in lavishly illustrated form, with input from all of the surviving Pythons.
"It contains things out of our old drawers and archives," Michael Palin tells Esquire. "Lots of things in envelopes. Eric Idle's in it, John Cleese is in it, Terry Jones is in it, Terry Gilliam is in it, and yes, even Michael Palin's in it."
Terry Gilliam's cartoon representation of the famous Gumby, who first appeared in Series One, Episode Five.
"And it contains brilliant artwork by a young Terry Gilliam," Gilliam adds, not to be outdone.
In fact, the book includes a plethora of removable facsimiles of rare memorabilia from the troupe's official archives, including hand-scribbled scripts, cue sheets, character lists and posters featuring Gilliam's pioneering animations. The Pythons were also actively involved in writing the book, which recounts the often-fraught making of their TV show in brisk, easily digestible, illustrated form, going back as far as their early days as members of the Cambridge Footlights, pre-Python work as writers for the BBC, and on to their collective brush with global stardom, feature films, inevitable fights and, finally, their 2014 reunion.
"Yes, it even contains the brilliantly designed poster for the Pythons' last stand at the O2 in 2014, when we were all together, all in one piece, all of our bits working properly, unlike now when most of our time is spent lying down in the middle of the day," Gilliam says of his artwork which promoted the record-setting London shows.
"It's wonderful, because it contains scripts of sketches that may or may not have been seen," John Cleese says of the book, which breaks down classic sketches as well as a handful of sketches that were abandoned along the way. "There's lots and lots of stuff in the book, and the surprising thing is how little of it I remember, honestly."
Terry Jones and Eric Idle performing the
"And everyone's done a silly forward, which is lovely," Cleese adds. "Python fans will love it. Everyone else will be bored stiff, of course."
One of the things Cleese seemed particularly pleased with are the QR codes included that, if you scan them with your smartphone, take you immediately to the Monty Python YouTube channel, where readers can see the corresponding sketch that's illustrated in the book.
As for the enduring appeal of Monty Python's Flying Circus, Cleese, of course, has a theory: "It's always surprising to me how many people in America come up to me and say they used to watch Monty Python because it was the only place you could get to see boobs," he says, chuckling.
Jeff Slate Jeff Slate is a New York City-based songwriter and journalist who has contributed music and culture articles to Esquire since 2013.
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Pierce: Sarah Palin Stands Up for Christmas
John Cleese Explains Donald Trump's Appeal
Dick Cavett Remembers Meeting John Lennon
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{
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We are very pleased to inform you that the problems relating to the AV equipment in Chemistry Lecture Theatre 2 have now been resolved. The TEL & AV Team have carried out work to ensure that the projector can be controlled as normal from the control panel and the issues relating to audio have been resolved with both the handheld microphone and the lapel microphone now fully functional. We would like to thank Timetabling for making adjustments to the teaching schedule in order to free up the room so that we were able to carry out this work.
The solution that has been provided in Chemistry LT2 means you cannot show 2 different inputs on the projectors, only one input will be shown on both screens. If two inputs are required on different screens please let us know either by adding a comment or sending an email to it@reading.ac.uk so that when the room is refurbished we can ensure this feature is reinstated.
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{
"redpajama_set_name": "RedPajamaC4"
}
| 6,593
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Q: Why my DEFAULT_DICT still change despite I use dict(DEFAULT_DICT) to init other dict? I want to have a python dictionary that never change.
In the following code, I was hoping that DEFAULT_DICT would not be changed :
DEFAULT_DICT = {
'history':{
'id':[]
}
}
my_dict = dict(DEFAULT_DICT)
print("my_dict is {}".format(my_dict))
print("DEFAULT_DICT is {}".format(DEFAULT_DICT))
my_dict['history']['id'].append("toto")
print("my_dict is {}".format(my_dict))
print("DEFAULT_DICT is {}".format(DEFAULT_DICT))
Can someone can tell me why DEFAULT_DICT is changing according to my_dict ?
I was thinking that use
my_dict = dict(DEFAULT_DICT)
will correction the problem but not.
A: The problem that when you wrote my_dict = dict(DEFAULT_DICT) shallow copy of DEFAULT_DICT was created, but you need a deep copy of this object.
To solve your problem you can use deepcopy function from copy module:
from copy import deepcopy
DEFAULT_DICT = {
'history': {
'id': []
}
}
my_dict = deepcopy(DEFAULT_DICT)
print("my_dict is {}".format(my_dict))
print("DEFAULT_DICT is {}".format(DEFAULT_DICT))
my_dict['history']['id'].append("toto")
print("my_dict is {}".format(my_dict))
print("DEFAULT_DICT is {}".format(DEFAULT_DICT))
For more information about shallow and deep copy follow this link.
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,133
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Q: ASP.Net file upload causing post back in update panel using triggers I have file upload control to upload the profile picture using update panel. I have used AsyncPostBackTrigger with update panel but still the page is causing full postback.
Below is my code inline.
<asp:UpdatePanel ID="pnlZerkerBasicProfile" runat="server">
<input type="file" id="myFile" name="myFile" class="file_input_hidden" onchange="javascript:FileUploadSubmit();" style="cursor: pointer;" />
<Triggers>
<asp:AsyncPostBackTrigger ControlID="btnSaveProfilePicture" />
</Triggers>
Can anyone help?
A: change the trigger t a postback trigger since file upload is not available in Request.Form.AllKeys when async postback occurs via update panel. See this:
http://www.codeproject.com/Articles/16945/Simple-AJAX-File-Upload
A: This should work
<asp:ScriptManager ID="ScriptManager1" runat="server" EnablePartialRendering="true" />
<div>
<asp:UpdatePanel ID="UpdatePanel1" runat="server" UpdateMode="conditional">
<Triggers>
<asp:PostBackTrigger ControlID="Button1" />
</Triggers>
<ContentTemplate>
<asp:FileUpload ID="FileUpload1" runat="server" />
<asp:Button ID="Button1" runat="server"Text="Upload" OnClick="Button1_Click" />
</ContentTemplate>
</asp:UpdatePanel>
</div>
A: This code should work. It will not cause postback.
<asp:UpdatePanel ID="pnlZerkerBasicProfile" runat="server">
<ContentTemplate>
<input type="file" id="myFile" name="myFile" class="file_input_hidden"
onchange="javascript:FileUploadSubmit();" style="cursor: pointer;" />
<asp:Button ID="btnSaveProfilePicture" runat="server"Text="Upload"
OnClick="btnSaveProfilePicture_Click" />
</ContentTemplate>
<Triggers>
<asp:PostBackTrigger ControlID="btnSaveProfilePicture" />
</Triggers>
</asp:UpdatePanel>
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 367
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Donut News
And The Winner of The Best Donut in St. Louis is…
by Andrew Corns
published in Rethink Essentials
After months of intense (and sugar-filled) research across every inch of St. Louis, Office Essentials is proud to announce the winner of our first-ever Essential Doughnut for the Workplace Award: Old Town Donuts!
Old Town Donuts has been a landmark location in the North County area for over 50 years and has fed three generations of St. Louis natives. Tim Cronin, a member of the Office Essentials sales force, has been an avid customer at Old Town for over 20 years and still gets a nostalgic feeling every time he walks in and remembers taking his daughter (now 21) to get her favorite chocolate Long John and strawberry milk. Tim's is just one of countless stories by members of the community that reinforce why Old Town Donuts is a very deserving winner of this prestigious honor.
When you go, don't be surprised to get a warm welcome from the owner, Keith Took, as you walk in the doors and gaze in awe at the myriad options in the counter window. Keith and his family love what they do and it's a testament to their craft when you see the wall behind the cash register adorned with dozens of plaques and awards. Old Town Donuts is unique to other shops in the area because they are open 24/7 (Florissant location) and have been an ideal destination for college students to come in, grab a donut & coffee and get some studying or homework done. Being open all day, every day also means Keith and his staff have to work around the clock to maintain fresh donuts, and they have that down to a science at this point. Inevitably though, there are donuts that don't sell through and instead of just discarding them, Keith donates them to several organizations in North County which further strengthens their deep community ties.
Whether you're having a meeting with a client or looking to get a couple of dozen donuts to show your appreciation to your coworkers, you can't get a better donut than the ones at either of Old Town's 2 area locations in Florissant and Cottleville. So go pay them a visit and load up on a mixture of classics or something more adventurous like a bacon-topped donut, one of their daily specials, or their signature gooey butter cake donut.
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,111
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Workers are configured by setting properties in the worker configuration. The common configuration options handled by the framework apply to all workers. In addition, there are worker specific properties, handled by the worker implementation.
Properties considered sensitive (currently PIN, KEYSTOREPASSWORD, and KEYDATA) are masked when displayed in the Administration GUI, configuration dumps (value replaced by the string _MASKED_), and in configuration change notifications in the Audit log.
You can comment out properties to temporarily disable them by adding a pre- or postfix underscore.
Commenting out masked sensitive properties will still protect the properties and mask them in the cases described above, see Sensitive Properties.
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{
"redpajama_set_name": "RedPajamaC4"
}
| 4,087
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{"url":"http:\/\/www.bernhardlearns.com\/2017\/04\/webscraping-with-r-and-rvest-how-can-i.html","text":"# Motivation\n\nI love the internet - all this information only a fingertip away. Unfortunately, most information is provided in unstructured text. Ready-made tabular data, as needed for most analytic purposes, is a rare exception.\nE.g., I enjoy reading Haiku and DailyHaiku hooks me up with my daily dosage. They even have a huge archive with all previously published Haiku. What interests me is which percentage of Haiku is in the traditional form: 5-7-5 syllables.\nNote: Haiku is a Japanese poem form and Japanese syllables are longer than their English siblings. Hence, many believe 17 English syllables are too verbose and aim at something around 11 syllables instead. These shorter Haiku are called free form Haiku.\nCounting one by one would take ages and isn\u2019t very reproducible. So this is a good job for web scraping. I.e., automated extraction of information from a website. This could be done in various environments and programming languages. For this example I am using R, because it allows for a wide range of consecutive NLP-analyses without having to implement them myself (Python would be a good alternative as well).\n\n# Preparations\n\nGet the needed R packages\nlibrary(tidyverse) # because I love tidy data and %>%\nlibrary(rvest) # for the actual webscraping\nlibrary(lubridate) # for date handling\nlibrary(stringr) # for working with strings\nSave URL of first page as a string\nstart_page <- \"http:\/\/www.dailyhaiku.org\/haiku\/\"\n\n# Step by Step\n\n## Get the CSS-selector\/XPath\n\nFrom the webpage we only want to extract the Haiku and the link to the previous archive page, so we need some way to identify these elements. The browser add-on SelectorGadget comes in handy for this task. By pointing and clicking it extracts the CSS-selector and the XPath of the selected object(s), which represent ways to address elements within a html document.\nFigure 1: Selection of the Haiku blocks\nWe see in Figure 1 that the first Haiku block, that is the one I\u2019ve clicked on, is highlighted in green. The others are highlighted in yellow, which means that they will be selected as well. If we don\u2019t want that, we can click on one of them. This would update the selection with the others removed. In the present case, however, the default behavior is exactly what we want. In the bottom we see the CSS-selector for the Haiku Blocks (if we prefer XPath we can change the address format). Let\u2019s store it for later use.\ncss_haiku <- c(\".haiku-archive-list\")\nNext we need the link for previous Haiku.\nFigure 2: Selection of the link to previous Haiku\nThis time the first click selected several links (e.g., to the authors), so I had to deselect them as indicated by the red highlight (see Fig. 2). Let\u2019s store the resulting CSS-selector.\ncss_link <- c(\".prev-next a\")\n\n## Extract the Information\n\nNow that we have the CSS-selectors we can try to extract their corresponding information from the webpage. Let\u2019s start by downloading the first page of the archive.\n\n### Extract Haiku Information\n\nfirst_page <- read_html(start_page)\nFrom the page we can extract the Haiku blocks.\nblocks <- first_page %>% html_nodes(css_haiku)\nA look into the first block shows us that it contains three elements. Their class names are - date - haiku - author\nwhich can be used as CSS-selectors.\n# peek into the first block\nblocks[[1]]\n#> {xml_node}\n#> <div class=\"haiku-archive-list\">\n#> [1] <h3 class=\"date\"><a href=\"http:\/\/www.dailyhaiku.org\/haiku\/2016-march ...\n#> [2] <p class=\"haiku\">balmy breeze<br>\\r\\nswarming bees circle<br>\\r\\nthe ...\n#> [3] <p class=\"author\"><a href=\"\/contributors\/Cycle-20-October-2015-to-Ma ...\nLet\u2019s create a functions that extract those information from a block.\nBeginning with date.\nextract_haiku_date <- function(block) {\n# test whether OS is Windows\nwindows <- Sys.info()[\"sysname\"] == \"Windows\"\n\n# test whether you have an English locale-setting\nloc <- sessionInfo()[[\"locale\"]]\nis_english <- str_detect(loc, \"LC_TIME=English\")\n\n# extract date with english locale\nif (is_english) {\ndate <- block %>% html_node(\".date\") %>% xml_text() %>% mdy()\n} else if (windows) {\ndate <- block %>% html_node(\".date\") %>% xml_text() %>% mdy(locale = \"English_United States.1252\")\n} else {\ndate <- block %>% html_node(\".date\") %>% xml_text() %>% mdy(locale = \"en_US.utf8\")\n}\n\nreturn(date)\n}\nNext, a function to extract the text.\nextract_haiku_text <- function(block) {\nblock %>% html_node(\".haiku\") %>% xml_text()\n}\nNext, a function to extract the author\u2019s name.\nextract_haiku_author <- function(block) {\nblock %>% html_node(\".author\") %>% xml_text()\n}\nFinally, put them all together.\nextract_haiku <- function(block) {\nlist(date = extract_haiku_date(block), text = extract_haiku_text(block),\nauthor = extract_haiku_author(block))\n}\nNow, try it on the whole block-set.\nblock_info <- blocks %>% map(extract_haiku) %>% map_df(~as.list(.))\n\nknitr::kable(block_info, format = \"html\", booktabs = TRUE)\ndate text author\n2016-03-26 balmy breeze swarming bees circle the river bank Polona Oblak\n2016-03-25 whitecaps on the bay the overhead cries of migrating birds Polona Oblak\n2016-03-24 deep within the lettuce a slug shaped hole Polona Oblak\n2016-03-23 siskins\u2019 trill sunlight floods the bare larch Polona Oblak\n2016-03-22 drifting fog an acquaintance i\u2019d rather not meet Polona Oblak\n2016-03-21 ferry harbour customs area swifts dart through the heat Polona Oblak\n2016-03-20 frost lingers i clean brussels sprouts in the kitchen sink Polona Oblak\n\nThat looks good! If you look at block_info in an unformatted table you might notice several \u201c\\r\\n\u201d in the text - those are line breaks. Depending on the task at hand we might need to remove them. For the time being I just leave them untouched.\n\n# Get all Haiku in the Archive\n\nWe build a little wrapper to parse all pages. Go get yourself a coffee after you start this chunk of code - it will take a while. By reducing or removing the Sys.sleep you can speed up things, but on the downside, this might get you banned. Furthermore, IMHO it is common courtesy not to hog the server all for yourself. Alternatively, you can download the result here. After downloading the file into your working directory, just type load(\"haiku.Rdata\") in your R-console.\n# run only if haiku data is not already present\nif (!file.exists(\"haiku.RData\")) {\npage_url <- start_page\n\nhaiku_list <- list()\ncounter <- 0\n\nwhile (page_url != \"stop\") {\ncounter <- counter + 1\n\nhaiku_list[[counter]] <- page %>% html_nodes(css_haiku) %>% map(extract_haiku) %>%\nmap_df(~as.list(.))\n\n# little break between page calls to avoid getting banned\nSys.sleep(5)\n\n# get the next page's url\nif (length(older_nr) == 0) {\npage_url <- \"stop\"\n} else {\n}\n\n}\n# combine list\nhaiku <- bind_rows(haiku_list)\n\n# save for later use\nsave(haiku, file = \"haiku.RData\")\n\n} else load(\"haiku.RData\")\nNote: If you are downloading larger amounts of data, then it might be a good idea to save regularly to your disk. Otherwise you have to start anew everytime there is a problem with your internet connection.\nTo check how many Haiku we got overall, we can look at the number of rows in the resulting data-frame.\nn <- nrow(haiku)\nn\n#> [1] 3633\nWow - so there were 3633 Haiku in the archive. That is more than I was expecting. But how many of them are in the traditional style? To classify the Haiku we need to count the number of syllables. 17 means classical, fewer means free form. For the syllable counting - a non-trivial task - we make use of the syllable package.\nhaiku <- haiku %>% mutate(syllables = syllable::compute_syllable_counts(text))\nLet\u2019s take a look at the distribution of syllable count per Haiku.\nhaiku %>% ggplot(aes(x = syllables)) + geom_histogram(color = \"black\", fill = \"white\")\n\nThis result was somewhat unexpected. Some entries are too short (I would consider 2 + 3 + 2 = 7 as the lower bound even for the free form) and some are too long (as mentioned earlier the long traditional form has 17 syllables). So what happened?\nFor the short ones multiple explanations are possible: 1. something went wrong in the web scraping 2. errors on the website 3. the entries are not Haiku 4. errors in the syllables counting 5. digits and special characters were used as words (and were not recognized for syllables counting) 6. something else\nBest we take a quick look at the shorter entries.\nhaiku %>% filter(syllables < 6) %>% knitr::kable(format = \"html\", booktabs = TRUE)\ndate text author syllables\n2015-05-23 t h e\u00a0\u00a0\u00a0 puck\u00a0\u00a0 !@#\u00a0\u00a0\u00a0 \\$%&\n*+\u201c?\u00a0\u00a0\u00a0 drops\nLeRoy Gorman 3\n2015-05-22 snowinterubric LeRoy Gorman 5\n2013-06-12 goinggoinggoinggon\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0e Alan S. Bridges 4\n2013-04-12 starving the darkness LeRoy Gorman 5\n2012-03-17 full bloom, full stop! Rafal Zabratynski 4\n2012-01-31 ki\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3\u2026 2\u2026 1\u2026 2012! \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ss Rafal Zabratynski 1\n2009-04-08 pond frogs\u00a0\u00a0\u00a0\u00a0\u00a0moon bats George Swede 4\n2008-12-30 the\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 smell \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0of snow Carol Pearce-Worthington 4\n2007-02-04 Just Sitting Around Bryak Webster 5\n\nWell, I\u2019m all but an expert and I\u2019m happy to be convinced otherwise, but the entries don\u2019t seem like Haiku to me.\nThe potential errors for the too long entries are similar. Best to check them anyways.\nhaiku %>% filter(syllables >= 20) %>% head() %>% knitr::kable(format = \"html\",\nbooktabs = TRUE)\ndate text author syllables\n2016-03-03 another glass of champagne\u2014 remembering what i choose to remember Sondra J. Byrnes 20\n2014-11-15 ice in the driveway she slips into something more comfortable kjmunro 20\n2014-01-08 altocumulus undulating above the town the chime of church bells J. Zimmerman 20\n2013-06-11 shuttle-bus-driver our daily conversation about the lottery numbers Alan S. Bridges 20\n2011-12-21 Dear Malvina,It\u2019s been a long time since we It\u2019s already autumn here . . . lonely evening Rafal Zabratynski 27\n2009-08-12 gallery opening the couple in the lobby kissing artistically Megan Arkenberg 20\n\nWell, for my taste they are too long. For the given task I will exclude both the extremely short and those with more than 17 syllables.\nNote: This is real world data and messy and irregular for that. Some kind of clean up is necessary in the most scenarios. In this case I just remove the irregularities, but in other scenarios a different approach might be preferable. E.g. If the too short Haiku were just too short because of the usage of digits instead of written out numbers, then replacing those digits by proper words might be a better choice.\nhaiku_clean <- haiku %>% filter(syllables >= 7) %>% filter(syllables <= 17)\nNext, we identify those in the traditional form.\nhaiku_clean <- haiku_clean %>% mutate(form = ifelse(syllables == 17, \"traditional\",\n\"free\"))\nFinally, we can try to answer the question: \u201cWhich percentage of Haiku is written in the traditional form?\u201d\nhaiku_clean %>% group_by(form) %>% summarise(n = n()) %>% mutate(percentage = n\/sum(n) *\n100)\n#> # A tibble: 2 \u00d7 3\n#> form n percentage\n#> <chr> <int> <dbl>\n#> 1 free 3041 94.294574\n#> 2 traditional 184 5.705426\nOnly 5.7% of the Haiku on DailyHaiku comply with the traditional form. Obviously, the contributors appreciate the English free form Haiku more.\n\n# Closing Remarks\n\nOf course this was only a first peek into web scrapping, but I hope it helps you start building your own solution. If you want to dive deeper into web scrapping:\nIf something is not working as outlined here, please check the package versions you are using. The system I have used was:\nsessionInfo()\n#> R version 3.3.2 (2016-10-31)\n#> Platform: x86_64-w64-mingw32\/x64 (64-bit)\n#> Running under: Windows 7 x64 (build 7601) Service Pack 1\n#>\n#> locale:\n#> [1] LC_COLLATE=German_Austria.1252 LC_CTYPE=German_Austria.1252\n#> [3] LC_MONETARY=German_Austria.1252 LC_NUMERIC=C\n#> [5] LC_TIME=German_Austria.1252\n#>\n#> attached base packages:\n#> [1] stats graphics grDevices utils datasets methods base\n#>\n#> other attached packages:\n#> [1] stringr_1.2.0 lubridate_1.6.0 rvest_0.3.2 xml2_1.1.1\n#> [5] dplyr_0.5.0 purrr_0.2.2 readr_1.1.0 tidyr_0.6.1\n#> [9] tibble_1.2 ggplot2_2.2.1 tidyverse_1.1.1\n#>\n#> loaded via a namespace (and not attached):\n#> [1] Rcpp_0.12.9 formatR_1.4 highr_0.6 plyr_1.8.4\n#> [5] forcats_0.2.0 tools_3.3.2 digest_0.6.12 jsonlite_1.2\n#> [9] evaluate_0.10 nlme_3.1-131 gtable_0.2.0 lattice_0.20-34\n#> [13] psych_1.6.12 DBI_0.5-1 yaml_2.1.14 parallel_3.3.2\n#> [17] haven_1.0.0 httr_1.2.1 knitr_1.15.1 hms_0.3\n#> [21] rprojroot_1.2 grid_3.3.2 R6_2.2.0 readxl_0.1.1\n#> [25] foreign_0.8-67 rmarkdown_1.4 modelr_0.1.0 reshape2_1.4.2\n#> [29] magrittr_1.5 codetools_0.2-15 backports_1.0.5 scales_0.4.1\n#> [33] htmltools_0.3.5 assertthat_0.1 mnormt_1.5-5 colorspace_1.3-2\n#> [37] stringi_1.1.2 lazyeval_0.2.0 munsell_0.4.3 broom_0.4.2\n\n1. That was a great deal of information. In respect to the same, is it possible to extract information based on a selected author from the dropdown (without having to extracting all archived data then sub-setting it by author)\n\n1. Sure - you just have to adjust the URL. Make your selection, look at the new address, and change your start url accordingly.\n\n2. That was quick reply. Actually I got stuck there. Trying to change the selection does not change the url. The url remains the same but the data changes. In addition, the selection field is not within a form that could have allowed the use of rvest::html_form(). I think the solution will lie in within the html_session() context but there is not guide in that\n\n1. Hm.. That's strange. When I select the first author in the list the url changes to http:\/\/www.dailyhaiku.org\/?s=haiku&c=Aaron-Marko\n\nThe parameter c=Name-Surname seems to me what you are looking for\n\n3. Sorry i realized i was trying to apply the functions to the url \"https:\/\/tradingeconomics.com\/\" instead of the url you applied, though with correct parameters\n\n4. Thank you so much for this nice information. Hope so many people will get aware of this and useful as well. And please keep update like this.\n\nteX-ai\n\nSentiment Analysis Tool\n\n## Recommended Post\n\n### Follow the white robot - Exploring retweets of Austrian politicians with Botometer in R\n\nbotometer_publish.utf8.md Hi folks! I guess you are aware that social medi...","date":"2020-04-01 11:46:07","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.20747144520282745, \"perplexity\": 8077.576139018252}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585370505730.14\/warc\/CC-MAIN-20200401100029-20200401130029-00362.warc.gz\"}"}
| null | null |
license: Licensed to the Apache Software Foundation (ASF) under one
or more contributor license agreements. See the NOTICE file
distributed with this work for additional information
regarding copyright ownership. The ASF licenses this file
to you under the Apache License, Version 2.0 (the
"License"); you may not use this file except in compliance
with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing,
software distributed under the License is distributed on an
"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
KIND, either express or implied. See the License for the
specific language governing permissions and limitations
under the License.
---
Coordinates
===========
位置情報で使用される座標を格納します。
プロパティ
----------
* __latitude__: 緯度を数値を表します _(Number)_
* __longitude__: 経度を数値で表します _(Number)_
* __altitude__: 海抜からの高度を表します _(Number)_
* __accuracy__: 位置の精度をメートル単位で表します_(Number)_
* __altitudeAccuracy__: 高度の精度をメートル単位で表します _(Number)_
* __heading__: 北から時計回りに図ったときのデバイスの方位を角度(数値)で表します _(Number)_
* __speed__: 現在のデバイスのスピードをメートル/秒で表します _(Number)_
概要
-----------
`Coordinates` オブジェクトは `Position` オブジェクトのプロパティとして作成されます。
`Position` オブジェクトはコールバック関数を通してユーザーに渡されます。
サポートされているプラットフォーム
-------------------
- Android
- BlackBerry (OS 4.6)
- BlackBerry WebWorks (OS 5.0 以上)
- iPhone
使用例
-------------
// 成功時のコールバック
//
var onSuccess = function(position) {
alert('緯度: ' + position.coords.latitude + '\n' +
'経度: ' + position.coords.longitude + '\n' +
'高度: ' + position.coords.altitude + '\n' +
'位置精度: ' + position.coords.accuracy + '\n' +
'高度精度: ' + position.coords.altitudeAccuracy + '\n' +
'方位: ' + position.coords.heading + '\n' +
'速度: ' + position.coords.speed + '\n' +
'タイムスタンプ: ' + new Date(position.timestamp) + '\n');
};
// 失敗時のコールバック
//
var onError = function() {
alert('エラーが発生しました。');
};
navigator.geolocation.getCurrentPosition(onSuccess, onError);
詳細な使用例
------------
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
"http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<title>Geolocation Position の例</title>
<script type="text/javascript" charset="utf-8" src="phonegap.0.9.5.js"></script>
<script type="text/javascript" charset="utf-8">
// イベントをセットし、PhoneGapの読み込みを待機
//
function onLoad() {
document.addEventListener("deviceready", onDeviceReady, false);
}
// PhoneGap準備完了
//
function onDeviceReady() {
navigator.geolocation.getCurrentPosition(onSuccess, onError);
}
// `Position` プロパティーを表示
//
function onSuccess(position) {
var div = document.getElementById('myDiv');
div.innerHTML = '緯度: ' + position.coords.latitude + '<br/>' +
'経度: ' + position.coords.longitude + '<br/>' +
'高度: ' + position.coords.altitude + '<br/>' +
'位置精度: ' + position.coords.accuracy + '<br/>' +
'高度精度: ' + position.coords.altitudeAccuracy + '<br/>' +
'方位: ' + position.coords.heading + '<br/>' +
'速度: ' + position.coords.speed + '<br/>';
}
// 問題発生時に警告を表示
//
function onError() {
alert('エラーが発生しました。');
}
</script>
</head>
<body onload="onLoad()">
<div id="myDiv"></div>
</body>
</html>
Android に関する注意点
-------------
__altitudeAccuracy:__ このプロパティはAndroidではサポートされておらず、常にnullを返します。
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,246
|
{"url":"http:\/\/elib.mi.sanu.ac.rs\/pages\/browse_issue.php?db=mm&rbr=22","text":"eLibrary of Mathematical Instituteof the Serbian Academy of Sciences and Arts\n > Home \/ All Journals \/ Journal \/\n\n Mathematica MoravicaPublisher: Faculty of Technical Sciences \u010ca\u010dak, University of Kragujevac, \u010ca\u010dakISSN: 1450-5932Issue: 16_2Date: 2012Journal Homepage\n\n Hybrid Pairs of Mappings with Some Weaker Conditions in Consideration of Common Fixed Point on 2-Metric Spaces 1 - 12 Bhavana Deshpande and Rohit Pathak\nAbstractKeywords:\u00a0Coincidence point; common fixed point; compatible maps; weak commutativity of type (KB)MSC:\u00a054H25 47H10DOI:\u00a010.5937\/MatMor1202001D\n Second-order method for Parabolic Volterra Integral Equations with Crank-Nicolson Method 13 - 20 Ali Filiz\nAbstractKeywords:\u00a0Parabolic Volterra integro-differential(integral) equation; Crank-Nicolson (CN) scheme; mixed rule; quadrature ruleMSC:\u00a065M06 45D05DOI:\u00a010.5937\/MatMor1202013F\n On ACVF of a Regime Switching AR(1) Process 21 - 24 Reza Habibi\nAbstractKeywords:\u00a0Auto-covariance function; Auto-regressive model; Markov chain; Non-stationary process; Regime switchingMSC:\u00a062G20; 62F20DOI:\u00a010.5937\/MatMor1202021H\n Fixed Point for Completely Norm Space and Map $T_{\\alpha}$ 25 - 35 S.A.M. Mohsenalhosseini and H. Mazaheri\nAbstractKeywords:\u00a0Fixed point; Completely norm space; Convex norm spaceMSC:\u00a054H25 54E50; 54E99; 68Q55DOI:\u00a010.5937\/MatMor1202025M\n Fixed Point Theorems for Monotone Mappings on Partial D*\u0003-metric Spaces 37 - 52 N. Shobkolaei, Shaban Sedghi, S.M. Vaezpour and K.P.R. Rao\nAbstractKeywords:\u00a0Fixed point; partial metricMSC:\u00a054H25 47H10DOI:\u00a010.5937\/MatMor1202037S\n A Remark on One Iterative Process for Finding the Roots of Equations 53 - 57 Dragomir Simeunovi\u0107\nAbstractKeywords:\u00a0Iteration formulas; approximate solutions of equationsMSC:\u00a065H05DOI:\u00a010.5937\/MatMor1202053S\n On the Location of Zeros of Some Polynomials 59 - 61 Dragomir Simeunovi\u0107\nAbstractKeywords:\u00a0Zeros of the polynomials; region of zerosMSC:\u00a012D10DOI:\u00a010.5937\/MatMor1202059S\n Acceleration of Convergence of One Iterative Method for Finding the Roots of Equations 63 - 68 Dragomir Simeunovi\u0107\nAbstractKeywords:\u00a0Iteration formulas; approximate solutions of equationsMSC:\u00a065H05DOI:\u00a010.5937\/MatMor1202063S\n Some Fixed Point Theorems for Certain Contractive Mappings on Metric and Generalized Metric Spaces 69 - 77 Amit Singh, M.S. Khan and Brian Fisher\nAbstractKeywords:\u00a0Fixed point; contractive mapping; sequently convergent; subsequently convergentMSC:\u00a054H25 47H10DOI:\u00a010.5937\/MatMor1202069S\n General System of Nonconvex Variational Inequalities and Parallel Projection Method 79 - 87 Balwant Singh Thakur and Suja Varghese\nAbstractKeywords:\u00a0System of nonconvex general variational inequality; fixed point problem; parallel algorithm; proximal normal cone; relaxed cocoercive mappingMSC:\u00a047J20 65K10; 65K15; 90C33DOI:\u00a010.5937\/MatMor1202079T\nArticle page: 12>>\n\n Remote Address: 34.204.179.0 \u2022 Server: elib.mi.sanu.ac.rsHTTP User Agent: CCBot\/2.0 (https:\/\/commoncrawl.org\/faq\/)","date":"2019-08-18 03:03:21","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\": 0.515082061290741, \"perplexity\": 6272.236026795609}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-35\/segments\/1566027313589.19\/warc\/CC-MAIN-20190818022816-20190818044816-00434.warc.gz\"}"}
| null | null |
{"url":"https:\/\/www.gradesaver.com\/textbooks\/science\/physics\/essential-university-physics-volume-1-3rd-edition\/chapter-7-exercises-and-problems-page-126\/36","text":"# Chapter 7 - Exercises and Problems - Page 126: 36\n\n#### Work Step by Step\n\n(a) We know that $U=-\\int Fdx$ $U=-\\int (\\frac{A}{x^2})dx$ $U=\\frac{A}{x}$ Thus, the potential energy difference is: $\\Delta U=\\frac{A}{x_2}-\\frac{A}{x_1}$ (b) The potential energy difference is given as $\\Delta U=\\frac{A}{\\infty}-\\frac{A}{x_1}=-\\frac{A}{x_1}$\n\nAfter you claim an answer you\u2019ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide\u00a0feedback.","date":"2018-10-22 05:15:05","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.5033700466156006, \"perplexity\": 708.1881864024872}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 5, \"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-2018-43\/segments\/1539583514708.24\/warc\/CC-MAIN-20181022050544-20181022072044-00014.warc.gz\"}"}
| null | null |
Q: PyQGIS problem with QgsRasterCalculator CRS definition from qgis.analysis import QgsRasterCalculator, QgsRasterCalculatorEntry import processing
from osgeo import osr, gdal from gdalconst import *
dataset1 = gdal.Open(input1, GA_Update) band1 = dataset1.GetRasterBand(1) dataset1.SetProjection( srs.ExportToWkt() ) dataset1 = None
layer1=QgsRasterLayer(dataset1,'test1')
#layer1.setCrs( QgsCoordinateReferenceSystem(3003, QgsCoordinateReferenceSystem.EpsgCrsId) )
print('load first layer')
input2='D:\\ascii2grids\\dati_ascii\\PR_2018091500UTCplus1.txt'
dataset2 = gdal.Open(input2, GA_Update) band2 = dataset2.GetRasterBand(1) dataset2.SetProjection( srs.ExportToWkt() ) dataset2 = None
layer2=QgsRasterLayer(dataset2,'test2')
print('load II layer')
exp = "%s - %s" % (layer1,layer2)
output='C:\\Users\\assis\\test.tif'
entries=[layer1,layer2]
calc = QgsRasterCalculator(exp,
output,
'GTiff',
layer1.extent,
QgsCoordinateReferenceSystem("EPSG:3003"),
layer1.width,
layer1.height,
entries
)
res = calc.processCalculation(feedback) if res == QgsRasterCalculator.ParserError:
raise QgsProcessingException(self.tr("Error parsing formula"))
This pyqgis script give me the following error:
Traceback (most recent call last): File "C:\OSGEO4~1\apps\Python37\lib\code.py", line 90, in runcode
exec(code, self.locals) File "<input>", line 1, in <module> File "<string>", line 57, in <module> TypeError: QgsRasterCalculator(): arguments did not match any overloaded call: overload 1: argument 4 has unexpected type 'builtin_function_or_method' overload 2: argument 4 has unexpected type 'builtin_function_or_method' overload 3: argument 1 has unexpected type 'str'
I do not understand the error. Perhaps the CRS definition in the QgsRasterCalculator function. Unfortunately I do not find any example of how to define CRS
A: You're specifying the function instead of calling it. I.e.
layer1.extent
should be:
layer1.extent()
Do this with width and height:
calc = QgsRasterCalculator(exp,
output,
'GTiff',
layer1.extent(),
QgsCoordinateReferenceSystem("EPSG:3003"),
layer1.width(),
layer1.height(),
entries
)
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,879
|
BioteQ's China Plant Ramps Up Production Ahead of Schedule Dexing Plant Now Operating at Maximum Capacity
VANCOUVER, B.C.– BioteQ Environmental Technologies, Inc. (TSX: BQE), a leader in the treatment of industrial waste water, announced today that its Dexing operation in China is operating at maximum design capacity, achieving this milestone well ahead of schedule.
The Dexing operation is BioteQ's largest water treatment plant, operating at one of the world's largest copper mine sites. The plant has been designed to recover 3.6 million pounds of copper per year, treating 1,000 cubic meters of water per hour. In early May, the plant reached the maximum design capacity, recovering almost 11,000 pounds of copper per day, treating a flow that exceeded 1,000 cubic meters per hour.
The plant was originally scheduled to gradually ramp up to full design capacity over several years, as new sources of water became available at the site. However, high seasonal rainfall, combined with improvements in the management of acid mine water at the Dexing Mine, has accelerated this schedule and enabled BioteQ to demonstrate the full scale operation of the plant. BioteQ expects that the increase in water will be seasonal, depending on variations in precipitation at the site. The plant is estimated to recover 1.3 million pounds of copper in 2009, and is presently on track to meet this estimate. In the first four months of the year, the plant recovered 436,000 pounds of copper. BioteQ shares the revenues and costs of the plant with its joint venture partner, Jiangxi Copper Company.
David Kratochvil, BioteQ's President and Chief Operating Officer stated, "We are very pleased that the Dexing operation has reached its design capacity ahead of schedule. The strong performance of the plant is a credit to our excellent operations staff and our project partner, Jiangxi Copper Company. We are confident that our technology and operating expertise will continue to deliver solid results in China."
BioteQ is an industrial water treatment company that applies innovative technologies to solve complex water problems, reducing environmental liabilities while generating revenue from wastewater. The Company's commercially proven technologies treat industrial wastewater contaminated with dissolved heavy metals and sulphate, producing saleable by-products and clean water that can be discharged safely to the environment. BioteQ has built 8 plants at sites in Canada, the US, China, Australia and Mexico, with additional projects in design and construction. BioteQ is headquartered in Vancouver, Canada, and trades on the TSX under the symbol BQE. For additional information, please go to www.bqewater.com.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 2,030
|
\section{Introduction}
\label{sec:intro}
Since the start-up of the Large Hadron Collider (LHC) in 2010, searches for direct particle dark matter (DM) production at colliders and their comparison with direct detection experiments have become a focal point for both the experimental and theoretical particle and astroparticle communities.
In the past, searches for DM production at colliders~\cite{ATLAS:2012ky,ATLAS:2012zim,Chatrchyan:2012me,CMS-PAS-EXO-12-048}, including signatures with missing transverse energy (MET) such as mono-jets and monophotons, were quantitatively compared with results from direct detection experiments in the framework of an effective field theory (EFT). In this case, bounds are placed on the contact interaction scale $\Lambda$ of various higher dimensional operators describing the interaction of DM with the Standard Model fields~\cite{Cao:2009uw,Beltran:2010ww,Goodman:2010yf,Bai:2010hh,Goodman:2010ku,Rajaraman:2011wf,Fox:2011pm}. While this is in principle a model-independent way of interpreting these searches, the EFT approach fails severely in a number of circumstances making it an inappropriate framework to interpret DM searches at colliders. As shown in a previous paper~\cite{Buchmueller:2013dya} by some of the present authors, the EFT ansatz is only valid for a heavy mediator for which the mediator width is larger than its mass, making a particle-like interpretation of the mediator doubtful. Furthermore, for lighter mediator masses the EFT approach provides constraints which are either over-conservative (because the process is resonantly enhanced) or too aggressive (because the missing energy distribution is too soft). Further work discussing inadequacies of the EFT approach can be found in~\cite{Bai:2010hh,Fox:2011fx,Fox:2011pm,Fox:2012ru,Goodman:2011jq,Shoemaker:2011vi,Busoni:2013lha,Busoni:2014sya,Busoni:2014haa}, and these arguments also extend to searches for other mono-objects such as mono-photons~\cite{Fox:2011fx}, mono-leptons~\cite{Bai:2012xg} and mono-Higgs~\cite{Carpenter:2013xra,Petrov:2013nia}.
As in~\cite{Buchmueller:2013dya}, a more appropriate approach to characterise DM searches at colliders is the use of simplified models~\cite{Alves:2011wf} (a similar approach was also advocated in~\cite{deSimone:2014pda}). This framework has proven to be very successful in searches for supersymmetry (SUSY) at the LHC~\cite{Aad:2013wta,Chatrchyan:2014lfa} and is by now the standard by which MET searches are compared in that context. Today, almost every ATLAS and CMS MET analysis provides an interpretation of their results in one or even several simplified models, which characterise the topologies probed by the search.
Although simplified models usually do not represent a full theory, valid constraints on more complete models such as the MSSM can be inferred if the simplified model approach is used with appropriate care~\cite{Buchmueller:2013exa,Barnard:2014joa,Papucci:2014rja,Kraml:2013mwa}.
Similarly, the advantage of the simplified model approach in the context of DM searches is that the full event kinematics over the whole parameter space is accurately captured. This allows for comprehensive studies of individual DM production topologies and for the optimisation of the experimental searches over all of the parameter space. In addition, the interpretation of collider searches in this framework can also be used to establish an equal-footing comparison with the results of direct detection experiments. This was not possible within the EFT approach where the collider limits were not valid in a large region of the relevant parameter space.
In this paper we suggest a minimal set of simplified models that can be used to characterise DM searches both at colliders as well as direct detection experiments. The parameter space of these models is defined by four variables: $M_{\rm{med}}$, $m_{\rm{DM}}$, $g_q$, and $g_{\rm{DM}}$, where $M_{\rm{med}}$ and $m_{\rm{DM}}$ are the masses of the mediator and the DM particle, while $g_q$ and $g_{\rm{DM}}$ represent the coupling of the SM particles to the mediator and the coupling of the mediator to the~DM. We use this minimal set of parameters to elucidate the true complementarity of mono-jet and direct detection searches. Continuing from~\cite{Buchmueller:2013dya}, we consider vector and axial- vector mediators to study the reach of the LHC and direct detection search from the LUX experiment. The mediator is produced in the s-channel at the LHC and in the t-channel at LUX (see figure~\ref{fig:OP}).
We focus on the development of a consistent and state-of-the-art framework within which collider limits and direct detection limits can be interpreted and compared in a general way. Other collider searches, such as jets plus MET~\cite{Fox:2012ee} or di-jet searches~\cite{An:2012va}, as well as DM indirect detection searches~\cite{Ackermann:2013uma} will also possess significant sensitivity in constraining the DM parameter space defined by our simplified model approach. The inclusion of these other searches in our framework is relatively straightforward and will be the subject of future work. In addition, it is also possible to extend our approach to include t-channel mediators, and DM particles and mediators with different spin. Describing DM interactions with a scalar or pseudoscalar mediator requires additional technical details~\cite{Haisch:2012kf} that we leave for follow-up work.
This paper is structured as follows: in section~\ref{sec:SMS} we define our Minimal Simplified Dark Matter (MSDM) framework in the context of s-channel vector and axial-vector mediators. Section~\ref{sec:valid} contains technical details related to the CMS mono-jet search (including a discussion on the optimal MET cut in the MSDM interpretation) and direct detection experiments. Section~\ref{sec:results} contains our main results: we show the current complementarity of mono-jet and direct detection searches for vector and axial-vector mediators in various two-dimensional projections of the four-dimensional parameter space. We also have a dedicated discussion (in section~\ref{sec:low}) of the low mass region where direct detection experiments lose sensitivity and show projected limits (in section~\ref{sec:pro}) from future scenarios, including limits from the LHC after $30~\mathrm{fb}^{-1}$, $300~\mathrm{fb}^{-1}$ and~$3000~\mathrm{fb}^{-1}$ and xenon direct detection experiments with multiple ton-year exposures. In section~\ref{sec:compEFTMSDM} we present a comparison of the limits obtained in the MSDM and EFT frameworks, which serves to highlight the inadequacies of the EFT framework. We present our conclusions in section~\ref{sec:conc}.
\section{Minimal Simplified Dark Matter models}
\label{sec:SMS}
The use of simplified models to characterise new physics searches at the LHC has become a standard procedure in both the experimental and theoretical communities. The advantage of simplified models is that they are fully described by a small number of fundamental parameters, such as masses, couplings and/or cross-sections. All these parameters are directly related to experimental observables, making this approach an effective framework for characterising searches in a well-defined, simple, and consistent manner.
In this paper we introduce a Minimal Simplified Dark Matter (MSDM) framework, which extends the SM matter content by two new fields whose properties are specified by (a minimum of) four parameters. The two fields are the dark matter and the mediator while the four basic parameters are the mass of the dark matter particle, $m_{\rm{DM}}$, the mass of the mediator, $M_{\rm{med}}$, the coupling of quarks to the mediator, $g_q$, and the coupling of the mediator to the dark matter, $g_{\rm{DM}}$. This set of parameters is sufficient to characterise the interactions of a variety of different UV completions (which we assume do not interact with each other) of the effective operators previously considered in the context of mono-jet searches (see e.g.~\cite{Goodman:2010ku} for a comprehensive list), including both s-channel and t-channel mediators~\cite{Chang:2013oia,An:2013xka,Bai:2013iqa,DiFranzo:2013vra,Papucci:2014iwa,Hamaguchi:2014pja,Garny:2014waa}.
In this paper we focus on the example of a vector mediator $Z'$ which is exchanged in the s-channel in mono-jet production. We consider the case when the dark matter is a Dirac fermion~$\chi$ and assume that the quark-mediator coupling~$g_q$ is equal for all quarks. In this case, as shown schematically in figure~\ref{fig:OP}, the model is completely characterised by the four parameters discussed above. These parameters are sufficient to determine the mono-jet production and direct detection scattering rate.
\begin{figure}[t!]
\centering
\includegraphics[width=0.99\columnwidth]{monoLHCDD.pdf}
\caption{The left diagram shows a contributing diagram for mono-jet production with an (axial) vector mediator at a hadron collider. The process is characterised by $M_{\rm{med}} ,\, m_{\rm{DM}} ,\, g_{\rm{DM}}$~and~$g_q$, which are the mediator and dark matter masses, and the mediator couplings to dark matter and quarks respectively. The right diagram shows the corresponding scattering process relevant for direct detection, which is characterised by the same four parameters.}
\label{fig:OP}
\end{figure}
In general a vector mediator can have vector or axial-vector couplings with quarks and the dark matter. In addition to the usual mass and kinetic terms for $\chi$ and $Z'$, our MSDM model with a vector mediator is defined by the interaction terms
\begin{align}
\label{eq:AV}
\mathcal{L}_{\mathrm{vector}}&\supset-\sum_q g_q Z'_{\mu} \bar{q}\gamma^{\mu}q- g_{\rm{DM}} Z'_{\mu} \bar{\chi}\gamma^{\mu}\chi \\
\mathcal{L}_{\rm{axial}}&\supset-\sum_q g_q Z'_{\mu} \bar{q}\gamma^{\mu}\gamma^5q- g_{\rm{DM}} Z'_{\mu} \bar{\chi}\gamma^{\mu}\gamma^5\chi
\end{align}
for vector and axial-vector couplings respectively, where the sum extends over all quarks. Models of a vector~$Z'$ mediator in the context of collider and direct detection searches have also been discussed elsewhere in the literature~\cite{Fox:2008kb,Cassel:2009pu,Bai:2010hh,Fox:2011pm,Fox:2011qd,Mambrini:2011dw,Gondolo:2011eq,Frandsen:2011cg,Shoemaker:2011vi,Frandsen:2012rk,An:2012va,An:2012ue,Alves:2013tqa,Arcadi:2013qia,Lebedev:2014bba,Davidson:2014eia,Fairbairn:2014aqa,Soper:2014ska}. Although the collider phenomenology of the vector and axial-vector mediators is similar, at direct detection experiments they are very different. In the non-relativistic limit the vector interaction gives a spin-independent interaction that is coherently enhanced by the number of nucleons, while the axial-vector interaction gives a spin-dependent signal which is not. In general it is also possible to have mixed vector and axial-vector couplings (so that e.g.~the quarks have vector couplings while the dark matter has axial-vector couplings). At tree-level, the mixed interaction is spin-dependent and velocity-squared suppressed~\cite{Kumar:2013iva} (where $v_{\rm{DM}}\simeq10^{-3}c$) so the loop-level spin-independent contribution, which is not velocity suppressed, dominates~\cite{Crivellin:2014qxa}. A treatment of the loop-induced contribution is beyond the scope of this work so we do not consider the case of mixed vector and axial-vector couplings further.
As both hadron collider and direct detection searches for dark matter primarily probe the interactions of dark matter with quarks, we set the mediator interactions with leptons to zero; the lepton couplings play no role (at tree-level) in the phenomenology in either hadron collider and direct detection searches~\cite{Kopp:2009et,Bell:2014tta}. While setting the mediator couplings to leptons to zero often introduces anomalies into the theory~\cite{Beringer:1900zz}, this does not have to be the case~\cite{Fox:2011qd,Buckley:2011vc,Buckley:2011mm,Duerr:2013dza,Duerr:2013lka}. If leptonic mediator couplings are introduced, di-lepton resonance searches will provide further constraints on the space of MSDM models.
As has been discussed in the literature~\cite{Fox:2011pm,An:2012va,Buchmueller:2013dya}, the mediator width~$\Gamma_{\rm{med}}$ plays an important role in mono-jet searches. In our MSDM models, we calculate the width from the four free parameters in the simplified model. We assume that no additional visible or invisible decays contribute to $\Gamma_{\rm{med}}$ so that the total width is
\begin{equation}
\Gamma_{\rm{med}}\equiv\Gamma(Z'\to\bar{\chi}\chi)\Theta\left(M_{\rm{med}}-2m_{\rm{DM}}\right)+\sum_q\Gamma(Z'\to\bar{q}q) \Theta\left(M_{\rm{med}}-2m_q\right)
\end{equation}
where the individual contributions for the vector and axial-vector cases are
\begin{equation}
\Gamma(Z'\to\bar{\chi}\chi)_{\rm{vector}}=\frac{g_{\rm{DM}}^2 M_{\rm{med}}}{12\pi}\left(1+\frac{2 m_{\rm{DM}}^2}{M_{\rm{med}}^2} \right)\sqrt{1-\frac{4 m_{\rm{DM}}^2}{M_{\rm{med}}^2}}\label{eq:Gamma1}
\end{equation}
\begin{align}
\Gamma(Z'\to\bar{q}q)_{\rm{vector}}&= \frac{3 g_q^2 M_{\rm{med}}}{12\pi}\left(1+\frac{2 m_q^2}{M_{\rm{med}}^2} \right)\sqrt{1-\frac{4 m_q^2}{M_{\rm{med}}^2}}\\
\Gamma(Z'\to\bar{\chi}\chi)_{\rm{axial}}&=\frac{g_{\rm{DM}}^2 M_{\rm{med}}}{12\pi} \left(1-\frac{4 m_{\rm{DM}}^2}{M_{\rm{med}}^2}\right)^{3/2}\\
\Gamma(Z'\to\bar{q}q)_{\rm{axial}}&= \frac{3 g_q^2 M_{\rm{med}}}{12\pi}\left(1-\frac{4 m_q^2}{M_{\rm{med}}^2}\right)^{3/2}\label{eq:Gamma4}\;.
\end{align}
It is straightforward to incorporate additional visible or invisible contributions to $\Gamma_{\rm{med}}$ but we do not consider that here.
Finally, while in this article we fix the mediator couplings to all quarks $g_q$ to be equal, we do not enforce that this must be equal to the mediator couplings to dark matter $g_{\rm{DM}}$.
Having different values for $g_{\rm{DM}}$ and $g_q$ is neither unreasonable nor unexpected: for instance, in the Standard Model there is a factor of six difference between the hypercharge couplings of the $\mathrm{SU}(2)_{\rm{L}}$ quark doublet and the right-handed electrons.
We end this section by again emphasising that our motivation here is to flesh out the framework of MSDM models so that the search results from collider and direct detection experiments can be accurately characterised. These minimal simplified models enable us to infer qualitative and quantitative properties of more complete DM models and allow a comparison of collider and direct detection experiments on equal footing. Variations of the assumptions which we have made in this paper should be explored in the future to fully map out the MSDM landscape; the approach should be extended to include, for instance, other spins for the mediator and dark matter particle, different coupling structures and additional experimental constraints.
\section{Experimental details and validation}
\label{sec:valid}
This section describes our technical implementation of the CMS mono-jet and LUX direct detection searches. Our limits agree with the respective collaboration's limits
to 10\% or better for both the mono-jet search and the LUX results, which is fully sufficient for our use-case. In addition, we check that the~MET ($\slashed{E}_T$) cut used by the mono-jet analysis, which was optimised assuming the EFT framework, is also appropriate within the MSDM framework. We also provide the prescription for translating between scattering cross-sections, on which the direct detection community quote limits, and $M_{\rm{med}} ,\, m_{\rm{DM}} ,\, g_{\rm{DM}}$ and~$g_q$, the parameters of interest for our MSDM models.
\subsection{LHC simulation details}
We generate LHC events for both the EFT and the MSDM using an extension of the POWHEG BOX described in~\cite{Haisch:2013ata,Nason:2004rx,Frixione:2007vw,Alioli:2010xd}. This allows us to generate the process where DM particles are pair produced in association with a parton from the initial state, resulting in a mono-jet signature. The implementation of this process in POWHEG allows for the generation of the signal to next-to-leading-order (NLO) accuracy and for this to be matched consistently with a parton shower. As shown in~\cite{Haisch:2013ata}, including NLO corrections results in a small enhancement of the cross-section compared to leading-order (LO). However, more importantly, it also leads to a substantial reduction in the dependence on the choice of the renormalisation and factorisation scales and hence the theoretical uncertainty on the signal prediction. Generating the signal to NLO accuracy should therefore lead to more robust bounds.
For the purposes of validating our framework against the results from the CMS mono-jet search~\cite{CMS-PAS-EXO-12-048}, events for the EFT process are generated at LO to enable a direct comparison with the limits provided by CMS. This is another advantage of implementing this process in the POWHEG BOX since it is capable of simulating both the EFT case (where the mediator is integrated out) and the MSDM case (where the mediator is correctly taken into account). For this validation process, we follow CMS and use the CTEQ6L1~\cite{Pumplin:2002vw} parton distribution functions (PDFs).
We set the renormalisation and factorisation scales to
\begin{equation}
\mu = \sqrt{m_{\chi\bar{\chi}}^{2} + p_{T,j_{1}}^{2}} + p_{T,j_{1}}
\end{equation}
where $m_{\chi\bar{\chi}}$ is the invariant mass of the DM pair and $p_{T,j1}$ denotes the transverse momentum of the leading jet $j_1$. As noted in~\cite{Haisch:2013ata}, this choice of scale leads to NLO corrections that are relatively independent of $m_{\rm{DM}}$. For all cases except the validation of the CMS EFT limits, we use the MSTW2008NLO~\cite{Martin:2009iq} PDFs.
The parton level process produced by POWHEG is matched to \texttt{Pythia}~8.180~\cite{Sjostrand:2007gs} for showering and hadronisation and put through a detector simulation using \texttt{Delphes3}~\cite{Ovyn:2009tx,deFavereau:2013fsa}, with parameters that are tuned to the CMS detector. Subsequently, the mono-jet selection cuts described in~\cite{CMS-PAS-EXO-12-048} are applied: Jets are reconstructed using the anti-$k_t$~\cite{Cacciari:2008gp} algorithm with a distance parameter of 0.5. Events are selected where the highest $p_T$ jet has transverse momentum above 110 GeV and $|\eta_{j_1}| < 2.4$. Another jet is allowed if it has $p_T > 30$ GeV and $|\eta| < 4.5$, but an event is vetoed if there are any additional jets satisfying this requirement. Thus, the mono-jet signature comprises of either one or two-jet events. If there are two jets in the event, it is further vetoed if the angular separation in azimuth between the two jets, $\Delta \phi_{j_1,j_2}$, is greater than 2.5. Seven signal regions are defined, with increasing thresholds for the missing transverse energy: $\slashed{E}_T > 250,\,300,\,350,\,400,\,450,\,500$ and 550~GeV. The CMS mono-jet analysis optimised the $\slashed{E}_T$ threshold by benchmarking it against exclusion sensitivity in the EFT interpretation framework. They found that the optimal threshold was 400 GeV.
As discussed in section~\ref{sec:optimise}, we have verified that this threshold is also a reasonable choice for placing limits in the MSDM models so we use it throughout this paper in our mono-jet analysis.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{EFT_validation.pdf}
\includegraphics[width=0.495\columnwidth]{res_validation.pdf}
\caption{A comparison of our 90\%~CL limits (solid lines) and the CMS 90\%~CL limits (dashed lines) on the contact interaction scale $\Lambda$. The left panel shows the results for the vector and axial-vector operators; our limits and the CMS limits agree to better than 5\%. The right panel shows the results for the vector interaction with two choices of the mediator width $\Gamma_{\rm{med}}$; our limits and the CMS limits agree to better than 10\%.}
\label{fig:validation}
\end{figure}
Figure~\ref{fig:validation} shows a comparison of our 90\%~CL limits (solid lines) and the CMS 90\% CL limits from~\cite{CMS-PAS-EXO-12-048} (dashed lines) on the contact interaction scale~$\Lambda$. The contact interaction scale~$\Lambda$ is the mass scale that gives the correct dimension to the vector and axial-vector higher dimensional operators
\begin{align}
\label{eq:EFT:vec}
\mathcal{L}^{\mathrm{EFT}}_{\mathrm{vector}}&\supset\sum_q \frac{1}{\Lambda^2} \bar{q}\gamma_{\mu}q\,\bar{\chi}\gamma^{\mu}\chi\\
\mathcal{L}^{\mathrm{EFT}}_{\rm{axial}}&\supset\sum_q\frac{1}{\Lambda^2} \bar{q}\gamma_{\mu}\gamma^5q\,\bar{\chi}\gamma^{\mu}\gamma^5\chi\;,
\label{eq:EFT:axvec}
\end{align}
where the sum extends over all quarks. The left panel shows the results for the vector (green and black lines) and axial-vector (red and blue lines) operators while the right panel shows the results for the vector operator for two choices of $\Gamma_{\rm{med}}$. Our limits and the CMS limits agree within 5\% (10\%) in the left (right) panel. We, therefore, conclude that we are able to reproduce the CMS mono-jet analysis to 10\% or better, which is fully sufficient for our use-case.
\begin{figure}[t!]
\begin{center}
\hspace{8mm}\includegraphics[width=0.65\columnwidth]{Mdm_Mmed_diffMet_90CL.pdf}
\caption{Exclusion limits at 90\%~CL for the vector mediator in the $m_{\rm{DM}}$-$M_{\rm{med}}$ plane for various different values of the $\slashed{E}_T$ threshold. The couplings are fixed to $g_q = 0.3,\,g_{\rm{DM}} = 1$. The optimum $\slashed{E}_T$ cut is~$\slashed{E}_T>450$~GeV, slightly larger than the $\slashed{E}_T>400$~GeV cut used in the CMS (and our) analysis. The 50~GeV increase in the $\slashed{E}_T>450$~GeV exclusion contour is modest so the $\slashed{E}_T>400$~GeV cut is a reasonable choice.}
\label{fig:multibin}
\end{center}
\end{figure}
\subsection{Optimising mono-jet searches in the MSDM framework}
\label{sec:optimise}
Fully exploiting the adoption of simplified models as a framework for the presentation and interpretation of mono-jet searches requires a re-optimisation of current experimental search cuts, which are based on signal samples generated in the EFT framework. While carrying out a complete re-optimisation of all cuts is beyond the scope of this paper, we can use the information provided by CMS to briefly examine the effects of varying the $\slashed{E}_T$ cut on the limits set in our MSDM framework. The $\slashed{E}_T$ cut is the most important cut of this analysis to separate background from a potential signal.
In figure~\ref{fig:multibin} we show the reach in the vector MSDM model using the expected limits provided by CMS for different values of $\slashed{E}_T$ from 250 to 550~GeV. In this example the couplings are fixed to $g_q = 0.3,\,g_{\rm{DM}} = 1$. We find that the optimum MET cut for the MSDM model is~$\slashed{E}_T>450$~GeV. This is slightly larger than the $\slashed{E}_T>400$~GeV cut which is optimal in the EFT framework. However, the 50~GeV increase in the exclusion contour is rather modest and thus we conclude that the use of the default cut of $\slashed{E}_T>400$~GeV is still reasonable.
\subsection{Facets of direct detection}
\label{sec:DD}
Dark matter interactions with nuclei lead to either spin-independent (SI) or spin-dependent (SD) scattering in the non-relativistic limit (recall that in the galaxy $v_{\rm{DM}}\simeq10^{-3}c$). Therefore, limits on the cross-section to scatter off a nucleon are presented separately for each case. In this paper we primarily use the limits from the LUX experiment, which currently sets the strongest published limit on SI interactions for $m_{\rm{DM}}\gtrsim6$~GeV. Two-phase xenon detector technology has a proven track record through the ZEPLIN~\cite{Alner:2005pa,Alner:2007ja,Akimov:2011tj}, XENON~\cite{Angle:2007uj,Aprile:2012nq,Aprile:2013doa} and LUX~\cite{Akerib:2013tjd} programs and is scalable to the much larger target masses required to probe very small scattering cross-sections. Xenon experiments also have the advantage that they are sensitive to both SI and SD interactions.
LUX has published the limit for SI interactions but not for SD interactions. We now describe our procedure for calculating both limits and assume that in the future, both limits will be provided directly by the collaboration. We model the differential scattering rate per kg-day at LUX with~\cite{Davis:2012vy,Davis:2012hn}
\begin{equation}
\frac{dR}{d\mathrm{S1}}=\xi(m_{\mathrm{DM}})\int_{3\,\rm{keV}}^{\infty}dE_{\rm{R}}\sum_{n=1}^{\infty}\epsilon_{\mathrm{S1}}(\mathrm{S1})\epsilon_{\rm{S2}}(E_{\rm{R}}) \mathrm{N}(\mathrm{S1};n,\sqrt{n}\sigma_{\mathrm{PMT}})\ \mathrm{P}(n;\nu(E_{R}))\frac{dR}{dE_{\rm{R}}}\;,
\end{equation}
where $\epsilon_{\mathrm{S1}}(\mathrm{S1})$ and $\epsilon_{\rm{S2}}(E_{\rm{R}})$ are the S1 and S2 efficiencies~\cite{Akerib:2013tjd}, S1 ranges from 2~PE to 30~PE, $\mathrm{N}(\mathrm{S1};n,\sqrt{n}\sigma_{\rm{PMT}})$ is a Normal distribution with mean and variance $n$ and $n \sigma_{\rm{PMT}}^2$ respectively, where $\sigma_{\rm{PMT}}\approx0.37$~\cite{Akerib:2012ys}, $\mathrm{P}(n;\nu(E_{R}))$ is a Poisson distribution with mean $\nu(E_R)\equiv8.8\, E_{\rm{R}}\,\mathcal{L}_{\rm{eff}}(E_{\rm{R}})$, where the numerical pre-factor is quoted in~\cite{Akerib:2013tjd} and we use $\mathcal{L}_{\rm{eff}}(E_{\rm{R}})$ from NEST (at 181~kV/cm)~\cite{NEST2013a}.
Following the event selection used by the LUX collaboration, in our analysis we only consider events that fall below the mean of the nuclear recoil band; the efficiency factor $\xi(m_{\rm{DM}})$ gives the DM mass-dependent fraction of events that fall below this mean. We calculate it by simulating the distribution of DM events in the $\log_{10}(\mathrm{S2}_{\rm{b}}/\mathrm{S1})$--$\mathrm{S1}$ plane for different values of $m_{\rm{DM}}$. We find that $\xi\approx1$ at $m_{\rm{DM}}=5$~GeV, falling to $\xi\approx0.5$ at $m_{\rm{DM}}=200$~GeV and remaining constant at 0.5 for higher masses.
The differential event rate for dark matter with local density $\rho_{\rm{DM}}=0.3~\text{GeV}\,\text{cm}^{-3}$ to scatter on a nucleus with mass $m_{\rm{N}}$ is~\cite{Lewin:1995rx}
\begin{equation}
\frac{dR}{dE_{\rm{R}}}=\frac{\rho_{\rm{DM}}}{m_{\rm{N}}m_{\rm{DM}}}\int_{v_{\rm{min}}}^{\infty}v f(\mathbf{v},\mathbf{v}_{\rm{E}})\frac{d \sigma}{d E_{\rm{R}}}\,d^3v\;,
\label{eq:dRdE1}
\end{equation}
where $f(v)$ is the local dark matter velocity distribution in the galactic frame, $v=|\mathbf{v}|$, $\mathbf{v}_{\rm{E}}$ is the Earth's velocity relative to the galactic rest frame~\cite{Lee:2013xxa,McCabe:2013kea} and $v_{\rm{min}}$ is the minimum speed required for a nucleus to recoil with energy $E_{\rm{R}}$. Here, we use the usual benchmark values for the astrophysical parameters that are used in the direct detection community. Uncertainties in these parameters lead to an uncertainty of around 50\% on the 90\%~CL nucleon scattering cross-section limit~\cite{McCabe:2010zh,Fairbairn:2012zs}.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{SI_validation.pdf}
\includegraphics[width=0.495\columnwidth]{SD_validation.pdf}
\caption{The left panel shows a comparison of our 90\% CL limits (solid lines) and published 90\%~CL limits (dashed lines) on spin-independent direct detection cross-sections $\sigma^0_{\rm{SI}}$. The right panel shows our limits for the corresponding spin-dependent direct detection cross-sections $\sigma^0_{\rm{SD}}$, for which no published results are available to compare with. Also shown in both plots is the expected reach of LZ with a 10 ton-year exposure, and the discovery reach accounting for the irreducible neutrino background from~\cite{Billard:2013qya} (dashed line) and our calculation of the same limit (solid line).}
\label{fig:DDvalidation}
\end{figure}
The input from particle physics (as opposed to astrophysics e.g.~the DM velocity distribution) enters through $d\sigma/dE_{\rm{R}}$, the differential cross-section to scatter off a nucleus. For SI and SD scattering, this is given by
\begin{align}
\frac{d \sigma_{\rm{SI}}}{d E_{\rm{R}}}&=\frac{m_{\rm{N}}\, A^2\, \sigma^0_{\rm{SI}}}{2 \mu^2_{n\chi} v^2}F^2(E_{\rm{R}})\label{eq:SI}\\
\frac{d \sigma_{\rm{SD}}}{d E_{\rm{R}}}&=\frac{4\pi}{3}\frac{m_{\rm{N}}\,\sigma^0_{\rm{SD}}}{2 \mu^2_{n\chi}v^2}\sum_i \frac{\mathfrak{f}_i}{2 J_i+1}S_i(E_{\rm{R}})\label{eq:SD}\;,
\end{align}
where $\mu_{n\chi}$ is the DM-nucleon reduced mass, $A\approx131$ is the atomic number of xenon, $F(E_{\rm{R}})$ is the Helm nuclear form factor~\cite{Duda:2006uk}, $S(E_{\rm{R}})$ is the spin structure function~\cite{Klos:2013rwa}, $J$ is the nucleus spin, the sum extends over all isotopes with non-zero spin and $\mathfrak{f}_i$ is the fractional abundance of the $i^{th}$ isotope with non-zero spin. The cross-sections $\sigma^0_{\rm{SI}}$ and $\sigma^0_{\rm{SD}}$ are the SI and SD cross-sections to scatter off a nucleon (in the limit of zero-momentum transfer) and are the quantities on which the experimental limits are quoted. The proton structure function is suppressed by over an order of magnitude relative to the neutron structure function for xenon isotopes therefore we ignore its contribution. This means that $\sigma^0_{\rm{SD}}$ is the cross-section to scatter off a neutron. Note that the dominant difference between the SI and SD cross-sections in eqs.~\eqref{eq:SI} and~\eqref{eq:SD} comes from the factor $A^2$. This enhancement ensures that the SI limits are over $10^4$ stronger than the corresponding SD limits, which plays an important role when comparing the LUX result with the mono-jet search (in section~\ref{sec:results}).
The left and right panels of figure~\ref{fig:DDvalidation} show the limits on $\sigma^0_{\rm{SI}}$ and $\sigma^0_{\rm{SD}}$ respectively. In order to validate our procedure we compare our $\sigma^0_{\rm{SI}}$ limit (solid lines) with the published ones (dashed lines). Our LUX limits (red) are calculated with the `pmax' method, introduced in ~\cite{Yellin:2002xd} and the limit on $\sigma^0_{\rm{SI}}$ agrees with the published LUX limit to better than 10\% over the whole mass range. Based on this observation we assume that our limits for $\sigma^0_{\rm{SD}}$, for which no published limits from the LUX Collaboration are available, are also a good approximation of the performance of the experiment. The limit we find for $\sigma^0_{\rm{SD}}$ is a factor $\sim2.5$ stronger than the published XENON100 SD limit to scatter off a neutron~\cite{Aprile:2013doa}. This is the same relative improvement as found in the SI limits of LUX and XENON100. As expected, the limit on $\sigma^0_{\rm{SD}}$ is significantly weaker than the limit on $\sigma^0_{\rm{SI}}$.
Also shown is the limit on~$\sigma^0_{\rm{SI}}$ from SuperCDMS~\cite{Agnese:2014aze}, which is stronger than LUX's for $m_{\rm{DM}}\lesssim6$~GeV, the projected limits from LZ (the successor to LUX) assuming an exposure of 10 ton-years~\cite{Malling:2011va}, and the discovery reach when coherent neutrino scattering is taken into account~\cite{Billard:2013qya}. For the LZ limit we assume that the efficiencies and background event rate remain the same as at LUX. The discovery reach indicates the cross-section at which 90\% of experiments can make a $3\sigma$ discovery of dark matter, taking into account the background contribution from coherent neutrino scattering. The result in~\cite{Billard:2013qya} is for SI only, therefore we reproduce that result here in the left panel of figure~\ref{fig:DDvalidation} (finding good agreement over the whole mass range) and extend the calculation to calculate the limit for SD scattering in the right panel of figure~\ref{fig:DDvalidation}. We make the same assumptions in our calculation as those used in~\cite{Billard:2013qya}. Namely, we assume that the low mass reach is from a xenon experiment with an exposure of 200~kg-years and an energy threshold of 3~eV, while the high mass reach is from a xenon experiment with a 4~keV energy threshold and the exposure is such that 500 neutrino events are expected. Furthermore, the magnitude, distribution and uncertainty of the neutrino fluxes are the same as those in~\cite{Billard:2013qya} and we assume that the experimental efficiencies and energy resolution is perfect, and we ignore the effect of neutrinos scattering on electrons. We make use of these results in sections~\ref{sec:low} and~\ref{sec:pro}.
Finally, we note that the discovery reach may be improved with new experimental and theoretical techniques (see e.g.~\cite{Grothaus:2014hja,Ruppin:2014bra}) but we do not discuss that further here.
Translating the limits on $\sigma^0_{\rm{SI}}$ and $\sigma^0_{\rm{SD}}$ to constraints on the parameters of interest in our MSDM models is now straightforward. For the vector model, the scattering interaction is SI and the cross-section to scatter off a point-like nucleon in the non-relativistic limit is
\begin{align}
\label{eq:SI2MSDM}
\sigma^0_{\rm{SI}}&=\frac{9\, g^2_{\rm{DM}}\,g_q^2\, \mu^2_{n\chi}}{\pi M^4_{\rm{med}}}\\
&\approx1.1\times 10^{-39}~\mathrm{cm}^2\cdot\left(\frac{g_{\rm{DM}} \,g_q}{1}\right)^2\left( \frac{1~\mathrm{TeV}}{M_{\rm{med}}}\right)^4\left(\frac{\mu_{n\chi}}{1~\mathrm{GeV}} \right)^2\;.
\end{align}
In the axial-vector model, the scattering interaction is SD and the analogous result for the cross-section to scatter off a point like neutron is
\begin{align}
\label{eq:SD2MSDM}
\sigma^0_{\rm{SD}}&=\frac{3\, g^2_{\rm{DM}}\,g_q^2 (\Delta_u+\Delta_d+\Delta_s)^2\, \mu^2_{n\chi}}{\pi M^4_{\rm{med}}}\\
&\approx 4.6\times 10^{-41}~\mathrm{cm}^2\cdot\left(\frac{g_{\rm{DM}} \,g_q}{1}\right)^2\left( \frac{1~\mathrm{TeV}}{M_{\rm{med}}}\right)^4\left(\frac{\mu_{n\chi}}{1~\mathrm{GeV}} \right)^2\;,
\end{align}
where $\Delta_u=-0.42$, $\Delta_d=0.85$ and $\Delta_s=-0.08$~\cite{Cheng:2012qr}. Other values for $\Delta_u$, $\Delta_d$ and $\Delta_s$ are also used in the literature (see e.g.~\cite{Ellis:2000ds,Gondolo:2004sc,Belanger:2008sj}) and differ by~$\mathcal{O}(10\%)$. We assume that the coupling~$g_q$ is equal for all quarks in both of these results. Note that the dependence on $m_{\rm{DM}}$ in eqs.~\eqref{eq:SI2MSDM} and~\eqref{eq:SD2MSDM} essentially vanishes for $m_{\rm{DM}}\gtrsim10$~GeV, since $m_{\rm{DM}}$ enters only through the reduced mass~$\mu_{n\chi}$. For large values of $m_{\rm{DM}}$, the dark matter mass only enters the scattering rate through its explicit dependence in eq.~\eqref{eq:dRdE1}. As a result (and as can be verified from figure~\ref{fig:DDvalidation}) the limits on $\sigma^0_{\rm{SI}}$ and $\sigma^0_{\rm{SD}}$ scale in proportion to $m_{\rm{DM}}$ at large $m_{\rm{DM}}$. Finally, we note that eqs.~\eqref{eq:SI2MSDM} and~\eqref{eq:SD2MSDM} are valid when the mediator mass is greater than the typical momentum transfer in the scattering process, which is $\sim100$~MeV. Therefore in the following, we do not consider direct detection limits for $M_{\rm{med}}<100$~MeV.
\section{Landscape of collider and direct detection searches}
\label{sec:results}
In this section we present our 90\% exclusion limits from the LHC mono-jet and LUX searches for the MSDM models defined in section~\ref{sec:SMS}. We discuss the vector and axial-vector cases in parallel, showing first the current constraints on the whole parameter space (in section~\ref{sec:current}) before zooming in on the low $m_{\rm{DM}}$ region where direct detection searches start to lose sensitivity (in section~\ref{sec:low}). We conclude this section with projections for future searches (in section~\ref{sec:pro}).
To explore the complementarity of collider and direct detection searches we map out the four-dimensional parameter space of the MSDM models by showing projections in two parameters. The following two-dimensional planes are considered:
\begin{itemize}
\item $m_{\rm{DM}}$ vs $M_{\rm{med}}$, for fixed values of couplings $g_q$ and $g_{\rm{DM}}$, both for the case where $g_q = g_{\rm{DM}}$ and $g_q \neq g_{\rm{DM}}$.
\item $M_{\rm{med}}$ vs ($g_{q}=g_{\rm{DM}}$), for fixed values of $m_{\rm{DM}}$.
\item $m_{\rm{DM}}$ vs ($g_{q}=g_{\rm{DM}}$), for fixed values of $M_{\rm{med}}$.
\item $g_{\rm{DM}}$ vs $g_q$, for fixed values of $m_{\rm{DM}}$ and $M_{\rm{med}}$.
\end{itemize}
We limit the parameter space by the requirement that the mediator width $\Gamma_{\rm{med}}$ is not larger than its mass $M_{\rm{med}}$. From eqs.~\eqref{eq:Gamma1} to~\eqref{eq:Gamma4}, we find that for the case $g_{\rm{DM}} =g_q$, this confines the maximal value of the two couplings $g_{\rm{DM}} =g_q \approx 1.45$, when the mediator couples to all quarks and $M_{\rm{med}}>2 m_t$. For a few plots we slightly extend beyond this coupling value to better visualise the limits. For all figures which show a direct comparison of the LHC and LUX searches, the axial-vector figures have linear scales while the vector figures have log scales. This is to better display the different features of collider and direct detection sensitivities.
\subsection{Limits from current searches}
\label{sec:current}
We first present our 90\% exclusion limits from the 8~TeV mono-jet and LUX 2013 searches for the MSDM models defined in section~\ref{sec:SMS}. In figure~\ref{fig:Mdm-Mmed} we compare the LHC mono-jet search with the LUX result in the $m_{\rm{DM}}$ vs~$M_{\rm{med}}$ plane for the vector (left panel) and axial-vector (right panel) MSDM models. The solid, dashed and dot-dashed lines show three different coupling scenarios: $(g_q,g_{\rm{DM}})$ = $(1,1)$, $(0.3,1)$ and $(0.5,0.5)$ respectively. The region to the left of the lines is excluded.
We begin by making some general comments which hold for all of the figures in this section. While the collider limits are similar in sensitivity for the vector and axial-vector cases, the LUX limits on $M_{\rm{med}}$ (for a given value of $m_{\rm{DM}}$) for a vector mediator exceed the axial-vector limits by almost two orders of magnitude. The significant difference in the LUX limits is explained by the atomic number squared ($A^2\simeq131^2$) enhancement of the SI cross-section in the case of a vector mediator. The axial-vector case, for which the scattering cross-section is SD, does not exhibit this enhancement (cf.~eqs.~\eqref{eq:SI} and~\eqref{eq:SD}). For the vector mediator, the LUX limits are significantly stronger than the LHC limits. The only exception is at smaller values of the DM mass ($m_{\rm{DM}}\lesssim5$~GeV) where direct detection experiments lose sensitivity. We discuss this region further in section~\ref{sec:low}. For axial-vector mediators, the mono-jet and direct detection searches show good complementarity, probing orthogonal directions in the parameter space. While the mono-jet search is more sensitive to large values of $M_{\rm{med}}$, the direct detection experiments extend the reach to large values of $m_{\rm{DM}}$.
For the different coupling scenarios the $g_q=g_{\rm{DM}}=1$ example provides the strongest limits for both mono-jet and direct detection searches, while the $g_{q}=g_{\rm{DM}}=0.5$ case possesses the weakest sensitivity. The behaviour of the direct detection limits is straightforward to understand: the cross-section scales like $g_q^2 g_{\rm{DM}}^2/M_{\rm{med}}^4$ (cf. eqs.~\eqref{eq:SI2MSDM} and~\eqref{eq:SD2MSDM}) and thus, for a given value of $m_{\rm{DM}}$, the limit on
$M_{\rm{med}}$ is proportional to $\sqrt{g_q g_{\rm{DM}}}$.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{mm_vec.pdf}
\includegraphics[width=0.495\columnwidth]{mm_ax.pdf}
\caption{The 90\% CL limits from current mono-jet (blue lines) and direct detection (red lines) searches in the $m_{\rm{DM}}$ vs~$M_{\rm{med}}$ plane for the vector (left panel) and axial-vector (right panel) mediators. The region to the left of the various curves is excluded. The solid, dashed and dot-dashed lines are for $(g_q,g_{\rm{DM}})=(1,1)$, $(0.3,1)$ and $(0.5,0.5)$ respectively. While the LHC limits are similar in both panels, the LUX limits are significantly more constraining for vector mediators. Note that the vector case has log scales for both axes while the axial-vector case has linear scales.}
\label{fig:Mdm-Mmed}
\end{figure}
The behaviour of the collider limits is more complex and can be understood as follows. First, consider the collider limits for fixed values of $m_{\rm{DM}}$ and at large values of $M_{\rm{med}}$. Here we again expect the cross-section to scale as $g_q^2 g_{\rm{DM}}^2$. However, unlike for direct detection, we must also take into account the effect of the mediator width $\Gamma_{\rm{med}}$ as discussed in~\cite{Fox:2011fx,Buchmueller:2013dya}. In this case the partonic cross-section scales approximately as $g_q^2 g_{\rm{DM}}^2/(M_{\rm{med}}^4 \Gamma_{\rm{med}})$ so that the limit on $M_{\rm{med}}\propto\sqrt{g_q g_{\rm{DM}}}\,\Gamma_{\rm{med}}^{-1/4}$. Although this approximation ignores the PDFs, we find numerically that it gives a good rule of thumb for the scaling at large values of $M_{\rm{med}}$. From eqs.~\eqref{eq:Gamma1} to~\eqref{eq:Gamma4} we see that at large values of $M_{\rm{med}}$ the width of the mediator $\Gamma_{\rm{med}}$ is proportional to $18g_q^2 + g_{\rm{DM}}^2$. This implies that the $(g_q,g_{\rm{DM}})=(0.3,1)$ case is enhanced with respect to the other cases because $\Gamma_{\rm{med}}$ is smallest for this case. This enhancement explains why the $(g_q,g_{\rm{DM}})=(0.3,1)$ mono-jet limit is closer to the $g_q=g_{\rm{DM}}=1$ limit rather than the $g_{q}=g_{\rm{DM}}=0.5$ limit as in the case of the direct detection limits.
Second, consider the collider limits for fixed values of $M_{\rm{med}}$. The limits on $m_{\rm{DM}}$ are constrained by the energy of the colliding partons since two DM particles must be produced in the final state. The phase-space suppression factors that enter the cross-section for vector and axial-vector mediators are typically of the form $\sqrt{Q_{\rm{tr}}^2-4m_{\rm{DM}}^2}(Q_{\rm{tr}}^2+2m_{\rm{DM}}^2)$ and $(Q_{\rm{tr}}^2-4m_{\rm{DM}}^2)^{3/2}$ respectively, where $Q_{\rm{tr}}\simeq700$~GeV is the s-channel momentum transfer~\cite{Busoni:2014sya}. It should be noted that these phase space factors also appear in the width calculation cf.~eqs.~\eqref{eq:Gamma1} to~\eqref{eq:Gamma4}. The axial-vector mediator is more strongly phase-space suppressed, which accounts for the greater suppression between the $g_q=g_{\rm{DM}}=1$ and $g_q=g_{\rm{DM}}=0.5$ limits at small $M_{\rm{med}}$ in the axial-vector case compared to the vector case in figure~\ref{fig:Mdm-Mmed}. Note that these phase-space suppression factors also account for the difference between the vector and axial-vector EFT limits in the left panel of figure~\ref{fig:validation}.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{med_g_vec.pdf}
\includegraphics[width=0.495\columnwidth]{med_g_ax.pdf}
\caption{The 90\% CL limits from the LHC mono-jet (blue lines) and LUX (red lines) searches in the $M_{\rm{med}}$ vs ($g_{q}=g_{\rm{DM}}$) plane; we have fixed $g_q=g_{\rm{DM}}$. The left and right panels show the limits for vector and axial-vector mediators respectively. The region to the right of the various curves is excluded. We show three different dark matter masses: $m_{\rm{DM}}=10$~GeV is solid, $m_{\rm{DM}}=100$~GeV is dashed and $m_{\rm{DM}}=200$~GeV is dot-dashed. Note that the $M_{\rm{med}}$-axis has a log (linear) scale in the left (right) panel.}
\label{fig:Mmed-couplings}
\end{figure}
Further insights into the dependence on the chosen coupling scenarios can be gained by looking at the projection in the $M_{\rm{med}}$ vs $g_q,g_{\rm{DM}}$ plane, shown in figure~\ref{fig:Mmed-couplings}. The solid, dashed and dot-dashed lines show the limits for $m_{\rm{DM}}=10,\,100$ and~$200$~GeV respectively. We have fixed $g_q=g_{\rm{DM}}$ in this figure and the region to the right of the lines is excluded.
In this plane the mono-jet limits are similar for axial-vector and vector mediators: both exclude down to $g_q=g_{\rm{DM}}\simeq0.2$ for light mediators (when $m_{\rm{DM}}=10$~GeV) and both show a characteristic turning point owing to the resonance of the s-channel mediator. The resonance occurs when $M_{\rm{med}}^2\gtrsim 4 m_{\rm{DM}}^2+\slashed{E}_T^2$ (where $\slashed{E}_T=400$~GeV). For values of $M_{\rm{med}}$ below this, the limits on the couplings become weaker because the production is through an off-shell mediator. The small difference in behaviour between the vector and axial-vector limits at large couplings and large $M_{\rm{med}}$ can again be understood by the different phase-space suppression factors. The axial-vector phase-space suppression is stronger so there is more of a difference between the limits at $m_{\rm{DM}}=10,\,100$ and~$200$~GeV. We again note that this behaviour is also found in the EFT limits in the left panel of figure~\ref{fig:validation} for the same reason.
The direct detection limit curves instead show a rather simple behaviour as there are no resonance effects in this case. The limits on $M_{\rm{med}}$ rise in proportion to the coupling strength cf.~eqs.~\eqref{eq:SI2MSDM} and~\eqref{eq:SD2MSDM}. In comparison to the collider limits where the limits are stronger for smaller $m_{\rm{DM}}$, the direct detection limit is strongest at $m_{\rm{DM}}=100$~GeV and weakest for $m_{\rm{DM}}=10$~GeV. This can be easily understood with reference to figure~\ref{fig:DDvalidation}.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{dm_g_vec.pdf}
\includegraphics[width=0.495\columnwidth]{dm_g_ax.pdf}
\caption{The 90\% CL limits from mono-jet (blue lines) and direct detection (red lines) searches in the $m_{\rm{DM}}$ vs ($g_{q}=g_{\rm{DM}}$) plane for the vector (left) and axial-vector (right) mediators. We have fixed $g_q=g_{\rm{DM}}$. The parameter space to the right of the various curves is excluded. We show two different mediator masses: $M_{\rm{med}}=500$~GeV is solid and $M_{\rm{med}}=1000$~GeV is dashed. Note that the $m_{\rm{DM}}$-axis scales are different for each panel.}
\label{fig:Mdm-couplings}
\end{figure}
Figure~\ref{fig:Mmed-couplings} again demonstrates the good complementarity between the mono-jet and direct detection searches for axial-vector mediators since they probe different regions in the MSDM parameter space. The direct detection experiments are better at probing small $M_{\rm{med}}$, which are not yet accessible to the collider searches as the mediator is very off-shell, while the LHC is a better probe at larger values of~$M_{\rm{med}}$.
In figure~\ref{fig:Mdm-couplings} we compare the two searches in the $m_{\rm{DM}}$ vs ($g_q=g_{\rm{DM}}$) plane. The solid and dashed lines show the limits for $M_{\rm{med}}=500$ and~$1000$~GeV respectively. The region to the right of the curves is excluded in both panels. The behaviour of the limits in this figure is similar to that shown already. The LUX limit is significantly stronger than the LHC limit for vector mediators, except in the low $m_{\rm{DM}}$ region. The LUX and LHC limits show good complementarity in the axial-vector case as they probe different regions of parameter space. The scalings of the collider limits can be understood with reference to the width and phase-space scalings discussed in connection with figure~\ref{fig:Mdm-Mmed}. As discussed previously, for a given value of $m_{\rm{DM}}$ the LUX limit on $\sqrt{g_q g_{\rm{DM}}}\proptoM_{\rm{med}}$.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{g_g_vec.pdf}
\includegraphics[width=0.495\columnwidth]{g_g_ax.pdf}
\caption{The current LHC mono-jet (blue lines) and LUX (red lines) 90\% CL limits in the $g_{\rm{DM}}$ vs $g_q$ plane for a vector (left panel) and axial-vector (right panel) mediator. The parameter space above and to the right of the various lines is excluded. We show three different sets of dark matter and mediator masses $(m_{\rm{DM}},M_{\rm{med}})$: $(100,1000)$~GeV is solid, $(200,500)$~GeV is dashed and $(200,800)$~GeV is dot-dashed. Note that the left (right) panel has log (linear) axes.}
\label{fig:couplings}
\end{figure}
\sloppy
Finally, we consider the limits in the $g_{\rm{DM}}$ vs $g_q$ plane, where we fix both $M_{\rm{med}}$ and $m_{\rm{DM}}$. Figure~\ref{fig:couplings} shows that the direct detection limits are fully symmetric in this plane. This is because the direct detection cross-section is sensitive only to the product $g_q^2 g_{\rm{DM}}^2$ cf.~eqs.~\eqref{eq:SI2MSDM} and~\eqref{eq:SD2MSDM}. However, the mono-jet search is able to break this degeneracy because it is also sensitive to the mediator width, which is not symmetric in $g_q$ and $g_{\rm{DM}}$ ($\Gamma_{\rm{med}}\propto18g_q^2 + g_{\rm{DM}}^2$ at large values of $M_{\rm{med}}$). Therefore in the event of a DM discovery at colliders and direct detection, the mono-jet analysis, or other collider searches like the dijet or jets plus~MET searches, could add important information in order to disentangle the coupling structure.
\fussy
\subsection{Low dark matter mass region}
\label{sec:low}
We now focus on the low $m_{\rm{DM}}$ region of the vector mediator parameter space. This is of particular interest as direct detection searches lose sensitivity for $m_{\rm{DM}}\lesssim 10$~GeV because the momentum transfer becomes small and the nuclear recoil energy falls below experimental thresholds. This is not an issue for collider searches and so it is interesting to understand how collider searches can help to constrain this parameter space. It is also an interesting region both from a theoretical perspective, since $m_{\rm{DM}}\simeq 5$~GeV is predicted in many models of asymmetric DM (see~\cite{Petraki:2013wwa} for a recent review), and from a phenomenological perspective, since it is the region where CoGeNT~\cite{Aalseth:2010vx,Aalseth:2011wp,Aalseth:2012if,Aalseth:2014eft}, CRESST-II~\cite{Angloher:2011uu}, CDMS-Si~\cite{Agnese:2013rvf} and DAMA/LIBRA~\cite{Bernabei:2013xsa} reported signal-like excesses in recent years. However, in 2013 both LUX and SuperCDMS reported results which naively exclude these signals. See also~\cite{Davis:2014bla},~\cite{Brown:2011dp,Kuzniak:2012zm,Angloher:2014dua} and~\cite{Blum:2011jf,Pradler:2012qt,Davis:2014cja} for additional non-DM explanations of the CoGeNT, CRESST-II and DAMA/LIBRA excesses. In this section we complement the LUX result with the recent result from SuperCDMS as it extends the sensitivity of direct detection experiments to lower values of $m_{\rm{DM}}$. Further details about the SuperCDMS result and how it is used are provided in section~\ref{sec:DD}.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{lightvec_mm.pdf}
\includegraphics[width=0.495\columnwidth]{lightvec_gg.pdf}
\caption{The 90\% CL limits from the LHC mono-jet (blue lines), LUX (red lines) and SuperCDMS (green lines) searches in the low $m_{\rm{DM}}$ region. The left and right panels show the $m_{\rm{DM}}$ vs $M_{\rm{med}}$ and $g_{\rm{DM}}$ vs $g_q$ planes for a vector mediator. In the left panel, the region to the left and above the lines is excluded. In the right panel, the region to the right and above the lines is excluded. In the $M_{\rm{med}}$-$m_{\rm{DM}}$ plane we show three different set of couplings: $(g_q,g_{\rm{DM}})=(1,1)$ is solid, $(0.3,1)$ is dashed and $(0.5,0.5)$ is dot-dashed. In the $g_q$-$g_{\rm{DM}}$ plane we fix $M_{\rm{med}}=1$~TeV and show two different choices of the dark matter mass: $m_{\rm{DM}}=3.5$~GeV and $m_{\rm{DM}}=6$~GeV. In the right panel, the mono-jet limit is identical for the two different $m_{\rm{DM}}$ values while there is no LUX limit for $m_{\rm{DM}}=3.5$~GeV.}
\label{fig:low-mass}
\end{figure}
In figure~\ref{fig:low-mass} we show the limits from the LHC mono-jet, SuperCDMS and LUX searches in the $m_{\rm{DM}}$ vs $M_{\rm{med}}$ plane (left panel) and the $g_{\rm{DM}}$ vs $g_q$ plane (right panel). In the left panel we show again the three different coupling scenarios: $(g_q,g_{\rm{DM}})$= $(1,1)$, $(0.3,1)$ and $(0.5,0.5)$. SuperCDMS and LUX exclude the region above the green and red lines, while the LHC limits exclude the region to the left of the blue lines. In the right panel we show the limits for $m_{\rm{DM}}=3.5$ and~$6$~GeV. We fix $M_{\rm{med}}=1$~TeV as this approximates the current sensitivity of the mono-jet searches (see figure~\ref{fig:Mdm-Mmed}) but a lower mediator mass would not significantly change our discussion. The region to the right of the various lines is excluded.
The left panel demonstrates that in the region of interest the LHC limits are independent of $m_{\rm{DM}}$. The LHC bounds are only limited by on-shell mediator production and currently extend to $M_{\rm{med}}\simeq1100$~GeV (for $g_q=g_{\rm{DM}}=1$). This is in contrast to LUX and SuperCDMS, whose sensitivity drops off rapidly below 6~GeV and 3.5~GeV respectively. This is also demonstrated in the right panel. While the LHC limit is independent of the choices for $m_{\rm{DM}}$, the LUX and SuperCDMS limits drop off rapidly. These examples demonstrate that direct detection and collider limits have good complementarity for vector mediators in the low $m_{\rm{DM}}$ region. This mass region is highly motivated in asymmetric DM models, where typically $m_{\rm{DM}}\simeq 5$~GeV, so mono-jet searches may have an important role to play in testing these models (see e.g.~\cite{MarchRussell:2012hi}).
\subsection{Projection for future searches}
\label{sec:pro}
In this section we provide extrapolations of how the limits and complementarity between the LHC and direct detection search avenues will continue to develop. Both the collider and direct detection communities have plans for mid- and long-term projects that possess the potential to significantly increase the sensitivity for DM searches.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{vec_proj.pdf}
\includegraphics[width=0.495\columnwidth]{ax_proj.pdf}
\caption{The blue and red lines show the current and projected 90\% CL limits from the LHC mono-jet and LUX searches in the $m_{\rm{DM}}$ vs $M_{\rm{med}}$ plane. The left and right panels show the limits for vector and axial-vector mediators respectively for $(g_q,g_{\rm{DM}})=(1,1)$. The region to the left of the various curves is excluded. The plot legend is the same for both panels. The short-dashed green lines shows the direct detection discovery reach after accounting for the neutrino background. While LUX has better sensitivity than mono-jet searches and approaches the neutrino limit for vector mediators, the opposite is true for axial-vector mediators. Note that the left (right) panel has log (linear) axes.}
\label{fig:proj:Mdm-couplings}
\end{figure}
For the LHC we provide projected limits for:
\begin{itemize}
\item LHC 13 TeV and 30 $\mathrm{fb}^{-1}$. This gauges the reach for the first year of LHC running in 2015.
\item LHC 14 TeV and 300 $\mathrm{fb}^{-1}$. This provides an estimate of the ultimate reach of the LHC.
\item HL-LHC 14 TeV and 3000 $\mathrm{fb}^{-1}$. This is the expected reach of a high-luminosity upgrade of the LHC.
\end{itemize}
The basis for these extrapolations are the 8 TeV limits of the CMS mono-jet search presented in section~\ref{sec:results}. These limits are scaled to the different future scenarios assuming that the underlying performances of the search in terms of signal efficiency and background suppression remains unchanged.
These assumptions were also used in the Snowmass~\cite{CMS:2013xfa} and ECFA~\cite{CMS-PAS-FTR-13-014,ATL-PHYS-PUB-2014-010,ATL-PHYS-PUB-2014-007} studies and form the basis of the Collider Reach~\cite{colliderreach} tool. Ref.~\cite{colliderreach} also shows the good agreement between using this extrapolation and using a full simulation. Furthermore, the underlying assumption of maintaining the present performance of the searches is supported by the ATLAS and CMS upgrade programmes, which both put forward this assumption as the main upgrade goal.
For the direct detection experiments we show two different scenarios:
\begin{itemize}
\item LZ with 10 ton year exposure. This is our estimated limit for the lifetime exposure of the LZ experiment~\cite{Malling:2011va}. The successor to XENON1T~\cite{Aprile:2012zx} should achieve a similar sensitivity.
\item The xenon discovery reach when accounting for the coherent neutrino scattering background~\cite{Billard:2013qya}.
\end{itemize}
These limits are based on the calculations described in section~\ref{sec:valid}.
Figure~\ref{fig:proj:Mdm-couplings} shows our estimates of future limits on the vector mediator (left panel) and axial-vector (right panel) mediators for $(g_q,g_{\rm{DM}})=(1,1)$. We see that the collider limits improve for each of the scenarios we consider. For the first year of operation of the LHC in 2015, we expect the reach of the mono-jet search to go up to $M_{\rm{med}}\simeq1.8$~TeV for $m_{\rm{DM}}\approx350$~GeV, while the ultimate reach of the LHC is expected to be around 3~TeV for $m_{\rm{DM}}$ up to 750~GeV. For the HL-LHC the mono-jet limit are projected to extend out to 5~TeV for $m_{\rm{DM}}$ up to 1~TeV. However, except at very low $m_{\rm{DM}}$ where the collider limit is stronger, the LZ limit will be stronger than even the high-luminosity LHC limit for a vector mediator. The LZ sensitivity even approaches the ultimate sensitivity of direct detection experiments determined by the neutrino background.
For the axial-vector mediator, the mono-jet reach is similar to the vector case. However, in this case the mono-jet reach extends beyond the LZ limit for $m_{\rm{DM}}\lesssim1$~TeV and nearly extends to the xenon discovery reach from the neutrino background for the choice of couplings we have made here: $(g_q,g_{\rm{DM}})=(1,1)$. For larger couplings the collider can even probe parameter space beyond the xenon discovery reach. However, LZ will be sensitive to mediator masses of 2~TeV for $m_{\rm{DM}}$ up to 2~TeV, thus complementing the collider searches by probing the large $m_{\rm{DM}}$ parameter space, which in turn will increase the discovery potential.
\section{Comparing EFT and MSDM limits}
\label{sec:compEFTMSDM}
Thus far we have presented results only in our MSDM models. In this section we contrast the results from these simplified models with those derived from the limit on the EFT suppression scale $\Lambda$. When valid, the advantage of the EFT approach is that the limits are model independent, where the suppression scale is simply related to the couplings and mediator mass of the full theory. We have argued in our previous paper~\cite{Buchmueller:2013dya} that the EFT limits for collider searches should be taken \textit{cum grano salis} as in practice, they apply only to a limited set of theories. However, as they are widely used in the theoretical community it is important to explore the failings of the EFT framework in more detail. In the following, we directly compare our MSDM limits with those derived from the model-independent EFT approach. This quantitatively demonstrates that a naive application of the EFT limits can lead to incorrect conclusions about the sensitivity of mono-jet searches and is an example of a well-defined model for which the model-independent EFT limits poorly approximate the underlying limits in a more-complete theory.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{EFT_ax_mm_2.pdf}
\includegraphics[width=0.495\columnwidth]{EFT_vec_med_g.pdf}
\includegraphics[width=0.495\columnwidth]{EFT_ax_mdm_g.pdf}
\includegraphics[width=0.495\columnwidth]{EFT_vec_gg.pdf}
\caption{Comparisons between the 90\% CL mono-jet limit in our MSDM models (blue solid line) and the EFT framework (green dashed) in the two-dimensional planes considered previously. The red dot-dashed line shows the LUX limit. The left and right panels are for axial-vector and vector mediators respectively.
The MSDM and EFT limits should agree in the domain where the EFT framework is valid. The EFT limits both underestimate the MSDM limit (by missing the resonant enhancement) or overestimate it (by missing off-shell production of the mediator). This may lead to a misleading conclusion regarding the relative sensitivity of mono-jet and direct detection searches. A simple criterion for the validity of the EFT approach is that $M_{\rm{med}} > 2m_{\rm{DM}}$. The line $M_{\rm{med}} =2m_{\rm{DM}}$ is shown in the upper left panel. Even in the valid region, the EFT limit fails to accurately reproduce the MSDM limit for these parameters.
}
\label{fig:EFTcomparison}
\end{figure}
When the mediator mass is sufficiently heavy to be safely integrated out, the effective higher dimension operators from our vector and axial-vector MSDM models are
\begin{align}
\mathcal{L}^{\mathrm{eff}}_{\mathrm{vector}}&\supset\sum_q \frac{g_q g_{\rm{DM}}}{M_{\rm{med}}^2} \bar{q}\gamma_{\mu}q\,\bar{\chi}\gamma^{\mu}\chi\\
\mathcal{L}^\mathrm{eff}_{\rm{axial}}&\supset\sum_q\frac{g_q g_{\rm{DM}}}{M_{\rm{med}}^2} \bar{q}\gamma_{\mu}\gamma^5q\,\bar{\chi}\gamma^{\mu}\gamma^5\chi\;,
\end{align}
where the sum is over all quarks. Comparing with eqs.~\eqref{eq:EFT:vec} and~\eqref{eq:EFT:axvec}, we observe that the relation $\Lambda=M_{\rm{med}}/\sqrt{g_q g_{\rm{DM}}}$ holds. Therefore, the EFT limits can be applied to the MSDM models by using the relation $\Lambda=M_{\rm{med}}/\sqrt{g_q g_{\rm{DM}}}$ and the CMS 90\%~CL limits on~$\Lambda$, which are shown in the left panel of figure~\ref{fig:validation} as a function of~$m_{\rm{DM}}$. In figure~\ref{fig:EFTcomparison} we show a comparison of the current MSDM mono-jet limit (blue solid line) with the naive limit obtained in the EFT framework (green dashed line) for each of the four parameter planes shown in figures~\ref{fig:Mdm-Mmed} to~\ref{fig:couplings}. The EFT limit is naive because we assume that it applies to the full parameter space of the MSDM model. For comparison, we also include the LUX 2013 limit as the red dot-dashed line. The left (right) panels show the limits for an axial-vector (vector) mediator. We again note that the EFT and MSDM provide identical results for the direct detection experiments in this paper, as long as $M_{\rm{med}} \gtrsim100$~MeV.
The first general observation that we can make is that the EFT limits consistently give a poor approximation to the underlying limits obtained in the MSDM model. Not only do the EFT limits exclude different parameter values but also the shape of the limit curve differs dramatically from those of the MSDM limits. This is because the EFT framework does not account for the mediator propagator, and thus does not include the effects of resonant enhancement or off-shell production of the mediator.
The top-left panel of figure~\ref{fig:EFTcomparison} shows the limits in the $m_{\rm{DM}}$ vs $M_{\rm{med}}$ plane for an axial-vector mediator when $g_q=g_{\rm{DM}}=1$. We observe that at low $m_{\rm{DM}}$ the EFT limit is too weak. This is because the EFT framework fails to take into account the resonant enhancement from on-shell mediator production. At larger $m_{\rm{DM}}$ the mediator is off-shell and the EFT framework dramatically overstates the limit. No limit is obtained in the MSDM model for $m_{\rm{DM}}\gtrsim300$~GeV while a naive application of the EFT limit gives the false impression that the limit extends beyond $m_{\rm{DM}}=1$~TeV. This overstating of the limit at high values of $m_{\rm{DM}}$ has sometimes led to the wrong conclusion that for spin-dependent interactions, the mono-jet searches outperform direct detection searches. However as the right panels of figures~\ref{fig:Mdm-Mmed} to~\ref{fig:couplings} demonstrate, the two searches probe different orthogonal and complementary regions of the axial-vector parameter space.
The bottom-left panel shows the limits in the $m_{\rm{DM}}$ vs ($g_{q}=g_{\rm{DM}}$) plane for an axial-vector mediator with $M_{\rm{med}}=500$~GeV. In this plane, it is particularly clear that naively applying the EFT limit obliterates the complementarity between the direct detection and mono-jet results. The MSDM model reveals that the collider limit on $g_q\,,g_{\rm{DM}}$ is stronger at smaller $m_{\rm{DM}}$ while the higher $m_{\rm{DM}}$ limit is kinematically suppressed because of off-shell mediator production.
The bottom-right panel shows the limits for a vector mediator when $M_{\rm{med}}=500$~GeV and $m_{\rm{DM}}=200$~GeV in the $g_{\rm{DM}}$ vs $g_q$ plane. We see again how the EFT framework misses important physical effects: the EFT limit is symmetric in $g_q$ and $g_{\rm{DM}}$ while the MSDM limit is asymmetric because the mediator width breaks the degeneracy between $g_q$ and $g_{\rm{DM}}$. Therefore, the collider possesses sensitivity to the underlying coupling structure, which is not resolved in the EFT approach.
The final panel in this figure is the top-right panel, which shows the limits for a vector mediator when $m_{\rm{DM}}=200$~GeV in the $M_{\rm{med}}$ vs ($g_{q}=g_{\rm{DM}}$) plane. We see that the EFT limit again overstates the limit at low $M_{\rm{med}}$ as the EFT framework does not account for the off-shell mediator production. This panel is also the only case where the EFT limit asymptotes to the MSDM limit. This occurs at large couplings and large mediator masses where $\Gamma_{\rm{med}}\gtrsimM_{\rm{med}}$, as discussed in our previous paper~\cite{Buchmueller:2013dya}.
\begin{figure}[t!]
\centering
\includegraphics[width=0.495\columnwidth]{EFT_SI.pdf}
\includegraphics[width=0.495\columnwidth]{EFT_SD.pdf}
\caption{A comparison between the 90\% CL mono-jet limit in our MSDM models (blue lines) and the EFT framework (green dashed) in the cross-section vs $m_{\rm{DM}}$ plane used by the direct detection community. The left and right panels show the limits on the SI and SD cross-sections appropriate for vector and axial-vector mediators respectively. The red dot-dashed line shows the current LUX limit. The MSDM and EFT limits should agree in the domain where the EFT framework is valid. For these choices of parameters, the EFT limit underestimates the MSDM limits for $m_{\rm{DM}}\lesssim300$~GeV and overestimates them for $m_{\rm{DM}}\gtrsim300$~GeV. The EFT limit gives a misleading representation
of the relative sensitivity of mono-jet and direct detection searches.
}
\label{fig:EFTcomparison2}
\end{figure}
For completeness, we also show in figure~\ref{fig:EFTcomparison2} a comparison of the MSDM and EFT limits in a format which may be more familiar. Here we map the MSDM limits for the cases $g_q=g_{\rm{DM}}=1$ (solid blue line) and $g_q=g_{\rm{DM}}=0.5$ (short dashed blue line) onto the usual cross-section vs DM mass plane used to present direct detection limits. The translation of the MSDM limits to the cross-section vs DM mass plane is performed by passing the mono-jet limits from figure~\ref{fig:Mdm-Mmed} through eqs.~\eqref{eq:SI2MSDM} and~\eqref{eq:SD2MSDM}. The left and right panels show the SI and SD cross-sections appropriate for vector and axial-vector mediators respectively. The red dot-dashed lines show the LUX limits and the long dashed green line shows the EFT limits.
We find that the EFT limit underestimates the MSDM collider limit by almost an order of magnitude for $m_{\rm{DM}}\lesssim300$~GeV (for $g_q=g_{\rm{DM}}=0.5$) and overestimates the MSDM limit for $m_{\rm{DM}}\gtrsim300$~GeV. As was discussed in section~\ref{sec:current}, the MSDM mono-jet production cross-section is resonantly enhanced in the region $m_{\rm{DM}}\lesssim300$~GeV. This enhancement is not accounted for in the EFT limits, which explains why the MSDM limit is more constraining than the EFT limit in this mass range.
The size of the enhancement in the 90\%~CL limit of scattering cross-sections $\sigma^0_{\rm{SI}}$ and $\sigma^0_{\rm{SD}}$ relative to the EFT limit can be estimated using the `rules of thumb' in Appendix~A of~\cite{Buchmueller:2013dya}. The MSDM and EFT scattering cross-sections are approximately related by $\sigma_{\rm{MSDM}} \approx \left(\Gamma_{\rm{med}}/ M_{\rm{med}}\right) \sigma_{\rm{EFT}}$. For the $g_q=g_{\rm{DM}}=1$ case, the ratio of the mediator width to the mediator mass is about 1/2, while for the $g_q=g_{\rm{DM}}=0.5$ case it is closer to 1/8. Accordingly we expect the MSDM direct detection limit to be lower than the EFT limit by a factor~2 and~8 respectively in the regime where the resonant enhancement occurs i.e.~at low to moderate DM masses. We see from figure~\ref{fig:EFTcomparison2} that this relation is a good approximation when $m_{\rm{DM}} \lesssim 300$~GeV for both the vector and axial-vector cases.
The EFT limits shown in figures~\ref{fig:EFTcomparison} and~\ref{fig:EFTcomparison2} are the result of a naive application of the limits on $\Lambda$ from figure~\ref{fig:validation}. Of course, in reality the EFT approach is only expected to be valid in a limited region of parameter space and various criteria have been proposed to designate the region where the EFT description is not valid. Perhaps the most naive criterion is to assume that the EFT limits are valid only when $\Lambda>m_{\rm{DM}}/(2\pi)$ (see e.g.~\cite{Goodman:2010yf}). This is a very weak criterion and does not restrict any of the EFT limits in figures~\ref{fig:EFTcomparison} and~\ref{fig:EFTcomparison2}. When applying the EFT limits to a more-complete model, a more reasonable minimum criterion for the validity of the EFT approach is to demand that $M_{\rm{med}} > 2m_{\rm{DM}}$. We have included the line $M_{\rm{med}} =2m_{\rm{DM}}$ in the upper left panel of figure~\ref{fig:EFTcomparison} to demonstrate how this restricts the domain of the EFT limit. In this case, only the dashed green line below the $M_{\rm{med}} =2m_{\rm{DM}}$ line is valid. While we see that this criterion excludes the EFT limit which differs most from the underlying MSDM limit (at large $m_{\rm{DM}}$), we find that the EFT limit in the valid region still fails to accurately reproduce the MSDM limit in this part of parameter space. For instance, at $m_{\rm{DM}}=100$~GeV the EFT limit on $M_{\rm{med}}$ underestimates the MSDM limit by 200~GeV. This highlights a general problem that even in regions where the EFT limit is valid, the limits are not model independent because the EFT framework does not include the mediator width, which strongly affects the mono-jet limits.
In summary, important physical effects are missed in the EFT framework because the full effect of the s-channel mediator propagator is ignored.
For instance, the limits in a full model may be substantially stronger than those found from the EFT limit on $\Lambda$ because the production can be resonantly enhanced. Furthermore, the LHC has sensitivity to the underlying coupling structure because the production cross-section is sensitive to the mediator width (which breaks the degeneracy between~$g_q$ and~$g_{\rm{DM}}$), but this is ignored because of the oversimplification of the EFT framework. The direct comparison of the MSDM and EFT limits highlights again how the EFT limits, when applied naively, lead to misleading conclusions about the real sensitivity of collider searches. Thus, the EFT framework is unsuitable for quantifying the true complementarity of collider and direct detection searches.
\section{Conclusions}
\label{sec:conc}
In many previous studies, the effective field theory (EFT) framework has been utilised to interpret and characterise studies of dark matter (DM) production at the LHC. The EFT framework is very powerful in its domain of validity. Unfortunately, as we discussed in our previous paper~\cite{Buchmueller:2013dya}, the limits from the EFT framework for collider searches apply only to a limited class of theories in which the mediator mass is very heavy and the couplings are very large. In particular, in the region where the EFT is valid, the mediator width is often larger than the mass of the mediator ($\Gamma_{\rm{med}}>M_{\rm{med}}$), meaning that a particle-like interpretation of the mediator is difficult (in the context of a single mediator).
In this paper we propose a Minimal Simplified Dark Matter (MSDM) framework, which is a more robust and accurate approach for interpreting and characterising collider searches of dark matter. In section~\ref{sec:SMS} we introduce MSDM models for vector and axial-vector mediators. In its most minimal variant our models are characterised by four free parameters: $m_{\rm{DM}},\, M_{\rm{med}},\, g_{\rm{DM}}$ and~$g_q$, which are the DM and mediator masses, and the mediator couplings to DM and quarks respectively. These parameters are sufficient to fully characterise DM production at colliders and scattering at direct detection experiments (see figure~\ref{fig:OP}). The advantage of the MSDM models is that the full event kinematics are captured and the dependence on all couplings and masses can be systematically studied.
After validating our implementation of the CMS mono-jet and LUX direct detection searches (see figures~\ref{fig:validation} to~\ref{fig:DDvalidation}), we map out the four-dimensional parameter space of our MSDM models by showing projections in two parameters. For vector mediators, we find that generally the LUX limits are much more constraining than the mono-jet limits (see left panels in figures~\ref{fig:Mdm-Mmed} to~\ref{fig:couplings}). The only exception is when $m_{\rm{DM}}\lesssim5$~GeV, where direct detection experiments lose sensitivity. In this DM mass range the LHC limits are more constraining (see figure~\ref{fig:low-mass}). In contrast, the LHC and LUX limits on axial-vector mediators generally show full complementarity, probing orthogonal directions in the parameter space (see right panels in figures~\ref{fig:Mdm-Mmed} to~\ref{fig:couplings}). For instance, the mono-jet search probes larger values of $M_{\rm{med}}$ while direct detection searches probe larger values of $m_{\rm{DM}}$.
We also provide estimates for the projected limits from the LHC for 14~TeV operation after $30~\rm{fb}^{-1}$, $300~\rm{fb}^{-1}$ and $3000~\rm{fb}^{-1}$, and from LZ after a 10 ton year exposure (see figure~\ref{fig:proj:Mdm-couplings}). It is interesting to note that the mono-jet reach in the axial-vector case approaches the neutrino noise, which, with current technology and calculations, is considered an irreducible background for direct detection experiments. It therefore seems critical to combine both search approaches in order to have the best possible coverage for discovery in the future.
We further explore the validity of the EFT framework by comparing the limits from our MSDM models with the EFT limits (see figures~\ref{fig:EFTcomparison} and~\ref{fig:EFTcomparison2}). The EFT limits fail to give a good approximation to the MSDM limits for both vector and axial-vector mediators over almost all of the parameter values considered. Confirming the results in~\cite{Buchmueller:2013dya}, we find that the EFT limits give a good representation of the MSDM limits only in the case of heavy mediator mass and large couplings. The EFT limits may also easily lead to misleading conclusions regarding the complementarity of collider and direct detection searches.
The MSDM framework is easily extendable to include scalar and pseudo-scalar interactions, Majorana fermion and scalar DM particles, as well as limits from indirect DM searches and additional collider searches, such as di-jet and $\rm{jets}+\slashed{E}_T$ searches. With these additions it should be possible to perform a global fit to a MSDM model, similar to the approaches already performed for supersymmetry (see for example~\cite{AbdusSalam:2009tr,Allanach:2011ya,Buchmueller:2013rsa}), to allow a more quantitative definition of the complementarity of collider and direct detection searches. This will become especially important in case of a discovery of a dark matter signal either at the LHC or at a direct detection experiment or ideally, at both.
\section*{Acknowledgements}
We thank Celine B\oe hm, Felix Kahlhoefer and Valya Khoze for productive discussions, and Emanuele Re for his extensive help with POWHEG throughout this project. Additionally, CM thanks Julien Billard, Enectali Figueroa-Feliciano and participants of the NORDITA `What is the dark matter?' program for helpful discussions regarding the limiting impact of coherent neutrino scattering on direct detection discovery. We also acknowledge the useful discussions at the Dark Matter brainstorming workshop at Imperial College London, and especially are grateful for input to our paper from Albert De Roeck and Greg Landsberg.
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"redpajama_set_name": "RedPajamaArXiv"
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The Agroforestry Group just announced a major upgrade to its durian plantations following a thorough review of its operations. A fertigation system has now been implemented which replaces its previous system of separate irrigation and fertilisation work. This new system will improve durian production yields and is more environmentally friendly relying on less water and fertiliser.
Mr. Paul Martin, Agroforestry Group's MD said "Agroforestry Group is constantly monitoring the changing landscape surrounding our business and we have been reviewing the effectiveness of fertigation systems for some time now. Although costly to implement, we feel it is necessary from an operational and environmental standpoint, particularly as the Agroforestry Group continues to grow further. Environmental concerns are part of Agroforestry Group's business model, and fertigation helps us expand and improve our products in a sound and efficient manner"
Mr. Martin added that traditional Agroforestry Group fertilisation and irrigation systems that most durian plantations employ are less efficient and harmful towards the environment as each activity is separate and not automated. Our fertigation system on the other hand combines both activities allowing for fertilisers to be administered along with irrigation water, through a fertilizer tank installed into the irrigation system. This ensures the even and timely distribution of water and fertilizer across all our durian. It also allows us to add additional necessary nutrients should they be needed to help growth.
The Agroforestry Group's decision to upgrade its entire durian plantations based in Johor, Malaysia, with fertigation comes only after an in-depth review of its effectiveness. It was found to be the most effective method for applying fertilizer and nutrients as it provides an easy means of precise doses to be delivered to its durian. It also provides the Agroforestry Group cost savings and improves production yield and quality in the long term, as it reduces fertilizer and water waste and ensures its durian are safe from issues relating to overfertilization or nutrient deficiencies.
Fertigation is just one of many new environmental-based improvements Agroforestry Group has made to its business and follows on the footsteps of its recently introduced reforestation environmental initiative which helps restore Malaysia's forests and protect its wildlife habitats. Agroforestry Group is constantly reviewing and monitoring its business operations and will be announcing further improvements later this year.
Agroforestry Group Launches Reforestation Initiative
Plantations International Separation with the Agroforestry Group Completed
Agroforestry Group Musang King Durian Tree Winner Announced
Agroforestry Group to Grow Black Thorn Durian in Malaysia
This entry was posted in Agroforestry Group and tagged Agroforestry Group. Bookmark the permalink.
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"redpajama_set_name": "RedPajamaCommonCrawl"
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\section{Introduction}
In recent years, topology and geometry blended with statistical methods have seen increasing application to the study of data analysis, visualization, and dimensionality reduction \cite{carlsson,carlsson_basics,CompyTopo,vasudevan2013,kusano2016,edelsbrunner2013,chung2015,munch2013,munch2016}. These applications range from classification and clustering in fields such as action recognition \cite{tda_action}, handwriting analysis \cite{tda_number}, and biology \cite{tda_wheeze,tda_clustering2015,gunnarcancer, HodgeCycle,CPD_me}, to classification of high entropy alloy \cite{Maroulas2020} and gas separation \cite{Townsend2020}, to the analysis of complex biological networks \cite{Maroulas2021}, and other complex dynamical systems \cite{tda_windows,tda_tracking} and sensor networks \cite{GdS06,GdS07,Ghrist12,CdS1,CdS2}.
Persistent homology \cite{persissensor, jholes, fullerene,tda_signal,persis_brain}, the workhorse of topological data analysis (TDA), has helped to compress nonlinear point cloud data from a new geometrically faithful point of view. In the realm of signal analysis, classification and clustering based on topological features of the signal identifies features that traditional signal analysis techniques fail to detect \cite{MaMa16,Marchese2018,tda_action,tda_timeseries,tda_wheeze}. Topological features, such as the number of connected components, cycles, and higher-dimensional voids, respectively, represent multi-stability, periodicity, and chaos in a dynamical system \cite{tda_wheeze, tda_windowgenes}.
The effective computation of persistence diagrams has become an area of intense active research, including a significant successful effort toward facilitating previously challenging computations. For example, the creation of persistence diagrams with packages such as Dionysus \cite{dionysus} and Ripser \cite{ripser} take advantage of certain properties of simplicial complexes \cite{persistwist}. Point clouds typically consist of many points. A set of $n$ such points possesses $2^n$ potential subsets that could contribute to the topology. The best classical algorithm for estimating these homological features of a data set with accuracy $\alpha$ takes time $O(2^n \log (1/\alpha)).$
More recently, quantum algorithms that compute topological features of data were developed. The first such algorithm was introduced in \cite{lloyd2016quantum} with run time $O(n^5/\alpha)$ -- exponentially faster than the best known classical algorithms. This algorithm was designed for a discrete-variable (DV) quantum system based on qubits, and it was extended to a continuous-variable (CV) substrate in \cite{siopsis2019quantum}. These two algorithms compute Betti numbers by analyzing a linear operator called the Dirac operator whose square is the combinatorial Laplacian. However, as was noted in \cite{gunn2019review}, these algorithms do not compute \emph{persistent} topological features so that one may track how topological features persist as the resolution of data changes and the underlying noise may vary. Recently, a quantum computation of persistent Betti numbers based on block-encoding and quantum singular value transformation was introduced in \cite{hayakawa2021quantum}. However, the study did not address any real implementation on data.
To that end, a few recent attempts on data for tracking the non-persistent topological features were studied. Indeed, the work in \cite{Huang2018} demonstrates a quantum algorithm presented in \cite{lloyd2016quantum} by employing a six-photon quantum processor to successfully analyze the topological features of a network including three data points. Moreover the work in \cite {1Qb} developed a quantum annealing approach for topologically analyzing point cloud data, and \cite{wie2017quantum} gives a quantum circuit to construct all maximal cliques of an $n$-node network using Grover's search algorithm.
The persistent combinatorial Laplacian is expressed as a quadratic function of a pertinent linear map called the boundary operator. However, it is computationally efficient to consider a map linear on the boundary. Here, we introduce a quantum algorithm that relies on a (persistent) Dirac operator which is linear in the boundary operator. Its square yields the persistent combinatorial Laplacian, hence the persistent Betti numbers, allowing us to track topological features across different scales and obtain persistence information. To that end, our algorithm is a generalization of the algorithm introduced in \cite{lloyd2016quantum}, and it similarly offers an exponential speedup over known classical algorithms of persistent homology.
Our discussion is organized as follows. In Section \ref{sec:2}, we review persistent homology introducing the important concepts relevant to the algorithm, such as the persistent combinatorial Laplacian and persistent Betti numbers. In Section \ref{sec:3}, we present our quantum algorithm introducing the persistent Dirac operator together with an outline of the quantum tools that are needed, such as quantum random access memory (QRAM), Grover's search algorithm, and phase estimation. In Section \ref{sec:4}, we apply our algorithm to a data set whose points are organized in squares, which was suggested in \cite{gunn2019review} as a case in which persistent Betti numbers differ from Betti numbers. Finally in Section \ref{sec:5}, we offer concluding remarks. Details of subroutines needed for our quantum algorithm are provided in Appendices \ref{app:A}, \ref{app:B}, and \ref{app:C} (Grover's algorithm, implementation of an exponential operator, and phase estimation, respectively).
\section{Persistent Homology}\label{sec:2}
Persistent homology studies objects called simplicial complexes. The classical algorithms that perform topological data analysis use the data to construct simplicial complexes, e.g., by connecting all the points in a point cloud within a certain distance from each other (Vietoris-Rips complex) and then varying the distance to obtain a filtration of simplicial complexes. After that, the algorithms proceed to compute the eigenvalues and eigenvectors of linear operators, such as the boundary operator and the persistent combinatorial Laplacian that act on the complexes.
Next, we briefly discuss simplicial complexes and homology, an algebraic descriptor for coarse shape in topological spaces. In turn, persistent homology, and its summary, persistence diagrams, are techniques for bringing the power and convenience of homology to the description of subspace filtrations of topological spaces.
We consider topological spaces of discernible dimension called manifolds.
\begin{defn}
A topological space $X$ is called a $k-$dimensional manifold if every point $x \in X$ has a neighborhood which is homeomorphic to an open neighborhood in $k$-dimensional Euclidean space.
\end{defn}
We generalize the fixed-dimension notion of a manifold in order to define simplicial homology for simplicial complexes.
We then discuss the Vietoris-Rips construction which is used to associate simplicial complexes to datasets.
\begin{defn} \label{simplex}
A $k$-simplex is a collection of $k+1$ linearly independent vertices along with all convex combinations of these vertices:
\begin{equation} \label{convex_combo}
\sigma=[ v_0,...,v_k ] = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { \sum_{i=0}^k \alpha_i v_i : \sum_{i=0}^k \alpha_i = 1 \textrm{ and } \alpha_i \geq 0 \, \forall i \RC.
\end{equation}
Topologically, a $k$-simplex is treated as a $k$-dimensional manifold (with boundary).
An oriented simplex is typically described by a list of its vertices, such as $[ v_0, v_1, v_2 ]$.
The faces of a simplex consist of all the simplices built from a subset of its vertex set;
for example, the edge $[v_1, v_2]$ and vertex $[v_2]$ are both faces of the triangle $[ v_0, v_1, v_2 ]$.
\end{defn}
\begin{defn} \label{simplicial_complex}
A simplicial complex $\K$ is a collection of simplices wherein \\
(i) if $\sigma \in \K$, then all its faces are also in $\K$, and \\
(ii) the intersection of any pair of simplices in $\K$ is another simplex in $\K$. \\
We denote the collection of $k$-simplices within $\K$ by $\K_{k}$.
\end{defn}
Conditions (i) and (ii) in Definition \ref{simplicial_complex} establish a unique topology on the realization of a simplicial complex which restricts to the subspace topology on each open simplex.
For finite simplicial complexes realized in $\R^{\dim}$, this topology is also consistent with the Euclidean subspace topology.
Here we define the homology groups for a simplicial complex through purely combinatorial means, which allows for automated computation.
\begin{defn} \label{defn_chain_group}
The chain group (over $\Z_3$) on a simplicial complex $\K$ of dimension $k$ is denoted by $C_k(\K)$ and is defined as formal sums of $k$-simplices in $\K$:
\begin{equation} \label{eqn_chain_group}
C_k(\K) = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { \sum_{\sigma \in \K_{k}} n_\sigma \sigma : n_\sigma \in \Z_{3} \RC.
\end{equation}
\end{defn}
\begin{defn} \label{defn_boundary_map}
The $k$-th boundary map is a homomorphism $\del{k} : C_k(\K) \goto C_{k-1}(\K)$ defined on each simplex as an alternating sum over the faces of dimension $k-1$:
\begin{equation} \label{eqn_boundary_map}
\del{k}[v_0,...,v_k] = \sum_{n=0}^k (-1)^n [v_0,...,v_{n-1},v_{n+1},...,v_k].
\end{equation}
\end{defn}
Chain groups give an algebraic way to describe subsets of simplices as a formal sum.
Toward this viewpoint, the chain group is often defined over $\Z_2 = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { 0 , 1 \RC$ instead of $\Z_{3}$.
In this case, the boundary maps can be understood classically; e.g., the boundary of a triangle yields (the sum of) its three edges and the boundary of an edge yields (the sum of) its endpoints.
When viewed over $\Z_{3}$, the presence of sign specifies simplex orientation.
Putting chain groups of every dimension together along with the boundary maps successively defined between them, we obtain a chain complex:
\begin{equation} \label{eqn_chain_complex}
\left\{} \newcommand{\RC}{\right\}}% Curly Braces { 0 \RC \xleftarrow{\bm 0} C_0(\K) \xleftarrow{\del{1}} C_1(\K) \xleftarrow{\del{2}} C_2(\K) \xleftarrow{\del{3}} ...
\end{equation}
The composition of subsequent boundary maps yields the trivial map \cite{CompyTopo};
this property is typically rephrased as $\im(\del{k+1}) \subset \ker(\del{k})$ which enables definition of the following modular groups.
\begin{defn} \label{defn_homology_group}
The homology group of dimension $k$ is given by
\begin{equation} \label{eqn_homology_group}
H_k(\K) = \ker(\del{k}) / \im(\del{k+1}) = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { \tilde{x} = x + \im(\del{k+1}) : x \in \ker(\del{k}) \RC\!,
\end{equation}
where $\tilde{x} = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { x + y : y \in \im(\del{k+1}) \RC$ defines the coset equivalence class of $x$.
\end{defn}
The dimension of $H_{k}$ is the $k$-th Betti number, denoted by $\beta_{k}$. It is shown in \cite{wang2020persistent} that the $k$-th Betti number is also the dimension of the kernel of the $k$-th combinatorial Laplacian $\mathcal{L}_{k}^{\K}:C_{k}(\K)\to C_{k}(\K)$ given by $\mathcal{L}_{k}^{\K} = \partial_{k}^{\dagger}\partial_{k} + \partial_{k+1}\partial_{k+1}^{\dagger},$
where $\partial_{k}^{\dagger}$ denotes the dual.
The generators of the homology group correspond to topological features of the complex $\K$;
for example, generators for the $0$-homology group correspond to connected components, generators of $1$-homology group correspond to holes in $\K$, etc.
The interpretation of these features is exemplified by taking the topological boundary of a $k+1$ ball (that is, a $k$-sphere);
for example, the boundary of an interval is two (disconnected) points while the boundary of a disc is a loop.
We wish to extend the notion of homology for a discrete set of data $\bm x = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { v_i \RC_{i=1}^N$ within a metric space $(X,d_X)$.
Treating the set itself as a simplicial complex, its homology yields only the cardinality of the data points.
So, we utilize the metric to obtain more information.
Here we denote by $B(x_0,r_0)$ a metric ball centered at $x_0$ of radius $r_0$.
Fix a radius $r > 0$ and consider the collection of neighborhoods $U = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { U_i \RC = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { B(v_i,r) \RC$ along with its union $\mathcal{U}_r = \cup_i B(v_i,r)$.
The collection of sets $\left\{} \newcommand{\RC}{\right\}}% Curly Braces { \mathcal{U}_r \RC_{r \in \R^+}$ naturally yields information about the arrangement within $X$ of the dataset $\bm x$ at various scales.
To make homology computations more tractable for $\mathcal{U}_r$, people often consider instead the associated Vietoris-Rips (VR) complexes which is (topologically) very similar.
\begin{defn} \label{defn_vr}
The Vietoris-Rips complex of the data $\left\{} \newcommand{\RC}{\right\}}% Curly Braces { v_{i}\RC$ at scale $\epsilon$, denoted by $S^{\epsilon}(\bm x)$ (or simply $S^\epsilon$), is the simplicial complex where a $k$-simplex $\sigma=[v_{i_0},..., v_{i_k}]$ is in $S^{\epsilon}(\bm x)$ if and only if $\text{diam}(\sigma) = \max_{j,j'}\left\{} \newcommand{\RC}{\right\}}% Curly Braces { d_{X}(v_{i_j},v_{i_{j'}})\RC\le \epsilon$.
\end{defn}
Examples of the VR complex for the same data at different scales are depicted in Fig. \ref{grow_cech}, where they are superimposed with the associated neighborhood space.
\begin{figure}
\begin{center}
\includegraphics[width=1.6in,height=1.4in]{figures/Cech_1.png}
\includegraphics[width=1.6in,height=1.4in]{figures/Cech_2.png}
\includegraphics[width=1.6in,height=1.4in]{figures/Cech_3.png}
\end{center}
\caption{The neighborhood space and VR complex of matching scale plotted at three different scales. Yellow indicates a triangle while orange indicates a tetrahedron. This family of simplicial complexes is the filtration utilized to compute and define persistent homology.} \label{grow_cech}
\end{figure}
Unfortunately the tools defined so far would only allow to obtain the Betti numbers of a fixed scale $\epsilon$, which is not very useful to analyze data because there is no way to differentiate between true topological features and noise. To tell them apart one must track the topological features across scales, those that persist for a long time are the true topological features, while those that persist for a short time are just noise. So, we must extend the notions above to include multiple simplicial complexes at once.
Consider a nested sequence or filtration of simplicial complexes
\begin{equation} \label{eqn_filtration}
\emptyset \subseteq \K_{1} \subseteq \K_{2} \subseteq ... \subseteq \K_{n}
\end{equation}
each complex $\K_{i}$ has associated chain groups $C_{k}(\K_{i})$, boundary operators $\partial_{k}^{i}$ and Homology groups $H_{k}^{i}$ as before. But now the inclusion maps $\iota:\K_{i}\goto\K_{j}$ between complexes induce homomorphisms $h_{k}^{i,j}=\iota_{*}:C_{k}(\K_{i})\goto C_{k}(\K_{j})$ between their corresponding chain groups.
\begin{defn} \label{defn_persist_hom_group}
For two nested simplicial complexes $\K_{i}\subseteq\K_{j}$ we define their $k$-th persistent Homology group $H_{k}^{i,j}$ as
\begin{equation}
H_{k}^{i,j} = \text{Im} (h_{k}^{i,j}) = \text{Ker}(\partial_{k}^{i})/(\text{Im}(\partial_{k+1}^{j}) \cap \text{Ker}(\partial_{k}^{i}))
\end{equation}
where $\text{Ker}(\partial_{k}^{i})$ is viewed as a subgroup of $\text{Ker}(\partial_{k}^{j})$. The dimension of $H_{k}^{i,j}$ is the $k$-th persistent Betti number $\beta_{k}^{i,j}$.
\end{defn}
Let $\tilde{C}_{k+1}^{i,j} = \left\{} \newcommand{\RC}{\right\}}% Curly Braces { x\in C_{k+1}(\K_{j}) : \partial_{k+1}^{j} x \in C_{k}(\K_{i})\RC$, that is, the subgroup of $C_{k+1}(\K_{j})$ defined by the $k+1$-simplices in $\K_{j}$ with boundary in $\K_{i}$. Then we can define the $k$-th persistent combinatorial Laplacian
\begin{equation}\label{eq:6}
\mathcal{L}_{k}^{i,j} = \tilde{\partial}_{k}^{i,i\dagger} \tilde{\partial}_{k}^{i,i} + \tilde{\partial}_{k+1}^{i,j} \tilde{\partial}_{k+1}^{i,j\dagger},
\end{equation}
where $\tilde{\partial}_{k+1}^{i,j}$ is the restriction of the boundary operator $\partial_{k+1}^{j}$ to $\tilde{C}_{k+1}^{i,j}$. Just as before, \cite{wang2020persistent} shows that the dimension of the kernel of $\mathcal{L}_{k}^{i,j}$ is the $k$-th persistent Betti number $\beta_{k}^{i,j}$.
Going back to the VR complexes introduced earlier, it follows from their definition that if $\epsilon\le\epsilon'$ then $S^{\epsilon}\subseteq S^{\epsilon'}$. Moreover, since there is only a finite number of data points, $S^{\epsilon}$ will remain unchanged for all $\epsilon>\text{diam}(\bm x)$. So, there is a maximal VR complex $S$ that contains all other VR complexes $S^{\epsilon}$, it's left to the reader to check that if the data consists of $n$ points then $S$ has exactly $2^n$ simplices. Choosing an increasing sequence of scales $0<\epsilon_1\le\epsilon_2\le\dots\epsilon_N$ yields a filtration of VR complexes $\emptyset \subseteq S^{\epsilon_{1}} \subseteq S^{\epsilon_{2}} \subseteq ... \subseteq S^{\epsilon_{N}}=S$.
\section{Quantum algorithm}
\label{sec:3}
Quantum algorithms proceed by first mapping the simplices, simplicial complexes, and filtrations onto quantum states, and then implementing linear unitary operators acting on them in order to extract topological features through measurements of quantum states. All $2^n$ possible simplices can be mapped onto quantum states in an $n$-qubit Hilbert space enabling an exponential speedup.
Our quantum algorithm uses a quantum Random Access Memory (QRAM) to access (or estimate) data in quantum parallel and create quantum states that encode the VR complexes. Indeed, the $k-$simplices, which are fully connected sets of $k+1$ vertices, are encoded as quantum states over $n$ qubits with $k+1$ qubits corresponding to the vertices of the simplex in the state $|1\rangle$ and the rest of the $n-k-1$ qubits in the state $|0\rangle$. The boundary of a $k$-simplex can be obtained as a superposition of all the $(k-1)-$simplices that result from flipping one of the qubits in the state $|1\rangle$ to $|0\rangle$. Furthermore, the projection operators necessary to express the persistent combinatorial Laplacian can be implemented using an oracle based on Grover's search algorithm. Then, one may form a superposition of simplices and use a quantum phase estimation algorithm to extract information about the kernel of the persistent combinatorial Laplacian, thus obtaining the desired persistent Betti numbers.
It is important to note that the resources needed to encode the simplicial complex (number of qubits) are only polynomial in the number of data points $n$, while in the classical case, the resources needed grow exponentially with $n$.
\subsection{Encoding simplices and filtrations as quantum states}
A $k$-simplex $\sigma = [v_{i_1},\dots,v_{i_k}]$ can be stored in a $n$-qubit register as $|\sigma\rangle = |v_1\rangle \otimes \dots \otimes |v_n\rangle$, with 1s at the positions of its $k+1$ vertices $v_{i_1},\dots,v_{i_k}$ and 0s elsewhere. Let $S$ denote the collection of all possible states of $n$ qubits, then $S$ effectively encodes the maximal VR complex described in section \ref{sec:2} with all possible simplices that can be formed with $n$ vertices or data points. Moreover, $\mathcal{H}$, the Hilbert space over $\Z_{3}$ with basis $S$ encodes the chain group of that complex.
We denote by $S_{k}$ the subset of states in $S$ encoding $k-$simplices, and by $\mathcal{H}_{k}$ the corresponding subspace of $\mathcal{H}$ which encodes the $k$-th chain group defined in \eqref{eqn_chain_group}. We can encode the order $k$ of a simplex $\sigma$ in a state $|k\rangle$ ($k=0,1,\dots,n-1$) by starting from $|0\rangle$ and performing permutations $0\to 1 \to \dots \to n-1 \to 0$, conditional upon the corresponding digit of $\sigma$ being 1. Thus, we perform $k$ permutations mapping $|0\rangle \to |k\rangle$. This can be implemented efficiently because the permutation is a 1-sparse matrix.
Similarly, we write $S^{\epsilon}$ for the subset of $S$ encoding simplices of diameter at most $\epsilon$, in other words the VR complex at scale $\epsilon$ as in Def. \ref{defn_vr}, and $\mathcal{H}^{\epsilon}$ for the corresponding subspace of $\mathcal{H}$. To encode the scale $\epsilon$ we need information on the data points that can be stored in quantum parallel in QRAM, if it is available, and accessed efficiently \cite{QRAM, giovannetti2008architectures}. For any $i,j = 1,2,\dots, n$,
$\mbox{QRAM}|i\rangle |j\rangle |0\rangle=|i\rangle |j\rangle |d(i,j)\rangle$, where $d(i,j)$ is the distance between points $i$ and $j$.
We introduce a register of qubits to record the parameter $\epsilon$ as $|\epsilon\rangle$. We need to know when $d(i,j) \le \epsilon$ to form a VR complex. This information will be stored in a qubit initially in the state $|0\rangle$, and flipped if the membership condition is satisfied. This is implemented with a unitary test that uses the qubit registers storing $d(i,j)$ and $\epsilon$ as controls to flip the last qubit,
\begin{equation}
U_{\text{test}}^\epsilon |d(i,j)\rangle |\epsilon\rangle |0\rangle = |d(i,j)\rangle |\epsilon\rangle |a^\epsilon(i,j)\rangle \ , \ \ a^\epsilon(i,j) = \left\{ \begin{array}{ccc}
0 & , & d(i,j) > \epsilon \\ 1 & , & d(i,j) \le \epsilon
\end{array} \right.
\end{equation}
Next, in order to know if $\sigma \in S^{\epsilon}$, we must check if $d(i,j) \le\epsilon$ for all $(i,j)$ pairs such that $v_i = v_j = 1$. To this end, we make $\mathcal{O} (k^2)$ calls to QRAM, where $k$ is the dimension of $\sigma$. For each pair $(i,j)$, we use $|\sigma\rangle$ as control to call QRAM and apply the test provided $v_i = v_j = 1$,
\begin{equation}
\text{QRAM}^\dagger U_{\text{test}}^\epsilon \text{QRAM} |\sigma\rangle |i\rangle |j\rangle |0\rangle |\epsilon\rangle |0\rangle = |\sigma\rangle |i\rangle |j\rangle |0\rangle |\epsilon\rangle |a^\epsilon (i,j)\rangle
\end{equation}
Membership of $\sigma$ in the VR complex $S^\epsilon$ is decided if for all $(i,j)$ we end up with $a^\epsilon (i,j) =1$.
The above steps allow us to implement the quantum oracle
\begin{equation}\label{eq:4}
\mathcal{O}_k^\epsilon |\sigma\rangle|0\rangle = |\sigma\rangle |a_{\sigma}^\epsilon\rangle \ , \ \ a_{\sigma}^\epsilon = \left\{ \begin{array}{ccc}
0 & , & \sigma\notin S_k^\epsilon \\ 1 & , & \sigma\in S_k^\epsilon
\end{array} \right.
\end{equation}
determining membership in $S_{k}^{\epsilon} = S_{k}\cap S^{\epsilon}$, which encodes the $k$-simplices in the $\epsilon$-complex.
The oracle in Eq. \eqref{eq:4} can be used for the implementation of the projection operators,
\begin{equation}\label{eq:P} P_k^\epsilon = \sum_{\sigma\in S_k^\epsilon} |\sigma\rangle\langle \sigma|, \end{equation}
onto $\mathcal{H}_k^\epsilon,$ the subspace of the Hilbert space $\mathcal{H}_k$
spanned by the simplices in $S_k^\epsilon$, which are needed to construct the persistent combinatorial Laplacian. To implement the projection $P_k^\epsilon$, we perform amplitude amplification \cite{brassard2002quantum} based on Grover's search algorithm \cite{grover} (for details, see Appendix \ref{app:A}).
\subsection{Persistent Dirac operator}
The boundary operator $\partial_k$ mapping $\mathcal{H}_{k}$ to $\mathcal{H}_{k-1}$ as defined in \eqref{eqn_boundary_map} may be encoded using 1-qubit Pauli X gates, and expressed similarly by its action on the bases $S_k$ and $S_{k-1}$
\begin{equation}\label{eq:b} \partial_k |\sigma_k\rangle := \sum_{l=0}^k (-)^lX_{i_l} |\sigma_k\rangle\ = \sum_{l=0}^k (-)^l |\sigma_{k-1} (l)\rangle , \end{equation}
where $|\sigma_{k-1} (l)\rangle$ is the $(k-1)$-simplex obtained from $|\sigma\rangle$ by flipping its $l$-th non-zero qubit. One easily deduces $\partial_{k-1} \partial_k = 0$.
For persistent homology we need to restrict the boundary operator \eqref{eq:b} as in the prelude to Eq.\ \eqref{eq:6},
\begin{equation}\label{eq:br} \tilde{\partial}_k^{\epsilon,\epsilon'} = P_{k-1}^\epsilon \partial_k P_k^{\epsilon'} \ , \end{equation}
where the projections are defined in \eqref{eq:P}. Then the persistent combinatorial Laplacian $\mathcal{L}_{k}^{\epsilon,\epsilon'}$ is as in \eqref{eq:6} with $\K_i = S^{\epsilon}$ and $\K_j = S^{\epsilon'}$.
Next, we introduce the persistent Dirac operator which plays a central role in our quantum algorithm. For quantum computation, it is advantageous to work with an operator which is linear in the boundary map. Unlike the persistent combinatorial Laplacian, the persistent Dirac operator is linear in the boundary operator, and its square yields the persistent combinatorial Laplacian given in Eq. \eqref{eq:6}.
We define the $k$-th persistent Dirac operator as the Hermitian operator
\begin{equation}\label{eq:18} {B}^{\epsilon,\epsilon'}_k = \left( \begin{array}{ccc} 0 & \tilde{\partial}_k^{\epsilon,\epsilon} & 0\\
\tilde{\partial}_k^{\epsilon,\epsilon\dagger} & 0 & \tilde{\partial}_{k+1}^{\epsilon,\epsilon'} \\
0 &\tilde{\partial}_{k+1}^{\epsilon,\epsilon'\dagger} & 0
\end{array}\right) - \xi \left( \begin{array}{ccc} P^\epsilon_{k-1} & 0 & 0\\
0 & -P^\epsilon_k & 0 \\
0 &0 & P^{\epsilon'}_{k+1}
\end{array}\right), \end{equation}
where $\xi\in\mathbb{R}$ is an arbitrary parameter. Its square is
\begin{equation} \left( {B}^{\epsilon,\epsilon'}_k \right)^2 = \left( \begin{array}{ccc} \tilde{\partial}_k^{\epsilon,\epsilon} \tilde{\partial}_k^{\epsilon,\epsilon\dagger} & 0 & \tilde{\partial}_k^{\epsilon,\epsilon} \tilde{\partial}_{k+1}^{\epsilon,\epsilon'} \\
0 & \mathcal{L}_k^{\epsilon,\epsilon'} & 0 \\
\tilde{\partial}_{k+1}^{\epsilon,\epsilon'\dagger} \tilde{\partial}_k^{\epsilon,\epsilon\dagger} &0 & \tilde{\partial}_{k+1}^{\epsilon,\epsilon'\dagger} \tilde{\partial}_{k+1}^{\epsilon,\epsilon'}
\end{array}\right) + \xi^2 \left( \begin{array}{ccc} P^\epsilon_{k-1} & 0 & 0 \\
0 & P^\epsilon_k & 0 \\
0 & 0 & P^{\epsilon'}_{k+1}
\end{array}\right) \end{equation}
written in block form with one of the blocks being the $k$th persistent combinatorial Laplacian shifted by $\xi^2$.
Let $\lambda$ be an eigenvalue of ${B}^{\epsilon,\epsilon'}_k$. Evidently, the corresponding eigenspace corresponds to an eigenspace of the Laplacian $\mathcal{L}_k^{\epsilon,\epsilon'}$ with eigenvalue
$ \gamma = \lambda^2 - \xi^2. $ Considering $\gamma = 0,$ one gets the the kernel of $\mathcal{L}_k^{\epsilon,\epsilon'},$ whose dimension is the $k$th persistent Betti number,
$ \beta_k^{\epsilon,\epsilon'} = |\ker \mathcal{L}^{\epsilon,\epsilon'}_k |.$
In other words, one is interested in the eigenspaces of ${B}^{\epsilon,\epsilon'}_k$ with eigenvalues $\lambda = \pm \xi$. For the persistent Betti numbers, we focus on the eigenspace with $\lambda = \xi$, because there is a one-one correspondence between its states and those in the null space of the Laplacian. Thus, although $\xi$ is arbitrary, we need to choose $\xi \ne 0$ in order to separate the eigenspaces with $\lambda = - \xi$ and $\lambda = \xi$. The choice $\xi =0$ leads to overcounting of the states in the null space of the Laplacian and an incorrect estimate of Betti numbers.
To see this, consider the action on vectors of the form $(X_{k-1}^\epsilon, Y_k^\epsilon, Z_{k+1}^{\epsilon'} )^T$ which satisfy the constraints $P^\epsilon X_{k}^\epsilon =X_k^\epsilon$, $P^\epsilon Y_k^\epsilon = Y_k^\epsilon$, and $P^{\epsilon'} Z_{k}^{\epsilon'} =Z_k^{\epsilon'}$.
For eigenvectors of $B^{\epsilon,\epsilon'}_k$ corresponding to eigenvalue $\lambda$, we obtain the system of equations
\begin{align}
- {\xi} X_{k-1}^\epsilon + \tilde{\partial}_k^{\epsilon,\epsilon} Y_k^\epsilon &= \l X_{k-1}^\epsilon \nonumber\\
{\xi} Y_k^\epsilon + \tilde{\partial}_k^{\epsilon,\epsilon\dagger} X_{k-1}^\epsilon + \tilde{\partial}_{k+1}^{\epsilon,\epsilon'} Z_{k+1}^{\epsilon'} &= \l Y_k^\epsilon \nonumber\\
- {\xi} Z_{k+1}^{\epsilon'} + \tilde{\partial}_{k+1}^{\epsilon,\epsilon'\dagger} Y_k^\epsilon &= \l Z_{k+1}^{\epsilon'}
\end{align}
For $\lambda \ne -\xi$, we can use two of the equations to express $X_{k-1}^\epsilon$ and $Z_{k+1}^{\epsilon'}$ in terms of $Y_k^\epsilon$, and the second equation to show that $Y_k^\epsilon$ is an eigenvector of the Laplacian with eigenvalue $\gamma$. Conversely, given an eigenvector $Y_k^\epsilon$ of the Laplacian with eigenvalue $\gamma$, the vector $(X_{k-1}^\epsilon, Y_k^\epsilon, Z_{k+1}^{\epsilon'} )^T$ with $X_{k-1}^\epsilon = \frac{1}{\lambda + \xi } \tilde{\partial}_k^{\epsilon,\epsilon} Y_k^\epsilon$ and $Z_{k+1}^{\epsilon'} = \frac{1}{\lambda + \xi } \tilde{\partial}_{k+1}^{\epsilon,\epsilon'\dagger} Y_k^\epsilon$ is an eigenvector of the Dirac operator with eigenvalue $\lambda$, demonstrating a one-one correspondence between the two eigenspaces.
For $\l = -\xi$, we obtain eigenvectors with $Y_k^\epsilon$ in the kernel of the Laplacian. We need to separate them from the eigenvectors with $\l = {\xi}$ in order not to overcount the vectors in the null space of the Laplacian.
The persistent Dirac operator \eqref{eq:18} can be decomposed as
\begin{equation}\label{eq:18a} {B}^{\epsilon,\epsilon'}_k = P_k^{\epsilon,\epsilon'} B_k P_k^{\epsilon,\epsilon'} \ , \ B_k = \left( \begin{array}{ccc} -\xi I & \partial_k & 0\\
\partial_k^{\dagger} & \xi I & {\partial}_{k+1} \\
0 & {\partial}_{k+1}^{\dagger} & -\xi I
\end{array}\right) \ , \ P_k^{\epsilon,\epsilon'} = \left( \begin{array}{ccc} P^\epsilon_{k-1} & 0 & 0\\
0 & P^\epsilon_k & 0 \\
0 &0 & P^{\epsilon'}_{k+1}
\end{array}\right), \end{equation}
To encode these $3\times 3$ block matrices, we introduce a qutrit label $|b\rangle$, with $b\in \{ -1,0,+1\}$, and consider the space spanned by $|b\rangle |\sigma_{k+b}^b\rangle$, where $\sigma_{k+b}^b \in S_{k+b}^{\epsilon_b}$, with $\epsilon_b = \epsilon$ for $b=-1,0$ and $\epsilon_b = \epsilon'$ for $b= +1$. Then we may write
\begin{equation} P_k^{\epsilon,\epsilon'} = \sum_{b\in \{ -1,0,+1 \} } |b\rangle\langle b| \otimes P_{k+b}^{\epsilon_b} \ , \end{equation}
and
\begin{equation}\label{eq:B} B_k = \sum_{b\in \{ 0,+1 \} } |b-1\rangle\langle b| \otimes \partial_{k+b} + \text{h.c.} + \xi \sum_{b\in \{ -1,0,+1 \} } (-)^b |b\rangle\langle b| \otimes I \end{equation}
The projections $P_k^{\epsilon,\epsilon'}$ can be implemented using Grover's algorithm as outlined above and described in detail in Appendix \ref{app:A}, whereas the unrestricted Dirac operator $B_k$ can be encoded in a qubit register. For $\xi =1$, a qutrit suffices for the encoding of $B_k$, because all of its matrix elements are in the set $\{ -1,0,+1 \}$.
\begin{comment}
\subsubsection{Obtaining the combinatorial Laplacian from the Dirac operator}
For a fixed $k$, $C^{\epsilon,\epsilon'}$ maps the Hilbert space spanned by $\{ |-1\rangle |k-1\rangle |s_{k-1}^{-1}\rangle , |0\rangle |k\rangle |s_{k}^{0}\rangle, |+1\rangle |k+1\rangle |s_{k+1}^{-1}\rangle \}$ onto itself. Let $C^{\epsilon,\epsilon'}_k$ be the restriction of $C^{\epsilon,\epsilon'}$ in this subspace. It can be written as a $3\times3$ block matrix with blocks labeled by the qutrit,
\begin{equation}\label{eq:C} {C}^{\epsilon,\epsilon'}_k = \left( \begin{array}{cccccc} \a P^\epsilon_k & \tilde{\partial}_k^{\epsilon,\epsilon} & 0\\
\tilde{\partial}_k^{\epsilon,\epsilon\dagger} & 0 & \tilde{\partial}_{k+1}^{\epsilon,\epsilon'} \\
0 &\tilde{\partial}_{k+1}^{\epsilon,\epsilon'\dagger} & \a P^{\epsilon'}_k
\end{array}\right) = P^{\epsilon,\epsilon'} C_k P^{\epsilon,\epsilon'} \ , \ \ C_k = \left( \begin{array}{cccccc} \a I & {\partial}_k & 0\\
{\partial}_k^\dagger & 0 & {\partial}_{k+1} \\
0 & {\partial}_{k+1}^{\dagger} & \a I
\end{array}\right) \ , \end{equation}
acting on vectors of the form $(X_{k-1}^\epsilon, Z_k^\epsilon, Y_{k+1}^{\epsilon'} )^T$ which satisfy the constraints $P^\epsilon X_{k}^\epsilon =X_k^\epsilon$, $P^\epsilon Z_k^\epsilon = Z_k^\epsilon$, and $P^{\epsilon'} Y_{k}^{\epsilon'} =Y_k^{\epsilon'}$. The modified Dirac operator can be written as a direct sum of these restrictions, $C^{\epsilon,\epsilon'} = \sum_k \oplus C^{\epsilon,\epsilon'}_k$.
For eigenvectors of $C^{\epsilon,\epsilon'}_k$ corresponding to eigenvalue $\lambda$, we obtain the system of equations
\begin{align}
\a X_{k-1}^\epsilon + \tilde{\partial}_k^{\epsilon,\epsilon} Z_k^\epsilon &= \l X_{k-1}^\epsilon \nonumber\\
\tilde{\partial}_k^{\epsilon,\epsilon\dagger} X_{k-1}^\epsilon + \tilde{\partial}_{k+1}^{\epsilon,\epsilon'} Y_{k+1}^{\epsilon'} &= \l Z_k^\epsilon \nonumber\\
\a Y_{k+1}^{\epsilon'} + \tilde{\partial}_{k+1}^{\epsilon,\epsilon'\dagger} Z_k^\epsilon &= \l Y_{k+1}^{\epsilon'}
\end{align}
For $\lambda \ne \alpha$, we can express $X_{k-1}^\epsilon$ and $Y_{k+1}^{\epsilon'}$ in terms of $Z_k^\epsilon$. We deduce
\begin{align}
\tilde{\partial}_k^{\epsilon,\epsilon} Z_k^\epsilon &= (\l -\a) X_{k-1}^\epsilon\nonumber\\
\tilde{\partial}_{k+1}^{\epsilon,\epsilon'\dagger} Z_k^\epsilon &= (\l - \a ) Y_{k+1}^{\epsilon'} \nonumber\\
\mathcal{L}^{\epsilon,\epsilon'}_k Z_k^\epsilon &= \l (\l - \a ) Z_k^\epsilon
\label{eq:20}\end{align}
Therefore, $Z_k^\epsilon$ is an eigenvector of the Laplacian with eigenvalue
\begin{equation}\label{eq:25} \gamma = \lambda (\lambda -\alpha) \end{equation}
If $\l = \a$, we obtain solutions with $Z_k^\epsilon$ in the kernel of the Laplacian. Had we chosen $\alpha =0$, these additional spurious solutions would have been in the kernel of the Dirac operator leading to overcounting of the dimension of the kernel of the Laplacian.
For $\alpha\ne 0$, there is a correspondence between the eigenspaces of the $k$th persistent Dirac operator and the $k$th persistent combinatorial Laplacian with corresponding eigenvalues related by \eqref{eq:25}.
Importantly, their respective null spaces have the same dimension.
Thus, the null space of the Dirac operator yields the null space of the Laplacian whose dimension is the $k$th persistent Betti number $\beta_k^{\epsilon,\epsilon'}$.
For simplicity we set $\alpha = 1$ in what follows, as its value does not affect Betti numbers.
\end{comment}
\subsection{Persistent Betti numbers}
As discussed earlier, the $k$th persistent Betti number
$\beta_k^{\epsilon,\epsilon'}$ is the dimension of the eigenspace of the persistent Dirac operator $B_k^{\epsilon,\epsilon'}$ (Eq.\ \eqref{eq:18}) with eigenvalue $\lambda = \xi$. To compute it, we apply phase estimation (for details, see Appendix \ref{app:C}), and derive the probability distribution
\begin{equation}\label{eq:9}
\mathcal{P} (p) = \frac{1}{\bm{N}} \sum_{\lambda} g_\lambda ( p) \ , \ \ g_\lambda (p) = \frac{1}{M^2} \frac{\sin^2 \pi l\lambda }{\sin^2 \frac{\pi(l\lambda -p)}{M}} \ ,
\end{equation}
where $l, M$ are arbitrary positive integers, $p=0,1,\dots, M-1$, and $\bm{N}$ is the number of eigenvalues $\lambda$ of $B_k^{\epsilon,\epsilon'}$. One easily checks that $\sum_{p=0}^{M-1} g_\lambda (p) = 1$ for any $\lambda$, therefore, $\sum_{p=0}^{M-1} \mathcal{P} (p) = 1$, as expected.
If one is interested in the spectrum of the persistent Dirac operator, $M$ and $l$ must be chosen in a way that the spectrum is covered with the different values of $p$, i.e., each eigenvalue is approximated as $\lambda \approx \frac{p}{l}$. Then $g_\lambda (p)$ is strongly peaked at $p \approx l\lambda$. At the peak, $g_\lambda (p) = 1$. Therefore, the probability distribution $\mathcal{P} (p)$ has a peak at each eigenvalue of the persistent Dirac operator whose height is proportional to the dimension of the corresponding eigenspace.
Since we are only interested in the eigenvalue $\lambda = \xi$, we only need to capture the peak at $p \approx l\xi$ and make sure it is resolved from other neighboring peaks. The persistent Betti number is obtained as $\beta_k^{\epsilon,\epsilon'} = \left. g_\xi (p) \right|_{p\approx l\xi}$.
\section{An application}
\label{sec:4}
This Section demonstrates how our algorithm computes persistence Betti numbers, which track topological features across different scales. This extends previous work in \cite{lloyd2016quantum} and \cite{siopsis2019quantum} where the proposed quantum algorithms calculated Betti numbers only without addressing persistence features. To do this, we apply our method to the data set suggested in \cite{gunn2019review} and described below for the sake of completeness.
\begin{figure}[ht]
\begin{center}
\includegraphics[width=\textwidth]{two-squares.png}
\end{center}
\caption{
\textit{(a)} The two squares example as appeared in \cite{gunn2019review}; \textit{(b)} Construction of the VR for $\epsilon_1$; \emph{(c)} VR for $\epsilon_2$} \label{fig:two_squares}
\end{figure}
Consider a point cloud of 8 points consisting of two well-separated squares, as in Figure \ref{fig:two_squares}. The smaller square has sides of length 1, while the larger square has sides of length $\sqrt{2}$. The distance between the two squares exceeds 2. It is easy to see (Figure \ref{fig:two_squares}) that the smaller square produces a loop in the VR complex at scale $1$ which disappears at scale $\sqrt{2}$, while at the same time the larger square produces a new loop.
It follows that for
$1 < \epsilon_{1} < \sqrt{2} < \epsilon_{2} < 2 $,
the one--dimensional persistent Betti numbers corresponding to the point cloud of Figure \ref{fig:two_squares} are
\begin{equation} \beta_{1}^{\epsilon_1,\epsilon_1} = 1 \ , \ \beta_{1}^{\epsilon_2,\epsilon_2} = 1 \ , \ \beta_{1}^{\epsilon_1,\epsilon_2} = 0 \ . \end{equation}
It should be pointed out that the algorithms proposed in \cite{lloyd2016quantum,siopsis2019quantum} can detect the number of loops in the VR complex at scales $\epsilon_1$ and $\epsilon_2$ by computing $\beta_{1}^{\epsilon_1,\epsilon_1}$ and $\beta_{1}^{\epsilon_2,\epsilon_2}$, respectively. However these Betti numbers do not hold any persistence information. The algorithms in \cite{lloyd2016quantum,siopsis2019quantum} cannot calculate the persistence Betti number $\beta_{1}^{\epsilon_1,\epsilon_2}$ which holds the persistence information (number of loops present at scale $\epsilon_1$ that persist to scale $\epsilon_2$). Thus, these algorithms cannot track topological features across different scales.
Moreover, even though $\beta_{1}^{\epsilon_1,\epsilon_1} = \beta_{1}^{\epsilon_2,\epsilon_2}$, the persistence Betti number cannot be deduced from $\beta_{1}^{\epsilon_1,\epsilon_1}$ and $\beta_{1}^{\epsilon_2,\epsilon_2}$. This is because it indicates that the loops at scales across $\sqrt{2}$ are different, which is additional information to the existence of a loop encoded in the other two Betti numbers.
\begin{figure}[ht]
\centering
\subfigure[]{\includegraphics[width=0.3\textwidth]{phase-estimation-11.png}}
\subfigure[]{\includegraphics[width=0.3\textwidth]{phase-estimation-22.png}}
\subfigure[]{\includegraphics[width=0.3\textwidth]{phase-estimation-12.png}}
\caption{Probability density corresponding to the persistent Dirac operator (a) $B_{1}^{\epsilon_1,\epsilon_1}$, (b) $B_{1}^{\epsilon_2,\epsilon_2}$, and (c) $B_{1}^{\epsilon_1,\epsilon_2}$, with $\xi = 1$, $l=3$, $M=16$. The heights at $p=3$, multiplied by the dimension of the Hilbert space (8, 22, and 12, respectively), yield the Betti numbers $\beta_1^{\epsilon_1,\epsilon_1} = \beta_1^{\epsilon_2,\epsilon_2} = 1$, and the persistent Betti number $\beta_1^{\epsilon_1,\epsilon_2} =0$.} \label{fig:2}
\end{figure}
\begin{figure}[ht]
\[
\xymatrix @*=<0em> @C=3em @R=.5em {
\lstick{\ket{0}} & \gate{H} & \ctrl{4} & \qw & \qw & \qw & \qw & \qw & \qw \\
\lstick{\ket{0}} & \gate{H} & \qw & \ctrl{4} & \qw &\qw &\qw &\qw & \qw \\
\lstick{\ket{0}} & \gate{H} & \qw & \qw & \ctrl{4} & \qw & \qw &\qw &\qw \\
\lstick{\ket{0}} & \gate{H} & \qw & \qw & \qw & \ctrl{4} & \qw & \qw &\qw \\
\lstick{\ket{0}} & \qw & *+<.02em,.02em>{\xy ="i","i"-<.39em,0em>;"i"+<.39em,0em> **\dir{-}, "i"-<0em,.39em>;"i"+<0em,.39em> **\dir{-},"i"*\xycircle<.4em>{} \endxy} \qw & \qw & \qw & \qw & \multigate{3}{U_B} & \qw & \qw \\
\lstick{\ket{0}} & \qw & \qw & *+<.02em,.02em>{\xy ="i","i"-<.39em,0em>;"i"+<.39em,0em> **\dir{-}, "i"-<0em,.39em>;"i"+<0em,.39em> **\dir{-},"i"*\xycircle<.4em>{} \endxy} \qw & \qw & \qw &\ghost{U_B} &\qw &\qw \\
\lstick{\ket{0}} & \qw & \qw & \qw & *+<.02em,.02em>{\xy ="i","i"-<.39em,0em>;"i"+<.39em,0em> **\dir{-}, "i"-<0em,.39em>;"i"+<0em,.39em> **\dir{-},"i"*\xycircle<.4em>{} \endxy} \qw & \qw & \ghost{U_B} & \qw &\qw \\
\lstick{\ket{0}} & \qw & \qw & \qw & \qw & *+<.02em,.02em>{\xy ="i","i"-<.39em,0em>;"i"+<.39em,0em> **\dir{-}, "i"-<0em,.39em>;"i"+<0em,.39em> **\dir{-},"i"*\xycircle<.4em>{} \endxy} \qw & \ghost{U_B} & \qw &\qw \\
\lstick{\ket{0}} & \gate{H} & \qw & \qw & \qw & \qw & \ctrl{-1} & \multigate{3}{U_{QFT}} & *=<1.8em,1.4em>{\xy ="j","j"-<.778em,.322em>;{"j"+<.778em,-.322em> \ellipse ur,_{}},"j"-<0em,.4em>;p+<.5em,.9em> **\dir{-},"j"+<2.2em,2.2em>*{},"j"-<2.2em,2.2em>*{} \endxy} \POS ="i","i"+UR;"i"+UL **\dir{-};"i"+DL **\dir{-};"i"+DR **\dir{-};"i"+UR **\dir{-},"i" \qw \\
\lstick{\ket{0}} & \gate{H} & \qw & \qw & \qw & \qw &\ctrl{-1} &\ghost{U_{QFT}} &*=<1.8em,1.4em>{\xy ="j","j"-<.778em,.322em>;{"j"+<.778em,-.322em> \ellipse ur,_{}},"j"-<0em,.4em>;p+<.5em,.9em> **\dir{-},"j"+<2.2em,2.2em>*{},"j"-<2.2em,2.2em>*{} \endxy} \POS ="i","i"+UR;"i"+UL **\dir{-};"i"+DL **\dir{-};"i"+DR **\dir{-};"i"+UR **\dir{-},"i" \qw\\
\lstick{\ket{0}} & \gate{H} & \qw & \qw & \qw &\qw & \ctrl{-1} & \ghost{U_{QFT}} & *=<1.8em,1.4em>{\xy ="j","j"-<.778em,.322em>;{"j"+<.778em,-.322em> \ellipse ur,_{}},"j"-<0em,.4em>;p+<.5em,.9em> **\dir{-},"j"+<2.2em,2.2em>*{},"j"-<2.2em,2.2em>*{} \endxy} \POS ="i","i"+UR;"i"+UL **\dir{-};"i"+DL **\dir{-};"i"+DR **\dir{-};"i"+UR **\dir{-},"i" \qw \\
\lstick{\ket{0}} & \gate{H} & \qw & \qw & \qw & \qw & \ctrl{-1} & \ghost{U_{QFT}} & *=<1.8em,1.4em>{\xy ="j","j"-<.778em,.322em>;{"j"+<.778em,-.322em> \ellipse ur,_{}},"j"-<0em,.4em>;p+<.5em,.9em> **\dir{-},"j"+<2.2em,2.2em>*{},"j"-<2.2em,2.2em>*{} \endxy} \POS ="i","i"+UR;"i"+UL **\dir{-};"i"+DL **\dir{-};"i"+DR **\dir{-};"i"+UR **\dir{-},"i" \qw
}
\] \caption{Quantum circuit for the calculation of Betti number $\beta_1^{\epsilon_1,\epsilon_2}$.}\label{fig:qc}
\end{figure}
Figure \ref{fig:qc} shows the quantum circuit for the calculation of Betti number $\beta_1^{\epsilon_1,\epsilon_2}$. The Dirac operator $B_1^{\epsilon_1,\epsilon_2}$ acts on an 12-dimensional Hilbert space. For $\xi =1$ are $\lambda = -1, \pm\sqrt{5}$, each of degeneracy 4. Notice that $1$ is not an eigenvalue, therefore $\beta_1^{\epsilon_1,\epsilon_2} =0$. This is confirmed by the quantum algorithm depicted in Figure \ref{fig:qc} as explained below.
A register of 4 qubits initially in the state $|0000\rangle_1$ is brought into the state $\frac{1}{4} \sum_{x=0}^{15} |x\rangle_1$, by acting with the Hadamard matrix on each. Then we use them as control to apply CNOT on each of 4 qubits in an additional register in the state $|0000\rangle_2$, thus entangling them to the state $\frac{1}{4} \sum_{x=0}^{15} |x\rangle |x\rangle_2$. We introduce a third register of 4 qubits (choosing $M=16$) in the state $|0000\rangle_R$ and act on each with the Hadamard gate to bring them into the state $\frac{1}{4} \sum_{y=0}^{15} |y\rangle_R$. We then use them as control to act on register 2 with the exponential Dirac operator (see Appendix \ref{app:C} for details). Finally, we measure all 4 qubits in the register $R$. The result is the probability distribution $\mathcal{P} (p)$, where $p=0,1,\dots, 15$ (Eq.\ \eqref{eq:9}) depicted in Figure \ref{fig:2}(c). With the choice $l=3$, $M=16$, a measurement of the register of 4 qubits yields no peak at $p=3$
, showing that $\beta_1^{\epsilon_1,\epsilon_2} =0$.
The persistent Betti number $\beta_1^{\epsilon_1,\epsilon_1}$ is calculated using an eight-dimensional Hilbert space. The eigenvalues of the persistent Dirac operator for $\xi =1$ are $\pm 1, \pm \sqrt{3}, \pm\sqrt{5}$. Two of the eigenvalues ($\pm\sqrt{3}$) are degenerate with multiplicity 2. We are interested in the multiplicity of the eigenvalue $\lambda = \xi = 1$, which is shown to be 1 by the peak at $p=3$ of height $1/8$ (see Fig.\ref{fig:2}(a)). The closest eigenvalue to $\lambda =1$ is $\lambda = \sqrt{3}$ which is near $p=5$. Thus, the peak at the nearest eigenvalue is well separated from the one of interest (in Figure \ref{fig:2}(a), one can see a dip at $p=4$, and the height $\mathcal{P} (5) \approx \frac{2}{8}$, confirming the double degeneracy of the eigenvalue $\lambda = \sqrt{3}$).The quantum circuit flows as the one in Figure \ref{fig:qc} but with registers 1 and 2 having 3 qubits each.
The calculation of Betti number $\beta_1^{\epsilon_2,\epsilon_2}$ proceeds similarly. The Hilbert space is 22-dimensional and for $\xi =1$, the eigenvalues are the same as for $\beta_1^{\epsilon_1,\epsilon_1}$, but with degeneracies 1, 3, 2, 7
for $\lambda = 1, -1, \pm\sqrt{3}, \pm\sqrt{5}$, respectively. The distance from the eigenvalue of interest ($\lambda =1$) to its closest one ($\lambda = \sqrt{3}$) is same as before, therefore we can choose $l=3, M=16$, again. The quantum circuit is similar to the one in Figure \ref{fig:qc} except that registers 1 and 2 need 5 qubits each. The resulting probability distribution is depicted in Figure \ref{fig:2}(b) showing that $\beta_1^{\epsilon_2,\epsilon_2} =1$.
\section{Conclusion}
\label{sec:5}
Our work established a quantum persistent homology algorithm that detects and computes the topological features of point cloud data as their resolution changes. Our method considered the persistent Laplacian operator, generalizing the Laplacian operator discussed in \cite{lloyd2016quantum, siopsis2019quantum}. We provided an implementation on the challenging problem of two particular point cloud squares proposed in \cite{gunn2019review} as an example in which persistent Betti numbers cannot be deduced from Betti numbers. Classical algorithms for persistent homology (e.g., see \cite{zomorodian2005computing}) typically need $\mathcal{O}(2^{3n})$ operations to diagonalize a $2^{n}\times 2^{n}$ boundary matrix and obtain the topological information. Our quantum algorithm estimates the same information after a number of operations which is only polynomial in the number of data points $n$. Moreover, our algorithm can encode the full simplicial complex using $n$ qubits, while a classical computer needs $2^n$ bits for the same process.
Last, our algorithm needs a small number of measurements to obtain reliable results, and thus, its application to scientific data including signal processing or image analysis problems is advantageous.
\acknowledgments
Research supported by the National Science Foundation award DMS-2012609.
G.\ Siopsis also acknowledges the Army Research Office award W911NF-19-1-0397, and the National Science Foundation award OMA-1937008.
\bibliographystyle{unsrt}
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Mopping up oil slicks the easy way
by Jon Cartwright
<h2>Mopping up oil slicks the easy way</h2><br /><p class="DefaultStyle">Many people remember vividly the Deepwater Horizon oil spill in 2010, when nearly five billion barrels of oil were emptied into the Gulf of Mexico. That disaster highlighted the inherent risk of drilling for oil, especially in deep wells and other difficult locations.</p> <p class="DefaultStyle">But while oil drilling has been finding new frontiers, the technology required to clean up spills has not. Today the most basic method is a primitive one: at least two boats cordon off an area of spillage with long booms, while a third boat moves inside to scoop the oil off the surface.<br /> <div class="quote-view quotesBlock"> <div class="quotesTop"><img src="https://horizon-magazine.eu/sites/all/themes/horizon/images/quotes_top.png" alt="" title="" /></div> <p>'An idea finally came to a product, and that's not something that can happen every day.'</p> <blockquote><p>Federico Meneghello, D'Appolonia, Milan, Italy</p></blockquote> <div class="quotesBottom"><img src="https://horizon-magazine.eu/sites/all/themes/horizon/images/quotes_bottom.png" alt="" title="" /></div> </div> </p> <p class="DefaultStyle">The problem is that in rough weather there is a risk of the thick crude oil slopping over the tops of the booms and escaping. Worse, the lengthy booms themselves can break, halting the clean-up process altogether.</p> <p class="DefaultStyle">To counter these issues, scientists from the EU-funded FORCE7 project have developed a new system for cleaning up oil spills without the need for booms, which consists of a net that is dragged behind a small boat, then squeezed dry<strong>. </strong></p> <p class="DefaultStyle">The new system could make it much easier to clean up oil spills, particularly in choppy water. Since the net rides on the waves, it is not troubled by rough waters and there is no risk of breakage.</p> <p class="DefaultStyle">The net can also work on a small area in a continuous loop, allowing it to work around troublesome objects such as icebergs – a real danger for prospective Arctic drillers. And tests have shown it to be remarkably efficient, mopping up 90 % of the oil it comes into contact with.</p> <p class="DefaultStyle"><strong>Monitoring dynamics</strong></p> <p class="DefaultStyle">On 26 February, representatives of FORCE7's partners gathered in Cardiff Bay in the UK to watch a demonstration of the system and monitor its dynamics on the water.</p> <p class="DefaultStyle">The net consists of several tails that can be dragged over waves by a single boat, collecting oil as they go. Once the net is saturated with oil, it is simultaneously hauled in and wrung dry with two rollers. After the oil is wrung out, the net is reeled out again for another pass.</p> <p class="DefaultStyle">'The most important point is that it has to follow the waves,' said Federico Meneghello of the Italian engineering firm D'Appolonia, who coordinates the project.</p> <p class="DefaultStyle">Although no oil was used in this particular demonstration, the fact that the net followed the waves without twisting, buckling or sinking suggested to Meneghello and colleagues that it would indeed work in rough waters. And that is probably thanks to the main research focus of the FORCE7 project: the material.<span class="img_legend" style="float: left;"><img src="/sites/default/files/lower%20res%20-%20Force%207%20mechanism%20-%20REA%20-%2020150226_133731.jpg" alt="The tails of the net are dragged over the waves to collect oil, before being hauled back on the boat and wrung dry. Image courtesy FORCE7." title="The tails of the net are dragged over the waves to collect oil, before being hauled back on the boat and wrung dry. Image courtesy FORCE7." width="200" height="150" /> <em>The tails of the net are dragged over the waves to collect oil, before being hauled back on the boat and wrung dry. Image courtesy FORCE7.</em></span></p> <p class="DefaultStyle">According to James Isley, managing director of the British engineering company OPEC which came up with the idea for the system, the partners experimented with a wide variety of materials during the two-year project, including those based on natural fibres. They tested the textiles' ability to clean up oil in confined tanks by <span>measuring the amount of oil collected in a given time for different oil mixes and textile structures.</span></p> <p class="DefaultStyle">In the end two materials did well: one sponge-like material made of polypropylene, which was particularly good at collecting heavy and light oils, and one net-like material made of polyethylene, which was suitably stiff. 'We thought, logically, let's combine the two best performers,' said Isley.</p> <p class="DefaultStyle">While the nets are not yet ready for market, the success of the demonstration means that the FORCE7 system could be ready for service in as little as one year. That would mean continued development of the system for market, said Meneghello – or they could start investigating other interesting avenues, such as recyclable versions.</p> <p class="DefaultStyle">'I am personally very pleased because I am a curious engineer,' he added. 'There was an idea and that idea finally came to a product, and that's not something that can happen every day.'</p> <br /> <img src="http://www.google-analytics.com/collect?v=1&tid=UA-40077089-1&cid=mopping-up-oil-slicks-the-easy-way&t=event&ec=republish&ea=read&el=mopping-up-oil-slicks-the-easy-way&cs=republish&cm=republish&cn=republish&cm1=1" /> This post <a href="https://horizon-magazine.eu/article/mopping-oil-slicks-easy-way.html">Mopping up oil slicks the easy way</a> was originally published on <a href="https://horizon-magazine.eu/">Horizon: the EU Research & Innovation magazine | European Commission</a>.
Following the demonstration, researchers predict the FORCE7 system could be ready for service in as little as a year. Image courtesy FORCE7
Engineers have successfully demonstrated a new technology to clean up oil spills, which could reduce the environmental danger of drilling for oil in cold, rough seas, such as those in the Arctic.
Many people remember vividly the Deepwater Horizon oil spill in 2010, when nearly five billion barrels of oil were emptied into the Gulf of Mexico. That disaster highlighted the inherent risk of drilling for oil, especially in deep wells and other difficult locations.
But while oil drilling has been finding new frontiers, the technology required to clean up spills has not. Today the most basic method is a primitive one: at least two boats cordon off an area of spillage with long booms, while a third boat moves inside to scoop the oil off the surface.
'An idea finally came to a product, and that's not something that can happen every day.'
Federico Meneghello, D'Appolonia, Milan, Italy
The problem is that in rough weather there is a risk of the thick crude oil slopping over the tops of the booms and escaping. Worse, the lengthy booms themselves can break, halting the clean-up process altogether.
To counter these issues, scientists from the EU-funded FORCE7 project have developed a new system for cleaning up oil spills without the need for booms, which consists of a net that is dragged behind a small boat, then squeezed dry.
The new system could make it much easier to clean up oil spills, particularly in choppy water. Since the net rides on the waves, it is not troubled by rough waters and there is no risk of breakage.
The net can also work on a small area in a continuous loop, allowing it to work around troublesome objects such as icebergs – a real danger for prospective Arctic drillers. And tests have shown it to be remarkably efficient, mopping up 90 % of the oil it comes into contact with.
Monitoring dynamics
On 26 February, representatives of FORCE7's partners gathered in Cardiff Bay in the UK to watch a demonstration of the system and monitor its dynamics on the water.
The net consists of several tails that can be dragged over waves by a single boat, collecting oil as they go. Once the net is saturated with oil, it is simultaneously hauled in and wrung dry with two rollers. After the oil is wrung out, the net is reeled out again for another pass.
'The most important point is that it has to follow the waves,' said Federico Meneghello of the Italian engineering firm D'Appolonia, who coordinates the project.
Although no oil was used in this particular demonstration, the fact that the net followed the waves without twisting, buckling or sinking suggested to Meneghello and colleagues that it would indeed work in rough waters. And that is probably thanks to the main research focus of the FORCE7 project: the material. The tails of the net are dragged over the waves to collect oil, before being hauled back on the boat and wrung dry. Image courtesy FORCE7.
According to James Isley, managing director of the British engineering company OPEC which came up with the idea for the system, the partners experimented with a wide variety of materials during the two-year project, including those based on natural fibres. They tested the textiles' ability to clean up oil in confined tanks by measuring the amount of oil collected in a given time for different oil mixes and textile structures.
In the end two materials did well: one sponge-like material made of polypropylene, which was particularly good at collecting heavy and light oils, and one net-like material made of polyethylene, which was suitably stiff. 'We thought, logically, let's combine the two best performers,' said Isley.
While the nets are not yet ready for market, the success of the demonstration means that the FORCE7 system could be ready for service in as little as one year. That would mean continued development of the system for market, said Meneghello – or they could start investigating other interesting avenues, such as recyclable versions.
'I am personally very pleased because I am a curious engineer,' he added. 'There was an idea and that idea finally came to a product, and that's not something that can happen every day.'
|
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{"url":"https:\/\/www.cfd-online.com\/W\/index.php?title=Nomenclature&diff=next&oldid=12965","text":"# Nomenclature\n\n(Difference between revisions)\n Revision as of 09:57, 11 June 2011 (view source)Peter (Talk | contribs) (Added SI base units for k)\u2190 Older edit Latest revision as of 20:23, 11 June 2011 (view source)Peter (Talk | contribs) Line 77: Line 77:\n$\\epsilon$ $\\epsilon$Dissipation of kTurbulence dissipation $J \/ kg s = m^2 \/ s^3$ $J \/ kg s = m^2 \/ s^3$\n- +\n\n## Latest revision as of 20:23, 11 June 2011\n\nAcronym Description Unit\n$C_p$ Specific heat at constant pressure $J\/kgK$\n$C_v$ Specific heat at constant volume $J\/kgK$\n$e$ Internal energy $J\/kg$\n$e_0$ Total energy $J\/kg$\n$h$ Enthalpy $J\/kg$\n$k$ Turbulent kinetic energy $J\/kg = m^2\/s^2$\n$p$ Static pressure $Pa$\n$R$ Specific gas constant $J\/kgK$\n$S_{ij}^*$ Trace-less viscous strain-rate tensor $s^{-1}$\n$t$ Time $s$\n$T$ Static temperature $K$\n$u^*$ Friction velocity $m\/s$\n$u_i$ Velocity $m\/s$\n$\\gamma$ Specific heat ratio = $C_p\/C_v$\n$\\epsilon$ Turbulence dissipation $J \/ kg s = m^2 \/ s^3$\n$\\delta_{ij}$ Kronecker's delta function\n$\\mu$ Dynamic viscosity $Ns\/m^2$\n$\\nu$ Kinematic viscosity $m^2\/s$\n$\\rho$ Density $kg\/m^3$\n$\\tau_{ij}$ Shear stress tensor $N\/m^2$\n$\\omega$ Specific dissipation $s^{-1}$\n$Y_k$ Mass Fraction of species k\n$X_k$ Molar Fraction of species k\n$[X_k]$ Molar Concentration of species k $mol\/m^3$\n$W_k$ Molecular weight of species k $kg\/mol$\n$\\overline{W}$ Mean molecular weight of a mixture $kg\/mol$\n$\\dot \\omega_k$ k-species reaction rate $kg\/m^3 s$\n\n## Dimensionless parameters:\n\nParameter Description Definition\n$Nu$ Nusselt number $\\frac{h L}{k}$\n$Pr$ Prandtl number $\\frac{\\mu C_p}{k}$\n$Re$ Reynolds number $\\frac{\\rho VL}{\\mu}$\n$St$ Strouhal number $\\frac{fL}{V}$\n$Ma$ Mach number $\\frac{v}{C}$\n\n## Subscript:\n\n $t$ Turbulent property $0$ Stagnation \/ total property\n\n## Superscript:\n\n $conv$ Convective part $diff$ Diffusive part $lam$ Laminar part $tot$ Laminar + turbulent part $turb$ Turbulent part $'$ Reynolds fluctuating part $''$ Favre fluctuating part $\\widetilde{\\cdot}$ Density weighted (Favre) average $\\overline{\\cdot}$ Normal average (time or space)","date":"2017-09-19 14:12:18","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 72, \"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\": 0.9377744793891907, \"perplexity\": 12444.866583872092}, \"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-2017-39\/segments\/1505818685698.18\/warc\/CC-MAIN-20170919131102-20170919151102-00456.warc.gz\"}"}
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Q: Render UITableView during background fetch for restoration I have a table which rows gets normally rendered from processes running in a background thread (not to slow down the scrolling). All works well but, when the app is launched from a background fetch, I struggle to render the table before calling the fetch completion handler. In facts it looks like the main thread (which is responsible to render the table after the reload data call) gets only processed after the fetch completion handler is called, leaving not much time for the table to render before its state is saved.
Is there a way to run a table reload data not in the main thread? Any other idea how I could make sure the table is rendered before calling the fetch completion?
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The James Bond 007 Dossier | Empire Magazine - Bond is Back
<< Too much for One James Bond | Vintage Diamonds Are Forever Trade Ad >>
15. April 2015 14:55 by m | 0 Comments
The first word on the movie formerly known as Bond 24, from the April Edition of Empire Magazine. No real spoilers here. Interesting that, while the editor describes the all important Gunbarrel beginning marking the start of another rollicking 007 adventure, the main article didn't touch upon whether or not we might see it restored to the start of the new film, Spectre .
The World's first look at Spectre
If you're 16 or 75, you'll know that moment. The lights go down, John Barry's immortal orchestral sting strikes up, and we see through the eye of that anonymous assassin — as perennially doomed as South Park's Kenny — trying to draw a bead on the well-dressed man... who twirls and fires a lethal pistol shot. Bond is back — always the same, always different. Simultaneously as homely as a hug from aunty on Boxing Day, and as exotic as a kiss from a supermodel in a Macau casino.
You can tell a lot about a country from its choice of hero, America has the preppy omnipotence of Superman by day, the gothic paranoia of Batman by night. Britain has Bond. Not quite super, often questionably heroic, but dogged, brave, witty and capable of high-beam charm and hardcore violence in the pursuit of a megalomaniac with a small army.
My first brush with Bond was 1985's A View To A Kill . Not a vintage year for wine or Bond, as a creaky Roger Moore lived the dream for all men touching 60: driving sports cars, sleeping with three beautiful women young enough to be his daughter and punching people at work. I was hooked.
Fast forward 30 years, and Bond movies are (like their star Daniel Craig) leaner, harder and more stylish. So when we were offered the first look at Spectre , 007's 24th outing, we reacted like you would. Arch nemesis Blofeld is rumoured to be back, and the delectable Monica Bellucci will be the first Bond girl since Goldfinger 's Pussy Galore to be older than the man himself. I sense a tour de force. See what you think on p.58.
THE ASTON MARTIN'S OUT OF THE GARAGE.
THE WALTHER PPK'S RELOADED.
HIS DEADLIEST-EVER FOES HAVE RETURNED.
EMPIRE WELCOMES BACK CLASSIC 007 WITH Spectre , THE MOVIE THAT'S GOING TO TOP Skyfall
Words Chris Hewitt, Additional Reporting Phil De Semlyen
007 HAS A SECRET. A TERRIBLE SECRET. A DARK SECRET.
And Empire has just stumbled right upon it.
It's late January, and we've come to Pinewood Studios to visit the set of Spectre , the 24th official James Bond movie, on a real scrotum-shrinker of a morning; so cold you could be forgiven for thinking that you're in the Austrian Alps. Which is precisely what we re meant to think when we walk through the doors of a soundstage (not the 007 stage — that's being reserved for the construction of something huge for the film's finale) and find ourselves in the rarefied five-star surroundings of the Hoffler Klinik.
A spa hotel for the seriously rich, the Klinik is a seriously impressive set, using so much steel that when it's dismantled, the framework will be turned into the film's brand-new MI6 headquarters. Empire enters through a lobby that's dominated by a giant fireplace in the middle of the room, around which sit sofas in a hexagonal arrangement. Above is a glass ceiling flecked with fake snow and surrounding the entire set, visible through every window, is a giant panoramic shot of the Austrian Alps. Turn off your phoned GPS and you could almost imagine that you were in Obertilliach.
Bond's secret lies two floors up, in a large glass-and-chrome office — the Beratungsraum, or Consultation Room — that is home to Madeleine Swann, the newest and, perhaps, most mysterious Bond girl to date. A quick browse through the reading material dotted around the room informs us she's a doctor, perhaps a shrink: The International Journal Of Psychoanalysis lies on one table, CBT For Worry & Generalised Anxiety Disorder on another.
And it's there, on Swann's desk, that we discover it, scribbled on a prescription pad. It's dated 25/4/15, placing us ever-so-slightly in the future, and it lists 60 Vicodin, 60 Xanax... and, most shockingly of all, 120 Viagra. The patient's name? James Bond.
His secret is out. When you've been as active between the sheets as he has over the years, it seems, you sometimes need a little help keeping the British end up. And let's face it, if Bond and Spectre are somehow going to surpass the secret agent's last cinematic outing, he's going to need all the help he can get...
Briefing:
RELEASED: October 23
DIRECTOR: Sam Mendes
STARRING: Daniel Craig, Christoph Waltz, Lea Seydoux, Monica Bellucci, Dave Bautista, Ralph Fiennes
STORY: The secret service is in danger of being dismantled, while James Bond (Craig] goes on the trail of a terrifying criminal organisation: Spectre .
LIKE FROM THE OLD BOND MOVIES!
Precisely. Returning director Sam Mendes is pushing the old-school feel he brought to Skyfall even further with this one.
Photo: Nice Spectre cals, James! Daniel Craig returns as Bond.
"EVERYBODY SEEMED TO LOVE Skyfall , AND that's what we're going for," says Barbara Broccoli who, along with Michael G. Wilson, is the producer of Spectre and keeper of the Bond flame. "We want to make a movie that people love, like they loved Skyfall ."
Easier said than done. Skyfall was a breakthrough for Bond in many ways. The franchise has always been huge, of course, but Skyfall was the first 007 flick to bust the billion-dollar barrier. It was also critically adored, restoring the lustre to the franchise that the misguided Quantum of Solace had rubbed off and picking up the series' first major BAFTA in almost 50 years (for Outstanding British Film in 2013). With Sam Mendes at the helm, it was a heavyweight of a movie, serious and sombre and testing Bond as a character in a way that he hadn't been in years.
How do you follow that up? Do you simply bung Skyfall a load of little blue pills and hope for the best? Or do you look elsewhere for a solution? For instance, now that you've reinstated Q and Moneypenny and the Aston Martin, back in the series' illustrious past? And the further back you look into someone's past, the more likely you are to chance upon a Spectre ...
The Special Executive for Counter-intelligence, Terrorism, Revenge and Extortion, aka Spectre , was a perennial thorn
"OUR Spectre IS NEW, EXCITING, DIFFERENT." Barbara Broccoli
in Bond's side through the early years of the franchise. Then it disappeared from Bond's cinematic life. Though ever-present in the Connery films, it troubled Moore just once. And that was the last we heard from it.
There was a good reason for this. 1965's Thunderball features a producer whose name doesn't appear on any other Bond movie: Kevin McClory. An Irish filmmaker/writer, McClory was instrumental in the creative process that led to Ian Fleming's novel, Thunderball , in which Spectre made its debut.
When he was subsequently deprived of credit, McClory sued Fleming and won, and as part of the deal became a producer on Thunderball . He also held the rights to the novel and all its characters, although he wasn't allowed to make a film version for ten years. When that time period elapsed, McClory started work on the non-official 007 movie that would become Never Say Never Again . Meanwhile, back in the official Eon films, Spectre vanished.
McClory tried several more times after that to get another version of Thunderball off the ground, most notably with Warhead 2000AD, which would have starred Pierce Brosnan before he became Bond, but nothing came to fruition. McClory died in 2006, and any desire to make a rival Bond seemed to die with him. Nevertheless, the tortuous tug-of-war over the rights to Spectre continued for a few years, during which time Eon rebooted Bond and, without recourse to 007's arch-rivals, forged its own Spectre -a-like villainous organisation, Quantum.
Photo: Returning Bond-wrangler Sam Mendes and newbie Lea Seydoux get serious on set.
Then, in 2013, a settlement was reached, and suddenly Spectre was back in play. There was speculation that the next Bond film would see the return of the evil organisation, and when Mendes confirmed the title back in December, it seemed nailed-on. But official confirmation that Spectre would, indeed, involve Spectre wasn't forthcoming until now. Michael G. Wilson describes Dave Bautista's Mr. Hinx as "an assassin... one of Spectre 'S top guys", while one lavish set Empire glimpses at Pinewood is a stunning Italian chamber, inspired by a building in Naples, all green, marble walls and columns, where we're informed a top-level Spectre meeting will take place. And Bond will gatecrash it. Rest assured, the title of this Bond film is not a double-bluff. Spectre is back.
"Spectre has, in the whole history of Bond, played an important role," says Broccoli. "We thought, 'Okay, now's the time to explore that again in a new and exciting and different way. We wouldn't be attempting to go there unless we knew we had a good way of doing it."
Today, though, Bond isn't fighting Spectre . Instead, on the set of a bar, Daniel Craig is giving what-for to two jobsworth security guards. His investigation having pointed him in the direction of Lea Seydoux's Dr. Swann, Bond has rocked up at the Hoffler Klinik ready to pump her vigorously for information. Madeleine, though, presents Bond with an icy front, and has
"SHE'S BOND'S EQUAL. STRONG AND SMART." Lea Seydoux
him escorted off the premises. That's the plan, anyway.
With Mendes positioned just a few feet away, Craig — dressed in a black ski vest and trousers — paces around, listening to something on his iPod, psyching himself up. He wipes his nose and stands up straight. He's ready.
Mendes yells, "Action!" and Craig stalks towards the right-hand exit of the bar, flanked by the actors playing the security guards. And then, without warning, he explodes into action, grabbing the guard in front and taking out the one behind him with a swift punch. The first guard whirls around to face Bond, Who jabs a Harrison Ford-like finger at him and barks, "Don't! Stay!", before taking off for the other exit. The guard thinks better of it, and Bond runs out of the room.
It's a neat snapshot of Bond as battering ram, but it doesn't feel like a signficant escalation from Skyfall 's largely internalised action. Where, Empire wonders, are the giant stunts? The enormous set-pieces? Where, for example, are the planes crashing down mountainsides?
GARY POWELL, Spectre STUNT COORDINATOR, squints into the harsh, cold sunlight of a beautiful Austrian February morning, and smiles. "We Could have put him on a set of skis, but a plane seemed better."
Now, this is more like it. Empire has come to Obertilliach in the Austrian Alps (no wrap-around backdrop here; this is the real thing) for a spot of snowbound second-unit skylarking.
Things have gotten out of hand since Bond evaded security back at the Hoffler Klinik. Whatever information Madeleine Swann has is valuable, so Spectre has dispatched Mr. Hinx to Austria to retrieve her. Much to Bond's chagrin, Hinx has bundled her into the back of a car and taken off at high-speed. Once upon a time, 007 would have strapped on a pair of skis, secured the Union Jack parachute, and started swishing down the mountainside in hot pursuit, Monty Norman's Bond theme blaring on the soundtrack and — quite possibly — inside Bond's head as well.
But skis are so 1970s. Instead, Craig's Bond commandeers a light aircraft, which he begins flying like a maniac, haphazardly piloting it through the snow-dusted pine forest, smashing through trees, divesting it of its wings, then its tail. Which brings us to today's shot.
Photo: Craig, Seydoux and Dave Bautista get their thermals on for filming in Solden, Austria.
The plane-turned-sled, having bashed its way through the forest on what production manager Martin Joy calls "the biggest aerial Scalextric you've ever seen" (the wires will be erased in post), will then smash through a barn, in classic Bond style, and continue out the other side. In less classic Bond style, it won't stir up a flock of panicked chickens. "We're not sure Daniel Craig is a chickens Bond," laughs art director Neal Callow.
That sound you can hear is Roger Moore's right eyebrow deflating in disappointment.
The production, under the auspices of second-unit director Alexander Witt, has brought in hundreds of crew members, and around 50,000 square metres of fake snow (the actual snow that fell overnight is the icing on top of the icing). As with any Bond set-piece, the shot has been months in the planning. Then Witt calls, "Action!", and the hull of the plane is shot out of the barn via a cannon and down the slope. It's all over in seconds, something Bond isn't used to.
This sequence, which arrives roughly mid-way through Spectre , is symptomatic of Mendes, Wilson and Broccoli's approach to the film. Skyfall largely stayed at home in Britain, while its big finale took place in Bond's family abode. It was insular, intimate, inward-looking. Its biggest stunt took place during the pre-credits sequence. Spectre is bigger and more extravagant, and Bond's whipped out the passport again. "We have a lot more locations going on," says Wilson. "Mexico (where the film's opening sequence will take place) and Rome and Austria and down in Morocco. And London. It's a lot."
Spectre featured prominently in the hack attack on Sony that took place late last year, with emails made public suggesting that the budget for the film would be around $300 million, making it comfortably the biggest 007 adventure to date, while a version of the script was also leaked. "We shut it down," says Broccoli. "It was stolen and then reproduced, and we didn't think that was right."
If you managed to get your hands on that script, don't smugly assume that it bears any resemblance to the finished product.
"It was a very old version," continues Broccoli. "This is a very organic — I hate the word organic, but I'm going to use it anyway — process, where everyone is continually coming up with ways to make things more exciting and more interesting and better."
Craig's Bond has been a breath of fresh air in many respects, but you couldn't accuse him of being a barrel of laughs. He's incredibly intense, super-serious, and generally treats one-liners as if they were henchmen to be punched. Yet the end of Skyfall , where a slightly breezier Bond stood at ease with his core MI6 support group of Q (Ben Whishaw), Moneypenny (Naomie Harris) and a new M (Ralph Fiennes), seemed to suggest that the rebooted series now has the confidence to embrace traditional Bondian humour. And while that won't extend to startled chickens in a barn or double-taking pigeons, we can expect this iteration of Craig's Bond to be a little looser, the sort of guy who might bark, "Stay!" at a security guard during a punch-up.
"IT'S GOOD, BOND IN FRONT OF AN <i>ADULT</i> WOMAN." Monica BELLUCCI
"You'll see Daniel's Bond in another way, in another form," says Broccoli. "I think we always try to have some lightness in the storytelling, but the story last time didn't really lend itself too much to humour because Bond started off being shot and left for dead. This film. Bond is on top of his game, top of his form, and then he's put through the rollercoaster."
WHO'S PUTTING BOND THROUGH THAT rollercoaster? Well, obviously, there's Mr. Hinx, the henchman with the throwback name and the first major role for Bautista since he made a stir as Drax in Guardians Of The Galaxy. That character was a lovable lunkhead; Mr. Hinx will be anything but. "When I came over to meet Sam, I only asked two questions," says Bautista. "I asked him if Mr. Hinx was a badass. He said, 'Yes, he's a badass.' I said, 'Well, is Mr. Hinx intelligent?' He said, 'Very.' That's what I like about Mr. Hinx. He's very well-dressed and very well-mannered. I'm not just here to fight people. He has a sense of humour. He definitely knows what a metaphor is."
A long-time Bond fan, Bautista's casting is interesting on several levels. Even though he slimmed down to a mere 265 lbs for the role, Mr. Hinx is the first proper brick shithouse-sized opponent that Craig has faced across his four movies, and has the potential to make an impact along the lines of Oddjob or Jaws. Bautista is loath to give things away, but will admit that all but one of his scenes (thus far) were with Craig, and that "James Bond and Mr. Hinx are not friends".
But if/when Mr. Hinx is dispatched, Spectre will still be standing. He's not pulling all the strings. When it comes to puppet masters, Spectre conjures up one name in particular. "And what might that be, by chance?" laughs Broccoli.
Ernst Stavro Blofeld, of course. The Joker to Bond's Batman, the Moriarty to his Sherlock Holmes, the Piers Morgan to his Alan Sugar. "Never heard of him!" she cackles. We suspect that the daughter of Cubby Broccoli, and producer of eight Bond movies in her own right, is not being entirely serious, but just in case, let's have a quick refresher.
Bald (unless we're talking about the Charles Gray version). Wears a Nehru suit. Strokes a white cat. The über-bastard at the head of Spectre . Seen first as a shadowy presence, Blofeld came into his own with You Only Live Twice (as Donald Pleasence), and was responsible for the murder of Bond's wife, Tracy, in On Her Majesty's Secret Service . But, with the McClory lawsuit looming, he became less significant in Bond's life, and was last seen being dropped unceremoniously (and symbolically) down a chimney at the beginning of For Your Eyes Only . In the years since, Mike Myers' Dr. Evil was such a spot-on piss-take of the character that it seemed pretty certain Blofeld would never darken Bond's doors again.
Yet here we are, with Spectre about to return and absorb Quantum (Jesper Christiansen, aka Casino Royale and Quantum of Solace 's Mr. White, will show up here, after Skyfall jettisoned the Quantum storyline entirely). Blofeld is surely set to make a comeback too, and with Christoph Waltz on board as the bad guy this time ("He might be Bond's ally," deadpans Wilson), it seemed like an open-and-shut case. Blofeld
"HINX IS A BADASS. AND HE HAS A SENSE OF HUMOUR" Dave Bautista
is back, and Waltz is Blofeld.
Not so fast. For starters, Waltz' character is called Oberhauser and Wilson and Broccoli are adamant that Waltz is not playing Blofeld. "He said no in his press conference," says Wilson (incidentally, the leaked script bears him out on this). "We have Spectre and the rest is speculation," adds Broccoli.
Here's some more speculation to add to the mix. If Blofeld doesn't show up this time, there's a very good chance that Team Eon are holding him back for the next Bond, which is — right now — scheduled to be Craig's last and, as chance would have it, is also going to be the 25th 007 adventure. Broccoli laughs at the suggestion. "One at a time," she says. "It's tough enough making one at a time..."
Spectre IS OUT ON OCTOBER 23 AND WILL BE REVIEWED IN A FUTURE ISSUE.
SPYING BY NUMBERS
WHAT ARE THE REST OF THE DOUBLE-O SECTION UP TO WHILE BOND IS BUSY SAVING THE WORLD?
JAMES BOND'S FELLOW SPIES are rarely spotted in the films or Ian Fleming's novels, but their adventures are hinted at throughout. 001 is never referred to (perhaps the designation is reserved for M ?], but 002 is named as Bill Fairbanks, shot by Scaramanga while, er, 'on the job' with a belly dancer before the events of The Man With The Golden Gun . Bond recovers a vital microchip from 003's corpse in A View To A Kill , and 004 took part in The Living Daylights ' Gibraltar training exercise along with Bond and another 002. There's no mention of 005, but 006 is referred to in Fleming's On Her Majesty's Secret Service : he and 007 bet on who will bed their secretary first. In Goldeneye , 006 Alec Trevelyan is revealed as a rogue agent.
008 seems on permanent standby — in both Goldfinger and The Living Daylights he's mentioned as a replacement if Bond refuses to follow orders or gets his knackers spliced by a laser. In Fleming's Thunderball , M puts 009 in charge of the Double-0 section while Bond is at a health farm, but the films' first 009 is less lucky: knifed in the back while dressed as a clown in Octopussy . Another 009 shot terrorist Renard in the head before the events of The World Is Not Enough , but failed to kill him. 0010 isn't mentioned. In Moonraker Fleming mentions 0011 and 008 as the only other Double-Os at the time (0011 is missing in Singapore, while 008 is resting in Berlin after a mission]. Fans have speculated that Skyfall bad guy Silva was once a 00, but writer John Logan denies this, telling us he was merely "an especially qifted spy".
NEIL ALCOCK
THE BLUE is THE WARMEST COLOUR STAR PROMISES A DIFFERENT-FLAVOURED BOND GIRL
IF YOU'RE STRUGGLING TO IMAGINE Lea Seydoux as a Bond girl., don't worry, you're not alone. "I don't consider myself as a Bond girl," she says. "I think I'm not really the stereotyped Bond girl. I feel quite different. You can't be like, 'Oh, James.' You have to find something else."
Which is certainly what Dr. Madeleine Swann appears to be: a girl who happens to be in a Bond movie, rather than a Bond girl. Whip-smart and beautiful, the good doctor could well be the first woman to defrost Bond's heart since that nasty business with Vesper Lynd at the end of Casino Royale . But she'll do it on her own terms; unlike other girls from the franchise's history, she won't be throwing herself at Bond first chance she gets.
"He can't really have her," she says. "She's not seduced at first sight, and she doesn't fall for his tricks. She resists. She's his equal, independent and strong and smart, and she doesn't need him or wait for him to save her."
Of course, there might be a scene or two where Bond has to save her, but otherwise Madeleine is resourceful. Don't expect her to suddenly start taking out bad guys with roundhouse kicks. In that sense, she's closer to Vesper than, say, Quantum of Solace 's Olga Kurylenko or Skyfall 's Naomie Harris. "She's not a fighter, she's a doctor," she confirms. "She fights in another way,"
Seydoux has dabbled with English-language blockbusters before, most notably her small role as a villainess in that other spooky-titled spy caper Mission: impossible — Ghost Protocol, but Spectre is her biggest movie to date. It's hard to imagine that the darling of French indie cinema would get nervous about chasing after roles in Hollywood blockbusters, much less become so nervous that she nearly screws up the audition, but that's exactly what happened with Spectre . "I did not really succeed during the audition," she laughs. "I was early for the appointment and I was a little anxious, so I thought I would have a little beer to relax me, and then I started to have a panic attack and lost my text (meaning forgot her lines)! I felt very stressed about it."
Let this be a lesson to any budding actors out there: never drink and audition. Although, when the fit of the vapours had subsided, Seydoux was composed enough to ask for another audition, which she aced. "I didn't have any beer," she confirms.
Franken-Henchman (Illustration Bill McConkey)
THE ULTIMATE SINISTER SIDEKICK PIECED TOGETHER TO DESTROY 007
Oddjob's lethal, steel-rimmed headgear (Goldfinger , 1964)
The jaws of Jaws, perhaps the most iconic of all elements of Bond villainy (The Spy Who Loved Me , 1977)
Tee Hee's robotic arm with the deadliest of grips (Live And Let Die , 1973)
Rosa Klebb's maid outfit, complete with spiked, poisoned shoe gives a false of sense of security (From Russia With Love , 1963)
Xenia Onatopp's thunder thighs will love you to death (Goldeneye , 1995)
Red Grant's wristwatch garrote, for when you have time to kill (From Russia With Love , 1963)
Baron Samedi bodypaint isn't deadly, but brings the fear of a voodoo hoodoo (Live And Let Die , 1973)
The facial accoutrements of one of Bond's lesser foes, Mr. Kidd (Diamonds Are Forever , 1971)
Zao's diamond-scars, to bring bling to your killing (Die Another Day , 2002)
Spectre : MEET THE TEAM
YOUR GUIDE TO THE BOND-HATING BUREAUCRACY
words KIM NEWMAN
Founder and Arch Villain
ERNST STAVRO BLOFELD
PLAYED BY; Anthony Dawson, Eric Pohlmann (voice); Donald Pleasence; Telly Savalas; Charles Cray; John Hollis, Robert Rietty (uncredited]; Max von Sydow APPEARS IN: From Russia With Love (1963); Thunderball (1965); You Only Live Twice (1967); On Her Majesty's Secret Service (1969); Diamonds Are Forever (1971); For Your Eyes Only (1981); Never Say Never Again (1983)
Projects include nuclear blackmail (Thunderball ), creating bioweapon; (On Her Majesty's Secret Service ), hijacking US/ Russian spacecraft to trigger World War III (You Only Live Twice ) and strafing Earth with an orbital laser (Diamonds Arc forever).
Head of Division
PLAYED Adolfo Celi; Klaus Maria Brandauer APPEARS IN: Thunderball (1965); Never Say Never Again (1983)
One-eyed, yacht-owning playboy, in charge of stealing a nuclear device for the purpose of extortion.
DR. JULIUS NO
PLAYED BY: Joseph Wiseman APPEARS IN: Dr. No (1962)
Communist-backed in the novel but a Spectre section head in the film, Dr. No tries to wreck the US space programme with radio interference.
High Ranking Minions
KRONSTEEN
PLAYED BY: Vladek Sheybal APPEARS IN: From Russia With Love (1963)
Russian chess expert who works out a plan to steal a Soviet code device while incidentally getting revenge on James Bond after the death of Dr. No .
ROSA KLEBB
PLAYED BY Lotte Lenya APPEARS IN: From Russia With Love (1963)
ASMERSH (Soviet counter-intelligence agency] commissar in the novel, she defects to Spectre for the film. Known for her poisoned shoe-tips.
FIONA VOLPE
PLAYED BY: Luciana Paluzzi APPEARS IN: Thunderball (1965)
Seductress, killer... shot in the back while dancing with Bond.
HELGA BRANDT
PLAYED BY: Karin Dor APPEARS IN: You Only Live Twice (1967)
Disappointing mid-level counter-intelligence operative... handier as fish food.
IRMA BUNT
PLAYED BY: Ilse Steppat APPEARS IN: On Her Majesty's Secret Service (1969)
A replacement for Klebb, Irma is Blofeld's secretary and vicious hit-woman. One of the few key Spectre personnel not to get killed in action.
PLAYED BY: Eric Coverly, Charles Edghill and Henry Lopez APPEAR IN: Dr. No (1962)
Jamaican calypso killers, they pose as blind beggars... in order to murder spies.
DONALD RED GRANT
PLAYED BY: Robert Shaw APPEARS IN From Russia With Love (1963)
Trained specifically to kill Bond. But doesn't know which wine to have with fish.
PLAYED BY: Philip Locke APPEARS IN: Thunderball (1965)
Celibate, teetotal killer -impaled by spear-gun.
MR. WINT AND MR. KIDD
PLAYED BY: Bruce Glover and Putter Smith
APPEAR IN: Diamonds Are Forever (1971)
Hit-men. And outmoded gay stereotypes.
BAMBI AND THUMPER
PLAYED BY: Lola Larson and Trina Parks
Martial-arts pin-up stereotype hit-women.
WHY THE BOND GIRL "THAT NEARLY GOT AWAY" FINALLY AGREED TO SIGN UP FOR THE 007 SPY GAMES
WHEN SAM MENDES WELCOMED Monica Bellucci onto the stage at the grand unveiling of Spectre and its cast at Pinewood back in December, it was almost as if you could hear the sound of thousands of palms hitting foreheads all at once. Sultry, seductive, impossibly glamorous, the Italian star of Irreversible and the Matrix sequels is, perhaps, the ultimate Bond girl.
The only question is, why didn't this happen sooner?
Well, it wasn't for the want of trying,
"We had wanted her a couple of times in the past, and it didn't work out," says producer Barbara Broccoli. "I was really afraid that she was going to be the one that got away. I couldn't be more pleased that we finally got her in a Bond movie, and in a really great role."
Bellucci doesn't want to name the 007 film she came close to doing, but she will admit that it "was almost 20 years ago", which would place it during Pierce Brosnan's tenure, and that the director in question sent her "a beautiful letter when I didn't do the film". Of her reasons for turning down the role of Bond girl then, she says, "When I was 20 or 30, it would be almost too obvious."
Now Bellucci is 50, and she looks upon her choice to take the role of Lucia Sciarra as a groundbreaking one. Bond usually dallies with women who are younger and more naive than he is — but not this time. Fifty years old, and 'James Bond?" she muses. "I think it's revolutionary It's good that James Bond is in front of a woman, an adult woman. Sam said, 'You're going to be the hero for women. 'A woman after 40, she freaks out, especially in this business. The possibility that a woman 50 years old can create desire, that's great for women today."
About Lucia, Bellucci can say little, other than, "Femininity is a sign of strength, instead of a sign of weakness," and that Bond encounters her in Rome. Empire's tour of the set includes a peek at Lucia's bedroom, littered with condolence cards written in Italian. We know of Spectre that a cryptic message from Bond's past triggers his investigation — is Lucia an echo from that past, and is her bereavement the spark that sets things off? Bellucci won't be drawn, offering only a knowing laugh.
She also brings to the table a keen knowledge of Bond-girl history. "All those James Bond girls in the past are images that become iconic, like Ursula Andress coming out of the water," she says. "These are moments that stay in the mind forever." So, can we expect something similar from Lucia in Spectre ? Again, that knowing laugh.
"I don't know," she says. "It's all about the costumes..." We reckon it's a pretty safe bet. After all, Bellucci has to make up for lost time...
[Source: Empire Magazine, April 2015, P1,4,6,37,58-71. Copyright © 2015 Bauer Consumer Media Limited. All rights reserved.]
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Bond XVI Script TreatmentRead the original treatment for the James Bond film, Licence to Kill, written by RICHARD MAIBAUM and...50 Years of BondIn late 2012 this 50th anniversary magazine went on sale just about everywhere - I picked mine up at...GoldenEye Official Movie Souvenir MagazinePierce Brosnan is James Bond 007 in GoldenEye - The Official Movie Souvenir Magazine. CHARACTER P...
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Edible Plants, Survival Guide
Yellow Water Lily – Nymphaeaceae
February 28, 2014 traderscreek
Yellow Water Lily
Water Lily, Brandy-bottle, pond lily, bullhead lily, spatterdock, yellow cowlily, water lily
My son built a small pond in the backyard several years ago. Along with the necessary koi we bought the flora we added included a plant native to the entire USA – a yellow pond lily. In researching this plant I found out its history and the many ways this wild food is used and useful.
As its name implies, the yellow pond lily is an aquatic plant. It is a long lived plant, a perennial, which grows from spongy rhizomes anchored into the bottom of a body of water. The floating leaves are thick, somewhat heart-shaped and have up to an 18" spread. The stalks connecting leaves and flowers to rhizomes can grow six feet long.
Flowers of the water lily emerge on separate stem stalks. They are cup-shaped, yellow-green, with small scale-like petals. Flowers bloom from May to October. Spent flowers give way to seed heads that burst upon ripening, broadcasting their seeds over the water surface.
Yellow pond-lily occurs in slow-moving streams, ponds, and lakes. The plant pictured here was in Pine Lake, NY, a shallow Adirondack lake. The plant grows in wet, poor sandy soils and grows best in 1' to 5' of water in full sun to part shade. It is however tolerant of shade and deep water. There is a boggy area fed by the Normans Kill in Albany, NY that gets choked up with these wild plants by mid-summer every year. This is where the lilies I have come from.
The yellow pond lily can basically be found from Alaska south to California East to Labrador and south to Florida.
The roots (rhizomes) are rich in starch and can be harvested any time of the year and either roasted or boiled. I understand that the root can be dried and ground into a flour substitute. The seeds can also be gathered in late summer into the fall and roasted and shelled. They can be eaten as is, boiled like you would rice or ground into a flour/meal.
Yellow Pond Lilies provides great cover for wildlife, including all types of fish, insects (aquatic, terrestrial and flying), amphibians and reptiles. It is also a food source for beaver, muskrats and waterfowl.
The plant's use dates back to pre-colonial times. Native Americans used the starchy rootstocks as a boiled or roasted vegetable. Additionally, they harvested the seed for grinding into flour.
Although water lily seeds are produced and deposited on the water surface, the yellow pond-lily reproduces more readily by spreading rhizomes – I can attest to this. The lily in the koi pond has a root system around 4' long with several spots that stems and flowers grow from. This native aquatic plant can readily take over a body of water – please do not help it spread. It is very difficult to eradicate
Back to edible plant index
Check out how to cook wild foods
flickerFragarianative plantsplantspond lilyRhus TyphinaWater Lily
Strawberry Plant Facts and Identification
Strawberry – Fragaria Virginiana
Woodland strawberry; California strawberry, Virginia Strawberry
The first time I came across strawberries in the wild, and knew it, I was 18 years old hiking with a friend in the coastal mountains of Oregon. He was the one that identified them. It was one of those times when it was all about camping, fishing for cutthroat trout and eating wild foods – with a lot of it being strawberries along with a smattering of blackberries, thimbleberries and a bit of wild greens. I found it strangely fulfilling camping in a tent for a week really living off the land.
The good news about strawberries is that they are easy to identify and widely distributed. The bad news is that the strawberry fruit can have a limited growing season. This is a perennial plant that spreads by seed, short rhizomes (a thick underground horizontal stem that produces roots and has shoots that develop into new plants) and leafless stolon (a long stem or shoot that arises from the central rosette of a plant and droops to the ground).
If you have ever seen a strawberry plant in Home Depot, Lowes or your local garden center then you know what a wild strawberry plant looks like – only the wild strawberry is smaller. The toothed leaves are thin and basal compound in groups of 3 with a petiole generally 1" – 4". They are sparsely hairy below. Leaf color is generally a bluish-green. The strawberry flower has 5 white petals with numerous pistils and 20-35 stamens. The flower is typically .25" – .5" wide. The fruit is white then turns red when ripe with the seeds on the outside. The plant is generally 2" – 6" tall.
Strawberries grow where there's lots of sun: in meadows, fields, on moist ground, along the edge of woods, and on hillsides. You can find them across the U.S. and Canada except in desert/arid areas.
The fruit ripens sometime between June and August. I have even come across strawberry fruit in the wild in late September. Obviously the fruit is edible and if you can pick enough, it can be canned, frozen or dried. The fruit of strawberries are nutritious and are full of essential vitamins and minerals.
The leaves and stems are edible and actually taste good when fresh and young. They are loaded with vitamin C – an important vitamin used to prevent scurvy. One way to enjoy the benefits of the leaves is make a tea with a handful of freshly picked leaves. For winter use you can dry out the leaves and store in a jar.
Native Americans used strawberries as a food source. The strawberry is an important food source for many wild animals from insects to deer and birds.
Growing your own strawberry patch: Strawberry plants are easy to grow if you want free fresh fruit. I like to plant my strawberries in long rows.
They should be planted in full sun in a light, loose soil, about 10" apart in rows 2' apart. You should plant in an area that has plenty of room for your patch to spread out. Lightly fertilize the plants during the growing season. After 2 – 3 years your plants will spread – mostly from "runners". Once a runner plant has established its own roots and is healthy I like to move it to avoid overcrowding. Keep the runners pruned back until after you pick the strawberry fruit. This allows the plant to focus on fruit production thus increasing yield. As they age plants will lose "vigor" so you should pull plants over three years old to maintain your patch's fruit production. Younger plants are more vigorous and produce more berries.
The biggest problems I have in the Northeast are rabbits (they will eat the plant right down to the ground) and gray squirrels (they will sneak in like the rats they are and eat the fruit just as it is ripening). I find the best way to protect plants and fruit is to cover the row with deer netting. It will let in the bees for pollination but keep out rabbits and squirrels.
FragariaFragaria Virginiananative plantsplantsstrawberrystrawberry fruitstrawberry plantwild food
Staghorn Sumac – Rhus Typhina
January 13, 2014 traderscreek
Staghorn Sumac
Driving around during September in New York you will eventually come across a group of small trees growing in dense stands. The leaves will be a deep red and large conical red hairy fruits called drupes may be at the end of branches. This is the common Staghorn Sumac which is a deciduous shrub to small tree. It grows quite aggressively. Because staghorn sumac can grow by its roots (rhizomes), and once established it can be a pain to remove.
Staghorn Sumac grows 10' – 35' tall. As can be seen in the picture, the leaves are alternate & compound growing approximately 24" long with 10 – 32 serrate leaflets. Each leaf grows to 12" long. The leaf stalks and the stems are densely covered in rust-colored hairs. Mature trunks are smooth and hairless. Interestingly, only female plants produce flowers and berries. The red berries grow at the end of branches. The plant flowers from May to July and fruit, the drupes, ripen from June to September. As can be seen in the pictures, they grow in upright bunches. Each cluster of drupes may contain 100 to 700 seeds
Staghorn sumac grows in gardens, lawns, the edges of forests, and wasteland. It can grow under a wide array of conditions, but is most often found in open areas which are not already established by other trees.
Staghorn sumac is found throughout the eastern half of the United States and Canada from western Ontario, south to Oklahoma into the Gulf Coast States and eastward to all the Atlantic States and eastern Canada.
The fruit of sumacs can be collected, soaked and washed in cold water, strained, sweetened and made into a lemonade-like drink.
Staghorn sumac spreads by seeds, and by its roots, rhizomes, to form "stands".
The staghorn sumac derives its name from the countless tiny hairs covering its branches and resembling the tines of a deer's antler when in velvet.
All parts of the staghorn sumac, except the roots, can be used as a natural dye.
Native Americans used the berries from staghorn sumac to make a drink.
The berries and bark are an important source of food for birds (upland games birds as well as song birds) and small mammals.
Staghorn sumac can form with either male or female plants.
Fragarianative plantsplantsRhus Typhinastaghornstaghorn sumacstaghorn sumac fruitstaghorn sumac plantsumacwild foodwild fruit
Leek Information
Frost Date Maps
Plant Hardiness Zone Map
White Baneberry Facts and Information
Partridgeberry
Outdoor News for Outdoor People
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,760
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The Best Attractions In Orchard
Jackson Lake State Park
Poudre River Trail
Wild Animal Sanctuary
Swetsville Zoo
Colorado Model Railroad Museum
Longmont Museum & Cultural Center
Orchard City is a statutory town in Delta County, Colorado, United States. The population was 3,119 at the 2010 census. There are three post offices serving Orchard City: Austin , Cory , Eckert .
Art Museum Beaches Breweries Food & Drink Museums Nature Specialty Museum State Park The Best Zoos & Aquariums
1. Jackson Lake State Park Orchard
This is a list of Confederate monuments and memorials that were established as public displays and symbols of the Confederate States of America , Confederate leaders, or Confederate soldiers of the American Civil War. Part of the commemoration of the American Civil War, these symbols include monuments and statues, flags, holidays and other observances, and the names of schools, roads, parks, bridges, counties, cities, lakes, dams, military bases, and other public works.Monuments and memorials are listed below alphabetically by state, and by city within each state. States not listed have no known qualifying items for the list. For monuments and memorials which have been removed, consult Removal of Confederate monuments and memorials. Some but by no means all are included below. This list do...
2. Colorado Model Railroad Museum Greeley
Colorado is a state of the Western United States encompassing most of the southern Rocky Mountains as well as the northeastern portion of the Colorado Plateau and the western edge of the Great Plains. It is the 8th largest geographically and 21st most populous U.S. state. The estimated population of Colorado was 5,540,545 on July 1, 2016, an increase of 10.17% since the 2010 United States Census.The state was named for the Colorado River, which Spanish travelers named the Río Colorado for the ruddy silt the river carried from the mountains. The Territory of Colorado was organized on February 28, 1861, and on August 1, 1876, U.S. President Ulysses S. Grant signed Proclamation 230 admitting Colorado to the Union as the 38th state. Colorado is nicknamed the Centennial State because it became...
3. Wild Animal Sanctuary Keenesburg
The Wild Animal Sanctuary is a 789-acre animal sanctuary located near Keenesburg, Colorado, United States. The sanctuary specializes in rescuing and caring for large predators which are being ill-treated, for which their owners can no longer care, or which might otherwise be euthanized. It is a 501 nonprofit organization and a state and federally licensed zoological facility. Created in 1980, The Wild Animal Sanctuary is situated on grassland northeast of Denver, and has helped over 1,000 animals since it first opened. By early 2018, home to more than 460 animals, the group announced the purchase of a major addition, a 9,004-acre ranch near Springfield, Colorado.
4. Left Hand Brewing Company Longmont
The Left Hand Brewing Company is a craft brewery located in Longmont, Colorado.
5. Longmont Museum & Cultural Center Longmont
Longmont is a Home Rule Municipality in Boulder and Weld counties of the U.S. state of Colorado. Longmont is located northeast of the county seat of Boulder and 33 miles north-northwest of the Colorado State Capitol in Denver. Longmont's population was 86,270 at the time of the 2010 U.S. Census. Longmont is the 13th most populous city in the state of Colorado. The word Longmont comes from Longs Peak, a prominent mountain named for explorer Stephen H. Long that is clearly visible from Longmont, and mont, from the French word montagne for mountain.
6. Poudre River Trail Greeley
The Cache la Poudre River , also known as the Poudre River, is a river in the state of Colorado in the United States.
7. Swetsville Zoo Timnath
Orchard Videos
10 Best Places to Visit in Utah - Travel Video
With five national parks, 43 state parks, and vast areas of breathtaking wilderness, Utah is one of the most popular states in the country for tourism. Along with what is recognized as the best snow on earth, visitors to Utah are also able to enjoy outdoor recreation, scenic vistas, and world-class shopping and dining. Thanks to Utah's ideal location, this lovely state presents the best of the Desert Southwest and the Rocky Mountains. Here's a look at the best places to visit in Utah:
The 10 Best Places To Live In Illinois (USA)
Top 10 Best Places To Live In Illinois (USA)
Illinois is as diverse a state as its cities and people. Located in the heartland of America, the Land of Lincoln may have cultivated a reputation as one of the worst run states, but it still remains a great choice for anyone looking to put down roots.
Unemployment rate is one of the major causes of the high migration rates out of the state in recent years, but Illinois continues to prove its economic resilience. Illinois is also home to dozens of cities with revitalized downtowns, excellent entertainment venues and endless outdoor recreation opportunities.
Universities in the state are on the leading edge of research and several of them, including the University of Illinois (Champaign Urbana) and Northwestern University,
are among the only 108 institutions nationally classified as "Very High Research Activity" on the Carnegie Classification of Institutions of Higher Education.
In the heart of the Midwest, Illinois has some crazy weather. The winters are harsh, the summers are hot, and several different seasons can show their face in a single day.
Every Illinoisan knows the importance of learning how to drive in snow and knows how to survive if their city gets shut down for a couple days.
Here are the 10 best places (cities and towns) to live in Illinois for 2018:
1. Northbrook.
2. Winnetka.
3. Buffalo Grove.
4. Naperville.
5. Galena.
6. Highland Park.
7. Wheaton.
8. Marion.
9. Park Ridge.
10. Elmhurst.
Original music by :
Savfk:
youtube.com/savfkmusic
facebook.com/savfkmusic
The 10 Best Places To Live In Maine | For 2018
The 10 Best Places To Live In Maine For 2018.
Maine is the north easternmost of the fifty US states. A versatile and vibrant landscape home to 1.3 million people.
With an impressive 3500-miles of coastline to enjoy, you are never far from the sandy shores in Maine.
The Atlantic coast is rugged and raw; waves crash against the rocks and the lighthouses stand proud above the choppy waters below.
When we said Maine offers a versatile landscape, we weren't kidding. Maine has a desert! Almost unheard of in a state that is so very coastal.
Outside the town of Freeport lies 40-acres of smooth, sandy desert; becoming an evermore popular attraction for both domestic and international visitors.
Maine is a keen fishing state, and in 2014 it produced nearly 90% of the United State's lobster yield. For those who are fans of seafood, you will feel right at home here in Maine.
When it comes to looking at this state as a potential place to live, you're already onto a winner with easy access to outstanding natural beauty.
We appreciate that proximity to the wild isn't the be all and end all, so in our list of 10 best places to live in Maine we have taken into consideration quality of public schools,
job opportunities, and general amenities.
Here are the 10 best places to live in Maine for 2018:
1. Portland.
2. Cape Elizabeth.
3. Caribou.
4. Farmington.
5. Brewer.
6. Gorham.
7. Yarmouth.
8. Falmouth.
9. Freepot.
10. Cumberland.
(This article is an opinion based on facts and is meant as infotainment).
Music by Nicolai Heidlas (
Top 15 Tourist Attractions & Things to Do in Grand Junction, Colorado
Top 15. Tourist Attractions & Things to Do in Grand Junction, Colorado: Grand Mesa, Downtown Grand Junction, Canyon View Park, Children's Nature Center, Two Rivers Winery, Museum of Western Colorado, John McConnell Math and Science Center, James M. Robb: Colorado River State Park, Grand Junction Visitors Center, Whitewater Hill Vineyards, Western Colorado Botanical Gardens, Western Colorado Center for the Arts, Cross Orchards Historic Site, Grand Junction Motor Speedway, Get Air At The Silo
Best Things To Do in Grand Junction, Colorado CO
Grand Junction Travel Guide. MUST WATCH. Top 10 things you have to do in Grand Junction. We have sorted Tourist Attractions in Grand Junction for You. Discover Grand Junction as per the Traveler Resources given by our Travel Specialists. You will not miss any fun thing to do in Grand Junction.
This Video has covered top 10 Best Things to do in Grand Junction.
List of Best Things to do in Grand Junction, Colorado (CO)
Grand Mesa
Two Rivers Winery
Canyon View Park
Children's Nature Center
Dominguez Canyon
John McConnell Math and Science Center
Grand Junction Visitors Center
Museum of the West
James M. Robb - Colorado River State Park
The 10 Best Towns To Live In Maryland For 2018
Subscribe for more videos:
Where are the best Towns to live in the state of Maryland?
To the untrained eye they are the places that have awesome economies. They're the places in Old Line State where people have the best jobs, residents are all above average, and the sun shines the most.
However, we don't trust the untrained eye and instead look to data to understand the best places to call home in Maryland.
There might be some surprises on this list, but when you look at the unbiased data, it's hard to argue against.
After analyzing 37 places in Maryland, we came up with this list of the best places:
1 - Hampstead.
2 - Rockville.
3 - Bowie.
4 - Poolesville.
5 - Walkersville.
6 - Mount Airy.
7 - La Plata.
8 - Thurmont.
9 - Cheverly.
10 - Takoma Park.
If you're looking for something more national, check out the best states in America or the best places to live in America.
Thank you for watching this video. I hope it's useful for you !
Music Title: Morning Sun
Artist: Nicolai Heidlas
This video is fair use under U.S. copyright law because it is noncommercial and transformative in nature, uses no more of the original than necessary, and has no negative effect on the market for the original work.
Copyright Disclaimer Under Section 107 of the Copyright Act 1976, allowance is made for fair use for purposes such as criticism, comment, news reporting, teaching, scholarship, and research. Fair use is a use permitted by copyright statute that might otherwise be infringing. Non-profit, educational or personal use tips the balance in favor of fair use. I DO NOT OWN ANY COPYRIGHTS. All rights goes to their respective owners, No copyright infringement intended.
If you have any issue with the content used in my channel or you find something that belongs to you, before you claim it to youtube, please SEND ME A MESSAGE and i will DELETE it right away. Thanks for understanding.
Palisade, Colorado Orchard in August
This is a beautiful spot; very peaceful.
Shooting Range at the Wild West Ghost Town Colorado Springs
Shooting the targets at the gun range... The Ghost Town Wild West Museum in Colorado Springs, CO is a throwback in time and a fun way to learn about history and this Wild Era!
(This Footage is a Small Part of the Bigger Video - To watch, visit
Turn Your Watch Back 100 Years!
As a true preservation of Colorado's western past, Ghost Town Museum is a fun and historic look back at kind of old west town that used to dot this region during the late1800's and early 1900's
An Authentic Ghost Town
Selected by Mobile Travel Guide and Family Circle Magazine as one of the fifty-five special attraction of America. See the USA Travel Edition Recognition of Merit. Explore the boardwalk connecting the Blacksmith's shop, Saloon, General and Merchants of main street, with the Livery Stable, and Victorian Home. Each is filled with thousands of fascinating artifacts. Ghost Town Museum delights young and old with lots of hands on activities, including old time arcades, panning for real gold (summer months), and much, much, more.
- See More at
Ghost Town History
Ghost Town Museum was created in 1954 to preserve a piece of Colorado's Wild West heritage.
In 1858 the cry Pikes Peak or Bust opened up the heartland of the Colorado territory to the gold prospector. Gold mining became a significant factor that led to the statehood of Colorado. The miners and the people who provided services to them quickly populated the western frontier of the United States. They needed transportation, and before long the twin steel ribbons of the railroads were pushing into the mountains to transport ore for processing.
Towns sprang up overnight and by the 1860's and 1870's people had blanketed the west. It was a rough and tumble time. Small encampments became small towns. Small cities along the rocky mountain Front Range provided a central location for supplies and services. The search for gold drove prospectors to every mountain valley, and every mountain peak. If gold or silver were not located, or if the mines played out, the towns were often abandoned to become ghost towns.
Little by little the raw spirit of the frontier died down. By the time gold was discovered in Cripple Creek in 1891, the frontier was almost gone. Today almost nothing remains of those exciting days of the old west. A scattered pile of old lumber, a tumbled pile of rocks marking an old mine, an occasional wagon wheel or a piece of equipment. The rip roaring camps of 100 years ago have become ghost towns now only a memory of a bygone era.
Louisville Colorado Town and Neighborhood Tour
Louisville Colorado has the distinction of being named Money Magazine's #1 best place to live in 2008, 2009, 2010 and 2011. The Money Magazine Study included crime rate, quality of life, health statistics, employment and housing measures. Obviously, Louisville was at or near the top in all of these categories to be #1 in the nation.
Louisville Colorado is a small town with easy access to both Boulder and Denver. It's a town where kids walk to school and friends meet for lunch at an old town restaurant.
Louisville Colorado was originally a coal mining town and was founded in the late 1800's. For many years Louisville's population was around 2,000 residents. Now it is a thriving town of 18,000.
The highly rated schools are part of the Boulder Valley School District. There is one high school, two middle schools and four elementary schools. The schools consistently rank among the states best.
There are many options for shopping and dining. Old Town features many quaint restaurants and is a great place to spend a relaxed evening. Louisville is surrounded by shopping; it is minutes from The Flatirons Crossing Mall and other large retailers like Super Target, Wild Oats Market and Costco. I'd be surprised if you had to go further than 10 minutes to find anything you would want to buy.
Real Estate: There is a diverse housing stock in Louisville Colorado. In Old Town you will find bungalows and remodeled Victorians. The rest of Louisville was mostly developed in the 1970's through the 1990's. A typical neighborhood is Louisville features quiet, winding streets of well kept homes within an easy walk to a park or open space.
Louisville's housing market is particularly strong. There is high demand and typically not many homes on the market.
All of Boulder County is an outdoor mecca and Louisville in particular has a great outdoor lifestyle. It's easy to get around on a bike and there are many parks, a city owned recreation center, a golf course and open space trails to enjoy.
So, if you are interested in living in Money Magazine's #1 Best Place To Live call me. I'm a Boulder County Native and one of the top Realtors in the area. I'd love to give you a personalized tour.
Neil Kearney 303.818.4055
The best places you must see in France during your trip
France - a country surrounded by love and romantic mood. France is a country of hundreds of pleasant aromas and bright lines of blooming orchards. France is also the homeland of gourmet dishes. The atmosphere of tenderness, calm and appeasement surrounds French streets. The most famous fashion shows are held in France, and the best couturiers of the world never get tired creating a fascination for this magical country. You will never be able to learn everything about France from books. Traveling France cannot be done within a week, month and even a year. France fascinates with her mysterious charm, she makes you want to dream. Weather in France is predictable, there are no abrupt changes in temperature, and the climate is pretty warm.
It is impossible to list all the attractions of France. Perhaps there are more of them here than anywhere else on Earth. Nobody else cares as much about their architectural heritage as French do. Lakes flooded with dense fog, quiet and snowy Alps, gentle sun on the green meadows - all of it calls for you, ready to share the secrets of many centuries.
like us at
Attractions In Orchard
Art Museum Attractions In Orchard Beaches Attractions In Orchard Breweries Attractions In Orchard Food & Drink Attractions In Orchard Museums Attractions In Orchard Nature Attractions In Orchard Specialty Museum Attractions In Orchard State Park Attractions In Orchard The Best Attractions In Orchard Zoos & Aquariums Attractions In Orchard
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,880
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Club Deportivo Elemental Unihockey-Floorball Leganés (CUF Leganes) er et floorballhold fra Madrid, Spanien, som spiller i den bedste række i Spanien både på herre- og damesiden. Klubben gør en stor indsats indenfor ungdomsfloorball.
Klubbens elitehold kvalificerede sig gennem det spanske mesterskab til EuroFloorball Cup-kvalifikation 2008 for herrer og for damer, som spilles i Frederikshavn.
Klubben opstod i 2002 som en fusion af Madrids to tophold KLER og Diablos Rojos.
Referencer
Eksterne henvisninger
Officiel hjemmeside
Floorballklubber
Sportsklubber i Spanien
Sport i Madrid
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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set -eu -o pipefail
# Return the collector main core version
get_collector_version() {
collector_module="$1"
main_mod_file="$2"
if grep -q "$collector_module" "$main_mod_file"; then
grep "$collector_module" "$main_mod_file" | (read mod version;
echo $version)
else
echo "Error: failed to retrieve the \"$collector_module\" version from \"$main_mod_file\"."
exit 1
fi
}
# Compare the collector main core version against all the collector component
# modules to verify that they are using this version as its dependency
check_collector_versions_correct() {
collector_module="$1"
collector_mod_version="$2"
incorrect_version=0
mod_files=$(find . -type f -name "go.mod")
# Loop through all the module files, checking the collector version
for mod_file in $mod_files; do
if grep -q "$collector_module" "$mod_file"; then
mod_line=$(grep "$collector_module" "$mod_file")
version=$(echo "$mod_line" | cut -d" " -f2)
# To account for a module on its own 'require' line,
# the version field is shifted right by 1. Match
# with or without a trailing space at the end to account
# for the space at the end of some collector modules.
if [ "$version" == "$collector_module" ] || [ "$version " == "$collector_module" ]; then
version=$(echo "$mod_line" | cut -d" " -f3)
fi
if [ "$version" != "$collector_mod_version" ]; then
incorrect_version=$((incorrect_version+1))
echo "Incorrect version \"$version\" of \"$collector_module\" is included in \"$mod_file\". It should be version \"$collector_mod_version\"."
fi
fi
done
echo "There are $incorrect_version incorrect \"$collector_module\" version(s) in the module files."
if [ "$incorrect_version" -gt 0 ]; then
exit 1
fi
}
# Note space at end of string. This is so it filters for the exact string
# only and does not return string which contains this string as a substring.
COLLECTOR_MODULE="go.opentelemetry.io/collector "
COLLECTOR_MODEL_PDATA="go.opentelemetry.io/collector/pdata"
COLLECTOR_MODEL_SEMCONV="go.opentelemetry.io/collector/semconv"
MAIN_MOD_FILE="./go.mod"
COLLECTOR_MOD_VERSION=$(get_collector_version "$COLLECTOR_MODULE" "$MAIN_MOD_FILE")
# Check the collector module version in each of the module files
check_collector_versions_correct "$COLLECTOR_MODULE" "$COLLECTOR_MOD_VERSION"
check_collector_versions_correct "$COLLECTOR_MODEL_PDATA" "$COLLECTOR_MOD_VERSION"
check_collector_versions_correct "$COLLECTOR_MODEL_SEMCONV" "$COLLECTOR_MOD_VERSION"
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,123
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New England Aviation History
from author and historian Jim Ignasher
Connecticut Aviation Accidents
Maine Aviation Accidents
Massachusetts Aviation Accidents
New Hampshire Aviation Accidents
Rhode Island Aviation Accidents
Vermont Aviation Accidents
Aviation Mysteries
Historic Articles
Airships & Flying Machines
Balloon Articles
New England "Firsts"
Forgotten Airports
Other Interest
Vintage Airport Views
Aviation Advertising
Aviation Memorials
Aviation Police/Fire
Civil Aviation Insignia
State Aviation Insignia
You are here: Home / Massachusetts - Civil / Saugus, MA – February 9, 1941
Saugus, MA – February 9, 1941
Saugus, Massachusetts – February 9, 1941
On February 9, 1941, a single-engine private biplane was stunt flying over Saugus. Witnesses recalled that the plane had just completed three loops and was beginning a fourth when it suddenly dove to the ground from an altitude of 400 feet. The plane crashed in the yard of a home belonging to Harry Butler, just missing the house by a few feet. Both men aboard the plane were killed.
The dead were identified as Laurence G. Hanscom, 34, of Worcester, Mass., and Dr. Anthony V. Carbone, 34, of Cambridge, Mass.
The plane had been a trainer aircraft, with a dual set of controls. Dr. Carbone had been a student pilot.
Hanscom was a well known newspaper correspondent working for the Worcester Telegram, and had been a pilot since 1919. He was also the commander of the Massachusetts Wing of the Civilian Air Reserve. The group numbered about 150 licensed pilots, and others interested in aerial photography and map making.
His death occurred the day before he was scheduled to enter the Royal Canadian Flying Corps as an instructor. (At the time of this accident, the United States hadn't entered World War II.)
In February 1943, Hanscom Air Force Base in Bedford, Massachusetts, was named in his honor.
(New Hampshire) The Nashua Telegraph, "No Explanation For Saugus Crash", February 10, 1941
(Maine) Lewiston Daily Sun, "Airplane Crash Kills Two Men At Saugus", February 10, 1941
Filed Under: Massachusetts - Civil Tagged With: Anthony V. Carbone, Laurence G. Hanscom, Saugus Airplane Crash, Saugus Massachusetts History, Saugus Plane Crash
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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Q: `fs-extra` integrate with `bluebird ` got `Cannot read property 'then' of undefined` error Here is my code
var Promise = require('bluebird');
var fse = Promise.promisifyAll(require('fs-extra'));
fse.remove('./myDir').then(function () {
console.log('Remove myDir done.')
});
I always get TypeError: Cannot read property 'then' of undefined error.
Version:
node: v6.9.2
bluebird: 3.4.7
fs-extra: 1.0.0
I searched and found a similar question but not exactly quite the same, and I tried that answer, unfortunately, it can't solve my problem.
Did I miss anything?
A: I found the correct way is fse.removeAsync, add Asyncsuffix to fse.remove, please see bluebird API here. Hope it can help others.
Update:
With the latest fs-extra, I don't need to import bluebird anymore.
See here, below syntax works well.
// Promise Usage
fs.remove('/tmp/myfile')
.then(() => {
console.log('success!')
})
.catch(err => {
console.error(err)
})
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{
"redpajama_set_name": "RedPajamaStackExchange"
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package onFailureCancelSuccessors;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileWriter;
import java.io.IOException;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.FileReader;
public class OnFailureCancelSuccessorsImpl {
public static int processParam(String filename) throws numberException {
File file = new File(filename);
BufferedReader br;
String st = "";
try {
// Read file contents
br = new BufferedReader(new FileReader(file));
st = br.readLine();
} catch (FileNotFoundException e) {
e.printStackTrace();
} catch (IOException e) {
e.printStackTrace();
}
// Content of file to integer
int n = Integer.parseInt(st);
System.out.println("The number readed is : " + n);
// The written string is the following number
String str = String.valueOf(n + 1);
BufferedWriter writer;
try {
// Erase file previous contents
new FileOutputStream(filename).close();
// Write the new number to the file
writer = new BufferedWriter(new FileWriter(file, false));
writer.write(str);
writer.close();
System.out.println("Writing to file");
} catch (IOException e) {
e.printStackTrace();
}
System.out.println("The written number is : " + str);
return n;
}
// Function called if the execution has to continue
private static void failOnce(int n) throws numberException {
File file = new File("/tmp/sharedDisk/onFailure1.txt");
// Delete previous occurrences of the file
System.out.println("The file exists ? " + file.exists());
// Exception thrown
if (n == 1) {
throw new numberException("The number is too low");
}
}
public static void processParamCancelSuccessors(String filename) throws numberException {
int n = processParam(filename);
failOnce(n);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
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Ethical Chic
The Inside Story of the Companies We Think We Love
Fran Hawthorne
Beacon Press, Boston
To my father, Edward Hawthorne
Contents
Author's Note
Introduction. The Image
1. Tom's of Maine: Woodstock Toothpaste
2. Timberland: How Green Is My Leather
3. Starbucks: Coffee as a Brand Name
4. Apple: The Coolest of Them All
5. Trader Joe's: Are We Having Fun Yet?
6. American Apparel: Sex and the T-Shirt
7. The Reality
Acknowledgments
Notes
Author's Note
Business may thrive on change and innovation, but too many changes sure make it hard to write a book about business. Of the six companies profiled in this book, three announced major and abrupt new developments within the last few months of my research and writing, and a fourth tossed in a small complication:
Three days before I was due to hand in the manuscript of this book to my editor, American Apparel revealed that it might file for bankruptcy.
Two months later, just as I was finishing the edit, Timberland was acquired by VF Corporation.
Two months after that, in the midst of yet another round of reviews, Apple's legendary chief executive, Steve Jobs, stepped down. And barely one month afterward, at the verge of the final edits for this book, Jobs died.
Also, I had known for months that Howard Schultz, Starbucks's chief executive, would be publishing the second volume of his autobiography a couple of weeks before my first deadline, which ultimately required a few updates in my manuscript.
So, who can guess what other surprises these companies may serve up between the day you start reading this book and the day you finish?
Introduction. The Image
Company X is an ideal progressive company. Its products have dramatically challenged conventional thinking while helping people from cerebral palsy patients to schoolkids in Africa to antigovernment protestors in Iran, Tunisia, and Egypt. Its cofounder, a vegetarian, was married in a Buddhist ceremony in Yosemite National Park. Its website posts detailed information about its carbon emissions; moreover, it was the first in its industry to eliminate the most common toxic ingredients. And it has done all this while competing against one of the biggest, most hated companies on Earth. Cutting-edge, creative people wouldn't think of using anyone else's products.
Company Y, on the other hand, is a terrible company for progressives. Its nonunion employees historically labored long hours at the whim of a micromanaging chief executive who changed his mind at the last minute and made impossible demands. Overseas, it uses Chinese sweatshops so dreadful that a dozen workers have committed suicide. It has been slow on environmental issues, acting only after intense prodding by socially responsible mutual funds and a big public campaign from Greenpeace. Actually, it's hard to know anything about this company because it's so secretive that its press people don't return phone calls.
Of course, Company X and Company Y are the same company. The name: Apple Inc.
In this age of consumer activism, pinpoint marketing, and unlimited and immediate information, we want the impossible: products and producers that will assure us that we are fashionable, and that don't pollute, harm animals, or contain weird chemicals, that run on alternative energy, pay their workers good salaries, recycle their scraps, use natural ingredients, buy from local suppliers, donate generously to charity, donate in particular to their neighborhoods, and don't throw their weight around by lobbying. (Or maybe they should lobby for the right causes?) Why should we pay good money for something that will make us look nerdy, or that will poison the Earth? We don't think we're being overly demanding. All we're asking for are the kinds of policies we try to follow in our own daily lives, and if we can manage to recycle and avoid animal products, then certainly big companies, with all their clout, can do likewise.
Hard as it is to be so many things to so many consumers, a handful of companies and products—like Apple, Ben & Jerry's ice cream, Converse sneakers, and the grocery store chain Trader Joe's—seem to have hit that magic bull's-eye, at least for a time. Almost no matter what they do, they maintain an image of being cool, fun, and innovative and, at the same time, an equally strong image as green, politically progressive, and ethical.
As a result, their customers are fiercely loyal. At Macworld, the annual conference for users and vendors of Apple products, held in San Francisco in 2010, I met fans who had traveled at their own expense from as far away as Iowa, Illinois, and Michigan just to meet kindred souls and to ooh and ahh over the newest add-ons. And mind you, this was a gathering without the magical presence of Apple's legendary cofounder, Steve Jobs. Meanwhile, Naomi A. Gardberg, an assistant professor at the City University of New York's Zicklin School of Business, has friends who will drive thirty miles to get to Trader Joe's.
Even during the 2008–2009 downturn and the weak recovery afterward, BusinessWeek magazine noted in amazement that stressed-out, debt-ridden, mortgage-foreclosed consumers still found spare change (or unused credit lines) for Apple iPads and Starbucks lattes. They would forgo a new car, switch from brand-name to generic toiletries, and pick up shampoo at discount outlets, the magazine said in an August 2010 cover story. But Apple and Starbucks were irreplaceable.
Investors, too, are more willing to cut certain firms a little slack. "Some companies have built so much trust that shareholders are less likely to vote against management," explained Laura Berry, executive director of the Interfaith Center on Corporate Responsibility (ICCR), a New York City–based organization that represents about three hundred religious institutions and is one of the pioneers of the movement for socially responsible investing. "In some ways, if shareholders bring a resolution that says, 'We want you to report more about your environmental sustainability,' and Apple says, 'We're making our best efforts—you should just trust us and don't vote against us,' we're going to believe them."
In return, more and more business executives are recognizing that ethical-trendy shoppers are a big and growing market. While the desire to be trendy is nothing new, the other factor—what's often called corporate social responsibility, or CSR—has burgeoned more recently.
When Walmart announced plans to run its trucks more efficiently, switch to solar energy at two dozen sites, promote energy-saving compact fluorescent lightbulbs (CFL), use recyclable cardboard cartons, and maybe even install windmills in its parking lots so customers could recharge their hybrid cars, it was clear that the environmental movement, at least, had gone Main Street. Institutional Investor, a trade journal that goes to the upper tier of business and finance, devoted a two-part cover package in November 2010 to socially responsible investing—a favorable package. The fortieth anniversary of Earth Day in 2010 "has turned into a premier marketing platform for selling a variety of goods and services, like office products, Greek yogurt, and eco-dentistry," the New York Times reported. Even the crusty British weekly the Economist reluctantly succumbed, in a special issue about CSR on January 19, 2008, with the cover headline "Just Good Business." It harrumphed, "This newspaper has argued that it is often misguided, or worse. But in practice few big companies can now afford to ignore it."
Thus, consumer-oriented businesses are trying to find the words, logo, and image—and, of course, products—that will indelibly brand themselves as the Apple or Trader Joe's of their industry. Unilever, which markets the chemical-laden Knorr soup mixes, reached out to the organic crowd by acquiring Ben & Jerry's. The Clorox Company—whose chlorine bleach is despised by environmental activists for damaging sewers and aquatic life—made a dual effort: It bought the homespun cosmetics company Burt's Bees, founded by a bearded guy who lived in a converted turkey coop in Maine. Plus, it has a new line of plant-based, "green" household cleaning products that touts an endorsement from the Sierra Club. McDonald's has recast some of its outlets with chocolate-colored seats and muted beige walls to look like Starbucks. (Sort of.)
The more that businesses incorporate the image of socially responsible hipness, however, the harder it is for consumers. How can they tell whether the picture of happy cows grazing in a meadow is a marketing mirage? Did Clorox co-opt Burt's Bees? When Starbucks says it buys fair-trade coffee, what does that mean?
Investigating a firm's ethical credentials would seem to be fairly straightforward, because plenty of organizations monitor and produce rosters of "best" companies in a whole range of categories. On the environmental front, according to a directory called the Ecolabel Index, there are at least 365 seals and certifications in 214 countries. For instance, Greenpeace publishes industry-specific lists, including a "Guide to Greener Electronics" for tech manufacturers and a "Supermarket Seafood Sustainability Scorecard"; the nonprofit coalition Ceres issues awards, reports on the sustainability efforts at particular businesses, and posts a list of the eighty-plus "network companies" that have met its green criteria; and the nonprofit environmental organization Climate Counts analyzes the efforts to reduce and measure carbon emissions at the largest firms in seventeen consumer industries.
Which companies treat their employees well? Fortune magazine each year publishes its choice of the "100 Best Companies to Work For," ranking nominees according to their internal communication, training, safety, work-life balance, pay, benefits, nondiscrimination, camaraderie, and so on. Working Mother has a different set of 100 companies that focuses on working moms and criteria such as flextime, parental leave, child-care benefits, family health coverage, and adoption reimbursement. Other magazines have offered their own lists centered on their particular specialties, including Latina Style's top 50 companies for Hispanic women and Black Enterprise's "40 Best Companies for Diversity." An arm of the AFL-CIO posts an annual roster called "The Labor Day List: Partnerships That Work" in order "to recognize successful partnerships between employers and their employees' labor unions that are working well in the global economy," as the accompanying report puts it.
In the federal Equal Employment Opportunity Commission's archives, you might find press releases announcing lawsuits alleging racial or sex discrimination at various businesses. Homing in specifically on the treatment of lesbian, gay, bisexual, and transgender workers, the Human Rights Campaign has a "Corporate Equality Index" that rates companies on factors like whether they have a formal nondiscrimination policy or offer domestic-partner benefits. In addition, a consumer might look at the number of women and minorities on a company's board of directors, at least for symbolic reasons, although Aaron Chatterji, an associate professor at Duke University's Fuqua School of Business, suggests that such percentages "may not reflect the way they treat people throughout the firm."
It's a little tougher to analyze working conditions at factories overseas. A lot of organizations monitor them, and activists disagree on which to trust. The Fair Labor Association? The Worker Rights Consortium? Verité? TransFair USA? Sweatshop Watch? Labour Behind the Label? Students & Scholars Against Corporate Misbehavior? The Global Union Federation? Specialized Technology Resources (better known as STR)? Regardless of the monitor, the brand-name multinational companies that contract out to those factories should have codes of conduct guaranteeing a right to collective bargaining and free association, labor experts say. Even better—but rare—would be a guarantee of a living wage, not merely that country's minimum wage (since the factory should theoretically pay the minimum anyway, with or without a code).
Still more. For ethical corporate behavior in general, there are lists from GoodGuide, Corporate Responsibility (or CR) magazine, Business for Social Responsibility (BSR), and Green America (which, despite the name, chooses members of its Green Business Network based on whether they are "values-driven" and "using business as a tool for social change," not greenness), to name only a few. Consumer Reports analyzes products' reliability, quality, repair record, price, and customer satisfaction. At People for the Ethical Treatment of Animals (PETA), the "Caring Consumer" database names businesses that do and don't test their products on animals. Concerned shoppers and investors can also check the names approved by the socially responsible mutual funds run by financial managers like the Calvert Group, Domini Social Investments, and Pax World Management Corporation. As a gauge of political leanings, the Center for Responsive Politics has detailed listings, going back more than a decade, of contributions to federal campaigns by companies and individual employees, as well as money spent on lobbying.
And I've left out dozens of others.
All these sources and rankings illustrate one big problem: ethically hip consumers are trying to follow too many—and often conflicting—criteria. Does the company use organic ingredients? Does it test its ingredients on animals? Does it obtain its ingredients from local suppliers? What if the sole source of organic, animal-safe supplies is imported? What if the organic item looks uglier than the one made with pesticides? What if it's twice as expensive? Furthermore, are its employees unionized? Does it recycle? Does a company have to pass every "test" to be considered ethical?
Since no company can be perfect in every category, consumers who are concerned about ethical business behavior have to set priorities. As with anything in life, they compromise and juggle among the questions raised above, and many more, depending on their personal values. Each person's priorities—and favorite companies—will be different. For instance, consider the following issues:
Can a company be socially responsible if it doesn't treat its employees well?
Assuredly not. Now rephrase the question: Can a company be said to treat its workers well if it has no unions? Or if it actively fights union organizing?
With barely 6.9 percent of the US private-sector labor force represented by a union, and with both corporate and public employee unions under severe attack from Republicans in states like Indiana, Michigan, Ohio, and Wisconsin, labor officials would be pretty unrealistic to insist on a union label. Some of them hedge. Warren Pepicelli, an executive international vice president of the apparel workers' union UNITE HERE, put it this way: "I think people should be in unions. That certainly is a criterion for a company being decent. The only way workers have respect is by having their own organization." Ron Blackwell, chief economist for the AFL-CIO, is more tolerant. If the wages, benefits, and working conditions are good and management seems to listen to the workforce, not having a union could be OK, he said. He draws the line, however, "if the company is using their power as an employer to suppress people's effective rights to form unions," by tactics such as threatening to shut down sites where a union drive is under way.
Well, Trader Joe's and Starbucks offer above-average pay and benefits for their industries, even without unions. But both have been accused of using nasty tactics to fight organizing drives—a particularly egregious issue in the case of Trader Joe's, because the supermarket industry is one of the few in the private sector that still has significant union representation. As if that weren't bad enough, Starbucks has had run-ins with CSR groups about whether it cheated impoverished Ethiopian coffee farmers.
And the labor questions don't end there, since being a decent boss is not simply a matter of pay. "Wages and benefits are the first thing an employer wants to give you. It's easy and meaningless; the employer just takes the money out of something else," said Christian E. Weller, an associate professor of public policy at the University of Massachusetts's McCormack Graduate School of Policy Studies, in Boston, and a senior fellow at the Center for American Progress, a liberal think tank based in Washington, DC.
"A union is also about due process," he went on. "Who gets hired, who gets fired, who gets promoted, under what circumstances. Can you complain about things that go wrong without being fired? Also, there should be a promotion-and-review process that has nothing to do with you being friends with the manager."
Can a company be socially responsible if its products are expensive?
Almost anything manufactured or sold in nonstandard ways charges a higher price than standard stuff. The main reason is that these items typically contain hard-to-find ingredients, are made by people who get above-minimum wages, or can't enjoy the economies of scale that come from mass production. Yet by most definitions, to be socially responsible is to care about the welfare of low-income and working-class people who can't afford $5.92-per-pound grass-fed, pasture-raised, no-antibiotic, no-added-hormones ground beef.
Optimistically, Patricia H. Werhane, a senior fellow at the University of Virginia's Olsson Center for Applied Ethics, predicts that prices will drop over time as public pressure forces more companies to follow CSR practices, creating an ethical version of mass production. Even if she's right, though, cash-strapped consumers need to eat and brush their teeth now.
Another suggestion comes from Jill Kickul, director of the Stewart Satter Program in Social Entrepreneurship at New York University's Stern School of Business. "Some of these companies would say, 'We are giving back to low-income people by some of the community service we do.'" Indeed, the glowing reputations of Timberland and Tom's of Maine are built in large part on exactly that sort of community service, because the two companies let employees take time off with pay to do volunteer work. Thus, rich shoppers, by buying expensive, socially responsible products, are subsidizing socially responsible projects for the poor—an organic Robin Hood arrangement.
Maybe. Still, there's something grating and patronizing about this explanation. The poor can't use Tom's healthful toothpaste, but they should be grateful that Tom's staffers might hand them mashed potatoes at a soup kitchen?
And then, when the juggling stops and the balls come to rest, the results can be meaningless or logically impossible.
Like Shell Oil Company getting a perfect score in both 2010 and 2011 on the Human Rights Campaign's corporate-equality list.
An oil company, whose basic function is to encourage the wasteful consumption of limited resources, thereby increasing global levels of dangerous carbon emissions? Even worse, Shell's parent company, Royal Dutch Shell, has been accused of environmental damage, oil spills, and human rights abuses in its operations in the Niger Delta in the 1990s. When Ken Saro-Wiwa, a Nigerian author and human rights advocate, led protests against the oil operations, Shell allegedly asked Nigeria's military rulers to stifle him. Saro-Wiwa and other activists were executed, and in 2009, the oil giant paid $15.5 million to settle some of the charges.
How does the Human Rights Campaign explain celebrating this corporate criminal? "In no way do we want to condone drilling or all the horrible environmental things they may be doing," said Eric Bloem, deputy director of the group's workplace project. Nevertheless, first things first, and for the HRC, diversity issues come first. Besides, the criteria for making the equality list are apparently so lax that almost any personnel office would qualify. Out of 615 large companies the HRC analyzed for 2011, fully 337 got a perfect score, and the average, on a scale of 0 to 100, was 87.
R. J. Reynolds Tobacco Company is another giant in another hated industry. Yet there it was, number 96 on the Fortune "Best Companies to Work For" roster in 2002. An independent organization called the Great Place to Work Institute, founded by journalists Milton Moskowitz and Robert Levering, compiles the annual ranking, based on a fifty-seven-question survey sent to at least four hundred employees at each company that applies, plus a survey filled out by corporate management. The questions focus on working conditions, not whether the product itself is socially responsible. "Using our methodology, [RJR employees] thought it was a great workplace," Levering told me.
To find a way through this morass, some socially concerned business managers, experts, and consumers have tried to craft an overarching definition to encompass all the contradictions and possibilities. The results are mind-boggling.
Timberland, for instance, has outlined its CSR mission in a grid with "pillars" and "core values." Gordon Peterson, the company's vice president for corporate social responsibility when I interviewed him in spring 2010, spelled it out: Energy, product, workplace, and service are the four pillars; humanity, humility, integrity, and excellence are the four core values; and transparency and accountability are a kind of combined supervalue connecting all of them. (Peterson later switched out of CSR to become vice president of change management and business transformation, overseeing a reworking of the company's business systems.)
The Geneva-based International Organization for Standardization, or ISO—best known for writing technical specifications for things like fasteners and oil burners—set up committees of consumer, business, government, labor, human rights, and other advocates to craft standards for various social values, such as "sustainability criteria for bioenergy." Its 106-page "Guidance on Social Responsibility" report includes seven "core subjects": community involvement and development, consumer issues, the environment, fair operating practices, human rights, labor practices, and organizational governance. Each of these subjects is then analyzed according to subcategories, like discrimination, health and safety, pollution, corruption, and economic, social, and cultural rights.
Not surprisingly, such formal definitions are rare. The National Consumers League doesn't have one; its annual Trumpeter Award almost always goes to individuals, not companies. "It's multiple-dimensional" is the description from Michael Gusmano, a research scholar at the Hastings Center, a think tank in the exurbs north of New York City that specializes in ethical issues in health and the environment. Patricia Werhane, of the Olsson Center for Applied Ethics, doesn't think the topic can ever be defined, "because you're going to leave something out."
So, if there isn't one single form of CSR, and each person or company has to set priorities, the priority that usually wins out is the environment. In fact, when business professors, ethicists, marketing experts, and company officials are asked about social responsibility, many of them launch immediately into a discussion of green products, as though that were the only kind of CSR.
One reason for the corporate emphasis is that "conservation is a little less politically aligned. In the conservation arena, you have both Republicans and Democrats," posits Christian Weller, the labor economist at the Center for American Progress. Thus, there's less risk of alienating customers. Some activists suggest that trying to be green is easier and cheaper for managers than, say, monitoring sweatshops in China, paying higher wages, or avoiding animal testing. "It's a technical fix," said Jeff Ballinger, a veteran antisweatshop activist. "If you have to replace a certain chemical that's a reproductive toxin, you just find the scientists to give you an alternative."
Consumers, for their part, may gravitate toward eco-activism because it's been part of the public discussion much longer than issues like animal welfare or workplace diversity, dating back at least to Rachel Carson's 1962 book Silent Spring. Certainly, the Millennial generation has been hearing about recycling and pollution since kindergarten. It's also easier to measure carbon emissions or water pollution than workplace morale.
When consumer groups do focus on work-related issues, they seem to be a lot more concerned about sweatshops overseas than wages, health insurance, family-friendly policies, discrimination, or union membership in the United States. Nike and the Gap changed their policies after public protests charging dangerous, exploitative working conditions at foreign subcontractors. However, where's the outrage when Starbucks is cited by the National Labor Relations Board for illegally firing American union organizers?
An obvious place where ethics-balancing occurs is in investing, which has morphed from the term "socially responsible investing" to "environmental, social, and governance" investing. If ESG activists like the religious ICCR members were to insist on finding corporations that had absolutely no history of pollution, nuclear power, Pentagon contracts, labor violations, outsourcing, nonunion work, ethnically insensitive product names, and animal testing, plus no ties to tobacco, alcohol, weapons, and gambling, their cash would still be under their mattresses. "Most companies are big, publicly traded, multinational companies that do some good things and do some bad things," said Adam Kanzer, the general counsel and a managing director at Domini, one of the largest of the ESG mutual fund families. "They're too big to carry a one-blanket reputation." Moreover, these are not charities, so in addition to all the touchy-feely social criteria, firms such as Domini, like any investment manager, have to worry about not losing their clients' money.
Thus, their criteria include wiggle room. Often, the final decision comes down to percentages. Boston's Trillium Asset Management allowed 3M Company onto its approved list, even though the manufacturer sold some weapons-related products, in consideration of its good record on the environment and employment, and the fact that just a tiny portion of its revenue came from weapons. Pax World Management and the Calvert Group took some heat in the early 2000s when they opened up their funds to utilities that owned existing nuclear plants. "If a utility company is doing everything right for alternative energy—it had some wind, some solar, but happened to have a legacy nuclear plant—we wouldn't exclude that company from consideration," Paul Hilton, Calvert's director of advanced equity research, said.
Domini juggles two sets of ethical values, along with standard financial criteria. As Steven D. Lydenberg, the chief investment officer, explained, one ethical set is focused on companies' sense of civic responsibility, whether they see themselves as having a responsibility to so-called stakeholders like employees, customers, and the local community, in addition to shareholders. The second ethical overlay, he added, looks for industries and business lines that are "particularly aligned with [Domini's] global standards." Then comes the juggling. "If the business is aligned with our standards, then the stakeholder relations don't have to be as strong as if it isn't aligned," Lydenberg said. "For instance, in pharmaceuticals, we distinguish between companies that have devoted themselves to vaccines, which we believe is most aligned with our goals of preventing illness, versus companies that make patent-protected lifestyle drugs."
Most ESG funds manage to draw some red lines for their bottom lines. Certain kinds of companies and products can never be ethical. Domini, like most socially responsible funds, will not invest in a company specializing in tobacco, weapons, gambling, or nuclear power. (No R. J. Reynolds dilemmas here.)
If it seems hard to define "socially responsible," try defining "cool."
The problem, for starters, is that the quality has to be mysterious, or by definition (if there were one) it wouldn't be cool, hip, fashionable, funky, trendy, and so on. If everything is cool, then nothing is. And if everyone knows what defines cool, then everyone will be able to imitate it.
"It is a universal complaint that hip ceases being hip the moment it spreads beyond one's own circle," pointed out pop-culture journalist John Leland in his 2004 book Hip: The History. "After all, once people fractionally more clueless than yourself are in the club, what is the value of membership?" Leland has a very narrow definition of hip, essentially tying it to black music, but his basic point applies to anything that claims the mantle of fashion.
Still, there do seem to be some commonly agreed-on indicators. For instance, coolness is more likely to be found among the young. "Teenagers and young adults, who have the least stake in the old order, tend to move fluidly in the uncertainty of the new," Leland wrote. Naomi Klein, in her best seller No Logo, said that corporate marketers actually didn't begin to focus on the youth audience until the early 1990s, because "1992 was the first year since 1975 that the number of teenagers in America increased"—that is, the audience was big enough to be worthwhile. Once business discovered the booming wallets of the boomers' kids, there was no turning back to old fogies. "Their parents might have gone bargain-basement, but kids, it turned out, were willing to pay up to fit in."
Historically, it was the upper crust who defined "cachet," and the lower classes strove as best as they could to emulate it (or, like Jay Gatsby and Tom Ripley, pretend they were of it). The post–World War II suburban ideal was a Cadillac and a fur coat like a movie star's. In the modern version, middle-class twentysomethings straight out of college dreamed of Rolexes, Jaguars, a converted loft in SoHo, or a ski house in Vail, then went into debt buying them if they could, or settled for Chinese knock-offs if they had to. In her 1998 book The Overspent American, Juliet B. Schor, then a senior lecturer at Harvard University, described how the ideal has been creeping ever higher, ever further from our means, from keeping up with the neighbors to keeping up with the boss at work to desperately trying to reach the exalted ranks of Beverly Hills, 90210.
That assumption of upward mobility has to be rethought now, however. As former Esquire editor in chief Lee Eisenberg wrote in his 2009 book Shoptimism: "Beginning in the sixties, it became apparent that tastes no longer just trickled down [emphasis in original], they trickled every which way. They trickled in from bohemians and hippie outer fringes, up from the ghetto and the grunge." Blue jeans began as workingman's garb, and when that was no longer grungy enough, they had to be torn and (intentionally) faded. "By the 1990s, inner-city tastes had become an important driver of middle-class fashion," Schor noted. Timberland certainly discovered that in the early 1990s when its traditional blue-collar boots suddenly became popular with the hip-hop crowd, and that popularity propelled the brand out into the broader fashion market.
And once you think you've defined a hip trend, you're too late. Trends come and go too fast to name. "After about a decade of looking at [a product], people say 'Ugh,'" said Arthur Caplan, chair of the Department of Medical Ethics at the University of Pennsylvania. "Familiarity breeds boredom." Starbucks, launched in its modern version in 1987, breached the ten-year line long ago, he said. Apple, founded in 1976, has managed to defy the time limit so far—partly by constantly inventing new product categories, partly because it almost went out of business in the mid-1990s and thus could be said to have restarted the countdown around the turn of the millennium, and partly because anything Steve Jobs ever did is inherently hip.
Robert Passikoff, founder and president of Brand Keys, a New York City–based consulting firm specializing in brand loyalty, said the timeline has actually speeded up in recent years. If a company brought to market something innovative in the 1960s or 1970s, he said, "it would take a year for rivals to copy you. As technology improved, rivals could copy you within six months, so all the products became the same."
Yet, even while it's impossible to categorize, in-ness is the essence of selling and, therefore, of corporate survival. The short cut to achieving this, whether during a thirty-second commercial or on a drive-by billboard or in a one-word Web banner, is by creating a brand. That doesn't mean merely a corporate logo or slogan. After all, ExxonMobil Corporation and McDonald's have recognizable logos, and no one would call them trendy. A true brand is an instant identity card, signage that separates the members from the outsiders. A community.
Unlike hip, the word community has lots of definitions. Passikoff: "It's people who feel an emotional bond to the product." Klein: "The products that will flourish in the future will be the ones presented not as 'commodities' but as concepts: the brand as experience, as lifestyle." Academics Dan Ariely (a professor of behavior economics at Duke University) and Michael I. Norton (an associate professor of business administration at Harvard Business School), in a paper in the 2009 Annual Review of Psychology: It's a way "to signal to ourselves and others our beliefs, attitudes, and social identities," which they label "conceptual consumption." New York Times Magazine consumer columnist Rob Walker, in his book Buying In, gives brand seekers a bit more power, arguing that manufacturers can no longer manipulate popularity the way they once did. A "brand that catches on in the marketplace does so," he claimed, "because of us: because enough of us decided that it had value or meaning and chose to participate."
Originally, especially when fashion meant emulating the wealthy, brands were affixed only to a few elite categories, like cars, clothes, and whiskey. Now, almost anything is branded—kitchen blenders, sunglasses, sneakers, baby strollers, and, the granddaddy of them all, coffee.
But wait—we're not done delineating yet. If there are ordinary corporate brands, like ExxonMobil, and then an inner circle of cool brands, like Starbucks, there is yet an even-more-inner circle of superelite cool brands. Consultants Matthew W. Ragas and Bolivar J. Bueno call them "cult brands"; Klein tags them "attitude brands." They might be the most expensive in their category, the ones used by big-name celebrities, the ones handmade in limited quantities, or the ones with the newest technology, but if so, those are all secondary traits. More important, superelite brands are trendy yet have stood the test of a certain amount of time. Their users may span a few generations, as long as they include the young. And these users build networks. They buy all the newest add-ons. They love these brands passionately. As Ragas and Bueno put it, in their book The Power of Cult Branding, these brands somehow evoke a community of "daring and determination" whose fans are so devoted that they will happily proselytize the unconverted—except not too many unconverted, since then of course the brand would lose its exclusivity.
All this may seem a lot to require of one pair of boots, one cup of coffee, or one company. Is it possible for a product to be both trendy and socially responsible? To be trusted and also loved? Yes, a few companies like Apple and Trader Joe's seem to have earned that double halo, but are they the rare exceptions?
This book set out to analyze six candidates, although they're hardly the sole companies in the world that might fit the dual definition. For that matter, the lessons here could be useful to any business. The driving idea is to understand how these privileged companies operate, what customers and activists say about them, why they are viewed as ethical and cool, what they do to try to achieve those images—and whether, in the end, they deserve their reputations.
To pull together a workable collection of names, I started writing down just about every company I could think of that could possibly claim both of the defining characteristics. I pored through notes from my four previous books and from three decades of reporting. I queried consumer, labor, environmental, human rights, and animal-welfare activists I had interviewed before, along with experts in business and ethics, including Steven Lydenberg, of Domini; Karen Ferguson, of the Pension Rights Center; Christian Weller, of the Center for American Progress; and longtime consumer advocate Carol Tucker Foreman. Then I overlaid those nominations against many of the "best" lists mentioned above. A company didn't have to make every ranking; indeed, I never found one that did. Nor did getting a negative vote—or a few—eliminate a company.
Although I tried to set logical ground rules, it had to be an idiosyncratic and subjective process. How else can something as subjective as image be measured? If trendiness is impossible to pin down, how could I grade it?
For instance, I knew instinctively that there was no way a big pharmaceutical, oil, or auto company could ever be accepted; I would be laughed out of bookstores if I suggested that they were either socially responsible or cool. However, small biotechs were possible, depending on the kind of drugs they were researching. One person suggested Zipcar, which rents cars by the hour, on the theory that this system encourages people to consolidate errands and thus drive less, even if its profits are based on carbon-spewing cars.
Coors Brewing Company? "Coors makes it high on almost any socially-responsible-investment list, since they push for environmentally friendly policies," Christian Weller said. "At the same time, they are staunchly antilabor." Unions boycotted the brewer for a decade in the 1970s and 1980s, and an arm of the AFL-CIO still urges customers to shun the beer. Moreover, Peter H. Coors, chairman of the parent company and a scion of the founding family, had run for the Republican nomination for US Senate from Colorado.
Newman's Own? You can't get much more socially responsible than a company that donates all its profits to charity. But is it a "real" company if it does that?
There's always a lot of back-and-forth on Whole Foods. Certainly, it has a hip image and lots of organic and humanely raised food. In fact, Whole Foods created the mass market for organic food almost singlehandedly. But it's expensive and antiunion. Arthur Caplan, the University of Pennsylvania ethicist, offered Wegmans Food Markets instead, arguing that it sells organic food at more reasonable prices and buys from local growers. He also praised UPS, which I have to confess I'd never considered trendy (or environmentally sustainable, considering that the entire business relies on driving). Caplan said the company uses propane gas to "green up their delivery."
From Richard Honack, a marketing professor at Northwestern University's Kellogg School of Management, came JetBlue Airways (for its flextime policies and hip image) and the small restaurant chain Panera Bread ("a comer," with its antibiotic-free chicken salads and a reputation as "a nice place to work").
Even Walmart got a surprising number of nominations. The City University of New York's Naomi Gardberg was one of several eco-advocates who pointed to its efforts to reduce energy use, with actions like promoting compact fluorescent lightbulbs and installing solar panels. Thanks to its reviled size, every ecological step Walmart takes reverberates across the global supply chain. However, what about all the lawsuits alleging sex discrimination and forced overtime, and the price-cutting that drives neighborhood stores out of business?
I'm not sure why so many people brought up Patagonia, North Face, REI, and L. L. Bean, except that maybe they assume that any business selling outdoor gear must be green.
In addition to those conceptual criteria, I had practical considerations. While gigantic multinational conglomerates were shunned almost automatically on the assumption that they are taking over the world, the nominees had to be big enough that people would have heard of them and be interested in what they're really like. I also tried to find companies from a variety of industries, in hopes of showing that corporate virtue isn't limited to just a few sectors of the business world. They had to be based in the United States so that I could feasibly visit their headquarters. (Sorry, Ikea and Ecover.) Similarly, I preferred publicly traded companies, which tend to provide information more readily, although I might let in one or two private firms.
And I looked for a story. Each example should illustrate at least one different and challenging facet of the dual reputations. Did Tom's of Maine and Ben & Jerry's sell their souls when they were bought by Colgate-Palmolive Company and Unilever, respectively? Does American Apparel push sexy hipness into sexual harassment? Did Starbucks get too big to be cool?
After a few weeks of name collecting, my list had nearly two dozen serious contenders: American Apparel, Apple, Ball Corporation, Ben & Jerry's, Burt's Bees, Chipotle Mexican Grill, Costco, Dell, Google, Herman Miller, In-N-Out Burger, Kiss My Face, Newman's Own, Nike, Patagonia, Seventh Generation, Starbucks, Stonyfield Farm, Symantec, Timberland, Tom's of Maine, Trader Joe's, and Whole Foods.
In an attempt to put some scientific order on this undertaking, I made a very careful chart. One checkmark for each positive recommendation, one minus sign for each negative. I tallied up the votes, then massaged the tally, based on the need for diversity plus gut instinct.
Kiss My Face, Burt's Bees, and Tom's of Maine were all too similar—kumbaya-Woodstock-hippie-organic little companies in the personal-care business. Kiss My Face had the disadvantage of being privately held. Tom's and Burt's had the same "story" of being bought by big conglomerates. Choose one.
Then, if I took one of those, should I dump Stonyfield and Seventh Generation, which are also kumbaya-Woodstock-hippie-organic little companies but in different lines of business?
For similar reasons, I couldn't have Whole Foods plus Trader Joe's, or Apple and Dell. Too similar.
Not even Apple plus Google. That was a tough call. They're really not alike at all, but with the entire business world to look at, I couldn't justify two tech companies.
And forget Ben & Jerry's and Whole Foods. They've been written about a zillion times.
By contrast, who ever heard of Ball Corporation? What does it do, anyway?
My editors and I conferred further.
Chipotle was too obscure. Costco was too frumpy. Nike still didn't pass the laugh test, even though there were intriguing arguments that it had vastly improved practices in its foreign sweatshops, and Greenpeace claimed it was actually a leader in protecting the Amazon rain forest.
That left around ten names, still too much for one book. We culled it to a manageable six: American Apparel, Apple, Starbucks, Timberland, Tom's of Maine, and Trader Joe's. As backups, I added Google and Seventh Generation, the maker of environmentally conscious household goods like paper towels and laundry detergent.
There were so many admirable ones left out. I could just as reasonably have had a list consisting of Ben & Jerry's, Google, Kiss My Face, Patagonia, Starbucks, and Whole Foods. (I still have lingering regrets over omitting those first two.)
Of course, compiling the roster wasn't the end of the investigation. Although these candidates had made the first cut, I now had to delve into the reality behind the labels, lists, and marketing. And I didn't want to look only at the usual Big Issues, like energy efficiency, recycling, hiring practices, animal treatment, and so on. I would also bring in topics that don't come up in the typical CSR questionnaire: Are the products priced beyond the reach of working-class consumers? Is the company active in political causes? Does it provide real information beyond advertising hype? Does it connect with the wider community, even with people who may not purchase its stuff? Do customers feel comfortable using the products, asking for help, and hanging out in the stores? To do that, not only would I interview the standard universe of sources, I would also go shopping.
Following those informal guidelines, the next six chapters will analyze the companies in depth, one per chapter, to reach a verdict on each: Do they deserve their haloes?
1. Tom's of Maine: Woodstock Toothpaste
It was more than an hour into our conversation—sitting in the eighteenth-century brick-and-wood building in downtown Kennebunk, Maine, that he'd salvaged and converted into offices—before Tom Chappell finally laughed. That came when I quoted a few portions from his 1993 book The Soul of a Business, in which he emphatically explained why he would never, ever, ever sell his beloved little natural-toothpaste company Tom's of Maine to a bigger company, and how he scorned the buyout offers that periodically made their way to Kennebunk.
For instance: "Family control gives us the chance to be a new model of a successful business, an inspiration to other corporations who also want to change the face of American business." And: "I wondered what life—and business—would be like if Tom's of Maine were under the tutelage of a large American corporation. . . . What if I asked my corporate parent to let me create a position like vice president of community life and to hire a woman who had no experience in corporate life, but a master's of divinity degree? What if I explained to my new bosses that one of the tasks of the department of community life was to give away $150,000 to community groups?"
What changed? I queried.
"You learn more about yourself—the journey of thirty-six years," Chappell replied, after he laughed. (He also demanded to know why I hadn't read his other book, Managing Upside Down.)
But he stumbled over the next few sentences, and then he became defensive as I pushed further, asking again in different ways the question that loyal Tom's of Maine customers are asking themselves, and would ask Chappell and his wife, Kate, if they could: Why did you sell out to Colgate-Palmolive?
Companies buy and sell each other all the time. In 1996, there were sixteen major pharmaceutical manufacturers; by 2010, half of those were gone as independent entities. Where are Northwest Airlines, America West, Manufacturers Hanover, Washington Mutual, Bethlehem Steel, and LTV? Small firms are especially prone to being acquired. In the global marketplace, they need the resources of a larger parent. And sometimes the founders want to cash out and retire rich.
What made the 2006 sale of Tom's to Colgate different was that Tom's wasn't supposed to be just any company. A mythology had developed around the place during its thirty-six years of independence somewhere up in Maine, whether factual or not: It used natural ingredients. It was founded by two hippies. It donated all its profits to charity. Everything was recycled. Working there was like belonging to a commune in the woods, although now and then the happy commune members presumably took time out from singing "Kumbaya" to make a few tubes of toothpaste.
Carol Holding, who runs a brand-strategies consulting firm, Holding Associates, in Seattle, considers Tom's one of only five brands—in addition to Ben & Jerry's, the yogurt maker Stonyfield Farm, the Body Shop, and Green Mountain Coffee Roasters—"that have that fabulous reputation of being a mission-led brand. Tom's defines the user as someone who is hip, who is a better parent, who cares about the world." In her 1998 book Green Marketing, consultant Jacquelyn A. Ottman listed just Tom's and outdoor-gear retailer Patagonia as "Two Companies That Do Everything Right." Citing the working conditions, philanthropy, natural ingredients, recycled and recyclable packaging, and other factors, she wrote, "Tom's of Maine is living proof that it is in fact possible to integrate personal values with managing for all traditional goals of business—making money, expanding market share, increasing profits, and building customer loyalty." Dan Shannon, director of youth outreach and campaigns at People for the Ethical Treatment of Animals (PETA) until April 2011, gushed that "Tom's is one of our favorite companies."
The myth has some truth, especially the all-natural and green part. Start inside the tube (since toothpaste constitutes 85 to 90 percent of the product line; the rest consists of dental floss, mouthwash, deodorant, and soap). According to the company, the items contain no animal-based ingredients, no ingredients tested on animals, and no artificial colors, flavors, fragrances, or preservatives. There are none of those strangely named chemicals found in other toothpaste brands that sound like they belong in lighter fluid—no tetrasodium pyrophosphate, sodium hydroxide, propylene glycol, PVM/MA copolymer, or carbomer 965. Instead, here's a partial listing from Tom's peppermint label: glycerin, water, organic Aloe barbadensis leaf juice, carrageenan (a seaweed extract that's a common vegetarian food additive), glycyrrhizic acid (derived from licorice root), and "natural flavor." (We'll get to that natural-flavor part a little later.) In addition, the toothpastes and most of the other goods are certified kosher and halal.
The scents of mint and apricot wafted through the headquarters factory, a short drive from Tom and Kate's office, on the day I visited, and just outside the front door mint, sage, thyme, and fennel grow in a small area labeled "Kate's Herb Garden."
Actually, that's another myth: The herbs used in Tom's products come from professional suppliers, not this garden. Nevertheless, plenty of green procedures are real. In his book, Chappell described eco-practices dating back to the early days, such as installing water-saving nozzles on the hoses that clean the equipment and packing the roll-on deodorant in glass rather than plastic, even though glass was more expensive. When recyclers said Tom's didn't generate enough paper to meet the minimum required for a pickup, the company pooled with other groups.
More modern efforts include motion-sensor lighting, vegetable-based inks, deodorant sticks made of recyclable plastic (replacing the troublesome glass), and recycling of almost every sort of material imaginable, including the backings of labels and shrink wrap. Through these and other steps, the company claims to save 250,000 kilowatt-hours per year of electricity, six thousand trees, and 2.5 million gallons of water, and to cut its garbage pickups in half. The restrooms have toilet paper made from unbleached, recycled paper.
Tom's boast that it buys wind-energy credits for all its energy consumption must be taken with some grains of (natural) salt. This is not the same as actually getting all its energy from wind. It simply means that Tom's is buying credits equal to all the power it gets from gas, oil, or other conventional sources, and the cash value of these credits is financing a wind farm so it will produce that same amount of power in a lower-emitting, renewable method. Offsets are controversial, because green activists question whether they simply shift money and emissions from the right hand to the left. Are offset buyers paying to plant trees or to set up wind farms that would have been planted or established anyway? (Of all the most common types of offsets, tree planting tends to be particularly distrusted, since it can take decades for those trees to grow big enough to absorb the carbon they're supposedly offsetting.)
Unfortunately, being natural can conflict with other important attributes, like product performance, cost controls, or customer appeal. "Nature doesn't always give you the same flexibility that a synthetic does," Tom Chappell pointed out. "You can't get long-lasting flavor or cool flavor." So, what gives? "You sacrifice the flavor," Tom said promptly. "You don't sacrifice your morality."
Or you become creative and change the assumptions. "You create a product that has a different taste," Kate said. For instance, Tom's at one point was trying to use ingredients like vitamin E and rosemary extract instead of the standard chemical antioxidants in its bar soap. So far, so good. When the company tried to limit the amount of packaging by ditching the usual cellophane wrapping, however, it turned out that the cellophane was necessary, even within a cardboard box, "to preserve the fragrance and freshness," Kate said. After a lot of searching, the company devised a wrapping made of natural, biodegradable cellulose.
Some things can't be finessed. Most famously, Tom's of Maine's promise to avoid testing on animals or using animal-derived products bumped up against another highly valued credential, the American Dental Association's seal of acceptance. Just as the federal Food and Drug Administration requires drugs to be tested on animals before humans take the risk, the ADA historically wanted dental products animal-tested before it would certify them. Although it's not illegal to market noncertified toothpaste (unlike the case with medicine), it can really hurt sales if customers think the product isn't safe. For years, Tom's haggled with the ADA and even explored an alternative certification. It also tried to substitute human tests on volunteers—including Kate. (Her teeth looked OK when I met her.)
The ADA seal was finally granted for the original toothpaste formula in 1995, which the company claims is the first for a toothpaste without animal testing. Eight other labels of Tom's toothpaste, mouthwash, and floss—though not the entire product line—have since been added. "They pushed the envelope on that issue," said Michael Markarian, chief operating officer of the Humane Society.
Yes, the primary factory really is located in a small town in Maine, albeit not in the middle of a forest. And while it's not a commune, the working conditions are definitely more easygoing, the benefits more generous, and the whole spirit more community minded than at almost any other company on earth. Tom's was a pioneer in granting parental leave to mothers and fathers, a decade before the federal Family and Medical Leave Act of 1993. There's a fitness center on site with a personal trainer who leads the production crew in stretch breaks every day, plus subsidized yoga classes and massages. Employees don't punch a time clock; they merely move a piece on a magnetic sign-in board to indicate whether they're in the building, and that's for safety reasons in case of fire, not for wage monitoring, my tour guide said. The production room itself is high ceilinged and brightly lit. On the afternoon I visited, when production was halted to check the alignment of the shrink wrap on a six-pack of deodorant, the half dozen workers didn't seem particularly anxious.
Probably the most outstanding aspect of working at Tom's is the community service. The company donates 10 percent of pretax profits to charitable causes, and employees can get full pay for spending 5 percent of their work time—twelve days a year—on volunteer activities. According to Tom Chappell, the corporate part began with a $25,000 donation to the town of Kennebunk for curbside recycling bins. (That wasn't a totally unselfish gesture, since it spurred the town to establish a recycling program, which ultimately benefited the company.) The $25,000 morphed into a policy of corporate "tithing," as Tom put it in his book, to support projects in education, the arts and humanities, environmental research and protection, and humanitarian needs, initially at 5 percent of profits and inching up to the current level.
The one glaring workplace omission is that the company is not unionized. That was also one of the few topics that got Tom angry. "There was no union that could have negotiated for benefits more generous than the ones we had," he asserted, mentioning the four weeks of paid parental leave, bonuses, flextime, and the time off for volunteering. One receptionist's husband was a labor organizer, Tom went on, and rather than try to organize the workers, whenever that man came to a Tom's company picnic, "he would commend us for what we were doing, and he would chuckle."
Tom and Kate seem to feel that a union wasn't necessary in an ostensibly egalitarian workplace where corporate values were discussed regularly in group meetings, time cards were unknown, and Tom himself might stop to chat with a secretary about the cost of their respective children's tuition. "I could see the boss-secretary relationship melt into an understanding between two parents," he wrote in The Soul of a Business.
"I don't think that the employees felt that they needed an advocate for them against management," Kate added in our interview. "We did as much as we could for them. The company was more like a web of relationships than a hierarchy." Maybe. But Tom Chappell's tuition payments were chiefly for private boarding school—a luxury available to the CEO and owner of a business—while the secretary's payments were for college, something the middle class is more likely to need.
And customers apparently buy the image, along with the toothpaste, floss, and deodorant. Most people I interviewed initially purchased Tom's products for the natural ingredients or the little-guy reputation, then gradually grew accustomed to the taste. Typically, Kate Bieger, a thirty-four-year-old New York City psychologist, said a friend had recommended the brand a few years ago, so she tried it because "I thought it would have fewer chemicals." She went on, "I didn't like it at first. It wasn't sweet enough." Today, she brushes with Tom's peppermint, her three-year-old son uses the kids' strawberry, and "now I can't stand the sugary taste of Colgate, the toothpaste I grew up with." (The irony of a Tom's user trashing the new corporate owner is, of course, tied up in the whole controversy.)
No one cited price as an ethical issue, which would actually be an argument against the brand. Tom's products, like most CSR goods, are more expensive than standard ones. The pricing has to cover ethical "frills" such as the time and resources to find the natural cellulose soap wrapper and the salaries paid to employees while they volunteer at animal shelters instead of churning out toothpaste. At one chain drugstore, a 5.5-ounce tube of Tom's was $5.59, while slightly larger tubes of Colgate, Crest, and Arm & Hammer cost at least $1.20 less. "People will pay for value," Tom argued. "Our customer is not buying a toothpaste. They're buying a toothpaste that meets their set of values."
Of course, even ethical products have to work. The Chappells said that when they ran surveys, respondents' first concerns were always how well the toothpaste cleaned their teeth and whether it made their breath smell fresh. Still, ethical factors like natural ingredients, lack of artificial dyes and sweeteners, recycled packaging, and no animal testing—rather than price or taste—came next, buttressing Tom's claim.
Effectiveness appears to be a particular issue with the deodorant. One twenty-nine-year-old art-gallery administrator I spoke to said he would like to use Tom's deodorant for the natural ingredients, especially the lack of aluminum. Unfortunately, he estimated, it's 25 percent less effective at eliminating odors than standard brands. His compromise: "I use it on the weekends when it doesn't matter as much, when I'm not at work." This is a problem that goes back at least twenty years, when the company had to recall a reformulated, more natural honeysuckle deodorant after angry customers complained that it didn't last as long as the predecessor, a petroleum-based version. Indeed, ineffectiveness is a common criticism of natural laundry detergents and cleansers, too.
Toothpaste may not seem like the kind of product that could be considered trendy, but using a brand famous for all those socially responsible virtues can be a quick and easy way for the purchaser to define himself or herself, as Carol Holding said. When a new girlfriend spends the night in your apartment for the first time, the toothpaste on your bathroom sink sends as much of a message as the brand of coffee in your kitchen and the contents of your refrigerator. If you want to prove your greenness, it's a lot simpler to buy a tube of Tom's than to clean up mountain trails and cheaper than a donation to the Sierra Club. Kate recalled that in the earliest days, when the name was barely known outside of health food stores, "musicians, artists, people who were the thinkers, creative types, bought it. It was very hip. The toothpaste for iconoclasts." Although the label is no longer quite so iconoclastic, Kate—who is a painter and printmaker—said it's still the one she sees in the dorms at art-school workshops.
There are competing natural brands, and some Tom's users do switch around. Others are loyal to particular Tom's flavors. And some stick with it out of convenience, finding it more widely available. That's a key point, because it gets to the heart of why Tom and Kate sold the company.
To gauge whether Tom's of Maine can maintain its personality and values without the namesake who created it, a key question is how important that namesake has been to the ongoing enterprise. Was the company really "Tom's," or was that merely a label?
Tom Chappell was (by his own description in his book) "the hottest young salesman" in what was then Aetna Casualty and Life Insurance Inc.'s Philadelphia office in 1968 when he got fed up with the hat-wearing conformity and tedium of office work and decided that "I had better find a career where I had a little more room for self-expression." His heart yearned for the great outdoors of western Massachusetts, where he grew up, and Maine, where he spent childhood vacations. In a step toward those goals, he moved to southern Maine to join his father's business manufacturing industrial detergents.
A skeptic might wonder how much self-expression there is in detergent, but Tom apparently found it by designing a nonpolluting cleaning agent. That led to environmentally conscious laundry detergent, shampoo, and body lotion. Interestingly, the toothpaste didn't come along until 1975.
From the beginning, it was Tom's of Maine, not Tom and Kate's. This was another topic that annoyed Tom. "Everybody asks that question," he growled. "Gloria Steinem asked that. We weren't thinking about the rights of women, necessarily. We were just a young couple starting out." By the accounts of both Chappells, the enterprise was Tom's baby. Kate was working as a paralegal plus teaching art and reading at their children's school, "because we really needed two sources of income." By the time she got more involved in the toothpaste business, the brand had been established and it was too late to change.
Whatever the name, it was in any case a personalized outfit. Even the packaging had a little note to "Dear friends," signed by "Kate and Tom," encouraging customers to write to them.
Sure, most entrepreneurs are directly and intimately involved in getting their new firms off the ground. For months or even years, they and their families may be the entire staff; they might sleep literally above the store. They have a hand in everything from designing the products to shipping the orders to making change (or taking debit cards) at the cash register. Tom and Kate's involvement, though, went beyond strategic business decisions and day-to-day operations to exactly what he talked about in his book—the soul.
In 1987, feeling stuck in a rut, fearing that his little antiestablishment venture had become too businesslike, Tom enrolled part-time in Harvard Divinity School. He wasn't aiming to become an ordained clergyman but rather was "on a search for meaning. . . . to recapture what had inspired me to start the business in the first place." Four years later, he returned full-time to his creation, brimming with renewed fervor and a clearer vision of how to elucidate the values he wanted the firm to share. As he wrote, "I persuaded my board of directors and my managers to make it our company's main 'mission' to seek financial success while behaving in a socially responsible and environmentally sensitive way. . . . I began to think about how I could transform Tom's of Maine into a company that could live its values—my values [emphasis in the original]." Out of Tom Chappell's personal transformation came a nine-part corporate mission statement, along with the philanthropic donations, the community service, a push for creative thinking, and lots of companywide meetings where people sat in circles. More than ever, toothpaste making was a manifestation of Tom Chappell's beliefs.
So, no wonder Tom insisted for so many years that, as he wrote in his book, "although our corporate suitors all assured us that they would not want to change Tom's of Maine, my response has been the same: My family will continue to control the company."
And then, in 2006, he sold.
Why did you sell out to Colgate-Palmolive?
The Chappells have given two chief reasons for their decision—lack of obvious heirs and lack of marketing clout.
By 2006, Tom and Kate were in their sixties and looking at those issues of mortality that divinity school may stir up. "I was genuinely tired," Tom said flatly. Kate sought to spend more time on her art. Every fifteen to eighteen months for the past few years, the Chappells and their five adult children had been holding family meetings with a psychologist to discuss issues like "how, as parents, we can empower our kids, and what do we need to know about being in business together," Tom explained. Now, it was time to discuss the future of the company. The parents wanted out, but who would take over?
Although all the offspring had at one time or another worked there, only the youngest, Luke, then age twenty-three, was interested in running the business. "He would have required a ten-year development," Kate said. And she and Tom didn't wish to wait ten years.
"We didn't necessarily want to saddle our children with the burden of carrying on the company," Kate added. By selling, "it released them. That seems to be more fulfilling ultimately than just maintaining a business your parents started."
Kate admitted that Luke was disappointed. However, by the time I talked with the Chappells, four years after their decision, they said that Luke had his own company in Northern California, Luke's Local, selling locally grown, minimally packaged, healthy—of course!—prepared food to commuters.
The other motivation involved commercial strategy. Back in 1993, when Tom wrote The Soul of a Business, annual sales were almost $20 million, his goal was $100 million, and in some pages he confessed that he wasn't sure the company could get there on its own. Thirteen years on, with sales still below $50 million, Tom said—and here's where he began to stumble in his answer—he was asking himself questions about "the role that the company needs. 'Do you have the skills to perform for the company?' I didn't think I was the right leader to take the company to $100 million in sales. I'm an entrepreneur. I don't rely on undue analytical research. When you are making decisions on a larger and larger scale, they need to be increasingly grounded in a complex level of objective data."
The industry was changing in contradictory ways that hurt small fry like Tom's. Mom-and-pop grocery stores were disappearing, even as dozens of new toothpastes were invented each year. That meant too much product for too few outlets. To get onto the shelves of the big stores that remained, Tom's of Maine needed more marketing muscle. "Unfortunately," Tom said, "toothpaste is dominated by a handful of retailers. If you want to be a mainstream player, you can't do it without those stores."
With the strategic decision made, all that really remained were the details of how to cede control. Since the business was too small to raise sufficient capital by publicly selling stock, the best route was to find an acquirer with money and experience in the consumer market. Tom emphasized that "we didn't just put the company up for sale" to the highest bidder; that wouldn't have allowed enough personal involvement in the selection. Rather, "we were researching the companies that best fit Tom's of Maine," Kate said. The couple came up with a list of twelve potential "strategic partners," narrowed that down to five, met with officials from those candidates, and finally pared the list to three. They won't reveal the two non-Colgate finalists, except to say that they were, in Tom's words, "global brands in consumer goods and personal care." He added that one of those two eliminated itself, fearing that it would destroy the intrinsic Tom's of Maine values.
Tom and Kate said they spent a lot of time with Colgate managers to see how they made their decisions and to gauge the kinds of questions the managers, in turn, were asking. "Their stated values are caring, commitment, continuous improvement," Kate said. "It's been around two hundred years. You don't hear a lot about it, because it doesn't blow its own horn." She praised Colgate for doing "a tremendous job in reducing waste," while Tom cited its frequent appearances on "Best Companies to Work For" lists. (More on that in a minute.) Finally, the deal was sealed, for $100 million.
Tom insisted that he had no regrets. "We made an incredibly good decision," he declared. "They don't want to do anything that would harm the brand. They are committed to natural."
It's important to remember, however, that he and Kate retain 16 percent ownership of the namesake Colgate subsidiary. If he trash-talks Colgate, its stock—and thus a portion of his personal wealth—will drop. There may be a touch of ego at stake, as well. Is he going to criticize his own business decision? Maybe in ten years he could say that the new Tom's management screwed up, but not yet.
If it really needed to sell out, Tom's of Maine could have done worse. While Colgate isn't as sterling as Tom's in terms of environmental sustainability, animal testing, natural ingredients, or working conditions—and what company is?—it scores moderately well in most indexes and wins solid, if not enthusiastic, praise.
In the rankings of Climate Counts and Ceres—the latter issued a December 2008 report, "Corporate Governance and Climate Change"—Colgate came in second out of six in the category of household and personal-goods products, trailing L'Oréal both times. With Climate Counts, Colgate scored best in measuring its carbon impact and lagged in actually reducing its emissions and in supporting public policy. Meanwhile, it notched a not-bad number 39 on BusinessWeek magazine's first annual roster of the five hundred "Greenest Big Companies in America" in 2009, but the purchase of Tom's was one of the three reasons cited, which is somewhat of a circular defense.
Wood Turner, the first executive director of Climate Counts, said Colgate had improved markedly, albeit in a category with a "somewhat low bar." He added, "We're seeing very little policy leadership in this sector, no American companies that have stepped forward and said, 'We support mandatory caps on emissions.'"
How about all those workplace rankings Tom Chappell mentioned? Working Mother magazine apparently adores Colgate; the company has made this list every year from 2002 through 2009. The magazine singled out a new mentoring initiative in 2008 plus admirable policies on flextime, telecommuting, health benefits for part-timers, emergency child-care help, and paid extra maternity leave. And on the Human Rights Campaign's "Corporate Equality Index," which analyzes companies' gay-friendly policies—and which is one of the easiest graders around—Colgate corrected some small deficiencies to attain a perfect score in 2011. Its reputation is less glowing at Fortune, where it has qualified for the bellwether list of best companies in the United States only in 2003 and (barely squeezing in at number 100) 2010.
Judged by a much broader set of over three hundred data points in areas such as the environment, employee relations, human rights, philanthropy, governance, and finance, Colgate was an impressive number 18 on Corporate Responsibility magazine's 2010 list of the "100 Best Corporate Citizens." That was a big improvement over the prior year, when it dawdled in seventy-third place.
Overall, Colgate's social-responsibility efforts have been good enough to pass the screens of environmental, social, and governance (ESG) investment funds like Domini Social Investments and Trillium Asset Management. Steven D. Lydenberg, the chief investment officer of Domini (which held a little more than $4 million in Colgate stock, or about 0.6 percent of the total portfolio, at the time we talked), praised Colgate for its openness in making detailed information about workplace safety, diversity, emissions, violation notices, and energy and water usage available on its website. He thought that the proportions of women and minorities in management—slightly over one-third and one-fourth, respectively—were "very strong" and that energy use per product, water use, and carbon emissions were all on the right track, going steadily down. (The ESG funds never had occasion to evaluate Tom's on its own, since it wasn't publicly traded.)
None of this praise, however, can turn Colgate-Palmolive into Tom's of Maine. It still puts PVM/MA copolymer, sodium lauryl sulfate, propylene glycol, and other weird-sounding stuff in its toothpaste—precisely the kinds of chemicals that Tom's brags that its products don't contain. Indeed, Tom's has singled out one of those Colgate ingredients, sodium lauryl sulfate, or SLS, for special concern. The packaging of certain Tom's flavors notes that "for some consumers [SLS] may cause irritation in the mouth. Our breakthrough formula uses the gentle ingredient glycyrrhizin (derived from licorice root) for natural low foaming." Even worse, the FDA and the Environmental Protection Agency are investigating another ingredient, triclosan, an antibacterial agent used in Colgate's superstrong "total" formulation—as well as in many manufacturers' liquid soap, scouring pads, toilet cleaners, kitchen cutting boards, and other items that don't normally go in people's mouths. "In 2006 it was found to act as a hormone disrupter in the North American bullfrog and must now be clearly labeled as an ingredient," warns the book A Good Life: The Guide to Ethical Living. In fairness, most of the focus has been on triclosan's use in liquid soap, but if it's not safe enough for the outside of the body, it hardly seems safe inside.
When I asked Tom Chappell about the parent company's chemicals, he simply said, "They have reasons why they use them. They also have reasons why they want to keep us the way we are."
Weird ingredients may not even be the worst of Colgate's sins. The Rough Guide to Shopping with a Conscience, an ethical guide published in 2007, stated that "when it comes to cosmetics, toiletries, and perfumes, the major worry for most consumers is animal testing." And according to PETA, Colgate-Palmolive conducts tests on animals.
Colgate outdoes Tom's in one area, however: workers at its St. Louis plant are represented by a union, Local 15C of the United Food and Commercial Workers International Union.
"You see a number of the iconic socially responsible brand names from the nineties and early 2000s having been acquired by large companies," Steven Lydenberg said. "There are people who are very concerned about how to preserve the model." Ice-cream maker Ben & Jerry's, perhaps the most famous of the CSR breed, was bought by Unilever in 2000. France's Groupe Danone acquired Stonyfield Farm, the yogurt company (and main financial backer of Climate Counts), in stages in the early 2000s. Burt's Bees, which produces natural lip balm, shampoos, and other personal-care products, fell to Clorox a year and a half after Tom's sale. And later, after Lydenberg and I spoke, Timberland would be sold to VF Corporation.
Sometimes the business strategy itself can provide reassurance. In the case of Tom's, the whole point was to gain access to the health niche. As Colgate said in a press release at the time, sales of "natural" oral and personal-care products were increasing 15 percent annually in the United States, and "Tom's of Maine gives Colgate the opportunity to enter the fast-growing health and specialty trade channel, where Tom's toothpaste is the clear market leader." For tactical reasons, it was better to buy its way in rather than try to create an organic Colgate brand from scratch. "You don't want to cannibalize your original line," explained Naomi A. Gardberg, an assistant professor at the City University of New York's Zicklin School of Business. (Gardberg's three children use Tom's strawberry toothpaste.) "If you make an organic line [with the Colgate name], that suggests the original line is dangerous. The acquisition of Tom's was brilliant, because you have a different name, and you already have a following." And the $100 million purchase price was nothing to Colgate, mere petty cash from its $15 billion in annual revenue. Thus, based on motivation and strategy, it would make no sense for Colgate to start messing around with the very qualities that inspired it to buy Tom's.
Another way to reassure Lydenberg's concerned consumers is to consider the guarantees that came with the purchase. Among them: Tom's of Maine headquarters and the primary factory would stay in Kennebunk, and no one would lose his or her job. Said Susan Dewhirst, the only person Colgate would offer up to comment (and who actually works for Tom's), "The deal was, they wouldn't change the fundamental, core things that made Tom's special."
Another part of the agreement guaranteed that Tom Chappell would continue to run the company during a two-year transition. In 2008, he was replaced by a different longtime Tom of Maine—Tom O'Brien, the chief operating officer. "That was great," Kate said. "We had worked with him for eleven years. He knew all the complexities of managing a socially responsible company." The Chappells remain on an advisory board that meets with the new Tom's management every three or four months. "They defer to Kate and me," Tom Chappell insisted.
Are these promises strong enough to ensure that Tom's stays Tom's? The Chappells didn't seek an official ten-year pledge from Colgate, as Ben & Jerry's supposedly did with Unilever. "That's not something that you can dictate in a formal agreement," Tom explained. "They have spent an enormous amount of time to understand the brand. If it doesn't work for 'Maine' and 'natural' to be at the heart of the identity of the brand, then the brand has lost its way. You have to trust the people you are turning it over to." That's nice for now, but what if different managers take over at Colgate? "It's about the culture that remains," he said. On the other hand, he added, "if they were pulling out of Maine or were making decisions that are strictly bottom-line based, I would be unhappy."
To answer Lydenberg's concerns, it's also crucial to see what is actually happening on the ground. Gardberg pointed to the commitment to keep churning out toothpaste at the Tom's factory and assembly lines, rather than shifting production to Colgate facilities. That can help save all those nice worker benefits—including the all-important paid volunteering time—by maintaining Tom's as a distinct place and culture, she said. "Companies feel pressured to standardize their HR practices across the company after an acquisition, especially to phase in new employees," she explained. "If they're running separate facilities, it's less likely they will be integrated." For his part, Lydenberg was glad to see that Tom's maintains its own website. There isn't even a Tom's sublink on the Colgate site. And Tom Chappell's mission statement is on the site, in an expanded version. Although Tom and Kate supposedly remain as advisers, Tom said he wasn't sure whether the corporate tithing is still in effect; the answer, according to Colgate, is yes.
Susan Dewhirst ticked off more ways that, she claimed, the Tom's values and milieu had been preserved, such as the natural ingredients, the stewardship model of environmental sustainability and sourcing, the wind-power credits—that is, the controversial offsets that many greens disdain—and the products themselves. Turnover had been minimal, she said, although she claimed not to have exact numbers. Press reports at the time of the sale mentioned a payroll of about 170, and in 2010, Dewhirst said, there were about 160 employees, which would mean a small net attrition.
If the Chappells really had to sell to gain marketing muscle, did they accomplish that business goal, at least? The answer can be found in almost any CVS, Target, or even Walmart.
"We've gone from one item to five [available] at Target," Tom boasted. At a convention a couple of weeks after the sale, he added, "one of the vice presidents of Walmart came up to me and he said, 'We will now work with you.'" (That memory evoked another rare laugh.) Moreover, Dewhirst suggested that Colgate's size and experience could help with social networking, global outreach, and negotiating FDA approvals.
Countering those benefits, however, Colgate has brought at least three changes that eat away at good old Tom's.
The most notorious is probably the packaging. Criticism of this factor has to be relative, because Tom's packaging, even post-Colgate, is still more informative than most. For instance, the side of the toothpaste box Crest wastes with its logo and ad copy ("Strengthens Enamel. Whitening. Minty Fresh Striped.") is where Tom's explains how it uses licorice-root extract instead of traditional sodium lauryl sulfate. On another side, where Crest puts yet more meaningless self-promotion ("With cleaning action to help prevent tartar buildup and remove surface stains"), Tom's has its socially responsible version of marketing copy—information about its community service, corporate donations, and policy forbidding animal testing.
However, there used to be a lot more information before Tom's redesigned the classic toothpaste packaging in 2010. No longer does the package spell out the source and purpose of each ingredient. (While the information is available online, that's simply not as convenient as being on the box.) Instead of the old label's specifics about the flavors—"cinnamon and organic clove oil with other natural flavors" derived from cinnamon leaves and bark and clove flowers, with the full scientific names included—the new version might just say "natural flavor." On the box side where the ingredient details previously were listed, there is now a short paragraph with more marketing than real facts. For the Wicked Fresh brand, that cute little paragraph gushes, "Our toothpaste uses powerful natural flavor oils and a patent-pending botanical extract to help neutralize stinky VSCs (volatile sulphur compounds) which can be largely responsible for bad breath." What oils? What extract? And gone—for obvious reasons—is the little note from "Kate and Tom." The only good change is that the bigger print and sharper white background are easier to read. But to read what?
Michael Myers, president of Palio Communications, an ad agency in upstate New York, thought the first-version packaging was merely "OK looking" from a design perspective, but, he added, "if you look at it from what it communicates, I think it's cool. They scream on their packaging that it's all about social responsibility and healthy and good products." The revised boxes, he said, still "communicate green" with symbols like little leaves. Yet he admitted that "it almost seems as if they've lessened their packaging focus here on the green aspect versus their older packaging."
Tom Chappell said that he had agreed with the necessity for new packaging because "it hadn't been redesigned for decades." Corporate management "checked with us to make sure they were going in the right direction," Tom continued. However, he and Kate did not oversee the details or the specific wording and design.
Another big shift came in 2011, when the recyclable aluminum toothpaste tube was replaced with plastic. Plastic! That symbol of everything unecological. Even the company's website confessed that "for many of you [customers] these aluminum tubes became synonymous with Tom's of Maine." In the surveys back in her day, Kate said, having recyclable tubes grew more important to respondents as time went by. Furthermore, the environment isn't the sole reason to prefer aluminum. The AFL-CIO endorses aluminum and steel beverage cans rather than plastic bottles, noting that the former industries are unionized.
The new Tom's said it made the switch after consumers complained that the aluminum tubes cracked and leaked, were hard to squeeze, and usually couldn't be recycled through their local programs anyway. The plastic-laminate tubes weigh only half as much, thus saving energy in manufacturing and shipping, the company claimed. And officials said they're seeking ways to recycle the plastic. All that may be. Nevertheless, it's hard to avoid the symbolism of Tom's of Maine turning plastic.
The third change: Four years after the sale, Tom's got a corporatized, automated phone-answering system. ("If this is a medical emergency, press 1. If you are a consumer with a question, press 2. If you are a health foods store with a question, press 3.") Both Dewhirst and another Tom's spokeswoman insisted that really, this was much nicer and more efficient for customers, and you could always get a human if you wanted.
It's hard to tell whether Tom's brushers have stayed faithful. Although the company still hasn't reached the $100 million goal that prompted the buyout, annual sales are up by about $10 million, to $60 million, and after all, a rather big recession has intervened. Toothpaste users tend to have a particularly strong brand loyalty, going back to what Mom put in the medicine cabinet, which could make it easier for Tom's to retain old customers yet harder to entice new ones. Tom Chappell asserted that the number of new buyers is "substantial" but wouldn't give me statistics.
When I randomly interviewed nearly two dozen people purchasing various brands of natural toothpaste, floss, mouthwash, and deodorant in New York City three years after the acquisition, only one, freelance writer Abby Scher, said she had deliberately dumped Tom's. Another, Melissa White, a public health researcher, said she hadn't been aware of the Colgate deal—but now that she knew, she added, she would try to find an alternative to Tom's. "If there were an equal product with similar price and ingredients, I would prefer to buy from an independent company," she said. At the least, she added, the name should be changed to Tom's of Maine, by Colgate.
Contributors on Tom's Good Matters blog have certainly not been happy with the acquisition, but blogs are, like any customer-complaint venue, self-selecting for kvetchers. Bloggers think the toothpaste and other products taste more artificial now; they miss the detailed labeling; their favorite flavors have become harder to find. And many of them blame Colgate. "I can only assume that the massive machine known as Colgate has decided to trim the margins, increase efficiency, and streamline the company," Sean wrote in October 2010.
Ethical activists, meanwhile, seem happy to have Tom's in any flavor. Soon after the takeover, recalled PETA's Dan Shannon, the Chappells "came to us and said they wanted to assure us they're going to remain a fully independent subsidiary and continue to follow all the [animal-free] policies," despite the new corporate owner's animal testing.
"There's a purist argument to be made; you're being bought by a big company that does test on animals," Shannon continued. "But at PETA, we really try to look at it from a practical perspective. Tom's is now more widely available than it was previously, because of the distribution power of Colgate. If you live in the middle of nowhere and Walmart is the only store you can go to, Tom's was probably not there before." Thus, while Tom's may now be helping bolster the profits of a company that causes pain to bunny rabbits, it's saving bunnies by reaching customers who might otherwise have bought toothpaste tested on those animals. Bottom line, are more bunnies saved, or hurt? Who knows?
There's one more twist to this tale: could Tom's change Colgate?
Tom Chappell claimed that it already had. "It's very clear that our presence in the Colgate family has impact," he asserted, pointing to two postacquisition examples. A year after the sale, he said, Colgate CEO Ian Cook "introduced a companywide commitment to sustainability," and members of Tom's staff were among the small advisory team that was supposed to explain what this meant. His second example was that Tom's employees were asked to help Colgate people "understand the potential for various herbs or plants, whatever their therapeutic benefit was, so Colgate would have an inventory of knowledge for using that in any of their formulations." Tom claimed that these two ideas came from Colgate, not him. He also said that they "weren't brewing before the acquisition," and thus must have been prompted by the arrival of Tom's, pointing out that Cook hadn't been the CEO prior to then. That's a bit disingenuous, since Cook was president and chief operating officer at the time of the sale, his promotion had already been announced, and he would probably have been involved in any major herb or sustainability initiative regardless of his title at that point. For that matter, the projects could have been "brewing" at lower levels for years. But they're nice ideas anyway.
Outside observers are more cautious. "We hope that it influences companies like Colgate, when they see that being a leader in this sector and being attentive to animal welfare and other issues can make Tom's of Maine a profitable, viable brand," said Michael Markarian of the Humane Society.
However, Wood Turner, the former executive director of Climate Counts, pointed out that big companies like Colgate buy little ones like Tom's precisely to fill a niche, not to replace the entire line—as New York University's Naomi Gardberg put it, not to cannibalize the rest of their products. "What they're inclined to do is to provide just enough availability to the conscientious consumer to satisfy their needs, but continue doing business otherwise," Turner said. Unfortunately, he couldn't compare Colgate's carbon-reduction scores before and after the Tom's purchase to see if Tom's had greened the larger company, because Climate Counts was launched the same year as the acquisition.
It's true that Clorox, since absorbing Burt's Bees, has initiated a brand of plant-based, "natural" cleaning products endorsed by the Sierra Club. Still, it's more likely that both decisions, to buy Burt's and to sell natural products, were spurred by Clorox management's awareness of the potential size of the ethical-consumer market, and not that Burt's founders or top managers—who didn't even stay after the acquisition—somehow persuaded Clorox to create the green brand.
THE QUESTION: Does Tom's of Maine deserve its reputation as an exemplar of ethical chic?
THE VERDICT: A worried yes.
Jill Kickul, director of the Stewart Satter Program in Social Entrepreneurship at New York University's Stern School of Business, said that negative press would be a strong sign that Tom's virtue had been corrupted. It's been five years since the sale. So far, the headlines have been pretty quiet.
So maybe things will be OK.
The good news? The factory in Maine, the corporate tithing, and the workers' benefits all seem solid, and the company keeps finding more ways to recycle and save energy. The ingredients certainly remain a lot less yucky and artificial than those in, well, Colgate toothpaste. On the negative side, the new packaging is a big step backwards, toward conventional marketing blather and away from the real information that the old version had provided about those nice ingredients. With so many strong reasons to prefer aluminum over plastic, the arguments about the switch in tubing are unconvincing. And I wish there had been a more firm ten-year pledge as part of the sale, rather than merely the soothing sentiment of "Trust the Chappells" or "Trust Colgate."
Basically, what Tom and Kate say in response to such complaints is, Suck it up. "If people want to feel the way they feel, there's nothing I can do," Tom snapped. "I know what took place. I don't have any discomfort about the decision."
Anyway, Tom and Kate are busy these days with new ventures. Kate is creating and exhibiting her artwork. Both are running Ramblers Way Farm, a business they founded in 2009 to make and sell wool clothing from humane, organic, environmentally sustainable US sheep farms and factories. Visitors walk into their offices, in that converted eighteenth-century building next to the Kennebunk Town Hall, by stepping on a circle of bricks engraved with sayings like, "Connect with goodness" and "Know thyself, be thyself."
If Tom was largely brusque throughout our long interview, sometimes angry, rarely laughing, there was one point where he got quiet: when I asked if they stayed in touch with Tom's of Maine employees, and if those employees felt the place had changed.
"I think people miss the founders," Tom replied. Then he paused. "I don't spend a lot of time with former Tom's people." Even though the factory is only a half-hour away from his new office, he said that, since the sale, "I don't think I've been in the building."
2. Timberland: How Green Is My Leather
Timberland Company's two-story brick headquarters is almost exactly what you would expect from its public image. It sits in a rustic version of an industrial park in Stratham, New Hampshire, adjoining a pond and enveloped by trees and the nonstop twittering of birds. There's a sculpture in the lobby made of recycled plastic soda bottles (used in some shoe parts), along with a stack of bamboo (crunched into the heels of women's shoes). Its oft-praised child-care center includes a half dozen rooms, an indoor gym, an outdoor playground, and a huge fish tank. In a garden just outside, employees grow organic squash, zucchini, and pumpkins that they sell in the corporate cafeteria, donating the proceeds to a food bank.
Next to the garden is a small array of solar panels. The press person guiding me around smiled a little apologetically. The panels are "symbolic," she admitted, because "New Hampshire doesn't get much sun." A facility in California has a much bigger, more practical array.
Timberland itself has become both a symbol and a working model of what to do right as a socially responsible business, winning all sorts of accolades for its environmental and workplace policies from raters like Business Ethics, Climate Counts, Ceres, the Dave Thomas Foundation for Adoption, Forbes, Fortune, Outside, the US Green Building Council, and Working Mother. Laura Berry, executive director of the New York City–based Interfaith Center on Corporate Responsibility (ICCR), which represents about three hundred religious institutional investors, said that "we have never filed or even put a [shareholder] resolution on the table, they're so darn good." Similarly, Steven Lydenberg, of Domini Social Investments, declared that "Timberland is a truly remarkable company. They've taken risks no one else has taken." The company has crafted a complex CSR matrix of "core values" and "pillars," and Gordon Peterson, Timberland's former vice president for corporate social responsibility, told me that the core values of CSR—humanity, humility, integrity, and excellence—are part of employees' performance review.
It's hard to believe that any company could be that perfect. It's particularly hard to believe such perfection of Timberland, for two reasons.
First, the main raw material for its most important products is leather. That requires killing cows. Even before they're killed, the cows present numerous ethical and environmental problems. To create grazing room and meet the growing demand for this raw material, irreplaceable rain forests may have been chopped down in Brazil. For that matter, deforestation anywhere can lead to soil erosion, which in turn pollutes lakes and rivers. Meanwhile, the methane produced by the cows' waste, and their unique digestive system (aka burping), is a serious factor in greenhouse gas emissions. Then, after they leave the grazing fields, the animals probably go to factory feedlots and slaughterhouses, where they are jammed into pens, forced to stand in their own waste, fed an unnatural diet of corn and animal parts, and injected with antibiotics and hormones to counter the effects of that diet. The chemicals used to grow their food pollute the ground and water, and the overuse of antibiotics is spurring resistance in bacteria to the point where we may run out of antibiotics that work when we actually need them. Finally, the process of tanning the leather from these cows can require vast amounts of energy and produce toxic chromium emissions. Thus, this "remarkable," "darn good" company is hurting rivers, lakes, soil, the rain forest, and the Earth's climate—plus the cows.
So, what should Timberland do—give up the leather boots that have been the foundation of its business for more than five decades?
All that is just the first reason for skepticism. Here's the second: if Timberland really is so wonderful, did it jeopardize that reputation by selling itself to a big conglomerate, VF Corporation, in 2011?
When Boston shoemaker Nathan Swartz bought the New Hampshire–based Abington Shoe Company in stages from 1952 to 1955, it was a contract manufacturer that made basic, sturdy, low-price footwear for other firms, which then sold the shoes under their own labels to army-navy surplus shops and discount outlets. In 1965, the company—still called Abington but now run by Nathan's sons Herman and Sidney—pioneered what became its trademark, a manufacturing process that melded soles to leather uppers without stitching, thus rendering the boots waterproof. The Timberland logo first appeared on a line of boots in 1973 and became the official corporate name five years later.
Like any company in the fashion business, Timberland has shifted its product line and image over time. Establishing its own label moved it upscale, from anonymous boots for other retailers to high-caliber, reliable work boots that shoppers could ask for by name. The marketing "was all about quality, materials, five hundred steps in the manufacturing process, ruggedness, long-lasting staff," recalled Carol Holding, the brand-strategies consultant, who worked at an agency that developed ads for Timberland in 1980. Then the Swartzes branched into casual shoes, and as those overtook boots in terms of sales, the company needed to reach a second target customer, "an upscale young man, eighteen to thirty-four, a fashion-conscious, quality-conscious young man," according to John Thorbeck, who was hired in 1983 as Timberland's first vice president of marketing.
And the images kept changing. In 1983, the company decided to emphasize outdoor performance, with ads featuring Timberland products that had been field-tested in the Iditarod, the grueling, 1,150-mile Alaskan sled-dog race. Around that same time, there was also a surge of interest from ultra-fashion-conscious Italians; New York City artist Peter Bornstein said that when he was in Turin in 1985, he was offered $120 for his Timberland boat shoes, right off his feet. (He declined.) A few years further on, the company took a different turn, introducing apparel and accessories in 1988, and children's shoes and more accessories such as watches and daypacks, under license, in 1996.
In the early 1990s, without any marketing push—in fact, without company officials even realizing it at first—the brand suddenly became popular among the urban hip-hop crowd. "We noticed some unusual patterns," Thorbeck recalled. "Why was the Four Dudes, a shop in inner-city Washington, DC, one of the best boot customers?" This client base might seem to be the complete opposite of lumberjacks and Iditarod mushers. However, Jim Davey, Timberland's current vice president for global marketing, outlined a connection: "One of the things that the [urban] market loved about the brand is that it was the toughest, best-made boot you could buy. It was a very authentic, plain-speaking brand that didn't try to put on airs."
Whatever the market, Davey said the company replaces about half of its 1,500 footwear products each year, which he claimed is typical of the industry. He added that the brand has different images in different countries—for "hard-core hikers" in Scandinavia, for instance, and as "a high-quality shoe for everyday life" in Asia. While some lower-cost lines can be found at discount outlets, in general it is unabashedly a "premium price" label, selling at perhaps 10 percent to 20 percent above competitors' prices, especially for boots, Davey said.
Ironically, one image Timberland didn't seek for a long time was to be a socially conscious brand. Then, in 1989, the cofounders of City Year—a Boston-based service organization that's often called a "youth urban Peace Corps"—asked Sidney Swartz's son, Jeffrey, to donate fifty pairs of boots. "I think he did it, saying, 'Yeah, yeah, I'd better do this service thing,'" Gordon Peterson said with a laugh. "But I think it transformed him." Some veteran employees cite another possible motivation, noting that there was gossip at the time that the younger Swartz had political ambitions.
Those boots were the first step on a wide path of corporate and employee community service. Within three years Jeffrey Swartz—who was not yet CEO—had started a program allowing staff to take up to sixteen hours' worth of paid time per year for volunteer work, and over the subsequent years would come efforts in recycling, alternative energy, and emissions reduction. In addition, the company's 1992 "Give Racism the Boot" ad campaign helped kick-start the concept of ethical marketing.
Even after Timberland got CSR religion, however, it didn't market any brand specifically as "environmental" until the Earthkeepers line—which sets strict standards for recycled content and other material—in the early 2000s. That remains a niche, accounting for only $100 million of the company's total $1.3 billion in sales in 2010. Timberland is trying to expand the concept both ways, to include more products as Earthkeepers, and to put higher green requirements on all clothing, accessories, and footwear.
Social responsibility, especially concerning the environment, would seem to be an obvious tie-in with the boots' image and customer base, whether it's Iditarod sledders or, as Davey described the current target market, "men and women in their twenties who have a little bit deeper appreciation for the outdoors." But company officials say CSR is actually not a major motivation for their customers. Anyone shopping for shoes or clothes, said Peterson, is more likely to ask, "What does it look like? How much money is it? Is it comfortable? Does it do what I want it to do?" Added Betsy Blaisdell, Timberland's senior manager for environmental stewardship, "The publicity related to how we look at sustainability is great, and it creates a great feel around our brand, but I think it's the durability, the price point, the look, the marketing, that's selling the most."
The customers I've interviewed bear that out. Graham Gaston, age thirty-two, a New York City television producer, was replacing the Timberland shoes he'd bought for a backpacking trip to Europe seven years ago. He talked about how well they had held up and how they were nice enough to wear to his office, but nary a word about the feel-good volunteer work and recycling. At another store, a twenty-nine-year-old cable television inspector said Timberlands are more stylish and less expensive than the boots he's required to buy for work.
Luckily, it's increasingly hip to be the kind of person who goes backpacking and hiking and who cares about the environment, so Timberland is happy to incorporate this image in its marketing today. Davey cited the "Nature Needs Heroes" TV spot for Earthkeepers in fall 2010: a young man, seeing his friend carelessly toss a plastic water bottle toward a trash can (and miss), chases the escaping bottle as it is carried off by the wind, leaping on top of a moving train, racing alongside a raging river—in his Timberland shoes, of course—until he finally catches and recycles the bottle. "We are really focusing on twentysomethings," Davey said, "and the environmental impact of products is a huge issue for them."
It thus seemed like a trifecta of a marketing strategy when, in October 2009, Timberland joined musician Wyclef Jean and his environmental and social charity Yéle Haiti to sponsor scholarships, tree planting, food distribution, sports, and other community-service initiatives in Jean's native Haiti. In one swoop, Timberland could reach out to those inner-city hip-hop fans, burnish its green and community-service cred, and sell more clothes and boots. Among the marketing plans was a world tour by Jean where specially branded "eco" T-shirts, hats, and other Timberland clothing would be sold. In addition, there would be sixteen new lines of boots made from organic and recycled material, store and website displays, promotions via social media, CDs, and a new album.
Barely three months later, a massive earthquake measuring 7.0 on the Richter scale hit Haiti. That should have made the partnership with Yéle Haiti even more important, as the shoemaker and the charity switched their focus temporarily to earthquake relief, promising to return to the more long-term environmental projects when the situation stabilized.
Instead, public scrutiny of the charity's messy finances accompanied the donations. News accounts started asking why Yéle Haiti hadn't filed tax returns for four years and was late in filing the next three, and why so much of its income seemed to go to businesses connected with Jean's musical career. For instance, the organization paid $250,000 to a TV station and recording studio controlled by Jean and a cousin. The charity replied that the payments were actually for rent—and discount rent at that—because its offices shared space with the studio, and for expenses relating to a benefit concert where Jean performed in 2006. It also claimed that it didn't need to file returns for years in which the charity wasn't active.
Timberland stood by its partnership, and after a few months, the publicity died down. Jean briefly considered running for president of Haiti; the charity turned its attention back to tree planting. Jim Davey declared that all the bad press hadn't hurt. "That's our primary goal, to reforest Haiti, and nothing changed with that," he said. And don't forget that Jean, he added, "is going to help us reengage with the urban market."
The ultimate social-responsibility quandary, of course, circles back to the cows. Timberland officials have a ready answer to any questions: "Our leather production is not responsible for killing animals," Betsy Blaisdell said promptly. "Meat production drives the killing of cattle. The hide is a waste product" that would get discarded anyway if Timberland didn't, in effect, recycle it for clothing. Problem solved.
Not completely.
The next problem lies in how the hides are processed, or tanned. Although Timberland doesn't do this part itself, it chooses the suppliers that do. And Blaisdell noted that "the tanning process is a beast of its own. It's one of those old dirty industries that's energy-intensive and polluting."
A primary tanner collects the hides, removes the hair and flesh, and soaks, pickles, and preserves them before selling the skins to a retannage facility. That facility then sells the stuff to Timberland and other leather-product manufacturers. The standard method of tanning uses a type of chromium salt, which can produce chromium emissions. While the US Environmental Protection Agency doesn't consider these emissions dangerous, it states that different kinds of chromium compounds can cause cancer and genetic diseases and can be toxic to wildlife.
To be more ecological, Timberland first switched to organic tanners that utilized vegetable-based dyes and materials such as corn sugar, oil, lime, and sodium bicarbonate. That led to a new concern, according to Blaisdell: "The amount of energy it takes to produce vegetable-based dyes is higher."
So the company decided to consider the matter as a question of process rather than ingredients, to seek out "the tanning that's managed best from an environmental standpoint." Joining other shoe manufacturers like Clarks, New Balance, and Nike, Timberland "met with tanners to establish a very detailed environmental protocol, with hundreds of questions" about the procedures and materials used, Blaisdell said. In 2005, they formally created the Leather Working Group, which now has over five dozen members. A detailed monitoring and rating system was established, and facilities are audited by outside experts every eighteen months. The gold-rated tanners, such as ISA Tan Tec facilities in Vietnam and China, track all the environmental inputs and outputs, treat waste water with top-of-the-line primary and secondary systems, even filter their water once more through reed beds, and are "very creative with how they reuse waste," Blaisdell said. "This is a tannery I would eat off the floor of." While Timberland still doesn't get all its leather from the gold scorers, that's the goal.
Lindsey Allen, a senior forest campaigner at Greenpeace, gave Timberland hefty credit for these efforts. "They led in creating the industry group that has made huge strides in trying to clean up the cattle sector, specifically around the tannery process," she said. "A lot of companies say, 'OK, OK, what do we have to do to make Greenpeace happy?' Timberland is working on a lot of initiatives without having to be pushed."
However, things got dicier when Greenpeace went a step further back in the process, back to where hides are a secondary waste product, to look at where the cows came from—specifically, whether Amazonian rain forests in Brazil were being destroyed to create grazing space for cattle ranches. Timberland wasn't chopping down the forests or running the ranches, of course, and the supply chain from rain forest to shoe is long and complex. Cattle farmers push into the rain forest—and other land—to raise their herds, then sell the cows to "fattening farms," which then sell the animals to slaughterhouses, which then sell the meat to food processors and the hides to the tanneries, and on through the tanning process to the ultimate shoe (or coat or briefcase) manufacturer. It can be almost impossible to know where a particular shipment of hides originally munched grass when it was a herd of cows. So Greenpeace wasn't demanding that Timberland stop cutting trees. The debate really revolved around what role Timberland was taking—and should take—in this convoluted process.
According to Allen, Greenpeace's research revealed that "three-fourths of the currently deforested areas in the Brazilian Amazon rain forest are occupied by cattle." While the meat from those cows was going mainly for local consumption, the leather demand was global, and "the footwear sector came up as a big player." She named almost the same list that launched the tanning-reform group, including Adidas, Clarks, the Italian company Geox, Nike, and Timberland.
Allen said Greenpeace contacted Timberland in early 2009 with what she called "a courtesy letter" stating that "we have concerns around the demand for leather"—in other words, a warning that the company was about to become a target. A questionnaire soon followed. At around that same time, Greenpeace also issued a report about the destruction of the Amazonian rain forests and the connection with cattle ranching. According to Allen, Greenpeace wanted Timberland and other shoemakers "to put pressure on your supplier to commit to a moratorium" on buying cattle from newly deforested rain forest land and to threaten to stop doing business with any supplier that refused.
Although Timberland first questioned why it was being lassoed in this whole campaign, both sides now acknowledge that the company may well have obtained some of its leather from a Brazilian slaughterhouse Greenpeace was targeting. What happened next, basically, is that Timberland said, "We'll handle this our own way, and you can trust us because you know we're wonderful." And Greenpeace replied, "That's not good enough."
Timberland's plan was to work privately with the slaughterhouse management in hopes of easing that processor out of the rain forest, but not to set a deadline, demand a moratorium, or say anything publicly. As Jeffrey Swartz described the situation on the Huffington Post website in March 2010, his company's response to Greenpeace was "not meant as a kiss-off, not meant to be empty promises—in fact the discovery was pretty startling and it did lead to some candid conversation with our supplier."
Greenpeace, however, felt that Timberland was being too cautious in using its clout as a major customer. While Timberland was talking quietly with mid-level managers at the slaughterhouse, moving step by step, other leather-goods manufacturers were being more aggressive and going straight to the executive suite—or the press. "What we were hearing is that if enough companies threaten to cancel contracts, it sends a very clear message all the way to the top" of the supplier, Allen said. "We think public accountability is almost always a good thing immediately." Even Nike was acting faster, apparently having learned a few lessons from the consumer protests over its Asian sweatshops. (As mortifying as it may be to Timberland, it seems to be generally accepted among social-activism types that Nike is often the CSR leader in the shoe industry. Domini's Steven Lydenberg agreed that "Nike these days really sets the standard for environmental initiatives when it comes to footwear and apparel.") So, Greenpeace essentially followed through on its warning letter, urging customers and activists to pressure Timberland, and Swartz felt unfairly singled out.
Eventually, Timberland caved. It joined the other shoemakers in demanding a moratorium on buying cattle from newly deforested rain forest area, as Greenpeace had sought, and that autumn the four largest Brazilian slaughterhouses agreed to phase it in. Swartz grudgingly wrote, "Did Greenpeace 'win' because we've adopted some of the terms and guidelines they proposed in working with our Brazilian supplier on this issue? I guess."
There's no question that it was a shock for Timberland to be seen as one of the bad guys, and Allen is sympathetic. "Their surprise was pretty fair," she acknowledged. "They were not experienced in being targeted publicly by environmental groups."
For her part, Blaisdell said she thinks Greenpeace "did the right thing." Then she added, "I won't say I didn't cry. They're my people!"
If it must rely on a business model that uses animals that burp methane gas, cuts down trees for their pasture, kills them, and tans their hides in ways that can pollute—and if it wants to be environmentally responsible—then Timberland needs to figure out how to compensate for the damage its production methods cause.
Start with the ingredients. One step is relatively easy: Blaisdell pointed out that leather, being so durable, fits right into the environmental mantra of "Reduce, reuse, and recycle." People don't have to waste the Earth's resources by buying new boots every year. Remember Graham Gaston, the TV producer, whose Timberland hiking shoes were still going strong after seven years? He was replacing them simply because he'd gotten tired of them. Moreover—at least, in theory—leather from the upper parts of shoes can be used again. In some of the newest lines of boots, 82 percent of the content is reusable. Of course, people first have to bring those boots back to the store for recycling, and Blaisdell conceded that that's not too likely to happen.
Nor do the shoes consist entirely of belching-cow, tanned-hide leather. Hemp, synthetics, recycled PET plastic (the plastic in beverage bottles, as seen in Timberland's lobby sculpture), and organic canvas are utilized in the linings, laces, and uppers. Sneakers are made of polyester blends and other synthetics, and Timberland is famous for being the first shoemaker to recycle rubber into soles.
Moreover, 30 percent of sales come from gear other than footwear—clothing and accessories—which certainly doesn't have to contain leather. These products, including a special "eco-conscious" line, are typically made of a combination of wool, organic and nonorganic cotton, leather, and synthetics. The stated position on the corporate website is to "increase renewable materials and recycled content in our products." Over one-third of the cotton is organic, and officials say they avoid cotton from Uzbekistan, because of that country's heavy use of child and forced labor, and shun fur altogether. Colleen Von Haden, Timberland's senior manager for code of conduct, said the company was trying to find sources of fair trade cotton in Africa, although standards for fair trade fabrics are not well established.
As for wool, animal rights advocates praise the company for steering clear of Australia and its merino sheep. Merinos are usually prized for their soft wool, but the problem is that they have extra folds of skin, under which debris such as blowfly larvae can build up. So the folds are usually cut away through a painful process known as mulesing. Then, after the sheep become too old to produce wool efficiently, they are shipped to the Mideast to satisfy the huge Muslim demand for halal meat. Dan Shannon of PETA claimed that "tens of thousands of sheep are crowded onto ships" without adequate food and water on voyages that can take weeks, and that "a huge percentage will die."
Presumably, Timberland could save a lot of cows and reduce pollution by using more synthetics like pleather rather than leather, but there are lines it cannot cross. When I asked Jim Davey, he said bluntly, "Leather is a huge part of what we do. It's consistent with our New England image. We're an outdoor brand; it always comes back to that."
Beyond the ingredients, the company has a detailed list of goals for shrinking its environmental footprint. In some cases, it's smartly ahead of schedule; in other cases, it's equally far behind.
The most important efforts probably have to do with energy usage. Officially, Timberland aims to get 60 percent of its energy from renewable sources by 2015, increase the number of buildings that are architecturally certified as green, and drastically reduce carbon emissions. It further pledges to work with outside energy auditors and to encourage employees to be more energy-conscious.
It's way past the obvious steps. CFL bulbs? Hah! Timberland is already onto the next generation, having replaced almost all its CFL bulbs with the even more efficient LED kind. There's a reflective white roof on the New Hampshire headquarters that's supposed to keep the building cooler in summer, and Consumer Reports cited the solar-panel system at the California distribution center—the real version of the symbolic array at headquarters—as one of the largest in the world. All new US stores are built to the highest green-certified standards, while renewable energy will soon be used in the United Kingdom. To inspire the troops, employees who carpool, drive hybrids, or bike get special parking spots, plus hybrid buyers get a $3,000 credit. Where the company had hoped to reduce emissions from staff travel by 25 percent as of year-end 2010, it actually achieved double that reduction.
The catch is that only about 4 percent of Timberland's climate impact comes from its own facilities worldwide—the New Hampshire headquarters, regional headquarters in the United Kingdom and Singapore, a design center in London, three distribution centers, one footwear factory in the Dominican Republic, and about two hundred stores—which means that those solar panels and LED bulbs aren't doing much. Maybe 5 percent more comes from shipping. Most of the energy usage, emissions, pollution, and other damage, not surprisingly, traces back to those cows, ranches, and tanneries Timberland doesn't directly control. Thus, the efforts to save the Amazon rain forest and find gold-level tanneries should help. The corporate website also promises to "leverage the relationship with our footwear supply chain" in order to pressure suppliers to reduce their own climate impact, a step that activists wish all companies would take. Still, these actions can't disguise the fact that Timberland is fairly powerless to compensate for the cows.
That leaves the energy offsets that ecology advocates deplore. Rolf Skar, a Greenpeace senior campaigner, said that the sole valid offsets are projects to increase efficiency and renewable energy. Timberland agrees, which is why it has amended its approach. The initial policy was to become carbon-neutral—that is, to add a net of zero carbon dioxide and other greenhouse gases to the Earth's climate problems—by the end of 2010. Well, by early that year, it was clear that the company could meet the goal only by buying offsets for at least half of the gases it emitted. Even with its LED lights, solar panels, and all the rest, it just couldn't reduce emissions enough. (In fact, as of the December 31, 2010, deadline, Timberland had cut its actual emissions by 38 percent—impressive, albeit far from the target.)
If it had to rely on offsets, the idea was to buy the "good" kinds and, even better, "use the [offset] fund to develop energy efficiency and renewable energy at the factories we source from," Blaisdell said. For instance, Timberland would cover some of the up-front expense of installing more environmentally sustainable power systems at these factories. Blaisdell claimed that suppliers are "very keen to do it," in hopes that efficiency projects would lower their own operating costs over the long term. So it would be a twofer for Timberland—green credits for itself plus lower costs for suppliers that, presumably, would get passed on to customers like Timberland in the form of lower prices. It would be nice if other shoemakers that source from these same suppliers would chip in to pay the installation expenses. Even if they won't, and they simply ride along on Timberland's dime, so be it, Blaisdell said.
Under its new approach, Timberland is still doing all that, but now it emphasizes how much it is actually reducing its own emissions, rather than the overall neutrality target. As for other eco-issues, the shoemaker fell about a year behind its goal of removing all toxic polyvinyl chlorides (PVCs) from its products by the end of 2010. It is using more water-based adhesives instead of the standard glues and solvents, which are made of volatile organic compounds that can cause irritation, headaches, rashes, nausea, and even cancer. Finally, these efforts are published in unusual detail on the Timberland website.
Timberland's first New York City store might even be considered an example of reusing and recycling. Built in the nineteenth century, it was a jewelry factory and an ice skate shop before taking on the Timberland logo in 2009, sales clerks told me. Its cast iron facade dates from 1860, and much of the wood inside is either 100 percent reclaimed or certified as environmentally sustainable. Scattered around the floor, walls, and ceiling are a pair of century-old skates, two refurbished leather jackets from the 1930s, and stools made with reclaimed leather seats. According to the staff, people come from all over the world to gape at the building (not the boots).
Pick up a cardboard box of Timberland refined chukka shoes, and the underside of the box top might tell you that the box is made of 100 percent postconsumer recycled material and printed with soy- and water-based ink. From other parts of the container, you could learn that
• Timberland uses 3.1 kwH of energy to produce each pair of shoes (or used that much energy to make this particular pair—it's not clear).
• Timberland-owned facilities use 5 percent renewable energy.
• No child labor was involved.
• 119,776 hours were spent (by whom? when?) serving "our" communities.
• 100 percent of facilities have been assessed against the company's code of conduct.
A label on the sole of the shoe itself might reveal (in English and French) that
• The box has 100 percent recycled content (again).
• Timberland, as of 2008, planted 919,524 trees.
• 74 percent of the company's products are free of PVCs.
• This pair of shoes contains 3.4 percent eco-conscious material.
• Producing this pair of shoes used 6.6 percent renewable energy.
You don't see labels like this on too many shoe boxes.
The consumer-information effort began around 2004, according to Blaisdell, because Jeffrey Swartz was constantly saying things like, "Why can't we make environmental reporting as simple as the nutrition label on a cereal box?" An environmental label couldn't really be that simple, of course, with so much of the impact coming from the tanneries Timberland doesn't control and the ranches it can't even name. It would thus be impossible to get exact figures, to trace a pair of refined chukka shoes back to Bessie the cow in Brazil.
To devise rough estimates for those ranches and tanneries, Timberland relies on off-the-shelf life-cycle software that calculates the environmental effects of standard production methods, depending on the type and amount of material—the number of cows, the number of hides, whatever. Then Timberland can take the real statistics from its own and subcontractors' factories and plug those into commonly accepted formulas, such as average emissions per unit of energy from the particular fuel used in that factory. This process produces more-or-less accurate data for the average shoe. These are still not the superindividualized labels Swartz wanted, since different styles of footwear require different material, different amounts of that material, and probably different amounts of time (and thus energy) on the assembly line. Obviously, producing a canvas deck shoe demands fewer cows (read: none) than a six-inch boot. The good news is that Timberland has gradually been narrowing the calculations down to a product-by-product level, although it slipped on its goal of having a "green index" label on all footgear by the end of 2011.
Environmentalists' major complaint is that these figures don't account for the energy and emissions attributable to leather scraps that never become part of a finished shoe. That seems awfully nitpicky, considering how meager the leather waste probably is relative to the amount used, and how little most other manufacturers are doing at all. Blaisdell said the "irregularity between hides and the amount of yield you get from each" makes these numbers hard to calculate, although she said Timberland is seeking a methodology to figure out the average amount of waste per measurement of hide. The only reason the company can even try is that the information gathering doesn't cost much—about ten dollars per product line and part of one employee's workweek.
When a customer finishes adding and multiplying, however, what do all these numbers actually reveal? How much is 3.1 kwH of energy? Is it a lot? It's nice to know that Timberland planted all those trees, and eco-activists and ESG investors praise the company for its openness and leadership. Still, Timberland officials, as well as the activists, wonder if it's too confusing and whether anyone pays attention.
Blaisdell thinks it would be more useful if other companies took on similar efforts and there were an industry standard—something like the government's Energy Star labels for appliances—that could enable buyers to match brands side by side. Greenpeace's Lindsey Allen suggested a scorecard showing red, yellow, and green lights. "What's reasonable with consumers is how the thing they're buying compares with another shoe, not the kilograms of carbon dioxide," Blaisdell said. "Consumers want simple, relative information." Lacking an industry standard, she said, Timberland would try to establish its own companywide comparison, labeling each of its products on a scale of zero to ten in terms of climate impact, resources, and chemicals. The next step: taking the data about the environmental impact of each shoe to the designers to see if they can find greener raw materials.
Remember the 119,776 hours "serving our communities" from the shoe label? That hearkens back to the roots of Timberland's social consciousness, the fifty pairs of boots that Jeffrey Swartz half-grudgingly donated to City Year in 1989.
Today's programs go way beyond boots. The main one, called the Path of Service, lets employees take paid time off for almost any type of community service except religious or political activity—launched at sixteen hours per year in 1992 and boosted to forty hours in 1997. People have spent these hours helping with disaster relief and coaching Little League, volunteering at homeless shelters and tutoring at local schools, and much more. In lauding Timberland as one of its "Best Companies" the year after the September 11, 2001, terrorist attacks, Fortune noted, "On Sept. 11, 130 employees of this retailer happened to be in the Bronx refurbishing a school. Two weeks later, in Boston, Timberland built a playground in memory of the victims." Two of the volunteer days are supposed to be allotted for activities organized by the company, called Earth Day and Serv-a-palooza Day. (OK, subtract points for the name being too cute.)
In a typical year, according to Gordon Peterson, 78 percent of the staff participates. He conceded that people could theoretically head to the beach on days they claim to be spooning out soup, but he said it would be hard to lie when coworkers ask about their day at the homeless shelter.
While the volunteer program is the most famous, other employee benefits certainly get kudos. Working Mother has repeatedly praised the flextime, job sharing, ability to work from home, paid leave for new moms and dads, and adoption aid, and it raves that part-timers who work as little as sixteen hours a week can get health benefits. The child-care center I saw at headquarters is nationally accredited, even accepting kids whose parents don't work for the company. Employees who want to stay healthy can use the free on-site fitness center, take yoga classes, and borrow outdoor gear like canoes, kayaks, and snowshoes. To appeal to health nuts as well as to traditionalists, the headquarters cafeteria has an odd mix of fair trade coffee and horribly unecological plastic water bottles, veggie burgers and breaded chicken fingers, cartons for recycling cans, bottles, and ink cartridges and unrecyclable clamshell takeout containers. All in all, Milton Moskowitz, one of the cofounders of the Fortune "Best Companies" ranking, told me, "I have fond memories of reviewing Timberland applications."
Yet the boots have sometimes stumbled. Timberland failed to respond to the Human Rights Campaign's questionnaires on gay and lesbian issues from 2006 through 2011, even though it seems laughably easy to score high. Moreover, the US facilities have never been unionized. "Why didn't we target that particular company? I don't know," said Warren Pepicelli of UNITE HERE, the apparel workers' union. No doubt one reason was that it wasn't his union's territory, because shoe workers had a separate organization in the 1950s and 1960s. Gordon Peterson's analysis, not surprisingly, is that "I don't think our workers needed or wanted it. I guess they're getting what they need." They may well be getting good benefits, but how about organized labor's other function—worker advocacy? "I think our workers' voices get heard pretty well at Timberland," Peterson said, noting that a "corporate culture" official meets with workers every two weeks.
And why, if it was such a wonderful place to work from 1998 through 2007, did both Fortune and Working Mother drop Timberland from their rankings in 2008?
The two magazines will not explain why companies don't make their lists or even how common it is for a company to slide off. They only point out that the application process can be time consuming and cumbersome. A prospective "Best Companies" candidate must complete a long questionnaire covering topics like pay, benefits, camaraderie, job satisfaction, and communication. For Fortune's list, four hundred or more randomly selected employees are surveyed, in addition to management. Jennifer Owens, the director of special projects at Working Mother, said her magazine's six-hundred-question survey can take one thousand "man-hours" (yes, that's the term this women's-magazine editor used) to fill out. She also said the number of applications has been increasing slightly each year, making it harder, by definition, to win a spot.
Peterson said Timberland stopped applying to get on Working Mother's list because the sole employee handling all the "Best Companies" submissions didn't have the hours and resources to compete everywhere—leaving the unspoken implication that this specific magazine was a low priority. Unable to dismiss the Fortune loss so easily, he cited a rough financial stretch, starting in late 2005, that undoubtedly hurt morale and, presumably, employees' responses to the Fortune survey. Sales and the stock price went on a three-year slide while the company took a $15 million restructuring hit and closed forty-three underperforming stores. (In interviews with me for a news article I wrote for the website Portfolio.com in January 2010, management blamed the slippage partly on a broad cultural shift toward dressier footwear.) Then came the disastrous 2008–2009 recession. "If your coworker just got laid off, do you think it's a good place to work?" Peterson asked rhetorically. As for Fortune, he added, "We want back on."
A year after that conversation, Timberland still hadn't made it back, and no one from the company would comment.
The benefits mentioned above apply only to employees at the facilities owned by Timberland. Which means they don't apply to virtually all the workers who actually make the shoes and other goods. According to Colleen Von Haden, Timberland's senior manager for code of conduct, about 90 percent of the output is manufactured by some 250,000 people in over three hundred factories run by subcontractors in thirty-six countries outside the United States, mainly in Brazil, China, India, Thailand, and Vietnam. (Timberland directly controls one shoemaking plant in the Dominican Republic.)
Forget about flextime or paid leave for community service. Ethical shoppers first have to make sure workers are getting their full wages for the hours they are working and that those hours and conditions aren't too grueling. In overseas sweatshops throughout a range of industries—as many activists, books, and news articles have documented—workers toil sixteen-hour days, six or seven days a week, for paltry wages, without bathroom breaks or overtime pay. Young women—the bulk of the sweatshop labor force—are sometimes sexually abused by their supervisors or watched in humiliating ways when they finally get to the toilet. Talking is forbidden. Then they go "home" to crowded, dark, overpriced, bare-bones, company-mandated dorms.
To counter these abuses, oversight generally starts with a code of conduct, and Timberland's is better than average. For instance, in forbidding child labor, it defines child as "younger than sixteen," whereas many codes put the bar at fifteen. Unlike other companies, Peterson said, Timberland grants no exceptions to its ban on working more than sixty hours a week, not even during peak seasons. The code gets extra credit for including the right not just to form unions—which is rare enough—but also to "an equivalent means of independent representation" in places where "the right to freedom of association is restricted under law."
So Timberland says the proper words. Everyone agrees that the real test is whether a trustworthy proctor is at the facility regularly to make sure the words are followed. Most activists say this proctor should absolutely not be from the big multinational brand whose name is on the merchandise, for reasons of obvious conflict of interest. "If anybody believes that internal monitors are going to blow the whistle on the company, it's naive," said Mark Levinson, chief economist of the Service Employees International Union. "The company pays the monitors."
(The relationship between the SEIU and the clothing union, UNITE HERE, is complex: the two big unions that historically represented textile and apparel workers—the International Ladies' Garment Workers' Union and the Amalgamated Clothing and Textile Workers Union—were stitched together in 1995 to create the Union of Needletrades, Industrial, and Textile Employees, or UNITE. In 2004, UNITE merged with the Hotel Employees and Restaurant Employees International Union, or HERE, becoming UNITE HERE, with some 850,000 workers and retirees. Then, in 2009, that group split, and the erstwhile textile leaders formed Workers United, which affiliated with Levinson's SEIU, representing health-care, public-sector, building-services, food-service, janitorial, and some textile-manufacturing workers, for a total of about 2 million members. The remaining garment workers, mainly in New England, stayed with UNITE HERE.)
However, Timberland takes the opposite view from Levinson and most activists, arguing that only the monitors it has trained and who answer to it can do the job right. It assigns ten employees full-time and two part-time who visit all the plants at least once a year. There is, in addition, some third-party involvement: two contractors are hired for about 9 percent of the site assessments, and every few years an outside firm audits the code and the inspectors. At the time I met with Timberland officials, in 2010, 22 percent of the plants had the lowest rating for environmental, health, or safety issues, and the company's stated aim was to reduce that to 20 percent by 2015, which seems an awfully easy goal.
If the oversight is a bit too cozy, the saving grace is that toughness may be less necessary here than with other companies. Timberland doesn't have a reputation for using particularly bad subcontractors. Also, Andrea Moffat, Ceres's vice president of corporate programs, cited what she called a "close to unique" project to supplement the official monitoring with local organizations, which is probably the best way to maintain any sort of ongoing supervision. "Audits can be effective, but audits are sporadic," she said. "If you can empower community organizations that are actually living next to these factories on a daily basis to understand what worker rights are, pollution, and these sorts of things, you end up with a more democratic supply-chain situation."
Jeff Ballinger, the antisweatshop activist, said Timberland could still do more by pressuring its subcontractors to lobby their local governments for stronger laws and enforcement. Levi Strauss & Company has publicly endorsed putting rigorous labor standards into international trade agreements, according to Mark Levinson.
In reply, Timberland officials plead their company's small size and inexperience. "Policy is a new area for Timberland," Peterson said, and indeed, it didn't rank among the top twenty companies in either the retail or clothing-manufacturing sectors in terms of political donations and lobbying, according to the records of the Center for Responsive Politics. Both Peterson and Colleen Von Haden said the company was starting to dip its toe into advocacy. If so, it's a pretty shallow dip. Von Haden said, "We are looking to engage in public-private partnerships and advocacy efforts" to make sure that existing minimum-wage levels are enforced in the countries it sources from, which is way below what Levinson and Ballinger call for. The two men would probably want Timberland to advocate to raise the minimum. Peterson might do exactly that; he said the company was considering working with local suppliers or perhaps other big brands to increase minimum wages. Still, if he were going to get involved in something like lobbying, he added, "I'd rather work on green issues to make better materials choices and reduce our footprint."
When I asked Peterson whether, in light of all the potential problems with overseas plants, he wishes Timberland made more of its stuff in the United States, he ducked the question. "I can't say I spend a lot of time on that," he said.
THE QUESTION: Does Timberland deserve its reputation as an exemplar of ethical chic?
THE VERDICT: Yes, but . . .
After more than twenty years of tutoring schoolkids, donating boots, recycling rubber, and other steps, Timberland has earned the trust of activists. They're willing to bend the rules on some touchy points.
Consider, for instance, all the problems associated with cows. Michael Markarian, of the Humane Society, allowed that "it would be a heavy lift for companies to be completely leather free." So, for him, it's more important that Timberland not use fur or ingredients from exotic, endangered, or threatened species. Similarly, Dan Shannon, at the more radical PETA, preferred to emphasize that Timberland avoids fur and doesn't obtain its wool from Australia or its leather from India, where, he claimed, cows are transported in "hideously abusive," hot, crowded conditions.
Even if Timberland abandoned its entire business model and stopped using leather altogether, Andrea Moffat at Ceres noted that almost every raw material has ethical problems. Cotton requires huge amounts of pesticides and water. Synthetics are probably petroleum based, thereby exacerbating all the environmental and political issues associated with oil drilling and emissions. Moffat wouldn't answer directly when I asked if Ceres would prefer for Timberland to use less leather, saying merely that her group had discussed the topic with officials there. "If companies can develop new materials, designs, or different types of products that have less impact, these are an improvement," she said. "I'm not an expert on how you replace leather."
More important, Moffat added, is that "they've really tried to integrate environmental-social issues into their business strategies. You'll hear Jeff Swartz talk about those issues to his shareholders and stakeholders. They're engaging their consumers, putting labeling on boxes." And despite that little business in Brazil, Greenpeace's Rolf Skar set a lot of value on the fact that Timberland is relatively open and willing to work with environmental groups. Indeed, noting how cooperative Nike had also been in the Amazon, Skar wondered whether there wasn't something about the shoe industry, particularly athletic and outdoor shoes, that encouraged eco-consciousness.
Activists thus say they have faith that Timberland's virtue can survive the takeover by VF, a North Carolina–based apparel conglomerate that already owns the Nautica, North Face, and Wrangler lines.
For one thing, VF presumably didn't pay $2 billion just for a bunch of leather. The community service, recycling, and eco-tanneries are "part of the brand image," pointed out Andrew Page, senior director of the Humane Society's fur campaign. "They would lose their customers if they changed that." And Jim Davey, Timberland's marketing director, noted that concern for the environment is an inherent corporate value in the boot business. "Our customers are people who love the outdoors, whether it's a park in Shanghai or a hike in the mountains or a puddly March day in the city," he said. "We are an outdoor company, and we need the outdoors."
Another reason for hope is that VF itself doesn't have a terrible reputation. ICCR records show only one episode—a resolution in approximately 2004 seeking better monitoring of the corporation's supply chain—according to the Reverend David Schilling, the ICCR's director of human rights and resources. PETA noted that "many" VF brands shun fur and merino wool. The official Timberland-VF press release quoted VF chief executive Eric Wiseman praising his new toy's "leadership position in sustainability." Then came a quote from Jeff Swartz: "Timberland is proud of . . . its reputation as a responsible and environmentally conscious global citizen, all of which will be preserved and enhanced by becoming part of the VF family."
Yet there are worrisome signs, too. At the time of the purchase, VF emphasized its plans for "expense management" and "operating disciplines"—in other words, cost cutting. It sure will have to save money somehow to justify that $2 billion purchase price, which most business analysts considered a bit rich. A CSR frill such as paying employees to take time off to build playgrounds is one obvious place for hard-nosed managers to cut. Moreover, some sense of ethics, philanthropy, or camaraderie—maybe noblesse oblige—is often lost when a founding family gives way to corporate control (as remains to be seen, perhaps, at Tom's of Maine). At the independent Timberland, Domini's Steven Lydenberg said, many of the policies were possible only "because they are family controlled and run, and the commitment comes from the very top."
In fairness, Schilling said, give the new company six months to a year—that is, around January to July 2012. Some key indicators of trouble would be a cutback in public reporting, fewer webinars with nongovernmental organizations (NGOs) and investors, reductions or reallocation of staff, and less CSR collaboration with other companies.
So a year from now, let's see if the folks from PETA, the Humane Society, Greenpeace, and elsewhere are still wearing Timberland boots.
3. Starbucks: Coffee as a Brand Name
Michael Tomasso, a retired telephone company technician, age fifty-nine, stops by the Starbucks outlet about a mile from his Brooklyn apartment several times a week, staying half an hour to do the newspaper's daily crossword puzzle. The rest of the week, he works the puzzle at home, but "sometimes I want the ambience at Starbucks." What does he drink? Bottled mocha, never any of the fresh-made coffee concoctions.
Ann Stein (not her real name) was "just killing some time" at the same Starbucks before picking up her five-year-old daughter from preschool. She made it clear that she doesn't do this often, maybe once every two or three weeks, when she's out on errands and it's not worth going home in between. She drinks the anonymous daily brewed coffee.
At a Starbucks a couple of miles away, high school senior Elizabeth Chavez (not her real name) did homework on her laptop until it was time to start her after-school job at a nearby gym. Chavez said she visited this café, as well as one closer to her school, two or three times a week, because "I like the environment. Nobody bothers me." Her beverages: vanilla lattes and the daily brewed coffee.
Barely three blocks further on, at yet a third Starbucks, Caroline Sausville, a thirty-seven-year-old personal shopper from France, was drinking black coffee. "It's so expensive, the fancy, fancy coffees, and I can do the same thing at home," she scoffed. However, she enjoys Starbucks' pastries, especially the Mallorca Sweet Bread.
About a half-mile down the street from Michael and Ann's Starbucks is a much smaller coffee house, one of three in a local chain called Café Grumpy. Thirty-three-year-old Web designer Jeff Meininger is a big fan of the coffee. "Starbucks is crap," he declared. "It tastes burnt."
Lily Meyers (not her real name), a writer and multimedia artist in her fifties, hangs out at Gorilla Coffee, another independent coffee bar, a half-mile in the opposite direction. "The music is better," she said. "At Starbucks, you hear Christmas music at Christmastime, the same thing over and over. Here, it's local bands and old stuff. You rarely hear the same thing twice." She added that the coffee at Gorilla has more flavor. The fact that it's not part of a big conglomerate appeals to her, too. "I really like supporting local places," she said.
Scott Schroeder, thirty-five, who runs an investment fund, brings his eleven-year-old daughter to Grumpy for the zucchini muffins. He prefers Grumpy's coffee to the Starbucks brand—but really, he added with a laugh, "I frequent just about every coffee establishment." It was around 5 P.M., and this was his third coffee stop that day.
A social anthropologist could no doubt find a thesis's worth of trends in this small survey. However, here's the main point: whether they love Starbucks or hate it, Michael, Ann, Elizabeth, Caroline, Jeff, Lily, and Scott were where they were, drinking what they were drinking, because of Starbucks.
Before Starbucks, people drank a generic beverage called coffee. Today, thanks to Starbucks, coffee is an experience. With gourmet beans, a squirt of foamed milk, and a few foreign-sounding (though sometimes made-up or misused) mix-n-match words, Starbucks claims that it enables anyone to feel as sophisticated as an Italian sipping espresso in Venice. Throw in big, comfortable armchairs, copies of the New York Times previous customers left behind, a homey brown-and-green decor, and free WiFi to create a "third place," or "an extension of the front porch," as CEO Howard Schultz described it in his first autobiography, Pour Your Heart into It. And if those coffee beans—or at least some of them—are grown in environmentally sustainable ways by farmers paid a bit more than average, and if the part-time employee serving them at the counter has corporate-sponsored health insurance, a Starbucks customer can vicariously be a sophisticated world traveler while sitting on a pseudo–front porch and feel virtuous about helping the environment, impoverished farmers, and struggling American workers. All for only, oh, three times the price of a plain old cup of coffee.
"At Starbucks, our product is not just great coffee but also what we call the 'Starbucks experience': an inviting, enriching environment in our stores that is comfortable and accessible yet also stylish and elegant," Schultz wrote.
The "Italian" product names are unabashedly phony. The coffee is genuine. And what about the rest?
Howard Schultz claims he didn't start his career seeking to create gourmet coffee or a front-porch meeting place. For that matter, he neither founded Starbucks nor imported the first cup of espresso to America. He was a businessman selling various products until, by 1979, he wrote, he'd been named head of US operations for the Hammarplast line of "stylish Swedish-designed kitchen equipment and housewares."
But Schultz says he was dreaming of bigger things, of making the world a better place, inspired by President John Kennedy and the Peace Corps. According to Dori Jones Yang, the veteran journalist who cowrote Schultz's autobiography, he was also driven by memories of how his father, Fred, a truck driver, lost his job when he broke his ankle in 1961, leaving the family with "no income, no health insurance, no workers' compensation, nothing to fall back on." Whatever business specialty Schultz eventually settled on, he wanted to run a company that treated its workforce decently. Yang said that's why the book begins with the story of his father. (Conflict-of-interest alert: I worked with Yang years ago at BusinessWeek, before she met Schultz.)
Coffee simply became the vehicle for Schultz's dreams. Noticing that Hammarplast was selling an unexpectedly large number of drip coffeemakers to a small, four-store retailer in Seattle named Starbucks Coffee, Tea, and Spice, he flew west to investigate. He drank a cup and visited the roasting plant, and soon he was begging for a job. "I felt as though I had discovered a whole new continent," Schultz said of that first cup. It was "stronger than any coffee I had ever tasted," with "full flavors as they slipped over my tongue." Company employees discoursed lovingly about the mountains where the beans were grown, the color of the beans, and the roasting process. After a yearlong courtship, Schultz was hired as head of marketing.
While savvy US consumers could find strong, gourmet, European coffee back then, the shops were usually tucked away near a university campus or in the beatnik fringe. What most Americans considered coffee was "light brown and almost see-through," as Temple University history professor Bryant Simon described it in his 2009 book about Starbucks, Everything but the Coffee. Schultz called it "dreadful" and "swill," pointing out that typical American coffee before the advent of his company was made with "inferior type [robusta beans] that the coffee traders of London and Amsterdam treated as a cheap commodity." US coffee consumption had actually been declining since the 1960s, replaced mainly by soft drinks.
Understandably, Schultz treads lightly with the two founders who hired him, Gerald Baldwin and Gordon Bowker—the third founder, Zev Siegl, sold out in 1980—but, reading between the lines, it's obvious he considered them overly cautious old fogies who didn't understand modern business practices, including the need to constantly grow. Schultz was, after all, a marketing man. He was also, like many converts, more enthusiastic than the original gurus.
A crucial fissure opened up after he took a business trip to Italy in 1983. Schultz realized he didn't want merely to sell coffee beans for people to take home like groceries, which was Starbucks's specialty. He wanted to operate cafés, the same as in Italy. "What we had to do was unlock the romance and mystery of coffee, firsthand, in coffee bars," he wrote. "The Italians understood the personal relationship that people could have to coffee, its social aspect." When this turned out to be a push too much for Baldwin and Bowker, Schultz severed ties and in 1985 founded his own pseudo-European gourmet-coffee shop, Il Giornale. (It was named, he said, for the Italian word for "daily," although that was also the title of the well-known Italian newspaper then owned by the man who would one day become that country's controversial right-wing prime minister, Silvio Berlusconi.) No hard feelings; Starbucks actually invested $150,000 in Schultz's new venture.
Everything came full circle in 1987, when Baldwin and Bowker decided to sell the business, and Schultz bought it. Now he had a chance to carry out his vision in full: a widespread chain of cafés with Italian-style ambience, high-quality coffee, and fair treatment of workers.
Schultz's description of his starting goals for Il Giornale works equally well for Starbucks. He wanted, he said, "to reinvent a commodity. We would take something old and tired and common—coffee—and weave a sense of romance and community around it. We would rediscover the mystique and charm that had swirled around coffee throughout the centuries. We would enchant customers with an atmosphere of sophistication and style and knowledge."
In many ways, Schultz succeeded, even beyond his dreams. Certainly, Starbucks today is a brand known worldwide, with outlets located everywhere from the Seattle birthplace to Shanghai, from Switzerland to Seoul. It's an icon of America. Everyone goes there: all ages, ethnicities, races, and clothing styles—business types, teenagers, tourists, backpackers, women in Muslim head scarves, nursing mothers, and much more—even if "latte-drinking" has become a pejorative shorthand for liberal, white-wine-sipping, tree-hugging Democrats who live in San Francisco. Dori Jones Yang, Schultz's coauthor, recalled that when she asked him who he was marketing to, he would say, "Go to Starbucks and look at the people in line. You get the cops and the construction people from nearby sites, as well as upper-income people."
(Almost the only place on Earth lacking a Starbucks latte is Israel, and the exception was a subject of some controversy in the blogosphere when the coffee company ended its joint venture there in 2003. While Starbucks, in a posting on its website, blamed business disagreements with its local partner, the company had come under tremendous pressure from Palestinian activists ever since Schultz spoke in defense of Israel at his synagogue, and supporters of the Jewish state expressed fears that the chain was knuckling under to anti-Israeli pressure.)
Has it built an extended front porch? Heck, it may be an entire house. People know they can stay for hours with their laptops and an empty cup, or stop in just to use the restroom, no questions asked. Bryant Simon, sitting in Starbucks venues ten to fifteen hours a week for nine months for his book, found real estate agents poring over maps with prospective tenants and entrepreneurs interviewing job seekers. In the heart of San Francisco, I saw one man snoring away in an easy chair.
Furthermore, Starbucks has helped provide some of the entertainment people might carry to its tables. In 1995, the chain began compiling and selling CDs of jazz, classical music, and blues. It followed up by acquiring the Hear Music label, producing original CDs and albums, publishing a quarterly magazine called Joe with Time Inc., cosponsoring the MSNBC show Morning Joe, promoting books and movies, and selling DVDs. It also established a private, in-store digital channel to give Starbucks-goers exclusive access to selected book excerpts, news articles, iTunes music, and educational games. (Not all those enterprises lasted.) To publicize the heartwarming 2008 novel For One More Day, the company brought author Mitch Albom to its flagship Manhattan store, and arranged phone chats in twenty-five cities. The ultimate achievement: it bagged eight Grammies in 2005 for Genius Loves Company, the final album by Ray Charles, which it coproduced.
However, Starbucks has discovered limits to its front porch. Even Schultz admitted that he hadn't quite created the "third place" he envisioned. That concept, first outlined by Florida sociology professor Ray Oldenburg in 1989, was supposed to mean "informal public places where [people] can gather, put aside the concerns of work and home, relax, and talk," Schultz wrote. In the Italian cafés he so much admired, he added, "you can hear the interplay of people meeting for the first time, as well as people greeting friends they see every day at the bar." It's the image, as well, of the traditional French café, with passionate artists arguing endlessly over strong coffee and stronger cigarettes (without the cigarettes). Thus, in the ideal Starbucks, a customer would sip a cup of cappuccino—or, better still, a few refills—while chatting amiably with whoever was in the next seat. Kind of like calling out to your neighbor while you rock on your real front porch.
Yet, for all the armchairs, Schultz said that when an ad agency did a survey in Los Angeles, "fewer than 10 percent of the people they observed in our stores at any given time actually ever talked to anybody." Making matter worse, barely 20 percent of patrons linger long enough to schmooze even if they wanted to; the vast majority get their caffeine hits to go.
Author Bryant Simon, during his nine months of Starbucks sitting, tried vainly to engage strangers in conversation. "No one talked with anyone they didn't seem to already know or hadn't come there to meet," he wrote in obvious frustration. Similarly, labor organizer Kim Fellner stayed an entire day, from 5 A.M. until 9 P.M., at her local outlet for her 2008 book Wrestling with Starbucks, and she reported only two instances where customers "leaped into" an ongoing conversation among strangers or joined in after "eavesdropping." I got the same sort of results every time I stopped by. It would seem that the most common activity at Starbucks is typing on a laptop, solo.
In 2009, the company tried to stir up some family-style dining and conversation by installing long wooden tables in the middle of some of its restaurants, replacing the individual chair-and-table arrangements. However, customers have simply converted those into individual tables, very carefully leaving an empty seat between themselves and other patrons, and proceeding to converse with their own companions or work on their laptops.
Whether or not the customers talk to each other, the baristas—despite the chain's vaunted reputation for friendly staff—don't talk much with them.
During more than three dozen visits over ten months at Starbucks venues of all sizes, in all sorts of neighborhoods, at all times of day, from the heart of San Francisco to suburban Massachusetts, from office-park Los Angeles to downtown Washington, DC, from a small town in upstate New York to the hippest niches of Manhattan, and more, I almost never saw any over-the-counter chitchat. Out of 420 customers at the counter during those visits, merely 25 talked with baristas. That's actually a far lower percentage than the amount of interaction I found at other coffee places like Gorilla, Grumpy, and the granddaddy of the movement, Peet's Coffee & Tea, where the ratio was 1 out of 10. Fellner's experience was apparently similar, although her book isn't always clear about who is talking with whom.
It's not that Starbucks baristas are terse or unfriendly. Most of them say, "May I help you?" cheerfully enough—perhaps a tad more cheerfully than elsewhere, perhaps not. Naturally, some are more outgoing than others. There was the Latino guy in San Francisco who seemed to find something warm to say to everyone, and the barista in upstate New York who sang out "Helloooo!" and the woman in Los Angeles who suggested another place I might find a bagel one evening when her store had run out, then remembered me the next morning. I overheard conversations about the most recent Redskins-Texans game, long hours at work, shopping for a new car, and a son going off to college. But those were the exceptions. Far more common were the customers who never took their mouths away from their cell phones and the baristas who were too busy talking with each other to spare any unnecessary words for their clientele. What about the iconic barista who supposedly knows the favorite beverage of all the regulars? I saw exactly two examples of that.
On the other hand, Richard Honack, a marketing professor at Northwestern University's Kellogg Graduate School of Management, seems to have had much more positive encounters. The staff, he claimed, give customers the sense that "you're the most important person, because we're talking with you." If someone doesn't quite know the name of a particular drink, the barista will try to figure it out, and if that fails, "people in line help them get it. Someone will say, 'I tried that macchiato—it really is good.'" If a customer wants to invent something, that's OK, too. Honack said that the manager of one nearby outlet makes sure to have a bottle of eggnog on hand every day for a friend of Honack's who likes eggnog latte, even when it's not in season. Of course Schultz, in his second book, Onward, offers plenty of examples of dedicated baristas who are BFFs with their customers, including one who donated a kidney to a longtime coffee drinker.
Then there's Michael Gates Gill, a son of the famed New Yorker columnist Brendan Gill, who became a barista at age sixty-three and actually titled his 2007 memoir How Starbucks Saved My Life. The book is full of examples of Gill and coworkers chattering away with regulars as well as newcomers, memorizing the drinks certain people ordered every day.
Schultz claimed that "we train baristas to make eye contact with customers" and that the staff are supposed to be "romancing" the public. "If we greet customers, exchange a few extra words with them, and then custom make a drink exactly to their taste, they will be eager to come back." In theory, sure. But, Howard, you try buying a latte—incognito.
The problem of depersonalization only worsened as Starbucks kept on growing. From 6 stores when Schultz took charge in 1987, it jumped to over 100 in 1992, when the company went public, to a staggering pace of one new opening per day by the end of 1995, culminating with 13,000 around the globe by 2007. After all, that was why Schultz had broken with the founders to begin with, because he envisioned a nationwide chain. Even after he resigned as CEO in 2000, the drive plowed on, as Schultz remained in the chairman's seat and "turned my attention to expanding Starbucks around the world," according to Onward.
It can get tough for any company that grows that fast to maintain its grip on quality and the personal touch. And—perhaps because Schultz was distracted by other interests, like his private equity fund and part ownership of the then Seattle SuperSonics—Starbucks handled matters particularly badly.
Most notoriously, in the name of efficiency, the stores stopped grinding their coffee on site and replaced their old-fashioned, hand-operated espresso machines with a semiautomated version. Customers could literally no longer smell the coffee. Furthermore, the new machines were bigger than their predecessors, blocking the public's view of the baristas at work. "It didn't sound or smell like European coffee shops anymore," pointed out Robert Passikoff, president and founder of Brand Keys, a New York City–based consulting firm that focuses on issues of brand loyalty. "People were paying 40 percent more for coffee they could get down the block, but they didn't see coffee being handcrafted." If any Starbucks workers really had gotten to know their customers, said Ashley Woodruff, a financial analyst at T. Rowe Price specializing in restaurants and grocery stores, the rapid corporate buildup killed the relationship. "One of the problems when you're expanding at the pace Starbucks was, there's constant churn," she said. "You never see the same person in the same store."
With chain size came complaints of big-chain mentality. Bryant Simon, in his book, asserted that the music became more commercial. So did the ambience, with outlets selling toys and tchotchkes that evoked the feel of a souvenir store at a highway rest stop. Some customers protested the corporate move into breakfast foods such as eggs and said the place smelled like McDonald's. Others faulted what they saw as a cookie-cutter sameness to the decor as each new store was slapped down and laid out in one of four official designs and color schemes. The finances felt the hit, from both a decline in customers and the costs of expansion. Starting in late 2006, the stock plunged, and same-store sales for outlets open more than a year (the standard retail yardstick) barely increased after sixteen years of 5 percent annual growth. Of course, the slide got worse during the 2008–2009 recession.
You just cease being the quirky, hip, neighborhood coffeehouse if someone can find three of you within six blocks. Jill Kickul, of New York University's social-entrepreneurship program, said that her undergraduate students "see Starbucks as too corporate now and too standardized and not unique enough, not edgy enough, not grimy enough." Added Carol Holding, the brand-strategies consultant who's based right in the company's hometown, "There's such Starbucks fatigue. The ubiquity reduced the exclusivity."
As the author Naomi Klein—no fan of Starbucks or any well-known chain—pointed out in her classic book No Logo, the key reason select companies like the Gap, Ikea, and Starbucks managed for so long to avoid being seen as another McDonald's or Walmart is that they "don't flash with the garish, cartoonlike plastic yellow shells and golden arches; they are more apt to glow with a healthy New Age sheen." That is, they look more sophisticated and trendy.
It was a shaky balancing act, and the weight of 13,000 stores finally pushed things over. By the 1999 meeting of the World Trade Organization in Seattle, Starbucks had become such a symbol of multinational McDonaldization that antiglobalization protesters hurled rocks through its café windows.
Howard Schultz didn't initially understand the criticism. In his first book—published in 1997, in the still-booming days—he wrote, "When Starbucks started being targeted, it caught us off guard. We were so used to regarding ourselves as the good guys, as the struggling underdogs." Yang, his coauthor, told me that "he was kind of surprised by [the comparisons to big chains], and a little bit hurt by that. He pointed out that it wasn't like Walmart, which goes in and offers lower prices than all the local companies and drives them out of business." (True enough: You can hardly accuse Starbucks of underpricing, as we'll discuss in more detail.)
Nevertheless, by winter 2007, even Schultz couldn't ignore the festering unhappiness. He penned a memo to his successor that quickly became public, conceding that, as a result of growth over the prior decade, "we have had to make a series of decisions that, in retrospect, have lead [sic] to the watering down of the Starbucks experience, and what some might call the commoditization of our brand." Among other issues, he cited the automated espresso machines and loss of fresh coffee beans.
Moreover, dissatisfied patrons had alternatives. Now that Starbucks had proved there's a broad demand for gourmet varieties, a slew of actual neighborhood places had sprung up offering the one-of-a-kind, funky, edgy image that Starbucks used to claim, like Café Grumpy. Gorilla, Think Coffee (favored by Kickul's New York University students), Ozzie's Coffee and Tea, Café Regular, Root Hill Café, Southside Coffee, Oslo, Verb, Mud, Ninth Street Espresso, Gimmel Coffee, Jack's Stir Brew, Abraço Espresso, Everyman Espresso—and those were merely a few of the names in New York City in the fall of 2009. Pushing from the other side, McDonald's and Dunkin' Donuts began offering less-expensive Italianate drinks.
Interestingly, labor activist and author Kim Fellner suggested that their very trendiness makes the little guys actually less socially responsible than Starbucks, if their highfalutin airs put off many of Schultz's construction-worker customers. "Neither an artisan shop like Murky [a coffeehouse in her Washington, DC, neighborhood she thinks has the best-tasting brew locally] nor an industrial shop like Dunkin', [Starbucks] broadcasts accessibility to all regardless of race or class, while retaining the music, the lighting, and the ambience that speak to high-end aspirations," she wrote. In addition, Starbucks is a lot more welcoming to laptops and other electronic gizmos than some of the quainter shops.
The world certainly has room for all these venues, Starbucks and small. Yang said that's what Schultz always felt: "His point of view was that the whole pie was growing larger, and Starbucks was just taking a larger portion of a larger pie." By his statistics, US gourmet coffee drinking had zoomed 18 percent annually between 1984 and the time his first book was published. For that matter, Starbucks itself owns the middle-market brand Seattle's Best.
Inevitably, some of the little guys go out of business, but that doesn't mean Starbucks pushed them over. About half of all start-ups fail within the first five years, according to the US Small Business Administration. Schultz in part blames landlords who, he said, "use Starbucks as a bargaining chip, informing another coffee company or another prospective tenant that we are interested in the space and then jacking up the rent." Without any help from Starbucks, Gorilla Coffee managed to shut itself down for more than two weeks in April 2010 in a dispute between staff and the owners.
In any case, apparently Schultz's memo wasn't enough to revive the brand, and Schultz returned in person as CEO in 2008. A whirlwind of changes followed. For starters, he closed all the stores for three hours to retrain the entire staff. Then he brought back in-store bean grinding, installed shorter espresso machines, ordered the baristas to make fresh batches more frequently, brewed a new, milder blend called Pike's Place Roast, acquired the manufacturer of a highly regarded brewing machine, the Clover, revamped the reviled breakfast sandwiches, and—shockingly for this maven of growth—shuttered nearly 1,000 stores, cutting costs by some $580 million. But that was just to get stabilized.
Looking ahead, Schultz introduced innovations such as a loyalty card with discounts, healthier and trendier food choices, a jazzed-up website, and the chain's first big ad campaign. Another surprising flourish was Via instant coffee for people to make at home. (So much for the "third place" and the communal experience of the Italian coffee bar.) Meanwhile, Schultz slightly redrew the logo—which he insists is a siren from Greek mythology but most people call a mermaid—and signed a partnership that paved the way to the biggest untapped market, India. For dessert, he bought Evolution Fresh, a maker of natural fruit and vegetable juices.
Hedging its bets, Starbucks in 2009 opened two outlets in its hometown incognito, under the monikers 15 Ave Coffee and Tea, and Roy Street Coffee and Tea, with nary a mermaid (or siren) in sight. Aficionados of the buy-local movement screamed that Starbucks was tricking coffee drinkers who specifically did not want to buy from a big chain. Starbucks officials retorted that they had to give the new places different names since they sell beer and wine, which classic Starbucks outlets don't. "We were not trying to hide anything," Schultz insisted, rather ridiculously, merely hoping to "experiment with other retail concepts that would further elevate our coffee authority."
Perhaps most important was the sheer fact of his return: even if Howard Schultz is no Steve Jobs, rarely can anyone boost morale like a company founder.
There were stumbles, of course. The sugary, yogurtlike Sorbetto flopped after a year; Starbucks trailed badly behind Green Mountain Coffee Roasters in the realm of take-home packets; and the redrawn logo has attracted criticism, as alterations of any traditional symbol often do. Overall, however, the changes were widely lauded. Via is considered a big success, and same-store sales and the stock perked up in late 2009. Many experts think Starbucks can recapture some of its magic.
But a good chunk is lost forever. It's been too many years, too many look-alike stores, too much fresh competition.
If coffee is Starbucks's key product, where and how it obtains the raw ingredient ought to be key to its social responsibility, or lack thereof. Indeed, coffee sourcing is one of the policies the company particularly likes to brag about, and most people seem to have a vague idea that all its coffee is fair trade, even if they don't quite know what the term means. Carol Holding, the branding consultant, said that "people absolutely support Starbucks for that. It balances out the price."
Well, the image is and isn't true. Starbucks does spell out a lot of policies to help struggling farmers in the poorest parts of the world where coffee is grown. But not all its coffee is fair trade. It's not the only coffee company trying to buy fair trade. And fair trade isn't the sole sourcing issue.
"Fair Trade Certified" is an official label that means a product has been audited by one of several NGOs to ensure that it follows a set of international standards. Among the standards, fair trade goods must be grown in environmentally sustainable ways; the workers must be treated decently and paid a living wage; they are guaranteed freedom of association and a safe workplace; forced child labor is forbidden; growers are promised a minimum payment level; and the producers must invest in long-term planning to improve both growing and social conditions. Coffee—by far the biggest fair trade crop—traditionally had some additional requirements to protect independent, small-scale growers. To cover the higher costs, middlemen pay a premium of, typically, 10 to 20 percent over market rates.
Does Starbucks do all that? According to its website, Starbucks and a respected environmental group called Conservation International jointly set guidelines for environmental and workplace matters at the farms that grow its coffee. By 2009, 81 percent of the beans it purchased, or 299 million pounds, met those standards, known as Coffee and Farmer Equity (CAFE) Practices, and Schultz declared a goal of reaching 100 percent by 2015. Under the CAFE Practices, outside parties must verify that there are "measures in place to manage waste, protect water quality, conserve water and energy, preserve biodiversity, and reduce agrochemical use" and must confirm that there are "measures in place that concern safe, fair, and humane working conditions." The CAFE definition for working conditions goes on to specify that "compliance with the indicators for minimum-wage requirements and [for] addressing child labor/forced labor and discrimination is mandatory." All that is fine. Nevertheless, it's not fair trade, strictly defined. The Starbucks standards don't specifically forbid child labor, forced labor, or discrimination. Moreover, relying on developing countries' minimum-wage requirements as a standard is almost meaningless since these are often far below the living wage required for fair trade certification. And what is "compliance with the indicators"?
Separately, Starbucks has set up support centers in Costa Rica and Rwanda to teach small local growers how to increase yields and improve coffee quality, and it has paid out some $2.5 million annually in small loans. But those efforts speak more to ensuring the quality of beans—a business necessity—than the quality of farmers' lives.
Starbucks does buy some genuinely fair trade coffee; in fact, it says it's the biggest purchaser in the world. (Green Mountain also claims to be number one.) As of 2009, however, that came to only about 40 million pounds, or one-ninth of the corporate total. In other words, just a small portion of the macchiatos and lattes you might drink are fair trade certified—even by the US group's more lax criteria.
Defenders say there aren't enough fair trade beans in the ground to satisfy Starbucks customers' voracious thirst. While that's true, it's circular: Starbucks has so much clout that if it demanded more fair trade beans, producers and shippers would find a way to comply. The same supposed dilemma occurred in 2002 with Ben & Jerry's and cage-free eggs (eggs laid by hens that have more freedom of movement than those in cramped traditional cages). When the Humane Society pressed B&J to use more of the humanely raised eggs in its ice cream, the company initially argued that it couldn't find enough, because 7,000 chickens are required to produce its annual supply of eggs. Somehow, however, it managed. Four years later, all the ice-cream maker's eggs were from cage-free chickens.
Some activists debate whether even fair trade does enough to protect the desperately poor people who grow the beans so beloved by customers who can afford more than three dollars for a cup of them in liquid form. When environmental consultant Fred Pearce trooped out to Tanzania for his 2008 book Confessions of an Eco-Sinner, coffee farmers pointed out that their fair trade "premium" price of $1.46 per pound might be 20 cents above average, but the buyers then turned around and sold that crop for the equivalent of $12 per pound retail. For a month's work—one sack of fair trade beans—a grower might get ten dollars. "No wonder that these farmers . . . struggle to send their own children to school," Pearce wrote. "No wonder their roofs leak. No wonder that no farmer I met had even a motorbike to take his beans to the shed." Similarly, in 2009 Time cited a survey of 179 fair trade coffee farmers in Central America and Mexico, in which "more than half said their families have still been going hungry for several months a year."
Sure, if Starbucks bought larger quantities of fair trade coffee or paid growers more, it would probably raise its retail prices. But for devotees already paying $3.20 and up, would an extra 10 cents be such a big deal?
Also on the menu are a number of noncoffee items. Starbucks' ethical policies for cocoa and tea are less developed, and it has not joined the big chocolate names Mars Inc., Cadbury Company, and Nestlé in working with the International Cocoa Initiative to set labor standards for infamous cocoa-growing countries such as Côte d'Ivoire, according to both the initiative's website and Linda Golodner, a former president of the National Consumers League. (Golodner was the consumer expert representing the United States on a special committee that wrote social-responsibility guidance for the International Organization for Standardization.)
It's important, as well, to consider what motivated Starbucks, and that probably wasn't its own conscience. The company came under tremendous criticism in the mid-1990s and again at the Seattle WTO meeting for buying beans grown by children and in other abusive circumstances. While Starbucks claimed it had no control over the growers and middlemen, it gave a token $75,000 to set up a revolving-loan fund for farmers in Guatemala, the site of the child-labor charge. Since then, it's become practically a competitive requirement for big-name brands—even McDonald's and Dunkin' Donuts—to offer some fair trade coffee.
Authors Kim Fellner and Bryant Simon separately went out to visit farmers who were selling to the coffee giant through some sort of ethical program, and each came back with a different conclusion. Fellner was more supportive, Simon more skeptical. Fellner said that Starbucks, "along with the Rainforest Alliance and a number of other NGOs, has become the toughest enforcer of environmental standards in the coffee fields," and she credited its payment premiums with saving small farmers when prices plunged in the early 2000s. Simon, meanwhile, said he could never find any "little farmers" from whom Starbucks claimed to buy its beans but instead met growers who told him that the company actually goes through large middlemen. As the book quotes one of them, "Starbucks bought almost exclusively from privately owned enterprises, from fairly wealthy investors." To add to the confusion, two of the three largest exporters of premium Coffea arabica beans are Brazil and Colombia, and the former is known for large, mechanized farms, while the latter relies more on small landowners. Plus, a surge in commodity prices in 2011 briefly uprooted the local-coffee cooperative system.
By 2005, Starbucks was certainly as aware as anyone of the need to maintain a socially responsible image regarding the people who were growing its basic crops (whether it deserved that image or not). That makes it hard to understand how the company could be so heavy-handed and lacking in PR savvy when it came to the farmers in the desperately poor country that discovered coffee a millennium ago, Ethiopia.
As has been widely reported by now, Ethiopia was trying to establish branding rights for certain regions famous for coffee, including Yirgacheffe, Harar (sometimes spelled Harrar), and Sidamo, so that it could trademark coffee sold with those regional names and, presumably, charge more. As Adam Kanzer, the general counsel for Domini, explained, "The names have acquired a certain value in the marketplace. It has a certain taste; it has a certain quality to it. [Ethiopian officials] felt that if they own the intellectual property, they could market the brand in a more effective way."
Many governments granted trademark protection to Ethiopia, including Canada, Japan, and the European Union, but the US Patent and Trademark Office rejected Harar and Sidamo on the grounds that Starbucks had already applied to register something called Shirkina Sun-Dried Sidamo. "Starbucks argued that you can't own the name of a region," Kanzer said. So, how could Starbucks itself register its label, if Ethiopia couldn't? The company claimed its situation was different, because it was using the word Sidamo as part of a longer, fancier brand name for a unique way of processing the coffee.
The dispute ran on for more than two years, played out in the press and public, as the Ethiopian government, Domini, Oxfam America, Trillium, and Light Years IP (an organization that helps developing countries profit from their intellectual property rights) all lobbied Starbucks. The Ethiopian ambassador wrote to Schultz; Domini brought an Ethiopian farmer to the Starbucks annual meeting; Oxfam circulated petitions and ran newspaper ads. The conflict even got a spot in a documentary about Ethiopia, Black Gold, that premiered at the Sundance Film Festival in 2006. Meanwhile, the National Coffee Association, a powerful trade group, filed a petition with the patent office opposing the Ethiopian government, allegedly at Starbucks's behest.
Beyond saying, "We got there first," Starbucks essentially argued that it would take better care of the farmers, and give them a bigger share of the proceeds, than their own government would. Even Kanzer conceded that "the Ethiopian government is not the most up-and-up government, and there were legitimate concerns raised about where is the revenue going to go—is it going to go to the farmers, or the government?" That may be, but how does that give Starbucks the right to the names? Kim Fellner, strongly siding with Starbucks again, asserted that the corporation meant well and that Ethiopian coffee had a poor reputation anyway.
In the end, and in the real world, there's no way a company can claim to be ethical and concerned about poor farmers, and then try to block those farmers from making money off the suddenly prestigious name of their homeland. "It's not good PR for a company to be on the wrong side of this issue," Kanzer pointed out, somewhat amazed at the coffee giant's stance. Starbucks finally saw the handwriting on the coffee-bean bag, and in June 2007 it signed a licensing deal agreeing to add the word Ethiopia to the regional names on its brands and to promote that nation's coffees. Today, you'll find Ethiopia Sidamo coffee with the trademark symbol at Starbucks. Coffees with non-Ethiopian geographic names, like Kenya and Sumatra, don't have the TM.
However well or badly it may deal with the people who grow its coffee, Starbucks claims bragging rights regarding the people who serve it. Indeed, that's how the whole story started, going back to 1961, when Howard Schultz was seven years old and his father broke his ankle and lost his job, with no medical insurance. So, as the corporate myth goes, Schultz created a workplace where employees are treated with respect. Since 1988, the chain has offered health coverage to anyone who works at least twenty hours a week, paying 75 percent of the premiums and expanding the benefit over the years to encompass preventive, mental health, chemical dependency, crisis counseling, vision, and dental care—for unmarried partners of either sex, too. Moreover, starting in 1991—even before the company went public—employees working at least twenty hours weekly have been granted stock options.
The staff are called partners to emphasize that they can be stockholders, just like Schultz, and not mere cogs, and there are solid opportunities for promotion, plus a 401(k) plan with a matching corporate contribution. Employees supposedly have a passion for coffee and are encouraged to learn more. The perks keep improving; after Schultz's return, for instance, tuition reimbursement was added. To cater to its diverse customer base, the company hires people of all races, ages, ethnic backgrounds, sexual preference, and tattoos—although perfume is forbidden, "because coffee beans have a bad tendency to absorb odors," Schultz said.
It's easy to scoff at the claims of happy barista-customer friendships and the moniker "partners," but the perks are genuine. Business experts like Jeffrey Bernstein, a senior analyst at Barclays Capital, say Starbucks's pay is at least in line with the industry average, or even slightly above, and the health benefits are unique in the trade. Those benefits are particularly amazing considering that more than 44 percent of Americans with jobs lacked any coverage at the time Congress passed health-care reform in 2010, according to the Kaiser Family Foundation; considering the tremendous political and business opposition to that reform law; and considering the pressure on Schultz to eliminate that "frill" when Starbucks was floundering.
Starbucks has also made the Fortune "Best Companies" list every year from 1998 through 2011 except for 2001, hitting as high as seventh place in 2008. Among the typical employee comments, according to one insider privy to the list making: "This place is unique because we all get to know each other really well, but we also are able to enjoy each other's company during work and outside of work," and "You are a partner in every store," and even—apparently some baristas do engage in customer chat—"Starbucks connects with customers in a way no other place does. We see a lot of people very day, and we get to know them and we make them feel at home." In addition, Starbucks is one of just three businesses to qualify for the "100 Best Corporate Citizens" roster of Corporate Responsibility magazine every year for the first nine years, based on its performance in areas such as the environment, employee relations, human rights, philanthropy, governance, and financial issues.
Richard Honack, the Northwestern University marketing professor and Starbucks admirer, said its business model couldn't succeed unless the workplace myth were true. "The employees have to buy in to the culture, and the employees do," he asserted. "When you walk in and talk to Starbucks employees, they're doing just fine. They like their health insurance, they like their training, they like that they're brought in as partners." That's pretty much what labor activist Kim Fellner found when she not only interviewed employees but also became one for her book, working a six-hour shift. Her conclusion: "For the most part, young workers consider a job at Starbucks miles above a job at McDonald's, Pizza Hut, or KFC."
"Treat people like family, and they will be loyal and give their all," Schultz wrote in his first book. "It's the oldest formula in business, one that is second nature to many family-run firms."
If you want dedication, turn to author-barista Michael Gates Gill. In his Starbucks-adoring memoir, Gill wrote that he was basically a psychological and financial mess—laid off as an executive at a prestigious advertising firm, recently divorced after an affair, alienated from most of his children, down nearly to his last dime, and in desperate need of health insurance to cover an operation for a brain tumor—when he stopped into Starbucks for a latte he probably couldn't afford and stumbled onto a recruiter. Along with a job and insurance, he gained a loving community of coworkers and, by the way, learned to respect low-income, poorly educated, young blacks and Latinos he would have shunned while at the ad agency and growing up in his famous father's shadow, when he hobnobbed with Jackie Kennedy, Ernest Hemingway, and Queen Elizabeth. (Really. Or so he says.) In Gill's Starbucks, the baristas are almost universally friendly and supportive, eager to help him adjust, and never jealous when one manager wins an award. As he wrote, "I could not deny the feeling of a growing happiness in my heart. This new, quiet, inner happiness kept catching me unawares in the midst of a rush of serving a big line at Starbucks." (With a job like that, who needs Jackie, Papa, or the queen?)
Nevertheless, for all the goodies—exaggerated or not—this is still a fast-food business. "The job won't give you the means to buy a house, raise a family, or even rent an apartment or make payments on a car," Kim Fellner noted. It can be physically demanding and emotionally rigorous, as customer-service work usually is; imagine chatting with strangers for six or eight straight hours. Fellner toiled hard on her shift, hauling ice, emptying trash, wiping tables, and trying to remember the damn Italianish names. Gill, behind the burbling, lays out a tough, almost nonstop regimen that sent him mopping bathrooms and carrying heavy bags of coffee grounds to the garbage whenever there was a minute's breather in the counter work. Schultz himself acknowledged, in Onward, "Being a barista is not an easy job. On their feet for hours, juggling multiple, complex drink orders." While turnover may be less than the triple-digit industry average, it's still around 60 to 90 percent.
Nor is every outside review glowing. Starbucks has never made Working Mother's "Best Companies" list—as mentioned in previous chapters, the magazine won't reveal why companies aren't listed—and it gets a mediocre 6.1 out of a possible 10 points for its overall score on GoodGuide.com, perhaps the most broad-based CSR-ranking website. Some of its lowest scores were in employee relations and working conditions.
Things got worse during the years the company overexpanded and brought in the superefficient new coffee machines, driving staff to work faster. The City University of New York's Naomi Gardberg said student baristas in her classes complained that they were no longer allowed to switch hours when they needed to study for a midterm or a final. Around 2008, Starbucks tried applying Japanese-style "lean" production methods to its counter work, such as measuring how long it takes to do routine tasks. Depending on whom you believe—news reports or Schultz's book—this was either a horribly pressured form of (ahem) bean-counting micromanagement or a way of "involving employees by asking for their opinions about how to improve their own work." But even Schultz conceded that the process "was not widely embraced as a big idea inside Starbucks." Later, in 2011—with profits booming again—Schultz burnished his CSR reputation with new programs to provide loans to small businesses and create jobs in poor neighborhoods, and a vow to stop making political donations in order to protest dysfunction in Washington, DC.
The chain's most famous labor confrontation came in 2004, when the Industrial Workers of the World began trying to unionize four shops in New York City. The attempt by the IWW—which used to be one of labor's radical leaders and is now nearly defunct—might seem oddly quixotic. As Barclays Capital's Jeffrey Bernstein pointed out, unions are rare in the fast-food industry, because of the scattered locations, part-time and short-term workforces, and diffuse franchise ownership. Even veteran union officials sounded tepid. Ron Blackwell, the AFL-CIO's chief economist, praised Starbucks for its code of ethics and its benefits. Kim Fellner—whose main career has been working in the labor movement, not writing—cast a skeptical eye on the IWW's motivation and tactics, implying that it was a bunch of intellectuals looking for a cause rather than actual workers.
Aaron Kocher, a Starbucks shift supervisor in Minneapolis who was one of the IWW's main organizers in New York City and at his own site, seemed to fumble when asked to explain the underlying grievances. He admitted that the company provides health benefits, the atmosphere is "pretty friendly," and "they tend to pay slightly higher than other places." However, he said that since the recession and the store closings, staffing cutbacks had intensified the pressure on the remaining workers. Also, there's no longer any time for the tastings the company used to encourage to teach baristas about their brews. And managers constantly changing shift assignments without advance warning is a perennial problem.
Facing such a half-baked effort, Starbucks could almost have ignored the whole thing. Instead, it fought back so nastily that a National Labor Relations Board judge in 2008 ruled that the company had broken the law. Among other violations, the judge found that management fired three employees for union activities; issued negative job evaluations to one of those employees; prohibited staff from discussing the union, wages, and other employment issues; prohibited them from posting union notices; and barred them from wearing more than one pro-union button. Starbucks was ordered to pay back wages and reinstate the fired employees and to end discriminatory treatment against workers sympathetic to the union.
At the time of that ruling, moreover, there had been at least three other sets of NLRB complaints in three states, two of which were settled. Kim Fellner's book describes heavy-handed efforts by Starbucks to block the International Union of Operating Engineers from organizing one roasting plant, including screening new hires for union sympathy, plus a personal visit from Schultz. When employees signed union cards, she said, "the company capriciously changed their work shifts" and "promoted new people over them." Kocher said that at nearly every store he and his colleagues tried to organize, "we would hear people saying, 'Managers are telling workers you can't talk about the union.'" The company, according to the Wall Street Journal, has also blocked organizing efforts in Europe and New Zealand.
Starbucks doesn't just fight the creation of new unions; it has also tried to wipe out any that were already established before Schultz took control. The CEO sounded positively gleeful as he described employees petitioning him in 1987 and 1992 to decertify the union that represented a warehouse, a roasting plant (a different plant from the one Fellner described), and a few retail workers in Seattle. "When so many of our people supported decertification, it was a sign to me that they were beginning to believe I would do what I had promised," he wrote. According to Naomi Klein in No Logo, the company shut down the Vancouver distribution plant in 1997 after it unionized. Only in Chile is a sizable percentage of the Starbucks workforce unionized.
In the company's defense, Dori Jones Yang said Schultz "strongly felt that unions would get in the way. He thought there should be a high level of trust between employees and management, and management should voluntarily go out of their way to treat employees well." Fellner's book cites similar arguments, including the visit by Schultz to the roasting plant, where he brought up the well-trod story of his father's broken ankle. Such an attitude is hardly unusual among socially progressive business executives. None of the companies profiled in this book are unionized. So is it silly to focus this much on the union question? Isn't there a distinction between, say, a nonunion Walmart and a nonunion Starbucks? Is it OK for a "good" company to be nonunion?
The answer is that of course it's better to have health insurance with no union, as opposed to no insurance plus no union, but those are not the only two options, or even the key issues. "A union is also about due process. Who gets hired, who gets fired, who gets promoted, under what circumstances," says Christian E. Weller, an associate professor of public policy at the University of Massachusetts's McCormack Graduate School of Policy Studies, in Boston, and a senior fellow at the Center for American Progress, a liberal think tank based in Washington, DC. Fellner also argues that workers' well-being should not depend on the "voluntary" whims of one manager, no matter how enlightened. This topic is discussed in more detail in the introduction.
The best opportunity for Starbucks to prove its CSR cred comes in the eco-realm, because the food business probably has more impact on the environment than any other industry. On top of the standard criteria regarding carbon emissions, recycled content, packaging, pollution, energy efficiency, and on and on, there are categories like organic, pesticide free, no added antibiotics, and non–genetically modified.
Starbucks has made a lot of effort in a lot of areas—which it happily emphasizes on its website—and it has a reputation among the general public for being pretty green. Yet professional environmentalists are not impressed. "I am disappointed," said Climate Counts's Wood Turner. "It is a company that people expect to be doing things differently."
The Climate Counts ranking of companies' efforts to reduce greenhouse-gas emissions is a perfect example of this mixed reputation. Sure, Starbucks usually leads the food-services category, but so what? "It's an amazingly low bar in that sector," Turner said with a shrug. The six rated companies—the others are Burger King, Darden Restaurants (owner of Olive Garden and Red Lobster), McDonald's, the Wendy's/Arby's Group, and Yum! Brands (owner of KFC, Long John Silver's, Pizza Hut, and Taco Bell)—are largely fast-food venues, "a very disposable sector," in Turner's words, with literally tons of throwaway take-out containers. Starbucks earns only about half the points possible in most categories, including measuring its impact on climate change, setting goals to reduce energy use, and posting public information.
More positively, Turner said that Starbucks managers have "been open and very nondefensive. They are strong supporters of our process, and they often will provide new information that we may have overlooked." Moreover, in 2011 Starbucks was one of Climate Counts's twenty-five "Gold Star" companies singled out for supporting mandatory federal action on climate change.
There's a similar halfway-done sense at Ceres, the coalition that reports on companies' sustainability efforts. As of 2011, Starbucks had not taken the full step of actually joining the Ceres Company Network, which would require it to pay a membership fee ranging from $2,000 to $25,000, officially support the group's principles, participate in some of the lobbying and publicity actions, and disclose its goals and efforts to reduce its own emissions. The fee would obviously be peanuts for Starbucks, with its annual revenues of over $10 billion, and even the other requirements wouldn't seem too taxing. According to Andrea Moffat, vice president of corporate programs at Ceres, the coffee chain has been fulfilling a lot of the requirements anyway. Schultz headed a committee that conducted a benchmarking study of industry rankings, and Starbucks officials have accompanied Ceres to meet with members of Congress, helped produce op-ed pieces, and spoken at conferences, she said. As with Climate Counts, Starbucks ranked first in its fairly crummy industry in the benchmark study. "I'd like them to become a member," Moffat conceded, "but we just haven't gotten there yet."
As for other CSR organizations, Starbucks belongs to Business for Social Responsibility, as does almost every big name you can think of—250 of them, including ExxonMobil and Walmart—and that group's standards are considered pretty easy to meet.
The biggest environmental problem is those ubiquitous, universally recognizable mermaid/siren carry-out cups—which the baristas automatically give you without asking whether you're staying in or running out. A customer who wants to be ecological has to take the effort to say, "Please put it in a ceramic mug." The barista is then likely to grimace and ask a coworker where the heck the mugs are. You can get a whopping 10-cent discount if you bring your own container, and the company also now sells such containers, but you'd better shove it in the barista's face before he or she has already poured your latte into a throwaway cup.
Baristas have told me that asking me what kind of cup I want and searching for ceramic would reduce their efficiency. They also say that the smaller outlets and those whose clientele are mainly take-out don't have storage space for the rarely used mugs. Then, once the paper cups leave the store, the staff can hardly run after them with recycling bins. Fine, but how come the counter workers at Wendy's, Burger King, and my local bagel store all manage to make their first sentence "Is it to stay, or to go?"
The Starbucks website sets as a goal to "serve 25% of beverages in reusable cups" by 2015. That's an interesting number, considering that only 20 percent of beverages are consumed on the premises, and of those, the website admits, paper and plastic cups "account for approximately 95 percent of our in-store beverage packaging." If it's really going to achieve that goal, Starbucks will need to shift all of its in-store purchases into reusable containers plus somehow capture 5 percent of the take-out. "They will have to train the workers"—as well as Wendy's does—said Sally Greenberg, executive director of the National Consumers League. And offer better than a 10-cent inducement to bring your own.
How much damage those little mermaid/sirens cause can be estimated. It's been frequently reported that 3 billion Starbucks cups end up in landfills each year. According to the environmental group Global Green, Americans annually use 58 billion paper cups of all kinds, producing a total of 645,000 tons of waste and 2.5 million metric tons of carbon emissions, or about one-third of an ounce of waste and about 0.00004 metric tons (about 1 1/2 ounces) of emissions per cup. Starbucks's paper profligacy is thus contributing nearly one-twentieth of that mess—clogging landfills with about 32,000 tons of unnecessary waste and contributing approximately 125,000 metric tons of emissions toward destructive climate change.
The chain has taken a few steps to rein in this impact. Schultz noted that as far back as 1995, Starbucks created a "hot-cup team" to find a more environmentally sustainable container that would still allow people to hold a steaming cup of coffee. If reusing or recycling mugs wasn't feasible, was there at least a way to reduce—the first environmental R—the amount of discarded, Earth-wrecking garbage? After some experimenting, the ultimate solution, premiered in 1997, was a cardboard "sleeve" fitting over the disposable cup that required just half as much material as the double cups the chain had previously used. As a bonus, the sleeve itself was made partly out of recycled paper. A decade later, Starbucks improved on that with a cup that included 10 percent postconsumer recycled fiber, and it replaced its cold cups with ones that use 15 percent less plastic.
In 2009, seven of its New York City outlets participated in an eight-week pilot project with Global Green to test whether its cups could be recycled along with ordinary corrugated cardboard. (Answer: The cups and sleeves could, though the lids couldn't.) The catch was that this recycling only involved beverages consumed on site, in order for the cups to be collected. While the practical limitations of the test are understandable, it's almost meaningless as an environmental solution. These to-stay paper cups are exactly the ones that are unnecessary and should be replaced with reusable mugs.
And Howard, if you really want to encourage reusable cups, why are you constantly being photographed holding disposables?
Beyond cups, Starbucks still has a mixed record on what ought to be easier recycling and waste issues. For instance, the corporate website asserts that 70 percent of stores recycle in-house material. However, there are caveats. As the website notes, "Recycling is dependent on the availability of commercial recycling services," it's mainly for nonconsumer material like cardboard boxes, and "for stores operating out of leased spaces"—the vast majority—"it is the landlords who control waste collection and recycling." Consumer recycling is an even sadder story. Frappuccino bottles? The newspapers that get left in the armchairs? Fewer than 400 stores in all of North America had consumer-recycling bins as of 2011. "If companies aren't doing the most basic things like putting recycling bins in, it's hard for me to get impressed by other things they're doing," said Conrad McKerron, director of the corporate-accountability program at As You Sow, a San Francisco–based nonprofit organization that works with ethical-investing funds. A more successful effort is the company's "Grounds for Your Garden" policy, which allows people to take home five pounds of used coffee grounds, gratis, for composting (and which everyone seemed to mention).
The buildings themselves can be big energy guzzlers, or savers. For instance, Starbucks is slowly switching to renewable energy—that factor accounted for 25 percent of power use in company-owned stores in 2009—and it saves on air conditioning by keeping venues a tad warmer in summer. Deciding that there was "no commercially available LED [energy-efficient lighting] that met our aesthetic and functional requirements," Starbucks got General Electric Company to design a new type. Plus, it tries to install recycled floor tiles, sustainable-certified wood, and cabinets made of postindustrial recycled material in its new construction and renovation. Community-development adviser Stacy Mitchell handed out rare praise, in her 2006 book Big-Box Swindle, noting that Starbucks is "one of the few chains that has a record of preserving and reusing historic buildings"—a form of recycling.
The problem is that most of these efforts apply solely to locations the company owns directly, whereas most outlets are rented. What can Starbucks do in the rentals? A lot, said Wood Turner of Climate Counts. Leasing millions of square feet worldwide, "Starbucks has leverage," he said. The same way that it could, if it wanted, spur farmers to grow more fair trade coffee, "it could begin to put pressure on building owners to make their buildings more efficient."
Food sourcing is an environmental issue because of the impact of pesticides, fertilizers, genetically modified ingredients, and animal waste. "Shade-grown" and "organic" methods try to reduce the environmental impact by banning chemical pesticides. And? Starbucks buys a minuscule 14 million pounds of certified-organic coffee beans per year, according to its own accounting.
When it comes to the various sandwiches and pastries, PETA's Dan Shannon gave the chain points for seeking more humane versions of animal-based ingredients, yet he described the efforts as "baby steps." These include "starting to source some cage-free eggs," "starting to give purchasing preference" to poultry suppliers that use a new method of slaughter that's supposed to be less painful, and "moving toward suppliers" that use less-cruel crates for the pigs that become the bacon–Gouda cheese–egg frittata sandwiches. And Shannon appreciates that he can get soy milk in his coffee.
Starbucks seems to have sought creative ways to resolve a big issue for many restaurants: the water that's wasted when employees keep the faucets running to save time on washing dishes. Starbucks said it now cleans blended-drink pitchers (one of the most water-intensive pieces) with "a blast of higher-pressure water" rather than "an open tap." The company also said it's saving H2O with a revised system for cleaning utensils and by reprogramming the way its espresso machines rinse shot glasses. What it's not doing, complained Aaron Kocher, the IWW organizer, is increasing "the amount of labor budgeted, so that perhaps workers won't feel so rushed."
Speaking of water, what on earth is Starbucks thinking with its Ethos water bottles? For every bottle sold (at, typically, $1.95 apiece), the company donates 5 cents to a special fund for "water, sanitation, and hygiene-education programs" for hundreds of thousands of people in countries without sufficient clean water. Even putting aside how small an amount that nickel takes from Starbucks's profits, any environmentalist will scream that selling bottled water in developed countries makes the world's problems worse, not better. More than 17 million barrels of oil are wasted to produce the water bottles Americans buy in a typical year—even while most Americans have access to perfectly safe, delicious drinking water from their own taps. The lovely lake and stream water that is poured into the Ethos bottles could have gone to those hundreds of thousands of impoverished people that Starbucks claims to be helping. No self-respecting environmental group, food co-op, or college campus will be seen with water bottles any more.
"You need to have your social issues lined up," says Conrad McKerron of As You Sow.
Finally, an analysis of Starbucks can't avoid the issue of price.
Of course Starbucks brews are expensive. They're meant to be. Howard Schultz made that clear from the start, happily comparing his brand to Nike, which set out "to design world-class running shoes" that could sell for $140 a pair in an era when good sneakers typically were only $20.
For the record, here are some comparisons: In my New York City neighborhood in 2010, a twelve-ounce ("tall") latte or cappuccino cost $2.49 at McDonald's, $2.69 at Dunkin' Donuts, and $3.20 at Starbucks. Consumer Reports found a similar range in August 2009, with $2.19 for ten ounces at Dunkin', $2.29 for twelve ounces at McDonald's, and $2.88 for twelve ounces at Starbucks. But the little, offbeat places were pricier: A twelve-ounce latte was $3.75 at Café Grumpy and a gorilla-size $4 at Café Gorilla. Meanwhile, a cup of regular coffee at a local diner went for $1.25.
During a few months in early 2011, prices throughout the world shot up as rising temperatures and volatile rainfall, probably linked to climate change, decimated the Colombian harvest—finally bringing the biggest lattes past the clichéd four-dollar mark, at least at my local Starbucks.
What do you get for that $3.20 or $4? Image.
Accountants and struggling actors, students and stay-at-home moms, Schultz's cops and construction workers could all savor the image of being richer and more worldly wise than they really were. "Starbucks gave yuppies, bobos, and their imitators a way to show off their wealth (or their desire for wealth), sophistication, and continental taste," Bryant Simon wrote (italics added). (Bobos are people with conflicting bohemian and bourgeois tastes.)
Not only that, but sophisticated Starbucks sippers have practically learned Italian, or at least a pseudo-Italian coffee language. "You could look at it as elitist," Northwestern University's Richard Honack acknowledged, although he prefers to consider the lingo and corporate culture "personalized." This is not an easy skill to master. Even Michael Gates Gill, the happy barista, several times admitted to getting flustered over the arcane coffee names.
No matter that very little of the image is accurate. Grande actually means "big" in Italian, so why does it refer to the medium size at Starbucks? Latte is just milk, and a glass of milk is exactly what you'd get if you ordered a latte in one of the real Italian cafés Schultz claims to love. A caffe latte, then? Ah, said my friend Paola, who was born in Bologna and raised in Milan, caffelatte is a breakfast dish, served in a bowl, consisting of espresso and lots of milk, and "the purpose of making this souplike thing is to be able to dunk bread, cookies, or pastries." And, by the way, you don't drink caffelatte in Italy; you eat it. Even the espresso at Starbucks is wrong, Paola said. It "lacks an essential ingredient—the crema, the foam that is created when the pressurized hot water goes through the coffee—not to be confused with cream."
Keep in mind, too, that coffee, Starbucks style, is not a health food. A simple "tall" latte packs 150 calories, and things pretty much go up from there: A venti, 240 calories. A grande caramel-brulée latte, 300. A venti Java-chip Frappuccino will feed you a whopping 600 calories. For one beverage. That's nearly one-third the federally recommended daily calorie intake for an average American adult.
And don't forget that basic ingredient, caffeine. The Mayo Clinic (to give one example) has warned that more than 500 milligrams of caffeine a day, which it translates to slightly over three Starbucks grande vanilla lattes, can cause insomnia, nervousness, restlessness, irritability, fast or irregular heartbeat, muscle tremors, headaches, anxiety, and nausea or other gastrointestinal problems. Nor is a "half-caff" or a decaf necessarily a free ride. When "secret shoppers" from Consumer Reports tested a total of thirty-six cups of decaffeinated coffee from Burger King, Dunkin' Donuts, McDonald's, Seattle's Best Coffee, 7-Eleven, and Starbucks sites near the magazine's suburban New York City headquarters in November 2007—all the cups ranging from ten to twelve ounces—the Starbucks cup had 21 milligrams of caffeine, one of the highest levels.
Sure, a hot drink—and image—isn't all that customers get. Their money pays rent on an armchair, a table, a bathroom, and free WiFi for several hours. Starbucks prides itself as well on teaching customers about the intricacies of brewing and types of coffee, if they're interested. Is $3.20 a lot to fork up for this? Maybe not if you have a steady paycheck, even as a construction worker or a cop. Certainly not if you're a lawyer or an investment banker. Among the diverse crowds that frequent Starbucks, no doubt many have the means. According to the Wall Street firm Morgan Stanley, in 2011 the average Starbucks customer earned over $75,000 a year. On the other hand, for Michael Gates Gill, ironically, right before he got hired at Starbucks, "a latte was becoming a luxury I could no longer afford." And the four-dollar latte has become the ultimate symbol of frivolous spending in virtually every retirement-advice article and book. If you skip one latte a day, that's nearly $120 per month, and starting at age twenty-two and investing that $120 in an IRA allocated 85 percent in stocks and 15 percent in bonds—why, by age sixty-five, you'd have over $300,000. Now is it worth the cost?
THE QUESTION: Does Starbucks deserve its reputation as an exemplar of ethical chic?
THE VERDICT: A lukewarm yes
There are two essential facts about Starbucks:
Its premise depends on making an everyday object expensive, even intimidating, and on encouraging consumers to be pretentious.
However, people don't go there only for the coffee. They go because the chain offers a community service that our government has failed to provide—a safe, inviting, all-weather public commons (with bathrooms).
I consider the second premise socially responsible and the first one the antithesis of social responsibility.
Howard Schultz probably sees both parts—and more—as socially responsible. In his view, he has given ordinary people a high-quality product plus a bit of romance, a bit of Italy, or at least an inviting place where they can take a break in their everyday lives, and for an Italian vacation it's certainly a bargain. Then don't forget the employee health insurance and the fair trade beans.
There's nothing wrong with making premium-quality coffee (or Nike sneakers) for those willing to pay. Even devotees of the not-Starbucks places told me they appreciate that Starbucks had brought the concept of gourmet coffee to the hinterland, paving the way for their little cafés. Nevertheless, I think it's stretching the definition to call that socially responsible. Culturally ennobling, maybe. Would you call Prada socially responsible for making a really good-quality, imported shoe for sophisticated consumers?
In fact, it is socially irresponsible for Starbucks to claim the ethical mantle while pricing out people who can't afford its wares—or even worse, as the financial advisers warn, siphoning off money that should go to more important uses. And it is patronizing to say that ordinary Joes can feel just as sophisticated as rich folks by drinking expensive joe. Even Schultz seems to be taking a step backward from the Italianate pretension. In his second book, he claimed that "for some customers, Starbucks is an aspirational brand or even a token of pride, but the latter is an unintended effect of what we originally set out to do." Yet take another look at his first justification for Il Giornale: "We would enchant customers with an atmosphere of sophistication and style and knowledge." Aspiration wasn't an "unintended side effect" back then.
Of course, price isn't the sole consideration in bestowing the ethical mantle on a business, but Starbucks's record in other aspects is similarly mixed. On the good side, its employee benefits are truly pioneering, and the consensus seems to be that, for what it is—a quick-serve eatery—the working conditions are better than most. The corporate interest in environmental issues, worker benefits, and fair trade seems to be genuine and long standing, perhaps dating back to Schultz's early inspirations from JFK, the Peace Corps, and his own father's struggles. On the so-so side, the company is obviously making some efforts to buy fair trade coffee and help struggling farmers, but there also seems to be a certain amount of hype, a willingness to let consumers believe that a lot more of the coffee is fair trade than it really is. And on the so-what side, in an era when even the hated Walmart is investigating renewable energy and pressuring its suppliers, Starbucks's measly steps to reduce energy and water use are simply par for the course.
Correction: Regarding eco-issues, Starbucks is making things worse.
With its huge market clout, it is hurting the environment by selling water bottles and automatically handing out paper cups. Would it be so hard to keep ceramic mugs under the counter and make it part of the baristas' routine to ask customers whether they're staying or going? They wouldn't even have to learn any fancy new words.
In short, Starbucks is a better-than-average company with a high-quality product that has changed the world. Not a bad epitaph. Still, I'd prefer to give my money to Café Regular or Gorilla or Grumpy or one of the other small fry that are undoubtedly having a much harder time staying in business—if they use ceramic mugs.
4. Apple: The Coolest of Them All
Is any brand in the world more cool, more hip, or more cutting edge in melding technology and design than Apple? Do any other computers look like works of art? Has any top executive, besides Apple's Steve Jobs, ever worn a black mock turtleneck and jeans?
Business managers have BlackBerrys. Artists, students, professors, techies, and other people you'd want to know have iPhones. Everyone has an iPod—or two or three or six. Apple users adore their Macs. PC users curse their Dell and HP clunkers.
Well, if Apple is cool, and I use Apple products, then I must be cool. And conversely, since I'm socially responsible—I recycle and I eat organic food and I care about animals—and I use Apple products, then obviously Apple must also be socially responsible.
Uh. . . .
"Apple has a very current, leading-edge brand—a drive to innovate," said Climate Counts's Wood Turner. "It's willing to change the way we engage with music and media and movies. So the consumer has always believed that the company must be environmentally and socially responsible as well. But it didn't follow. It hasn't been meeting the same bar that other companies in the [electronics] sector were." Similarly, Adam Kanzer, the general counsel at Domini, mused, "I think the perception of the brand for a long time was that this is a company that does the right thing. Apple carries that aura. But when you dig into it, we started to have some questions."
In fact, the Apple orchard isn't nearly as ethically well stocked as many people assume. Apple has historically been less environmentally responsible, less worker friendly, and much less open than other tech companies and merely average in the conditions at its overseas plants, even as it has been more beloved by the public. Nor do activists expect that corporate emphasis to change significantly now that Jobs has died. But here's the hopeful part: starting around 2005, even while Jobs was still alive and in charge, the company, concerned about its poor image, began paying more attention to environmental and sweatshop problems. And if there's one thing Apple knows, it's image.
Although the history of Apple has been widely told, a brief recap is needed to dig beneath the myths.
First, the company didn't start in Steve Jobs's garage. It started in his Silicon Valley bedroom in 1976 and then moved to the garage. And Jobs was not a tech whiz. The brains behind the earliest Apple technology was the "other" Steve, cofounder Steve Wozniak.
Jobs and Wozniak were both loners and geeks, introduced by a mutual friend when Jobs was thirteen and Wozniak was eighteen. They each stumbled around college, not graduating, eventually working at some of the Valley's earliest tech companies—video-game maker Atari (Jobs) and Hewlett-Packard Company (both).
The pair started Apple because Jobs thought they could parlay Wozniak's tinkering with phones and crude computers into something bigger. Their first order came from a local store, the Byte Shop. Jobs negotiated the deal, based on the hardware designed by Woz (as he is often known). Jobs also dreamed up the corporate name, probably in honor of some friends' apple farm in Oregon. (Whether the name was stolen from the Beatles' recording label has been one aspect of back-and-forth lawsuits since 1978.) And that was the pattern that would largely continue throughout Apple's existence: someone else designed the hardcore technology, while Jobs (sometimes disastrously, but usually brilliantly) handled the business negotiations, dreamed the long-range dreams, and crafted the image—until, eventually, he became the image.
Jobs "believed the computer was eventually going to become a consumer product. That was an outrageous idea back in the early 1980s," when computers were for corporations or really nerdy hobbyists, recalled John Sculley, the PepsiCo executive who in 1983 was hired as Apple's CEO and president, in an interview with Bloomberg Businessweek in October 2010. Nevertheless, the weird little company grew. A follow-up computer, the Apple II, was a huge success. Apple pulled itself into corporate shape, got funding from banks and venture capitalists, wrote a formal business plan, hired a professional president, and finally, in December 1980, began selling stock to the public.
Almost immediately thereafter, troubles hit. IBM Corp., which until then had focused on business clients, invaded Apple's turf in personal computers with all its 800-pound-gorilla muscle. A next-generation product, the Lisa, was a market failure. So was the Apple III. Several dozen employees were laid off, and some shaky projects were killed. With Woz on an indefinite leave of absence after a near-fatal plane crash, many questioned whether Apple could rebound.
Enter the Macintosh, lightweight and easy to use, and the answer seemed to be yes. The Mac was introduced with perhaps the most famous commercial in history even to this day, the 1984-themed Super Bowl spot, which evoked George Orwell's dystopian novel, with the Mac in the guise of an attractive blonde runner challenging IBM-as-Big Brother.
Yet a year later, in 1985, Jobs was essentially fired by his own company. Despite all the hype, Mac sales had faltered. It turned out that the first models had very little software. Jobs had miscalculated, devoting a bloated staff to his pet project, overestimating potential demand, and saddling the company with a mound of unsold inventory. In the second quarter of 1985, Apple suffered its first loss. Moreover, the management situation was tense and unsustainable. Although Jobs had wanted to be president, the board, back in 1983, had hesitated at naming a flaky twenty-eight-year-old—even a flaky twenty-eight-year-old genius who had cofounded the company—and brought in Sculley from Pepsi. Jobs was technically just running the Mac project and thus reporting to Sculley. However, Jobs was also chairman, and therefore Sculley's boss. After the Mac fiasco, the board yanked all of his operating roles, offering Jobs a face-saving title, "product visionary"—whatever that was. Jobs tried to charm and manipulate his way back to power, then finally took his multimillion-dollar marbles and left to form another computer company, called (with typically quirky Valley spelling) NeXT.
From the mid-1980s to the mid-1990s, without either of the founding Steves, Apple continued to stumble while IBM and Microsoft charged ahead. Its market share plummeted to a measly 8 percent from 20 percent. No products seemed to catch the public imagination. One CEO after another came and went. Red ink flowed. Bankruptcy was a real possibility. For that matter, NeXT wasn't doing too well, either, and Jobs had gambled a good part of his Apple fortune on a struggling company that did computer animation for movies, called Pixar.
Now, part two of the legend begins: Jobs the genius steps in to save all three companies. Seeing the potential in Pixar, he poured in the resources to keep it alive until the first full-length movie using its technology, Toy Story, could bound into theaters and emerge a blockbuster. The Apple board, in 1997, begged him to return, buying NeXT in the process. He coyly came back as "interim" CEO, finally admitting the obvious and becoming full CEO in 2000.
Over the next decade, everything Apple and Jobs touched turned to gold. Even more important, they changed the world.
The new era started with the iMac, which Jobs launched almost the minute he arrived. The iMac didn't look like a computer. It was cute, rounded, and translucent blue. Nor did it act like most computers; amazingly, it had no floppy disks and no external hard drive, instead cramming circuits, modems, plugs, monitor, and everything else into that cute blue plastic case. It was a forerunner of what Apple would stand for: Style. Simplicity. Radical innovation. Fun. And for only $1,300.
Moreover, according to the book Apple Confidential 2.0, by Owen W. Linzmayer, a poll by the research firm Audits and Surveys showed that 29.4 percent of iMac buyers had never owned a computer before. Apple truly had turned computers into a product for the mass market, not just for nerds.
Still, different as it was, the iMac was a computer. The real Apple revolution began with iTunes and the iPod, expanding the company beyond computers into technology that would take over every aspect of even nontech consumers' lives.
Steve Jobs didn't invent the concept of downloading music from CDs to play on computers or portable devices, of course; MP3 and Napster had already done that, illegally. But Apple made it easy, widespread, beautiful, and legal. Most crucially, the company negotiated deals with the five major music producers for the rights to their products at an affordable price through its iTunes Store. And how to play that music? With typical Jobs micromanagement and flair, Apple designed the lightweight, sleek iPod in what would become trademark Apple white. Later, it added an online music-storage-and-syncing service. Ten years after the iPod's launch in 2001, there is still no rival.
The third of the big iProducts was the iPhone. Again, the idea of a mobile phone that does more than make calls didn't originate at Apple. The stolid business executive's BlackBerry was already on the market, along with offerings from Nokia, Palm, and Sony Ericsson. And BlackBerry would continue to dominate even after the iPhone arrived in 2007. However, BlackBerry was the brand corporate managers forced their employees to use. The iPhone was what younger, more creative, more daring, cooler people chose of their own accord.
With the next innovation, the iPad, observers at first were skeptical. What did it do that an iPhone, an iPod touch, or a laptop didn't do already? And hadn't its forerunner tablet, Apple's Newton, been a much-mocked failure in the 1990s? As Newsweek tech columnist Daniel Lyons wrote at the official product unveiling in February 2010, "Jobs and his team kept using words like 'breakthrough' and 'magical,' but the iPad is neither, at least not right now." To make matters worse, the name sounded like a brand of sanitary napkin.
However, by the time the thing actually hit the market, two months after Lyons's column, the standard Apple adoration had kicked in. Novelist-screenwriter-actor Stephen Fry, in an April 2010 cover story for Time, couldn't stop drooling, comparing using the tablet to "one's relationship with a person or an animal" and "like a gun lobbyist's rifle: the only way you will take it from me is to prise it from my cold, dead hands." The night before it officially went on sale, fans lined up outside Apple Stores in New York City and San Francisco, willing to camp out all night or longer to be sure to bag their gadgets and apps. That initial day, more than 300,000 iPads were swept off the shelves. By November, Time had declared it one of the "50 Best Inventions of the Year." Rivals like BlackBerry, as well as Acer, Amazon, Barnes & Noble, HP, and Samsung, were months behind. Even before some of them hit the market, the next-generation iPad was released—and it sold out in major cities and online within hours.
Barely a dozen years after Jobs rode to the rescue, the once-upon-a-time laggard of the computer industry was now the undisputed champ of both the tech and hip cultures, bigger than Microsoft in terms of market capitalization, more profitable than IBM, the largest business other than an oil company in the world. It was so huge that in 2011, the Nasdaq 100 index actually had to reduce its share of the total weighting, because any blip in its sales or profits tilted the index too much. British prime minister David Cameron and his iPad were "inseparable," as Time put it; Russian president Dmitri A. Medvedev flaunted his iPhone and iPad. Everyone except the family of Microsoft cofounder Bill Gates, apparently, has an iPod. (At least Melinda Gates, Bill's wife, claimed in an interview with the New York Times Magazine in October 2010 that her household was iPod-free.)
True, it's tough to stay number one in all areas forever. Google's Android operating system overtook the iPhone in 2010, and its $12.5 billion purchase of Motorola's cell phone business the following year put its smartphone power on steroids. Microsoft—finally—learned about marketing, launching its Windows 7 in 2009 with ads that challenged Apple for hipness. On the other hand, Apple is constantly branching into new fields and adding updates; at the same time that Google and Microsoft were beefing up, Apple put out an improved version of its middling TV device and won an important victory that will inhibit Android. Even with growing competition, it has, by a long shot, more smartphone applications than anyone. Each iteration of the iPhone immediately sells out. And no gadget maker—never, nowhere, nohow—makes products as beautiful, as easy to use, or as beloved.
In short, the story of Apple has everything you'd want in a heroic myth: David versus Goliath. Near-death and resurrection. Beautiful heroine (or products). Brilliant young hero-genius, misunderstood by the common world, who dares to challenge the status quo. And, apparently, a happy ending.
Until the hero is struck down at the height of his powers.
If there's a myth, then there must be true believers. This is not the same thing as having a huge customer base. Apple has that base, as the range of buyers from the Kremlin to 10 Downing Street proves; but so do Walmart and Toyota and, yes, Microsoft. What Apple also has are fans whose homes, cars, and offices are stocked with every version of the brand's merchandise, who read magazines and follow blogs solely about the company, who wait in long lines to grab each new product as it comes out.
Fast Company magazine, in July 2010, dubbed Apple "the Coolest Company Anywhere," citing, in part, the "religious fervor among its adherents." The iPod is virtually a character in Arthur Phillips's 2009 novel This Song Is You. Apple was one of just nine companies, people, or other entities that met the strict criteria for being "premier" cults as defined by consultants Matthew W. Ragas and Bolivar J. Bueno in their book about cult branding. (The rest were Harley-Davidson, musician Jimmy Buffett, the Linux operating system, Oprah Winfrey, Star Trek, Vans shoes, Volkswagen, and World Wrestling Entertainment.) This devotion can go beyond a desire for mere physical products. "The real Apple believers see some sort of 'I'm in touch with the universe' thing, that 'my computer is spiritual,'" claimed David Eiswert, a stock analyst who manages T. Rowe Price's global technology fund. (When I interviewed him in October 2009, Apple comprised 5.5 percent of the $350 million fund, the largest single holding.) Some branding consultants studied the brain activity of Apple users through functional magnetic resonance imaging and found amazing similarities to the way the subjects' brains responded to images of rosary beads and the pope or to the proximity of a girlfriend.
To meet such true believers, go to Macworld, the annual convention of Apple customers and vendors. Even in a year like 2010—when Steve Jobs, although still alive, didn't attend—more than 30,000 devotees poured into San Francisco's Moscone Center. Many of them had taken time off from work and were paying with their own hard-earned cash, $195 to $1,595 apiece in registration fees alone (depending on how many events they wanted to access), plus hotel, food, transportation, and other travel costs. I talked with people from Chicago and Las Vegas, from Arizona and Minnesota, and from throughout the length of California. They were mostly white but of all ages, sporting styles from polyester to pierced noses. There were couples with babies and local high school students; would-be iPhone app sellers and IT geeks; teachers and graphic designers; and at least one yoga instructor, one archaeology professor, one US Navy welder, and one Greek Orthodox priest. Only one of more than a dozen I interviewed thought she might go to a similar conference for another company's products. Consider some of them:
Mary Lee and her husband have a PowerBook G4, an iPhone, a Mac Pro, two Apple TVs, and an assortment of Mac computers in their Chicago home. "It's more than just a company that makes products that I buy," said the forty-one-year-old Lee, an IT assistant. "I feel some kind of connection to the company. I feel happy when they do well."
George Van Houton, age sixty-two, an electronics technician from Las Vegas, was at his tenth Macworld. "You see products you wouldn't be aware of" otherwise, he said. With three iPods, a Mac Pro, two Mac minis, and countless other Macs at home, he was eyeballing an iPod touch and more memory for his Mac Pro. "Why do rock fans go to a rock concert? Macworld is my version of Woodstock."
John Swayze, a forty-five-year-old welding-program manager for the Navy, likes Apple products because they're easy to use: he should know, since he and his family own seven iPods, an iMac, a laptop, and a PowerBook. He had driven the five hundred miles from San Diego to every Macworld since 2001, making a whole extended-family vacation of it with his kids, brother, nephews, nieces, and other relatives.
Leo Gesday, forty-six, manages a consumer-electronics store and had been at all the Macworlds save one since they began in 1985. "There's nothing so pervasive in my life as the products from Apple"—a laptop, a Mac mini, an iMac, an iPhone, and four iPods.
I found the same kind of devotion among people waiting overnight for the inaugural iPads in New York City. At 9 P.M., twelve hours before the gadget officially went on sale, there were already about twenty people in line, with sleeping bags and folding chairs, including a half dozen who had preordered and were thus guaranteed one no matter how late they came by, but who wanted accessories or the shared experience of an Apple all-nighter. Dean Vassallo, a twenty-seven-year-old systems engineer from Long Island, was among the latter. He had taken the day off work, arriving at around noon—but that was nothing. For the first iPhone, he had camped out for two days. "I've owned almost every single product Apple has come out with since before Steve Jobs came back," he said. "Apple is in a class of their own. They're magical devices."
Woodstock. Magical. Can you imagine standing in line nearly twenty-four hours to pick up something you've already reserved? Can you imagine being happy when your washing machine company does well?
Experts use a lot of jewelry analogies when talking about Apple. The iPod "likens itself to a watch and pendant," said Michael Myers, the advertising veteran from upstate New York. For Michael Tchong, a technology-trends consultant who founded the trade journal MacWeek and ran it from 1987 to 1991, "Tiffany comes to mind. There are so many tiny details [in the iPhone], like the elegant little drop shadows around the lettering."
Even when Apple messes up, fans blame themselves, or the store where they bought the item, or United Parcel Service, or Microsoft, or the weather—anyone except Apple. For instance, the iPhone got so popular by late 2009 that all those millions of Americans texting, downloading, video streaming, Web surfing, and talking overwhelmed the network of its sole carrier at the time, AT&T. Particularly in New York City and San Francisco, calls and other services were dropped and delayed.
And? AT&T took the blame. "People are still buying iPhones," T. Rowe Price's David Eiswert said at the height of the turmoil. "But people don't like AT&T's network." Many customers were waiting for AT&T's exclusive contract to end in early 2011; however, after Apple added Verizon, that carrier, too, warned of undercapacity.
It was harder, in June 2010, for Apple to dodge a different case of dropped calls and other reception trouble with the iPhone 4. For a while, the company tried to dismiss the situation as an old software bug that simply displayed the wrong number of reception bars or even say it was the customer's fault for holding the phone wrong. Finally, in July, when venerable Consumer Reports said that it couldn't recommend the phone because of a hardware flaw with the antenna, Apple conceded that it had a problem. Sort of. Jobs held a rare news conference at corporate headquarters to admit that there was an antenna issue and to temporarily offer free bumpers that would wrap around the rim of the phone, which seemed to improve the reception. "We are human, and we make mistakes sometimes," he said. Then he promptly went on to claim that other smartphones had the same flaw, iPhone complaints were rare, the media were exaggerating, and the iPhone is the greatest phone in the world anyway.
And? Customers rushed out to buy more iPhones. Less than a week after the mea culpa press conference, there was a three-week wait for the gadgets. Apple has "created that community, so no one cares," said branding expert Robert Passikoff. "That's the beauty of getting the benefit of the doubt." Steve Wozniak himself can't figure it out. "Apple has a community, millions of people who love its products. I don't know why it's loved," he admitted when I met him at a conference in 2010.
It's not just the products that are the object of Apple fans' devotion. So is Steve Jobs.
No wonder, really. A guy rated one of "The World's Most Influential People" by Time in 2010, called one of "27 Brave Thinkers" by the Atlantic in 2009 and one of just 21 in 2011, listed under "Revolutionaries"—not merely zillionaires—in the 2009 Forbes "400 Richest People in America" roster, even hailed as "CEO of the Decade" by Fortune in 2009. The book Apple Confidential 2.0 describes the reaction at the 2000 Macworld, when Jobs announced that he would be the permanent CEO: "The Mac faithful that filled San Francisco's Moscone Center rose to their feet, chanting, 'Steve! Steve! Steve!'" There were similar frenzies when he introduced the Mac in 1984 and when he came back to Apple from exile in 1997. Stephen Fry—the writer-actor who drooled over the iPad in Time—offered that "I have met five British Prime Ministers, two American Presidents, Nelson Mandela, Michael Jackson, and the Queen. My hour with Steve Jobs certainly made me more nervous than any of those encounters."
So when Jobs got a rare form of pancreatic cancer in 2004, then inexplicably lost weight and took a mysterious health leave in 2009, followed by a liver transplant, and again in early 2011 announced that he was taking another indefinite leave of absence to deal with medical issues, terror coursed through the Apple world. What if he didn't . . . ? The thought was too horrible to contemplate. The stock price gyrated with each medical report, shooting up after the liver transplant, plunging briefly at the news of the 2011 medical leave, rising smartly again when Jobs interrupted his 2011 leave to introduce, in person, a new version of the iPad. At his first news conference upon returning to work after the transplant, employees and even journalists (journalists?) gave Jobs a standing ovation.
Then, in late August 2011, the first unthinkable happened: Apple announced that Jobs was stepping down as CEO, to be replaced by Chief Operating Officer Timothy D. Cook—although Jobs would presumably keep a lot of fingers on the keyboard as chairman of the board.
The universe shook: The announcement led the news at the Wall Street Journal and other newspapers; hundreds of thousands of messages were posted on Twitter and elsewhere, fans flocked to Apple stores in a kind of makeshift wake, and the stock slid more than 5 percent in after-hours trading. The New York Times called him "the da Vinci of our time."
Things calmed down within a couple of days. The stock picked up nicely; after all, the company's product line was strong, and it had some $76 billion in cash to cushion any problems. The experts' consensus was that there were enough Jobs-created gizmos in the pipeline to carry the karma another two or three years, and Jobs would still be sort-of around as chairman, but a key issue was how many other people would leave. The headlines faded, replaced by a hurricane on the East Coast and the ongoing fall of Libyan dictator Muammar Qaddafi.
Still, the Apple world was holding its breath. "If Wall Street says, 'Jobs is gone, so Apple is dying,' then it loses the hipness," Northwestern University's Richard Honack suggested. From Wall Street, T. Rowe Price's David Eiswert was a bit reassuring, on the Street's unique terms. "Apple has built a culture and philosophy that's bigger than Jobs," he said. "The stock will go down, but it's a buying opportunity."
Less than two months later came the even-more-dreaded follow-up blow: Jobs died of complications from his cancer. There could be no more fantasies that he might still hover over the shoulders of Apple designers.
Now the tributes were even more intense. His photo was splashed on the covers of magazines ranging from the New Yorker to People to the Economist to Rolling Stone, while Bloomberg Businessweek, Fortune, and Newsweek each devoted an entire issue to tributes to him. President Barack Obama hailed him as one of "the greatest of American innovators." The State of California declared an official Steve Jobs Day.
Although Jobs was still CEO when I went to Macworld, I had asked the attendees about the dire possibility. They weren't about to dump their iPhones and PowerBooks if Jobs were to leave—"The Apple products would have to get really bad, or Microsoft would have to get really good," Ann Pfaff-Doss, a retired graphic designer, told me—but they would definitely be nervous. "When he's there, I'm more reassured that things are going to go in the right direction," said Jeffrey Boerner, a graduate student in math at the University of Iowa who had written some iPhone apps and who had come to the conference with his wife and mother.
Of course, there's nothing ethically wrong with selling products that people love. And consumer and political movements often rely on building a sense of community, seen in groups like food co-ops and MoveOn.org. So, why does the Apple fan club make a lot of activists nervous?
Perhaps it's because they worry that love and community can too easily edge into blind devotion—when community risks becoming a cult. And there are hints of cultism in the way no one seemed to blame the company for the iPhone problems in 2009 and 2010, in the Jobsmania, in the loving comparisons to Tiffany and jewels, and, most troubling, in the company's extreme secrecy.
Jobs and his spokespeople were coy—verging on outright lying—about his second medical scare. When they couldn't hide his severe weight loss any longer, they initially claimed that he was suffering from a "hormone imbalance," then conceded only that he was taking time off because, as Jobs put it, his "health-related issues are more complex than I originally thought." The third medical leave, too, followed months of mysterious weight loss and was announced in a terse, six-sentence e-mail sent to Apple staff on a federal holiday, Martin Luther King Jr. Day, when many employees and reporters were presumably not working. Jobs didn't return journalists' phone calls. While he certainly had a right to medical privacy, that didn't include a right to lie, especially when so many people thought the company's fortunes—and maybe the value of their stock holdings, their paychecks, or the warranties on their products—were directly tied to his heartbeat.
When I wrote an article in 2009 about the company's lagging environmental policies for the website Portfolio.com—details on that topic follow a little further in this chapter—and again for this book, the company never responded to my repeated requests for an interview. OK, that happens with reporters all the time. Then, the minute my environmental article posted online, a press person called to complain that I hadn't said enough about the good things Apple is doing. That, too, happens regularly. Now, here's the weird Apple twist: the press person said I was not allowed to quote her, nor would she let me talk to anyone else at the company. What's the point of complaining to the press if you don't want the public to hear your side?
The obsessive secrecy has grown worse over time. Michael Tchong told me that when he was in charge of MacWeek during the non-Jobs years, from 1987 to 1991, "people would come to our booth at trade shows and tell us if it weren't for us, they wouldn't know what was going on. People would get fired if they talked to us. [Members of Apple management] were checking phone records, checking for our number in San Francisco." Still, Tchong and his writers were able to glean some information "because it wasn't as insane as it is today. I could not publish MacWeek today." The book iCon, by Jeffrey S. Young and William L. Simon, picks up the story from there, saying that after Jobs returned he instituted "an absolute ban on talking to anyone outside the company who uses words as a tool of his trade," with limited exceptions. That remark proved more prescient and ironic than the authors could have foreseen: presumably annoyed that it couldn't control what was being written in that book, Apple removed all titles published by iCon's publisher, John Wiley & Sons, from Apple Stores—even though this particular book ends up quite positive about Jobs. (Conflict-of-interest alert: I guess the Apple Store ban would include four of my books, which were published by Wiley or a firm subsequently acquired by Wiley.)
In spring 2010, an unfortunate employee accidentally left a prototype of the not-yet-released iPhone 4 in a Silicon Valley bar. As news reports later revealed, another customer found it and sold it to the tech blog Gizmodo, which then posted photos and a story. Although Gizmodo returned the phone, as the company requested, Apple immediately filed a criminal complaint, and the next thing anyone knew, the county sheriff's office had raided the home of the Gizmodo blogger who'd written the post. It took more than a year before the local district attorney finally announced that he wouldn't be filing charges against the blogger.
Apple's secrecy is internal as well. Multiple articles have been written about the oversight systems, ID badges, numeric-code door locks, and security cameras. New-product R&D is as shrouded as nuclear weapons development in Iran. The New York Times reported in June 2009, "Some Apple workers in the most critical product-testing rooms must cover up devices with black cloaks when they are working on them, and turn on a red warning light when devices are unmasked." According to iCon, when the iPod was under development, "Steve was manic about leaks, so each unit was sealed in a separate reinforced plastic box, much larger than the actual unit—closer to the size of a shoe box. Wires for the controls were strung to random spots on the exterior of the box. On some, the scroll wheel was on the side, for example, and the screen on the top; anyone looking at the box would have no idea how the controls were placed on the actual unit."
Sure, no company likes bad publicity, no company agrees to every media request, and many companies insist that a PR person be present at all interviews. To a certain degree, secrecy is even a standard business tactic. The hush-hush build-up to a product launch can—so executives hope—create a sense of drama and then stoke demand. Apple, however, takes these common uses of secrecy too far.
And when it comes to social responsibility, extreme secrecy may be the single most anti-responsible quality a business could have, because without information, how can activists know whether a company really is providing decent working conditions, cutting back on energy use, or undertaking any of the other efforts considered responsible? That's why "report" is one of the four areas Climate Counts measures when it analyzes companies' efforts to reduce emissions, asking questions like, "Is the company publicly reporting on emissions, risks, and actions?" And why union officials like Mark Levinson insist that outside organizations need to monitor overseas sweatshops and then issue detailed descriptions. The consumer movement began, in part, with a demand for information, such as data about the pollutants that local businesses were discharging into the air and water. Nor is it socially responsible to treat your employees like potential spies.
Openness is especially important to investors, and not just ESG types. The foundation of the modern financial industry is full and fair disclosure, the concept that everyone has access to the same information at the same time. Particularly with such a leader-driven company, investors during Jobs's long illness needed to know more than "Steve is still the CEO." For instance, how much was he actually working? Who was being groomed as a successor? "Apple would benefit from Jobs giving more of the limelight to the best talents," suggested Jeffrey Sonnenfeld, a senior associate dean at the Yale School of Management, in an article in Newsweek soon after the 2011 medical leave was announced and before Jobs stepped down. Even one member of the Apple board—Jerome B. York, a former top finance officer at IBM and Chrysler, who died in 2010—criticized the company in 2009 for being so tight-lipped regarding Jobs's health, according to the Wall Street Journal. An official at the giant California Public Employees' Retirement System pension fund (CalPERS) was quoted in another Wall Street Journal piece saying that the federal Securities and Exchange Commission should require all companies to disclose more information about a chief executive's serious illness. The commission briefly investigated whether Apple's corporate disclosure had been sufficient but took no action.
Brushing aside such advice, Apple management beat back a shareholder resolution in early 2011 that would have required it to disclose its succession planning, claiming that would give rivals an unfair advantage; nevertheless, the resolution garnered 30 percent of the stockholders' votes, which is an amazing figure considering that resolutions not proposed by management usually disappear unseen.
"A company that considers itself progressive shouldn't resist transparency of reporting," said the ICCR's Laura Berry. "Apple tends to be resistant to the whole idea of anyone outside of Apple telling them what to do." Her group of religious investor-activists filed a shareholder resolution in 2009, also opposed by management, pushing Apple to be more open about its sustainability efforts and attracted an impressive 8 percent yes vote. As You Sow's Conrad MacKerron gave the example of companies that install a code of conduct for overseas sweatshops: "You can have a code of conduct in place, but unless you can show us how it's being carried out, we can't know the companies are rigorously enforcing it. Like everything else, the devil is in the details."
Lack of information was consistently a key factor dragging down Apple's scores in Greenpeace's Guide to Greener Electronics, an industry ranking, as well as, until recently, Climate Counts's lists. "Disclosure has probably not been their strength, compared to their competitors," said Casey Harrell, a coordinator for Greenpeace's global electronics campaign. MacKerron said that Dell and HP publicized lots of details about worker-injury rates, energy efficiency, greenhouse-gas-emissions goals, and corporate philanthropy; Apple was silent. Students and Scholars Against Corporate Misbehavior, an organization in Hong Kong that investigates working conditions, found HP more open to monitoring groups, according to Jeff Ballinger, the antisweatshop activist.
The only privacy Apple seems to ignore is that of its customers. A transatlantic furor erupted in spring 2011 over the discovery that iPhones, iPads, and Google products were secretly collecting information on users' locations. Although the data were supposedly anonymous, to be used for targeted ads and geography-based services, Steve Jobs was forced to leave his sickbed and admit that the project was mishandled.
The obsession with control—and its ethical implications—also plays out in Apple's basic business philosophy. Under the dominance of Microsoft, and spurred by the Internet, technology has long thrived via widespread sharing. Any computer maker can install Windows. Anyone with a browser can surf the Web. But Apple historically hasn't shared.
It provides almost everything itself: the hardware, the software, and the doorway to content. Because it controls the spigot, the company can control what flows through the spigot. Notoriously, it has refused to allow certain political or pornographic material, often without explanation, including an app with cartoons about golf superstar Tiger Woods, another mocking President Obama, and one by a Republican challenger to California Congress member Henry A. Waxman—although, in fairness, it later relented on the last two. When Apple released its first guidelines for its App Store in September 2010, supposedly to clarify the rules, some of the standards remained vague and micromanaging: "Apps that are not very useful or do not provide any lasting entertainment value may be rejected" and no apps will be allowed if they look like they were "cobbled together in a few days." To avoid potential hitches, Playboy removed most of the photos from its iPad version. (Playboy without the centerfold?)
Business strategists could reasonably debate the effectiveness of this approach. Apple claims that if it doesn't control every step, it can't be sure that outside contributors meet the superhigh quality standards for which it is famous. But from an ethical standpoint, this strategy is wrong. In fact, there's a well-known word for it: censorship.
Trillium Asset Management—which runs about $900 million in ESG investments for churches, endowments, foundations, nonprofit organizations, and individuals, including shares in Apple—wrote to Apple in late 2009 asking "why and what you're doing to avoid making political determinations" in vetting apps, according to Jonas Kron, deputy director for shareholder advocacy at the firm. "It's an opaque process," he added in an interview. "They're the gatekeeper, and it puts them at the forefront of issues relating to freedom of speech and expression and association and privacy."
"Buy into the World According to Steve, and you're making a Faustian bargain," warned Daniel Lyons, the Newsweek tech columnist and a longtime critic of the Apple model. "You sacrifice freedom for the sake of a lovely device that (mostly) works just the way it's supposed to."
Even fans are starting to grumble. While they may adore Apple's quality, innovation, stylishness, ease of use, and former CEO, they're the ones who aren't getting the Playboy centerfolds or Tiger Woods cartoons. "Rejections from the Apple Store should only be for very obvious, glaring reasons," John Gruber, who writes the blog Daring Fireball, devoted to Apple issues—and who usually loves the company—said at Macworld. "It should only be about quality control, not content control. That's one of the lines they've crossed that rubs people the wrong way."
In any case, the wall may be cracking. Between summer 2009 and summer 2010, according to news reports, the US Department of Justice and the Federal Trade Commission launched investigations into whether Apple was blocking various sorts of outside content, while the Library of Congress ruled against the company in another blocking case and European and US regulators, in 2011, began looking into possible antitrust issues with Apple's subscription requirements for the iPad dating to September 2010. Apple caved a bit by issuing the App Store guidelines and relaxing its requirements for outside applications for the iPhone and the iPad, even allowing long-banned Adobe some limited access. Moreover, as powerful players like Google, Microsoft, and Motorola bring out smartphones and tablets with features and prices as good as or better than the iPhone's and the iPad's, Apple will be ruling a smaller and smaller piece of turf.
Other than the ultrasecurity and black cloaks, working at Apple is, more or less, like the cliché of working anywhere in Silicon Valley. Devotion, excitement, and adrenaline. Ping-Pong and stock options, but long hours. Creativity and independence—as long as Steve Jobs didn't interfere. For that matter, it's the same kind of passionate commitment I found when I interviewed veteran employees of the pharmaceutical maker Merck & Company for my book The Merck Druggernaut, as they described the glory days of the mid-1980s to mid-1990s, when Merck was discovering one groundbreaking medicine after another.
At Apple, "it wasn't just a job," recalled Kristina Woolsey, who was a senior engineer, director of a multimedia lab, and an HR official from 1985 to 1998. "It was a calling or a fascination or a passion. It became a way of life. People had a common vision in terms of wanting to change the computing environment." Her sentiment was shared by Kris Lawley, a senior service manager in the Austin, Texas, office who has spent more than two decades at Apple. "You work hard on a project, and then it ends and you take a vacation," Lawley said. "And then you plunge in again." In a rare inside look at the place, Fortune, in 2011, quoted a former designer this way: "If you're a diehard Apple geek, it's magical. But it's also a really tough place to work."
Employees have some flexibility in choosing which hours they work. "You could take the afternoon off and go see a movie, as long as you're there the core hours" of 11 A.M. to 4 P.M., said Lawley's mother, Gail, who recently retired as a quality-control manager in Tucson. The famous Silicon Valley perks were available: Kris Lawley mentioned Ping-Pong, Nerf guns, and nap rooms; at the Cupertino headquarters, said Woolsey, "they set up an incredible cafeteria," with everything from health food to pizza. Woolsey even nursed her infant daughter at the office.
However, Fortune claimed that "the vibe is the opposite of the jocularity that Google—with its wear-your-pajamas-to-work day and all-you-can-eat cafeterias—has fostered." If so, that may stem at least in part from the secrecy and micromanaging. At the Apple Store, according to the Wall Street Journal, employees are given a detailed script for almost every interaction with customers. Certainly, it was no picnic to answer to Steve Jobs, who could stalk into a lab and tear up a design or demand an impossible change at the drop of a chip. Some of Gail Lawley's colleagues left as soon as he returned in 1997, she said, "because they didn't want to work with him." Authors Jeffrey Young and William Simons, in iCon, described how employees tried to avoid the boss: "You didn't want to encounter him in a hallway, because he might not like an answer you gave. . . . And you sure as hell didn't want to get trapped on an elevator with him, because by the time the doors opened, you might not have a job."
Janet Gray Hayes didn't work for Jobs, but she sometimes had to work with him when she was the mayor of San Jose—the biggest city near Apple headquarters—from 1975 to 1983. One time when he came to her office, "he lay on my table, like he was the center of the universe," she sniffed in an interview with me, years later. More diplomatically, Kristina Woolsey offered, "He manages to the product. He doesn't manage [in order] to be a nice guy." But she never felt he was looking over her shoulder, she added.
Moreover, not everyone gets the same perks. The initial Mac developers directly under Jobs famously were a privileged group, with cars, video games, their own basketball court, subsidized babysitters, and free massages. Other employees resented those deals, but then again, the Mac team resented the non-Mac staff's higher pay. When Apple first went public by selling stock in 1980, and again with Pixar's initial public offering, some longtime colleagues were inexplicably left out or got a measly allocation of shares, according to the books iCon and Apple Confidential 2.0.
Labor expert Christian Weller is a bit skeptical about the perks but sympathetic on the whole to the workplace style. Things like Ping-Pong are "flim-flam," he scoffed. "When people move into their thirties, a Ping-Pong table becomes a lot less important, and health care and work-flex rules become more important." In that sense, he added, "one place where Silicon Valley companies tend to be very good is giving workers plenty of flexibility in the hours they work."
To its credit, Apple has not been a major actor in the tech industry's biggest workplace controversy, the use of "permatemps"—long-term contract employees who work almost identical jobs and hours as full-timers yet are denied benefits. Microsoft, by contrast, had to pay a $97 million settlement in a class-action lawsuit in 2005.
In another crucial way, however, Apple is worse than the rest of Silicon Valley. Microsoft, Google, IBM, HP, and other rivals regularly appear on Fortune magazine's "Best Companies to Work For" list. Apple has never been seen there (although it was included in a 1984 book by the same journalists who compile the Fortune project). What's wrong with Apple? Since companies must proactively apply, it's possible Apple wouldn't even deign to ask a magazine to judge it. Or, it's possible that the staff actually doesn't like working there. Because the editors of the list won't discuss why companies don't qualify, we'll never know.
Domini's Steven Lydenberg offered a historical explanation for Apple's omission from the "best" lists. In the early days, he said, "it had a reputation for being a great place to work, better than any other Silicon Valley place. It had AIDS education in the workplace and a big community volunteerism program; it was good on diversity issues." Then the revenues and stock collapsed, and "all the socially responsible programs were understandably set to one side, and they just concentrated on getting their business model and getting back on line," he suggested. (Apple constitutes about 3 percent of Domini's $1 billion holdings.)
It's still too soon to tell how much the atmosphere may change under the new CEO, Tim Cook. Descriptions of him emphasize his skill at operations and efficiency, which may sound a lot more boring than inventing the iPod but could also mean a more grueling working environment without much time for Ping-Pong. Cook is also described as intense and a workaholic—no change from Jobs there. On the optimistic side, he is considered calmer and more polite than his predecessor. In any case, it's probably safe to assume that Jobs's handpicked successor is no flower child.
Stressful as the milieu at headquarters might be, matters are far worse, of course, in the developing-world factories where Apple products are manufactured. In fairness, Apple is hardly the only company outsourcing. Everything we use nowadays seems to be made in sweatshops in China or in other desperately poor locales like Bangladesh, El Salvador, Honduras, and Vietnam. Tech factories like Apple's can be especially dangerous because of the lead, beryllium, and other toxic materials that go into a computer or iPhone. And don't expect the facilities always to provide safety gloves or masks. But again, to be fair to Apple, the whole electronics industry "was kind of late to the game in terms of dealing with overseas-labor issues," trailing the apparel industry, according to Adam Kanzer, the general counsel at Domini.
Even with those caveats, Apple was a step behind the rest of the Valley. Dell, HP, and IBM cofounded the Electronic Industry Citizenship Coalition (EICC) in 2004 and crafted a code of conduct for monitoring working conditions in the supply chain, but Apple didn't join until 2006.
According to Kanzer, in 2004, Domini began writing to Jobs about the factory conditions, emphasizing an angle that the investment firm figured would appeal to the image-conscious CEO. "They have such a strong base of young consumers who probably care about these issues more than most," as Kanzer put it. "This could have a significant impact on the company. What if people found out something like, children were making iPods?" Domini followed up with a shareholder resolution seeking a corporate code of conduct for the supply chain and a system of monitoring and reporting. Perhaps the threat of looking like an ugly capitalist got Apple's attention, or perhaps it was the $21.5 million worth of its stock Domini holds; in any case, Apple said it would consider the ideas. Then negotiations dragged on for a year and a half. Domini agreed to withdraw its resolution if Apple adopted a code, Apple missed the deadline for doing so, and Domini refiled the resolution. Drafts went back and forth. Finally, in November 2005, Apple adopted a code.
True to Apple's modus operandi, when it finally came out with a product—in this case, a code of conduct—it was arguably the best on the market. One key area involves freedom of association and union activity, which too many codes omit. The EICC version requires participating members "to respect the rights of workers as established by local law to associate freely on a voluntary basis, seek representation, join or be represented by Works Councils, and join or not join labor unions and bargain collectively." Apple's is more pointed in placing similar freedom-of-association requirements on suppliers—not just on itself—and in specifying that suppliers may not fire or refuse to hire people because of union membership. Moreover, within four years, Apple had audited 288 supplier factories, cutting ties with 3 that hired underage workers—and, perhaps most amazing, issuing public annual reports on its suppliers. "I was impressed how quickly the company got up to speed," Kanzer said.
Apple soon had a test of its intentions. Barely six months after its code was adopted, a British newspaper published an investigation of iPod factories in China run by the subcontractor Foxconn Technology, charging, among other things, that people worked fifteen hours a day for less than $50 a month and were housed in crowded dormitories, forced to work overtime, guarded by armed police, and punished harshly.
It took Apple a mere two months to investigate and post a detailed report on its website. According to that report, its audit team "interviewed over 100 randomly selected employees" and "visited and inspected factory floors, dormitories, dining halls, and recreation areas," as well as reviewing "thousands of documents." The upshot was fairly tame. Apple claimed that "we found the supplier to be in compliance in the majority of the areas audited," including "no evidence whatsoever of the use of child labor or any form of forced labor." However, the company-that-never-apologizes did concede a few "violations to our Code of Conduct," most notably that "employees worked longer hours than permitted" by the code. The report additionally cited "impersonal" and crowded conditions at three dorms—ah, trust Apple to notice the decor!—and a pay structure that "was unnecessarily complex." To remedy these problems, Apple hired the respected outside monitoring firm Verité.
Scandal struck Foxconn and Apple again four years later. A dozen young Chinese workers at two Foxconn plants committed suicide in winter and spring 2010, most of them dramatically by leaping from corporate dorms. Tens of thousands of other unhappy workers had quit, charging long hours, low pay, military-style drills, forced overtime, verbal abuse, and harsh punishments. This time, Apple wasn't alone; Foxconn made products for Dell, HP, and others as well. By summer, as the headlines raced around the world, several of the tech giants promised to investigate. Apple sent an inspection team led by Tim Cook (not yet the CEO) that interviewed, by its own count, more than one thousand workers. Foxconn denied that its working conditions had any connection to the suicides but nevertheless responded by doubling salaries, setting up a twenty-four-hour counseling center, and installing yards of netting.
In China, sadly, tales of horrible workplaces don't end. Six months after the Foxconn controversy seemed to die down, Apple acknowledged that some 137 laborers at another subcontractor, Wintek, had suffered nerve damage, weakness, headaches, dizziness, and other serious injuries from a toxic chemical used in manufacturing iPhone screens in 2009. Apple claimed it had ordered Wintek to stop using the chemical and to improve safety and said it would monitor conditions. Wintek said almost everyone had recovered, but employees told the New York Times that they had never heard from Apple, even as the subcontractor was pressuring them to quit, take cash settlements, and shut up. Students and Scholars Against Corporate Misbehavior, the Hong Kong advocacy group, also accused Apple of dragging its feet.
The area where Apple should do best—and disappoints most—is the environment. For a lot of reasons, the tech industry is usually a star of the green world. "The electronics sector, since Day One, has had the highest average scores of any sectors" in the Climate Counts ranking of large companies' carbon-emissions policies, said Wood Turner, the organization's former executive director. As he explained it, "People that are early adopters of technology are typically the leading edge of thinking on issues, whether it be the gadget they're using or how business should be focusing on sustainability." Similarly, Greenpeace's Casey Harrell opined that "you've got a much younger industry that's built around a lot of means of innovation. Comparatively, they're relatively green." Three of the top four companies cited by Ceres (the group that reports on business sustainability efforts) are tech companies. So were the first three—and six of the first nine—of Newsweek's "100 Greenest Companies in America" in 2010, and three of the top five in 2011.
But not Apple.
The company didn't make Newsweek's 2009 and 2011 lists at all and came in at a paltry Number 65 in 2010. It consistently ranks at the bottom of Climate Counts's twelve names in its industry. When IBM, Nokia, and Sony, among others, formed the Eco-Patent Commons in 2008 to share new environmental ideas, Apple was AWOL. It has refused to join Ceres, despite years of discussions. "Apple was one of the personal-computer companies that was later to the table in terms of allowing recycling of older computers," said the ICCR's Laura Berry. As noted by As You Sow's Conrad MacKerron, Dell and HP are more open about disclosing goals for all sorts of environmental issues, such as emissions cuts, energy efficiency, reduced packaging, and greener packaging, and Greenpeace specifically targeted Apple in a special consumer campaign called Green My Apple in 2006.
This is not the image people expect of Apple. Not the Apple where former US vice president Al Gore—winner of the Nobel Peace Prize and an Academy Award for his global-warming film An Inconvenient Truth—sits on the board. Consider the name, with its evocation of nature, trees, organic fruit, and the precursor farm owned by Jobs's friends. "A lot of people think Apple is an environmental leader just because it's Apple and it's a cool company," said Conrad MacKerron with a sigh. "When you scratch below the surface, I would not say they are an environmental leader."
Along with many activists, MacKerron suspects that Apple's culture has gotten in the way. The secrecy and insistence on handling everything itself make it harder for environmental advocates to figure out exactly what Apple is doing. "A lot of companies would have given a nod to shareholders on those issues, saying, 'We've been glad to work with our partners' [to fix environmental problems]," suggested Trillium's Jonas Kron. "Apple didn't see the shareholders as useful partners." Even worse, Wood Turner, of Climate Counts, worries that Apple's obsession with being the hippest, most innovative guy on the block could keep it from being the most ethical guy on the block. "They have to be first, and once they're not the first, I think they fight tooth and nail against being pressured into doing anything," he said. So, if all of its tech rivals are already recycling old computers or pressuring their suppliers to reduce packaging, Apple certainly isn't going to copy them, no matter how much better that would be for the environment.
Of course, the reverse could be true. It might be that Apple is doing a lot more than the critics realize, but because Apple keeps it hidden, nobody knows.
And in other ways, Apple's culture works both for and against greenness. The tendency toward minimalist design and packaging means that fewer ingredients need to be mined to create the gadgets, less is dumped in a landfill at the end, and less energy is consumed in manufacturing and shipping. That's the good part. However, all those efforts are undermined by the imperative to constantly produce newer, more innovative versions of whatever is already on the market. Each time the next iPhone or iPod comes out, fans must have it. How much energy and how many resources are used up in that serially speedy obsolescence? And what happens to the outdated models?
The situation began improving around 2006. Perhaps Apple wasn't immune to the shareholder resolutions, poor rankings, and comparisons with hated rivals. Conrad MacKerron's group, for instance, finally managed to meet with Al Gore and (it took a year longer to arrange) with Jobs. In October 2009, Apple, along with a handful of lesser-known companies like California utility PG&E, dramatically quit the US Chamber of Commerce to protest the chamber's foot dragging on climate change. And in 2011, it was one of only twenty-five companies, out of the nearly one hundred ranked by Climate Counts, to get an extra gold star for supporting mandatory federal action on carbon emissions.
Environmentalists said they have even noticed a greater willingness by Apple to share information. In some cases, it's now an industry leader, rather than a follower. The corporate website has product-by-product environmental statistics, including greenhouse gas emissions in kilograms and power consumption for various operating modes. Greenpeace's Casey Harrell particularly praised the company for educating suppliers about less toxic alternatives. "They did a lot of the early-adapter costs," he said. "They pulled the rest of the industry along." It was the first company to stop using lead-containing monitors, a pioneer in banning glass containing arsenic, and at least a year ahead of HP and Dell in getting rid of toxic PVCs. Neither Harrell nor other activists expect Tim Cook to alter this trend, in part because Cook and Jobs both said as much.
The Apple PR person who wouldn't let me quote her (so I'll paraphrase) emphasized three areas where, she asserted, my Portfolio.com article hadn't given the company enough green credit: detailed environmental reports about each product; elimination of brominated flame retardants, PVCs, mercury, and other toxic ingredients; and measurement of the emissions when people use the products, in addition to the emissions from manufacturing and corporate headquarters. Moreover, she claimed that the company had been doing some of this for years. As a result of these efforts, and more, Apple jumped a whopping forty-one points on Climate Counts's ranking from 2008 to 2009. It briefly flew up six notches on the Greenpeace guide in January 2010, from eleventh to a five-way tie for fifth out of seventeen, then dropped four places the following October, and then shot back up to fourth in November 2011.
Yet Apple's efforts start from such a low point that it still has a long way to go. It remains the worst-ranking electronics company on Climate Counts's list.
Secrecy continues to drag down its Greenpeace rankings. "Apple would score more points on the other criteria with greater transparency of its data" regarding suppliers' emissions and use of dangerous chemicals, the November 2011 report said. On the Climate Counts chart, the worst ratings come in the most important category, that of setting goals and actually doing something to reduce emissions—as opposed to simply mouthing off about federal mandates and such. Moreover, as the ICCR's Laura Berry and Climate Counts's Wood Turner mentioned, Apple lags rival big tech firms in enabling customers to return old computers for recycling.
(The issue of recycling is separate from the problem of obtaining the tantalum, coltan, tin, tungsten, and other minerals that are vital components of tech products like cell phones. Many of these are dug up in habitats of endangered animals or war zones controlled by vicious militia leaders, or else mined in ways that pollute the environment. In this controversy, Apple shines no brighter—but no worse—than any other manufacturer. It says it is seeking to ensure that its raw materials don't come from regions with human rights abuses or in the midst of fighting.)
A major dispute centers on how to measure emissions. The company argues that customer usage must be included because the gases emitted after an iPhone, MacBook, or anything else leaves the Apple Store—taking it home, manufacturing the battery or providing the electricity that powers it, disposing of it—account for 46 percent of the total carbon footprint. Jobs, in a rare interview that may indicate how important this topic suddenly became to the company, told BusinessWeek in October 2009 that measuring emissions without including the end user is "like asking a cigarette company how green their office is." He added, "A lot of companies publish how green their building is, but it doesn't matter if you're shipping millions of power-hungry products with toxic chemicals in them." Apple may want to include this part of the emissions trail because it claims its gizmos are the most energy-efficient in the world, as detailed on the website. And the company knows this, the unquotable spokesperson said, because it microanalyzes even down to the level of how much power goes into each keystroke.
Activists like MacKerron and Turner are skeptical about this whole argument. First, they question whether product usage really has such a significant greenhouse impact. By Apple's own figures, after all, the nonconsumer aspects like manufacturing and transportation from the factory to the store are responsible for 54 percent of the emissions. "Extraction of raw materials, design, production, a vast distribution network, retail stores—there's a huge amount of energy that goes into getting that product into the consumer's hands," Turner said. "How much are you pressuring your supply chain [to reduce this energy consumption]?" There have been contradictory studies of whether reading something electronically is greener than using old-fashioned paper, but even if it is, skeptics don't necessarily buy Apple's assertion that its electronic products are the greenest. And finally, even if all of Apple's claims are true, customer usage is one area the company really doesn't control. Maybe fans love its products so much that they use them more than they would use clunky PCs and BlackBerrys, in which case Apple is actually increasing total emissions.
Ideally, Apple could leverage its customers' devotion to really move the industry. Greenpeace aimed to do exactly that with its international Green My Apple campaign, beginning in 2006. The environmental group found Apple users by going to Mac trade shows and reaching out online "through the echo chamber that is the Mac fan world," as Casey Harrell put it. It directed them to a special website, where users were asked to design an Apple ad campaign that would emphasize environmental topics. Greenpeace stepped carefully, knowing the fans' feelings. "Our campaign wasn't, 'Apple, you're horrible.' Our campaign was, 'Apple, you're great, but we want you green,'" Harrell recalled. For instance, the home page said, "We love Apple. Apple knows more about 'clean' design than anybody, right? So why do Macs, iPods, iBooks, and the rest of their product range contain hazardous substances that other companies have abandoned?" Customers were thrilled at the chance to design an ad for their idol, Harrell said, and the campaign ended up with thousands of submissions. (He conceded that there was also "a subsegment of the population that said, 'Piss off, Greenpeace, Apple can do no wrong.'")
Did the campaign work? Naturally, Harrell said yes. But so did Jobs, in the BusinessWeek interview. At any rate, it was around that time that Apple began to change.
And why did Greenpeace choose to target Apple instead of Dell or Motorola or Sony? Partly because of the fan base. Partly because it was a laggard. And, Harrell said, because "we hoped it will have a domino effect on the rest of the industry."
Maybe critics are defining "social responsibility" too narrowly.
When describing Apple's efforts in classically CSR areas like overseas sweatshops or green initiatives, Domini's Steve Lydenberg used cautious terms like "incrementally" and "satisfactory" and "phasing in, in an orderly manner," and he admitted that the company had taken "what I would not necessarily call a leadership role." Nevertheless, his ethical-investing firm has taken a $21.5 million bite of that Apple. So what makes it a socially responsible investment? "We value innovation and customer quality and service, and Apple has always been a true leader in that area," Lydenberg explained. "We look for innovations that are related to access." In particular, he cited mobile phones, the Internet, and computers in general as technologies that have "had a tremendously empowering and economically positive effect in the developing world."
Journalist Chrystia Freeland made a similar point in a 2011 cover story in the Atlantic about what she called the global superelite. She distinguished techno-zillionaires like Jobs (and Bill Gates), who built their fortunes on "advances that have broadly benefited the nation and the world," from "TARP-recipient bankers," who took federal bailout money in the Troubled Asset Relief Program during the 2008 financial crisis.
Certainly, there are many uplifting stories of schools in Africa, Asia, and Latin America that are able to run solar-powered laptops or of impoverished farmers who have established cell phone networks to market their produce and crafts. Even some American schools have found that students focus better if they get their assignments via iPad. One iPad app helps children who have cerebral palsy. The Iranians who took to the streets in June 2009 to protest their country's stolen presidential election used cell phones to organize and send information to the outside world, and undoubtedly many of those were iPhones. The same goes for the Facebook- and Twitter-wielding protestors in Tunisia and Egypt who brought down their authoritarian governments in 2011. If all that is CSR, Apple clearly fits.
It's not only political protesters and impoverished farmers who benefit sociopolitically from Apple technology. In an era of information aggregation and Web surfing, experts ranging from New York Times media columnist David Carr to Unilever's chief marketing officer to Walter Isaacson, author of the only authorized biography of Steve Jobs, have predicted that the iPad may be the innovation that will keep books, magazines, and newspapers alive (no small matter for this author and freelance writer). Perhaps the $4.99 copy of the New Yorker on the iPad is the middle ground between the $5.99 print edition and free downloads to a computer or a smartphone, allowing readers the convenience of e-versions while still funneling some income to the publishers and authors. (And if the first-round prices for tablet editions were too close to the print ones and if publishers didn't like Apple's subscription terms, those are basically problems of monopoly and technology that competition and more tech can solve; indeed, pressure from publishers forced Apple to alter its subscription policies within less than a year.) The iPad is easier to read than a smartphone, the picture quality is better than on a computer, and the pages look identical to the hard copy. Probably most important to publishers in the long run, the tablet offers the kind of flexibility that the digital world demands, including interactive ads, multimedia links, and ways to measure consumer viewing of ads.
Condé Nast, for one, decided the iPad made it worthwhile to revive its defunct magazine Gourmet, albeit as a mobile app, not the original publication. Rupert Murdoch even created a brand-new newspaper, the Daily, specifically for that platform. As for e-books, publishers hoped that Apple, by breaking Amazon's Kindle monopoly, would give them pricing leverage down the road, even if the publishers' and authors' royalties were actually lower at the beginning. In fact, one day after the iPad was introduced, Macmillan Publishing forced Amazon to raise its e-book prices by threatening to pull its titles (and, presumably, transfer to Apple). True, competition from Google and Barnes & Noble could accomplish those same goals—but Apple was first.
But speaking of old-fashioned virtues like reading: whatever happened to the concept of walking down the street or in a park, noticing the people around you, smelling the flowers, listening to the birds, letting your mind daydream, or thinking deep thoughts? No time for that anymore, because we're plugged into our iPods 24/7. Steve Jobs and Apple have a lot to answer for in that destruction of social responsibility.
When it comes to more mundane aspects of community service, ironically, Apple seems far less polished. Outside of a few standard-issue gestures, like donating a portion of the proceeds from specific iPod and iTunes purchases to fighting AIDS in Africa, it's not particularly known for its philanthropy. According to a long analysis by noted New York Times business writer Andrew Ross Sorkin—in the same 2011 article in which he called Jobs "the da Vinci of our time"—Apple doesn't even do standard big-company actions like matching employees' charitable donations, and Jobs shut down the existing philanthropic programs when he returned in 1997. Furthermore, Sorkin pointed out, Jobs didn't join fellow famous moguls Bill Gates and Warren Buffett in the Giving Pledge, in which superwealthy families promise to give away at least half of their fortunes. Nor did his cancer turn Jobs into a public advocate for health issues. In fairness, of course, he and Apple could have been handing out a ton of money anonymously.
Apple has been busier on the political side. Since 1998, it's been steadily increasing its profile and now is "a significant lobbying force," according to Dave Levinthal, who until 2011 was the spokesperson for the Center for Responsive Politics, the nonpartisan research group that's considered the best source for this sort of data. By 2008, the company was spending $1.71 million on nineteen lobbyists, including, said Levinthal, "some very high-powered" outside firms. It's been a bit stingier with campaign donations, but by 2008 it reached number 16 in the tech industry. (That was obviously a busy year for Apple.) Nearly 90 percent of the money goes to Democrats. Jobs and his wife, Laurene, were major Democratic Party donors for years, and Laurene was even a delegate to the Democratic National Convention in 2000. Among specific beneficiaries, the Human Rights Campaign's Eric Bloem praised the company for being one of the few to give money in 2008—that same busy year—to defeat Proposition 8, a constitutional amendment in California banning same-sex marriage. (The measure passed anyway.)
The scorecard on shareholder governance issues—the G in ESG—is fairly weak, perhaps because governance by its very nature means being open to pressure from outsiders, in this case shareholders. Rubber-stamp though the process usually is, management does have to bring resolutions and board elections to a public vote, while shareholders get the opportunity to bring up their own issues. Remember all those resolutions and threatened resolutions about Apple's environmental initiatives and the global supply chain? Another popular activist target is the board membership and the process of electing it, since directors throughout the corporate world are notoriously cozy with their CEOs. CalPERS, the giant California pension fund, managed—against Apple management's opposition—to push through a resolution in February 2011 changing the rules so that directors running unopposed couldn't simply assume reelection; they would actually have to win a majority of the votes. On any board, gender and racial diversity makes a symbolic statement to activists, and Apple's lack of both long bothered ESG investors like the ICCR and Domini. Apple didn't get its first nonwhite or nonmale board member until 2008, when it managed a twofer by appointing Andrea Jung, the chair and chief executive of Avon Products.
Cost has always been the big rap against Apple, because its high price tags discriminate against lower-income people. "They are the product of choice of elite, preppy Ivy Leaguers who have the money to afford the price," Sally Greenberg of the National Consumers League asserted.
But look again at those issues of quality and service Steven Lydenberg mentioned. Apple desktops, in a Consumer Reports survey of 62,500 users between 2005 and 2009, required the fewest repairs among seven leading brands. Putting aside the antenna problem with the iPhone 4, "Apple has been at or near the top consistently" in Consumer Reports computer rankings, according to a spokesperson. David Eiswert, the T. Rowe Price portfolio manager, compared the 12-inch MacBook Pro ($1,200, when we spoke) with an equivalent PC (maybe $750). "With MacPro, you get ease of software, iMovie and iPhoto, and a seven-hour battery. That's what people want," he said. "It would take you an hour just to install the software in the PC." The computers famously get hit by far fewer viruses than Windows-using rivals (although that may be due less to Apple antivirus wizardry than to virus mongers' calculation that its single-digit market share isn't worth attacking).
Plus, Apple customers and noncustomers alike have access to more than three hundred beautiful, airy, glass-and-steel Apple Stores, where they can use the restrooms, the display Macs, and the WiFi, no purchase necessary. Best of all are the stores' Genius Bars, whose technicians will answer almost any question and fix almost any problem at no cost. Compare that with what most tech companies offer: a call center somewhere in Mumbai or Bangalore, or no live voices at all, just computerized answering services or websites that never return messages.
The price issue may finally have gotten to Apple. By 2011, it was mulling a cheaper version of the iPhone, and the iPad sold at a lower cost than rivals for its first year. (More likely, however, the iPhone move was spurred by the competition from Google, not CSR guilt, and the iPad was no doubt partly subsidized by fat profits from all the other pricey gizmos.)
For true believers, all this microanalysis is beside the point. They know that Apple is socially responsible, because—well, because Al Gore is on the board, and Gandhi was in the 1997 "Think Different" ad campaign, and all the cool people they know use Apple products. "It's equated with California, and California is organic food and driving a Prius," Michael Tchong, the former MacWeek publisher (and former California resident), said with a laugh.
The people I met at Macworld didn't spend much time fretting about the company's social responsibility. Jeffrey Boerner, the grad student from Iowa, was vaguely aware that Apple was taking some steps on recycling. His wife, Nora, accepted the company's claims about its environmental efforts at face value, because, as she put it, "I do believe they are the leader in so many ways."
"It's not the compelling thing for me," said Lynn Goldstein, a fifty-nine-year-old archaeology professor at Michigan State University. "The compelling issue is how easy it is for me to do the things I do" on Apple products.
THE QUESTION: Does Apple deserve its reputation as an exemplar of ethical chic?
THE VERDICT: Inching closer to yes
Because its image of social responsibility is so much more glowing than Apple deserves, the first temptation is to issue a flat-out negative verdict. And that would have been accurate in the early 2000s. Today, however, any analysis has to be a combination of maybes, yes-buts, and back-and-forths.
For instance, the company deserves recognition for the improvements it has made on the environmental and sweatshop fronts, even if the green ones don't go far enough. In some ways, it's ahead of its peers, and in some ways behind. That's OK, but can a company be hailed as socially responsible if it's average? And how much credit should it get if the action was forced on it by public pressure? For a company to be truly ethical, CSR concerns should be built into the corporate culture. The purchasing manager shouldn't even have to ask whether to buy recycled or virgin-tree paper.
Another yes-but involves working conditions. While Apple isn't the most nurturing place to work, prospective employees either buy into the pressured creativity, or they don't have to apply. It can be invigorating to work ninety hours a week when you feel as though you are changing the world. Still, can a company be considered socially responsible if employees live in mortal terror of a mercurial and micromanaging CEO? In this case, the answer will now depend on our evolving insight into the new CEO.
Steven Lydenberg, Chrystia Freeland, and David Eiswert have a point in saying that it's socially responsible to help the public—to expand access and communication, to go overboard in making products easy to use, and to offer prompt help. That may be the most unsung value of all. Yet is that CSR, or just good business?
Maybe most important, there is the question of corporate soul. The secrecy. The self-satisfaction. The obsessive need for control. Can any company really be socially responsible if it's so secretive that no one can be sure whether it's even doing the socially responsible things it claims? This trait is particularly troubling if Apple is arbitrarily rejecting apps for the iPad and iPhone because of their content, whether political, pornographic, or otherwise. While government investigations, competition, and public protest seem to be eroding some of the micromanagement at the edges, the changes are not hitting the core. Even worse, they are not self-motivated. Apple doesn't really want to change.
Will things be different now that Steve Jobs is no longer around to smother the corporate culture with his personality, paranoia, and whims? Here's one reason for hope: because Tim Cook does not start out with Jobs's cultlike following, he will need to nurture goodwill, love, respect, and adoration. It may be easier to accomplish that by actually talking to reporters, investors, activists, and customers. Moreover, Andrea Matwyshyn, a professor of legal studies and business ethics at the University of Pennsylvania's Wharton School, predicted that, as is often the case when a strong founding leader leaves, the company is more likely to be run by a team leadership, and a team pretty much requires some communication. Indeed, a whole bevy of executives, not a solo Jobs, was hauled before reporters to announce the iPhone 4S, just one day before Jobs died.
Now, here are all the reasons not to hope: the New York Times, Newsweek, and other publications regularly describe Cook with words such as "intensely private," and Cook and Apple both clammed up, Jobs-like, about the former CEO's health every time he took a medical leave. Apple also refused to make Cook available to the press when Jobs made his farewell announcement. Besides, why should Apple change its culture? It's worked at least since Jobs returned in 1997.
As long as the pixie dust holds out.
5. Trader Joe's: Are We Having Fun Yet?
If you bring your own shopping bags, a cashier in a navy-and-white flowered shirt told the customer ahead of me in line, you can enter your name in a lottery.
"What's the lottery prize?" I butted in.
"A cryogenic chamber," deadpanned the cashier.
When I gave him a skeptical glance, the cashier laughed. He was an athletic-looking blond, maybe in his twenties. "A twenty-five-dollar gift certificate and a Trader Joe's bag," he amended.
"But I wouldn't need a bag, because I brought my own," I pointed out. "That's how I'd get in the lottery."
"Yeah, Joe didn't think about that. But he's still a nice guy."
Shopping at Trader Joe's is like that. The employees will slip into easygoing conversations at the drop of an organic banana. And if there are no organic bananas, there may be Formosa papaya, heirloom leaf lettuce, six types of pita bread, nine varieties of mushrooms, seven kinds of feta cheese, free-range organic chicken, no-antibiotic/vegetarian-fed chicken, and minimally raised chicken. Plastered on the walls are nautical and South Sea knickknacks such as surfboards, fake-bamboo picture frames, and Polynesian masks, plus perky sayings written on wooden signs. By the lettuce bin: "The fact 'Romaines,' TJ's has unbeatable prices on salad! 'Lettuce' be your go-tos for greens." At the meat section: "You can 'butcher' bottom dollar that TJ's meat values are a 'cut' above the rest."
No one loves grocery shopping, not the way Paris Hilton might love cruising through the Sydney Michelle boutique. But people love Trader Joe's.
Before an outlet opened in New York City in 2006, Willa Edwards, a credit-collection clerk then in her mid-sixties, would take a one-hour bus ride from her Manhattan home once a month to get to the Trader Joe's in the Westchester suburbs. The New York Times found an even more devoted Brooklynite who regularly trekked five hours round-trip via train and bus in pursuit of the chain's egg rolls and minestrone.
Those bereft of a local Trader Joe's beg for one. The Times Union, in Albany, New York, in 2008 wrote about a group called We Want Trader Joe's in the Capital District—the Capital District is the region that encompasses Albany, the state capital—and reported that some locals "believe the Capital Region cannot become a center for technology or high-wage employment until it has stores like Whole Foods, Trader Joe's, and Nordstrom."
There are as many varieties of shoppers and reasons for shopping at Trader Joe's as there are types of feta cheese and mushrooms. My mother goes there, and so does my vegetarian cousin. According to a 2010 cover story in Fortune magazine, "[Y]oung Hollywood types like Jessica Alba are regularly photographed brandishing Trader Joe's shopping bags—but Supreme Court Justice Sonia Sotomayor reportedly is a fan too." Willa Edwards cited "the gourmet food," including honey-plantain strips, and the fact that the offerings are "natural, no MSG or any of that crap." Tatiana Boureau, a twentysomething dance student, likes the chain "because it's cheap," while Ronnie Worthen, a forty-nine-year-old corrections officer from Brooklyn, mentioned the assortment of nuts, berries, organic breads, and vegetables. I know one couple who go out of their way for the low-sodium lox. Anton Chatterji, an associate professor at Duke University's Fuqua School of Business, is happy to find prepared, ethnic-Indian food like chicken tandoori. It seems impossible to find anyone who doesn't love Trader Joe's.
But which Trader Joe's do these fans love?
"They didn't bill themselves as a socially responsible company, just a well-run company in the gourmet and natural business. Well run, and ethical."
—Tom Chappell, the Tom of Tom's of Maine, whose toothpaste is sold there
"A commercial version of the neighborhood store."
—Arthur Caplan, chair of the University of Pennsylvania's medical-ethics department
"A Tiki Room with Aisles of Discounts"
—the headline on the New York Times article when the first outlet opened in that city
"The corporate culture can be described as dorky."
—a different New York Times article by a different writer, ten days earlier
"They combine almost a warehouse-grocery experience, which on some level feels hip and green, with some unique foods."
—Michael Myers, president of the ad agency Palio Communications
"An offbeat, fun discovery zone."
—Fortune cover story, 2010
"They're not a supermarket; they're a specialty market."
—consumer-branding expert Robert Passikoff
"Your Neighborhood Grocery Store."
—the Trader Joe's website
The Rough Guide to Shopping with a Conscience essentially throws up its hands, saying that "[w]hether Trader Joe's, incidentally, is classified as a 'health food' store or 'specialist foods' retailer seems to vary according to what source you read."
Some basic facts appear to be undisputed: The chain specializes in unusual foods not available in standard supermarkets, often imported or at least with international-style names, and in particular, precooked frozen entrees that can be easily warmed up for a quick, gourmet-seeming dinner. A "tasting panel" scours the globe to bring back exciting new treats. The company stocks mainly its own private-label products, which, by and large, cost less than national brands. A few famous names are available, but Trader Joe's deliberately does not try to sell all things to all people—no diapers, no baby food, no Diet Coke. Where a typical grocery store might carry 30,000 to 50,000 SKUs (stock-keeping units—essentially, items), Trader Joe's could have a mere 4,000. The stores themselves are small by industry standards, with a decor variously described as Hawaiian, Polynesian, Tahitian, South Seas, nautical, and tropical kitsch, and a superfriendly staff. Beyond that, let's take a closer look at some of the popular images.
Image: "A well-run company in the gourmet and natural business" that "on some level feels hip and green"
For its 3,000 private-label goods, which constitute about 80 percent of the items on its shelves, Trader Joe's indeed sets stringent "natural" and "green" standards, including no trans fats, genetically modified ingredients, or artificial preservatives, colors, or flavors. A lot of the house products are fully organic, as are about half of the fruits and vegetables. Since 2005, all TJ's-brand eggs must be laid by cage-free hens—that is, hens not crammed into the horrendous cages of mainstream egg factories. According to PETA, Trader Joe's does not test its products on animals.
These promises apply solely to the specific Trader Joe's labels, however. The outside brands could well be full of chemicals or produced in inhumane ways. The Hebrew National hot dogs on Trader Joe's shelves contain sodium nitrite, which has been linked to cancer, as well as heapings of fat, saturated fat, and salt. Some non-TJ's eggs are laid by mistreated hens. "They could certainly do a lot more, as companies like Whole Foods have done," said the Humane Society's Michael Markarian. For instance, he'd like the chain to use roomier crates for pigs. It's also important to remember that when tasting-panel members scout out a perfect tiramisu on the coast of Italy, they're not focusing on whether it's organic or free of GMOs (genetically modified organisms). They simply want a mouth-watering dish that isn't available commercially in the United States.
(By the way, the shelves have more national brands than shoppers realize. Many products are actually made by big manufacturers like Kiss My Face and Tasty Bite, with a TJ's label slapped on.)
And some of the most well-known ethical requirements, including the GMO ban and the cage-free eggs, were instituted only after pressure from groups like Greenpeace and the Humane Society. Perhaps the nastiest food fight involved fish. According to Casson Trenor, a senior markets campaigner at Greenpeace who specializes in seafood, the Trader Joe's seafood section at one time was "appalling." It was selling species like orange roughy, Greenland halibut, Alaska pollock, Atlantic cod, South Atlantic albacore, and yellowfin tuna, all of which are endangered, at risk, or caught in environmentally damaging ways, Trenor said. (The respected Monterey Bay Aquarium Seafood Watch and Blue Ocean Institute seafood guide are a lot more forgiving, urging consumers to avoid orange roughy and some types of Atlantic cod and yellowfin tuna but permitting or not commenting on the rest of Trenor's list.)
While admirers said TJ's tuna was caught without nets, to protect dolphins, Trenor argued that the fishing process used a long-line network of thousands of hooks that could unintentionally snag endangered species, rather than the less-destructive, though less common, pole-and-line system, which has fewer hooks. Furthermore, Trenor accused the company of putting an "egregious" sign right above a pile of orange roughy proclaiming that "all of our seafood was caught in a sustainable and environmentally friendly manner." (Trader Joe's rarely talks to the press and declined to comment for this book.)
For eighteen months in 2008 and 2009, while Greenpeace pelted Trader Joe's officials with e-mails, phone messages, and surveys, the company "stonewalled us," Trenor claimed. So the environmental organization went public, urging shoppers to contact corporate headquarters in Monrovia (a town on the outskirts of Los Angeles), and briefly set up a website called Traitor Joe's. "Groups of people went up and down the West and East Coasts engaging with their customers and staff in front of different stores," according to Trenor.
Apparently, the pressure worked. In March 2010, Trader Joe's posted "A Note to our Customers" on its website declaring that "all of our seafood purchases will shift to sustainable sources by December 21, 2012." The company said, in fact, that it had already ceased selling orange roughy, Chilean sea bass, and red snapper. The announcement added that the company promised to work with "third-party, science-based organizations to establish definitions and parameters" for its sustainability goals and to include information on the seafood's procurement or production method in its policies.
OK, maybe the food isn't all pure. But doesn't Trader Joe's deserve green credit for rewarding customers who supply their own bags? That's one of the biggest issues among environmentalists, who point to the trees that are chopped down to become paper bags and the oil that's drilled to make plastic bags, which most shops—including Trader Joe's—blithely hand out. Yet, once again, Trader Joe's seemed to give a few eco-inches only after public pressure. The Rainforest Alliance, back in 2004, was planning demonstrations against some Trader Joe's branches because the grocer obtained its paper bags from Weyerhaeuser Company, which the Alliance and the Forest Stewardship Council had singled out for using particularly destructive lumbering methods. Then, Trader Joe's dropped Weyerhaeuser. The chain claimed that was purely for business reasons, to consolidate its paper bag purchasing nationwide.
In any case, Trader Joe's is not as ecologically progressive as Costco, which provides no packaging material at all except the empty cartons in which the food was delivered. San Francisco, Seattle, and other cities ban standard plastic bags completely at most grocery stores, while many supermarkets refund shoppers two cents for each bag they bring from home. As a final indication of how pale green Trader Joe's really is, the ethical-ranking website GoodGuide.com gave it a lousy score of 5.8, out of a possible 10, for environmental issues.
Image: "Your neighborhood grocery store"
Perhaps this was true back in 1958, when it all began. An entrepreneur named Joe Coulombe, four years out of business school, bought a small chain of three convenience stores near Los Angeles known as Pronto Markets. It was great timing: Southern California was at the beginning of its postwar boom, fed by Hollywood, sunshine, the federal highway system, and the aerospace industry. Pronto prospered.
Unfortunately for Coulombe, by the 1960s, the much bigger chain of 7-Eleven convenience stores had discovered California. To fight off the incursion, Pronto needed a gimmick. So in 1967, Coulombe reinvented his little company. It would be offbeat, off-price, and sophisticated. He scouted out overstocked and discontinued gourmet food items from manufacturers, distributors, and importers, then sold them at steep discounts. In addition, Coulombe redecorated, establishing a Polynesian decor and renaming the business Trader Joe's. The "Joe" part would seem to be in honor of himself. But why Polynesian? Len Lewis, a veteran trade journalist and author of a fawning book about the company, The Trader Joe's Adventure, cited a couple of common theories. "Legend has it that Coulombe was vacationing on a beach somewhere in the Caribbean, trying to figure out what to do about this new competition" from 7-Eleven. Or, "He also took inspiration from the novel Trader Horn"—written in 1927 by Alfred Aloysius Horn—"which chronicled the travels of a trader and adventurer in Equatorial Africa during the 19th century."
Over the years, Coulombe tweaked the product line, bringing in more organic food and starting the private labels in 1972. Yet the basic image remained. The chain added the brands Trader Ming's (for its Chinese food), Trader José's (Spanish), and Trader Giotto's (Italian). Things seemed to be going great. But in 1979, Coulombe sold the whole shebang to a reclusive German billionaire, Theo Albrecht, who along with his older brother, Karl, owned the Aldi discount-grocery chain in Europe.
Why he sold remains a big retail mystery, and the answer may never be known, since Coulombe shuns interviews. Money was presumably a motive, although the purchase price has not been publicly revealed. Coulombe could have been bored with the business, yet he stayed on for another decade. Maybe Albrecht wore him down. Various accounts have said that the German magnate pursued the purchase for two years.
With about two dozen stores at the time of the deal, all in Southern California, Trader Joe's was already too big to be "your neighborhood grocer." It might have been accurately described as a small regional chain, until that, too, changed. Gradually, it moved into Northern California, Arizona, Oregon, Washington, Nevada, and then cross-country in 1996 to Boston. By 2011, there were more than three hundred and fifty locations in thirty states plus the District of Columbia, from Maine to New Mexico, from Minnesota to South Carolina, with new branches constantly opening. If it's not as huge as Kroger Company, Safeway Inc., or, of course, Walmart, it's about the same size as, or maybe larger than, Whole Foods.
More broadly, Trader Joe's is part of a supersecretive, $68 billion global conglomerate, the eighth-largest retailer on Earth. Its owners, the Albrecht brothers, who divided Aldi in 1960, each qualified for Forbes magazine's ranking of the world's billionaires, until Theo died in 2010 at age eighty-eight. At that time, Bloomberg Businessweek reported that Theo had made just three confirmed public statements in his lifetime and that the last known photograph of either brother dated from the 1980s. (Understandably, Theo grew especially publicity shy after he was kidnapped and held for seventeen days in 1971.) Officials of the parent company, like those of the TJ's subsidiary, almost never grant interviews.
In keeping with the brothers' personal secrecy, the company is privately owned. There are plenty of pros and cons about private versus public ownership of a business, which will be discussed in more detail in chapter 7, but a key issue is that secrecy is the antithesis of social responsibility. Secrecy makes it impossible for shoppers to learn about the sourcing of the paper bags, tuna, eggs, chicken, or any other products unless management decides that it's in its own interest to reveal the information. Yes, Trader Joe's succumbed to the Greenpeace campaign about sustainable fish, but it would have been forced to reply—and perhaps change—a lot sooner if it had to face questions from shareholders at an annual meeting. If you go on the Trader Joe's website and read its timeline, you will learn when it put handles on its paper bags (1992). However, you would have no idea that it was ever sold to Theo Albrecht.
Then why does the little-old-general-store image stick? For a combination of genuine reasons (the limited selection and square footage) and phony ones (the corny signs). "It's a marvelous coup on their part to have created branding like that," Greenpeace's Casson Trenor said, "this company that feels like it's owned by a couple of surfers from San Diego, when in reality it's owned by a couple of octogenarian billionaires from Germany." (In fairness, he said this while he was still fighting over fish and at the height of his annoyance with the firm.)
After the Times Union ran its article about the Albany-area group begging for a Trader Joe's, an advocate for local shopping replied on the newspaper's blog that, while she loved the nuts, coffee, and olive oil, "I am under no illusions that this international corporation is my hometown neighborhood grocery store. . . . It is an international chain, trying to make lots of money for the home office in Germany."
Image: "A Tiki Room with Aisles of Discounts"
Producing and selling ethical products is almost always more expensive than doing things the standard way, as discussed in the introduction. Items are often handmade, rather than in bulk. Animals raised grass-fed, cage-free, or free-range need more space and more expensive feed than those in factory farms. Fair trade workers overseas are paid better than sweatshop wages.
Except, magically, for Trader Joe's.
One of the most common reasons customers give for shopping there is its low prices. Particularly famous is Two-Buck Chuck, the award-winning wine that sells in many TJ's outlets for a mere $1.99 per bottle. After all, discounting was an essential part of Joe Coulombe's gimmick for fighting off 7-Eleven, way back when.
This is one image that is, in fact, largely true. In Consumer Reports surveys in 2008 and 2009, Trader Joe's ranked as one of only eight and six (respectively) national chains that "gave our readers the biggest bang for the buck," as the magazine wrote in April 2008.
I tried to do some market-basket comparisons over a three-day period in October 2009 and a six-day period in December 2010, taking an actual basket around six stores within a three-and-a-half-mile radius: Whole Foods, Trader Joe's, my local food co-op, Costco, and two regular, regional chains: Key Food (in the New York City area) and Pathmark (Delaware, New Jersey, New York, and Pennsylvania). By definition, it was tough to find identical items to compare, since Trader Joe's prides itself on its unique lineup. Forget the canned vegetable soup, which I thought would be a staple; did I want Trader Joe's low-sodium minestrone? Organic vegetable and lentil? And don't even get me started on the eggs: Cage-free omega-1? Cage-free organic omega-3? Large organic free roaming? Cage-free large? Cage-free extra-large? Brown large cage-free? Brown large organic? Making matters even more difficult, most Trader Joe's fruit is sold either by the piece or in unit-priced bags, whereas other stores typically sell it per pound.
Still, I was able to pull together fifteen similar-enough items in a variety of food groups, and the result was that Trader Joe's was the cheapest in six categories and tied with Whole Foods in a seventh—the best showing of any contender. (The items were a pound of nonorganic baby carrots, a loaf of raisin bread, a six-ounce container of yogurt, an eleven-ounce package of Hebrew National hot dogs, barbecue-flavor potato chips, and organic Fuji apples and nonorganic Granny Smith apples, but only if you buy those last two in bags of two pounds and five pounds, respectively.) From all these comparisons, however, shoppers would have to subtract any double coupons and special discounts that rivals might offer, because Trader Joe's doesn't stoop to such measures.
To the degree that Trader Joe's genuinely keeps prices down, how does it manage? Part of the explanation is precisely that it doesn't sell only goods that are organic, pesticide-free, cage-free, and all those other socially responsible qualities that cost more to produce. Moreover, in many locations, especially the original ones, it saves on rent by seeking out-of-the-way sites, like mini-malls without big-name anchor tenants. The dearth of expensive national brands helps, too.
Moreover, the basic business model includes some inherent savings. If a store carries merely two brands of toothpaste or three brands of bar soap—and one of them is the house brand—rather than a dozen or more, as at a traditional big supermarket, then it's probably buying from just two or three suppliers. (Many manufacturers make more than one brand of the same type of product, so the number of brand names is a little misleading as a strict guide to the number of sources, but the essential principle holds.) Add to that the fact that by offering only a few choices, Trader Joe's is probably selling more of each choice than a traditional supermarket, even if that bigger market sells far more toothpaste tubes or soap bars per week in total. Thus, the odd little store probably has more clout per item and can exert more price pressure on each supplier. Then add one more factor: As much as possible, Trader Joe's sources directly from the manufacturer rather than via distributors, thereby avoiding extra distribution fees.
A double socially responsible area of savings is that Trader Joe's runs almost zero advertising. It's not spending its money trying to persuade customers to spend their money on things they don't need. Furthermore, according to the records of the Center for Responsive Politics, the chain apparently wastes very little on political contributions and lobbying. (It also, obviously, spends nothing on a PR department.)
Maybe it's skimping too much on its social responsibility. "Trader Joe's makes it crystal clear that it does not buy advertising, program space, or tickets to [charitable] events under any circumstances," Len Lewis wrote in his book. "It also does not underwrite any organization . . . or donate gift certificates . . . it is simply being practical and holding down unnecessary costs."
And take a second look at that beloved Two-Buck Chuck: the name comes from Charles F. Shaw, an investment banker who owned a vineyard that he sold to another vintner, who now produces the wine for Trader Joe's. According to The Trader Joe's Adventure, Shaw has publicly protested the use of his name on a cheap wine that, he said, unfairly competes with classier labels bottled by his friends. Other critics complain that the whole concept of discount wine has turned an art form into a commodity.
Image: "An offbeat, fun discovery zone" (for workers)
For a lot of objective reasons, Trader Joe's wouldn't seem to be a fun place to work. Len Lewis wrote that "to control labor costs, overall store payrolls are kept down by having a lower head count in each location per dollar of sales." That sounds like the notorious practice of speed-up, or pushing fewer workers to do extra tasks that should be shared by more people, without added pay—in other words, lousy working conditions.
Nor has the company apparently made it onto the major "Best Companies" rosters. Although Lewis claimed in his book that "Fortune magazine has consistently ranked the company among its 100 best places to work," I couldn't find a single mention of it in a search of the entire Fortune "Best Companies" database when I was given special access. Like most retailers, Trader Joe's might be at a disadvantage in these contests by following a business model that typically relies on part-timers who don't qualify for benefits. However, after Working Mother launched a special list for hourly workers in 2010, Trader Joe's still didn't make the cut—even as companies like Marriott International, with lots of hourly workers, actually get on the regular list. Meanwhile, GoodGuide gave the chain a middling 5.2 (out of a possible 10) in its overall rating, and a dreadful 4.4 in the "workers" category, dragged down by "labor and human rights" and "workplace diversity." The "working conditions and benefits" subcategory was a better 6.7. Maybe the Trader Joe's scores are hurt by its union situation. Supermarkets are one of the last bastions of union strength in the US business world. The United Food and Commercial Workers International Union represents 70 percent of the labor force at large national supermarket chains. But Trader Joe's isn't among them.
Why not? For one thing, the union hasn't tried very hard. Although a few small, unsuccessful efforts have been reported in California, in 1998 and 2003, Jim Papian, a UFCW spokesman, said, "I don't think we made a major attempt on a national basis. We had our hands full with Walmart and other major operators." Certainly, Walmart is a much bigger, juicier, and still-unreached target, with a long roster of accusations, including sex discrimination, cheating workers out of pay, illegally denying them breaks, skimping on health benefits, and much more. Papian further said he's not surprised at the lack of unions at Trader Joe's, given the tough organizing climate nationally. The chain was also a target of several farmworkers' groups in 2011 for refusing to sign agreements to improve working conditions and pay for the laborers who pick the tomatoes it sells.
Of course, another reason unions haven't taken hold could be that workers like Trader Joe's just fine the way it is. Pay and benefits, for instance, appear to be at least as good as those at unionized shops. As of 2005, Len Lewis said that the average Trader Joe's salary was about 15 percent above the union average. Five years later, Fortune reported that "full-time crew members"—which the company defines as supervisors working 40 to 47.5 hours per week—"can start in the $40,000 to $60,000 range." That could be noticeably more than the median pay for "first-line supervisors/managers" at grocery stores, which, according to the US Bureau of Labor Statistics, would come to about $35,150 for a 40-hour week and $41,750 for the longer hours.
(The BLS publishes hourly pay, so to get an annual comparison, I multiplied the BLS rate by Trader Joe's lowest and highest weekly hours and then multiplied those two figures by fifty-two weeks. Two caveats: The BLS median is for all grocery stores, nonunion as well as union, but with the high unionization rate in the industry, it's probably fair enough to consider the BLS numbers equivalent to union rates. Also, the most recent BLS data at the time of the 2010 Fortune article were two years older, dating to May 2008; however, inflation was virtually nonexistent then, so raises between 2008 and 2010 would have been low, and the year-to-year comparisons are reasonable.)
Less clear was an article in the Atlantic in 2011, which reported that "Trader Joe's sets wages so that full-time employees earn at least a median income within their community." But that community median could be a very low, nonunion rate.
To those wages, add in the benefits. Trader Joe's has been putting an amount equal to 15.4 percent of pay into a 401(k)-style retirement plan for years. That's a heck of a lot more generous than the typical 401(k) formula, whereby companies contribute just 3 percent of pay, and only if the employee contributes first. In addition, the Trader Joe's website says that "eligible" full- and part-time employees get medical, dental, and vision coverage. It doesn't define "eligible," except to say that "most" people qualify after a couple of months.
Many on-the-spot reports are positive. Sally Greenberg, of the National Consumers League, said that a niece and a friend's wife who have worked at Trader Joe's "seem really happy" with their jobs and pay. "If you ask them," said Patricia Werhane, a senior fellow at the University of Virginia's Olsson Center for Applied Ethics, "employees say they really do love to work there. They can chat; they can do what they want. They seem to not have so many rules." When I got to know a checkout worker well enough to feel comfortable asking a few questions, the one thing she complained about was pressure to wear turkey hats at Thanksgiving.
Personally, I don't put much stake in the celebrated hats, flowered shirts, and nautical names as proof of good working conditions. Trader Joe's staffers are called captains, first mates, crew members, and so on. Other than having a theme, how is that any different from Starbucks's "partners" or Target's "team members"? All the cute titles are simply ways to pretend that these aren't low-status, low-paid employees working at tedious jobs. And the so-called Hawaiian shirts? Well, McDonald's, Starbucks, Target, and many other retailers have uniforms, aprons, or dress codes for their workforces (by whatever name). Supposedly, the Trader Joe's flowered version is more playful. However, the designs have been getting steadily less flowery, and in any case it's not fair to call them Hawaiian, because they are nowhere near as garish as a genuine Hawaiian shirt with a splash of loud colors.
It's also debatable whether people are really enjoying their work if "Have fun!" is a mandatory part of the job description. I've certainly run into Trader Joe's staff who don't seem to be having the best time of their life, like the bored-looking woman sitting at the free-samples counter who never offered any samples. But those are rare. Then again, perhaps the most sullen staffers get hidden in the stockroom.
Image: "An offbeat, fun discovery zone" (for shoppers)
Yes, it's a show. And maybe you hate the too-adorable signs as much as I do, or you don't even notice the plastic lobsters and fake bamboo any more. Still, those props are not what create the Trader Joe's milieu. The real differences between Trader Joe's and just any old store are genuine customer service and personal warmth.
There's usually free coffee and some exotic free sample. I saw one worker at a New York outlet take several minutes to explain the different varieties of vitamins to a shopper, and a staffer at another store, rather than waiting for harried customers to grab her in desperation, walked around asking, "Does anyone need help finding anything?" One cashier in California got to know my mother so well that she called her "Nana" and gave her a plant at Christmastime. Restrooms are available, with prominent signs. Even the customers seem to pick up the mood. At the Chelsea site in New York City, a total stranger who saw me at the soap shelf suddenly started telling me which scents of soap she preferred and how much she liked the layout of the aisles.
If all the types of eggs are confusing, a sign at the egg display at the flagship Union Square outlet in Manhattan outlined the differences among organic, cage-free, white, and brown. At the Brooklyn store, a sign asked and answered the question "What is free-range chicken?" While the Fearless Flyer newsletter may lack coupons, it explains why Northern California's climate is good for growing orchids and where Fuji apples come from. Respondents in the 2009 Consumer Reports survey, in addition to citing low prices, gave Trader Joe's top marks for service. And the magazine singled it out, along with Wegmans, as "among the most satisfying chains to shop at."
The main consumer complaint involves the notoriously long lines. You could look at that as proof of the store's popularity or of its penny-pinching in not hiring enough cashiers.
The real problem with Trader Joe's isn't that it doesn't live up to its image. The problem is the image itself—the subtle implications of the chain's basic operating principles: a limited selection of exotic food, carefully plucked from around the world, precooked and ready to eat. We need to take a second look behind the scenes:
Limited selection. Yummy as the food may be to most shoppers, we all need more than low-sodium lox and honey-plantain strips. Like toothpaste (which not all outlets carry). Scouring pads (ditto). Maybe some of us (me) drink Diet Coke. Maybe we would like more than two choices of cake mix (lemon or chocolate). Therefore, customers will have to make an extra trip to a "real" supermarket now and then, and in almost every city or state where Trader Joe's is located—especially in California—that means driving. Thus, Trader Joe's customers must waste gas and spew unnecessary carbon emissions by shopping double. This could negate any environmental benefit from bringing reusable shopping bags.
Exotic food. Average Trader Joe's shoppers, according to a finding by researcher and ratings guru ACNielsen cited in Len Lewis's book, are childless younger couples, young singles, middle-aged singles, or middle-aged childless couples. Elsewhere, the book discusses an analysis from another lifestyle-and-shopping research firm, Scarborough Research, showing that "the typical Trader Joe's customer in the Pacific Northwest is a college-educated, white homeowner with a median age of 44 and a median household income [in the early 2000s] of $64,000. . . . About two-thirds have no kids at home."
These are not descriptions of the average American supermarket customer. Most notable is the lack of children. Remember, Trader Joe's doesn't carry diapers or baby food, and it's not clear how many three-year-olds really want double cream champagne brie. On the other hand, if your kid has to have the little packages of chocolate chip cookies that everyone else brings for lunch at school, but Trader Joe's doesn't sell that brand, you're in big trouble.
Jill Kickul, the director of the entrepreneurial program at New York University, pointed out another demographic issue: "[I]t's not located in some of the lower-income communities." Although the company may have sought cheaper sites off the fashion track in its early days, by the time it got to New York City in 2006, it was pitching its fake-bamboo tent poles in such reliably yuppie areas as Manhattan's Upper West Side and the edge of Brooklyn Heights.
In short, if you're an average American who needs staples to feed your family, Trader Joe's isn't interested in you. Or, to put it another way, Trader Joe's is elitist. Can being elitist also be socially responsible?
The focus on exotic food troubled me for one more reason. Until I walked into an outlet and leafed through the Fearless Flyer, I had no idea that things like chicken chilaquiles or inside-out carrot-cake cookies existed, let alone that I might want to try them. So, Trader Joe's has created a false demand for unnecessary consumption. Isn't that socially irresponsible?
That theory doesn't seem to bother consumer activists. On the contrary, many consider that one of Trader Joe's best qualities, since it can teach insular Americans about other cultures—and far more authentically than Starbucks. "Consumers want choices, and it opens consumers to a whole range of ethnic choices they may never have known about," said the National Consumers League's Sally Greenberg.
Carefully plucked from around the world. In 2006, the New York Times described the work of the fifteen members of Trader Joe's tasting panel who "perpetually travel the world visiting all kinds of food businesses—restaurants, farmers' markets, artisanal pasta makers, street stalls, and supermarkets—and then translate their finds to the stores." They bring back grass-fed cheddar cheese from New Zealand, goat's-milk cream cheese from France, and lime-and-chili peanuts from Thailand. That means it isn't only customers who are racking up the carbon emissions and burning gallons of fossil fuels. Trader Joe's completely violates every tenet of the locavore movement, which advocates buying locally grown food—usually defined as being within one hundred to two hundred miles—in order to support neighborhood businesses and to limit the environmental impact of shipping the food. Again, this makes it hard to describe Trader Joe's as green.
Precooked and ready to eat. The more processing involved in a food product, the more energy and packaging it usually demands. Fresh fruits and vegetables can pretty much go straight from field to carton to truck to produce bins at the store. By contrast, Climate Counts's Wood Turner pointed out that Trader Joe's uses a lot of excess packaging to ship its cleaned, shelled, diced, sliced, sautéed, mixed, and otherwise cooked foods from their exotic locales to the cute store aisles—while admitting that he likes being able to "buy products that don't have tons of preservatives and maybe are organic, in some cases at a lower cost than I might otherwise get."
"I wouldn't call them environmentally friendly," said Russell Winer, chair of the marketing department at New York University's Stern School of Business, "because they sell a lot of fast stuff in plastic packages—convenience foods."
Even the noncooked items are overpackaged. In its quest to make meal preparation a breeze for customers, Trader Joe's is increasingly switching to precut, prewashed salads and other veggies, all in plastic bags rather than loose in bins. As one of the world-traveling tasters told a New York Times reporter, in a rare occasion when the company granted any access, "Who buys head lettuce anymore?"
I know that these precooked meals can be a great option for busy shoppers, healthier than TV dinners, and less expensive than restaurant take-out. Yet I worry: What will happen to the old-fashioned art of home cooking?
THE QUESTION: Does Trader Joe's deserve its reputation as an exemplar of ethical chic?
THE VERDICT: No, but who cares?
Hey, I like going to Trader Joe's. You can drool through the unusual entrees and cheeses, and the staff really makes you feel happy to be there. There is a clear public value to a business model that emphasizes friendly, helpful service. As Sally Greenberg asserts, Trader Joe's may be increasing Americans' awareness of other cultures, which also is an important social value. If people never cook any more, Trader Joe's isn't the cause; blame dual-working families and the fast-food culture—in which case, it's a lot better to serve a Trader Joe's salmon mojito-marinated filet than a Big Mac with fries. And really, even if the whole atmosphere is too cute by half, what's wrong with making grocery shopping fun?
So, fine; it's a nice set of stores. Nevertheless, very few of the good points have much to do with social responsibility.
On the contrary, the carbon footprint is horrendous, while the few gestures toward greenness are trivial. Other stores do a lot more to encourage customers to bring their own bags, for instance. Although Trader Joe's may carry more organic, cage-free, and natural-type food than the average supermarket, the whole industry is moving in that direction. Virtually every major chain now sells big-name, factory-organic brands like Horizon milk and Earthbound Farm baby carrots, along with cage-free eggs. Moreover, for all the image of open friendliness, Trader Joe's is way too secretive about issues that really matter to the public.
Perhaps most important, this is an industry where ethical shoppers have lots of good choices, including food co-ops, farmers' markets, health food stores, community-supported-agriculture programs, local specialty shops, and—the easiest of all—unionized supermarket chains. Surely we can find enough to eat in those places.
6. American Apparel: Sex and the T-Shirt
The coral-colored, seven-story factory towers over its neighbors in the industrial downtown of Los Angeles—the LA Wholesale Produce Market, Bravo Brand Food, Canton Food Company, Angel Toy Corporation, a Los Angeles Times printing plant. A set of long-abandoned trolley tracks runs alongside, down Alameda Street. It's a far cry from the Santa Monica oceanfront or the fashionable streets just east of Beverly Hills where shops sell the clothing made at the coral-colored factory, although geographically they're only about fifteen miles away.
On the outside of the factory, huge signs proclaim "Legalize LA" and "Immigration Reform Now" and (in English and Spanish) "American Apparel Is an Industrial Revolution." Inside, in large, open, light-filled rooms, hundreds of middle-aged Latina women stitch skimpy shorts and tight-fitting T-shirts under blown-up photos of women crouched on all fours, pulling out their T-shirt necklines to reveal their cleavage, and suggestively shoving their hands down the waistbands of their jeans.
All of this—the industrial grime and retail chic, the outreach to immigrants and the outright sexualization, the hip, the socially responsible, the socially irresponsible—are equally part of the image of American Apparel. Indeed, they are the most famous aspects of its brand.
Theoretically, CSR activists should admire American Apparel for stubbornly resisting the garment industry's trend to shift production to the lowest-paying sweatshops in the poorest countries in the world, workers' rights be damned. Every piece of American Apparel is created in the United States, from fabric to ad photos, nonunion but with what is widely considered union-quality pay and benefits. If its ads are really, really sexy, well, that's what sells fashion.
Yet for all its advocacy of immigrants' rights, its subsidized lunches and bus passes, its free bikes and English classes, American Apparel makes liberal activists squirm.
"American Apparel?" I heard repeatedly, in horrified tones, when I rattled off the list of companies for this book. And: "It's soft porn." On top of that, by 2011, the company's finances were such a mess that it was in serious danger of shutting its doors, and it wasn't clear how much was due to standard business problems like overexpansion and the recession, and how much came from the same self-indulgent lawlessness and carelessness that the founder, Dov Charney, has allegedly exhibited in sexual harassment of his employees.
This was undoubtedly the most controversial of my picks.
"Made in Downtown LA—Sweatshop Free" proclaim the ads. It's true, and it's important. Five thousand workers at the coral-colored factory, an adjoining warehouse, and two smaller knitting-and-dyeing facilities nearby churn out the company's entire line: some 1.2 million brightly colored, snug-fitting, highly fashionable T-shirts, leggings, tank tops, miniskirts, button-down shirts, short shorts, swimsuits, jeans, sweaters, underwear, and more each week. These wares are then sold by another five thousand or so sales clerks at over 285 company-owned stores throughout the world—including China, thus putting American Apparel in the rare, and possibly unique, position of shipping clothing from the United States to China. The company claims to operate—and no one disputes this—"the largest garment factory in the United States."
By contrast, its competitors mainly send the drudge sewing work to Bangladesh, China, Honduras, Vietnam, and other countries that pay workers a fraction of US wages. The typical rate in these countries might range from 15 cents an hour to $1, judging by news reports; meanwhile, the US minimum wage was $7.25 an hour in 2010, and American Apparel at that point was paying $9 to $10 an hour as a base, plus productivity bonuses that, the company asserted, brought its average hourly wage to $13 to $18. Here's another comparison: the standard US workweek is 40 hours; in overseas sweatshops, it's easily 100 or more hours, with a typical schedule running sixteen-hour days, seven days a week.
After laborers at electronics and auto factories like Apple's in China staged protests and even jumped to their deaths in a rash of suicides in 2010, they got their pay hiked from around $130 per month to $176. However, as Chinese wages rose "too high," manufacturers moved operations to cheaper Bangladesh and Vietnam. Even for an (unlikely) forty-hour week, that "raise" would bring the pay rate to little more than $1 an hour. Workplace conditions in these countries are also much, much worse than at American Apparel, with the toxic materials, sexual abuse, and lack of breaks described in earlier chapters.
Some social-justice advocates, such as New York Times columnist Nicholas Kristof and author Fred Pearce, argue that these jobs are actually good deals in countries where any paycheck is a luxury. The alternatives—trying to scrabble a living from a tiny family farm, prostitution, scrounging in dumps, starvation—are worse.
While Kristof and Pearce raise important issues, and companies like Apple and Nike are trying to improve conditions, American Apparel undeniably spends more and offers better conditions—which we'll get to shortly—by basing its manufacturing in California. And if it's depriving women in Bangladesh, China, Honduras, Vietnam, and other struggling countries of job opportunities, it is providing those opportunities for low-skilled Americans and preserving the last remnants of what was once a thriving sector of the US industrial base. "American Apparel is showing that you can produce domestically," said Mark Levinson, the economist from the SEIU, whose affiliate Workers United represents textile-industry workers. However, his praise is qualified, and organized labor's relationship with American Apparel is complicated, as will be discussed a little later.
Having spent twenty years fighting sweatshops, Jeff Ballinger is more accustomed to castigating clothing makers than complimenting them. Yet he echoed Levinson's qualified appraisal of American Apparel: "For me, it boils down to 'Are people making a living wage?' I think it's a terrific operation, because it's built a factory in Los Angeles. You can't pay [Los Angeles workers] less than $300 a week. They showed that you can compete [by operating in the United States] and win."
Let's not go overboard with the praise. American Apparel chose to centralize its operations in the United States not for charitable reasons but because it believes this arrangement offers solid business advantages. As the company itself emphasizes, it is "vertically integrated"—that is, it can oversee every step of the production process in one spot and thus, presumably, ensure quality. By sewing in California, it also saves on shipping costs and can get supplies to North American stores fast to keep up with ever-moving fashion trends.
Moreover, these vaunted American jobs are boring, repetitive, and sometimes physically demanding. It's an assembly line, not Wall Street or Silicon Valley. "Teams" of five to twenty-five men and women sit at long tables of sewing machines doing the same limited task over and over: Sew a pocket on a pair of jeans. Sew a sleeve to a T-shirt. The noise level varies, depending on the number of machines clacking away, but it can be roughly the decibel level of a New York City subway train arriving in a station, brakes screeching. Many workers wear face masks or ear plugs. There's little chitchat.
Still, as factories go, the American Apparel version—a converted railroad warehouse—is particularly pleasant. Sunlight streams through floor-to-ceiling windows filling three or even all four outer sides of the block-long work rooms—windows that workers are actually allowed to open. One full side of windows looks out on a panoramic view of downtown Los Angeles. The inner walls are painted white, which adds to the sense of airiness, and a few green plants are scattered about.
Most incredible are the benefits: A subsidized health clinic next to the main lunchroom, open two days a week for ten hours each day and available to workers' families, too. Free on-site English and yoga classes. Discount bus passes and catered meals (in several ethnic choices, including Spanish and Korean). Free ten-minute massages during breaks, plus a voluntary twenty-minute exercise routine—on company time—before the shift begins. A bank of three or four phones on every floor for free international calls. (Ryan Holiday, a company spokesperson, said that perk alone probably costs American Apparel "hundreds of thousands" of dollars.) A few hundred free bicycles that can be used for pleasure as well as for commuting. This is not merely the official list outlined by Holiday; on a tour, I saw much of it in action, such as an exercise session, the phone banks, a food truck, two massage therapists, the health clinic (closed that day), signs about the buses and bikes, and the cavernous lunchroom with plenty of microwave ovens, hot-storage facilities, and vending machines.
(This description applies only to the factory. The milieu at the retail outlets is a totally different and more controversial matter, which will be discussed later.)
The company brags about its egalitarian philosophy, as well. Chief executive Dov Charney's office is on the same floor as one of the main sewing areas, past the "development room" with its bolts of fabric for making samples, then through a set of industrial double doors. Workers call him Dov, and he holds a weekly phone conference with the retail managers, in which any store staffer supposedly can join. "There's no middleman between the employee and the CEO," boasted Holiday (who doubles as head of Web design and also works on advertising). A 2005 article in BusinessWeek described how "anyone can walk into the boss's office at any time."
"A lot of them love him. He will walk the floor, and they will hug him," said Angelica M. Salas, executive director of the Coalition for Humane Immigration Rights of Los Angeles (known as CHIRLA), an immigrant-advocacy organization, who has known Charney since he came to Los Angeles in 1997. One time when she was visiting, she recalled, a worker came up to Charney with an offer to go from town to town in Mexico selling T-shirts. As Salas recounted it, Charney told the worker, "'If you can have a plan for me, go for it.' The worker was so happy," Salas added. "He was basically going to be a distributor."
For all the "Dov-ing" and hugs and phone chats, however, there is clearly a caste system. The lower-skilled staff—sewers, maintenance workers, guards—are mainly Hispanic men and women (especially women, at the sewing machines) who look to be in their thirties and older. The office jobs—marketing, advertising, technology, Web design—go to Anglo twentysomethings. These latter employees work in offices that were cooler than the sewing floors on a hot summer day, with doors that can shut out the subway-brake noise.
Another negative: American Apparel has never appeared on Fortune or Working Mother's "Best Companies" lists, and it's impossible to know why. The benefits would certainly seem to rank up there with the "best." Nor can size explain the omission, since Fortune requires merely that a company have more than one thousand employees, which American Apparel does, and the list has at times included companies with similar or lower sales volume, such as the Container Store, the Atlanta-based law firm Alston & Bird, and Shared Technologies, a Texas telecom. In 2010, Working Mother even added a list for hourly workers, giving American Apparel a second shot. No go.
With the subsidized meals, bus fare, and other fringe benefits, does it matter that American Apparel isn't unionized? Neither are its overseas sweatshop competitors, after all. Nor, for that matter, are 93.1 percent of private businesses in the United States. Yet in an industry that was one of the keystones of the nation's labor movement—a movement forged by the infamous Triangle Shirtwaist Factory fire of 1911—are American Apparel's wages, benefits, and overall atmosphere so good that, as it claims, a union is unnecessary?
Jason Coulter is now pastor of Chicago's Ravenswood United Church of Christ. However, for thirteen years in the 1990s and early 2000s, he was an organizer for the old Amalgamated Clothing and Textile Workers Union and the textile union UNITE. In 2003, he came to American Apparel.
It was an unusual target from the start. "Some of our members had family members that were working there, and they described kind of a crazy scene," Coulter recalled. "The owner would ride around the factory on a skateboard. He was a gringo from Canada who spoke Spanish and didn't wear a suit and tie, the classic patrón model: you drive people hard and then show great fits of generosity. He led a group of hard-driving Mexican supervisors and then would say, 'We're having a fiesta!'" Contrary to American Apparel's image now, Coulter said that "the wages and benefits at that time were maybe at standard or below standard, comparable to nonunion local wages." And the vaunted health-care coverage, he claimed, consisted merely of arranging for "one of those county health care trucks to come by the plant" once a week. Still, he said the union didn't see the company as evil. It just wanted to find out what was really happening.
(The sole person American Apparel would make available for an interview was Holiday, the spokesman, who basically cited all the workplace benefits when I asked about working conditions.)
Once UNITE got serious and started holding meetings and handing out leaflets, the charmingly erratic T-shirt maker "behaved exactly like every other nonunion company," Coulter charged. "They sought to have us thrown off the property. They restricted the workers' access to information. They tried to find out who had signed union cards and monitored closely those people who were union supporters, to see who they were talking to." For instance, he said, company officials ordered organizers off the public sidewalk outside the factory and refused requests to hold informational meetings on the premises or post union information on factory bulletin boards.
As Coulter told it, when Charney, the CEO, finally met with union officials at UNITE's Los Angeles office, it was a disaster: "He was an incredibly difficult guy to talk with. He never lets you speak, he's so blustery and controlling and domineering. He accused us of manipulating the workers and misrepresenting how well he treats them. He held on dearly to this belief that he is this lovable and benevolent employer that everyone would want to work for. He started attacking the union, [saying] all we were out for was dues money."
By late 2003, UNITE filed a complaint with the National Labor Relations Board, alleging that American Apparel illegally attempted to block the organizing drive. The two sides settled, with the company paying no financial damages and acknowledging no wrongdoing but agreeing to post a notice on site stating that it promised not to interfere with the workers' right to organize.
What that meant was that Charney won. UNITE gave up. Coulter conceded that "at some level the patrón model of management, throwing people a few crumbs here and there, can be effective in forestalling unionization, especially if people feel they have to risk their jobs in order to have a union." He nevertheless claimed some credit, saying that the union efforts forced the company to improve its pay and health coverage. American Apparel, of course, would argue that those "crumbs" are exactly the point: the wages and benefits it voluntarily gives are far better than anyone could get in a typical labor contract.
Portfolio magazine, in a long article in November 2008, wrote that in light of the decent pay, benefits, and working conditions, "union leaders in LA have arrived at a kind of cease-fire with Charney." Some top labor officials seemed to confirm that assessment, although it may simply be that they're not very familiar with the situation. For instance, Carl Proper, communications director for the UNITE HERE offshoot that remains independent of the SEIU, said he didn't know why the organizing drive failed at American Apparel and conceded that "it's plausible" the pay and benefits were generous enough to dissipate any interest. "They paid fairly well, for a nonunion place" was his recollection. Another major labor leader, who didn't want to be named because praising a nonunion shop could be politically delicate, described the company as "formed with a worker-friendly attitude, trying to mine that niche in a very dirty industry." The SEIU's Mark Levinson, however, bristled at the Portfolio description, asserting that the American Apparel fight "was as vicious an antiunion campaign as you can find." Despite his praise for the company's effort to "produce domestically," he added, "I wouldn't rule out [another organizing drive] by any means."
But as labor leaders like Levinson, Coulter, the AFL-CIO's Ron Blackwell, and the Center for American Progress's Christian Weller point out, wages and benefits are not the only criteria for judging a company. There are also important considerations like respect and the ability to speak out. "An essential aspect of a good place to work is the people have a right to join a union," Blackwell said. "Whether they do [join] or not depends on their choices." In the International Organization for Standardization's detailed definition of human rights, under "Fundamental principles and rights at work," the first item listed is "freedom of association and collective bargaining," even before important principles like nondiscrimination and the elimination of forced labor and child labor. In Levinson's and Coulter's view, American Apparel, for all its freebies, didn't provide that basic freedom.
American Apparel's other unique claim to socially responsible fame, in addition to keeping presumably well-paying garment jobs in the United States, is its strong advocacy of immigrant rights.
Until around 2006, it wasn't unusual for US businesses to welcome high levels of immigration, including unskilled factory, farm, and construction workers. However, that was simply as a source of cheap labor. If the immigrants didn't have legal papers, well, companies winked and gave a quick glance at forged Social Security cards, and the workers didn't dare complain about low pay and poor conditions.
After 2006, even that sort of immigration-exploitation tolerance became rare, as the federal government cracked down on the hiring of workers without proper documentation. The mood grew nastier over the next few years when recession rolled in, unemployment spiked past 10 percent, and politicians revved up fears about Latinos swarming across the border to "steal" jobs. Polls showed wide national support for an unprecedentedly harsh law passed by Arizona in April 2010 that made it a crime to be an illegal immigrant and actually required local police officers to check the immigration status of anyone they stopped for any cause, if they had "reasonable suspicion" of the person's status.
That pervasive mood of suspicion and antagonism is what made—and still makes—American Apparel so different. It actively tries to help its Spanish-speaking workers. The free English classes, subsidized arroz con pollo lunches, and bilingual signs throughout the building are part of it. In addition, the plant gives staff time off on May Day to march in Los Angeles's traditional immigrant rights parade. Sometimes Charney joins. He likes to point out that after all, he's an immigrant, too—albeit from Canada—and one year he let the immigrant rights group CHIRLA use his own green card in a fund-raising ad. The corporate website has myriad links to pro-immigration news articles, fact sheets, interviews, photos from the May march, a TV series, and more. Among the rare logos allowed on its T-shirts are political ones, like "Legalize LA"—meaning the city's immigrant workforce. CHIRLA's Angelica Salas said Charney has donated thousands of T-shirts to her organization and others and to the marches, as well as at least $50,000 in cash to her group, and has opened the factory to CHIRLA speakers to talk about workers' legal rights. Other immigrant advocacy groups also say the efforts seem to be genuine and serious.
Toward the end of 2007, in the heat of the federal crackdown, American Apparel began a major advertising push, featuring its own Latino workers and supporting immigrant rights in strong language. "The government and politicians exploit and misrepresent this matter to advance their own careers," newspaper ads declared. And, "At what point are we going to recognize that the status quo amounts to an apartheid system?" Union organizers, too, praise American Apparel for that part of its philosophy. The AFL-CIO in the mid-1990s officially dropped its historic opposition to immigration, and Mark Levinson of the SEIU (which represents a large number of foreign-born members) said that American Apparel's "view on immigration is the same as ours: all workers, regardless of status, should have the same rights in the workplace." Still, Jason Coulter, the organizer turned pastor, maintained some skepticism about the company's motives. "LA is a teeming mass of people who, because they don't have papers, can't negotiate the same type of employment situation" as legally documented workers, he said. "American Apparel benefits from that."
In the furious politics of the early 2000s, it was inevitable that a company as in-your-face as American Apparel would be busted.
Sure enough, in January 2008, the federal Immigration and Customs Enforcement (ICE) agency demanded to see the company's personnel files. Over the next year and a half, American Apparel cooperated with the feds as they pored through the records in search of phony Social Security cards and other suspect IDs. By September 2009, the company had axed some 1,500 employees who couldn't prove their legal status, more than one-fourth of its manufacturing workforce—or, as Ryan Holiday, the spokesperson put it, "Because of a broken immigration process, American Apparel was forced to lay off 1,500 hard-working employees and lose 1,500 good jobs. Some of the workers had worked for the company for ten years." Holiday said the people weren't immediately replaced, in part because it was the middle of a severe recession, and in part because of the helter-skelter nature of the firings, with some teams decimated and others almost intact. "That really threw off the production process," he said. Nine months later, about 1,000 spots had been filled.
The whole episode was awkward for a company that had so proudly advocated against the very laws it was now forced to obey. Still, matters could have been far worse. In other well-publicized cases—most notably at the Iowa-based slaughterhouse Agriprocessors in 2008—government agents have swooped down in surprise raids and arrested company officials on criminal charges. American Apparel's relatively clean record—the fact that it didn't seem to have knowingly hired undocumented workers and had no history of abusing its workforce—undoubtedly protected it from worse legal treatment, its own lawyer said.
Politicians' reactions immediately afterward summed up the extremes of the public mood:
The mayor of Los Angeles, Antonio Villaraigosa, a Democrat of Hispanic background, was quoted calling the firings "devastating" and telling ICE to focus instead on employers that mistreat their workers. Meanwhile, a Republican congressman from nearby San Diego, Brian P. Bilbray, said that American Apparel managers "seem to think that somehow the law doesn't matter, that crossing the line from legal to illegal is not a big deal."
Even before the federal probe, hints had popped up in the press from time to time implying that Charney's passion for immigrant rights was cooling. New York Times Magazine columnist Rob Walker asserted in his 2008 book Buying In that the company had deliberately switched its marketing strategy away from emphasizing social values like being sweatshop-free to trumpeting its sexiness. Bloomberg Businessweek, in August 2010, indirectly quoted the CEO saying that, among the things he could have done differently to avoid the serious financial weaknesses facing the company at that point, he could have moved "manufacturing offshore while he resolved his worker problems."
Yet it's hard to see any CSR de-emphasis at the company itself. A year after the firings, signs throughout the factory were still in English and Spanish. Employees chatted in Spanish; guards' uniforms were emblazoned with the word "security" in both languages. The staff had marched on May Day, as always. There was a new line of "Legalize Arizona" T-shirts, protesting that state's anti-immigration law. Ryan Holiday said the company continued to hire Latino workers, although he conceded that HR might now check identification "more strenuously." Pointing to the huge banners on the building, he claimed, "I don't think American Apparel has toned down its ads in any way."
Ultimately, when discussing American Apparel, the elephant in the room—the naked elephant—is sex.
Of course the fashion industry reeks of sex. And it's not the fashion world alone. Sex sells, and always has sold, everything from Coke to cars, from cigarettes to Cialis. Former Esquire editor-in-chief Lee Eisenberg described in his 2009 book Shoptimism the advice that Ernest Dichter, a pioneering social scientist who specialized in consumer marketing, gave to Esquire editors years ago: They should tell potential advertisers that when men look at photos of nearly nude women, such as those in Esquire, "their pupils open wide, which in turn makes men 'more attentive to visual stimuli' of any sort," such as ads on the next page.
Whether or not Dov Charney has gotten bored with CSR, he certainly knows that sex, not immigrant rights campaigns, is what draws his customers. So American Apparel's ads, website, in-store posters, and mannequins show people (or figures) in provocative poses revealing lots of flesh. That goes without saying. The real question should be, "Are American Apparel's displays significantly worse than those of other companies?" A fair and comprehensive answer has to consider three elements: the clothing itself, the marketing, and the working conditions.
Are the clothes sexy? That depends on which clothes.
American Apparel sells crotch-high shorts and skimpy bikinis, bodysuit thongs and see-through blouses, skintight pencil skirts and strapless "dresses" no bigger than an oversize shirt. It also markets plenty of modestly cut crew-neck T-shirts, button-down Oxford-style shirts, and zippered hoodies. Like it or not, body-clinging or androgynous, this is what fashionable young women in their teens and twenties wear. People could debate whether a thirteen-year-old should dress like a twenty-eight-year-old, but plenty of them aim to, and that's a problem that would exist even if American Apparel didn't. (Judging by the customers—and their mothers—that I interviewed, along with marketing experts and college professors with a sense of their students' wardrobes, the typical American Apparel customer ranges from about thirteen to thirty-two.)
Overall, these are the same sorts of clothes available at American Apparel's rivals, places like Abercrombie & Fitch, Aéropostale, Forever 21, the Gap, Hollister, H&M, and Urban Outfitters. The last-named offers backless shirts and bustiers. Hollister displays short shorts and spaghetti-strap tops. H&M has short shorts and tight, short skirts. As their customers might say, "Duh."
Perhaps American Apparel's wares are a tad sexier. After all, it's known for its form-fitting T-shirts that are cut for women, rather than boxy and unisex like most. Loretta Lurie, a veteran advertising executive in New York City and Chicago—and the mother of a teenage girl, Sydney Bornstein, who considers the brand "cool"—grimaced a bit. "You go into Hollister and Abercrombie, and then American Apparel: Their shirts are cut a little lower. The dresses are too short or too tight. It encourages teenage girls to dress like sluts." Not surprisingly, one of her daughter's friends, fifteen-year-old Faye Honig, agreed with the daughter, not the mother, about the chain's coolness; nevertheless, certain American Apparel items were too much for her. "Some of the stuff you laugh at. Who would wear that netted, see-through stuff—which if you'd buy, you'd layer?" (And what mother and teenage daughter will ever have the same opinion about which clothes are appropriate?) Meanwhile, from the opposite point of view, Rachel Gilman, a thirty-three-year-old New York City advertising stylist, said she likes American Apparel's turtlenecks and tank tops because "they make them long, not cropped"—that is, less revealing of the midriff.
In any case, American Apparel clothing has more attributes, unrelated to sexiness, that make it popular among the target audience. The T-shirts are softer than most others and of higher-quality fabric, often all-cotton. They don't have silly logos. "They're a step up from casual T-shirts," Jessie, a thirty-two-year-old New York City nursing student, commented. "I can wear the shirts out and not feel like a slob."
The biggest problems are the occasional children's items that seem to copy the adult versions. In fairness, most of the gear is age appropriate ('tween girls like to wear leggings and tank tops) or even too sedate (try getting a squirming two-year-old into an Oxford button-down). But the slinky rib racerback dress? The baby rib spaghetti tank dress? It's one thing for a thirteen-year-old to dress like twenty-eight; it's another matter for an eight-year-old to do so.
Is the marketing sexy? Consider the following examples.
The window displays of an American Apparel store on the Upper East Side of Manhattan in April 2010: One female mannequin stands with her hand on her buttocks, her blouse unbuttoned so far down that half of one breast is revealed. A real woman, in a blown-up poster, is perched on hands and knees, her rear end high in the air. However, a half dozen other mannequins are posed much more innocently, arms and legs akimbo, striding, or even slouching almost pigeon-toed like shy little kids.
The window and outside-wall displays of an H&M store a few blocks away, the same day: Headless mannequins are set in positions similar to those at American Apparel—for instance, one has a hip thrust out, with her feet pigeon-toed. Huge posters show head-and-shoulder shots of attractive youths who look to be in their teens and twenties. They're usually fresh faced and fully clothed, but in one strategically placed poster, the much-larger-than-life-size crotch of a blonde in a tight, short skirt is right about at a passerby's eye level.
The window displays of an Urban Outfitters store in the same neighborhood, same day: The mannequins lack heads and sometimes arms and legs, which inherently renders them fairly sexless. However, the posters make up for any sexual slack. There's a blow-up of a young blonde woman in a vest with deep cleavage, and in another, a woman is seen from behind walking on a beach, wearing high boots and bikini panties that reveal generous portions of her buttocks.
The window display for Abercrombie & Fitch, Northridge Mall, in Northridge, California, March 2011: A huge black-and-white photo shows a blonde teenage girl lying on top of a bare-chested teen boy, almost kissing, with his hands stroking her hips.
The window display for Forever 21, same mall, same day: The mannequins are wearing miniskirts and short shorts, but their mops of curly hair, lack of faces, and playful stances evoke a completely asexual, childlike mood.
The back-page ad for American Apparel in the Onion, June 3–9, 2010: A brunette arches her back in an impossible yoga-style pose on the sand, wearing a black swimsuit that reveals plenty of buttocks and torso, her legs stretched apart suggestively, her head leaning back so that it almost touches her upraised bare foot, eyes closed in ecstasy, as her curly hair cascades down.
The back-page ad for American Apparel in the Onion, April 22–28, 2010: In a series of three photos, a young, long-haired Asian woman in beige slacks and a plain white, short-sleeved, somewhat loose-fitting blouse kneels demurely, with her head tilted in a different direction in each shot, her arms usually down at her sides.
A full-age ad for H&M in Seventeen, December 2009-January 2010: Three women strut or lean against each other, clad in various configurations of body-hugging black leather, silk, spandex, and other clingy fabrics—a very short skirt, bicycle-style shorts, a front-zippered minidress, a half-unbuttoned blouse.
A double-truck ad for H&M in Teen Vogue, March 2010: Two young women with frizzy red hair, laughing, arm in arm, are sporting bright yellow-and-pink striped sweaters with black skirts.
Seductive? Yes, some of the American Apparel images certainly are. And some of them are playful or straightforward. Furthermore, they're not noticeably different from the ads, posters, and mannequins of rival brands—and far, far less raunchy than ads in the same magazines for Valentino and Jimmy Choo.
So, is American Apparel's marketing sexy compared with the competition's?
To answer that, I pored through a stack of copies of Allure, Girls' Life, Harper's Bazaar, InStyle, Marie Claire, the New York Times Magazine, the Onion, Seventeen, Teen Vogue, and the Village Voice, from October 2009 through July 2010, and studied window and store displays at American Apparel, Banana Republic, the Gap, H&M, Hollister, Uniqlo, Urban Outfitters, and Victoria's Secret throughout the course of several months. (It's a tough job, but somebody's got to do it.)
In analyzing the various examples, it's important to remember that American Apparel has a wide target market, encompassing readers of Girls' Life and of Allure. The ads in Girls' Life, Seventeen, and Teen Vogue ought to be more demure than those in magazines aimed at adults. American Apparel solves the problem to some degree by not advertising in the PG-13 publications. Going for edgier outlets, like the satirical weekly the Onion and the Village Voice (famous for its sex-of-all-sorts classified ads), it gets more leeway. Yes, thirteen-year-olds may read Mom's Allure rather than Seventeen, but that's another one of the broader social problems that can't be blamed on American Apparel.
For that matter, American Apparel doesn't push the limits as far as it could. Take another look at those back-page ads in the Onion. Of a half dozen from February through June 2010, four were not sexual at all, or were only minimally so. The models were sitting or standing in casual positions, with serious or cheerful faces, not come-hither looks. Two of them were fully clothed in slacks and shirts, and the others—one in a bikini top and jacket, and one in a black lace blouse—still didn't look any sexier than someone wearing a "Legalize LA" T-shirt. They seemed almost bored with their poses. (By contrast, the two more provocative back pages featured a young woman in a short skirt and form-fitting long-sleeve shirt, and the yoga-stretching model described above.)
Too sexy for teens? Hardly. These six ads could have fit comfortably into the November 2009 issue of Teen Vogue, which boasted a demure profile of a young woman in a lacy-sleeved white blouse and jeans, for PRVCY Premium; the back view of a young woman modeling Emu boots and wearing a white bikini bottom that revealed as much of her buttocks as American Apparel's yoga performer displayed; and eight pages of ads for Jimmy Choo shoes "for H&M" that included (among other images) a couple of women sprawled seductively in black leather, a woman with half of one breast falling out of her dress while she caressed a partner, and a seated woman with a black skirt slit up to her crotch.
Moving up (or down) the ladder of raunchiness, American Apparel's website is certainly more erotic than those of rivals like Hollister and Urban Outfitters. However, it's a crapshoot. Clicking onto the American Apparel page for women's dresses, you might see a woman in a slinky tank dress sprawled on an unmade bed. Or you might see a woman sitting on a chair in a pink dress with a wide, twirly skirt.
Most troubling are the store displays, because they are harder to avoid. While no one has to buy a magazine or surf online, anybody walking down the street or the mall, from age three to eighty-three, can see the mannequins splayed in sexy poses, maybe lying on one side or sitting with legs stretched wide. The display photos are usually worse, showing lots of black lace and up-on-all-fours poses. Yet the mannequins are just as likely to be unobjectionable, merely standing, striding, even (apparently) doing jumping jacks or gymnastic stretches and wearing long sleeves, jackets, and slacks in a splatter of bright colors.
The colors actually gave American Apparel a more innocent look than H&M and Hollister on that April day. Those other two stores exuded an air of sophistication and sexiness—H&M with its sultry black-white-beige-brown color scheme, and Hollister with its black-painted walls and wafts of incense. At the Hollister door, moreover, shoppers were met by bikini-clad greeters.
Certainly, American Apparel has a reputation for being worse than its rivals, and that reputation can even alienate the target audience. Faye Honig, the teenager, complained that in its marketing, "it's like, whoa! It's crazy, they're showing off underwear, and they're basically naked. They show everything." A fifteen-year-old boy in Manhattan told me that when American Apparel ads are on the Onion's back page—which can be every other week—it's so embarrassing that he won't read the newspaper on the subway. His friends called the ads "weird" (from a boy) and "pornographic" (a girl). When I visited the Hastings Center, a think tank in suburban New York that specializes in ethical issues relating to health and the environment, one researcher said she felt uncomfortable bringing her teenage niece to the stores, while another said the shops "are known as a place to go look at soft porn."
Viewing the marketing strategy from a hard-nosed business angle, Robert Passikoff, the branding expert, said, "It does provide some level of image differentiation for the brand, but it's a dangerous game."
Yet the bottom-of-the-line reputation is not universal. Several mothers of teenage girls I talked with didn't think American Apparel's ads are particularly different from those of other stores or manufacturers. Although Loretta Lurie (who is married to Peter Bornstein, the artist who wears Timberland shoes) considers the clothing sexier, she said the commercials blend in with the TV programs where they're featured—something she should know about, as an advertising expert herself. "Didn't Abercrombie & Fitch set the bar on sexy marketing?" asked Carol Holding, the brand-strategies consultant. "They had ads where the men's pants were cut so low that you can see the pubic hair." The New York Times media writer David Carr, too, pointed to other examples, noting in a January 2011 column that "Abercrombie & Fitch built a brand out of writhing, half-naked teenagers, as Calvin Klein once did."
Defending their company, Dov Charney and Ryan Holiday argue that the extra-sexy reputation actually stems from American Apparel's policy of using its own employees in its ads, rather than professional models. "I don't think the sexuality of American Apparel is necessarily any more explicit or extreme than any other fashion company," Holiday told me, "but because we are not using professional stylists and they're not Photoshopped, people are sometimes caught off guard by the realness of our ads. They conflate that with being more explicit." Indeed, the manufacturer is proud of the policy, claiming it proves that the clothes are for real people. "We try to use our employees and friends, because that's who we design our clothes around—not what people should look like, but what they are," Holiday said.
Then, essentially conceding that the marketing might in fact be extra edgy, he added, "These are the images we choose to use because we think they are evocative and interesting and exciting. We consider our ad space as a conversation. Sometimes we use our ad space to speak out about politics like immigration." And sometimes, apparently, sex.
In truth, sexuality in marketing and fashion alike has grown increasingly explicit over time. A century ago in Europe and the United States, a glimpse of a woman's ankle was risqué; now, bikinis barely cover what's still considered the tiniest scrap of private parts, and if you want more, just see what people voluntarily post on YouTube without even getting paid. What in the American Apparel repertoire can hold a candle to the Neiman Marcus ad in Marie Claire where the model—close-up, full-frontal view almost to the navel—is wearing nothing except a couple of strategically placed necklaces?
Okay, so sex sells. Fashion designs, store displays, clothing ads, and even nonclothing ads use sex. That still leaves the most serious charge against American Apparel, and the one that most sets it apart from its competitors—that the work place itself oozes sex.
The tales have been repeated in news articles and lawsuits for years and to some degree even confirmed by Dov Charney. Allegedly, he walks around nearly nude in the office and has held business meetings in a similar state of undress, calls employees "sluts" and "whores," favors staffers who sleep with him, hires young women on the basis of their looks, screams at employees, grabs their hair, describes graphic sex to them, and more. The Portfolio article talked about a half dozen male employees in their twenties who lived with Charney in his mansion, including one "loud, pear-shaped" PR apprentice who called the boss "Daddy." New York Times Magazine consumer columnist Rob Walker wrote in his book that he was in the CEO's office with one male and two female staffers while "Dov Charney was naked from the waist down"—but the punch line is that Charney was trying on prototypes of a new line of men's underwear. He has certainly dated female staffers, at least three of them seriously. Most notoriously, writer Claudine Ko, in the June–July 2004 issue of Jane magazine, described a female employee presumably performing oral sex on Charney in a hotel room in front of Ko. A week afterward, the article continued, Ko was in a corporate apartment with Charney while the CEO masturbated and "we casually carry on our interview, discussing things like business models, hiring practices and the stupidity of focus groups."
Nine female employees or ex-employees have filed lawsuits or legal complaints officially asserting sexual harassment. One was dropped, one was settled, and the rest were pending at the time of this book's publication, one of them for years.
Nikky Yang—a former girlfriend of Charney's who, according to her lawyer, Keith A. Fink of Los Angeles, helped found the clothing chain—charged that the company had created "a hostile work environment based on sex." For instance, "while working naked Mr. Charney grabbed his penis and stated to Ms. Yang, 'pet my dick.'" In another situation, Yang's lawsuit accused Charney of "forcing Ms. Yang to sit and watch him shower to discuss business." (The lawsuit includes nonsexual issues, as well, alleging that the CEO screamed at her, physically abused her, and cheated her out of pay.) Although Fink would not discuss a second client, Mary Nelson, whose case was still pending, published reports have mentioned claims that Charney made sexual advances and inappropriate comments to her and "wore a skimpy thong that barely covered his genitals."
Yet more Fink clients have filed cases that include sexual angles almost as a side charge. In December 2008, Bernhard-Axel Ingo Brake, who was hired to set up American Apparel's retail operations in Europe, sued the company and Charney mainly for issues relating to wrongful termination, breach of contract, failure to pay bonuses and commissions, and emotional distress. However, he also claimed that "American Apparel employs many women who have had sex with Mr. Charney. These women are commonly referred to as 'Dov's girls,' his 'girls,' 'lovers of Dov,' or 'F.O.D.' (meaning 'Friends of Dov'). 'Dov's girls' receive preferential treatment from American Apparel due to their 'special relationship' with American Apparel's largest shareholder."
Brake said that Charney would send these women to "take over management tasks [in Europe] despite their lack of qualifications," leading to "mismanagement of the retail store operations to the financial detriment of American Apparel and its shareholders in the hundreds of thousands of dollars"—and, not coincidentally, making it difficult for Brake to do his job. The lawsuit further alleged that Charney "purchased hundreds of sex videos using company funds," saying they were for research, and "attempted to charge his payment for the services of a prostitute at his hotel to American Apparel."
Things seemed to quiet down for a couple of years, until, within less than three weeks in March 2011, five more women filed charges. Most dramatically, a New York City woman claimed that when she was only eighteen, she'd been "held prisoner" in Charney's apartment for several hours and threatened with being fired if she refused to perform sex acts over the next eight months.
The fact that some of the women say they felt forced to have sex with Charney in order to keep their jobs ties in with the controversy over using employees in ads. Even without any sex, there's always an implicit coercion when your boss asks you to do a task.
If the charges focus on Charney, it's impossible to separate him from the company. He founded it, nearly destroyed it, revived it, saw the potential of form-fitting and no-logo shirts, set the sexually charged mood, and still is the public face and ultimate arbiter of everything from designs to hiring to advertising to immigration advocacy.
As Charney himself lays out the history on the corporate website, he essentially launched the business through the back window while he was a high school student at the elite Connecticut prep school Choate Rosemary Hall. He would buy up huge numbers of "iconic" Hanes T-shirts when stores like Kmart had supersales, then load them onto trains bound for his hometown of Montreal for resale, undercutting the official Canadian distributors. He carried the business concept over to his dorm room at Tufts University, where a partner—a local Hanes wholesaler—conceived the name American Apparel. (That partnership didn't last long. By Charney's own admission on the website, the wholesaler "thought I was a little difficult to deal with," and Charney had to return the man's $16,000 investment.)
During Charney's sophomore year, American Apparel began manufacturing its own unique garments in the barn of a South Carolina farm. Charney eventually dropped out of Tufts and moved to South Carolina to devote himself to the burgeoning business full-time. Already, the firm was becoming known for its fitted designs, in contrast to the standard unisex cut. At that point it was a wholesaler, not a retail brand, often selling to companies that would imprint their own logos.
However, in 1996, Charney filed for bankruptcy. This is one portion of his history that the CEO does not discuss on the website—although he manages to find space to muse about his mother's Syrian roots and his favorite bagels. Outsiders have variously attributed the problems to low-cost imports and Charney's disorganization, both of which would become recurring themes in his career.
In any case, by 1997 he was in Los Angeles, starting over, thanks to the financial backing of either one or two Korean partners, depending on who's telling the story. The brush with bankruptcy apparently didn't sober him. Airily, Charney wrote on the website, "The Korean garment community was vigorously supportive of my work . . . . Many suppliers extended me credit even after I bounced so many checks on them and continuously failed to pay them on time." Still, the company seemed to do well enough—at least for a while—that in 2003 Charney decided to open his own stores, rather than sell through middlemen.
That decision changed everything: it made the chain famous, but it also opened the door to the notorious advertising and probably overexpansion that are among the company's worst problems today.
Sexual or not, Charney is clearly a charismatic and hands-on (no double entendre intended) manager. According to published reports, he selects some of the employees to pose in those sexy ads and may even photograph them himself. (For that matter, spokesman Ryan Holiday said that Charney's two dogs have been featured in spots.) During my visit, employees were constantly checking his opinion on things like a marketing plan, and the Portfolio article describes him striding through downtown Los Angeles handing out job fliers. Jason Coulter, the erstwhile union organizer, said that when he and his labor colleagues met with Charney, "he tried to seduce us"—not literally, of course.
Thus, nine lawsuits. That may not seem like a lot, within the context of 10,000 employees and 285 stores. Yet there are larger companies with fewer, or none.
Charney's main defense has been essentially that the whole industry is motivated by sex, that fashion workplaces are inevitably sexually charged, so why pick on him? For instance, responding to Mary Nelson's lawsuit, he asserted, as Portfolio put it, that "in addition to being the company's creative director, he is also one of its fit models—a simple explanation for why he would stride around his offices half-dressed. . . . He has also said he 'test-drives' the underwear to see how it fits 'in action.' . . . In a deposition, he said he 'frequently' had been in his 'underpants' because he was 'designing an underwear line' while Nelson was working at the company."
That jibes with Rob Walker's account, as well.
In other specific cases, Charney has claimed that the women suing him did substandard work or that they were trying to extort money from him. "Dov Charney's celebrity status in the fashion industry is being publicly exploited," the company said in a statement to the press, in response to the New York teenager's lawsuit in 2011. Regarding the four women who jointly filed soon afterward, Charney showed reporters sexually explicit e-mails, text messages, and photos that he said the women had sent to him—in other words, they were hounding him, not vice versa.
Others in the industry scoff at his "everybody does it" defense. Sure, famous models regularly hang out in design studios in various states of semidress. That doesn't mean the company owner fondles them or strolls around in thongs himself. "I have been in Liz Claiborne shops, in a bunch of other places," Jason Coulter said. "They are run professionally." Karen Erickson has been part of the industry since she started New York City–based Showroom Seven, a designer-fashion sales firm, in 1983. "Everyone I know who is in fashion works too hard to have affairs in the office," she snapped. "My husband has been working with me for thirty years. He would be backstage helping with models; he sees top models naked. Whether I have problems with him? Absolutely not, any more than a gynecologist's wife has problems with him seeing patients naked."
Still, there is other evidence to indicate that all is not sex and foreplay at American Apparel. When I visited the Los Angeles factory, I saw no one running around half-naked or flirting, nor anyone who looked drop-dead gorgeous. In fact, some of the white-collar, younger, presumably hip employees were unfashionably chubby, and the two massage therapists who were starting their work shift—one middle-aged man, one twentyish woman—were modestly dressed in pale-blue T-shirts and shorts. Angelica Salas, the immigrant rights advocate, said that she's never heard any complaints from factory workers she talks with. "In my own interactions, personally, as a woman, he has always been super respectful of me," she added. (She was twenty-six when she first met Charney in 1997, presumably within his target age for hitting on.)
The website Gawker.com, in June 2010, posted a couple of supposedly leaked American Apparel memos spelling out the guidelines for employee grooming, and the requirements were, if anything, amazingly modest. For females, "Makeup is to be kept to a minimal [sic]. . . . Liquid eyeliner, pencil eyeliner and eyeshadow are advised against; mascara must look very natural. . . . Blush must not be overdone—should not have glitter or sparkles. . . . Please do not use a shiny gloss on your lips; any lipcolor must be subtle. . . . Hair must be kept your natural color." And among the "guidelines for dudes" are the warnings that "[h]air should look natural. Excessive product to the extent of creating stiffness and an unnatural or greasy appearance to your hair is advised against."
In describing the look that the company seeks in its staff, Ryan Holiday said, "The idea that we're hiring on attraction is false. We hire based on a sense of personal style: How do you hold yourself? What do you wear that with? It's that they're stylish and creative and expressive with their clothes."
The teenage employees I interviewed who had worked at the retail stores, males and females alike, didn't report any uncomfortable situations. For instance, Matt Jacobs (not his real name) spent about six months as a part-time stock clerk and sales clerk at an outlet in Manhattan's Greenwich Village during his senior year in high school in 2006. In addition, friends of both genders worked at other American Apparel stores. True to the stereotype, he said that the sales staff upstairs were thin, pretty, young white women, while the stockroom employees in the basement were older, often Hispanic and black, and often married with kids themselves. "There definitely was a [sales-clerk] look," Jacobs said. However, it wasn't always a sexy look: "There were different body types. A lot had tattoos. They were interesting looking. Hipster." And, yes, he heard plenty of rumors about Charney sleeping with employees or taking photos of them. When Charney paid a call, people were on their toes, the same as anyone would be at any company when the boss comes by. Still, the mood never took on a sexual edge, with or without the presence of the CEO. "It wasn't uncomfortable at all. I liked how everyone worked together. There wasn't that kind of [sexually charged] feeling," Jacobs said with a shrug. "I don't know where that whole reputation comes from."
The charges in the lawsuits are serious, yet anyone can claim anything in legal papers. The proof is in the end result—and even that can be ambiguous. Of these American Apparel suits, one was dismissed at the request of the woman who filed it, which might or might not mean that it was baseless; sometimes lawsuits are dropped because a big, rich, corporate defendant applies so much pressure that the plaintiff can't hold out any longer. Another American Apparel case was settled, which usually implies either that there was some merit or that the company just paid off the plaintiff to get rid of the nuisance. A third lawsuit had been pending for years at the time this book was published, which could simply indicate obstinacy on both sides. One had gone against the company in the first round with the federal Equal Employment Opportunity Commission, but lawyers on both sides were negotiating. Five others were too new to have been resolved in any fashion.
Keith Fink, the attorney for the two longer-pending suits, has a controversial history of his own. According to various news reports, he has been fined for fabricating evidence, has repeatedly sued famous people to obtain quick nuisance settlements, has stalled and changed his mind on an arbitration offer, and has demanded money from American Apparel. The clothing company has reportedly countersued, charging him with extortion. Fink proudly told me, "I represent all sorts of celebrities," although the ones he cited are hardly household names, other than bad girl/rock musician Courtney Love. He claimed that American Apparel has paid people to write negative articles about him and manipulated Google's search optimization. "They will stop at nothing" to badmouth him, he said. So, which side of the legal debate is sleazier?
In a way, my visit to the corporate headquarters epitomized the contradictions. There were the airy and well-lighted production floors, the free bikes, the subsidized food, the professional-looking massage therapists. And then there were all those middle-aged seamstresses, probably from traditional Latino backgrounds, soberly dressed themselves, sewing skimpy shorts and bikinis under huge photos of woman crouched seductively on hands and knees. The store clerks may be cool with this. But are the factory workers comfortable?
As for other topics often of concern to socially responsible shoppers, American Apparel doesn't have much of a reputation either way. On balance, it ends up slightly on the positive side of the ethical spectrum.
The only social issue on which the company has publicly taken a major stand, besides immigration reform, is gay rights. After its home-state voters approved Proposition 8, a constitutional amendment to ban same-sex marriage, in 2008, American Apparel jumped into the ensuing protests. It produced and donated tens of thousands of "Legalize Gay" T-shirts, put those shirts in its store windows, cosponsored a march in Washington with the Human Rights Campaign, donated some proceeds from sales of the shirts to the HRC, and advocated on its website.
That kind of sensitivity to sex-based discrimination might seem out of alignment with the charges of sexual harassment and the ads that exploit women. However, it fits an industry where homosexual designers are a cliché and customers are often young and unafraid of breaking taboos. As the American Apparel website declared, "With many of our employees and customers identifying as gay, lesbian, bisexual or transgendered, we are a company that is vocal about our support for the protection of gay rights." Both the immigration and gay rights advocacy have helped make the chain popular with San Francisco–area teenagers I interviewed. And if American Apparel is about anything, it's about in-your-face sexuality, whether it's half-nude women in sexy poses, or two women kissing.
To the HRC's Eric Bloem, the anti–Proposition 8 activism (and no doubt the cash from the T-shirt sales) earns the company a lot of breathing room to make up for the allegations of sexism. While HRC's annual survey asks large companies about all sorts of policies regarding gay, lesbian, transgendered, and bisexual employees and consumers—topics like their domestic-partner benefits, marketing, and donations—Bloem said that sexual harassment is "not so much in our portfolio." He went on, "Obviously, we do not condone any sort of sexual harassment, but with the firm stance [American Apparel] has taken on LGBT inclusion, we'd like to try to see if their policies match up with the programs they have in place. I'd like to see what the allegations are." He didn't know exactly what policies American Apparel has or how it might rate on the various human resources issues, since the company isn't big enough to be actually included in the annual survey.
Meanwhile, its environmental record is mixed. It's also too small to qualify for Climate Counts's rankings, although Wood Turner, the organization's founder and former executive director, said he wears some of the T-shirts because "they're sweatshop-free, and that matters to me." By not shipping garments all the way from China or other far-off points, the company certainly uses less fuel and produces fewer emissions than other brands.
The Rough Guide to Shopping with a Conscience gave American Apparel credit for "offering its most popular styles in certified organic cotton and recycling, according to its own count, over a million pounds of fabric scraps every year." The recycling part may be true. Company officials say that T-shirt fabric left over from adult shirts goes into making smaller items such as bathing suits (which, at American Apparel, can get really small), children's clothes, and hair bows. The littlest scraps are used to tie up bundles of garments. "Everything is designed to reduce waste," Ryan Holiday said.
The cotton claim is more dubious. Consumers often rave about how much of the clothing is all-cotton and thus not made from petroleum-based synthetics, with the mess of attendant environmental and political problems that come from using oil. That's only partly true; obviously, the leggings and other stretch garments are synthetic. Moreover, cotton creates plenty of its own environmental damage as well as human rights violations. For starters, instead of propping up Russia or Saudi Arabia, cotton buying probably supports the police state of Uzbekistan, one of the world's three main sources of raw cotton, which uses forced labor. Standard cotton growing demands huge amounts of chemical fertilizers, insecticides, and water, and Uzbekistan has drained the Aral Sea to feed this industry. What about American Apparel's supposed use of organic cotton? In a search for "organic cotton" on the company's website, a mere fourteen items emerged. Only three of those were specifically labeled for babies, a category where many customers think being organic is most important.
PETA and the Humane Society give the brand credit for not using fur or leather, although that's rather meaningless, considering that the vast majority of its products—T-shirts, button-down shirts, underwear, jeans, bathing suits—aren't normally made of animal skins. Then PETA subtracts points for wool, which it doesn't like due to the painful mulesing and shipping processes. On balance, however, PETA calculates that the lack of fur and leather tips the scales in favor of American Apparel; indeed, the chain makes some of the T-shirts PETA sells.
On another important ethical topic—free speech and politics—the record is similarly mixed. American Apparel has never been a big force in political lobbying or donations, according to the Center for Responsive Politics. Of course, the company asserts that its whole attitude toward sexuality is really about being open and frank. But Keith Fink, the lawyer handling some of the sexual-harassment suits, accused American Apparel during our interview of forcing newly hired staff to sign arbitration provisions far more restrictive than the norm. Although arbitration agreements are common enough among "sophisticated employers," he said, the usual formula is that employees must accept the ruling of a private arbitrator and keep the charges and settlement from the public. "Nobody else has in their agreement the provision that American Apparel does," Fink added. "[New hires] are forced to agree not to discuss with the media anything that goes on with American Apparel."
Price is also a CSR issue, albeit one too often ignored. It's hard to figure out where to place American Apparel in that category. Among customers I talked with, there seemed to be a general feeling that its most stylish clothes were probably worth the somewhat high cost but that twenty dollars—a typical American Apparel price tag—was a little dear for a plain T-shirt. Several New York City teenage girls singled out Urban Outfitters as usually cheaper, while another rival, H&M, is known for bargains. Then again, some American Apparel T-shirts were just fifteen or eighteen dollars at the time I wrote this book, and I talked to shoppers who actually go to the chain for what they consider its low prices. Carol Holding, the brand-strategies consultant, said her twenty-two-year-old daughter likes American Apparel clothes in part because "they're disposable—they cost nothing."
A fashion designer wondered how it could be competitive if it's paying such high, nonsweatshop salaries. Company officials say they save money by controlling the whole design-to-retail process through their vertical integration. As the American Apparel website proclaims, "A smaller portion of the margins goes towards fuel, transocean container ships, middlemen, boxes, pallets and entropy." The best answer is probably that, while it's no discount house, it's not the most expensive shop in town.
A discussion of American Apparel's ethics also needs to consider its finances. There are serious questions of fiscal irresponsibility, or at least really lousy judgment. It might seem that a key requirement for a socially responsible company would be honesty about basic business issues. A second requirement might simply be to stay in business.
From the prep school beginnings, American Apparel's corporate history is sprinkled with ethical envelope pushing (the resales to Canada) and shaky finances (the 1996 bankruptcy). The newest problems probably go back to what seemed like its era of greatest success, the happy days in the early 2000s when the reincarnated company was expanding into retail. The initial three stores burgeoned to over 280 in seven years. The stock started trading on the then American Stock Exchange (now part of the New York Stock Exchange), by virtue of the fact that, in 2007, American Apparel was bought by a publicly traded special-purpose acquisition company—essentially, a shell that exists to buy other companies—called Endeavor Acquisition Corporation. The chain hired an industry veteran as vice president of operations, praised by author Rob Walker as "quiet, serious, soft spoken."
Then, as 2010 wended its way into summer, the house of T-shirts began unraveling. As numerous press reports have recounted, its accounting firm, Deloitte & Touche, quit, with a warning of "material weaknesses" in the internal controls, and the company revealed that the Securities and Exchange Commission and the US Justice Department were investigating. It teetered on the brink of violating the covenants of a private equity loan, the second time it had had trouble with a key lender. On top of all that, it risked being kicked off the NYSE for repeatedly filing its quarterly papers late. The stock price plummeted.
By year-end, the manufacturer had cobbled together fresh financing, brought in a new acting president and chief financial officer, and rehired its old, pre-Deloitte auditor, but Charney had to buy up nearly $4 million worth of shares to keep things going. And that didn't seem to be enough. The debt kept rising, sales and revenue fell, thirteen underperforming stores were closed, two board members left, angry shareholders filed class-action lawsuits, and loan terms were repeatedly renegotiated. Losses for 2010 reached $86 million. In its annual SEC report in March 2011, the company warned that it might have to file for bankruptcy. Again, financial salvation arrived at the last minute—at least, temporarily—in the form of a package of stock purchases and warrants to purchase more, worth up to $43 million, from a group of Canadian investors.
Maybe it was all just a mix of overexpansion, recession, and sloppiness, aggravated by the need to quickly hire and train 1,500 new employees to replace the ones forced out by the immigration raid. The company claimed—plausibly enough—that such a mass talent search hurt its productivity. Charney told Bloomberg News that with replacement workers now in place, seventy new stores set to open, and a program to sell its wares at other retailers, the company was poised to return to profitability. The bankruptcy warning, he claimed, was just a technicality.
Maybe. However, some of the lawsuits filed by Keith Fink go beyond bad luck and run-of-the-mill poor business decisions to allege actual malfeasance. For example, Bernhard-Axel Ingo Brake, the head of American Apparel's European operations, brought incendiary charges against Charney. Brake alleged that, in addition to hiring incompetent "Dov's girls" and using company money for sex videos, Charney ordered him to avoid paying French taxes by illegally attributing part of employees' salaries as reimbursement for expenses; tried to inflate the value of the stock by lying about the prices of goods that were sold; and demanded that he fiddle with the way rent and other expenses for unopened stores would be booked. Another plaintiff, Roberto Hernandez, said he was fired for refusing to manipulate the inventory figures.
THE QUESTION: Does American Apparel deserve its reputation as an exemplar of ethical chic?
THE VERDICT: No (but it's not hopeless)
To oversimplify, the debate comes down to this: is extreme sexism so egregious that it outweighs American Apparel's efforts to improve its employees' work lives in other ways, including giving them jobs in the United States to begin with?
If many of my friends think the answer to the sexism question is obvious, activists had a much harder time. They seemed to find the question excruciating. They really wanted to endorse the company for its support for immigrants and gay rights, keeping jobs in America, not using leather, or whatever other ethical reason. They wanted someone to prove that the sexual-harassment charges weren't true; failing that, they avoided answering by pleading lack of information (especially since the company is too small to hit the radar of a lot of "Best Companies" surveys). Or perhaps nine lawsuits really aren't so many? Eric Bloem of the Human Rights Campaign mused that if female employees are treated crudely, "it may be indicative of a lack of appropriate human resources policies and procedures." Nevertheless, he added that he couldn't be sure.
Nor has the ICCR (the shareholder activist group for religious institutions) paid much attention to the clothing manufacturer. "We have been aware of more general concerns regarding images in advertising," said Laura Berry, the executive director. "There are definitely members who are concerned about pornography and violent media portrayals." But, after all, American Apparel's photos and harassment are nowhere near as horrible as child sex slavery. "We choose our battles," she added.
Aaron Chatterji, the Duke University professor, even used the company—along with ExxonMobil!—in a guest lecture at California's Monterey Institute of International Studies in November 2009 as an example of how difficult it can be to juggle competing aspects of CSR. Pretending that he was discussing four anonymous companies rather than just two, he told the students, "Here's a company with the best safety record in the industry, here's a company that's a bad polluter, here's a company that has good working conditions, here's a company that's been sued for sexual harassment. Which do you value more?" The students quickly nixed the supposed companies with pollution records and sexual-harassment lawsuits, favoring the "other two." Then Chatterji revealed that the safe company and the polluter were actually both ExxonMobil, and the good working conditions and the lawsuits both applied to American Apparel.
To some activists, however, the very fact that American Apparel aspires to be seen as socially responsible in areas like workers' rights and immigration gives it an extra obligation to be a good citizen all around. The charges of sexual harassment are even more troubling than they would be at a less socially active employer. So American Apparel considers itself a protector of immigrants? Well, pointed out the National Consumers League's Sally Greenberg, "immigrant women are very vulnerable. [Charney] has to clean up his act." In other words, Latina employees at American Apparel might be doubly at risk.
In a typical company, the sexually charged image "would not raise an eyebrow. It would be 'Yeah, look at the clothes, these are sexy clothes,'" suggested Carol Holding, the brand strategist from Seattle. "But because this brand is so rooted in this social ethos, all of a sudden, it becomes a very big deal. It negates the whole social-responsibility thing."
Certainly, American Apparel deserves acknowledgment for what it does right. It seems to be genuine about providing decent benefits (albeit without allowing unions) and fighting for better treatment of immigrants without exploiting those who are illegal. These qualities are in its DNA. And to his credit—or perhaps as a result, finally, of the bad PR backlash—Charney has apparently toned down the underwear parades and other particularly outrageous flaunting.
Nevertheless, CSR is a little like the Hippocratic oath: first, do no harm, before you try to whitewash your harm with good works. Were the robber barons of the late nineteenth century good guys if they built libraries and universities? Is Goldman Sachs a paragon if its CEO, Lloyd Blankfein, donates $1.3 million a year to philanthropic causes, even as the firm sold risky subprime-mortgage-backed loans to customers without revealing that a key client was hedging against those same loans, ultimately paying a fine worth five hundred times Blankfein's yearly donation?
Winning the sexual-harassment trials (if they ever happen) wouldn't solve American Apparel's problem, because those cover only a few examples. The sexuality is the company's whole identity.
To earn a social-responsibility badge, American Apparel would have to take a major step: dump Charney.
OK, OK, he's the founder and head designer and inspiration and guiding light and micromanager and chief underwear model, so ease him upstairs as founding CEO or chief consultant or CEO emeritus. In fact, let him keep suggesting designs and colors. And then hire a real CEO with management expertise to go along with the other grown-up managers recently brought in. (Bonus: That might also help the company dig out of its financial mess and stay in operation.)
The problem is that Charney doesn't inspire only the fashion designs, ad campaigns, and political causes. His cavalier (or worse) personal attitudes toward sex and women have set the tone of the workplace. Most of the complaints are directed at actions he himself—not the company—is said to have taken. As long as he is a physical and psychological presence in that coral-colored factory in downtown Los Angeles, so are the poisons. At the same time, if he has truly built a made-in-the-USA business model that works, not simply a one-man admiration society, it should succeed without him.
7. The Reality
Perhaps this book could have been written 240 years ago. Arguably, the first time that consumer power was deployed to make a political point was the Boston Tea Party, in 1773.
The consumer movement grew, alongside political populism, union organizing, and the campaign for women's suffrage, in the late nineteenth and early twentieth centuries. That was the era when the Interstate Commerce Act, the Sherman Antitrust Act, the American Federation of Labor, and the Food and Drug Act came into being, while muckrakers at Collier's Weekly and the Ladies' Home Journal investigated phony patent medicines. Corporate management, for its part, recognized a sense of responsibility. The new Harvard Business School's mission statement vowed, "We educate leaders who make a difference in the world"—that is, a nonbusiness difference.
The Depression, World War II, and postwar rebuilding temporarily pushed aside the public's interest in social causes as people made basic survival a priority. Then the second great era of political-consumer activism was ignited by the civil rights movement in the 1960s, antiwar protests in the 1960s and 1970s, and the growing revulsion against South Africa's apartheid in the 1970s and 1980s. Shoppers and investors discovered that their dollars could buy political pressure as well as stuff. Why should they give their money to bus companies that forced black passengers to give up seats to whites? Why should the universities they attended purchase products from Dow Chemical, which also made the napalm used in Vietnam? Socially responsible investing, for one, is now a $2.7 trillion business. People wanted to feel that they were making a difference for good, and it was so much easier to do it as part of their daily routine, while buying something they needed to buy anyway, rather than seeking out a special activity.
The targets continued to spread. Student groups demanded investigations into the foreign sweatshops that manufactured their official college gear. Advocates for farm workers boycotted California grapes. Gay rights advocates boycotted orange juice.
And increasingly, since the 1990s, business has been responding to this demand.
Frito-Lay plans to make half of its junk food with natural ingredients. International Paper is burning biomass debris to save fuel. The average Climate Counts score has risen nearly 20 points since the website was launched in 2007. Trader Joe's stopped selling orange roughy and other endangered fish and agreed to work with outside groups. Starbucks signed a licensing deal with Ethiopia. Nike has transformed itself from the evil sweatshop abuser to being greener than Timberland in the Amazon. And on and on.
The burgeoning of social-responsibility themes in marketing makes a particularly good yardstick, since ads are the means by which businesses project the image they think will appeal to shoppers. "Companies are trying to move in that direction because it does give them some cachet with the press and customers," said Michael Myers, of the ad agency Palio Communications. "In a few more years, it's going to be expected." As a typical example, Donald Schepers, director of the City University of New York's Robert Zicklin Center for Corporate Integrity, described a recent television commercial for a Honda Civic, a car known for good gas mileage: "It starts out with a car from the seventies. A thin young man gets out, cool looking; he looks like a guy who'd be fun to be with. He walks along, and his T-shirt progresses through the years, but the T-shirts always have eco-friendly things on them. He doesn't age. He's still in his twenties. Now, he's getting into a brand-new Civic. There's a great deal of transference that the company is trying to set up, that being eco-friendly goes along with being cool."
Experts say that certain industries are more susceptible to social-action pressure, whether because their sins seem to stand out, because alternatives are readily available, or because their customer bases are particularly CSR attuned. Among these sectors are clothing, autos, food, and architecture.
"Fashion companies had better be pretty green and socially conscious, because they're very much about image," said Arthur Caplan, the University of Pennsylvania ethicist. "They're selling products that induce guilt. Who needs all that high-end stuff? You'd better do what you can to make it guilt-free." Indeed, while couture designers started slathering on more furs around 2010, they are countered by the growing breed of younger, "ethical" designers like Stella McCartney who offer faux-fur choices. Caplan's logic applies as well to cars: automakers must find trendy and green ways to compensate for their unhip, irresponsible use of fossil fuels, their carbon emissions, and their pollution. (Hello, Prius and Lexus hybrids.) Meanwhile, food is a key sector because "consumers care about something that goes into your body," as Timberland's Gordon Peterson pointed out a little enviously. (If only they cared as much about what goes on their feet!) It may be relatively easier for the food and construction industries to be virtuous, New York University's Russell Winer suggested, since organic food and architectural eco-certifications are becoming widely available.
The businesses that most need a CSR patina are probably those with a client base in the teens to early thirties. They're the Timberland target. They're fine with Trader Joe's limited, prepackaged selection, because they don't have kids and they're too busy with dual careers (and social activism) to cook an old-fashioned meal. And they basically define the Apple and American Apparel communities. Said Jill Kickul, who teaches this age group in New York University's entrepreneurship program, "You have a younger generation in their twenties and thirties that want to see and are expecting business-as-usual to be socially responsible."
Ethical, environmental, political, and other policy concerns are still not—and never will be—the prime reason people buy anything. There are too many other practical factors, like convenience, size, taste, color, fashion, quality, allergies, friends' recommendations, religious requirements, that spark of joy you can get from the right item, and, most of all, price.
Tom Chappell asserted that people will accept a higher price for "natural" goods, and there is some evidence to back him up. Starbucks, Timberland, and Apple customers obviously pay more, although it's not clear how much they're paying for milieu, gourmet taste, sturdiness, and the Genius Bar and how much for the ethical image. As well, a few weakly supportive surveys are floating around. The Humane Society's Michael Markarian mentioned a January 2005 Ohio State University survey in which 43.1 percent of the respondents said they would fork over a 10 percent premium for humane animal products, and 12.4 percent reported that they would pay as much as 25 percent more. On the other hand, 40.6 percent wouldn't pay extra at all, which comes to a pretty high "unwilling" faction.
Brand strategist Carol Holding cited a different set of analyses, done by Cone, a Boston-based consulting company that specializes in cause branding. This research, she said, found that "an enormous number of people will buy a product that's socially responsible, assuming the price and quality are equal."
Isn't that kind of comparison meaningless, I asked; of course anyone would take a product that came with an extra attribute (ethics) for no extra price. "Consumer-products companies are looking for a hair's difference," Holding replied. That tiny preference for ethics could be enough to outsell a non-CSR rival.
All those calculations go out the window when the economy goes down the tubes. Numerous polls showed that, not surprisingly, outlays on expensive organic food and green products dropped during the 2008–2009 recession. If regular food, clothes, cars, or anything else seemed unaffordable, who is going to pay 10 or 50 percent more to feel virtuous?
To ethicist Arthur Caplan, these surveys are missing the key part of the affordability problem. "It's very much a class issue," he said. "People shopping at Walmart and BJ's [Wholesale Club] and Sam's Club are less interested in being green than people buying Volvos and hybrid cars are. I think the rich have a little more room for it than the poor." In that case, being socially responsible in terms of the environment, working conditions, animal rights, organic and natural ingredients, and other typical standards by definition requires a company to be socially irresponsible in terms of bias against working-class and low-income consumers.
Horrified officials at supposedly progressive companies immediately disavow any thought of class prejudice, enumerating all the ways that discounted versions of their goods are available. "There's a range of price points" for Timberland shoes, marketing vice president Jim Davey said, from the $300 boots at Saks Fifth Avenue and Nordstrom to $100 and $120 versions at DSW and the Timberland Factory Outlet. Kate Chappell, of Tom's of Maine, insisted that "there are plenty of low-income people, like students, that buy our products." She cited Tom's outlet stores, and of course, thanks to the Colgate marketing clout, the label is now at Walmart. In the long term, optimists like the University of Virginia's Patricia Werhane say, mass production and economies of scale could bring the price down—if only more of us would pay the few extra pennies now.
So, a lot of consumers are demanding ethics with their Big Macs. How well did the six companies in this book respond, and what do their actions say about business attitudes?
To start, I broke down the basic criteria from the introduction into smaller, measurable chunks, like "reduce energy use" and "reduce or recycle waste" under the broad heading of "climate change and energy." Next, I set up a four-part scoring system: a "good" rating got 3 points, "better than average" got 2, "average" or not applicable got 0, and "bad" got minus 1. Then I scoured the facts, data, interviews, opinions, and analyses in the six chapters to determine how to rate each company. They earned a higher rating if they acted on their own initiative, like Timberland's bringing in outside certification of its overseas factories, versus doing it after a public uproar, as with the environmental campaigns against Apple. Being a pioneer added points, too.
It is, admittedly, an arbitrary and subjective process. Should Timberland's long history of making "Best Companies" lists earn it a "good," or should the fact that it fell off in 2008 drop it to merely "better than average"? Is Tom's of Maine's revamped toothpaste packaging still "good" in the "information" category, or should it be downgraded to "better than average"? Here's what I came up with (omitting the zeroes, to keep it simple):
ENVIRONMENTAL/HUMANE
Reduce energy use: Timberland and Tom's are Good / Starbucks is Better Than Average / Trader Joe's is Bad
Alternative energy: Timberland and Tom's are Good / Starbucks is Better Than Average
Recycle/reduce waste (including packaging): Timberland and Tom's are Good / American Apparel is Better Than Average / Apple, Starbucks, and Trader Joe's are Bad
No animal cruelty: American Apparel and Tom's are Good / Starbucks and Trader Joe's are Better Than Average / Timberland is Bad
Natural/organic/no PVCs, etc.: Timberland and Tom's are Good / Apple, Starbucks, and Trader Joe's are Better Than Average
Local sourcing: Tom's is Good / Trader Joe's is Bad
WORKING CONDITIONS
Unions: All are Bad
Pay and benefits: All but Apple are Good
"Best Companies" lists: Starbucks is Good / Timberland is Better Than Average / Apple is Bad
Overseas sweatshops (absence or monitoring): American Apparel, Starbucks, and Timberland are Good / Apple is Better Than Average
Sexual harassment: American Apparel is Bad
PUBLIC SERVICE
Price: Trader Joe's is Good / Apple and Starbucks are Bad
Community and public service: American Apparel, Starbucks, Timberland, and Tom's are Good
Customer service: Apple, Starbucks, Timberland, and Trader Joe's are Good
Public information: Timberland, Tom's, and Trader Joe's are Good / Apple and Trader Joe's are Bad
(In the category of "public information," Trader Joe's is unusually good in providing consumer information, such as explaining the different types of eggs, yet it is also unusually bad in its corporate secretiveness—which is why it counts twice.)
Putting aside, for the moment, the issue of labor unions, good US working conditions would appear to be the most popular "virtue," with five of the six companies claiming some plaudits for pay, benefits, or "Best Companies." The reason is that it's not just an ethical value. It's an important business practice to treat your workforce well, as Henry Ford discovered nearly a century ago, when he began paying his workers a wage high enough that they could afford to buy his Model Ts. CSR experts say that ethical values can lead to lower turnover, higher morale, and a recruiting edge. At Timberland, Gordon Peterson pointed out, the time off for volunteering was a key attraction for job applicants. When Tom's of Maine employees take their paid volunteer time, Kate Chappell said, "they come back to their jobs reenergized."
But what about unions? Since fewer than 7 percent of private-sector employees are unionized, and collective bargaining among government workers has become a political football, it shouldn't be surprising that a group of six companies would have no unions—except for the fact that these are supposed to be especially socially responsible companies. Wouldn't at least one of them be more open to an organizing drive then the average American manager? Actually, no, say some labor veterans. "I don't think union shops are as much needed at socially responsible workplaces," said Ron Blackwell, the AFL-CIO's chief economist. "A lot of these [CSR] programs are about managing reputational risk, especially about workplace issues." In other words, these companies have already checked off the "working conditions" box by providing long maternity leaves or flextime or whatever nice benefits, so they don't need a union in order to qualify as a good place to work. It's the Tom-and-Kate/Howard Schultz philosophy of the benevolent, socially responsible boss.
The trouble with the benevolent-CEO philosophy is that no CEO lasts forever. Even if generous benefits or community service are supposedly intrinsic to the company's self-definition and have come to be expected by staff and customers alike, expectations erode over time. If the new chief executive doesn't feel as strongly, if rivals aren't providing such benefits, if profit margins are shrinking, if a new generation of workers and customers is less aware of the CSR history—all those factors can make it too easy to snip away at the supposedly sacred corporate mission statement.
The next two most popular categories, with three or four "goods" apiece—which, combined, encompass all six companies—are a set of virtues that usually get ignored by social-responsibility campaigners and investors: community, public, and customer service. The most obvious examples are Timberland's and Tom's of Maine's paid volunteering time and American Apparel's ads, donations, marching, and other support for immigration rights. But these categories also can mean openness and availability to the world at large. Things like Starbucks creating a space where people can sit for hours without being required to buy an overpriced latte. Or Apple Stores staff answering questions at the Genius Bar and letting anyone check e-mail at the display computers.
Why do these two categories rate such high billing? As with wages and benefits, probably because they help basic business operations. Happy customers—especially customers who are encouraged to linger—will buy more. Local organizations that are grateful for a company's donations will spread the word.
After those top categories, the scores drop dramatically. Unfortunately, the cynics are right that many CSR attributes interfere with business operations: low price is hard to achieve if companies pay their workers above-average wages and use expensive organic ingredients. Trying to avoid animal products might limit the kind of fashions American Apparel and Timberland can design. And how can a Starbucks in Manhattan, San Francisco, or Seattle possibly buy local, when the climate in those cities is too wet and cold for growing coffee beans?
Another value that's not usually considered as part of CSR is the corporate structure itself, whether ownership is public or private. Public companies—generally the largest and best known—sell stock to any investors. Private companies are owned by a limited group of people that have committed their own capital—typically, the founders, their friends and relatives, and a few professional investors such as hedge funds. Virtually all companies begin this way, and most, but not all, private companies are small. (Some notable exceptions are Hearst Corporation and Mars Inc., which makes M&Ms.)
The big problem with a public company is that investors are constantly comparing the profit margins, earnings per share of stock, and other data against rival businesses' numbers. So there is tremendous pressure to cut costs here and raise prices there in order to eke out pennies more in returns. Even worse, shareholders tend to focus on the short term—to demand returns right now—rather than support investments in, say, solar installations that may pay for themselves over the long run. "Big institutional investors drive companies to increase shareholder values, which often results in oppressive working conditions," said the AFL-CIO's Ron Blackwell. By contrast, privately held companies have the freedom to pay extra for natural ingredients or give their employees time off for community projects. Indeed, that's what Tom Chappell said—before he sold Tom's of Maine to publicly traded Colgate.
All these are powerful points. However, there are stronger arguments in favor of public ownership.
Of course, ordinary stockholders with a few hundred shares don't "own" a company like Apple the way they might own their house and decide whether to put in a solar array. The real power belongs to management, the board of directors, and the large institutions that Blackwell mentioned, such as pension funds, that own millions of shares. Nevertheless, because all shareholders technically own the company, and anyone could become an "owner" in the future, these companies are legally required to provide a wealth of operating and financial information buyers and sellers might need to make informed decisions. The general citizenry can thus learn about top officials' pay and perks, or pending lawsuits over pollution or sexual harassment. "Keeping all of that information private is a problem," said the National Consumers League's Sally Greenberg. "It's really hard for consumers to figure out if you're sharing the price discounts you should. Nobody really knows what you're paying your CEO."
Public companies are also subject to the much more sophisticated and potentially rigorous oversight of the Securities and Exchange Commission. (That oversight may not seem to be doing much to help American Apparel, but the company's ownership structure is really a tangle of private and a veneer of public.) Plus, shareholders have the right to propose changes in corporate policy and ask uncomfortable questions at the annual meeting—exactly what has opened the door to activism by groups like As You Sow and the ICCR. While most resolutions may fail, Domini and Oxfam would have had no influence over Starbucks's policy in Ethiopia without the risk that shareholders would dump the stock.
So far, so good. Businesses have discovered that having a socially responsible reputation is a great way to appeal to the public and to differentiate themselves from competitors. Yet that leads to an obvious risk: when is the CSR claim just a marketing gimmick and when is it real, and how can consumers tell the difference?
"I'm skeptical that you can," Arthur Caplan, the University of Pennsylvania ethicist, said bluntly. Advertising is built on manipulating images and words, after all. "It's simple for a company to create an image that makes them appear to be socially responsible," said Robert Passikoff, the president of the brand-loyalty consulting firm Brand Keys.
With environmental issues, phony marketing is called greenwashing, and the vast majority of companies do it, according to surveys by TerraChoice, an environmental-marketing outfit that's part of Underwriters Laboratories. Common tactics include assertions that aren't backed up by respected certifications, vague claims like "all-natural," and meaningless claims such as touting a product as "CFC-free"—meaningless because all use of chlorofluorocarbons (CFCs), which deplete the Earth's protective ozone layer, has been banned internationally since the 1990s.
Consultant Jacquelyn Ottman has written an entire book telling companies how to eco-pitch themselves, entitled, appropriately, Green Marketing. "Use highly illustrative visuals to strengthen the upbeat emotional appeal of environmental advertising," she suggests. And, "Make illustrations big, bright, and beautiful" by showing, for instance, "a close-up shot of a spotted owl looking all feathery and cute or a nest of little owls." To be fair, Ottman isn't simply pushing image; she further advises business readers that there has to be genuine green action behind the owls. Yet, as she admitted to me in an e-mail interview, "Not sure if [consumers] are equipped to catch the fakes."
Food is another area where questionable marketing abounds. Food writer Michael Pollan, in his book The Omnivore's Dilemma, described buying a free-range, organic chicken at Whole Foods, sold by a company called Petaluma Poultry, whose packaging boasted that Petaluma's "farming methods strive to create harmonious relationships in nature, sustaining the health of all creatures and the natural world." The label even gave the chicken a name: Rosie. But when Pollan tracked down his chicken, its ostensibly "harmonious" farm "turns out to be more animal factory than farm," he wrote. "She lives in a shed with twenty thousand other Rosies," and her supposed free range is a door that "remains firmly shut until the birds are at least five or six weeks old."
The mass-production chicken giant Perdue Farms ran a TV commercial in 2009 showing company chairman Jim Perdue strolling through a barn with a bunch of happy hens waddling around, while bragging that all Perdue chickens are cage-free. Wow. So Perdue has become, like, organic and stuff? No. All factory-farmed roasters are technically cage-free. The only time that "cage-free" matters is for egg-laying hens.
As for apparel, two University of Missouri researchers published a paper in 2011 asserting that shoppers are willing to pay an extra 15 to 20 percent for clothing manufactured via "sustainable and ethical" practices—but these same shoppers were skeptical when manufacturers claimed to be doing exactly what they sought.
In theory, the kinds of standards cited in the introduction could help consumers find their way through the marketing. But there are far too many labels, and far too little proof behind them. For the environment, the Ecolabel Index has catalogued 365 seals and certifications. Food can be barn roaming, local, natural, vegetarian fed, grass fed, antibiotics-free, preservatives-free, free of added hormones, free of artificial flavors, free of GMOs, minimally treated, family farmed, certified humane raised, sustainable, dolphin safe, trans fat–free, and a lot more. On top of that, add the lists compiled by consumer organizations like PETA, the Monterey Bay Aquarium's Seafood Watch, and Climate Counts.
Only a few terms are actually defined. The US Department of Agriculture has pretty strict standards for organic produce and meat, and much more vague ones for free range and free roaming. Dolphin Safe is a trademark of Earth Island Institute, a nonprofit environmental group, and is supposed to set standards for catching tuna in a way that doesn't harm dolphins. The so-called leaping-bunny logo of the Coalition for Consumer Information on Cosmetics, for personal care and household products, is one way to show that no animal testing was done. However, Tom's of Maine uses a different no-animal-testing bunny from PETA, and Trader Joe's has yet a third bunny. "Fair trade" has—or had—a specific meaning if the label is on coffee, cocoa, rice, sugar, tea, roses, and soccer balls, because an internationally recognized group called the Fairtrade Labelling Organizations International administers those certifications. But the US affiliate, Transfair USA, has now split off. And, in any case, the same term on clothing is meaningless.
How much time does a concerned consumer want to devote to this research? Labor activists suggest checking clothing labels to see where a garment was made. The SEIU's Mark Levinson favors Caribbean factories, because at least they use US-made textiles. Until recently, Jeff Ballinger had been advising shoppers to "go for the countries that are further up the ladder of democracy," on the theory that the workers there have more rights than in dictatorships. "If it's made in Taiwan or South Korea, maybe they don't have a union, but they can vote their governments out," he explained. He's had second thoughts about that tactic ever since a fellow activist pointed out that a lot of sweatshop workers in those countries may be undocumented foreigners who can't vote.
Ah, the Web will save us! And to some degree, that's true. A company that's polluting, using sweatshop labor, or cheating its workers has a tougher time keeping its nefarious deeds secret nowadays. "The guy that was standing by the Dumpster ten years ago watching them pour chemicals, now he can take out his BlackBerry with a camera and have it out to the world within minutes, or videotape it and put it on YouTube," said Palio Communications's Michael Myers.
Yet if social networking can uncover phony greenwashing, it can equally spread phony green attacking. The Body Shop suffered from that in 2006, brand strategist Carol Holding recalled, after it was bought by French cosmetics giant L'Oréal. While the Body Shop is famous for its policy of not testing on animals, L'Oréal does test, and rumors raced online that the Body Shop would knuckle under to its new owner. Animal rights groups called for a boycott, even as company officials insisted that their policies wouldn't change. Indeed, the Body Shop ultimately retained its policies and its place on PETA's list of nontesting companies.
A positive image "is hard to gain and very easy to lose," warned Northwestern University's Richard Honack. "You can lose it with one bad incident. It goes out viral, and [people begin saying,] 'I'm not using those products anymore.'"
The best way to judge whether to trust a corporate image is to remember that these companies are out to make a buck, and they will be most likely to go green, humane, and squishy if it makes business sense. "It has to be integrated into the business itself," Carol Holding said. "That's when it's authentic." She gave the example of Liz Claiborne Inc.'s long-running campaign, ever since the early 1990s, to raise awareness of domestic abuse. "They do it because their customers are women," Holding explained. "If you have IBM picking up abused women as a cause, it's totally phony. There is no connection to the business."
Fortune's 2004 "Best Places" citation of Timberland noted that employees used their company-paid volunteer time "at the Nashville Rescue Mission this December to fit 217 men with shoes and boots." While those 217 pairs of footwear were presumably donated, the mission employees and any volunteers from other organizations might want to buy shoes someday and would remember Timberland fondly.
CSR ethics can also be reflected in the corporate culture. It shows up in qualities like having an ombudsman or a place where whistle-blowers feel comfortable reporting violations, or quickly recalling faulty products without threats from regulators. In February 2010, Fortune profiled a management consultant, Dov Seidman, who has built an entire business of more than 400 big-name clients on this concept, asserting, as the magazine put it, that "in today's wired and transparent global economy, companies that 'outbehave' their competitors ethically will also tend to outperform them financially." The classic example dates to 1982 but is still evoked frequently: Johnson & Johnson's reaction when seven deaths were traced to its Extra Strength Tylenol. The Food and Drug Administration asked J&J to withdraw the four manufacturing lots that the suspect capsules had come from. Of its own volition, J&J went further, recalling all 31 million containers of the pills—the entire production line.
Certainly, companies have an incentive to be socially responsible if it can save hard cash, and sometimes it does. By now, the corporate world is overflowing with environmental money-saving examples, including CFL and LED lightbulbs, better insulation, and motion-sensor lights. Timberland officials cite the solar panels at the California distribution center, and the reflective white roof and a "new premium-efficiency" heating, air-conditioning, and ventilation system at the New Hampshire headquarters. Moreover, contracting with the most reliable eco-tanneries means less need for oversight, while some of the materials for the ecological Earthkeeper line are less expensive than standard material.
Even if it's only image, by now, CSR has become an integral part of many companies' brands. Timberland would just be a bunch of sturdy boots without it. American Apparel would have no protection against accusations of sleaze. Starbucks would be another chain selling gourmet coffee, perhaps no better than Dunkin' Donuts, certainly less cool than a neighborhood café. Trader Joe's would still be a cute alternative grocer, but it wouldn't be a cuter version of Whole Foods. Tom's wouldn't exist.
Or, in the end, is the whole exercise pointless?
If everyone in the business world from Walmart to Nike to the Economist is now touting the virtues of corporate social responsibility—and their own CSR PR, in particular—consumer activists who have been fighting these companies for years might have a moment of doubt. Is that really it? Victory? The worries go deeper than image and marketing, to the basic question of whether CSR is, by definition, a contradiction in terms. Skeptics tend to fall into two camps.
One position is that CSR is meaningless because it's limited and voluntary. No company can survive in today's economy if it ignores fundamentals like globalization, competition, and cost pressures, and those business considerations don't allow for ethics on a company-by-company basis. So LED bulbs save a few pennies and attract a few customers; most CSR efforts are expensive. The network of subcontractors is too long and diffuse to monitor. The few companies that try to be ethical will go bankrupt. And since actions like using recycled ingredients or solar energy are voluntary decisions, the easiest and most logical choice is to stop.
Thus, this camp of skeptics argues, overcoming these powerful, built-in, worldwide, competition-driven pressures requires a counterforce equally powerful, an infrastructure that doesn't depend on a particular CEO's whim and can't be bypassed by a business with cold feet. That's also why a union is so important, with its legally binding contracts, independent voice to counter management, and outside monitoring.
"It was always misguided that, rather than relying on laws, we're going to rely on the conscience, the largesse, of corporations to do the right thing," the SEIU's Mark Levinson scoffed. "It's very easy and comforting. You don't have to have the messy business of passing laws." Former US labor secretary Robert Reich wrote in his 2007 book Supercapitalism, "The only way for the citizens in us to trump the consumers and investors in us is through laws and regulations that make our purchases and investments a social choice as well as a personal one." As one example, he endorsed paid leave, going beyond the Family and Medical Leave Act, "so workers can upgrade their skills or take the time to attend to a newborn or sick parent." Maybe there could be harsh penalties for pollution, a tax on carbon emissions, or more subsidies for alternative energy.
Yet even those sorts of rules might not be enough. Just watch a big company declare that unless it's exempted from a particular regulation, it will take its jobs to Bangladesh, China, or some other place with weaker laws.
The other position is that CSR is meaningless because all businesses encourage unnecessary consumption. Everyone needs food, toothpaste, shoes, and clothing. And in the modern world, let's concede that mobile phones and computers are a basic necessity. But how many pairs of shoes, and how many computers? Do we really need $3.75 lattes? Or Trader Joe's chicken-sausage calzone with two cheeses and red onions? Or iPods?
Starbucks, Trader Joe's, and Steve Jobs all invented markets that never existed before. Who knew that we could have a device that could easily, cheaply, and legally download our specific taste in music? Who knew that we needed fancy coffee every day? As Howard Schultz said in his second book, "The best innovations sense and fulfill a need before others realize the need even exists."
These invented "needs" do more than waste consumers' money. Trees are cut down, oil is dug up, climate-destroying gases are emitted, and water is siphoned from depleted lakes to create these "natural" and "ethical" products.
Obviously, such criticisms can get carried to ridiculous extremes. If no one ever shopped at Starbucks, Trader Joe's, and all the rest, those businesses would go bankrupt. Their employees would lose their jobs and, therefore, also stop shopping at Starbucks, Trader Joe's, and the rest. Then the companies that supply, ship, advertise, and do the accounting for the first tier of companies would go bankrupt.
"Can you have a transnational corporation that is built on a business model of continuing expansion, selling more things every year, and be sustainable?" Greenpeace's Rolf Skar asked rhetorically. "They are valid questions, but if you answer no, we can't have continual growth, even as the population expands globally."
Well, few people live by absolutes, and activists really would like to believe they can nudge business in the direction of social responsibility—as well as keep drinking their lattes and using iPods. So they find niches of hope.
On the question of globalization, antisweatshop activist Jeff Ballinger noted that brands like Hanes, Russell Athletic, and Timberland own some of the factories that produce their underwear and shoes and therefore can maintain a bit more oversight. In addition to American Apparel's wares, a limited amount of clothing continues to be manufactured in the United States, including about 20 percent of the New Balance label, according to Ballinger, plus the highest-end designer jeans and 20 to 30 percent of what's sold at the youth chain Forever 21. The website StillMadeinUSA.com lists dozens of clothing lines that it says are American sewn, along with stores that sell them.
These are not the greatest solutions. By and large, the StillMadeinUSA.com offerings are frumpy or no-name clothes, without the cachet of the name brands made in sweatshops in Bangladesh, and a lot of the US work is done in a subindustry of microsubcontractors paying wages below the federal minimum, in hidden enclaves in Los Angeles, New York City, and other cities. Nevertheless, presumably the lousy conditions at these shops are easier to uncover than the overseas versions, and in fact lawsuits have ferreted out some of them. At least these ideas are a start.
Although the AFL-CIO's Ron Blackwell considers most codes of conduct too weak, he allowed that having a code, a mission statement, or some other expression of ethics is better than not having one: "If they say they endorse certain practices and you show violations, there is at least a moral force to change that." For similar reasons, he pointed to the way Starbucks brags about its health coverage for part-timers. With so much publicity, it would be a huge PR disaster for Starbucks to renege. "This is a customer-service business, and they want their employees to exude pride in the company," he said. Finally, Blackwell puts some faith in activist shareholders, who can hit publicly traded companies where it hurts.
As for the issue of overconsumption, luckily, more people are worrying about this and tying to limit their resource use, through everything from municipal recycling programs to the consumer-trading website Freecycle to vintage shops. Economists are rethinking the way gross domestic product is measured, so that the consumption of resources doesn't automatically get counted on the positive side of the ledger. Timberland claims its boots are really ecological because they last forever.
Greenpeace, Rolf Skar said, doesn't try to tackle the basic philosophy of consumerism. That would be too overwhelming. "We're looking at pretty discrete questions," he said, like the deforestation caused by one pulp-and-paper mill or one cattle ranch in the Amazon. One acre of rain forest at a time.
Acknowledgments
If you want a good conversation starter or pickup line, ask people what companies they consider socially responsible and also hip.
During the past couple of years, when friends and colleagues would question me about the topic of my next book, I'd briefly describe the theme—"I'm writing about six companies that are seen as trendy and ethical"—and immediately, like a good reporter, I'd turn the question around: "Which companies would you choose?" Most people love "best" lists, and they also love being asked their opinions, so the suggestions would flood in. Anecdotes, arguments, agreement, sources, head-slapping, eye-rolling, laughter, groans. Someone's friend had worked at Trader Joe's. Someone else knew someone who once was a manager at Apple. Everyone adored Apple. Everyone hated Starbucks, but did they prefer Gorilla Coffee, or Café Regular, or Ozzie's, and was Café Regular du Nord as good as the original Café Regular? I got into discussions at all sorts of places—at my book club and at dinner parties, with my running partners and at my French class, on a charity fund-raising walk and at Jewish funeral shiva minyans.
So thank you, Adriana, Ann, Ben, Cara, Dan, Dan, Ed, Elaine, Elizabeth, Erik, Gabriel, Greg, Jan, Jeanne, Jennifer, Jo, Joe, Karen, Kathleen, Les, Lillian, Lisa, Lisa, Mari, Marta, Mary, Michael, Michael, Mike, Mike, Moira, Mort, Nancy, Nancy, Paola, Patty, Reba, Rick, Scott, Sharon, Sharon, Susana, Theresa, Tom, Trina . . . I won't name you all—I don't even know all your names—but you know who you are.
(Also, thanks to those of you who donated your copies of Allure, Harper's Bazaar, InStyle, Marie Claire, Seventeen, and Teen Vogue for my research.)
In addition, special thanks to my agent, Lauren Abramo, of Dystel & Goderich Literary Management, and my editors at Beacon Press, Allison Trzop and Joanna Green, who had faith in my selections—and one more thanks to Joanna, who was absolutely right about where the excess could be trimmed. Thanks to those who agreed to a formal interview. And finally, as always, thanks to my family for putting up with my frantic intensity in those last (many) months of finishing the manuscript.
Notes
As a guide for curious readers, these notes indicate the most important books, reports, and newspaper and magazine articles that I consulted for particular points, but no list could possibly encompass all my research. My main source of information was the interviews I conducted between August 2009 and March 2011, plus my direct observations from visits to dozens of stores. In addition, I browsed the six companies' websites along with various consumer, advocacy, and government sites and read voluminous press releases and other official handouts from these companies, most of which are clearly identified in the text. When a news event has been widely reported—such as Apple's problem with the antennas on its iPhones in 2010 or Walmart's green initiatives—I give no specific citation, because I consulted a variety of news sources.
As for the companies themselves, I was able to interview many executives at Timberland and Tom and Kate Chappell at Tom's of Maine, as well as tour both headquarters and Tom's main factory. Trader Joe's rarely grants press interviews and outright declined my request. American Apparel and Starbucks said they would consider my requests but ultimately failed to reply to numerous queries from winter 2010 through spring 2011, though American Apparel did allow me to tour its facility and interview a press spokesperson. Apple failed to respond to any queries.
INTRODUCTION. THE IMAGE
The information about Steve Jobs's wedding is from Jeffrey S. Young and William L. Simon, iCon: Steve Jobs, the Greatest Second Act in the History of Business (Hoboken, NJ: Wiley, 2005), p. 193.
The Bloomberg Businessweek cover story about debt-ridden consumers who splurge on lattes is Devin Leonard, "The New Abnormal," August 2, 2010.
The two articles in the November 2010 issue of Institutional Investor were Imogen Rose-Smith, "No Turning Back," p. 38, and Katie Gilbert, "Money from Trees," p. 42.
The New York Times's Earth Day reference is from Leslie Kaufman, "On 40th Anniversary, Earth Day Is Big Business," April 22, 2010.
The specific quote from the Economist's cover package of January 19, 2008, is on p. 1.
The report from the International Organization for Standardization is "Guidance on Social Responsibility" (final draft, as of summer 2010), ISO/FDIS 26000.
Robert Levering's quote about R. J. Reynolds comes from my book The Overloaded Liberal: Shopping, Investing, Parenting, and Other Daily Dilemmas in an Age of Political Activism (Boston: Beacon Press, 2010), p. 179.
I actually interviewed Calvert's Paul Hilton in July 2008 for The Overloaded Liberal, although I didn't use that particular quote in that book.
John Leland's quote comes from the paperback edition of his book Hip: The History (New York: Harper Perennial, 2005), pp. 69 and 61.
The quotes from No Logo, by Naomi Klein, are from the paperback edition (New York: Picador, 2002), pp. 68, 21, 16, respectively.
Lee Eisenberg's quote is from Shoptimism: Why the American Consumer Will Keep on Buying No Matter What (New York: Free Press, 2009), pp. 186–87.
There are a couple of references from Juliet B. Schor, The Overspent American: Why We Want What We Don't Need (New York: Harper Perennial, 1999). The bulk of the information about how people's role models have become ever more ritzy is found on pp. 3–10, and the direct quote about inner-city tastes is from p. 40.
"Conceptual Consumption" is by Dan Ariely and Michael I. Norton, Annual Review of Psychology 60 (2009): 475–99.
Rob Walker, Buying In: The Secret Dialogue Between What We Buy and Who We Are (New York: Random House, 2008), p. xiii.
The ideas about cult branding come from Matthew W. Ragas and Bolivar J. Bueno, The Power of Cult Branding: How 9 Magnetic Brands Turned Customers into Loyal Followers (and Yours Can, Too!) (New York: Crown Business, 2002).
1. TOM'S OF MAINE: WOODSTOCK TOOTHPASTE
Tom Chappell's book is The Soul of a Business: Managing for Profit and the Common Good (New York: Bantam, 1993), and the quotes (in order) are on pp. 216 and 158, regarding why he wouldn't sell the company; pp. 187–88, for the descriptions of early eco-practices; p. 49, for the history of corporate "tithing"; p. 65, for the chat with the secretary; pp. 111–12, for the description of himself as a young insurance salesman; p. xi, for the explanation of why he enrolled at Harvard Divinity School; pp. x and 24, for what he learned from Harvard; and p. 215, for the later reference about why he wouldn't sell.
Jacquelyn A. Ottman, Green Marketing: Opportunity for Innovation (Lincolnwood, IL: NTC Business Books, 1998), describes Tom's of Maine on pp. 196–99; the quote is on p. 196.
The information about the government investigations into triclosan is from Andrew Martin, "Popular Antibacterial Chemical Raises Safety Issues," New York Times, August 20, 2011.
The citation from Leo Hickman, ed., A Good Life: The Guide to Ethical Living (London: Transworld, 2008), is from p. 159.
Also, Duncan Clark and Richie Unterberger, The Rough Guide to Shopping with a Conscience (New York: Rough Guides, 2007), p. 195.
2. TIMBERLAND: HOW GREEN IS MY LEATHER
Some good sources about Timberland's history, in addition to the timeline on its website, are Steven Flax, "Boot Camp," Inc., September 1, 1987, and the above-cited Buying In, pp. 81–84.
A lot has been written about Wyclef Jean, his work in the Haiti hurricane, the financial investigations into his charity, and his campaign for president of Haiti—including an article I wrote for Portfolio.com in January 2010 titled "A Foot Soldier for Haiti (and Timberland)," <http://www.portfolio.com/>.
I got some great background about leather tanning and chromium from the US Environmental Protection Agency website at "9.15 Leather Tanning," <http://www.epa.gov/>.
In addition to material found at the Timberland website, there was good information about the company's carbon footprint in a couple of Wall Street Journal articles: Jeffrey Ball, "Six Products, Six Carbon Footprints," October 6, 2008, and Jeffrey Ball, "Green Goal of 'Carbon Neutrality' Hits Limit," December 30, 2008.
The reference to my Portfolio.com article is the one cited above, "A Foot Soldier for Haiti (and Timberland)."
3. STARBUCKS: COFFEE AS A BRAND NAME
Howard Schultz's story of how he created and then returned to Starbucks comes from his two books: Pour Your Heart Into It: How Starbucks Built a Company One Cup at a Time (and Dori Jones Yang; New York: Hyperion, 1997) and Onward: How Starbucks Fought for Its Life without Losing Its Soul (with Joanne Gordon; New York: Rodale, 2011).
First, the quotes from Pour Your Heart into It: The quote at the beginning of the chapter about the front porch is from p. 5, and the one about "the Starbucks experience" is on p. 251. The description of Hammarplast is on p. 22, and the quote about his father is on p. 3. The description of his first taste of Starbucks coffee is on p. 26. The descriptions of "dreadful" and "swill" American coffee pre-Starbucks are on pp. 26 and 30, while the quote about Italy is from p. 52. The description of his goals for Il Giornale is found on p. 77. Schultz's acknowledgement of not quite being the "third place" is on p. 120, and the quote about the Italian cafés is on p. 51. His claim about baristas making eye contact is on pp. 250–51. The quote about Starbucks being targeted is on p. 294. The statistics about the growth of gourmet-coffee consumption are on p. 181, while the quotes are on pp. 278–79. The quote about landlords is on p. 279; the quote about perfume is on p. 252; and the one about treating workers like family is on p. 127. The union decertifications are discussed on pp. 108–9 and 137. The "hot-cup team" quotes are on pp. 303–4. The comparison to Nike is from p. 77.
Now, from Onward. The quotes about turning his attention to expanding Starbucks and getting bored with day-to-day operations are from p. 16; the quote about the 15th Avenue and Roy Street shops is on p. 279; the quote about how hard baristas work is on p. 122; the quotes about the "lean" production methods are on pp. 281 and 181; the complaint about four-dollar lattes is on p. 146; and the quote about reducing fat content is on p. 167. The quote denying aspirational motivation is on p. 159.
Bryant Simon, Everything but the Coffee: Learning About America from Starbucks (Berkeley: University of California Press, 2009): for the description of old-type coffee, p. 23; Simon's fruitless attempts to start a conversation, p. 100; his complaint about the music, p. 163; his interview with farmers, p. 217; and his comment about yuppies and bobos, p. 11.
The fourth book heavily used for this chapter is Kim Fellner, Wrestling with Starbucks: Conscience, Capital, Cappuccino (New Brunswick, NJ: Rutgers University Press, 2008). The description of trying to talk with other customers is on pp. 116–19; the discussions about whether Starbucks is more socially responsible than other cafés are on p. 134; the praise of its environmental work is on p. 102; and the comparison with the stringency of Rainforest Alliance standards is on p. 94. The author's interviews with Starbucks workers are on p. 111, as is the description of the low pay; the description of her work shift is from p. 151; and the discussion of the unionizing effort at the roasting plant is found on pp. 145–47.
Michael Gates Gill tells his story in How Starbucks Saved My Life: A Son of Privilege Learns to Live Like Everyone Else (New York: Gotham Books, 2007). The arcane coffee names are on p. 134; the descriptions of his coworkers and working life are on pp. 51, 217, and 224; the anecdote about working during his break is on p. 139; and the quote about not being able to afford a latte is on p. 13.
Numerous articles have been written about how Starbucks overexpanded, hurt its image, alienated its client base, and faced new competition in the early 2000s. Here are some I used: Ted Botha, "Bean Town," New York Times, October 26, 2009; Brad Stone, "Starbucks Plans Return to Its Roots," New York Times, March 20, 2008; Barbara Kiviat, "Starbucks Looks for a Fresh Jolt," Time, March 27, 2008; Brad Stone, "Original Team Tries to Revive Starbucks," New York Times, October 30, 2008; and Sara Kiesler, "Neighbor: Starbucks Stole My Ambience," SeattlePI.com, July 16, 2009; Susan Berfield, "Starbucks: Howard Schultz vs. Howard Schultz," BusinessWeek, August 6, 2009; Barbara Kiviat, "Starbucks Can Smell Growth," Time, January 21, 2010; Claire Cain Miller, "Now at Starbucks: A Rebound," New York Times, January 21, 2010.
The No Logo quote about garish decor is found on p. 131, and the anecdote about the Vancouver union is on p. 241.
There are a lot of sources of information about fair trade. I particularly relied on Rough Guide (cited above), pp. 23–24, and the website of TransFair USA (<http://transfairusa.org>). The specifics about price premiums came from Fred Pearce, Confessions of an Eco-Sinner: Tracking Down the Sources of My Stuff (Boston: Beacon Press, 2008), p. 22, and Ezra Fieser, "What Price for Good Coffee?" Time, October 5, 2009, p. 61. The later quotes from Eco-Sinner are from p. 23.
Two Wall Street Journal articles in particular discussed the attempt at Japanese-style production: Julie Jargon, "Latest Starbucks Buzzword: 'Lean' Japanese Techniques," August 4, 2009, and Julie Jargon, "At Starbucks, Baristas Told No More Than Two Drinks," October 13, 2010.
The information about loans to small businesses and job-creation partnerships is from "Howard's Way," Economist, October 8–14, 2011.
The Wall Street Journal article about unionizing efforts in Europe, New Zealand, and Chile is Julie Jargon's "Starbucks Workers Plan Chile Strike," July 11, 2011.
A few examples of Howard Schultz being photographed with paper cups—and I am limiting this to examples from after the publication of his second book, to give him the benefit of a raised eco-consciousness: photos accompanying the articles Julie Jargon, "Coffee Talk: Starbucks Chief on Prices, McDonald's Rivalry," Wall Street Journal, March 7, 2011; John H. Ostdick, "Heart of the Brand," Success, April 2011, p. 44; and Howard Schultz, "How Starbucks Got Its Mojo Back," Newsweek book excerpt, March 31, 2011, p. 50.
The book by Stacy Mitchell is Big-Box Swindle: The True Cost of Mega-Retailers (Boston: Beacon Press, 2006), p. 91.
The Shoptimism quote is from p. 178.
The Mayo Clinic reference is from its website (<http://www.mayoclinic.com/>), particularly the articles "Caffeine Content for Coffee, Tea, Soda, and More" and "Caffeine: How Much Is Too Much?"
The Morgan Stanley data on Starbucks's customers' income is from John Jannarone, "Grounds for Concern at Starbucks," Wall Street Journal, May 3, 2011.
The calculations about how much you'd save by skipping a latte are adapted from an online retirement-plan calculator from Fidelity Investments.
4. APPLE: THE COOLEST OF THEM ALL
The history and general information about Apple and Steve Jobs come mainly from the following books and articles: iCon (cited above); Owen W. Linzmayer, Apple Confidential 2.0: The Definitive History of the World's Most Colorful Company (San Francisco: No Starch Press, 2004); Fortune magazine's cover package "CEO of the Decade," November 23, 2009; Stephen Fry, "On the Mothership: A Confessed Apple Fanboy Gets Finger Time with the iPad—and Face Time with Steve Jobs," Time, April 12, 2010, p. 40; Farhad Manjoo, "Invincible Apple: 10 Lessons from the Coolest Company Anywhere," Fast Company, July–August 2010; Randall Stross, "What Steve Jobs Learned in the Wilderness," New York Times, October 2, 2010; and Leander Kahney, "Being Steve Jobs' Boss," Bloomberg Businessweek, October 24, 2010. And for a little insight into Jobs's personality, I read Daniel Lyons, Options: The Secret Life of Steve Jobs (Cambridge, MA: Da Capo Press, 2007).
But, of course, I also perused dozens of other articles in my research for this chapter, some of which are cited below in connection with specific topics. News events such as problems with the iPhone antenna, suicides at the Foxconn factory in China, and Steve Jobs's resignation have been widely reported.
The specific quotes from iCon are (in the order in which they're quoted) from pp. 235, 282, and 236; and the information about the Jobs family's political activity is on pp. 254–55.
The particular quotes from the Linzmayer book are (also in quote order) from pp. 295 and 298.
The Daniel Lyons quote is from "In iPad We Trust," Newsweek, February 8, 2010.
The reference to British prime minister David Cameron is from Catherine Mayer, "Reshaping British Politics from Within," Time, November 8, 2010.
The interview with Melinda Gates is Deborah Solomon, "The Donor," New York Times Magazine, October 22, 2010.
The iPod is a character in Arthur Phillips, This Song Is You (New York: Random House, 2009).
The reference to the branding consultants who studied the brain activity of Apple users is from Martin Lindstrom, "You Love Your iPhone, Literally," New York Times, October 1, 2011.
The Fortune "Business Person of the Year" ranking was in the issue dated January 10, 2011.
The Steve Jobs accolades come from the following: "The World's Most Influential People," Time, May 10, 2010; "27 Brave Thinkers," Atlantic, November 2009, "Brave Thinkers 2011," Atlantic, November 2011; "The 400 Richest Americans," Forbes, September 30, 2009 (although Jobs has made the list in other years as well); and "CEO of the Decade," cited above. And then, when Jobs announced his resignation, the New York Times quote is from Andrew Ross Sorkin, "The Mystery of Jobs's Public Giving," August 30, 2011.
The quote about secrecy in the product testing room is from Brad Stone and Ashlee Vance, "Apple Obsessed with Secrecy on Products and Top Executives," New York Times, June 23, 2009.
Jeffrey Sonnenfeld's comment is from "The Genius Dilemma," Newsweek, January 31, 2011, p. 12.
The article citing Jerome York is Joann S. Lublin and Scott Thurm, "Mum on Succession, Board Got Heat," Wall Street Journal, August 25, 2011.
The information about the CalPERS official asking the SEC to require more disclosure about CEO health came from Joann S. Lublin, "Investors Want Right to Know," Wall Street Journal, January 24, 2011.
Many, many stories have been written about Apple's obsessive micromanagement and its all-in-one business model. For the specific references to the rejected apps and the new guidelines, I used the following: Ryan Singel, "Now Apple Bans Tiger Woods Satire App. Does Big Media Care?" Wired.com, April 27, 2010; Joshua Brustein, "Apple's Struggle on Political Apps," New York Times, May 31, 2010; Jeff Bercovici, "Dirty Apps? How Magazines Are Handling Apple's Erratic Censorship," Daily Finance, August 11, 2010; Yukari Iwatani Kane and Thomas Catan, "Apple Blinks in Apps Fight," Wall Street Journal, September 10, 2010; and Jenna Wortham, "Apple Plays to App Developers by Revealing Its Policy Guidelines," New York Times, September 10, 2010. Also, the quote about the Faustian bargain is from Daniel Lyons, "Think Really Different," Newsweek, April 5, 2010, p. 46.
The rare inside look at working at Apple is from Adam Lashinsky, "Inside Apple," Fortune, May 23, 2011, p. 124.
The Wall Street Journal describes training at the Apple Stores in Yukari Iwatani Kane and Ian Sherr, "Secrets from Genius Bar: Full Loyalty, No Negativity," June 15, 2011.
The interview with the Wintek workers is from David Barboza, "Workers Poisoned at Chinese Factory Wait for Apple to Fulfill a Pledge," New York Times, February 23, 2011.
The formation of the Eco-Patent Commons was mentioned in Mary Tripsas, "Everybody in the Pool of Green Innovation," New York Times, November 1, 2009.
The interview with Steve Jobs about environmental issues was from Peter Burrows, "Apple Launches Major Green Effort," BusinessWeek, October 5, 2009, p. 68.
The Atlantic cover story about the global elite is Chrystia Freeland, "The Rise of the New Global Elite," Atlantic, January–February 2011, p. 44.
The discussion about Apple taking advantage of bulk discounts on iPad components was in Jenna Wortham, "So Far Rivals Can't Beat iPad's Price," New York Times, March 7, 2011.
Of course, numerous articles have been written about the impact of the iPad on publishing, but here are the three examples specifically cited in which experts predicted the tablet could save books and newspapers: David Carr, "A Savior in the Form of a Tablet," New York Times, January 4, 2010; Walter Isaacson, "Information Wants to Be Paid For," Atlantic, July–August 2010, p. 47; and "'iPads Will Save Newspapers,' Says Unilever CMO," Marketing, October 13, 2010.
I read about the accidental social benefits of iPads in two articles: Jennifer Valentino DeVries, "Using the iPad to Connect," Wall Street Journal, October 13, 2010; and Winnie Hu, "Math That Moves: Schools Embrace the iPad," New York Times, January 5, 2011.
The quote describing Timothy Cook is from Miguel Helft, "The Understudy Takes the Stage," New York Times, January 24, 2011.
5. TRADER JOE'S: ARE WE HAVING FUN YET?
The reference to the Brooklyn shopper is from Anthony Ramirez, "A Tiki Room with Aisles of Discounts Makes Its City Debut," New York Times, March 18, 2006.
For the Albany reference, Chriss Churchill, "Trendsetter Shops Bypass Region," (Albany, NY) Times Union, May 11, 2008.
All the Fortune references are from Beth Kowitt, "Inside the Secret World of Trader Joe's," Fortune, September 13, 2010.
Here are the references from Len Lewis, The Trader Joe's Adventure: Turning a Unique Approach to Business into a Retail and Cultural Phenomenon (Chicago: Dearborn, 2005): the history of the name, p. 3; the lack of philanthropy, p. 187; Charles Shaw complaint, p. 123; and about labor costs, p. 145. The "Best Companies" claim is made several times, but the specific quote is on p. ix; the starting salaries are on pp. 143–44; and the two demographic descriptions are on pp. 112 and 72, respectively.
From The Rough Guide to Shopping with a Conscience (cited above), pp. 156–57.
Theo Albrecht's obituary was written by Patrick Donahue and Holger Elfes in Bloomberg Businessweek, August 2, 2010.
The unionizing attempts were mentioned in Trader Joe's Adventures (p. 143) and The Rough Guide to Shopping with a Conscience (p. 157).
The Atlantic article is Don Peck, "Can the Middle Class Be Saved?" September 2011, p. 60.
The description of the tasting-panel members traveling the world is from Julia Moskin, "For Trader Joe's, a New York Taste Test," New York Times, March 8, 2006.
6. AMERICAN APPAREL: SEX AND THE T-SHIRT
Almost any book or article you pick up will cite a different country, year, or methodology for calculating pay rates and weekly hours worked in foreign sweatshops. I took some examples from the following books and newspaper articles: Confessions of an Eco-Sinner, cited above (pp. 102–3); my book The Overloaded Liberal, cited above (p. 146); Vikas Bajaj, "As Labor Costs Rise in China, Textile Jobs Shift Elsewhere," New York Times, July 15, 2010; Steven Greenhouse, "A Factory Defies Stereotypes, but Can It Thrive?" New York Times, July 18, 2010; Vikas Bajaj and Julfikar Ali Manik, "Bangladesh Arrests 21 After Rallies," New York Times, August 17, 2010; Patrick Barta and Alex Frangos, "Southeast Asia Linking Up to Compete with China," Wall Street Journal, August 23, 2010; and Wayne Arnold, "Vietnam Holds Its Own Within China's Vast Economic Shadow," New York Times, January 1, 2011.
Regarding Fred Pearce's and Nicholas Kristof's arguments about the relative advantages of sweatshops: Pearce's comments come from his book Confessions of an Eco-Sinner. Kristof has written extensively about these topics in the New York Times, so I'll cite just one example: "Where Sweatshops Are a Dream," January 15, 2009.
The BusinessWeek quote is from Christopher Palmeri, "Living on the Edge at American Apparel," June 27, 2005.
The Portfolio quote is from Claire Hoffman, "Barely Legal," November 2008, p. 114.
The particular citations in the ISO report (cited above) begin on p. 31.
The sentiments about moving work offshore are in Allison Abell Schwartz, "American Apparel's Unhip Finances," BusinessWeek, August 9, 2010.
Regarding the ICE investigation of American Apparel, the lawyer's explanation and the politicians' comments were reported in several news stories, including Julia Preston, "A New Strategy on Illicit Work by Immigrants," New York Times, July 3, 2009, and Julia Preston, "Immigrant Crackdown Leads to 1,800 Pink Slips," New York Times, September 20, 2009. The number of layoffs was later recalculated by the company.
Rob Walker discussed the supposed changes in American Apparel's marketing on pp. 223–26 of Buying In.
The Eisenberg reference is from p. 52 of the above-cited book Shoptimism.
For the specific American Apparel and other ads in the various magazines, here are the dates and page numbers: Harper's Bazaar, September 2009, pp. 2 and 213; Marie Claire, January 2010, p. 67; Seventeen, December 2009–January 2010, p. 21; Teen Vogue, March 2010, pp. 4–5, 41, 47, and the Jimmy Choo insert between p. 42 and p. 43. In the case of the Onion, it's always the back page: February 25–March 3, March 11–17, March 25–31, April 8–14, April 22–28, and June 3–9, all in 2010. There isn't space to list all the rest of the publications I looked at—and, really, you could probably pick up any issue of the named magazines and find the same thing.
The reference to Abercrombie & Fitch's marketing is from David Carr, "A Naked Calculation Gone Bad," New York Times, January 24, 2011.
As the chapter notes, numerous publications have discussed the allegations of sexual harassment and a sexually charged workplace at American Apparel. To name just the ones specifically quoted: Claudine Ko, "Meet Your New Boss," Jane, June–July 2004; the Portfolio article "Barely Legal," cited above; and the book Buying In (pp. 217, 225–26), cited above. As well, I have read the complaints filed by Nikky Yang, Bernhard-Axel Ingo Brake, and Roberto Hernandez.
Again, many of the sources cited above talk about the history of American Apparel and about Dov Charney and his operating style, including "Barely Legal," in Portfolio; "Living on the Edge at American Apparel," in BusinessWeek; and "Meet Your New Boss," in Jane; plus pp. 218–20 of Buying In. On the American Apparel website (<http://www.americanapparel.net/>), go to "About Us," then "Meet Dov Charney," then "My Name Is Dov Charney."
The Gawker.com posting about the employee-grooming memos was reported on New York magazine's website (<http://www.nymag.com/>) on June 18, 2010, under the headline "Revealed in Remarkable Detail: American Apparel's Beauty Guidelines."
The allegations against attorney Keith Fink have been covered in numerous publications, including Saabira Chaudhuri, "American Apparel Aims to Bring Down 'Celebrity Ambulance Chasing' Lawyer," FastCompany.com, December 1, 2008; "The Story Behind American Apparel's Sham Arbitration," Wall Street Journal online, November 4, 2008; and James Covert, "Suits Fly at American Apparel," New York Post, December 2, 2008.
The Rough Guide to Shopping with a Conscience reference is from p. 193.
The company's financial troubles have been discussed in many news articles, but the specific interview with Charney about the 2011 bankruptcy warning is from the online post by Matt Townsend, "American Apparel Glamour Fades Amid Cash Crunch" Bloomberg.com, April 1, 2011. Other good sources: Laura M. Holson, "He's Only Just Begun to Fight," New York Times, April 14, 2011; Matt Townsend, "American Apparel Gets Adult Supervision," Bloomberg Businessweek, April 18–24, 2011, p. 21; and "American Apparel Gets up to $43M in Rescue Financing, Avoiding Bankruptcy," New York Post, April 21, 2011.
Rob Walker's praise of industry veteran Marty Baily is from p. 224 of the above-cited Buying In.
Finally, the teenagers named in this article were interviewed with the permission of their parents.
7. THE REALITY
Frito-Lay's plan for healthier junk food was reported in Mike Esterl, "You Put What in This Chip?" Wall Street Journal, March 24, 2011.
The quotes from Green Marketing (cited above) are from pp. 119 and 46, respectively.
Michael Pollan's book is The Omnivore's Dilemma: A Natural History of Four Meals (New York: Penguin, 2006), pp. 135, 140.
The University of Missouri survey is Jung Ha-Brookshire and Gargi Bhaduri, "Do Transparent Business Practices Pay? Exploration of Transparency and Consumer Purchase Intention," Clothing and Textile Research Journal 29, no. 2 (April 2011): 135–49.
The details about the Fairtrade Labelling Organizations International came from The Rough Guide to Shopping with a Conscience (cited above), pp. 25–26 and 143.
The "Best Places" citation about Timberland is from Robert Levering and Milton Moskowitz, "The 100 Best Companies to Work For," Fortune, January 12, 2004, p. 56.
The article on Dov Seidman is Richard McGill Murphy, "Why Doing Good Is Good for Business," Fortune, February 8, 2010, p. 90.
The quotes from Robert B. Reich, Supercapitalism: The Transformation of Business, Democracy, and Everyday Life (New York: Knopf, 2007), are on p. 127.
The Howard Schultz quote about fulfilling a need is from p. 251 of Onward.
The information about Forever 21 is from Susan Berfield, "Forever 21's Fast (and Loose) Fashion Empire," Bloomberg Businessweek, January 24, 2011.
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Ethical chic : the inside story of the companies we think we love /
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THE ABBATIAL CROSIER
THE FULL SERIES OF
The Mysteries of the People
OR
History of a Proletarian Family
Across the Ages
By EUGENE SUE
_Consisting of the Following Works_:
THE GOLD SICKLE; or, _Hena the Virgin of the Isle of Sen_.
THE BRASS BELL; or, _The Chariot of Death_.
THE IRON COLLAR; or, _Faustine and Syomara_.
THE SILVER CROSS; or, _The Carpenter of Nazareth_.
THE CASQUE'S LARK; or, _Victoria, the Mother of the Camps_.
THE PONIARD'S HILT; or, _Karadeucq and Ronan_.
THE BRANDING NEEDLE; or, _The Monastery of Charolles_.
THE ABBATIAL CROSIER; or, _Bonaik and Septimine_.
THE CARLOVINGIAN COINS; or, _The Daughters of Charlemagne_.
THE IRON ARROW-HEAD; or, _The Buckler Maiden_.
THE INFANT'S SKULL; or, _The End of the World_.
THE PILGRIM'S SHELL; or, _Fergan the Quarryman_.
THE IRON PINCERS; or, _Mylio and Karvel_.
THE IRON TREVET; or _Jocelyn the Champion_.
THE EXECUTIONER'S KNIFE; or, _Joan of Arc_.
THE POCKET BIBLE; or, _Christian the Printer_.
THE BLACKSMITH'S HAMMER; or, _The Peasant Code_.
THE SWORD OF HONOR; or, _The Foundation of the
French Republic_.
THE GALLEY SLAVE'S RING; or, _The Family Lebrenn_.
Published Uniform With This Volume By
THE NEW YORK LABOR NEWS CO.
28 CITY HALL PLACE NEW YORK CITY
THE
ABBATIAL CROSIER
OR
BONAIK AND SEPTIMINE
A Tale of a Medieval Abbess
By EUGENE SUE
TRANSLATED FROM THE ORIGINAL FRENCH BY
DANIEL DE LEON
NEW YORK LABOR NEWS COMPANY, 1908
Copyright 1908, by the
NEW YORK LABOR NEWS CO.
INDEX
TRANSLATOR'S PREFACE v
PROLOGUE.
CHAPTER.
I. NARBONNE 3
II. ABD-EL-KADER AND ROSEN-AER 6
PART I--THE CONVENT OF ST. SATURNINE.
I. THE LAST OF THE MEROVINGIANS 15
II. CHARLES MARTEL 23
III. FATHER CLEMENT'S REFECTORY 33
IV. MORDECAI THE SLAVE-DEALER 40
PART II--THE ABBEY OF MERIADEK.
I. ELOI THE GOLDSMITH 47
II. THE INTENDANT RICARIK 57
III. THE ABBESS MEROFLEDE 62
IV. IN SIGHT OF THE ABBEY 69
V. ASYLUM 78
VI. WARRIOR AND ABBESS 83
VII. THE MOUSE-TRAP 89
VIII. THE MIRACLE OF ST. LOUP'S TEETH 94
IX. BRENN--KARNAK 102
X. MISTRESS AND MAN 117
XI. THE FLIGHT 122
XII. MOTHER AND SON 129
TRANSLATOR'S PREFACE
The turbulent epoch that rocked the cradle of the Carlovingian dynasty,
the dynasty from which issued the colossal historic figure of
Charlemagne, is the epoch of this touching story--the eighth of the
series of Eugene Sue's historic novels known collectively under the
title "_The Mysteries of the People; or, History of a Proletarian Family
Across the Ages_." From the seething caldron of the valleys of the
western Rhine, inundated by the Arabs from the south, the Frisians from
the north, the Saxons from the west, and in which the chants of Moslems,
of Christians and of barbarians mixed into the one common cry of
desolating war, the feudal social system, previously introduced by
Clovis, and now threatened to be engulfed, emerged from the chaos as a
social institution. Many a characteristic of feudalism would be missed
if this, a crucial period of its existence, is not properly apprehended.
As in all the others of this series of Eugene Sue's stories, the
information is imparted without the reader's knowledge. What may be
termed the plot seizes and keeps the interest from start to finish,
steadily enriching the mind with knowledge historically inestimable,
besides connecting with the era described in the previous story--_The
Branding Needle; or, The Monastery of Charolles_--and preparing the
ground for the thrilling events that are the subject of the succeeding
narrative--_The Carlovingian Coins; or, The Daughters of Charlemagne_.
DANIEL DE LEON.
New York, 1904.
PROLOGUE
CHAPTER I.
NARBONNE.
Cruel intestine wars between the descendants of the Frankish conquerors
were devastating Gaul when the Arab invasion took place in 719. The
invaders poured down from the Pyrenees and drove back or subjugated the
Visigoths. The exchange of masters was almost a gain to the inhabitants
of the region. The conquerors from the south were more civilized than
those from the north. Many of the Gauls,--either freemen, or colonists
or slaves--took so strongly to the southern invader that they even
embraced his religion, the religion of Mahomet, allured thereto by the
promises of a paradise peopled with houris. "The virtuous believer,"
declared the Koran, "will be taken to the delicious home of Eden,
enchanted gardens, through which well-shaded rivers flow. There,
ornamented with bracelets of gold, clad in green clothes of woven silk
and resplendent with glory, the faithful will recline upon nuptial beds,
the happy prize in the dwelling of delights." Preferring, accordingly,
the white houris promised by the Koran to the winged seraphs of the
Christian paradise, many Gauls embraced Mohamedanism with ardor. Mosques
rose in Languedoc beside Christian churches. More tolerant than the
bishops, the Arabs allowed the Christians to follow their own religion.
Moreover, Mohamedanism, founded by Mahomet during the previous century,
608, acknowledged the divinity of the Scriptures and recognized Moses
and the Jewish prophets as beings chosen by God, only it did not
recognize the godship of Jesus. "Oh, ye, who have received the
Scriptures, keep within the bounds of the faith. Speak only the truth
about God. Jesus is the son of Mary, and he was sent by the All-High,
but is not his son. Say not that God is a trinity. God is one. Jesus
will not blush at being the servant of God. The angels that surround the
throne of God obey God!"--thus spoke the Koran.
The town of Narbonne, capital of Languedoc under the dominion of the
Arabs, had in 737 quite an Oriental aspect, due as much to the clearness
of the sky as to the dress and customs of a large number of its
inhabitants. The laurel shrubs, the green oaks and palm trees recalled
the vegetation of Africa. Saracen women were seen going to or coming
from the fountains with earthen vessels nicely balanced on their heads,
and draped in their white clothes like the women of the time of Abraham,
or of the young master of Nazareth. Camels with their long necks and
loaded with merchandise left the town for Nimes, Beziers, Toulouse or
Marseilles. The caravans passed on these journeys, along the fields, a
great variety of settlements--mud hovels thatched with straw and
inhabited by Gallic peasants, who were successively the slaves of the
Visigoths and of the Musselmen; tents of a Barbary tribe, Arabian
mountaineers who had descended to the plains from the peak of Mt. Atlas,
and who preserved in Gaul the nomad habits of their old home, warriors,
ever ready to mount their tireless and swift horses in answer to the
first call of battle from the emir of the province; finally, and at long
distances apart, on the crests of the mountains, high towers where,
during war, the Saracens lighted fires for the purpose of signaling the
approach of the enemy to one another.
In the almost Musselman town of Narbonne, the same as in all the other
towns of Gaul under the sway of the Franks and the bishops, there were,
sad to say, public market-places where slaves were set up for sale. But
that which imparted a peculiar character to the market of Narbonne was
the diversity of the races of the captives that were offered to
purchasers. There were seen <DW64>s and negresses in large numbers, as
well as Ethiopians of ebony blackness; copper- mestizos; handsome
young Greek girls and boys brought from Athens, Crete or Samos and taken
prisoner on some of the frequent maritime raids made by the Arabs. A
skilful politician, Mahomet, their prophet, had incited in his
sectarians a passion for maritime expeditions. "The believer who dies on
land feels a pain that is hardly comparable with the bite of an ant,"
says the Koran, "but the believer who dies at sea, feels on the contrary
the delicious sensation of a man, who, a prey to burning thirst, is
offered iced water mixed with citron and honey." Around the slave market
stood numerous Arabian shops filled with merchandise mainly manufactured
at Cordova or Granada, centers, at the time, of Saracen art and
civilization: brilliant arms inlaid in arabesques with gold and silver,
coffers of chiseled ivory, crystal cups, rich silk fabrics, embroidered
hose, precious collars and bracelets. Around the shops pressed a crowd
of as various races as costumes: aboriginal Gauls in their wide hose, an
article that gave this section of Gaul the name of "Bracciata" with the
Romans; descendants of the Visigoths who remained faithful to their old
Germanic dress, the furred coat, despite the warmth of the climate;
Arabians with turbans of all colors. From time to time, the cry of the
Musselman priests, calling the believers to prayer from the height of
the minarets, mixed with the chimes of basilicas that summoned the
Christians to their devotions.
"Christian dogs!" said the Arabs or Musselman Gauls. "Accursed heathens,
damned degenerates!" answered the Christians; whereupon both proceeded
to exercise their own cult in peace. More tolerant than the bishops of
Rome, Mahomet said in the Koran: "Do not do violence upon men for reason
of their religion."
CHAPTER II.
ABD-EL-KADER AND ROSEN-AER.
Abd-el-Kader, one of the bravest chiefs of the warriors of Abd-el-Rhaman
during the life of this emir, who was killed five years before on the
field of Poitiers where he delivered a great battle to Charles Martel
(the Hammer)--Abd-el-Kader, after ravaging and pillaging the country and
the churches of Tours and of Blois, occupied one of the handsomest
dwellings in Narbonne. He had the house arranged in Oriental
fashion--the outside windows were closed up, and laurels were planted in
the inner courtyard, from the center of which a fountain jetted its
steady stream. His harem occupied one of the wings of the house. In one
of the chambers of this harem, covered with rich carpets of gay colors,
furnished with silk divans, and lighted by a window with gilded bars,
sat a woman of rare beauty, although about forty years of age. It was
easy to recognize by the whiteness of her skin, the blondness of her
hair and the blue of her eyes that she was not of Arabian stock. Her
pale and sad face revealed a settled and profound sorrow. The curtain
that covered the door of the chamber was pushed aside and Abd-el-Kader
entered. The swarthy-complexioned warrior was about fifty years of age;
his beard and moustache were grizzled; his face, calm and grave,
expressed dignity and mildness. He stepped slowly towards the woman and
said to her: "Rosen-Aer, we meet to-day for the last time, perhaps."
The Gallic matron seemed surprised and replied: "If I am not to see you
again, I still shall remember you. I am your slave, but you have been
kind and generous to me. I shall never forget that six years ago, when
the Arabians invaded Burgundy and raided the valley of Charolles, where
my family lived in happiness for more than a century, you respected me
when I was taken to your tent. I declared to you then that at the first
act of violence on your part, I would kill myself ... you ever treated
me as a free woman--"
"Mercy is the badge of the believer. I only obeyed the voice of the
prophet. But you, Rosen-Aer, did you not, shortly after you were brought
here a prisoner and Ibraham, my youngest son, was nearly dying, did you
not ask to take care of him the same as a mother would? Did you not
watch at his bedside during the long nights of his illness as if he were
your own son? It was, accordingly, in recompense for your services, as
well as in obedience to the behest of the Koran--_deliver your brothers
from bondage_--that I offered you your freedom."
"What else could I have done with my freedom? I am all alone in the
world.... I saw my brother and husband killed under my own eyes in a
desperate fight with your soldiers when they invaded the valley of
Charolles; and before those days I wept my son Amael, who had
disappeared six years before. I wept him then, as I do still every day,
inconsolable at his absence."
Rosen-Aer spoke these words and could not keep back the tears that
welled in her eyes and inundated her face. Abd-el-Kader looked at her
sadly and replied: "Your motherly sorrow has often touched me. I can
neither console you, nor give you hope. How could your son now be found,
seeing he disappeared when barely fifteen years of age! It is a question
whether he still lives."
"He would now be twenty-five; but," added Rosen-Aer drying her tears,
"let us not now talk of my son; I am afraid he is lost to me
forever.... But why say you that we see each other to-day, perhaps, for
the last time?"
"Charles Martel, the chief of the Franks, is advancing with forced
marches at the head of a formidable army to drive us out of Gaul. I was
notified yesterday of his approach. Within two days, perhaps, the Franks
will be upon the walls of Narbonne. Abd-el-Malek, our new emir, is of
the opinion that our troops should go out and meet Charles.... We are
about to depart. The battle will be bloody. God may wish to send me
death. That is why I came to tell you we may never meet again.... If God
should will it so, what will become of you?"
"You have several times generously offered me freedom, money and a guide
to travel through Gaul and look for my child. But I lacked the courage
and strength, or rather my reason told me how insane such an undertaking
would be in the midst of the civil wars that are desolating our unhappy
country. If I am not to see you again and I must leave this house, where
at least I have been able to weep in peace, free from the shame and the
trials of slavery, there will be nothing left to me but to die."
"I do not like to see you despair, Rosen-Aer. This is my plan for you.
During my absence you shall leave Narbonne. My forces are to take the
field against the Franks; my army is brave, but the will of God is
immovable. If it be his pleasure that victory fall to Charles and that
the Franks prevail over the Crescent, they may lay siege to this town
and take it. In that event you and all its inhabitants will be exposed
to the fate of people in a place carried by assault--death or slavery.
It is with an eye to withdrawing you from so sad a fate that I would
induce you to leave the town, and to take temporary shelter in one of
the Gallic colonies nearby that cultivate my fields."
"Your fields!" exclaimed Rosen-Aer with bitterness; "you should rather
say the fields that your soldiers seized by force and rapine, the
inseparable companions of conquest."
"Such was the will of God."
"Oh, for the sake of your race and of yourself, Abd-el-Kader, I hope the
will of God may save you the pain of some day seeing the fields of your
fathers at the mercy of conquerors!"
"God ordains ... Man submits. If God decrees against Charles Martel at
the approaching battle and we are victorious, you can return here to
Narbonne; if we are vanquished, if I am killed in the battle, if we are
driven out of Gaul, you shall have nothing to fear in the retreat that I
am providing for you. You can remain with the family of my servant. Here
is a little purse with enough gold pieces to supply your wants."
"I shall remember you, Abd-el-Kader, as a generous man, despite the
wrong your race has done mine."
"God sent us hither to cause the religion preached by Mahomet to
triumph, the only true religion. May his name be glorified."
"But the Christian bishops, priests and monks also pretend that their
religion is the only true one."
"Let them prove it ... we leave them free to preach their belief. Barely
a century since its foundation, the Musselman faith has subjugated the
Orient almost entirely, Spain and a portion of Gaul. We are instruments
of the divine will. If God has decided that I shall die in the
approaching battle, then we shall not meet again. Should I die and yet
our arms triumph, my sons, if they survive me, will take care of you....
Ibraham venerates you as his own mother."
"Do you take Ibraham to battle?"
"The youth who can manage a steed and hold a sword is of battle age....
Do you accept my offer, Rosen-Aer?"
"Yes; I tremble at the very thought of falling into the hands of the
Franks! Sad days these are for us. We have only the choice of
servitudes. Happy, at least, are those who, like myself, meet among
their masters compassionate hearts."
"Make yourself ready.... I myself shall depart in an hour at the head of
a part of my troops. I shall come for you. We shall leave the house
together; you to proceed to the colonist who occupies my country house,
and I to march against the Frankish army."
When Abd-el-Kader returned for Rosen-Aer, he had donned his battle
costume. He wore a brilliant steel cuirass, and a red turban wrapped
around his gilded casque. A scimitar of marvelous workmanship hung from
his belt; its sheath as well as its handle of massive gold was
ornamented with arabesques of corals and diamonds. The Arab warrior said
to Rosen-Aer with suppressed emotion: "Allow me to embrace you as a
daughter."
Rosen-Aer gave Abd-el-Kader her forehead, saying: "I pray that your
children may long retain their father."
The Arab and the Gallic woman left the harem together. Outside they met
the five sons of the chief--Abd-Allah, Hasam, Abul-Casem, Mahomet and
Ibraham, the youngest, all in full armor, on horseback and carrying over
their arms long and light white woolen cloaks with black tufts. The
youngest of the family, a lad of barely fifteen, alighted from his horse
when he saw Rosen-Aer, took her hand, kissed it respectfully and said:
"You have been a mother to me; before departing for battle I greet you
as a son."
The Gallic woman thought of her son Amael, who also was fifteen years
when he departed from the valley of Charolles, and answered the young
man: "May God protect you, you who are now to incur the risk of war for
the first time!"
"'Believers, when you march upon the enemy, be unshakable,' says the
prophet," the lad replied with mild yet grave voice. "We are going to
deliver battle to the infidel Franks. I shall fight bravely under the
eyes of my father.... God alone disposes of our lives. His will be
done."
Once more kissing the hand of Rosen-Aer, the young Arab helped her mount
her mule that was led by a black slave. From the distance the martial
bray of the Saracen clarions was heard. Abd-el-Kader waved his last
adieu to Rosen-Aer, and the Arab, with whom age had not weakened the
martial ardor of younger years, leaped upon his horse and galloped off,
followed by his five sons. For a few moments longer the Gallic woman
followed with her eyes the long white cloaks that the rapid course of
the Arab and his five children raised to the wind. When they had
disappeared in a cloud of dust at a turning of the street, Rosen-Aer
ordered the black slave to lead the mule towards the main gate of the
town in order to ride out and reach the colonist's house.
PART I.
THE CONVENT OF ST. SATURNINE
CHAPTER I.
THE LAST OF THE MEROVINGIANS.
About a month had elapsed since the departure of Abd-el-Kader and his
five sons to meet Charles Martel in battle.
A boy of eleven or twelve years, confined in the convent of St.
Saturnine in Anjou, was leaning on his elbows at the sill of a narrow
window on the first floor of one of the buildings of the abbey, and
looking out upon the fields. The vaulted room in which the boy was kept
was cold, spacious, bare and floored with stone. In a corner stood a
little bed, and on a table a few toys roughly cut out of coarse wood. A
few stools and a trunk were its only furniture. The boy himself, dressed
in a threadbare and patched black serge, had a sickly appearance. His
face, biliously pale, expressed profound sadness. He looked at the
distant fields, and tears ran down his hollow cheeks. While he was
dreaming awake, the door of the room opened and a young girl of about
sixteen stepped in softly. Her complexion was dark brown but extremely
fresh, her lips were red, her hair as well as her eyes jetty black, and
her eyebrows were exquisitely arched. A more comely figure could ill be
imagined, despite her drugget petticoat and coarse apron, the ends of
which were tucked under her belt and which was full of hemp ready to be
spun. Septimine held her distaff in one hand and in the other a little
wooden casket. At the sight of the boy, who remained sadly leaning on
his elbows at the window, the young girl sighed and said to herself:
"Poor little fellow ... always sorry ... I do not know whether the news
I bring will be good or bad for him.... If he accepts, may he never
have cause to look back with regret to this convent." She softly
approached the child without being heard, placed her hand upon his
shoulder with gentle familiarity and said playfully: "What are you
thinking about, my dear prince?"
The child was startled. He turned his face bathed in tears towards
Septimine, and letting himself down with an air of utter dejectment on a
stool near the window, said: "Oh, I am weary!... I am weary to death!"
and the tears flowed anew from his fixed and red eyes.
"Come now, dry those ugly tears," the young maid replied affectionately.
"I came to entertain you. I brought along a large supply of hemp to spin
in your company while talking to you, unless you prefer a game of
huckle-bones--"
"Nothing amuses me. Everything tires me."
"That is sad for those who love you; nothing amuses you, nothing pleases
you. You are always downcast and silent. You take no care of your
person. Your hair is unkempt ... and your clothes in rags! If your hair
were well combed over your forehead, instead of falling in disorder, you
would not look like a little savage.... It is now three days since you
have allowed me to arrange it, but to-day, will ye, nill ye, I shall
comb it."
"No; no; I won't have it!" said the boy stamping his foot with feverish
impatience. "Leave me alone; your attentions annoy me."
"Oh, oh! You can not frighten me with your stamping," Septimine replied
mirthfully. "I have brought along in this box all that I need to comb
you. Be wise and docile."
"Septimine.... Leave me in peace!"
But the young girl was not to be discouraged. With the authority of a
"big sister" she turned around the chair of the recalcitrant boy and
forced him to let her disentangle his disordered hair. While thus giving
him her care with as much affection as grace, Septimine, standing behind
him said: "Are you not a hundred times better looking this way, my dear
prince?"
"What is the difference, good looking or not?... I am not allowed to
leave this convent.... What have I done to be so wretched?"
"Alack, poor little one ... you are the son of a king!"
The boy made no answer, but he hid his face in his hands and fell to
weeping, from time to time crying in a smothered voice: "My father....
Oh, my father.... Alas!... He is dead!"
"Oh, if you again start crying, and, worst of all, to speak of your
father, you will make me also cry. Although I scold you for your
negligence, I do pity you. I came to give you some hope, perhaps."
"What do you mean, Septimine?"
Having finished dressing the boy's hair, the young girl sat down near
him on a stool, took up her distaff, began to spin and said in a low and
mysterious voice: "Do you promise to be discreet?"
"Whom do you expect I can talk to? Whom could I reveal secrets to? I
have an aversion to all the people in this place."
"Excepting myself.... Not true?"
"Yes, excepting you, Septimine.... You are the only one who inspires me
with some little confidence."
"What distrust could a little girl, born in Septimany, inspire you with?
Am not I as well as my mother, the wife of the outside porter of this
convent, a slave? When eighteen months ago you were brought to this
place and I was not yet fifteen, I was assigned to you, to entertain you
and play with you. Since then we have grown up together. You became
accustomed to me.... Is it not of course that you should have some
confidence in me?"
"You just told me you had some hope to give me.... What hope can you
give me? I want to hear?"
"Do you first promise to be discreet?"
"Be easy on that score. I shall be discreet."
"Promise me also not to begin to weep again, because I shall have to
speak about your father, a painful subject to you."
"I shall not weep, Septimine."
"It is now eighteen months since your father, King Thierry, died on his
domain in Compiegne, and the steward of the palace, that wicked Charles
Martel, had you taken to this place and kept imprisoned ... poor dear
innocent boy!"
"My father always said to me: 'My little Childeric, you will be a king
like myself, you will have dogs and falcons to hunt with, handsome
horses, chariots to ride in, slaves to serve you'; and yet I have none
of these things here. Oh, God! Oh, God! How unhappy I am!"
"Are you going to start weeping again?"
"No, Septimine; no, my little friend."
"That wicked Charles Martel had you brought to this convent, as I was
saying, in order to reign in your place, as he virtually reigned in the
place of your father, King Thierry."
"But there are in this country of Gaul enough dogs, falcons, horses and
slaves for that Charles to have an abundance and I also. Is it not so?"
"Yes ... if to reign means simply to have all these things ... but I,
poor girl, do not understand these things. I only know that your father
had friends who are enemies of Charles Martel, and that they would like
to see you out of this convent. That is the secret that I had for you."
"And I, Septimine, would also like to be out of here! The devil take the
monks and their convent."
After a moment's hesitation, the young girl stopped spinning and said
to the young prince in a still lower voice and looking around as if
fearing to be heard: "It depends upon you to get out of this convent."
"Upon me!" cried Childeric. "That would be quickly done on my part. But
how?"
"Mercy! Do not speak so loud," replied Septimine uneasily and casting
her eyes towards the door. "I always fear some one is there listening."
She rose and went on tip-toe to listen at the door and peep through the
keyhole. Feeling reassured by the examination, Septimine returned to her
seat, again started to spin, and went on talking with Childeric: "You
can walk in the garden during the day?"
"Yes, but the garden is surrounded by a high wall, and I am always
accompanied by one of the monks. That is why I prefer to remain in this
room to walking in such company."
"They lock you up at night--"
"And a monk sleeps outside before my door."
"Just look out of this window."
"What for?"
"To see whether the height of the window above the ground would frighten
you."
Childeric looked out of the window. "It is very high, Septimine; it is
really very high."
"You little coward! It is only eight or ten feet at most. Suppose a rope
with large knots were fastened to that iron bar yonder, would you have
the courage to descend by the rope, helping yourself with your feet and
hands?"
"Oh, I never could do that!"
"You would be afraid? Great God, is it possible!"
"The attempt looks to me above my strength."
"I would not be afraid, and I am only a girl.... Come, have courage, my
prince."
The boy looked once more out of the window, reflected and proceeded to
say: "You are right.... It is not as high as it looked at first. But
the rope, Septimine, how am I to get it? And then, when I am down there,
at night.... What shall I do then?"
"At the bottom of the window you will find my father. He will throw upon
your shoulders the caped cloak that I usually wear. I am not really much
taller than you. If you wrap the mantle well around you and lower the
cape well over your face, my father could, with the help of the night,
make you pass for me, traverse the interior of the convent, and reach
his lodge outside. There, friends of your father would be waiting on
horseback. You would depart quickly. You would have the whole night
before you, and in the morning, when your flight was discovered, it
would be too late to start in your pursuit.... Now answer, Childeric,
will you have the courage to descend from this window in order to regain
your freedom?"
"Septimine, I have a strong desire to do so ... but--"
"But you are afraid.... Fie! A big boy like you! It is shameful!"
"And who will give me a rope?"
"I.... Are you decided? You will have to hurry; your father's friends
are in the neighborhood.... To-night and to-morrow night they will be
waiting with horses not far from the walls of the convent ... to take
you away--"
"Septimine, I shall have the courage to descend, yes ... I promise you."
"Forget not, Childeric, that my mother, my father and I are exposing
ourselves to terrible punishment, even death perhaps, by favoring your
flight. When the proposition was made to my father to help in your
escape, he was offered money. He refused, saying: 'I want no other
reward than the satisfaction of having contributed in the deliverance
of the poor little fellow, who is always sad and weepful all these
eighteen months, and who is dying of grief.'"
"Oh, be easy. When I shall be king, like my father, I shall make you
handsome presents; I shall give you fine clothes, jewelry--"
"I do not need your presents. You are a child that one must sympathize
with. That is all that concerns me. 'It is not because the poor little
fellow is the son of a king that I take an interest in him,' my father
has said to me, 'because, after all, he is of the race of those Franks
who have held us in bondage, us the Gauls, ever since Clovis. No, I wish
to help the poor little fellow because I pity him.' Now, remember,
Childeric, the slightest indiscretion on your part would draw terrible
misfortunes upon my family."
"Septimine, I shall say nothing to anybody, I shall have courage, and
this very night I shall descend by the window to join my father's
friends. Oh! What happiness!" the child added, clapping his hands, "what
happiness! I shall be free to-morrow!... I shall be a king like my
father!"
"Wait till you are away to rejoice!... And now, listen to me carefully.
You are always locked in after evening prayers. The night is quite dark
by that time. You will have to wait about half an hour. Then tie the
rope and let yourself down into the garden. My father will be at the
foot of the window--"
"Agreed.... But where is the rope?"
"Here," said Septimine, taking from amidst the flax that she held in her
apron a roll of thin but strong rope, furnished with knots at intervals.
"There is at the end, as you see, an iron hook; you will fasten that to
this bar, and you will then let yourself down from knot to knot till you
reach the ground."
"Oh! I am no longer afraid! But where shall I hide the rope? Where shall
I keep it until evening?"
"Under the mattress of your bed."
"Good! Give it to me!" and the young prince, helped by Septimine, hid
the rope well under the mattress. Hardly had they re-covered the bed
when trumpets were heard blowing at a distance. Septimine and Childeric
looked at each other for a moment in astonishment. The young girl
returned to her seat, took up her distaff and observed in great
excitement:
"Something unusual is going on outside of the abbey.... They may come
here.... Take up your huckle-bones and play with them."
Childeric mechanically obeyed the orders of the young girl, sat down on
the floor, and began to play huckle-bones, while Septimine, with
apparent unconcern, spun at her distaff near the window. A few minutes
later the door of the room opened. Father Clement, the abbot of the
convent, came in and said to the young girl: "You can go away; I shall
call you back if I want you."
Septimine hastened to leave; but thinking she could profit by a moment
when the monk did not see her, she placed her finger to her lips in
order to convey to Childeric a last warning of discretion. The abbot
happening to turn around suddenly, the girl hardly had time to carry her
hand to her hair in order to conceal the meaning of her first gesture.
Septimine feared she had aroused the suspicion of Father Clement, who
followed her with penetrating eyes, and her apprehensions ripened into
certainty when, having arrived at the threshold of the door and turning
a last time to salute the Father, her eyes met his scrutinizing gaze
fixed upon her.
"May God help us," said the poor girl seized with mortal anxiety and
leaving the room. "At the sight of the monk the unhappy prince became
purple in the face.... He did not take his eyes from the bed where we
hid the rope. Oh, I tremble for the little fellow and for us!... Oh!
What will come of it?"
CHAPTER II.
CHARLES MARTEL.
Charles the Hammer, or Martel, had arrived at the convent of St.
Saturnine escorted by only about a hundred armed men. He was on the way
to join a detachment of his army that lay encamped at a little distance
from the abbey. The steward of the palace and one of the officers of the
squad that accompanied him were installed in a room that served as the
refectory of Father Clement, while the latter went for the little
prince.
At this period in the full vigor of his age, Charles Martel exaggerated
in his language and costume the rudeness of his Germanic stock. His
beard and hair, which were of a reddish blonde, were kept untrimmed and
shaggy, and framed in a face of high color, that bore the imprint of
rare energy coupled with a good nature that was at times both jovial and
sly. His keen eyes revealed an intelligence of superior order. Like the
lowest of his soldiers, he wore a coat of goat-skin over his tarnished
armor. His boots, made of heavy leather, were armed with rusty iron
spurs. From his leather baldric hung a long sword of Bordeaux, a town
renowned for its manufacture of arms.
The officer who accompanied Charles Martel seemed to be twenty-five
years of age--tall, slender, powerfully built. He wore his brilliant
steel armor with military ease, half-hidden under a long white cloak
with black tufts, after the Arabian fashion. His magnificent scimitar,
with both handle and scabbard of solid gold and ornamented with
arabesques of coral and diamonds, likewise was of Arabian origin. The
young man's face was of rare manly beauty. He had placed his casque upon
a table. His wavy black hair, divided in the middle of his head, fell in
ringlets on both sides of his forehead, which was furrowed by a deep
scar, and shaded his manly face that bore a slight brown beard. His eyes
of the blue of the sea, usually mild and proud, seemed however to reveal
a secret sorrow or remorse. At times a nervous twitch brought his
eyebrows together, and his features would for a while become somber.
Soon, however, thanks to the mobility of his impressions, the ardor of
his blood, and the impetuosity of his character, his face would again
resume its normal expression.
Charles, who for a while had been silently contemplating his young
companion with a kind and sly satisfaction, at last broke the silence,
saying in his hoarse voice:
"Berthoald, how do you like this abbey and the fields that we have just
traversed?"
"The abbey seems to me large, the fields fertile. Why do you ask?"
"Because I would like to make you a present to your taste, my lad."
The young man looked at the Frankish chief with profound astonishment.
Charles Martel proceeded: "In 732, it is now nearly six years ago, at
the time that those heathens from Arabia, who had settled in Gaul,
pushed forward as far as Tours and Blois, I marched against them. One
day I saw arrive at my camp a young chief followed by fifty daring
devils. It was you, the son, as you told me, of a Frankish seigneur, who
was dead and had been dispossessed of his benefice, like so many others.
I cared nothing about your birth. When the blade is well tempered I care
little about the name of the armorer," Charles explained as he noticed a
slight quiver in the eyelashes of Berthoald whose forehead swiftly
mantled with a blush and whose eyes dropped in involuntary confusion.
"You searched your fortune in war and had assembled a band of determined
men. You came to offer me your sword and your services. The next day, on
the plains of Poitiers, you and your men fought so bravely against the
Arabs that you lost three-fourths of your little troop. With your own
hands you killed Abd-el-Rhaman, the general of those heathens, and you
received two wounds in disengaging me from a group of horsemen who were
about to kill me, and would thereby have ended the war to the lasting
injury of the Franks."
"It was my duty as a soldier to defend my chief. I deserve no praise for
that."
"And it is now my duty as your chief to reward your soldierly courage. I
shall never forget that I owe my life to your valor. Neither will my
children. They will read in some notes I have left on my campaign: 'At
the battle of Poitiers, Charles owed his life to Berthoald; let my
children remember it every time they see the scar that the brave warrior
carries on his forehead.'"
"Charles, your praises embarrass me."
"I love you sincerely. Since the battle of Poitiers I have looked upon
you as one of my best companions in arms, although at times you are as
stubborn as a mule and quite odd in your tastes. If the matter in hand
is a war in the east or the north against the Frisians or the Saxons, or
in the south against the Arabs, there is no more rageful hammerer on the
enemies' heads than yourself; but when we had to suppress some revolts
of the Gauls you fought gingerly, almost against your will.... You no
longer were the same daring champion.... Your sword did not leave its
scabbard."
"Charles, tastes differ," answered Berthoald laughing with so obvious an
effort that it betrayed some poignant recollection. "In matters of
battle it is as in matters of women, tastes differ. Some like blondes,
others brunettes; they are all fire for the one, and all ice for the
other. And so my preference is for war against the Frisians, Saxons and
Arabs."
"I have no such predilections. As true as I have been surnamed Martel,
so long as I can strike and crush what stands in my way, all enemies are
equally to my taste.... I believed that those Arabian dogs who had been
so roughly hammered would recross the Pyrenees in a hurry after their
rout at Poitiers. I was mistaken. They still hold their ground firmly in
Languedoc. Despite the success of our last battle we have not been able
to seize Narbonne, the place of refuge of those heathens. I am now
called back to the north of Gaul to resist the Saxons who are returning
with more threatening forces. I regret to have to leave Narbonne in the
hands of the Saracens. But we have at least ravaged the neighborhood of
that large town, made an immense booty, carried away a large number of
slaves, and devastated in our retreat the countries of Nimes, of
Toulouse and of Beziers. It will be a good lesson for the populations
who took the side of the Arabs. They will long remember what is to be
gained by leaving the Gospels for the Koran, or rather, because, after
all, I care as little for the Pope as I do for Mahomet, what is to be
gained by an alliance with the Arabs against the Franks. For the rest,
although they remain masters of Narbonne, these pagans worry me little.
Travelers from Spain have informed me that civil war has broken out
between the Caliphs of Granada and of Cordova. Busy with their own
internal strifes, they will not send fresh troops into Gaul, and the
accursed Saracens will not dare to advance beyond Languedoc, whence I
shall drive them away later. At rest about the south, I now return
north. But before doing so I wish to provide, to their own taste and
mine, for a large number of soldiers, who, like yourself, have served
me valiantly, and turn them into fat abbots, rich bishops or other large
beneficiaries."
"Charles, would you make out of me an abbot or a bishop? You are surely
joking."
"Why not? It is the abbey and the bishopric that make the abbot and the
bishop, whoever be the incumbent."
"Please explain yourself more clearly."
"I have been able to sustain my great wars in the north and south only
by constantly recruiting my forces from the German tribes on the other
side of the Rhine. The descendants of the seigneurs who were the
beneficiaries of Clovis and his sons have degenerated. They have become
do-nothings like their kings. They seek to escape their obligations of
leading their columns to war, under the pretext that they need hands to
cultivate the soil. Apart from a few fighting bishops, old men with the
devil in them, who changed the casque for the mitre, and who, redonning
their cuirasses brought their men to my camp, the Church has not wished
and does not wish to contribute to the expenses of the war. Now, upon
the word of Martel, that will not do! My brave warriors, fresh from
Germany, the chiefs of the bands that have served me faithfully, have a
right to a share of the lands of Gaul. They have more right thereto than
the rapacious bishops and the debauched abbots who keep harems like the
Caliphs of the Arabs. I want to restore order in the matter; to reward
the brave and to punish the cowards and do-nothings. I propose to
distribute a part of the goods of the Church among my men who have
recently arrived from Germany. I shall in that manner provide for my
chiefs and their men, and instead of leaving so much land and so many
slaves in the hands of the tonsured brothers, I shall form a strong
reserve army of veterans, ever ready to take the field at the first
signal. And to begin, I present this abbey to you, its lands, buildings,
slaves, with no other charge upon you than to contribute a certain sum
into my treasury and to turn out with your men at my first call."
"I a count of this country! I the possessor of such broad estates!" the
young chief cried with joy, hardly believing so magnificent a gift
possible. "But the goods of this abbey are immense! Its lands and
forests extend more than two leagues in a circle!"
"So much the better, my lad! You and your men will settle down here.
Handsome female slaves are sure to abound on the place. You will raise a
good breed of soldiers. Moreover this abbey is bound, due to its
situation, to become an important military post. I shall grant to the
abbot of this convent some more land ... if any is left. And that is not
all, Berthoald; I entertain as much affection for [you] as I place
confidence in you. I make the gift to you out of affection; now, as to
my confidence. I shall give you a strong proof of it by establishing you
here and charging you with so important a duty ... that, in the end, it
will be I who remain your debtor...."
"Why do you halt, Charles?" asked Berthoald noticing the chief of the
Franks reflect instead of continuing.
After a few seconds of silence, Charles resumed: "During the century and
a half and more that we have reigned in fact, we the stewards of the
palace ... of what earthly use have the kings been, the descendants of
Clovis?"
"Have I not heard you say a hundred times that those do-nothings spend
their time drinking, eating, playing, hunting, sleeping in the arms of
their concubines, going to church and building churches in atonement for
some crime committed in the fury of their drunkenness?"
"Such has been the life of those 'do-nothing' kings--well named such. We
the stewards of the palace govern in fact. At every assembly of the
Field of May, we pulled one of our royal mannikins out of his residence
of Compiegne, of Kersey-on-the-Oise, or of Braine. We had him set up in
a gilded chariot drawn by four oxen according to the old Germanic
custom, and, with a crown upon his head, a scepter in his hand, purple
on his back, his face ornamented with a long artificial beard, if he had
no beard, so as to impart to him a certain degree of majesty, the image
was promenaded around the Field of May, and received the pledge of
homage from the dukes, counts and bishops, gathered at the assembly from
all parts of Gaul.... The comedy over, the idol was thrust back into its
box until the next year. But what useful purpose can these mummeries
serve? He only should be king who governs and fights. Consequently, as I
have no taste for what is superfluous, I have suppressed the royalty....
I confiscated the King."
"You deserve to be praised for that, Charles; the Frankish kings
descended from Clovis, have inspired me with hatred and contempt--"
"But whence the hate?"
Berthoald blushed and puckered up his brows: "I have always hated
idleness and cruelty."
"The last one of these kings, Thierry IV, dead now eighteen months, left
a son behind ... a child of about nine years.... I had him deported to
this abbey--"
"What do you purpose to do with him?"
"To keep him.... We Franks are fickle folks. For a century and a half we
fell into the habit of despising the kings that one time we
worshipped.... Accordingly, when the first Field of May took place
without the royal mummery, not one of the dukes and bishops missed the
idol that was absent from the feast. This year, however, some did ask
where was the king; and others answered: 'What is the use of the king?'
It may, nevertheless, happen that one of these days they may demand to
see the royal mannikin make the tour of the Field of May according to
the old custom.... I do not care, provided I reign. Accordingly, I keep
in reserve for them the child that is here. With the aid of a false
beard on his chin and a crown on his head, the little monkey will play
his role in the chariot neither better nor worse than so many other
kings of twelve or fifteen years who preceded him. In case of need, next
year he will be Childeric III, if I think it advisable."
"Kings of twelve!... How low can royalty fall!... How low the
degradation of the people!"
"The stewardship of the palace, a post that became hereditary, came very
near dropping to the same level.... Did I not have a brother of eleven
who was the steward of the palace to a king of ten?"
"You joke, Charles!"
"No, indeed, I do not, because those days were far from pleasant for
me.... My step-mother, Plectrude, had me cast into prison after the
death of my father Pepin of Heristal.... According to the dame, I was
only a bastard, good either for the gibbet or the priest's frock, while
my father left to my brother Theobald the post of steward of the palace;
hereditary in our family.... And so it happened that my brother, then
only eleven, became the steward of the palace of the then king, who was
only ten, and who became the grandfather of this little Childeric, who
is a prisoner in this convent. That king and steward could exercise no
rivalry over each other except at tops or huckle-bones. Thus the good
dame Plectrude expected to rule in the place of the two urchins, while
they would be at play. Such audacity and folly aroused the Frankish
seigneurs. At the end of a few years Plectrude was driven away with her
son, while I, Charles, for whom she had only bad names, came out of
prison, and now became steward of the palace of Dagobert III. Since then
I have made so much noise in the world, hammering here and yonder upon
the heads of Saxons, Frisians and Saracens, that the name of Martel has
stuck to me. Dagobert III left a son, Thierry IV, who died eighteen
months ago, and he was the father of little Childeric, the prisoner of
this place. While having to cross the region, I wished to pay a visit to
the royal brat and learn how he stood his captivity. I said I had a
token of confidence to give.... I confide to you the keeping of that
child, the last scion of the stock of Clovis, of the Merovingian
conquerors of Gaul."
"I shall keep this last scion of Clovis?" cried Berthoald, at first
stupefied, but immediately thrilled with savage joy. "I shall keep him?
The boy who has among his ancestors a Clotaire, the murderer of
children! a Chilperic, the Nero of the Gauls! a Fredegonde, a second
Messalina! a Clotaire II, the executioner of Brunhild, and so many other
crowned monsters! Shall I be the jailor of their last issue?... The fate
of man is often strange.... I to be the guardian of the last descendant
of that conqueror of Gaul so much abhorred by my fathers!... Oh, the
gods are just!"
"Berthoald, are you going crazy? What is there so astonishing in your
becoming the watcher of this child?"
"Excuse me, Charles," answered Berthoald recollecting and fearing to
betray himself. "I was greatly struck with the thought that I, an
obscure soldier, should watch and hold as a prisoner the last scion of
so many kings! Is it not a strange fate?"
"Indeed this stock of Clovis, once so valiant, ends miserably!... But
how else could it be! These kinglets--fathers before fifteen, decayed at
thirty, brutified by wine, dulled by idleness, unnerved by youthful
debauchery, emaciated, stunted, and stupid--could not choose but end
this-wise.... The stewards of the palace, on the contrary--rough men,
always on the march from north to south, from east to west, and back
again, always on horseback, always fighting, always governing--they run
out into a Charles, and he is not frail, he is not stunted! Not he! His
beard is not artificial; he will be able to raise a breed of true
kings.... Upon the word of Martel, this second breed of kings will not
allow themselves to be exhibited in carts neither before nor after the
assemblies of the Field of May by any stewards of palaces!"
"Who can tell, Charles! It may happen that if you raise a breed of
kings, their stock will run down just as that of Clovis has done, whose
last scion you wish to put under my charge."
"By the devil! By the navel of the Pope! Do you see any sign of decay in
us, the sons of Pepin of Old, who have been the hereditary stewards of
the palace since the reign of Queen Brunhild?"
"You were not kings, Charles; and royalty carries with it a poison that
in the long run enervates and kills the most virile stock--"
At this moment Father Clement came tumbling into the room in great
excitement, and broke the thread of the conversation between Charles
Martel and Berthoald.
CHAPTER III.
FATHER CLEMENT'S REFECTORY.
"Seigneur," said Father Clement to Charles, as he precipitately broke
into the room, "I have just discovered a plot! The young prince
obstinately refused to accompany me hither--"
"A plot! Ho, ho! The folks of your abbey indulge in conspiracies!"
"Thanks be to heaven, seigneur, myself and brothers are utter strangers
to the unworthy treason. The guilty ones are the miserable slaves who
will be punished as they deserve!"
"Explain yourself! And stop circumlocutions!"
"I must first of all inform you, sir, that when the young prince first
arrived at this convent, Count Hugh who brought him, recommended to me
to place near the child some young female slave, a pretty girl, if
possible, above all one that would provoke love ... and who would be
willing to submit to the consequences--"
"In order, I suppose, that he be educated after the fashion that old
Queen Brunhild followed towards her own grandchildren.... Count Hugh
exceeded my orders; and you, holy man, did you not blush at the role of
coupler in the infamous scheme?"
"Oh, seigneur! What an abomination! The two children remained pure as
angels.... To make it short, I placed a young female slave near the
prince. The girl, an innocent creature, together with her father and
mother took pity on the fate of Childeric. They listened to detestable
propositions, and this very night and by means of a rope, the child was
to slip from his room with the connivance of the porter slave, and join
some faithful adherents of the deceased King Thierry who are lying in
hiding near the convent. That was the plot."
"Ha! Ha! The old royal party is stirring! They thought I would be long
kept busy with the Arabs! They planned to restore the royalty in my
absence!"
"A minute ago, as I entered the room of the young prince, my suspicions
were awakened. The confusion he was in and the redness in his face told
of his guilt. He would not take his eyes from his bed. A sudden idea
occurred to me. I raised the mattress, and there I found a rope
carefully stowed away. I pressed the child with questions, and amidst
tears he confessed to me the full project of escape."
"Treason!" cried the chief of the Franks, affecting more rage than he
really felt. "How came I to confide this child to the care of monks who
are either traitors or incapable of defending their prisoner!"
"Oh, seigneur!... We traitors!"
"How many men did this abbey contribute to the army?"
"Seigneur, our colonists and slaves are hardly enough to cultivate the
land; our vines are neglected; our fields lie fallow. We could not spare
a single man for the army."
"How much did you pay into the treasury towards the expenses of the
war?"
"All our revenues were employed in charitable works ... in pious
foundations."
"You extend fat charities to yourselves. Such are these churchmen!
Always receiving and taking, never giving or returning! Ye are a race of
vipers! Under whom does this old abbey hold the land?"
"From the liberalities of the pious King Dagobert. The charter of our
endowment is of the year 640 of our Lord Jesus Christ."
"Do you, monk, believe that the Frankish kings made these endowments to
you of the tonsured fraternity to the end that you might grow fat in
idleness and abundance, and without ever contributing towards the
expenses of the war with either men or money?"
"Seigneur ... remember the obligations of the monastery ... keep in mind
the expenses of the cult!"
"I confide an important prisoner to you and you prove unable to watch
him ... you miserable tonsured idlers ... topers and do-nothings!"
"Seigneur, we are innocent and incapable of betraying you!"
"That will never do. I shall settle soldiers on the domain ... men who
will be able to watch the prisoner, and, when need be, defend the abbey,
if the folks of the royal party should attempt to carry off the prince
by force," and turning to Berthoald, Charles said: "You and your men
will take possession of this abbey. I present it to you!"
The abbot raised his hands to heaven in sign of mute desolation, while
Berthoald, who had pensively stood near, said to Charles Martel:
"Charles, the commission of jailor is repugnant to my character of a
soldier. I feel thankful to you, but I must decline the gift."
"Your refusal afflicts me. You have heard the monk. I need here a
vigilant guardian. This abbey is, by its position, an important military
post."
"Charles, there are other soldiers in your army whom you can charge with
the child and to whom you can confide the defence of the post. You will
find men enough who will not be restrained by any scruples such as
restrain me."
For a few minutes the chief of the Franks remained silent and
thoughtful, then he said: "Monk, how much land, how many colonists and
slaves have you?"
"Seigneur, we have five thousand eight hundred acres of land, seven
hundred colonists, and nineteen hundred slaves."
"Berthoald ... you hear it! That is what you decline for yourself and
your men. Moreover, I would have created you count of the domain."
"Reserve for others than myself the favor you meant to bestow upon me. I
absolutely refuse the function of jailor."
"Seigneur," put in Father Clement with a holy resignation that, however,
but ill-concealed his anger at Charles: "You are the chief of the Franks
and all-powerful. If you establish your armed men on this domain, we
shall have to obey, but what will become of us?"
"And what will become of my companions in arms, who have valiantly
served me during the war while you were counting your beads?... Are they
to steal or beg their bread along the roads?"
"Seigneur ... there is a way of satisfying both your companions in arms
and ourselves. You wish to change this abbey into a military post. I
admit it, your armed men would be better keepers of the young prince
than we poor monks. But since you dispose of this abbey, deign,
illustrious seigneur, to bestow another one upon us. There is near
Nantes the abbey of Meriadek. One of our brothers, who died recently,
lived there several years as the intendant. He left with us an inventory
containing an exact list of the goods and persons of that abbey. It was
at the time under the rule of St. Benoit. We have learned that later it
was changed into a community of women. But we have no positive
information on that head. But that would matter little."
"And that abbey," Charles asked, rubbing his beard with a sly look, "you
ask me for it as a charity to you and your monks?"
"Yes, seigneur; since you dispossess us of this one, we solicit
indemnity."
"And what is to become of the present holders of the abbey of Meriadek?"
"Alack! what we would have become. The will of God be done. Charity
begins at home."
"Yes, provided the will of God turn in your favor. Is the abbey rich?"
"Seigneur, with the aid of God, we could live there humbly and in
seclusion and prayer and with a little privation."
"Monk, no false pretences! Is that abbey worth more or is it worth less
than this one? I wish to know whether it is a cow or a goat I am giving
away. If you deceive me, I may some day go back upon my gift. Moreover,
you just said you had an exact inventory of the abbey's havings. Come,
speak up, you old dotard!"
"Yes, seigneur," answered the abbot biting his lips and proceeding to
look in a drawer among several rolls of parchment for the inventory of
the abbey of Meriadek. "Here," said he, producing the document, "you
will see from this that the revenues of Meriadek are worth about as much
as those that we draw here.... We may even, by retrenching upon our good
works, by reducing our charities, contribute two hundred gold sous
annually to your treasury."
"You say that rather late," replied Charles turning the leaves of the
inventory which did, indeed, accurately set forth the extent and limits
of the domain of Meriadek. "Have you parchments to write on? I wish to
make the bequest in due form."
"Yes, seigneur," cried the monk in great glee, running to his trunk and
believing himself in full possession of the abbey of Meriadek. "Here is
a roll of parchment, gracious seigneur. Be kind enough to dictate the
terms of the bequest ... unless you prefer to adopt the usual formula."
Saying this the abbot was about to sit down and take pen in hand, when,
pushing him away from the table, Charles said: "Monk, I am not like the
do-nothing and ignorant kings; I know how to write; and I like to
transact my business myself."
Consulting from time to time the parchments that the abbot had handed to
him, and from time to time casting a look upon Berthoald, who had
remained steeped in thought and a stranger to what was going on near
him, Charles began to write. A few steps from the table, and following
the hand of Charles with greedy eyes, the monk was congratulating
himself upon his having thought of the abbey of Meriadek, and he no
doubt was computing the advantage that would accrue to himself by the
exchange. Addressing the chief of the Franks, who was silently writing,
the monk said: "Mighty seigneur, my names are Bonaventure Clement, an
unworthy priest and monk of the order of St. Benoit."
Charles raised his head, looked fixedly at the abbot and a singular
smile played around his lips. He then proceeded to write, and a few
minutes later said: "Wax!... I wish to place my seal on this charter as
a last formality."
The abbot hastened to fetch what he was ordered; Charles pulled from his
finger a large gold ring and placed it on the burning wax. "Now the
charter of the bequest is in good shape."
"Gracious seigneur," cried the abbot extending his hands, "we shall
every day pray that heaven may protect you."
"You have my thanks, monk; disinterested prayers are particularly
agreeable to the Almighty;" and turning towards his young officer:
"Berthoald, by this charter I make you count of the county of Nantes,
and I donate to you and your men the abbey of Meriadek, together with
its dependencies."
The abbot remained petrified. Berthoald trembled with joy, and cried in
accents of profound gratitude: "Charles, will your generosity never
tire?"
"No, no, my valiant boy! No more than your arm tires in battle.... And
now, to horse, noble count. Should the abbey of Meriadek turn out to be
a convent of tonsured friars with some fighting abbot at their head who
refuses to make room for you, you have your sword; your men have their
lances. If it happens to be a convent of women and that the nuns are
young and handsome, by the devil!--"
Again the conversation in the monk's refectory was suddenly broken in
upon; this time by Septimine.
CHAPTER IV.
MORDECAI THE SLAVE-DEALER.
Pale, affrighted, her face in tears, her hair unloosened, Septimine
broke into the room and threw herself at the feet of the abbot, crying:
"Mercy, Father, mercy!"
Close upon the heels of Septimine entered two slaves armed with whips,
and carrying rolls of rope. They had run after the young girl, but now
stood respectfully awaiting the abbot's orders. Septimine was so
beautiful, her distress so touching, her suppliant attitude, accentuated
by the tears that flowed down her charming face, so pathetic, that
Berthoald was struck with admiration and suddenly felt an irrepressible
interest in the distracted girl. Charles Martel himself could not hold
back the cry of admiration: "My faith, what a pretty girl!"
"What do you want here?" brutally asked Father Clement, smarting under
the pain of having seen the gift of the abbey of Meriadek slip from him;
and turning to the two slaves, who remained motionless at the door: "Why
have you not punished this wretch?"
"Father, we were about to strip off her clothes and tie her to the
whipping-post. But she fought us so hard that she slipped away from us."
"Oh, Father!" cried Septimine in a voice suffocated with sobs and
raising her suppliant hands to the abbot; "order me killed, but spare me
the disgrace!"
"Charles," said Father Clement, "this slave girl sought to help the
young prince to escape!... Drag her away!" he added to the slaves at
the door; "Have her well whipped!"
The slaves took a step forward, but Berthoald held them back with a
menacing gesture. Approaching Septimine he took her hand and said: "Fear
not, poor child; Charles the chief of the Franks will not allow you to
be punished."
The young woman, not yet daring to rise, turned her charming face
towards Berthoald, and remained no less struck by the generosity of the
young man than by his comely looks. Their eyes met. Berthoald felt a
profound emotion, while Charles said to Septimine: "Come, I pardon you;
but why the devil, my little girl, did you want that royal urchin to run
away?"
"Oh, seigneur, the child is so unhappy! My father and mother, the same
as myself, felt pity for him.... That is all our crime, seigneur.... I
swear by the salvation of my soul;" and sobs again choked her voice.
Again joining her hands, she could only utter the words: "Mercy; mercy
for my father and mother! Have pity upon us, noble seigneur!"
"You are weeping fit to choke yourself," said Charles, touched, despite
his roughness, at the sight of such youth, anguish and beauty: "I forbid
that your father and mother be punished."
"Seigneur ... they want to sell me and to separate me from my
parents.... Have pity upon us!"
"What about that, monk?" asked Charles, while Berthoald, who felt his
sorrow, admiration and pity increase by the second, could not take his
eyes from the charming maid.
"Seigneur," answered Father Clement, "I gave orders that, after being
severely whipped, the three slaves, father, mother and daughter, be sold
and taken far away from the convent. One of those slave-dealers who
travel through the country came this morning to offer me two carpenters
and a smith that we stand in need of. I offered him the young girl in
exchange together with her father and mother. But Mordecai refused the
exchange."
"Mordecai!" involuntarily exclaimed Berthoald, whose face, suddenly
turning pale, now expressed as much fear as anxiety. "That Jew!"
"What the devil is the matter with you?" said Charles to the young man.
"You look as white as your cloak."
Berthoald sought to control his emotions, dropped his eyes and answered
in a quivering voice: "The horror that these accursed Jews inspire me
with is such ... that I can not see them, or even hear their names
mentioned, without shuddering, despite myself." Saying this, Berthoald
quickly took his casque from the table and put it on his head, pushing
it down as far as he could so that the visor might conceal his face.
"I can understand your horror for the Jews," replied Charles; "I share
your aversion for that race. Proceed, monk."
"Mordecai consented to take the girl, for whom he has a place; but he
does not want either the father or the mother. I, accordingly, sold him
the girl, reserving the right of having her punished before delivery to
him. I shall sell her parents to some other slave-dealer."
"Seigneur!" cried Septimine breaking out into a fresh flood of tears,
"slavery is a cruel condition, but it seems less hard when borne in the
company of those whom we love--"
"The bargain is closed," said the abbot. "Mordecai paid me earnest
money; he has my word; he is waiting for the girl."
When Berthoald heard that the Jew was in the convent he trembled anew,
retreated into a niche in the wall, and threw the cape of his long
Arabian cloak over his casque so as to conceal his face. He then
addressed the Frankish chief in a hurried voice like a man in fear of
some imminent danger and anxious to leave the place:
"Charles, before I bid you good-bye, perhaps for a long time, cap the
climax of your generosity towards me. Give the father and mother of this
child their freedom, and buy her back from the Jew to prevent her being
separated from her parents. Guilty though she was, it was only pity that
led her astray. You are about to place vigilant soldiers in this place.
The little prince's escape will not need to be feared."
Hearing the tender words of Berthoald, Septimine raised her face to him,
full with ineffable gratitude.
"Rest assured, Berthoald," said Charles; "and you, my girl, rise; this
abbey, where I wish to establish my warriors, shall have three slaves
less. I can refuse nothing to this valiant officer."
"Take this, my child," said the young man putting several Arabian gold
pieces into the hand of Septimine. "This is to help you, your father and
mother to live. May you be happy! Bless the generosity of Charles
Martel; and remember me occasionally."
With an unconscious movement that absolutely controlled her will,
Septimine took the hand that Berthoald reached out to her, and without
taking the gold pieces that he tendered and that rolled down over the
floor, she kissed the young man's hand with such passionate
thankfulness, that his own eyes were moistened with tears. Charles
Martel noticed the circumstance, and pointing at the young folks, cried
with the boisterous laugh peculiar to himself:
"Upon the word of Martel, I believe he weeps!"
Berthoald pulled the cape of his cloak further down over his face,
leaving it now almost wholly covered.
"You are right, my brave fellow, to lower your cape and conceal your
tears."
"I shall not long treat you to the spectacle of my weakness, Charles;
allow me to depart immediately with my men for the abbey of Meriadek."
"Go, my good companion in arms. I excuse your impatience. Be vigilant!
Keep your men in daily exercise; let them be ever ready to answer my
first call. I may have to use them against the accursed Bretons who have
withstood our arms since the days of Clovis. You are the count of the
county of Nantes, close to the frontiers of that bedeviled Armorica.
Your loyal sword may yet have occasion to render me such service that in
the end it may yet be I who will be your debtor. May we soon meet again!
A happy trip and a fat abbey are my best wishes to you."
Thanks to the cape that almost wholly veiled Berthoald's face, he was
able to conceal from Charles the cruel agony that he became a prey to
the moment he heard Charles say that some day he might receive orders to
invade the country of the Bretons that had so far remained indomitable.
He bent a knee before the chief of the Franks and left the refectory in
such a state of wild and complex anxiety that he did not even have a
parting look for Septimine, who remained upon her knees amidst the
Saracen gold pieces that lay strewn around her.
The young officer crossed the courtyard of the abbey to reach his horse,
when, turning the corner of a wall, he found himself face to face with a
little grey-bearded man. It was the Jew Mordecai. Berthoald shivered and
walked quickly by; but although his face was hidden under the cape of
his cloak, his eyes encountered the piercing ones of the Jew, who smiled
sardonically while the young chief walked rapidly away.
The Jew had recognized Berthoald.
PART II.
THE ABBEY OF MERIADEK
CHAPTER I.
ELOI THE GOLDSMITH.
A gold and silversmith's shop is a sight agreeable to the eye of the
artisan who, freeman or slave, has grown old at the beautiful art made
illustrious by Eloi, the most celebrated of all Gallic goldsmiths. The
eye rests with pleasure upon the burning furnace, upon the crucible
where the metal boils, upon the anvil that seems to be of silver veined
with gold--so much gold and silver has been beaten on it. The
work-bench, equipped with its files, its hammers, its chip-axes, its
burins, its bloodstone and agate polishing stones is no less pleasing to
the eye. Then there are also the earthen molds into which the metal is
poured, and here and there upon little tables some models taken from the
debris of antique art that have been found among the ruins of Roman
Gaul. There is nothing from the grinding of the files to the panting
breath of the bellows, that is not like sweet music to the ear of the
artisan grown old at the trade. Such is the passion of this art that the
slave at times forgets his bondage, and has no thought but for the
marvels that he fashions for his master.
Like other rich convents of Gaul, the abbey of Meriadek had its little
gold and silver shop. An old man, almost ninety-six years of age, was
overseeing the work of four young apprentices, slaves like himself, all
busy in a vaulted ground floor room, lighted by an arched window, that
was furnished with iron bars and that opened upon a moat full of water,
the convent having been built upon a sort of peninsula almost wholly
surrounded by deep ponds. The forge was placed against one of the walls,
into the thick body of which a kind of vault was dug that led below by
several steps. It contained the supply of charcoal required for the
work. The old goldsmith, whose face and hands were blackened by the
smoke of the forge, wore a smock-frock half hidden by a large leathern
apron, and was engaged in chiseling with great professional delight a
little silver abbatial crosier that he held on his knees.
"Father Bonaik," said one of the young slaves to the old man, "this is
the eighth day that our comrade Eleuthere has not come at all to the
workshop ... where can he be?"
"God knows, my boys ... but let us talk of something else."
"I am half of your opinion, old father; on the matter of Eleuthere I
have as strong a desire to speak as to hold my tongue. I have discovered
a secret. It burns my tongue. And I fear it will be cut off if I talk."
"Come, my lad," replied the old man, chiseling away at his work, "keep
your secret. That's the most prudent thing you can do."
But more inquisitive than the old man, the other young apprentices
insisted so much with their comrade that, overcome by their
importunities, he told them: "Day before yesterday--it was the sixth day
since the disappearance of Eleuthere--I took, by order of Father Bonaik,
a silver bowl to the abbey. The attendant at the turning-box told me to
wait while she went inside to inquire whether there were any articles of
silver that needed mending. Left alone during her absence, I had the
curiosity to step upon a stool so as to look out of a high window that
opened upon the garden of the monastery. And what did I see? Or, rather,
what is it that I thought I saw? Because there are resemblances that are
so striking ... so extraordinary--"
"Well, what did you see in the garden?"
"I saw the abbess, distinguished by her high stature, walking between
two young nuns with an arm resting upon the shoulder of each."
"You talk as though our abbess were almost a hundred years old, like
Father Bonaik--she who rides like a warrior, who hunts with falcons, and
whose upper lip is shaded by a slight reddish moustache neither more nor
less than that of a youth of eighteen!"
"It surely was not out of feebleness but tenderness that the abbess
leaned upon the two nuns. One of them having stepped upon her robe, lost
her balance, tripped and turned her head ... and I recognized, or
believed I recognized ... guess whom ... Eleuthere!"
"Dressed like a nun?"
"Dressed like a nun."
"Go away!... You must have been dreaming."
"And yet," replied another and less incredulous slave, "that is quite
possible. Our comrade is not yet eighteen, and his chin is as innocent
of a beard as any young girl's."
"I maintain that if that nun is not Eleuthere, she is his sister ... if
he has one."
"I tell you," put in the old goldsmith with marked impatience, "I tell
you that you are ninnies, and that if you are anxious for a trip to the
whipping-post and to renew your acquaintance with the thongs of the
whip, all you have to do is to persevere in talks like that."
"But Father Bonaik--"
"I allow chattering at work; but when the words may translate themselves
into the strokes of a whip on your backs, then the subject seems to me
badly chosen. You know, as well as I, that the abbess--"
"Is hot-tempered and bedeviled, Father Bonaik."
"Are you anxious to have the flesh flayed off your backs, unhappy lads!
I order you to hold your tongues."
"And what are we to talk about if not of our masters and the abbess?"
"Here," said the old man anxious to have the subject drop, "I have often
promised you to tell you the story of the illustrious master of our
trade, the glory of the artisans of Gaul. Let us talk of that artist."
"About the good Eloi? The great and saintly Eloi, Father Bonaik, the
friend of the good King Dagobert?"
"Call him the 'good' Eloi, my boys; never was there a better; but do not
say the 'good' King Dagobert. That King had everybody who displeased him
throttled; he pillaged, he levied ransom upon the poor, and he kept a
harem like an Arabian Caliph. Listen, children. The good Eloi was born
in 588 or thereabouts, at Catalacte, a small village in the neighborhood
of Limoges. His parents were freemen, but of obscure and poor
condition."
"Father Bonaik, if Eloi was born in 588, that must have been about a
hundred and fifty years ago. That is a century and a half."
"Yes, my boys, seeing we are now almost at 738."
"And did you know him?" asked one of the lads with an incredulous smile.
"Did you know the good Eloi?"
"Certainly, I did, seeing I shall soon be ninety-six, and that he died
last century, in 659, nearly eighty years ago."
"You were then quite young?"
"I was sixteen and a half years old the last time I saw him.... His
father was called Eucher and his mother Terragie. Noticing that his son
was since early boyhood ever fashioning in wood some figure or small
utensil of pretty design, his father apprenticed him to a skilful
goldsmith of Limoges, named Master Abbon, who at that epoch also
directed the mint in the town of Limoges. After having acquired a good
deal of skill in his art, to the point that he surpassed his master,
Eloi left the neighborhood and his family, much regretted by everybody,
he being beloved by all on account of his cheerful disposition, the
mildness of his nature and his excellent heart. He went to seek his
fortune in Paris, one of the residential towns of the Frankish kings.
Eloi was recommended by his old master to a certain Bobbon, a goldsmith
and treasurer of Clotaire II. Having accepted Eloi as a workman, Bobbon
soon perceived the young man's talent. One day King Clotaire ordered a
chair of solid gold, wrought with art and ornamented with precious
stones."
"A chair of solid gold! Father Bonaik, what magnificence! Nothing is too
costly to these kings."
"Alack, my boys, the gold cost the Frankish kings in Gaul only the
trouble of picking it up, and they were not slow at it. Well, then,
Clotaire II had the fancy to own a gold chair. But nobody in the
workshops of the palace was able to accomplish such a task. The
treasurer Bobbon knew the skill of Eloi and proposed to him to undertake
the work. Eloi accepted; he went to the forge and the crucible, and out
of the large quantity of gold given for one chair he fashioned two. He
then took to the palace one of the two chairs and hid the other--"
"Ho! Ho!" said one of the young slaves laughing. "The good Eloi did as
millers do who are sharp, artful and not very scrupulous. He drew double
pay for one bag--"
"Wait, my boys, wait before you judge our venerable master. Charmed at
the elegance and delicacy of the artisan's work, Clotaire II issued
orders on the spot to recompense him generously. Eloi thereupon showed
the second chair to Bobbon saying: 'This is what I spent the rest of
your gold in so as to lose nothing of the stuff. I have acted as you
would have wished.'"
"You are right, Father Bonaik, we were too quick in judging the good
Eloi."
"That act of probity, so honorable in the poor artisan, was the start
of his future fortune. Clotaire II wished to attach him to his court as
a goldsmith. It was then that Eloi achieved his finest productions:
vases of chiseled gold ornamented with rubies, pearls and diamonds;
pieces of furniture of solid silver and admirable design and set off
with chiseled stone; reliquaries, curtain pins, Bible cases encrusted
with carbuncles.... I saw the chalice of enameled gold more than a foot
high that he made for the abbey of Chelles. It was a miracle in enamel
and gold."
"It is enough to dazzle one to hear you tell of such beautiful works,
Father Bonaik."
"Oh, children, this room could not contain the masterpieces of that one
artisan, the glory of Gallic artisanship. The coins that he has struck
as the minter of Clotaire II, of Dagobert and of Clovis II have
admirable reliefs: they are gold thirds of a sou of a superb stamp. Eloi
succeeded in all the branches of the goldsmith's art. He excelled, like
the goldsmiths of Limoges, in the incrustation of enamel and the setting
of precious stones; he also excelled, as did the goldsmiths of Paris, in
statuaries of hammered gold and silver. He chiseled jewelry as
delicately as the jewelers of Metz. The cloths of woven gold thread
manufactured under his eyes and after his designs, were not less
magnificent than those of Lyon. My boys, what a hard worker was Eloi.
Ever at his forge from earliest dawn, ever with his leathern apron on
his loins, and the file, the hammer or the burin in his hand. He often
did not leave his workshop until a late hour in the night, and had ever
at his side his favorite apprentice, a Saxon named Thil. I knew that
Thil. He was then an old man, and he also was a great artist. They
should be models for you."
"Eloi was not a slave, and as he enjoyed the fruit of his labor he must
have become very rich, Father Bonaik?"
"Yes, my boys, very rich. Dagobert, upon succeeding to the throne of
his father Clotaire II, kept Eloi as his goldsmith. But the good Eloi,
mindful of his hard condition as an artisan, and of the cruel fate of
the slaves who had often been his fellow-workmen, when he became rich
spent all his income in ransoming slaves. He used in that way to
emancipate twenty, thirty and even fifty on one day. He often went to
Rouen and bought whole cargoes of slaves of both sexes taken from all
countries to that town, celebrated for its market of human flesh. Among
those unfortunate people were Romans, Gauls, English, and even Moors,
but above all Saxons. If it happened that the good Eloi did not have
money enough to purchase the slaves, he used to distribute among them
all the money he had in order to relieve their misery. 'How often,'
Thil, his favorite apprentice said to me, 'his purse being exhausted, I
saw my master sell his cloak, his belt and even his shoes.' But you must
know, my boys, that that mantle, that belt, those shoes were embroidered
with gold and often enriched with pearls. The good Eloi, who ornamented
the robes of others, also took pleasure in ornamenting his own. In his
younger years he was magnificently dressed."
"It was the least he could do to deck himself out well--he who decked
others so well. It is not as with us who work on gold and silver, and
never have but rags."
"My poor boys, we are slaves, while Eloi had the fortune of being free;
but he utilized his freedom for the benefit of his fellows. He had
around him several servants who adored him. I knew some of them, among
others, Bauderic, Tituen, Buchin, Andre, Martin and John. So you see old
Bonaik has a good memory. But how can one fail to remember anything
connected with Eloi!"
"Do you know, master, that it is an honor to us poor goldsmith slaves,
to number such a man in our profession?"
"A great honor, my boys! Certes, we should be proud of it. Imagine that
the reputation of the good Eloi for charity was such that his name was
known all over Gaul, and even in other countries. Strangers considered
it an honor to call upon the goldsmith who was at once so great an
artist and so good a man. If anyone asked in Paris where he lived, the
first passer-by would answer: 'Do you want to know where the good Eloi
lives? Go where you will find the largest number of poor people gathered
together. He lives there.'"
"Oh, the good Eloi," said one of the lads with eyes moist with tears.
"Oh, the good Eloi, so well named!"
"Yes, my friends, he was as active in charity as at his trade. In the
evening, at his meal hour, he would send out his servants in different
directions to gather people who suffered hunger, and also travelers in
distress. They were taken to him and he fed them. Filling the office of
a servant when they came, he helped some to unload their packs,
sprinkled warm water on the hands of others, poured out wine into their
cups, broke their bread, carved their meat and distributed it--all
himself. After having thus served all with sweet pleasure, he would sit
down himself, and only then did he himself share in the meal that he
offered these poor people. That was his way of practicing charity."
"And how did the good Eloi look, Father Bonaik? Was he tall or short?"
"He was tall and of a florid complexion. In his younger days, his
apprentice Thil said to me, his black hair was naturally curly. His
hand, though hardened by the hammer, was white and well-shaped; there
was something angelic in his expression; yet his straightforward eyes
were full of keenness."
"That is just the way I would picture him to myself, dressed in the
magnificent robes that he used to sell in order to ransom slaves."
"When he grew in years, the good Eloi renounced splendor altogether. He
wore only a robe of coarse wool, with a cord for belt.... When about
forty he was appointed bishop of Noyon at his own request."
"He? Did so great an artist aspire after a bishopric?"
"Yes, my lads.... Grieved at the sight of so many covetous and wicked
prelates, who devoured the substance of his well-beloved poor, the good
Eloi applied to the King for the bishopric of Noyon, saying to himself
that at least that bishopric would be ruled by the sweet morality of
Jesus. And he put that morality into practice up to the last day of his
life, without thereby renouncing his art. He founded several
monasteries, where he set up large gold and silversmiths' shops under
the direction of the apprentices whom he raised in the abbey of Solignac
and elsewhere in Limousin. It was thither, my lads, that I was taken as
a slave at sixteen after having undergone many trials. But I was born in
Brittany ... in that Brittany that is still free to this day, and that I
never expect to see again, although this abbey lies not far from the
cradle of my family," and the old man, who during the whole of his
narrative had kept steadily at work at the abbatial crosier that he was
chiseling, dropped on his knee the hand that held the burin. He remained
silent and pensive for a few seconds. Then, waking up with a start, he
proceeded addressing the young slaves under him, who wondered at his
silence: "My lads, I have allowed myself to be carried away despite
myself by recollections that are at once sweet and painful to my
mind.... Where did I leave off?"
"You were telling us, Father Bonaik, that you were taken as a slave at
the age of sixteen to the abbey of Solignac in Limousin."
"Yes; well, it was there that I first saw the great artist. Once every
year he left Noyon to visit the abbey. He had inducted his apprentice
Thil abbot of the place, and the abbot directed the goldsmith's
workshop. The good Eloi was quite old then; but he loved to come to the
workshop to oversee and direct the work. He often took the file or the
burin from our hands to show us how to use it, and in such a paternal
manner did he act that all our hearts went out to him. Oh! those were
good days.... The slaves were not allowed to leave the territory of the
monastery, but they felt as happy there as one can under bondage. At
every visit that he paid the place, Eloi inquired after them to
ascertain whether they were kindly treated. After his death, however,
everything changed."
The old goldsmith had reached this epoch in his narrative when the door
of the workshop opened and two personages stepped in.
CHAPTER II.
THE INTENDANT RICARIK.
One of the persons who entered Father Bonaik's workshop was Ricarik, the
intendant of the abbey, a Frank of a low and vulgar appearance; the
other was Septimine, the slave of the abbey of St. Saturnine, whose
freedom, together with her father's and mother's, Berthoald had a few
days previous sued for and obtained at the hands of Charles Martel.
Since her departure from the abbey of St. Saturnine, the poor child had
become hardly recognizable. Her charming face had thinned and was
pale--so much had she suffered and wept. She followed the intendant
silent and confused.
"Our holy dame, Abbess Meroflede, sends you this slave," said Ricarik to
the old goldsmith, pointing at Septimine, who, ashamed at finding
herself among the young apprentices, did not dare to raise her eyes.
"Meroflede bought her yesterday from the Jew Mordecai.... You are to
teach her to polish jewelry; our holy abbess wishes to keep her near her
for that work. Within a month at the latest, she must be versed in her
work; if not, both she and you shall be punished."
At these words Septimine trembled and took courage to raise her eyes to
the old man, who stepped forward and said to her kindly: "Do not be
afraid, my child; with a little good will on your part, we shall be able
to teach you how to polish jewelry and meet the wishes of our holy
abbess. You shall work there, near me."
For the first time in several days did the features of the young girl
express sentiments other than those of fear and sadness. She timidly
raised her eyes to Bonaik, and, struck by the kindness of his face,
answered him in an accent of profound gratitude: "Oh! Thank you, good
father! Thank you for being kind to me!"
While the apprentices were exchanging in a low voice their views on the
looks of their new shopmate, Ricarik, who carried a little casket under
his arm, said to the old man: "I bring you here the gold and silver with
which to fashion the belt that you know of, and also the Greek vase. Our
dame Meroflede is anxious to have the two articles."
"Ricarik, I told you before that the stuff that you brought me in bits
and in gold and silver sous is not enough. It is all in that iron trunk
whose key you hold. Moreover, in order to make one of those beautiful
belts, similar to those that I saw manufactured in the workshops that
the illustrious Eloi established, about twenty pearls and as many other
precious stones will be needed."
"I have in this purse and this casket all the gold, silver and precious
stones that you will need," saying which, Ricarik emptied out the
contents of a purse upon the old goldsmith's work-bench, and took out of
the casket a sufficient number of gold sous, several twisted lumps also
of gold, that looked as if they had been forcibly wrenched from some
article that they had served as ornament to, and finally a gold
reliquary studded with precious stones. "Have you now enough gold and
stones?"
"I think so; these stones are superb; the reliquary is ornamented with
matchless rubies."
"This reliquary was presented to our holy abbess; it contains a thumb of
St. Loup, of the great St. Loup, and two teeth from his jaw."
"Ricarik, after I shall have detached the rubies and melted the gold of
the reliquary, what am I then to do with the thumb and teeth?"
"The thumb and teeth?"
"The bones of the blessed St. Loup that are inside."
"Do with them what you like ... keep them as relics to prolong your old
age."
"I would then live at least two hundred years."
"What are you examining with so much attention?"
"I am examining the silver sous that you have just brought in. Some of
them do not seem sound."
"Some colonist must have cheated me.... This is the day they pay their
rents and imposts. When these people pay in money you would think they
were having their teeth extracted. It is unfortunately too late now to
discover the cheats who paid with false sous. But you shall come along
with me so that you may examine the pieces that are now to be paid in.
Woe to the thief who should then try to pass false coin upon me! His
skin will boil for it!"
"I shall do as you order.... We shall lock these precious metals and
stones in the iron chest, if you please, until I have time to start to
work on them."
While the Frank was examining the contents of the chest, the old
goldsmith approached his young apprentices and said to them in a low
voice: "Now, lads, so far I have always taken your side against our
masters, palliating or hiding your faults, to spare you the punishments
that you sometimes did deserve."
"That is so, Father Bonaik."
"In return, I demand of you that you treat that poor girl that stands
trembling there, as if she were your own sister. I am to go out with the
intendant, and shall be away, perhaps, for an hour. Promise me that you
will be decorous and reserved in your talk before her."
"Fear not, Father Bonaik; we shall say nothing that a nun may not hear."
"That is not enough; certain nuns can hear everything; promise me you
will say nothing that you would not say before your own mothers."
"We promise you, Father Bonaik."
This whispered conversation took place at the other end of the workshop,
while Ricarik was taking an inventory of the contents of the iron chest.
The old man then returned to Septimine and said to her also in a low
voice: "My child, I shall leave you for a little while; but I have
recommended those lads to treat you as a sister. Be at ease. You will
hear nothing to hurt your ears."
Septimine had hardly thanked the old jeweler with a look of gratitude,
when the intendant closed the chest and said: "Have you heard any news
of that runaway Eleuthere?"
The old goldsmith made a sign to the young slaves, all of whom had
raised their heads at the name of Eleuthere; but catching Father
Bonaik's eyes, all resumed work without answering a word to the
intendant's question, and without even seeming to hear him.
"His disappearance must be a matter of surprise to you, is it not?"
asked Ricarik, letting his penetrating eye wander over the apprentices.
"He must have found a way to escape," said the lad who believed he had
recognized Eleuthere in the cloister. "He long went with the idea of
escaping from the monastery."
"Yes, yes," answered two other apprentices; "Eleuthere told us he would
run away from the monastery."
"And why did you not post me, you dogs?" cried the intendant. "You are
his accomplices."
The lads remained quiet with their eyes down. The Frank proceeded:
"Oh! You kept the secret! Your backs will ring for it under the whip!"
"Ricarik," replied the old goldsmith, "these lads chatter like jays, and
have no more brains than fledgling birds. Eleuthere often said as so
many others have: 'Oh, how I would like to roam over the fields, instead
of being bound to the workshop from morning till evening!' That is what
these lads call secrets. Pardon them. Then, you should remember that our
holy dame Meroflede is impatient for her belt and vase. But if you have
my apprentices whipped, they will spend more time rubbing their sores
than plying the hammer and the file, and our work will make but slow
progress. It would cause a great delay."
"Very well, then; they shall be punished later. All of you will have to
work hard, not by day only, but also by night. By day you will work upon
gold and silver. By night you shall furbish iron. There is a double task
for you."
"What do you mean?"
"There will be a stack of arms brought here this evening--axes, swords,
and lances that I have bought at Nantes."
"Arms!" cried the old man in astonishment. "Arms! Do the Arabs still
threaten the heart of Gaul?"
"Old man, the arms will be brought to you this evening. See to it that
the lances have good points, that the swords are well sharpened, the
axes trenchant. Never you mind the rest. But this is the hour when the
colonists must bring their money taxes. Follow me, in order to ascertain
whether the thieves try to pass false coin upon me. Come, Father
Bonaik!"
CHAPTER III.
THE ABBESS MEROFLEDE.
Upon leaving the workshop, the intendant Ricarik, followed by the old
goldsmith, proceeded to a vast shed located outside of the abbey. Almost
all the slaves and colonists who had ground-rent to pay to the monastery
were gathered at the place. There were four days in the year set aside
for the payment of major rents. At these periods, the products of the
land that was cultivated, and with so much labor, by the Gauls, flowed
in a strong and steady stream into the abbey. Thus abundance and leisure
reigned within the holy precincts of this, the same as of all the other
monasteries, while the enslaved populations, barely sheltered in
thatched hovels, lived in perpetual and atrocious misery, borne down by
all manner of exactions. Few sights could be imagined, more lively and
yet so sad, than those presented at the payment of the ground-rent. The
peasants, barely clad, whether slaves outright or only colonists, whose
leanness told of their trials, arrived carrying on their shoulders or
pushing in carts provisions and products of all sorts. To the tumultuous
noise of the crowd was added the bleating of sheep and calves, the
grunting of pigs, the lowing of cattle, the cackling of poultry--animals
that the rent payers had to bring alive. Some of the men bent under the
weight of large baskets filled with eggs, cheese, butter and honeycombs;
others rolled barrels of wine that were taken to the abbey's gate on a
sort of sled; yonder, wagons were unloaded of their heavy bags of wheat,
of barley, of spelt, of oats or of mustard grain; here, hay and straw
were being heaped up in high piles; further away, kindling wood or
building material, such as beams, planks, boards, vine poles, stakes;
forester slaves brought in bucks, wild boars and venison to be smoked;
colonists led by the leash hunting dogs that they had to train, or
carried in cages falcons and sparrow-hawks that they had taken from
their nests for falconry; others, taxed in a certain quantity of iron
and lead, necessary articles in the construction of the buildings of the
abbey, carried these metals, while others brought rolls of cloth and of
linen, bales of wool or of hemp for spinning, large pieces of woven
serge, packages of cured hides, ready for use. There were also tenants
whose rent consisted in certain quantities of wax, of oil, of soap and
even resinous torches; baskets, osier, twisted rope, hatchets, hoes,
spades and other agricultural implements. Finally, others had to pay
with articles of furniture, and household utensils.
Ricarik sat down at one of the corners of the shed near a table to
receive the money tax of the colonists who were in arrears, while
several turning-box sisters of the convent, dressed in their long black
robes and white veils, went from group to group with a parchment scroll
on which they entered the rent in kind. The old goldsmith stood behind
Ricarik and examined one after another the sous and the silver and
copper deniers that were being paid in. He approved them all. The
venerable old man feared to expose the poor people to bad treatment if
he rejected any coin, seeing the intendant was merciless. The colonists
who were unable to pay on that day made a considerable group, and
anxiously awaited their names to be called. Many of them were
accompanied by their wives and children. Those who had the money to pay
having acquitted themselves, Ricarik called in a loud voice:
"Sebastian!" The colonist advanced all in a tremble with his wife and
two children at his side, all of them as miserably dressed as himself.
"Not only have you not paid your rent of twenty-six sous," said the
intendant, "but last week you refused to cart to the abbey the woolen
and linen goods that the abbess sent to Rennes. A bad payer, a
detestable servant."
"Alack, seigneur! If I have not paid my rent it is because shortly
before harvest time the storm destroyed my ripe wheat. I might still
have saved something if I could have attended to the crop immediately,
but the slaves who work the field with me were requisitioned away five
out of seven days in order to work at the enclosures of the new park of
the abbey and in draining one of the ponds. Left alone, I could not take
in the remnants of the harvest; then came the heavy rains; the wheat
rotted on the ground and the whole harvest was lost. All I had left was
one field of spelt; it had not been badly treated by the storm; but the
field is contiguous to the forest of the abbey, and the deer ravaged the
crops as they did the year before."
Ricarik shrugged his shoulders and proceeded: "You owe besides, six
cart-loads of hay; you did not fetch them in, yet the meadows that you
cultivate are excellent. With the surplus of six cart-loads you could
easily get money and fulfill your engagements."
"Alack, seigneur! I never get to see the first cut of those meadows. The
herds of the abbey come to pasture on my lands from early spring. If I
set slaves to keep them off, a fight breaks out between my slaves and
those of the abbey; one day mine are beaten, the next mine beat the
others. But however it be, I am deprived of the help of their arms.
Besides, seigneur, almost every day has its special duties; one day we
have to prune the vines of the abbey, another we have to plow, harrow
and plant its fields; yet another, we have its crops to cart away;
another day it is the fences that have to be repaired. We have lately
also had ditches to dig when the abbess feared that the convent was to
be attacked by some bands of marauders. At that time we also had to
mount guard.... If out of three nights one is compelled to spend two on
his feet, and then to work from early dawn, strength fails and the work
is neglected."
"What about the cartage that you refused?"
"No, seigneur, I did not refuse to make the cartage. But one of my
horses was foundered with too heavy a load and too long a stretch for
the abbey. It was not possible to execute your orders for the last
cartage."
"If you have only one foundered horse, how do you expect to cultivate
your fields? How will you pay your back rent and the rent of next year?"
"Alack, seigneur! I am in a cruel fix. I have brought with me my wife
and children. Here they are. They join me in beseeching you to remit
what I owe. Perhaps in the future I shall not meet so many disasters one
after another."
At a sign from the unhappy Gaul, his wife and children threw themselves
at the feet of the intendant and with tears in their eyes implored him
to remit the debt. Ricarik answered the colonist: "You have done wisely
in bringing your wife and children with you; you have saved me the
trouble of sending for them. I know of a certain Jew of Nantes called
Mordecai, who loans money on bodily security. He will advance at least
ten gold sous on your wife and two children, both of whom are old enough
to work. You will be able to invest the money in the purchase of a horse
to replace the one that was foundered. Later, after you shall have
reimbursed the Jew his loan, he will return you your wife and children."
The colonist and his family heard with stupor the words of the
intendant, and broke out into sobs and prayers. "Seigneur," said the
Gaul, "sell me if you like as a slave; my condition will not be worse
than it is now; but do not separate me from my wife and children.... I
never shall be able to pay my back rent and reimburse the Jew; I prefer
slavery to my present life as a colonist. Have pity upon us!"
"That will do!" said Ricarik. "You have too numerous a family to feed;
that is what is ruining you.... When you will have only your own needs
to attend to, you will be able to pay your rent, and with Mordecai's
loan you will be enabled to continue to work." Turning thereupon to one
of his men: "Take the wife and children of Sebastian to the Jew
Mordecai, he happens to be here now."
Bonaik sought to mollify the Frank, but in vain, and Ricarik proceeded
to call up by their names other colonists who were in arrears with their
rent. The intendant was at this work when a lad of from seventeen to
eighteen was dragged before him. The lad offered violent resistance to
his captors and cried: "Let me go! I have brought three falcons and two
goshawks for the abbess' perch as my father's rent.... I took them from
their nests at the risk of breaking my bones.... What is it you want?"
"Ricarik," said one of the slaves of the abbey who was dragging the lad,
"we were near the fence of the abbey's perch when we saw a sparrow-hawk,
still hooded, that had escaped from the falconer's hand. The bird flew
only a little distance. Being impeded by its hood, it fell down close to
the fence. This lad immediately threw his cap upon the bird and put it
into his bag. We caught the thief in the act. Here is the bag. The
sparrow-hawk is inside with its hood still on."
"What have you to say?" asked Ricarik of the young lad who remained
somber and silent. "Do you know how the law punishes the theft of a
sparrow-hawk? It condemns the thief to pay three silver sous or to allow
the bird to eat six ounces of flesh from his breast. I have a good mind
to apply the law to you as a salutary example to other hawk thieves....
What have you to say?"
"If our abbess," the lad answered boldly, "gives our flesh for pasture
to her hunting birds, as true as my name is Broute-Saule, sooner or
later I shall have my revenge on her and you!"
"Seize him!" cried Ricarik. "Let him be tied down to a bench outside of
the shed so that his punishment be public.... Let the flesh on his
breast be offered to the sparrow-hawk for pasture!"
"Butcher!" cried the lad. "If I ever catch you or your abbess of the
devil alone, you will make the acquaintance of my knife!"
The crowd of slaves who witnessed the scene broke out into violent
shouts against Broute-Saule, who was impious enough to express himself
in such terms on the abbess Meroflede, and the wretches crowded each
other in their curiosity to witness the punishment. The young Gaul was
stripped of his clothes to the waist and tied down, face up, to a stout
bench that stood outside of the shed. Ricarik then made a slight
incision on the right breast of the lad so as to whet the hawk's
appetite. Attracted by the blood, the bird pounced upon the breast of
Broute-Saule, into whose flesh it stuck its beak.
At this moment the tramp of several horses was heard, and immediately
the slaves and colonists who stood near the bench on which Broute-Saule
lay, and with a greedy gap watched his punishment, fell upon their
knees. The abbess Meroflede had ridden in among them, mounted upon a
vigorous grey stallion. Curious to ascertain the cause of the excited
crowd that stood outside of the shed, the abbess reined in her horse
with a sudden tug at the reins. Meroflede was dressed in a long black
robe; a white veil, fastened under her chin, framed in her face. Clasped
at the height of her neck, a sort of caped red cloak floated in the
breeze over her monastic garb. Slender, tall and graceful, the woman was
about thirty years of age. Her features would have been handsome but for
their combined expression that was alternately sensuous, haughty or
savage. Her face, wan from excess, rivaled by its pallor the whiteness
of the veil that surrounded it, the same as the color of her cloak vied
with her red and lascivious lips that were shaded by a light moustache
of reddish gold. Her hooked nose terminated in palpitating and inflated
nostrils. Her large eyes of sea-green color glistened under thick and
reddish eyebrows. Meroflede reined in her horse near the crowd, which
knelt down, and in doing so discovered to her sight the half-naked
youth, whose breast the sparrow-hawk had begun to peg into. Broute-Saule
turned towards her his face that nestled in his black and wavy hair, and
despite the pain that the bird's beak gave him, the young Gaul, whose
features were expressive of involuntary admiration, cried: "How
beautiful she is!"
Motionless, with the gloved hand that held her whip reclining upon her
thigh, Meroflede looked steadily upon the slave whose flesh the hawk was
eating up; on the other hand, insensible to his own pain, Broute-Saule
contemplated the abbess and repeated in a low voice as if in a rapture:
"How beautiful she is! Oh, madam, the Queen Mary and mother of God is
not more beautiful!"
For a few seconds Meroflede contemplated the spectacle; she then called
Ricarik, leaned down over her saddle, whispered a few words to him, and
casting a last look at Broute-Saule she departed at a gallop without
bestowing upon the kneeling slaves and colonists the benediction that
the poor wretches expected from their abbess.
CHAPTER IV.
IN SIGHT OF THE ABBEY.
Upon leaving the convent of St. Saturnine, Berthoald took with his men
the road to the abbey of Meriadek. The march of the troop was delayed by
the condition in which they found two of the bridges on their route; the
roads, moreover, were in such a state that the carts containing the
booty of the warriors, together with the Arabian and Gallic women whom
they had captured in the environs of Narbonne, frequently sank to the
axles of the wheels in the mud.
Two days after Broute-Saule had been delivered to the claws and beak of
the sparrow-hawk, Berthoald and his men arrived near Nantes. The sun was
going down, night was near. The young chief on horseback rode a few
paces ahead of his companions, among whom were several fresh recruits
raised by Charles from the other side of the Rhine--men as savage and
fierce as the first soldiers of Clovis, and, like them, dressed in skins
and wearing their hair tied at the top of their heads--just as, more
than two centuries before, Neroweg, one of the leudes of the Frankish
king, had worn his. The other warriors were casqued and cuirassed.
Berthoald was reserved, almost haughty towards the men of his band. They
grumbled at his coolness and general bearing towards them. But the
ascendency of his courage, his redoubtable physical strength, his rare
dexterity in arms, the promptitude of his war expedients, finally, the
high favor that he enjoyed with Charles held the savage men of war in
control. Accordingly, Berthoald rode alone at the head of his troop.
Often, since his departure from the abbey of St. Saturnine, he had
dropped into a reverie at the thought of the charming Septimine. He was
thinking of the young girl when Richulf, one of his men, rode up to his
chief and said to him:
"According to the information that we gathered on the way, our abbey
must lie hereabouts. If you will, let us interrogate the slaves that we
see on the fields."
Awakening from his reverie, Berthoald made an affirmative sign with his
head, and the two hastened the pace of their horses.
"As for me," said Richulf, a sort of German giant of an enormous girth,
"I am enjoying in advance the face that our abbot will make when we
shall tell him: 'We are here by the grace of Charles Martel. Vacate the
place, priest of Satan, and give us the key of the cellar and pantry for
us to eat and drink our fill!'"
Being now near the slaves towards whom they had ridden, Berthoald asked
one of them where the abbey of Meriadek was.
"Not far from here, seigneur; the crossroad that you see there down
below, bordered with poplars, leads straight to the abbey."
"Is an abbot or an abbess at the head of the abbey of Meriadek?"
"It is our holy abbess Meroflede."
"An abbess!" repeated Berthoald in surprise. And laughing he asked
again: "Is she young and handsome, this abbess Meroflede?"
"Seigneur, I could not answer your question, never having seen her but
from a distance and enveloped in her veils."
"If she envelops herself in her veils she must be ugly," put in Richulf,
shaking his head doubtfully. "Are the lands of the abbey fertile? Has it
many herds of swine? Does it gather in good wine?"
"The lands of the abbey are very fertile, seigneur ... the herds of
swine and sheep are very large. Two days ago we carried our rent to the
abbey and the colonists their money. It was with difficulty that the
large shed of the monastery could contain all the cattle and provisions
taken there."
"Berthoald," said Richulf, "Charles Martel has dealt generously by us.
But we arrive two days too late. The rents are paid, perhaps also
consumed by the abbess and her nuns. We will find neither pork nor wine
left."
The young chief did not seem to share the apprehensions of his
companion, and said to the slave: "Well, my poor fellow, that road lined
with poplars, there ahead of us, leads to the abbey of Meriadek?"
"Yes, seigneur; you can reach the place in half an hour."
"Thank you for the information."
Berthoald and Richulf were about to turn their horses' heads and rejoin
their troop when the latter, breaking out into a loud guffaw, observed:
"By my beard, I have never seen anyone so kind and civil towards these
dogs as you, Berthoald."
"It pleases me to be so--"
"And that makes you an odd man in everything that concerns these slaves.
One would think that it hurts you to see them.... We have about twenty
female slaves in the carts that we are dragging after us as part of the
booty. Some of them are very beautiful. You never as much as had the
curiosity of looking at them ... yet they belong to you as much as to
the rest of us."
"I have told you that I lay no claim whatever to my share of human
flesh," impatiently answered Berthoald. "The sight of those poor
creatures is painful to me. You refused to give them their freedom....
Have your way.... But do not mention them again to me."
"Well, it is no loss to us. After having amused ourselves with them on
the road we can sell them for at least from fifteen to twenty gold sous
each, according to what a Jew, who looked at them, said to us."
"Enough!... I have heard enough about the Jew and the slaves!" and
wishing to put an end to a conversation that was painful to him, he
touched the flanks of his horse with his spurs to join his Frankish
companions whom he hailed from afar. "Friends, good news! Our abbey is
rich, well stocked with cattle, and fertile; and we are to succeed an
abbess; whether she be young or old, handsome or ugly, I do not yet
know. We shall see her within an hour and shall be able to judge."
"Long live Charles Martel!" cried one of the warriors. "There's no
abbess without nuns.... We shall have a good laugh with the nuns!"
"I would have preferred to have dispossessed some fighting abbot. But I
console myself with the thought that we are to be masters of numerous
herds of swine."
"Richulf, you can think of nothing but loins of beef and ham!"
Thus gaily conversing, the warriors followed the avenue bordered with
poplars. The abbey was presently descried from the distance, rising in
the center of a sort of peninsula, and reached from this side by a
narrow road that was built between two ponds.
"Hurrah for Charles Martel!"
"What a magnificent building! Look at it, Berthoald!"
"Vast domains! And that grand forest in the horizon--it surely all
belongs to our abbey. We shall be able to hunt at our ease."
"It must be full of game. We shall hunt deer, bucks and wild boars....
Long live Charles Martel!"
"And the ponds that extend down there on either side of the road, they
must be full of fish.... We shall fish carp, tench and pike that I like
so well!... Long live Charles!"
"Do you not find, comrades, that this abbey has a certain martial
aspect, with its high battlements, its counter forts, its ramparts, its
few and narrow windows and its ponds that surround it like a natural
defence?"
"So much the better! Within its walls we shall be entrenched as within a
fortress; and should it please the successors of our good Charles, or
the phantom kings, to dispossess us in turn, as we are about to
dispossess this abbess, we shall be able to prove that we wear hose and
not skirts."
"Our tapers are lances, our benedictions sabre cuts."
"Let us hasten our horses; it will soon be night and I am hungry....
Upon the word of Richulf, two whole hams, four pikes and a whole
mountain of cabbage will barely suffice to appease my hunger."
"Sharpen your teeth, glutton! As to me, I propose to invite the abbess
and her nuns. The feast will then be complete."
"I shall invite the young and handsome ones to share our lodgings at the
abbey. What say you, comrades?"
"What! Invite them, Sigewald!... They must, by my beard! They shall be
forced to remain with us.... The good Charles will laugh at the move. If
the Bishop of Nantes should raise a howl, we shall tell him to come and
take his sheep from the wolves."
"The devil take the Bishop of Nantes! The day of these tonsured people
has gone by, that of the soldier has come!... We are masters in our
house!"
While his companions were delivering themselves of these gross jokes,
Berthoald preceded them silent and pensive. Charles had invested him
with the high dignity of count; he dragged a rich booty behind him in
his carts; the donation of the abbey insured to him the possession of a
large income; all notwithstanding, the young chief seemed troubled in
mind; at times a bitter and painful smile curled his lips. The Frankish
riders were presently on the narrow road at either side of which an
immense pond extended as far as the eye could reach. Richulf presently
said to the young chief: "I do not know whether it is the dusk that
impedes my sight, but it looks to me as if this road is cut off by a
mound of earth a little distance ahead of us."
"Let us look at that a little closer," said Berthoald, putting his horse
to a gallop. Richulf and Sigewald followed him. Soon the three found
their advance intercepted by a deep and wide moat cut into the road and
filled with water that flowed into it from two ponds. On the other side
of the moat rose a kind of breastwork of earth protected with enormous
piles. The obstacle was serious. Night drew near, and on either side the
ponds extended as far as the eye could reach. Berthoald turned around to
his companions who were no less surprised than himself: "The breastwork,
like the abbey, has a decidedly martial mien."
"This ground has been recently thrown up. The bark of the piles is still
fresh, as also the leaves of the hedge that crowns the parapet.... What
the devil can these precautions of defence mean?"
"By the hammer of Charles!" said Berthoald. "Here we have an abbess who
is well up in the art of entrenchment! But there must be some other
route to reach the abbey and--" Berthoald did not finish the sentence. A
volley of stones thrown by slingers hid behind the hedge that crowned
the parapet, reached the three warriors. Their casques and cuirasses
broke the shock, but the young chief was rudely struck in the shoulder,
while the horse of Richulf, that was near the edge of the road and was
hit in the head, reared so violently that it fell over upon its rider
and both rolled into the pond, which was so deep at that spot that horse
and rider disappeared completely. The Frank soon rose back to the
surface and managed with great difficulty to clamber up the bank, while
his horse swam away frightened towards the center of the pond, where,
finally exhausted, it rolled over and sank.
"Treason!" cried Berthoald.
The deep moat filled with water was thirty feet wide. In order to cross
it, according to the art of war, it would have been necessary to fetch
lumber from a great distance and commence a regular siege. Night,
moreover, was on. While the young chief consulted with his companions
upon the unexpected occurrence, a voice from behind the hedge called
out: "This first volley of stones is but a shower of roses to what is in
store for you if you attempt to force a passage."
"Whoever you be, you shall pay dearly for this assault," cried
Berthoald. "We are come by orders of Charles, chief of the Franks, who
made a gift of the abbey of Meriadek to me and my men. I command here.
It is for you to obey."
"And I," replied the voice, "make you a gift, preparatory to something
better, of that volley of stones that you just got."
"We can not to-night force a passage; but we shall encamp on this road.
To-morrow, at break of day, we shall storm your entrenchment. So, I warn
you, the abbess of this convent and her nuns will be treated like women
of conquered towns. The young ones will be distributed among us, the old
ones will be whipped, and the men will be slaughtered."
"Our holy abbess, Dame Meroflede, minds not such threats," answered the
voice. "The abbess consents to admit the chief of those bandits, but
alone, into the convent.... His companions will camp for the night on
the causeway. To-morrow at break of day he shall rejoin his troop. And
when he shall have reported to them what he saw in the monastery, and in
what style preparations are making to receive them, they will realize
that the very best thing for them to do will be to return and fight
near Charles, the heathen who dares to dispose of the goods of the
Church! By the horns of Satan, we shall know how to chase you hence!"
"I shall punish your insolence!"
"My horse is drowned," added Richulf in a rage; "the water streams from
my armor; I am chilled through; my stomach is empty; and yet we are
condemned to spend the night in the open!"
"Enough words! Decide!" replied the voice. "From the top of this
breastwork a long plank will be lowered over to you. However unsteady of
foot your chief may be, he will be able to cross the moat in safety. I
shall take him to the abbey; to-morrow he shall rejoin his companions,
and may the devil, who brought you here, lead you back to hell!"
During this debate the other Franks of Berthoald's troop and presently
also the carts and baggages, all of which entered without mistrust upon
the narrow causeway, had come up to where the young chief stood. He
explained what had happened, and showed them the moat and the opposite
breastwork, which, under the circumstances, could neither be cleared nor
taken. The straggling beneficiaries of the abbey, no less nonplussed and
no less furious than Berthoald himself, broke out into threats and
imprecations against the abbess. Nevertheless, night having now fallen,
there was no choice but to camp upon the road. It was also decided that
Berthoald should proceed alone to the abbey, and that early the next
morning they were to consider what to do, according to his report; but
whatever their decision might be upon Berthoald's report, it was
determined that if Berthoald should fall a victim to treason and not
return in the morning, force would be immediately resorted to. As to
himself, wholly disregarding any danger that might threaten, Berthoald
insisted upon accepting the offer of admitting him to the monastery. The
young chief yielded in this as much to the spirit of adventure as to an
overpowering curiosity to see the fighting abbess. Agreeable to the
tender made by Ricarik, who guarded the breastwork, a plank was pushed
out horizontally from within the parapet, it swayed to the right and
left for a moment and then dropped so that one end rested on the side of
the ditch where Berthoald stood and the other remained firmly fastened
to the parapet. Berthoald left his horse in charge of one of his
companions, and with a firm and light step walked over the plank,
quickly reaching the parapet, into which the plank was immediately drawn
back.
CHAPTER V.
ASYLUM.
Berthoald was received by the intendant, whom, controlling his own
anger, he followed to a near spot where two horses stood saddled.
Ricarik left about a dozen slaves and colonists behind to watch the
trench under the starry sky, and motioning Berthoald to one of the
horses, leaped upon the other and galloped ahead. The young chief rode
in the wake of his guide, rage alternating in his breast with curiosity
concerning the fighting abbess who gave such unsatisfactory tokens of
resignation to the decree that dispossessed her of her benefice. In the
course of the ride towards the abbey, Berthoald encountered two other
protected ditches, like the first, but crossable by means of drawbridges
that were let down to allow him and his guide to pass. A short while
after crossing the second of these two ditches, Berthoald stood near the
outer enclosure of the abbey. The enclosure consisted of thick joists
well fastened together and planted from bank to bank of the two ponds
that lay on both sides. The buildings of the abbey rose upon a vast
peninsular field, accessible only from the side of the causeway that had
just been put in a state of defence. Behind the monastery, a tongue of
land connected with the forest, whose crest bordered the horizon, thus
offering another passage. Berthoald noticed many lights inside of the
enclosure, projected, no doubt, by torches. The intendant took a copper
horn that hung from the pommel of his saddle and blew a call. An
iron-barbed door facing the jetty opened slowly. Preceded by his guide,
Berthoald entered the first courtyard of the abbey, and found himself
face to face with the abbess on horseback, surrounded by several
torch-bearing slaves. Meroflede had lowered the cape of her scarlet
cloak half over her forehead. At her side hung a gold-handled hunting
knife in a steel sheath. Berthoald was seized with astonishment at the
sight of the woman as she sat in the light of the torches. Her costume,
at once monastic and martial, set off the supple and easy frame of the
abbess. The young chief found her handsome as far as he could judge
across the shadow projected upon her face by her half-drawn cowl.
"I know that you are Berthoald," said Meroflede in a vibrating and
sonorous voice; "and so you have come to take possession of my abbey?"
"This abbey has been given me and my companions of war by Charles, the
chief of the Franks. Yes, I have come to take possession."
Meroflede indulged in a laugh of disdain, and despite the shadow that
veiled her face, her laughter exposed to the eyes of Berthoald two rows
of pearly white teeth. The abbess gave her horse a slight touch of her
heel and bade the young man follow.
At the moment when Meroflede's horse was put on the march,
Broute-Saule--now healed of the peckings of the sparrow-hawk, and no
longer clad in rags, but wearing on the contrary an elegant green
jacket, buck-skin hose, neat leather shoes and a rich fur cap--placed
himself at the horse's head with his hands on the reins. Thus walking
between the abbess and Berthoald, the young hawk thief watched
attentively the slightest motion of Meroflede and covered her with
ardent and jealous eyes. From time to time he cast an uneasy glance at
the young chief. The torch-bearing slaves followed close behind the
abbess and Berthoald to the inner courtyard. Meroflede entered with
Berthoald and indicated to him fifty colonists in martial order and
armed with bows and slings.
"Do you think these premises are sufficiently protected, my valiant
captain?" asked Meroflede.
"For me and my men, a slinger or an archer is no more dangerous than a
dog that barks at a distance. We let the arrows whiz, the stones fly and
get within our sword's length. To-morrow at break of day you will know
what you have to expect, dame abbess ... should you insist upon
defending the abbey."
Meroflede again laughed and said: "If you love a fight at close quarters
your taste will be suited to-morrow."
"Not to-morrow!" cried Broute-Saule, casting upon Berthoald a look of
concentrated hatred and mistrust; "if you wish to fight, fight on the
spot ... right here in this yard, by the light of the torches and under
the eyes of our holy abbess; although I have neither casque nor cuirass,
I am your man!"
Meroflede playfully struck Broute-Saule's cap with her whip and said
smiling: "Hold your tongue, slave!"
Berthoald made no answer to the challenge of the hot-headed lad, and
silently followed the abbess, who, riding out of this second yard, moved
towards a spacious building from which confused cries were heard to
proceed. She leaned over her horse, and said a few words in the ear of
Broute-Saule. The latter seemed to hesitate before obeying. Seeing this,
she added imperiously:
"Did you hear me?"
"Holy dame--"
"Will you obey!" cried Meroflede impetuously, striking Broute-Saule with
her whip. "Do as you are told, slave!"
The face of Broute-Saule became livid and his furious eyes fell not upon
Meroflede but upon Berthoald. But the lad made a violent effort to
control himself; he obeyed, and ran forward to execute his mistress'
orders. Immediately after, about a hundred men of sinister and
determined mien and dressed in rags came out of the building, drew up
in line and brandished their lances, swords and axes, shouting: "Long
live our holy abbess, Meroflede!" Several women who were among the men
cried no less noisily: "Long live our abbess! Long live our holy dame!"
"Do you, who have come to take possession of this monastery," said
Meroflede to the young chief with a caustic smile, "know what the right
of asylum imports?"
"A criminal who takes refuge in a church is protected from the justice
of men."
"You are a treasure of science, worthy of carrying the crosier and the
mitre! Well, these good folks that you see there are the flower of the
bandits of this region; the least guilty of them has committed one or
two murders. Apprised of your approach, I offered them to leave the
asylum of the basilica of Nantes by night, and promised them asylum in
the chapel of the abbey, and the indulgence of the good old times. If
they leave this place the gibbet awaits them. That will give you an idea
of the fury with which they will defend the monastery against your men,
who would not be Christian enough to extend to them a similar
protection. It is easy enough to accept the gift of an abbey, it is more
difficult to take possession of it. You now know what forces I have at
my command. Let us enter the monastery. After so long a journey, you
must feel tired. I extend hospitality to you. You shall sup with me....
To-morrow, at daybreak, you shall rejoin your companions. You surely are
a prudent councilor. You will induce your band to look for some other
abbey, and you will lead them in the search."
"I see with pleasure, holy abbess, that solitude and the austerities of
the cloister have not impaired the joviality of your temper."
"Ah! You think I am jovial?"
"You suggest with an amusing seriousness that I and my men who have
been fighting the Arabs, Frisians and Saxons since the battle of
Poitiers, shall now turn tail to this handful of murderers and robbers,
reinforced by poor colonists who have left the plow for the lance, and
the hoe for the sling!"
"You braggart!" cried Broute-Saule, who had returned to his place at the
head of Meroflede's horse. "Will you have us two take an axe? We shall
strip to the waist, and you will find out whether the men of this place
are cowards!"
"You look to me to be a brave lad," answered Berthoald smiling. "If you
would like to remain with us at the abbey, you will find a place in the
ranks of my companions."
"We must have a truce from now till to-morrow.... You are surely tired.
You shall be taken to a bath. That will refresh you. After that we shall
sup. I can not treat you to a feast such as St. Agnes and St. Radegonde
treated their favorite poet, Bishop Fortunat, to at their abbey of
Poitiers, in short skirts. But you will not starve." Meroflede then
turned to Ricarik: "You have my orders, obey them!"
While speaking, Meroflede had drawn near the interior door of the abbey.
With a light leap she alighted from her horse and disappeared within the
cloister, after throwing the bridle to Broute-Saule. The lad followed
the fascinating woman with looks of despair, and he then slowly returned
to the stables, after shaking his fist at Berthoald. The latter, who was
more and more struck by the oddities of the abbess, did not notice
Broute-Saule's threatening gesture but was steeped in thought when
Ricarik recalled him to his surroundings, saying: "Alight; the slaves
will conduct you to the bath; they will help you take off your armor,
and as your baggage is not here they will furnish you with proper
vestments--they are a new hose and coat that I never used. You may put
them on should you prefer them to your iron shell. I shall later come
for you to sup with our holy dame."
CHAPTER VI.
WARRIOR AND ABBESS.
Refreshed by his bath and daintily dressed, Berthoald was half an hour
later led by Ricarik to the apartment of the abbess. When he appeared in
the hall where Meroflede awaited him, he found her alone. The abbess had
doffed her black vestments to array herself in a long white robe. A
light veil half hid the tresses of her thick and reddish hair. A
necklace and bracelets of precious stones ornamented her neck and bare
arms. The Franks, having preserved the custom, introduced before them in
Gaul by the Romans, of surrounding their banquet tables with couches,
the abbess, extended almost at full length upon a long and wide lounge
furnished with cushions, made a sign to the young chief to sit down near
her. Berthoald obeyed, increasingly taken with the unusual beauty of
Meroflede. A large fire flamed in the hearth. Rich vessels of silver
glistened on the table, which was covered with embroidered linen;
daintily carved flagons stood near gold cups; the plates held toothsome
dishes; a candelabrum, on which two little wax candles were burning,
barely lighted the spacious apartment, which was thrown into
semi-obscurity a few paces away from Meroflede and her guest, and into
complete darkness at its further ends. The lounge stood against a
wainscoted wall from which hung two portraits, one of them, coarsely
painted on an oak panel in Byzantine style, representing a Frankish
warrior barbarously accoutred after the fashion of the leudes of Clovis
three centuries earlier. Below the painting was the inscription:
"Gonthram Neroweg." Beside this picture was one of the abbess Meroflede
herself, draped in her long black and white veils; in one hand she held
her abbatial crosier, in the other a naked sword. The second picture was
much smaller than the first; it was painted on parchment, in the style
of the miniatures that sacred books were then commonly illuminated with.
Berthoald's eyes fell upon the two pictures at the moment when he was
about to sit down beside his hostess. At their sight a tremor ran
through him, and he remained as if thunder-struck. Presently he looked
from Gonthram Neroweg to Meroflede, and from the abbess back to the
former. He seemed to compare the resemblance between the two, an obvious
resemblance; like Neroweg, Meroflede's hair was reddish, her nose
beaked, her eyes green. The young chief could not conceal his
astonishment.
"You seem to contemplate with deep interest the portrait of one of my
ancestors, deceased several centuries ago!"
"You are of the race of Neroweg!"
"Yes, and my family still inhabits its vast domains of Auvergne,
conquered by my ancestors' swords, or bestowed upon them by royal
gifts.... But that is quite enough for the past. Glory to the dead, joy
to the living! Sit down here near me, and let us take supper.... I am an
odd abbess. But by Venus, I live like the other abbots and bishops of my
time, with the only difference that these mitred folks sup with young
girls, while I shall spend the night with a handsome soldier.... Will
that be to your taste?" and raising one of the heavy silver flagons with
a virile hand, she filled to the brim the gold cup that was placed near
her guest. After merely moistening her own red lips in the cup, she
reached it to the young chief and said resolutely:
"Let us drink your welcome to this convent!"
Berthoald held the cup for a moment between his two hands, and casting
one more look at the portrait of Neroweg, he smiled caustically, fixed
upon the abbess a look as bold as that which she cast at him, and
replied: "Let us drink, beautiful abbess!" and emptying the cup at one
draught, he added: "Let us drink to love!... which overpowers the
abbesses as it does the simple maids!"
"Aye! Let us drink to love, the god of the world, as the pagans used to
say!" answered Meroflede, and filling her own cup from a little red
flagon, and replenishing the cup of the young chief, who fixedly gazed
at her with eyes that shot fire, she added: "I have drunk to your toast;
now drink to mine!"
"Whatever it be, holy abbess, and even though this cup be filled with
poison, I shall empty it to your toast, I swear by your snow-white
arms!--by your beautiful eyes!--by your voluptuous lips! I drink to
Venus Callipyge!"
"Well, then," said the abbess, fixing a penetrating look upon the young
man, "let us drink to the Jew Mordecai!"
Berthoald had his cup at his lips, but at the name of the Jew he
shivered, laid his cup down abruptly, his face grew dark and he cried in
terror:
"Drink to the Jew Mordecai?"
"Come, by Venus, the patroness of lovers, do not tremble like that, my
brave friend!"
"Drink to the Jew Mordecai!... I----"
"You said to me: 'Let us drink to Love!'" replied the abbess, without
losing the effect of her words upon Berthoald; "you swore by the
whiteness of this arm," and she raised her sleeves, "you swore to drink
my toast. Fulfill your promise!"
"Woman!" cried Berthoald with impatience and embarrassment, "what whim
is that? Why do you wish me to drink to the Jew Mordecai, to a merchant
of human flesh?"
"I shall satisfy your curiosity.... Had not Mordecai sold you as a slave
to the Seigneur Bodegesil, you would not have stolen your master's horse
and armor to go in search of adventures, and palmed yourself off upon
that devil of a Charles Martel--you, a Gaul of the subject race--for a
noble of the Frankish race and son of a dispossessed beneficiary, and
finally, Charles, one of whose best captains you have become, would not
have presented you with this abbey. Consequently, you would not be here
now, at my side, at this table, where we are together drinking to
Love.... That is the reason why, my valiant warrior, I empty this cup to
the memory of that filthy Jew! And now, will you drink to the Jew
Mordecai?"
While Meroflede was uttering these words, Berthoald contemplated her
with increased astonishment, now mixed with fear, and could find not one
word in answer.
"Ah! Ah! Ah!" said the abbess laughing, "see how dumb he has become. Why
grow alternately pale and red? What does it matter whether you are of
Gallic or Frankish race? Does that render your eyes less blue, your hair
less black, your shape less comely? Come, shame upon you, my warrior!
Must I teach a soldier how cups are emptied, and how love is made?"
Berthoald felt as if in a dream. Meroflede did not seem to despise him;
she did not seem to triumph at the advantage that she had gained over
him by the knowledge of his secret. Frank in her cynicism, she
contemplated the young chief with mild and ardent eyes. Her looks that
at once troubled his mind and fired his veins; the strangeness of the
adventure; the effect of the large cup that he had just drained at one
draught, either a heady wine or perchance mixed with some philtre, and
that began to throw his brain into disorder;--all these thoughts crowded
upon Berthoald's mind. He took a sudden resolve--to vie with the abbess
in audacity, and said resolutely to her: "You are of the race of
Neroweg, I of that of Joel!"
"We shall drink to Joel ... he has raised a breed of handsome soldiers."
"Are you acquainted with the death of the son of Gonthram Neroweg, whose
portrait I see there on the wall?"
"A tradition in my family has it that he was killed in his domain of
Auvergne by the chief of a troop of bandits and revolted slaves. May the
devil keep his soul!"
"The chief of those bandits was named Karadeucq ... he was the great
grandfather of my grandfather!"
"By heaven! That is a singular coincidence! And how did the bandit kill
Neroweg?"
"Your ancestor and mine fought valiantly with axes, and the count
succumbed. The Gaul triumphed over the Frank!"
"Indeed ... you refresh the recollections of my childhood. Did not your
ancestor cut some words in the trunk of a tree with the point of a
dagger after the combat?"
"Yes--'_Karadeucq, a descendant of Joel, killed Count Neroweg_'!"
"A few months after her husband's death, the count's wife, Godegisele,
gave birth to a son, who was the grandfather of my grandfather."
"Strange coincidence, indeed ... and you, my beautiful abbess, listen to
the story with great calmness!"
"What are those combats of our ancestors and of our races to me? By
Venus! By her beautiful hips! I know but one race in all the world--the
race of lovers! Empty your cup, my valiant warrior, and let us sup
merrily. To-night there is a truce between us two.... War to-morrow!"
"Shame! Remorse! Reason! Duty!--let them all be drowned in wine!... I
know not whether I am awake or dreaming on this strange night!" cried
the young chief, and taking up his full cup, he rose and proceeded with
an air of feverish defiance while turning towards the somber and savage
portrait of the Frankish warrior: "To you, Neroweg!" Having emptied his
cup, Berthoald felt seized with a vertigo and threw himself upon the
lounge, saying to Meroflede: "Long live Love, abbess of the devil! Let
us love each other to-night, and fight to-morrow!"
"We shall fight on the spot!" cried a hoarse and strangling voice, that
seemed to proceed from the extremity of the large hall that lay in utter
darkness, and, the curtains of one of the doors being thrust aside,
Broute-Saule, who, without the knowledge of the abbess and driven by
savage jealousy, had managed to penetrate into the apartment, rushed
forward agile like a tiger. With two bounds he reached Berthoald, seized
him by the hair with one hand and raised a dagger over him with the
other, determined to plunge the weapon into the young chief's throat.
The latter, however, although taken by surprise, quickly drew his sword,
held with his iron grip the armed hand of Broute-Saule, and ran his
weapon through the unfortunate lad. Deadly wounded, Broute-Saule
staggered about for a few seconds and then dropped, crying: "Meroflede
... my beautiful mistress ... I die under your eyes!"
Still holding his bloody sword in his hand, and aware that the powerful
wine was making further inroads upon his senses, Berthoald mechanically
fell back upon the lounge. The dazed chief for a moment scrutinized the
darkness of the apartment, apprehensive of further attempts upon his
life, when he saw the abbess knock over with her fist the candelabrum
which alone lighted the room, and in the midst of the total darkness
that now pervaded the place he felt himself in the close embrace of the
monster. Hardly any recollection remained to him of what happened during
the rest of that night of drunkenness and debauchery.
CHAPTER VII.
THE MOUSE-TRAP.
Dawn was about to succeed the night in which Broute-Saule was killed by
Berthoald. Profoundly asleep and with his hands pinioned behind his
back, the young chief lay upon the floor of Meroflede's bedchamber.
Wrapped in a black cloak, her face pale and half veiled by her now loose
thick red hair that almost reached the floor, the abbess proceeded to
the window, holding in her hand a lighted torch of rosin. Leaning over
the sill whence the horizon could be seen at a distance, the abbess
waved her torch three times, while intently looking towards the east
which began to be tinted with the approaching day. After a few minutes,
the light of a large flame, that rose from a distance behind the
retreating shades of night, responded to Meroflede's signal. Her
features beamed with sinister joy. She dropped her torch into the moat
that surrounded the monastery, and then proceeded to awaken Berthoald by
shaking him rudely. Berthoald was with difficulty drawn from his
lethargy. He sought to take his hand to his forehead, but found that he
was pinioned. He raised himself painfully upon his leaden feet, and
still unclear of mind he contemplated Meroflede in silence. The abbess
extended her bare arms towards the horizon, that dawn was feebly
lighting, and said: "Do you see yonder, far away, the narrow road that
crosses the pond and prolongs itself as far as the outer works of the
abbey?"
"Yes," said Berthoald, struggling against the strange torpor that still
paralyzed his mind and will, without thereby wholly clouding his
intellect; "yes, I see the road surrounded by water on all sides."
"Did not your companions in arms camp on that road during the night?"
"I think so," replied the young chief, seeking to collect his confused
thoughts; "last evening ... my companions--"
"Listen!" put in the abbess nervously and placing her hand upon the
young man's shoulder. "Listen ... what do you hear from the side on
which the sun is about to rise?"
"I hear a great rumbling noise ... that seems to draw nearer towards us.
It sounds like the rush of waters."
"Your ear does not deceive you, my valiant warrior;" and leaning upon
Berthoald's shoulder: "Yonder, towards the east, lies an immense lake
held in by dikes and locks."
"A lake? What of it?"
"The level of its waters is eight to ten feet above those of the
ponds.... Do you understand what will follow?"
"No, my mind is heavy ... I hardly remember ... our charming night ...
but why am I pinioned?"
"For the purpose of checking your joy when, as will soon be the case,
you will have recovered your senses.... Now, let us continue our
confidential chat. You will understand that the moment the dikes are
broken through and the locks opened, the water will rise in these ponds
to the extent that they will submerge the narrow road on which your
companions encamped for the night with their horses and the carts that
held their booty and slaves.... Now, watch.... Do you notice how the
water is rising? It is now up to the very edge of the jetty.... Within
an hour, the jetty itself will be entirely submerged. Not one of your
companions will have escaped death.... If they seek to flee, a deep
trench, cut at my orders over night, will stop their progress.... Not
one will escape death.... Do you hear, my handsome prisoner?"
"All drowned!" murmured Berthoald, still under the dominion of a dull
stupor; "all my companions drowned----"
"Oh, does not yet that new piece of confidential news wake you up?...
Let us pass to another thing," and the abbess proceeded with a voice of
ringing triumph: "Among the female slaves, taken from Languedoc, that
your band brought in its train, there was a woman ... who will drown
with the rest, and that woman," said Meroflede, emphasizing each word in
the hope of each being a dagger in Berthoald's heart, "is--your--mother!"
Berthoald trembled violently, leaped up in his bonds, and vainly sought
to snap them. He uttered a piercing cry, cast a look of despair and
terror upon the immense sheet of water that, tinted with the first rays
of the rising sun, now extended in every direction. The wretched man
called aloud: "Oh, my mother!"
"Now," said Meroflede with savage joy, "the water has almost completely
invaded the causeway. The tent-cloths that cover the carts can hardly be
seen. The flood still rises, and at this very hour your mother is
undergoing the agonies of death ... agonies that are more horrible than
death itself."
"Oh, demon!" cried the young man, writhing in his bonds. "You lie! My
mother is not there!"
"Your mother's name is Rosen-Aer, she is forty years of age; she lived
one time in the valley of Charolles in Burgundy."
"Woe! Woe is me!"
"Fallen into the hands of the Arabs at the time of their invasion of
Burgundy, she was taken to Languedoc as a slave. After the last siege of
Narbonne by Charles, your mother was captured in the vicinity of the
town together with other women. When the division of the booty took
place, Rosen-Aer having fallen to the lot of your band was brought as
far as here.... If still you should doubt, I shall give you one more
token. That woman carries on her arm, like you, traced in indelible
letters the two words: '_Brenn_' and '_Karnak_'.... Are these details
accurate enough?"
"Oh, my mother!" cried the unfortunate Berthoald casting upon the waters
of the pond a look of most poignant pain.
"Your mother is now dead.... The jetty has disappeared under the waters,
and still they rise.... Aye, your mother was drowned in the covered
cart, where she was held confined with the other slaves."
"My heart breaks," murmured Berthoald, crushed by the weight of pain and
despair: "My suffering is beyond endurance!"
"Are you so soon at the end of your strength?" cried Meroflede with a
peal of infernal laughter. "Oh! no, no! You have not yet suffered
enough. What! You stupid slave! You Gallic renegade! Cowardly liar, who
brazenly deck yourself with the name of a noble Frank! What, did you
imagine vengeance did not boil in my veins because you saw me smile last
evening at the death of my ancestor, who was killed by a bandit of your
race! Aye! I smiled because I thought how at daybreak I would have you
witness from a distance the death agonies of your own mother! I was but
preparing my vengeance."
"Monster of lewdness and ferocity!" cried Berthoald, making superhuman
efforts to break his bonds. "I must punish you for your crimes!... Yes,
by Hesus, I shall throttle you with my own hands!"
The abbess realized the impotence of Berthoald's fury, shrugged her
shoulders and continued: "Your ancestor, the bandit, set fire a century
and a half ago to the castle of my ancestor, Count Neroweg, and killed
him with an axe. I reply to the fire with the inundation, and I drown
your mother! As to the fate that awaits you, it will be terrible!"
"Did my mother know that I was the chief of the Franks who took her
prisoner?"
"My vengeance lacked only that!"
"But who, miserable woman, could have told you what you know about my
mother?"
"The Jew Mordecai."
"How did he know her? Where did he see her?"
"At the halt that you made at the convent of St. Saturnine with Charles
Martel; it was there that the Jew recognized you."
"God was merciful to me! My mother did not live to know my shame. Her
death would have been doubly terrible.... And now, monster, deliver me
of your presence and of life. I am in a hurry to die!"
"Have patience! I have prepared for you a refined punishment, and a
prolonged agony."
CHAPTER VIII.
THE MIRACLE OF ST. LOUP'S TEETH.
On the morning of the fateful day when the abbess Meroflede drowned, as
in a mouse-trap, the troop of Frankish warriors that had presumed to
dispossess her, the goldsmith Bonaik entered his workshop at the
accustomed hour. He was soon joined by his slave apprentices. After
lighting the fire in the forge, the old man opened the window that
looked over the fosse, to let the smoke escape. With no little
astonishment Bonaik observed that the water in the moat had risen so
high as to be within a foot of the window sill. "Oh, my lads," said he
to the apprentices, "I fear some great calamity happened last night! For
very many years the water of this moat did not reach the height of
to-day, and then it happened when the dike of the upper lake broke, and
caused widespread disasters. Look yonder at the other end of the moat.
The water is almost up to the air-hole cut into the cavern under the
building opposite us."
"And it looks as if the water were still rising, Father Bonaik."
"Alack, yes, my lad! It is still rising. Oh, the bursting of the dikes
will bring on great calamities. There will be many victims!"
While Bonaik and his apprentices were looking at the rising water in the
moat, the voice of Septimine was heard calling on the outside: "Father
Bonaik, open the door of the workshop!" One of the apprentices ran to
the door and the girl entered, supporting a woman whose long hair
streamed with water; her clothes were drenched, her face livid; she was
barely able to drag herself along; so weak was she that after taking a
few steps in the shop she fell fainting in the arms of the old goldsmith
and Septimine.
"Poor woman! She is cold as ice!" exclaimed the old man, and turning to
his apprentices: "Quick, quick boys! Fetch some coal from the vault, ply
the bellows and raise the fire in the forge to warm up this unfortunate
woman. I thought so! This inundation must have caused much damage."
At the words of the goldsmith, two apprentices ran down into the vault
behind the forge for charcoal, and the other blew upon the fire, while
the old man approached Septimine, who, on her knees before the
unconscious woman, wept and said: "Oh, she is going to die!"
"Reassure yourself," the old man said; "this poor woman's hands, icy
cold a minute ago, are becoming warmer. But what has happened? Your
clothes also are drenched. You look strangely shocked."
"Good father, at daybreak this morning, the girls who sleep in my room
and I woke up and went into the courtyard. There we heard other slaves
crying that the dikes had burst. The girls all ran to see the progress
of the inundation. I went along without knowing why. They dispersed. I
advanced to a tongue of land that is washed by the water of the pond. A
large willow stands near the spot. I presently saw a half-submerged cart
floating a little way off. It was being turned around by the opposite
currents, and it was covered by a tent-cloth."
"Thanks be to God! The spreading tent-cloth acted like a balloon and
kept the cart from sinking."
"The wind blew into this sort of a sail, driving the cart towards the
shore where I stood. I then saw this unfortunate woman, holding to the
tent-cloth, the rest of her body in the water."
"And what happened then, my daughter?"
"There was not a second to lose. The failing hands of the poor woman,
whose strength was exhausted, were about to drop. I fastened one end of
my belt to one of the branches of the willow-tree and the other to my
wrist and I leaned forward towards the poor woman calling out to her:
'Courage!' She heard me, and seized my right hand convulsively. The
sudden pull caused my feet to slip from the edge and I fell into the
water."
"Fortunately your left wrist was tied to one of the ends of the belt
that you had fastened to the tree!"
"Yes, good father. But the shock was violent. I thought my arm was
wrenched from its socket. Fortunately the poor woman took hold of the
edge of my dress. My first pain having passed I did my best, and with
the aid of my belt that remained fastened to the tree and on which I
tugged away, I succeeded in reaching the shore and pulling out this
woman, on the point of drowning. Our workshop being the nearest place
that I could think of, I brought her here; she could hardly support
herself; but, alack!" added the girl at the sight of the still inanimate
face of Rosen-Aer, for it was Berthoald's mother that Septimine had just
saved, "I may only have retarded the supreme moment for a few seconds!"
"Do not lose hope," answered the old man, "her hands are growing
warmer."
With the aid of the apprentices, who were no less compassionate than
Septimine and the old man, Rosen-Aer was drawn sitting on a stool near
the forge. Little by little she felt the salutary effect of the
penetrating heat, she gradually recovered her senses, and finally awoke.
Gathering her thoughts, she stretched out her arms to Septimine and said
in a feeble voice: "Dear child, you saved me!"
Septimine threw herself around Rosen-Aer's neck, shedding glad tears,
and answered: "We have done what we could; we are only poor slaves."
"Oh! my child, I am a slave like yourselves, brought to this country
from the center of Languedoc. We spent the night on the road between the
two ponds of this monastery. The oxen had been unhitched from the carts.
We were caught in the inundation that began at daybreak----" But
Rosen-Aer suddenly broke off and rose to her feet. Her face was at first
expressive of stupor, but immediately a delirious joy seized her, and
precipitating herself towards the open window, she passed her arm
through the thick iron bars, crying: "My son! I see my son Amael
yonder!"
For a moment both Septimine and Bonaik believed the unhappy woman had
become demented, but when they approached the window the young girl
joined her hands and cried out: "The Frankish Chief, he in an
underground passage of the abbey?"
Rosen-Aer and Septimine saw on the other side of the moat Berthoald
holding himself up with both hands by the iron bars of the air-hole of
the cavern. He suddenly saw and as quickly recognized his mother, and,
delirious with joy, he cried in a thrilling voice that, despite the
distance, reached the workshop: "Mother!... My dear mother!"
"Septimine," Bonaik said anxiously to the girl, "do you know that young
man?"
"Oh, yes! He was as good to me as an angel from Heaven! I saw him at the
convent of St. Saturnine. It is to that warrior that Charles donated
this abbey."
"To him!" replied the old man, bewildered. "How, then, comes he in that
cavern?"
"Master Bonaik," one of the apprentices ran by saying, "I hear outside
the voice of the intendant Ricarik. He stopped under the vault to scold
some one. He will be here in a minute. He is coming on his morning
round, as is his habit. What is best to be done?"
"Good God!" cried the old man in terror. "He will find this woman here,
and will question her. She may betray herself and acknowledge that she
is the mother of that young man--undoubtedly a victim of the abbess."
And the old man, running to the window, seized Rosen-Aer by the arm and
said to her while he dragged her away: "In the name of your son's life,
come! Come quick!"
"What threatens my son's life?"
"Follow me, or he is lost, and you also." And Bonaik, without further
explanations to Rosen-Aer, pointed out to her the vault behind the
forge, saying: "Hide there, do not stir," and turning to his apprentices
while he put on his apron: "You, boys, hammer away as loud as you can,
and sing at the top of your voices! You, Septimine, sit down and polish
this vase. May God prevent that poor young man from remaining at the
air-hole or from being seen by Ricarik!" Saying this the old goldsmith
started to hammer upon his anvil, striking with a sonorous voice the old
and well-known goldsmith's song in honor of the good Eloi:
"From the station of artisan
He was raised to that of bishop,--
With his duties of pastor,
Eloi purified the goldsmith.
His hammer is the authority for his word,
His furnace the constancy of zeal,
His bellows the inspirer,
His anvil, obedience!"
Ricarik entered the workshop. The goldsmith seemed not to notice him,
and proceeded with his song while flattening with hammer blows a silver
leaf into which the abbatial cross terminated. "You are a jolly set,"
remarked the intendant stepping to the center of the workshop; "stop
your singing ... you dogs ... you deafen my ears!"
"I have not a drop of blood in my veins," Septimine whispered to Bonaik.
"That wicked man is drawing near the window.... If he were to see the
Frankish chief--"
"Why have you so much fire in the forge?" the intendant proceeded to
say, taking a step towards the fireplace, behind which was the cave that
Rosen-Aer was concealed in. "Do you amuse yourself burning coal
uselessly?"
"No, indeed! This very morning I shall melt the silver that you brought
me yesterday."
"Metal is melted in crucibles, not in forges--"
"Ricarik, everyone to his trade. I have worked in the workshops of the
great Eloi. I know my profession, seigneur intendant. I shall first
subject my metal to the strong fire of the forge, then hammer it, and
only after that will it be ready for the crucible. The cast will then be
more solid."
"You never lack for an answer."
"Because I always have good ones to give. But there are several
necessary things that I shall want from you for this work, the most
important of any that I shall have made for the monastery, seeing the
silver vase is to be two feet high, as you may judge from the cast on
the table."
"What do you need, dotard?"
"I shall need a barrel that I shall fill with sand, and in the middle of
which I shall place my mold.... That is not all.... I have often found
that, despite the hoops that hold the staves of the barrel, where molds
are placed inside of the sand, the barrel bursts when the molten metal
is poured into the hollow. I shall need a long rope to wind tightly
around the barrel. If the hoops snap, the rope will hold. I shall also
need a long thin string to hold the sides of the mold."
"You shall have the barrel, the rope and string."
"These young folks and I shall be forced to spend part of the night at
the work. The days are short at this season. Order a pouch of wine for
us, who otherwise drink only water. The good cheer will keep up our
strength during our hard night's work. On casting days, at the workshops
of the great Eloi, the slaves were always treated to something extra....
Eatables were not spared."
"You shall have your pouch of wine ... seeing that this is a holy-day at
the convent. A miracle has taken place--"
"A miracle! Tell us about it!"
"Yes.... A just punishment of heaven has struck a band of adventurers
upon whom Charles the accursed had the audacity of bestowing this abbey
that is consecrated to the Church. They camped last night upon the
jetty, expecting to attack the monastery at daybreak. But the Lord, by
means of a redoubtable and astonishing prodigy opened the cataracts of
heaven. The ponds swelled and the whole band of criminals was drowned!"
"Glory be to the Lord!" cried the old goldsmith, making a sign to his
apprentices to imitate him. "Glory be to the Lord, who drowns impious
wretches in the cataracts of his wrath!"
"Glory be to the Lord!" repeated the young slaves in chorus at the top
of their voices. "Glory be to the Lord, who drowns impious wretches in
the cataracts of his wrath! Amen!"
"It is a miracle that does not at all surprise me, Ricarik," added the
goldsmith; "it is surely due to the teeth of St. Loup, to the holy relic
that you brought me yesterday."
"That's probable ... it is certain.... You do not need anything else?"
"No," answered the old man, rising and looking into several boxes; "I
have here for the mold enough sulphur and bitumen, there is also enough
charcoal; one of my apprentices shall go with you, Ricarik, and bring
the barrel, rope and cord, and do not forget the pouch of wine and the
victuals, seigneur intendant!"
"You will get them later, together with your pittances at double
rations."
"Ricarik, we shall not be able to leave the workshop one instant, on
account of the mold. Let us have our daily pittance this morning, if you
please, so that the work may not be interrupted. We shall lock the door
to keep out intruders."
"Let one of your apprentices come with me; he shall bring all the
things, but be sure and have the vase cast to-morrow so as to please our
holy abbess; if you fail your backs will have to pay for it."
"You may assure our holy and venerable abbess that when the vase shall
come out of the mold it will be worthy of an artisan who saw the great
Eloi handle the file and burin." Bonaik then said in a low voice to one
of the apprentices, while Ricarik was moving towards the door: "Pick up
on your way a dozen stones of the size of walnuts; keep them in your
pockets, and bring them to me." He then said aloud: "Accompany the
seigneur intendant, my boy; and be sure not to loiter on the way back."
"Rest assured, master," said the apprentice with a significant gesture
to the old man while following the intendant out of the shop; "your
orders will be obeyed to the letter."
CHAPTER IX.
BRENN--KARNAK.
The goldsmith remained a few moments at the threshold of the workshop
listening to the retreating steps of the intendant; he then closed and
bolted the door and went to the vault where Rosen-Aer was in hiding,
while Septimine ran to the window to see whether Berthoald was still in
sight. But the sight that presented itself to her eyes made her exclaim
with terror: "Great God, the young chief is lost!... The water has
reached the air-hole!"
"Lost!... My son!" cried Rosen-Aer in despair, rushing to the window
despite the old man's efforts to restrain her. "Oh, my son! To have seen
you again only to lose you.... Amael, Amael!... Answer your mother!"
"The woman will betray us ... if she is heard outside!" said the
fear-stricken old man, vainly endeavoring to drag Rosen-Aer from the
window bars to which the distracted woman clung, hysterically calling
out to her son. But Amael did not reappear. The flood had gained the
opening of the air-hole, and despite the width of the moat that
separated the two buildings, the muffled sound of the water was heard
pouring through the opening and falling into the cavern. Pale as death,
Septimine could not utter a word. In the frenzy of her despair,
Rosen-Aer sought to break the stout iron bars of the window, while she
sobbed aloud: "To know that he is there ... in agony ... dying ... and
we unable to save him!"
"Have hope!" cried the old man with tears in his eyes at the sight of
the mother's anguish; "hope!... I have been watching the moss-covered
stone at the corner of the air-hole. The water does not rise to it....
It has stopped rising.... See for yourselves!"
Septimine and Rosen-Aer dried their tears and looked at the stone that
Bonaik pointed out. In fact it was not submerged. Presently even the
noise of the water flowing down through the air-hole sounded with less
distinctness, and finally ceased altogether. The flood seemed checked.
"He is saved!" cried Septimine. "Thank God, the young chief will not
drown!"
"Saved!" stammered Rosen-Aer in a heart-rending tone of doubt. "And if
enough water has poured into the cavern to drown him.... Oh! If he were
still alive he would have answered my voice.... No, no! He is dying! He
is dead!"
"Master Bonaik, some one knocks," an apprentice said. "What shall I do?
Open?"
"Return to your hiding place," the old man said to Rosen-Aer, and as she
did not seem to hear, he added: "Are you determined to perish and have
us all perish with you, we who are ready to sacrifice ourselves for you
and your son?" Rosen-Aer left the window and returned to the vault,
while the old man walked to the door and inquired: "Who is there?"
"I," answered from the outside the voice of the apprentice who had gone
out with Ricarik; "I, Justin, I have executed your commissions, Father
Bonaik."
"Come in, quick," said the goldsmith to the lad who carried an empty
barrel on his shoulders and had in his hand a basket of provisions, the
wine pouch, and a large roll of rope and cord. Re-bolting the door, the
old man took the wine pouch out of the basket and going to the vault
where Rosen-Aer was hiding said to her: "Take a little wine to comfort
you."
But Amael's mother pushed the pouch aside, crying in despair: "My son!
My son! What has become of my son Amael?"
"Justin," the old man said to the apprentice, "give me the stones I told
you to pick up."
"Here, Master Bonaik, are they. I filled my pockets with them."
The old man picked out a small stone and went to the window, saying: "If
the unfortunate man is not drowned, he will understand, when he sees
this stone drop into the cave, that it is a signal." Father Bonaik took
accurate aim and threw the stone through the air-hole. Rosen-Aer and
Septimine awaited the result of Bonaik's attempt in mortal anguish. Even
the apprentices observed profound silence. A few seconds of intense
anxiety passed. "Nothing," murmured the old goldsmith with his eyes
fixed upon the air-hole.
"He is dead!" cried Rosen-Aer, held by Septimine in her arms. "I shall
never more see my son!"
The old man threw a second stone. Another interval of anxiety ensued.
All held their breath. A few seconds later, as Rosen-Aer raised herself
on tip-toe, she cried: "His hands! I see his hands! He is holding to the
bar of the air-hole. Thanks, Hesus! Thanks! You have saved my son!" and
the woman fell upon her knees in an attitude of prayer.
Bonaik thereupon saw the pale face of Amael, framed in his long black
hair that now streamed with water, rise between the iron bars of the
air-hole. The old man made him a sign to withdraw quickly, while saying
in a low voice as if he expected to be heard by the prisoner: "Now, hide
yourself, disappear and wait!" and turning to Rosen-Aer: "Your son has
understood me. No imprudence. Be calm." Bonaik then went to his
work-bench, took a piece of parchment from a little roll that he used to
trace his models on, and wrote these words:
* * * * *
"If the water has not invaded the cavern so that you cannot stay there
without danger until night, then give three pulls to the string at the
end of which will be attached the stone tied in this note. This cord can
then serve as a means of communicating. When you see it shake get ready
for further information. Until then do not show yourself at the
air-hole. Courage!"
* * * * *
Having written these words, the goldsmith rolled the stone in the
parchment, happily impermeable to water, and tied both in a knot to one
end of the string, at about the middle of which he attached a piece of
iron in order that the body of the rope might be held under water, and
thus the means of communication between the workshop and the cavern
remain invisible. Bonaik slung the stone through the air-hole, retaining
in his hand the other end of the string. Almost immediately after, three
pulls given to the string announced to Bonaik that Amael could remain
until evening without danger in his prison, and that he would follow the
orders of the old man. Hope revived the spirits of Rosen-Aer. In the
fulness of her thanks she took the goldsmith's hands and said to him:
"Good father, you will save him, will you not? You will save my son?"
"I hope so, poor woman! But let me collect my thoughts.... At my age,
you know, such experiences are trying. In order to succeed, we must be
prudent. The task is difficult.... We cannot be too cautious."
While the goldsmith, leaning on his elbows at his work-bench, held his
head in his hands, and the apprentices remained silent and uneasy,
Rosen-Aer, struck by a sudden recollection, said to Septimine: "My
child, you said my son had been good to you, like an angel from
heaven.... All that concerns you interests me. Where did you meet him?"
"Near Poitiers, at the convent of St. Saturnine.... My family and I,
touched with pity for a young prince, a boy, who was kept confined in
the monastery, wished to help him to escape; all was discovered, they
meant to punish me in a shameful, infamous manner," Septimine said
blushing; "and they decided to sell me and separate me from my father
and mother.... It was at that moment that your son, a favorite of
Charles, the Chief of the Franks, interceded in my behalf and took me
under his protection--"
"My son, say you, dear child?"
"Yes, madam, the seigneur Berthoald."
"You call him Berthoald?"
"That is the name of the young Frankish chief who is locked up in that
cavern--"
"My son Amael with the name of Berthoald! My son a favorite of the
Frankish chief!" cried Rosen-Aer struck with amazement. "My son, who was
raised in horror for the conquerors of Gaul, those oppressors of our
race! My son one of their favorites! No, no.... It is impossible!"
"Live a hundred years, and never shall I forget what happened at the
convent of St. Saturnine--the touching kindness of the seigneur
Berthoald towards me, whom he had never seen before. Did he not obtain
my liberty from Charles, and also the liberty of my father and mother?
Was he not generous enough to give me gold to meet my family's wants?"
"I am lost in the attempt to penetrate this mystery. The troop of
warriors, that brought us slaves in their train, did indeed stop at the
abbey of St. Saturnine," replied Rosen-Aer in great agony, and she
added: "but if he whom you call Berthoald obtained your freedom from the
chief of the Franks, how come you to be a slave here, my poor child?"
"The seigneur Berthoald trusted the word of Charles, and Charles trusted
the word of the abbot of the convent. But after the departure of the
chief of the Franks and your son, the abbot, who had previously sold me
to a Jew named Mordecai, kept his bargain with the Jew.... In vain did I
beseech the warriors whom Charles left behind in possession of the
monastery, and as a guard over the little prince, to stand by me. I was
torn away from my family. The Jew kept the gold that your son had
generously given me, and brought me to this country. He sold me to the
intendant of this abbey that was donated by Charles to the seigneur
Berthoald, as I learned at the convent of St. Saturnine."
"This abbey was donated to my son!... He a companion in arms of these
accursed Franks!... He a traitor! a renegade! Oh, if you speak truly,
shame and perdition upon my son!"
"A traitor! A renegade!... The seigneur Berthoald! The most generous of
men! You judge your son too severely!"
"Listen, poor child, and you will understand my sorrow.... After a great
battle, delivered near Narbonne against the Arabs, I was taken by the
warriors of Charles. The booty and slaves were divided by lot. I and my
female fellow prisoners were told that we belonged to the chief
Berthoald and his men."
"You, a slave of your own son!... But, God, he did not know it!"
"Yes, the same as I did not know that my new master, the young Frankish
chief Berthoald, was my son Amael."
"And probably your son, who marched at the head of his troop, did not
see you on the journey."
"We were eight or ten female slaves in a covered cart. We followed the
army of Charles. Occasionally the men of chief Berthoald visited us, and
... but I shall spare your blushes, poor child, and shall not dilate
upon their infamous conduct!" added Rosen-Aer shuddering at the
disgusting and horrible recollection. "My age protected me from a shame
that, however, I was determined to escape by death.... My son never
joined in those orgies, frequently stained with blood and moistened in
tears--the men beat the girls to the point of shedding their blood when
they sought to resist being outraged. In that way we arrived in the
vicinity of the convent of St. Saturnine. We stopped there several
hours. The Jew Mordecai happened to be at the monastery. Learning, no
doubt, that there were slaves to buy in the train of the army, he came
to us accompanied by some men of the band of Berthoald. You were sold,
poor child; you know the disgraceful examination that these dealers in
Gallic flesh submit the slaves to."
"Yes, yes; I had to undergo the shame before the monks of the abbey of
St. Saturnine when they sold me to the Jew," answered Septimine, hiding
her face, purple with shame.
Rosen-Aer proceeded:
"Women and young girls, despite their prayers and resistance, were
stripped of their clothes, profaned and spoiled by the looks of the men
who wanted either to sell or to buy us. My age could not spare me this
general disgrace--" and breaking out into tears and wringing her arms in
despair, the mother of Amael added amidst moans: "Such are the Franks
whose companion of war my son is!"
"It is horrible!"
"The baseness confounds my senses and makes my heart to sicken. At the
age of fifteen my son disappeared from the valley of Charolles, where he
lived free and happy ... before the Saracen invasion. What happened
since? I do not know."
Hearing the name of the valley of Charolles, Bonaik, who had remained
steeped in thought, trembled and listened to the conversation between
Septimine and the mother of Amael, who proceeded to say: "Perhaps the
Jew holds the secret of my son's life."
"That Jew?... How?"
"When, despite the pain it gave me, the Jew came to inspect me, I had to
undergo the fate of the rest. I was stripped of my clothes.... Oh, may
my son never know of my shame! The thought alone would haunt him as a
perpetual remorse through life, if he should live," Rosen-Aer
interjected in a low voice. "While I underwent the fate of my companions
in slavery ... the Jew observed with a start on my left arm these two
words traced in indelible letters: '_Brenn_,' '_Karnak_.'"
"'_Brenn_,' '_Karnak_'!" cried the old goldsmith.
"The custom of doing so was adopted in my family several generations
back, because, alack, in those troubled days of continuous war, families
were exposed to being rent apart and dispersed far and wide. 'Twas an
indelible sign which might help them to recognize one another."
Rosen-Aer had hardly pronounced these words when, drawing near her in
deep emotion, Bonaik cried: "Are you of the family of Joel, the brenn of
the tribe of Karnak?"
"Yes, father!"
"Did you live in Burgundy in the valley of Charolles, once ceded to
Loysik, the brother of Ronan, by King Clotaire I?"
"But, good father, how do you know all that?"
For only answer, the old man rolled up the sleeve of his blouse and
pointed with his finger to two words indelibly traced on his left arm:
"_Brenn_," "_Karnak_."
Rosen-Aer remained stupified, and recovering said: "You also?... You
also.... You, good father.... Are you of the family of Joel?"
"One of my ancestors was Kervan, the uncle of Ronan. That is my
affiliation."
"Does your family live in Brittany, near Karnak?"
"My brother Allan or his children remained at the cradle of our stock."
"And how did you fall into slavery?"
"Our tribe crossed the frontier and came, according to their custom from
time immemorial, to trade arms for the vines of the Franks near the
county of Rennes. I was then fifteen, and accompanied my father on his
journey. A troop of Franks attacked us. I was separated during the fight
from my father, was captured and taken far away into bondage. Sold from
one master to another, accident brought me to this country where I am
now twelve years. Alack! Often have my eyes wandered towards the
frontier of our old Brittany, ever free! My advanced age coupled to the
habit of a profession that I love and that consoles me, have kept me
from thinking of escape. And so we are relatives!... The unhappy young
man yonder, near us, imprisoned in the cavern, is of our blood?... But
how did he become chief of this Frankish troop that the inundation has
just swallowed up?"
"I was telling this poor child that a Jew, a dealer in slaves, having
noticed these two words--'_Brenn_,' '_Karnak_'--on my arm seemed
astonished, and said to me: 'Have you not a son who must be about
twenty-five years old, and who carries like you, those two words traced
on his arm?' But despite the horror that the Jew inspired me with, his
words revived in me the hope of finding my son again. 'Yes,' I answered
him, 'ten years ago my son disappeared from the place where we lived.'
'And you lived in the valley of Charolles?' the Jew asked. 'Do you know
my son?' I cried. But the infamous man refused to answer me, and he
walked away casting a cruel look upon me."
"And you have seen him since?" asked Septimine.
"Never again. The carts resumed their march to this country, where I
arrived with my fellow female slaves. All the women must have perished
this morning ... and without the efforts of this brave girl I would have
perished also."
"The Jew Mordecai," replied the goldsmith reflecting, "that dealer in
the flesh of Gauls, a great friend of the intendant Ricarik, arrived
here a few days ago. He was at the convent of St. Saturnine when the
donation of this abbey was made to your son and his band. He must,
undoubtedly, have run ahead to warn the abbess, and she, accordingly,
made her preparations of defence against the warriors who came to
dispossess her."
"The Jew was in a great hurry to arrive here after his departure from
the convent of St. Saturnine, where he took me from," replied Septimine.
"We were only three slaves and he packed us on his light wagon that was
drawn by two horses. He must have arrived here two or three days ahead
of the troop of the seigneur Berthoald, who must have been delayed on
his march by his large baggage."
"So that the Jew must have notified Meroflede in advance, and must also
have revealed to her the secret of the alleged Frankish chief being of
the Gallic race," observed Bonaik. "Hence the terrible vengeance of the
abbess, who must have had your son cast into that subterranean prison,
expecting to expose him to certain death. The thing now is how to save
him, and to protect ourselves from the vengeance of Meroflede. To remain
here after your son's escape would be to expose these poor apprentices
and Septimine to death."
"Oh, good father! What shall we do?" put in Septimine, joining her
hands. "No one can penetrate into the building under which the seigneur
Berthoald is imprisoned."
"Call him Amael, my child," said Rosen-Aer bitterly. "The name of
Berthoald constantly reminds me of a shame that I would forget."
"To extricate Amael out of the cavern is not an impossible feat," said
the old goldsmith, raising his head. "I have just been thinking it over.
We have a fair chance of success."
"But, good father," asked Rosen-Aer, "what about the iron bars at the
window of this workshop, and those at the air-hole of the cave in which
my son is confined? And then that large and deep moat? What obstacles!"
"These are not the most difficult obstacles to surmount. Suppose night
has set in and Amael is with us, free. What then?"
"Leave the abbey," said Septimine; "escape ... we shall all flee--"
"And how, my child? Do you forget that with nightfall the gate of the
jetty is locked? A watchman is there on guard. But, even if we cleared
the gate, the inundation covers the road. It will take two or three days
for the waters to withdraw. Until then this abbey will remain surrounded
by water like an island."
"Master Bonaik," said one of the young apprentices, "there are the
fishing boats."
"Where are they usually fastened, my boy, at what part of the pond?"
"On the side of the chapel."
"To reach them we would have to cross the interior court of the
cloister, and its door is every evening bolted and barred from within!"
"Alack!" exclaimed Rosen-Aer, "must we renounce all hope of escape?"
"Never give up hope. Let us first think of Amael. Whatever may happen,
once he is out of the cavern, his fate will not be worse. Now, my lads,"
the goldsmith added, addressing the apprentices, "what we are about to
attempt is grave ... your lives and ours are at stake. You have no
choice but to help us or betray us. To betray us would be a base act.
Nevertheless your only interest in this flight is the uncertain hope of
recovering your freedom. Do you prefer to betray us? Say so frankly, and
now.... In that event I shall not undertake anything, and the fate of
the worthy woman and her son is sealed.... If, on the contrary, we
succeed with your help to save Amael and leave this abbey, this is my
plan: I am told it is about four days' march from here to Armorica, the
only territory in all Gaul that is still free. Arrived in Brittany, we
shall take the road to Karnak. There we shall find my brother or his
descendants. My tribe will receive us all as children of its own family.
From goldsmith's apprentices you will become apprentices in field-labor,
unless you should prefer to pursue your trade in some town of Brittany,
only no longer as slaves but as free artisans. Reflect ripely, and
decide. The day is slipping by. Time is precious."
Justin, one of the apprentices, consulted with his companions in a low
voice, and then answered: "Our choice is not doubtful, Master Bonaik. We
shall join you in restoring a son to his mother; hap what hap may, we
shall share your fate."
"Thank you, my generous boys!" said Rosen-Aer, with her eyes full of
tears. "Alack! All I can offer you in exchange for your noble conduct is
the gratitude of a mother!"
"Now," said the goldsmith, who seemed to have regained the agility and
vivacity of his youth, "no more words! To work! Two of you will see to
the sawing of the bars of the window. But do it so that they remain in
position."
"We understand, Father Bonaik," said Justin; "the bars will remain in
position; all that will be needed to throw them down will be a slight
tap of the hammer when you tell us."
"There is no fear of being seen from without. The opposite building has
no windows facing us."
"But how are the bars of the air-hole to be sawed?"
"The prisoner will do that himself with the aid of this file that I
shall throw over to him wrapped in another note directing him what to
do." Saying this the old man sat down upon his work-bench and wrote the
following lines which Septimine, leaning over his shoulders, read aloud
as fast as he wrote:
* * * * *
"Saw off with this file the iron bars of the air-hole, keeping them,
however, in position. When it is dark remove them. Three pulls given to
the string, one end of which you hold, will announce to us that you are
ready. You will then draw towards the air-hole an empty barrel that we
shall have tied to the end of the string."
* * * * *
"What! Good father! You had so much presence of mind as to think of all
these means of escape and prepare for them? How grateful my heart is to
you!"
"We must find means of escape," answered the old man, starting to write;
"the lives of us all are now at stake----"
"And we who are of the trade, we really believed you were preparing
these articles for the cast," said Justin. "This is a fine trick! The
wicked Ricarik will himself have furnished us the barrel and ropes."
Septimine continued to read as Bonaik wrote:
* * * * *
"When the barrel is near enough to the air-hole, you will take firm hold
of a rope that is wound around the barrel and throw yourself into the
water. You will push the barrel, and we will pull it gently toward the
window, which you will then be able to scale easily with our help. We
shall consider the rest."
* * * * *
"Oh, good father," exclaimed Rosen-Aer tenderly, "thanks to you, my son
is saved!"
"Alack! Not so fast, poor woman! I told you before, to take him out of
the cavern is possible; but after that the need will be to get out of
this accursed convent.... Well, we shall try!" and he proceeded to write
these last lines:
* * * * *
"Perhaps you can swim; no imprudence! The best swimmers get drowned.
Reserve your strength so as to be able to help your mother to escape
from this abbey. When you receive this parchment tear it up in little
bits; the same with the first, throw them into the darkest corner of
your prison because it is possible that you may be sent for and taken
from there before evening."
* * * * *
"Oh, God!" exclaimed Rosen-Aer joining her hands in terror. "We never
thought of that. Such a misfortune is possible."
"We must foresee every eventuality," replied the old man closing his
letter with these words:
"Do not despair, and place your hope in Hesus, the God of our fathers!"
"Oh!" murmured Rosen-Aer in distress, "the faith of his fathers, the
teachings of his family, the sufferings of his race, and the hatred for
the stranger--he has forgotten it all!"
"But the sight of his mother will have brought all back again to him,"
answered the old man. Saying this he gave a pull to the string to notify
Amael. The latter answered the signal in the same way. Bonaik then
wrapped the file in the parchment and threw it to the other side of the
moat. The aim was again accurate. The missive, together with the file,
flew through the air-hole and dropped on the floor of the cavern. After
having informed himself on these further instructions from the old man,
Amael showed himself behind the bars. His eager eyes seemed to ask for
his mother.
"He is looking for you," said Septimine to Rosen-Aer; "show yourself to
him; do not deny him this consolation."
The Gallic matron sighed, and leaning upon Septimine took two steps
towards the window. There, with a solemn and resigned mien, she raised a
finger to heaven, as if to say to her son to trust the God of his
fathers. At the sight of his mother and Septimine, the sweet image of
whom had never left him since he first saw her at the convent of St.
Saturnine, Amael joined his hands, and raised them above his head. His
face indicated at once resignation, respect and happiness.
"And now, my boys," the goldsmith said to the young apprentices, "take
your files and start filing off the bars of the window; I and one of you
shall place the crucible on the brasier and melt the metal. Ricarik may
come back. He must be made to believe that we are busy at the cast. The
door is bolted inside. You, Rosen-Aer, remain near the entrance of the
vault so as to escape into it quickly should that accursed intendant
take it into his head to return here, a probable thing. His early
morning round being done, we hardly ever see him again, thanks to God!
But the least imprudence may be fatal."
CHAPTER X.
MISTRESS AND MAN.
Night has returned. Clad in her monastic vestments, the abbess Meroflede
reclines on the lounge in the banquet hall where the evening before
Amael was seated near her. The woman's pale face has a sinister aspect.
Seated opposite her at the table lighted by a wax taper, Ricarik had
been writing under the dictation of the abbess.
"Madam," said Ricarik, "you need only to attach your signature to the
letter for the Bishop of Nantes," and seeing that, absorbed in her own
thoughts, Meroflede did not answer, the intendant repeated in a louder
voice: "Madam, I am waiting for your signature."
Her forehead resting on her hand, her eye fixed, her bosom heaving,
Meroflede said to her intendant in a slow and hollow voice: "What did
Berthoald have to say this morning when you went to see him in his
prison?"
"He remained silent and somber."
The abbess rose brusquely and paced the hall in great agitation.
Overpowering the storm within her breast she said to the intendant:
"Go and bring me Berthoald."
"Madam!... Is it you who issue such an order?"
"I have commanded; obey without delay."
"But the messenger whom you sent for is waiting for this letter to the
Bishop of Nantes. The boat is ready with its oarsmen."
"The Bishop of Nantes will receive my missive a day later. Fetch me
Berthoald!"
"I obey the orders of my noble mistress."
Ricarik walked slowly towards the entrance of the hall and was about to
disappear behind the curtain when, after another equally violent
struggle, Meroflede called to him: "No ... come back!" and letting
herself heavily down upon the lounge, the abbess covered her face with
her hands, uttering prolonged and woeful moans that resembled the
howlings of a wounded she-wolf. The intendant drew near and waited in
silence for the crisis that was convulsing his mistress to spend itself.
A few seconds later the abbess rose again. Her cheeks were inflamed; her
eyes shot fire, her lips curled disdainfully. "I am too weak!" she
cried. "Oh, that man! that man! He shall pay dearly for what he makes me
suffer!" Again Meroflede paced the hall in violent agitation, but
presently she grew calmer, sat down upon the lounge and said to the
intendant: "Read me the letter over again.... I was temporarily insane!"
The intendant read:
* * * * *
"Meroflede, the maid-servant of the maid-servants of the Lord, to her
beloved father in Christ, Arsene, Bishop of the diocese of Nantes,
respectful greeting. Very beloved father, the Lord has shown by a
wonderful miracle what terrible punishment he reserves for the wicked
who wrong him in the person of his poor hand-maids. Charles, the chief
of the Franks, contemner of all divine laws, desolator of the Church,
devastator of faithful women, had the sacrilegious audacity of bestowing
upon a band of his warriors the possession of this abbey, a patrimony of
God. The chief of these adventurers summoned me outrageously to vacate
this monastery, adding that if I did not obey, he would attack us by
main force at daybreak. In order to be nearer to their damnable work,
these accursed men camped over night behind one of the approaches of the
abbey. But the eye of the Lord watched over us. The Almighty has known
how to defend us against the ravishing wolf. During the night the
cataracts of heaven opened with a frightful crash. The waters of the
ponds, miraculously swollen, swallowed up the sacrilegious warriors. Not
one of them escaped the punishment of heaven! It was a terrible prodigy!
Red lights shimmered at the bottom of the waves as if a mouth of hell
had opened to recover its detestable prey. The justice of the Lord being
accomplished, the waters again became calm and limpid, and peacefully
returned to their bed. So that, after the deluge the white dove of peace
and hope winged its flight out of the holy ark. This letter, oh, my
venerable father in Christ, is to notify you of the miracle. This fresh
proof of the omnipotence of the Lord will serve to edify, comfort,
console and delight all pious, and terrify the impious. I close asking
your apostolic benediction."
* * * * *
After Ricarik had finished reading this pious letter he again said to
the abbess: "Madam, may it please you to sign."
Meroflede took the pen and wrote at the bottom, "MEROFLEDE, ABBESS OF
MERIADEK," after which she said with a satanic leer: "The Bishop of
Nantes is a skilful man; he will know how to make the miracle tell; a
century hence people will speak of the prodigy to which the virgins of
the convent of Meriadek owed their deliverance." An instant later she
said distractedly: "The fires of hell are burning in my veins!"
"What, madam, are you still thinking of Berthoald? How strong an
impression must he have made upon you!"
"What I feel for that man is a mixture of contempt, hatred and amorous
frenzy.... I am frightened at my own feelings.... No other man ever
inspired me with such a passion!"
"There is a very simple method of ridding yourself of these agonies....
I proposed the method to you.... I am ready to apply it."
"Take care! No violence upon him! Your life answers to me for his!"
"What are your intentions?"
"I do not know what to decide upon.... One moment I wish him to undergo
a thousand deaths ... the next I am ready to fall at his knees, and ask
pardon.... I am out of my mind ... out of my mind with love!" And the
abbess wrung her hands, bit into the cushions of the lounge, and tore
them with her nails in savage fury. Suddenly rising, her eyes wet with
tears and glistening with passion, she cried: "Give me the key of
Berthoald's prison!"
"It is on this bunch," answered the intendant pointing to several keys
that hung from his belt.
"Give me that one quick!"
"Here it is," said the intendant, detaching a large iron key from the
bunch. Meroflede took the key, contemplated it in silence, and fell into
a revery.
"Madam," said Ricarik, "I shall order the messenger in waiting to depart
with your letter to the Bishop of Nantes."
"Go.... Go.... Take the letter and return!"
"I shall also take a look at the old goldsmith's shop.... He is to cast
the large silver vase to-day!"
"Oh! What do I care!"
"There is a vague suspicion in my mind. I imagined this morning I
noticed a sign of embarrassment on the face of the wily old man. He told
me he was to lock himself in the whole day. I suspect he has a plot with
his apprentices to pilfer a portion of the metal. He also notified me
the casting would not commence until night. I wish to see how it is
done. I shall then come back, madam. Have you any other orders for me,
my abbess?"
Meroflede remained plunged in revery, holding in her hand the key of
Amael's prison. After a few seconds of silence, and without raising her
eyes that remained fixed upon the floor, she said to the intendant:
"When you go out, tell Madeleine to bring me my cloak and a lighted
lamp."
"Your cloak, madam? Do you expect to go out? Do you need it to go to
Berthoald in his prison----?"
Meroflede interrupted the intendant by stamping her foot in a rage, and
pointed him to the door with an imperious gesture, saying:
"Begone, vile slave!"
CHAPTER XI.
THE FLIGHT.
Bonaik, his apprentices, Rosen-Aer, and Septimine, confined since
morning in the workshop, had impatiently waited for night. Everything
was in readiness for the escape of Amael from the cavern when darkness
should set in. The glare of the brasier in the forge and the furnace
alone lighted the workshop.
"You are young and strong," said the old man to his apprentices; "for
want of better weapons, the iron bars that have been removed from the
window may serve you to defend us. Deposit them in a corner. Now pass
the barrel out of the window, and fasten to one of the hoops this
string, the other end of which is in Amael's hands. He is ready. He has
just answered my signal."
Their hearts beating with hope and anxiety, Rosen-Aer and Septimine
stood near the window in a close embrace. The apprentices pushed out the
barrel. The darkness was thick. Not even the whiteness of the building
in whose lower part lay Amael's prison, was distinguishable. Drawn
towards himself by the latter, the barrel soon disappeared in the dark.
In the measure that it went, one of the apprentices paid out the rope
attached to it. The rope was to help pull the barrel back as soon as
Amael had seized it. At that critical moment a profound silence reigned
in the workshop. All seemed to hold their breath. Despite the pitchy
darkness of the night that prevented anything being seen without, the
eyes of all sought to penetrate the obscurity. Finally, after a few
minutes of anxiety, the apprentice, who, leaning out of the window,
held the cord that was to pull the barrel back, said to the old man:
"Master Bonaik, the prisoner is out of the cavern; he is holding the
barrel; I feel the cord tighten."
"Then, you pull, my boy!... Pull gently.... Do not jerk!"
"He is coming," replied the apprentice joyfully; "the prisoner's weight
is upon the barrel."
"Great God!" suddenly cried Rosen-Aer, pointing out of the window. "Look
in the cavern! There is a light!... All is lost!"
Indeed, a strong light, shed by a lamp, suddenly appeared in the
subterranean prison. The semi-circular opening of the air-hole was
luminously marked across the darkness. The reverberation of the light
projected itself upon the water in the moat--and revealed the fugitive,
who, half submerged, held himself up with his two hands on the floating
barrel. Immediately after, Meroflede appeared at the air-hole wrapped in
her scarlet cloak with its hood thrown back, and leaning against the
remaining bars which Amael had not had time to remove. At the sight of
the fugitive, the abbess uttered a scream of rage and cried twice,
"Berthoald! Berthoald!" She then disappeared, taking her lamp with her,
so that again all was left in thickest darkness without. Frightened at
the appearance of the abbess, the apprentice who drew the barrel threw
himself back and dropped the cord. Fortunately the goldsmith seized it
as soon, and amidst the mortal fear of all, drew the barrel close to the
window, saying: "Let us first save Amael."
Thanks to the barrel, which floated almost on a level with the window
sill, the latter was easily scaled by the prisoner. His first movement
upon stepping into the workshop was to throw himself on his mother's
neck. Mother and son for a moment forgot their common danger and were
holding each other in a passionate embrace when a rap was heard at the
door.
"Woe is us!" muttered one of the apprentices. "It is the abbess!"
"Impossible!" said the goldsmith. "To ascend from the prison, pass the
cloister, cross the courtyard, and come as far as our workshop she would
need more than ten minutes."
"Bonaik!" cried from the outside the rough voice of Ricarik, "open the
door instantly."
"Oh! what shall we do! The coal vault is too narrow to conceal Rosen-Aer
and her son," muttered the old man; then raising his voice, he answered:
"Seigneur intendant, we are just at the cast, we cannot leave it----"
"That is the very operation I want to witness," cried back the
intendant. "Open immediately."
"You, Septimine, and your son remain near the window, lean out your
heads; you will otherwise be suffocated," hastily said the old man to
Rosen-Aer, taking a swift resolution. And pushing Amael, his mother and
Septimine to the casement, he whispered to one of the apprentices: "Pour
the full contents of the box of sulphur and bitumen upon the forge
brasier.... We shall fill the workshop with smoke."
The young slave obeyed mechanically. At the moment when Ricarik began
again to knock at the door with redoubled force, a sulphurous and
bituminous smoke began to spread in the workshop, and soon was so
intense that one could hardly see his hand before his eyes. Thus, when
the old man finally proceeded to open the door to the intendant, the
latter, blinded and suffocated by a puff of the pungent and thick vapor,
instead of stepping in, jumped back.
"Walk in, seigneur intendant," said Bonaik, "this is the effect of the
casting after the fashion of the great Eloi.... We could not open to you
sooner out of fear of chilling the liquid metal, which we were pouring
into the mold.... Step forward, seigneur intendant; come and see the
casting."
"Go to the devil!" answered Ricarik, coughing fit to strangle and
stepping further away from the threshold. "I am suffocated ... blinded!"
"It is the effect of the casting, dear seigneur," and watching the bunch
of keys at the belt of the intendant, who was rubbing his smarting
eyelids with both hands, Bonaik seized him by the throat and cried:
"This way, boys! He has the keys of the gates!"
At the call of the old man, the apprentices and Amael rushed forward,
precipitated themselves upon the intendant and smothered his cries by
holding his throat tight, while Bonaik, seizing the bunch of keys, said:
"Drag this fellow into the workshop and throw him out of the window into
the moat. That will settle him quickly, and he will no longer punish and
kill poor slaves!"
The old man's orders were immediately executed. Despite the resistance
of the Frank, the noise of his body was soon heard, dropping into the
water.
"Now," cried the old man, "all come here! Follow me and let us run!"
Hardly had the old man taken a few steps in the alley when he saw the
slave who watched the gate approaching from a distance with a lighted
lantern in his hand. "Remain hidden in the shadow," the goldsmith said
in a low voice to the fugitives, and he walked briskly toward the
gateman, who met him with a look of surprise:
"Helloa, old Bonaik! Is not the intendant in your workshop? I do not
know what the man is thinking about. It is two hours since the boat and
oarsmen are waiting for his messenger.... They are growing impatient and
want to go."
"They will not have long to wait; I am the messenger."
"Are you going to fill the functions of messenger?"
"Do you know this bunch of keys?"
"Surely I know this bunch of keys. It is the one the intendant always
carries at his belt."
"He confided it to me so that I could get out of the abbey yard in case
you were not at your lodge. Let us go quick to the boat. Walk ahead."
Convinced by the sincerity of the old man, whose presence of mind seemed
to grow with the difficulties that arose in his way, the gateman marched
ahead of him. Bonaik, however, slackened his pace, and, calling to one
of the apprentices, in a low voice said: "Justin, you and the others
follow me at a distance; the night is dark, the light of the gateman's
lantern will guide us, but the moment you hear me whistle, all run up to
me." Having attended to that, Bonaik addressed the gateman who had gone
far ahead: "Helloa, Bernard! Do not walk so fast; you forget that at my
age one's legs are not as nimble as yours." Thus, preceded by the
gateman and followed at a distance in the dark by the rest of the
fugitives, Bonaik arrived at the outer court of the monastery. Bernard
stopped and seemed to listen.
"What's the matter?" asked the goldsmith. "Why do you halt?"
"Do you not see the flare of torches lighting the top of the wall of the
inside court? Do you not hear voices?"
"March, man! March! I have other business in hand than to stop to look
at torches, or listen to noises. I must obey our holy abbess and deliver
Ricarik's message as soon as possible. I have not a second to lose.
Quick, let's hurry."
"But something out of the usual order is going on in the monastery!"
"It is for that very reason that the intendant sent me off with so much
haste on this message.... Hurry up! Time presses!"
"Oh, that is something else, old Bonaik," answered Bernard, quickening
his steps. The gateman hurried on, arrived in a minute at the outside
enclosure, and opened the gate. Immediately the old man whistled.
Greatly surprised at this, the gateman asked him: "What are you
whistling for? The door is open. Go out, if you are in such a hurry. But
I hear steps. They seem to be running this way. Who are these people?"
and he raised his lantern in order to obtain a better view. "There are
two women; who may they be?"
Bonaik cut short the gateman's observations with the peremptory order to
the fugitives: "Take the key out of the lock and close it after you.
That will keep the gateman locked in." Hardly had the old man pronounced
these words when Amael, the apprentices, Rosen-Aer and Septimine rushed
through the opening. One of the apprentices pushed Bernard roughly back
into the court, took out the key, pulled the door after him and locked
it on the outside. Bonaik took up the lantern and cried: "Helloa, there!
The boat! Come here for us to embark!"
"Come this way!" answered several voices. "This way! The boat is tied to
the large willow tree."
"Master Bonaik," said one of the apprentices in great trepidation, "we
are pursued. The porter is calling for help. Look at the glimmer of
approaching torches! They seem to be in the garden that we have just
left."
"There is now nothing to fear, my lads, the gate is studded with iron
and locked from without. Before they can have time to break it down, we
shall have embarked," saying which the old man proceeded at a rapid pace
towards the willow tree. Observing on his way a full bag on Justin's
shoulder, Bonaik said to him: "What have you got in that bag?"
"Master Bonaik, while you were talking to the intendant, Gervais and I,
fearing some oversight on your part, took, out of precaution, I, my bag
in which I stowed away the rest of our provisions, and Gervais the wine
pouch which is still half full."
"You are wise lads; we have a long tramp before us after we shall have
disembarked."
A few minutes later and the old man, together with his companions,
arrived at the old willow tree. A boat stood ready. Four slave oarsmen
sat on the benches, with the steersman at the rudder. "At last!" said
the steersman in a peevish tone. "Here we have been waiting over three
hours; we are chilled through, and have more than two hours to row--"
"I am going to give you a piece of good news, my friends," answered the
goldsmith to the boatmen. "I have brought oarsmen with me to relieve
you. You can go back to the monastery. The steersman alone will have to
remain to pilot the boat."
Glad and quickly the slaves jumped out of the boat. The steersman
resigned himself not without a murmur. Bonaik let Rosen-Aer and
Septimine enter first. Amael and the apprentices took hold of the oars,
the steersman the rudder, and the boat swiftly left the bank behind,
while Bonaik, wiping the sweat from his brow, said with a sigh of relief
and joy:
"Oh, my boys, this was a casting day such as I never saw in the workshop
of the great Eloi!"
CHAPTER XII.
MOTHER AND SON.
At noon of the day following the exciting night in which the fugitives
left the abbey, they halted for rest after having been uninterruptedly
on the march from the time that they disembarked at the other shore of
the abbey's pond. Thanks to the precaution of the apprentices, one of
whom had brought provisions and another a pouch of wine, their strength
was speedily restored. The travelers had sat down upon the grass under a
wide-spreading oak whose foliage was yellowed by the late season. At
their feet flowed a stream of limpid water, behind them rose a hill that
they had just traveled over, following the track of an old Roman road
that had fallen into decay. The road continued for a long distance until
the turning of a wooded headland behind which it disappeared. Far away
in the distant horizon stood outlined the dark blue mountain-tops that
form the boundaries and frontier of Brittany. Guided by one of the
apprentices who was familiar with the surroundings of the abbey, the
fugitives had struck the old Roman road. It led to Nantes, at the
boundary line of Armorica, and in the neighborhood of which, seven
centuries earlier, Julius Caesar established several entrenched camps in
order to protect his military colonies. Accustomed through his
profession of war to measure distances, Amael calculated that by
marching until sunset, resting an hour, and then resuming their tramp,
it would be possible to reach Brittany at the end of the next day.
Septimine sat near Rosen-Aer and Amael, and the apprentices, spread out
upon the grass, had just finished their frugal meal. The old goldsmith
having also repaired his forces, pulled out of the pocket of his blouse
a little packet that was carefully wrapped up in a piece of smooth skin.
The young folks followed the old man's movements with curiosity, and to
their great surprise they saw him take from its wrapping the little
abbatial crosier of silver, at which he had for some time been
chiseling. There were also two burins in the package. Noticing the look
of astonishment on the faces of the apprentices, he said to them:
"You seem surprised, my children, to see that I carried this jewel from
the abbey. It is not the value of the metal that tempted me."
"I believe that, Master Bonaik; the little crosier has but little silver
in it. But we still wonder why you brought it along."
"Well, my boys, I love my trade.... I shall have no further
opportunities to exercise it during the remaining days of my life.... I
preserved my two best burins.... I mean to chisel this crosier so nicely
that by working upon it a little every day I shall consume the rest of
my life at it. It will be the masterpiece of my long career."
"You congratulated us upon our foresight, Master Bonaik, because we
thought of the pouch of wine and the provisions. But we must admit that
your foresight exceeds ours."
"Good father, and you, my friends," said Amael, addressing himself to
the goldsmith and his apprentices, "please draw near; I wish you to hear
what I have to say to my mother. I have committed a wrong, I should now
have courage to make a public confession ... and beseech forgiveness."
Rosen-Aer sighed and listened with sad and severe curiosity to her son's
account of his conduct and career since she saw him as a boy. Looking at
her with a surprised face Septimine seemed to beseech the indulgence of
the mother, of this Gallic mother who felt so justly and so painfully
mortified at her son.
"From the moment that all peril to me was over," Amael began, "my mother
has not spoken to me during this long journey, either by day or night;
she has refused the support of my arm, preferring that of this poor
girl, who saved her life. My mother's severity is just, I cannot
complain of it, though it pains me.... May the truthful account of my
faults, the confession of my errors, and my sincere repentance merit her
pardon."
"A mother always forgives," said Septimine timidly, looking at
Rosen-Aer, but the latter answered in a tremulous and grave voice,
without deigning to look at Amael:
"My son's abandonment has torn my heart; a prey to unceasing and ever
renewing anxieties on his behalf, I gave myself up alternately to
despair and to insane hope.... These torments have lasted long years. I
can pardon my son for having caused them; but what is not in my power to
pardon is his criminal alliance with the oppressors of our race, with
those accursed Franks, who enslaved our fathers, outraged our mothers,
and who continue to hold our children in bondage!"
"My crime is great. But I swear to you, mother, that long before I saw
you again remorse gnawed at my heart. It is ten years since I left the
valley of Charolles, where I lived happily with my family. But I yielded
to curiosity, to an overpowering thirst for adventure. I believed that
beyond our own confines I was to see an entirely new world. One evening
I left, but not without shedding many a tear, not without turning more
than once to take a parting look at our valley."
"In my youth," said the old man, "my father often told me how Karadeucq,
one of our ancestors, also left his family to run what then was called
the 'Bagaudy'--to tramp free through the woods and lie in ambush for
our oppressors. May, Rosen-Aer, the remembrance of our ancestor soften
your heart towards your son."
"The Bagauders and the Vagres warred against the Romans and then against
the Franks; they did not ally themselves with our oppressors, and fight
on their side, as my son has done."
"Your reproaches are merited, mother! You will see in the course of my
account that I often made them to myself. Almost immediately upon
quitting the valley I fell into the hands of a band of Franks. They were
on their way back from Auvergne and were traveling north. They made me a
slave. Their chief kept me for a time to oversee and tend his horse, and
to furbish his weapons. I had the instinct of war. The sight of arms or
of a fine horse always fascinated me since childhood. You know it,
mother."
"Yes, your holidays were those on which the colonists of the valley
exercised themselves in arms ... or ran races on horseback."
"Led a slave by that Frankish chief, I never sought to flee. He treated
me kindly. Besides, it was to me a pleasure to polish armors and to ride
on the march. At least, and at last, I was seeing a new country....
Alas, quite new! The fields were ravaged, the harvest was neglected, the
frightful distress of the subjugated populations of the districts that
we traversed contrasted cruelly with the independent and happy life of
the inhabitants of our valley. It was on such occasions that, thinking
of our happy region, of you, and of my father, tears dropped from my
eyes, and my heart felt like breaking. Occasionally, the thought came to
me of running away from the Franks and returning to you. But the fear of
a severe reprimand held me back."
"I would have felt the same way, had I committed the same fault," said
Septimine, who listened to Amael's report with tender interest. "I
never would have dared to return to my family."
"After being more than a year with the Frankish chief, I had become a
good groom, and I could master the most spirited horses. By cleaning the
weapons I had learned to handle them. The Frank died. I was to be sold
with all his other slaves. A Jew named Mordecai, who traveled over Gaul
as a trafficker in slaves, happened to be in Amiens at the time; he
inspected my deceased master's slaves. He bought me and told me in
advance that he was to sell me to a rich Frankish seigneur named
Bodegesil, Duke of the country of Poitiers. The seigneur, said the Jew,
owned the finest horses and the finest armors imaginable. 'If you flee'
said the Jew to me, 'I would lose a fat sum of money, because I bought
you for a large amount, knowing I could dispose of you to the seigneur
Bodegesil at a good profit. If you run away you will lose a chance of
making your fortune. Bodegesil is a generous seigneur. Serve him
faithfully and he will take you to war with him whenever he is called to
take the field with his men, and we have seen in these days of war more
than one manumitted slave become a count.' The Jew's words fired my
ambition, pride intoxicated me, I believed what he said, and did not try
to run away. He himself, in order to confirm my purpose, treated me at
his best; he even promised me to have a letter that I wrote to you reach
you through another Jew who was to go to Burgundy."
"The man did not keep his promise," said Rosen-Aer. "No tidings from you
ever reached me."
"I am not surprised at his breach of promise. That Jew was greedy and
faithless. He took me to Duke Bodegesil. That Frank did indeed raise
superb horses on the immense meadows of his domain, and one of the halls
of his burg, an ancient Roman castle, was fitted out with splendid
armors. But the Jew had lied to me on the duke's character. He was a
violent, cruel man. Still, struck almost immediately after my arrival at
the manner in which I broke in a savage colt that had until then been
the terror of the stable slaves, he treated me with less severity than
he did my Gallic or Frankish companions, because, you know, mother,
that, thanks to the ups and downs of the times, a large number of the
descendants of the conquerors of the Gauls have fallen into poverty, and
from poverty into slavery. Bodegesil was as cruel towards his slaves of
his own German extraction as towards those of the Gallic race. Always on
horseback, always busy furbishing and handling weapons, I now steadily
pursued an idea that was destined to be realized. The renown of Charles,
the steward of the palace, had reached my ears; I had heard some of the
Frankish friends of Bodegesil say that Charles, being compelled to
defend Gaul in the north against the Frisians and in the south against
the Arabs, and finding himself ill-supported by the old lay and clerical
seigneurs, who furnished him little money and only small forces, gave a
friendly reception to adventurers, several of whom by bravely fighting
under his orders, had arrived at unexpected wealth. I was twenty years
old when I learned that Charles was approaching Poitiers for the purpose
of driving back the Arabians, who then threatened to invade the region.
The moment, long dreamed of by my ambition, had arrived. One day I took
the handsomest suit of armor from Bodegesil's racks, I sequestered a
sword, a battle-axe, a lance and a buckler. When night fell I picked out
of the stable the finest and most spirited horse. I put on the armor,
and rode rapidly away from the castle. I wished to join Charles and
decided to conceal my extraction and pass for the son of a Frankish
seigneur so as to interest Charles in my fortunes. About five or six
leagues from the castle, I was attacked early the next morning by
bandits who infested the roads. I defended myself vigorously. I killed
two of the robbers and said to the others: Charles needs brave men. He
leaves a large part of the booty to them. Come with me. It is better to
fight in an army than to attack travelers on the road. The danger is the
same, but the profit is larger! The bandits took my advice and followed
me. Our little troop was increased on the route by other idle but
determined men. We arrived at the camp of Charles on the eve of the
battle of Poitiers. I claimed to be the son of a noble Frank who died
poor and left me his horse and arms as only inheritance. Charles
received me with his habitual roughness. 'There will be a fight
to-morrow,' he answered me, 'if you and your men behave well you will be
pleased with me.' Accident willed it that at that battle against the
Arabs I saved the life of the Frankish chief by helping him to defend
himself against a group of Berbery riders who attacked him furiously. I
was wounded in several places. That day secured the affection of Charles
to me. I shall not tell you, mother, of the many proofs of favor that he
gave me. My great fortune was ever poisoned by the thought ever present
in my mind: 'I have lied; I have denied my race; I have allied myself to
the oppressors of Gaul; I have given them the aid of my sword in
repelling the Saxons and Arabs, who are neither more nor less barbarous
than our accursed Frankish conquerors.' More than once, during the
incessant struggles between the seigneurs of Austrasia and those of
Neustria or Aquitaine--impious wars in which the counts, the dukes, and
the bishops drafted their Gallic colonists as soldiers--I fought against
the men of my own race.... I reddened my sword with their blood. These
are crimes."
"Oh, shame and sorrow," murmured Rosen-Aer, covering her face with her
hands, "to be the mother of such a son!"
"Yes, shame and sorrow ... not for you only, but also for me. Alack! I
yielded to the consequence of a first false step; I fought the men of my
race, out of fear to be taken for a coward by Charles, out of fear to
betray my extraction. Pride intoxicated me when I saw myself admiringly
surrounded by the proudest of our conquerors--I, the son of that
conquered and subjugated people. But after such moments of vertigo were
over, I often envied the fate of the most miserable slave. They at least
were entitled to the respect that undeserved misfortune inspires. Vainly
did I look for death in battle. I was condemned to live. Only in the
intoxication of battle, in perilous undertakings did I find temporary
relief from the remorse that haunted me. Oh, how often did I not think
with sorrow of our valley of Charolles, where my family lived! When I
afterward learned of the ravages of the region by the Arabs, of the
desperate resistance that its inhabitants had offered ... my relatives,
my friends; when I thought that my sword might have defended you, or at
least avenged you, mother, from that time forward remorse embittered my
life. I never since had one instant of happiness."
"Your father fought up to his last breath for freedom and for the
freedom of his kin. I saw him fall at my feet riddled with wounds! Where
were you when your father was defending his hearth, his freedom and his
family?... Near the Frankish chief, fawning for his favor! Perchance
even fighting your own brothers!"
Amael covered his face with his hands and answered only with a smothered
sob.
"Oh, for pity's sake, do not overwhelm him!" said Septimine to
Rosen-Aer. "See how wretched he feels ... how contrite he is!"
"Rosen-Aer," added the old man, "remember that yesterday your son was
still the favorite of the sovereign chief of Gaul, and that to-day he
renounces the favors that intoxicated him. He is no less wretched than
we, and has no other wish than to live a poor and hard but free life in
the old Armorica that is the cradle of our family."
"By Hesus!" cried Rosen-Aer. "Did my son voluntarily renounce those
goods, those lands, those favors, the accursed gifts of Charles? Did you
not extract him from a prison, where, without you, he would have
perished? Oh! The gods are just. My son owed his fortune to an impious
ambition ... and the fortune came near being fatal to him. Glorified and
enriched by the Franks, he has been shamefully punished and stripped of
all by a woman of their race."
"Oh!" cried Septimine, breaking down in tears, "do you believe that
Amael, even if in full possession, would not have renounced all to
follow you, his mother?"
"The man who falls away from his duty to his country and his race can
also fall away from his duty to his mother! I am justified to question
the goodness of my son's heart!"
"Master Bonaik," suddenly cried one of the apprentices in an accent of
fear, "look down below there, at the turning of the road ... there are
soldiers. They are approaching rapidly. They will be here within short!"
At these words of the lad the fugitives jumped to their feet. Amael
himself, forgetting for a moment the sorrow into which his mother's just
severity plunged him, dried his face that was moist with tears and took
a few steps forward to reconnoiter.
"Great God!" cried Septimine. "They may be in pursuit of Amael.... Good
father Bonaik, let us hide in this thicket----"
"My child, that would be to expose ourselves to being pursued. The
riders have seen us.... Our flight would awaken their suspicion.
Besides, they come from the side opposite to Nantes; they cannot have
been sent in our pursuit."
"Master Bonaik," said one of the apprentices, "three of the riders are
hastening their horses' steps, and motion us with their hands to come to
them."
"Perhaps a new danger now threatens us!" said Septimine, drawing close
to Rosen-Aer, who had alone remained seated, and seemed indifferent to
what went on around her. "Alack, what is to become of us!"
"Oh, poor child!" said Rosen-Aer, "I care little for life at this
moment!... And yet the mere hope of some day finding again my son,
served to sustain my sad life!"
"But you have found again that son whose loss you so tenderly regretted.
He is here, near you!"
"No!" answered the Gallic mother with sorrow, "no, that is not my son!"
Feeling not a little uneasy, Amael had walked toward the three Frankish
horsemen, who rode at the head of a more numerous troop. One of them
reined in his steed, and said to Rosen-Aer's son: "Does this road lead
to Nantes?"
"Yes; it is the nearest road."
"Does it also lead to the abbey of Meriadek?"
"Yes," answered Amael, as much surprised at the meeting as at the
questions.
"Arnulf," said the rider to one of his companions, "ride back and tell
Count Bertchram that we are on the right road; while waiting for your
return to us, I shall let my horse drink at this stream."
The rider departed, and while his two companions were allowing their
horses to take a few throatfuls of water, Amael, who had not been able
to overcome the growing curiosity that seized him at hearing the name of
Count Bertchram, asked the two riders: "What brings Count Bertchram to
this country?"
"He comes as a messenger of Charles, the chief of the Franks. Tell us,
young man, whether we still have a long way to ride before we reach the
abbey of Meriadek."
"You could not reach the place until late to-night."
"Is that abbey as rich as they claim?"
"It is rich.... But why do you ask?"
"Why?" said the soldier with a merry smile, "because Bertchram and we
are to take possession of the abbey, which the good Charles has bestowed
upon us."
"But I heard it said that Charles had bestowed the monastery and all its
dependencies upon one Berthoald."
During this conversation the other riders had joined their vanguard,
followed by several carts drawn by mules and a few horses led by the
bridle. The carts were loaded with baggage. Bertchram rode at the head
of the main body. He was an elderly warrior of rude and stupid
physiognomy. Amael took a few steps toward the count. The latter
suddenly stopped his horse, dropped the reins, and rubbed his eyes as if
he could not believe the evidence of their sense. He contemplated the
son of Rosen-Aer for a few seconds in utter amazement, and then cried:
"Berthoald! Count Berthoald!"
"Yes, it is I.... Good-day to you, Bertchram!"
Bertchram alighted from his horse and ran toward the young man to
contemplate him closer. "It is he ... and no mistake! And what are you
doing here, valiant count, in the company of these beggars?"
"Speak not so loud. I am on a mission from Charles."
"Bareheaded in that way? Without arms, your clothes soiled with mud and
almost in rags?"
"It is a disguise that I have assumed."
"You are a wily customer! Whenever the good Charles had some delicate
matter in hand, it was always you he charged with it, because you are
more subtle than any of us others. Charles always said to me:
'Bertchram, you would be a terrible man if your brain were as powerful
as your fist!' You probably do not know that I am the bearer of a
message to you?"
"What is the message about?"
"Simply this, that I come to replace you as abbot at the abbey of
Meriadek."
"Charles is master, he can give and take back again."
"Do not look upon the substitution as a disgrace, Berthoald! Far from
it! Charles raises you to the rank of duke, and he reserves for you the
command of his vanguard in the war he is about to undertake against the
Frisians. 'Upon the word of the Hammerer,' he said to us, 'I was a fool
in confining to an abbey one of my youngest captains, and at this season
when wars break out so unexpectedly; it is now, when I have not
Berthoald at my side, that I feel how much I need him. The post I gave
him is good for an aged soldier; it fits you better than him, old
Bertchram, go and take the place of Berthoald and his men; you shall
give him this letter from me, and as a pledge of my constant friendship,
take to him two of my best horses; besides that, take to him from me a
magnificent armor of Bordeaux. He loves fine armor and fine horses. It
will please him.' And there they are with me," added Bertchram. "The
horses are led by the bridle. They are beautiful, one is as black as a
raven, the other white as a swan. As to the armor, it is carefully
packed up in my baggage, I cannot show it to you now. It is a
masterpiece of the most famous armorer of Bordeaux. It is enriched with
gold and silver ornaments. The casque is a marvel."
"I am truly touched with this fresh proof of Charles' affection,"
answered Amael, "I shall report to him as soon as I have fulfilled his
mission."
"But he wishes you to join him immediately, as you will see by the
letter that I have carefully put away in my cuirass," said the warrior
hunting for the parchment.
"Charles will not regret to see me arrive a day or two later if I return
to him after successfully attending to the mission that he confided to
me. I shall find the horses and the armor at the abbey, where I shall
see you again, and now I shall move on with my men. But you must have
made a wide circuit, to judge by the road you are on!"
"Charles gave me the command of a large troop that he has cantonned on
the frontiers of Brittany."
"Does he expect to attack Armorica?"
"I do not know. I left the troops entrenched in two old Roman camps, one
to the right, the other to the left of a long road that winds up there."
"Is the troop large?"
"About two thousand men distributed in two camps."
"Charles can undertake nothing against Brittany with so small a number
of soldiers."
"All he expects to do is to reconnoiter the frontier of the country
until after the war with the Frisians is ended, when he will be able to
give his attention in person to the accursed Armorica. This province has
resisted our arms for more than three centuries, since the glorious
Clovis conquered Gaul. Indeed it is a shame to us!"
"Yes, the independence of Armorica is a shame to the arms of the
Franks."
"Here is Charles' letter," said Bertchram pulling from under his cuirass
a scroll of parchment that he delivered to Amael, and ordering the two
horses which his slaves had unsaddled to be brought forward, he added:
"Look at them! Are there any nobler or more spirited animals in the
world?"
"No," answered Amael unable to avoid admiring the two superb stallions,
that were with difficulty held by the slaves. The horses reared and
caracoled, daintily striking the ground with their hoofs; one was ebony
black, with a bluish tinge; the other, white as snow, shone like silver.
Their nostrils were inflated, their eyes sparkled under their long
manes, and they lashed the air with their flowing tails.
"These are noble horses!" said Amael smothering a sigh; and motioning to
the slaves to re-cover the animals with their housings, he muttered:
"Adieu, fine battle horses! Adieu magnificent armors!" Turning to the
Frank, Amael said: "I wish you a happy journey.... I shall see you again
at the abbey of Meriadek where I hope you may enjoy yourself."
"Adieu, Berthoald; but ... a thought strikes me. Should your men refuse
to admit me during your absence, what shall I do?"
"Keep Charles' letter; it will notify my men of Charles' pleasure. You
may break the seal before them."
"I shall do it that way. Adieu, I shall take your place at the abbey,
where I expect to have a dull time until your return. Adieu, and come
back soon."
"One more question.... Who are the chiefs of the troops that are
cantonned near the frontiers of Brittany?"
"Two friends of yours, Hermann and Gondulf. They asked me to remember
them to you."
"Now, good-bye."
"Good-bye, Berthoald."
The chief of the Frankish troops, having resumed his march, followed by
his troops and train, soon disappeared before the eyes of the fugitives.
Amael returned to the tree under which his traveling companions were
assembled. Hardly had he taken a few steps towards them when his mother
opened her arms to him: "Come, my son; I have heard every word. Now, at
least, your renunciation of a brilliant career, that might have dazzled
you, is voluntary!"
"You were near me, mother, and yonder I saw the frontiers of Brittany.
Could I be dazzled by any favors from Charles against my mother and my
country?"
"Oh!" cried the matron tenderly pressing Amael to her breast. "This day
makes me forget all that I have suffered!"
"And this, mother, is the first happy day that I have had in years--a
day of unalloyed happiness."
"You see I was right, your son's heart remained true," said Septimine to
Rosen-Aer with touching kindness.
"Septimine!" replied Amael with a look of tenderness, "would you doubt
my heart in the future?"
"No, Amael," she answered naively, looking at the young man with an
expression of timidity and surprise. "I shall never doubt you."
"Mother, this sweet and brave girl saved your life; she is now a
fugitive, forever separated from her family. If she should consent to
give me her hand, would you accept her as a daughter?"
"Oh, with joy! With thankfulness!" said Rosen-Aer. "But would you
consent to the union, Septimine?"
Blushing with surprise, with happiness and confusion, the girl threw
herself on the neck of Amael's mother, and holding her face on the
matron's breast, murmured:
"I loved him since the day he showed himself so generous toward me at
the convent of St. Saturnine. Did he not there protect me?"
"Oh, Rosen-Aer!" now exclaimed the old man who had stood near wrapped in
thought, "the gods have blessed my old age, seeing they reserved such a
day for me." And after a few seconds of silent emotion, shared in by the
young apprentices, the old man proceeded, saying: "My friends, if you
will take my advice, let us resume our march. We shall have to walk
briskly in order to arrive to-morrow evening at the frontier of
Armorica."
"Mother," said Amael, "lean upon me; you will not now refuse the support
of my arm?"
"No, oh, no! my child!" answered the matron with tenderness, and brimful
of happiness, taking her son's arm.
"And you, good father," said Septimine to the old goldsmith, "you lean
on me."
The fugitives resumed their march. After having traveled without
accident until night and the following day, they arrived at moon-rise
not far from the first spurs of the wild and high mountains that serve
both as boundary and as ramparts to Armorica. The sight of his native
soil awoke in Bonaik the recollections of his boyhood days as if by
enchantment. Having before now crossed the frontiers with his father in
order to attend the Breton fairs, he remembered that four druid stones
of colossal size rose not far from a path that was cut between the
rocks, and that was so closely hemmed in, that it allowed only one
person to march abreast. The fugitives entered the path one after the
other and began climbing the steep ascent. Amael marched first.
Presently they arrived at a little clearing or platform, surrounded by
precipices and beetled over by huge rocks.
Suddenly the fugitives heard from a far distance above their heads a
sonorous voice, that, quivering through the surrounding and profound
silence of the night, melancholically chanted these words:
"She was young,
She was fair,
And holy was she;
Hena her name,
Hena, the Maid of the Island of Sen."
Rosen-Aer, Bonaik and Amael, the three descendants of Joel, remained for
a moment transfixed with exaltation, and yielding to an irresistible
impulse all three fell upon their knees. Tears ran down their cheeks.
Septimine and the apprentices, sharing the emotion which they were
unable to account for, also fell upon their knees, and all listened,
while the sonorous voice which seemed to descend from the skies,
concluded the Gallic chant now eight centuries old.
"Oh, Hesus!" finally exclaimed Rosen-Aer, raising her tear-stained face
toward the starry vault where the sacred luminary of Gaul was shining in
its splendor, "Oh, Hesus! I see a divine omen in this chant, so dear to
the descendants of Joel.... Blessed be the chant! It salutes us at this
solemn hour when, at last setting foot on this free soil, we return to
the ancient cradle of our family!"
Guided by the old goldsmith, Amael, his mother, Septimine and the
apprentices, arrived in the vicinity of the sacred stones of Karnak, and
were tenderly received by the sons of Bonaik's brother. Amael became a
field laborer, the young apprentices followed his example and settled in
the tribe. At the death of Bonaik, the abbatial crosier, which he had
finished at his leisure, was joined to the relics of the family of Joel
accompanied by this narrative which I, Amael, the son of Guen-Ael, who
was the son of Wanoch, who was the son of Alan a grandson of Ronan the
Vagre through Ronan's son Gregory, wrote shortly after our return to
Brittany.
THE END.
End of the Project Gutenberg EBook of The Abbatial Crosier, by Eugene Sue
***
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BC Beat
Chase Carey: Does Not Expect the White House To Be 'vindictive'
marisa guthrie
Fox News has made much hay of the White House's strenuous attempts to de-legitimize the news channel. Greta Van Susteren has called it "silly" and "patently absurd." Hannity is running promos boasting: "Not approved by the White House."
On Wednesday, Chase Carey, deputy chairman, president and COO of News Corp., weighed in.
"It's probably been PR and marketing we couldn't have bought," he said.
Carey was speaking at Broadcasting & Cable's OnScreen Media Summit at the Edison Ballroom.
Asked if he is concerned that the White House would let its campaign against Fox News bleed into FCC- or media-related policy issues, Carey said: "I don't think they'll conduct themselves in a vindictive way. They are running a government for the people."
"I think Fox News is quite comfortable where it is," he added. "We try to present an honest presentation of the issues from both sides. It has clearly struck a raw nerve. We're not trying to pick a fight. We' trying to present an honest and in [Fox News chairman] Roger [Ailes'] words, a fair and balanced perspective of the issues. We're quite comfortable with where we are."
Cribs: White House Edition
White House Spokesperson Dunn Steps Down
Fox News' Hume on McCain's Chances: "Very Difficult If Not Impossible"
Salahis' 15 Minutes May Be Just Beginning
Apology Expected
Jonathan Wald To CNN?
Law & Order White House
CBS Sources: Cronkite Not in Dire Straits
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People: Black Ridge Acquisition Corp (BRAC.OQ)
BRAC.OQ on NASDAQ Stock Exchange Capital Market
$0.09 (+0.88%)
Eisele, Michael
Mr. Michael Eisele is Chief Operating Officer of the company since May 2017. Mr. Eisele has been the chief operating officer of our sponsor since August 2013, and prior to that had served as our sponsor's vice president of land from August 2012 to August 2013, overseeing its acreage portfolio and managing acquisitions and divestitures. Prior to joining our sponsor, Mr. Eisele was the co-owner and landman of High West Resources, Ltd. from 2011 to July 2012, the owner of Eisele Resources LLC from 2009 to 2012, and a self-employed landman from 2007 to 2009. Mr. Eisele is a graduate of Luther College (B.A.).
Kenneth DeCubellis
James Moe
Bradley Berman
Lyle Berman
Joseph Lahti
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\section{Introduction}
Stability of two-dimensional (2D) plasma crystals is a fundamental problem of complex (dusty) plasmas. Such crystals --
which are monolayers of hexagonally ordered monodisperse microparticles -- can be (routinely) created in a rf plasma
\cite{Fortov20051,RevModPhys.81.1353}: Particles get negatively charged in a plasma and therefore the electric force exerted
on them in the sheath above a horizontal electrode can compensate for gravity, thus providing a stable levitation. There are
several mechanisms operating in complex plasmas that can result in the melting of 2D crystals. These mechanisms can
generally be divided into two categories -- {\it generic} and {\it plasma-specific}.
Generic mechanisms of melting are those operating in any (classical) system with a given pair interaction between particles,
provided the interaction can be described by a Hamiltonian. The melting in 2D systems can either be a two-step process
(which involves consecutive unbinding of weakly interacting dislocation and disclination pairs, respectively, with the
intermediate hexatic phase) \cite{PhysRevLett.41.121,0022-3719-6-7-010,PhysRevB.19.2457,PhysRevB.19.1855} or a one-step
process (where the hexatic phase is preempted by the formation of dislocation chains) \cite{PhysRevB.28.178}. These generic
melting mechanisms can operate in very different 2D systems including complex plasmas
\cite{PhysRevLett.58.1200,nosenko:nzikm,PhysRevE.53.R2049,sheridan:083705,sheridan:103702,PhysRevLett.85.3656}.
Plasma-specific melting mechanisms can only operate in complex plasmas. Such mechanisms are associated with the energy
exchange between microparticles and ambient plasma and can be considered as a result of the system openness. For instance,
2D plasma crystals can be strongly perturbed by single particles moving above or below the monolayer
\cite{PhysRevE.62.1238,Nunomura05}, or they can melt due to fluctuations of particle charges
\cite{PhysRevLett.83.1970,Morfill99,vaulina:vknp}.
The most universal among the plasma-specific mechanisms is that associated with the {\it wake-mediated} interaction between
microparticles: In the presence of strong plasma flow the screening cloud around each charged particle becomes highly
asymmetric \cite{ishihara:357,ishihara:69,vladimirov:3867,vladimirov:vs}. These clouds are usually referred to as ``plasma
wakes'' \cite{Lampe00,Miloch08,PhysRevE.64.046406,kompaneets:052108,Kompaneets08} and play the role of a ``third body'' in
the interparticle interaction, making it nonreciprocal \cite{PhysRevLett.83.3194}. Under certain conditions, this makes the
system non-Hamiltonian and provides effective conversion of the energy of flowing ions into the kinetic energy of
microparticles \cite{Fortov20051,RevModPhys.81.1353,PhysRevE.54.R46,Joyce02}.
The wake-induced mechanism of melting of crystalline monolayers was discovered theoretically a decade ago by Ivlev and
Morfill \cite{PhysRevE.63.016409}. Based on a simple model of a particle chain, it was shown that the longitudinal in-plane
and transverse out-of-plane dust-lattice (DL) wave modes are no longer independent -- they are coupled due to the
wake-mediated interactions. When the modes intersect they become modified by the coupling and form a {\it hybrid} mode in a
narrow vicinity of the crossing. This can trigger the {\it mode-coupling instability} which causes the melting. This melting
mechanism had received strong confirmation later on, when the instability threshold predicted by the theory was compared
\cite{PhysRevE.68.026405} with the experimental observations by U. Konopka and numerical simulations by G. Joyce. However,
the direct comparison of theory and experiment became possible only recently, after an experimental method of measuring the
out-of-plane mode was developed \cite{couedel:215001} and therefore the essential fingerprint of the mode-coupling
instability -- the hybrid mode -- became observable. In recent experiment by Cou\"edel {\it et al.}
\cite{PhysRevLett.104.195001} an implementation of this method unambiguously demonstrated that the melting indeed occurs due
to the resonance coupling between the longitudinal in-plane and transverse out-of-plane modes. The variation of the wave
modes with the experimental conditions, including the emergence of the hybrid branch, revealed exceptionally good agreement
with the theory of mode-coupling instability generalized for 2D case by Zhdanov {\it et al.} \cite{zhdanov:zim}.
The theory of mode-coupling instability \cite{PhysRevE.68.026405,PhysRevE.63.016409,zhdanov:zim} predicts a number of
distinct fingerprints to be observed upon the instability onset: Along with the emergence of hybrid mode mentioned above,
these are a critical angular dependence -- the hybrid mode first appears only for wave vectors oriented along one of the
principal lattice axes, a mixed polarization -- the two DL modes that form the hybrid mode are no longer purely longitudinal
and transverse close to the merging point, and distinct thresholds -- the instability sets in only when (i) the particle
number density in the monolayer is high enough or/and vertical confinement eigenfrequency is low enough (so that the two DL
modes can cross and form the hybrid mode) and (ii) the gas pressure is low enough (so that the growth rate of the hybrid
mode exceeds the damping rate).
All these fingerprints have been mentioned in our previous theoretical publications
\cite{PhysRevE.63.016409,PhysRevE.68.026405,zhdanov:zim}, some of them were also illustrated in the followup experimental
paper \cite{PhysRevLett.104.195001}. However, their discussion was apparently too concise to address all these important
properties in necessary detail. The need for in-depth discussion of the wake-mediated mode coupling became evident now, when
new publications have appeared where some essential properties of the instability were misinterpreted (see, e.g., recent
experimental paper \cite{PhysRevLett.105.085004} and the subsequent Erratum \cite{PhysRevLett.105.269901} by Liu {\it et
al.}). Therefore, in this paper we summarize the key features of the mode coupling and provide a detailed discussion,
analyze the critical dependence on experimental parameters, and highlight the outstanding issues.
\section{Summary of Mode-Coupling Theory}\label{theory}
In 2D plasma crystals, two in-plane wave modes can be sustained (here we naturally leave aside polydisperse mixtures). Both
modes have an acoustic dispersion, one of them is longitudinal and the other is transverse. Since the strength of the
vertical confinement in such systems is finite, there is a third fundamental wave mode which has an optical dispersion and
is associated with the out-of-plane oscillations
\cite{PhysRevLett.71.2753,PhysRevE.63.016409,PhysRevE.68.046403,samsonov:026410,PhysRevE.56.R74,vladimirov:030703,zhdanov:zim}.
Theory predicts that all three modes depend critically on the parameters of the plasma wakes. Yet the role of the wakes is
not only the modification of the modes themselves. What is far more important is that the modes are {\it coupled} to each
other due to the wake-mediated interactions between particles. It is worth noting that this {\it coupling is linear} and
therefore does not depend on the wave amplitude. Below we identify the conditions when the wake-mediated coupling becomes
crucial for waves in 2D crystals.
\subsection{DL modes for nonreciprocal interactions}
In general, linear dispersion relations $\omega({\bf k})$ are determined by eigenvalues (eigenmodes) of a dynamical matrix
$\textsf{D}$. The latter is derived by considering small perturbations of individual particles (with respect to a stable
configuration, e.g., a hexagonal monolayer for 2D crystals) of the form $\propto\exp(-i\omega t+i{\bf k}\cdot{\bf r})$.
Elements of $\textsf{D}$ are determined by properties of interparticle interactions and are functions of ${\bf k}$. If the
interactions are reciprocal then $\textsf{D}$ is Hermitian, and therefore the eigenvalues are always real (i.e., the modes
are stable) and the eigenvectors are orthogonal. The situation changes if the interactions are nonreciprocal -- the
eigenvalues in this case can become complex.
\begin{figure}
\includegraphics[width=8.3cm,clip=]{fig1.eps}
\caption{\label{fig1} (a) Elementary hexagonal lattice cell with the frame of reference, the lattice constant is $\Delta$.
(b) The reciprocal lattice in ${\bf k}$-space, the basis vectors of the lattice are ${\bf b}_{1,2}=2\pi\Delta^{-1} (1,\pm
\frac1{\sqrt{3}})$. Due to the lattice symmetry, it is sufficient to consider the wave vectors ${\bf k}$ at $0^{\circ}\leq
\theta\leq30^{\circ}$ and from within the first Brillouin zone (gray region enclosed by dashed lines), so that $|{\bf k}|
\Delta\leq\frac43\pi$ for $\theta=0^{\circ}$ and $|{\bf k}|\Delta\leq\frac2{\sqrt{3}}\pi$ for $\theta=30^{\circ}$.}
\end{figure}
Before specifying a particular functional form of interparticle interactions in 2D crystals, let us generally assume the
non-reciprocity and discuss common properties of the DL waves in this case. The dynamical matrix has the following form:
\begin{equation}\label{matrix}
\textsf{D}=
\left(
\begin{array}{ccc}
\alpha_{\rm h}-\beta & 2\gamma & i\sigma_y \\
2\gamma & \alpha_{\rm h}+\beta & i\sigma_x \\
i\sigma_y & i\sigma_x & \Omega_{\rm conf}^2-2\alpha_{\rm v} \\
\end{array}
\right).
\end{equation}
The elements $\alpha_{\rm h}({\bf k})$, $\beta({\bf k})$, and $\gamma({\bf k})$ determine the dispersion of two in-plane
(horizontal) modes and $\alpha_{\rm v}({\bf k})$ characterizes the out-of-plane (vertical) mode. The elements
$\sigma_{x,y}({\bf k})$ emerge due to non-reciprocity and make $\textsf{D}$ non-Hermitian. The matrix is calculated for the
reference frame shown in Fig.~\ref{fig1}(a) assuming that vertically the particles are confined in a (parabolic) potential
well characterized by the eigenfrequency $\Omega_{\rm conf}=2\pi f_{\rm conf}$. To derive the dispersion relations
$\omega({\bf k})$, we add a friction force $m\nu\dot{\bf r}$ in equations of motion (with $\nu$ being the damping rate)
which yields:
\begin{equation}\label{dispersion}
\det[\textsf{D} -\omega(\omega+i\nu)\textsf{I}]=0,
\end{equation}
where $\textsf{I}$ is the unit matrix. Thus, $\omega(\omega+i\nu)\equiv\Omega^2$ are the eigenvalues of $\textsf{D}$, i.e.,
the DL wave modes.
For reciprocal interactions $\sigma_{x,y}=0$ and then Eqs (\ref{matrix}) and (\ref{dispersion}) yield
\begin{equation}\label{dispersion1}
(\Omega^2-\Omega_{{\rm h}\|}^2)(\Omega^2-\Omega_{{\rm h}\perp}^2)(\Omega^2-\Omega_{\rm v}^2)=0.
\end{equation}
There are three independent and real DL modes: Two {\it acoustic} in-plane modes $\Omega^2({\bf k})=\alpha_{\rm
h}\pm\sqrt{\beta^2+4\gamma^2}\equiv\Omega_{{\rm h}\|,\perp}^2({\bf k})$ (where $\|$ and $\perp$ indicate the longitudinal
and transverse polarizations and correspond to the plus and minus signs, respectively) and an {\it optical} out-of-plane
mode $\Omega^2({\bf k})=\Omega_{\rm conf}^2-2\alpha_{\rm v}\equiv\Omega_{\rm v}^2({\bf k})$. When solved for $\omega({\bf
k})$, each mode yields a couple of conjugate branches.
When interactions are nonreciprocal the modes are modified -- they are described by Eq. (\ref{dispersion1}) with nonzero
right-hand side (r.h.s.) which is proportional to $\sigma_x^2+\sigma_y^2$. The DL modes become coupled with each other and
complex \footnote{Matrix $\textsf{D}$ is symmetric and hence can be reduced to the diagonal form also for
$\sigma_{x,y}\ne0$, but with complex eigenvalues.}.
Now let us specify interparticle interactions. For the direct interaction between charged grains we naturally adopt the
Yukawa potential which is characterized by (negative) particle charge $Q$ and the screening length $\lambda$. For the wake
we employ the commonly used simple model \cite{PhysRevE.54.R46} of a point-like (positive) charge $q$ located at the
distance $\delta$ downstream each particle and also interacting with the neighboring particles via the Yukawa potential. The
elements of the dynamical matrix (\ref{matrix}) for such interactions are calculated in Appendix~\ref{appendix1},
Eqs~(\ref{elements1}) and (\ref{elements2}). For brevity, theoretical results in this paper are written in the dimensionless
form -- the frequency is normalized by the DL frequency scale,
\begin{displaymath}
\Omega_{\rm DL}=\sqrt{\frac{Q^2}{m\lambda^3}},
\end{displaymath}
and the wave vector is normalized by the lattice constant $\Delta$: $\Omega/\Omega_{\rm DL}\to\Omega$ and ${\bf
k}\Delta\to{\bf k}$.
\subsection{Types of mode coupling}\label{types}
After the normalization, the DL modes depend on three dimensionless parameters (along with the normalized wave vector): The
screening parameter $\kappa=\Delta/\lambda$ as well as the relative wake charge $\tilde q=|q/Q|$ and distance
$\tilde\delta=\delta/\Delta$. In experiments, $\kappa$ is typically about unity whereas both wake parameters are usually
small. Elements $\sigma_{x,y}$ [Eq.~(\ref{elements2})] are proportional to the product $\tilde q\tilde\delta$ and hence the
coupling between the DL modes is very small [$\propto(\tilde q\tilde\delta)^2$]. It becomes important only if different DL
modes intersect (or they are very close to each other); otherwise the coupling can be neglected and then the modes can be
treated independently, as described by Eq. (\ref{dispersion1}). Let us elaborate on this point.
\begin{figure}
\includegraphics[width=0.99\columnwidth,clip=]{fig2.eps}
\caption{\label{fig2} Modification of coupled modes [Eq. (\ref{dispersion2})] in the vicinity of their crossing. The sketch
depicts the modes in the $(\Omega,|{\bf k}|)$-plane (a) in the absence of coupling, (b) with negative coupling ($\epsilon<0$),
and (c) with positive coupling ($\epsilon>0$). Negative coupling results in the formation of a hybrid mode which can be unstable
(see text); positive coupling causes the mode reconnection, while the modes remain stable and form a ``forbidden band''.}
\end{figure}
Behavior of two coupled modes, $\Omega_{1,2}({\bf k})$, in a close proximity of their intersection can generally be
described by the following equation:
\begin{equation}\label{dispersion2}
\left[\Omega-\Omega_0-{\bf U}_1\cdot({\bf k}-{\bf k}_0)\right]\left[\Omega-\Omega_0-{\bf U}_2\cdot({\bf k}-{\bf k}_0)
\right]=\epsilon.
\end{equation}
Here ${\bf U}_{1,2}=\partial\Omega_{1,2}/\partial{\bf k}$ are the group velocities of the two modes calculated at a point
${\bf k}_0$ of the intersection line $\Omega_0({\bf k})$ (the latter is determined by the shape of the crossing modes) and
$\epsilon$ characterizes the coupling. From Eq.~(\ref{dispersion2}) one readily concludes that the effect of the coupling
critically depends on the sign of $\epsilon$. This is illustrated in Fig.~\ref{fig2}: When $\epsilon<0$ the crossing modes
merge and form a complex hybrid mode in a narrow range $|{\bf k}-{\bf k}_0|\propto\sqrt{\epsilon}$, with Re~$\Omega_{\rm
hyb}\simeq \Omega_0+\frac12({\bf U}_1+{\bf U}_2)\cdot({\bf k}-{\bf k}_0)$ and Im~$\Omega_{\rm hyb}\sim\pm\sqrt{\epsilon}$.
Thus, one of the branches of the hybrid mode has a positive imaginary part and hence can be unstable. When $\epsilon>0$ the
coupling is accompanied by reconnection (formation of a ``forbidden band'') and the modes remain stable (real). Furthermore,
the sign of the product ${\bf U}_1\cdot{\bf U}_2$ in the unstable case determines the type of the instability, which is
absolute for ${\bf U}_1\cdot{\bf U}_2<0$ (the case illustrated in Fig.~\ref{fig2}) and convective otherwise.
Now we can consider the DL modes described by Eqs (\ref{matrix}) and (\ref{dispersion}), with the dispersion and coupling
elements from Eqs (\ref{elements1}) and (\ref{elements2}). The detailed analysis shows that the intersection of the
transverse in-plane mode $\Omega_{{\rm h}\perp}({\bf k})$ with the longitudinal in-plane, $\Omega_{{\rm h}\|}({\bf k})$, as
well as with the out-of-plane mode $\Omega_{\rm v}({\bf k})$ is characterized by positive coupling and therefore is
accompanied by reconnection illustrated in Fig.~\ref{fig2}c, so that the modes remain stable. Moreover, the coupling for
these two pairs of modes exactly disappears (Fig.~\ref{fig2}a) if ${\bf k}$ is parallel to one of the principal lattice axes
(i.e., when $\theta=0^{\circ}$ or $30^{\circ}$ in Fig.~\ref{fig1}a).
In contrast, for the remaining pair of $\Omega_{\rm v}({\bf k})$ and $\Omega_{{\rm h}\|}({\bf k})$ the coupling is {\it
always negative}. As illustrated in Fig.~\ref{fig2}b, this results in the formation of the {\it hybrid} mode with the
imaginary part Im~$\Omega_{\rm hyb}\sim\pm\tilde q\tilde\delta$ (by the order of magnitude). If damping is low enough, this
triggers the {\it mode-coupling instability}.
Thus, only the intersection between the out-of-plane and longitudinal in-plane modes is critical for stability of 2D plasma
crystals \footnote{For 2D plasma crystals, the ``trivial'' origin of the non-Hamiltonial behavior associated with neutral
gas friction can often be neglected, since the corresponding damping rate is typically one-to-two orders of magnitude
smaller that the Einstein frequency \cite{RevModPhys.81.1353}.}.
\begin{figure*}
\includegraphics[width=0.9\textwidth,clip=]{fig3.eps}
\caption{Fluctuation spectra for ``shallow'' mode intersection (molecular dynamics simulations). Shown are the DL modes
(positive branches) for ${\bf k}$ at (a) $\theta=0^{\circ}$ and (b) $\theta=30^{\circ}$, and (c) spectrum in the ${\bf
k}$-plane integrated over frequency (in the range between 10~Hz~$\leq f\leq$~14~Hz). Simulations are for $N=16384$ particles
of a mass $m=6.1\times10^{-13}$~kg and charge $Q=-18500~e$, the screening length is $\lambda=600~\mu$m, the damping rate is
$\nu=0.87$~s$^{-1}$. The horizontal and vertical confinements have eigenfrequencies $f_{\rm conf}^{\rm(h)}=0.11$~Hz and
$f_{\rm conf}^{\rm(v)}=14.03$~Hz, respectively. The lattice constant in the center is $\Delta\simeq612~\mu$m
($\kappa=\Delta/\lambda\simeq1.02$). The wake parameters are $q=-0.2Q$ and $\delta=0.3\lambda$. The dashed lines show the
border of the first Brillouin zones, solid lines in (a) and (b) are theoretical curves. In (c) (as well as in other figures
depicting spectra in the ${\bf k}$ plane) the calculations for the upper right quadrant are mirrored in other three (shown
in lighter colors).}\label{fig3}
\end{figure*}
\subsection{Mode-coupling theory for 1D model}
\label{1D_theory}
It is instructive to present a brief summary of the mode-coupling theory which was originally developed for a 1D string
assuming the nearest-neighbor (NN) interactions \cite{PhysRevE.68.026405,PhysRevE.63.016409}. As it follows from the
subsequent analysis (see Sec.~\ref{Fingerprints}), this approach yields very simple expressions which can be conveniently
implemented for practical purposes (e.g., to calculate the instability thresholds, see Sec.~\ref{threshold}).
In the framework of 1D NN model \cite{PhysRevE.63.016409}, the coupling between horizontal (``longitudinal in-plane'') and
vertical (``out-of-plane'') DL modes,
\begin{equation}\label{Modes_1D}
\begin{array}{l}
\Omega_{{\rm h}}^2(k)=4(1-\tilde q)\left(\kappa^{-1}+2\kappa^{-2}+2\kappa^{-3}\right){\rm e}^{-\kappa}\sin^2\frac12k,\\[.3cm]
\Omega_{{\rm v}}^2(k)=\Omega_{\rm conf}^2-4(1-\tilde q)\left(\kappa^{-2}+\kappa^{-3}\right){\rm e}^{-\kappa}\sin^2\frac12k,
\end{array}
\end{equation}
is described by the following (exact) equation:
\begin{equation}\label{Coupling_1D}
(\Omega^2-\Omega_{{\rm h}}^2)(\Omega^2-\Omega_{\rm v}^2)+\sigma^2=0.
\end{equation}
The range of $k$ is limited by the first Brillouin zone $|k|\leq\pi$ (we use the same normalization as above), and the 1D
coupling coefficient is
\begin{equation}\label{Coupling_coefficient_1D}
\sigma(k)=2\tilde q\tilde\delta\left(\kappa^{-1}+3\kappa^{-2}+3\kappa^{-3}\right){\rm e}^{-\kappa}\sin k.
\end{equation}
All characteristics of the hybrid mode (e.g., width, growth rate, etc.) can be easily derived from Eqs
(\ref{Modes_1D})-(\ref{Coupling_coefficient_1D}), see Appendix~\ref{appendix1a}.
These results are obtained in the limit of ``small'' $\tilde\delta$ (for general case, see Ref. \cite{PhysRevE.63.016409}).
In Sec.~\ref{threshold} they will be compared with the exact 2D results derived in this limit.
\subsection{Additional remarks}
\label{remarks}
To conclude this Section, we should make two specific remarks which might be useful when considering DL waves and their
coupling:
(i) The dynamical matrix $\textsf{D}$ is solely characterized by interparticle interactions, i.e., does not depend on the
damping rate $\nu$. Thus, the {\it wave modes} $\Omega^2({\bf k})$ -- which are the eigenvalues of $\textsf{D}$ -- do not
depend on $\nu$ either. As regards the {\it dispersion relations} $\omega({\bf k})$, their dependence on $\nu$ is determined
by the solutions of the quadratic equation $\omega(\omega+ i\nu)-\Omega^2=0$. Therefore the effect of friction on waves is
straightforward: For weakly damped waves (when $|\Omega|\gg\nu$, which is typical for experiments), one readily obtains
$\omega({\bf k})\simeq\Omega({\bf k})-\frac12i\nu$. From the practical point of view this implies that one can analyze
undamped dispersion relations (i.e., put $\omega=\Omega$) and afterwards simply add $-\frac12\nu$ to the resulting imaginary
part \footnote{The real part of the dispersion relations remains unaffected by damping. This is only violated for the
acoustic modes $\Omega_{{\rm h}\|,\perp}({\bf k})$ in a close proximity of ${\bf k}={\bf 0}$ and therefore is unimportant
for the analysis.}, which simultaneously identifies the instability threshold for the hybrid mode \footnote{This also shows
that the analysis of wave modes does not require any distinction in terms of friction, as it has been done by Liu {\it et
al.}~\cite{PhysRevLett.105.085004} (where our previous theoretical results
\cite{PhysRevE.63.016409,PhysRevE.68.026405,zhdanov:zim} were erroneously referred to as ``frictionless'').} (see
Sec.~\ref{threshold2}).
(ii) For the analysis of wave modes in a crystal it is {\it sufficient} to consider the wave vectors from within the first
Brillouin zone \cite{kittel1961,lifshitz1981} which is shown in Fig.~\ref{fig1}b. This zone is nothing but the
Wigner-Seitz cell of the reciprocal lattice formed by the basis vectors ${\bf b}_{1}$ and ${\bf b}_{2}$. Hence, the wave
vectors ${\bf k}$ and ${\bf k}'={\bf k}+{\bf G}$ which are different by a linear combination of the basis vectors (${\bf
G}=m{\bf b}_1+n{\bf b}_2$) are equivalent for wave modes, i.e., $\Omega({\bf k}+{\bf G})\equiv\Omega({\bf k})$.
One has to remember this fact when analyzing dispersion relations at large $|{\bf k}|$. For instance, recently Liu {\it et
al.}~\cite{PhysRevLett.105.085004} identified one of the ``hot spots'' seen in their fluctuation spectra (in their Fig.~4c)
as a new hybrid mode. This spot is centered at $|{\bf k}|\Delta\simeq6.3(\simeq2\pi)$, $\theta=0^{\circ}$ and therefore is
located outside the first Brillouin zone; after the mapping with, say, ${\bf G}={\bf b}_2$, its position is $|{\bf
k}|\Delta\simeq \frac2{\sqrt{3}}\pi$, $\theta=90^{\circ}$ (equivalent to $30^{\circ}$, see Fig.~\ref{fig1}b; note also the
change in the polarization, from the transverse to longitudinal). This naturally coincides with the position of the
``regular'' hybrid mode at the border of the first zone, whereas the ``original'' spot is merely its image outside it (as
illustrated in Figs~\ref{fig3}c and \ref{fig4}b).
\begin{figure}
\includegraphics[width=0.8\columnwidth,clip=]{fig4.eps}
\caption{(a) Contour plot of the growth rate Im~$\omega_{\rm hyb}({\bf k})$ calculated from theory and (b) fluctuation
spectra in the ${\bf k}$-plane obtained from simulations (integrated over frequency in the range between 10~Hz~$\leq
f\leq$~14~Hz). To facilitate comparison with theory, the simulations are performed with periodic boundary conditions
in the horizontal plane, otherwise the parameters are the same as in Fig.~\ref{fig3}. }\label{fig4}
\end{figure}
\section{Fingerprints of Mode Coupling}
\label{Fingerprints}
In this Section we present detailed discussion and analysis of distinct fingerprints characterizing the wake-mediated
coupling of DL modes in 2D crystals. Based on the results of Sec.~\ref{types} we naturally focus only on the coupling
between the out-of-plane and longitudinal in-plane modes, which causes the formation of the hybrid mode and can trigger the
mode-coupling instability.
To illustrate key features of the mode coupling, the theoretical calculations were combined with the results of molecular
dynamics (MD) simulations (see description in Appendix~\ref{appendix2}). The DL wave modes were obtained from the
simulations by plotting the so-called ``fluctuation spectra'' -- intensity distributions of thermal velocity fluctuations in
the $(\omega,{\bf k})$ space.
\subsection{Hybrid mode}\label{hybrid}
Figure~\ref{fig3} represents a characteristic example of fluctuation spectra measured at the onset of the mode-coupling
instability. It was obtained from MD simulations performed for the conditions close to those of experiment by Cou\"edel {\it
et al.}~\cite{PhysRevLett.104.195001} (experiment II in Table~\ref{tab1}). In this case the out-of-plane and longitudinal
in-plane modes are just barely touching. Such ``shallow'' intersection is nevertheless sufficient to form a distinct hybrid
mode and to trigger the instability.
Figures~\ref{fig3}a and b depict the DL modes in the $(\omega,|{\bf k}|)$ plane (positive branches). They are obtained for
two directions of ${\bf k}$ at $\theta=0^{\circ}$ and $\theta=30^{\circ}$, respectively (corresponding to the principal
lattice axes, see Fig.~\ref{fig1}a). Figure~\ref{fig3}c shows the intensity distribution in the ${\bf k}$-plane (integrated
over frequency), which provides a ``top view'' on the fluctuation spectra (dotted line shows the direction of
$\theta=30^{\circ}$). The hybrid mode can be identified in Figs~\ref{fig3}b and c as ``hot spots'' located near the border
of the first Brillouin zone, where the intersection occurs (note also images of the hybrid mode outside the first zone). The
theoretical curves calculated from Eqs (\ref{matrix}), (\ref{dispersion}), (\ref{elements1}), and (\ref{elements2}) for the
same set of parameters demonstrate excellent agreement with simulations.
The reason why the fluctuation intensity is anomalously high at the position of the hybrid mode is the heating induced by
the wake-mediated coupling. Figure~\ref{fig3} represents the marginally unstable regime, when Im~$\omega_{\rm
hyb}(\simeq{\rm Im}~\Omega_{\rm hyb}-\frac12\nu)\gtrsim0$. In this regime (also observed in experiment
\cite{PhysRevLett.104.195001}) the effective growth rate of the instability is low, which allows us to obtain the
fluctuation spectra before the crystal is eventually destroyed. It is worth noting, however, that the hybrid mode would
usually appear as a ``hot spot'' even if the instability is suppressed by friction and Im~$\omega_{\rm hyb}<0$. This is
because the heating due to mode coupling is present also in stable regime. It becomes negligible only when Im~$\Omega_{\rm
hyb}\ll\frac12\nu$, and then the fluctuation intensity coincides with the intensity of DL modes outside the hybrid zone
(where it is determined by the background neutrals or temperature of thermostat in simulations).
At the initial stage of the instability (and, of course, when the instability is suppressed) the effect of nonlinearity on
the DL modes is not significant. In this case the contour plot of the growth rate Im~$\omega_{\rm hyb}({\bf k})$ reasonably
reproduces the distribution of fluctuation intensity in the vicinity of the hybrid mode. This is illustrated in
Fig.~\ref{fig4} where we plotted Im~$\omega_{\rm hyb}({\bf k})$ predicted by theory and the (frequency-integrated)
fluctuation spectra from simulations. At a later stage, however, a nonlinear coupling between different modes becomes
essential. This results in a variety of new phenomena, such as the energy cascades from the ``hot spots'' in the ${\bf k}$
space and the generation of secondary harmonics at the double frequency of the hybrid mode (which are clearly seen in Fig.~3
of Ref.~\cite{PhysRevLett.104.195001}). Nevertheless, since the principal aim of this paper is to focus on distinct features
of the {\it linear mode coupling}, we leave aside the discussion of numerous nonlinear coupling effects.
For the plots shown in Fig.~\ref{fig4} we used the same set of parameters as for Fig.~\ref{fig3}, but for simulations we
assumed periodic boundary conditions. The latter not only allowed us to directly compare the theory and simulations, but
also to probe the effect of weak deviation from periodicity caused by the horizontal confinement. We see that the only
noticeable difference between Figs~\ref{fig3}c and \ref{fig4}b is the intensity of the hybrid mode. This reflects the fact
that the growth rate of the instability critically depends on the interparticle distance $\Delta$ (resulting in
exponentially growing difference in the heating at the initial stage). Therefore in the case of parabolic confinement (where
$\Delta$ in the center is somewhat smaller than the average value) the intensity of the hybrid mode is higher than in the
homogeneous case shown in Figs~\ref{fig4}b. Otherwise, the positions and the overall shape of the ``hot spots'' in these two
plots practically coincide, suggesting that weak inhomogeneity which is always present in experiments due to the horizontal
confinement does not really affect the periodic structure of the Brillouin zones.
\begin{figure}
\includegraphics[width=0.8\columnwidth,clip=]{fig5.eps}
\caption{Illustration of ``deep'' mode intersection (simulations). The eigenfrequency of the vertical confinement is
$f_{\rm conf}^{\rm(v)}=13.12$~Hz (spectra are integrated over frequency in the range between 9~Hz~$\leq f\leq$~13~Hz), the
damping rate is $\nu=2.19$~s$^{-1}$. Otherwise the parameters are the same as in Fig.~\ref{fig3}.}\label{fig5}
\end{figure}
Finally, to illustrate the difference between ``shallow'' and ``deep'' intersections of the out-of-plane and longitudinal
in-plane modes, in Fig.~\ref{fig5} we demonstrate the fluctuation spectra obtained for the eigenfrequency of vertical
confinement $f_{\rm conf}^{\rm(v)}$ which is slightly lower than that in Fig.~\ref{fig3}. This naturally shifts the
out-of-plane mode down and thus makes the resulting hybrid mode much more pronounced: Figure~\ref{fig5} shows that for deep
intersections the separate ``islands'' of the hybrid mode merge into a joint broad ``ring'' (within the first Brillouin
zone) and the ``hot'' region occupies substantially larger part of the ${\bf k}$-plane. The magnitude of Im~$\Omega_{\rm
hyb}$ for deep intersections is usually much larger than for the shallow intersections and therefore the threshold
conditions to trigger the mode-coupling instability in the former case are substantially relaxed (see discussion in
Sec.~\ref{threshold}). Note that in this case, in order to keep the crystal in the marginally unstable regime (which allows
us to recover the fluctuation spectra) we increased the damping rate to $\nu=2.19$~s$^{-1}$.
\subsection{Angular dependence}\label{angular}
The dependence of DL modes on the direction of ${\bf k}$ is evident from the discussion above. For the hybridization and the
onset of the mode-coupling instability this dependence becomes crucial and therefore it deserves a separate discussion.
Figures~\ref{fig3} and \ref{fig4} show that the first crossing of the out-of-plane and longitudinal in-plane modes always
occurs at $\theta\simeq30^{\circ}$, at the border of the first Brillouin zone. The area of the hybrid mode in the ${\bf k}$
plane rapidly grows as the intersection gets deeper, and eventually the hybrid mode exists for any $\theta$, as in
Fig.~\ref{fig5}. The crossing depth is controlled by changing the particle density or/and the eigenfrequency of the vertical
confinement (see Sec.~\ref{threshold}).
Therefore, when the DL fluctuation spectra are measured in experiments, under conditions close to the onset of hybridization
(and, if not suppressed -- of the mode-coupling instability), special attention should be paid to the orientation of ${\bf
k}$ with respect to the crystalline lattice. Under these circumstances the direction should be chosen according to the
purpose of the experiment: If detection of the mode coupling is the goal, then $\theta=30^{\circ}$ is the best choice; if
unperturbed modes are to be measured, then $\theta=0^{\circ}$ should be used. The experimental technique must therefore
provide angular resolution, which is easily done for the in-plane modes, but is not always possible for the out-of-plane
mode (since it is difficult to achieve angular positioning of the plasma crystal in an experiment). For instance, if the
out-of-plane mode is measured with a fixed side-view camera~\cite{PhysRevLett.105.085004} then the angle $\theta$ is set
during the experiment and cannot be adjusted at the analysis stage, but if it is measured with a top-view camera (from the
variation of individual particle intensity)~\cite{couedel:215001} then $\theta$-resolved wave spectra can be obtained.
\subsection{Mixed polarization}
\begin{figure}[h]
\includegraphics[width=0.92\columnwidth]{fig6.eps}
\caption{Mixed polarization near the hybrid mode (simulations). Shown are the fluctuation spectra with the transverse
out-of-plane (a) and longitudinal (b) polarization, for ${\bf k}$ at $\theta=30^{\circ}$ and parameters of Fig.~\ref{fig3}.
Arrows indicate traces of mixed polarization. Far from the hybrid mode (``hot spots'') the modes become purely out-of-plane
(a) and in-plane (b).}\label{fig6}
\end{figure}
As we pointed out in Sec.~\ref{theory}, the DL wave modes are independent only when the wake-mediated coupling can be
neglected: Far from the intersection or if the modes do not cross at all, the out-of-plane mode is purely transverse, one of
the in-plane modes is longitudinal and the other is transverse. However, near the hybrid mode, where the coupling between
the first two modes is strong, the theory predicts the emergence of {\it mixed polarization}\cite{zhdanov:zim}: As the modes
approach the junction point, their polarizations become {\it oblique} (in the plane formed by ${\bf k}$ and the vertical
axis), but the eigenvectors remain {\it mutually orthogonal}. At the point where they merge the polarization exhibits a
discontinuity -- the eigenvectors of the two modes form a single (hybrid) eigenvector with the elliptic polarization.
Traces of the mixed polarization for the out-of-plane mode have been observed in our recent
experiment~\cite{PhysRevLett.104.195001} (supplemental Fig.~S2 therein) as well as in the experiment by Liu {\it et
al.}~\cite{PhysRevLett.105.085004} (shown in their Fig.~4b and erroneously interpreted as a ``new mode''). In
Fig.~\ref{fig6} we illustrate the mixed polarization observed in simulations (performed for the conditions of our
experiment~\cite{PhysRevLett.104.195001}). The magnitude of this effect ($\propto\tilde q\tilde\delta<1$) is quite small for
typical experimental conditions, so that its detection requires very careful analysis and high signal-to-noise ratio.
\subsection{Thresholds}\label{threshold}
The mode-coupling theory predicts two distinct thresholds: (i) {\it Confinement threshold}, which determines when the
out-of-plane and longitudinal in-plane modes intersect; it depends on the combination of the vertical confinement frequency
and the lattice constant (particle number density). This threshold identifies the sufficient condition for the hybrid mode
to form, but only the necessary condition for the instability to set in. The sufficient condition for the instability is
determined by (ii) {\it damping threshold} -- this identifies the critical value of the damping rate (controlled by
pressure) below which the instability is not suppressed. Let us discuss thresholds (i) and (ii) separately (we recall that
all frequencies are normalized by $\Omega_{\rm DL}$).
\begin{figure}
\includegraphics[width=7.5cm,clip=]{fig7.eps}
\caption{Universal mode-coupling thresholds (limit of small $\tilde\delta$). (a) Critical value of the vertical confinement frequency,
$\Omega_{\rm conf}^{\rm(cr)}$ (confinement threshold, upper curves), which identifies the formation of the hybrid mode, shown
versus the screening parameter $\kappa=\Delta/\lambda$. Also plotted is the minimum value $\Omega_{\rm conf}^{\rm(min)}$
(below which only multilayer crystals can exist, lower curves). (b) Critical value of the damping rate, $\nu^{\rm(cr)}$ (damping
threshold), which determines the sufficient condition for the instability to set in, shown versus the confinement control
parameter, $\Pi=(\Omega_{\rm conf}^{\rm(cr)})^2 -\Omega_{\rm conf}^2$, for $\kappa=0.5$, 1, 1.5, and 2. The upper bound for the
critical damping rate, $\nu^{\rm(cr,max)}$, is reached when $\Omega_{\rm conf}=\Omega_{\rm conf}^{\rm(min)}$
(marked by bullets). The inset in (b) shows $\nu^{\rm(cr,max)}$ for different $\kappa$, the mode-coupling instability is always
suppressed above the dotted line. In both panels, solid lines are exact 2D results derived in this paper, dashed lines represent
results of a 1D NN theory\cite{PhysRevE.63.016409}. Tilde denotes universal normalization (see text for details).}\label{fig7}
\end{figure}
\subsubsection{Confinement threshold}\label{threshold1}
The first intersection of the out-of-plane and longitudinal in-plane modes takes place at the border of the Brillouin zone
\cite{zhdanov:zim}, for ${\bf k}$ at $\theta=30^{\circ}$. Then, using the expressions for $\Omega_{\rm v}({\bf k})$ and
$\Omega_{{\rm h}\|}({\bf k})$ we readily obtain the condition for the hybrid mode to form (confinement threshold),
\begin{equation}\label{threshold_confinement1}
\Omega_{\rm conf}<\Omega_{\rm conf}^{\rm(cr)}=\left.\sqrt{\alpha_{\rm h}+2\alpha_{\rm v}+|\beta|}\right|_{{\bf k}
={\bf k}_{\rm cr}},
\end{equation}
where $|{\bf k}_{\rm cr}|=\frac2{\sqrt{3}}\pi$.
\begin{figure}
\includegraphics[width=8cm,clip=]{fig8.eps}
\caption{Role of ``finite'' $\tilde\delta$. Shown is the relative deviation of $\Omega_{\rm conf}^{\rm (cr)}$ (solid line) and
$\Omega_{\rm conf}^{\rm (min)}$ (dashed line) from the values calculated in the limit of small $\tilde\delta$
(see Fig.~\ref{fig7}a). The results are illustrated for $\kappa=1$ and three different values of $\tilde q$.}\label{fig8}
\end{figure}
Generally, the critical confinement frequency $\Omega_{\rm conf}^{\rm(cr)}$ is a rather complicated function of $\kappa$,
$\tilde\delta$, and $\tilde q$; it is given in Appendix~\ref{appendix3}, Eq. (\ref{app_confinement1}). However, Eq.
(\ref{elements1}) suggests that to the accuracy $O(\tilde\delta)$ the r.h.s. of Eq. (\ref{threshold_confinement1}) is
independent of $\tilde\delta$ and is proportional to $\sqrt{1-\tilde q}$. Thus, in this limit of ``small'' $\tilde\delta$
the combination $\Omega_{\rm conf}^{\rm(cr)}/\sqrt{1-\tilde q}\equiv\widetilde\Omega_{\rm conf}^{\rm(cr)}$ is a function of
$\kappa$ only (i.e., of the particle density) which is given by Eq. (\ref{app_confinement2}). Figure~\ref{fig7}a shows this
universal dependence in the useful range $0.5<\kappa<2$ (upper solid line).
One should always keep in mind that $\Omega_{\rm conf}$ cannot be arbitrarily small
\cite{PhysRevE.63.016409,PhysRevE.68.026405}: The out-of-plane mode $\Omega_{\rm v}^2({\bf k})= \Omega_{\rm
conf}^2-2\alpha_{\rm v}$ decreases monotonically with $|{\bf k}|$ and attains a minimum at the border of the first Brillouin
zone. If $\Omega_{\rm v}^2<0$ this formally implies instability. Physically, this is because the vertical confinement in
this case becomes too weak to keep the particles in the monolayer and the bifurcation to a multilayer crystal occurs (i.e.,
a monolayer crystal is no longer a ground state). Thus, irrespective of the value of damping rate, a monolayer plasma
crystal can only exist if the vertical confinement frequency exceeds the minimum value defined by \footnote{$\Omega_{\rm
v}^2({\bf k})$ is practically independent of $\theta$ at the border of the Brillouin zone \cite{zhdanov:zim} (the variation
is $\lesssim1~\%$), so that in order to facilitate the calculations we substitute ${\bf k}$ at $\theta=30^\circ$.}
\begin{equation}\label{threshold_confinement3}
\Omega_{\rm conf}>\Omega_{\rm conf}^{\rm(min)}\simeq\left.\sqrt{2\alpha_{\rm v}}\right|_{{\bf k}={\bf k}_{\rm cr}}.
\end{equation}
This value is given by Eqs (\ref{app_confinement3}) and (\ref{app_confinement4}) for arbitrary and small values of
$\tilde\delta$, respectively. In the latter case we obtain a universal dependence $\Omega_{\rm conf}^{\rm(min)}/
\sqrt{1-\tilde q}\equiv\widetilde \Omega_{\rm conf}^{\rm(min)}$ on $\kappa$ which is also plotted in Fig.~\ref{fig7}a (lower
solid line).
The effect of ``finite'' $\tilde\delta$ [i.e., beyond the accuracy $O(\tilde\delta)$] is illustrated in Fig.~\ref{fig8} for
$\kappa=1$ (results are practically independent of $\kappa$ in the range considered here). We plot the {\it relative
deviations} of $\Omega_{\rm conf}^{\rm (cr)}$ and $\Omega_{\rm conf}^{\rm (min)}$ from the values given by Eqs
(\ref{app_confinement2}) and (\ref{app_confinement4}), respectively. The deviations increase as $\propto\tilde\delta^2$ for
$\tilde\delta\lesssim0.3$ and then rapidly saturate at the level $(1-\tilde q)^{-1/2}-1$. [The latter is because both
$\Omega_{\rm conf}^{\rm (cr)}$ and $\Omega_{\rm conf}^{\rm (min)}$ do not depend on the wake parameters for
$\tilde\delta\gg1$, whereas at $\tilde\delta\ll1$ they scale as $\propto\sqrt{1-\tilde q}$.] Note that the curves have
almost identical shape at different $\tilde q$, which indicates that the shown correction approximately scales as
$\propto(1-\sqrt{1-\tilde q})$. Given typical experimental errors (see Table~\ref{tab1} and Fig.~\ref{fig10}), we conclude
that the corrections shown in Fig.~\ref{fig8} can generally be neglected, i.e., the accuracy of universal dependencies
obtained in the limit of small $\tilde\delta$ is sufficient for practical purposes. In some cases, however, the effect of
``finite'' $\tilde\delta$ can nevertheless play an important role (see Sec.~\ref{large_delta}).
Finally, let us compare the ``exact'' 2D results (in the limit of small $\tilde\delta$) with the results of approximate 1D
NN mode-coupling theory summarized in Sec.~\ref{1D_theory}. For the 1D case, the critical and minimum confinement
frequencies are derived from Eq.~(\ref{Modes_1D}) using the conditions $\Omega_{\rm h}^2(\pi)=\Omega_{\rm v}^2(\pi)$ and
$\Omega_{\rm v}^2(\pi)=0$, respectively. For the comparison with the 2D results, we multiply the 1D results by constant
``form factors'' reflecting mismatch of 1D and 2D environments, which yields
\begin{equation}\label{threshold_confinement_1D}
\begin{array}{l}
\widetilde\Omega_{\rm conf}^{\rm(cr)} \simeq 2F_{\rm conf}^{\rm(cr)}\sqrt{\left(\kappa^{-1}+3\kappa^{-2}
+3\kappa^{-3}\right){\rm e}^{-\kappa}},\\[.3cm]
\widetilde\Omega_{\rm conf}^{\rm(min)} \simeq 2F_{\rm conf}^{\rm(min)}\sqrt{\left(\kappa^{-2}+\kappa^{-3}\right)
{\rm e}^{-\kappa}}.
\end{array}
\end{equation}
The form factors $F_{\rm conf}^{\rm(cr)}=1.25$ and $F_{\rm conf}^{\rm(min)}=1.49$ are determined from a fit to the 2D
results, Eqs (\ref{app_confinement2}) and (\ref{app_confinement4}). The dependencies given by
Eq.~(\ref{threshold_confinement_1D}) are shown in Fig.~\ref{fig7}a by dashed lines.
Thus, we see that the 1D NN theory provides excellent qualitative description of the confinement thresholds -- even for
small $\kappa$; by multiplying these results with {\it constant} factors about unity we also get very good quantitative
agreement with 2D results.
\subsubsection{Damping threshold}\label{threshold2}
As pointed out in Sec.~\ref{types}, for $\theta=30^{\circ}$ (as well as for $0^{\circ}$) the transverse in-plane mode
becomes exactly decoupled. In this case the out-of-plane and longitudinal in-plane modes are governed by the following
equation [similar to that for the 1D NN model, Eq.~(\ref{Coupling_1D})]:
\begin{equation*}
(\Omega^2-\Omega_{{\rm h}\|}^2)(\Omega^2-\Omega_{\rm v}^2)+\sigma_{y}^2=0.
\end{equation*}
In the vicinity of the intersection $(\Omega_0,{\bf k}_0)$ the coupled modes are described by Eq. (\ref{dispersion2}) with
$\epsilon\simeq(\sigma_y/2\Omega_0)^2$. The group velocities ${\bf U}_{{\rm h}\|}$ and ${\bf U}_{\rm v}$ are collinear with
${\bf k}$ due to the azimuthal symmetry at $\theta=30^{\circ}$, so that the hybrid mode is given by
\begin{eqnarray*}
\Omega_{\rm hyb}({\bf k})=\Omega_0+\frac12({\bf U}_{{\rm h}\|}+{\bf U}_{\rm v})\cdot({\bf k}-{\bf k}_0)\hspace{2cm}\\
\pm\frac12i\sqrt{\sigma_y^2({\bf k}_0)/\Omega_0^2-|{\bf U}_{{\rm h}\|}-{\bf U}_{\rm v}|^2|{\bf k}-{\bf k}_0|^2}.
\end{eqnarray*}
Thus, the width of the hybrid mode is $|{\bf k}-{\bf k}_0|=\sigma_y({\bf k}_0)/(\Omega_0|{\bf U}_{{\rm h}\|}-{\bf U}_{\rm
v}|)^{-1}$, and the maximum of Im~$\Omega_{\rm hyb}({\bf k})$ is attained at the crossing point ${\bf k}_0$. From this we
immediately obtain the sufficient condition for the instability (damping threshold),
\begin{equation}\label{threshold_pressure1}
\nu<\nu^{\rm(cr)}=\sigma_y({\bf k}_0)/\Omega_0,
\end{equation}
where $\Omega_0$ and ${\bf k}_0$ are determined from the crossing condition,
\begin{equation}\label{threshold_pressure1a}
\Omega_0=\left.\sqrt{\alpha_{\rm h}+\beta}\right|_{{\bf k}={\bf k}_{0}}=\left.\sqrt{\Omega_{\rm conf}^2-2\alpha_{\rm
v}}\right|_{{\bf k}={\bf k}_{0}}.
\end{equation}
In order to relate Eq. (\ref{threshold_pressure1}) to the necessary instability condition [confinement threshold, Eq.
(\ref{threshold_confinement1})] we introduce the {\it confinement control parameter},
\begin{displaymath}
\Pi=(\Omega_{\rm conf}^{\rm(cr)})^2-\Omega_{\rm conf}^2,
\end{displaymath}
which varies in the range from zero to $(\Omega_{\rm conf}^{\rm(cr)})^2-(\Omega_{\rm conf}^{\rm(min)})^2$. It is obtained
from Eq. (\ref{threshold_pressure1a}),
\begin{equation}\label{threshold_pressure2}
\Pi=\left.\left(\alpha_{\rm h}+2\alpha_{\rm v}+\beta\right)\right|_{{\bf k}_0}^{{\bf k}_{\rm cr}},
\end{equation}
where the r.h.s. is calculated as the difference at ${{\bf k}_{\rm cr}}$ and ${{\bf k}_0}$. Thus, Eqs
(\ref{threshold_pressure1}) and (\ref{threshold_pressure2}) determine the dependence of the critical damping rate
$\nu^{\rm(cr)}$ on the control parameter $\Pi$ via the parametric dependence on $|{\bf k}_0|$. For arbitrary $\tilde\delta$,
this dependence is derived in Appendix~\ref{appendix3}, Eqs (\ref{app_pressure1}) and (\ref{app_pressure2}).
Similar to the confinement threshold discussed in the previous subsection, for the damping threshold one can also obtain a
universal dependence in the limit of small $\tilde\delta$. It is calculated in Eqs~(\ref{app_pressure3}) and
(\ref{app_pressure4}), where the r.h.s. are functions of $\kappa$ only (along with the parameter $|{\bf k}_0|$) and the
dependence on the wake parameters is explicitly given by the l.h.s. By introducing the universal normalization for the
critical damping rate and the confinement control parameter,
\begin{equation}\label{universal_norm}
\tilde\nu^{\rm(cr)}\equiv\frac{\sqrt{1-\tilde q}}{\tilde q\tilde\delta}\nu^{\rm(cr)},\quad
\widetilde\Pi\equiv\frac{\Pi}{1-\tilde q},
\end{equation}
we conclude that $\tilde\nu^{\rm(cr)}$ is a universal function of $\kappa$ and $\widetilde\Pi$. Figure~\ref{fig7}b shows
$\tilde\nu^{\rm(cr)}$ versus $\widetilde\Pi$ for four characteristic values of $\kappa$ (solid lines). For ``shallow''
intersections, when $\Omega_{\rm conf}$ is slightly below the critical value $\Omega_{\rm conf}^{\rm(cr)}(\kappa)$ the
critical damping rate increases as $\tilde\nu^{\rm(cr)}\propto \sqrt{\widetilde\Pi}$, which can be readily derived from
Eqs~(\ref{app_pressure3}) and (\ref{app_pressure4}). Thus, for given $\kappa$ and $\widetilde\Pi$ (with $\Omega_{\rm
conf}^{\rm(min)}< \Omega_{\rm conf}<\Omega_{\rm conf}^{\rm(cr)}$) monolayer plasma crystals are unstable if $\nu<(\tilde
q\tilde\delta/\sqrt{1-\tilde q})\tilde\nu^{\rm(cr)}(\kappa,\widetilde\Pi)$ and stable otherwise.
The critical damping rate is always bound from above, $\tilde\nu^{\rm(cr)}\leq \tilde\nu^{\rm(cr,max)}$. For a given
$\kappa$, the upper bound $\tilde\nu^{\rm(cr,max)}(\kappa)$ corresponds to $\Omega_{\rm conf}=\Omega_{\rm
conf}^{\rm(min)}(\kappa)$ and is marked by bullets in Fig.~\ref{fig7}b. These points shown in the inset as a function of
$\kappa$ identify the {\it absolutely stable} region: The mode-coupling instability in monolayer crystals is always
suppressed when $\nu$ exceeds $(\tilde q\tilde\delta/\sqrt{1-\tilde q})\tilde\nu^{\rm(cr,max)}(\kappa)$.
\begin{table*}[htbp]
\caption{Parameters of 2D crystals for different experiments (marked I to XII). The mode crossing is indicated as observed
in that study.}\label{tab1}
\begin{tabular}{lcccccccc|c|cc}
\hline
\hline
& $m$ & $|Q|$ & $\Delta$ & $\lambda$ & $\kappa$ & $f_{\rm conf}^{\rm(v)}$ & $\nu$ & $\omega_0$ & Mode & ~$2\pi f_{\rm conf}^{\rm(v)}/\omega_0$~ & ~$\nu/\omega_0$~ \\
& ($10^{-13}$~kg) & ($e$) & ($\mu$m) & ($\mu$m) & & (Hz) & (s$^{-1}$) & (s$^{-1}$) & crossing & & \\
\hline
I \cite{PhysRevLett.104.195001}$^{\ddag}$ & 6.1 & 17400 & 600 & 570 & 1.05 & 16.5 & 0.9 & 23.0 & No & 4.5 & 0.04 \\
II \cite{PhysRevLett.104.195001}$^{\ddag}$ & 6.1 & 18300 & 640 & 610 & 1.05 & 14.5 & 0.9 & 22.0 & Yes & 4.1 & 0.04 \\
III \cite{couedel:215001}$^{\ddag}$ & 5.3 & 14000 & 525 & 400 & 1.30 & 23.3 & 1.0 & 24.3 & No & 6.0 & 0.04 \\
IV \cite{couedel:215001}$^{\ddag}$ & 5.3 & 14200 & 514 & 514 & 1.00 & 20.5 & 1.0 & 25.4 & No & 5.1 & 0.04 \\
V \cite{couedel:215001}$^{\ddag}$ & 5.3 & 14600 & 1060 & 815 & 1.30 & 18.3 & 1.0 & 8.8 & No & 13.0 & 0.11 \\
VI \cite{couedel:215001}$^{\ddag}$ & 5.3 & 18000 & 600 & 600 & 1.00 & 16.3 & 1.1 & 25.6 & Yes & 4.0 & 0.04 \\
VII \cite{PhysRevLett.105.085004} & 4.2 & 9000 & 1000 & 700 & 1.40 & 13.9 & 3.5 & 6.7 & No & 13.0 & 0.52 \\
VIII \cite{PhysRevLett.105.085004} & 4.2 & 9000 & 600 & 700 & 0.86 & 13.9 & 3.5 & 14.4 & Yes & ~6.1$^{\dag}$ & 0.24 \\
IX \cite{PhysRevLett.105.269901} & 4.2 & 12000 & 600 & 760 & 0.79 & 13.9 & 3.5 & 19.2 & Yes & 4.5 & 0.18 \\
X \cite{PhysRevE.68.026405} & 5.5 & 15500 & 550 & 500 & 1.10 & 15.5 & 3.3 & 24.6 & Yes & 4.0 & 0.14 \\
XI \cite{samsonov:026410} & 5.6 & 16000 & 700 & 930 & 0.75 & 16.0 & 1.2 & 17.6 & No & 5.7 & 0.07 \\
XII \cite{samsonov:026410} & 5.6 & 13000 & 540 & 635 & 0.85 & 21.0 & 2.2 & 21.1 & No & 6.3 & 0.10 \\
\hline
\hline
\end{tabular}\\
{$^{\dag}$ The value is too high for the mode crossing (see Fig.~\ref{fig10}), amended in Erratum \cite{PhysRevLett.105.269901}.}\\
{$^{\ddag}$ For these data, error bars are available: $\pm15~\%$ for $\kappa$ and $\lambda$, $\pm10~\%$ for $|Q|$, $\pm8~\%$ for $f_{\rm conf}^{\rm(v)}$, and $\pm4~\%$ for $\Delta$.}
\end{table*}
According to the 1D NN theory [see Appendix~\ref{appendix1a}, Eq. (\ref{hybrid_1D})] the critical damping rate is
\begin{equation*}
\tilde\nu^{\rm(cr)}=\sqrt{\frac{\kappa^2+3\kappa+3}{\kappa^2+2\kappa+2}}\sqrt{\widetilde\Pi},
\end{equation*}
i.e., it also scales as a square root of the control parameter. The upper bound for $\nu^{\rm(cr)}(\kappa)$ is obtained by
substituting Eq. (\ref{threshold_confinement_1D}) for the maximum of $\Pi$, which yields
\begin{equation}\label{threshold_damping_1D}
\tilde\nu^{\rm(cr,max)}\simeq2F^{\rm(cr,max)}\sqrt{\left(\kappa^{-1}+3\kappa^{-2}+3\kappa^{-3}\right){\rm e}^{-\kappa}},
\end{equation}
where the corresponding form factor is $F^{\rm(cr,max)}=1.28$. Equation (\ref{threshold_damping_1D}), which is plotted in
the inset of Fig.~\ref{fig7}b by the dotted line, also provides excellent agreement with the 2D model. Hence, this is a
convenient formula to identify conditions of absolute stability for a 2D crystal.
\section{Comparison with experiments}\label{conclusion}
\begin{figure*}
\includegraphics[width=0.9\textwidth,clip=]{fig9.eps}
\caption{In-plane fluctuation spectra for ``shallow'' mode intersection (experiment II \cite{PhysRevLett.104.195001} in
Table~\ref{tab1}). Shown are the DL modes (positive branches) for ${\bf k}$ at (a) $\theta=0^{\circ}$ and (b)
$\theta=30^{\circ}$, and (c) spectrum in the ${\bf k}$-plane integrated over frequency (in the range between 10.5~Hz~$\leq
f\leq$~14.5~Hz). The dashed lines show the border of the first Brillouin zones, solid lines in (a) and (b) are theoretical
curves for all tree principal DL modes (assuming $\tilde q=0.3$ and $\tilde\delta=0.33$). Fluctuation spectra in (a) and (b)
reveal clear traced of the out-of-plane mode (mixed polarization). In order to reduce noise in (c), the spectrum is an
average of six spectra corresponding to equivalent directions in the crystal (using the invariance of hexagonal lattice to
$60^{\circ}$ rotations). }\label{fig9}
\end{figure*}
Wake-induced mode coupling has been observed in several experiments
\cite{couedel:215001,PhysRevLett.104.195001,PhysRevLett.105.085004,PhysRevE.68.026405}. However, the analysis of
experimental results can be fastidious and needs to be done carefully. The fingerprints of the mode-coupling must be
identified properly in order to avoid misinterpretations of the results. Therefore, in this Section we use the experiment of
Ref.~\cite{PhysRevLett.104.195001} as a characteristic example to demonstrate the principal features of the wake-induced
mode coupling. Then, we give an overview of literature currently available on experiments with 2D crystals (stable and
unstable) \cite{couedel:215001,PhysRevLett.104.195001,PhysRevLett.105.085004,PhysRevE.68.026405,samsonov:026410}, the
summary of experimental parameters is given in Table~\ref{tab1}. Finally, we discuss the stability of crystals in terms of
thresholds introduced in the previous Section.
One of the most clear experimental evidence of mode-coupling in a 2D plasma crystal was reported in
Ref.~\cite{PhysRevLett.104.195001} (experiment II in Table~\ref{tab1}). A monolayer of microparticles was formed by
levitating them in a plasma sheath above the lower rf electrode in a capacitively coupled discharge in a (modified) GEC
chamber. The microspheres were made of melamine-formaldehyde and had a diameter of $9.19\pm0.09~\mu$m. The low argon
pressure of $0.76$~Pa ensured that the particle motion was only slightly damped. A high quality of the monolayer (with no
detected particles above or below) was verified by using a side-view camera. Details of the experimental procedure are given
in Refs.\cite{couedel:215001,PhysRevLett.104.195001}.
\begin{figure}
\includegraphics[width=7.5cm,clip=]{fig10.eps}
\caption{Comparison of the vertical confinement frequency measured in experiments (Table~\ref{tab1}) with the theoretical
confinement threshold (Fig.~\ref{fig7}a): Blue diamonds are for experiments I and II, red circles for III-VI,
green up triangles for VII and VIII, open green up triangle for IX, blue square for X, and purple down triangles for XI and XII.
The vertical resonance frequency is normalized to $\omega_0=\sqrt{Q^2/m\Delta^3}$. For experiments I to VI, error bars are
available: $\pm15\%$ for $\kappa$, $\pm8\%$ for $f_{\rm conf}^{\rm(v)}$, and $\pm12\%$ for $\omega_0$.}
\label{fig10}
\end{figure}
The experimentally measured fluctuation spectra of two in-plane DL modes are shown in Fig.~\ref{fig9}. Since this experiment
was performed at conditions close to the onset of instability, all essential fingerprints of mode coupling are clearly
visible:
\begin{itemize}
\item{The mode coupling critically depends on the direction of the wave vector ${\bf k}$. The comparison of wave spectra
calculated for $\theta=0^{\circ}$ (Fig.~\ref{fig9}a) and $\theta=30^{\circ}$ (Fig.~\ref{fig9}b) reveals that the
onset of mode coupling first occurs at $\theta=30^{\circ}$ -- this results in the prominent ``hot spots'' in
Fig.~\ref{fig9}b. Colored red, they are almost two orders of magnitude more intense than the ``normal'' branches of
the fluctuation spectra. The hot spot that lies within the first Brillouin zone (left one) represents the hybrid
mode, the other one is its image in the higher Brillouin zone. These observations are in agreement with theory and
complimentary simulations (Fig.~\ref{fig3}), which predicts that the mode coupling first takes place at
$\theta=30^{\circ}$ for ``shallow'' mode intersection.}
\item{The less intense spot seen in Fig.~\ref{fig9}a at $\theta=0^{\circ}$ and $k\Delta\simeq6.5$ is outside the first
Brillouin zone (in Fig.~\ref{fig9}c the location is along $k_x$-axis, at the right edge). As explained in
Sec.~\ref{remarks}, this spot should be mapped into the first Brillouin zone, where it represents the gap between
two hot spots of the hybrid mode (in Fig.~\ref{fig9}c, along the border of the Brillouin zone at
$\theta\simeq30^\circ$), and therefore its intensity is almost one order of magnitude smaller than the intensity of
the hot spots.}
\item{Traces of mixed polarization (out-of-plane mode) are clearly seen next to the hybrid mode in Figs.~\ref{fig9}a and
\ref{fig9}b. This gives a direct experimental proof that the out-of-plane mode becomes oblique close to the
intersection point. A discrepancy of $\simeq5~\%$ between the experimentally measured in-plane projection of the
out-of-plane mode and its theoretical dispersion relation can be explained by ``finite-$\tilde\delta$'' correction
to the theory shown in Fig.~\ref{fig8} (which is about $4~\%$ for the chosen values of wake parameters).}
\item{Finally, all ``hot spots'' predicted by the theory and observed in simulations can be simultaneously seen in the
experimental wave spectrum in ${\bf k}$-plane, which is shown in Fig.~\ref{fig9}c. }
\end{itemize}
Next, we analyze the stability of 2D plasma crystals in terms of the confinement threshold (which determines when the hybrid
mode emerges). Available literature data on stable and unstable crystals is summarized in Table~\ref{tab1}, and the measured
vertical confinement frequency $2\pi f^{\rm(v)}_{\rm conf}$ is compared to the theoretical threshold $\Omega ^{\rm
(cr)}_{\rm conf}$ in Fig.~\ref{fig10}. Note that for the comparison we change the normalization of $2\pi f^{\rm(v)}_{\rm
conf}$: Instead of using $\Omega_{\rm DL}$ -- a natural frequency scale in theory, now we employ the 2D analogue of dust
plasma frequency,
\begin{equation*}
\omega_0=\sqrt{\frac{Q^2}{m\Delta^3}}\equiv\kappa^{-3/2}\Omega_{\rm DL}.
\end{equation*}
This normalization allows us to minimize the experimental errors, since the interparticle distance is usually measured with
much higher accuracy than the screening length (see footnote to Table~\ref{tab1}).
Figure~\ref{fig10} shows that all experiments listed in Table~\ref{tab1} as having no mode crossing are indeed represented
by points well above the confinement threshold line. To the contrary, the points for experiments marked by mode crossing are
located very close to the threshold line or below it. The only exception is the experiment VIII
\cite{PhysRevLett.105.085004} by Liu \textit{et al.}: The wake-induced mode coupling was clearly seen in the fluctuation
spectra measured in \cite{PhysRevLett.105.085004}, but the reported experimental parameters (yielding $2\pi f_{\rm
conf}^{\rm(v)}/\omega_0\simeq6$, marked by green up triangle in Fig.~\ref{fig10}) certainly do not allow the mode crossing,
which indicates large measurement errors (amended in the subsequent Erratum \cite{PhysRevLett.105.269901}). This example
demonstrates that, by comparing experimental parameters to the theoretical confinement threshold near the point where the
hybrid mode (hot spot) emerges in the fluctuation spectra one can perform very sensitive consistency test for the deduced
parameters.
\subsection{Effective charge and wake parameters}
At this point, let us briefly discuss the relation between the actual charge carried by particles and the effective charge
which determines the dispersion properties of DL waves in 2D plasma crystals.
The common method to determine $Q$ and $\lambda$ in 2D crystals is to fit the measured fluctuation spectra for the in-plane
modes by theoretical curves. The method is based on the {\it assumption} that the interparticle interaction potential can be
approximated by the Yukawa form \footnote{The functional form of the interaction potential can deviate from the Yukawa
dependence at large distances, but within several $\lambda$ this deviation is negligible indeed (see Ref.
\cite{kompaneets:052108}).} and provides rather high accuracy. However, the dispersion relations are determined by the
combined effect of direct interparticle interactions and the wake-mediated interactions. While the former contribution
scales as $\propto Q^2$, the latter depends on a particular form of the wake. For the model of a point-like wake charge used
in this paper the wake-mediated interactions scale as $\propto qQ$, which modifies the dispersion elements of the dynamical
matrix (\ref{elements1}). In the limit of small $\tilde\delta$ (which turns out to be a remarkably accurate approximation,
see Fig.~\ref{fig8}) this yields the common renormalizing factor $(1-\tilde q)$ in Eq. (\ref{elements1}), and therefore the
dispersion relations are determined by the {\it effective} charge $Q_{\rm eff}=\sqrt{1-\tilde q}\:Q$.
This fact should always be kept in mind when fitting the fluctuation spectra by theoretical dispersion relations: In theory,
frequencies are normalized by $\Omega_{\rm DL}\propto |Q|$ and hence the explicit dependence on the factor $(1-\tilde q)$
naturally disappears. This allows us, e.g., to directly compare the experimentally measured values of $2\pi f_{\rm
conf}^{\rm(v)}/\omega_0$ with the theoretical confinement threshold without knowing the wake parameters (see
Fig.~\ref{fig10}).
Of course, the comparison of theory and experiments in terms of the damping threshold requires knowledge of $\tilde q$ and
$\tilde\delta$, since the growth rate of the hybrid mode is directly proportional to the effective ``dipole moment'' of wake
$\tilde q\tilde\delta$. As was shown in Sec.~\ref{threshold2}, in order to compare the measured value of $\nu/\omega_0$
(last column of Table~\ref{tab1}) with the theoretical damping threshold plotted in Fig.~\ref{fig7}b, we need to known the
factor $\tilde q\tilde\delta/(1-\tilde q)$ [see Eq. (\ref{universal_norm}); additional factor $\sqrt{1-\tilde q}$ in the
denominator here is because $\omega_0$ in experiments is determined by $Q_{\rm eff}$]. In experiments, however, the wake
parameters are generally unknown, so that a reasonable assumption should always be made in order to perform the analysis in
terms of the damping threshold.
\subsection{Effect of ``finite'' $\tilde\delta$}
\label{large_delta}
As we mentioned in Sec.~\ref{threshold2}, under certain conditions the ``finite-$\tilde\delta$'' correction shown in
Fig.~\ref{fig8} can become important. In particular, this happens in ``marginal cases'', when the normalized value of the
confinement frequency is very close to the corresponding threshold line (viz., when the distance to the line is comparable
or less than the correction). For instance, such situation might occur for experiments II, VI, IX, and X shown in
Fig.~\ref{fig10}. However, typical experimental errors are relatively large, so that accounting for the corrections is
hardly required in these cases.
As regards the comparison of theory with numerical simulations, where all input parameters are known precisely, the
``finite-$\tilde\delta$'' corrections can become crucial. To illustrate this, let us consider simulations of the shallow
mode intersection shown in Fig.~\ref{fig3}. The (normalized) confinement frequency in this case is $\simeq1~\%$ {\it larger}
than $\widetilde\Omega_{\rm conf}^{\rm(cr)}$, i.e., according to the universal criterion for the confinement threshold the
system is still marginally stable. However, by taking into account the correction to the confinement threshold from
Fig.~\ref{fig8} (which is about $+4~\%$ in this case) we conclude that the system is in fact marginally unstable -- as
observed in the simulations. In contrast, for the case of the deep mode intersection shown in Fig.~\ref{fig5} (where the
confinement frequency is just $\simeq6.5~\%$ smaller) the correction plays practically no role.
\section{Conclusions and outlook}
The theory of mode-coupling instability \cite{PhysRevE.63.016409,zhdanov:zim} provides detailed picture of a {\it
plasma-specific} melting scenario operating in 2D plasma crystals. The melting associated with the wake-mediated coupling
between the longitudinal in-plane and out-of-plane modes can only be triggered if (i) the modes intersect and (ii) the
neutral gas damping is sufficiently low. Even if the instability is suppressed by the damping and the melting does not
occur, the coupling always results in the formation of a hybrid mode which is revealed in fluctuation spectra by anomalous
``hot spots'' emerging at distinct positions in the ${\bf k}$-plane. In the vicinity of the hybrid mode, one can observe
traces of mixed polarization for the two intersecting wave branches.
In this paper we showed that all these features can be considered as distinct fingerprints to identify the onset of the
wake-induced mode coupling. This, in turn, allows us to determine certain combinations of the crystal parameters with a
fairly good accuracy. For instance, the theory predicts a well-defined confinement threshold (for the ratio of the vertical
confinement frequency to the dust-lattice frequency) at which the ``hot spots'' emerge. It is noteworthy that the effect of
wakes on the dispersion relations is automatically taken into account via the charge renormalization, which yields the
effective charge -- the value which is deduced from the analysis of experimental fluctuation spectra.
On the other hand, the damping threshold as well as the evolution of the mode-coupling instability (if not suppressed) are
determined by parameters of the wake -- which are still poorly known for experiments. By identifying the onset of the
instability and comparing it with the damping threshold derived above, one could obtain effective ``dipole moment'' of the
wake. Furthermore, one could measure the energy growth rate at the initial instability stage and compare it with the
theoretical prediction. Systematic studies in this direction would be highly desirable. However, we note that such
measurements would only give us some mean characteristics of the wake, e.g., the first (``dipole'') moment in the multipole
expansion.
We believe that future research into the stability of 2D plasma crystals should be focused, in particular, on the
implementation of self-consistent wake models \cite{PhysRevE.64.046406,kompaneets:052108,Kompaneets08} for the calculation
of the mode coupling (which should also account for the spatial variation of the interaction parameters
\cite{Kompaneets05,Yaroshenko05}). Such studies will allow us to gain deeper insight into the plasma-specific mechanisms of
melting operating in 2D systems and provide more reliable basis for future research into generic melting mechanisms.
\begin{appendix}
\section{Elements of dynamical matrix $\textsf{D}$ [Eq. (\ref{matrix})]}\label{appendix1}
In Ref.~\cite{zhdanov:zim} we calculated the elements of $\textsf{D}$ with the accuracy $O(\tilde\delta)$. Although usually
$\tilde\delta$ is small indeed, such a linear expansion might not be always sufficient for some experimental conditions (see
Sec.~\ref{large_delta}). Below we present the results for arbitrary $\tilde\delta$. For brevity, we introduce the following
auxiliary functions:
\begin{equation}\nonumber
\begin{array}{l}
\Psi(x)=(x^{-1}+x^{-2}+x^{-3}){\rm e}^{-x},\\[.2cm]
\Xi(x)=(x^{-1}+3x^{-2}+3x^{-3}){\rm e}^{-x},\\[.2cm]
\Lambda(x)=\frac12[\Xi(x)-\Psi(x)].\\[.3cm]
\end{array}
\end{equation}
Then the dispersion elements of Eq. (\ref{matrix}) are given by the following sums over integer $m$ and $n$ with excluded
$(0,0)$:
\begin{equation}\label{elements1}
\begin{array}{l}
\alpha_{\rm h}=\sum\limits_{m,n}\left\{\Psi(\kappa s)-\tilde q \left[\Psi(\kappa s_{\delta})-
\tilde\delta^2s_{\delta}^{-2}\Xi(\kappa s_{\delta})\right]\right\}\\
\hspace{5.8cm}\times\sin^2\frac12{\bf k}\cdot{\bf s},\\[.6cm]
\alpha_{\rm v}=\sum\limits_{m,n}\left\{\Lambda(\kappa s)-\tilde q \left[\Lambda(\kappa s_{\delta})-
\tilde\delta^2s_{\delta}^{-2}\Xi(\kappa s_{\delta})\right]\right\}\\
\hspace{5.8cm}\times\sin^2\frac12{\bf k}\cdot{\bf s},\\[.6cm]
\beta=\sum\limits_{m,n}\left[\Xi(\kappa s)-\tilde qs^2s_{\delta}^{-2}\Xi(\kappa s_{\delta})\right]\\
\hspace{3.9cm}\times(s_y^2-s_x^2)s^{-2}\sin^2\frac12{\bf k}\cdot{\bf s},\\[.6cm]
\gamma=\sum\limits_{m,n}\left[\Xi(\kappa s)-\tilde qs^2s_{\delta}^{-2}\Xi(\kappa s_{\delta})\right]
s_xs_ys^{-2}\sin^2\frac12{\bf k}\cdot{\bf s}.
\end{array}
\end{equation}
Here, the vector ${\bf s}$ with the components $s_x=\frac12m+n$ and $s_y=\frac{\sqrt{3}}2m$ and the absolute value
$s=\sqrt{m^2+mn+n^2}$ characterizes the relative positions of all neighbors in the hexagonal lattice; we also introduced
$s_{\delta}=\sqrt{s^2+\tilde\delta^2}$. The coupling elements are given by
\begin{equation}\label{elements2}
{\textstyle\sigma_{x,y}=\tilde q\tilde\delta\sum\limits_{m,n}\Xi(\kappa s_{\delta})s_{x,y}s_{\delta}^{-2}\sin{\bf
k}\cdot{\bf s}}.
\end{equation}
In the NN approximation (formally applicable for $\kappa\gg1$), the modes $\Omega_{\rm v}^2({\bf k})$ and $\Omega_{{\rm
h}\|}^2({\bf k})$ (whose coupling causes the hybridization) obtained from Eqs (\ref{elements1}) and (\ref{elements2})
coincide with Eqs. (\ref{Modes_1D})-(\ref{Coupling_coefficient_1D}) for a 1D string. In the limits $\tilde q\to0$ or
$\tilde\delta\to\infty$, Eqs (\ref{elements1}) and (\ref{elements2}) reduce to conventional (wake-free) results for DL modes
in 2D crystals. For $\tilde\delta\to0$ and finite $\tilde q$ one also obtains the wake-free results, but with the particle
charge renormalized by the factor $\sqrt{1-\tilde q}$.
\section{Hybrid mode for 1D model}\label{appendix1a}
The intersection point between the horizontal and vertical modes, $(\Omega_0,k_0)$, is readily derived from Eq.
(\ref{Modes_1D}):
\begin{equation*}
\Omega_0=\sqrt{\frac{\kappa^2+2\kappa+2}{\kappa^2+3\kappa+3\kappa}}\;\Omega_{\rm conf},\quad
\sin\frac12k_0=\frac{\Omega_{\rm conf}}{\Omega_{\rm conf}^{\rm(cr)}},
\end{equation*}
where $\Omega_{\rm conf}^{\rm(cr)}$ is given by the first Eq. (\ref{threshold_confinement_1D}) with $F_{\rm
conf}^{\rm(cr)}=1$. The maximum growth rate of the hybrid mode is obtained from Eq. (\ref{Coupling_1D}),
\begin{equation}\label{hybrid_1D}
{\rm Im}~\Omega_{\rm hyb}(k_0)=\frac{\sigma(k_0)}{2\Omega_0},
\end{equation}
where $\sigma(k)$ is given by Eq. (\ref{Coupling_coefficient_1D}). This yields the critical damping rate
$\nu^{\rm(cr)}=\sigma(k_0)/\Omega_0$.
\section{Molecular dynamics simulations}\label{appendix2}
The charged particles were confined in a vertical parabolic well with an eigenfrequency which was varied in the range of
15~Hz~$<f_{\rm conf}^{\rm(v)} <$~25~Hz. In the horizontal plane, two options were investigated: parabolic confinement with
an eigenfrequency $f_{\rm conf}^{\rm(h)}<0.5$~Hz and periodic boundary conditions (with $f_{\rm conf}^{\rm(h)}=0$). The
equation of motion for each particle is
\begin{displaymath}
m\ddot{\mathbf{r}}_i +m\nu \dot{\mathbf{r}}_i =\sum_{j\neq i}\mathbf{F}_{ij} + {\bf C}_{i} + \mathbf{L}_{i}
\end{displaymath}
where $m$ is the particle mass, $\nu$ is the damping rate, $\mathbf{r}_i$ the position of the $i$th particle, and ${\bf
C}({\bf r}_i)$ represents the confinement force. The force of interparticle interaction is
\begin{eqnarray}
\mathbf{F}_{ij} & = & -\frac{Q^2}{r_{ij}^2}\exp\Big({-\frac{r_{ij}}{\lambda}}\Big)\Big(1+\frac{r_{ij}}{\lambda}\Big)
\frac{\mathbf{r}_{ij}}{r_{ij}}\nonumber \\
& & +\frac{Qq}{r_{{\rm w}_{ij}}^2} \exp\Big({-\frac{r_{{\rm w}_{ij}}}{\lambda}}\Big)\Big(1+
\frac{r_{{\rm w}_{ij}}}{\lambda}\Big)\frac{\mathbf{r}_{{\rm w}_{ij}}}{r_{{\rm w}_{ij}}}\nonumber
\end{eqnarray}
where ${\bf r}_{ij}$ is the distance from the particle $i$ to the particle $j$, ${\bf r}_{{\rm w}_{ij}}$ is the distance to
the wake of the particle $j$, $Q$ is the particle charge, and $q$ is the point-like charge of the wake placed at a distance
$\delta$ below each particle. The Langevin force is defined as
\begin{displaymath}
\langle\mathbf{L}_i(t)\rangle={\bf 0},\qquad \langle\mathbf{L}_i(t+\tau)\mathbf{L}_j(t)\rangle = 2\nu
mT\delta_{ij}\delta(\tau),
\end{displaymath}
where $T$ is the temperature of the thermostat (here, $\delta$ is the Kronecker delta or the Dirac delta function).
In order to simulate systems of a size comparable to experimental (with $N\gtrsim10^4$ particles) without any approximation
(i.e., without cutoff radius in the interactions), the code was written in CUDA C and run on NVIDIA Tesla C1060 GPU or C2050
GPU computing cards. The equations of motion were solved using Beaman algorithm with predictor-corrector.
\section{Calculation of thresholds for 2D model}\label{appendix3}
To derive the confinement threshold, we substitute the dispersion elements from Eq. (\ref{elements1}) in Eq.
(\ref{threshold_confinement1}) which yields
\begin{widetext}
\begin{equation}
\Omega_{\rm conf}^{\rm(cr)}=\sqrt{\sum\limits_{m,n}\eta_m\left\{\left(1+p\right)
\left[\Xi(\kappa s)-\tilde q\Xi(\kappa s_{\delta})\right]+\tilde q\tilde\delta^2s_{\delta}^{-2}\left(3+p\right)
\Xi(\kappa s_{\delta})\right\}}.\label{app_confinement1}
\end{equation}
\end{widetext}
Here the fact that $|{\bf k}_{\rm cr}|s_y=m\pi$ is taken into account, so that it is convenient to introduce the parameter
$\eta_m=\frac12 \left[1-(-1)^m\right]$ (which is equal to 1 or 0 for odd or even $m$, respectively). Furthermore, for
brevity we use $p\equiv s^{-2}(s_x^2-s_y^2)$.
For the accuracy $O(\tilde\delta)$, we can neglect in Eq. (\ref{app_confinement1}) the second term in curly braces and set
$s_{\delta}=s$, which results in the following expression:
\begin{equation}
\frac{\Omega_{\rm conf}^{\rm(cr)}}{\sqrt{1-\tilde q}}=\sqrt{\sum\limits_{m,n}\eta_m\left(1+p\right)\Xi(\kappa s)},
\label{app_confinement2}
\end{equation}
where the r.h.s. is a function of $\kappa$ only. Thus, Eq. (\ref{app_confinement2}) determine the universal dependence of
$\Omega_{\rm conf}^{\rm(cr)}$ on $\kappa$.
The minimum value of the confinement frequency defined in Eq. (\ref{threshold_confinement3}) is
\begin{widetext}
\begin{equation}
\Omega_{\rm conf}^{\rm(min)}=\sqrt{2\sum\limits_{m,n}\eta_m\left\{\Lambda(\kappa s)-\tilde q\Lambda(\kappa s_{\delta})
+\tilde q\tilde\delta^2s_{\delta}^{-2}\Xi(\kappa s_{\delta})\right\}},\label{app_confinement3}
\end{equation}
\end{widetext}
for the accuracy $O(\tilde\delta)$ it is reduced to
\begin{equation}
\frac{\Omega_{\rm conf}^{\rm(min)}}{\sqrt{1-\tilde q}}=\sqrt{2\sum\limits_{m,n}\eta_m\Lambda(\kappa s)}.\label{app_confinement4}
\end{equation}
For the damping threshold, we substitute the coupling element [Eq. (\ref{elements2})] in Eq. (\ref{threshold_pressure1}) and
the dispersion elements in Eqs (\ref{threshold_pressure1a}) and (\ref{threshold_pressure2}). After some algebra we get
\begin{widetext}
\begin{eqnarray}
\nu^{\rm(cr)} & = &
\frac{\tilde q\tilde\delta\sum\limits_{m,n}s_{\delta}^{-2}s_y\Xi(\kappa s_{\delta})\sin|{\bf k}_0|s_y}{\sqrt{\sum\limits_{m,n}
\left\{\Psi(\kappa s)-\tilde q \Psi(\kappa s_{\delta})+p\left[\Xi(\kappa s)-\tilde q\Xi(\kappa s_{\delta})\right]
+\tilde q\tilde\delta^2s_{\delta}^{-2}\left(1+p\right)\Xi(\kappa s_{\delta})\right\}\sin^2\frac12|{\bf k}_0|s_y }}
\label{app_pressure1}, \\
\Pi & = &
\sum\limits_{m,n}\left(\eta_m-\sin^2{\textstyle\frac12}|{\bf k}_0|s_y\right)\left\{\left(1+p\right)\left[\Xi(\kappa s)
-\tilde q\Xi(\kappa s_{\delta})\right]+\tilde q\tilde\delta^2s_{\delta}^{-2}\left(3+p\right)
\Xi(\kappa s_{\delta})\right\}. \label{app_pressure2}
\end{eqnarray}
\end{widetext}
For the accuracy $O(\tilde\delta)$, we neglect the last terms in curly braces and set $s_{\delta}=s$. Then Eqs
(\ref{app_pressure1}) and (\ref{app_pressure2}) are reduced to
\begin{widetext}
\begin{eqnarray}
\frac{\sqrt{1-\tilde q}}{\tilde q\tilde\delta}\nu^{\rm(cr)} & = &
\frac{\sum\limits_{m,n}s^{-2}s_y\Xi(\kappa s)\sin|{\bf k}_0|s_y}{\sqrt{\sum\limits_{m,n}\left[\Psi(\kappa s)+p\Xi(\kappa s)\right]
\sin^2\frac12|{\bf k}_0|s_y }},\label{app_pressure3}\\
\frac{\Pi}{1-\tilde q} & = &
\sum\limits_{m,n}\left(\eta_m-\sin^2{\textstyle\frac12}|{\bf k}_0|s_y\right)\left(1+p\right)\Xi(\kappa s),\label{app_pressure4}
\end{eqnarray}
\end{widetext}
where the r.h.s. depend only on $\kappa$ and $|{\bf k}_0|$. Thus, Eqs (\ref{app_pressure3}) and (\ref{app_pressure4})
determine the universal dependence of the critical damping rate $\nu^{\rm(cr)}$ on the confinement control parameter $\Pi$
via the parametric dependence on $|{\bf k}_0|$.
\end{appendix}
|
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"redpajama_set_name": "RedPajamaArXiv"
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| 9,701
|
<?php
declare(strict_types=1);
use Doctrine\Common\Cache\PhpFileCache;
use Doctrine\Common\Persistence\Mapping\Driver\MappingDriverChain;
use Doctrine\ORM\EntityManager;
use Doctrine\ORM\EntityManagerInterface;
use Ramsey\Uuid\Doctrine\UuidBinaryOrderedTimeType;
use Ramsey\Uuid\Doctrine\UuidBinaryType;
use Ramsey\Uuid\Doctrine\UuidType;
use Roave\PsrContainerDoctrine\EntityManagerFactory;
return [
'dependencies' => [
'factories' => [
'doctrine.entity_manager.orm_default' => EntityManagerFactory::class,
],
'aliases' => [
EntityManager::class => 'doctrine.entity_manager.orm_default',
EntityManagerInterface::class => 'doctrine.entity_manager.default',
'doctrine.entitymanager.orm_default' => 'doctrine.entity_manager.orm_default'
]
],
'doctrine' => [
'connection' => [
'orm_default' => [
'doctrine_mapping_types' => [
UuidBinaryType::NAME => 'binary',
UuidBinaryOrderedTimeType::NAME => 'binary',
]
]
],
'driver' => [
// default metadata driver, aggregates all other drivers into a single one.
// Override `orm_default` only if you know what you're doing
'orm_default' => [
'class' => MappingDriverChain::class,
'drivers' => [],
],
],
'types' => [
UuidType::NAME => UuidType::class,
UuidBinaryType::NAME => UuidBinaryType::class,
UuidBinaryOrderedTimeType::NAME => UuidBinaryOrderedTimeType::class,
],
'cache' => [
PhpFileCache::class => [
'class' => PhpFileCache::class,
'directory' => getcwd() . '/data/cache/doctrine'
]
]
],
'resultCacheLifetime' => 300
];
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,478
|
{"url":"https:\/\/www.gradesaver.com\/textbooks\/science\/physics\/physics-principles-with-applications-7th-edition\/chapter-3-kinematics-in-two-dimensions-vectors-problems-page-70\/31","text":"# Chapter 3 - Kinematics in Two Dimensions; Vectors - Problems - Page 70: 31\n\n481m\n\n#### Work Step by Step\n\nLet x= 0 and y = 0 directly below where the package is launched, and let upward be the positive y direction. The projectile\u2019s initial vertical velocity is $(69.4 m\/s)(sin 0 ^{\\circ}) = 0$. The vertical acceleration is $-9.8 \\frac{m}{s^{2}}$, negative because it is directed downward. It starts at a height of y = 235 m, and the final vertical position is 0 m. Use equation 2.11b to find the time of flight of 6.925 s. The horizontal distance covered is the constant horizontal velocity multiplied by the time. $$(69.4 m\/s)(cos 0 ^{\\circ})(6.925 s) = 481 m$$ That\u2019s how far in advance the goods should be dropped.\n\nAfter you claim an answer you\u2019ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide\u00a0feedback.","date":"2019-05-21 23:01:45","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\": 0.8421191573143005, \"perplexity\": 600.0673519226455}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"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-2019-22\/segments\/1558232256586.62\/warc\/CC-MAIN-20190521222812-20190522004812-00304.warc.gz\"}"}
| null | null |
Q: Connection Pool - OkHttp We are using OkHttp in WAS environment Could you please help us with the below queries -:
*
*Question 1: What should be the ideal connection pool size and keep Alive for a container environment , is there any formula to calculate it, we will be using Okhttp client to connect to two different URL's
*Question 2: We don't want to have any client side failures , how does OkHttp handle stale connections , I don't see any parameter in OkHttp to check for stale connections?
HTTP Java client Java has this parameter to turn on stale connection check:
http.connection.stalecheck
We are using OkHttp client as mentioned below , is there any important configuration am I missing?
new OkHttpClient.Builder()
.readTimeout(10,TimeUnit.SECONDS)
.retryOnConnectionFailure(false)
.connectTimeOut(5,TimeUnit.SECONDS)
.connectionPool(new ConnectionPool(10,5,TimeUnit.SECONDS)
.build();
A:
What should be the ideal connection pool size and keep Alive for a container environment
Take 256 as a starting point. It's big enough that you'll get a good hit rate and small enough that you won't notice the memory used.
If you hit lots of different hosts frequently you may adjust it up. If you are running on very small containers or have memory sensitivity you may adjust it down.
We dont want to have any client side failures
There's a setting on OkHttpClient.Builder, retryOnConnectionFailure. It's true by default and will handle client-side failures for you. If you did want to handle client-side failures you'd set this to false.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,146
|
Health, Mind and Body
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Challenges to The Second Law of Thermodynamics
By Vladislav Čápek & Daniel P. Sheehan
Release Date - Published: 2006-03-30
Book Genre: Physics
Author: Vladislav Čápek & Daniel P. Sheehan
Our rating: 5/5 stars
Score: (From 0 Ratings)
➲ "Challenges to The Second Law of Thermodynamics" ♫ Challenges to The Second Law of Thermodynamics AudioBook
Challenges to The Second Law of Thermodynamics Vladislav Čápek & Daniel P. Sheehan read online review & book description:
The second law of thermodynamics is considered one of the central laws of science, engineering and technology. For over a century it has been assumed to be inviolable by the scientific community. Over the last 10-20 years, however, more than two dozen challenges to it have appeared in the physical literature - more than during any other period in its 150-year history. The number and variety of these represent a cogent threat to its absolute status. This is the first book to document and critique these modern challenges. Written by two leading exponents of this rapidly emerging field, it covers the theoretical and experimental aspects of principal challenges. In addition, unresolved foundational issues concerning entropy and the second law are explored. This book should be of interest to anyone whose work or research is touched by the second law.
@2019 – Go Read a Book. All Right Reserved. goreadabook.org is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for website owners, to earn advertising fees by linking and advertising to amazon.com and any other website that may be affiliated with Amazon Service LLC Associates Program; As an Amazon Associate I earn from qualifying purchases.
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|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3,122
|
A Lazy Person's Guide to the CBD Products Actually Worth Trying
I went to Europe's biggest CBD expo to test a bunch of samples (and try to push past their placebo effect).
photos by Bekky Lonsdale
July 24, 2019, 8:50am
The author, with a CBD gummy worm
This article originally appeared on VICE UK.
Like air, or pollution, CBD products are everywhere. From coffee to moisturiser to gummy bears, basically if you can swallow, smoke or bathe with it, chances are you can get your favourite thing with some cannabidiol (aka CBD, aka the non-psychoactive ingredient in weed) slathered onto it.
Right now, this swelling industry is so big that it's been called The Next Gold Rush. One study has even predicted it could be worth $20 billion by 2024. And so, where there's money, there are business conferences, which is why, last month, London hosted Europe CBD Expo, the UK's first of its kind, with more than 80 exhibitors. Here's a bit of what it looked like:
The author, at The Hemp Plug's stand (well, on a giant 'gummy', but you get the idea)
A CBD smoothie bar at the expo
But perhaps in order to be taken seriously, and to distance themselves from the negative image of layabout potheads and hippies, the CBD world is keen to stress that CBD has no psychoactive element and will NOT get you high. Repeat: It will NOT get you high! Instead it's there to help with various ailments – including but not limited to, basically everything TBQH with you.
This is all well and good, but personally I refuse to take advice about a cannabis product from people who seem intent on distancing their weed product as much from weed as possible. Still, I headed down to the conference anyway, hoping that in the sea of exhibitors I would be able to find some people who actually like getting stoned and then go from there. First though: some tips.
I called up LA-based stoner and journalist Michelle Lhooq (full disclosure: she used to work for VICE in the US). She's written book Weed: Everything You Want to Know But Are Always Too Stoned to Ask, so I figured she could provide some expert instruction on what to look for. "I would start with addressing why you are taking CBD in the first place," she tells me. "What are you trying to remedy? Is it anxiety? Menstrual pain? Do you want better skin? From there, you'd figure out routes of administration – how you wanna take it basically. There are tinctures – which is CBD oil that you can take sublingually – or you can vape it, which is pretty trendy these days, just for the ease of it."
She also tells me to look for labels that say 'full spectrum', which describes the extraction process. "You want CBD that has trace amounts of THC in it – CBD requires a bit of THC in order to be activated. Some people love to take a super concentrated form of just isolated CBD, and that doesn't work". Other than that, she swears by CBD flower: "it's been cultivated to not have any THC, but it looks and tastes exactly like weed." Yum.
Without further ado, here is a list of everything I tried in a two-hour time period before I felt weird and wanted to go home. Consider it your handy guide to which sort of products really 'work' and which are more about clever marketing.
QUALIA CBD, GUMMIES
This brand does both full spectrum (good) and CBD isolate (absolute nonsense) tinctures. More importantly, they specialise in CBD sweets, popcorn, and honey sticks. Both the sour snakes and the gummy bears were delicious.
But did it work? Each gummy has only 10mg of CBD in them so you'd have to eat a load to feel any health benefits, which will probably be cancelled out by the sugar? I don't know, I'm not a scientist. But also I don't really care, because sweets are good.
THE HEMP PLUG (THP), TINCTURES AND BATH BOMBS
Reassuringly, the guy I spoke to at THP is both a stoner, and a surfer with back problems. He swears by CBD for inflammation of any kind, although points out that that it's a nutraceutical, not a pharmaceutical, and so needs to be taken regularly for a couple of weeks before you feel the benefits, just as you would a supplement. They do their own white-label CBD tinctures in various concentrations for both day and night (with melatonin), depending on what you want to achieve. He was also kind enough to give me a bath bomb to use at home, which I'm excited to use to potentially drown myself in the tub with later.
But did it work? I did not drown in the bath-tub but I did sleep like a baby afterwards, so it's a thumbs up from me.
HOLY LEAF, CBD FLOWER
The holy grail!
But did it work? Well… sadly it was not available to try or purchase at the expo because you can't legally sell CBD flower here yet. Though it is legal to buy it, and you can purchase it via Switzerland or several of the vape shops in London if you so desire. We love arbitrary laws!
CANNIANT… LOADS OF STUFF
These guys had a CBD vending machine (???), CBD coffee pods (bad for the environment!!), and…CBD lubricant, which I will be using until I can get my hands on a competing product, which has THC in it (Foria, CBD lube OGs, if you are reading this……please……).
But did it work? Mind your business.
PRÁSINO, CBD+ SUPERFOOD
This product would be great and potentially life-changing if I ever woke up as the kind of person who bothers to look after themselves (eats breakfast). There are two 'flavour' options available: 'Calm Comfort' and 'Alpha Sport'. We tried some of the former: they'd just added the supplement to yoghurt and berries and mixed it all up, to admittedly tasty effect. One for the health gang.
But did it work? I don't have any scientific basis for this but I feel like this is legit? Plus the supplement had loads of other good stuff in it (chia seeds, blueberry powder, cinnamon) so I feel like it's just generally good for you regardless.
SO, DOES ANY OF THIS WORK?
I mean, it definitely does something, because by 3PM I was feeling really spaced out and ready for a lie-down. Of course, it could be due to a placebo effect; one of the exhibitors I spoke to told me an anecdote about how CBD helped his wife with her insomnia: "It could be a placebo, but whether it's a placebo or not, it worked. It helped her sleep."
Realistically there's enough research at this point to show that weed, and as a byproduct CBD, has healing properties – at least as much you'd expect for anything else plant-based and holistic, that claims health benefits. Like, for example, the fact medical marijuana has been proven to help alleviate chronic pain symptoms and offer therapeutic care. Or that there's strong scientific evidence suggesting CBD can help in treating childhood epilepsy when other anti-seizure medication doesn't work.
Please though, for the love of god don't buy a mango-flavoured vape, because you look like a nerd and it smells gross. Grow up.
@niluthedamaja / @bekkylonsdalephoto
Tagged:CBDExpostonerscannabidiol
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,170
|
\section{Introduction and the Main Results}
The Mittag-Leffler function arises naturally in the solution of fractional order integral equations or fractional order differential equations and especially in the investigations of the fractional generalization of the kinetic equation, random walks, super-diffusive transport and in the study of complex systems. The ordinary and generalized Mittag-Leffler functions interpolate between a purely exponential law and power-law like behavior. The Mittag-Leffler function has been successfully applied in many areas of sciences and engineering. Due to its vast potential of its applications in solving problems on physical, biological, engineering and earth sciences, the Mittag-Leffler function is an important function that finds widespread use in fractional modeling \cite{sergei}. As the exponential function naturally arises in the solution of integer order differential equations, the Mittag-Leffler function plays an analogous role in the solution of non-integer order differential equations. The detailed treatment of Mittag-Leffler functions can be found in \cite{sergei1,gupta,shukla} and in the references therein, see also \cite{ca,fe,ga,le,li} for more details and applications. Geometric properties of Mittag-Leffler functions such as univalence, starlikeness, convexity and close-to-convexity, were established recently in \cite{gonzalez,haubold,bansal}. Special functions have great importance in geometric function theory, and because of this there is an extensive literature dealing with various geometric properties of certain subclasses of analytic univalent functions involving special functions such as Bessel, Struve and Lommel functions of first kind. Baricz and his coauthors investigated in details the determination of the radii of starlikeness and convexity of some normalized forms of these special functions, see for example \cite{baricz, baricz1,baricz2,baricz3,baricz4,baricz5,baricz6,baricz7,baricz8,baricz9} and the references therein for more details. One of the most important things which we have learned in these studies is that the radii of univalence, starlikeness and convexity are obtained as solutions of some transcendental equations and the obtained radii satisfy some interesting inequalities. The positive zeros of special functions and the Laguerre-P\'{o}lya class of real entire functions played an important role in these papers. Motivated by the above series of papers, in this paper our aim is to present some similar results for the generalized three parameter Mittag-Leffler function. For this, three different normalizations are applied in such way that the resulting functions are analytic. By using the Hadamard factorization of the generalized Mittag-Leffler function and combining the methods from \cite{baricz2,baricz1,baricz7,baricz}, we investigate the radii of starlikeness and convexity for each of the three functions. Moreover, we deduce the interlacing properties of the zeros of Mittag-Leffler function and its derivative, and this result is quite useful in the proof of the main results. Furthermore, our aim is also to give some lower and upper bounds for the radii of starlikeness and convexity of order zero by using Euler-Rayleigh inequalities for the smallest positive zeros of some transcendental equations.
\subsection{Characterization of starlike and convex functions}
In order to present our results we need the following basic definitions. Let $\mathbb{D}_{r}$ be the disk $\{z \in \mathbb{C}:|z|<r\},$ where $r>0.$ Moreover, let $\mathcal{A}$ be the class of analytic functions defined in $\mathbb{D}_r,$ which satisfy the normalization conditions $f(0)=f^{\prime}(0)-1=0.$ Denote by $\mathcal{S}$ the class of functions belonging to $\mathcal{A},$ which are univalent in $\mathbb{D}_{r}.$ The class of starlike functions, denoted by $\mathcal{S}^{*},$ is the subclass of $\mathcal{S},$ which consists of functions $f$ for which the domain $f(\mathbb{D}_r)$ is starlike with respect to $0.$ The analytic description of $\mathcal{S}^{*}$ is
$$\mathcal{S}^{*}=\left\{f \in \mathcal{A}:\operatorname{Re} \left(\frac{zf^{\prime}(z)}{f(z)}\right)>0~~ \text{for}~~~ \text{all}~~ z \in \mathbb{D}_r\right\}.$$
Moreover, let $\mathcal{S}^{*}(\rho)$ be the subclass of $\mathcal{S}$ consisting of functions which are starlike of order $\rho$ in $\mathbb{D}_{r},$ where $0\leq \rho <1,$ that is,
$$\mathcal{S}^{*}(\rho)=\left\{f \in \mathcal{A}:\operatorname{Re} \left(\frac{zf^{\prime}(z)}{f(z)}\right)>\rho~~ \text{for}~~~ \text{all}~~ z \in \mathbb{D}_r\right\}.$$
The real numbers
$$r^{*}(f)=\sup \left\{r>0:\operatorname{Re} \left(\frac{zf^{\prime}(z)}{f(z)}\right)>0~~ \text{for}~~~ \text{all}~~ z \in \mathbb{D}_{r}\right\}$$
and
$$r^{*}_{\rho}(f)=\sup \left\{r>0:\operatorname{Re} \left(\frac{zf^{\prime}(z)}{f(z)}\right)>\rho~~ \text{for}~~~ \text{all}~~ z \in \mathbb{D}_{r}\right\}$$
are called the radius of starlikeness and the radius of starlikeness of order $\rho$ of the function $f,$ respectively. We note that $r^{*}(f)=r^{*}_{0}(f)$ is the largest radius such that the image region $f(\mathbb{D}_{r^{*}(f)})$ is a starlike domain with respect to the origin.
The class of convex functions, denoted by $\mathcal{C},$ is the subclass of $\mathcal{S}$ which consists of functions $f$ for which the image domain $f(\mathbb{D}_r)$ is a convex domain. The analytic description of $\mathcal{C}$ is
$$\mathcal{C}=\left\{f \in \mathcal{A}:\operatorname{Re} \left(1+\frac{zf^{\prime\prime}(z)}{f^{\prime}(z)}\right)>0~~ \text{for}~~~ \text{all}~~ z \in \mathbb{D}_r\right\}.$$
Moreover, let $\mathcal{C}(\rho)$ be the subclass of $\mathcal{S}$ consisting of functions which are convex of order $\rho$ in $\mathbb{D}_{r},$ where $0\leq \rho <1,$ that is,
$$\mathcal{C}(\rho)=\left\{f \in \mathcal{A}:\operatorname{Re} \left(1+\frac{zf^{\prime\prime}(z)}{f^{\prime}(z)}\right)>\rho~~ \text{for}~~~ \text{all}~~ z \in \mathbb{D}_r\right\}.$$
The real numbers
$$r^{c}(f)=\sup \left\{r>0:\operatorname{Re} \left(1+\frac{zf^{\prime\prime}(z)}{f^{\prime}(z)}\right)>0~~ \text{for}~~~ \text{all}~~ z \in \mathbb{D}_{r}\right\}$$
and
$$r^{c}_{\rho}(f)=\sup \left\{r>0:\operatorname{Re} \left(1+\frac{zf^{\prime\prime}(z)}{f^{\prime}(z)}\right)>\rho~~ \text{for}~~~ \text{all}~~ z \in \mathbb{D}_{r}\right\}$$
are called the radius of convexity and the radius of convexity of order $\rho$ of the function $f,$ respectively. We note that $r^{c}(f)=r^{c}_{0}(f)$ is the largest radius such that the image region $f(\mathbb{D}_{r^{c}(f)})$ is a convex domain.
\subsection{The Laguerre-P\'olya class of real entire functions}
An entire function is a complex-valued function that is holomorphic over the
whole complex plane. An entire function is called real if it maps the real line into itself. A real entire function $\Omega$ belongs to the Laguerre-P\'{o}lya class $\mathcal{LP}$ if it can be represented in the form $$\Omega(x)=cx^{m}e^{-ax^2+bx}\prod_{n\geq1}\left(1+\frac{x}{x_n}\right)e^{-\frac{x}{x_n}},$$ with $c,b,x_n\in\mathbb{R},$ $a\geq0,$ $m\in\mathbb{N}\cup\{0\}$ and $\sum1/{x_n}^2<\infty.$ We note that the class $\mathcal{LP}$ consists of entire functions which are uniform limits on the compact sets of the complex plane of polynomials with only real zeros. It is important to mention that that $\mathcal{LP}$ is closed under differentiation, that is, if $\Omega\in\mathcal{LP},$ then $\Omega^{(m)}\in\mathcal{LP}$ for each $m\in\{2,3,\dots\}.$
\subsection{The three parameter generalization of the Mittag-Leffler function}
Now, let us consider the function $\phi(\alpha,z)$ defined by
\begin{equation}
\label{radd1}
\phi(\alpha,z)=\sum_{n\geq 0}\frac{z^{n}}{\Gamma(\alpha n+1)},
\end{equation}
where $\Gamma$ denotes the Euler gamma function. This function was introduced by Mittag-Leffler in 1903 and therefore it is known as the Mittag-Leffler function.
Another function having similar properties was introduced later by Wiman \cite{wiman} and it is defined by the following series
\begin{equation}\label{radd2}
\phi(\alpha,\beta,z)=\sum_{n\geq 0} \frac{z^{n}}{\Gamma(\alpha n+\beta)}.
\end{equation}
In 1971 Prabhakar \cite{prabhakar} introduced the three parameter function $\phi(\alpha,\beta,\gamma,z)$ in the form of
\begin{equation}\label{radd3}
\phi(\alpha,\beta,\gamma,z)=\sum_{n \geq 0}\frac{(\gamma)_{n}z^{n}}{n!\Gamma(\alpha n+\beta)},
\end{equation}
where $(\gamma)_{n}$ denotes the Pochhammer symbol (or shifted factorial) given in terms of the gamma function by $(a)_n=\Gamma(a+n)/\Gamma(a).$
Some particular cases of $\phi(\alpha,\beta,\gamma,z)$ are
\begin{gather*}
\phi(1,1,1,z)=e^{z}, \qquad
\phi(1,1,2,z)=e^{z}(z+1),\\
\phi(2,1,1,z)=\cosh(\sqrt{z}), \qquad \phi(2,1,2,z)=\cosh(\sqrt{z})+\frac{1}{2}\sqrt{z}\sinh(\sqrt{z}),\\
\phi(2,2,1,z)=\frac{1}{\sqrt{z}}\sinh(\sqrt{z}),\qquad \phi(2,2,2,z)=\frac{1}{2z}(\sqrt{z}\sinh(\sqrt{z})+z\cosh(\sqrt{z})),\\
\phi(2,3,1,z)=\frac{1}{z}\left(\cosh(\sqrt{z})-1 \right),\qquad \phi(2,4,1,z)=\frac{1}{z}\left(\frac{\sinh(\sqrt{z})}{\sqrt{z}}-1 \right).
\end{gather*}
\subsection{A preliminary result on the Mittag-Leffler function}
To state our first preliminary result, we define the following three transformations mapping the set
$$\left\{\left(\frac{1}{\alpha},\beta\right):\alpha>1,\beta>0\right\}$$ into itself:
$$A:\left(\frac{1}{\alpha},\beta\right)\to \left(\frac{1}{2\alpha},\beta\right), \ \ \ B:\left(\frac{1}{\alpha},\beta\right)\to \left(\frac{1}{2\alpha},\alpha+\beta\right),$$
$$C:\left(\frac{1}{\alpha},\beta\right)\to \left\{\begin{array}{ll}\displaystyle\left(\frac{1}{\alpha},\beta-1\right),&\mbox{if}\ \ \beta>1\\ \\ \displaystyle\left(\frac{1}{\alpha},\beta\right),&\mbox{if}\ \ 0<\beta\leq1\end{array}\right..$$
We put $W_b=A(W_a)\cup B(W_a),$ where
$$W_a=\left\{\left(\frac{1}{\alpha},\beta\right):1<\alpha<2,\beta\in[\alpha-1,1]\cup[\alpha,2]\right\},$$
and we denote by $W_i$ the smallest set containing $W_b$ and invariant with respect to $A,$ $B$ and $C,$ that is, if $(a,b)\in W_i,$ then
$A(a,b),$ $B(a,b),$ $C(a,b)\in W_i.$ By using a result of Peresyolkova \cite{peres}, Kumar and Pathan \cite{kumar} recently proved that if
$\left(\frac{1}{\alpha},\beta\right)\in W_i$ and $\gamma>0,$ then all zeros of the generalized Mittag-Leffler function $\phi(\alpha,\beta,\gamma,z)$ are real and negative. It is worth mentioning that
the reality of the zeros as well as their distribution in the case of $\gamma=1,$ that is of Wiman's extension $\phi(\alpha,\beta,z),$ has a rich literature. For more details see for example the papers of Dzhrbashyan \cite{dzhr}, Ostrovski\u{i} and Peresyolkova \cite{ostrov}, Popov and Sedletskii \cite{sedlet}.
The following lemma, which may be of independent interest, plays an important role in the proof of our main results.
\begin{lemma}\label{lemma}
If $\left(\frac{1}{\alpha},\beta\right)\in W_i$ and $\gamma>0,$ then the function $z \mapsto \phi(\alpha,\beta,\gamma,-z^{2})$ has infinitely many zeros which are all real. Denoting by $\lambda_{\alpha,\beta,\gamma,n}$ the $n$th positive zero of $z\mapsto\phi(\alpha,\beta,\gamma,-z^{2}),$ under the same conditions the Weierstrassian decomposition
$$\phi(\alpha,\beta,\gamma,-z^{2})=\frac{1}{\Gamma(\beta)} \prod_{n\geq 1}\left(1-\frac{z^{2}}{\lambda_{\alpha,\beta,\gamma,n}^{2}}\right)$$
is valid. Moreover, if $\xi_{\alpha,\beta,\gamma,n}$ denotes the $n$th positive zero of $\Psi'(\alpha,\beta,\gamma,z),$ where $\Psi(\alpha,\beta,\gamma,z)=z^{\beta}\phi(\alpha,\beta,\gamma,-z^{2}),$ then the positive zeros $\lambda_{\alpha,\beta,\gamma,n}$ and $\xi_{\alpha,\beta,\gamma,n}$ are interlaced.
\end{lemma}
Observe that the function $z \mapsto \phi(\alpha,\beta,\gamma,-z^{2})$ does not belong to $\mathcal{A}.$ Thus first we perform some natural normalization. We define three functions originating from $\phi(\alpha,\beta,\gamma,z)$ as follows:
$$f_{\alpha,\beta,\gamma}(z)=\left(z^{\beta}\Gamma(\beta)\phi(\alpha,\beta,\gamma,-z^{2})\right)^{1/\beta},$$
$$g_{\alpha,\beta,\gamma}(z)=z\Gamma(\beta)\phi(\alpha,\beta,\gamma,-z^{2}),$$
$$h_{\alpha,\beta,\gamma}(z)=z\Gamma(\beta)\phi(\alpha,\beta,\gamma,-z).$$
Obviously these functions belong to the class $\mathcal{A}.$ Of course, there exist infinitely many other normalizations. The main motivation to consider the above ones is that they are similar to the frequently studied normalizations in the literature of Bessel, $q$-Bessel, Struve, Lommel and Wright functions.
\subsection{Radii of starlikeness of the generalized Mittag-Leffler functions}
Now, our aim is to investigate the radii of starlikeness of the normalized forms of the generalized three parameter Mittag-Leffler function, that is of $f_{\alpha,\beta,\gamma},$ $g_{\alpha,\beta,\gamma}$ and $h_{\alpha,\beta,\gamma}.$ Our aim is to show that the radii of starlikeness of order $\rho$ of the generalized three parameter Mittag-Leffler functions are actually solutions of some transcendental equations. Moreover, we will also find some lower and upper bounds for the radii of starlikeness of order zero. Throughout of this paper for simplicity we use the notation $\lambda(\alpha,\beta,\gamma,z)=\phi(\alpha,\beta,\gamma,-z^2).$ The technique of determining the radii of starlikeness in the next theorem follows the ideas from \cite{baricz3}, \cite{baricz1} and \cite{baricz2}. The results of the next theorem are natural extensions of some recent results (see \cite{prajapat}, where the special case of $\gamma=1$ was considered) on the Mittag-Leffler function in \eqref{radd2}.
\begin{theorem}\label{theorem1}
Let $\left(\frac{1}{\alpha},\beta\right)\in W_i,$ $\gamma>0$ and $\rho \in [0,1).$
\begin{enumerate}
\item[\bf a.] The radius of starlikeness of order $\rho$ of $f_{\alpha,\beta,\gamma}$ is $r^{*}_{\rho}(f_{\alpha,\beta,\gamma})=x_{\alpha,\beta,\gamma,1},$ where $x_{\alpha,\beta,\gamma,1}$ is the smallest positive zero of the transcendental equation
$$r\lambda'(\alpha,\beta,\gamma,r)-\beta (\rho-1)\lambda(\alpha,\beta,\gamma,r)=0.$$
\item[\bf b.] The radius of starlikeness of order $\rho$ of $g_{\alpha,\beta,\gamma}$ is $r^{*}_{\rho}(g_{\alpha,\beta,\gamma})=y_{\alpha,\beta,\gamma,1},$ where $y_{\alpha,\beta,\gamma,1}$ is the smallest positive zero of the transcendental equation
$$r\lambda'(\alpha,\beta,\gamma,r)- (\rho-1)\lambda(\alpha,\beta,\gamma,r)=0.$$
\item[\bf c.] The radius of starlikeness of order $\rho$ of $h_{\alpha,\beta,\gamma}$ is $r^{*}_{\rho}(h_{\alpha,\beta,\gamma})=z_{\alpha,\beta,\gamma,1},$ where $z_{\alpha,\beta,\gamma,1}$ is the smallest positive zero of the transcendental equation
$$\sqrt{r}\lambda'(\alpha,\beta,\gamma,\sqrt{r})-2(\rho-1)\lambda(\alpha,\beta,\gamma,\sqrt{r})=0.$$
\end{enumerate}
\end{theorem}
The following theorem provides some tight lower and upper bounds for the radii of starlikeness of the functions considered in the above theorem.
The technique used in the proof of this theorem follows the ideas from \cite{baricz4} and \cite{baricz5}, and the main idea is to deduce some Euler-Rayleigh inequalities for the first positive zero of some entire functions, which are connected with the transcendental equations in the above theorem. We mention that it is possible to get more sharp results in the next theorem by using higher order Euler-Rayleigh inequalities for $k\in\{2,3,\dots\},$ however we omitted them due to their complicated form.
\begin{theorem}\label{theorem2}
Let $\left(\frac{1}{\alpha},\beta\right)\in W_i$ and $\gamma>0.$
\begin{enumerate}
\item[\bf a.] The radius of starlikeness $r^{*}(f_{\alpha,\beta,\gamma})$ satisfies the inequalities
$$\frac{\gamma(\beta+2)\Gamma(\beta)}{\beta\Gamma(\alpha+\beta)}-\frac{(\gamma+1)(\beta+4)\Gamma(\alpha+\beta)}{(\beta+2)\Gamma(2\alpha+\beta)}
<{\left(r^{*}(f_{\alpha,\beta,\gamma})\right)^{-2}}<\frac{\gamma(\beta+2)\Gamma(\beta)}{\beta\Gamma(\alpha+\beta)}.$$
\item[\bf b.] The radius of starlikeness $r^{*}(g_{\alpha,\beta,\gamma})$ satisfies the inequalities
$$\frac{3\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}-\frac{5(\gamma+1)\Gamma(\alpha+\beta)}{3\Gamma(2\alpha+\beta)}<
\left(r^{*}(g_{\alpha,\beta,\gamma})\right)^{-2}<\frac{3\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}.$$
\item[\bf c.] The radius of starlikeness $r^{*}(h_{\alpha,\beta,\gamma})$ satisfies the inequalities
$$\frac{2\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}-\frac{3(\gamma+1)\Gamma(\alpha+\beta)}{2\Gamma(2\alpha+\beta)}<
\left(r^{*}(h_{\alpha,\beta,\gamma})\right)^{-1}<\frac{2\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}.$$
\end{enumerate}
\end{theorem}
\subsection{Radii of convexity of the generalized Mittag-Leffler functions}
Now, we are going to investigate the radii of convexity of order $\rho$ of the functions $f_{\alpha,\beta,\gamma},$ $g_{\alpha,\beta,\gamma}$ and $h_{\alpha,\beta,\gamma}.$ In addition, we find tight lower and upper bounds for the radii of convexity of order zero for the functions $g_{\alpha,\beta,\gamma}$ and $h_{\alpha,\beta,\gamma}.$ The technique used in the process of finding the radii of convexity in the next theorem is based on the ideas from \cite{baricz7} and \cite{baricz8}.
\begin{theorem}\label{theorem4}
Let $\left(\frac{1}{\alpha},\beta\right)\in W_i,$ $\gamma>0$ and $\rho \in [0,1).$
\begin{enumerate}
\item[\bf a.] The radius of convexity $r_{\rho}^c(f_{\alpha,\beta,\gamma})$ is the smallest positive root of the transcendental equation $(rf_{\alpha,\beta,\gamma}(r))'=\rho f'_{\alpha,\beta,\gamma}(r).$
\item[\bf b.] The radius of convexity $r_{\rho}^c(g_{\alpha,\beta,\gamma})$ is the smallest positive root of the transcendental equation $(rg_{\alpha,\beta,\gamma}(r))'=\rho g'_{\alpha,\beta,\gamma}(r).$
\item[\bf c.] The radius of convexity $r_{\rho}^c(h_{\alpha,\beta,\gamma})$ is the smallest positive root of the transcendental equation $(rh_{\alpha,\beta,\gamma}(r))'=\rho h'_{\alpha,\beta,\gamma}(r).$
\end{enumerate}
\end{theorem}
Finally, we present some lower and upper bounds for the radii of convexity of the functions $g_{\alpha,\beta,\gamma}$ and $h_{\alpha,\beta,\gamma}$ by using the corresponding Euler-Rayleigh inequalities.
\begin{theorem}\label{theorem5}
Let $\left(\frac{1}{\alpha},\beta\right)\in W_i$ and $\gamma>0.$
\begin{enumerate}
\item[\bf a.] The radius of convexity $r^{c}(g_{\alpha,\beta,\gamma})$ satisfies the inequalities
$$\frac{9\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}-\frac{25(\gamma+1)\Gamma(\alpha+\beta)}{9\Gamma(2\alpha+\beta)}<
\left(r^{c}(g_{\alpha,\beta,\gamma})\right)^{-2}<\frac{9\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}.$$
\item[\bf b.] The radius of convexity $r^{c}(h_{\alpha,\beta,\gamma})$ satisfies the inequalities
$$\frac{4\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}-\frac{9(\gamma+1)\Gamma(\alpha+\beta)}{4\Gamma(2\alpha+\beta)}<
\left(r^{c}(h_{\alpha,\beta,\gamma})\right)^{-1}<\frac{4\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}.$$
\end{enumerate}
\end{theorem}
\section{Proofs of the main results}
\setcounter{equation}{0}
\begin{proof}[\bf Proof of Lemma \ref{lemma}]
Recall that Kumar and Pathan \cite{kumar} recently proved that if
$\left(\frac{1}{\alpha},\beta\right)\in W_i$ and $\gamma>0,$ then all zeros of the generalized Mittag-Leffler function $z\mapsto\phi(\alpha,\beta,\gamma,z)$ are real and negative. Moreover, it is well known that $z\mapsto\phi(\alpha,\beta,\gamma,z)$ is an entire function of order $1/\alpha$ (see \cite{sergei1}), and this is a non-integer number and lies in $(0,1)$ if $\left(\frac{1}{\alpha},\beta\right)\in W_i.$ It follows that the generalized Mittag-Leffler function has infinitely many zeros, which are all real, and its infinite product exists. Now, from the infinite product representation we get
\begin{equation}\label{deriv1}
\frac{\Psi'(\alpha,\beta,\gamma,z)}{\Psi(\alpha,\beta,\gamma,z)}=\frac{\beta}{z}+\frac{\lambda'(\alpha,\beta,\gamma,z)}{\lambda(\alpha,\beta,\gamma,z)}=\frac{\beta}{z}+\sum_{n \geq 1}\frac{2z}{z^{2}-\lambda^{2}_{\alpha,\beta,\gamma,n}}.
\end{equation}
Differentiating both sides of \eqref{deriv1}, we have
\begin{equation*}
\frac{d}{dz}\left(\frac{\Psi'(\alpha,\beta,\gamma,z)}{\Psi(\alpha,\beta,\gamma,z)}\right)=-\frac{\beta}{z^{2}}-2\sum_{n \geq 1}\frac{z^{2}+\lambda^{2}_{\alpha,\beta,\gamma,n}}{(z^{2}-\lambda^{2}_{\alpha,\beta,\gamma,n})^{2}},\quad z \neq \lambda_{\alpha,\beta,\gamma,n}.
\end{equation*}
The right hand side of the above expression is real and negative for each $z$ real, $\left(\frac{1}{\alpha},\beta\right)\in W_i$ and $\gamma>0.$ Thus, the quotient on the left side of \eqref{deriv1} is a strictly decreasing function from $+\infty$ to $-\infty$ as $z$ increases through real values over the open interval $(\lambda_{\alpha,\beta,\gamma,n}, \lambda_{\alpha,\beta,\gamma,n+1}),$ $n \in \mathbb{N}.$ Hence the function $z\mapsto\Psi'(\alpha,\beta,\gamma,z)$ vanishes just once between two consecutive zeros of the function $z\mapsto\lambda(\alpha,\beta,\gamma,z).$
\end{proof}
\begin{proof}[\bf Proof of Theorem \ref{theorem1}]
We need to show that the inequalities
\begin{equation}\label{rad1}
\operatorname{Re} \left(\frac{zf^{\prime}(z)}{f(z)}\right) \geq \rho,\qquad \operatorname{Re} \left(\frac{zg^{\prime}(z)}{g(z)}\right) \geq \rho \qquad \mbox{and} \qquad \operatorname{Re} \left(\frac{zh^{\prime}(z)}{h(z)}\right) \geq \rho
\end{equation}
are valid for $z \in \mathbb{D}_{r^{*}_{\rho}(f_{\alpha, \beta,\gamma})},$ $z \in \mathbb{D}_{r^{*}_{\rho}(g_{\alpha, \beta,\gamma})}$
and $z \in \mathbb{D}_{r^{*}_{\rho}(h_{\alpha, \beta,\gamma})},$ respectively, and each of the above inequalities does not hold in any larger disk. Recall that under the corresponding conditions the zeros of the Mittag-Leffler function $\phi(\alpha,\beta,\gamma,z)$ are all real. Thus, according to Lemma \ref{lemma} the Mittag-Leffler function admits the Weierstrassian decomposition of the form
$$\phi(\alpha,\beta,\gamma,-z^{2})=\frac{1}{\Gamma(\beta)} \prod_{n\geq 1}\left(1-\frac{z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}}\right)$$
and this infinite product is uniformly convergent on each compact subset of $\mathbb{C}.$ Denoting, as above, the above expression by $\lambda(\alpha,\beta,\gamma,z),$ and by logarithmic differentiation we get
\begin{equation*}
\frac{\lambda'(\alpha,\beta,\gamma,z)}{\lambda(\alpha,\beta,\gamma,z)}=\sum _{n \geq 1}\frac{-2z}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z^{2}},
\end{equation*}
which in turn implies that
$$\frac{zf^{\prime}_{\alpha,\beta,\gamma}(z)}{f_{\alpha,\beta,\gamma}(z)}=1-\frac{1}{\beta}\sum _{n \geq 1}\frac{2z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z^{2}}, \ \ \
\frac{zg^{\prime}_{\alpha,\beta,\gamma}(z)}{g_{\alpha,\beta,\gamma}(z)}=1-\sum _{n \geq 1}\frac{2z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z^{2}}$$ and
$$\frac{zh^{\prime}_{\alpha,\beta,\gamma}(z)}{h_{\alpha,\beta,\gamma}(z)}=1-\sum _{n \geq 1}\frac{z}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z}.$$
We know that \cite{baricz2} if $z \in \mathbb{C}$ and $\theta \in \mathbb{R}$ are such that $\theta > |z|,$ then
\begin{equation}\label{cov}
\frac{|z|}{\theta-|z|} \geq \operatorname{Re} \left(\frac{z}{\theta-z}\right).
\end{equation}
Thus the inequality
\begin{equation*}
\frac{|z|^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-|z|^{2}} \geq \operatorname{Re} \left(\frac{z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z^{2}}\right),
\end{equation*}
is valid for every $\left(\frac{1}{\alpha},\beta\right)\in W_i,$ $\gamma>0,$ $n \in \mathbb{N}$ and $|z|< \lambda_{\alpha,\beta,\gamma,1},$ and therefore
under the same conditions we have that
$$
\operatorname{Re} \left(\frac{zf^{\prime}_{\alpha,\beta,\gamma}(z)}{f_{\alpha,\beta,\gamma}(z)}\right)=1-\frac{1}{\beta}\operatorname{Re} \left(\sum _{n \geq 1}\frac{2z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z^{2}}\right)\geq 1-\frac{1}{\beta}\sum _{n \geq 1}\frac{2|z|^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-|z|^{2}}=\frac{|z|f^{\prime}_{\alpha,\beta,\gamma}(|z|)}{f_{\alpha,\beta,\gamma}(|z|)},
$$
$$
\operatorname{Re} \left(\frac{zg^{\prime}_{\alpha,\beta,\gamma}(z)}{g_{\alpha,\beta,\gamma}(z)}\right)=1-\operatorname{Re} \left(\sum _{n \geq 1}\frac{2z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z^{2}}\right)\geq 1-\sum _{n \geq 1}\frac{2|z|^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-|z|^{2}}=\frac{|z|g^{\prime}_{\alpha,\beta,\gamma}(|z|)}{g_{\alpha,\beta,\gamma}(|z|)}
$$
and
$$
\operatorname{Re} \left(\frac{zh^{\prime}_{\alpha,\beta,\gamma}(z)}{h_{\alpha,\beta,\gamma}(z)}\right)=1-\operatorname{Re} \left(\sum _{n \geq 1}\frac{z}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z}\right)\geq 1-\sum _{n \geq 1}\frac{|z|}{\lambda^{2}_{\alpha,\beta,\gamma,n}-|z|}=\frac{|z|h^{\prime}_{\alpha,\beta,\gamma}(|z|)}{h_{\alpha,\beta,\gamma}(|z|)},
$$
where equalities are attained only when $z=|z|=r.$ The minimum principle for harmonic functions and the previous inequalities imply that the corresponding inequalities in \eqref{rad1} are valid if and only if we have $|z|<x_{\alpha,\beta,\gamma,1},$ $|z|< y_{\alpha,\beta,\gamma,1}$ and $|z|< z_{\alpha,\beta,\gamma,1},$ respectively, where $x_{\alpha,\beta,\gamma,1},$ $y_{\alpha,\beta.\gamma,1}$ and $z_{\alpha,\beta,\gamma,1}$ are the smallest positive roots of the following equations
\begin{equation*}
\frac{rf^{\prime}_{\alpha,\beta,\gamma}(r)}{f_{\alpha,\beta,\gamma}(r)}=\rho, \quad \frac{rg^{\prime}_{\alpha,\beta,\gamma}(r)}{g_{\alpha,\beta,\gamma}(r)}=\rho \quad \mbox{and} \quad \frac{rh^{\prime}_{\alpha,\beta,\gamma}(r)}{h_{\alpha,\beta,\gamma}(r)}=\rho,
\end{equation*}
which are equivalent to $$r\lambda'(\alpha,\beta,\gamma,r)-\beta(\rho-1)\lambda(\alpha,\beta,\gamma,r)=0, \ \ r\lambda'(\alpha,\beta,\gamma,r)- (\rho-1)\lambda(\alpha,\beta,\gamma,r)=0$$
and
$$\sqrt{r}\lambda'(\alpha,\beta,\gamma,\sqrt{r})-2(\rho-1)\lambda(\alpha,\beta,\gamma,\sqrt{r})=0.$$
\end{proof}
\begin{proof}[\bf Proof of Theorem \ref{theorem2}]
{\bf a.} The radius of starlikeness of the normalized Mittag-Leffler function $f_{\alpha,\beta,\gamma}$ corresponds to the radius of starlikeness of the function $\Psi(\alpha,\beta,\gamma,z)=z^{\beta}\lambda(\alpha,\beta,\gamma,z).$ The infinite series representation of the function $z\mapsto\Psi'(\alpha,\beta,\gamma,z)$ and its derivative are as follows:
\begin{equation}\label{rad4}
\Psi'(\alpha,\beta,\gamma,z)=\sum_{n \geq 0} \frac{(-1)^{n}(\gamma)_{n}(2n+\beta)z^{2n+\beta-1}}{n! \Gamma(\alpha n +\beta)},
\end{equation}
\begin{equation}\label{rad5}
\Psi''(\alpha,\beta,\gamma,z)=\sum_{n \geq 0} \frac{(-1)^{n}(\gamma)_{n}(2n+\beta)(2n+\beta-1)z^{2n+\beta-2}}{n!\Gamma(\alpha n +\beta)}.
\end{equation}
In view of Lemma \ref{lemma}, the function $z\mapsto \Psi(\alpha,\beta,\gamma,z)$ belongs to the Laguerre-P\'olya class $\mathcal{LP}.$ This class of functions is closed under differentiation, and therefore $z\mapsto \Psi'(\alpha,\beta,\gamma,z)$ belongs also to the Laguerre-P\'{o}lya class $\mathcal{LP}.$ Hence the zeros of the function $z\mapsto \Psi'(\alpha,\beta,\gamma,z)$ are all real, and in fact according to Lemma \ref{lemma} they are interlaced with the zeros of $z\mapsto \Psi(\alpha,\beta,\gamma,z).$ Thus, $\Psi'(\alpha,\beta,\gamma,z)$ can be written as
\begin{equation}\label{rad6}
\Psi'(\alpha,\beta,\gamma,z)=\frac{\beta}{\Gamma(\beta)}z^{\beta-1}\prod_{n \geq 1} \left(1-\frac{z^{2}}{\xi^{2}_{\alpha,\beta,\gamma,n}}\right).
\end{equation}
Logarithmic differentiation of both sides of \eqref{rad6} for $|z|<\xi_{\alpha,\beta,\gamma,1}$ gives
\begin{align}\label{rad7}
\frac{z\Psi''(\alpha,\beta,\gamma,z)}{\Psi'(\alpha,\beta,\gamma,z)}-(\beta-1)&=\sum_{n \geq 1} \frac{-2z^{2}}{\xi^{2}_{\alpha,\beta,\gamma,n}-z^{2}}=-2\sum_{n \geq 1} \sum_{k \geq 0} \frac{z^{2k+2}}{\xi^{2k+2}_{\alpha,\beta,\gamma,n}}\\&=-2\sum_{k \geq 0} \sum_{n \geq 1} \frac{z^{2k+2}}{\xi^{2k+2}_{\alpha,\beta,\gamma,n}}=-2\sum_{k \geq 0}\chi_{k+1}z^{2k+2},\nonumber
\end{align}
where $\chi_{k}=\sum_{n \geq 1}\xi^{-2k}_{\alpha,\beta,\gamma,n}.$ On the other hand, by using \eqref{rad4} and \eqref{rad5} we get
\begin{equation}\label{rad8}
\frac{z\Psi''(\alpha,\beta,\gamma,z)}{\Psi'(\alpha,\beta,\gamma,z)}=\left.\sum_{n\geq 0}a_{n}z^{2n}\right/\sum_{n \geq 0}b_{n}z^{2n},
\end{equation}
where $$a_{n}=\frac{(-1)^{n}(\gamma)_{n}(2n+\beta)(2n+\beta-1)}{n!\Gamma(\alpha n+\beta)}\ \ \ \mbox{and}\ \ \ b_{n}=\frac{(-1)^{n}(\gamma)_{n}(2n+\beta)}{n!\Gamma(\alpha n+\beta)}.$$
By comparing the coefficients of \eqref{rad7} and \eqref{rad8} we have
$$(\beta-1)b_{0}=a_{0},\ \ (\beta-1)b_{1}-2\chi_{1}a_{0}=a_{1},\ \ (\beta-1)b_{2}-2\chi_{1}b_{1}-2\chi_{2}b_{0}=a_{2},$$
which implies that
$$\chi_{1}=\frac{\gamma(\beta+2) \Gamma(\beta)}{\beta \Gamma(\alpha+\beta)},\ \ \chi_{2}=\frac{\gamma^{2}(\beta+2)^{2}\Gamma^{2}(\beta)}{\beta^{2}\Gamma^{2}(\alpha+\beta)}-\frac{\gamma(\gamma+1)(\beta+4)\Gamma(\beta)}{\beta
\Gamma(2\alpha+\beta)}.$$
By using the Euler-Rayleigh inequalities $$\chi_{k}^{-1/k}< \xi^{2}_{\alpha,\beta,\gamma,1}<\frac{\chi_{k}}{\chi_{k+1}}$$ for $k=1$ we have the inequalities of the first part of the theorem.
{\bf b.} If $\rho=0$ in the second part of Theorem \ref{theorem1}, then we have that the radius of starlikeness of order zero of the function $g_{\alpha,\beta,\gamma}$ is the smallest positive root of the equation $(z\lambda(\alpha,\beta,\gamma,z))'=0.$ Therefore, it is of interest to study the first positive zero of
\begin{equation}\label{rad9}
\omega(\alpha,\beta,\gamma,z)=(z\lambda(\alpha,\beta,\gamma,z))'=\sum_{n \geq 0}\frac{(-1)^{n}(2n+1)(\gamma)_{n}z^{2n}}{n!\Gamma(\alpha n+\beta)}.
\end{equation}
We know that the function $z\mapsto \lambda(\alpha,\beta,\gamma,z)$ belongs to the Laguerre-P\'{o}lya class $\mathcal{LP},$ which is closed under differentiation. Therefore, we get that the function $z\mapsto \omega(\alpha,\beta,\gamma,z)$ belongs to the Laguerre-P\'{o}lya class, and hence all its zeros are real. Suppose that $\zeta_{\alpha,\beta,\gamma,n}$ is the $n$th positive zero $z\mapsto \omega(\alpha,\beta,\gamma,z)$. Then the function $z\mapsto\omega(\alpha,\beta,\gamma,z)$ has the following infinite product representation
\begin{equation}\label{rad10}
\omega(\alpha,\beta,\gamma,z)=\frac{1}{\Gamma(\beta)}\prod_{n \geq 1}\left(1-\frac{z^{2}}{\zeta^{2}_{\alpha,\beta,\gamma,n}}\right),
\end{equation}
since its growth order corresponds to the growth order of the generalized Mittag-Leffler function itself. If we take the logarithmic derivative of both sides of \eqref{rad10}, for $|z|<\zeta_{\alpha,\beta,\gamma,1}$ we have
\begin{equation}\label{rad11}
\frac{\omega'(\alpha,\beta,\gamma,z)}{\omega(\alpha,\beta,\gamma,z)}=\sum_{n\geq1}\frac{-2z}{\zeta_{\alpha,\beta,\gamma,n}^2-z^2}=
\sum_{n\geq1}\sum_{k\geq0}\frac{-2z^{2k+1}}{\zeta_{\alpha,\beta,\gamma,n}^{2k+2}}=\sum_{k\geq0}\sum_{n\geq1}\frac{-2z^{2k+1}}{\zeta_{\alpha,\beta,\gamma,n}^{2k+2}}
=-2 \sum_{k \geq 0}\delta_{k+1}z^{2k+1},
\end{equation}
where $\delta_{k}=\sum_{n \geq 1}\zeta^{-2k}_{\alpha,\beta,\gamma,n}.$ Moreover in view of \eqref{rad9}, we have
\begin{equation}\label{rad12}
\frac{\omega'(\alpha,\beta,\gamma,z)}{\omega(\alpha,\beta,\gamma,z)}=-2\left.\sum_{n \geq 0}c_{n}z^{2n+1}\right/\sum_{n \geq 0}d_{n}z^{2n},
\end{equation}
where $$c_{n}=\frac{(-1)^{n}(2n+3)(\gamma)_{n+1}}{n!\Gamma(\alpha n+\alpha +\beta)} \ \ \ \mbox{and}\ \ \
d_{n}=\frac{(-1)^{n}(\gamma)_{n}(2n+1)}{n! \Gamma(\alpha n+\beta)}.$$
Comparing the coefficients in \eqref{rad11} and \eqref{rad12} we have that $\delta_{1}d_{0}=c_{0}$ and
$\delta_{2}d_{0}+\delta_{1}d_{1}=c_{1},$ which yields the following Rayleigh sums
$$\delta_{1}=\frac{3\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)} \ \ \ \mbox{and}\ \ \ \delta_{2}=\frac{9\gamma^2 \Gamma^{2}(\beta)}{\Gamma^{2}(\alpha+\beta)}-\frac{5\gamma(\gamma+1)\Gamma(\beta)}{\Gamma(2\alpha+\beta)}.$$
By using the Euler-Rayleigh inequalities $$\delta_{k}^{-1/k}< \zeta^{2}_{\alpha,\beta,\gamma,1}<\frac{\delta_{k}}{\delta_{k+1}}$$
for $k=1$ we obtain the inequalities of the second part of the theorem.
{\bf c.} Taking $\delta=0$ in the third part of Theorem \ref{theorem1} we obtain that the radius of starlikeness of order zero of the function $h_{\alpha,\beta,\gamma}$ is the smallest positive root of the equation $(z\lambda(\alpha,\beta,\gamma,\sqrt{z}))^{\prime}=0.$ Therefore, it is of interest to study the first positive zero of
\begin{equation}\label{rad13}
\sigma(\alpha,\beta,\gamma,z)=(z\lambda(\alpha,\beta,\gamma,\sqrt{z}))^{\prime}=\sum_{n \geq 0}\frac{(-1)^{n}(\gamma)_{n}(n+1)z^{n}}{ n!\Gamma(\alpha n+\beta)}.
\end{equation}
We know that the function $z\mapsto \lambda(\alpha,\beta,\gamma,z)$ belongs to the Laguerre-P\'{o}lya class $\mathcal{LP},$ and consequently we get that the function $z\mapsto\sigma(\alpha,\beta,\gamma,z)$ belongs also to the Laguerre-P\'{o}lya class. Hence the zeros of the function $z\mapsto \sigma(\alpha,\beta,\gamma,z)$ are all real. Let $\eta_{\alpha,\beta,\gamma,n}$ be the $n$th positive zero of the function $z\mapsto \sigma(\alpha,\beta,\gamma,z)$. Then the next infinite product representation is valid
\begin{equation}\label{rad14}
\sigma(\alpha,\beta,\gamma,z)=\frac{1}{\Gamma(\beta)}\prod_{n \geq 1}\left(1-\frac{z}{\eta_{\alpha,\beta
,\gamma,n}}\right).
\end{equation}
This is in agreement with the fact that according to Kumar and Pathan \cite{kumar} if
$\left(\frac{1}{\alpha},\beta\right)\in W_i$ and $\gamma>0,$ then all zeros of the generalized Mittag-Leffler function $z\mapsto \phi(\alpha,\beta,\gamma,z)$ are real and negative, and consequently all zeros of $z\mapsto \lambda(\alpha,\beta,\gamma,\sqrt{z})$ and then of $z\mapsto \sigma(\alpha,\beta,\gamma,z)$ are all real and positive.
Logarithmic differentiation of both sides of \eqref{rad14} for $|z|<\eta_{\alpha,\beta,\gamma,1}$ gives
\begin{equation}\label{rad15}
\frac{\sigma'(\alpha,\beta,\gamma,z)}{\sigma(\alpha,\beta,\gamma,z)}=-\sum_{n\geq1}\frac{1}{\eta_{\alpha,\beta,\gamma,n}-z}
=-\sum_{n\geq1}\sum_{k\geq0}\frac{z^k}{\eta^{k+1}_{\alpha,\beta,\gamma,n}}=-\sum_{k\geq0}\sum_{n\geq1}\frac{z^k}{\eta^{k+1}_{\alpha,\beta,\gamma,n}}
=-\sum_{k \geq 0}\theta_{k+1}z^{k},
\end{equation}
where $\theta_{k}=\sum_{n \geq 1}\eta^{-k}_{\alpha,\beta,\gamma,n}.$ On the other hand, logarithmic differentiation of both sides of \eqref{rad13} gives
\begin{equation}\label{rad16}
\frac{\sigma'(\alpha,\beta,\gamma,z)}{\sigma(\alpha,\beta,\gamma,z)}=-\left.\sum_{n \geq 0}u_{n}z^{n}\right/\sum_{n \geq 0}v_{n}z^{n},
\end{equation}
where $$u_{n}=\frac{(-1)^{n}(n+2)(\gamma)_{n+1}}{n!\Gamma(\alpha n+\alpha+\beta)} \ \ \ \mbox{and}\ \ \ v_{n}=\frac{(-1)^{n}(n+1)(\gamma)_{n}}{n!\Gamma(\alpha n+\beta)}.$$
By comparing the coefficients of \eqref{rad15} and \eqref{rad16}, we get the following Rayleigh sums
$$\theta_{1}=\frac{2\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}\ \ \ \mbox{and}\ \ \ \theta_{2}=\frac{4\gamma^2\Gamma^{2}(\beta)}{\Gamma^{2}(\alpha+\beta)}-\frac{3\gamma(\gamma+1)\Gamma(\beta)}{\Gamma(2\alpha+\beta)}.$$
By using the Euler-Rayleigh inequalities $$\theta_{k}^{-1/k}< \eta_{\alpha,\beta,\gamma,1}<\frac{\theta_{k}}{\theta_{k+1}}$$ for $k=1$ the corresponding part of this theorem is proved.
\end{proof}
\begin{proof}[\bf Proof of Theorem \ref{theorem4}]
{\bf a.} First note that
$$1+\frac{zf^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{f^{\prime}_{\alpha,\beta,\gamma}(z)}=1+\frac{z\Psi''(\alpha,\beta,\gamma,z)}{\Psi'(\alpha,\beta,\gamma,z)}+
\left(\frac{1}{\beta}-1\right)\frac{r\Psi'(\alpha,\beta,\gamma,z)}{\Psi(\alpha,\beta,\gamma,z)},$$
and let us recall the following infinite product representations from the proof of Theorem \ref{theorem1}
\begin{gather*}
\Gamma(\beta)\Psi(\alpha,\beta,\gamma,z)=z^{\beta}\prod_{n \geq 1}\left(1-\frac{z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}}\right),\quad \Gamma(\beta)\Psi'(\alpha,\beta,\gamma,z)=\beta z^{\beta-1}\prod_{n \geq 1}\left(1-\frac{z^{2}}{\xi^2_{\alpha,\beta,\gamma,n}}\right),
\end{gather*}
where $\lambda_{\alpha,\beta,\gamma,n}$ and $\xi_{\alpha,\beta,\gamma,n}$ are the $n$th positive roots of $z\mapsto\Psi(\alpha,\beta,\gamma,z)$ and $z\mapsto\Psi'(\alpha,\beta,\gamma,z),$ respectively, as in Lemma \ref{lemma}. Logarithmic differentiation of both sides of the above relations yields
\begin{gather*}
\frac{z\Psi'(\alpha,\beta,\gamma,z)}{\Psi(\alpha,\beta,\gamma,z)}=\beta-\sum_{n \geq 1}\frac{2z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z^{2}},\quad \frac{z\Psi''(\alpha,\beta,\gamma,z)}{\Psi'(\alpha,\beta,\gamma,z)}=\beta-1-\sum_{n \geq 1}\frac{2z^{2}}{\xi^2_{\alpha,\beta,\gamma,n}-z^{2}},
\end{gather*}
which implies that
$$ 1+\frac{zf^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{f^{\prime}_{\alpha,\beta,\gamma}(z)}=1-\left(\frac{1}{\beta}-1\right)\sum_{n \geq 1}\frac{2z^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-z^{2}}-\sum_{n \geq 1}\frac{2z^{2}}{\xi^2_{\alpha,\beta,\gamma,n}-z^{2}}.$$
By using the inequality \eqref{cov} for $\beta \in (0,1]$ we have
\begin{equation}\label{rad17}
\operatorname{Re} \left(1+\frac{zf^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{f^{\prime}_{\alpha,\beta,\gamma}(z)}\right)\geq 1-\left(\frac{1}{\beta}-1\right)\sum_{n \geq 1}\frac{2r^{2}}{\lambda^{2}_{\alpha,\beta,\gamma,n}-r^{2}}-\sum_{n \geq 1}\frac{2r^{2}}{\xi^{2}_{\alpha,\beta,\gamma,n}-r^{2}},
\end{equation}
where $|z|=r.$ Moreover, in view of the following inequality (see \cite[Lemma 2.1]{baricz7})
$$\alpha \operatorname{Re} \left(\frac{z}{a-z}\right)-\operatorname{Re} \left(\frac{z}{b-z}\right)\geq \alpha \frac{|z|}{a-|z|}-\frac{|z|}{b-|z|},$$
where $a>b>0,$ $\alpha\in[0,1],$ $z \in \mathbb{C}$ such that $|z|<b,$ we obtain that \eqref{rad17} is also valid when $\beta > 1$ for all $z \in \mathbb{D}_{\xi_{\alpha,\beta,\gamma,1}}.$ Here we used that the zeros of $\lambda_{\alpha,\beta,\gamma,n}$ and $\xi_{\alpha,\beta,\gamma,n}$ interlace, according to Lemma \ref{lemma}. Now, the above deduced inequalities imply for $r \in (0,\xi_{\alpha,\beta,\gamma,1})$
$$\inf_{z \in \mathbb{D}_r}\left\{\operatorname{Re} \left(1+\frac{zf^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{f^{\prime}_{\alpha,\beta,\gamma}(z)}\right)\right\}=1+\frac{rf^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{f^{\prime}_{\alpha,\beta,\gamma}(r)}.$$
The function $u_{\alpha,\beta,\gamma}:(0,\xi_{\alpha,\beta,\gamma,1}) \rightarrow \mathbb{R},$ defined by
$$u_{\alpha,\beta,\gamma}(r)=1+\frac{rf^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{f^{\prime}_{\alpha,\beta,\gamma}(r)},$$
is strictly decreasing since
\begin{align*}
u^{\prime}_{\alpha,\beta,\gamma}(r)&=-\left(\frac{1}{\beta}-1\right)\sum_{n\geq 1}\frac{4r\lambda^{2}_{\alpha,\beta,\gamma,n}}{(\lambda^{2}_{\alpha,\beta,\gamma,n}-r^{2})^{2}}-
\sum_{n\geq 1}\frac{4r\xi^{2}_{\alpha,\beta,\gamma,n}}{(\xi^{2}_{\alpha,\beta,\gamma,n}-r^{2})^{2}}\\
&<\sum_{n\geq 1}\frac{4r\lambda^{2}_{\alpha,\beta,\gamma,n}}{(\lambda^{2}_{\alpha,\beta,\gamma,n}-r^{2})^{2}}-
\sum_{n\geq 1}\frac{4r\xi^{2}_{\alpha,\beta,\gamma,n}}{(\xi^{2}_{\alpha,\beta,\gamma,n}-r^{2})^{2}}<0
\end{align*}
for $r \in (0,\xi_{\alpha,\beta,\gamma,1}),$ where we used again the interlacing property of the zeros stated in Lemma \ref{lemma}. Observe that $\lim_{r\searrow 0} u_{\alpha,\beta,\gamma}(r)=1$ and $\lim_{r\nearrow \xi_{\alpha,\beta,\gamma,1}} u_{\alpha,\beta,\gamma}(r)=-\infty,$ which means that for $z \in \mathbb{D}_{r_{1}}$ we get
$$\operatorname{Re} \left(1+\frac{zf^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{f^{\prime}_{\alpha,\beta,\gamma}(z)}\right)>\rho$$ if and only if $r_{1}$ is the unique root of
$$1+\frac{zf^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{f^{\prime}_{\alpha,\beta,\gamma}(r)}=\rho$$ situated in $(0,\xi_{\alpha,\beta,\gamma,1}).$
{\bf b.} According to \eqref{rad10} we have
$$g'_{\alpha,\beta,\gamma}(z)=\prod_{n \geq 1}\left(1-\frac{z^{2}}{\zeta^{2}_{\alpha,\beta,\gamma,n}}\right). $$
Now, taking logarithmic derivatives on both sides, we get
$$1+\frac{zg^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{g^{\prime}_{\alpha,\beta,\gamma}(z)}=1-\sum_{n \geq 1}\frac{2z^{2}}{\zeta^{2}_{\alpha,\beta,\gamma,n}-z^{2}}.$$
Application of the inequality \eqref{cov} implies that $$\operatorname{Re} \left(1+\frac{zg^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{g^{\prime}_{\alpha,\beta,\gamma}(z)}\right)\geq 1-\sum_{n \geq 1}\frac{2r^{2}}{\zeta^{2}_{\alpha,\beta,\gamma,n}-r^{2}}, $$
where $|z|=r.$ Thus, for $r \in (0,\zeta_{\alpha,\beta,\gamma,1}),$ we get
$$\inf_{z \in \mathbb{D}_r}\left\{\operatorname{Re} \left(1+\frac{zg^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{g^{\prime}_{\alpha,\beta,\gamma}(z)}\right)\right\}=
1+\frac{rg^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{g^{\prime}_{\alpha,\beta,\gamma}(r)}.$$
The function $v_{\alpha,\beta,\gamma}:(0,\zeta_{\alpha,\beta,\gamma,1})\rightarrow \mathbb{R},$ defined by
$$v_{\alpha,\beta,\gamma}(r)=1+\frac{rg^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{g^{\prime}_{\alpha,\beta,\gamma}(r)},$$
is strictly decreasing and take the limits $\lim_{r\searrow 0} v_{\alpha,\beta,\gamma}(r)=1$ and $\lim_{r\nearrow \zeta_{\alpha,\beta,\gamma,1}} v_{\alpha,\beta,\gamma}(r)=-\infty,$ which means that for $z \in \mathbb{D}_{r_{2}}$ we get
$$\operatorname{Re} \left(1+\frac{zg^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{g^{\prime}_{\alpha,\beta,\gamma}(z)}\right)>\rho$$ if and only if $r_{2}$ is the unique root of
$$1+\frac{zg^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{g^{\prime}_{\alpha,\beta,\gamma}(r)}=\rho$$ situated in $(0,\zeta_{\alpha,\beta,\gamma,1}).$
{\bf c.} According to \eqref{rad14} we have
$$h'_{\alpha,\beta,\gamma}(z)=\prod_{n \geq 1}\left(1-\frac{z}{\eta_{\alpha,\beta,\gamma,n}}\right),$$
which implies that
$$1+\frac{zh^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{h^{\prime}_{\alpha,\beta,\gamma}(z)}=1-\sum_{n \geq 1}\frac{z}{\eta_{\alpha,\beta,\gamma,n}-z}.$$
Let $r \in (0,\eta_{\alpha,\beta,\gamma,1})$ be a fixed number. The minimum principle for harmonic function and inequality \eqref{cov} imply that for $z \in \mathbb{D}_{r}$ we have
\begin{align*}
\operatorname{Re} \left(1+\frac{zh^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{h^{\prime}_{\alpha,\beta,\gamma}(z)}\right)
&=\operatorname{Re} \left(1-\sum_{n \geq 1}\frac{z}{\eta_{\alpha,\beta,\gamma,n}-z}\right)\geq
\min_{|z|=r}\operatorname{Re} \left(1-\sum_{n \geq 1}\frac{z}{\eta_{\alpha,\beta,\gamma,n}-z}\right)\\
&=\min_{|z|=r}\left(1-\sum_{n \geq 1}\operatorname{Re} \frac{z}{\eta_{\alpha,\beta,\gamma,n}-z}\right)
\geq 1-\sum_{n \geq 1}\frac{r}{\eta_{\alpha,\beta,\gamma,n}-r}
=1+\frac{rh^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{h^{\prime}_{\alpha,\beta,\gamma}(r)}.
\end{align*}
Consequently, it follows that
$$\inf_{z \in \mathbb{D}_r}\left\{\operatorname{Re} \left(1+\frac{zh^{\prime\prime}_{\alpha,\beta,\gamma}(z)}{h^{\prime}_{\alpha,\beta,\gamma}(z)}\right)\right\}=1+\frac{rh^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{h^{\prime}_{\alpha,\beta,\gamma}(r)}.$$
Now, let $r_{3}$ be the smallest positive root of the equation
\begin{equation}\label{rad18}
1+\frac{rh^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{h^{\prime}_{\alpha,\beta,\gamma}(r)}=\rho.
\end{equation}
For $z \in \mathbb{D}_{r_{3}},$ we have
$$\operatorname{Re}\left(1+\frac{rh^{\prime\prime}_{\alpha,\beta,\gamma}(r)}{h^{\prime}_{\alpha,\beta,\gamma}(r)}\right)>\rho.$$
In order to complete the proof, we need to show that equation \eqref{rad18} has a unique root in $(0,\eta_{\alpha,\beta,\gamma,1}).$ But the equation \eqref{rad18} is equivalent to
$$w_{\alpha,\beta,\gamma}(r)=1-\rho-\sum_{n\geq 1} \frac{r}{\eta_{\alpha,\beta,\gamma,n}-r}=0$$
and we have
$\lim_{r \searrow 0}w_{\alpha,\beta,\gamma}(r)=1-\rho>0,$ and $\lim_{r \nearrow \eta_{\alpha,\beta,\gamma}}w_{\alpha,\beta,\gamma}(r)=-\infty.$
Now, since the function $w_{\alpha,\beta,\gamma}:(0,\eta_{\alpha,\beta,\gamma,1})\to\mathbb{R},$ defined above, is strictly decreasing, it follows that the equation $w_{\alpha,\beta,\gamma}(r)=0$
has indeed a unique root in $(0,\eta_{\alpha,\beta,\gamma,1}).$ This completes the proof of the theorem.
\end{proof}
\begin{proof}[\bf Proof of Theorem \ref{theorem5}]
{\bf a.} By using the infinite series representations of the generalized Mittag-Leffler function and its derivative we obtain
$$\varphi(\alpha,\beta,\gamma,z)=(zg^{\prime}_{\alpha,\beta,\gamma}(z))^{\prime}=1+\sum_{n \geq 1}\frac{(-1)^{n}(\gamma)_{n}\Gamma(\beta)(2n+1)^{2}z^{2n}}{n!\Gamma(\alpha n+\beta)}.$$
We know that $g_{\alpha,\beta,\gamma}\in\mathcal{LP}$ and this in turn implies that $z\mapsto\varphi(\alpha,\beta,\gamma,z)$ belongs also to the Laguerre-P\'{o}lya class and consequently all its zeros are real. Assume that $\tau_{\alpha,\beta,\gamma,n}$ is the $n$th positive zero of the function $z\mapsto\varphi(\alpha,\beta,\gamma,z).$ Then we have that
$$\varphi(\alpha,\beta,\gamma,z)=\prod_{n \geq 1}\left(1-\frac{z^{2}}{\tau^{2}_{\alpha,\beta,\gamma,n}}\right)$$
and for $|z|<\tau_{\alpha,\beta,\gamma,1}$
\begin{equation}\label{rad19}
\frac{\varphi'(\alpha,\beta,\gamma,z)}{\varphi(\alpha,\beta,\gamma,z)}=\sum_{n\geq1}\frac{-2z}{\tau_{\alpha,\beta,\gamma,n}^2-z^2}=
\sum_{n\geq1}\sum_{k\geq0}\frac{-2z^{2k+1}}{\tau_{\alpha,\beta,\gamma,n}^{2k+2}}=\sum_{k\geq0}\sum_{n\geq1}\frac{-2z^{2k+1}}{\tau_{\alpha,\beta,\gamma,n}^{2k+2}}
=-2 \sum_{k \geq 0}\mu_{k+1}z^{2k+1},
\end{equation}
where $\mu_{k}=\sum_{n \geq 1}\tau^{-2k}_{\alpha,\beta,\gamma,n}.$ On the other hand, we have
\begin{equation}\label{rad20}
\frac{\varphi'(\alpha,\beta,\gamma,z)}{\varphi(\alpha,\beta,\gamma,z)}=-2\left. \sum_{n \geq 0}q_{n}z^{2n+1}\right/\sum_{n \geq 0} r_{n}z^{2n},
\end{equation}
where $$q_{n}=\frac{(-1)^{n}(\gamma)_{n+1}\Gamma(\beta)(2n+3)^{2}}{n!\Gamma(\alpha (n+1)+\beta)}\ \ \ \mbox{and}\ \ \ r_{n}=\frac{(-1)^{n}(\gamma)_{n}\Gamma(\beta)(2n+1)^{2}}{n!\Gamma(\alpha n+\beta)}.$$
By comparing the coefficients of \eqref{rad19} and \eqref{rad20} we obtain
$$\mu_{1}=\frac{9\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)},\quad \mu_{2}=\frac{81\gamma^2\Gamma^{2}(\beta)}{\Gamma^{2}(\alpha+\beta)}-\frac{25\gamma(\gamma+1)\Gamma(\beta)}{\Gamma(2\alpha+\beta)}$$
and by using the Euler-Rayleigh inequalities $$\mu_{k}^{-1/k}< \tau^2_{\alpha,\beta,\gamma,1}<\frac{\mu_{k}}{\mu_{k+1}}$$
for $k=1$ we have the inequalities of this part of the theorem.
{\bf b.} In view of the definition of the generalized Mittag-Leffler function we have
$$\varpi(\alpha,\beta,\gamma,z)=(zh^{\prime}_{\alpha,
\beta,\gamma}(z))^{^\prime}=1+\sum_{n \geq 1}\frac{(-1)^{n}\Gamma(\beta)(\gamma)_{n}(n+1)^{2}z^{n}}{n!\Gamma(\alpha n+\beta)}$$
and consequently
\begin{equation}\label{rad23}
\frac{\varpi'(\alpha,\beta,\gamma,z)}{\varpi(\alpha,\beta,\gamma,z)}=-\left.\sum_{n\geq 0}t_{n}z^{n}\right/\sum_{n\geq0}s_{n}z^{n},
\end{equation}
where
$$t_{n}=\frac{(-1)^{n}\Gamma(\beta)(\gamma)_{n+1}(n+2)^{2}}{n!\Gamma(\alpha (n+1)+\beta)}\ \ \
\mbox{and}\ \ \ s_{n}=\frac{(-1)^{n}\Gamma(\beta)(\gamma)_{n}(n+1)^{2}}{n!\Gamma(\alpha n+\beta)}.$$
Since $h_{\alpha,\beta,\gamma}\in \mathcal{LP},$ it follows that $h'_{\alpha,\beta,\gamma}\in\mathcal{LP},$ and consequently $z\mapsto \varpi(\alpha,\beta,\gamma,z)$ belongs also to the Laguerre-P\'{o}lya class $\mathcal{LP},$ and hence all its zeros are real. If we suppose that $\varsigma_{\alpha,\beta,\gamma,n}$ is the $n$th positive zero of the function $z\mapsto \varpi(\alpha,\beta,\gamma,z),$ then we get
$$\varpi\alpha,\beta,\gamma,z)=\prod_{n \geq 1}\left(1-\frac{z}{\varsigma_{\alpha,\beta,\gamma,n}}\right)$$
and for $|z|<\varsigma_{\alpha,\beta,\gamma,1}$
\begin{equation}\label{rad22}
\frac{\varpi'(\alpha,\beta,\gamma,z)}{\varpi(\alpha,\beta,\gamma,z)}=-\sum_{n\geq1}\frac{1}{\varsigma_{\alpha,\beta,\gamma,n}-z}
=-\sum_{n\geq1}\sum_{k\geq0}\frac{z^k}{\varsigma^{k+1}_{\alpha,\beta,\gamma,n}}=-\sum_{k\geq0}\sum_{n\geq1}\frac{z^k}{\varsigma^{k+1}_{\alpha,\beta,\gamma,n}}
=-\sum_{k \geq 0} \nu_{k+1}z^{k},
\end{equation}
where $\nu_{k}=\sum_{n \geq 1}\varsigma^{-k}_{\alpha,\beta,\gamma,n}.$
By comparing the coefficients of \eqref{rad22} and \eqref{rad23}, we have
$$\nu_{1}=\frac{4\gamma\Gamma(\beta)}{\Gamma(\alpha+\beta)}, \ \ \nu_{2}=\frac{16\gamma^2\Gamma^{2}(\beta)}{\Gamma^{2}(\alpha+\beta)}-\frac{9\gamma(\gamma+1)\Gamma(\beta)}{\Gamma(2\alpha+\beta)}$$
and by using the Euler-Rayleigh inequalities $$\nu_{k}^{-1/k}< \varsigma_{\alpha,\beta,\gamma,1}<\frac{\nu_{k}}{\nu_{k+1}}$$ for $k=1$ we have the inequalities of the second part of the theorem.
\end{proof}
\section*{Acknowledgements} The research of A. Prajapati was supported under the INSPIRE fellowship, Department of Science and
Technology, New Delhi, Government of India, Sanction Letter No. REL1/2016/2/2015-16.
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{"url":"https:\/\/www.ncatlab.org\/nlab\/show\/Brown-Comenetz+duality","text":"# nLab Brown-Comenetz duality\n\nContents\n\n### Context\n\n#### Stable Homotopy theory\n\nstable homotopy theory\n\nIntroduction\n\nduality\n\n# Contents\n\n## Idea\n\nBrown-Comenetz 76 introduced the spectrum $I_{\\mathbb{Q}\/\\mathbb{Z}}$ which represents the cohomology theory that assigns to a spectrum $X$ the Pontrjagin duals $Hom_{\\mathbb{Z}}(\\pi_{- \\ast} X, \\mathbb{Q}\/\\mathbb{Z})$ of its homotopy groups.\n\nIf $X$ is a spectrum whose stable homotopy groups are finite groups, then the natural \u201cdouble-duality\u201d map $X \\to I_{\\mathbb{Q}\/\\mathbb{Z}} I_{\\mathbb{Q}\/\\mathbb{Z}} X$ (the unit of the corresponding continuation monad) is an equivalence (see at dualizing object in a closed category).\n\nThe Brown-Comenetz spectrum $I_{\\mathbb{Q}\/\\mathbb{Z}}$ has an \u201cintegral\u201d refinement which is the Anderson spectrum $I_{\\mathbb{Z}}$ inducing Anderson duality.\n\n## Properties\n\n\u2022 Eilenberg-Mac Lane spectra are Brown-Comenetz self-dual: $I_{\\mathbb{Q}\/\\mathbb{Z}} H \\mathbb{F}_p \\cong H \\mathbb{F}_p$.\n\n## References\n\n\u2022 E. H. Brown, Jr. and M. Comenetz, Pontrjagin duality for generalized homology and cohomology theories, Amer. J. Math. 98 (1976), no. 1, 1\u201327.\n\nLast revised on April 6, 2017 at 11:31:47. See the history of this page for a list of all contributions to it.","date":"2020-01-17 16:46:15","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 8, \"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\": 0.8326503038406372, \"perplexity\": 1462.5935025922674}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-05\/segments\/1579250589861.0\/warc\/CC-MAIN-20200117152059-20200117180059-00252.warc.gz\"}"}
| null | null |
Q: Catch exception when connection to database Spring Data JPA I want to check every time my application runs that I am connected to the database, if not I want to generate an alert. I am using Spring Boot with Spring Data JPA and I have my database details configured in my application.properties. My question is, where does database connection happen in Spring Data JPA, and can I catch exception so I can perform some logic?
A: You can getConnection from DataSource.
If is connection is not ok, then getConnection will throw a exception.
@SpringBootApplication(scanBasePackages = "packages")
public class MyApp {
public static void main(String[] args) {
ConfigurableApplicationContext springContext = SpringApplication.run(MyApp.class);
DataSource dataSource = springContext.getBean(DataSource.class);
try {
// if connection is not ok, then getConnection throw exception
dataSource.getConnection();
} catch (SQLException e) {
// try connection error here
}
}
}
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"redpajama_set_name": "RedPajamaStackExchange"
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This month we have Work Wise Woman Award Winner 2018 member Liz Drury as our speaker.
Liz Drury has been working as a professional voiceover artist since 2013 working from a studio at her home in North Lincs for clients all over the world. Some of the big names that have used her voice include Bulgari, Prada, VW, BMW, the NHS, Hilton Garden Inn and more. Liz has voiced commercials, website videos, museum guides, online training courses, telephone prompts etc., but she has yet to be the voice of a character in one of the computer games her kids are playing….however in taking part in "Baring All For Hull" Liz tells us how and why she got involved with Spencer Tunick's 'Sea of Hull' project (the one with the naked, blue people!), and how this experience changed her life, and improved her voiceover business.
Copyright © 2014 Getextra All rights reserved.
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{
"redpajama_set_name": "RedPajamaC4"
}
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\section{Introduction}
Reading someone else's handwriting is often a challenging task; some of the characters are unclear, the text is cursive, there is background clutter and the image quality can be low. When deciphering each character, we often rely on the surrounding area to compensate for the occasional obscurity of local areas in the text.
The automation of reading text images has been a thriving field of research in computer vision for decades. Recent deep learning methods have significantly improved recognition results \cite{Baek2019clova,zhang2019sequence,luo2020learn,Litman_2020_CVPR,aberdam2020sequence}.
Nevertheless, a close investigation reveals that state-of-the-art text recognizers are prone to overly rely on local image statistics\footnote{In this work, statistics are defined as the mean and standard deviation calculated from the corresponding distribution.}, ignoring cues from the surrounding areas.
Similarly, previous works suggested the susceptibility of image classifiers to develop a bias towards global image statistics~\cite{nuriel2020permuted}. Adaptive Instance Normalization (AdaIN)~\cite{huang2017arbitrary} was utilized for the purpose of reducing this bias. Specifically, Nuriel \etal~\cite{nuriel2020permuted} proposed to probabilistically apply AdaIN between the activations of random samples in a batch during training. Thus, randomly swapping channel-wise feature statistics accumulated over the entire image, as depicted in \cref{fig:teaser_fig}(a).
\begin{figure}[t]
\centering
\includegraphics[width=0.95\columnwidth]{Figures/teaser_fig_v8.pdf}
\caption{{\bf Fine-grained TextAdaIN.} (a) Recent works suggested utilizing AdaIN, swapping instance-level feature statistics, to remedy classifiers' bias towards global information. (b) Our method, TextAdaIN, leverages a fine-grained variation of AdaIN to swap feature statistics between slices along the width axis. This moderates the observed reliance of text recognizers on local statistics. }
\label{fig:teaser_fig}
\vspace{-0.4cm}
\end{figure}
In classification tasks, global statistics can contain relevant label cues. For example, an image of a fish will normally have the global statistics of water. As a result, the model learns to depend on this information and is prone to develop a bias towards these statistics~\cite{nuriel2020permuted,geirhos2018}. However this is not the case in text recognition, as the global statistics contain little information regarding the transcript of the text in the image. Thus, as we will show, text recognizers are already robust to global image statistics.
This work proposes a simple, yet powerful, technique for moderating the reliance on local statistics, which enhances the performance of text recognizers. The key idea of our approach is to probabilistically swap fine-grained feature statistics in a manner which is adjusted to the task at hand.
To that end, we propose TextAdaIN, a local variation of AdaIN~\cite{huang2017arbitrary}, depicted in \cref{fig:teaser_fig}(b). In contrast to AdaIN which operates on the entire image, TextAdaIN operates on vertical slices of the sequential feature map. In addition, the normalization is performed over multiple dimensions and as a consequence, the granularity level in which the statistics are modified is increased. Effectively, local distortions are injected into the feature space at a sub-word level, forcing the encoder to account for information in surrounding areas.
To gain insights on the effect of swapping local feature statistics in the domain of text images, we utilize a trained autoencoder, similarly to~\cite{nuriel2020permuted}. As illustrated in \cref{fig:reconst_vis}(c), TextAdaIN provides two noticeable modifications to the reconstructed images. Firstly, local perturbations are injected from an induced distribution which represents the natural feature statistics of text images. Additionally, we notice that local regions containing textual information occasionally undergo masking. These domain specific distortions act as a regularization method to the network. They prevent the network from overfitting to the local statistics of the training data and restrict its reliance on specific features to identify characters. To verify that our method indeed regulates this reliance, we numerically quantify its robustness towards local image corruptions, demonstrating its distinct advantage. This regularization is most critical in the case of handwriting, where the training data is typically very limited.
We validate our method experimentally, comparing its performance with state-of-the-art approaches on several handwritten text benchmarks.
TextAdaIN achieves state-of-the-art results, reducing the word error rate by $\textbf{1.4\%}$, $\textbf{2.0\%}$ and $\textbf{0.4\%}$ on IAM, RIMES and CVL, respectively. Furthermore, our method shows a consistent improvement across multiple architectures and in the domain of scene text recognition.
Not only does our model surpass other, more complicated methods (\cite{bhunia2019handwriting, fogel2020scrabblegan, zhang2019sequence, luo2020learn, aberdam2020sequence}), but it is simple to implement and can effortlessly be integrated into any mini-batch training procedure.
To summarize, the key contributions of our work are:
\begin{enumerate}[nolistsep]
\item We identify the problem of text recognizers' heavy dependence on local statistics and suggest to regulate it.
\item We introduce TextAdaIN, a simple yet effective normalization approach to remediate the reliance on local statistics in text recognizers.
\item Extensive experimental validation shows our method achieves state-of-the-art performance on several popular handwritten text benchmarks. In addition, it is applicable to the domain of scene text and can be used independent of the chosen architecture.
\end{enumerate}
\begin{figure*}[t]
\centering
\includegraphics[width=0.95\textwidth]{Figures/vis_autoencoder_v8.pdf}
\caption{\label{fig:reconst_vis}
\textbf{Autoencoder visualization.} We visualize the effect of applying different variations of AdaIN at intermediate layers of a trained autoencoder. The input, donor and reconstructed images are shown on the left. As seen in (a), applying vanilla AdaIN yields only global effects for text images. In (b), we see the effect of applying AdaIN on both the height and channel dimensions, increasing the granularity level. (c) TextAdaIN further increases the granularity level and allows for multiple donors by splitting the feature map into separate elements along the width axis. L.=layer; Recon=Reconstruction.
}
\end{figure*}
\section{Related Work and Background}
\paragraph{Normalization and style transfer.}
Normalizing feature tensors is an effective and powerful technique that has been explored and developed over the years for a variety of tasks. Ioffe \& Szegedy~\cite{ioffe2015batch} were the first to introduce Batch Normalization which inspired a series of normalization-based methods such as Layer Normalization \cite{ba2016layer}, Instance Normalization \cite{ulyanov2016instance}, and Group Normalization \cite{wu2018group}.
The style of an image was characterized by \cite{gatys2016image} to be the statistics of activation maps in intermediate layers of convolutional neural networks. Instance Normalization (IN) \cite{ulyanov2016instance} is a normalization layer which normalizes these statistics, removing the style representation from the activation map. Formally, given an instance $x\in \mathbb{R}^{C\times H \times W} $, where $C,H$ and $W$ are the channels, height, and width respectively, Instance Normalization is defined to be:
\begin{equation*}
\textrm{IN}(x)= \gamma\left(\frac{x-\mu(x)}{\sigma(x)}\right)+\beta\,.
\end{equation*}
Where $\gamma, \beta \in \mathbb{R}^{C}$ are learned parameters and $\mu(x), \sigma(x) \in \mathbb{R}^{C}$ are calculated by taking the mean and standard deviation over $H,W$ of $x$.
Adaptive Instance Normalization (AdaIN), proposed in \cite{huang2017arbitrary} changes the input image style by incorporating the statistics of an additional image into the feature space. Given two image representations, $x_a,x_b\in \mathbb{R}^{C \times H \times W}$, AdaIN shifts the statistics of the representation of $x_a$ to the representation of $x_b$. This is done in two steps. First, Instance Normalization is applied on $x_a$ to remove $x_a$'s style information. Then, the normalized activation map is scaled and shifted to match $x_b$'s statistics. This operation is thus perceived to transfer $x_b$'s style onto $x_a$.
\begin{equation*}
\label{eq:2}
\textrm{AdaIN}_c(x_a,x_b)= \sigma(x_b)\left(\frac{x_a-\mu(x_a)}{\sigma(x_a)}\right)+\mu(x_b)\,.
\end{equation*}
$\textrm{AdaIN}_c$ denotes the standard AdaIN operation in which $\sigma,\mu$ are calculated over the spatial dimensions, resulting in shifting corresponding channel statistics.
Leveraging the benefits of this operation, Geirhos \etal~\cite{geirhos2018} created Stylized-ImageNet, a stylized version of ImageNet. They demonstrated that classifiers trained on this dataset rely more on shape rather than texture.
More recently, Zhou \etal~\cite{zhou2021mixstyle} proposed to probabilistically mix instance-level feature statistics during training across different domains, thus increasing the generalizability of the model.
Furthermore, Nuriel~\etal~\cite{nuriel2020permuted} demonstrated that a similar approach can be utilized to reduce classifiers' reliance on global statistics, therefore increasing classification performance.
In this work, we reveal that text recognizers exhibit a similar bias, yet on a local scale. To remediate this problem, we also leverage AdaIN. However, instead of swapping statistics on a word (instance) level, we swap fine-grained statistics on a sub-word level, thus regulating the reliance on local feature statistics in text recognizers.
\paragraph{Text Recognition.}
Text recognition has attracted considerable attention over the past few years. In particular, deep learning approaches have achieved remarkable results \cite{shi2016end,Liu2016STARNetAS,Baek2019clova,luo2020learn,wan2020vocabulary,slossberg2020calibration,aberdam2020sequence}.
Still, current state-of-the-art methods struggle to train robust models when the amount of data is insufficient to capture the magnitude of handwriting styles.
Various methods have been suggested to cope with this problem. Bhunia \etal~\cite{bhunia2019handwriting} proposed an adversarial feature deformation module that learns ways to elastically warp extracted features, boosting the network's capability to learn highly informative features. Luo \etal~\cite{luo2020learn} introduced an agent network that learns from the output of the recognizer. The agent controls a set of fiducial points on the image and uses a spatial transformer to generate "harder" training samples.
In a different line of work, utilizing unlabeled data was proposed to improve recognition results.
Zhang \etal~\cite{zhang2019sequence} and Kang \etal~\cite{kang2020unsupervised} have introduced adversarial domain adaptation approaches between a labeled source domain and an unlabeled target domain.
Aberdam~\etal~\cite{aberdam2020sequence} suggested a framework for sequence-to-sequence contrastive learning named SeqCLR, which yields effective visual representations for text recognition by pre-training the network on unlabeled data.
Unlike previous methods, our method does not require additional data, new models or complex training paradigms.
Instead, we suggest a normalization-based method adjusted to text images and to sequence-to-sequence approaches.
TextAdaIN is extremely easy to implement and can fit into any encoder as part of a mini-batch training process.
Throughout this work, unless mentioned otherwise, we integrate our proposed method with a state-of-the-art recognizer named SCATTER~\cite{Litman_2020_CVPR}.
The SCATTER architecture consists of four main components:
\begin{enumerate}[nolistsep]
\item Transformation: A rectification module which aligns the input text
image using a Thin Plate Spline (TPS) transformation \cite{Liu2016STARNetAS,shi2016robust}.
\item Feature extraction: A convolutional neural network
(CNN) that extracts features from the rectified image. Similar to~\cite{cheng2017focusing,Baek2019clova,Litman_2020_CVPR,aberdam2020sequence}, a 29-layer ResNet is employed as the backbone. Subsequently, the features are mapped to a sequence of frames, denoted by $V = [v_1, v_2, ..., v_T]$, each corresponding to different receptive fields in the image.
\item Visual feature refinement: An intermediate supervision in the form of a CTC decoder \cite{Graves2006ctc} is employed to provide direct supervision for each frame in the visual features $V$.
\item Selective-Contextual Refinement Block: Contextual features are extracted using a two-layer bi-directional LSTM encoder. These features are concatenated to the visual features, $V$. The features are then fed into a selective decoder and into a subsequent block if it exists.
These blocks can be stacked together to improve results. In this work, for convenience, we set the number of blocks to two.
\end{enumerate}
For further details about the baseline architecture, we refer the reader to~\cite{Litman_2020_CVPR}.
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{Figures/fig_text_recog_v3.pdf}
\caption{{\bf TextAdaIN block.} (a) A standard residual block and (b) a TextAdaIN block. TextAdaIN is probabilistically employed after every Conv layer during training.}
\label{fig:arch_fig}
\vspace{-0.3cm}
\end{figure}
\section{Method}
Our method is inspired by two key observations in the context of text recognition. First, text recognition approaches define the recognition task as a sequence character classification problem. The characters appear across a series of frames along the width axis of the image.
This leads us to the second observation, that the model's predictions are mostly based on local information which lies in consecutive frames~\cite{Bai2015crnn,qiao2020seed}. Therefore, text recognizers are at the risk of developing a bias towards local statistics and thus may not sufficiently take the surrounding information into account.
Leveraging the recent development proposed by \cite{nuriel2020permuted, zhou2021mixstyle},
we suggest two modifications that correspond to the aforementioned observations:
\begin{enumerate}[nolistsep]
\item Viewing the feature map as a sequence of individual elements and swapping the feature statistics between elements instead of entire images.
\item Modifying AdaIN to operate on two dimensions - the height and channels of the feature map.
\end{enumerate}
These modifications increase the granularity level in which statistics are calculated and modified, thus regulating the reliance on local statistics. Both are crucial for our method's success, as shown in the ablation study.
Similarly to \cite{nuriel2020permuted}, in \cref{fig:reconst_vis}, we illustrate the effect of our approach by applying it to an autoencoder trained on natural images. We compare between applying vanilla AdaIN to applying TextAdaIN exemplifying the distinction between the two. In (a), we apply vanilla AdaIN. When applied to natural images the change is apparent. However, when applied to text images the change is subtle. Correspondingly, in the experimental section we provide further evidence that text recognizers are already invariant to global statistics.
In (b), a local variation of AdaIN is applied, in which statistics from each channel and height are swapped. In this setting the visual impact is more noticeable. In the last row (c), we apply TextAdaIN, which takes it a step further and splits the sequential feature map into separate elements created from every few consecutive frames. Thus, increasing the scale in which the feature statistics are swapped and allowing the use of multiple donor images.
\input{tables/hw_sota}
Formally, given an image representation $x\in \mathbb{R}^{C\times H\times W}$, we define $\mu_{c,h}$, $\sigma_{c,h}$ to be the following:
\begin{equation*}
\mu_{c,h}(x) = \frac{1}{W}\sum_{w=1}^{W} x_{c,h,w} \,,
\end{equation*}
\begin{equation*}
\sigma_{c,h}(x) = \sqrt{\frac{1}{W}\sum_{w=1}^{W}(x_{c,h,w} - \mu_{c,h}(x))^{2} + \epsilon}\ \,.
\end{equation*}
A local variation of $\textrm{AdaIN}_c$ is defined as:
\begin{equation*}
\textrm{AdaIN}_{c,h}(x_a,x_b)= \sigma_{c,h}(x_b)\left(\frac{x_a-\mu_{c,h}(x_a)}{\sigma_{c,h}(x_a)}\right)+\mu_{c,h}(x_b) \,.
\end{equation*}
This variant of AdaIN swaps statistics for every corresponding channel and height, thus impacting the feature map's statistics at a higher level of granularity. We note that backpropagating gradients only occur through $\mu_{c,h}(x_a), \sigma_{c,h}(x_a)$.
Given the definitions above, we formulate the TextAdaIN operation used during training. Let $X=\{x_i\}_{i=1}^B$ denote a mini-batch of $B$ feature maps. We divide each sample $x_i$ into $K$ windows along its width. The result is a batch of elements pertaining to $B\cdot K$ windows. This operation can be defined as a mapping:
\begin{equation*}
X\in \mathbb{R}^{B\times C \times H \times W} \rightarrow \widehat{X}\in \mathbb{R}^{B\cdot K \times C \times H \times \frac{W}{K}} \,.
\end{equation*}
Then, we employ a similar procedure to the one used in pAdaIN \cite{nuriel2020permuted}. We randomly draw a permutation of the modified batch $\widehat{X}$ and apply $\textrm{AdaIN}_{c,h}$ between the modified batch and the permuted one. Namely, let
\begin{equation*}
\pi(\widehat{X}) = [\hat{x}_{\pi(1)},\hat{x}_{\pi(2)}...\hat{x}_{\pi(B\cdot K)}] \,
\end{equation*} denote applying a permutation $\pi: [B\cdot K] \rightarrow [B\cdot K]$ on $\widehat{X}$. Then the output of TextAdaIN on the $i^{th}$ window of $\widehat{X}$ is defined by:
\begin{equation*}
\textrm{TextAdaIN }(\hat{x}_i) = \textrm{AdaIN}_{c,h}(\hat{x}_i,\hat{x}_{\pi(i)}) \,.
\end{equation*}
Subsequently, the batch of windows is rearranged back to its original form using the inverse mapping operation.
TextAdaIN is applied batch-wise with probability $p$ after every convolutional layer in the encoder, as illustrated in \cref{fig:arch_fig}(b). The permutation $\pi$ is sampled uniformly, and $p$ is a hyperparameter fixed ahead of training. TextAdaIN is only applied during training and not during inference.
\section{Experiments}
In this section, we begin by comparing our method's performance against state-of-the-art methods on several public handwritten datasets. Then, we demonstrate that TextAdaIN can be integrated into additional recognition architectures and applied to natural scene text images.
\noindent
\textbf{Datasets}~ We conduct experiments on several public handwritten and scene text datasets.
For handwriting, we consider the English datasets IAM~\cite{marti2002iam} and CVL~\cite{kleber2013cvl}, and the French dataset RIMES~\cite{grosicki2009icdar}. For scene text, we train on the synthetic datasets SynthText~\cite{Zisserman206st} and MJSynth~\cite{Zisserman2014mj} and test on four real-world regular text datasets: IIT5K~\cite{Mishra2012sj}, SVT~\cite{Wang2011bottom}, IC03~\cite{Lucas2003ic03}, IC13~\cite{Karatzas2013ic13} and three real-world irregular text datasets: ICDAR2015~\cite{Karatzas2015ic15}, SVTP~\cite{Phan2013svtp} and CUTE 80~\cite{Risnumawan2014cute}.
We present samples from each dataset and include more details in \cref{app:dtatsets}.
\noindent
\textbf{Metrics}~ To evaluate recognition performance, word-level accuracy is measured. For handwritten text recognition state-of-the-art comparison, Word Error Rate (WER) and Character Error Rate (CER) are adopted similar to the convention used in \cite{sueiras2018offline, zhang2019sequence, aberdam2020sequence}.
\noindent
\textbf{Implementation Details}~ Unless mentioned otherwise, in all of our experiments TextAdaIN is fused into the backbone of SCATTER~\cite{Litman_2020_CVPR}. The experimental settings, including the optimizer, learning rate, image size, and training datasets, are identical to SCATTER~\cite{Litman_2020_CVPR}. Full implementation details are described in \cref{app:implementation_det}.
\subsection{Comparison to State-of-the-Art}
In \cref{tab:htr_sota_results}, we measure the accuracy of our proposed method on public handwritten text benchmarks.
Our method achieves state-of-the-art results across all datasets. Compared to current state-of-the-art methods, incorporating TextAdaIN achieves a performance increase of \textbf{+1.4} pp (85.9\% vs. 87.3\%) on IAM, \textbf{+2.0} pp (92.4\% vs. 94.4\%) on RIMES and \textbf{+0.4} pp (77.8\% vs. 78.2\%) on CVL. We wish to emphasize that previous methods, such as \cite{bhunia2019handwriting,kang2020unsupervised,luo2020learn,aberdam2020sequence}, introduced complex modifications to the training phase, including adversarial learning and contrastive pre-training. In contrast, TextAdaIN can be easily implemented in a few lines of code and seamlessly fit into any mini-batch training procedure. In addition, the effect of applying MixStyle~\cite{zhou2021mixstyle} and pAdaIN~\cite{nuriel2020permuted} is displayed in \cref{tab:htr_sota_results}. Both have little to no effect on the results, indicating that handwritten text recognizers are already invariant to changes in global statistics.
In \cref{fig:fail_case}, we display failure cases of our method on the IAM dataset. The failure cases are mostly composed of highly cursive text, unclear handwriting styles and character occlusions. Adding additional context by employing a line-level approach can assist in rectifying these types of errors, nevertheless line-level recognition has its own caveats.
\begin{figure}[t]
\centering
\includegraphics[width=0.95\columnwidth]{Figures/error_ana_v2.pdf}
\caption{{\bf Failure cases.} Samples of failure cases on the IAM dataset. GT stands for the ground truth annotation, and Pred is the predicted result. Prediction errors are marked in red, and missing characters are annotated by strike-through.}
\label{fig:fail_case}
\vspace{-0.3cm}
\end{figure}
\subsection{Generalization of Proposed Method}
In this subsection, we explore our method's transferability to both the domain of scene text and to different recognition architectures. In addition to the SCATTER architecture, we utilize the Baek \etal~\cite{Baek2019clova} framework, which can describe the building blocks of many text recognizers, including~\cite{Bai2015crnn,Zisserman2015large,shi2016end,shi2016robust, liu2016star, Hu2017grccn,bai2017accurate,cheng2017focusing, zhang2019sequence, Litman_2020_CVPR, fogel2020scrabblegan, yousef2020origaminet}.
We choose to present TextAdaIN's performance when integrated into the Baek \etal~\cite{Baek2019clova} framework while employing either a CTC~\cite{graves2006connectionist} or an attention decoder~\cite{cheng2017focusing, shi2016robust}. As in \cite{Litman_2020_CVPR}, weighted (by size) average word accuracy is adopted where regular and irregular text datasets are distinguished.
As observed in \cref{tab:str_sota_results_avg}, TextAdaIN shows consistent improvement on both regular and irregular text benchmarks. The results are competitive with recent state-of-the-art methods. Furthermore, TextAdaIN is flexible and can be easily integrated into any general text recognizer.
Contrary to handwritten text recognition models, scene text models are trained on synthetic data~\cite{Baek2019clova,Litman_2020_CVPR}. This synthetic data is over a hundred times the size of handwriting training data and thus can cover a variety of text appearance. Therefore, scene text models are less prone to develop a reliance on local feature statistics. Despite this, TextAdaIN still shows improvement.
\input{tables/str_sota_avg}
\section{Ablation Study}
In this section, we conduct a series of experiments to further understand the performance improvements and analyze the impact of our key contributions. For this purpose, we adopt the IAM dataset, and the baseline model is the SCATTER architecture~\cite{Litman_2020_CVPR}. Similar to our previous experiments, implementation details are described in \cref{app:implementation_det}.
We begin by exploring the different variants of AdaIN, demonstrating that our method significantly outperforms other variants. To analyze the performance as a function of the granularity level, we then measure the accuracy while varying the number of windows. Subsequently, we demonstrate the reliance of text recognizers on local feature statistics by increasing the hyperparameter $p$. Lastly, we perform an analysis of our method's robustness demonstrating its effectiveness on fine versus coarse corruptions.
\input{tables/SpAdaIN_breakdown}
\begin{figure*}[t]
\centering
\includegraphics[width=0.8\textwidth]{Figures/feature_viz_v6.pdf}
\caption{{\bf Feature visualization.} An intensity map of the features after the first convolution layer of the encoder is visualized. TextAdaIN has two noticeable effects: (1) injecting background distortions drawn from an induced distribution (2) introducing masking on a local scale. Both regulate the reliance on local feature statistics in text recognizers as further investigated in \cref{sec:corruption}.}
\label{fig:adain_config}
\vspace{-0.3cm}
\end{figure*}
\begin{figure}[t]
\centering
\includegraphics[width=0.9\columnwidth]{Figures/app_fig_window_short.png}
\caption{{\bf Number of windows.} Varying the number of windows extracted per sample has multiple effects, including the granularity level and the number of donor images.}
\label{fig:window_size}
\vspace{-0.3cm}
\end{figure}
\subsection{AdaIN Variations}
Each dimension of the feature space represents different information about the input. Hence, modifying AdaIN to operate across different dimensions can influence the model accordingly. Our method is employed over both the channel and height dimensions between different elements of samples in a batch. Each element consists of a pre-defined number of consecutive frames in the sequential feature map. As seen in \cref{tab:spAdaIN_configuration}, TextAdaIN significantly improves recognition performance as opposed to all other AdaIN variations.
To better understand the information encompassed in each of the dimensions, we visualize the feature maps of a trained baseline model in \cref{fig:adain_config}. For this purpose, we apply PCA on the spatial dimensions of the first convolutional layer's output, thus obtaining an $H\times W \times 1$ intensity map. An image depicting the spatial intensities is displayed after normalization.
As depicted in \cref{fig:adain_config}, applying pAdaIN has almost no effect on the learned features. This is in alignment with the quantitative results indicating that text recognizers are relatively invariant to changes in global statistics. As for $\textrm{AdaIN}_{c,w}$, modifying individual vertical frames introduces subtle changes to the feature map. The network can easily compensate for the distortions leading to minimal impact on the training process.
Interestingly, applying $\textrm{AdaIN}_{h,w}$ injects text from the donor image into the feature map. This phenomenon originates from shifting each corresponding spatial location in the representation space. Clearly, without the modification of the labels, this effect will not improve the performance.
TextAdaIN has two major effects as visualized in both \cref{fig:reconst_vis} and \cref{fig:adain_config}.
The first is injecting local perturbations drawn from an induced distribution into the feature space. The distribution is induced from the manner in which TextAdaIN operates, providing a correct balance between the coarse to fine distortion level. Namely, TextAdaIN's impact is more local than pAdaIN's, yet more global in the sequence dimension than $\textrm{AdaIN}_{c,w}$. Therefore, the impact aligns with both the nature of the data and sequence-to-sequence approaches.
Occasionally, statistics of smooth areas (without text) are injected into regions of the feature space which represent text. This generates the second effect of local masking, in which part of the textual features undergo masking. We hypothesize that this forces the model to rely on semi-semantic information, which compensates for the missing visual cues. This was partially observed by Aberdam \etal~\cite{aberdam2020sequence} while applying horizontal cropping and in the context of speech recognition by Baevski \etal~\cite{baevski2020wav2vec}. As this analysis was performed on the feature space, we also show the influence of TextAdaIN on the input space in \cref{sec:corruption}.
\input{tables/corruption}
\input{tables/padain_vs_spadain}
\subsection{Number of Windows}
TextAdaIN splits the feature map into windows along the width axis. Each window is perceived as an individual element in the AdaIN operation. As the features vary in size at different layers, we define $K$ to represent the number of elements created per sample. Thus, $K$ determines the window size at each layer. Modifying $K$ has several different effects. For example, it controls the granularity level in which the statistics are calculated and modified and the number of donors.
Therefore, an optimal value of $K$ can be found to balance the different effects. In \cref{fig:window_size}, we plot the performance as a function of $K$. The best result is achieved when using $K=5$. We note that the average length of English words is 4.7 characters. Thus, when $K=5$, the statistics are normalized per character on average.
\subsection{Reliance on Local Statistics}
\label{sec:reliance}
In this subsection, we wish to assert text recognizers' reliance on local statistics. Nuriel et al. \cite{nuriel2020permuted} observed that applying pAdaIN at high values of $p$ resulted in a significant degradation of classification performance. We can thus infer that global statistics contain label-relevant information for classifiers.
For text recognizers, as shown in \cref{tab:spadain_vs_padain}, this is not the case.
Increasing the value of $p$, when applying pAdaIN, only slightly affects the results. This indicates that global statistics are less significant in the domain of text images.
In contrast, applying TextAdaIN with a high value of $p$ decreases performance substantially. This implies that profusely applying TextAdaIN distorts important information that the model relies on. Therefore, text recognizers are prone to develop a bias towards local statistics. If applied correctly, with the right $p$, TextAdaIN can alleviate this bias.
\subsection{Robustness Towards Local Corruption}
\label{sec:corruption}
To demonstrate that TextAdaIN indeed regulates the reliance on local statistics, in \cref{tab:corruption}, we evaluate its performance on several types of corruptions, comparing it to the baseline model. The corruptions are divided into three categories: (1) local masking, (2) kernel-based methods and (3) geometric transformations. The columns are roughly sorted by the locality scale of the corruptions. In the kernel-based columns, they are ordered by kernel size.
For each corruption, we display the gap between the performance of the baseline versus the TextAdaIN model. To accentuate the improvement provided by our method, we also display the normalized gap - the ratio between the gap on the corrupted data and the gap on the original data. This normalization removes the performance advantage of TextAdaIN on the original data.
We note that there is a distinct correlation between locality and the normalized gap. This provides further evidence that TextAdaIN regulates the reliance on local statistics in text recognizers. We refer the reader to \cref{app:corruption} for more details on and visualizations of the corrupted datasets.
\section{Conclusion}
Text recognizers leverage convolutional layers to extract rich visual features, and hence are extremely powerful. However, in many cases, they exhibit sensitivity towards subtle modifications that preserve image content. This is in contrast to classifiers that exhibit a bias on a global scale~\cite{nuriel2020permuted}. To relieve text recognizers' oversensitivity, we introduce TextAdaIN, a normalization-based method which distorts the feature space in a local manner and effectively regulates the reliance on local statistics.
Our method achieves state-of-the-art results on handwritten text recognition benchmarks. TextAdaIN is also applicable to various recognition architectures and to the domain of scene text images. In contrast to previous methods, our method does not require complex adversarial training, contrastive pre-training or the incorporation of additional data. It can be implemented simply in a few lines of code and effortlessly integrated into a mini-batch training procedure.
{\small
\bibliographystyle{ieee_fullname}
\section{Datasets}
\label{app:dtatsets}
In this work, we consider the following public datasets for handwriting and scene text. Samples from the different datasets are depicted in \cref{fig:dataset_samples}.
\subsection{Handwritten text}
For handwriting recognition, we consider three datasets:
\begin{itemize}[noitemsep]
\item \textbf{IAM} \cite{marti2002iam} handwritten English text dataset, written by 657 different writers. This dataset contains 101,400 correctly segmented words, partitioned into writer independent training, validation and test.
\item \textbf{CVL} \cite{kleber2013cvl} handwritten English text dataset, written by 310 different writers. 27 of the writers wrote 7 texts, and the other 283 writers wrote 5 texts. This dataset contains 84,990 correctly segmented words, partitioned into writer independent training and test.
\item \textbf{RIMES} \cite{grosicki2009icdar} handwritten French text dataset, written by 1300 different writers. This dataset contains 66,480 correctly segmented words, partitioned into training, validation and test sets that are independent of writers.
\end{itemize}
\subsection{Scene text}
For training the scene text models we utlized only synthetic datasets:
\begin{itemize}[noitemsep]
\item {\textbf{MJSynth}} (MJ) \cite{Zisserman2014mj} a synthetic text in image dataset which contains 9 million word-box images, generated from a lexicon of 90K English words.
\item \textbf{SynthText} (ST) \cite{Zisserman206st} a synthetic text in image dataset, containing 5.5 million word, designed for scene text detection and recognition.
\item \textbf{SynthAdd} (SA) \cite{Wang2019sar} only when training SCATTER for scene text, as in the original paper~\cite{Litman_2020_CVPR}, SA was also utilized for training data. This dataset was generated using the same synthetic engine as in ST, and contains 1.2 million word box images. SA is used for compensating the lack of non-alphanumeric characters in the training data.
\end{itemize}
\begin{figure}[t]
\centering
\includegraphics[width=0.9\columnwidth]{supp_files/dataset_samples.pdf}
\caption{\label{fig:dataset_samples} \textbf{Dataset samples.}
Examples of images from each dataset.
}
\vspace{-0.5cm}
\end{figure}
\begin{figure*}[t]
\centering
\includegraphics[width=\textwidth]{supp_files/corruption_v1.pdf}
\caption{\label{fig:corruptions}
{\bf Visualization of selected corruptions}. To assert TextAdaIN's regularization effect we compare it's performance to the baseline while applying different types of corruptions. We visualize the different corruptions, sorted by their locality impact in each category.
}
\end{figure*}
Aligned with many scene text recognition manuscripts (e.g. \cite{Bai2018aster, Baek2019clova, Wang2019sar, Litman_2020_CVPR}), we evaluate our models using seven scene text datasets: ICDAR2003, ICDAR2013, IIIT5K, SVT, ICDAR2015, SVTP and CUTE. Those datasets are commonly divided into regular and irregular text according to the text layout.
\newline
\textbf{Regular text} datasets are composed of:
\begin{itemize}[noitemsep]
\item \textbf{IIIT5K}~\cite{Mishra2012sj} consists of 2000 training and 3000 testing images that are cropped from Google image searches.
\item \textbf{SVT}~\cite{Wang2011bottom} is a dataset collected from Google Street View images and contains 257 training and 647 testing cropped word-box images.
\item \textbf{ICDAR2003}~\cite{Lucas2003ic03} contains 867 cropped word-box images for testing.
\item \textbf{ICDAR2013}~\cite{Karatzas2013ic13} contains 848 training and 1,015 testing cropped word-box images.
\end{itemize}
\textbf{Irregular text} datasets are composed of:
\begin{itemize}[noitemsep]
\item \textbf{ICDAR2015}~\cite{Karatzas2015ic15} contains 4,468 training and 2,077 testing cropped word-box images, all captured by Google Glass, without careful positioning or focusing.
\item \textbf{SVTP}~\cite{Phan2013svtp} is a dataset collected from Google Street View images and consists of 645 cropped word-box images for testing.
\item \textbf{CUTE 80}~\cite{Risnumawan2014cute} contains 288 cropped word-box images for testing, many of which are curved text images.
\end{itemize}
\section{Implementation Details}
\label{app:implementation_det}
In our experiments, we utilize three types of architectures. The first is SCATTER, and the two others are variants of Baek~\etal\cite{Baek2019clova} framework. All models are trained and tested using the PyTorch
framework on a Tesla V100 GPU with 16GB memory.
We follow the training procedure performed in \cite{Litman_2020_CVPR}. Accordingly, models are trained using the AdaDelta optimizer with: a decay rate of 0.95, gradient clipping with a magnitude of 5 and batch size of 128. During training, 40\% of the input images are augmented by randomly resizing them and adding extra distortion. Models trained on handwriting and scene text datasets are trained for 200k iterations and 600k iterations, respectively. Model selection is performed on the validation set, which for scene text is the union of the IC13, IC15, IIIT5K, and SVT training splits and for handwriting is the predefined validation sets. When utilizing SCATTER all images are resized to $32\times 128$ and are in RGB format. For evaluation, word accuracy measured is case insensitive. We refer the reader for any additional implementation details, both during inference and training to the original papers \cite{Baek2019clova, Litman_2020_CVPR}.
For TextAdaIN, we use $p=0.01$ and split images into $K=5$ windows. In the cases where the number of windows doesn't divide the width, we use the maximum width that can be divided and ignore the remainder.
\section{TextAdaIN Pseudo-Code}
\label{app:code}
In this section, we provide pseudo-code for TextAdaIN. The code includes two functions not explicitly implemented: \textit{create\_windows\_from\_tensor}, \textit{revert\_windowed\_tensor}.
The first function represents the mapping:
\begin{equation*}
X\in \mathbb{R}^{B\times C \times H \times W} \rightarrow \widehat{X}\in \mathbb{R}^{B\cdot K \times C \times H \times \frac{W}{K}} \,,
\end{equation*} and the second represents the corresponding inverse mapping. As mentioned in the paper, we don't backpropogate through $\mu_{c,h}(\hat{x}_{\pi(i)}), \sigma_{c,h}(\hat{x}_{\pi(i)})$ and thus detach is used.
\input{supp_files/psudo_code}
\section{Image Corruptions}
\label{app:corruption}
In Section 5.4, we compare between the performance of the baseline model and the TextAdaIN version on corrupted versions of the IAM test set. \cref{fig:corruptions} contains original images from the test set on the first column, and the results of applying each of the corruptions on the following columns. The corruptions are applied utilizing the \textit{imgaug}~\cite{imgaug} package as explicitly written below.
\input{supp_files/corruptions}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 248
|
#pragma once
#include <aws/iottwinmaker/IoTTwinMaker_EXPORTS.h>
#include <aws/core/utils/memory/stl/AWSString.h>
namespace Aws
{
namespace IoTTwinMaker
{
namespace Model
{
enum class ErrorCode
{
NOT_SET,
VALIDATION_ERROR,
INTERNAL_FAILURE
};
namespace ErrorCodeMapper
{
AWS_IOTTWINMAKER_API ErrorCode GetErrorCodeForName(const Aws::String& name);
AWS_IOTTWINMAKER_API Aws::String GetNameForErrorCode(ErrorCode value);
} // namespace ErrorCodeMapper
} // namespace Model
} // namespace IoTTwinMaker
} // namespace Aws
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,195
|
Hyperacanthomysis longirostris is een aasgarnalensoort uit de familie van de Mysidae. De wetenschappelijke naam van de soort werd in 1936 voor het eerst geldig gepubliceerd door Ii.
Verspreiding
Hyperacanthomysis longirostris is een aasgarnaal. Het is inheems in de kustwateren van de noordoostelijke Stille Oceaan, inclusief het zuiden van Japan, Korea en China. Het wordt geïntroduceerd in de Sacramento-San Joaquin Delta, Californië, waar het is geconcentreerd in estuariene leefomgevingen met een laag zoutgehalte. Het handhaaft een populatie in 0-5 psu, grotendeels door een patroon van verticale migratie, dat opwaarts migreert bij inkomende getijden. Het is de overheersende aasgearnaal in de delta geworden en vervangt grotendeels een inheemse aasgarnalensoort (Neomysis mercedis), die een belangrijk voedselorganisme is voor jonge vissen.
Aasgarnalen
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,039
|
\section{Introduction}
Recent research indicates that quantum computing can effectively solve
some problems that are considered intractable on classical Turing machines.
A sample of such problems is the factorization of large composite numbers into primes,
a problem which is the basis of the security of many classical key cryptosystems \cite{Nielsen00}.
The task of designing a quantum computer is equivalent to finding a physical system of
quantum bits (qubits) and quantum gates between the bits.
Such a physical system has to fulfill several basic criteria~\cite{DiVincenzo00}.
First, one needs a system with two eigenstates for each qubit
which can be identified as the two logic states $|0\rangle$ and $|1\rangle$.
One should be able to perform one-qubit operations
on an arbitrary qubit without affecting the other qubits.
The operations should be able to create a state which is the superposition of the two
eigenstates.
Second, the qubits must interact with each other to provide a set of universal logic gates.
It has been shown that any operation can be
decomposed into controlled-not gates (CNOT) of two qubits between the nearest neighbor
and rotations on individual qubits \cite{DiVincenzo95}.
Third, one must be able to initialize the qubits to a known state at the beginning
of each operation sequence since the results of computation generally depend on the input states.
Fourth, one should be able to extract the results from the qubits by some measurements.
Fifth, the quantum mechanical feature of the
qubits also require that they are well isolated from environment so that the
coherence time is long compared with an average logic gate duration
such that many logic gates can be implemented within the coherence
time. This means for each qubit, the quantum state which is a superposition
of two eigenstates, should sustain itself long enough before relaxing to the state determined
by the environment.
Furthermore, a useful register for a quantum computer needs at least
$10^3$ qubits. Scalability of proposed quantum computer
architecture to many qubits is of central importance \cite{Cirac95}.
Meeting all these criteria simultaneously pose a significant
experimental challenge.
For example, how can one gain access to a
quantum system and at the same time keep the coherence time long?
So far only a few systems have been identified as potential
viable quantum computer models.
Atoms \cite{Monroe02} and ions in traps \cite{Kielpinski02},
cavity quantum electrodynamic system \cite{Raimond01},
nuclei in complex molecules \cite{Cory97},
quantum dots and other solid state devices \cite{Maklin01}
and electrons confined on top of liquid helium \cite{Platzman02}
have been studied as possible implementations.
In this paper, we propose a system where individual
electrons merged inside superfluid liquid helium are used as qubits.
The paper is arranged in such a way that first we will describe
some properties of single electrons inside liquid helium,
then we will discuss how to confine a chain of such electrons inside a trap.
In the remainder of the paper, we will focus on how such a system can fulfill
the criteria for a quantum register.
\section{Single Electron Bubbles}
When an energetic electron enters liquid helium, it dissipates its
energy quickly through producing excited state helium atoms and
quasi-particles like rotons and phonons. After the electron comes to rest,
it will expel the surrounding helium atoms and produce a
spherical cavity of approximately 17 \AA~in radius (see below) which is almost free of helium atoms.
The properties of such single electron
bubbles have been studied extensively \cite{Maris03}.
Here we just focus briefly on some features which are relevant to the implementation of qubits.
The total energy of such an electron bubble can be estimated by
\begin{equation}
E=E_{\rm el} + \gamma A +PV
\end{equation}
where $E_{\rm el}$ is the energy of the electron,
$\gamma$ is the surface energy of liquid helium,
$A$ is the surface area of the bubble,
$P$ is the pressure inside the liquid and $V$ is the volume of the bubble.
In the first order approximation,
we can consider that the electron is confined inside a spherical square well
and the wave function of the electron goes to zero at the wall of the bubble.
The ground state (1s) energy of the electron $E_{\rm el}$ can be written as
\begin{equation}
E_{el}=\frac{h^2}{8mR^2},
\label{electron_energy}
\end{equation}
where $m$ is the mass of the electron, $R$ is the bubble radius.
The radius of the bubble thus can be determined by minimizing the total energy $E$.
If assuming the pressure $P$ is zero,
this gives
\begin{equation}
R=\left(\frac{h^2}{32\pi m \gamma} \right)^{1/4}
\label{bubble_radius}
\end{equation}
If the value of $0.37~$erg/cm$^2$ is taken for the surface tension of liquid helium-4~\cite{Vicente02},
Eq.~\ref{bubble_radius} gives $R=19$~\AA.
Several factors such as the finite thickness of the liquid vapor interface,
the penetration of the electron wave function into the liquid helium can give some corrections to the
above calculated $R$ value \cite{Maris00}.
Comprehensive reviews of electrons in helium can be found in reference \cite{Fetter74}.
From the size of an electron bubble,
the effective mass of such an object can be estimated to be equal to
the amount of liquid helium expelled.
Experimentally, the effective mass was
measured, which gives the value of $243$~m$_{\rm He}$,
m$_{\rm He}$ is the mass of one helium atom~\cite{Poitrenaud72, poitrenaud74}.
In the next section, this should be the value to be used to calculate the effective trapping potential
of a linear quadrupole trap.
The energy spectra of single electron bubbles were investigated both theoretically
and experimentally \cite{Maris03, Grimes90}.
Here we are interested in the laser induced fluorescence when the electron is excited from 1s to 1p or
2p state.
The photons emitted from the bubbles can be used to indicate their locations.
We will discuss how to use such information in reading out the qubits.
The transition energy of 1s$\rightarrow$1p is 0.11 eV and 1s$\rightarrow$2p is 0.52 eV.
The two-level system of an electron bubble is due to two eigenstates
of the spin 1/2 electron in a magnetic field.
The $g$ value of such an electron spin was measured and it is equal to the $g$ value of
a free electron within 10~ppm \cite{Reichert74}.
For the convenience of later discussions,
we define the lower energy state in which the spin is parallel to the magnet field, $|0\rangle$,
and the higher energy state in which it is anti-parallel to the field, $|1\rangle$.
These two states are the two logic states of a quantum qubit.
Similarly, for two qubits (two single electron bubbles),
we use the symbols $|00\rangle$, $|10\rangle$, $|01\rangle$ and $|11\rangle$
to represent the combined states.
Here we emphasize that the multi-bits system are
multiple single electron bubbles with one electron in each bubble in contrast to
a multiple electron bubble in which many electrons are confined in a single bubble.
An important requirement of the implementation of quantum computing is that the
coherence time of an individual qubit should be much longer than the duration of a quantum operation.
The electron in the helium void has very weak interactions with its surroundings.
The source of decoherence is the spin-lattice relaxation.
Some theoretical calculation predicts that the spin-lattice relaxation time $T_1$
could be in the order of $10^5$ seconds~\cite{Huang71}.
So far there was only one experimental investigation on $T_1$ through an ESR measurement,
which showed that $T_1$ was longer than 100 ms \cite{Reichert74}.
It will be useful to extend the investigations.
Liquid helium is such a pure system that away from the walls of its container
there are no impurities (except the isotope helium 3) that can introduce spin-lattice relaxation.
It is worth mentioning that helium~3 which has nuclear spin 1/2 can
influence $T_1$~\cite{Reichert83}.
There is around 0.1-0.2 ppm of helium~3 in helium~4.
But it is not clear if the trace amount of helium~3 will have any significant effect on $T_1$.
\section{Trapping single electron bubbles}
The technique of using radio frequency trap (Paul trap) to confine
ions in vacuum have been developed in the research of
precision spectroscopy and standards,
laser cooling and recently in the implementation of quantum computing \cite{Paul90, Brewer92}.
A single electron bubble is not much different from a very heavy ion.
It has a mass of 243 times the mass of a helium atom and a charge of an electron.
It is inside a dissipative environment if the temperature is not too low.
Since trapping single or multi-electron bubbles can be a useful technique in the study such as
bubble fission \cite{Maris00} and degenerate two dimensional electron systems \cite{Silvera05},
we will devote a separate paper to describe various trapping schemes.
Here we describe briefly a linear quadrupole trap to confine a chain of single electron bubbles as a quantum register.
\begin{figure}[htbp]
\centering \includegraphics[scale=0.5]{trap.eps}
\caption{A quadrupole trap. The periodical static potential is produced by the
rings to confine the bubbles in the z direction. In some situations as described in the text,
several neighboring rings' potential should be tuned individually.}
\label{fig_trap}
\end{figure}
The device consists of four parallel rods as shown in Fig.~\ref{fig_trap}.
Typically, each rod has a circular cross section.
A time-varying RF potential $V_0\cos\Omega t$ is applied to the two opposing rods.
The remaining two rods are held at RF ground.
The time-varying potential near the axis can be approximated by
\begin{equation}
V=\frac{V_0}{2}\left(1+\frac{x^2-y^2}{r^2}\right) \cos \Omega t,
\end{equation}
where $r$ is the distance from the axis to the surface of the electrodes.
For sufficiently high driving frequency $\Omega$,
a particle with mass $m$ and charge $q$ moves in the effective pseudo-potential
\begin{equation}
\Phi=\frac{qV_0^2}{4m\Omega^2r^4}(x^2+y^2)=\frac{m}{2q}w_r^2(x^2+y^2),
\label{eq_trap}
\end{equation}
where
\begin{equation}
w_r=\frac{qV_0}{\sqrt{2}m\Omega r^2}
\end{equation}
To make a stable parabolic trap as described by Eq.~\ref{eq_trap},
the RF driving frequency $\Omega$ has to satisfy
\begin{equation}
\frac{2qV}{mr^2\Omega^2} \le 0.92
\end{equation}
If $r \sim 1$~mm and $V \sim 1$~Volt,
this will give a minimum value of 74~kHz.
From Eq.~\ref{eq_trap}, one can see for moderate voltages and frequencies,
the trap is very steep.
After a bubble is trapped inside the trap,
its amplitude of thermal motion in x-y plane is very small.
So all the bubbles form a one dimensional chain
and they can not interchange their positions.
The confinement in the $z$ direction is achieved by a static electric field
produced by the rings at different potential
which is schematically shown in Fig.~\ref{fig_trap}.
\section{Single Qubit and Multiple Qubits}
The chain of electron bubbles in the Fig. \ref{fig_trap}
is similar to a big artificial one-dimensional molecule.
A magnetic field is applied along the $z$ direction.
For a single qubit operation,
a RF pulse at the Larmor frequency can be applied to rotate the spin.
By introducing a magnetic field gradient along the z axis,
$B=\alpha z$,
each spin experiences a different field and has a unique Larmor frequency.
This way, all the spins can be addressed individually.
The situation discussed here is very similar to the NMR quantum
computing where the quantum computer consists of several
individual atoms with spin $1/2$ nuclei~\cite{Cory97}.
Different nuclei experience different total (external plus internal)
magnetic field thus have different Larmor frequency.
The interaction between two neighboring spins is via magnetic coupling.
At the beginning of each computation sequence,
the quantum register,
here is the chain of spins,
has to be set to a known initial state, usually to its ground state.
This can be achieved by establishing thermal equilibrium between the spin ensemble and the external
thermal reservoir of the liquid helium.
At 4.2 K and a field of 1 T, the probability of finding a spin in the ground state is $58\%$;
if $B/T$ is increased by a factor of 20 and at 0.2 K, $99.98\%$.
As mentioned above, the coupling between the electron spin with the surrounding helium
is very weak.
On one hand, the qubits benefit from such weak interaction and have very long coherence time.
On the other hand, this makes thermalization a very slow procedure.
The time needed can be estimated by
\begin{equation}
\frac{dp}{dt}=-\frac{p-p_{\rm eq}}{T_1},
\end{equation}
where, $p$ is the polarization, $p_{\rm eq}$ is the equilibrium polarization,
and $T_1$ is the spin-lattice relaxation time.
So, a waiting period of several $T_1$ is needed to let the system being
settled to the ground state before each operation sequence.
This is certainly not practical if $T_1$ is in the order of $10^5$~s.
Another possible solution to this issue is that during the loading procedure of the bubble chain,
one can sort the bubbles according to their spin orientations and let only the bubbles
with desired spins enter the trap. Since $|0\rangle$ bubbles tend to
move toward high field regime and $|1\rangle$ bubbles move the other way, the separation can
be accomplished by a magnetic field gradient.
After a sequence of operations, we need a mechanism to read out the result of each qubit.
The following is a scheme which is similar to the Stern Gerlach experiment.
By lowering the electric potential barrier on the end of the chain,
the bubble at the end will start to drift. Owing to the gradient of the magnetic field,
the bubble will experience a force whose direction depends on the spin orientation.
The force,
\begin{equation}
F= -g \mu_B s \frac{\partial B}{\partial z}=-g \mu_B s \alpha,
\end{equation}
where $\mu_B$ is the Bohr magneton, $s$ is the spin, and $g$ is the g-value of the spin.
There will be two different drift velocities corresponding to the two spin orientations.
After a period of time,
we can take a snap picture by shining a laser bean toward the two possible locations of the bubble and
we should see the bubble at only one place. This information will tell the spin orientation.
And repeating the same procedure for all the bubbles, one can get a measurement of the whole register.
The scalability of the scheme depends on how large the magnetic gradient can be applied and how well
the RF instruments can separate the frequencies to address the individual spins.
The higher the gradient, the denser the bubbles in the trap.
\section{Two qubit controlled-not operation}
The two qubit controlled-not operation is defined as
\begin{eqnarray}
| 00 \rangle \rightarrow |00 \rangle~~ | 10 \rangle \rightarrow |10 \rangle \\
| 01 \rangle \rightarrow |11 \rangle~~ | 11 \rangle \rightarrow |01 \rangle
\label{eq_two_bit}
\end{eqnarray}
where the second bit is the control bit.
The CNOT operation in NMR quantum computing was achieved through
the spin-spin interaction. The magnetic resonant frequency of a particular spin
depends on the orientations of its neighboring spins.
Such interaction is strong only within interatomic distance in a molecule.
To bring a pair of electron bubbles to such a distance,
the external electric field has to be exceedingly large.
\begin{figure}[htbp]
\centering \includegraphics[scale=0.38]{two_bit.eps}
\caption{Two-bit controlled not operation.
For $|00\rangle$ and $|11\rangle$, the centers of the pair shift
due to the magnetic field gradient but the distances between the bubbles keep the same.
While for $|10\rangle$ and $|01\rangle$,
the centers keep the same but the distances change.}
\label{fig_two_bit}
\end{figure}
The following scheme is designed to address the two qubit operation by making use of the magnetic
field gradient.
By lowering the electric potential barrier that separates the neighboring bubbles,
the two bubbles can be brought closer inside the same trap.
Due to the Coulomb repulsion,
the two bubbles will be separated by a distance which can be controlled by the strength of
the static potential. Besides the Coulomb interaction,
the spins will also experience a force due to the magnetic field gradient.
As shown in Fig. \ref{fig_two_bit},
there exist four sets of locations for the pair. And for bubble 1,
$z1$ and $z2$ are the locations for states $|11\rangle$ and $|01\rangle$, respectively.
As indicated also in the figure, frequency $f(z1)$ will cause $|11 \rangle \rightarrow |01 \rangle$
and $f(z2)$ will cause $| 01 \rangle \rightarrow |11 \rangle$ transition.
By applying a $\pi$ pulse which contains the two frequencies simultaneously,
we can execute the operation specified in Eq.~\ref{eq_two_bit} without altering the other states.
This is the two bit controlled-not.
After the operation,
the two bubbles can be re-separated by raising barrier between them again.
In the above discussion, we assume that a bubble's motion follows Stokes law that
the velocity is proportional to the force applied on it. When the force
is reduced to zero, the bubble stops moving. This condition is satisfied at temperatures
above 0.5 K in pure helium-4 when there are still enough photons and rotons to dissipate the
energy of the bubbles.
At lower temperatures, some other dissipation mechanism has to be introduced since the density of those
quasi-particles becomes very low. The issue can be solved by simply adding several tens of ppm of helium-3
into the system which will significantly increase the dissipation since the helium-3 inside will not become
superfluid at the lowest temperature ever achieved.
In this paper, we discussed the possibility of the implementation of quantum computing with a chain of single
electron bubbles inside liquid helium.
The method combines the schemes of trapped ions and NMR quantum computation.
Such a system should be able to scale up to $10^2$ bits without major technical obstacles.
Finally, we would like to mention that similar schemes may also work for positive ions with
one unpaired electron.
For example, the alkaline earth metal ion Ba$^+$, Mg$^+$ and Sr$^+$.
Some spectroscopic studies have been carried out recently on those specimens immersed inside liquid
helium \cite{Tabbert95}.
One possible advantage of those systems is that there may exist some optical transitions
that can be used to manipulate and measure the spin orientation of individual ions through laser pulses.
Positive helium ions can also be made.
A difference between positive ions and
electrons inside helium is that positive ions attract the neighboring helium atoms and form solid
balls instead of cavities. Some further work is still needed in the investigation of those
systems in the possible applications in quantum computing.
The author would like to thank Dr. S. Balibar, Prof. G. Seidel and Prof. I. Silvera
for very helpful discussions and suggestions.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 563
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Zarda pulao or sweet rice is a popular dish of South Asia. It's equally popular in India and Pakistan and is mainly made on celebration and festivals like weddings, diwali etc..
Zarda pulao is also popular as meethe chawal in Punjab, kangra valley and many states of India. This pulao is so aromatic with saffron strands and vibrant yellow colour and mild fragrance and also its name.
Our today's Foodie Monday Bloghop theme is based on "North Indian Cuisine" So I made this aromatic and flavourful pulao on the occasion of Vasant Panchami.
Vasant Panchami - it's a famous festival when Saraswati, the goddess of intellect, learning and wisdom is worshipped.
The colour yellow holds a special meaning for this celebration as it signifies the brilliance of nature and the vibrancy of life. So I made both saffron rice and rava kesari halwa.
This is one of our family favourite dish and I usually made on every festival season. This recipe has been passed on to me by my mother, and to her from her mother, and so on! I just made a change in this recipe I added a fennel seeds(saunf)..something different flavour...hmmmmm yumm !!
This pulao is actually loaded with lots of dry fruits and desi ghee, brings out the taste from whole spices, kewra water.
Sweet rice is very easy to make and a perfect desert for small pooja, party and get together at home.
This is one of the desert which is liked by every person and loved by kids also. It is easy to make and consists of simple ingredients.
Learn how to make zarda pulao with very simple and easy steps.
1. Soak rice in water for 1 hour.
2. Mix milk, food colour, kesar, rose water and sugar in a bowl.
3. Heat 4-5 cups of water in a pan. Once it comes to boil, add the soaked rice without water.
4. Cook till the rice is about 80 % done, then strain the water and mix half of desi ghee.
5. Heat the remaining half of desi ghee in a pan. Add dry fruits, fennel seeds and fry till golden-brown.
6. Add whole spices and fry for about half a minute. Add the milk mixture and boil.
7. Add the rice and cook on low flame for 10-12 minute with cover.
8. Mix rice with a fork for better presentation.
9. Garnish with few chopped almonds and Serve hot.
Looks yummy !! Lovely share dear.
Love the color of the pulao. Looks so delicious!
Oh I like this...sure to try..
Thanks a lot dear Jeena..waiting !!
You know Zarda Pulao, Punjabi gur ke chawal and Sindhi recipe Tahiri has more or less similar preparation. And this rice preparation is absolutely delicious and mainly prepared on special occasions like the arrival of a new year or when you'll start something new. Your preparation is looking healthy, flavorful and super delicious!
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{
"redpajama_set_name": "RedPajamaC4"
}
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\section{Introduction}
Anomaly mediation is an attractive alternative to the MSUGRA paradigm for
low energy supersymmetry~\cite{lrrs}-\cite{aprr}. In Ref.~\cite{hjjr} we
showed how augmenting the MSSM with an extra $U_{1}$ broken at high energies
provides a natural solution to the AMSB tachyonic slepton problem if the
extra $U_{1}$ has a Fayet-Iliopoulos term; this model being the explicit
construction associated with the scenario first explored in detail in Ref.~%
\cite{jja}. Here we show that a similar low energy theory can in fact arise
from a \textit{scale invariant} $MSSM\otimes U_{1}^{\prime }$ theory, with
the scale of $U_{1}^{\prime }$ breaking arising by dimensional
transmutation, and the only explicit terms of dimension two and three in the
Lagrangian being those associated with AMSB. The $U_{1}^{\prime }$ breaking
scale also determines the right handed neutrino masses, which in turn
determine the observable neutrino masses via the usual see-saw mechanism.
The low energy theory differs, however, from that of Ref.~\cite{hjjr}, in
that a light MSSM singlet survives the $U_{1}^{\prime }$ breaking; this
raises subtle issues concerning decoupling, as described by Pomarol and
Rattazzi (PR)~\cite{aprr}.
\section{$U(1)^{\prime }$ radiative breaking}
\subsection{The superpotential}
\label{sec:superpot} The superpotential for our theory is
\begin{equation}
W = W_1 + W_2 +W_3, \label{eq:spot}
\end{equation}
where $W_1$ contains the Yukawa terms responsible for the quark and lepton
Dirac masses (including the neutrino Dirac masses):
\begin{equation}
W_1 = Q Y_u t^c H_2 + Q Y_d d^c H_1 + L Y_{e} e^c H_1 + L Y_{\nu} \nu^c H_2
\label{eq:spota}
\end{equation}
and $W_2$ contains additional terms involving an MSSM singlet sector; a pair
of fields $\phi$, ${\overline{\phi}}$ charged under $U^{\prime }_1$, and
gauge singlet fields $U$, $Z$:
\begin{equation}
W_2 = U(\lambda\phi{\overline{\phi}} - {\textstyle{\frac{{1}}{{2}}}}\rho
Z^2) + {\textstyle{\frac{{1}}{{6}}}}kU^3. \label{eq:spotb}
\end{equation}
$W_3$ contains terms coupling the two sectors, the purpose of which which
will be to generate the Higgs $\mu$-term and the right-handed neutrino
masses. We will consider two slightly different forms for $W_3$:
\begin{equation}
W_3^A = \lambda^{\prime \prime }U H_1 H_2 + {\textstyle{\frac{{1}}{{2}}}}%
Y_{\nu^c}\phi \nu^c\nu^c \label{eq:spotca}
\end{equation}
and
\begin{equation}
W_3^B = \lambda^{\prime \prime }Z H_1 H_2 + {\textstyle{\frac{{1}}{{2}}}}%
Y_{\nu^c}\phi \nu^c\nu^c. \label{eq:spotcb}
\end{equation}
Here $\lambda$, $\lambda^{\prime \prime }$, $\rho$, $k$ are coupling
constants while $Y_{u,d,e,\nu}$ and $Y_{\nu^c}$ are $3\times 3$ matrices in
flavour space. The superpotential $W$ is natural in that it contains all
possible cubic terms allowed by the symmetry $MSSM\otimes U^{\prime }_1
\otimes Z_2$, where, under $Z_2$, $Z \to -Z$. and the remaining fields are
invariant (in the case of $W_3^A$) or arranged so that $H_1 H_2 \to - H_1
H_2 $ (in the case of $W_3^B$).
Note that $W$ contains no explicit mass scale. The electroweak scale (and
the associated supersymmetry-breaking scale) are generated via anomaly
mediation, while the $U^{\prime }_1$-breaking scale is generated by
dimensional transmutation, as we shall discuss.
The $U^{\prime }_1$ charge assignments of the various fields are shown in
Table~1.
\begin{table}[tbp]
\begin{center}
\begin{tabular}{|ccccccc|}
\hline
$q_Q$ & $q_{u^c}$ & $q_{d^c} $ & $q_{H_1}$ & $q_{H_2}$ & $q_{\nu^c}$ & $%
q_{\phi} = -q_{{\overline{\phi}}}$ \\ \hline
& & & & & & \\
$-\frac{1}{3}q_L$ & $-q_e-\frac{2}{3}q_L$ & $q_e+\frac{4}{3}q_L$ & $-q_e-q_L$
& $q_e+q_L$ & $-2q_L-q_e$ & $4q_L + 2q_e$ \\
& & & & & & \\ \hline
\end{tabular}%
\end{center}
\caption{Anomaly free $U_1$ symmetry for arbitrary lepton doublet and
singlet charges $q_L$ and $q_e$ respectively.}
\label{anomfree}
\end{table}
\subsection{The scalar potential}
\label{sec:potmin} Our theory is defined by the superpotential Eq.~(\ref%
{eq:spot}), with the addition of anomaly mediation soft-breaking terms of
the general form
\begin{eqnarray}
L_{\mathrm{SOFT}} &=&\sum_{\phi }m_{\phi }^{2}\phi ^{\ast }\phi +\left[
m_{3}^{2}H_{1}H_{2}+\sum_{i=1}^{3}\frac{1}{2}M_{i}\lambda _{i}\lambda _{i}+%
\mathrm{h.c.}\right] \notag \\
&+&\left[ H_{2}Qh_{t}t^{c}+H_{1}Qh_{b}b^{c}+H_{1}Lh_{\tau }\tau ^{c}+\mathrm{%
h.c.}\right],
\end{eqnarray}%
where
\begin{subequations}
\begin{eqnarray}
M_{i} &=&m_{0}\beta _{g_{i}}/g_{i} \label{eq:amsba} \\
h_{Y} &=&-m_{0}\beta _{Y} \label{eq:amsbb} \\
m_{\phi }^{2} &=&{\textstyle{\frac{{1}}{{2}}}}m_{0}^{2}\mu \frac{d}{d\mu }%
\gamma _{\phi }. \label{eq:amsbc}
\end{eqnarray}%
Here $m_{0}$ is the gravitino mass, $\beta _{g_{i}}$ are the gauge $\beta $%
-functions, $\gamma $ the chiral supermultiplet anomalous dimension, $Y$
stands for any Yukawa coupling and $\beta _{Y_{t,b,\tau }}$ are the Yukawa $%
\beta $-functions. (We will discuss presently the origin of the Higgs $\mu $%
-term and associated soft breaking term).
Let us seek an extremum of the scalar potential such that $\phi, {\overline{%
\phi}}, Z$ obtain vacuum expectation values which are of the same order and
much bigger than $m_0$. We therefore begin by writing down the scalar
potential corresponding to the superpotential $W_2$. Note that this
superpotential has no accidental additional continuous symmetries;
consequently at the extremum there will be no pseudo-Goldstone bosons. The
relevant tree potential may be written
\end{subequations}
\begin{eqnarray}
V &=& {\textstyle{\frac{{1}}{{2}}}}m_1^2 x^2 + {\textstyle{\frac{{1}}{{2}}}}%
m_2^2 y^2 +{\textstyle{\frac{{1}}{{2}}}}m_3^2 z^2 + {\textstyle{\frac{{1}}{{2%
}}}}m_u^2 u^2 + h_1 uxy + {\textstyle{\frac{{1}}{{2}}}} h_2 u z^2 + {%
\textstyle{\frac{{1}}{{6}}}}h_3 u^3 \notag \\
&+& {\textstyle{\frac{{1}}{{4}}}}\lambda^2 (xy-z^2+ {\textstyle{\frac{{1}}{{2%
}}}}{\overline{k}}u^2)^2 +{\textstyle{\frac{{1}}{{4}}}}\lambda^2 u^2
(x^2+y^2)+{\textstyle{\frac{{1}}{{2}}}}\lambda\rho u^2 z^2 + {\textstyle{%
\frac{{1}}{{8}}}}g_{\phi}^2 (x^2 - y^2)^2. \label{eq:epot}
\end{eqnarray}
Here $g_{\phi} = q_{\phi}g^{\prime }$ where $g^{\prime }$ is the $U^{\prime
}_1$ coupling, $x /\sqrt{2} = \mathopen\langle \phi\mathclose\rangle $, $y /%
\sqrt{2} = \mathopen\langle {\overline{\phi}}\mathclose\rangle $, $z = \sqrt{%
\frac{\rho}{\lambda}}\mathopen\langle Z\mathclose\rangle $, $u /\sqrt{2} = %
\mathopen\langle U\mathclose\rangle $, $m_{\phi} = m_1$, $m_{{\overline{\phi}%
}} = m_2$, $m_3^2 = 2m_Z^2\lambda/\rho$ and ${\overline{k}}= k/\lambda$. The
cubic couplings $h_{1,2,3}$ are related to $\beta_{\lambda,\rho,k}$
according to Eq.~(\ref{eq:amsbb}):
\begin{subequations}
\begin{eqnarray}
h_1 & = & {\textstyle{\frac{{1}}{\sqrt{2}}}}h_{\lambda} = -{\textstyle{\frac{%
{m_0}}{\sqrt{2}}}}\beta_{\lambda} \label{eq:hamsba} \\
h_2 & = & -{\textstyle{\frac{{\sqrt{2}\lambda}}{{\rho}}}}h_{\rho} = {%
\textstyle{\frac{{\sqrt{2}\lambda m_0}}{{\rho}}}}\beta_{\rho}
\label{eq:hamsbb} \\
h_3 & = & {\textstyle{\frac{{1}}{\sqrt{2}}}}h_{k} = - {\textstyle{\frac{{m_0}%
}{\sqrt{2}}}}\beta_{k}. \label{eq:hamsbc}
\end{eqnarray}
For an extremum we have
\end{subequations}
\begin{subequations}
\begin{eqnarray}
x\left[ m_{1}^{2}+{\textstyle{\frac{{1}}{{2}}}}g_{\phi }^{2}(x^{2}-y^{2})+{%
\textstyle{\frac{{1}}{{2}}}}\lambda ^{2}u^{2}\right] +y\left[ {\textstyle{%
\frac{{1}}{{2}}}}\lambda ^{2}(xy-z^{2}+{\textstyle{\frac{{{\overline{k}}}}{{2%
}}}}u^{2})+h_{1}u\right] &=&0 \label{eq:minA} \\
y\left[ m_{2}^{2}-{\textstyle{\frac{{1}}{{2}}}}g_{\phi }^{2}(x^{2}-y^{2})+{%
\textstyle{\frac{{1}}{{2}}}}\lambda ^{2}u^{2}\right] +x\left[ {\textstyle{%
\frac{{1}}{{2}}}}\lambda ^{2}(xy-z^{2}+{\textstyle{\frac{{{\overline{k}}}}{{2%
}}}}u^{2})+h_{1}u\right] &=&0 \label{eq:minB} \\
z\left[ m_{3}^{2}-\lambda ^{2}(xy-z^{2}+{\textstyle{\frac{{{\overline{k}}}}{{%
2}}}}u^{2})+\lambda \rho u^{2}+h_{2}u\right] &=&0 \label{eq:minC} \\
u\left[ m_{u}^{2}+{\textstyle{\frac{{1}}{{2}}}}\lambda ^{2}(x^{2}+y^{2})+{%
\textstyle{\frac{{1}}{{2}}}}{\overline{k}}\lambda ^{2}(xy-z^{2}+{\textstyle{%
\frac{{{\overline{k}}}}{{2}}}}u^{2})+\lambda \rho z^{2}\right] && \notag \\
+h_{1}xy+{\textstyle{\frac{{1}}{{2}}}}h_{2}z^{2}+{\textstyle{\frac{{1}}{{2}}}%
}h_{3}u^{2} &=&0. \label{eq:minD}
\end{eqnarray}%
We seek an an extremum such that the $U_{1}^{\prime }$ is broken at a scale
much larger than $m_{0}$. For this to be a minimum, we see from Eq.~(\ref%
{eq:epot}) that it must correspond to $x\sim y\sim z>>u$. Then, setting $%
x\approx y\approx z\approx M$, we have from Eq.~(\ref{eq:minD}) that
\end{subequations}
\begin{equation}
u\approx -\frac{2h_{1}+h_{2}}{2(\lambda ^{2}+\lambda \rho )},
\label{eq:uvev}
\end{equation}%
so that $u$ is naturally of $O({\textstyle{\frac{{m_{0}}}{{16\pi ^{2}}}}})$.
Now in anomaly mediation we have (for a typical $\hbox{TeV}$ sparticle
spectrum) $m_{0}\sim 40\hbox{TeV}$; we thus obtain, in the case $W_{3}\equiv
W_{3}^{A}$, a contribution to the Higgs $\mu $-term from Eqs.~(\ref%
{eq:spotca}), (\ref{eq:uvev}) of appropriate magnitude (around $0.5\hbox{TeV}
$) without having to assume a small value of the coupling $\lambda ^{\prime
\prime }$. It is also easy to show (from Eqs.~(\ref{eq:minA}), (\ref{eq:minB}%
)) that (to leading order in $M$)
\begin{equation}
x^{2}-y^{2}=\frac{m_{2}^{2}-m_{1}^{2}}{g_{\phi }^{2}}, \label{eq:xydiff}
\end{equation}%
so that the contribution to the slepton doublet mass is simply
\begin{equation}
\Delta m_{L}^{2}=\frac{1}{2}g_{\phi }^{2}\frac{q_{L}}{q_{\phi }}%
(x^{2}-y^{2})=\frac{m_{2}^{2}-m_{1}^{2}}{2}\frac{q_{L}}{q_{\phi }}
\end{equation}%
(with a similar formula for the slepton singlet mass) so, as long as we pick
charges such that $q_{L}$ and $q_{e}$ have the same sign (depending on the
sign of $m_{2}^{2}-m_{1}^{2}$), we have a potential solution to the
tachyonic slepton problem. Since $m_{1,2}^{2}$ depend on unknown couplings
we can write
\begin{equation}
\frac{m_{2}^{2}-m_{1}^{2}}{2q_{\phi }}=\xi
\end{equation}%
where $\xi $ is an effective Fayet-Iliopoulos parameter.
Setting $x = R\cos\Omega$ and $y = R\sin\Omega$, we find also from Eqs.~(\ref%
{eq:minA}), (\ref{eq:minB}) that
\begin{equation}
\sin 2 \Omega = -\frac{m_3^2 + (2h_1+h_2)u + \lambda\rho u^2}{m_1^2 + m_2^2
+ \lambda^2 u^2}. \label{eq:omegadef}
\end{equation}
Now our desired extremum corresponds to $\Omega \approx \pi/4$; we see
easily from Eq.~(\ref{eq:omegadef}) and using Eq.~(\ref{eq:uvev}) that at
this extremum we require
\begin{equation}
\Delta = m_1^2 + m_2^2 + m_3^2 - \frac{(h_1 + {\textstyle{\frac{{1}}{{2}}}}%
h_2)^2}{\lambda(\lambda + \rho)} = 0 + O\left[(m_0^4/M^2)\right].
\label{eq:deltadef}
\end{equation}
Now this looks like a fine-tuning of the fundamental parameters; however
when we bear in mind that all these parameters are functions of scale then
this interpretation changes. The crucial point is that if we are interested
in the effective potential of a set of fields at an (approximately common)
value of these fields much larger than any explicit mass parameters, then
the appropriate scale to evaluate the potential is one equal to the the
scale set by the value of the fields themselves. This simply minimises the
effect of radiative corrections on the tree potential.
Now from Eq.~(\ref{eq:epot}) it is clear that for $m_1^2 + m_2^2 + m_3^2\le
0 $, the potential $V$ is unbounded from below as for $u=0$ and $x = y = z
\to \infty$. Crucially, however, it is quite natural to have $\Delta \le 0$
at some scale (corresponding to $\mu < M$) and then $\Delta > 0$ for $\mu > M
$. We will demonstrate that this mechanism works explicitly in the next
section by examining the variation of $\Delta$ with renormalisation scale.
It follows that the potential will develop a minimum at the scale such that
Eq.~(\ref{eq:deltadef}) is satisfied. It is easy to show from Eq.~(\ref%
{eq:epot}) that in the neighbourhood of the minimum,
\begin{equation}
V = \frac{1}{2}\Delta M^2 + O\left[m_0^4\right].
\end{equation}
This is, of course, an example of dimensional transmutation as originally
described by Coleman and Weinberg~\cite{coleman}; the relation Eq.~(\ref%
{eq:deltadef}) is analogous to the relation CW wrote down between the
quartic scalar and gauge couplings (valid at the extremum of the potential)
in massless scalar QED. In describing the breaking of a gauge symmetry at
high energies our approach here is reminiscent of Witten's inverted
hierarchy model~\cite{witten}.
The upshot of all this is that without fine-tuning, our scale invariant
potential can quite naturally have an extremum such that $x\sim y\sim z\sim
M>>m_{1,2,3}$, thus achieving $U_{1}^{\prime }$ breaking in a manner similar
to that envisaged in Ref.~\cite{hjjr}, but without the explicit introduction
of the breaking scale in the form of an FI term.
\subsection{The anomalous dimensions}
At one loop the anomalous dimensions of the various fields which only appear
in $W_2$ and $W_3$ are given by (for $W_3 \equiv W_3^A$)
\begin{subequations}
\begin{eqnarray}
16\pi^2\gamma_{\phi} &=& \lambda^2 + {\textstyle{\frac{{1}}{{2}}}}\mathrm{Tr
} (Y_{\nu^c})^2 - 2 g^{\prime 2 }q_{\phi}^2 \label{eq:anoma} \\
16\pi^2\gamma_{{\overline{\phi}}} &=& \lambda^2 - 2 g^{\prime 2 }q_{\phi}^2
\label{eq:anomb} \\
16\pi^2\gamma_{U} &=& \lambda^2 + {\textstyle{\frac{{1}}{{2}}}}\rho^2 + {%
\textstyle{\frac{{1}}{{2}}}}k^2 + 2\lambda^{\prime \prime 2}
\label{eq:anomc} \\
16\pi^2\gamma_{Z} &=& \rho^2 \label{eq:anomd}
\end{eqnarray}
while for $W_3 \equiv W_3^B$, Eqs.~(\ref{eq:anomc}) and (\ref{eq:anomd}) are
replaced by
\end{subequations}
\begin{subequations}
\begin{eqnarray}
16\pi^2\gamma_{U} &=& \lambda^2 + {\textstyle{\frac{{1}}{{2}}}}\rho^2 + {%
\textstyle{\frac{{1}}{{2}}}}k^2 \label{eq:anomce} \\
16\pi^2\gamma_{Z} &=& \rho^2 + 2\lambda^{\prime \prime 2}. \label{eq:anomf}
\end{eqnarray}
For the MSSM non-singlet fields and $\nu^c$ we have
\end{subequations}
\begin{eqnarray}
16\pi^2(\gamma_L)^i_j &=& (Y_e)^{ik}(Y_e)_{jk} +
(Y_{\nu})^{ik}(Y_{\nu})_{jk} -2C_H\delta^i_j, \notag \\
16\pi^2(\gamma_{e^c})^i_j &=& (Y_e)^{ki}(Y_e)_{kj} -2C_{e^c}\delta^i_j,
\notag \\
16\pi^2(\gamma_{\nu^c})^i_j &=& (Y_{\nu^c})^{ik}(Y_{\nu^c})_{jk}+
2(Y_{\nu})^{ki}(Y_{\nu})_{kj}- 2g^{\prime 2 }q_{\nu^c}^2\delta^i_j \notag \\
16\pi^2(\gamma_Q)^i_j &=& (Y_d)^{im}(Y_d)_{jm} +
(Y_u)^{im}(Y_u)_{jm}-2C_Q\delta^i_j, \notag \\
16\pi^2(\gamma_{d^c})^i_j &=& 2(Y_d)^{mi}(Y_d)_{mj} -2C_{d^c}\delta^i_j,
\notag \\
16\pi^2(\gamma_{u^c})^i_j &=& 2(Y_u)^{mi}(Y_u)_{mj} -2C_{u^c}\delta^i_j,
\notag \\
16\pi^2\gamma_{H_1} &=& 3(Y_d)^{ij}(Y_d)_{ij} + (Y_e)^{ij}(Y_e)_{ij} +
\lambda^{\prime \prime 2 }-2C_H, \notag \\
16\pi^2\gamma_{H_2} &=& 3(Y_u)^{ij}(Y_u)_{ij} + (Y_{\nu})^{ij}(Y_{\nu})_{ij}
+\lambda^{\prime \prime 2 }-2C_H,
\end{eqnarray}
where
\begin{eqnarray}
C_{Q}&=& {\textstyle{\frac{{4}}{{3}}}}g_3^2 + {\textstyle{\frac{{3}}{{4}}}}%
g_2^2 +{\textstyle{\frac{{1}}{{60}}}}g_1^2 + q_{Q}^2 g^{\prime 2}, \notag \\
C_L &=& {\textstyle{\frac{{3}}{{4}}}}g_2^2 +{\textstyle{\frac{{3}}{{20}}}}%
g_1^2 + q_{L}^2 g^{\prime 2} \notag \\
C_{u^c}&=& {\textstyle{\frac{{4}}{{3}}}}g_3^2 +{\textstyle{\frac{{4}}{{15}}}}%
g_1^2 + q_{u^c}^2 g^{\prime 2}, \notag \\
C_{d^c}&=& {\textstyle{\frac{{4}}{{3}}}}g_3^2 +{\textstyle{\frac{{1}}{{15}}}}%
g_1^2 + q_{d^c}^2 g^{\prime 2}, \notag \\
C_{e^c}&=& {\textstyle{\frac{{3}}{{5}}}}g_1^2 + q_{e}^2 g^{\prime 2}, \notag
\\
C_H &=& {\textstyle{\frac{{3}}{{4}}}}g_2^2 +{\textstyle{\frac{{3}}{{20}}}}%
g_1^2 + q_{H}^2 g^{\prime 2} \label{eq:Cterms}
\end{eqnarray}
and we have written $q_{H}^2 = q_{H_1}^2 = q_{H_2}^2$, since $q_{H_1} = -
q_{H_2}$.
\subsection{RG evolution and radiative breaking}
In this section we work in the simplified approximation where we neglect $%
\lambda^{\prime \prime }$ and $Y_{\nu}$. As a result the renormalisation
group evolution equations of $\lambda$, $Y_{\nu^c}$, $\rho$ $k$ and $%
g^{\prime }$ become (at one loop) a closed system, which simplifies the
analysis, and makes it the same whether we use $W_3^A$ or $W_3^B$. Moreover
we will assume a simplified form for $Y_{\nu^c}$, to wit
\begin{equation}
Y_{\nu^c} = \left(\begin{array}{ccc}
0&0&0\\ 0&0&0\\ 0&0&\lambda^{\prime}\\
\end{array}\right).\end{equation}
The $\beta$-functions for the Yukawa couplings are then:
\begin{eqnarray}
16\pi^2\beta_{\lambda} &=& \lambda (\gamma_{\phi}+\gamma_{{\overline{\phi}}%
}+\gamma_U) \notag \\
&=& \lambda \left[3\lambda^2 + {\textstyle{\frac{{1}}{{2}}}}\lambda^{\prime
2 }+ {\textstyle{\frac{{1}}{{2}}}}\rho^2 +{\textstyle{\frac{{1}}{{2}}}}k^2 -
4g^{\prime 2 }q_{\phi}^2\right] \notag \\
16\pi^2\beta_{\lambda^{\prime }} &=& \lambda^{\prime
}(\gamma_{\phi}+2\gamma_{\nu^c}) \notag \\
&=& \lambda^{\prime }\left[\lambda^2 + {\textstyle{\frac{{5}}{{2}}}}%
\lambda^{\prime 2 }- 2g^{\prime 2 }(q_{\phi}^2 + 2q_{\nu^c}^2)\right] \notag
\\
16\pi^2\beta_{\rho} &=& \rho (\gamma_{U}+2\gamma_Z) = \rho\left[\lambda^2 + {%
\textstyle{\frac{{5}}{{2}}}}\rho^2 + {\textstyle{\frac{{1}}{{2}}}}k^2\right]
\notag \\
16\pi^2\beta_k &=& 3k\gamma_U = 3k\left[\lambda^2 +{\textstyle{\frac{{1}}{{2}%
}}}\rho^2 + {\textstyle{\frac{{1}}{{2}}}}k^2\right]. \notag \\
\end{eqnarray}
The $\beta$-function for the $U^{\prime }_1$ gauge coupling is
\begin{equation}
16\pi^2\beta_{g^{\prime }} = b^{\prime }g^{\prime 3},
\end{equation}
where
\begin{equation}
b^{\prime }= 3(q_e^2+3(q_{u^c}^2+q_{d^c}^2)+6q_Q^2+2q_L^2+q_{\nu^c}^2)
+2(q_{H_1}^2+q_{H_2}^2)+2q_{\phi}^2.
\end{equation}
We then find using the AMSB mass formula
\begin{equation}
(m^2)^i{}_j = \frac{1}{2}m_0^2\mu\frac{d}{d\mu}\gamma^i{}_j
\label{eq:amsbmass}
\end{equation}
that
\begin{eqnarray}
16\pi^2 m_{\phi^2} &=& {\textstyle{\frac{{1}}{{2}}}}m_0^2(
2\lambda\beta_{\lambda} +\lambda^{\prime }\beta_{\lambda^{\prime }}
-4g^{\prime }\beta_{g^{\prime }}q_{\phi}^2) \notag \\
16\pi^2 m_{{\overline{\phi}}^2} &=& {\textstyle{\frac{{1}}{{2}}}}m_0^2(
2\lambda\beta_{\lambda} -4g^{\prime }\beta_{g^{\prime }}q_{\phi}^2) \notag
\\
16\pi^2 m_Z^2 &=& {\textstyle{\frac{{1}}{{2}}}}m_0^2( 2\rho\beta_{\rho}).
\end{eqnarray}
Substituting in Eq.~(\ref{eq:deltadef}) we thus have
\begin{eqnarray}
(16\pi^2)^2\frac{\Delta}{m_0^2} &=& [32 \lambda^5 +16 \lambda^2 k^2 \rho + 8
\lambda \rho^2 k^2 +64 \lambda^4 \rho+4 \lambda^3 \lambda^{\prime 2} +56
\lambda^3 \rho^2 \notag \\
&+&48 \lambda^2 \rho^3 + 8 \lambda^3 k^2 +12 \lambda^2 \lambda^{\prime 2}
\rho +9 \lambda^{\prime 4} \lambda+10 \lambda^{\prime 4} \rho +24 \lambda
\rho^4 +8 \lambda \lambda^{\prime 2} \rho^2 \notag \\
&-&g^{\prime 2} (1024\lambda^2 q_L^2 \rho +256 \lambda^2 q_e^2 \rho -64
\lambda^{\prime 2} q_L^2 \lambda +192 \lambda^{\prime 2} q_L^2\rho -16
\lambda^{\prime 2} q_e^2 \lambda \notag \\
&+&48 \lambda^{\prime 2} q_e^2 \rho +1024 \lambda q_L^2 \rho^2+256 \lambda
q_e^2 \rho^2 +1024 \lambda^2 q_L q_e \rho -64 \lambda^{\prime 2} q_L q_e
\lambda \notag \\
&+&192 \lambda^{\prime 2} q_L q_e \rho +1024 \lambda q_L q_e \rho^2) -
g^{\prime 4} (4608q_e^4 \rho+55296 q_L^4 \lambda \notag \\
&+&38912 q_L^4 \rho +5632 q_e^4 \lambda +97792q_e^2 q_L^2\lambda+73216 q_e^2
q_L^2 \rho +37888 q_e^3 q_L \lambda \notag \\
&+& 29696 q_e^3 q_L \rho +116736 q_L^3 q_e \lambda +83968 q_L^3 q_e
\rho)]/(8(\lambda+\rho)].
\end{eqnarray}
\includegraphics[angle=-90, width= 5.4in]{amsbnewfig.eps} \medskip \leftskip %
= 40 pt\rightskip = 40pt \textit{%
\centerline{ Fig.~1:
Plot of $\Delta$ against $t=\ln {{\textstyle{\frac{{\mu }}{{\mu_{0}}}}}}$}}
\medskip \leftskip = 0 pt\rightskip = 0pt
In Fig.~1 we plot $\Delta $ against $t=\ln {{\textstyle{\frac{{\mu }}{{%
\mu_{0}}}}}}$, choosing initial values so that $\Delta =0$ when $\mu =\mu
_{0}$. (Specifically, we have taken, at $\mu =\mu _{0}$, $\rho =\lambda/10$,
$\lambda ^{\prime }= k = 2 \lambda $, $\lambda =0.4784$, $g^{\prime }=1$, $%
\xi = 1\hbox{TeV}^2$ and $q_{L}=q_{e}=0.08$. We see that $\Delta$ indeed has
the desired behaviour, with $\Delta <0$ at $\mu <\mu _{0}$ to $\Delta >0$ at
$\mu >\mu _{0}$. Clearly the potential will have a minimum for $\mu \sim \mu
_{0}$.
\section{The low energy theory}
\subsection{The Higgs spectrum}
If we take the superpotential Eq.~(\ref{eq:spotb}) and shift the fields by
their vacuum expectation values ($U\rightarrow u/\sqrt{2}+U,\phi \rightarrow
x/\sqrt{2}+\phi ,{\overline{\phi }}\rightarrow y/\sqrt{2}+{\overline{\phi }}%
,Z\rightarrow \sqrt{\frac{\lambda }{\rho }}z+Z$), it is easy to see that, to
$O(\frac{u}{x}),$ the linear combination
\begin{equation}
H=\frac{1}{R^{\prime }}\left[ x{\overline{\phi }}+y\phi -\sqrt{\frac{2\rho }{%
\lambda }}zZ\right]
\end{equation}%
where
\begin{equation}
R^{\prime 2}=x^{2}+y^{2}+{\textstyle{\frac{{2\rho }}{{\lambda }}}}z^{2}
\label{eq:rp}
\end{equation}%
combines with $U$ so that both get large supersymmetric mass terms. The
combination
\begin{equation}
G=\frac{1}{R}\left[ y{\overline{\phi }}-x\phi \right]
\end{equation}%
where%
\begin{equation*}
R^{2}=x^{2}+y^{2}
\end{equation*}%
is the Higgs/Goldstone multiplet, combining with the $U_{1}^{\prime }$ gauge
multiplet to produce a spin 1 massive supermultiplet. The orthogonal
combination
\begin{equation}
L=\frac{1}{R^{\prime \prime }}\left[ x{\overline{\phi }}+y\phi +\sqrt{\frac{%
\lambda }{2\rho }}\frac{x^{2}+y^{2}}{z}Z\right]
\end{equation}%
where
\begin{equation}
R^{\prime \prime 2}=x^{2}+y^{2}+\frac{\lambda }{2\rho }\frac{%
(x^{2}+y^{2})^{2}}{z^{2}}, \label{eq:rpp}
\end{equation}%
has a large vacuum expectation value but obtains a mass of order $u$, which
from Eq.~(\ref{eq:uvev}) is of order $\,\hbox{TeV}$. Examined in more
detail, we find that the two scalar components of $L$ have masses of $O(u%
\sqrt{\rho })$ and its fermionic component a mass of order $u\rho $ if, as
we shall motivate later, we choose $\rho <<\lambda $. It is interesting to
note that the $UH_{1}H_{2}$ or $ZH_{1}H_{2}$ terms in the alternative
superpotential terms $W_{3}^{A}$ or $W_{3}^{B}$ of Eqs.~(\ref{eq:spotca})
and (\ref{eq:spotcb}) means that part of our theory resembles the NMSSM.
However, unlike the NMSSM, the light singlet state decouples to $O(\frac{u}{x%
})$ or almost decouples from the MSSM fields, in the first case because $U$
has no $L$ component while in the latter case the coefficient of the
trilinear term must be chosen to be very small for phenomenological reasons.
In both cases however the existence of the light field causes a phenomenon
of AMSB non-decoupling, described by Pomarol and Rattazzi (PR)~\cite{aprr},
which effects the low energy mass spectrum as discussed below.
\subsection{The Higgs $\protect\mu $-term and $b$-term}
\subsubsection{A fine tuned solution}
Let us consider first the case $W_{3}\equiv W_{3}^{A}$ (Eq.~(\ref{eq:spotca}%
)). The vacuum described in Section~\ref{sec:potmin} clearly generates a
Higgs $\mu $-term $\mu _{1}=\lambda ^{\prime \prime }\mathopen\langle U%
\mathclose\rangle $ which is naturally of the right order of magnitude. It
also, however, generates a soft breaking Higgs $b$-term of the form $%
b_{1}=m_{0}\mu _{1}$ which is too large; a generic problem with the scenario
which has been noticed by a number of authors.
There is, however another Weyl invariant operator which generates both $\mu $%
-term and a $b$-term, to wit
\begin{equation}
\delta L=\sigma \int \,d^{4}\theta \,\frac{\Phi ^{\dagger }}{\Phi }H_{1}H_{2}
\end{equation}%
where $\Phi =1+m_{0}\theta ^{2}$ is the conformal compensator field. This
gives $\mu _{2}=\sigma m_{0}$ and $b_{2}=-m_{0}\mu _{2}$. Thus we have $\mu
=\mu _{1}+\mu _{2}$ and $b=m_{0}(\mu _{1}-\mu _{2})$. It is clear that if we
proceed to determine $\mu $ and $b$ via the electroweak minimisation
conditions in the customary way then this amounts to a degree of fine-tuning
in order to achieve $b\sim \mu ^{2}$
\subsubsection{An unnatural solution}
PR~\cite{aprr} propose an ingenious solution to this problem as follows.
They introduce the further contribution to the superpotential
\begin{equation}
W_{4}=\lambda ^{\prime \prime }SH_{1}H_{2}+{{\frac{{1}}{{6}}}}k^{\prime
}S^{3}+{{\frac{{1}}{{2}}}}k^{\prime \prime }ZS^{2}. \label{eq:spotd}
\end{equation}
The superpotential $W_4$ produces at one loop kinetic mixing of $Z$ and $S$:
\begin{equation}
\delta L \sim k^{\prime }k^{\prime \prime} \int\, d^4 \theta\, Z^{\dagger} S.
\end{equation}
The large vev for $Z$ produces a large supersymmetric mass term for $S$, so
that it decouples at low energies and can be eliminated via its equation of
motion which for small $k^{\prime }$ is
\begin{equation}
S = - k^{\prime \prime }\frac{H_1 H_2}{Z}
\end{equation}
giving rise to a contribution to the effective low energy theory of the form
\begin{equation}
\delta L \sim \int\, d^4 \theta\, \frac{Z^{\dagger}}{Z}H_1 H_2
\end{equation}
and hence via anomaly mediation a contribution to the $\mu$ term $\mu =
\mu_3 $ and an associated contribution to the $b$-term of the form
\begin{equation}
b_3 = -m_0 \beta_{\mu_3}. \label{eq:prmu}
\end{equation}
Thus one achieves a $b$ of the right order of magnitude (relative to $\mu_3$%
). Then if $\lambda^{\prime \prime }$ and $\rho$ were sufficently small that
the contributions to $b$ associated with them were of similar size to $b_3$
then we would have $\mu \sim \mu_3$ and $b \sim b_1 + b_2 + b_3$, so that
once more we can determine $\mu, b$ via electroweak minimisation. (If we
assume that the PR mechanism is the only source of $\mu, b$ then it is
difficult to achieve the electroweak vacuum~\cite{jja}, because Eq.~(\ref%
{eq:prmu}) would mean $\mu$ and $b$ were not independent.)
The problem with this scenario is that in order to write down the
superpotential $W_{4}$ we must abandon the $Z\rightarrow -Z$ symmetry which
rendered our theory natural. This is because the simultaneous presence of
the $S^{3}$ term and the $ZS^{2}$ term requires $Z$ and $S$ have the same
symmetry properties. As a result a natural theory would also allow
additional terms in Eq.~(\ref{eq:spotb}) of the form $Z^{3}$ and $Z^{2}S$
which unfortunately spoil the mechanism proposed by PR.
\subsubsection{A natural solution without fine tuning}
Here we propose a very simple mechanism which does not involve additional
fields to generate the $\mu $ and $b$ terms of the correct magnitude in a
way consistent with the $Z_{2}$ symmetry. This is achieved through the case $%
W_{3}\equiv W_{3}^{B}$ (Eq.~(\ref{eq:spotcb})).
The $U^{\prime }_1$-breaking proceeds exactly as before and so from Eq.~(\ref%
{eq:spotcb}) we obtain a $\mu$-term of the form $\mu = \lambda^{\prime
\prime }\mathopen\langle Z\mathclose\rangle $. Since $\mathopen\langle Z%
\mathclose\rangle $ is of order the $U^{\prime }_1$ breaking scale it is
therefore necessary to assume that $\lambda^{\prime \prime }$ is very small.
We will return to this point presently.
The reason that we can achieve a suitable $b$-term is that since
\begin{equation}
Z=\frac{1}{\sqrt{R^{\prime 2}+R^{\prime \prime 2}}}\left( -R^{\prime
}H+R^{\prime \prime }L\right),
\end{equation}%
we can, c.f. Eqs.~(\ref{eq:rp}) and (\ref{eq:rpp}), arrange by making $\rho
\ll \lambda $ that $Z\sim L$. This will suppress the $B$ term since while $%
F_{H}= \mathopen\langle H\mathclose\rangle m_{0}$, $F_{L}=0$. Quantitatively
we have
\begin{equation}
b=\sqrt{2}\frac{\rho }{\lambda }\mu m_{0}.
\end{equation}%
Thus we retain naturalness by avoiding the need for cancellation between
distinct contributions to $b$. Although we do require two dimensionless
couplings ($\rho $ and $\lambda ^{\prime \prime }$) to be small this can be
achieved by, for example, the Froggatt-Nielsen mechanism, generating these
terms through higher dimension terms suppressed by a large messenger mass.
\subsection{The Low Energy Theory}
The existence of a light singlet field, $L,$ introduces additional
contributions to the soft supersymmetry breaking terms due to the
non-decoupling phenomenon discussed in PR \cite{aprr}. Following PR we have,
in place of Eqs.~(\ref{eq:amsba}), (\ref{eq:amsbb}) and (\ref{eq:amsbc}),
the equations
\begin{subequations}
\begin{eqnarray}
M_{i} &=&m_{0}\beta _{g_{i}}/g_{i} \\
h_{Y} &=&-m_{0}\left( \frac{\partial }{\partial \ln \mu }+\frac{\partial }{%
\partial \ln M}\right) \ln Z_{Y}(\mu ,M) \\
m_{\phi }^{2} &=&{-{\frac{{1}}{{2}}}}m_{0}^{2}\left( \frac{\partial }{%
\partial \ln \mu }+\frac{\partial }{\partial \ln M}\right) ^{2}\ln Z_{Y}(\mu
,M),
\end{eqnarray}
where $M$ is the $U(1)^{\prime }$ breaking scale and $\mu $ is the
low-energy scale parameter ($\mu \ll M).$ The $\mu $ dependent terms are the
normal anomaly mediated terms while the $M$ dependent terms are the
non-decoupling terms due to the light scalar. These equations apply in the
limit $\rho \ll \lambda $ where $F_{L}=0.$ One sees that the effect of these
non-decoupling terms is simply to retain the contributions of the $%
U_{1}^{\prime }$ gauge boson to the soft breaking terms even though the $%
U_{1}^{\prime }$ gauge coupling freezes out at the breaking scale $M.$ Thus
for example we have for the soft $Qt^{c}H_{2}$ coupling, $h_{t}$,
\end{subequations}
\begin{equation}
16\pi ^{2}h_{t}=-m_{0}\lambda _{t}\left( 6\lambda
_{t}^{2}-2(C_{H}+C_{Q}+C_{t^{c}})\right),
\end{equation}%
where we have for simplicity retained only the top-quark Yukawa coupling.
The gauge pieces $C_{Q}$ etc. are as given in Eq.~(\ref{eq:Cterms}), but the
$U_{1}^{\prime }$ coupling is to be evaluated at the $U_{1}^{\prime }$
breaking scale.
\subsection{Phenomenological implications}
For both the cases $W_{3}\equiv W_{3}^{A}$ and $W_{3}\equiv W_{3}^{B},$ in
the limit $g^{\prime }\rightarrow 0,$ the additional soft terms due to
non-decoupling associated with the light scalar state are negligible and, to
a good approximation, we recover the spectrum of Ref.~\cite{hjjr} for the
MSSM states. This is because, as discussed earlier, the coupling of the
light singlet $L$ to the Higgs is very small. The fermionic component, $%
\widetilde{L},$ of $L$ will, however be the LSP. The accelerator lower
limits of around $46\,\hbox{GeV}$ will not apply because of the weak
coupling of the state; in our favoured scenario for Higgs $\mu $-term
generation we estimate its mass to be around $10\,\hbox{GeV}$. The
cosmological and phenomenological implications of a $\widetilde{L}$ LSP are
similar to that of a gravitino LSP and will be discussed in detail
elsewhere.
For the case when the new gauge interaction is not negligible there will be
additional supersymmetry breaking soft contributions to the MSSM states. We
will also return elsewhere to a consideration of the phenomenology in this
case too.
\section*{\protect\large Acknowledgements}
Both DRTJ and GGR visited CERN and KITP (Santa Barbara)
while part of this work was done. This
work was partially supported by the EC 6th Framework Programme
MRTN-CT-2004-503369, and by the National Science Foundation
under Grant No. PHY99-07949.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,147
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The location: The Bloody Socks crime scene.
Q. What is it supposed to be on the show?
A. A residential road.
Q. Where is it supposed to be on the show?
A. Somewhere in Miami.
Q. When did we see it on the show?
A. In Episode 7 (of Season 3), "Easy As Pie".
In this short scene, we see Debra driving up an uncurbed road.
She sees Anton up ahead waiting for her.
She pulls the car over, and Anton walks over and gets in her car.
She warns him, rather cryptically, that he is in danger - that the police have leaked word that he gave them information about The Skinner - who will now be looking for revenge.
Anton says he didn't say anything, and Debra says she knows that, but he's still in danger, and she urges him to get out of town.
Anton refuses.
Q. What is it actually in real life?
A. A residential road - but not in Miami.
Q. Where can I find it in real life?
A. This scene was shot at the same time as the bloody socks crime scene, and the scene with Prado & Dexter hitting balls at the double-decker driving range.
Both of those scenes were shot in an unusual area for Dexter: the city of Downey, California.
So, since all they needed was a road, there was no reason to go far.
They simply went one block east of the bloody socks house and filmed there.
The scene was shot on the 8500 block 11th Street, in Downey. That's between Birchdale Ave (on the east) and Brookshire Ave (on the west), just south of Florence Ave.
Debra is driving east on the street. Anton's car is parked on the north side.
They probably opted for that particular street because it has a number of palm trees on it, and fact that most of the road is uncurbed (which is unusual for Southern California) gives it a somewhat rural look. (The city has since curbed the street.)
Despite the natural palm trees, they added a cluster of smaller palms to the foreground, to make it look even more tropical.
The city of Downey is located about 9 miles southeast of downtown Los Angeles, and about 13 miles north/northeast of their usual stomping ground of Long Beach. The city is in a triangle formed by the Long Beach (710) freeway (on the west), the Century (105) freeway (on the south), and the 605 freeway to the east.
( A historical footnote: The nearby McDonald's, just east of this location, at the southwest corner of Florence Ave & Lakewood Blvd, is the oldest surviving McDonald's in the world, built in 1953 by the original McDonald brothers, before Ray Kroc bought the chain. There's no drive-thru, just walk-up, and they've added a small museum of sorts next to it. The address is 10207 Lakewood Blvd., Downey, CA. )
I shot these photos in November 2010.
The tall house with green shutters that you see on
the right side of the photo above is at 8500 11th St.
The house with the red tile roof that Debra passes on the way in
(seen in the photo above) is at 8529 11th Street.
Here is an aerial photo of the street. And here is a map link.
Q. How the heck did you figure out where it was?
A. I didn't. I searched for months on this one, to no avail.
Finally, I got a tip from Geoff (who also found the "bloody socks" house nearby). (Thanks, Geoff !)
Google StreetView made it clear that it was the right street.
Then I went there in person and shoot the matching photos that you see above.
I noted a number of changes since the 2008 filming. They have curbed the street, and one notable wall (seen behind Anton) has been replaced.
By Episode - By Category - By Geographical Location - Clickable Map of All Dexter Locations - Go To Main Menu
The Dexter screenshots from the show and all related characters & elements are trademarks of and © Showtime.
All other photos & text are Copyright � 2020-Gary Wayne and may not be used without written permission.
Return to Seeing-Stars.com
Looking for something in particular? Search the Seeing-Stars website!
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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{"url":"https:\/\/premedicaluniversity.com\/steak-grilling-msk\/how-to-multiply-improper-fractions-by-improper-fractions-d44d2a","text":"1. Students must answer problems involving multiplying fractions and mixed numbers to move their game piece around the game board. fractions, mathematics, math, multiplying. Let\u2019s say that you want to know the result of \u2075\u2044\u2083 \u00d7 \u2077\u2044\u2086. Required fields are marked *. Multiply the left and right denominators to obtain the answer's denominator. Otherwise keep it as it is. Then, write the result into the upside of the result fraction. Fractions Mixed and Improper DRAFT. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math. For more like this, use the search bar to look for some or all of these keywords: fractions, mathematics, math, multiplying. You multiply two fractions by multiplying the numerators and multiplying the denominators. Procedure: 1. Step 2 \u2013 Multiply the numerators. Welcome to The Multiplying Proper and Improper Fractions (A) Math Worksheet from the Fractions Worksheets Page at Math-Drills.com. Step 3 \u2013 Multiply the denominators. Divide the numerator by the denominator. Simplified and Mixed Number Answers: Multiply 7 with 2 in the given example, 2(1\/7). Multiplying improper fractions is just like multiplying proper fractions. Positive improper fractions are always greater than or equal to 1. If there are more versions of this worksheet, the other versions will be available below the preview images. Applications of fraction operations. Improper fractions are fractions that their numerators are larger than or equal to their denominators. Enter your \u2026 In this method, You have to use the long division. Mixed Numbers to Improper Fractions . Worksheets > Math > Grade 5 > Fractions: multiply \/ divide > Multiplying improper fractions . Multiply fractions can discuss under three main categories. Landing on a. Step 4: The Improper fraction obtained is: 15\/7. Then multiply the Improper Fractions (Note: negative times negative gives positive) : \u2212149 \u00d7 \u2212157 = \u221214 \u00d7 \u2212159 \u00d7 7 = 21063 . What part of the mixed number do you KEEP in an improper fraction? A number which is the sum of a whole number and a proper fraction written in this manner defined as Mixed Numbers, Step 1 \u2013 Convert the mixed number into improper fractionStep 2 \u2013 Multiply the numeratorsStep 3 \u2013\u00a0Multiply the denominatorsStep 4 \u2013 Express the answer as a mixed number. Just continue with 2. again, we can see that 3 is a common factor. This mixed fraction calculator by calculator-online is the smart tool that helps you in adding, subtracting, multiplying, and dividing mixed numbers fraction. Improper fractions are fractions with a value greater than 1 (numerator is greater than the denominator). To change 1 of the mixed fractions, multiply the denominator by... 2. 17 Qs . You can continue to simplify the fraction with any common factor that you remember. Convert Mixed to Improper Fractions: 1 59 = 99 + 59 = 149 2 17 = 147 + 17 = 157. Step 1 \u2013 Convert the mixed number into improper fraction. A proper fraction is a fraction that is less than one, with the numerator less than the denominator. Often the resulting product will not be in lowest terms, so you must also simplify. Write down the whole number answer. Divide the numerator by denominator. These are equivalent fractions. Multiply the numerators of the improper fractions. Below are six versions of our grade 5 math worksheet on multiplying improper fractions together. Now you will get the same answer. Pingback: Learn Calculating Perimeter of Circle with Equations | Math Tutor, Your email address will not be published. Fraction Fever (Improper Fraction Edition) is a board game that helps students practice multiplying fractions (including improper fractions) and mixed numbers. You do this by multiplying the whole number and the denominator of the fraction then add the product to the numerator of the fraction. Example 01 : Step 01. as our answer. Multiplying Improper Fractions Games. Dividing fractions and mixed numbers. Also, we perform various arithmetic operations on these fractions, such as addition, division, multiplication\u2026 Before multiplying, simplify the fractions if you can. Change all the mixed numbers to improper fractions. Don\u2019t get confused. 1.4k plays . Multiplying three fractions seems a little more complicated than multiplying two fractions. Teaching children to multiply any fractions is complicated, and multiplication of improper fractions can feel like an extra step. Write the result into the denominator side of the result fraction. Math worksheets: Multiplying improper fractions. 12. An improper fraction is one whose numerator is greater than its denominator. Improper fractions can be converted to mixed numbers. Simply put, there is no difference in terms of multiplication of proper and improper fractions. Step 4 \u2013 Express the answer as a mixed number. Proper fraction, improper fraction, and mixed fraction. In step 03, we have to simplify the fraction. Step 01\u00a0and\u00a0Step 02\u00a0 ( if it is difficult for you to multiply you can use a multiplication table\u00a0), By following step 01 and step 02 we got our answer as. Put the result 13 over the denominator 5, then prefix the resulting improper fraction with a \u2026 It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math. Again, you just need to follow the previous steps: On the other hand, mixed numbers, also known as compound fractions, are numbers that have both a whole number and a fraction. Copyright \u00a9 2005-2020 Math-Drills.com The improper fraction has a numerator larger than the denominator. Try it yourself! If it is necessary, make some simplified operation on the result. Convert 52\/9 from an improper fraction to a mixed number. Solution: Answer: It will take 6 and 2\/3 yards of fabric to make 8 dresses. Example 2: Renee had a box of cupcakes, of which she gave We can simplify now. Subjects: Math, Fractions. Welcome to The Multiplying Proper and Improper Fractions (A) Math Worksheet from the Fractions Worksheets Page at Math-Drills.com. Preview this quiz on Quizizz. Learn all about mixed numbers and improper fractions in this quick, free lesson for 4th and 5th grade. Then, multiply denominators like numerators. Step 3: Keep the Denominator same i.e. An Improper Fraction is a fraction in which the numerator is greater than the denominator, Step 1 \u2013 Multiply the numeratorsStep 2 \u2013 Multiply the denominatorsStep 3 \u2013 Convert the improper fraction into a mixed number. Example 1: If it takes 5\/6 yards of fabric to make a dress, then how many yards will it take to make 8 dresses? Students can use math worksheets to master a math skill through practice, in a study group or for peer tutoring. If the inputs are mixed fractions or whole numbers, convert them to improper fractions. Now let\u2019s solve this one by following the above three simple steps. It\u2019s the revolutionary math study guide just for middle school students from the brains behind\u00a0Brain Quest. Step 1: Multiply the denominator with the whole number, i.e. 11. A mixed number contains a whole number and a fraction. In Sadie\u2019s case, you have two mixed numbers, 10 2\/3 and 1 1\/2, that need to become improper fractions. In arithmetic, there are three types of fractions. 7. Step 2: Add the numerator of the Fraction to the result in step 1. i.e Add 1+ 14 =15. ). Multiplying improper fractions and mixed numbers. For this numerator and denominator, we have several common factors such as 2,3 and 6. out of those factors you have to select the greatest common factor (and also called as the Highest Common Factor \u2013 HCF). Save my name, email, and website in this browser for the next time I comment. Don't just watch, practice makes perfect. But in the above answer, we can see that there are no common factors (a number which divides both 2 and 15). Change the mixed number into its improper fraction form. First multiply the integer by the bottom number (the denominator) of the fraction (in this example; 3 x 4) and add to the top number of the fraction (in this example; 3). Back to Course Index. Here we use two steps, first by 7 (21 and 63 are both multiples \u2026 Divide 63 by 12, Then the quotient is 5 and the remainder is 3. So, in our exercise above, answers 1 and 2 are improper fractions. To multiply mixed numbers you have to follow four simple steps. In this section, a model will be used as a way to multiply mixed numbers and improper fractions. And mixed numbers have a whole number sitting next to a proper fraction -- for example, 4 3\/6 or 1 1\/2. Practice this topic. Multiply the left and right numerators to obtain the answer's numerator. 10 Qs . Your email address will not be published. Preview images of the first and second (if there is one) pages are shown. Fractions in which the whole number in the numerator is greater than or equal to the whole number in the denominator are called positive improper fractions. Using a Calculator Make a fraction into a decimal to solve equations on the calculator. The Multiplying Proper and Improper Fractions (A) Math Worksheet from the Fractions Worksheets Page at Math-Drills.com. There are several methods to do the conversion. 506 times ... Mixed Multiplication HARD MODE . To change $$\u22122 \\frac{3}{5}$$ to an improper fraction, ignore the minus sign, proceed as before, then prefix the minus sign to the resulting improper fraction. In this article, you will find all the topics related to improper fractions. Dividing fractions and mixed numbers. You can remove the common factors as follows. Multiply numerator by numerator and denominator by denominator, Convert the improper fraction to mixed number. There general steps to multiply fractions are described below. We need to multiply the numerators and the denominators to find the product. Multiply the numerators firstly. Follow this formula to convert each mixed number into an improper fraction: In a fraction, the Numerator is always North of (above) the fraction \u2026 Use the buttons below to print, open, or download the PDF version of the Multiplying Proper and Improper Fractions (A) math worksheet. Nevertheless, when some students see an improper fraction, they simply block. 7 \u00d7 2 =14. Multiplying Proper and Improper Fractions (A). Improper Fractions. Parents can work with their children to give them extra practice, to help them learn a new math skill or to keep their skills fresh over school breaks. This math worksheet was created on 2013-02-14 and has been viewed 224 times this week and 434 times this month. Then we will multiply the two fractions. To convert a mixed number to an improper fraction, multiply the denominator by the whole number and add the numerator. Definition: Positive Improper Fractions. Convert the mixed fractions to improper fractions. 3rd - 5th grade. You already know that proper fractions have numerators smaller than the denominators, such as 1\/2, 2\/10 or 3\/4, making them equal less than 1. Multiplying Mixed Fractions by Mixed Fractions 1. Let\u2019s think that you could only find 2 as a common factor. 2. Then multiply as \u2026 Improper Fractions Definition. Learn Calculating Perimeter of Circle with Equations | Math Tutor. Improper Fractions and Mixed Numbers I am a little obsessed with acronyms when it comes to teaching Math methods. But the multiplication method is the same. Now that you have 2 improper fractions \u2026 Step 1\u00a0\u2013 Multiply the numeratorsStep 2 \u2013 Multiply the denominatorsStep 3 \u2013 Simply the fraction to it\u2019s the simplest form (You have to follow this step, only when we have common factors for the numerator and denominator. So, let\u2019s take a look at a practical example. We can see that both 15 and 24 can. So we need to convert 3\u00be into an improper fraction (check the definition of improper fraction above). Analysis: To solve this problem, we will convert the whole number to an improper fraction. You multiply the numerators (top number) of each fraction to come up with the numerator of the answer. 6.1k plays . Write each mixed number as an improper fraction. Think that you cannot find the greatest common factor,which is 6 in the above example. Then write down any remainder above the denominator. You may use the math worksheets on this website according to our Terms of Use to help students learn math. For example, in the fraction 5 3\/8, multiply the denominator 8 and the whole number 5, then add the numerator 3: (8 x 5) + 3 = 43 The answer becomes your new numerator. Teachers can use math worksheets as tests, practice assignments or teaching tools (for example in group work, for scaffolding or in a learning center). Mixed fraction to Improper Fraction. This calculator for simply mixed fractions and allows you to change a mixed number to an improper fraction\/proper fraction or vice versa.","date":"2021-08-01 10:33:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.8233285546302795, \"perplexity\": 764.0575746908631}, \"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-2021-31\/segments\/1627046154175.76\/warc\/CC-MAIN-20210801092716-20210801122716-00411.warc.gz\"}"}
| null | null |
ACCEPTED
#### According to
International Plant Names Index
#### Published in
null
#### Original name
Verbesina myrtifolia Chodat
### Remarks
null
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,793
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There are no contents, the information for this collection has beenmoved to the Iowa Author's Manuscript Collection, MsC0869.
To access the materials of Waldemar Argow reference MsC0869, the Iowa Author's Manuscript Collection. All information is located there.
The contents of this collection have been moved to the Iowa Author's Manuscript Collection, MsC0869.
Waldemar Argow. University of Iowa Special Collections. http://aspace.lib.uiowa.edu/repositories/2/resources/526 Accessed April 23, 2019.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 563
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The Missouri Small Business and Technology Development Centers (MO SBTDC) is part of a national program authorized in the 1980s. Headquartered at the University of Missouri, the SBTDC is a critical component of contractual relationships with nearly all of Missouri's state colleges and universities.
In addition, the programs assisted clients in creating 754 jobs and 66 new businesses.
In the past three years, SBTDC have counseled or educated more than 40,000 business owners/managers.
Click here for case studies on businesses we've helped create.
Why do business in Missouri?
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 7,226
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package ikube.search;
import org.apache.lucene.analysis.Analyzer;
import org.apache.lucene.search.Searcher;
/**
* This search is for all the fields in all the indexes.
*
* @see Search
* @author Michael Couck
* @since 22.08.08
* @version 01.00
*/
@SuppressWarnings("deprecation")
public class SearchAll extends SearchMultiAll {
public SearchAll(final Searcher searcher) {
this(searcher, ANALYZER);
}
public SearchAll(final Searcher searcher, final Analyzer analyzer) {
super(searcher, analyzer);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,498
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<?php get_header(); ?>
<section id="content" role="main">
<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
<?php get_template_part( 'entry' ); ?>
<?php endwhile; endif; ?>
<?php get_template_part( 'nav', 'below' ); ?>
</section>
<?php get_sidebar(); ?>
<?php get_footer(); ?>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,175
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Odzala is een kevergeslacht uit de familie van de boktorren (Cerambycidae). De wetenschappelijke naam van het geslacht werd voor het eerst geldig gepubliceerd in 1968 door Villiers.
Soorten
Odzala is monotypisch en omvat slechts de volgende soort:
Odzala bicolorata Villiers, 1968
Boktorren
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 2,492
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Q: How to send email in Xcode with Version 6.2? I have looked at various tutorials for sending email in an app using Xcode, but most of the tutorials I have tried will not work for the current version of Xcode 6.2. When I run the IOS simulator, the email view will either instantly disappear or I can't type anything in any of the fields. I made sure to update the framework to use the MessageUI.framework. I will also post the current code I am using for the app. I want to use objective C as the language, as the app I am creating is using Objective C. Does anyone know how I can implement email in the current version(6.2)?
.h file
#import <UIKit/UIKit.h>
#import <MessageUI/MessageUI.h>
@interface IntakeViewController : UIViewController <MFMailComposeViewControllerDelegate>{
}
- (IBAction)emailClicked:(id)sender;
@end
.m file
#import "IntakeViewController.h"
@interface IntakeViewController ()
@end
@implementation IntakeViewController
- (IBAction)emailClicked:(id)sender {
if ([MFMailComposeViewController canSendMail]) {
MFMailComposeViewController *mail = [[MFMailComposeViewController alloc]init];
mail.mailComposeDelegate = self;
[mail setSubject:@"Review"];
NSArray *toRecipients = [NSArray arrayWithObjects:@"cbailey92@gmail.com", nil];
[mail setToRecipients:toRecipients];
NSString *body = @"You need more passion";
[mail setMessageBody:body isHTML:NO];
mail.modalPresentationStyle = UIModalPresentationPageSheet;
[self presentViewController:mail animated:YES completion:nil];
} else{
UIAlertView *alert = [[UIAlertView alloc] initWithTitle:@"Run Away!" message:@"You need more passion" delegate:nil cancelButtonTitle:@"Cancel" otherButtonTitles:nil];
[alert show];
}
}
-(void)mailComposeController:(MFMailComposeViewController *)controller didFinishWithResult:(MFMailComposeResult)result error:(NSError *)error
{
switch (result) {
case MFMailComposeResultCancelled:
NSLog(@"Cancelled");
break;
case MFMailComposeResultSaved:
NSLog(@"Saved");
break;
case MFMailComposeResultFailed:
NSLog(@"Failed");
break;
case MFMailComposeResultSent:
NSLog(@"Sent");
break;
default:
NSLog(@"Default");
break;
}
[self dismissViewControllerAnimated:YES completion:nil];
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,364
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\section{Introduction}
The negative refraction index media, first considered by Veselago \cite{Veselago}, and recently realized in the form of metamaterials~\cite{Smith,Shelby} exhibit many fascinating properties \cite{Veselago2,Pendry1} and potential applications such as imaging beyond the diffraction limit \cite{Pendry2}. In such materials, commonly called left-handed media (LHM) due to left-handed triada of vectors $\vec E$, $\vec H$ and $\vec k$ of propagating waves, many usual optical phenomena become reversed, however some of them are unreversed, just to mention the so-called rotational Doppler effect \cite{Luo} as well as the spin Hall effect in LHM \cite{Luo2}. The class of reversed phenomena includes
refraction \cite{Pendry1,Shelby}, Goos - H\"{a}nchen shift~\cite{GHshift} and the Doppler effect \cite{Veselago}. The reversed Doppler shift has been observed in a variety of systems such as magnetic thin film~\cite{Spinwave}, photonic crystals~\cite{Dop_Opt}, transmission lines~\cite{Seddon} and acoustical metamaterials~\cite{Sound_Lee}. In dispersive media, the so-called complex Doppler effect occurs, when a monochromatic source generates wave modes of multiple frequencies \cite{Ziemkiewicz}.
Another example of reversed phenomena in LHM is the Cherenkov effect \cite{Veselago}. This radiation, which was discovered experimentally in 1934 by Cherenkov \cite{Cherenkov} and later described theoretically by Frank and Tamm \cite{Tamm} occurs when a charged particle moves at a speed exceeding the phase velocity of the waves in a medium and has been extensively applied for particle detection. In usual, right-handed materials, the angle of radiation is smaller than $\pi/2$, so that the energy is emitted in the forward direction.
One of the important feature of negative index materials is a negative value of the phase velocity so the Cherenkov effect is reversed and the waves are emitted in backward direction \cite{Veselago}. It has been observed experimentally by Xi \emph{et al.}\cite{Xi}. The Cherenkov radiation in LHM has been studied by Lu \emph{et al.} \cite{Lu} for both lossless and lossy cases and they found that maintaining a forward $k$ vector of radiation in negative index media exhibits a backward emission. An elegant review of Cherenkov radiation in photonic crystals describing a backward-pointing radiation cone and backward direction of emission was presented by Luo \emph{et al.} \cite{Luo_Phot}. More recently in \cite{Chen} it was pointed out that the reversed Cherenkov radiation has a distinct advantage which allows the photons and charged particle to naturally separate in opposite directions, minimizing their interference. Nowadays there is a considerable interest in developing a new class of velocity-sensitive particle detectors based on left-handed materials \cite{Lu} which can be used to enhance the radiation \cite{Duan} or control its emission angle \cite{Ginis}.
Here we present a simple, unified analytical description of the Doppler and Cherenkov phenomena in an idealized, dispersive medium. The description of the complex Doppler effect presented in our previous paper \cite{Ziemkiewicz} is extended to the two-dimensional case. It is shown that a moving, monochromatic source generates two distinct frequency modes and the generated field exhibits features of both the Doppler and the Cherenkov effects.
Starting from the first principles, we are able to explain the angular distribution of the energy for the fast and slow frequency modes of the two-dimensional, complex Doppler effect in LHM. Moreover, the reversed Cherenkov radiation emerges as a particular case of the presented theory as the source with the frequency $\omega_0=0$ is shown to be formally equivalent to a moving charge. The intrinsic feature of the reversed Cherenkov effect in the considered LHM is the lack of a source velocity threshold above which this phenomenon occurs. This fact is explained in a general way and is shown to have a different origin than in the case of periodic media such as nanowire structures \cite{Fernandes}.
The theoretical findings are confirmed by numerical simulations based on the Finite Difference Time Domain (FDTD) method which is a common tool in the study of electromagnetic wave propagation in various media \cite{Veselago2,KS_Taflove}. The performed numerical simulations are in agreement with our theoretical predictions based on the first principle approach.
This paper is organized as follows. In section 2 we present the theory of the complex Doppler effect in two-dimensional LHM, section 3 is devoted to the description of the simulation setup. A spatial structure of fields emitted by a moving source characterized by nonzero and zero frequency, describing the complex Doppler and the reversed Cherenkov effect respectively, is discussed in section 4. Conclusions are drawn in section 5. Finally, in Appendix A we prove that the Cherenkov cone angle varies only within small interval and is almost insensible to the source velocity.
\section{Theory}
Consider an observer C receiving wavefronts emitted by a point source moving at a velocity $\vec v$, where the initial angle between source-observer line and $\vec v$ is $\theta$, as shown on the Fig. \ref{Doppler_rys}. The radiation source has a nominal frequency $\omega_0 = \frac{2\pi}{T_0}$ in its own reference frame.
\begin{figure}[ht!]
\begin{center}
\includegraphics[scale=0.6]{Fig1.eps}
\caption{Source of radiation moving with velocity $v$ emits two subsequent wave fronts at points A and B, towards observer C.}\label{Doppler_rys}
\end{center}
\end{figure}
Assuming that the first wavefront was emitted at $t=0$, the time instant in which it will be registered is
\begin{equation}
t_1 = \frac{a+b}{v_p(\omega)} = \frac{n(\omega)(a+b)}{c},
\end{equation}
where $v_p(\omega)$ is the phase velocity in the medium, and $n(\omega)$ is the refraction index. These quantities are observed in the reference frame of the detector and are functions of the detected frequency $\omega$. The second wavefront will arrive at the receiver at the time instant
\begin{equation}
t_2 = \frac{T_0}{\sqrt{1-\beta^2}} + \frac{n(\omega)d}{c},
\end{equation}
where $\beta = v/c$. The period measured by the observer will be
\begin{equation}
T = \left|\frac{T_0}{\sqrt{1-\beta^2}} - \frac{n(\omega)}{c}(a+b-d)\right|,
\end{equation}
where the absolute value was used to ensure that the period is a positive quantity. In a typical case, the distance $e$ traveled during a single period is negligible. Therefore, the angle $\alpha \approx 0$ and $b \approx d$. By using the relation
\begin{equation}
a = e \cos \theta = v\frac{T_0}{\sqrt{1-\beta^2}}\cos \theta,
\end{equation}
one obtains
\begin{equation}\label{DOPP1}
\omega = \omega_0 \left|\frac{\sqrt{1-\beta^2}}{1 - n(\omega)\beta \cos \theta}\right|,
\end{equation}
similar to the result obtained in \cite{Bazhanova},
where in our case the absolute value is necessary to ensure that the frequency is a positive quantity. The above relation is implicit and has multiple solutions in a dispersive medium, leading to the so-called the complex Doppler effect \cite{Frank}, where a monochromatic source generates multiple detected frequencies.
To solve the Eq. \ref{DOPP1}, one has to specify the dispersion relation of the medium. A remarkably simple description discussed by Veselago \cite{Veselago} in the context of the left-handed media is given by the Drude model, with the permittivity and permeability given by $\epsilon(\omega)= 1 - \frac{\omega_{pe}^2}{\omega^2}$ and $\mu(\omega)= 1 - \frac{\omega_{pm}^2}{\omega^2}$ respectively, where $\omega_{pe}$ and $\omega_{pm}$ depend on the metamaterial structure \cite{Pendry_6}. The proposed relations are applicable to a wide range of metamaterials \cite{Veselago2,Pendry_6}. For further simplification, one can assume $\omega_{pe} = \omega_{pm} = \omega_p$, so that the dispersion relation for the refraction index $n$ is
\begin{equation} \label{modDRU}
n(\omega) = 1 - \frac{\omega_p^2}{\omega^2}.
\end{equation}
With the above dispersion model, from Eq. (\ref{DOPP1}) one obtains two explicit solutions of the following form
\begin{eqnarray}\label{DOPP2}
\omega_1(\beta,\theta) = \frac{\omega_0\sqrt{1-\beta^2} + \sqrt{(1-\beta^2)\omega_0^2 - 4x(1-x)\omega_p^2}}{2(1-x)},\nonumber\\
\omega_2(\beta,\theta) = \frac{\omega_0\sqrt{1-\beta^2} - \sqrt{(1-\beta^2)\omega_0^2 - 4x(1-x)\omega_p^2}}{2(1-x)},
\end{eqnarray}
where
\begin{equation}
x = \beta\cos\theta.
\end{equation}
The important property of the Eqs. (\ref{DOPP2}) is the range of parameters where the frequencies $\omega_{i}$ are real, indicating non-evanescent wave modes detectable in the far field of the source. By taking, for simplicity, $\omega_0^2 = \frac{1}{2}\omega_p^2$ so that $n(\omega_0)=-1$, one obtains
\begin{equation}
\cos \theta \leq \frac{2 - \sqrt{2 + 2\beta^2}}{4 \beta}
\end{equation}
so that for sufficient source velocity, no propagating modes will be observed for the angle $\theta$ smaller than some limit value $0 \geq \theta_0 \geq \pi/2$. By inspecting the implicit Eq. (\ref{DOPP1}), one can see that for the negative value of the refraction index, the Doppler shift is reversed, so that the frequency of waves emitted in the forward direction ($\theta < \pi/2$) will be downshifted. In the considered model, the frequency of the upshifted modes at $\theta > \pi/2$ is inherently limited; as $\omega \rightarrow \omega_p$, the refraction index $n \rightarrow 0$ and the denominator of Eq. (\ref{DOPP1}) is equal to $1$. Therefore, the frequency $\omega_p$ cannot be exceeded when $\omega_0<\omega_p$. This means that a source having frequency $\omega_0$ such that $n(\omega_0)<0$ will generate only negative phase velocity modes with $n(\omega) < 0$.
\section{Simulation setup}
The performed simulations were based on a standard FDTD algorithm \cite{Yee} where the Maxwell's equations are solved in the time domain. A two-dimensional system with transverse magnetic field is chosen to facilitate the simulation of Cherenkov radiation \cite{Chen}; the electric field has two components in the plane of propagation $\vec E = [E_x,E_y,0]$, and the magnetic field has a single component $\vec H = [0,0,H_z]$. To model the dispersive medium, the Auxiliary Differential Equations (ADE) method is used \cite{KS_Taflove}. The implementation is a straightforward extension of the method used in our preceding work \cite{Ziemkiewicz} and is based on the time domain calculation of the polarization and magnetization in the medium. In the considered Drude model, these quantities are given by equations of motion $\ddot{P} = \omega_p^2 E$ and $\ddot{M} = \omega_p^2 H$.
The source with frequency $\omega_0$ moving at a velocity $V$ along $\hat x$ axis is modeled as a time varying current density in the form
\begin{equation}
J = J_0 \exp\left[\frac{-(x-Vt)^2}{2\sigma^2}\right]\exp\left(\frac{-y^2}{2\sigma^2}\right)\exp(-i\omega_0 t).
\end{equation}
The above representation describes an oscillating dipole oriented along $x$ axis \cite{Luo_Phot}, where the usual Dirac delta function is replaced with sufficiently narrow Gaussian width, with the width $\sigma$ significantly smaller that the source wavelength $\lambda(\omega_0)$. The only relativistic effect taken into account is the time dilation affecting the frequency $\omega_0$, which is needed to keep the consistency with the relativistic description of the Doppler shift presented above. In the performed simulations, the Lorentz contraction and other factors affecting the field amplitude can be disregarded, as the following discussion of the radiation intensity is qualitative in nature and the relativistic effects at the considered speeds are not significant.
The simulation space is divided into 300x300 grid and is surrounded by absorbing boundaries to reduce reflections. The frequency $\omega_0$ was chosen to minimize the effect of the numerical dispersion and anisotropy \cite{KS_Taflove}. This is especially important in the case of a dispersive medium described above, where the high frequency modes are limited by the finite time step, and the low frequency, short wavelength modes are constrained by the spatial step.
\section{Spatial structure of the field}
Let's assume that the moving source emits a quasi-monochromatic wave packet with central frequency $\omega_0$. According to Eq. (\ref{DOPP2}), for any emission angle $\theta$, there are two wave modes $\omega_i(\theta)$, $i=1,2$. Therefore, the wavefronts will propagate at an angle-dependent phase velocity $V_{pi}(\theta)=V_{pi}[\omega(\theta)]$. However, their envelopes will move at a group velocity $V_{gi}(\theta) = c/\left(n(\omega) + \omega\frac{\partial n}{\partial \omega}\right)$ which is assumed to be positive. When $V_g \cos \theta < V$, the emitted field will be detectable only behind the source, forming the so-called group cone \cite{Carusotto}. In dispersive media, its apex angle may differ significantly from the usually considered wave cone formed by the wavefronts. The situation is shown on the Fig. \ref{fig:2}. Assuming that the medium is isotropic and lossless, the phase velocity will be parallel to the group velocity.
\begin{figure}[ht!]
\begin{center}
\includegraphics[scale=0.4]{Fig2.eps}
\caption{Radiation cone formed by a single mode emitted at a given angle $\theta$. Dashed line indicates the wavefront.}\label{fig:2}
\end{center}
\end{figure}
As it follows from the geometry of the~Fig.~\ref{fig:2}, the cone half apex angle $\alpha$ can be expressed as
\begin{equation}\label{rw0}
\tan \alpha = \frac{V_g(\theta) \sin \theta}{V - V_g(\theta) \cos \theta}.
\end{equation}
To deduce the whole radiation pattern of the moving source, one has to consider the wave modes for all angles $\theta$. An elegant way of presentation was pointed out in \cite{Luo_Phot} and it consists of plotting the group velocity $V_g(\theta)$ as a contour and comparing it to the source velocity. By doing this, one can visualize the distance traveled by the source and the wave envelope at some given time, recreating the spatial structure of the radiated field. An example of such construction for $\beta=0.3c$ and $n(\omega_0)=-1$ is shown on the Fig. \ref{fig:3a} and the corresponding field snapshot is presented on the Fig. \ref{fig:3b}. The solutions of Eq. (\ref{DOPP2}) define two contours $V_{gi}(\theta)$. The high frequency modes $\omega_1(\theta)$ are comparable to the nominal frequency $\omega_0$ and are characterized by relatively high group velocity $V_{g1}(\theta)$. This solution can be associated with the usual Doppler effect; the backwards moving waves ($\theta > \pi/2$) are upshifted, with their group velocity exceeding the value of $V_g(\omega_0) = c/3$. Also, the transverse Doppler shift for the waves emitted in a direction perpendicular to the source motion is caused only by the relativistic effects, so in the low velocity regime $\omega_1(\pi/2)\approx\omega_0$. For the forward moving waves, the frequency and the group velocity drops quickly as $\theta \rightarrow \theta_0$, possibly becoming much smaller than $V$ and leading to the Cherenkov-like radiation pattern. The second wave mode $\omega_2$ is characterized by small group velocity. A characteristic point of this solution is $\theta=\pi/2$, where $\omega_2 = 0$. As the angle approaches this value, the frequency becomes arbitrarily small. In a realistic scenario, the amount of the downshift is limited to the range where the dispersion model in Eq. (\ref{modDRU}) is applicable. Moreover, the low frequency modes are more affected by the absorption \cite{Ziemkiewicz}, making their detection difficult.
\begin{figure}
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.37]{Fig3a.eps}
\subcaption{}\label{fig:3a}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.27]{Fig3b.eps}
\subcaption{}\label{fig:3b}
\end{minipage}
\caption{(a) Radiation cones of the two Doppler modes at $\beta=0.3c$ and $n(\omega_0)=-1$. The angles $\theta_1$ and $\theta_2$ mark the direction of radiation forming the cone. (b) The group velocity contour imposed on the field snapshot calculated with FDTD method.}\label{fig:3}
\end{figure}
The space taken by the radiated field is limited by the maximum value of cone angle $\alpha$ measured between the source velocity and a line tangent to the group velocity contour (Fig. \ref{fig:3a}). Its value can be determined by solving $\partial \tan \alpha/\partial \theta = 0$, which leads to
\begin{equation}\label{rw1}
V_g^2 = V \frac{\partial V_g}{\partial \theta}\sin \theta + V V_g \cos \theta.
\end{equation}
The angle $\theta$ obtained from the above equation marks the point of intersection and, according to the Fig. \ref{fig:2}, describes the direction of radiation forming the cone. As it was shown in \cite{Carusotto} at this angle, the maximum of the radiation maximum intensity is expected. This is due to the fact that for all angles near $\theta$, the cone angle $\alpha$ is almost the same, so that constructive interference occurs.
In a dispersionless medium (e. g. $V_g=V_p$ and $\partial V_g/\partial \theta = 0$), the Eq. (\ref{rw1}) reduces to the classic relation for the Cherenkov radiation angle
\begin{equation}\label{rw2}
\cos \theta = \frac{V_p}{V}.
\end{equation}
In the case of a dispersive material, the Eq. (\ref{rw1}) can be solved separately for the two modes $V_{gi}(\theta)$, yielding characteristic angles $\theta_i$. These critical angles, as well as and the associated cones described by Eq. (\ref{rw0}) are shown on the Fig. \ref{fig:3a}. One can see that the first, wide cone is formed by the high frequency modes $\omega_1$. The radiation is emitted at an angle $\theta_1<\pi/2$ and the wavefronts are roughly parallel to the cone surface, in a manner similar to the Cherenkov radiation (Fig. \ref{fig:3b}). The low frequency modes $\omega_2$ form a much narrower cone. The emission angle $\theta_2 > \pi/2$ and the wavefronts are almost perpendicular to the cone surface which is a characteristic feature of the reversed Cherenkov effect \cite{Chen}. The first contour $V_{g1}(\theta)$ becomes almost circular for $\theta>\theta_1$. In this area, the radiated field is very similar to the case of the Doppler effect in dispersionless medium - a detector positioned at an angle $\theta$ will register only single wave mode, so that the wave frequency $\omega(\theta)$ can be readily measured.
On the other hand, as the angle approaches $\theta_0$, the frequency of the both modes changes quickly, so the field measured along some finite angle range around $\theta_0$ has a wide spectrum.
Further analysis of this case is presented on the Fig. \ref{fig:4}. The field snapshot from the FDTD simulation is presented in Fig. \ref{fig:4a}. Clearly, the obtained cones divide the radiated field into three distinct regions. The highest field amplitude is generated by the modes traveling along the direction $\theta_1$ and forming the outer cone. The inner cone is formed by the $\omega_2(\theta_2)$ modes. Another significant direction is $\theta_0$, where the field is a superposition of many modes with a wide range of group velocities, so that it is spreading over time. These findings are confirmed by the calculated time-averaged value of the Poynting vector $\vec S = \vec E \times \vec H$ shown on the Fig. \ref{fig:4b}. One can see that the initial radiation pattern shows a wide peak at $\theta \approx \theta_1$ which is formed by the fast modes $\omega_1$. After the time needed for these modes to leave the simulation area, the intensity peaks formed by the slow modes $\omega_2$ can be observed. They are centered around $\theta_0$ and $\theta_2$. As it is shown on the Fig. \ref{fig:4c}, there is significant difference in the absolute value of the phase velocity between the fast modes $\omega_1$ and slow modes $\omega_2$. In the latter case, it is significantly smaller than $V$. Finally, the measured frequencies presented in Fig. \ref{fig:4d} are also in a good agreement with the predicted value. To illustrate the influence of the source velocity on the field structure, another simulation was performed for $\beta=0.1$. The results are shown on Figs. \ref{fig:4e} and \ref{fig:4f}. In this case, the group velocity of the first mode $\omega_1$ is always significantly higher than $V$, so that no cone is formed and the radiation pattern differs only slightly from the field of radiating, stationary dipole. The second mode $\omega_2$ is characterized by a very low group velocity, forming a very narrow cone, barely visible in the field snapshot in Fig. \ref{fig:4e}.
\begin{figure}
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.21]{Fig4a.eps}
\subcaption{}\label{fig:4a}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.33]{Fig4b.eps}
\subcaption{}\label{fig:4b}
\end{minipage}
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.33]{Fig4c.eps}
\subcaption{}\label{fig:4c}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.33]{Fig4d.eps}
\subcaption{}\label{fig:4d}
\end{minipage}
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.21]{Fig4e.eps}
\subcaption{}\label{fig:4e}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.33]{Fig4f.eps}
\subcaption{}\label{fig:4f}
\end{minipage}
\caption{Simulation results for the complex Doppler effect at $\beta = 0.3$ and $n(\omega_0)=-1$. (a) Field snapshot at t=500. The cones clearly divide the space into distinct areas. (b) Angular distribution of energy for the fast modes centered around $\theta_1$ and the low frequency modes at $\theta_0$ and $\theta_2$. (c) The phase velocity contour. The radius of the black circle is equal to the source speed. (d) The frequency as a function of angle measured in the area where the field is monochromatic. (e) Field snapshot for $\beta=0.1$. (f) The group velocity contour for $\beta=0.1$.}\label{fig:4}
\end{figure}
\begin{figure}
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.33]{Fig5a.eps}
\subcaption{}\label{fig:6a}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.21]{Fig5b.eps}
\subcaption{}\label{fig:6b}
\end{minipage}
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.33]{Fig5c.eps}
\subcaption{}\label{fig:6c}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.21]{Fig5d.eps}
\subcaption{}\label{fig:6d}
\end{minipage}
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.33]{Fig5e.eps}
\subcaption{}\label{fig:6e}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.33]{Fig5f.eps}
\subcaption{}\label{fig:6f}
\end{minipage}
\caption{Cherenkov radiation for $\beta = 0.3$. (a) Group velocity contour in dispersionless dielectric with $n=4$. (b) Field snapshot at t=500, showing typical Cherenkov cone. (c) Group velocity contour in left-handed medium. (d) Field snapshot at t=500, showing reversed Cherenkov effect. (e) Radiation pattern for $\beta = 0.3$, exhibiting a narrow peak at $\theta_1$. (f) Radiation pattern for $\beta = 0.8$.}\label{fig:6}
\end{figure}
It is important to note the difference between the obtained radiation patterns and the Cherenkov effect. Here, the source of radiation is characterized by the nominal frequency $\omega_0$. Moreover, the absolute value of the phase velocity of the first mode is significantly larger than $V$ (Fig. \ref{fig:4c}), so that the condition in Eq. (\ref{rw2}) cannot be met. One can also see that the cone angle $\theta_1 < \pi/2$ which characterizes a non-reversed Cherenkov effect, despite the fact that the phase velocity is negative. Finally, for $\theta>\theta_1$, the cone transforms in a continuous manner into the typical Doppler shifted field pattern, generated by radiating point source. On the other hand, the second, narrower cone is formed by the modes characterized by $|V_{p2}| < V$ and $V_{g2} < V$; the radiation pattern is simpler, closely resembling the case of the reversed Cherenkov effect.
To compare the results to the generic Cherenkov radiation, our source model can be adapted to simulate a moving charge by assuming $\omega_0=0$. Under such condition, the Eq. (\ref{DOPP1}) describes wave modes with frequency $\omega=\vec k \cdot \vec V = n \beta \cos \theta$, generating the spectrum of a point charge moving with velocity $V$. A particle of small but finite dimension moving along x axis can be modeled as a charge density \cite{Burlak}
\begin{equation}
\rho(x,y,t) = \rho_0 \exp\left[\frac{-(x-Vt)^2}{2\sigma^2}\right]\exp\left(\frac{-y^2}{2\sigma^2}\right),
\end{equation}
which corresponds to the source current \cite{Lu}
\begin{equation}
J = \rho_0V \exp\left[\frac{-(x-Vt)^2}{2\sigma^2}\right]\exp\left(\frac{-y^2}{2\sigma^2}\right).
\end{equation}
As a test case, a simulation was performed in a dispersionless dielectric characterized by $n=4$. The charge moving at a velocity $V=0.3~c$ is expected to create a cone at the angle $\theta_1 = \arccos (V_p/V) \approx 34^o$. The geometrical construction based on the group velocity contour is presented on the Fig. \ref{fig:6a}. The field snapshot is shown on the Fig. \ref{fig:6b}. The Cherenkov cone is clearly visible and its angle matches the theoretical prediction.
In the case of a dispersive medium described by Eq. (\ref{modDRU}), the Doppler shift Eqs. (\ref{DOPP2}) remain valid for $\omega_0=0$, reducing to a single solution
\begin{equation}\label{DOPP5}
\omega_1(\beta,\theta) = \omega_2(\beta,\theta)= \omega_p\sqrt{\frac{-\beta\cos\theta}{1-\beta\cos\theta}}.
\end{equation}
One can check that for any angle $\theta$, the phase velocities of the wave modes described by above relation fulfill the Eq. (\ref{rw2}). This important property should be stressed; in the classical Cherenkov radiation, the single radiation angle is a function of the two constants - the phase velocity and the source velocity. Here, the phase velocity of the emitted mode varying, being a function of the source speed and angle $\theta$. In other words, the radiation pattern is a superposition of cones corresponding to different group velocities \cite{Luo}. The real value of the frequency associated with propagating waves is obtained from Eq. (\ref{DOPP5}) only for $\theta>\theta_0=\pi/2$. This means that the Cherenkov effect is reversed which is consistent with the negative value of the refraction index \cite{Veselago}. The group velocity contour for $V=0.3c$ is shown on the Fig. \ref{fig:6c}. In contrast to the Cherenkov effect in dispersionless medium, the frequency range of the emitted modes is limited, and their group velocities vary from $V_g=0$ at $\theta=90^0$ to $V_g \approx 0.19~c$ at $\theta=180^0$. Due to the low values of the group velocity, the outer cone is relatively narrow, and the radiation angle $\theta_1 \approx 120^o$. Again, the structure of the field in the snapshot presented in Fig. \ref{fig:6d} is in an excellent agreement with the analytical prediction. As expected, the radiation pattern presented in Fig. \ref{fig:6e} shows a narrow initial peak at $\theta=\theta_1$, followed by the slow modes at $\theta_0>\theta>\theta_1$.
When a single frequency is measured, the radiation angle agrees with the generic Cherenkov condition given by Eq. (\ref{rw2}) for the appropriate value of $n(\omega)$. Therefore, the performed simulations show a good agreement with prior simulations where a window function has been used to reduce frequency range \cite{Chen} and with experimental data obtained by Xi \emph{et al.}\cite{Xi}.
Surprisingly, the dependence of the cone angle on the source velocity is insignificant; the result for $V=0.8 c$ shown on the Fig. \ref{fig:6f} is almost indistinguishable from the case of $V=0.3 c$. This is confirmed on the Fig. \ref{fig:7a}, where the numerically computed relation $\theta_1(\beta)$ based on Eq. (\ref{rw1}) is shown. This interesting property depends on the dispersion relation of the medium and has been observed in various physical systems; for example, in the so-called Kelvin wake in water waves \cite{Georgi}, the group velocity is directly proportional to the phase velocity, which is given by Eq. (\ref{rw2}). This causes the Eq. (\ref{rw1}) to independent of the source speed; the details are presented in Appendix A.
One can see another significant departure from the typical Cherenkov effect in a dispersionless medium; the Eq. (\ref{DOPP5}) has a solution for any $1 \geq \beta \geq 0$. Therefore, there is no source velocity threshold above which the phenomenon occurs. Unless additional constraints are put on the dispersion model, the frequency and phase velocity of the wave modes can become arbitrarily small, matching the source velocity in accordance with the Eq. (\ref{rw2}) and producing radiation at any $\beta$. Such radiation without a velocity threshold has been observed with metallic gratings \cite{Purcell} and predicted to occur in periodic structures \cite{Luo} such as nanowire metamaterial \cite{Fernandes}. The Cherenkov radiation frequency varies considerably with source velocity (Fig. \ref{fig:7b}) but, in general, it is comparable to the resonant frequency of the medium $\omega_p$, so that it is defined by the material properties \cite{Burlak}.
\begin{figure}
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.25]{Fig6a.eps}
\subcaption{}\label{fig:7a}
\end{minipage}%
\begin{minipage}[b]{.5\linewidth}
\centering
\includegraphics[scale=0.25]{Fig6b.eps}
\subcaption{}\label{fig:7b}
\end{minipage}
\caption{(a) The dependence of the cone angle on the source velocity. (b) The dependence of the wave frequency on the source velocity for $\theta=120^0$.}\label{fig:7}
\end{figure}
\section{Conclusion}
We presented an unified analytical description of the two-dimensonal Doppler and Cherenkov effects in an idealized, dispersive metamaterial. It was shown that a moving, monochromatic source generates two distinct frequency modes and the generated field exhibits features of both, the Doppler and the Cherenkov effects. We prove,
starting from the first principles, that the reversed Cherenkov radiation emerges as a particular case of the presented theory. The characteristic peculiarities
of the reversed Cherenkov effect in LHM, namely the backward direction of emission, the constant angle of maximum radiation intensity and the lack of a source velocity threshold above which this phenomenon occurs are explained on the basis of presented theory and confirmed by numerical simulations. Our results are in agreement with measurements obtained in the experiment performed by Xi \emph{et al.}\cite{Xi}. All these interesting features of the Cherenkov radiation in metamaterials characterized by Drude-like dispersion model might possibly provide a new way of frequency-based charged particle speed measurement, with the mechanical simplicity enabled by the constant radiation angle.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,541
|
\section{Introduction}
The Sudbury Neutrino Observatory (SNO) is a heavy water Cherenkov detector
located 2092~m underground near Sudbury, Ontario.\cite{nim} The
neutrino target consists of 1000 tonnes of ultra-pure D$_2$O housed in a
clear acrylic vessel 12 m in diameter. SNO detects the neutrinos from
\iso{8}B decays in the sun through three reactions:
\begin{eqnarray}
\mbox{Charged Current Reaction (CC): \,\,\,\,\,\,\,\,\, }\nu_e+\mbox{d}&\longrightarrow&\mbox{p}+\mbox{p}+e^{-}\nonumber\\
\mbox{Elastic Scattering Reaction (ES): \,\,\,\,\,\,\,\, }\nu_x+e^{-}&\longrightarrow&\nu_x+e^{-}\nonumber\\
\mbox{Neutral Current Reaction (NC): \,\,\,\,\,\,\,\,\,
}\nu_x+\mbox{d}&\longrightarrow&\nu_x + \mbox{p}+\mbox{n}.
\end{eqnarray}
The charged current reaction is sensitive only to electron neutrinos,
while the neutral current reaction is sensitive to any active flavor,
$\nu_x$, $ x = e, \mu, \tau$.
The elastic scattering reaction has some sensitivity to non-electron
flavors, but is primarily sensitive to electron neutrinos. The NC reaction
in SNO allows a measurement of the total flux of all active \iso{8}B
solar neutrinos,
while a comparison of the neutrino fluxes measured through the NC and CC
reactions tests for solar neutrino flavor change.
Cherenkov radiation from the electrons produced in the CC and ES
reactions is detected in an array of approximately 9500
photomultiplier tubes (PMTs). The neutrons liberated in the NC reaction must
be detected through a secondary capture reaction. The SNO experiment
was designed to run in three phases, incorporating three distinct
neutron capture signatures to ensure a robust NC measurement.
In each phase, the neutron response features, systematic
uncertainties, background characteristics, and analysis techniques differ.
In the first phase of the experiment, neutrons were detected using the
6.25~MeV gamma signature from neutron capture on deuterium.
Results from the first phase confirmed solar model predictions
of the \iso{8}B flux, demonstrated solar neutrino flavor change, and
contributed to determination of the underlying neutrino oscillation
parameters.~\cite{prl1}~\cite{prl2}~\cite{prl3}
In the second phase of the experiment, ultra-pure salt (NaCl) was
dissolved in the D$_2$O, to a concentration of ($0.196\pm0.002)\%$ by
weight. The higher cross section for neutron capture on
\iso{35}Cl and the higher energy (8.6~MeV) released in the reaction
improve SNO's efficiency for detecting NC neutrons. In addition, the multiple
gammas produced in the \iso{35}Cl capture reaction result in a more
isotropic distribution of Cherenkov light relative to the distribution
of light in single-electron events. Using the
isotropy of light produced in a neutrino event, the CC and NC
signals can be statistically separated without requiring constraints
on the solar neutrino energy spectrum. First
neutrino flux results for 254 days of salt data
were published in 2004.\cite{prl4} Results for the 391-day salt data set
have recently been reported \cite{nsp} and are summarized in this
article.
Finally, the third phase of the SNO experiment began in the fall of 2004,
following the deployment of 36 strings of \iso{3}He proportional
counters and 4 strings
of \iso{4}He proportional counters
inside the heavy water volume. Neutron capture in the \iso{3}He
counters allows an event-by-event determination of the NC
rate, completely decoupled from the PMT detection of the CC and ES signals.
\section{Data Analysis in the Salt Phase}
The effect of the added salt on SNO's neutron detection efficiency is
illustrated in figure \ref{fig:ncapt}(a), which shows the neutron
capture efficiency for a \iso{252}Cf calibration source as a function of
the radial position of the source in the detector volume. Accounting for the
fiducial volume and energy cuts used in the solar neutrino analysis,
the neutron capture efficiency in the salt phase is
40.7\%, compared to 14.4\% in the pure-D$_2$O phase.
The higher energy of neutron capture events in the salt phase also
boosts the NC signal further above the analysis energy threshold. A
Monte Carlo comparison of the energy spectrum for neutrons in the salt
and pure-D$_2$O phases is shown in figure \ref{fig:ncapt}(b).
\begin{figure}[h]
\begin{center}
$\begin{array}{c@{\hspace{0.2cm}}c}
\epsfxsize=3.0in \epsfysize = 2.2in
\epsffile{salt_d2o_comp.eps} &
\epsfxsize=3.0in
\epsffile{salt_d2o_energy.eps}\\ [0.1cm]
\mbox{\bf (a)} & \mbox{\bf (b)}
\end{array}$
\end{center}
\caption{(a) Comparison of the neutron capture efficiency in the salt
and D$_2$O phases. The capture efficiency is shown for neutrons
from a \iso{252}Cf fission source of known strength, as a function of
the radius of the source in the detector. (b)
Comparison of the energy spectrum of neutrons events in the salt
phase to the D$_2$O phase, as calculated by Monte Carlo. }
\label{fig:ncapt}
\end{figure}
A fiducial volume cut of 550~cm and an analysis energy threshold of
$T_{eff} > 5.5$~MeV are used to reduce the number of background events in the final
salt event sample, where $T_{eff}$ is the effective electron kinetic
energy for the event, $T_{eff} = E - 0.511$~MeV. The final data set
consists of 4722 events recorded over 391.4 days of detector live time between July 2001 and
August 2003. This data set contains
some remaining backgrounds as well as neutrino
interaction events. The dominant background in SNO is
neutrons from the photodisintegration of deuterium by gammas with
energies above 2.2~MeV. Radioactive contaminants from the U and
Th decay chains are the primary source of these gammas, which can
originate within the D$_2$O or in the acrylic vessel and external regions
of the detector. The total contribution of neutron backgrounds from
inside the D$_2$O region is determined, using a variety of in-situ and
ex-situ techniques, to be $125.1^{+37.3}_{-32.0}$ events.
Additionally, an estimated $3.2^{+4.6}_{-4.4}$ events in the salt data
set are gamma rays from the products of atmospheric neutrino
interactions. These ``internal'' neutron and gamma backgrounds are held
fixed in the statistical signal extraction process that is used to
determine the CC, NC, and ES reaction rates. Neutrons and gamma rays
produced outside the D$_2$O region can also propagate into the
fiducial volume. Neutron backgrounds due to these ``external''
sources will have a characteristic radial profile that can be used to
distinguish them from signal neutrons.
To extract the numbers of CC, NC, ES, and external neutron (EN)
events in the data set, event distributions in several variables are
fit to characteristic signal distributions derived from
Monte Carlo calculations. The event variables used are the effective
electron kinetic energy $T_{eff}$, the radius
of the reconstructed event vertex $\rho = (r/600.5\mbox{cm})^3$, the
cosine of the angle between the reconstructed event direction and a
vector from the sun $\cos\theta_{\odot}$, and a
parameter characterizing the light isotropy in the event, $\beta_{14}$.
The $\beta_{14}$ parameter is based on
Legendre polynomials in terms of the angle between each pair
of hit PMTs relative to the event vertex. Events with a
more isotropic distribution of light have smaller values of $\beta_{14}$.
\begin{figure}[h]
\begin{center}
$\begin{array}{c@{\hspace{0.2cm}}c}
\epsfxsize=2.4in
\epsffile{teff_pdf.eps} &
\epsfxsize=2.4in
\epsffile{rho_pdf.eps} \\ [0.2cm]
\epsfxsize=2.4in
\epsffile{b14_pdf.eps} &
\epsfxsize=2.4in
\epsffile{cossun_pdf.eps}
\end{array}$
\end{center}
\caption{Monte Carlo probability density functions used in signal
extraction, for (a) energy, (b) radius of the event vertex, (c)
isotropy, and (d) direction relative to the sun. Normalizations are
arbitrary. Where external neutron backgrounds are indistinguishable
from internal neutrons
(including those produced by the NC signal), the distribution is
simply labeled ``neutrons''. The CC energy shape shown in (a)
corresponds to an undistorted \iso{8}B neutrino spectrum.}
\label{fig:pdfs}
\end{figure}
Detailed Monte Carlo simulations are used to generate probability
density functions (PDFs) characterizing signal distributions in these
variables. These PDFs are shown in figure \ref{fig:pdfs}.
In a statistical fit, the isotropy distributions
provide a powerful tool for distinguishing neutrons from CC and ES events,
the direction distributions help to identify the ES contribution,
and the radial distributions separate the external neutron background.
The energy distribution shown for the CC signal
assumes an undistorted \iso{8}B neutrino spectrum. To make
measurements that are independent of model assumptions about the
energy spectrum, we can extract the CC and ES signals separately in
each energy bin. In such an ``energy unconstrained'' analysis, the
extracted CC spectrum can be used to test models of neutrino
oscillation. This model-independent signal extraction is possible
because of the power of the $\beta_{14}$ distribution for separating
event classes
in salt. In the D$_2$O phase, the CC and ES spectra had to be
constrained to break statistical correlations between the signals.
\section{Systematic Uncertainties}
Systematic uncertainties in detector response are evaluated
through comparisons of Monte Carlo simulations and calibration data.
The primary calibration sources used to study systematic uncertainties
are a \iso{16}N 6.13~MeV gamma-ray source and a \iso{252}Cf fission
neutron source. The \iso{16}N source is used to study energy
response, event reconstruction performance, and
detector stability over time. The \iso{252}Cf source is used to
evaluate neutron response characteristics.
Systematic uncertainties are
propagated by perturbing the PDFs according to the estimated 1$\sigma$
variation in each response parameter, and then repeating the signal
extraction process.
The dominant systematic uncertainties on the CC and NC extracted
fluxes in the energy-unconstrained analysis are due to uncertainty in
the $\beta_{14}$ parameter. Uncertainties of less than a percent in the
mean isotropy values translate to uncertainties of around 4\% in the CC and
NC fluxes. The energy scale uncertainty in the salt phase is
estimated to be 1.15\%, which contributes an uncertainty of around
3.5\% in the NC flux, but has a smaller effect on the CC and ES
fluxes. An uncertainty of 1\% in radial reconstruction accuracy
is also one of the larger
contributions to the overall systematic error, resulting in a $\sim3$\%
uncertainty in each flux. The ES flux uncertainty is dominated by
a 5\% systematic uncertainty due to uncertainty in angular resolution.
A much more detailed discussion of calibrations and systematic
uncertainties can be found in the recent salt phase publication.\cite{nsp}
\section{Solar Neutrino Flux Results from an Energy-Unconstrained Analysis}
From an energy-unconstrained extended maximum likelihood fit to extract
the contributions of each signal to the data set, the
number of NC events is $2010\pm85$, the number of
CC events is $2176\pm78$, and the number of ES events is
$279\pm26$. The external neutron background is $128\pm42$ events.
Accounting for acceptance factors and detector live time, we can
convert these extracted event numbers into equivalent fluxes of
\iso{8}B solar neutrinos, in units of $10^6\,\mbox{cm}^{-2}\mbox{s}^{-1}$,
\begin{eqnarray}
\phi_{\mbox{\small{CC}}}& =& 1.68^{+0.06}_{-0.06}\mbox{(stat.)}^{+0.08}_{-0.09}\mbox{(syst.)}\nonumber\\
\phi_{\mbox{\small{ES}}}& =& 2.35^{+0.22}_{-0.22}\mbox{(stat.)}^{+0.15}_{-0.15}\mbox{(syst.)}\nonumber\\
\phi_{\mbox{\small{NC}}}& =& 4.94^{+0.21}_{-0.21}\mbox{(stat.)}^{+0.38}_{-0.34}\mbox{(syst.)}.
\end{eqnarray}
\begin{figure}
\begin{center}
\psfig{figure=pnt.eps,height=2.8in}
\caption{\label{fig:pnt} Flux of $\mu$ and $\tau$ neutrinos versus flux of
electron neutrinos. CC, NC, and ES flux measurements are indicated
by the filled bands. The total \iso{8}B solar neutrino flux
predicted by the Standard Solar Model is shown as dashed lines,
parallel to the NC measurement. The narrow band parallel to the SNO
ES measurement corresponds to the Super-Kamiokande elastic
scattering result. The best-fit point is determined using only the SNO data.}\end{center}
\end{figure}
The flavor
composition of \iso{8}B solar neutrinos detected by SNO is
summarized in figure \ref{fig:pnt}, which also shows comparisons to
the ES flux measured by the Super-Kamiokande experiment~\cite{sk} and
the Standard Solar Model predicted total flux.~\cite{ssm} The best-fit
point indicates the appearance of non-electron neutrino flavors in the
solar neutrino flux.
\section{Charged Current Spectrum and Day-Night Asymmetries}
The favored model for explaining solar neutrino flavor
change invokes matter-enhanced neutrino oscillation in the solar
interior, through the so-called Mikheyev-Smirnov-Wolfenstein (MSW) effect.
In addition to predicting solar neutrino flavor change, the MSW effect
has two other predictions that are potentially testable in SNO.
Matter effects in the sun
could distort the energy spectrum of solar neutrinos, and additional
matter effects in the earth could affect the flavor composition of
neutrinos that pass through terrestrial material before reaching a
detector. The energy-unconstrained analysis of SNO's salt phase data allows an
extraction of the CC electron energy spectrum, which can be
used to test for spectrum distortions. Matter effects in the earth
can be tested by looking for day-night asymmetries in the rate of
charged current interactions.
For both the spectrum and day-night analyses, a number of differential
systematic uncertainties were evaluated. Calibration sources were
used to study energy-dependent systematic effects.
In-situ techniques using low-energy backgrounds and secondary products
from cosmic-ray muon interactions were used to study diurnal variations
for the day-night analysis.
\begin{figure}
\begin{center}
\psfig{figure=model.eps,height=2.8in}
\caption{Extracted electron energy spectrum from the CC
reaction, with statistical uncertainties. Systematic uncertainties
are shown with
respect to the predicted spectrum for an undistorted \iso{8}B solar
neutrino spectrum. The spectrum shape for the best-fit MSW point
(in the ``LMA'' region of the parameter space) is also shown.
\label{fig:spec}}
\end{center}
\end{figure}
The extracted CC energy spectrum is shown in figure \ref{fig:spec},
with statistical uncertainties. Systematic
uncertainties are shown with respect to the prediction assuming an
undistorted \iso{8}B solar neutrino spectrum. The measured spectrum
is consistent with no distortions, and is also consistent
with the spectrum predicted by the best-fit MSW model, corresponding
to the so-called Large Mixing Angle (LMA) region of the neutrino
oscillation parameter space.
To search for day-night effects, we
construct asymmetry parameters in terms of the measured day and night fluxes,
$A_\alpha=
2(\Phi_{\alpha,N}-\Phi_{\alpha,D})/(\Phi_{\alpha,N}+\Phi_{\alpha,D})$,
where $\alpha$ = CC, NC, ES.
The asymmetries determined in an energy-unconstrained analysis of the
salt phase data are
\begin{eqnarray}
A_{{CC}} &=&
-0.056\pm0.074(\mbox{stat.})\pm0.053(\mbox{syst.})\nonumber\\
A_{{NC}} &=&
0.042\pm0.086(\mbox{stat.})\pm0.072(\mbox{syst.})\nonumber\\
A_{{ES}} &=& 0.146\pm0.198(\mbox{stat.})\pm0.033(\mbox{syst.}).
\end{eqnarray}
All asymmetries are consistent with zero.
The extracted day and night CC spectra from this analysis
can be used to construct the CC asymmetry as a function of energy,
shown in figure \ref{fig:acc_vs_e}. Neutrino oscillation parameters
in the LMA region predict very small
day-night asymmetries, and a comparison to the LMA predicted asymmetry
is shown in the figure.
\begin{figure}
\begin{center}
\psfig{figure=acc_vs_e_unc.eps,height=2.8in}
\caption{Charged current day-night asymmetry as a function of energy,
with statistical uncertainties only. The final bin extends from
13.5~MeV to 20~MeV. The dashed line shows the prediction from the
previous best-fit point in the MSW parameter space.
\label{fig:acc_vs_e}}
\end{center}
\end{figure}
Since an asymmetry in the NC rate is not expected for standard
neutrino oscillations, a statistically significant NC asymmetry would
be evidence for sterile neutrinos or exotic physics. Within the
standard neutrino oscillation picture, we can constrain the neutral
current asymmetry to be zero to reduce the statistical correlations in
the extraction of the day-night asymmetries. With this
additional constraint, the asymmetries become
\begin{eqnarray}
A_{{CC}} &=&
-0.037\pm0.063(\mbox{stat.})\pm0.032(\mbox{syst.})\nonumber\\
A_{{ES}} &=& 0.153\pm0.198(\mbox{stat.})\pm0.030(\mbox{syst.}).
\end{eqnarray}
Repeating this analysis with the assumption of an undistorted
\iso{8}B neutrino energy spectrum further reduces the uncertainties,
and allows the salt phase charged-current asymmetry to be combined with the
energy-constrained asymmetry results from the first phase of SNO. The
combined day-night asymmetry from both phases is $A_{\mbox{\tiny{salt+D$_2$O}}} =
0.037\pm0.040$(stat.+syst.). The day-night asymmetry results from SNO
are consistent with no asymmetry, and also with the best-fit MSW
model, which predicts an asymmetry of $\sim3.5$\%.
\section{MSW Parameter Constraints}
The salt phase results for the fluxes, spectra, and day-night
asymmetries can be combined with SNO's previous results and the
results of other solar neutrino experiments to
produce constraints on the fundamental neutrino parameters in the MSW
model. Figure \ref{fig:msw}(a) shows the results of a global
chi-squared analysis in a two-neutrino oscillation framework,
including SNO's salt phase and D$_2$O phase data as well as results
from Chlorine~\cite{cl} and Gallium~\cite{ga1}~\cite{ga2} experiments and the
Super-Kamiokande experiment~\cite{sk}. The best-fit point is $\Delta m^2 =
(6.5^{+4.4}_{-2.3})\times10^{-5}\mbox{eV}^2$, $\tan^2\theta =
0.45^{+0.09}_{-0.08}$. Including
the results from the KamLAND experiment~\cite{kl1}~\cite{kl2} gives the contours shown in
figure \ref{fig:msw}(b). The best fit point for the global analysis
including the KamLAND data is $\Delta m^2 =
(8.0^{+0.6}_{-0.4})\times10^{-5}\mbox{eV}^2$, $\tan^2\theta = 0.45^{+0.09}_{-0.07}$.
\begin{figure}
\begin{center}
\psfig{figure=global_side.eps,height=2.8in}
\caption{(a) Parameter constraints from a global neutrino oscillation analysis including fluxes and
day and night energy spectra from SNO's salt and D$_2$O phases, as
well as rate measurements from the Chlorine, SAGE, and Gallex/GNO
experiments, and zenith spectra from Super-Kamiokande. (b)
Constraints from a global
analysis including the KamLAND 766 ton-year
results as well. Best fit points are marked with stars.
\label{fig:msw}}
\end{center}
\end{figure}
\section{Conclusions}
Solar neutrino results from the salt phase of the SNO experiment have been
summarized in this paper. These results include
measurements of the flux of \iso{8}B solar
electron neutrinos through the CC reaction, and
of the flux of \iso{8}B solar neutrinos of
all active flavors through the NC reaction. Use of the isotropy
parameter in the salt phase
allows NC and CC events to be statistically
separated without any assumptions about the underlying neutrino
energy spectrum.
The new flux
results confirm and improve previous results, demonstrate solar
neutrino flavor change, and contribute to evidence for solar neutrino
oscillations.
Salt phase results also include the first
presentation of the extracted charged current electron energy spectrum
with statistical and systematic uncertainties fully evaluated. This
spectrum is consistent with the spectrum predicted for an undistorted
\iso{8}B neutrino spectrum, and is also consistent with the
spectrum predicted by the best-fit MSW model.
Day-night asymmetries have been constructed to test for possible MSW
effects in the earth. Measured asymmetries are consistent with zero,
and also with the predictions for the best-fit MSW model. A global
analysis of the salt phase results along with other solar and reactor
neutrino measurements has been performed, giving best-fit values of
$\Delta m^2 =
(8.0^{+0.6}_{-0.4})\times10^{-5}\mbox{eV}^2$,$\tan^2\theta =
0.45^{+0.09}_{-0.07}$.
More details as well as additional
results can be found in the recent salt phase publication.\cite{nsp}
\section*{Acknowledgments}
This research was supported by: Canada: Natural Sciences and
Engineering Research Council, Northern Ontario Heritage Fund, Atomic
Energy of Canada, Ltd., Ontario Power Generation, High Performance
Computing Virtual Laboratory, Canada Foundation for Innovation; US:
Dept. of Energy, National Energy Research Scientific Computing Center;
UK: Particle Physics and Astronomy Research Council.
\section*{References}
|
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Хэси́ () — район городского подчинения города центрального подчинения Тяньцзинь (КНР).
История
Во времена феодального Китая именно здесь размещались руководящие учреждения провинции Чжили и города Тяньцзинь.
Район Хэси был образован в 1956 году.
Административное деление
Район Хэси делится на 13 уличных комитетов.
Язык
Местные жители говорят на тяньцзиньском диалекте.
Достопримечательности
Народный парк
Образование
Тяньцзиньский университет экономики и финансов
Тяньцзиньский институт иностранных языков
Тяньцзиньский научно-технический университет
Ссылки
Районы Тяньцзиня
|
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\section{\bf Introduction}\label{intro}
A spacetime is a 4-dimensional connected Lorentzian manifold. The class of pp-wave metrics (\cite{EK62}, \cite{ste03}) arose during the study of exact solutions of Einstein's field equations. The term ``pp-wave'' is given by Ehlers and Kundt \cite{EK62}, where ``pp'' stands for ``plane-fronted gravitational waves with parallel rays'', which means that the generalized pp-wave spacetimes admit geodesic null vector field whose twist, expansion and shear are zero. The ``plane rays'' implies that the rotation of the vector field vanishes. For vacuum type N, this implies the existence of a covariantly constant vector field which is parallel to the null vector field. There are various forms of generalized pp-wave metrics in different coordinates. The pp-wave belongs to the class of solutions admitting a non-expanding, shear-free and twist-free null congruence and it admits a null Killing vector.\\
\indent The family of pp-wave space-times was first discussed by Brinkmann \cite{Brin25} and interpreted in terms of gravitational waves by Peres \cite{Pere59}. According to Brinkmann, a pp-wave spacetime is any Lorentzian manifold
whose metric tensor can be described, with respect to Brinkmann coordinates, in the form
\be\label{pp-bc}
ds^2 = H(u, x, y) du^2 + 2 du dv + dx^2 + dy^2,
\ee
where $H$ is any nowhere vanishing smooth function. Again it is well known that a Lorentzian manifold with parallel lightlike (null) vector field is called Brinkmann-wave (\cite{Brin25}, \cite{GL10}). A Brinkmann-wave is called pp-wave if its curvature tensor $R$ satisfies the condition ${R_{ij}}^{pq}R_{pqkl}= 0$ (\cite{GL10}, \cite{MS16}, \cite{SG86}). In 1984, Radhakrishna and Singh \cite{RS84} presented a class of solutions to Einstein-Maxwell equation for the null electrovac Petrov type $N$ gravitational field. They presented a metric of the form
\beb
ds^2=-2U du^2+2dudr-\frac{1}{2}P[(dx^3)^2+(dx^4)^2],
\eeb
where $U=U(u,x^3,x^4)$ and $P=P(x^3,x^4)$ are two nowhere vanishing smooth functions.
For the simplicity of notation, we write the variable $u$ as $x$, and the function $U$ as $h$ and $P$ as $f$. Then the aforesaid metric can be written as
\be\label{gppwm}
ds^2=-2 h(x,x^3,x^4) (dx)^2 + 2 dx dr-\frac{1}{2}f(x^3,x^4)[(dx^3)^2+(dx^4)^2].
\ee
\indent In section \ref{se-gpp} we show that the metric \eqref{gppwm} admits a covariantly constant null vector field and it satisfies the condition ${R_{ij}}^{pq}R_{pqkl}= 0$ if
\be\label{cond}
\left(f f_{33} - f^2_{3}\right)+\left(f f_{44} - f^2_{4}\right) = 0.
\ee
Thus we can say that the metric \eqref{gppwm} is a Brinkmann-wave and it becomes a pp-wave if \eqref{cond} holds. Hence we can say the metric \eqref{gppwm} as ``generalized pp-wave metric''. We note that for $f\equiv -2$ and $h = -\frac{1}{2}H(u,x^3,x^4)$, the solution \eqref{gppwm} reduces to the pp-wave metric \eqref{pp-bc}.\\
\indent In the study of differential geometry the notion of manifold of constant curvature has been generalized by many authors in different directions such as locally symmetric manifold by Cartan \cite{Cart26}, semisymmetric manifold by Cartan \cite{Cart46} (see also \cite{Szab82}, \cite{Szab84}, \cite{Szab85}), pseudosymmetric manifold by Adam\'{o}w and Deszcz \cite{AD83}, recurrent manifold by Ruse (\cite{Ruse46}, \cite{Ruse49a}, \cite{Ruse49b}, see also \cite{Walk50}), weakly generalized recurrent manifold by Shaikh and Roy (\cite{SAR13}, \cite{SR11}), hyper generalized recurrent manifold by Shaikh and Patra (\cite{SP10}, \cite{SRK15}), super generalized recurrent manifold by Shaikh et al. \cite{SRK16}. We note that in such geometric structures the first order and second order covariant derivatives of the Riemann curvature tensor and other curvature tensors involved. We mention that the notion of pseudosymmetry by Deszcz is important in the study of differential geometry due to its application in relativity and cosmology (see \cite{DDVV94}, \cite{DHV04}, \cite{DVV91} and also references therein). The notion of pseudosymmetry is extended by considering other curvature tensors in its defining condition, such as conformal pseudosymmetry, pseudosymmetric Weyl conformal curvature tensor, Ricci generalized pseudosymmetry etc. and they are called pseudosymmetric type conditions. It may be mentioned that different pseudosymmetric type conditions are admitted by various spacetimes, such as G\"{o}del spacetime (\cite{DHJKS14}, \cite{Gode49}), Som-Raychaudhuri spacetime (\cite{SK16srs}, \cite{SR68}), Reissner-Nordstr\"{o}m spacetime \cite{Kowa06} and Robertson-Walker spacetime (\cite{ADEHM14}, \cite{DDHKS00}, \cite{DK99}).\\
\indent The main object of the present paper is to investigate the geometric structures admitted by the generalized pp-wave metric \eqref{gppwm}. It is interesting to note that the metric \eqref{gppwm} without any other condition admits several geometric structures, such as Ricci generalized pseudosymmetry, 2-quasi Einstein and generalized quasi-Einstein in the sense of Chaki \cite{Chak01}. Again it is shown that the pp-wave metric (i.e., \eqref{gppwm} with condition \eqref{cond}) is Ricci recurrent but not recurrent, semisymmetric, $R$-space by Venzi, conformal curvature 2-forms are recurrent, Ricci tensor is Riemann compatible and fulfills a pseudosymmetric type condition due to the projective curvature tensor $P$. For the study of pseudosymmetric type conditions with projective curvature tensor we refer the reader to see the recent papers of Shaikh and Kundu (\cite{SKppsn}, \cite{SKppsnw}). It is interesting to note that for such a metric $P\cdot R = 0$ but $P\cdot\mathcal R \ne 0$.\\
\indent It is also shown that the metric is weakly Ricci symmetric and weakly cyclic Ricci symmetric for different associated 1-forms, which ensures the existence of infinitely many solutions of associated 1-forms of such structures. Again we investigate the condition for which such a spacetime is locally symmetric and recurrent.\\
\indent The paper is organized as follows. Section 2 deals with defining conditions of different curvature restricted geometric structures, such as recurrent, semisymmetry, pseudosymmetry, weakly symmetry etc. as preliminaries. Section 3 is devoted to the investigation of curvature restricted geometric structures admitted by the generalized pp-wave metric \eqref{gppwm}. Section 4 is mainly concerned with the geometric structures admitted by pp-wave metric and plane wave metric. Section 5 deals with the investigation of the conditions under which the energy-momentum tensor of such spacetimes are parallel, Codazzi type and cyclic parallel. Finally, the last section is devoted to make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric as well as pp-wave metric.
\section{\bf Preliminaries}
Let $M$ be a connected smooth semi-Riemannian manifold of dimension $n$ $(\geq 3)$ equipped with the semi-Riemannian metric $g$. Let $R$, $\mathcal R$, $S$, $\mathcal S$ and $\kappa $ be respectively the Riemann-Christoffel curvature tensor of type $(0,4)$, the Riemann-Christoffel curvature tensor of type $(1,3)$, the Ricci tensor of type $(0,2)$, the Ricci tensor of type $(1,1)$ and the scalar curvature of $M$.\\
\indent For two symmetric $(0,2)$-tensors $A$ and $E$, their Kulkarni-Nomizu product $A\wedge E$ is defined as (see e.g. \cite{DGHS11}, \cite{Glog02}):
\begin{eqnarray*}
(A\wedge E)(X_1,X_2,X_3,X_4) &=& A(X_1,X_4)E(X_2,X_3) + A(X_2,X_3)E(X_1,X_4)\\
&-& A(X_1,X_3)E(X_2,X_4) - A(X_2,X_4)E(X_1,X_3),
\end{eqnarray*}
where $X_1,X_2,X_3,X_4 \in \chi(M)$, the Lie algebra of all smooth vector fields on $M$. Throughout the paper we will consider $X, Y, X_1, X_2, \cdots \in \chi(M)$.\\
\indent In terms of Kulkarni-Nomizu product, the conformal curvature tensor $C$, the concircular curvature tensor $W$, the conharmonic curvature tensor $K$ (\cite{Ishi57}, \cite{YK89}) and the Gaussian curvature tensor $\mathfrak G$ can be expressed as
\beb
C &=& R-\frac{1}{n-2}(g\wedge S) + \frac{r}{2(n-2)(n-1)}(g\wedge g),\\
W &=& R-\frac{r}{2n(n-1)}(g\wedge g),\\
K &=& R-\frac{1}{n-2}(g\wedge S),\\
\mathfrak G &=& \frac{1}{2}(g\wedge g).
\eeb
Again the projective curvature tensor $P$ of type $(0,4)$ is given by
$$
P(X_1, X_2, X_3, X_4) = R(X_1, X_2, X_3, X_4) - \frac{1}{n-1}[g(X_1, X_4)S(X_2, X_3)-g(X_2, X_4)S(X_1, X_3)].
$$
\indent For a symmetric $(0, 2)$-tensor $A$, we get an endomorphism $\mathcal A$ defined by $g(\mathcal AX,Y) = A(X,Y)$. Then its $k$-th level tensor $A^k$ of type $(0,2)$ is given by
$$A^k(X,Y) = A(\mathcal A^{k-1}X,Y),$$
where $\mathcal A^{k-1}$ is the endomorphism corresponding to $A^{k-1}$.\\
\begin{defi} (\cite{Bess87}, \cite{SKgrt})
A semi-Riemannian manifold $M$ is said to be $Ein(2)$, $Ein(3)$ and $Ein(4)$ respectively if
$$S^2 + \lambda_1 S + \lambda_2 g = 0,$$
$$S^3 + \lambda_3 S^2 + \lambda_4 S + \lambda_5 g = 0 \ \mbox{and}$$
$$S^4 + \lambda_6 S^3 + \lambda_7 S^2 + \lambda_8 S + \lambda_9 g = 0$$
holds for some scalars $\lambda_i, \, 1\le i \le 9$.
\end{defi}
\begin{defi} (\cite{Bess87}, \cite{SKgrt})
A semi-Riemannian manifold $M$ is said to be generalized Roter type (\cite{SKgrt}, \cite{SK16}) if its Riemann-Christoffel curvature tensor $R$ can be expressed as a linear combination of $g\wedge g$, $g\wedge S$, $S\wedge S$, $g\wedge S^2$, $S\wedge S^2$ and $S^2\wedge S^2$. Again $M$ is said to be Roter type (\cite{Desz03}, \cite{Desz03a}) if $R$ can be expressed as a linear combination of $g\wedge g$, $g\wedge S$ and $S\wedge S$.
\end{defi}
\indent Again for a $(0,4)$-tensor $D$, an endomorphism $\mathscr{D}(X,Y)$ and the corresponding $(1,3)$-tensor $\mathcal D$ can be defined as
$$\mathscr{D}(X,Y)X_1 = \mathcal D(X,Y)X_1, \ \ D(X_1,X_2,X_3,X_4) = g(\mathcal D(X_1,X_2)X_3, X_4).$$
Again for a symmetric $(0,2)$-tensor $A$, another endomorphism $X\wedge_A Y$ (\cite{DDHKS00}, \cite{DGHS11}) can be defined as
$$(X\wedge_A Y)X_1 = A(Y,X_1)X-A(X,X_1)Y.$$
\indent By operating $\mathscr{D}(X,Y)$ and $X\wedge_A Y$ on a $(0,k)$-tensor $B$, $k\geq 1$, we can obtain two $(0,k+2)$-tensors $D\cdot B$ and $Q(A,B)$ respectively given by (see \cite{DG02}, \cite{DGHS98}, \cite{DH03}, \cite{SDHJK15}, \cite{SK14} and also references therein):
$$D\cdot B(X_1,X_2,\cdots,X_k,X,Y) = -B(\mathcal D(X,Y)X_1,X_2,\cdots,X_k) - \cdots - B(X_1,X_2,\cdots,\mathcal D(X,Y)X_k).$$
\beb
\mbox{and } \ &&Q(A,B)(X_1,X_2, \ldots ,X_k,X,Y) = ((X \wedge_A Y)\cdot B)(X_1,X_2, \ldots ,X_k)\\
&&= A(X, X_1) B(Y,X_2,\cdots,X_k) + \cdots + A(X, X_k) B(X_1,X_2,\cdots,Y)\\
&& - A(Y, X_1) B(X,X_2,\cdots,X_k) - \cdots - A(Y, X_k) B(X_1,X_2,\cdots,X).
\eeb
In terms of local coordinates system, $D\cdot B$ and $Q(A,B)$ can be written as
\beb
(D\cdot B)_{i_1 i_2\cdots i_k j l} &=& -g^{pq}\left[D_{jli_1 q}B_{p i_2\cdots i_k} + \cdots + D_{jli_k q}B_{i_1 i_2\cdots p}\right],
\eeb
\beb
Q(A, B)_{i_1 i_2\cdots i_k j l} &=& A_{li_1}B_{j i_2\cdots i_k} + \cdots + A_{li_k}B_{i_1 i_2\cdots j}\\
& & -A_{ji_1}B_{l i_2\cdots i_k} - \cdots - A_{ji_k}B_{i_1 i_2\cdots l}.
\eeb
\begin{defi}$($\cite{Ruse46}, \cite{Ruse49a}, \cite{Ruse49b}, \cite{Patt52}$)$
A semi-Riemannian manifold $M$ is said to be $B$-recurrent if $\nabla B = \Pi \otimes B$ for an 1-form $\Pi$. In particular for $B = R$ (resp., $S$), the manifold $M$ is called recurrent (resp., Ricci recurrent) manifold.
\end{defi}
\begin{defi}$($\cite{AD83}, \cite{Cart46}, \cite{Desz92}, \cite{SK14}, \cite{Szab82}$)$
A semi-Riemannian manifold $M$ is said to be $B$-semisymmetric type if $D\cdot B = 0$ and it is said to be $B$-pseudosymmetric type if $\left(\sum\limits_{i=1}^k c_i D_i\right)\cdot B = 0$ for some scalars $c_i$'s, where $D$ and each $D_i$, $i=1,\ldots, k$, $(k\ge 2)$, are (0,4) curvature tensors. In particular, if $c_i$'s are all constants, then it is called $B$-pseudosymmetric type manifold of constant type or otherwise non-constant type.
\end{defi}
\indent In particular, if $i =2$, $D_1 = R$, $D_2 = \mathfrak G$ and $B = R$, then $M$ is called Ricci generalized pseudosymmetric \cite{DD91a}.\\
\begin{defi}
A semi-Riemannian manifold $M$ is said to be quasi-Einstein (resp., 2-quasi-Einstein) if at each point of $M$, rank$(S - \alpha g)\le 1$ (resp., $\le 2$) for a scalar $\alpha$. Also $M$ is said to be generalized quasi-Einstein in the sense of Chaki \cite{Chak01} if
$$S = \alpha g + \beta \Pi \otimes \Pi + \gamma [\Pi \otimes \Omega + \Pi \otimes \Omega]$$
form some 1-forms $\Pi$ and $\Omega$.
\end{defi}
\begin{defi}\label{def2.8}
Let $D$ be a $(0,4)$-tensor and $E$ be a symmetric $(0, 2)$-tensor on $M$. Then $E$ is said to be $D$-compatible (\cite{DGJPZ13}, \cite{MM12b}, \cite{MM13}) if
\[
D(\mathcal E X_1, X,X_2,X_3) + D(\mathcal E X_2, X,X_3,X_1) + D(\mathcal E X_3, X,X_1,X_2) = 0
\]
holds, where $\mathcal E$ is the endomorphism corresponding to $E$ defined as $g(\mathcal E X_1, X_2) = E(X_1, X_2)$. Again an 1-form $\Pi$ is said to be $D$-compatible if $\Pi\otimes \Pi$ is $D$-compatible.
\end{defi}
\begin{defi}
A Riemannian manifold $M$ is said to be weakly cyclic Ricci symmetric \cite{SJ06} if its Ricci tensor satisfies the condition
\bea\label{crs}
&&(\nabla_X S)(X_1,X_2) + (\nabla_{X_1} S)(X,X_2) + (\nabla_{X_2} S)(X_1,X)\\\nonumber
&&=\Pi(X)\, S(X_1,X_2) + \Omega(X_1)\, S(X,X_2) + \Theta(X_2)\, S(X_1,X),
\eea
for three 1-forms $\Pi$, $\Omega$ and $\Theta$ on $M$. Such a manifold is called weakly cyclic Ricci symmetric manifold with solution $(\Pi, \Omega, \Theta)$. Moreover if the first term of left hand side is equal to the right hand side, then it is called weakly Ricci symmetric manifold \cite{TB93}.
\end{defi}
\begin{defi}
Let $D$ be a $(0,4)$ tensor and $Z$ be a $(0,2)$-tensor on $M$. Then the corresponding curvature 2-forms $\Omega_{(D)l}^m$ (\cite{Bess87}, \cite{LR89}) are called recurrent if and only if (\cite{MS12a}, \cite{MS13a}, \cite{MS14})
\beb\label{man}
&&(\nabla_{X_1} D)(X_2,X_3,X,Y)+(\nabla_{X_2} D)(X_3,X_1,X,Y)+(\nabla_{X_3} D)(X_1,X_2,X,Y) =\\
&&\hspace{1in} \Pi(X_1) D(X_2,X_3,X,Y) + \Pi(X_2) D(X_3,X_1,X,Y)+ \Pi(X_3) D(X_1,X_2,X,Y)
\eeb
and 1-forms $\Lambda_{(Z)l}$ \cite{SKP03} are called recurrent if and only if
$$(\nabla_{X_1} Z)(X_2,X) - (\nabla_{X_2} Z)(X_1,X) = \Pi(X_1) Z(X_2,X) - \Pi(X_2) Z(X_1,X)$$
for an 1-form $\Pi$.
\end{defi}
\begin{defi}$($\cite{Prav95}, \cite{SKppsn}, \cite{Venz85}$)$
Let $\mathcal L(M)$ be the vector space formed by all 1-forms $\Theta$ on $M$ satisfying
$$\Theta(X_1)D(X_2,X_3,X_4,X_5)+\Theta(X_2)D(X_3,X_1,X_4,X_5)+\Theta(X_3)D(X_1,X_2,X_4,X_5) = 0,$$
where $D$ is a $(0,4)$-tensor. Then $M$ is said to be a $D$-space by Venzi if $dim \mathcal L(M) \ge 1$.
\end{defi}
\section{\bf Curvature properties of generalized pp-wave metric}\label{se-gpp}
We can now write the metric tensor $g$ of the generalized pp-wave metric \eqref{gppwm} as follows:
$$g = \left(
\begin{array}{cccc}
-2 h & 1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
0 & 0 & -\frac{1}{2} f & 0 \\
0 & 0 & 0 & -\frac{1}{2} f
\end{array}
\right).$$
Then the non-zero components of its Riemann-Christoffel curvature tensor $R$, Ricci tensor $S$ and scalar curvature $\kappa$ of \eqref{gppwm} are given by
$$R_{1313}=\frac{-f_3 h_3+f_4 h_4+2 f h_{33}}{2 f}, \ \ R_{1314}=\frac{-f_4 h_3-f_3 h_4+2 f h_{34}}{2 f},$$
$$R_{1414}=\frac{f_3 h_3-f_4 h_4+2 f h_{44}}{2 f}, \ \ R_{3434}=\frac{-f_3^2-f_4^2+f f_{33}+f f_{44}}{4 f},$$
$$S_{11}=\frac{2 \left(h_{33}+h_{44}\right)}{f}, \ \ S_{33}= S_{44}=\frac{-f_3^2-f_4^2+f f_{33}+f f_{44}}{2 f^2},$$
$$\kappa = \frac{2 \left(f_3^2+f_4^2-f \left(f_{33}+f_{44}\right)\right)}{f^3}.$$
Again the non-zero components of $C$ and $P$ are given by
$$C_{1313}= -C_{1414}=\frac{-f_3 h_3+f_4 h_4+f h_{33}-f h_{44}}{2 f}, \ \ C_{1314}=\frac{-f_4 h_3-f_3 h_4+2 f h_{34}}{2 f},$$
$$P_{1211}=\frac{2 \left(h_{33}+h_{44}\right)}{3 f}, \ P_{1313}=\frac{-3 f_3 h_3+3 f_4 h_4+4 f h_{33}-2 f h_{44}}{6 f},$$
$$P_{1314}= -P_{1341}= P_{1413}= -P_{1431}=\frac{-f_4 h_3-f_3 h_4+2 f h_{34}}{2 f}, \ \ P_{1441}=-\frac{f_3 h_3-f_4 h_4+2 f h_{44}}{2 f},$$
$$P_{1331}=-\frac{-f_3 h_3+f_4 h_4+2 f h_{33}}{2 f}, \ \ P_{1414}=-\frac{-3 f_3 h_3+3 f_4 h_4+2 f h_{33}-4 f h_{44}}{6 f}.$$
Now the non-zero components (upto symmetry) of the energy momentum tensor
$$T= \frac{c^4}{8\pi G}\left[S-\left(\frac{\kappa}{2}-\Lambda\right)g\right],$$
where $c=$ speed of light in vacuum, $G=$ gravitational constant and $\Lambda=$ cosmological constant, are given by
$$T_{11}=-\frac{c^4 \left(f^3 h \Lambda -f^2 h_{33}-f^2 h_{44}+f_{33} f h+f_{44} f h-f_3^2 h-f_4^2 h\right)}{4 \pi f^3 G},$$
$$T_{12}=\frac{c^4 \left(f^3 \Lambda +f_{33} f+f_{44} f-f_3^2-f_4^2\right)}{8 \pi f^3 G}, \ \ T_{33}= T_{44}=-\frac{c^4 f \Lambda }{16 \pi G}.$$
Then the non-zero components (upto symmetry) of covariant derivative $\nabla T$ of the energy momentum tensor $T$ are given by
$$T_{11,1}=\frac{c^4 \left(h_{133}+h_{144}\right)}{4 \pi f G},$$
\beb
T_{11,3}=\frac{c^4}{4 \pi f^4 G} &&\left(-f^2 h f_{344}-f^2 h f_{333}+f^3 h_{333}+f^3 h_{344}-f_3 f^2 h_{33}-f_3 f^2 h_{44}\right.\\
&&\left.+4 f_3 f_{33} f h+2 f_4 f_{34} f h+2 f_3 f_{44} f h-3 f_3^3 h-3 f_3 f_4^2 h\right),
\eeb
\beb
T_{11,4}=\frac{c^4}{4 \pi f^4 G} &&\left(-f^2 h f_{444}-f^2 h f_{344}+f^3 h_{334}+f^3 h_{444}-f_4 f^2 h_{33}-f_4 f^2 h_{44}\right.\\
&&\left.+2 f_4 f_{33} f h+2 f_3 f_{34} f h+4 f_4 f_{44} f h-3 f_4^3 h-3 f_3^2 f_4 h\right),
\eeb
$$T_{12,3}=\frac{c^4 \left(f^2 f_{344}+f^2 f_{333}+3 f_3^3+3 f_4^2 f_3-4 f f_{33} f_3-2 f f_{44} f_3-2 f f_4 f_{34}\right)}{8 \pi f^4 G},$$
$$T_{12,4}=\frac{c^4 \left(f^2 f_{444}+f^2 f_{334}+3 f_4^3+3 f_3^2 f_4-2 f f_{33} f_4-4 f f_{44} f_4-2 f f_3 f_{34}\right)}{8 \pi f^4 G},$$
$$T_{13,1}=\frac{c^4 \left(-f_3^2-f_4^2+f f_{33}+f f_{44}\right) h_3}{8 \pi f^3 G},$$
$$T_{14,1}=\frac{c^4 \left(-f_3^2-f_4^2+f f_{33}+f f_{44}\right) h_4}{8 \pi f^3 G}.$$
\indent From above we see that the Ricci tensor $S$ of \eqref{gppwm} is of the form
\be\label{eqchqe}
S(X, Y) = \alpha g(X, Y) + \beta \eta(X)\eta(Y) + \gamma [\eta(X)\delta(Y)+\eta(Y)\delta(X)],
\ee
where $\alpha = \frac{f_3^2+f_4^2-f f_{33}-f f_{44}}{f^3}, \ \beta = 1, \ \gamma = 1, \ \eta = \{1,0,0,0\}$\\
\indent \indent and $\delta = \left\{\frac{2 f^2 \left(h_{33}+h_{44}\right)-2 \left(f_{33}+f_{44}\right) f h+2 \left(f_3^2+f_4^2\right) h - f^3}{2 f^3}, \frac{f \left(f_{33}+f_{44}-f_3^2-f_4^2\right)}{f^3},0,0\right\}.$\\
Therefore the metric \eqref{gppwm} is generalized quasi-Einstein in the sense of Chaki. Moreover $||\eta|| = 0$, $||\delta||^2 = \frac{\left(f_3^2+f_4^2-f \left(f_{33}+f_{44}\right)\right) \left(f-2 \left(h_{33}+h_{44}\right)\right)}{f^4}$, $g(\eta, \delta) = -\frac{f_3^2+f_4^2-f \left(f_{33}+f_{44}\right)}{f^3}$ and $\nabla \eta = 0$. So there exists a null covariantly constant vector field $\zeta$, where $\zeta$ is the corresponding vector field of $\eta$ (i.e., $g(\zeta, X) = \eta(X)$, $\forall \ X$). Hence we can conclude that the spacetime with the metric \eqref{gppwm} is a generalized pp-wave metric.\\
\indent Now from the value of the components of various tensors related to \eqref{gppwm}, we can state the following:
\begin{thm}\label{maingppwm}
The generalized pp-wave metric \eqref{gppwm} possesses the following curvature restricted geometric structures:
\begin{enumerate}[label=(\roman*)]
\item Ricci generalized pseudosymmetric such that $R\cdot R = Q(S, R)$,
\item 2-quasi-Einstein, since Rank$(S - \frac{f_3^2+f_4^2-f f_{33}-f f_{44}}{f^3}g) = 2$,
\item generalized quasi-Einstein in the sense of Chaki such that \eqref{eqchqe} holds,
\item Ricci tensor is Riemann compatible as well as Weyl compatible,
\item $Ein(3)$ manifold such that $S^2 = -\frac{f_3^2+f_4^2-f \left(f_{33}+f_{44}\right)}{f^3} S^3$.
\end{enumerate}
\end{thm}
\indent Now from the components of $R$, we see that the only non-zero (upto symmetry) the tensor $D_{ijkl} = R_{ij}^{pq}R_{pqkl}$ is given by $D_{3434} = \frac{\left(f_3^2+f_4^2-f \left(f_{33}+f_{44}\right)\right)^2}{2 f^4}$. Hence from definition, we can state the following.
\begin{thm}
The generalized pp-wave metric \eqref{gppwm} becomes a pp-wave metric if
$$f_3^2+f_4^2-f \left(f_{33}+f_{44}\right) = 0.$$
\end{thm}
\section{\bf Curvature properties of pp-wave and plane wave metric}\label{se-pp}
In this section we investigate the curvature restricted geometric structures admitted by the pp-wave metric. Since under the condition \eqref{cond} the generalized pp-wave metric \eqref{gppwm} becomes a pp-wave metric, putting this condition we get the non-zero components of $R$, $S$, $C$ and $P$ of the pp-wave metric given as follows:
$$R_{1313}=\frac{-f_3 h_3+f_4 h_4+2 f h_{33}}{2 f}, \ R_{1314}=\frac{-f_4 h_3-f_3 h_4+2 f h_{34}}{2 f}, \ R_{1414}=\frac{f_3 h_3-f_4 h_4+2 f h_{44}}{2 f},$$
$$S_{11}=\frac{2 \left(h_{33}+h_{44}\right)}{f},$$
$$C_{1313}= -C_{1414}=\frac{-f_3 h_3+f_4 h_4+f h_{33}-f h_{44}}{2 f}, \ \ C_{1314}=\frac{-f_4 h_3-f_3 h_4+2 f h_{34}}{2 f},$$
$$P_{1211}=\frac{2 \left(h_{33}+h_{44}\right)}{3 f}, \ P_{1313}=\frac{-3 f_3 h_3+3 f_4 h_4+4 f h_{33}-2 f h_{44}}{6 f},$$
$$P_{1314}= -P_{1341}= P_{1413}= -P_{1431}=\frac{-f_4 h_3-f_3 h_4+2 f h_{34}}{2 f}, \ \ P_{1441}=-\frac{f_3 h_3-f_4 h_4+2 f h_{44}}{2 f},$$
$$P_{1331}=-\frac{-f_3 h_3+f_4 h_4+2 f h_{33}}{2 f}, \ \ P_{1414}=-\frac{-3 f_3 h_3+3 f_4 h_4+2 f h_{33}-4 f h_{44}}{6 f}.$$
Using the values of the components of $g$, $R$, $S$ and $C$ we get\\
(i) $\kappa = 0$, (ii) $R\cdot R = 0$, (iii) $R\cdot S = 0$, (iv) $Q(S, R) = 0$, (v) $R\cdot C = 0$, (vi) $C\cdot R = 0$, (vii) $C\cdot C = 0$ and (viii) $Q(S, C) =0$.\\
\indent The energy momentum tensor $T$ is given by
\be\label{tcom}
T_{11}=-\frac{c^4 \left(f h \Lambda -h_{33}-h_{44}\right)}{4 \pi f G}, \ \ T_{12}=\frac{c^4 \Lambda }{8 \pi G}, \ \ T_{33}=T_{44}=-\frac{c^4 f \Lambda }{16 \pi G}.
\ee
Then the non-zero components of covariant derivative of $T$ are given by
\be\label{dtcom}
\left.\begin{array}{l}
T_{11,1}=\frac{c^4 \left(h_{144}+h_{133}\right)}{4 \pi f G},\\
T_{11,3}=\frac{c^4 \left(f h_{344}+f h_{333}-f_3 h_{33}-f_3 h_{44}\right)}{4 \pi f^2 G},\\
T_{11,4}=\frac{c^4 \left(f h_{444}+f h_{334}-f_4 h_{33}-f_4 h_{44}\right)}{4 \pi f^2 G}.
\end{array}\right\}
\ee
\indent From the above calculations, we can state the following:
\begin{thm}\label{mt}
The pp-wave metric (\eqref{gppwm} with the additional condition \eqref{cond}) possesses the following curvature properties:
\begin{enumerate}[label=(\roman*)]
\item $\kappa = 0$ and hence $R=W$ and $C=K$.
\item $R$-space and $C$-space by Venzi for $\{1,0,0,0\}$. Hence from second Bianchi identity, the curvature 2-forms $\Omega_{(R)l}^m$ are recurrent for the 1-form $\{1,0,0,0\}$.
\item It is semisymmetric and hence Ricci semisymmetric, conformally semisymmetric and projectively semisymmetric.
\item If $\alpha_{_3}+\alpha_{_4}\ne 0$, then the conformal 2-forms $\Omega_{(C)l}^m$ are recurrent with 1-form of recurrency
$$\Pi = \left\{1,0,\frac{\alpha_{_1}+\alpha_{_2}}{\alpha_{_3}+\alpha_{_4}},\frac{\alpha_{_5}+\alpha_{_6}+\alpha_{_7}}{\alpha_{_3}+\alpha_{_4}}\right\},$$
where $\alpha_{_1} = \left(f_3 h_3-f_4 h_4-f \left(h_{33}-h_{44}\right)\right) \left(f_3 \left(h_{33}+h_{44}\right)-f \left(h_{333}+h_{344}\right)\right)$,\\
$\alpha_{_2}= \left(-f_4 h_3-f_3 h_4+2 f h_{34}\right) \left(f \left(h_{334}+h_{444}\right)-f_4 \left(h_{33}+h_{44}\right)\right),$\\
$\alpha_{_3}= f^2 \left(4 h_{34}^2+\left(h_{33}-h_{44}\right){}^2\right)+f_3^2 \left(h_3^2+h_4^2\right)+f_4^2 \left(h_3^2+h_4^2\right),$\\
$\alpha_{_4}= 2 f f_4 \left(h_4 \left(h_{33}-h_{44}\right)-2 h_3 h_{34}\right)-2 f f_3 \left(2 h_4 h_{34}+h_3 \left(h_{33}-h_{44}\right)\right),$\\
$\alpha_{_5}= f^2 \left(2 h_{34} \left(h_{333}+h_{344}\right)+\left(h_{44}-h_{33}\right) \left(h_{334}+h_{444}\right)\right)+f_3^2 h_4 \left(h_{33}+h_{44}\right)+f_4^2 h_4 \left(h_{33}+h_{44}\right),$\\
$\alpha_{_6}= f f_3 \left(-2 h_{34} \left(h_{33}+h_{44}\right)-h_4 \left(h_{333}+h_{344}\right)+h_3 \left(h_{334}+h_{444}\right)\right)$,\\
$\alpha_{_7}= -f f_4 \left(-h_{33}^2+h_{44}^2+h_3 \left(h_{333}+h_{344}\right)+h_4 \left(h_{334}+h_{444}\right)\right)$.
\item It is not recurrent but if $h_{33}+h_{44}\ne 0$, then it is Ricci recurrent with 1-form of recurrency
$$\Pi = \left\{\frac{h_{144}+h_{133}}{h_{33}+h_{44}}, 0,\frac{f h_{344}+f h_{333}-f_3 h_{33}-f_3 h_{44}}{f\left(h_{33}+h_{44}\right)},\frac{f h_{444}+f h_{334}-f_4 h_{33}-f_4 h_{44}}{f\left(h_{33}+h_{44}\right)}\right\}.$$
\item If $h_{33}+h_{44}\ne 0$, then it is weakly cyclic Ricci recurrent with solution $(\Pi, \Omega, \Theta)$, given by
$$\Pi = \left\{\Pi_1, 0, \frac{f \left(h_{333}+h_{344}\right)-f_3 \left(h_{33}+h_{44}\right)}{f \left(h_{33}+h_{44}\right)}, \frac{f \left(h_{334}+h_{444}\right)-f_4 \left(h_{33}+h_{44}\right)}{f \left(h_{33}+h_{44}\right)}\right\},$$
$$\Omega = \left\{\Omega_1, 0, \frac{f \left(h_{333}+h_{344}\right)-f_3 \left(h_{33}+h_{44}\right)}{f \left(h_{33}+h_{44}\right)}, \frac{f \left(h_{334}+h_{444}\right)-f_4 \left(h_{33}+h_{44}\right)}{f \left(h_{33}+h_{44}\right)}\right\},$$
$$\Theta = \left\{\frac{3 \left(h_{133}+h_{144}\right)}{h_{33}+h_{44}}-\Pi_1-\Omega_1, 0, \frac{f \left(h_{333}+h_{344}\right)-f_3 \left(h_{33}+h_{44}\right)}{f \left(h_{33}+h_{44}\right)}, \frac{f \left(h_{334}+h_{444}\right)-f_4 \left(h_{33}+h_{44}\right)}{f \left(h_{33}+h_{44}\right)}\right\},$$
where $\Pi_1$ and $\Omega_1$ are arbitrary scalars.
\item Ricci simple (i.e., $S = \alpha \eta\otimes\eta$) for
$$\alpha = \frac{2(h_{33}+h_{44})}{f} \ \ \mbox{ and } \ \ \eta = \left\{1, 0, 0, 0\right\}$$
and hence $S\wedge S =0$ and $S^2 = 0$. Again $||\eta|| = 0$ and $\nabla\eta = 0$.
\item $Q(S, R) = Q(S, C) =0$ but $R$ or $C$ is not a scalar multiple of $S\wedge S$ as $S$ is of rank 1.
\item $C\cdot R =0$ and hence $C\cdot S =0$, $C\cdot C =0$ and $C\cdot P =0$.
\item $P\cdot R = 0$ but $P\cdot \mathcal R \ne 0$. Also but $P\cdot S =P\cdot \mathcal S =0$.
\item Ricci tensor is Riemann compatible as well as Weyl compatible.
\item $P\cdot P = -\frac{1}{3}Q(S,P)$.
\end{enumerate}
\end{thm}
\begin{rem}
From the value of the local components (presented in Section \ref{se-pp}) of various tensors of the pp-wave metric, we can easily conclude that the metric is
\begin{enumerate}[label=(\roman*)]
\item not conformally symmetric and hence not locally symmetric or projectively symmetric,
\item not conformally recurrent and hence not recurrent or not projectively recurrent,
\item not super generalized recurrent \cite{SRK16} and hence not hyper generalized recurrent \cite{SP10}, weakly generalized recurrent \cite{SR11},
\item not weakly symmetric \cite{TB89} for $R, C, P, W$ and $K$ and hence not Chaki pseudosymmetric \cite{Chak87} for $R, C, P, W$ and $K$,
\item neither cyclic Ricci parallel \cite{Gray78} nor of Codazzi type Ricci tensor although its scalar curvature is constant,
\item not harmonic, i.e., $div R \ne 0$ and moreover $div C \ne 0$, $div P \ne 0$.
\end{enumerate}
\end{rem}
\begin{rem}
In \cite{DD91a} Defever and Deszcz showed that if $Q(S,R) = 0$, then $R = L S\wedge S$ for some scalar $L$ if $S$ is not of rank 1. Recently, Shaikh and Kundu \cite{SKppsn} presented a metric (Example 1, \cite{SKppsn}) with $Q(S, R) = 0$, on which $S$ is not of rank 1 and $R = e^{x^1} S\wedge S$. It is interesting to mention that the rank of the Ricci tensor of the pp-wave metric is 1 and here $R\ne 0$ but $S\wedge S = 0$.
\end{rem}
\begin{rem}
It is well-known that every Ricci recurrent space with $\Pi$ as the 1-form of recurrency, is weakly Ricci symmetric with solution $(\Pi, 0, 0)$. It is interesting to mention that there may infinitely many solutions for a weakly Ricci symmetric manifold. The pp-wave metric (\eqref{gppwm} with condition \eqref{cond}) is weakly Ricci symmetric with solution
$$\Pi = \left\{\Pi_1, 0, \frac{f \left(h_{333}+h_{344}\right)-f_3 \left(h_{33}+h_{44}\right)}{f \left(h_{33}+h_{44}\right)}, \frac{f \left(h_{334}+h_{444}\right)-f_4 \left(h_{33}+h_{44}\right)}{f \left(h_{33}+h_{44}\right)}\right\},$$
$$\Omega = \left\{\Omega_1,0,0,0\right\} \ \mbox{ and}$$
$$\Theta = \left\{\frac{h_{133}+h_{144}}{h_{33}+h_{44}}-\Pi_1- \Omega_1, 0, 0, 0\right\},$$
where $\Pi_1$ and $\Omega_1$ are arbitrary scalars.
\end{rem}
\indent Again it is clear that the pp-wave metric \eqref{pp-bc} in Brinkmann coordinates, is a special case of \eqref{gppwm} for $f\equiv -2$ and $h = -\frac{1}{2}H$ and hence satisfies \eqref{cond}. Therefore from Theorem \ref{mt}, we can state the following about the geometric properties of the metic \eqref{pp-bc}.
\begin{cor}\label{cor1}
The metric given in \eqref{pp-bc} possesses the following curvature properties:
\begin{enumerate}[label=(\roman*)]
\item $\kappa = 0$ and hence $R=W$ and $C=K$.
\item $R$-space and $C$-space by Venzi for $\{1,0,0,0\}$. Hence from second Bianchi identity, the curvature 2-forms $\Omega_{(R)l}^m$ are recurrent for the 1-form $\{1,0,0,0\}$.
\item Semisymmetric and hence Ricci semisymmetric, conformally semisymmetric and projectively semisymmetric.
\item If $4H_{34}^2+ \left(H_{33}-H_{44}\right)^2 \ne 0$, then its conformal curvature 2-forms $\Omega_{(C)l}^m$ are recurrent with 1-form of recurrency $\Pi$, given by
$$\Pi_1 = 1, \ \ \Pi_2 = 0,$$
$$\Pi_3 = \frac{2 H_{34} \left(H_{334}+H_{444}\right)+\left(H_{33}-H_{44}\right) \left(H_{333}+H_{344}\right)}{4H_{34}^2+ \left(H_{33}-H_{44}\right)^2},$$
$$\Pi_4 = \frac{2 H_{34} \left(H_{333} + H_{344}\right) - \left(H_{33}-H_{44}\right) \left(H_{334}+ H_{444}\right)}{4H_{34}^2+ \left(H_{33}-H_{44}\right)^2}.$$
\item If $H_{33}+H_{44} \ne 0$, then it is Ricci recurrent with 1-form of recurrency $\Pi$, given by
$$\Pi = \left\{1, 0, \frac{H_{333}+H_{344}}{H_{33}+H_{44}}, \frac{H_{334}+H_{444}}{H_{33}+H_{44}}\right\}.$$
\item If $H_{33}+H_{44} \ne 0$, then it is weakly Ricci symmetric with solution $(\Pi, \Omega, \Theta)$, given by
$$\Pi = \left\{\Pi_1, 0, \frac{H_{333}+H_{344}}{H_{33}+H_{44}}, \frac{H_{334}+H_{444}}{H_{33}+H_{44}}\right\},$$
$$\Omega = \left\{\Omega_1, 0, 0, 0\right\} \ \mbox{and}$$
$$\Theta = \left\{\frac{H_{133}+H_{144}}{H_{33}+H_{44}}-\Pi_1-\Omega_1, 0, 0, 0\right\},$$
where $\Pi_1$ and $\Omega_1$ are arbitrary scalar.
\item If $H_{33}+H_{44} \ne 0$, then it is weakly cyclic Ricci symmetric with solution $(\Pi, \Omega, \Theta)$, given by
$$\Pi = \left\{\Pi_1, 0, \frac{H_{333}+H_{344}}{H_{33}+H_{44}}, \frac{H_{334}+H_{444}}{H_{33}+H_{44}}\right\},$$
$$\Omega = \left\{\Omega_1, 0, \frac{H_{333}+H_{344}}{H_{33}+H_{44}}, \frac{H_{334}+H_{444}}{H_{33}+H_{44}}\right\} \ \mbox{and}$$
$$\Theta = \left\{\frac{3 \left(H_{133}+H_{144}\right)}{H_{33}+H_{44}}-\Pi_1-\Omega_1, 0, \frac{H_{333}+H_{344}}{H_{33}+H_{44}}, \frac{H_{334}+H_{444}}{H_{33}+H_{44}}\right\},$$
where $\Pi_1$ and $\Omega_1$ are arbitrary scalar.
\item Ricci simple \cite{MS16} (i.e., $S = \alpha \eta\otimes\eta$) for
$$\alpha = \frac{1}{2}\left(H_{33}+H_{44}\right) \ \ \mbox{ and } \ \ \eta = \left\{1, 0, 0, 0\right\}$$
and hence $S\wedge S =0$ and $S^2 = 0$. Here $||\eta|| = 0$ and $\nabla \eta = 0$.
\item $Q(S, R) = Q(S, C) =0$ but $R$ or $C$ is not a scalar multiple of $S\wedge S$ as $S$ is of rank 1.
\item $C\cdot R =0$ and hence $C\cdot S =0$, $C\cdot C =0$ and $C\cdot P =0$.
\item $P\cdot R = 0$ but $P\cdot \mathcal R \ne 0$. Also but $P\cdot S =P\cdot \mathcal S =0$.
\item Ricci tensor is Riemann compatible as well as Weyl compatible.
\item $P\cdot P = -\frac{1}{3}Q(S,P)$.
\end{enumerate}
\end{cor}
\indent Again the non-vacuum pp-wave solution presented by Sippel and Goenner \cite{SG86} is a special case of \eqref{pp-bc} for $H(x,x^3,x^4) = 2 a_1 e^{a_2 x^3 - a_3 x^4}$. Hence the line element is explicitly given by:
\be\label{gppsg}
ds^2 = 2 a_1 e^{a_2 x^3 - a_3 x^4} (dx)^2 + 2 dx dr+[(dx^3)^2+(dx^4)^2].
\ee
Now the geometric properties of the metric \eqref{gppsg} can be stated as follows:
\begin{cor}\label{cor2}
The metric given in \eqref{gppsg} possesses the following curvature properties:
\begin{enumerate}[label=(\roman*)]
\item it satisfies the curvature conditions (i)-(xiii) of Corollary \ref{cor1} with different associated 1-forms of the corresponding structures,
\item moreover it is recurrent for the 1-form of recurrency $\{0,0,2 a_2,-2 a_3\}$. Hence it is Ricci recurrent, conformally recurrent and projectively recurrent. Also it is semisymmetric and hence Ricci semisymmetric, conformally semisymmetric and projectively semisymmetric.
\end{enumerate}
\end{cor}
\indent Again the generalized plane wave metric \cite{ste03} is given by
\be\label{gpwm}
ds^2 = 2 H(x,x^3,x^4) (dx)^2 + 2 dx dr+(dx^3)^2+(dx^4)^2,
\ee
where $H(x,x^3,x^4) = a_1 (x^3)^2 + a_2 (x^4)^2 + a_3 x^3 x^4 + a_4 x^3 + a_5 x^4 + a_6$, $a_i$'s are scalar. Hence it is a special case of \eqref{pp-bc} and we can state the following.
\begin{cor}\label{cor3}
The metric given in \eqref{gpwm} possesses the following curvature properties:
\begin{enumerate}[label=(\roman*)]
\item it satisfies the curvature conditions (i)-(ix) of Corollary \ref{cor1} with different associated 1-forms of the corresponding structures,
\item moreover it is locally symmetric and hence Ricci symmetric, conformally symmetric and projectively symmetric.
\end{enumerate}
\end{cor}
\indent From Corollary \ref{cor1}, Corollary \ref{cor2} and Corollary \ref{cor3}, we can state the following about the recurrent structure on a semi-Riemannian manifold.
\begin{rem}
From Corollary \ref{cor2} we see that the metric \eqref{gppsg} is recurrent but not locally symmetric and from Corollary \ref{cor1} we see that the metric \eqref{pp-bc} is Ricci recurrent but not recurrent. These results support the well-known facts that every locally symmetric manifold is recurrent but not conversely, and every recurrent manifold is Ricci recurrent but not conversely.
\end{rem}
\section{\bf Energy-momentum tensor of generalized pp-wave metric}\label{E-M}
In this section we discuss about the energy-momentum tensor of the generalized pp-wave metric \eqref{gppwm} and also the other special forms, such as \eqref{pp-bc}, \eqref{gppsg} and \eqref{gpwm}. From the values of the energy momentum tensor $T$ of the generalized pp-wave metric \eqref{gppwm}, we can conclude that $T$ is of rank 1 if the cosmological constant is zero and \eqref{cond} holds. In this case
$$T = \frac{c^4 \left(h_{33} + h_{44}\right)}{4 \pi f G} \eta\otimes\eta, \ \ \eta=\{1,0,0,0\}.$$
Again it is easy to check that $\eta$ is null. Thus we can state the following:
\begin{thm}
For zero cosmological constant, the generalized pp-wave metric \eqref{gppwm} is a pure radiation metric if and only if it is a pp-wave metric.
\end{thm}
\begin{cor}
For zero cosmological constant, the pp-wave metric (\eqref{gppwm} with \eqref{cond} or \eqref{pp-bc}) is a pure radiation metric.
\end{cor}
Again from the values of the components of $\nabla T$ of the metric \eqref{gppwm}, we get
$$T_{11,1} + T_{11,1} + T_{11,1}=\frac{3 c^4 \left(h_{133}+h_{144}\right)}{4 \pi f G},$$
\beb
T_{11,3} + T_{13,1} + T_{31,1}&=&\frac{c^4}{4 \pi f^4 G} \left(f^3 h_{333}+f^3 h_{344}-f_{333} f^2 h\right.\\
&&-f_{344} f^2 h+f_{33} f^2 h_3+f_{44} f^2 h_3-f_3 f^2 h_{33}-f_3 f^2 h_{44}+4 f_3 f_{33} f h\\
&&\left.+2 f_4 f_{34} f h+2 f_3 f_{44} f h-f_3^2 f h_3-f_4^2 f h_3-3 f_3^3 h-3 f_3 f_4^2 h\right),
\eeb
\beb
T_{11,4} + T_{14,1} + T_{41,1}&=&\frac{c^4}{4 \pi f^4 G} \left(f^3 h_{334}+f^3 h_{444}-f_{334} f^2 h-f_{444} f^2 h\right.\\
&&+f_{44} f^2 h_4-f_4 f^2 h_{33}-f_4 f^2 h_{44}+2 f_4 f_{33} f h+2 f_3 f_{34} f h+f_{33} f^2 h_4\\
&&\left.+4 f_4 f_{44} f h-f_3^2 f h_4-f_4^2 f h_4-3 f_4^3 h-3 f_3^2 f_4 h\right),
\eeb
$$T_{12,3} + T_{23,1} + T_{31,2}=\frac{c^4 \left(f^2 f_{333}+f^2 f_{344}+3 f_3^3+3 f_4^2 f_3-4 f f_{33} f_3-2 f f_{44} f_3-2 f f_4 f_{34}\right)}{8 \pi f^4 G},$$
$$T_{12,4} + T_{24,1} + T_{41,2}=\frac{c^4 \left(f^2 f_{334}+f^2 f_{444}+3 f_4^3+3 f_3^2 f_4-2 f f_{33} f_4-4 f f_{44} f_4-2 f f_3 f_{34}\right)}{8 \pi f^4 G}$$
and
\beb
T_{11,3} - T_{13,1} &=& \frac{c^4}{8 \pi f^4 G} \left(2 f^3 h_{333}+2 f^3 h_{344}-2 f_{333} f^2 h-2 f_{344} f^2 h\right.\\
&&-f_{33} f^2 h_3-f_{44} f^2 h_3-2 f_3 f^2 h_{33}-2 f_3 f^2 h_{44}+8 f_3 f_{33} f h+4 f_4 f_{34} f h\\
&&\left.+4 f_3 f_{44} f h+f_3^2 f h_3+f_4^2 f h_3-6 f_3^3 h-6 f_3 f_4^2 h\right),
\eeb
\beb
T_{11,4} - T_{14,1} &=& \frac{c^4}{8 \pi f^4 G} \left(2 f^3 h_{334}+2 f^3 h_{444}-2 f_{334} f^2 h-2 f_{444} f^2 h-f_{33} f^2 h_4\right.\\
&&-f_{44} f^2 h_4-2 f_4 f^2 h_{33}-2 f_4 f^2 h_{44}+4 f_4 f_{33} f h+4 f_3 f_{34} f h+8 f_4 f_{44} f h\\
&&\left.+f_3^2 f h_4+f_4^2 f h_4-6 f_4^3 h-6 f_3^2 f_4 h\right),
\eeb
$$T_{12,3} - T_{13,2} = T_{23,1} - T_{21,3} = -\frac{c^4 \left(f^2 f_{333}+f^2 f_{344}+3 f_3^3+3 f_4^2 f_3-4 f f_{33} f_3-2 f f_{44} f_3-2 f f_4 f_{34}\right)}{8 \pi f^4 G},$$
$$T_{12,4} - T_{14,2} = T_{24,1} - T_{21,4} = -\frac{c^4 \left(f^2 f_{334}+f^2 f_{444}+3 f_4^3+3 f_3^2 f_4-2 f f_{33} f_4-4 f f_{44} f_4-2 f f_3 f_{34}\right)}{8 \pi f^4 G}.$$
Now putting the condition \eqref{cond} to above, we get
\be\label{codtcom}
\left.\begin{array}{l}
T_{11,3} - T_{13,1} = \frac{c^4 \left(f h_{344}+f h_{333}-f_3 h_{33}-f_3 h_{44}\right)}{4 \pi f^2 G},\\
$$T_{11,4} - T_{14,1} = \frac{c^4 \left(f h_{444}+f h_{334}-f_4 h_{33}-f_4 h_{44}\right)}{4 \pi f^2 G},
\end{array}\right\}
\ee
and
\be\label{cstcom}
\left.\begin{array}{l}
T_{11,1} + T_{11,1} + T_{11,1}=\frac{3 c^4 \left(h_{144}+h_{133}\right)}{4 \pi f G},\\
T_{11,3} + T_{13,1} + T_{31,1}=\frac{c^4 \left(f h_{344}+f h_{333}-f_3 h_{33}-f_3 h_{44}\right)}{4 \pi f^2 G},\\
T_{14,1} + T_{41,1} + T_{11,4}=\frac{c^4 \left(f h_{444}+f h_{334}-f_4 h_{33}-f_4 h_{44}\right)}{4 \pi f^2 G}.
\end{array}\right\}
\ee
Now from \eqref{dtcom} and \eqref{cstcom} we can state the following:
\begin{pr}
The energy momentum tensor $T$ of the pp-wave metric \eqref{gppwm} with the condition \eqref{cond} is\\
i) parallel if
$$h_{144}+h_{133} = f h_{344}+f h_{333}-f_3 h_{33}-f_3 h_{44} = f h_{444}+f h_{334}-f_4 h_{33}-f_4 h_{44} = 0,$$
(ii) Codazzi type if
$$f h_{344}+f h_{333}-f_3 h_{33}-f_3 h_{44} = f h_{444}+f h_{334}-f_4 h_{33}-f_4 h_{44} = 0,$$
(iii) cyclic parallel if $$h_{144}+h_{133} = f h_{344}+f h_{333}-f_3 h_{33}-f_3 h_{44} = f h_{444}+f h_{334}-f_4 h_{33}-f_4 h_{44} = 0.$$
\end{pr}
\begin{pr}
The energy-momentum tensor of the generalized pp-wave metric of the form \eqref{pp-bc} is
(i) parallel if
$$h_{144}+h_{133} = h_{344}+h_{333} = h_{444}+h_{334} = 0,$$
(ii) Codazzi type if
$$h_{344}+h_{333} = h_{444}+h_{334} = 0,$$
(iii) cyclic parallel if $$h_{144}+h_{133} = h_{344}+h_{333} = h_{444}+h_{334} = 0.$$
\end{pr}
Now we can conclude the following:
\begin{thm}
On a pp-wave spacetime (endowed with the metric \eqref{gppwm} with \eqref{cond} or with the metric \eqref{pp-bc})\\
(i) the energy-momentum tensor is parallel if and only if it is cyclic parallel,\\
(ii) the energy-momentum tensor is Codazzi type if it is cyclic parallel but not conversely (see Example \ref{ex1}),\\
(iii) the Ricci tensor is zero, i.e., the space is vacuum if $h$ is harmonic in $x^3$ and $x^4$, i.e., $h_{33} + h_{44} = 0$ and in this case $\nabla T = 0$.
\end{thm}
\begin{exm}\label{ex1}
We now consider a special form of the generalized pp-wave metric \eqref{gppwm} as
\be\label{spec}
ds^2=-2 e^{x+x^3-x^4} (dx)^2 + 2 dx dr - \frac{1}{2}e^{x^3-x^4}[(dx^3)^2+(dx^4)^2].
\ee
Then the non-zero components of its $R$, $\nabla R$, $S$ and $\nabla S$ are given by
$$R_{1313} = R_{1414} = e^{x+x^3-x^4}, \ \ \ R_{1313,1}= R_{1414,1}=e^{x+x^3-x^4},$$
$$S_{11}=4 e^x, \ \ \ S_{11,1}=4 e^x.$$
It is easy to check that the scalar curvature of this metric is zero and it is conformally flat. Now the non-zero components of its energy momentum tensor $T$ and its derivative $\nabla T$ are given by
$$T_{11}=\frac{c^4 e^{x-x^4} \left(2 e^{x^4}-\Lambda e^{x^3}\right)}{4\pi G}, \ \ T_{12}=\frac{c^4 \Lambda }{8\pi G}, \ \ T_{33}=T_{44}=-\frac{c^4 \Lambda e^{x^3-x^4}}{16\pi G},$$
$$T_{11,1}=\frac{c^4 e^x}{2\pi G}.$$
Thus we can easily check that the Ricci tensor and the energy momentum tensor of \eqref{spec} are codazzi type but not cyclic parallel.
\end{exm}
\section{\bf Robinson-Trautman metric and generalized pp-wave metric}\label{compar}
Recently, Shaikh et al. \cite{SAA17} studied the curvature properties of Robinson-Trautman metric. The line element of Robinson-Trautman metric in $\{t,r,x^3,x^4\}$-coordinate is given by
\be\label{rtm}
ds^2 = -2(a - 2 b r - q r^{-1})dt^2 + 2 dt dr - \frac{r^2}{f^2} [(dx^3)^2+(dx^4)^2],
\ee
where $a, b, q$ are constants and $f$ is a function of the real variables $x^3$ and $x^4$. In this section we make a comparison between the curvature properties of the Robinson-Trautman metric \eqref{rtm} and generalized pp-wave metric \eqref{gppwm} as well as the pp-wave metric \eqref{pp-bc}.
\begin{thm}
The Robinson-Trautman metric \eqref{rtm} and generalized pp-wave metric \eqref{gppwm} have the following similarities and dissimilarities: \\
\textbf{A. Similarities:}\\
(i) Both the metrics are 2-quasi-Einstein,\\
(ii) both are generalized quasi-Einstein in the sense of Chaki,\\
(iii) Ricci tensors of both the metrics are Riemann compatible as well as Weyl compatible,\\
\textbf{B. Dissimilarities:}\\
(iv) \eqref{rtm} is Deszcz pseudosymmetric whereas \eqref{gppwm} is Ricci generalized pseudosymmetric,\\
(v) the conformal curvature 2-forms are recurrent for \eqref{rtm} but not recurrent for \eqref{gppwm},\\
(vi) the metric \eqref{rtm} is Roter type and hence $Ein(2)$ but \eqref{gppwm} is not Roter type but $Ein(3)$.
\end{thm}
\begin{thm}
The Robinson-Trautman metric \eqref{rtm} and pp-wave metric \eqref{pp-bc} have the following similarities and dissimilarities: \\
\textbf{A. Similarities:}\\
(i) for both the metrics, the conformal curvature 2-forms are recurrent,\\
(ii) Ricci tensor of both the metrics are Riemann compatible as well as Weyl compatible,\\
\textbf{B. Dissimilarities:}\\
(iii) the metric \eqref{rtm} is 2-quasi-Einstein, where as \eqref{pp-bc} is Ricci simple and hence quasi-Einstein,\\
(iv) \eqref{rtm} is Deszcz pseudosymmetric whereas \eqref{pp-bc} is semisymmetric,\\
(v) \eqref{rtm} is pseudosymmetric due to conformal curvature tensor whereas \eqref{pp-bc} is semisymmetric due to conformal curvature tensor,\\
(vi) the metric \eqref{rtm} is $S\wedge S \ne 0$ but \eqref{gppwm} $Ein(3)$,\\
(vii) the metric \eqref{rtm} is Roter type and hence $Ein(2)$ but \eqref{gppwm} is not Roter type but $Ein(3)$.
\end{thm}
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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Ralphs Grocery Store is a historic building in the Westwood Village section of Westwood, Los Angeles, California. Built in 1929 as a Ralphs Grocery Store, it was one of the original six buildings in the Westwood Village development. The building was noted for its cylindrical rotunda capped by a low saucer dome, with a pediment over the entrance and arcaded wings extending north and east. It was photographed by Ansel Adams in 1940, declared a Historic-Cultural Monument in 1988, and listed on the National Register of Historic Places in 1992.
Origins of Westwood Village
The history of Westwood Village began in 1925, when the Regents of the University of California purchased a large block of land from the Janss Investment Company for the construction of the new UCLA campus. The Janss family retained ownership of the land south of the campus and there developed Westwood Village — a carefully planned commercial center that was to be "a model college town." The university and the Janss family agreed to harmonize the architecture of the campus and the village in a "Mediterranean style."
Architecture and opening of Ralphs Grocery Store
The new Westwood Village began to open in 1929, and one of its original buildings was the Ralphs Grocery Store located on Westwood Boulevard, one block north of Wilshire Boulevard. The store's most prominent feature was its low rotunda, at the corner of Westwood Boulevard and Lindbrook Drive. The building's exterior walls were built with imitation stone, but were later covered with stucco. The building's style has been described as having Mission Revival, Spanish Colonial Revival, Romanesque Revival and Renaissance Revival elements, and is said to have served as a model for other low-rise commercial structures in the village. Early advertising materials for the Westwood Village development featured images of the Ralphs tower and the Janss dome, which became area landmarks. The opening of the store in the fall of 1929 was timed to coincide with the opening of the UCLA campus, and the Los Angeles Times proclaimed the store "one of the most beautiful exclusive grocery marts in the West." The opening was celebrated with a free food show, as Ralphs boasted a new feature at their Westwood store — "the employment of uniformed boys to wrap each purchase of merchandise while it is being paid for at the cashier's stand, and then carry it to the customer's car."
In 1940, Ansel Adams took a series of photographs of Westwood Village, some featuring the Ralphs building. The photographs are part of the collections of the Los Angeles Public Library and can be viewed here, here and here.
Businesses operating in the building
Ralphs operated a grocery store on the site until the mid-1960s, when it left Westwood Village. Ralphs returned to Westwood Village nearly 40 years later, converting the old Bullock's department store into a grocery store (formerly sharing the space with a Best Buy and an Expo Home Design Center). Since Ralphs vacated the building in the mid-1960s, it has housed a number of different businesses. In 1970 a large portion of the space facing Lindbrook Drive was converted into a movie theater, which was known over the years as the United Artists Theater, (where The Rocky Horror Picture Show made its US debut on September 26, 1975) the UA Egyptian, the Odeon Cinema, and finally as the Mann Festival which closed on July 30, 2009. The Bratskeller restaurant, popular with UCLA students, also operated at the building from the late 1960s through the mid-1980s. In the late 1990s and early 2000s the prime corner space at the base of the tower was split between Daphne's Greek Cafe and Togo's Sandwich Restaurant. In late 2008, they were replaced with a Peet's Coffee & Tea, which remains currently. In early 2012, part of the shuttered movie theater was converted into 800 Degrees Neapolitan Pizzeria.
Historic preservation and designation
Since the 1970s, the demand for office and residential space around the UCLA campus has resulted in much of the original Mediterranean architecture giving way to large modern high rises, as depicted in the photograph to the right. Preservationists sought to preserve what could be saved of the original Westwood architecture, and in 1988 the Ralphs-Bratskeller-Egyptian Theater building was designated as a Historic Cultural Monument (HCM #360) by the Los Angeles Cultural Heritage Commission. Eight other historic buildings in Westwood Village (including the Fox Bruin Theater, the Fox Village Theater and the Janss Investment Company Building) were given monument status at the same time. In 1992, the Ralphs building was also added to the National Register of Historic Places.
See also
List of Registered Historic Places in Los Angeles
References
External links
Commercial buildings in Los Angeles
Retail buildings in California
Kroger
Los Angeles Historic-Cultural Monuments
Commercial buildings completed in 1929
Commercial buildings on the National Register of Historic Places in Los Angeles
Mission Revival architecture in California
Romanesque Revival architecture in California
Spanish Colonial Revival architecture in California
Spanish Revival architecture in California
Westwood, Los Angeles
Grocery store buildings
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
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Choosing iPad Pro Keyboard – iPad Pro is currently the biggest and fastest iPad. It arrives with some accessories to make it complete like iPad Pro keyboard called the smart keyboard, the Apple Pencil, and more. Today we will discuss about iPad Pro keyboard.
iPad Pro keyboard can help us ease our typing works. Yes, this is about the additional keyboard which is available to be applied for iPad Pro when we want to type just like typing on a laptop or computer. However, the keyboard is different from the appearance. This iPad keyboard has slim and lighter body that is very different with laptop and computer keyboard.
Speaking of iPad Pro Keyboard, this kind of keyboard is being supplied by Apple itself where we can find it originally through Apple stores. This is called smart keyboard. Apple makes the smart keyboard with much superiority from the material and also the system.
Yes, through this Smart Keyboard, people will get their typing works in an easy mode where we can connect our iPad to the keyboard and fold the keyboard part in being the place for our iPad to lean on. This method brings us in typing experience like typing using a touch screen laptop. More, the material of Smart Keyboard from Apple is also the high quality and we can feel the 64 seamless keys on the keyboard. To get this Smart Keyboard for iPad pro, we have to purchase it with $169 for the original one.
However, in case of getting the iPad Pro Keyboard, there are the other brands which produce the compatible keyboard for iPad Pro. We can see from Logitech which is being a technology stuffs producers. Here, Logitech is producing the keyboard for iPad Pro too. Seeing the specification, Logitech keyboard has a good quality too.
However, speaking of originality, when we need to have our iPad Pro suited with the keyboard, it is better to get the original keyboard that comes from Apple itself. But, if you wish to try the other brand keyboard, its OK. Sometimes, the other brands' keyboard has the same specification with cheaper price where people like it the most.
Good day especially admin iosmanuals.com.
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{
"redpajama_set_name": "RedPajamaC4"
}
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Limaria rotundata is een tweekleppigensoort uit de familie van de Limidae. De wetenschappelijke naam van de soort is voor het eerst geldig gepubliceerd in 1843 door Sowerby II.
Limidae
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,763
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Q: Content for second div is not being alerted using $(this) This is my full code:
<input id="storecipient">
<div class="hidbdsp">
<div class="hidname">tomato</div>
<div class="hidname">orange</div>
</div>
<script type="text/javascript">
$(document).ready(function() {
$("#storecipient").on('input', function() {
var thisFstchar = $(this).val();
var name = $(this).siblings(".hidbdsp").children(".hidname").html();
if (thisFstchar.charAt(0) == name.charAt(0)) {
alert(name);
}
});
});
</script>
What my js code does is alerts the full word that contains the first letter of the word typed on the input. So when the letter "t" is typed, the word "tomato" shows up, but when "o" is typed on the input, "orange" does not show up. Even though both "orange" and "tomato" have the same class ".hidname", the $(this) selector only will select tomato but skips over orange. Why is this?
A: As @misner3456 stated, jQuery.html() returns the HTML of the first matched element only. To get the HTML for all of the matched elements, try something like looping over all of the classes and appending each element's HTML to a string. For example:
let html;
$(".hidname").each(function() {
html += $(this).html();
});
A: Try this
$(document).ready(function() {
$("#storecipient").on('input', function() {
var thisFstchar = $(this).val();
$(this).siblings(".hidbdsp").children(".hidname").each(function() {
var name = $(this).html();
if (thisFstchar.charAt(0) == name.charAt(0)) {
alert(name);
}
});
});
});
<input id="storecipient">
<div class="hidbdsp">
<div class="hidname">tomato</div>
<div class="hidname">orange</div>
</div>
<script src="https://code.jquery.com/jquery-3.1.0.js"></script>
A: You can refactor to directly iterate $(".hidbdsp .hidname").each() rather than finding the sibling.
$(document).ready(function() {
$("#storecipient").on('keyup', function() {
var thisFstchar = $(this).val();
$(".hidbdsp .hidname").each(function() {
var name = $(this).html();
if (thisFstchar.charAt(0) == name.charAt(0)) {
alert(name);
}
});
});
});
<script src="https://code.jquery.com/jquery-3.1.0.js"></script>
<input id="storecipient">
<div class="hidbdsp">
<div class="hidname">tomato</div>
<div class="hidname">orange</div>
</div>
A: To get all children and descendant:
$('.hidbdsp *')
To get only direct children:
$('.hidbdsp > *')
.
<!DOCTYPE html>
<html>
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.4.1/jquery.min.js"></script>
</head>
<body>
<input id="storecipient">
<div class="hidbdsp">
<div class="hidname">tomato</div>
<div class="hidname">orange</div>
</div>
<script type="text/javascript">
$(document).ready(function() {
$("#storecipient").on('input', function() {
var thisFstchar = $(this).val();
$('.hidbdsp *').each(function() {
var name = $(this).html();
if (thisFstchar.charAt(0) == name.charAt(0)) {
alert(name);
}
});
});
});
</script>
</body>
</html>
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,661
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Google Tuesday unveiled a new product that will allow publishers to create tailor-made search engines for their sites.
The tool will allow publishers to put query boxes on their sites and also choose which sites Google indexes for the customized search engine. Publishers can choose to only include their own sites, or can expand the index to any sites in their industry--including sites operated by competitors.
Ultimately, however, the usefulness of the product will depend on the work that publishers put into crafting an index, search industry watchers said.
David Berkowitz, director of strategic planning for search engine marketing firm 360i, said that publishers might inadvertently create a search engine that has little to no utility for their users. "When it comes down to it, it's a great service that Google is offering, but it falls on the publishers to implement it well," he said. "It's very easy to implement this halfheartedly and create a disservice for your users."
Both having an engine that returns too many results and one that returns too few could lead the engine not to be useful, Berkowitz said. If it's too broad, then users have no reason to use the customized product instead of the general Google search, Berkowitz said. On the other hand, he said, "if it's too narrow, users might just want to go to other sites instead of using yours."
Greg Sterling, principal of Sterling Marketing Intelligence, said that with enough work, the service could yield better results than Google for users. "The richness of the experience will be directly correlated to how much work they put in," he said. "It potentially is much more relevant than general Web search. There's a lot more noise in general Web search."
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 543
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Goldmund Mimesis DAC | What's Best Audio and Video Forum. The Best High End Audio Forum on the planet!
Does anyone know which DACS Goldmund used in the mimesis 12+ dac ?
I have a Goldmund Mimesis 12+ that I use for a long time: dynamic, great sound image, transparency, softness, fluidity and total lack of aggressiveness.
We often hear that older generations of high-end converters sound more "analog" compared to newer models equipped with sophisticated chips (like ESS or others). Converters for "music lovers" rather than "audiophiles". The kind of ready-made formula that does not mean much from my point of view.
But the current mode of resistor network DACs would tend to show that technological progress in the field of conversion chips does not necessarily translate into musical gain.
In my case, the reasons why I did not find it useful to replace the Mimesis are simple: I mainly listen to a repertoire that use a lot of instruments sometimes sound a little "green" (harpsichord, baroque violin , etc.) that does not support ultra-analytical renditions, a little unbalanced and therefore tiring in the long run.
Moreover, the added value of a change of DAC seems harmless compared to a change of speakers, amp or listening room.
Interesting feedback Hal1...as a Zanden digital owner myself (which is also an older design, certainly by digital standards), i have some appreciation for how happy you are with your current digital. Enjoy.
I do wonder,Progress,but in which direction?
In 17 years, apart from an Orpheus and a dCS Elgar + I have never listened to a DAC that makes me want to change. And no recent DAC has succeeded, although I do not dispute the fact that some are of very high quality (for example a Bricasti listened to qlq months ago but in a system that I did not know at all). And as we know, the conversion chip is only one of the variables (power supply, output stages, etc.) of the equation. Not persuaded that equivalent level of implementation a recent Saber chip is musically "superior" to a PCM63K. But I admit that I have not done the test.
I hear you...i have been impressed with some of the latest digital, but not found anything i truly loved more than the Zanden, particularly have had several years to tweak it. Enjoy your Goldmund!
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,677
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\section{Overview}
\label{sec:overview}
\begin{quote}
{\em
``The coherence provided by QCD means that insights [into hadron
structure] may arise from unexpected quarters. It is more than ever
advisable to take a broad view that integrates across hadronic physics,
and to connect with the rest of subatomic physics.''
} C. Quigg, 2011 \cite{Quigg:2011sb}
\end{quote}
\noindent
The across-the-board connection I will focus on here is between the fields of high-energy particle physics and of lower energy hadronic and nuclear physics. This connection is made possible by the universality of the parton distribution functions (PDFs) of the proton, which allows one to calculate a variety of processes from a common set of quark and gluon momentum distributions. These processes range from high-energy physics interactions such as in $\bar p+p$ collisions at the Tevatron or $p+p$ collisions at the Large Hadron Collider (LHC) to lower energy electron or hadron collisions on proton as well as nuclear targets. The former are designed to study QCD and electroweak interactions at the parton level, as well as to search for the Higgs boson and for physics beyond the standard model. The latter are designed to explore how QCD builds a hadron out of 3 valence quarks, how its quantum numbers are built up from these and from the ``sea'' of quark-antiquark pairs and gluons, how its properties change in a nuclear medium, and how a nucleus as a bound state of protons and neutrons emerges from the underlying microscopic quark and gluon degrees of freedom.
One powerful set of tools that exploit the PDF universality are the so called ``global PDF fits\cite{Forte:2013wc,Jimenez-Delgado:2013sma,Rojo:2013fta}''. Their original \emph{ra\^ison d'\^etre} is to utilize experimental data from a number of processes, combined with perturbative QCD calculations of the relevant partonic cross sections, in order to extract the non perturbatively calculable parton distributions. These in turn can be used to calculate processes not included in the fits, for example the expected rates of Higgs boson production in several channels, or various standard or beyond-the-standard model cross sections, such as production of $W'$ and $Z'$ gauge bosons, Kaluza-Klein resonances, gluinos, and so on. In this sense, increasing the number of data points to be fitted by including more processes, and improving the theoretical calculations to include a larger portion of the available kinematics, is extremely useful to reduce the uncertainties in the extracted PDFs, thus yielding more accurate theoretical predictions. This is one way in which lower energy hadronic and nuclear data, which typically access lower momentum scales and larger parton momentum fractions $x$ inside a proton than at colliders, can improve the study of high-energy processes.
However, as I will argue here, this phenomenologically very important connection is not necessarily the most far reaching. Indeed, a novel aspect of large-$x$ global fits is their ability to connect elements of high-energy physics with hadronic and nuclear physics at medium energy. For example, data on $W$ and $Z$ forward rapidity boson production at the Tevatron and LHC, which can reach large values of $x$, can constrain the extrapolation to $x=1$ of the down-quark to up-quark ratio in the proton. With enough statistical precision this can indicate which nonperturbative proton structure model best captures the effects of confinement on hadron structure. Here we have collider physics providing insights on hadronic physics.
Likewise, but less obviously, global PDF fits can be used as a tool to study the structure of the nucleus and the differences between bound and free protons and neutrons, for which current models display large theoretical uncertainties. This is possible, {\it e.g.}, by exploiting the interplay of Deep Inelastic Scattering (DIS) data \emph{on deuteron targets}, which allow one to extract a nuclear-model dependent $d$ quark distribution at large $x$ \cite{Accardi:2009br,Accardi:2011fa,Owens:2012bv}, and weak interaction processes \emph{on proton targets}, such as the mentioned $W$ and $Z$ production at hadronic colliders, which also depend on the $d$ quark but are naturally free from nuclear effects. Since an unrealistic nuclear correction would pull the $d$ quark extracted from a global fit away from that required by the proton target data, constraints on the viable nuclear models can then be obtained by studying tensions in these two data sets under global fits.
Global fits can thus relate high-energy experiments at the Tevatron
\cite{Grannis-Tevatron,Denisov-Tevatron} or LHC\cite{Dissertori:2012cra} with nuclear physics experiments at lower energy facilities such as Jefferson Lab\cite{JLab10,Dudek:2012vr}. Otherwise stated, one can now use proton targets to study QCD in nuclei.
It is the goal of this review to substantiate these claims.
\section{The CTEQ-Jefferson Lab global PDF fits}
\begin{figure}
\vskip-.3cm
\parbox{0.6\linewidth}{\center
\includegraphics[width=0.95\linewidth,trim= 0 120 0 25,clip=true]
{fig.DIS_ps_lin.eps}
}
\parbox{0.35\linewidth}{
\caption{Kinematic coverage in Bjorken $x_B$ and $Q^2$ of the DIS data used in the CJ12 fits \protect\cite{Owens:2012bv}. The $W^2 \gtrsim 14$~GeV$^2$ cut typically used in global PDF fits and the $W^2>3$ GeV$^2$ cut used in the CJ12 analysis are indicated by the dashed and dot-dashed lines, respectively.
\protect\label{fig:DISdata} }
}
\vskip-.5cm
\end{figure}
\noindent
Deep-inelastic lepton-hadron scattering experiments have provided
a wealth of data over the past few decades that have yielded
considerable information on PDFs over a wide range of $x$ and $Q^2$.
However, most global fits\cite{Martin:2009iq,JimenezDelgado:2008hf,JimenezDelgado:2009tv,Lai:2010vv,Aaron:2009aa,Ball:2012cx} have focused on the extraction of
leading twist PDFs, utilizing cuts on $Q^2$ and the hadronic final
state mass $W^2 = M^2 + Q^2 (1-x)/x$, where $M$ is the nucleon mass,
of $Q^2 \gtrsim 4$~GeV$^2$ and $W^2 \gtrsim 14$~GeV$^2$. The aim
of such cuts is to eliminate regions of kinematics where effects
that do not scale with $log(Q^2)$ may be important, which unfortunately
has the effect of excluding a considerable amount of high-precision
data that have been collected at intermediate and large values of $x$, see Figure~\ref{fig:DISdata}.
On the other hand, there are many reasons why accurate information
on PDFs at high $x$ is important. For example, it is necessary to
have control over uncertainties on QCD backgrounds in searches for
new physics in collider experiments with final states at large $p_T$, large invariant mass, or large rapidity\cite{Rojo:2013fta}.
Also, the behavior of PDF ratios, such as the $d/u$ ratio, as $x \to 1$
can provide insight into the dynamics of quarks and gluons in the
nonperturbative region \cite{Holt:2010vj}. In addition, the uncertainty in the extraction of the spin-dependent gluon PDF at small $x$ in forward particle
production in polarized $pp$ collisions is limited by the uncertainties
on the quark PDFs at large $x$.
The CTEQ-Jefferson Lab (CJ) collaboration\cite{CJweb} was formed with the initial aim to include large-$x$ and ${\cal O}(1/Q^2)$ theoretical corrections into perturbative calculations, in order to maximize the use of available experimental data (in particular from fixed target DIS experiments) and produce accurate fits with a quantitative evaluation of the associated theoretical errors. Earlier efforts in this direction include the work of Alekhin {\it et al.}\cite{Alekhin:2000ch,Alekhin:2012ig} and Martin {\it et al.}\cite{Martin:2003sk}
\begin{figure}
\vskip-.3cm
\center
\includegraphics[width=0.7\linewidth,trim= 0 230 0 0,clip=true]
{fig.stdW_err.eps}
\caption{Ratio of relative errors of the CJ12mid fit with $W^2>3$ GeV$^2$ and a a similar fit using $W^2>12.5$ GeV$^2$.
\label{fig:improvedstat}
}
\end{figure}
The CJ global PDF fits utilize the world's data on charged lepton
DIS on proton and deuteron targets, lepton pair production with a
proton beam on proton and deuteron targets, $W$ asymmetries and $Z$ rapidity distribution as well as jet production data in $\overline p p$ collisions.
The theoretical treatment of inclusive DIS includes subleading ${\cal O}(1/Q^2)$ effects, such as target mass correction and (a fit of) higher twist terms, and nuclear corrections for the deuterium target data.
The resulting fits\cite{Accardi:2009br,Accardi:2011fa,Owens:2012bv} can thus incorporate data down to $W \approx 1.7$~GeV, and have culminated in the release of the ``CJ12'' PDF sets\cite{CJweb,CJ-LHAPDF}, valid in the
range $10^{-5} \lesssim x \lesssim 0.9$.
The fits were performed at next-to-leading order in the zero
mass variable flavor number scheme, with $\alpha_s(M_Z)$ fixed to the
world average value.
(Full heavy quark treatments, fits of the strong coupling constant,
and inclusion of the available LHC data will be considered in a
subsequent analysis.)
The CJ PDFs have been shown\cite{Accardi:2009br} to be stable with the weaker cuts on $W$ and $Q^2$, and the increased DIS data sample (of about 1000 additional points) has led to significantly reduced uncertainties of up to 80\% on the $d$ quark PDF at large $x$, where precise data are otherwise scarce (see figure \ref{fig:improvedstat}). Since $d$ quark flavor separation at large $x$ is currently almost entirely dependent on DIS on deuterium targets, corrections for nuclear Fermi motion and binding effects are included by convoluting the nucleon structure functions with a smearing function computed from the deuteron wave function \cite{Accardi:2011fa,Kulagin:2004ie}. As the $u$ quark is well constrained by data on proton targets, the $d$ quark becomes directly sensitive to the nuclear corrections. The effect is a large suppression at high $x$, and a mild but non-negligible increase at intermediate $x$, still inside the ``safe'' region defined by the larger $W$ cut discussed above\cite{Accardi:2009br}. These findings have subsequently been confirmed by Ball {\it et al.}\cite{Ball:2013gsa}.
\begin{figure}
\center
\includegraphics[width=0.47\linewidth,trim= 0 0 0 0,clip=true]
{relerrNODd.eps}
\hspace{.5cm}
\includegraphics[width=0.462\linewidth,trim= 0 0 0 0,clip=true]
{relerrCJdu.eps}
\caption{
{\it Left:} PDF uncertainties for the CJ12mid $d$ quark
compared with the total uncertainty including nuclear
corrections and with a fit excluding all deuterium
data relative to the CJ12mid set.
{\it Right:} $d/u$ ratio for the CJ12min, CJ12mid and CJ12max PDFs
\protect\cite{Owens:2012bv}. Note that these ratios are to
a good approximation independent of the $Q^2$ scale.
\label{fig:CJ12d}
}
\end{figure}
The uncertainties on the CJ12 $d$ quark PDF from theoretical modeling of
nuclear corrections (which I refer to as ``nuclear uncertainties'')
have been quantified\cite{Accardi:2011fa,Owens:2012bv}.
In particular, the size of the nuclear corrections range from mild, corresponding to the hardest of the deuteron
wave functions (WJC-1) coupled to a 0.3\% nucleon off-shell
correction, to strong, corresponding to the softest wave function
(CD-Bonn) and a large, 2.1\% nucleon off-shell correction; the
central value corresponds to the AV18 deuteron wave function with
a 1.2\% off-shell correction\cite{Owens:2012bv}. The resulting PDFs
are labeled ``CJ12min'', ``CJ12max'', and ``CJ12mid'', respectively.
The uncertainties on the CJ12 $d$ quark distribution are illustrated
in the left panel of Figure~\ref{fig:CJ12d}, with the central (red) band indicating the PDF error calculated with the Hessian method and a tolerance
factor $T=10$. The central (blue) band represents the theoretical
nuclear uncertainty, obtained as an envelope of the CJ12min and
CJ12max fits, and is of the same order of magnitude as the PDF error.
Finally, the outer (green) band is the PDF error in a fit that excludes
all deuterium data, and exceeds the combined PDF and nuclear uncertainties.
This demonstrates the usefulness of the deuterium data, even in
the presence of the nuclear uncertainties that its use introduces.
A further source of theoretical uncertainty was investigated by utilizing a more flexible parametrization for the valence $d_v$ quark at large-$x$, which now includes a small admixture of the valence $u_v$ PDF,
\begin{align}
d_v(x) \rightarrow d'_v(x) =
a_0^{d} \Big[ d_v(x) / a_0^{d} + b\, x^c u_v(x) \Big],
\label{eq:newd}
\end{align}
where $a_0^{d}$ is the $d$ quark normalization, and $b$ and $c$ are
two additional parameters\cite{Accardi:2011fa,Owens:2012bv}. The result is that the $d/u$ ratio at $x \to 1$ can now span the range $[0,\infty)$ rather than being limited to either 0 or $\infty$ as in all previous PDF fits.
A finite, nonzero value of this ratio is in fact expected from several nonperturbative models of nucleon structure\cite{Jimenez-Delgado:2013sma,Holt:2010vj}.
It is also required from a purely practical point of view because it avoids potentially large biases on the fitted $d$ quark PDF, as illustrated in the left and middle panels of Figure~\ref{fig:d2uparams} and discussed in more detail in Section~\ref{sec:theorybiases}.
\begin{figure}
\center
\vskip-.3cm
\parbox{0.9\linewidth}{
\includegraphics[width=\linewidth,bb=18 330 592 718,clip=true]
{plot.du_sequence.eps}
}
\caption{The CJ11 $d/u$ ratio at $Q^2=10$ GeV$^2$ obtained with different
$d$ quark parametrization and nuclear corrections:
({\it left}) standard $d$ quark \protect\cite{Accardi:2009br}
and AV18 deuteron wave function for several off-shell
corrections models;
({\it middle}) modified $d$ quark parametrization;
({\it right}) dependence on the wave function
for a fixed off-shell correction (mKP).
The shaded bands and bottom panels show the $\Delta\chi=1$
(tolerance $T=1$) absolute and relative PDF errors, respectively.
For details, see the original paper \protect\cite{Accardi:2011fa}.}
\label{fig:d2uparams}
\vskip-.1cm
\end{figure}
\section{Applications}
Let us now discuss in turn a hadronic physics and a collider physics application of the fitted CJ12 PDFs, and explore the consequences of the nuclear uncertainties in either case.
The ratios of the $d$ to $u$ PDFs for the three CJ12 sets are shown in Figure~\ref{fig:CJ12d} right. These are constrained up to $x\approx 0.8$ by the enlarged data set considered in the CJ fits, but can be confidently extrapolated to $x=1$ thanks to the modified $d$ quark parametrization \eqref{eq:newd}.
As the magnitude of the nuclear corrections increases, the $d/u$ intercept at $x=1$ rises\cite{Owens:2012bv}. Including the PDF errors, it was found that
\begin{align}
d/u \,\xrightarrow[\,x\rightarrow 1\,]{} \, 0.22
\pm 0.20 \, \text{({\small PDF})}
\pm 0.10 \,\text{(nucl)},
\label{eq:dulimit}
\end{align}
where the central value is obtained as an average of the CJ12max and CJ12min PDFs, the first error is from the PDF fits, and the second error reflecting
the theoretical nuclear uncertainty is obtained by considering the difference between the CJ12min and CJ12max PDFs. These values encompass the full 0-0.5 range of available theoretical predictions\cite{Feynman:1973xc,Close:1973xw,Farrar:1975yb,Melnitchouk:1995fc,Wilson:2011aa}.
However, it is also clear that a relatively modest
improvement in statistical precision and reduction of nuclear
uncertainty would allow one to restrict the range of allowable
physical mechanisms\cite{Roberts:2013mja}.
The large nuclear uncertainty in the quark PDF (and that in the
gluon PDF arising from jet-data induced anticorrelation with the $d$ quark\cite{Accardi:2011fa}), have also potentially profound implications for collider experiments. To illustrate this in general terms, consider the differential parton luminosities for production of an object of mass $\sqrt{\hat s}$ at rapidity $y$ in a hadronic collision of center of mass energy $\sqrt s$,
\begin{align}
dL_{ij} / dy
= \big[ f_i\left( x_1, \hat{s} \right)
f_j\left( x_2, \hat{s} \right)
+ (i \leftrightarrow j)
\big] / \big[ s (1+\delta_{ij}) \big] ,
\end{align}
where $x_{1,2} = \tau e^{\pm y}$ with $\tau = \sqrt{\hat s / s}$.
The differential luminosities, normalized to the reference fit calculation, are shown in Figure~\ref{fig:lum_y} as a function of
$\tau$ for three values of rapidity. (Since the ratios are largely
independent of the hard scattering scale, these plots are also independent of $s$).
The sensitivity to large $x$ PDFs, hence to nuclear uncertainties, grows the larger the mass of the produced object and the larger its rapidity at a given mass. For example, the nuclear uncertainty becomes relevant for $W$ production at rapidity larger than 2 at the Tevatron, and larger than 3.5 at the LHC\cite{Brady:2011hb}, as we shall see in more detail.
For particles of heavier mass, such as the putative $W'$ and $Z'$ bosons, the nuclear uncertainty at large $x$ may become large also in the inclusive production cross section\cite{Brady:2011hb}, as illustrated in Figure~\ref{fig:WZprime_incl}.
As the current LHC limits put the $W'$ and $Z'$ masses approximately above 2.5 TeV for Standard-Model like couplings\cite{Dissertori:2012cra}, one can appreciate how nuclear uncertainties and other large-$x$ theoretical uncertainties may significantly affect the interpretation of signals of new particles and an accurate measurement of their properties.
\begin{figure}[t]
\center
\includegraphics[width=0.95\linewidth,bb=18 485 565 700,clip=true]
{plot.partlumi_y.eps}
\vskip-.3cm
\caption{CJ11 differential parton luminosities for
$gg$, $gd$ and $d\bar u$ parton collisions
at fixed rapidity $y=1,2$ and 3, as a function of
$\tau = \sqrt{\hat s / s}$, illustrating the variations
due to the choice of nuclear corrections
\protect\cite{Accardi:2011fa}.}
\label{fig:lum_y}
\end{figure}
\begin{figure}[t]
\parbox{0.6\linewidth}{
\rotatebox{-90}{\includegraphics[height=0.94\linewidth,clip=true]{fig.WZprime_inclusive.eps}}
}
\parbox{0.39\linewidth}{
\caption{Ratio of $W'$ boson
$\sigma_{W'} = \sigma_{W'^+} + \sigma_{W'^-}$ cross section,
versus the $Z'$ boson cross section $\sigma_{Z'}$ for varying
$Z'$ boson masses (in TeV next to
the points). The cross sections are computed for $\sqrt s = 7$ GeV
from CJ11 PDFs \protect\cite{Accardi:2011fa} with minimum
(filled red circle) and maximum (open blue circle) nuclear
corrections, relative to the reference cross section calculated
from the central CJ11
PDFs\protect\cite{Brady:2011hb}.\newline\newline }
\label{fig:WZprime_incl}
}
\vskip-0.5cm
\end{figure}
\section{Theoretical biases at $x \rightarrow 1$}
\label{sec:theorybiases}
The importance of using a more flexible $d$-quark parametrization than
in traditional fits cannot be overemphasized. Figures~\ref{fig:CJ12-udg}
and \ref{fig:d-biases} show a comparison of the CJ12mid fits to a fit
obtained with the standard $W>3.5$~GeV cut, and a fit obtained with
$W>1.7$~GeV but standard $d$-quark parametrization (namely, $b=c=0$
in Eq.~\eqref{eq:newd}).
\begin{figure}
\center
\vskip-.45cm
\includegraphics[width=0.89\linewidth,trim=20 250 20 0,clip=true]
{fig.du-pdfs.eps}
\vskip-.3cm
\caption{Comparison of PDFs obtained with a conventional $W>3.5$~GeV
cut, and using the old $d_v$ quark parametrization with $W>1.7$~GeV
to the CJ12mid set. A tolerance $T=1$ is used for clarity.}
\label{fig:CJ12-udg}
\end{figure}
In Figure~\ref{fig:CJ12-udg}, the ratios of the $u$, $d$ and gluon
PDFs in the two new fits to the CJ12mid fit are presented with a
tolerance $T=1$ (for clarity). The fit using the standard
parametrization starts deviating from the CJ12mid fit at
$x \gtrsim 0.5$. This behavior is clearly not data driven
(it starts already inside the covered kinematic range), but is
forced by the use of the functional form $d \propto (1-x)^{a_d}$
rather than the more flexible parametrization \eqref{eq:newd}.
The dramatic decrease of the standard $d$ quark PDF towards 0 can
be compensated in the fit by a slightly increased $u$ quark and gluon distributions, due to the correlation induced by the large-$x$ DIS data and jet data, respectively.
Further insight can be obtained by considering the $d/u$ ratio in
Figure~\ref{fig:d-biases}. In this case the standard parametrization
forces $d/u$ to take either the value of 0 or $\infty$.
In contrast, the extended $d'$ parametrization allows for limiting
values in the entire range between 0 and $\infty$. In the CJ12 fit,
the data does not seem to warrant the behavior of the standard
parametrization, which lies at the edge of the PDF error band
of the CJ12mid fit. Not only does the standard $d$
parametrization underestimate the central fitted value at
$x \gtrsim 0.5$, it also underestimates the PDF uncertainty,
as well as the nuclear uncertainty. As a consequence one could risk, {\it e.g.}, to interpret as signal of new physics what instead is an artificially small calculated cross section, as it has already happened in the past in analogous situations\cite{Huston:1995tw,Kuhlmann:1997wd}.
Other potential biases exist at large $x$, related to theoretical
corrections not yet included included in the perturbative QCD
calculations utilized in the CJ12 analysis. These include large-$x$
resummation\cite{Anderle:2012rq,Courtoy:2013qca}, jet mass corrections\cite{Accardi:2008ne}, and higher-order terms in the perturbative expansion\cite{Blumlein:2008kz}. However, these typically scale as $1/Q^2$ (or resemble such a power correction at low $Q^2$) and will mainly affect the extraction of the HT term, leaving the
leading-twist PDFs largely unchanged, as was found, {\em e.g.}, for the model
dependence of target mass corrections\cite{Accardi:2009br}.
This makes the choice of parametrization possibly the largest remaining
theoretical bias in the determination of the $d$-quark PDF at
large $x$. A full theoretical unbiasing should be pursued by
generalizing the $d'$ quark functional form adopted in the CJ12
fits and investigating the related quantitative extraction of
$d$-quark PDF errors at $x \to 1$.
\begin{figure}[t]
\center
\vskip-.2cm
\includegraphics[width=0.43\linewidth,trim=0 120 120 0,clip=true]
{fig.du-old.eps}
\hspace{.5cm}
\includegraphics[width=0.43\linewidth,trim=0 120 120 0,clip=true]
{fig.du-old-nucl.eps}
\vskip-.2cm
\caption{
PDF errors with tolerance $T=10$ and nuclear uncertainties
for the fits in Fig.~2.
}
\label{fig:d-biases}
\end{figure}
\section{Constraining the nuclear corrections}
Given the current size of nuclear uncertainties and their impact on phenomenology across low-energy hadron physics and high-energy particle physics, it is imperative to reduce this source of theoretical uncertainty.
On the theory side the main difficulty resides in the interplay of the hard interaction at the nucleon level, described in terms of partonic degrees of freedom and calculable directly from the QCD Lagrangian, and the comparatively soft nucleon-nucleon interactions described in terms of hadronic degrees of freedom with effective interactions fitted to nucleon elastic scattering data. Oftentimes the soft nuclear and hard nucleonic interactions are assumed to factorize, even though this is not formally guaranteed the way QCD factorization theorems allow to separate the hard partonic interactions from nonperturbative PDFs\cite{Jaffe:1985ci}.
Moreover, the medium modifications of the nucleons are almost unknown experimentally, especially in the nucleon momentum range relevant for inclusive DIS. Therefore, theoretical models of nuclear corrections seem at present irreducibly unconstrained, and comparison to non-inclusive DIS experimental data is mandatory for further theoretical progress.
If, however, one's purpose was solely to obtain a precise enough but nuclear uncertainty free extraction of the $d$ quark, one would need new experimental data to compensate for the loss in statistics deriving from excluding the deuteron data shown in Figure~\ref{fig:CJ12d} left. This new data can come from 2 sources. The first is data on nuclear targets, but with observables designed to minimize the impact of nuclear corrections, for example, DIS on deuteron targets with detection of a slow spectator proton, which guarantees that the electron scatters on a quasi-free neutron, or inclusive DIS on 3-Helium and Tritium, where the nuclear effects largely cancel in the ratio of the respective cross sections (future BONUS 12 and MARATHON experiments at Jefferson Lab, respectively\cite{MARATHON,BONUS12}). The second source is weak interactions in proton target collisions.
These contribute, through photon-$Z$ boson interference, to electron and positron DIS cross sections at large $Q^2$ only (for which, unfortunately, the combined run-I HERA data\cite{Aaron:2009aa} have insufficient large $x$ coverage), but are of leading order in parity violating charge asymmetries (recent limited large-$x$ coverage $F_{2,3}^{\gamma Z}$ measurements at HERA\cite{Aaron:2012qi,Abramowicz:2012bx}, and future SOLID\cite{SOLID} and PVDIS\cite{PVDIS} experiments at Jefferson Lab). In principle, weak charged currents can also be directly measured in neutrino and anti-neutrino scattering on proton targets, for which however the old WA21/25 data\cite{Jones:1987gk,Jones:1994pw} cannot be easily used in global fits, and no new data is planned for the foreseeable future.
This leaves one with $W$ and $Z$ boson production in $p+\bar p$ collisions at Tevatron and $p+p$ collisions at RHIC and the LHC, which I shall focus on next.
\begin{figure}[t]
\center
\rotatebox{-90}{\includegraphics[height=0.5\linewidth]{fig.Wasy_LHC.eps}}
\hspace*{-0.5cm}
\rotatebox{-90}{\includegraphics[height=0.5\linewidth]{fig.Wasy_Tevatron.eps}}
\vskip-.3cm
\caption{$W$ boson asymmetry $A_W$ as a function of the $W$ rapidity
$y_W$ at LHC and Tevatron,
computed from CJ11 PDFs with minimum (upper blue solid)
and maximum (lower blue solid) nuclear
corrections~\protect\cite{Brady:2011hb}.
The asymmetries using the ABKM, CT10 and MSTW
PDF sets are also shown.}
\label{fig:W_asym}
\end{figure}
As discussed at the end of Section~\ref{sec:overview}, global QCD fits allow for the intriguing possibility to combine deuteron and proton target data to obtain experimental constraints on the nuclear models, and at the same time fully utilize the available statistics of the nuclear target data. This is very well demonstrated by considering the directly reconstructed $W$ asymmetry at Tevatron. As shown in Figure~\ref{fig:W_asym}, this process is very sensitive to nuclear corrections at $y\gtrsim 2$, and the comparison\cite{Brady:2011hb} with the very precise CDF data\cite{Aaltonen:2009ta}, as well as the total $\chi^2$ values in the CJ12 fits, suggests that nuclear effects are somewhere between the minimum and central ones considered in the CJ12min and CJ12mid fits, respectively. This was also confirmed in a similar analysis by Martin {\it et al.}\cite{Martin:2012da}, where however the nuclear correction was assumed to be $Q^2$ independent and directly fitted to data rather than calculated in a model. On the phenomenological side, this result disfavors nonperturbative proton models based on the SU(6) spin-flavor symmetry, which predict $d/u \rightarrow 1/2$ as $x\rightarrow 1$. More importantly, it exemplifies the power of global fits in combining data from across the board, and is the first step in establishing the experimental foundation that was until now missing for a qualitative jump in our ability to theoretically understand and describe high-energy processes in nuclei -- and this with proton targets! Interestingly, this procedure is not limited to deuteron targets, but can in principle be adapted to provide a new line of experimental constraints of nuclear effects in heavier nuclei, thus shedding new light on the EMC effect that for more than 30 years has eluded a satisfying theoretical explanation\cite{Higinbotham:2013hta,Norton:2003cb,Frankfurt:2012qs}.
The $W$ charge asymmetry at CDF unfortunately seems the only observable that currently has this potential. The asymmetry in lepton production from $W$ decays has insufficient large $x$ coverage due to decay vertex smearing, while $Z$ rapidity distributions from CDF and D\O\ have insufficient precision\cite{Owens:2012bv}. At the LHC one would need measurements with better than 10\% precision at $y\gtrsim 3.5$, namely, at the edge of the LHCb acceptance for $\sqrt{s}=7$ TeV, and the experimental accuracy of the $W$ asymmetry is inherently reduced due to the difference between $p+p$ scattering compared to $p+\bar p$ \cite{Brady:2011hb,Lohwasser:2010sp}. Nonetheless, inclusion of the available LHC data in the CJ fits is underway to quantify its impact on nuclear uncertainty constraints.
The potential of large rapidity $W$ and $Z$ measurements in proton-proton collisions at the RHIC\cite{Bourrely:1993dd,Melnitchouk:1996fh,Surrow-DIS2013,Bourrely:2013qfa} should also be explored.
In particular\cite{W_at_RHIC_private}, the STAR detector can in principle provide directly reconstructed $W$ asymmetries at pseudorapidity $-1\leq \eta \leq 1$ using the central detector, accessing the $d$ quarks at $0.05<x<0.5$, and possibly up to $\eta \approx 2$ using the end cap, which will access the $x>0.5$ region we have been focusing on in this review. Although this is a challenging measurement\cite{Lohwasser:2010sp}, it would provide one with an important validation of the CDF measurement\cite{Aaltonen:2009ta}, as well as a test of its energy dependence.
Of further interest would be measurements of $W$, $Z$ and dilepton production in proton-deuteron collisions at large rapidity in the deuteron direction\cite{Kamano:2012yx,Ehlers_etal}: these would access large-$x$ quarks in the deuteron and test theoretical nuclear corrections in a complementary way to electron-deuteron DIS measurements.
Looking at the future, one could also envisage utilizing the sensitivity of large-$x$ gluons to nuclear corrections (induced by their correlation with $d$-quark in jet data) to further constrain nuclear models analogously to what I am proposing here for the $d$ quark. This would require a further observable sensitive to large-$x$ gluons in protons, {\it e.g.}, data on top quark production from Tevatron and LHC, which is directly sensitive to large-$x$ gluons\cite{Czakon:2013tha}, and furthermore free from the subleading in $1/Q^2$ corrections that limit the sensitivity of longitudinal $F_L$ structure function or cross section measurements in fixed target DIS experiments.
The planned Electron-Ion Collider\cite{Boer:2011fh,Accardi:2012hwp} and Large Hadron-electron Collider\cite{AbelleiraFernandez:2012ty} projects will be able to perform a complete set of structure function measurements for gluon and quark flavor separation at large $x$ (and large $Q^2$).
Finally, new experiments focused on large rapidity particle production, such as the proposed AFTER@LHC experiment\cite{Brodsky:2012vg}, would provide invaluable data to not only obtain precise large-$x$ PDFs, but also and more in general to investigate QCD in the nuclear medium.
\section{Conclusion}
The recent CTEQ-Jefferson Lab collaboration investigations, culminating in the public CJ12 PDF release\cite{Owens:2012bv,CJweb,CJ-LHAPDF}, have demonstrated the intimate interconnection of hadronic and high-energy physics, exemplifying one of the across-the-board connections called for in the opening quote by C.~Quigg for further progress in these fields. Namely, global QCD fits have become capable of constraining theoretical models of nuclear corrections in the deuteron (as well as in heavier nuclei). Not only will this reduce the nuclear uncertainty on the fitted PDFs with important phenomenological consequences on physics ranging from nonperturbative proton structure to beyond the standard model interactions, it will also provide a new avenue for progress in the theoretical understanding of high-energy processes involving \emph{nuclei}, using weak interactions on \emph{proton} targets from Jefferson Lab to the LHC.
\vskip.6cm\noindent
{\bf Acknowledgments:}
I am very grateful to my CJ colleagues for the enjoyable and productive collaboration. While the opinions expressed in this paper are the author's responsibility only, interesting discussions with E.Aschenauer, S.Forte, J.Rojo, E.Sichtermann, and R.Thorne are gratefully acknowledged.
This work was supported by the DOE contract No.~DE-AC05-06OR23177,
under which Jefferson Science Associates, LLC operates Jefferson Lab, and by the DOE contract No. DE-SC008791.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 958
|
Q: Word to describe an informal, mutually beneficial interaction between two or more people Context
Consider a language exchange group. In other words, people are teaching and learning foreign languages from each other. There are no monetary transactions.
I'm looking for a word that's friendly in tone to summarize this mutually beneficial concept. It should be more informal and "marketing" friendly than exchange. The best I've come up with is "mutual help," but it sounds a bit redundant to me.
Sample sentence
A community based on mutual help.
Other options
Reciprocity - too transactional
Mutual benefit - similar to mutual help and a bit sterile
A: The word symbiosis nicely captures the idea of cooperating for mutual benefit.
a cooperative relationship (as between two persons or groups)
You could use it in a sentence like this:
The members of a language exchange group are in symbiosis, teaching each other, and learning from each other at the same time.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,047
|
Learn to the Read the Bible Effectively – an online course which will help you understand the Bible better.
The Evidence, You Decide – a site which challenges you to look at the Bible.
Lifes Big Questions – tries to show the answers contained in the Bible for many of life's big questions.
This is your Bible – a site run by Christadelphians Worldwide with information on finding your nearest ecclesia.
TheChristadelphians.org.uk – General Christadelphian Site including more details of what we believe.
The Bible Toolshed – A growing site covering many aspects of Bible knowledge.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 1,658
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\section{Introduction}
Measuring the extent to which cultural communities overlap via the knowledge they preserve can paint a picture of how culturally proximate or diverse they are. Wikipedia, the largest crowd-sourced encyclopedia today, is a platform that documents knowledge from different cultural communities via different language editions. The collective traces left by editors of Wikipedia can be utilized to identify cultural communities that are most similar with regard to the knowledge they document. Certainly, co-editing similarities among language communities of Wikipedia editors are just a particular dimension of culture and are not representative of cultural similarities among the communities in general. Yet, Wikipedia plays a critical role in today's information gathering and diffusion processes and Wikipedians constitute an important cultural subset of educated and technology-savvy elites who often drive the cultural, political, and economic processes \cite{Ronen}. In this paper, we tap into the traces left by editors of Wikipedia to gain new insights into how language communities on Wikipedia relate to each other via common co-editing interests.
\textbf{Problem.}
We are thus interested in seeking answers to the following overarching research question: What are common editing interests between language communities on Wikipedia, and how can they be explained? In addition, we also aim to establish a computational method which would allow measuring culture-related similarities based on the topics the editors document in Wikipedia.
We assume that collective interest of a language-speaking community is reflected through the aggregation of articles documented in the corresponding language edition of Wikipedia. These articles are an approximation of the topics which are culturally relevant to that language community, though by no means are representative of the entire underlying cultural community. We define \textit{cultural similarity} as a significant interest of communities in editing articles about the same topics; in other words, language communities are similar when they significantly agree regarding the topics they choose to edit.
\textbf{Methods.}
Our approach consists of several steps. We first use statistical filtering to identify language pairs which show consistent interest in articles on the same topics. Based on this dyadic information, we create a network of interest similarity where nodes are languages and links are weighted as the strength of shared interest. We cluster the network and inspect it visually to inform the generation of hypotheses about the mechanisms that contribute to cultural similarity. Finally, we express these hypotheses as transition probability matrices, and test their plausibility using two statistical inference techniques -- HypTrails~\cite{hyptrails} and MRQAP \cite{krackardt1987qap} (Multiple Regression Quadratic Assignment Procedure). Using both Bayesian and frequentist approaches, we obtain similar results, which suggests that our findings are robust against the chosen statistical measure.
\textbf{Contribution and findings.}
Our main contribution is empirical. We expand the literature on culture-related research by (a)~presenting a large-scale network of interest similarities between 110 language communities, (b)~showing that the set of languages covering a concept of Wikipedia is not a random choice, and (c)~by statistically demonstrating that similarity in concept sets between Wikipedia editions is influenced by multiple factors, including bilinguality, proximity of these languages, shared religion, and population attraction. We also combine multiple techniques from network theory, Bayesian and frequentist statistics in a novel way, and present a generalisable approach to quantify and explain culture-related similarity based on editing activity of Wikipedia editors.
We find that the topics that each language edition documents are not selected randomly, however small the underlying community of editors. We test several hypotheses about the underlying processes that might explain the observed nonrandomness, and find that bilingualism, linguistic similarity of languages, and shared religion provide the best explanations for the similarity of interests between cultural communities. Population attraction and geographical proximity are also significant, but much weaker factors bringing communities together.
The remainder of the paper is structured as follows. In Related Literature (Section \ref{literature}) we will give a brief overview of work on how cultural differences find reflection in multilingual online platforms, as well as on how Wikipedia has been used to compare cultural and linguistic points of view, and cultural biases involved in knowledge production. In the Data, Section \ref{data} we will describe in detail the process of data sampling and collection. Sections \ref{4} and \ref{5} will focus on identifying and explaining co-editing interests, give a technical overview of the quantitative methods, and report the results. We will offer our reflection upon the findings in the Discussion (Section \ref{discussion}), and Conclusions and Implications (Section \ref{conclusions}).
\section{Related literature} \label{literature}
Definition of culture and its borders is a long-debated and still unresolved issue in Anthropology and Social Sciences; a 1951 review of the works on the issue already contained close to 300 definitions of culture \cite{Kroeber}. Cultural communities have fuzzy boundaries: several distinct cultures might co-exist in one state, or alternatively, reach beyond and across continents. This is especially true for multilingual countries or those with colonial past. While there are many non-verbal expressions of material culture, language is an important bearer of culture -- its meanings have to be learnt socially and represent the way of life as seen by a particular community \cite{Bloomfield, Hoijer, Silvia, Voegelin}. Language-speaking communities form distinct and unique cultures around themselves \cite{Bucholtz, Geertz-1973}, and overlap of interests between these communities might signify cultural proximity between them. Language is central to culture for several reasons: it reflects the collective agreement of a language community to view the world in a certain way, and helps a community to perpetuate its culture, develop its identity, and archive accumulated knowledge \cite{Kramsch}. It is the latter feature of collective knowledge selection and archiving that this paper focuses on.
\textbf{Wikipedia as a lens for studying cultural repertoires of language communities. }
The online encyclopedia Wikipedia is a prominent example of collective knowledge accumulation, and it is becoming one of the most interesting and convenient sources for academics to study cultural and historical processes \cite{Schich-15}. Wikipedia is one of the most linguistically diverse projects online, with a constant base of editors contributing in almost 300 languages \cite{WP:list}, ranging from almost 5 million in the largest edition (English) to just 89 in Cree, the smallest one \cite{WP:list}. This makes it accessible to more than 5 billion people, or 75\% of the world's population \cite{Petzold}. There is no central authority that dictates which topics must be covered, and every editor is free to select their own, as long as they are consistent with the notability guidelines \cite{WP:notability}. All language editions have their own notability guidelines and are edited independently from each other, although an editor can also co-edit several editions in parallel. Large language editions like English are not supersets of smaller ones, and each edition contains unique concepts which are not covered by others. For example, concept overlap between the two largest editions, English and German, is only 51\% \cite{Hecht:2010content}. Opposite to the common misconception, even when articles on the same concept exist in different language editions, they are not translated replicas of each other, but instead reveal consistent cultural biases \cite{Hecht:2009bias, Callahan-2011} and introduce various linguistic viewpoints \cite{Bao-2012, Massa-2012, Massa-2011}.
These differences in number, selection, and content of articles across languages are not accidental, but relate to the cultural differences between the underlying language communities. Contributing to Wikipedia means more than writing encyclopedic content: it allows communities to store cultural memories of events \cite{Keegan-2011, Keegan-newswork-2013, Pentzold-12}, document their point of view \cite{Massa-2012, Massa-2011}, and give prominence to people \cite{Samoilenko-2014}. This collective sifting of culturally-relevant knowledge is such an important social process that conflicts and edit wars frequently emerge before reaching consensus \cite{Yasseri-book}. Finally, the language communities not yet represented on Wikipedia seek the inclusion as an opportunity to establish and promote their language and culture in the digital realm \cite{Kornai-2013}. There are currently 160 open requests for new Wikipedia language editions in the Wikimedia Incubator \cite{WP-incubator}. Wikipedia is rich in cultural material, and all data are recorded and openly available, which makes the encyclopedia an attractive object for research on culturally-mediated behaviour.
\textbf{Quantifying cultural similarity. }
Multiple numerical measures have been proposed to assess the degree of cultural similarity, although many of them suffer from practical scalability issues or focus on a narrow aspect of culture. The most often cited measure is known as Hofstede's dimensions of culture, which delineates cultures by national borders \cite{Hofstede-1980}. Evidence of national cultural differences has been found in the style of collaborative authoring of Wikipedia articles \cite{Pfeil-2006, Hara-2010}. West \cite{West-2004} quantifies cultural distance through linguistic distance between languages. Several studies delineated cultures by language, and focused on Wikipedia data. In particular, Laufer and colleagues~\cite{Laufer-2014} developed measures of cultural similarity, understanding, and affinity through comparing how food cultures are described by self- and foreign communities. Eom et al.~\cite{Eom-2015} applied ranking algorithms to biographical articles and obtained a network of cultural agreement on what historical figures are viewed as important, which includes 24 language points of view. Finally, the value of Wikipedia for such anthropological questions as assessing cultural chauvinism or differences in historical world view between cultures has been discussed in \cite{Gloor}. Cultural differences have also been found in other modalities of online communication and collaboration, on such multilingual platforms as Facebook \cite{Barnett-FB}, Twitter \cite{Eleta-4, Garcia-6, Mocanu-11}, and YouTube \cite{Platt-14}.
Although previous research has advanced scientific understanding of cultural similarity, attempts to quantify it, for practical reasons, were mostly limited to comparing a small number of cultures along a selected topical dimension. The literature shows a need to establish a scalable approach to quantifying cultural similarity which allows comparing multiple permutations of language dyads and obtaining a bird's-eye view on global intercultural relationships.
\section{Data} \label{data}
There are almost 300 language editions of the encyclopedia, which vary greatly in size. This makes sampling a nontrivial decision: on the one hand, many editions are rather small, and sampling from them would not provide data sufficient for statistical analysis. On the other hand, downloading full data on every language edition over a long period of time would be computationally expensive. As a compromise, we focused the analysis on a sample of 126 largest editions which contained more than 10,000 article pages, as of July 2014 ~\cite{WP:list}.
\textbf{Sampling procedure. }
To account for variations in editions' age, number of active contributors, and growth rates, we selected the time frame such that (1) to ensure a sufficient amount of editions existed in the beginning of the observation; (2) to allow enough time for each edition to accumulate concepts. We traced back each edition to its first registered article page, and found out that 110 out of 126 largest editions had been created before 01.01.2005. We excluded 11 editions which appeared later (min, vo, be, new, pms, pnb, bpy, arz, mzn, sah, vec) and those whose language codes could not be mapped to the ISO 639-1 standard (be-x-old, zh-yue,bat-smg, map-bms, zh-min-nan). These remaining 110 editions became the focus of our subsequent analysis which covers the period of 9 years between 01.01.2005 and 31.12.2013.
We sampled from each edition separately, collecting IDs of all article pages created between 2005 and 2013 (excluding other types of pages, redirects, and pages created by bots). For each ID we also collected the entire editing history in all linked language editions. Thus, each ID corresponds to a concept (the topic of the article regardless of the language), and all interlinked language editions represent various linguistic points of view on the concept. After removing duplicates, our dataset includes 3,066,736 unique concepts and a total of 1,360,647,795 article pages in different languages. The data were collected between 20.12.2015 and 25.01.2016 from Wikimedia servers directly, using the access provided by Wikimedia Tool Labs~\cite{toolserver}.
One algorithmic limitation of our approach is the fact that we rely on Wikipedia's interlanguage link graph to identify articles on the same concepts in different language editions. This approach has some known issues with the lack of triadic closure and dyadic reciprocity \cite{Bao-2012}. To ensure that the maximal set of interlanguage links related to a concept is retrieved, we collect all articles with their interlanguage links from each edition separately, removing duplicates afterwards. Thus, all existing interlanguage links are extracted.
\section{Extraction of co-editing patterns} \label{4}
In this section, we describe the procedure of extracting cultural similarities from co-editing activity in Wikipedia, and present the network of significant shared interests between 110 language communities. The section begins with summarising our pre-analysis check of whether the language-concept overlap in Wikipedia is random.
\subsection{Testing for non-randomness of co-editing patterns}
Theoretically, each concept covered in Wikipedia could exist in all 288 language editions of the encyclopedia. This is possible because Wikipedia does not censor topic inclusion depending on the language of edition, and anyone is free to contribute an article on any topic of significance. However in practice, such complete coverage is very rare, and concepts are covered in a limited set of language editions. Is this set of languages random? To answer this question, we analyse matrices of language co-occurrences based on a 6.5\% random sample of the data (200,748 concepts).
We construct the matrix of empirical co-occurrences $C_{ij}$, based on the probability of languages ${i,j}$ to have an article on the same concept.
We also construct a synthetic dataset where we preserve the distribution of languages and the number of concepts, $N = 200{,}748$, but allow languages to co-occur at random. We use the resulting data to produce the matrix of random co-occurrences $C^{\mathrm{rand}}_{ij}$, and compare it to the matrix of co-occurrences $C_{ij}$. Our null model corresponds to belief that in Wikipedia each concept has equal chances to be covered by any language, with larger editions sharing concepts more frequently purely because of their size. Comparing the two matrices (Figure~\ref{fig:SI} in the Appendix) allows us to get a preliminary intuition of the extent to which co-editing patterns are non-random.
We establish that language dyads do not edit articles about the same concept (co-occur) by chance. Large editions share concepts more frequently than expected: although in the data \emph{EN-DE} and \emph{EN-FR} overlap in 45\% of cases, only 15\% is expected by the null model. To little surprise, the amount of overlap between editions in the data decreases with the size of the editions. One notable exception is the Japanese edition which, despite being among the ten largest Wikipedias, co-occurs with other top editions noticeably less frequently. Similarly, the Uzbek edition, being among the ten smallest in the dataset, shows high concept overlap with large editions. By simply plotting frequencies of co-occurrences, we do not observe any local blocks or clusters, neither among large nor small editions (see Fig.~A1).
These overlap differences are statistically significant, and the null model explains only 1,386 out of 11,990 language pairs (11\% of observed data, 95\% confidence level). Such low explained variation suggests that concept overlap is not random and cannot be explained only by edition sizes. Instead, there are non-random, possibly cultural processes, that influence which languages cover which concepts on Wikipedia. Having evidence that the data contain a signal, we continue our investigation by performing network analysis.
\subsection{Inferring the network of shared interest}
We look for the languages that are consistently interested in editing articles on the same topics by comparing the differences between observed and expected co-editing activity on each concept. We give a $z$-score to every language pair, and compare it to the threshold of significance to filter out insignificant pairs. This logic is demonstrated in Fig.~\ref{fig1}. The result is a weighted undirected network of languages, where languages are connected based on shared information interest.
\begin{figure}
\centering
\includegraphics[width=0.97\textwidth]{img/fig1}
\caption{\csentence{Illustration of the $z$-score-based filtering method.} The method requires three steps: (a)~to retrieve all edits to each concept in all linked language editions; (b)~to compare the empirical and expected probabilities of each language pair to co-edit a concept; and (c)~to create a filtered network of languages with significant shared interests. In the final network, `heavier' links signify stronger co-editing similarity between the nodes.}
\label{fig1}
\end{figure}
We first compute the empirical weight $w_{ij}^{c}$ of a link between languages $i$, $j$ which co-edit a concept $c$:
\begin{equation}
w_{ij}^{c} = k_{i}^{c} k_{j}^{c}.
\label{eq:empirical_weight}
\end{equation}
Here, $k_{i}^{c}$ is the number of edits to the concept $c$ in the language edition $i$, which we use as a proxy to the amount of editing work invested in the concept. This is done across all concepts and language permutations. To determine which links are statistically significant, and which exist purely by chance or due to size effects, we construct a null model where we assume that links between languages $i$ and $j$ are random.
Let the total editing probability of a language be $p_{i} = \frac 1 M \sum_{c}k_{i}^c$, where $M$ is the total number of edits for all concepts and language editions. Then the expected probability $\mathrm{E}[w_{ij}^{c}]$ that languages $i$ and $j$ co-edit the same concept $c$ is:\begin{equation}
\mathrm E[w_{ij}^{c}] = n_{c} (n_{c} - 1) p_{i} p_{j},
\label{eq:expected_weight}
\end{equation}
where $n_{c}$ is the total number of edits to a concept from all language editions. To compare the difference between observed and expected link weights, we compute a $z$-score $z_{ij}^{c}$ for each concept and pair of languages ${i,j}$, defined as
\begin{equation}
z_{ij}^{c} = \frac{w_{ij}^{c} - \mathrm E[w_{ij}^{c}]}{\sigma_{ij}^{c}},
\label{eq:z_scores}
\end{equation}
where $\sigma_{ij}^{c}$ is the standard deviation of the expected link weight \cite{Karimi}.
Finally, to find the cumulative $z$-score for a pair of languages ${i,j}$, we sum their $z$-scores over all concepts\begin{equation}
z_{ij} = \sum_{c}z_{ij}^{c}.
\label{eq:final_z}
\end{equation}
The relationship between $i$ and $j$ is significant if the cumulative probability of their total $z$-score, $z_{ij}$ in the right tail falls beyond the $p$-value $p = 1 - 0.05 / N$, where $N$ is the total number of languages. We use the Bonferroni correction \cite{dunn1961multiple} to account for the multiple comparisons and size effects in the data. This corresponds to a $z$-score of 3.32. Since $z$-scores are sums across many independent variables, their distribution can be approximated by the normal distribution, and the threshold for link significance in the right tail is $t = 3.32 \sqrt{L}$, where $L = 3{,}066{,}736$ is the number of concepts. We create a link between a pair of languages ${i,j}$ if the observed $z$-score, $z_{ij}$, is above the threshold $t$~\cite{Karimi}.
We use the resulting $z$-scores to build a network of shared topical interests, where the edges are weighted by the similarity of interest, quantifies via $z$-scores. In summary, this approach allows for discovering significant language pairs of shared interest, accounting for editions of different sizes, and avoiding over-representing the large editions \cite{Karimi}.
Other methods exist to extract significant weights in graphs. For example, \cite{Tumminello} used the hypergeometric distribution for finding the expected link weights for bipartite networks and measured the global $p$-value. Serrano et al.~\cite{Serrano} used a disparity filtering method to infer significant weights in networks. Similar to our work, \cite{Dianati} proposed pair-wise connection probability by the configuration model and used the $p$-value to measure statistical significance of the links.
The network consists of 110 nodes (language editions) and 11,986 undirected edges, and is a complete graph. This means that most languages show at least some similarity in the concepts they edit, however the strength of similarity differs highly across language pairs. The distribution of edge weights is highly skewed with the lowest $z$-score between Korean and Buginese and the highest $z-$-score between Javanese and Indonesian.
\subsection{Clustering the network of significant shared interests}
We use the Infomap algorithm~\cite{rosvall} to identify language communities that are most similar in their interests. We release a random walker on the network, and allow it to travel across links proportional to their weights. By measuring how long the random walker spends in each part of the network, we are able to identify clusters of languages with strong internal connections \cite{rosvall}. Additionally, we compare these results with the Louvain clustering algorithm~\cite{louvain} and establish that both methods show high agreement.
Our cluster analysis suggests that no language community is completely separated from other communities, and in fact, there are significant topics of common interest between almost any two language pairs. We reveal 21 clusters of two and more languages, plus 9 languages that are identified as separate clusters (see SI for full information on the clusters). Notably, English forms a self-cluster, and this independent standing means little interest similarity between English and other languages. This is an interesting finding in the light of the recent discussions on whether English is becoming a global language and the most suitable \textit{lingua franca} for cross-national communication \cite{crystal:global}.
\begin{figure*}
\centering
\includegraphics[width=0.97\textwidth]{img/network}
\caption{\csentence{The network of significant Wikipedia co-editing ties between language pairs.} Nodes are coloured according to the clusters found by the Infomap algorithm \cite{Edler-2013}, and link weights within clusters represents the positive deviation of $z$-scores from the threshold of randomness; links are significant at the 99\% level. For visualisation purposes we display only 23 clusters and the strongest inter-cluster links in the network. The inter-cluster links show the aggregated z-scores between all nodes of a pair of clusters. The network suggests that local factors such as shared language, linguistic similarity of languages, shared religion, and geographical proximity play a role in interest similarity of language communities. Notably, English forms a separate cluster, which suggest little interest similarity between English speakers and other communities.
\label{fig:network}
}
\end{figure*}
The resulting network is visualised in Fig.~\ref{fig:network}. The links within clusters are weighted according to the amount of positive deviation of $z$-score per language pair from the threshold of randomness. Stronger weights indicate higher similarity. The links are significant at the 99\% level. The inter-cluster links should be interpreted with care in the context of this study, as they are weighted according to the aggregated strength of connection between all nodes of both clusters. The network is undirected since it depicts mutual topical interest of both language communities, which is inherently bidirectional. For visualisation purposes, we display only the strongest inter-cluster links and 23 language clusters. Cluster membership information is detailed in Table~\ref{SI_table} (in the Appendix).
\textbf{Cluster interpretation. }
Visual inspection of language clusters suggests a number of hypotheses which might explain such network configuration. For example, (1) geographical proximity might explain the Swedish-Norwegian-Danish-Faroese-Finnish-Icelandic cluster (light blue), since those are the languages mostly spoken in Scandinavian countries. Other groups of languages form around (2) a local \textit{lingua franca}, which is often an official language of a multilingual country, and include other regional languages which are spoken as second- and even third language within the local community. This way, Indonesian and Malay form a cluster with Javanese and Sundanese (brown), which are the two largest regional languages of Indonesia. Similarly, one of the largest clusters in the network (purple) consists of 11 languages native to India, where cases of multilingualism are especially common, since one might need to use different languages for contacts with the state government, with the local community, and at home \cite{crystal:global}. Another interesting example is the cluster of languages primarily spoken in the Middle Eastern countries (yellow), which apart from geographical proximity are closely intertwined due to (3) a shared religious tradition. Finally, some clusters illustrate (4) the recent changes in sociopolitical situation, which can also be partially traced through bilingualism. Following the civil war of the 1990s in former Yugoslavia, its former official Serbo-Croatian language is now replaced by three separate languages: Serbian, Croatian, and Bosnian (green cluster). Notably, there is still a separate Serbo-Croatian Wikipedia edition. To give another example, Russian held a privileged position in the former Soviet Union, being the language of the ideology and a priority language to learn at school \cite{crystal:global}. Even twenty years after the dissolution of the Soviet Union, Russian remains an important language of exchange between the post-Soviet countries. Similarity of interests between speakers of Russian and the languages spoken in nearby countries, as seen in the magenta cluster, comes as little surprise.
We use this anecdotal interpretation of the clusters to inform our hypotheses about the mechanisms that affect the formation of co-editing similarities. In the next section we will build on these initial interpretations and formulate them as quantifiable hypotheses. To evaluate the validity of the hypotheses, we will compare their plausibility against one another using statistical inference approach.
\section{Explanation of co-editing patterns} \label{5}
In this section we show how the network of significant shared interests could be used to inform hypothesis formulation. We compare the plausibility of hypotheses using two statistical approaches. First, we use Bayesian approach and visually compare the strengths of hypotheses. Then we apply frequentist approach to report the explanatory power of different models. We begin by outlining the necessary methodology and continue with reporting the results.
\subsection{Hypothesis formulation}
We convert our initial interpretation of the network clusters into quantifiable hypotheses, which we express through transition probability matrices illustrated in Fig.~\ref{fig2}. The hypotheses aim to explain the link weights in the network of co-editing similarities, which correspond to the obtained $z$-scores. The transition probability matrices are square with dimensions $N = 110$, corresponding to the number of language editions studied. The diagonal is empty, since self-loops are not allowed. The formulas, the definitions, and data sources for hypotheses formulation are summarised for reference in Table \ref{hypotheses_table}. Below we give more extended explanations on the process of hypotheses construction.
\begin{itemize}
\item{\textbf{H0: Uniform}}
All language co-occurrences are possible with the same probability. A concept can be randomly covered by any language edition. The transition probability $t_{ij}$ for all permutations of languages $i$ and $j$ is \begin{equation*}t_{ij} = 1.\end{equation*}
\item{\textbf{H1: Shared language family}}
We retrieve the whole family tree profile of each language and count the number of branches overlapping between each language dyad. For example,
\begin{itemize}
\item{Arabic: Afro-Asiatic; Semitic; Central Semitic; Arabic languages; Arabic}
\item{Hebrew: Afro-Asiatic; Semitic; Central Semitic; Northwest Semitic; Canaanite; Hebrew}
\end{itemize}
Arabic and Hebrew share three levels of language tree hierarchy (Afro-Asiatic; Semitic; Central Semitic) and thus will have the transition score of 3 in the hypothesis table.
If $f_i$ is the set of branches describing the full language family profile of language $i$, the transition probability $t_{ij}$ corresponds to the count of shared branches in the family tree of languages $i$ and $j$, and is computed as \begin{equation*}t_{ij} = |f_i \cup f_j|.\end{equation*}
\item{\textbf{H2: Bilingual population within a country}}
To formalise other hypotheses, we needed to map languages to countries where they are spoken. We list all countries where a pair of languages are co-spoken; for each country we compute the probability of a person to speak both languages. The hypothesis table contains the average probability of a person to speak both languages computed across all countries where both languages are spoken by more than 0.1\% of the population. The transition probability is described by \begin{equation*} t_{ij} = \frac{1}{N_{ij}} \sum_A p(i)_A p(j)_A,\end{equation*} where $p(i)_A$, $p(j)_A$ are proportions of speakers of languages $i$, $j$ in a country $A$, $N_{ij}$ is the number of countries where $i$,$j$ are co-spoken. The more bilinguals speaking $i$ and $j$ live in the same country, the higher the transition belief.
\item{\textbf{H3: Geographical proximity of language speakers}}
We assign each country with its primary language (the language that the majority of its population speaks) and compute the average distance between all permutations of countries where language $i$ or $j$ are spoken. All inter-country distances are scaled between 0 and 1. Thus, \begin{equation*} t_{ij} = \frac{1}{N_{ij}} \sum_{A,B}\frac{ d_{\mathrm{min}} }{ d_{AB}},\end{equation*} where $N_{ij}$ is the number of country permutations where $i$ or $j$ are spoken as primary language, $d_{AB}$ is Euclidean distance between each pair of countries, and $d_{\mathrm{min}}$ is the smallest distance between countries in the dataset. The smaller the distance between speakers of $i$ and $j$ living in separate countries, the higher the chances for languages $i,j$ to cover the same concept.
\item{\textbf{H4: Gravity law -- demographic force attracting language communities}}
Like in the previous example, we allow one (primary) language per country and consider all country permutations where languages $i$ or $j$ are spoken. Demographic attraction is strongest between large population of speakers who live in separate counties which are located closely. Consider the example of France and Germany, where large numbers of French and German speakers correspondingly, live at close distance. We compute average demographic attraction between all permutations of country pairs. We define \begin{equation*} t_{ij} = \frac{1}{N_{ij}} \sum_{A,B} \frac{m_{A,i} m_{B,j}}{d_{AB}^2},\end{equation*} where $m_{A,i}$, number of speakers of the primary language $i$ in a country $A$, $d_{AB}$ is Euclidean distance between each pair of counties (in kilometers), $N_{ij}$ is the number of country pairs where $i$ or $j$ are spoken as primary language. The larger the language-speaking population and the smaller the distance between the countries $A,B$, the more the attraction between $i$ and $j$.
\item{\textbf{H5: Shared primary religion}}
For each country we identified its primary language and its most widespread religion (Christian, Muslim, Hindu, Buddhist, Folk, other or unaffiliated). The religion we assign to a language is the most common religion in the list of countries where the language is spoken as primary. For a language pair, if they share the religion, we add 1 to the hypothesis matrix, and 0 otherwise. Thus the linguistic communities which profess the same religion will show consistent interest in the same topics.
\end{itemize}
\begin{table}
\centering
\caption{
Formalisation of hypotheses to explain the probability of language dyads to co-edit a Wikipedia article about the same concept.
The hypotheses aim to explain the values of link weights ($z$-scores) in the network of co-editing similarity (see Fig.\ref{fig:network} for illustrative purposes). The transition probability matrices are square with dimensions $N$ = 110, corresponding to the number of language editions studied. The diagonal is empty, since self-loops are not allowed. The value $t_{ij}$ expresses the hypothesised probability of Wikipedia language editions $i$ and $j$ to cover the same concept. After construction of the hypotheses matrices, the matrices undergo Laplacian smoothing of weight 1 (for HypTrails hypotheses testing only), and are further normalised row-wise. The precess is illustrated in Fig.\ref{fig2}. The results of hypothesis testing are represented in Fig.\ref{fig:hyptrails} for the HypTrails approach, and in Fig.\ref{table:mrqap} for the MRQAP approach, and are discussed in sections \ref{Hyptrails} and \ref{mrqap} correspondingly.
}
\label{hypotheses_table}
\makebox[\textwidth]{
\scalebox{0.93}{
\begin{tabular}{m{4cm}|m{3.3cm}|m{3.3cm}|m{3.3cm}}
\toprule
\textbf{Hypothesis and Formalisation} & \textbf{Notation} & \textbf{Description} & \textbf{Data Source} \\
\midrule
H0: Uniform hypothesis \begin{equation*} t_{ij} = 1 \end{equation*} & -- &
All co-occurrences are equally probable, i.e. every edition $i$ covers the same concept as edition $j$ with a constant probability. & --
\\
\midrule
H1: Shared language family
\begin{equation*}t_{ij} = |f_i \cup f_j|\end{equation*}
& $f_i$ is the set of branches describing the full language family profile of language $i$, $t_{ij}$ is the count of shared
branches in the family tree of $i$ and $j$.
& Language communities of linguistically related languages will show more co-editing similarity.
& The data on language family classification was taken from English Wikipedia infoboxes of articles on each of 110 languages, such as `Hebrew language'.
\\
\midrule
H2: Bilingual population within a country \begin{equation*} t_{ij} = \frac{1}{N_{ij}} \sum_A p(i)_A p(j)_A\end{equation*} &
$p(i)_A$, $p(j)_A$ are proportions of speakers of $i$, $j$ in a country $A$, $N_{ij}$ is the number of countries where $i$,$j$ are co-spoken. &
Multilingual editors belong to multiple cultural communities and might serve as bridges between them. The more bilinguals speaking $i$ and $j$ live in the same country, the higher the transition belief.
& Territory--language information was downloaded from \cite{data:lang}, and is based on the data from the World Bank, Ethnologue, FactBook, and other sources, including per-country census data.
\\
\midrule
H3: Geographical proximity of languages \begin{equation*} t_{ij} = \frac{1}{N_{ij}} \sum_{A,B}\frac{ d_{\mathrm{min}} }{ d_{AB}}\end{equation*} &
$N_{ij}$ is the number of country permutations where $i$ or $j$ are spoken as primary language, $d_{AB}$ is Euclidean distance between each pair of countries, and $d_{\mathrm{min}}$ is the smallest distance between countries in the dataset. &
The smaller the distance between speakers of $i$ and $j$ living in separate countries, the higher the chances for languages $i,j$ to cover the same concept. We consider one (primary) language per country.
& Distance between countries is computed as Euclidean distance in kilometers between country capitals \cite{CIA_factbook}.
\\
\midrule
H4: Gravity law -- demographic force attracting language communities
\begin{equation*} t_{ij} = \frac{1}{N_{ij}} \sum_{A,B} \frac{m_{A,i} m_{B,j}}{d_{AB}^2}
\end{equation*}
&
$m_{A,i}$, number of speakers of the primary language $i$ in a country $A$, $d_{AB}$ is Euclidean distance between each pair of counties, $N_{ij}$ is the number of country pairs where $i$ or $j$ are spoken as primary language. &
The larger the language-speaking population and the smaller the distance between the countries $A,B$, the more the attraction between $i$ and $j$. Based on the countries' primary languages.
& Country population data is taken from CIA Factbook \cite{CIA_factbook}.
\\
\midrule
H5: Shared religion \begin{equation*} t_{ij}= \begin{cases} 1, & \text{if } r_{i}=r_{j}\\ 0 & \text{otherwise}\end{cases}\end{equation*}&
$r_i$ is the dominating religion of a language community. It is defined as the most common religion in the list of countries whose primary language is $i$. &
Cultures which profess the same religion will show consistent interest in the same topics.
& The data on world religions was taken from the most recent 2010 Report on Religious Diversity provided by the Pew Research Center \cite{data:religion}.
\\
\bottomrule
\end{tabular}
}}
\end{table}
\begin{figure}
\centering
\includegraphics[width=0.97\textwidth]{img/fig3}
\caption{\csentence{A toy example of expressing a hypothesis through a transition probability matrix.} The matrices are symmetrical. The diagonal is empty since the data do not allow self-loops. According to each hypothesis, the cells with more likely transitions are coloured in darker shades of blue. In (a) Uniform hypothesis -- all transitions are equally possible, i.e. the editions are covering random topics. In (b) Shared religion hypothesis -- the dyads Russian-Ukrainian and Polish-Estonian are given more belief on the basis of shared religion. Finally, in (c) Geographical proximity hypothesis -- the shorter the distance between languages, the stronger belief in the transition.
}
\label{fig2}
\end{figure}
\subsection{Bayesian inference -- HypTrails} \label{Hyptrails}
In order to explain why certain languages form communities of shared interest, we need to explain the link weights, or $z$-score values. We formulate multiple hypotheses based on real-world statistical data, and compare their plausibility using HypTrails \cite{hyptrails}, a Bayesian approach based on Markov chain processes. We input the $z$-scores into a matrix, and express hypotheses about their values via Dirichlet priors -- matrices of transition probabilities between each possible state (in our case -- language edition). We use the trial roulette method to compare different hypothesis. This approach allows to visualise how plausibility of the hypotheses changes with the increasing belief and decreasing allowed variation. Although it was initially designed to compare hypotheses about human trails, in this paper we show that HypTrails is also useful in explaining link weights in networks.
\textbf{Data preparation. }
Using the formalisations detailed in Table \ref{hypotheses_table}, we fill out corresponding transition probabilities matrices. We apply Laplacian smoothing of weight 1 to all matrices to avoid sparsity issues and to account for the cases when editions co-edit a topic of a general encyclopedic importance which might be relevant for multiple language communities. All matrices are normalised row-wise; diagonals are zero as no self-loops are allowed.
\textbf{Hyptrails ranking. }
The Hyptrails algorithm does not output the absolute values for plausibility of hypotheses, but only compares them one to another. Thus, one must always compare the hypotheses to a uniform hypothesis, and discard those hypotheses that are ranked below the uniform. For the upper bound of comparison, we use the $z$-scores data itself, since no hypothesis can explain the data better than the data itself.
The results suggest that multiple factors play role in how shared interests are shaped, including geographical proximity, population attraction, shared religion, and especially strongly, linguistic relatedness of the languages and the number of bilingual speakers. No hypothesis explains perfectly all variations in the data, however and all Bayes Factors for all pairs of hypotheses are decisive. Geographical proximity only explains the data to a limited extent, and decays for higher values of $k$, while the number of bilinguals in the same country, shared language family, and shared religion hypotheses grow stronger with more belief, which suggests that they explain the data most robustly. The explanatory power of hypotheses should be compared for the same values of $k$, which expresses how strongly we believe in the hypotheses and how much variation is allowed. Fig.~\ref{fig:hyptrails} summarises the results of the HypTrails algorithm. All hypotheses are compared against the uniform hypotheses of random co-occurrence.
\begin{figure}
\centering
\includegraphics[width=0.70\textwidth]{img/hyptrails}
\caption{
\csentence{HypTrails-computed Bayesian evidence for hypotheses plausibility on shared editing interest Wikipedia data.}
Higher values of the Bayesian evidence denote that a hypothesis fits the data well. The bottom black line represents the hypothesis of random shared interests and the top grey line is the fit of data on itself -- together forming an upper and lower limit for fitting hypothesis. The ranking of hypotheses should be compared for the same $k$. All hypotheses are significant, but the most plausible ones to explain cultural proximity are the shared language family, the bilingual, the shared religion, and the gravity law hypotheses. The results show that cultural factors such as language and religion play a larger role in explaining Wikipedia co-editing than geographical factors. }
\label{fig:hyptrails}
\end{figure}
\subsection{Frequentist approach -- MRQAP} \label{mrqap}
In addition to the HypTrails analysis, we use Multiple Regression Quadratic Assignment Procedure (MRQAP) \cite{hubert1976} to assess statistical significance of association between the concept co-editing network ties and various hypothesis. This method has a long established tradition in social network analysis as a way to sift out spuriously observed correlations~\cite{dekker2003}, and is well-suited for analysing dyadic data where observations are autocorrelated if they are in the same row or column \cite{krackardt1987qap}. We treat the network of concept co-editing as a dependent variable matrix; the independent variable contains the set of hypotheses about the configuration of the network, expressed via hypotheses matrices. Formulation of hypotheses is given in Table~\ref{hypotheses_table}. We normalise the matrices row-wise in order to standardise the values across matrices. MRQAP is a nonparametric test -- it permutes the dependent variables to account for dyadic inter-dependencies. It is also robust against various underlying data distributions \cite{dekker2007sensitivity}. We used 1,000 permutations, which usually suffices for the procedure \cite{jackson1989}.
\textbf{MRQAP ranking. }
The results of the test are in agreement with the hypothesis ranking obtained from applying HypTrails. The number of bilinguals, shared language family, shared religion and demographic attraction are the factors significantly contributing to cultural similarity, as suggested by the $t$-statistic. By including all five hypotheses into Model 1, we are able to explain 15\% of variation in the data. Geographical distance, although a significant factor in several models, is not a very strong one: after excluding the distance hypothesis (Model 2), precision does not decrease. Excluding other hypotheses one by one (Models 3, 4, 5 and 6) lowers precision considerably. Finally, shared language family and bilinguals alone (Models 21 and 22) explain 5\% and 7\% variation in shared interests correspondingly. The results of the MRQAP are reported in Table \ref{table:mrqap}. Different models include variations of hypotheses combinations that explain the variation in language co-editing ties.
\begin{table}
\centering
\caption{MRQAP decomposition of pairwise correspondence between concept co-occurrence and cultural factors. The combination of all hypotheses explains most of the variation in the data (15\%). The most plausible explanations are the number of bilinguals and shared religion. The results of MRQAP agree with the ranking of hypotheses by the HypTrails algorithm. All statistics except those labelled with $^*$ are significant at the 0.05 level.
\label{table:mrqap}
}
\makebox[\textwidth]{
\scalebox{0.90}{
\begin{tabular}{ l l | rrrrr | rrrr }
\toprule
\multicolumn{2}{c|}{\textbf{Model}} &
\textbf{Bilinguals} &
\textbf{Lang. family} &
\textbf{Religion} &
\textbf{Gravity} &
\textbf{Distance}\textsuperscript{1} &
\textbf{$R^2$ adj.} & \textbf{F-stat.} & \textbf{dF} & \textbf{Intercept} \\
\midrule
\midrule
1 & Estimate & $0.0688$ & $0.1074$ & $0.0900$ & $0.0470$ & $-0.0042^*$ & $\mathbf{0.1458}$ & $410.3$ & $11984$ & $0.0066$ \\
& $t$-statistic & $\mathbf{27.6524}$ & $\mathbf{23.6158}$ & $\mathbf{13.4772}$ & $\mathbf{10.2732}$ & $\mathbf{-1.3422^*}$ & \\
\midrule
\midrule
2 & Estimate & $0.0676$ & $0.1075$ & $0.0894$ & $0.0464$ & --$^{\phantom *}$ & $0.1458$ & $512.4$ & $11985$ & $0.0067$ \\
& $t$-statistic & $29.1517$ & $23.6428$ & $13.4200$ & $10.1893$ & --$^{\phantom *}$ & \\
\midrule
3 & Estimate & $0.0703$ & $0.1129$ & $0.1022$ & -- & $-0.0009^*$ & $0.1384$ & $482.3$ & $11985$ & $0.0067$ \\
& $t$-statistic & $28.1932$ & $24.8853$ & $15.4831$ & -- & $-0.2989^*$ & \\
\midrule
4 & Estimate & $0.0685$ & $0.1080$ & -- & $0.0581$ & $-0.0016^*$ & $0.1329$ & $460.5$ & $11985$ & $0.0074$ \\
& $t$-statistic & $27.3119$ & $23.5817$ & -- & $12.7773$ & $-0.5225^*$ & \\
\midrule
5 & Estimate & $0.0716$ & -- & $0.0916$ & $0.0598$ & $-0.0055^*$ & $0.1061$ & $356.9$ & $11985$ & $0.0075$ \\
& $t$-statistic & $28.1697$ & -- & $13.4180$ & $12.8396$ & $-1.7256^*$ & \\
\midrule
6 & Estimate & -- & $0.1134$ & $0.0881$ & $0.0546$ & $0.0272^{\phantom *}$ & $0.09140$ & $302.5$ & $11985$ & $0.0070$ \\
& $t$-statistic & -- & $24.2095$ & $12.7958$ & $11.5815$ & $9.0453^{\phantom *}$ & \\
\midrule
7 & Estimate & $0.0700$ & $0.1129$ & $0.1020$ & -- & --$^{\phantom *}$ & $0.1386$ & $643.1$ & $11986$ & $0.0067$ \\
& $t$-statistic & $30.2487$ & $24.8885$ & $15.5098$ & -- & --$^{\phantom *}$ & \\
\midrule
8 & Estimate & $0.0703$ & $0.1151$ & -- & -- & $0.0030^*$ & $0.1212$ & $552.2$ & $11986$ & $0.0076$ \\
& $t$-statistic & $27.9237$ & $25.1460$ & -- & -- & $0.9388^*$ & \\
\midrule
9 & Estimate & -- & -- & $0.0898$ & $0.0684$ & $0.0272^{\phantom *}$ & $0.0470$ & $198.2$ & $11986$ & $0.0079$ \\
& $t$-statistic & -- & -- & $12.7323$ & $14.2619$ & $8.8191^{\phantom *}$ & \\
\midrule
10 & Estimate & $0.0700$ & -- & $0.0909$ & $0.0590$ & --$^{\phantom *}$ & $0.1060$ & $474.8$ & $11986$ & $0.0075$ \\
& $t$-statistic & $29.5521$ & -- & $13.3370$ & $12.7297$ & --$^{\phantom *}$ & \\
\midrule
11 & Estimate & -- & $0.1140$ & -- & $0.0654$ & $0.0296^{\phantom *}$ & $0.0790$ & $344.0$ & $11986$ & $0.0077$ \\
& $t$-statistic & -- & $24.1755$ & -- & $13.9808$ & $9.7791^{\phantom *}$ & \\
\midrule
12 & Estimate & $0.0712$ & $0.1151$ & -- & -- & --$^{\phantom *}$ & $0.1212$ & $827.8$ & $11987$ & $0.0076$ \\
& $t$-statistic & $30.4703$ & $25.1430$ & -- & -- & --$^{\phantom *}$ & \\
\midrule
13 & Estimate & $0.0738$ & -- & -- & -- & $0.0027^{\phantom *}$ & $0.0749$ & $486.5$ & $11987$ & $0.0085$ \\
& $t$-statistic & $28.6184$ & -- & -- & -- & $0.8295^{\phantom *}$ & \\
\midrule
14 & Estimate & -- & -- & -- & $0.0794$ & $0.0296^{\phantom *}$ & $0.0342$ & $213.4$ & $11987$ & $0.0086$ \\
& $t$-statistic & -- & -- & -- & $16.7162$ & $9.5508^{\phantom *}$ & \\
\midrule
15 & Estimate & $0.0733$ & -- & $0.1072$ & -- & --$^{\phantom *}$ & $0.0940$ & $622.8$ & $11987$ & $0.0076$ \\
& $t$-statistic & $30.9368$ & -- & $15.9020$ & -- & --$^{\phantom *}$ & \\
\midrule
16 & Estimate & -- & $0.1222$ & -- & -- & $0.0357^{\phantom *}$ & $0.0641$ & $411.6$ & $11987$ & $0.0080$ \\
& $t$-statistic & -- & $25.9063$ & -- & -- & $11.8512^{\phantom *}$ & \\
\midrule
17 & Estimate & -- & -- & $0.0936$ & $0.0741$ & --$^{\phantom *}$ & $0.0409$ & $256.8$ & $11987$ & $0.0080$ \\
& $t$-statistic & -- & -- & $13.2534$ & $15.5280$ & --$^{\phantom *}$ & \\
\midrule
18 & Estimate & -- & -- & -- & -- & $0.0372^{\phantom *}$ & $0.0118$ & $144.1$ & $11988$ & $0.0090$ \\
& $t$-statistic & -- & -- & -- & -- & $12.0025^{\phantom *}$ & \\
\midrule
19 & Estimate & -- & -- & -- & $0.0861$ & --$^{\phantom *}$ & $0.0269$ & $333.1$ & $11988$ & $0.0087$ \\
& $t$-statistic & -- & -- & -- & $18.2514$ & --$^{\phantom *}$ & \\
\midrule
20 & Estimate & -- & -- & $0.1144$ & -- & --$^{\phantom *}$ & $0.0217$ & $267.1$ & $11988$ & $0.0081$ \\
& $t$-statistic & -- & -- & $16.3447$ & -- & --$^{\phantom *}$ & \\
\midrule
21 & Estimate & -- & $0.1233$ & -- & -- & --$^{\phantom *}$ & $0.0532$ & $674.9$ & $11988$ & $0.0081$ \\
& $t$-statistic & -- & $25.9798$ & -- & -- & --$^{\phantom *}$ & \\
\midrule
22 & Estimate & $0.0746$ & -- & -- & -- & --$^{\phantom *}$ & $0.0749$ & $972.2$ & $11988$ & $0.0085$ \\
& $t$-statistic & $31.1808$ & -- & -- & -- & --$^{\phantom *}$ & \\
\bottomrule
~\\
\multicolumn{10}{l}{\textsuperscript{1} primary language}
\end{tabular}
}}
\end{table}
\section{Discussion} \label{discussion}
In this paper, we have used edit co-occurrences data to investigate cultural similarities between language communities on Wikipedia. We have applied a statistical filtering approach to quantify co-editing similarities and build a network of mutual interests. We have utilised the logic of Bayesian and frequentist hypothesis testing to examine what societal features can explain the observed language clusters. Both approaches render similar results, suggesting that cultural proximity and similarity of interests are best explained by bilingualism, linguistic relatedness of languages, shared religion, and demographic attraction of communities. Geographical distance is a weak, and not very significant factor.
\textbf{Limitations. }
Our study is not free of limitations, some of which are inherent to the nature of the chosen data. Although we found in the literature mounting evidence that Wikipedia is a promising and rich data source for those interested in mining cultural relations, we agree that it is only one of many possible media where culture might find reflection. Moreover, Wikipedia itself is not free from structural biases, as it reflects the activity of selected technology-savvy, mostly white and male \cite{Hill-7, Antin-1}, educated, and economically stable social elites. It by no means is representative of the views of general population. However, it is the elites that often drive the cultural, political, and economic processes \cite{Ronen}, and thus Wikipedia editors represent a group worthy of being studied. Furthermore, we point out that even though we focus on 110 largest language editions, we still compare the editions at different growth stages and levels of topical saturation. Although this might introduce unforeseen biases, we do not see it as a major limitation, since we focus on aggregated editing activity and only on the articles created between 2005 and 2013. We leave for future research the interesting task of incorporating the time dimension in the analysis and examining how interests shape and change over time.
Additionally, while our approach is quantitative, it requires some subjectivity in interpreting the clusters and formulating hypotheses. To strengthen the internal validity of the study, we inform our reasoning about the hypotheses both in visual analysis of the clusters and in previous literature on the subject. Still, we do not claim to have exhausted all possible hypotheses which could explain the data. Moreover, other formalisations of the selected hypotheses might render different results.
One of the benefits of our approach is that it is free of biases related to topic selection, since we avoid focusing on specific kinds of topics where cultural similarities might be expected. It also scales well in terms of the number of communities and hypotheses that could be analysed. In case of research on multilingual data, an important benefit of our approach is that it only uses metadata on user interactions, and understanding the language itself is not required. Finally, it is applicable for any example of collaborative production of a common good where individual activity of participants is recorded.
\textbf{Discussion of results.} Culture is a very complex concept without a definition that is unanimously accepted by Anthropologists, Social Scientists, or Linguists. Although it is universally agreed that cultural communities exist, their borders are very fuzzy and depend on how the researcher defines the term 'culture'. In this work, we focus on the relation between language and culture, and particularly, on how online linguistic expressions can help distil cultural similarities between multilingual communities of Wikipedia editors. An inseparable part of culture, language is only one way of cultural expression, and more studies are needed to explore how other aspects of culture manifest themselves in off- and online world.
Our analysis shows that the decision to write or not to write an article on a certain topic is not a random one. Similar to the idea of national cultural repertoires in the traditional Cultural Sociology \cite{Lamont-10}, we find that various linguistic communities apply different grammars of worth and criteria of evaluation when selecting the topics to cover, that would appeal to the common interest of the language community. Thus, each language edition represents a community of shared understanding with unique linguistic point of view \cite{Bao-2012, Massa-2012, Massa-2011}, its own controversial topics \cite{Yasseri-book}, and concept coverage \cite{Callahan-2011}.
We demonstrate that similarity of co-editing interests between language communities can be partially explained by the number of bilinguals and by linguistic similarity of the languages themselves. This comes as little surprise, since language is a fundamental part of identity, self-recognition, and culture \cite{Kramsch, Castells-2011, Whorf, Bloomfield}. It is hard to separate the effects of the number of bilinguals and shared language family from one another, since both might be related: shared vocabulary and grammatical features of the languages from the same language family might explain higher level of bilingualism for these language dyads. Moreover, language choice and bilingualism are an effect of factors galore, such as post-colonial history, education, language and human right policies, free travel, and migration due to political instability, poverty, religious persecutions or work \cite{Rassool-1998, Crystal-2000}. Finally, cultural similarity defined through Hofstede's four dimensions of values \cite{Hofstede-1980} has also been found to relate to language~\cite{Pfeil-2006, West-2004}.
Shared religion is another uniting factor for language communities. Our finding is in line with Huntington's thesis which argues that cultural and religious identities of people form the primary source of potential conflict in the post-Cold War era~\cite{Huntington}. The studies of email and Twitter communication \cite{State-2015} and similarity in country information interests \cite{Karimi} also reveal the patterns that echo religious ``fault lines''.
Population attraction and geographical proximity are the uniting factors that have been extensively discussed in the literature, most relevantly in the context of mobile communication flows \cite{Krings-2009} and migration \cite{Simini-2012}. Similar to our results, several studies report gravity laws in online settings, including \cite{Backstrom} and \cite{Karimi}. Not only choice of topics to edit, but also online trade in taste-dependent products is affected by distance. For example, \cite{Blum-2006} finds that proximate countries show more similarity in taste. Notably, this effect only holds for culture-related products such as music. This further supports our finding that there is a relationship between geographical distance and culture, and allows us to speculate that the Internet fails to defy the law of gravity.
The question of whether English is becoming the world's \textit{lingua franca} is an intriguing one \cite{crystal:global}. Its central, influential position in the global language network has been reported in networks of book translations, multilingual Twitter users, and Wikipedia editors \cite{Ronen, Hale-2014, Hale-2014-Twitter}. On the one hand, such high visibility allows information to radiate between the more connected languages. On the other hand, our study shows that global language centrality plays a minor role in shared interests. Moreover, we show that the domination of English disappears in the network of co-editing similarities, and instead local interconnections come to the forefront, rooting in shared language, similar linguistic characteristics, religion, and demographic proximity. A similar effect has been observed in international markets, where economic competitiveness is linked to the ability to speak a local \textit{lingua franca}, rather than English \cite{Bel-2011}.
\section{Conclusions and Implications} \label{conclusions}
Out of almost 300 Wikipedia's language editions, 76\% have less than 100 active users \cite{WP:list}. Linguistically, this means that those languages are in danger of extinction \cite{Crystal-2000}, at least in the online space \cite{Netlang}. Nevertheless, \cite{Kornai-2013} emphasises the role of Wikipedia in helping peripheral languages cross the digital divide, acquire digital functions and prestige as their speakers go online. At the same time, Pentzold \cite{Pentzold-12} describes Wikipedia as a global cultural memory place, access to which depends on the language skills. In his view, Wikipedia is not a mere encyclopedia where facts are documented, but rather a space where the entire collective memories of important events are constructed during a discursive, social process. We show that the topics that each language edition documents are not selected randomly, however small the underlying community of editors. These non-random processes might relate to the fact that each Wikipedia language edition presents a cultural memory place, where the linguistic point of view and the memorable events of that community are negotiated.
Our findings bring some important policy questions for the Wikimedia Foundation, such as: What are the cultural implications of populating editions with automatically translated concepts present in other language editions? Should English Wikipedia aim at becoming an all-inclusive collection of information from other language editions? Should the decision on who and what will be remembered belong to the community of editors, however small, or to an automated algorithm? We hope that our research will inspire dialogue on how similarities between language communities can be used to improve participation of editors speaking peripheral languages and expand the content of smaller editions.
In addition, Wikipedia has a power to mobilise cultural communities around a very important collective task -- selecting and archiving important knowledge for future generations. Our analysis sheds light on how cultural similarities are reflected in this process. We also demonstrate that global cultural interconnections are not dominated by one powerful player, but instead follow the locally established ``fault lines'' of bilingualism, shared religion and population attraction. We hope that these results will be useful for managers, economists and politicians working in multicultural settings, enthusiastic Wikipedians, academics wishing to study culture via the web, as well as for the public curious about global, intercultural relationships.
\begin{backmatter}
\section*{Competing interests}
The authors declare that they have no competing interests.
\section*{Author's contributions}
AS, MS, FK conceived and designed the research. AS acquired the data. AS, FK and DE analysed the data. AS and FK interpreted the results. All authors discussed, wrote, and approved the final version of the manuscript.
\section*{Acknowledgements}
We would like to thank Michael Macy, Florian Lemmerich, and Philipp Singer for inspiring discussions and useful comments. We also thank the Wikimedia Foundation for developing and hosting the Wikimedia Labs infrastructure and granting access to its servers. JK acknowledges the funding from the European Community's Seventh Framework Programme under grant agreement n\textsuperscript{o}~610928, REVEAL.
\bibliographystyle{bmc-mathphys}
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| 9,020
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{"url":"https:\/\/www.reddit.com\/r\/Jekyll\/comments\/cp7ggo\/katex_not_properly_parsing\/","text":"Press J to jump to the feed. Press question mark to learn the rest of the keyboard shortcuts\n2\n\n# KaTeX Not Properly Parsing \\\\\n\n2\nPosted by6 days ago\n\n# KaTeX Not Properly Parsing \\\\\n\nIt seems that I can't use the aligned environment in KaTeX, and I've narrowed it down to \\\\ not working. It works just fine in the KaTeX preview box, but not when rendered as a Jekyll site. Is there something Jekyll is doing in preprocessing that could be stripping or tampering with the \\\\?\n\nExample syntax:\n\n\\begin{aligned}\n1 + 1 &= 2 \\\\\n2 + 2 &= 4 \\\\\n4 + 4 &= 8\n\\end{aligned}\n\n100% Upvoted\nSort by\n\nBe the first to share what you think!","date":"2019-08-18 15:07:23","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\": 0.999474823474884, \"perplexity\": 2930.4988205537275}, \"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-2019-35\/segments\/1566027313936.42\/warc\/CC-MAIN-20190818145013-20190818171013-00342.warc.gz\"}"}
| null | null |
Asia's AFC Cup matches postponed over coronavirus
Feb 11, 2020 10:51 PM PHT
KUALA LUMPUR, Malaysia – AFC Cup football matches involving teams from East Asia have been postponed until April over the deadly coronavirus, the Asian Football Confederation said on Tuesday, February 11.
The two-month suspension comes after several countries imposed travel restrictions aimed at stopping the outbreak, which has killed more than 1,000 people in China.
"Taking into consideration the overall logistical arrangements as well as match preparations of the East Zone participating clubs, the AFC has decided that... the AFC Cup 2020 (East Zone) preliminary, playoff and group stage matches will be postponed and will recommence on April 7, 2020," an AFC statement said.
It added that the home and away games between Mongolia's Ulaanbaatar City and Taipower Company of Taiwan had already been postponed because of travel restrictions.
Teams from Hong Kong and Macau are also among those affected by the postponement in Asia's second-tier continental competition.
The AFC had earlier been forced to change the dates of home games for Vietnamese clubs after Vietnam cancelled all sports events in February because of the virus.
The top-tier AFC Champions League has also been disrupted by the epidemic, with Chinese clubs mainly sidelined until April.
– Rappler.com
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\section{Introduction}
The two-dimensional ($n+1$)-periodic Toda lattice with opposite sign is the system
\begin{eqnarray}
\left\{
\begin{array}{l}2 (w_i)_{z\bar z} =-e^{2 (w_{i+1}-w_i)}+e^{2 (w_i-w_{i-1})}\\
w_{i+n+1}=w_i
\end{array}
\right. ,
\label{Toda-N}
\end{eqnarray}
where $\bar z$ denotes the complex conjugate of $z \in \mathbb{C}$ and $w_i=w_i(z,\bar z) \in \mathbb{R}$.
System (\ref{Toda-N}) admits both the $l$-anti-symmetry constraints
\begin{eqnarray}
\left\{
\begin{array}{lll}
w_0+w_{l-1}=0, &w_1+w_{l-2}=0, &\cdots \\
w_l+w_n=0, &w_{l+1}+w_{n-1}=0, &\cdots
\end{array}
\right. ,
\label{l-anti}
\end{eqnarray}
where the fixed $l \in \{0,1,\cdots, n\}$,
and the radial constraints
\begin{eqnarray}
w_i(z,\bar z)=w_i(|z|), \quad i \in \{0,1,\cdots, n\}.
\label{Radical}
\end{eqnarray}
The tt* (topological–anti-topological fusion) equation is (\ref{Toda-N}) constrained by
(\ref{l-anti}) and (\ref{Radical}).
The special case of $l=0$ was introduced by Cecotti and Vafa when they deformed the superpotentials
to study the fusion of topological $N=2$ supersymmetric quantum field theory with its conjugate,
the anti-topological one \cite{CV-1}.
It also appeared in the extraction of exact results for supersymmetric $\sigma$ models \cite{CV-2}
and in the classification of $N=2$ supersymmetric theories \cite{CV-3}.
Dubrovin gave the zero-curvature representation of tt* equations
and also studied their geometry aspects \cite{Dub}.
All concrete examples of the tt* equations were reduced to the third Painlev\'{e} equation
before the work of Guest and Lin \cite{GL-1},
where they initiated the direct study of differential system with two unknowns
\begin{eqnarray}
\left\{
\begin{array}{l}
u_{z \bar z}=e^{a u}-e^{v-u} \\
v_{z \bar z}=e^{v-u}-e^{-b v}\\
\end{array}
\right. ,
\label{TT}
\end{eqnarray}
where $a,b>0$,
subject to the boundary condition
\begin{eqnarray}
\left\{\begin{array}{ll}
u(z)\xlongrightarrow{ |z| \rightarrow \infty} 0, & v(z)\xlongrightarrow{ |z| \rightarrow \infty} 0 \\
u(z) \xlongrightarrow{ z \rightarrow 0} (\gamma+o(1)) \log |z|, &v(z) \xlongrightarrow{z \rightarrow 0} (\delta+o(1)) \ln |z|
\end{array} \right. .
\label{BC}
\end{eqnarray}
The tt* equations with two dependent variables are the cases $a,b \in \{1,2 \}$, exhausted in \cite{GL-1}.
So, \cite{GL-1} studied a generalized version of them.
In \cite{GIL-1}, Guest, Its and Lin proved the following comprehensive property for Equation (\ref{TT}) with boundary condition (\ref{BC}).
\begin{theorem} \label{thm-GIL-1}
\textup{\cite{GIL-1} }\quad
For $a,b>0$ and any $(\gamma,\delta)$ in the triangular region
$$\gamma \ge -\frac{2}{a}, \quad \delta \le \frac{2}{b}, \quad \gamma-\delta \le 2, $$
the system (\ref{TT}) has a unique solution that satisfies the boundary condition (\ref{BC}).
Further, the unique solution is radially-invariant, i.e., it depends only on $|z|$.
\end{theorem}
\input{Figure1.tikz}
Therefore, any point in the triangular region represents a smooth solution of the (generalized) tt* equation
in $\mathbb{C}^*=\mathbb{C} \backslash \{0\}$.
So, Theorem \ref{thm-GIL-1} characterizes a two-parameter family of smooth solutions for the tt* equation
in $\mathbb{C}^*$.
Note that a similar result to Theorem \ref{thm-GIL-1} had been obtained by Guest and Lin in \cite{GL-1},
where they demanded $\gamma, \delta>0$.
But the difference is crucial since Theorem \ref{thm-GIL-1} characterize
{\sl all} smooth radial solution of Equation (\ref{TT}) \cite{GIL-2}.
The work of \cite{GL-1} also triggered some other researches, such as \cite{Mochi-1} and \cite{Mochi-2}.
By the Riemann-Hilbert approach, Guest et al. obtained all connection formulae for the tt* equation, i.e., $a,b \in \{1, 2\}$ \cite{GIL-2}.
The complete picture of the monodromy data, holomorphic data, and asymptotic data
were eventually obtained in \cite{GIL-3}.
In \cite{GIL-3}, some fine structures (more detailed asymptotics) of the solutions of tt* equation near $z=0$ were revealed.
However, the fine structures are complicated, lacking of intuitional explanation
or other relevant results that could directly support them.
The first aim of this paper is to verify them numerically up to $100$ digits in all cases:
the general case, the edge case, and the vertex case.
To be more specific,
we will only consider the tt* equation with $a=b=2$, which is the case 4a studied in detail in \cite{GIL-1, GIL-2, GIL-3}.
In this case, $u=2 w_0$, $v=2 w_1$. So (\ref{TT}) becomes
\begin{eqnarray}
\left\{
\begin{array}{l}
2 (w_0)_{z \bar z}=e^{4 w_0}-e^{2 w_1-2 w_0} \\
2 (w_1)_{z \bar z}=e^{2 w_1-2w_0}-e^{-4 w_1}
\end{array}
\right.
. \label{TT-1}
\end{eqnarray}
According to the radical constraint (\ref{Radical}),
system (\ref{TT-1}) is written as an ordinary differential equations (ODEs) with variable $r=|z|$
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{1}{2} w_0''+\frac{1}{2 r} w_0' =e^{4 w_0}-e^{2 w_1-2 w_0} \\
\frac{1}{2} w_1''+\frac{1}{2 r} w_1' =e^{2 w_1-2w_0}-e^{-4 w_1}
\end{array}
\right.
, \label{TT-2}
\end{eqnarray}
where the prime denotes $\frac{d}{dr}$.
Near $r=0$, by (\ref{BC}), $w_0$ and $w_1$ have properties
\begin{eqnarray}
\left\{
\begin{array}{l}
2 w_0(r) \xlongrightarrow{r \rightarrow 0} (\gamma_0 +o(1) ) \ln r\\
2 w_1(r) \xlongrightarrow{r \rightarrow 0} (\gamma_1+o(1) ) \ln r
\end{array}
\right. . \label{OAsymp}
\end{eqnarray}
Near $r=\infty$, the asymptotics of $w_0$ and $w_1$ are expressed
by the Stokes data $s_1^\mathbb{R}$ and $s_2^\mathbb{R}$ \cite{GIL-2}:
\begin{eqnarray}
\left\{
\begin{array}{l}
w_0(r)+w_1(r)\xlongrightarrow{r \rightarrow \infty}-s_1^\mathbb{R} 2^{-\frac{3}{4}} \left( \pi r\right)^{-\frac{1}{2}} e^{-2 \sqrt{2}r}\\
w_0(r)-w_1(r)\xlongrightarrow{r \rightarrow \infty}s_2^\mathbb{R} 2^{-\frac{3}{2}} \left( \pi r\right)^{-\frac{1}{2}} e^{-4 r}
\end{array}
\right. .\label{InfAsymp}
\end{eqnarray}
The map from $(\gamma_0, \gamma_1)$ to $(s_1^\mathbb{R}, s_2^\mathbb{R})$
is the connection formula \cite{GIL-2}
\begin{eqnarray}
\left\{
\begin{array}{l}
s_1^\mathbb{R}=-2 \cos \left( \frac{\pi}{4} (\gamma_0+1) \right)-2 \cos \left( \frac{\pi}{4}(\gamma_1+3) \right) \\
s_2^\mathbb{R}=-2 -4 \cos \left( \frac{\pi}{4} (\gamma_0+1) \right) \cos \left( \frac{\pi}{4}(\gamma_1+3) \right)
\end{array}
\right. . \label{ConnectFormula}
\end{eqnarray}
Let us take the general case, which refers to a solution represented by a inner point of the triangular region in Figure \ref{fig-1},
as an example to explain the fine structure near $r=0$.
In this case, the fine structure states that
\begin{eqnarray}
\left\{
\begin{array}{l}
2 w_0(r) \xlongrightarrow{r \rightarrow 0} \gamma_0 \ln r +\rho_0 \\
2 w_1(r) \xlongrightarrow{r \rightarrow 0} \gamma_1 \ln r+\rho_1
\end{array}
\right. , \label{OAsymp-Fancy}
\end{eqnarray}
where
\begin{eqnarray}
\left\{
\begin{array}{l}
\rho_0= -\ln \left( 2^{2 \gamma_0}
\frac{\Gamma(\frac{1+\gamma_0}{4}) \Gamma(\frac{4+\gamma_0+\gamma_1}{8}) \Gamma(\frac{6+\gamma_0-\gamma_1}{8})}
{ \Gamma(\frac{3-\gamma_0}{4})\Gamma(\frac{4-\gamma_0-\gamma_1}{8}) \Gamma(\frac{2-\gamma_0+\gamma_1}{8})} \right) \\
\rho_1=-\ln \left( 2^{2 \gamma_1}
\frac{\Gamma(\frac{3+\gamma_1}{4}) \Gamma(\frac{4+\gamma_0+\gamma_1}{8}) \Gamma(\frac{2-\gamma_0+\gamma_1}{8})}
{ \Gamma(\frac{1-\gamma_1}{4})\Gamma(\frac{4-\gamma_0-\gamma_1}{8}) \Gamma(\frac{6+\gamma_0-\gamma_1}{8})} \right)
\end{array}
\right. . \label{rhos-DEF}
\end{eqnarray}
We will see (\ref{OAsymp-Fancy}) is appropriate to verify numerically.
Also, the fine structures in the edge case and the vertex case can be managed to verify numerically.
The $r=\infty$ asymptotics (\ref{InfAsymp}) is able to
fix the solution of the tt* equation (\ref{TT-2}) uniquely.
This is an initial value problem from $r=\infty$.
However, the rough asymptotics (\ref{OAsymp}) itself is not enough to fix the solution.
To fix the solution, it has to be accompanied with the rough $r=\infty$ asymptotics
$w_0(r) \xlongrightarrow{r \rightarrow \infty}0$ and
$w_1(r) \xlongrightarrow{r \rightarrow \infty} 0$.
But it is a boundary value problem.
To get an initial value problem from $r=0$,
it is necessary and enough to begin with the fine structure (\ref{OAsymp-Fancy}).
Then, $r=\infty$ and $r=0$ become symmetrical.
This explains why the fine structure is important.
The connection formula (\ref{ConnectFormula}) maps the $(\gamma_0, \gamma_1)$ region
to the $(s_1^\mathbb{R}, s_2^\mathbb{R})$ region.
Coming down to Equation (\ref{TT-2}), the region map can be represented by Figure \ref{fig-2}.
\input{Figure2.tikz}
Any solution represented by a point $(s_1^\mathbb{R}, s_2^\mathbb{R})$
in the curved triangle (including the edges and the vertexes) in Figure \ref{fig-2}
must have asymptotic (\ref{OAsymp-Fancy}) near $r=0$,
where $(\gamma_0, \gamma_1)$ is determined from $(s_1^\mathbb{R}, s_2^\mathbb{R})$ by the connection formula (\ref{ConnectFormula}).
One would wonder what happens if the point $(s_1^\mathbb{R}, s_2^\mathbb{R})$ lies out of the curved triangle.
Based on our numerical results,
we will give a conjecture to generalize the range and explanation of the connection formula and the fine structures.
If $\rho_0$ and $\rho_1$ are exactly given by (\ref{rhos-DEF}),
then $w_0(r)\xlongrightarrow{r \rightarrow \infty} 0$ and $w_1(r)\xlongrightarrow{r \rightarrow \infty} 0$.
In \cite{GIL-2}, they had shown that the smooth solutions in $\mathbb{C}^*$ are all of such type.
So, if $\rho_0$ and $\rho_1$ differ from (\ref{rhos-DEF}), the solutions must have singularities.
We would give a more detailed picture for these singular solutions.
One may also wonder about the solutions that associated with the points $(\gamma_0, \gamma_1)$ that lies out of the triangle.
But this is, in fact, not a question since the triangle is optimal \cite{GL-1},
i.e. there is no such solution that has asymptotics (\ref{OAsymp}) with $(\gamma_0, \gamma_1)$ out of the triangle.
This can also be explained by noticing that (\ref{tu0tu1}) has no solution of order $o(s)$.
The paper is organized as follows.
In Section 2, we verify numerically the fine structures given in \cite{GIL-3}.
In Section 3, we consider the case that $(s_1^\mathbb{R}, s_2^\mathbb{R})$ lies out of the curved triangle.
In Section 4, a more detailed picture is given for the case that $\rho_0$ and $\rho_1$ differ from (\ref{rhos-DEF}).
This paper may be viewed as a supplement of work \cite{GIL-1,GIL-2,GIL-3}.
Acknowledgement.
Part of this work was done while Y. Li was visiting the Department of Mathematical Sciences of IUPUI.
Y. Li would like to thank A. Its for his hospitality and the suggestion of verifying their Corollary 8.3 in \cite{GIL-3}.
The work is partly supported by NSFC(11375090) and
Science and Technology Commission of Shanghai Municipality (No. 18dz2271000).
\section{Verifying the fine structures \label{sec-verify}}
The fine structures are different for the general case, the edge cases and the vertex cases.
Both the edge cases and the vertex cases include three subcases: E1, E2, E3 for the edge case and V1, V2, V3 for the vertex case.
The tt* equation (\ref{TT-2}) has symmetry
\[ \left\{ \begin{array}{l}w_0\rightarrow -w_1 \\w_1\rightarrow -w_0 \end{array} \right. , \]
i.e, if $(w_0(r), w_1(r))=(f(r), g(r))$ is a solution of the tt* equation,
then $(w_0(r), w_1(r))=(-g(r), -f(r))$ is also a solution of the tt*.
Therefore, if the solution $(w_0(r), w_1(r))=(f(r), g(r))$ has data
$(\gamma_0,\gamma_1)=(\mu_0,\mu_1)$ and $(s_1^\mathbb{R}, s_2^\mathbb{R})=(\nu_1,\nu_2)$,
then the solution $(w_0(r), w_1(r))=(-g(r), -f(r))$ will have data
$(\gamma_0,\gamma_1)=(-\mu_0,-\mu_1)$ and $(s_1^\mathbb{R}, s_2^\mathbb{R})=(-\nu_1,\nu_2)$ by (\ref{OAsymp}) and (\ref{InfAsymp}).
In this way, the formulae for the E2 case and the V3 case can be obtained from the E1 case and V1 case respectively.
Further, as has been mentioned in \cite{GIL-3}, the V2 case is just the sinh-Gordon,
for which the asymptotic is already well known.
So, we will only verify four cases: the general, E1, E3 and V1.
For convenient, we will also list the formulae for the E2 case, the V2 case and the V3 case.
We will find that each fine structure is associated with a special truncation of (\ref{TT-2}).
This kind of truncation will keep working in Section \ref{CONJ}.
\subsection{Preliminary for the numerical experiments: an approximation proper for calculations near $r=\infty$}
Considering the solutions of (\ref{TT-2}) with asymptotics
$w_0(r)\xlongrightarrow{r \rightarrow \infty} 0$ and $w_1(r)\xlongrightarrow{r \rightarrow \infty} 0$.
The primary asymptotics of the solutions can be obtained by the linearization of (\ref{TT-2}):
\begin{eqnarray}
\left\{ \begin{array}{l}
\left( \frac{1}{2} \frac{d^2}{dr^2}+\frac{1}{2 r} \frac{d}{d r} \right) w_0^L=6 w_0^L -2 w_1^L \\
\left( \frac{1}{2} \frac{d^2}{dr^2}+\frac{1}{2 r} \frac{d}{d r} \right) w_1^L=6 w_1^L -2 w_0^L
\end{array}
\right. . \nonumber
\end{eqnarray}
Then, $(w_0^L,w_1^L)$ will be a good approximation of $(w_0^L,w_1^L)$ near $r=\infty$.
Define
\begin{eqnarray}
\left\{ \begin{array}{l}
w_p^L=w_0^L+w_1^L\\
w_m^p=w_0^L-w_1^L
\end{array}
\right. .\label{wpwL-DEF}
\end{eqnarray}
Then, $w_p^L$ and $w_m^L$ satisfy
\begin{eqnarray}
\left\{ \begin{array}{l}
\left( \frac{1}{2} \frac{d^2}{dr^2}+\frac{1}{2 r} \frac{d}{d r} \right) w_p^L=4 w_p^L\\
\left( \frac{1}{2} \frac{d^2}{dr^2}+\frac{1}{2 r} \frac{d}{d r} \right) w_m^L=8 w_m^L
\end{array}
\right. . \label{wpwm-L}
\end{eqnarray}
Considering $w_p^L$ and $w_m^L$ should vanish at $r=\infty$, the solution of (\ref{wpwm-L}) is
\begin{eqnarray}
\left\{ \begin{array}{l}
w_p^L=c_p K_0(2 \sqrt{2} r)\\
w_m^L=c_m K_0(4 r)
\end{array}
\right. . \label{vpvml-sol}
\end{eqnarray}
Comparing (\ref{vpvml-sol}) with (\ref{InfAsymp}), we immediately obtain
\begin{eqnarray}
\left\{ \begin{array}{l}
c_p=-\frac{\sqrt{2}}{\pi} s_1^\mathbb{R} \\
c_m=\frac{1}{\pi} s_2^\mathbb{R}
\end{array}
\right. . \label{cpcm-sol}
\end{eqnarray}
Corresponding to (\ref{wpwL-DEF}), let us define
\begin{eqnarray}
\left\{ \begin{array}{l}
w_p=w_0+w_1\\
w_m=w_0-w_1
\end{array}
\right. . \label{wpm-DEF}
\end{eqnarray}
Then, the equations for $w_p$ and $w_m$ are
\begin{eqnarray}
\left\{ \begin{array}{l}
\left( \frac{1}{2} \frac{d^2}{dr^2}+\frac{1}{2 r} \frac{d}{d r} \right) w_p=e^{2 w_p+2 w_m}-e^{2 w_p-2 w_m}
=2 e^{2 w_m} \sinh \left( 2 w_p \right) \\
\left( \frac{1}{2} \frac{d^2}{dr^2}+\frac{1}{2 r} \frac{d}{d r} \right) w_m=e^{2 w_p+2 w_m}+e^{2 w_m-2w_p}-2 e^{-2 w_m}
=4 e^{2 w_m} \sinh^2(w_p)+4 \sinh (2 w_m)
\end{array}
\right. . \label{wpwm}
\end{eqnarray}
Note that (\ref{wpwm}) is written to a form better for keeping the high precision of the numerical integration.
Also note Equations (\ref{wpwm-L}) are the linearization of (\ref{wpwm}).
The errors of approximating $(w_p, w_m)$ by $(w_p^L, w_m^L)$ are caused by the nonlinear terms in the expansion of (\ref{wpwm}).
In general, the most significant correction to $w_p$ is proportional to $ w_p^L w_m^L$, i.e.,
$w_p =c_p K_0(2 \sqrt{2} r)+O(r^{-1} e^{-(2 \sqrt{2}+4)r})$.
Meanwhile, the most significant correction to $v_m$ is proportional to the square of $w_p^L$, i.e.,
$ w_m =c_m K_0(4 r)+O(r^{-1} e^{-4 \sqrt{2} r})$.
These results are sufficient for the rough numerical investigations for smooth solutions of the tt* equation.
It is called rough since they can be refined.
In the high-precision numerical integration of (\ref{wpwm}), the relative error will not enlarge too much when $r$ is still large.
For $w_m(r)$, the relative error is about $O(r^{-\frac{1}{2}} e^{-4 (\sqrt{2}-1) r})$.
If we give the initial values by $w_p(r)=w_p^L(r)$ and $w_m(r)=w_m^L(r)$ with $r=45$,
the relative error of the initial values are of order $10^{-33}$, which is not so satisfying.
If we want to reach a relative error of order $10^{-100}$ by this way,
$r=138$ is needed to give the initial values.
We will see, after considering the most significant contribution of the nonlinear terms,
the starting $r$ can be greatly reduced.
Suppose
\begin{eqnarray}
\left\{ \begin{array}{l}
w_p(r)=w_p^{(0)}(r)+w_p^{(1)}(r)+w_p^{(2)}(r)+\cdots\\
w_m(r)=w_m^{(0)}(r)+w_m^{(1)}(r)+w_m^{(2)}(r)+\cdots
\end{array}
\right. , \nonumber
\end{eqnarray}
where
\begin{eqnarray}
\left\{ \begin{array}{l}
w_p^{(0)}(r)=w_p^L(r)= -\frac{\sqrt{2}}{\pi} s_1^\mathbb{R} K_0(2 \sqrt{2} r)\\
w_m^{(0)}(r)=w_m^L(r)=\frac{1}{\pi} s_2^\mathbb{R} K_0(4 r)
\end{array}
\right. . \nonumber
\end{eqnarray}
Then $w_p^{(1)}$ and $w_m^{(1)}$ satisfy
\begin{eqnarray}
\left\{ \begin{array}{l}
\left( \frac{1}{2} \frac{d^2}{dr^2}+\frac{1}{2 r} \frac{d}{d r} \right) w_p^{(1)}-4 w_p^{(1)}=8 w_p^{(0)} w_m^{(0)}\\
\left( \frac{1}{2} \frac{d^2}{dr^2}+\frac{1}{2 r} \frac{d}{d r} \right) w_m^{(1)}-8 w_m^{(1)}
=4 \left(w_p^{(0)} \right)^2
\end{array}
\right. \nonumber
\end{eqnarray}
with $w_p^{(1)}(\infty)=0$ and $w_m^{(1)}(\infty)=0$.
The solution of $w_p^{(1)}$ and $w_m^{(1)}$ is:
\begin{eqnarray}
\left\{ \begin{array}{l}
w_p^{(1)}=2 I_0(2 \sqrt{2} r) \int_\infty^r K_0(2 \sqrt{2}r) \bigg(8 w_p^{(0)}(r) w_m^{(0)}(r) \bigg) r dr
-2 K_0(2 \sqrt{2} r) \int_\infty^r I_0(2 \sqrt{r}) \bigg(8 w_p^{(0)}(r) w_m^{(0)}(r) \bigg) r dr\\
w_m^{(1)}=2 I_0(4 r) \int_\infty^r K_0(4 r) \bigg(4 ( w_p^{(0)}(r) )^2 \bigg) r dr
-2 K_0(4 r) \int_\infty^r I_0(4 r) \bigg( 4 ( w_p^{(0)}(r) )^2 \bigg) r dr
\end{array}
\right. . \nonumber
\end{eqnarray}
Then
\begin{eqnarray}
\left\{ \begin{array}{l}
w_p(r)=w_p^{(0)}(r)+w_p^{(1)}(r)+O\left(r^{-\frac{3}{2}} e^{-6 \sqrt{2} r} \right)\\
w_m(r)=w_m^{(0)}(r)+w_m^{(1)}(r)+O\left(r^{-\frac{3}{2}} e^{-(4+ 4\sqrt{2}) r} \right)
\end{array}
\right. . \label{iniApprox}
\end{eqnarray}
The relative errors are both of order $ r^{-1} e^{-4 \sqrt{2} r}$.
To acquire a relative error of order $10^{-100}$, it should be enough to start the numerical integration from $r=45$.
Higher order nonlinear terms should not be considered,
else we will meet high-dimensional integration that is difficult to calculate to our precision goal.
The truncation of (\ref{iniApprox}) will be used to given initial values for the numerical integration of (\ref{wpwm})
both in this section and in Section \ref{CONJ}.
\subsection{The general case: in the triangular \label{GeneralCase}}
This subsection is devoted to verify (\ref{OAsymp-Fancy}).
To be specific, we will fix $(\gamma_0, \gamma_1)=(1, \frac{1}{3} )$.
Then, $(s_1^\mathbb{R}, s_2^\mathbb{R})=(\sqrt{3},-2 )$ by (\ref{ConnectFormula}).
(\ref{iniApprox}) means that we can start our numerical integration from $r=45$
for moderate $(s_1^\mathbb{R},s_2^\mathbb{R})$ to guarantee our precision goal $10^{-100}$.
Also, we will find it is convenient to do transform
\begin{eqnarray}
s=\ln r \label{s-DEF}
\end{eqnarray}
near $r=0$.
So, the numerical integration is divided into two parts:
on $r \in [r_m, 45]$ and on $s \in [s_f, s_m=\ln r_m]$.
For convenience, $r_m$ is always chosen as $r_m=1$.
$s_f$ vary with $(s_1^\mathbb{R},s_2^\mathbb{R})$
and will be given after the determination of the associated truncation of (\ref{TT-2}).
\subsubsection{Numerical integration from $r=45$ to $r=1$}
By the truncation of (\ref{iniApprox}), the initial values for the numerical integration of (\ref{wpwm})
are calculated up to more than $100$ digits
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(45)=-4.5763465910740842210810671823515633075572030760030... \times 10^{-57} \\
w_p'(45)=1.2994612025622450236510718743064448909150132699101... \times 10^{-56}\\
w_m(45)=-3.9902150828859022626192436154419670328254784177405... \times 10^{-80}\\
w_m'(45)=1.6005134816454403480052616718328017176197600655449... \times 10^{-79}
\end{array}
\right. .\label{ini-General}
\end{eqnarray}
To save space, we only list the first $50$ digits in (\ref{ini-General}).
Immediately, one notice there is not so much need to list the first few digits of the initial values:
$w_m(45)$ in (\ref{ini-General}) coincides $w_m^L(45)=-\frac{\sqrt{6}}{\pi} K_0(90 \sqrt{2})$ with $33$ digits
while $w_p(45)$ in (\ref{ini-General}) coincides with $w_p^L(45)=-\frac{2}{\pi} K_0(180) $ with all the listed $50$ digits.
Formula (\ref{iniApprox}) only provides the order of error, not the actual.
We obtain the errors of (\ref{ini-General})
by comparing the initial values (\ref{ini-General}) with a more accurate numerical solution starting from $r=55$.
Table \ref{tab1} shows both the absolute error and the relative error of the initial values at $r=45$.
\begin{table}[ht]
\caption{Errors of the initial values for the general case with $(\gamma_0,\gamma_1)=(1,\frac{1}{3})$.}
\label{tab1}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=45$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$1.98 \times 10^{-170}$ &$1.68 \times 10^{-169}$ &$2.43 \times 10^{-193}$&$2.36\times 10^{-192}$ \\
| Relative Error | &$4.32\times 10^{-114}$ &$1.30 \times 10^{-113}$ &$6.09 \times 10^{-114}$&$1.47\times 10^{-113}$
\end{tabular}
\end{table}
In this paper, we use the Gauss-Legendre method,
which is an implicit Runge-Kutta method suitable for high-precision numerical integration,
to integrate ODEs numerically.
After integrating (\ref{wpwm}) numerically from $r=45$ to $r=1$
by a $100$-stage Gauss-Legendre method with step size $\frac{1}{100}$,
we obtain the numerical values of $w_p$, $w_p'$, $w_m$ and $w_m'$ at $r=1$:
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(1)=-3.2972969594742103001480456261339460432792854660454...\times 10^{-2}\\
w_p'(1)=1.0829838290019404254859616425541702465151021916881...\times 10^{-1}\\
w_m(1)=-6.6648017026562016812805168052539563362254856278250...\times 10^{-3}\\
w_m'(1)=2.8961723214345113722967491163879906375020596216242...\times 10^{-2}
\end{array}
\right. . \label{values-general-1}
\end{eqnarray}
Note that (\ref{values-general-1}) lists only the first $50$ digits of the numerical solution.
Also note the precision of the numerical method itself is of order
$\text{stepsize}^{2 \times \text{stages}}=10^{-400}$, which is far more accurate than our precision goal.
Comparing (\ref{values-general-1}) with the more accurate solution starting from $r=55$,
we obtain the errors of (\ref{values-general-1}) as Table \ref{tab2}.
\begin{table}[ht]
\caption{Errors of the numerical solution at $r=1$ for the general case with $(\gamma_0,\gamma_1)=(1,\frac{1}{3})$.}
\label{tab2}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=1$ & $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$2.85 \times 10^{-115}$ &$9.31 \times 10^{-115}$ &$6.64 \times 10^{-116}$&$2.82\times 10^{-115}$ \\
| Relative Error | &$8.63\times 10^{-114}$ &$8.60 \times 10^{-114}$ &$9.97 \times 10^{-114}$&$9.75\times 10^{-114}$
\end{tabular}
\end{table}
\subsubsection{Near $r=0$}
Inspired by the form of (\ref{OAsymp-Fancy}), we use independent variable $s$
and dependent variables
\begin{eqnarray}
\left\{
\begin{array}{l}
\tilde w_0 =2 w_0-\gamma_0 s \\
\tilde w_1 =2 w_1-\gamma_1 s
\end{array}
\right. . \label{transform-general}
\end{eqnarray}
Please recall that $s=\ln (r)$ is defined by (\ref{s-DEF}).
From the numeric point of view, the advantage of using $s$ rather than $r$
is that it can avoid the frequent adjusting of the step size when we compute numerically near $r=0$.
The equations for $\tilde w_0$ and $\tilde w_1$ are
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{1}{4} \frac{ d^2\tilde w_0}{ds^2}= e^{2 \tilde w_0 +2 (\gamma_0+1) s}-e^{\tilde w_1- \tilde w_0+(\gamma_1-\gamma_0+2)s} \\
\frac{1}{4} \frac{ d^2\tilde w_1}{ds^2}=e^{\tilde w_1- \tilde w_0+(\gamma_1-\gamma_0+2)s}-e^{-2 \tilde w_1+2 (1-\gamma_1) s}
\end{array}
\right. .\label{tu0tu1}
\end{eqnarray}
We expect $\tilde w_0 \xlongrightarrow{s \rightarrow -\infty} \rho_0$
and $\tilde w_1 \xlongrightarrow{s \rightarrow -\infty} \rho_1$.
In the triangular: $\gamma_0>-1$, $\gamma_1<1$, $\gamma_1>\gamma_0-2$.
So, all terms in the right of (\ref{tu0tu1}) can be neglected at first.
Thus,
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{1}{4} \frac{ d^2\tilde w_0^{(0)}}{ds^2}= 0 \\
\frac{1}{4} \frac{ d^2\tilde w_1^{(0)}}{ds^2}=0
\end{array}
\right. \label{tu0tu1-truc}
\end{eqnarray}
is the primary approximation of (\ref{tu0tu1}), which is equivalent to (\ref{TT-2}).
So (\ref{tu0tu1-truc}) can be viewed as the truncation structure of the tt* equation in the general case.
The initial values of $\tilde w_0$, $\frac{ d\tilde w_0}{ds}$, $\tilde w_1$ and $\frac{ d\tilde w_1}{ds}$ at $s=0$
can be inferred from $w_p$, $w_p'$, $w_m$ and $w_m'$ at $r=1$
\begin{eqnarray}
\left\{
\begin{array}{l}
\tilde w_0|_{s=0}= w_p|_{r=1}+w_m|_{r=1} \\
\frac{ d \tilde w_0}{ds}|_{s=0}= w_p'|_{r=1}+w_m'|_{r=1} -\gamma_0 \\
\tilde w_1|_{s=0}= w_p|_{r=1}-w_m|_{r=1} \\
\frac{ d\tilde w_1}{ds}|_{s=0}= w_p'|_{r=1}-w_m'|_{r=1} -\gamma_1
\end{array}
\right. . \label{ini-s0-General}
\end{eqnarray}
In the truncation of (\ref{tu0tu1} ) to (\ref{tu0tu1-truc}),
the neglected terms are of order $O(e^{2 (\gamma_0+1) s})$, order $O(e^{(\gamma_1-\gamma_0+2) s})$
and order $O(e^{2 (1-\gamma_1)s})$.
Now, $(\gamma_0, \gamma_1)=(1, \frac{1}{3})$.
Thus, $(\tilde w_0, \tilde w_1)$ will approach $(\rho_0,\rho_1)|_{\gamma_0=1,\gamma_1=\frac{1}{3}}$
with distance $O(e^{\frac{4}{3} s})$, where
\begin{eqnarray}
\left\{
\begin{array}{l}
\rho_0|_{\gamma_0=1,\gamma_1=\frac{1}{3}} = 0.89156581440748831917188012305422345475702308262231...\\
\rho_1|_{\gamma_0=1,\gamma_1=\frac{1}{3}} = 0.22017225140694662756648980530049931068839656816740...
\end{array}
\right. \nonumber
\end{eqnarray}
by (\ref{rhos-DEF}).
So, when $e^{\frac{4}{3} s} \approx 10^{-100}$, ie., $s \approx -172.7$,
$(\tilde w_0, \tilde w_1)$ will be indistinguishable from $(\rho_0,\rho_1)|_{\gamma_0=1,\gamma_1=\frac{1}{3}}$ within our precision tolerance.
Therefore, it is enough to integrate (\ref{tu0tu1}) numerically from $s=0$ to $s_f=-175$.
\begin{table}[ht]
\caption{Errors of the numerical solution at $s=-175$ for the general case with $(\gamma_0,\gamma_1)=(1,\frac{1}{3})$.}
\label{tab3}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$s=-175$ & $\tilde w_0$ & $\frac{d\tilde w_0}{ds}$ & $\tilde w_1$ &$\frac{d \tilde w_1}{ds}$\\
\hline
| Absolute Error | &$1.33 \times 10^{-111}$ &$7.66 \times 10^{-114}$ &$6.54 \times 10^{-112}$&$3.76\times 10^{-114}$\\
| Relative Error | &$1.50 \times 10^{-111}$ &$1.08 \times 10^{-12}$ &$2.97 \times 10^{-111}$&$2.04\times 10^{-12}$
\end{tabular}
\end{table}
Table \ref{tab3} shows that the numerical solution is accurate as we expect.
The relative error of $\frac{d\tilde w_0}{ds}$ or $\frac{d\tilde w_1}{ds}$ in Table \ref{tab3} seems to be large.
But this is really nothing since it is only another demonstration of the fact that$\frac{d\tilde w_0}{ds}$ and $\frac{d\tilde w_1}{ds}$ are small.
Table \ref{tab4} shows how good the asymptotic solution (\ref{OAsymp-Fancy}) is.
\begin{table}[ht]
\caption{Approximate derivation from the asymptotic solution for the general case with $(\gamma_0,\gamma_1)=(1,\frac{1}{3})$.}
\label{tab4}
\centering
\begin{tabular}[h]{ c|c c c c c c c}
\hline \hline
$s$ & $-25$ & $-50$ & $-75$ &$-100$ &$-125$& $-150$&$-175$\\
\hline
$\ln(\rho_0-\tilde w_0)$ &$-33.1938$ &$-66.5271$&$-99.8605$&$-133.194$&$-166.527$&$-199.860$&$-233.194 $\\
$\ln(\rho_1-\tilde w_1)$ &$-34.5412$ &$-67.8745$ &$-101.208$&$-134.541$&$-167.875$&$-201.208$&$-234.541$
\end{tabular}
\end{table}
Table \ref{tab4} not only numerically verifies the asymptotics of the general case for $(\gamma_0,\gamma_1)=(1,\frac{1}{3})$,
but also confirms our estimation that $(\tilde w_0, \tilde w_1)$ is close to its asymptotics $(\rho_0,\rho_1)|_{\gamma_0=1,\gamma_1=\frac{1}{3}}$ with a distance of order $O(e^{\frac{4}{3} s})$.
In fact, the asymptotics (\ref{OAsymp-Fancy}) can still be refined, see Section \ref{DFG}.
\subsection{Case E1 \label{E1Case}}
The E1 case is $-1<\gamma_0<3$ and $\gamma_1=1$.
This subsection is devoted to verify the fine structure of the E1 case
\begin{eqnarray}
\left\{
\begin{array}{l}
2 w_0(r) \xlongrightarrow{r \rightarrow 0} \gamma_0 \ln r +a_{E1} \\
2 w_1(r) \xlongrightarrow{r \rightarrow 0} \ln r+\ln(-2 s+b_{E1})
\end{array}
\right. , \label{Asymp-E1}
\end{eqnarray}
where
\begin{eqnarray}
&&a_{E1}=-\ln \left( 2^{2 \gamma_0}
\frac{\Gamma(\frac{\gamma_0+1}{4}) \left( \Gamma(\frac{\gamma_0+5}{8}) \right)^2}
{ \Gamma(\frac{3-\gamma_0}{4}) \left(\Gamma(\frac{3-\gamma_0}{8}) \right)^2 } \right) ,\nonumber\\
&&b_{E1}=\frac{1}{2} \psi(\frac{3-\gamma_0}{8})+\frac{1}{2} \psi(\frac{5+\gamma_0}{8}) -\gamma_{\text{eu}} +4 \ln 2.\nonumber
\end{eqnarray}
Note that $s=\ln (r)$ as defined by (\ref{s-DEF}), $a_{E1}=\rho_0|_{\gamma_1=1}$
and $\psi$ is the digamma function $\psi(t)=\frac{d}{dt} \ln (\Gamma(t))=\frac{\Gamma'(t)}{\Gamma(t)}$.
Please also recall the denotation $s=\ln(r)$, see (\ref{s-DEF}).
To fix the problem, we take $\gamma_0=1$,
as an example to verify the E1 case. Substituting $(\gamma_0,\gamma_1)=(1,1)$
to the connection formula (\ref{ConnectFormula}),
we immediately get $(s_1^\mathbb{R}, s_2^\mathbb{R})=(2, -2)$.
Similar to the general case of Subsection \ref{GeneralCase},
the numerical integration is divided into two parts: on $r\in [1,45]$ and on $s\in [s_f,0]$.
\subsubsection{Numerical integration from $r=45$ to $r=1$}
By the truncation of (\ref{iniApprox}), the initial values at $r=45$ are obtained (only the first $50$ digits are listed)
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(45)= -5.2843098725232974899221393911204991207504443469367... \times 10^{-57} \\
w_p'(45)= 1.5004885502015739552694025310567337731833237644509... \times 10^{-56}\\
w_m(45)=- 3.9902150828859022626192436154419666864562950795650... \times 10^{-80}\\
w_m'(45)= 1.6005134816454403480052616718328015209213735935410... \times 10^{-79}
\end{array}
\right. .\label{ini-E1}
\end{eqnarray}
Comparing with the more accurate solution starting from $r=55$,
the errors of the initial values (\ref{ini-E1}) are obtained as shown by Table \ref{tab5}.
\begin{table}[ht]
\caption{Errors of the initial values of case E1 with $\gamma_0=1$.}
\label{tab5}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=45$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$3.04 \times 10^{-170}$ &$2.59 \times 10^{-169}$ &$3.24 \times 10^{-193}$&$3.14\times 10^{-192}$ \\
| Relative Error | &$5.76\times 10^{-114}$ &$1.73 \times 10^{-113}$ &$8.12 \times 10^{-114}$&$1.96\times 10^{-113}$
\end{tabular}
\end{table}
Numerically integrating the tt* equation (\ref{wpwm}) from $r=45$ to $r=1$
by the Gauss-Legendre method with parameters as same as in Subsection \ref{GeneralCase},
the values of $w_p$, $w_p'$, $w_m$ and $w_m'$ at $r=1$ are obtained
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(1)=-3.8076020447615564848336037555396597913276640146800...\times 10^{-2} \\
w_p'(1)=1.2507257120725277318359466237894266588814464453818...\times 10^{-1}\\
w_m(1)=-6.5181931373519405060356987540333399617643482502891...\times 10^{-3}\\
w_m'(1)=2.8018632441288063804071518136255604932977444116709....\times 10^{-2}
\end{array}
\right. .\label{values-E1-1}
\end{eqnarray}
Comparing with the more accurate solution starting from $r=55$,
the errors of (\ref{values-E1-1}) are obtained as shown by Table \ref{tab6}.
\begin{table}[ht]
\caption{Errors of the numerical solution at $r=1$ of case E1 with $\gamma_0=1$.}
\label{tab6}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=1$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$4.38 \times 10^{-115}$ &$1.43 \times 10^{-114}$ &$8.52 \times 10^{-116}$&$3.55\times 10^{-115}$ \\
| Relative Error | &$1.15\times 10^{-113}$ &$1.15 \times 10^{-113}$ &$1.31 \times 10^{-113}$&$1.27\times 10^{-113}$
\end{tabular}
\end{table}
\subsubsection{Near $r=0$}
Let
\begin{eqnarray}
\left\{
\begin{array}{l}
\tilde w_0 =2 w_0-\gamma_0 s \\
\tilde w_1 =2 w_1 - s
\end{array}
\right. , \label{transform-r0-E1}
\end{eqnarray}
where $s=\ln(r)$ as defined by (\ref{s-DEF}).
Then the differential equations for $\tilde w_0$ and $\tilde w_1$ are
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{1}{4} \frac{ d^2\tilde w_0}{ds^2}= e^{2 \tilde w_0 +2 (\gamma_0+1) s}-e^{\tilde w_1- \tilde w_0+(3-\gamma_0)s} \\
\frac{1}{4} \frac{ d^2\tilde w_1}{ds^2}=e^{\tilde w_1- \tilde w_0+(3-\gamma_0)s}-e^{-2 \tilde w_1 }
\end{array}
\right. .\label{tu0tu1-E1}
\end{eqnarray}
(\ref{tu0tu1-E1}) can also be simply obtained from (\ref{tu0tu1}) by substituting $\gamma_1=1$ to it.
We expect $\tilde w_0$ is of order $O(1)$ and that $\tilde w_1$ is of order $O(\ln(-s))$.
Also considering $-1<\gamma_0<3$, we get the primary truncation of (\ref{tu0tu1-E1}) near $s=-\infty$:
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{1}{4} \frac{ d^2\tilde w_0^{(0)}}{ds^2}=0\\
\frac{1}{4} \frac{ d^2\tilde w_1^{(0)}}{ds^2}=-e^{-2 \tilde w_1^{(0)} }
\end{array}
\right. .\label{tu0tu1-trunc-E1}
\end{eqnarray}
(\ref{tu0tu1-trunc-E1}) is the truncation structure of the tt* equation for the E1 case.
The general solution of (\ref{tu0tu1-trunc-E1}) is
\begin{eqnarray}
\left\{
\begin{array}{l}
\tilde w_0^{(0)}=k_{0E1}+k_{1E1} s\\
\tilde w_1^{(0)}=\ln \left( \pm \frac{2}{k_{2E1} } \sinh(k_{2E1} (s+k_{3E1})) \right)
\end{array}
\right. .\label{SOL-trunc-E1}
\end{eqnarray}
By (\ref{Asymp-E1}) and (\ref{transform-r0-E1}),
we know the asymptotics of the tt* equation corresponds to
$k_{0E1}=a_{E1}$, $k_{1E1}=0$, $k_{2E1}\rightarrow 0$ and $k_{3E1}=b_{E1}$.
In the truncation from (\ref{tu0tu1-E1}) to (\ref{tu0tu1-trunc-E1}),
the neglected term for the differential equation of $\tilde w_1$ is $e^{\tilde w_1- \tilde w_0+(3-\gamma_0)s}$,
which is of order $O(s e^{(3-\gamma_0) s})$.
Similarly, the neglected terms for the differential equation of $\tilde w_0$ are of orders $O(s e^{(3-\gamma_0) s})$
and $O(e^{2 (\gamma_0+1)s})$.
In the current numerical experiment, $\gamma_0=1$.
Therefore, the difference between the asymptotic solution and the exact solution is of order $O(s e^{2 s})$.
So, we should do high-precision numerical integration from $s=0$ to about $s=s_f=-120$
since $120 \times e^{2 \times (-120)} \approx 7.055 \times 10^{-103}$.
Similar to the general case of Subsection \ref{GeneralCase},
the values of $\tilde w_0$, $\frac{ d\tilde w_0}{ds}$, $\tilde w_1$ and $\frac{ d\tilde w_1}{ds}$ at $s=0$
are obtained by formula (\ref{ini-s0-General}).
Then, integrating (\ref{tu0tu1-E1}) numerically by the Gauss-Legendre method, the high-precision numerical solution is obtained.
Comparing it with the more accurate numerical solution starting from $r=55$,
the errors of the numerical solution are obtained.
\begin{table}[ht]
\caption{Errors of the numerical solution at $s=-120$ for the E1 case with $\gamma_0=1$.}
\label{tab7}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$s=-120$ & $\tilde w_0$ & $\frac{d\tilde w_0}{ds}$ & $\tilde w_1$ &$\frac{d \tilde w_1}{ds}$\\
\hline
| Absolute Error | &$1.06 \times 10^{-111}$ &$8.84 \times 10^{-114}$ &$3.56 \times 10^{-110}$&$5.94\times 10^{-112}$ \\
| Relative Error | &$1.35 \times 10^{-111}$ &$6.84 \times 10^{-12}$ &$6.50 \times 10^{-111}$&$7.12\times 10^{-110}$\\
\end{tabular}
\end{table}
Table \ref{tab7} shows our numerical solution is accurate as we expect.
The large relative error of $\frac{d\tilde w_0}{ds}$ is nothing
because $\frac{d\tilde w_0}{ds}|_{s=-120} \approx -1.29\times 10^{-102} $ is so small.
Table \ref{tab8} shows how good the asymptotic solution (\ref{Asymp-E1}) is.
\begin{table}[ht]
\caption{Approximate derivation from the asymptotic solution for the E1 case with $\gamma_0=1$.}
\label{tab8}
\centering
\begin{tabular}[h]{ c|c c c c c c}
\hline \hline
$s$ & $-20$ & $-40$ & $-60$ &$-80$ &$-100$& $-120$\\
\hline
$\ln(a_{E1}-\tilde w_0)$ &$-37.0566$ &$-76.3821$&$-115.983$&$-155.698$&$-195.477$&$-235.296$ \\
$\ln(\tilde w_1-\ln(-2 s+b_{E1}))$&$-37.0553$&$-76.3818$ &$-115.983$&$-155.698$&$-195.477$&$-235.296$
\end{tabular}
\end{table}
Table \ref{tab8} not only numerically verifies the asymptotics of the E1 case for $\gamma_0=1$,
but also confirms our estimation that $(\tilde w_0, \tilde w_1)$ differs with its asymptotic solution
by an order of $O(s e^{2 s})$.
\subsection{Case E2}
In this case, $\gamma_0=-1$ and $-3<\gamma_1<1$.
As explained in the beginning of Section \ref{sec-verify}, the fine structure of the E2 case can be obtained from the E1 case.
For convenience, the fine structure of the E2 case is listed below explicitly
\begin{eqnarray}
\left\{
\begin{array}{l}
2 w_0(r) \xlongrightarrow{r \rightarrow 0} -\ln (r) -\ln \left(-2 s+ a_{E2} \right)\\
2 w_1(r) \xlongrightarrow{r \rightarrow 0} \gamma_1 \ln (r)+b_{E2}
\end{array}
\right. , \label{Asymp-E2}
\end{eqnarray}
where
\begin{eqnarray}
&&a_{E2}=\frac{1}{2} \psi(\frac{3+\gamma_1}{8})+\frac{1}{2} \psi(\frac{5-\gamma_1}{8}) -\gamma_{\text{eu}} +4 \ln 2 ,\nonumber\\
&&b_{E2}=-\ln \left( 2^{2 \gamma_1}
\frac{\Gamma(\frac{\gamma_1+3}{4}) \left( \Gamma(\frac{\gamma_1+3}{8}) \right)^2}
{ \Gamma(\frac{1-\gamma_1}{4}) \left(\Gamma(\frac{5-\gamma_1}{8}) \right)^2 } \right).\nonumber
\end{eqnarray}
Please also recall that $s=\ln (r)$ and $\psi$ is the digamma function. Note $b_{E2}=\rho_1|_{\gamma_0=-1}$.
\subsection{Case E3}
In this case $\gamma_1=\gamma_0-2$ and $-1<\gamma_0<3$.
This subsection will numerically verify the fine structure of the E3 case
\begin{eqnarray}
\left\{
\begin{array}{l}
2 w_0(r)+ 2 w_1(r) \xlongrightarrow{r \rightarrow 0} 2(\gamma_0-1)\ln (r) +a_{E3}\\
2 w_1(r)- 2 w_0(r) \xlongrightarrow{r \rightarrow 0} -2 \ln (r)-\ln \left( 4 (s+b_{E3})^2 \right)
\end{array}
\right. , \label{Asymp-E3}
\end{eqnarray}
where
\begin{eqnarray}
&&a_{E3}=4(1-\gamma_0) \ln 2-4 \ln \left( \Gamma \left( \frac{1+\gamma_0}{4}\right) \right)+
4 \ln \left( \Gamma \left( \frac{3-\gamma_0}{4}\right) \right), \nonumber\\
&&b_{E3}=-\frac{1}{4}\psi\left(\frac{3-\gamma_0}{4}\right)
-\frac{1}{4}\psi\left(\frac{\gamma_0-3}{4}\right) +\frac{1}{3-\gamma_0}+\frac{\gamma_{EU}}{2}
-2 \ln(2).
\end{eqnarray}
Note that $s=\ln (r)$ and $\psi$ is the digamma function.
Also, we should notice
\begin{eqnarray}
a_{E3}
&=&\lim_{\gamma_1 \rightarrow \gamma_0-2} (\rho_0(\gamma_0,\gamma_1)+\rho_1(\gamma_0,\gamma_1)), \nonumber
\end{eqnarray}
where $\rho_0$ and $\rho_1$ are defined by (\ref{rhos-DEF}).
Let us take $\gamma_0=\frac{1}{3}$ as an example to verify (\ref{Asymp-E3}) numerically.
Then $(s_1^\mathbb{R},s_2^\mathbb{R})=(-2,-3)$.
Similar to the general case of Subsection \ref{GeneralCase},
the numerical integration is divided into two parts: on $r\in [1,45]$ and on $s\in [s_f,0]$.
\subsubsection{Numerical integration from $r=45$ to $r=1$}
By the truncation of (\ref{iniApprox}), the initial values at $r=45$ are obtained (only the first $50$ digits are listed)
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(45)= 5.2843098725232974899221393911204991207504443469367... \times 10^{-57} \\
w_p'(45)=-1.5004885502015739552694025310567337731833237644509... \times 10^{-56}\\
w_m(45)=- 5.9853226243288533939288654231629507224228092956986... \times 10^{-80}\\
w_m'(45)= 2.4007702224681605220078925077492026747788333343193... \times 10^{-79}
\end{array}
\right. .\label{ini-E3}
\end{eqnarray}
It is not surprising that $w_p(45)$ and $w_p'(45)$ of (\ref{ini-E3}) coincide with that of (\ref{ini-E1}) with many digits
since in the numerical examples $s_1^\mathbb{R}=-2$ for this case and $s_1^\mathbb{R}=2$ for the E1 case.
Comparing with the more accurate solution starting from $r=55$,
the errors of the initial values (\ref{ini-E3}) are obtained as shown by Table \ref{tab9}.
\begin{table}[ht]
\caption{Errors of the initial values of case E3 with $\gamma_0=\frac{1}{3}$.}
\label{tab9}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=45$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$3.04 \times 10^{-170}$ &$2.59 \times 10^{-169}$ &$4.86 \times 10^{-193}$&$4.71\times 10^{-192}$ \\
| Relative Error | &$5.76\times 10^{-114}$ &$1.73 \times 10^{-113}$ &$8.12 \times 10^{-114}$&$1.96\times 10^{-113}$
\end{tabular}
\end{table}
Numerically integrating the tt* equation (\ref{wpwm}) from $r=45$ to $r=1$
by the Gauss-Legendre method with parameters as same as in Subsection \ref{GeneralCase},
the values of $w_p$, $w_p'$, $w_m$ and $w_m'$ at $r=1$ are obtained
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(1)= 3.8027004168653915145363303284447255846983739527888...\times 10^{-2} \\
w_p'(1)=-1.2469806975938122928142121636698878096900701362539...\times 10^{-1}\\
w_m(1)= -1.0071686775204061495316019356342162460012952192431...\times 10^{-2}\\
w_m'(1)= 4.3926896299159549125370306923225572137558540540015....\times 10^{-2}
\end{array}
\right. .\label{values-E3-1}
\end{eqnarray}
Comparing with the more accurate solution starting from $r=55$,
the errors of (\ref{values-E3-1}) are obtained as shown by Table \ref{tab10}.
\begin{table}[ht]
\caption{Errors of the numerical solution at $r=1$ of case E3 with $\gamma_0=\frac{1}{3}$.}
\label{tab10}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=1$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$4.37 \times 10^{-115}$ &$1.42 \times 10^{-114}$ &$1.35 \times 10^{-115}$&$5.76\times 10^{-115}$ \\
| Relative Error | &$1.15\times 10^{-113}$ &$1.14 \times 10^{-113}$ &$1.34 \times 10^{-113}$&$1.31\times 10^{-113}$
\end{tabular}
\end{table}
\subsubsection{Near $r=0$}
Near $r=0$, we still use the transformation (\ref{transform-general}).
So the differential equations for $\tilde w_0$ and $\tilde w_1$ are also (\ref{tu0tu1}).
We expect $\tilde w_0$ and $\tilde w_1$ are of order $o(s)$.
Also considering $-1<\gamma_0<3$ and $\gamma_1=\gamma_0-2$, we get the primary truncation of (\ref{tu0tu1}) near
$s=-\infty$ for the E3 case:
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{1}{4} \frac{ d^2\tilde w_0^{(0)}}{ds^2}=-e^{\tilde w_1-\tilde w_0}\\
\frac{1}{4} \frac{ d^2\tilde w_1^{(0)}}{ds^2}=e^{\tilde w_1-\tilde w_0}
\end{array}
\right. .\label{tu0tu1-trunc-E3}
\end{eqnarray}
(\ref{tu0tu1-trunc-E3}) is the truncation structure of the tt* equation for the E3 case.
By (\ref{tu0tu1-trunc-E3}) we get
\begin{eqnarray}
\left\{
\begin{array}{l}
\tilde w_0^{(0)}+\tilde w_1^{(0)}=k_{0E3}+k_{1E3} s\\
\tilde w_1^{(0)}-\tilde w_0^{(0)}=\ln \left(- \frac{k_{2E3}^2}{8 \pm 8 \cosh(k_{2E3} (s+k_{3E3}))} \right)
\end{array}
\right. .\label{SOL-trunc-E3}
\end{eqnarray}
By (\ref{Asymp-E3}) and (\ref{transform-general}),
we know the asymptotics of the tt* equation corresponds to
$k_{0E3}=a_{E1}$, $k_{1E3}=0$, $k_{2E3} \rightarrow 0$ and $k_{3E2}=b_{E1}$.
In the truncation from (\ref{tu0tu1}) to (\ref{tu0tu1-trunc-E3}),
the neglected terms for the differential equation of $\tilde w_0+\tilde w_1$
are $e^{2 \tilde w_0+2 (\gamma_0+1)s}$ and $e^{-2 \tilde w_1+2 (1-\gamma_1)s}$,
which are of order $O(s^2 e^{2(\gamma_0+1) s})$ and $O(s^{-2} e^{2(\gamma_0+1) s})$.
Similarly, the neglected terms for the differential equation of $\tilde w_1$ are also
of orders $O(s^{-2} e^{2(3-\gamma_0) s})$ and $O(s^{-2} e^{2(\gamma_0+1) s})$.
In the current numerical experiment, $\gamma_0=\frac{1}{3}$.
Therefore, the difference between the asymptotic solution and the exact solution is of order $O(s^2 e^{\frac{8}{3} s})$.
So, we should do high-precision numerical integration from $s=0$ to about $s=s_f=-90$
since $90^2 \times e^{\frac{8}{3} \times (-90)} \approx 4.76 \times 10^{-101}$.
Just as the general case,
the values of $\tilde w_0$, $\frac{ d\tilde w_0}{ds}$, $\tilde w_1$ and $\frac{ d\tilde w_1}{ds}$ at $s=0$
are obtained by formula (\ref{ini-s0-General}).
Then, integrating (\ref{tu0tu1}) numerically by the Gauss-Legendre method, the high-precision numerical solution is obtained.
Comparing it with the more accurate numerical solution starting from $r=55$,
the errors of the numerical solution are obtained.
\begin{table}[ht]
\caption{Errors of the numerical solution at $s=-90$ for the E3 case with $\gamma_0=\frac{1}{3}$.}
\label{tab11}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$s=-90$ & $\tilde w_0$ & $\frac{d\tilde w_0}{ds}$ & $\tilde w_1$ &$\frac{d \tilde w_1}{ds}$\\
\hline
| Absolute Error | &$1.30 \times 10^{-110}$ &$2.95 \times 10^{-112}$ &$1.41 \times 10^{-110}$&$3.08\times 10^{-112}$ \\
| Relative Error | &$2.74 \times 10^{-111}$ &$2.66 \times 10^{-110}$ &$2.51 \times 10^{-111}$&$2.77\times 10^{-110}$\\
\end{tabular}
\end{table}
Table \ref{tab11} shows our numerical solution is accurate as we expect.
Table \ref{tab12} shows how good the asymptotic solution (\ref{Asymp-E3}) is.
\begin{table}[ht]
\caption{Approximate derivation from the asymptotic solution for the E3 case with $\gamma_0=\frac{1}{3}$.}
\label{tab12}
\centering
{\small
\begin{tabular}[h]{ c|c c c c c c}
\hline \hline
$s$ & $-15$ & $-30$ & $-45$ &$-60$ &$-75$& $-90$\\
\hline
$\ln(\tilde w_0+\tilde w_1-a_{E3})$ &$-34.5568$ &$-73.2186$&$-112.424$&$-151.857$&$-191.415$&$-231.054$ \\
$\ln\left(\tilde w_0-\tilde w_1-\ln\left(4 (s+b_{E3})^2\right) \right)$ &$-34.5556$ &$-73.2183$ &$-112.424$&$-151.857$&$-191.415$&$-231.054$
\end{tabular}
}
\end{table}
Table \ref{tab12} not only numerically verifies the asymptotics of the E3 case for $\gamma_0=\frac{1}{3}$,
but also confirms our estimation that $\tilde w_0+\tilde w_1$ and $\tilde w_1-\tilde w_0$ deviate from their asymptotics
by an order of $O(s^2 e^{\frac{8}{3} s})$.
More detailed analysis shows that $\tilde w_0$ and $\tilde w_1$ deviate from their asymptotics
by an order of $O(s^2 e^{\frac{8}{3} s})$ and an order of $O(e^{\frac{8}{3} s})$, respectively.
\subsection{Case V1}
In this case, $\gamma_0=3$ and $\gamma_1=1$.
This subsection is devoted to verify the fine structure of the V1 case
\begin{eqnarray}
\left\{
\begin{array}{l}
2 w_0(r) \xlongrightarrow{r \rightarrow 0} 3 \ln (r)+\ln \left( P_3\right) \\
2 w_0(r)+ 2 w_1(r) \xlongrightarrow{r \rightarrow 0} 4 \ln(r)+ \ln \left( P_4 \right)
\end{array}
\right. , \label{Asymp-V1}
\end{eqnarray}
where
{\small
\begin{eqnarray}
\hspace*{-0.5cm}&&P_3=-\frac{4}{3} (s-\ln 4)^3-4 \gamma_{eu} (s-\ln 4)^2-4 \gamma_{eu}^2 (s-\ln 4)-\frac{1}{24} \zeta(3)-\frac{4}{3} \gamma_{eu}^3,
\label{P3}\\
\hspace*{-0.5cm}&&P_4=\frac{4}{3} (s-\ln 4)^4+ \frac{16 }{3}\gamma_{eu} (s-\ln 4)^3+8 \gamma_{eu}^2 (s-\ln 4)^2
+(\frac{16\gamma_{eu}^3}{3} -\frac{\zeta(3)}{12}) (s-\ln 4)-\frac{ \gamma_{eu} \zeta(3)}{12}+\frac{4\gamma_{eu}^4 }{3}.
\label{P4}
\end{eqnarray}
}
Note that $s=\ln (r)$.
$(s_1^\mathbb{R},s_2^\mathbb{R}) =(4,-6)$ by (\ref{ConnectFormula}).
Similar to the general case of Subsection \ref{GeneralCase},
the numerical integration is divided into two parts: on $r\in [1,45]$ and on $s\in [s_f,0]$.
\subsubsection{Numerical integration from $r=45$ to $r=1$}
By the truncation of (\ref{iniApprox}), the initial values at $r=45$ are obtained (only the first $50$ digits are listed)
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(45)= -1.0568619745046594979844278782240998241500888693873... \times 10^{-56}\\
w_p'(45)= 3.0009771004031479105388050621134675463666475289019... \times 10^{-56}\\
w_m(45)= -1.1970645248657706787857730846325898673892151885992... \times 10^{-79}\\
w_m'(45)= 4.8015404449363210440157850154984037759705748926074... \times 10^{-79}
\end{array}
\right. .\label{ini-V1}
\end{eqnarray}
Comparing with the more accurate solution starting from $r=55$,
the errors of the initial values (\ref{ini-V1}) are obtained as shown by Table \ref{tab13}.
\begin{table}[ht]
\caption{Errors of the initial values of case V1.}
\label{tab13}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=45$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$2.43 \times 10^{-169}$ &$2.07 \times 10^{-168}$ &$3.89 \times 10^{-192}$&$3.77\times 10^{-191}$ \\
| Relative Error | &$2.30\times 10^{-113}$ &$6.91 \times 10^{-113}$ &$3.25 \times 10^{-113}$&$7.85\times 10^{-113}$
\end{tabular}
\end{table}
Numerically integrating the tt* equation (\ref{wpwm}) from $r=45$ to $r=1$
by the Gauss-Legendre method with parameters as same as the ones in Subsection \ref{GeneralCase},
the values of $w_p$, $w_p'$, $w_m$ and $w_m'$ at $r=1$ are obtained
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(1)= -7.5811708202722819337886291345224915096864160866088...\times 10^{-2} \\
w_p'(1)= 2.4764894905832982616275785124301997778251205645956...\times 10^{-1}\\
w_m(1)= -1.8985818420083245736824441481547286887104902789335...\times 10^{-2}\\
w_m'(1)= 8.0472024534463364925338502074404317836916130555680....\times 10^{-2}
\end{array}
\right. .\label{values-V1-1}
\end{eqnarray}
Comparing with the more accurate solution starting from $r=55$,
the errors of (\ref{values-V1-1}) are obtained as shown by Table \ref{tab14}.
\begin{table}[ht]
\caption{Errors of the numerical solution at $r=1$ of case V1.}
\label{tab14}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=1$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$3.47 \times 10^{-114}$ &$1.12 \times 10^{-113}$ &$9.71 \times 10^{-115}$&$3.94\times 10^{-114}$ \\
| Relative Error | &$4.58\times 10^{-113}$ &$4.54 \times 10^{-113}$ &$5.11 \times 10^{-113}$&$4.89\times 10^{-113}$
\end{tabular}
\end{table}
\subsubsection{Near $r=0$}
Near $r=0$, the transformation is still (\ref{transform-general}).
Hence, the differential equations for $\tilde w_0$ and $\tilde w_1$ are also (\ref{tu0tu1}).
Now, $(\gamma_0,\gamma_1)=(3,1)$ and we expect $\tilde w_0$ and $\tilde w_1$ are of order $o(s)$.
So the primary truncation of (\ref{tu0tu1}) near $s=-\infty$ for the V1 case is
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{1}{4} \frac{ d^2\tilde w_0^{(0)}}{ds^2}=-e^{\tilde w_1^{(0)}-\tilde w_0^{(0)}}\\
\frac{1}{4} \frac{ d^2\tilde w_1^{(0)}}{ds^2}=e^{\tilde w_1^{(0)}-\tilde w_0^{(0)}}-e^{-2 \tilde w_1^{(0)}}
\end{array}
\right. .\label{tu0tu1-trunc-V1}
\end{eqnarray}
(\ref{tu0tu1-trunc-V1}) is the truncation structure of the tt* equation for the V1 case.
Let
$$\tilde w_p^{(0)}= w_0^{(0)}+ w_1^{(0)}.$$
Then, we have
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{1}{4} \frac{ d^2\tilde w_0^{(0)}}{ds^2}=-e^{\tilde w_p^{(0)}-2 \tilde w_0^{(0)}}\\
\frac{1}{4} \frac{ d^2\tilde w_p^{(0)}}{ds^2}=-e^{-2 \tilde w_p^{(0)}+2 \tilde w_0^{(0)}}
\end{array}
\right. .\label{tu0tu1-trunc1-V1}
\end{eqnarray}
Unlike the cases discussed before,
we have not achieved the general solution of (\ref{tu0tu1-trunc1-V1}).
Anyhow, Equation (\ref{tu0tu1-trunc1-V1}) itself deserves an independent investigation. Let us leave it as a future work.
Surprisingly, a two parameter family of explicit solutions of (\ref{tu0tu1-trunc1-V1}) can be constructed
and the asymptotic solution near $r=0$ is just among them!
By the hint of the asymptotic solution and for the convenience of comparison,
we seek the solutions of (\ref{tu0tu1-trunc1-V1}) with form
\begin{eqnarray}
\left\{
\begin{array}{l}
\tilde w_0^{(0)}= \ln \left( \tilde{a}_3 (s-\ln 4)^3+\tilde{a}_2 (s-\ln 4)^2+\tilde{a}_1 (s-\ln 4)+\tilde{a}_0 \right)\\
\tilde w_p^{(0)}= \ln \left(\tilde{b}_4 (s-\ln 4)^4+ \tilde{b}_3 (s-\ln 4)^3+\tilde{b}_2 (s-\ln 4)^2+\tilde{b}_1 (s-\ln 4)+\tilde{b}_0 \right) \nonumber
\end{array}
\right. . \label{formAnsaz}
\end{eqnarray}
There are only 2 sets of solutions that has form (\ref{formAnsaz}).
Set A:
\begin{eqnarray}
&&\tilde{a}_3=\frac{4}{3}, \quad \tilde{b}_4=\frac{4}{3}, \nonumber\\
&&\tilde{a}_1=\frac{1}{4}\tilde{a}_2^2, \quad \tilde{b}_3=\frac{4}{3} \tilde{a}_2, \quad \tilde{b}_2=\frac{1}{2} \tilde{a}_2^2,\nonumber\\
&&\tilde{b}_1=\frac{1}{8}(\tilde{a}_2^3-16 \tilde{a}_0), \quad \tilde{b}_0=\frac{1}{64} (\tilde{a}_2^4-32 \tilde{a}_0 \tilde{a}_2). \nonumber
\end{eqnarray}
Set B:
\begin{eqnarray}
&&\tilde{a}_3=-\frac{4}{3}, \quad \tilde{b}_4=\frac{4}{3}, \nonumber\\
&&\tilde{a}_1=-\frac{1}{4}\tilde{a}_2^2, \quad \tilde{b}_3=-\frac{4}{3} \tilde{a}_2, \quad \tilde{b}_2=\frac{1}{2} \tilde{a}_2^2,\nonumber\\
&&\tilde{b}_1=\frac{1}{8}(16 \tilde{a}_0-\tilde{a}_2^3), \quad \tilde{b}_0=\frac{1}{64} (\tilde{a}_2^4-32 \tilde{a}_0 \tilde{a}_2). \nonumber
\end{eqnarray}
The asymptotic solution is in Set B with
\begin{eqnarray}
&&\tilde{a}_2=-4 \gamma_{eu}, \nonumber\\
&&\tilde{a}_0=-\frac{1}{24} \zeta(3)-\frac{4}{3} \gamma_{eu}^3. \nonumber
\end{eqnarray}
The error of the truncation from (\ref{tu0tu1}) to (\ref{tu0tu1-trunc-V1})
is caused by the term $e^{2 \tilde w_0 +8 s}$, which is of order $O(s^6 e^{8s})$.
So we set $s_f=-32$ since $(-32)^6 e^{8\times (-32)} \approx 7.1 \times 10^{-103}$
has been smaller than our precision goal.
Integrating (\ref{tu0tu1}) numerically by the Gauss-Legendre method, the high-precision numerical solution is obtained.
Comparing it with the more accurate numerical solution starting from $r=55$,
the errors of the numerical solution are obtained.
\begin{table}[ht]
\caption{Errors of the numerical solution at $s=-32$ for the V1 case.}
\label{tab15}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$s=-32$ & $\tilde w_0$ & $\frac{d\tilde w_0}{ds}$ & $\tilde w_1$ &$\frac{d \tilde w_1}{ds}$\\
\hline
| Absolute Error | &$1.14 \times 10^{-109}$ &$1.49 \times 10^{-110}$ &$3.94 \times 10^{-109}$&$4.77\times 10^{-110}$ \\
| Relative Error | &$1.06 \times 10^{-110}$ &$1.62 \times 10^{-109}$ &$1.13 \times 10^{-109}$&$1.57\times 10^{-108}$\\
\end{tabular}
\end{table}
Table \ref{tab15} shows our numerical solution is accurate as we expect.
Table \ref{tab16} shows how good the asymptotic solution (\ref{Asymp-V1}) is.
\begin{table}[ht]
\caption{Approximate derivation from the asymptotic solution for the V1 case.}
\label{tab16}
\centering
\begin{tabular}[h]{ c| c c c c c c}
\hline \hline
$s$ & $-7$ & $-12$ &$-17$ &$-22$& $-27$ & $-32$\\
\hline
$\ln(\tilde w_0-\ln(P_3))$ &$-45.6682$&$-82.7772$&$-120.834$&$-159.368$&$-198.191$
&$-237.207$ \\
$\ln\left(\tilde w_0+\tilde w_1-\ln (P4) \right)$
&$-45.6691$ &$-82.7775$&$-120.834$&$-159.368$&$-198.191$ & $-237.207$
\end{tabular}
\end{table}
Table \ref{tab16} not only numerically verifies the asymptotics of the V1 case,
but also confirms our estimation that $\tilde w_0$ and $\tilde w_1+\tilde w_0$ differ from their asymptotics
by an order of $O(s^6 e^{8 s})$.
\subsection{Case V2}
In this case $(\gamma_0,\gamma_1)=(-1,1)$.
By the connection formula (\ref{ConnectFormula}), we have
$(s_1^\mathbb{R}, s_2^\mathbb{R})=(0,2)$.
$s_1^\mathbb{R}=0$ means $w_1=-w_0$ at $r=\infty$.
This leads to $w_1 \equiv -w_0$ for $r \in (0 ,\infty)$, considering (\ref{TT-2}).
Let
$$ w=w_0=-w_1.$$
Then, the differential equation for $w$ is
\begin{eqnarray}
\frac{1}{2} (\frac{d^2}{dr^2}+ \frac{1}{r}\frac{d}{dr}) w=e^{4 w}-e^{-4 w}, \nonumber
\end{eqnarray}
which is the radical reduction of the sinh-Gordon equation.
For convenience, we also give the fine structure of the V2 case
\begin{eqnarray}
2 w(r) \xlongrightarrow{r \rightarrow 0} -\ln (r) -\ln\left(-2 s -2 \gamma_{eu}+2 \ln 2\right) . \label{Asymp-V2}
\end{eqnarray}
Near $r=0$, $2 w(r)$ differs from its asymptotics by an order of $O(s^2 e^{4 s})$.
\subsection{Case V3}
In this case, $(\gamma_0,\gamma_1)=(-1,-3)$. Thus, $(s_1^\mathbb{R},s_2^\mathbb{R})=(-4,-6)$ by (\ref{ConnectFormula}).
As explained in the beginning of Section \ref{sec-verify},
the fine structure of the V3 case can be read out from the V1 case.
For convenience, we list the fine structure of the V3
\begin{eqnarray}
\left\{
\begin{array}{l}
2 w_1(r) \xlongrightarrow{r \rightarrow 0} -3 \ln (r)-\ln \left( P_3\right) \\
2 w_0(r)+ 2 w_1(r) \xlongrightarrow{r \rightarrow 0} -4 \ln(r)- \ln \left( P_4 \right)
\end{array}
\right. , \label{Asymp-V3}
\end{eqnarray}
where $P_3$ and $P_4$ are defined by (\ref{P3}) and (\ref{P4}).
\section{Out of the curved triangle: generalizing the connection formula and the fine structure \label{CONJ}}
First, let us divide the real plane of $(s_1^\mathbb{R}, s_2^\mathbb{R})$ into $19$ parts:
regions $\Omega_0$, $\Omega_1$, $\Omega_2$, $\Omega_3$, $\Omega_4$, $\Omega_5$, $\Omega_6$;
edges E1, E2, E3, $E_1^U$, $E_2^U$, $E_1^D$, $E_2^D$, $E_3^R$, $E_3^L$;
and vertices V1, V2, V3. See Figure \ref{fig-3} for the details.
Note the boundaries of $\Omega_i$ are
line $s_2^\mathbb{R}=2 s_1^\mathbb{R}+2$, line $s_2^\mathbb{R}=-2 s_1^\mathbb{R}+2$
and parabola $s_2^\mathbb{R}=-\frac{1}{4} \left( s_1^\mathbb{R} \right)^2 -2 $.
\input{Figure3.tikz}
By the connection formula (\ref{ConnectFormula}) (also see Figure \ref{fig-2}), on the Stokes data side,
the solutions studied in Theorem (\ref{thm-GIL-1}) are those associated with a point in the region $\Omega_0$,
on the edges E1, E2, E3 or at the vertices V1, V2, V3.
Those solutions are all smooth for $r \in (0,\infty)$.
Let us consider the case
that $(s_1^\mathbb{R}, s_2^\mathbb{R})$ lies out of the curved triangular.
Then the corresponding $w_0(r)$, $w_1(r)$ or both of them must develop to singularity
somewhere as $r$ decreases from $r=\infty$.
Numerical experiments show there is a cut around each singularity.
But we have evidences that hint these singularities and cuts are artificial:
they can be avoided by choosing appropriate variables.
For example, if we use variables $v_0=e^{2 w_0}$ and $v_1=e^{2 w_1}$,
then $v_0$ and $v_1$ will have no cuts near $r>0$.
$v_0$ or $v_1$ may still have singularities,
i.e., in general $v_0$ and $v_1$ are not the final smooth variables.
Fortunately, we could find two smooth variables for each part of Figure \ref{fig-3},
see Conjecture \ref{Conj}.
From this point of view, Theorem (\ref{thm-GIL-1}) studies only those solutions
that have ``positiveness" property so that after taking logarithm they are still real.
\subsection{The conjecture}
The fine structures for the cases of $\Omega_0$, E1, E2, E3, V1, V2 and V3
have been rigorously proven in \cite{GIL-3} and numerically verified in Section \ref{sec-verify}.
So the following conjecture only deal with the other remaining $12$ cases:
$\Omega_1$, $\Omega_2$, $\Omega_3$, $\Omega_4$, $\Omega_5$, $\Omega_6$, $E_1^U$, $E_2^U$, $E_1^D$, $E_2^D$, $E_3^R$ and $E_3^L$.
Similar to the explanation in the beginning of Section \ref{sec-verify}, the formulae of $\Omega_3$, $\Omega_4$, $E_1^U$,
$E_2^D$ and $E_3^L$ are symmetrical to that of $\Omega_1$, $\Omega_6$, $E_2^U$,
$E_1^D$ and $E_3^R$, respectively.
But, for convenience we will list all formulae for the $12$ cases.
\begin{conjecture} \label{Conj}
Let the inverse of connection formula (\ref{ConnectFormula}) be
\begin{eqnarray}
\left\{
\begin{array}{l}
\gamma_0=\frac{4}{\pi}\arccos\left(-\frac{1}{4}s_1^\mathbb{R}+\frac{1}{4}\sqrt{8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R}} \right)-1\\
\gamma_1=\frac{4}{\pi}\arccos\left(-\frac{1}{4}s_1^\mathbb{R}-\frac{1}{4}\sqrt{8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R}} \right)-3
\end{array}
\right. ,\label{CF-Inverse}
\end{eqnarray}
where the values of the $\arccos$ terms may be complex and should be given by their principal values.
Suppose $w_0(r)$ and $w_1(r)$ have asymptotic (\ref{InfAsymp}) at $r=\infty$
and that $(\gamma_0, \gamma_1)$ is calculated from (\ref{CF-Inverse}).
Define $(\rho_0,\rho_1)$ by (\ref{rhos-DEF}) and $s=\ln (r)$.
Denote $\gamma_i^\mathbb{R}=\Re(\gamma_i)$, $\gamma_i^\mathbb{I}=\Im(\gamma_i)$, $\rho_i^\mathbb{R}=\Re(\rho_i)$, $\rho_i^\mathbb{I}=\Im(\rho_i)$, $i=0,1$.
Then, the characteristics of a solution parameterized by a point in region $\Omega_i$, $i=1,\cdots,6$, are the following.
\begin{itemize}
\item[$\Omega_1:$] $\sqrt{8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R}} \in \mathbb{R}$,
$\gamma_0 \in \mathbb{R}$, $\gamma_1 \not\in \mathbb{R}$.
$e^{2 w_0(r)}$ and $e^{2 w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{l}
e^{2 w_0} \xlongrightarrow{ s \rightarrow -\infty} e^{\gamma_0 s+\rho_0} \\
e^{2 w_1} \xlongrightarrow{ s \rightarrow -\infty} 2\, \Re \left( e^{\gamma_1 s+\rho_1} \right)
\end{array}
\right. .
\]
\item[$\Omega_2:$] $\sqrt{8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R}} \in \mathbb{R}$,
$\gamma_0 \not\in \mathbb{R}$, $\gamma_1 \not\in \mathbb{R}$.
$e^{-2 w_0(r)}$ and $e^{2 w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{l}
e^{-2 w_0} \xlongrightarrow{ s \rightarrow -\infty} 2\, \Re \left( e^{-\gamma_0 s-\rho_0} \right) \\
e^{2 w_1} \xlongrightarrow{ s \rightarrow -\infty} 2\, \Re \left( e^{\gamma_1 s+\rho_1} \right)
\end{array}
\right. .
\]
\item[$\Omega_3:$] $\sqrt{8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R}} \in \mathbb{R}$,
$\gamma_0 \not\in \mathbb{R}$, $\gamma_1 \in \mathbb{R}$.
$e^{-2 w_0(r)}$ and $e^{-2 w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{l}
e^{-2 w_0} \xlongrightarrow{ s \rightarrow -\infty} 2\, \Re \left( e^{-\gamma_0 s-\rho_0} \right) \\
e^{-2 w_1} \xlongrightarrow{ s \rightarrow -\infty} e^{-\gamma_1 s-\rho_1}
\end{array}
\right. .
\]
\item[$\Omega_4:$] $\sqrt{8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R}} \in \mathbb{R}$,
$\gamma_0 \not\in \mathbb{R}$, $\gamma_1 \not\in \mathbb{R}$.
$e^{-2w_1(r)}$ and $e^{-2w_0(r)-2w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{lll}
e^{-2w_1} &\xlongrightarrow{ s \rightarrow -\infty}& e^{-\gamma_1^{\mathbb{R}} s} \left( \frac{8 e^{-\rho_0^{\mathbb{R}}}}{(\gamma_0^\mathbb{I}-\gamma_1^\mathbb{I})^2}
\cos \left(\gamma_0^{\mathbb{I} } s+\rho_0^{\mathbb{I}} \right)
+2\, e^{-\rho_1^{\mathbb{R}}} \cos\left( \gamma_1^{\mathbb{I}}s+\rho_1^{\mathbb{I}}\right) \right)\\
e^{-2w_0-2w_1} &\xlongrightarrow{ s \rightarrow -\infty}& e^{-(\gamma_0^\mathbb{R}+\gamma_1^\mathbb{R})s}
\bigg\{ 2\,e^{-\rho_0^\mathbb{R}-\rho_1^\mathbb{R}} \frac{(\gamma_0^\mathbb{I}+\gamma_1^\mathbb{I})^2}{(\gamma_0^\mathbb{I}-\gamma_1^\mathbb{I})^2}
\cos\left( (\gamma_0^\mathbb{I}-\gamma_1^\mathbb{I})s+\rho_0^\mathbb{I}-\rho_1^\mathbb{I} \right) \\
&& +\frac{16 e^{-2 \rho_0^\mathbb{R}} (\gamma_0^\mathbb{I})^2}{(\gamma_0^\mathbb{I}-\gamma_1^\mathbb{I})^4}
+e^{-2 \rho_1^\mathbb{R}} (\gamma_1^\mathbb{I})^2
+2\,e^{-\rho_0^\mathbb{R}-\rho_1^\mathbb{R}} \cos\left( (\gamma_0^\mathbb{R}+\gamma_1^\mathbb{R})s+\rho_0^\mathbb{I}+\rho_1^\mathbb{I}\right) \bigg\}
\end{array}
\right. .
\]
\item[$\Omega_5:$] $\sqrt{8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R}} \not\in \mathbb{R}$,
$\gamma_0 \not\in \mathbb{R}$, $\gamma_1 \not\in \mathbb{R}$.
$e^{2 w_0(r)}$ and $e^{-2 w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{l}
e^{2 w_0} \xlongrightarrow{ s \rightarrow -\infty}
2\, \Re \left( e^{\gamma_0 s+\rho_0} \right) \\
e^{-2 w_1} \xlongrightarrow{ s \rightarrow -\infty} 2\, \Re \left( e^{-\gamma_1 s-\rho_1} \right)
\end{array}
\right. .
\]
\item[$\Omega_6:$] $\sqrt{8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R}} \in \mathbb{R}$,
$\gamma_0 \not\in \mathbb{R}$, $\gamma_1 \not\in \mathbb{R}$.
$e^{2w_0(r)}$ and $e^{2w_0(r)+2w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{lll}
e^{2w_0} &\xlongrightarrow{ s \rightarrow -\infty}& e^{\gamma_0^{\mathbb{R}} s} \left( \frac{8 e^{\rho_1^{\mathbb{R}}}}{(\gamma_0^\mathbb{I}-\gamma_1^\mathbb{I})^2}
\cos \left(\gamma_1^{\mathbb{I} } s+\rho_1^{\mathbb{I}} \right)
+2\, e^{\rho_0^{\mathbb{R}}} \cos\left( \gamma_0^{\mathbb{I}}s+\rho_0^{\mathbb{I}}\right) \right) \\
e^{2w_0+2w_1} &\xlongrightarrow{ s \rightarrow -\infty}& e^{(\gamma_0^\mathbb{R}+\gamma_1^\mathbb{R})s}
\bigg\{ 2\,e^{\rho_0^\mathbb{R}+\rho_1^\mathbb{R}} \frac{(\gamma_0^\mathbb{I}+\gamma_1^\mathbb{I})^2}{(\gamma_0^\mathbb{I}-\gamma_1^\mathbb{I})^2}
\cos\left( (\gamma_0^\mathbb{I}-\gamma_1^\mathbb{I})s+\rho_0^\mathbb{I}-\rho_1^\mathbb{I} \right) \\
&& + \frac{16 e^{2 \rho_1^\mathbb{R}} (\gamma_1^\mathbb{I})^2}{(\gamma_0^\mathbb{I}-\gamma_1^\mathbb{I})^4}
+e^{2 \rho_0^\mathbb{R}} (\gamma_0^\mathbb{I})^2
+2\,e^{\rho_0^\mathbb{R}+\rho_1^\mathbb{R}} \cos\left( (\gamma_0^\mathbb{R}+\gamma_1^\mathbb{R})s+\rho_0^\mathbb{I}+\rho_1^\mathbb{I}\right) \bigg\}
\end{array}
\right. .
\]
\end{itemize}
On the edges, $ 8+\left(s_1^\mathbb{R}\right)^2+4 s_2^\mathbb{R} $ is always non-negative.
Define
\begin{eqnarray*}
&& b_1= \frac{1}{2} \psi(\frac{3-\gamma_0}{8})+\frac{1}{2} \psi(\frac{5+\gamma_0}{8}) -\gamma_{\text{eu}} +4 \ln 2,\\
&& b_2= \frac{1}{2} \psi(\frac{3+\gamma_1}{8})+\frac{1}{2} \psi(\frac{5-\gamma_1}{8}) -\gamma_{\text{eu}} +4 \ln 2,\\
&& b_3=-\frac{1}{4} \psi(\frac{3-\gamma_0}{4}) -\frac{1}{4}\psi(\frac{\gamma_0-3}{4})
+\frac{1}{3-\gamma_0}-2 \ln 2+\frac{\gamma_{eu} }{2}.
\end{eqnarray*}
Then, the characteristics of a solution parameterized by a point on an edge are the following.
\begin{itemize}
\item[$E_1^U:$]$\gamma_0 \not\in \mathbb{R}$, $\gamma_1 =1$, $\gamma_0^\mathbb{R}=-1 $, $\rho_0 \not\in \mathbb{R}$
and $\rho_1$ is not defined.
$e^{-2w_0(r)}$ and $e^{2w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{l}
e^{-2 w_0} \xlongrightarrow{ s \rightarrow -\infty} 2\, \Re \left( e^{-\gamma_0 s-\rho_0} \right) \\
e^{2w_1(r)} \xlongrightarrow{ s \rightarrow -\infty} -2 s+ b_1
\end{array}
\right. .
\]
\item[$E_2^U:$]$\gamma_0 =-1$, $\gamma_1 \not\in \mathbb{R}$, $\gamma_1^\mathbb{R}=1$, $\rho_1 \not\in \mathbb{R}$
and $\rho_0$ is not defined.
$e^{-2w_0(r)}$ and $e^{2w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{l}
e^{-2 w_0} \xlongrightarrow{ s \rightarrow -\infty} -2 s+b_2\\
e^{2w_1(r)} \xlongrightarrow{ s \rightarrow -\infty} 2\, \Re \left( e^{\gamma_1 s+\rho_1} \right)
\end{array}
\right. .
\]
\item[$E_1^D:$]$\gamma_0 =3$, $\gamma_1 \not\in \mathbb{R}$, $\gamma_1^\mathbb{R}=1$, $\rho_1 \not\in \mathbb{R}$
and $\rho_0$ is not defined.
$e^{2w_1(r)}$ and $e^{2w_0(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{l}
e^{2w_0(r)} \xlongrightarrow{ s \rightarrow -\infty} e^{\gamma_0 s} \left( -\frac{8}{(\gamma_1^\mathbb{I})^2} s+d_0 -\frac{8}{(\gamma_1^\mathbb{I})^3}\cos\left( \gamma_1^\mathbb{I} s+\rho_1^\mathbb{I} \right) \right) \\
e^{2 w_1} \xlongrightarrow{ s \rightarrow -\infty} 2\, e^{\gamma_1^\mathbb{R} s+\rho_1^\mathbb{R}}
\left( \cos\left( \gamma_1^\mathbb{I} s+\rho_1^\mathbb{I} \right) + \frac{(1-\sin(\gamma_1^\mathbb{I}s+\rho_1^\mathbb{I}) )^2}{\gamma_1^\mathbb{I}s-\frac{(\gamma_1^\mathbb{I})^3}{8}d_0 +\cos(\gamma_1^\mathbb{I} s+\rho_1^\mathbb{I})} \right)
\end{array}
\right. ,
\]
where $d_0=\lim\limits_{s_1^\mathbb{R} \rightarrow 1-\frac{s_2^\mathbb{R}}{2}+0_-} 2\, e^{\rho_0^\mathbb{R}}
\left(\rho_0^\mathbb{I}+\frac{\pi}{2}\right)$.
\item[$E_2^D:$]$\gamma_0 \not\in \mathbb{R}$, $\gamma_1=-3$, $\gamma_0^\mathbb{R}=-1$, $\rho_0 \not\in \mathbb{R}$
and $\rho_1$ is not defined.
$e^{-2w_0(r)}$ and $e^{-2w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{
\begin{array}{l}
e^{-2 w_0} \xlongrightarrow{ s \rightarrow -\infty} 2\, e^{-\gamma_0^\mathbb{R} s-\rho_0^\mathbb{R}}
\left( \cos\left( \gamma_0^\mathbb{I} s+\rho_0^\mathbb{I} \right) + \frac{8(1+\sin(\gamma_0^\mathbb{I}s+\rho_0^\mathbb{I}) )^2}{-8\gamma_0^\mathbb{I}s+ (\gamma_0^\mathbb{I})^3 \tilde{d}_0+8 \cos(\gamma_0^\mathbb{I} s+\rho_0^\mathbb{I})} \right) \\
e^{-2w_1(r)} \xlongrightarrow{ s \rightarrow -\infty} e^{-\gamma_1 s} \left(-\frac{8}{(\gamma_0^\mathbb{I})^2} s+\tilde{d}_0+\frac{8}{(\gamma_0^\mathbb{I})^3}\cos(\gamma_0^\mathbb{I} s+\rho_0^\mathbb{I})\right)
\end{array}
\right. ,
\]
where $\tilde{d}_0=\lim\limits_{s_1^\mathbb{R} \rightarrow \frac{s_2^\mathbb{R}}{2}-1+0_+} 2\, e^{-\rho_1^\mathbb{R}}
\left( \frac{\pi}{2}-\rho_1^\mathbb{I} \right)$.
\item[
$E_3^R:$]$\gamma_0 \not\in \mathbb{R}$, $\gamma_1 \not\in \mathbb{R}$,
$\gamma_0^\mathbb{R}=3$, $\gamma_1^\mathbb{R}=1$ and $\gamma_0^\mathbb{I}=\gamma_1^\mathbb{I}$.
Both $\rho_0$ and $\rho_1$ are not defined.
$e^{2w_0(r)}$ and $e^{2w_0(r)+2w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{ \begin{array}{l}
e^{2 w_0} \xlongrightarrow{ s \rightarrow -\infty}-e^{\gamma_0^\mathbb{R} s} \left( \frac{4}{(\gamma_0^\mathbb{I})^2} (s+ \Re(b_3) ) \sin(\gamma_0^\mathbb{I} s+\theta_0)+\frac{4}{(\gamma_0^\mathbb{I})^3} \cos(\gamma_0^\mathbb{I} s+\theta_0) \right) \\
e^{2w_0+2w_1(r)} \xlongrightarrow{ s \rightarrow -\infty} e^{(\gamma_0^\mathbb{R}+\gamma_1^\mathbb{R} )s} \left( \frac{4}{(\gamma_0^\mathbb{I})^2} (s+\Re(b_3))^2
-\frac{4}{(\gamma_0^\mathbb{I})^4} \left( \cos(\gamma_0^\mathbb{I} s+\theta_0) \right)^2 \right)
\end{array}
\right. ,
\]
where $\theta=\lim\limits_{s_1^\mathbb{R} \rightarrow 2 \sqrt{-2-s_2^\mathbb{R}} +0_+} \rho_0^\mathbb{I} $.
\item[$E_3^L:$]$\gamma_0 \not\in \mathbb{R}$, $\gamma_1 \not\in \mathbb{R}$,
$\gamma_0^\mathbb{R}=-1$, $\gamma_1^\mathbb{R}=-3$ and $\gamma_0^\mathbb{I}=\gamma_1^\mathbb{I}$.
Both $\rho_0$ and $\rho_1$ are not defined.
$e^{-2w_1(r)}$ and $e^{-2w_0(r)-2w_1(r)}$ are smooth for $r \in (0,\infty)$.
Their asymptotics at $s=-\infty$ are
\[
\left\{ \begin{array}{l}
e^{-2 w_1} \xlongrightarrow{ s \rightarrow -\infty} e^{-\gamma_1^\mathbb{R} s}
\left( \frac{4}{(\gamma_1^\mathbb{I})^2} (s+ \Re(b_3) )
\sin(\gamma_1^\mathbb{I} s-\tilde{\theta}_0)
+\frac{4}{(\gamma_1^\mathbb{I})^3} \cos(\gamma_1^\mathbb{I} s-\tilde{\theta}_0) \right) \\
e^{-2w_0-2w_1(r)} \xlongrightarrow{ s \rightarrow -\infty} e^{-(\gamma_0^\mathbb{R}+\gamma_1^\mathbb{R} )s} \left( \frac{4}{(\gamma_1^\mathbb{I})^2} (s+\Re(b_3))^2
-\frac{4}{(\gamma_1^\mathbb{I})^4} \left( \cos(\gamma_1^\mathbb{I} s-\tilde{\theta}_0) \right)^2 \right)
\end{array}
\right. ,
\]
where $\tilde{\theta}_0=-\lim\limits_{s_1^\mathbb{R} \rightarrow -2 \sqrt{-2-s_2^\mathbb{R}} +0_-} \rho_1^\mathbb{I} $.
\end{itemize}
\end{conjecture}
\subsection{Verify the conjecture numerically: the $\Omega_1$ case as an example}
In this subsection, we will verify Conjecture \ref{Conj} for the $\Omega_1$ case with $(s_1^\mathbb{R}, s_2^\mathbb{R})=(2,1)$.
Then by (\ref{CF-Inverse}) we get
\begin{eqnarray}
\left\{
\begin{array}{l}
\gamma_0|_{s_1^\mathbb{R}=2, s_2^\mathbb{R}=1}=\frac{1}{3}\\
\gamma_1|_{s_1^\mathbb{R}=2, s_2^\mathbb{R}=1}=\frac{4}{\pi}\arccos(-\frac{3}{2})-3
=1+\frac{4 \mathrm{i}}{\pi}\ln(\frac{3-\sqrt{5}}{2})
\end{array}
\right. .\label{gam12-Omega1}
\end{eqnarray}
With $(s_1^\mathbb{R}, s_2^\mathbb{R})=(2,1)$, $w_0$ and $w_1$ keep real as $r$ decreasing from $r=\infty$ to $r=1$.
So we do not need adjust our numerical integration for $r>1$.
By the truncation of (\ref{iniApprox}), the initial values at $r=45$ are obtained (only the first $50$ digits are listed)
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(45)= -5.2843098725232974899221393911204991207504443469367... \times 10^{-57}\\
w_p'(45)= 1.5004885502015739552694025310567337731833237644509... \times 10^{-56}\\
w_m(45)= 1.9951075414429511313096218077209854214432475688359... \times 10^{-80}\\
w_m'(45)=-8.0025674082272017400263083591640194065100562879396... \times 10^{-80}
\end{array}
\right. .\label{ini-Omega1}
\end{eqnarray}
Comparing with the more accurate solution starting from $r=55$,
the errors of the initial values (\ref{ini-Omega1}) are obtained as shown by Table \ref{tab17}.
\begin{table}[ht]
\caption{Errors of the initial values of case $\Omega_1$ with $(s_1^\mathbb{R}, s_2^\mathbb{R})=(2,1)$.}
\label{tab17}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=45$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$3.04 \times 10^{-170}$ &$2.59 \times 10^{-169}$ &$1.62 \times 10^{-193}$&$1.57\times 10^{-192}$ \\
| Relative Error | &$5.76\times 10^{-114}$ &$1.73 \times 10^{-113}$ &$8.12 \times 10^{-114}$&$1.96\times 10^{-113}$
\end{tabular}
\end{table}
Integrating numerically the tt* equation (\ref{wpwm}) from $r=45$ to $r=1$
by the Gauss-Legendre method with parameters as same as the ones in Subsection \ref{GeneralCase},
the values of $w_p$, $w_p'$, $w_m$ and $w_m'$ at $r=1$ are obtained
\begin{eqnarray}
\left\{
\begin{array}{l}
w_p(1)= -3.8224055163443861381648888321249635590437848425393...\times 10^{-2} \\
w_p'(1)= 1.2620798170393397054252193737795545512207073701669...\times 10^{-1}\\
w_m(1)= 4.1421810495867924927295926159960489963050832028643...\times 10^{-3}\\
w_m'(1)=-1.9704834137414281607395710259152505912708048802280....\times 10^{-2}
\end{array}
\right. .\label{values-Omega1-1}
\end{eqnarray}
Comparing with the more accurate solution starting from $r=55$,
the errors of (\ref{values-V1-1}) are obtained as shown by Table \ref{tab18}.
\begin{table}[ht]
\caption{Errors of the numerical solution at $r=1$ of case $\Omega_1$ with $(s_1^\mathbb{R}, s_2^\mathbb{R})=(2,1)$.}
\label{tab18}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$r=1$& $w_p$ & $w_p'$ & $w_m$ &$w_m'$\\
\hline
| Absolute Error | &$4.42 \times 10^{-115}$ &$1.46 \times 10^{-114}$ &$6.30 \times 10^{-116}$&$3.09\times 10^{-115}$\\
| Relative Error | &$1.16\times 10^{-113}$ &$1.16 \times 10^{-113}$ &$1.52 \times 10^{-113}$&$1.57\times 10^{-113}$
\end{tabular}
\end{table}
When $r<1$, $w_0$ and $w_1$ may be complex.
As Conjecture \ref{Conj} suggests, we use $v_0$ and $v_1$
\begin{eqnarray}
\left\{
\begin{array}{l}
v_0=e^{2 w_0}\\
v_1=e^{2 w_1}
\end{array}
\right. . \label{v0v1-DEF1}
\end{eqnarray}
as dependent variables for the $\Omega_1$ case.
Then, $v_0$ and $v_1$ will be real for $r>0$.
To improve computation efficiency, we use $s=\ln(r)$ as independent variable.
Then the equations for $v_0$ and $v_1$ are
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{d^2 v_0}{ds^2}=4 e^{2 s} (v_0^3-v_1) +\frac{1}{v_0} (\frac{d v_0}{ds})^2 \\
\frac{d^2 v_1}{ds^2}=4 e^{2 s} \left( \frac{v_1^2}{v_0}-\frac{1}{v_1} \right)
+\frac{1}{v_1} (\frac{d v_1}{ds})^2
\end{array}
\right. . \label{v0v1-DEQ1}
\end{eqnarray}
The truncation structure of (\ref{v0v1-DEQ1}) should be
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{d^2 v_0^{(0)}}{ds^2}=\frac{1}{v_0^{0}} \left(\frac{d v_0^{(0)}}{ds} \right)^2 \\
\frac{d^2 v_1^{(0)}}{ds^2}=-\frac{4 e^{2 s}}{v_1^{(0)}}
+\frac{1}{v_1^{(0)}} \left(\frac{d v_1^{(0)}}{ds} \right)^2
\end{array}
\right. . \label{v0v1-trunc-DEQ1}
\end{eqnarray}
In fact, after substituting (\ref{gam12-Omega1}) to the $\Omega_1$ case of Conjecture \ref{Conj},
it becomes obvious which terms of (\ref{v0v1-DEQ1}) should be ignored.
The solution of (\ref{v0v1-trunc-DEQ1}) is known
\begin{eqnarray}
\left\{
\begin{array}{l}
v_0^{(0)}(s)= e^{a_{1\Omega_1} s+b_{1\Omega_1}} \\
v_1^{(0)}(s)=-2 e^s \frac{ \cos( a_{2\Omega_1} s+b_{2\Omega_1} ) }{a_{2\Omega_1}}
\end{array}
\right. . \label{v0v1-trunc-DEQ1-Sol}
\end{eqnarray}
Comparing (\ref{v0v1-trunc-DEQ1-Sol}) with Conjecture \ref{Conj}, we know $a_{1\Omega_1}=\gamma_0$,
$b_{1\Omega_1}=\rho_0$, $a_{2\Omega_1}=\Im (\gamma_1)$ and $b_{2\Omega_1}=\Im (\rho_1)$.
Also we note $-\frac{1}{\Im (\gamma_1)}=e^{\Re (\rho_1)}$ in the $\Omega_1$ case.
The neglected terms of the truncation from (\ref{v0v1-DEQ1}) to (\ref{v0v1-trunc-DEQ1})
are $ 4 e^{2 s} (v_0^3-v_1)$ and $4 e^{2 s} \frac{v_1^2}{v_0} $,
which are of order $O(e^{3 s})$ and $O(e^{\frac{11}{3}s})$ respectively (considering (\ref{gam12-Omega1})).
So the relative errors are both of order $O(e^{\frac{8}{3}s})$ except near the zeros of $v_1(s)$.
Since $v_0$ and $v_1$ are both small in this case, only the relative errors are relevant.
To avoid the inconvenience brought by the relative error,
we will take
\begin{eqnarray}
\left\{
\begin{array}{l}
\Delta_0(s)=|e^{2 w_0} e^{-\gamma_0 s-\rho_0}-1|\\
\Delta_1(s)=|\frac{1}{2}e^{2 w_1} e^{-\Re(\gamma_1) s-\Re(\rho_1)} -\cos(\Im(\gamma_1)s+\Im(\rho_1))|
\end{array}
\right. \label{DelDel1-DEF}
\end{eqnarray}
as the measurement of error.
So, $\Delta_0$ and $\Delta_1$ are both of order $O(e^{\frac{8}{3}s})$.
Solving $e^{\frac{8}{3}s_f}=10^{-100}$, we get $s_f \approx 86.35$. For safety and convenience, we set $s_f=-87$.
Numerical results show $v_0(s)$ has no zero for $s \in (-\infty, 0]$ but $v_1(s)$ has, just Conjecture \ref{Conj} predicts.
For the sake of numerical integration, it is better to integrate around the zeros of $v_1(s)$.
In order to keep away from the zeros of $v_1(s)$, we first compute $v_0(s+\mathrm{i} \epsilon)$ with $\epsilon=10^{-2}$
to determine the approximate zeros of $v_1(s)$ by solving $\mathrm{Re}(v_1(s+\mathrm{i} \epsilon))=0$.
Then we get the approximate zeros $s_i$ of $v_1(s)$ within the range $-87 \le s \le 0$.
The first few of them are listed as Table \ref{tab19}.
\begin{table}[ht]
\caption{The first few approximate zeros $s_i$ of $v_1(s)$ for the $\Omega_1$ case with $(s_1^\mathbb{R}, s_2^\mathbb{R})=(2,1)$.}
\label{tab19}
\centering
\begin{tabular}[h]{c|c c c c c c c c}
\hline \hline
$s_i$ & $s_1$ & $s_2$ & $s_3$ &$s_4$&$s_5$&$s_6$&$s_7$&$s_8$\\
\hline
value& $-2.506$ &$-5.069$ &$-7.633$& $-10.197$ &$-12.760$ & $-15.324$&$-17.888 $&$-20.452 $
\end{tabular}
\end{table}
Obviously, the distance between two adjacent zeros in Table \ref{tab19} is about $2.5$.
To avoid the numerical instabilities caused by those zeroes, we use a contour in the complex plane of $s$,
as shown by Figure \ref{fig-4}.
\input{Figure4.tikz}
The radius of the circles surrounding the zeroes are set to $\frac{1}{5}$.
In principle, the values of $v_i$ can be evaluated by the Cauchy's integral formula
$ v_i(s)=\frac{1}{2 \pi \mathrm{i}} \oint \frac{v_i(\xi)}{\xi-s} d\xi$.
But $v_i(\xi)$ has high-precision values only at some fixed points on the circle.
At a point other than those, interpolation must be used, which is not proper for high-precision purpose.
Since $v_i$ are periodic functions on the circle, we use the trapezoidal rule to calculate them
\begin{eqnarray}
v_i(s)=\frac{1}{2 \, n} \sum_j \frac{\tilde v_i(\theta_j)}{R e^{\mathrm{i} \theta_j}-s} R e^{\mathrm{i} \theta_j},
\quad i=0,1, \label{Trapezoidal}
\end{eqnarray}
where $R=\frac{1}{5}$ denotes the radius of the circle,
and $\tilde v_i(\theta_j)$ the value of $v_i$ at $\theta_j$ on the circle.
The distance between the adjacent $\theta_j$ is $\frac{\pi}{n}$.
Obviously, formula (\ref{Trapezoidal}) is not proper for a point near the circle.
It is why the contour has $2$ line segments in each circle. We use line segment of length $\frac{1}{10}$.
In our numerical experiments, $n$ is equal to $1000$, which is far more enough to guarantee our $100$-digits precision goal.
The plots of $v_0$ and $v_1$ is shown by Figure \ref{fig-5}.
\input{Figure5.tikz}
Table \ref{tab20} shows our numerical solution is accurate as we expect.
\begin{table}[ht]
\caption{Errors of the numerical solution at $s=-87$ for the $\Omega_1$ case with $(s_1^\mathbb{R},s_2^\mathbb{R} )=(2,1)$.}
\label{tab20}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$s=-87$ & $v_0$ & $\frac{dv_0}{ds}$ & $v_1$ &$\frac{d v_1}{ds}$\\
\hline
| Absolute Error | &$4.06 \times 10^{-125}$ &$1.31 \times 10^{-125}$ &$2.75 \times 10^{-149}$&$2.30\times 10^{-149}$ \\
| Relative Error | &$1.48 \times 10^{-112}$ &$1.43 \times 10^{-112}$ &$7.69 \times 10^{-111}$&$6.35\times 10^{-112}$
\end{tabular}
\end{table}
Table \ref{tab21} shows how good the asymptotic solution is.
\begin{table}[ht]
\caption{Approximate derivation from the asymptotic solution
for the $\Omega_1$ case with $(s_1^\mathbb{R},s_2^\mathbb{R} )=(2,1)$.}
\label{tab21}
\centering
\begin{tabular}[h]{ c| c c c c c c c}
\hline \hline
$s$ &$-27$ & $-37$ & $-47$ &$-57$ &$-67$& $-77$ & $-87$\\
\hline
$\ln(\Delta_0(s))$&$-73.2379$ &$-100.773$&$-130.684$&$-155.003$&$-181.988$&$-208.457$ &$-233.699$ \\
$\ln(\Delta_1(s))$
&$-72.5076 $ &$-98.9279$ &$-125.524$&$-152.287$&$-179.229$&$-206.373$ & $-233.697$
\end{tabular}
\end{table}
\section{Deviating from (\ref{rhos-DEF}) \label{DFG}}
This section concerns with how the solution looks like if (\ref{rhos-DEF}) is dissatisfied.
First, we derive a better asymptotics near $r=0$, which is suitable to give initial values for the numerical integration.
Also, it shows how the truncation structure works.
Then, the tt* equation is integrated numerically.
The integrating contour on the complex plane of $r$ is used to surround the singularities.
We will find the singularities distribute regularly.
However, we should understand the difficulties here are much larger than the ones encountered in Section \ref{CONJ},
where we could formulate conjecture based on the numerical results.
This is also understandable since we have in fact four independent parameters $\gamma_0$, $\gamma_1$, $\rho_0$ and $\rho_1$
while in Section \ref{CONJ} we have essentially only two parameters $s_1^\mathbb{R}$ and $s_2^\mathbb{R}$.
For convenience, in this section we will always use dependent variables $v_0$ and $v_1$
as defined by (\ref{v0v1-DEF1}).
As independent variable, we use $s=\ln(r) $ for $r \le 1$ as before.
So the equations for $v_0$ and $v_1$ are still (\ref{v0v1-DEQ1}).
Let us take the following assumption first.
\begin{itemize}
\item[]{{\bf Assumption 1}: Both terms $4 e^{2 s} (v_0^3-v_1)$ and $4 e^{2 s} \left( \frac{v_1^2}{v_0}-\frac{1}{v_1} \right)$
in (\ref{v0v1-DEQ1}) are negligible near $s=-\infty$.}
\end{itemize}
So, (\ref{v0v1-DEQ1}) becomes
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{ d^2 v_0^{(0)} }{ds^2} =\frac{1}{ v_0^{(0)}} \left( \frac{ d v_0^{(0)}}{ds} \right)^2 \\
\frac{ d^2 v_1^{(0)} }{ds^2}=\frac{1}{v^{(0)}_1}\left( \frac{d v_1^{(0)}} {ds} \right)^2
\end{array}
\right. . \label{wv0wv1-DEQ}
\end{eqnarray}
The solution of (\ref{wv0wv1-DEQ}) is
\begin{eqnarray}
v_0^{(0)}= c_0 e^{\gamma_0 s}, \quad v_1^{(0)}= c_1 e^{\gamma_1 s} , \label{wv0wv1-SOLU}
\end{eqnarray}
where $c_0$, $c_1 $, $\gamma_0$ and $\gamma_1$ are constants,
which should be real if we only interest in the real solutions of (\ref{v0v1-DEQ1}).
The immediate results of Assumption 1 is that $\gamma_0$ and $\gamma_1$ satisfy the constraints
$3 \gamma_0+2 >\gamma_0$, $\gamma_1+2 >\gamma_0$, $2 \gamma_1-\gamma_0+2 >\gamma_1$
and $2-\gamma_1>\gamma_1$, which is just the inner of the triangle in Figure \ref{fig-2}.
So, if $(\gamma_0,\gamma_1)$ is a point in the inner of the triangle in Figure \ref{fig-2},
then $(v_0^{(0)}, v_1^{(0)})$ of (\ref{wv0wv1-SOLU}) is the primary approximate solution of $(v_0, v_1)$ near $s=-\infty$.
If $c_0=e^{\rho_0}$ and $c_1=e^{\rho_1}$ with $\rho_0$ and $\rho_1$ defined by (\ref{rhos-DEF}),
then the solution is the one dealt by Theorem \ref{thm-GIL-1}.
Here we are interested in the case that $c_0 \neq e^{\rho_0}$ or $c_1 \neq e^{\rho_1}$.
Now, let us transform (\ref{v0v1-DEQ1}) to its integral form
\begin{eqnarray}
\left\{
\begin{array}{l}
v_0(s) = c_0 e^{\gamma_0 s} e^{ 4 \int_{-\infty}^s d\xi \int_{-\infty}^\xi
d\zeta \left[ v_0(\zeta)^2- \frac{v_1(\zeta)}{v_0(\zeta)} \right]
e^{2 \zeta} } \\
v_1(s) = c_1 e^{\gamma_1 s} e^{ 4 \int_{-\infty}^s d\xi \int_{-\infty}^\xi
d\zeta \left[ \frac{v_1(\zeta)}{v_0(\zeta)} -\frac{1}{v_1(\zeta)^2}\right]
e^{2 \zeta} }
\end{array}
\right. . \label{v0v1-inteEQ}
\end{eqnarray}
In principle, near $s=-\infty$, (\ref{v0v1-inteEQ}) can be solved recursively:
$v_0^{(0)}$ and $v_1^{(0)}$ are given by (\ref{wv0wv1-SOLU});
$v_0^{(1)}$ and $v_1^{(1)}$ are
\begin{eqnarray}
\left\{
\begin{array}{l}
v_0^{(1)}(s) =c_0 e^{\gamma_0 s} \exp\left\{ \frac{c_0^2}{(1+\gamma_0)^2}e^{2(1+\gamma_0)s}-
\frac{4 c_1}{c_0 (2-\gamma_0+\gamma_1)^2} e^{(2-\gamma_0+\gamma_1)s} \right\} \\
v_1^{(1)}(s)=c_1 e^{\gamma_1 s} \exp\left\{ \frac{4 c_1}{c_0 (2-\gamma_0+\gamma_1)^2} e^{(2-\gamma_0+\gamma_1)s} -\frac{1}{c_1^2 (1-\gamma_1)^2}e^{2(1-\gamma_1)s} \right\}
\end{array}
\right. ,\label{v0v1-SOLU-1}
\end{eqnarray}
which are obtained by substituting $v_0=v_0^{(0)}$ and $v_1=v_1^{(0)}$ to the right of (\ref{v0v1-inteEQ});
And so on and so forth.
If $(\gamma_0,\gamma_1)$ lies in the inner of the triangle in Figure \ref{fig-2}, $v_0^{(i)}$ and $v_1^{(i)}$ converge as $i$ increases.
\subsection{Numerical solution}
As Subsection \ref{GeneralCase}, we still use $(\gamma_0,\gamma_1)=(1,\frac{1}{3})$.
To have some deviation from Subsection \ref{GeneralCase},
$c_0$ and $c_1$ should be chosen as
\begin{eqnarray}
c_0=e^{\rho_0}+\delta c_0, \quad c_1=e^{\rho_1}+\delta c_1, \nonumber
\end{eqnarray}
where $\delta c_0$ and $\delta c_1$ can not be $0$ simultaneously.
In our numerical experiment, we use
$$\delta c_0=\frac{1}{2}, \quad \delta c_1=\frac{1}{5} . $$
To solve (\ref{v0v1-DEQ1}) numerically, the initial values of $(v_0,\frac{dv_0}{ds},v_1,\frac{dv_1}{ds})$ must be given.
We start from $s_1=-100$ and give the initial values by (\ref{v0v1-SOLU-1}).
Since one can easily compute initial values by (\ref{v0v1-SOLU-1}), the details of the initial values are omitted.
We just list the errors of the initial value by Table \ref{tab22}.
\begin{table}[ht]
\caption{Errors of the numerical solution at $s=-100$ with $(\gamma_0,\gamma_1,c_0,c_1))=(1,\frac{1}{3},e^{\rho_0}+\frac{1}{2},e^{\rho_1}+\frac{1}{5})$.}
\label{tab22}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$s=-100$ & $v_0$ & $\frac{dv_0}{ds}$ & $v_1$ &$\frac{d v_1}{ds}$\\
\hline
| Absolute Error | &$5.32 \times 10^{-160}$ &$1.95 \times 10^{-159}$ &$2.47 \times 10^{-131}$&$7.42\times 10^{-131}$ \\
| Relative Error | &$4.86 \times 10^{-117}$ &$1.78 \times 10^{-116}$ &$5.12 \times 10^{-117}$&$4.61\times 10^{-116}$
\end{tabular}
\end{table}
The error of the values at $s=-100$ are obtained by comparing them with the numerical solution starting from $s=-140$,
which is far more accurate.
The numerical solution is smooth for $s \in [-100,0]$.
As a comparison to (\ref{values-general-1}), the values of $v_0$ et al. at $s=0$ are
\begin{eqnarray}
\left\{
\begin{array}{l}
v_0|{s=0}= 1.3324864759152155716932764336782719490481063559703... \\
\frac{dv_0}{ds}|_{s=0}= 0.49495834671586092263807187324781656576576424051419...\\
v_1|{s=0}= 2.6783375094329925626474416219547736732331423595096...\\
\frac{dv_1}{ds}|_{s=0}= 6.2948008049596612397631881197126092308528410458148....
\end{array}
\right. .\label{values-Deviation-0}
\end{eqnarray}
Table \ref{tab23} gives the errors of (\ref{values-Deviation-0}).
\begin{table}[ht]
\caption{Errors of the numerical solution at $s=0$.}
\label{tab23}
\centering
\begin{tabular}[h]{ c|c c c c}
\hline \hline
$s=0$& $v_0$ & $\frac{dv_0}{ds}$ & $v_1$ &$\frac{dv_1}{ds}$\\
\hline
| Absolute Error | &$ 3.37 \times 10^{-113}$ &$ 1.69 \times 10^{-112}$ &$ 5.96 \times 10^{-113}$&$ 3.43\times 10^{-112}$ \\
| Relative Error | &$2.53 \times 10^{-113}$ &$ 3.41 \times 10^{-112}$ &$ 2.23 \times 10^{-113}$&$5.44 \times 10^{-113}$
\end{tabular}
\end{table}
Again, the errors are evaluated by comparing the two numerical solutions staring from $s=-140$ and from $s=-100$ respectively.
For $s>0$, i.e. $r>1$, it is convenient to use variable $r$ itself rather than $s$:
the pattern of the singularities is more transparent with respect to $r$ than with respect to $s$.
Then (\ref{v0v1-DEQ1}) is converted to
\begin{eqnarray}
\left\{
\begin{array}{l}
\frac{dv_0}{dr}=\frac{1}{r} p_0\\
\frac{dp_0}{dr}=\frac{p_0^2}{r v_0}+4 r v_0^3-4 r v_1 \\
\frac{dv_1}{dr}=\frac{1}{r}p_1\\
\frac{dp_1}{dr}=\frac{p_1^2}{r v_1}-\frac{4 r}{v_1}+\frac{4 r v_1^2}{v_0}
\end{array}
\right. . \label{v0v1-DEQr}
\end{eqnarray}
Then, we compute the numerical solution of (\ref{v0v1-DEQr}),
for which the initial values are given by (\ref{values-Deviation-0}).
Near $r \approx 1.539167317$, the numerical solution blows up.
Figure \ref{fig-6} and \ref{fig-7} show the plots of $v_0$ and $v_1$ on the circle with a radius of about $0.239167317$ around the singular point.
\input{Figure6.tikz}
\input{Figure7.tikz}
Clearly, $v_0$ and $v_1$ are smooth functions on the circle.
Numerical results show the singularity at $r \approx 1.539167317$ is a simple pole of $v_1$.
By (\ref{v0v1-DEQr}), either $v_0=\text{infinity}$ or $v_0=0$ at the singularity of $v_1$.
Numerical results indicate $v_0=0$ at this singularity of $v_1$.
To show the pattern of the singularities of $v_0$ and $v_1$,
we plot $v_i(r+10^{-2}\mathrm{i}) $, $i=0,1$ as Figure \ref{fig-8} and Figure \ref{fig-9}.
\input{Figure8.tikz}
\input{Figure9.tikz}
Though we can not give a precise description of Figure \ref{fig-8} and Figure \ref{fig-9},
we still have several heuristic observations from the two figures.
First, we can safely say both $v_0(r)$ and $v_1(r)$ have infinity of singularities
since some adjacent singularities are almost equidistant.
Second, $v_0(r)$ and $v_1(r)$ should be real since the imaginary part of $v_0(r+10^{-2}\mathrm{i})$ and $v_1(r+10^{-2}\mathrm{i})$
are small except near the singularities.
Third, $v_1(r_{singular}+0_-)>0$ and $v_1(r_{singular}+0_+)<0$ and the imaginary part of $v_1(r+0_+ \mathrm{i})$ is always positive.
Fourth, the singularities of $v_0(r)$ have two frequencies:
the class of singularities with $v_0(r_{singular}+0_+ \mathrm{i})<0$ have one frequency
and the class of singularities with $v_0(r_{singular}+0_+ \mathrm{i})>0$ have another frequency.
The first two observations should be general for cases deviating from (\ref{rhos-DEF}).
It seems there is no simple combination of $v_0$ and $v_1$ such that the result variable is smooth for $r \in (0,\infty)$.
|
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| 1,923
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namespace ColladaDOM150 {
daeElementRef
domTrifans::create(DAE& dae)
{
domTrifansRef ref = new domTrifans(dae);
return ref;
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daeMetaElement *
domTrifans::registerElement(DAE& dae)
{
daeMetaElement* meta = dae.getMeta(ID());
if ( meta != NULL ) return meta;
meta = new daeMetaElement(dae);
dae.setMeta(ID(), *meta);
meta->setName( "trifans" );
meta->registerClass(domTrifans::create);
daeMetaCMPolicy *cm = NULL;
daeMetaElementAttribute *mea = NULL;
cm = new daeMetaSequence( meta, cm, 0, 1, 1 );
mea = new daeMetaElementArrayAttribute( meta, cm, 0, 0, -1 );
mea->setName( "input" );
mea->setOffset( daeOffsetOf(domTrifans,elemInput_array) );
mea->setElementType( domInput_local_offset::registerElement(dae) );
cm->appendChild( mea );
mea = new daeMetaElementArrayAttribute( meta, cm, 1, 0, -1 );
mea->setName( "p" );
mea->setOffset( daeOffsetOf(domTrifans,elemP_array) );
mea->setElementType( domP::registerElement(dae) );
cm->appendChild( mea );
mea = new daeMetaElementArrayAttribute( meta, cm, 2, 0, -1 );
mea->setName( "extra" );
mea->setOffset( daeOffsetOf(domTrifans,elemExtra_array) );
mea->setElementType( domExtra::registerElement(dae) );
cm->appendChild( mea );
cm->setMaxOrdinal( 2 );
meta->setCMRoot( cm );
// Add attribute: name
{
daeMetaAttribute *ma = new daeMetaAttribute;
ma->setName( "name" );
ma->setType( dae.getAtomicTypes().get("xsToken"));
ma->setOffset( daeOffsetOf( domTrifans , attrName ));
ma->setContainer( meta );
meta->appendAttribute(ma);
}
// Add attribute: count
{
daeMetaAttribute *ma = new daeMetaAttribute;
ma->setName( "count" );
ma->setType( dae.getAtomicTypes().get("Uint"));
ma->setOffset( daeOffsetOf( domTrifans , attrCount ));
ma->setContainer( meta );
ma->setIsRequired( true );
meta->appendAttribute(ma);
}
// Add attribute: material
{
daeMetaAttribute *ma = new daeMetaAttribute;
ma->setName( "material" );
ma->setType( dae.getAtomicTypes().get("xsNCName"));
ma->setOffset( daeOffsetOf( domTrifans , attrMaterial ));
ma->setContainer( meta );
meta->appendAttribute(ma);
}
meta->setElementSize(sizeof(domTrifans));
meta->validate();
return meta;
}
} // ColladaDOM150
|
{
"redpajama_set_name": "RedPajamaGithub"
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Share this Story: Cenotaph crash case set to begin
Cenotaph crash case set to begin
Terry Bridge
Aug 21, 2018 • August 21, 2018 • 1 minute read • Join the conversation
The damaged wall next to the cenotaph is seen here on Tuesday August 21, 2018 in Stratford, Ont. Terry Bridge/The Beacon Herald
A man hit with impaired driving charges after police allege he crashed his vehicle into a stone wall next to a Stratford war memorial is heading to court next week.
Nathaneal Tewelde, 20, from Kitchener is facing four charges including dangerous operation of a motor vehicle and a pair related to drunk driving, multiple sources confirmed Tuesday.
Cenotaph crash case set to begin Back to video
20 year old arrested after crashing vehicle into Cenotaph retaining wall. He now faces charges of Dangerous Driving, Impaired, Over 80 and Mischief to Police Property. His breath samples were over twice the legal limit. #ArriveAlive @maddcanada
— Stratford Police Service (@SPSmediaoffice) August 13, 2018
A 2007 Jeep Compass was heading north on Erie Street between York and Cobourg streets shortly before midnight on Aug. 12 when it left the road, police said the next day. It veered down a grass hill and smashed into a stone wall near the cenotaph and a walking path.
Two people were outside the car when police arrived. Both of the vehicle's airbags deployed, but the pair declined medical attention.
The driver, a 20-year-old G2 licence holder from Kitchener-Waterloo, was arrested for impaired driving and two breath samples were both twice the legal limit, police said. A fourth charge, mischief under $5,000, stemmed from an incident at police headquarters after the arrest, according to police.
None of the allegations have been proven in court.
As for the damage to the monument, Quin Malott, the city's manager of parks, forestry and cemeteries, said a contractor was tentatively scheduled to begin repairs late last week.
"It should take one-and-a-half to two weeks to fix," Malott said. "I can't get into costs right now because we'll be dealing with courts and insurance companies for the incident."
David St. Louis, the city's director of community services, confirmed Tuesday the cost of the repair will be about $8,000.
The area has been closed off with temporary fencing and pylons since about 7 a.m. the day after the incident.
"Just because (Stratford) Summer Music is down there and the wall is going to be a little bit unstable," Malott said.
tbridge@postmedia.com
|
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| 6,559
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Cătrunești este un sat în comuna Sinești din județul Ialomița, Muntenia, România.
Cătrunești, Sinești
|
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| 2,484
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If you would like to reproduce this article or any part of it, please contact us for permission.
As if being pregnant isn't hard enough, suddenly you have all these new things to learn about. Although the shopping can be fun, deciding what you need to buy and which product to choose can be very confusing for first time parents. This article aims to help you to find out more about some of the slings and baby carriers that are available, and will help you to decide which will best suit your needs.
There are many advantages to using a sling or carrier: it keeps your baby safe, happy and close; using a sling allows you to have your hands free for other tasks or older children; and it's a great way of settling a tired fretful baby.
When you're out and about a sling is a great way of transporting a baby – your baby is kept warm and snug in the winter, and a fabric sling will keep them well covered in the summer sun. Plus you don't have the added hassle of manoeuvring a pushchair around shops or up and down steps.
A sling is ideal for keeping a tiny baby where they are happiest - close to your body where they are reassured by your heartbeat, and can enjoy the rhythm of your movements. An older baby will love being held up high with a good view of the world, and get lots of opportunity to interact with you and with other adults.
You want a sling or baby carrier that is going to be comfortable for you to wear. A comfortable carrier is one which holds the baby high up and tucked close against your body. Carriers which hang from your shoulders can be very uncomfortable when worn for any length of time, even with a newborn. You may have a baby who wants to be carried a lot, so you will need to choose a carrier which distributes the weight evenly. Slings or baby carriers with broad straps that distribute the weight across the back and torso tend to be more comfortable that those with thinner straps.
Research suggests that upright baby carriers which spread the baby's legs wide in a seated 'M' position are preferable to ones with narrower bases where the baby hangs from the crotch with their weight directly above the pelvis. Although this wide legged position may look alarming it is actually the optimal position for the development of the baby's pelvis. The carrier should then hold your baby close in against your body with support right along the length of the spine and it is important to follow the TICKS principles for safe babywearing.
If you have a newborn or young baby, would you like a sling or baby carrier that will be suitable for carrying a toddler in too? Or will you be able to afford to buy another carrier more suitable for carrying a toddler in the future? This may sound extravagant but you can buy two baby carriers for the price of most pushchairs!
There are so many to choose from, that it can seem overwhelming at first. This section describes most of the main types of sling, and gives some of their advantages and disadvantages.
This is a sling which is made from a single piece of fabric which threads through two rings to form a loop. The sling is worn over one shoulder like a sash and can be tightened by pulling the fabric through the rings which then lock it into place. Some ring slings have padding in the shoulder and in the edges or 'rails' - this padding can make it more comfortable to wear, but can also make it bulkier and less easy to adjust. For this reason some people prefer unpadded slings, or ones with only very slight padding.
This is a single piece of fabric which is sewn together at the ends to form a loop. It is worn over one shoulder like a sash and the fabric is folded in on itself lengthways to form a pocket for the baby. Many can not be adjusted, however there are some which are adjustable with poppers or zips.
• Can be difficult to get a nice snug carrying position as you can't adjust the top edge separately as you can with a ring sling.
A wraparound sling or carriers consists of a single piece of fabric which is wrapped around and tied in such a way that the baby is held securely against your body. There are two main sub-categories of wraparound; those which are made of a woven fabric, and those which are made of stretchy knitted fabric (like T-shirt material). They come in a variety of lengths, partly to suit different sized wearers, but also dependent on which type of carrying positions you would like to be able to use.
Generally the Stretchy Wraps are less supportive than the Woven Wraps.
Stretchy Wraps are slightly easier to put on as you tend to use one tying method for all carrying positions. Plus you can put your baby down while you tie the wrap on, the stretch in the fabric will allow you to pull the fabric apart to put them in after you've tied the knot.
The Woven Wraps have a bit more of a learning curve as most carrying positions involve tying the wrap around yourself and your baby which is a little more fiddly for those who are new to wraps. However the woven fabric gives superior back support so these wraps work well even with heavy toddlers.
This is quite a large category that lots of carriers fall into, so it's hard to give an accurate description that will cover all of them. If you want to find out exactly what features a particular carrier offers you will need to look at a website which sells them. Broadly speaking though, this term refers to a more structured carrier than those described above.
A soft carrier will have shoulder straps for securing the carrier and will often have a waist strap too. The baby is either supported by their crotch or across their entire bottom. Some are suitable from birth, but not all. Some are suitable for carrying on the hip or the back as well as on the front. Some fasten with clips, others wrap and tie.
Those that are suitable for smaller babies usually have a smaller 'body' to the carrier or fold down so that a newborn won't be lost in them. Some allow adjustment of the seat/crotch to make it narrower for smaller babies. Those that are designed for older babies and toddlers have a larger 'body' so they offer good back support even for older, taller children.
It's not really possible to give a list of advantages and disadvantages as there is so much variety within this category. If you want to know more about a particular type of carrier then it's best to get in touch with us for advice. Generally those that can be used for back carrying are suitable for carrying older, heavier babies. Most are fairly easy to get on and off for a front carry. Getting a baby into a back carrier is always harder but with practise it is possible to do this on your own.
At Little Possums you can shop online for baby slings and carriers. Feel free to Contact us at Little Possums for more advice before making your purchase if required.
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| 2,484
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{"url":"https:\/\/mathoverflow.net\/questions\/291229\/invariant-two-form-under-symplectic-group","text":"Invariant two form under symplectic group\n\nLet $m,n\\in\\mathbb{N}$, $l$ be a prime number, let $J$ be the standard symplectic matrix\n\n$$J=\\left[ \\begin{array}[cc] \\\\0 & I_n \\\\ -I_n & 0\\\\ \\end{array}\\right]$$\n\nLet $$\\mathrm{Sp}(2n,\\mathbb{Z}\/l^m)=\\{A\\in\\mathrm{Gl}_{2n}(\\mathbb{Z}\/l^m)|A^TJA=J\\}.$$\n\nLet $N\\in \\mathrm{Mat}_{2n}(\\mathbb{Z}\/l^m)$ be a skew symmetric matrix, such that for any $A\\in\\mathrm{Sp}(2n,\\mathbb{Z}\/l^m)$ $$A^TNA=N$$\n\nThen is it true $N$ is a scalar multiple of $J$?\n\nIf not, will the conclusion be true for $m$ large enough or replace $\\mathbb{Z}\/l^m$ by $\\mathbb{Z}$?\n\n\u2022 is $l$ a prime? \u2013\u00a0Venkataramana Jan 22 '18 at 4:59\n\n1 Answer\n\nYes. Let $(q_k,p_k)$ be a symplectic basis to $\\mathbb{R}^{2n}$ so that $J(q_k)=p_k$ and $J(p_k)=-q_k$ for all $k$. Consider matrices $A_k$ and $B_{k,l}$ such that\n\n\u2022 $A_k (q_k)=p_k \\quad$and$\\quad A_k (p_k) = -q_k$\n\u2022 $A_k (q_l)=q_l \\quad$and$\\quad A_k (p_l) = p_l$ for $l \\neq k$\n\u2022 $B_{k,l}(q_k)=q_l, \\quad B_{k,l}(q_l)=q_k, \\quad B_{k,l}(p_k)=p_l,\\quad B_{k,l}(p_l)=p_k\\quad$ and $B_{k,l}$ is the identity away from the subspace spanned by the vectors $q_k,p_k,q_l,p_l$.\n\nThe matrices $A_k$ and $B_{k,l}$ are symplectic, as can easily be checked. If $E_k$ is the subspace spanned by the vectors $q_k,p_k$, we have $E_k=\\text{Ker}(A_k^2+I)$. Also, note that $A_k^{T}=A_k^{-1}$ and $B_{k,l}^T=B_{k,l}$.\n\nNow, since these matrices are symplectic, we can subsitute them into the formula for $N$ to get $A_k^{-1} N A_k = N$ and $B_{k,l} N B_{k,l}= N$. Taking the first equation and applying it to the vector $q_k$, we have $A_k^{-1}NA_k(q_k)=N(q_k)$, so $N(p_k)=A_kN(q_k)$. Similarly, $N(q_k)=-A_kN(p_k)$. In particular, $A_k^2 N(q_k)=-N(q_k)$ and $A_k^2N(p_k)=-N(p_k)$. Hence, $N(q_k), N(p_k) \\in E_k$, and so there are numbers $a_k,b_k,c_k,d_k$ such that $$N(q_k)=a_k q_k+b_k p_k \\\\ N(p_k)=c_k q_k+d_k p_k .$$ Applying $A_k$ to either of these equations and using $N(q_k)=-AN(p_k)$ or $N(p_k)=AN(q_k)$, respectively, we have that $a_k=d_k$ and $c_k=-b_k$. Applying $B_{k,l}$ to these formulas for each $k,l$ shows that $a_k=a_l=:a$ and $b_k=b_l =: b$. So putting this all together, we get $N=aI+bJ$. Since $N$ is skew symmetric, it follows that $a=0$, and hence the result.\n\n\u2022 Thanks! Also may I know if there is a reference for such results? \u2013\u00a0Qixiao Jan 23 '18 at 13:28\n\u2022 Sadly I do not know of a reference. \u2013\u00a0David Hughes Jan 23 '18 at 15:50","date":"2019-03-26 03:02:41","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9856750965118408, \"perplexity\": 76.01990309493604}, \"config\": {\"markdown_headings\": false, \"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-2019-13\/segments\/1552912204768.52\/warc\/CC-MAIN-20190326014605-20190326040605-00551.warc.gz\"}"}
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Baseball|Ivan Nova Returns as Yankees Avoid a Phillies Sweep
Yankees 10, Phillies 2
Ivan Nova Returns as Yankees Avoid a Phillies Sweep
Ivan Nova left the game after throwing 92 pitches, tipping his cap during a prolonged ovation in appreciation of holding the Phillies to three hits.CreditCreditKathy Willens/Associated Press
By Seth Berkman
Thirty minutes before the first pitch was thrown at Yankee Stadium on Wednesday, the center-field scoreboard showed a preview of the matchup between the Philadelphia Phillies' ace, Cole Hamels, and Ivan Nova, who was making his first start since April 19, 2014.
It showed Hamels tossing a ball in left field and then reeled off a résumé that should make him a highly desired trade target over the next month: Hamels was the 2008 World Series most valuable player, was a three-time all-star and, more recently, had 12 strikeouts over seven scoreless innings against the Pittsburgh Pirates in his previous outing.
After Hamels's list of credentials was completed, Nova's introduction was succinct, announcing simply that this was his first appearance of the season.
Nova, though, showed no ill effects of Tommy John surgery, which he had on April 29, 2014. He outdueled Hamels as the Yankees prevented a sweep by the Phillies, the team with the worst record in the major leagues, with a 10-2 win.
Nova said he had been awaiting this opportunity for the last 14 months. He left the Stadium before last night's rain-delayed game began and was in bed by 10 p.m. Someone had told him he would rest well.
"I told him he's a liar," Nova said. "I didn't sleep."
Nova's performance — shutting out the Phillies over six and two-thirds innings — provided a boost to a team looking for stability among a collection of arms that have been inconsistent. The Yankees had allowed 11 or more runs in their last three games.
With a number of scouts on hand, Hamels (5-6) did not pitch poorly, but he was undone by fielding gaffes. In the second, third baseman Andres Blanco skipped a throw home that catcher Carlos Ruiz could not cleanly scoop, and two runs scored.
Two innings later, Didi Gregorius hit a pop-up to shortstop Freddy Galvis, who lost its trajectory in the sun. Galvis put his glove over his head and scampered away as the ball fell to the ground. Gregorius was awarded a double, the first of four Yankees hits in the inning as they tacked on three runs.
One came on a single by Mark Teixeira, who returned after sitting out the last two games with neck pain. Teixeira was 3 for 5 and drove in two runs.
The Yankees' Chris Young scored past the Phillies' Carlos Ruiz in the second inning.CreditJim Mcisaac/Getty Images
Hamels has reportedly piqued the interest of the Yankees, who have used 23 pitchers this month. The Phillies are rebuilding around younger players such as Maikel Franco, who had three home runs and 10 R.B.I. over the first two games of the series.
But Hamels carries a hefty price. Aside from the quality prospects the Phillies would want in return, Hamels's total salary for 2015 is $23.5 million, which he is scheduled to earn in each of the next three years. Hamels also has a no-trade clause, but the Yankees present an appealing option as a playoff contender.
Hamels largely deflected trade talk, saying he did not pay attention to speculation. But he realizes the Phillies are not in a position to win this year, he added.
"It is tough, but we all understand what's kind of going on," he said.
Hamels also gave credit to Nova, who injured the ulnar collateral ligament in his right elbow during a 2014 game against the Tampa Bay Rays.
Manager Joe Girardi had said that Nova would be limited to about 95 pitches, and he exited after his 92nd, tipping his cap during a prolonged ovation in appreciation of holding the Phillies to three hits.
Girardi was not around to see most of Nova's performance. He was ejected in the third by the first-base umpire, Alan Porter, for arguing a checked-swing call on an 0-2 pitch to Franco.
"I told him he swung, and he said, 'Knock it off,' " Girardi said. "And I said, 'I'd knock it off if you got the call right,' and he threw me."
Girardi had been emotional from the start. In the first, Hamels drilled Alex Rodriguez on the left thigh with a fastball. Both benches were warned, and Girardi left the dugout to have an animated discussion with the home-plate umpire, Brian O'Nora, who believed that Hamels's pitch might have been in retaliation for Justin Wilson's hitting Franco the previous night.
The early exit allowed Girardi to get a closer view of Nova by watching on television in the clubhouse.
"You put the combination of being able to watch their swings from the bench, and then you get a chance to see the movement inside — you actually get a pretty good read of what he had today," Girardi said.
His final analysis was overwhelmingly positive.
"I thought his sinker was really good, his curveball was really good, his command of the strike zone," Girardi said. "Everything he did."
A version of this article appears in print on , Section B, Page 13 of the New York edition with the headline: Yanks' Nova Barely Sleeps, Then Leaves Bats in Stupor in His Return. Order Reprints | Today's Paper | Subscribe
Cubs Fan Catches Foul Ball in One Hand With Baby in Other
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F.B.I. Struggles to Pinpoint the Fingers Behind a Hacking
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"redpajama_set_name": "RedPajamaCommonCrawl"
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\section{INTRODUCTION}
\label{section:Paper1Introduction}
The radio continuum -- far-infrared (RC--FIR) relation of galaxies holds over 4 orders of magnitude in luminosity, irrespective of galaxy type \cite[][]{Helou1985,deJong1985,Yun2001}. It displays a mere $0.26$\,dex scatter \cite[][]{Yun2001} and has been observed to hold at least out to a redshift of $3$ \cite[][]{Appleton2004}. The radio continuum \cite[RC; see][for a review]{Condon1992} and the far-infrared (FIR) have long been attributed to the input of energy following a star formation (SF) event. At 6\,cm the RC is comprised of two main contributions: a thermal component (${\rm RC_{Th}}$) from thermal electrons in HII regions, and a non-thermal component (${\rm RC_{Nth}}$) generated by cosmic ray electrons (\mbox{CR$e$}) accelerated in supernova shocks. The ${\rm RC_{Th}}$\ and ${\rm RC_{Nth}}$\ emission both have an unambiguous link to recent SF, while the FIR originates from the modified blackbody radiation of interstellar dust that is heated by the interstellar radiation field \cite[][]{Li2010}.
The classical scenario leading to the RC--FIR relation assumes a galaxy behaves as a calorimeter \cite[][]{Voelk1989}. This model assumes that galaxies are optically thick to dust-heating UV photons which are absorbed by dust within the galaxy that goes on to reradiate the energy gained in the FIR. It also requires that magnetic fields retain all \mbox{CR$e$}, which eventually produce synchrotron radiation. Since all the energy contained within the \mbox{CR$e$}\ is radiated, the strength of the magnetic field is irrelevant, i.e., whether the energy contained in the \mbox{CR$e$}\ is radiated over $1$\,Myr in a relatively strong magnetic field, or over $1$\,Gyr in a weaker magnetic field, the total energy emitted is the same. The calorimeter assumption implies that the mean-free-path of dust-heating photons is less than the galaxy disk scale height, and that the typical energy loss timescale of \mbox{CR$e$}\ is less than the diffusion timescale to traverse the scale height.
Clearly, the calorimeter model is not perfect. Dust-heating photons {\em are} observed to be coming from galaxies and ${\rm RC_{Nth}}$\ emission {\em is} observed in the haloes of larger spiral galaxies \cite[][]{Heesen2009}. Therefore, for galaxies to follow the RC--FIR relation, the escape of \mbox{CR$e$}\ from galactic magnetic fields must be in proportion to the escape of dust-heating photons from the disk \citep{Helou1993}. Some of the earliest evidence of this comes from \cite{Klein1991} who stated that the deficiency of ${\rm RC_{Nth}}$\ `happens to be balanced' by a lack of dust in a study of Blue Compact Dwarfs (BCDs). This is known as the `conspiracy' between the emission at RC and FIR wavelengths (e.g., \citealp{Bell2003}; \citealp{Dale2009}; \citealp{Lacki2010}). The first paper with a quantitative model of the RC-FIR correlation for non-calorimeter galaxies and the "conspiracy" between the processes involved was that by \cite{NiklasB1997} who predicted a slightly nonlinear correlation for the synchrotron emission. To complicate the picture yet further, heating of the diffuse cold dust by photons may not be sufficient to make the RC--FIR relation as tight as is observed; \cite{Xu1990} found that a significant fraction of the heating of diffuse cool dust could not be accounted for by UV radiation in their sample of $40$ spiral galaxies. An alternative source to compensate for this insufficient UV--heating could be heating by \mbox{CR$e$}\ \cite[as for example in Ultra--Luminous Infrared Galaxies;][]{Papadopoulos2010}.
It is difficult to disentangle the many factors that lead to the RC--FIR relation. This is especially true in large spiral galaxies where within any kpc--size area the \mbox{CR$e$}\ population stemming from recent SF can be contaminated by older \mbox{CR$e$}\ from neighbouring areas. The interstellar medium (ISM) in spirals likewise is in a constant state of flux with differential rotation and spiral arms transporting material in and out of such a kpc--size region. We argue therefore that dwarf galaxies create a more accessible route to understanding the relationship between the RC and FIR emission and SF. The low mass of dwarf galaxies leads to SF which simulations suggest is episodic \cite[e.g.,][liken the SF history of isolated dwarf galaxies to `breathing']{Stinson2007}. If this is the case then within a set region one is ever only receiving emission from one generation of \mbox{CR$e$}. However, observational evidence suggests that the duration of bursts of SF in dwarf galaxies may actually be quite long in some cases ($0.5$--$1.3$\,Gyr; \citealt{McQuinn2010}) which may complicate this interpretation. Dwarf galaxies also contain proportionally less dust than spirals, as confirmed by several authors \cite[e.g.,][]{Lisenfeld1998,Bigiel2008}, and should therefore be fainter in the FIR for a given level of radio emission. Understanding the origin of ${\rm RC_{Nth}}$\ emission generated should also be more straightforward in dwarf galaxies. They lack differential rotation \cite[][]{Gallagher1984} and thus lack the associated dynamo action present in larger, grand--design spirals that leads to amplification of the magnetic field and ordered fields of $\sim 5\mathrm{\mu G}$ between spiral arms \citep{Beck2009}. Observations suggest that dwarf galaxies differ markedly from spirals in terms of their magnetic field strength \cite[e.g.,][]{Chyzy2011,Roychowdhury2012}. These features make dwarf galaxies ideal laboratories in which to study the RC--FIR relationship.
Historically, spatially resolved studies of the RC in dwarf galaxies have been limited by their intrinsically low surface brightness. To date, resolved observations of dwarf galaxies have been restricted to the few brightest: the near and bright IC\,10 \cite[][]{Heesen2011}, IC\,1613 \cite[][]{Chyzy2011}, NGC\,4214 \cite[][]{Kepley2011}, NGC\,1569 (\citealp{Lisenfeld2004}; \citealp{Kepley2010}; \citealp{Westcott2017}), and the Magellanic Clouds (e.g., \citealp{Filipovic1995}; \citealp{Filipovic1998}; \citealp{Leverenz2013}). The NRAO\footnote{The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.} Karl G.\ Jansky Very Large Array (VLA), after recently benefiting from a major upgrade, provided the prospect of routinely delivering quality, good signal-to-noise (S/N) observations of nearby dwarf galaxies. This opportunity is exploited here to revisit the relationship between the RC, FIR and star formation rate (SFR) in the dwarf galaxy regime.
The study presented here is based on VLA {\em C-}band\ (4--8\,GHz) images of the 40 dwarf galaxies corresponding to the LITTLE THINGS sample \cite[][]{Hunter2012}, mainly focussing on the relation of RC emission with SFR indicators. The ultimate aim is to increase our understanding of the RC--SFR relation of low mass, low metallicity systems. With the development of the Square Kilometre Array (SKA; \citealt{Dewdney2015}), calibrating the RC--SFR relation in quiescent/low SFR galaxies will become more important than ever. The benefit of the RC is that observations can be carried out with ground based instruments rather than expensive (cryogenically cooled) IR satellites. Our calibration of the RC--SFR relation may provide a better understanding of how this indicator may work at higher redshift, in the domain that will be accessible to the SKA.
This paper is organised as follows: in Section~\ref{section:Paper1sample_and_data_reduction} we describe the observations, calibration, and imaging of our sample. We present our results (images and integrated emission) in Section~\ref{section:Paper1Results}. We then discuss our results, including the RC--SFR, FIR--SFR, and RC--FIR relations in Sections~\ref{section:Paper1rc--sfr_relation}, \ref{section:Paper1fir--sfr_relation}, and \ref{section:Paper1rc--fir_relation}, respectively. We summarise our results in Section~\ref{section:Paper1Summary}.
\begin{landscape}
\notetoeditor{Table~\ref{Table:tab-sample} should be able to fit on a landscape-orientated page with tabletypesize=tiny. There is something wrong with the formatting that pushes the table off the page. Can this be sorted? I have copied this table to the end of the document to show how it should be viewed.}
\begin{deluxetable}{lccccccccccc}
\tabletypesize{\tiny}
\tablecolumns{12}
\tablewidth{689pt}
\tablecaption{The Galaxy Sample\label{Table:tab-sample} }
\tablehead{ & & \colhead{D} & & \colhead{M$_V$} & \colhead{$R_H$\tablenotemark{c}} & \colhead{$R_D$\tablenotemark{c}} &
& \colhead{log$_{10}$ $\Sigma_\mathrm{SFR}\mathrm{(H\alpha)}$} & \colhead{log$_{10}$ $\Sigma_\mathrm{SFR}\mathrm{(FUV)}$} & & \\ \colhead{Galaxy} & \colhead{Other names\tablenotemark{a}} & \colhead{(Mpc)} & \colhead{Ref\tablenotemark{b}} & \colhead{(mag)} & \colhead{(arcmin)} & \colhead{(kpc)} & \colhead{E($B-V$)\tablenotemark{d}} & \colhead{(\mbox{${M_\odot}$} yr$^{-1}$ kpc$^{-2}$)\tablenotemark{e}} & \colhead{(\mbox{${M_\odot}$} yr$^{-1}$ kpc$^{-2}$)\tablenotemark{e}} & \colhead{$12+\log_{10} {\rm O/H}$\tablenotemark{f}} & \colhead{Ref\tablenotemark{g}} }
\startdata
\cutinhead{Im Galaxies}
\object[CVn I dwA]{CVnIdwA} & UGCA 292 & 3.6 & 1 & -12.4 & 0.87 & $0.57 \pm 0.12$ & 0.01 & $-2.58 \pm 0.01$ & $-2.48 \pm 0.01$ & $7.3 \pm 0.06$ & 24 \\
\object{DDO 43} & PGC 21073, UGC 3860 & 7.8 & 2 & -15.1 & 0.89 & $0.41\pm 0.03$ & 0.05 & $-1.78 \pm 0.01$ & $-1.55 \pm 0.01$ & $8.3 \pm 0.09$ & 25 \\
\object{DDO 46} & PGC 21585, UGC 3966 & 6.1 & \nodata & -14.7 & \nodata & $1.14 \pm 0.06$ & 0.05 & $-2.89 \pm 0.01$ & $-2.46 \pm 0.01$ & $8.1 \pm 0.1$ & 25 \\
\object{DDO 47} & PGC 21600, UGC 3974 & 5.2 & 3 & -15.5 & 2.24 & $1.37 \pm 0.06$ & 0.02 & $-2.70 \pm 0.01$ & $-2.40 \pm 0.01$ & $7.8 \pm 0.2$ & 26 \\
\object{DDO 50} & PGC 23324, UGC 4305, Holmberg II, VIIZw 223 & 3.4 & 1 & -16.6 & 3.97 & $1.10 \pm 0.05$ & 0.02 & $-1.67 \pm 0.01$ & $-1.55 \pm 0.01$ & $7.7 \pm 0.14$ & 27 \\
\object{DDO 52} & PGC 23769, UGC 4426 & 10.3 & 4 & -15.4 & 1.08 & $1.30 \pm 0.13$ & 0.03 & $-3.20 \pm 0.01$ & $-2.43 \pm 0.01$ & (7.7) & 28 \\
\object{DDO 53} & PGC 24050, UGC 4459, VIIZw 238 & 3.6 & 1 & -13.8 & 1.37 & $0.72 \pm 0.06$ & 0.03 & $-2.42 \pm 0.01$ &$-2.41 \pm 0.01$ & $7.6 \pm 0.11$ & 27 \\
\object{DDO 63} & PGC 27605, Holmberg I, UGC 5139, Mailyan 044 & 3.9 & 1 & -14.8 & 2.17 & $0.68 \pm 0.01$ & 0.01 & $-2.32 \pm 0.01$ & $-1.95 \pm 0.01$ & $7.6 \pm 0.11$ & 27 \\
\object{DDO 69} & PGC 28868, UGC 5364, Leo A & 0.8 & 5 & -11.7 & 2.40 & $0.19 \pm 0.01$ & 0.00 & $-2.83 \pm 0.01$ & $-2.22 \pm 0.01$ & $7.4 \pm 0.10$ & 29 \\
\object{DDO 70} & PGC 28913, UGC 5373, Sextans B & 1.3 & 6 & -14.1 & 3.71 & $0.48 \pm 0.01$ & 0.01 & $-2.85 \pm 0.01$ & $-2.16 \pm 0.01$ & $7.5 \pm 0.06$ & 30 \\
\object{DDO 75} & PGC 29653, UGCA 205, Sextans A & 1.3 & 7 & -13.9 & 3.09 & $0.22 \pm 0.01$ & 0.02 & $-1.28 \pm 0.01$ & $-1.07 \pm 0.01$ & $7.5 \pm 0.06$ & 30 \\
\object{DDO 87} & PGC 32405, UGC 5918, VIIZw 347 & 7.7 & \nodata & -15.0 & 1.15 & $1.31 \pm 0.12$ & 0.00 & $-1.36 \pm 0.01$ & $-1.00 \pm 0.01$ & $7.8 \pm 0.04$ & 31 \\
\object{DDO 101} & PGC 37449, UGC 6900 & 6.4 & \nodata & -15.0 & 1.05 & $0.94 \pm 0.03$ & 0.01 & $-2.85 \pm 0.01$ & $-2.81 \pm 0.01$ & $8.7 \pm 0.03$ & 25 \\
\object{DDO 126} & PGC 40791, UGC 7559 & 4.9 & 8 & -14.9 & 1.76 & $0.87 \pm 0.03$ & 0.00 & $-2.37 \pm 0.01$ & $-2.10 \pm 0.01$ & (7.8) & 28 \\
\object{DDO 133} & PGC 41636, UGC 7698 & 3.5 & \nodata & -14.8 & 2.33 & $1.24 \pm 0.09$ & 0.00 & $-2.88 \pm 0.01$ & $-2.62 \pm 0.01$ & $8.2 \pm 0.09$ & 25 \\
\object{DDO 154} & PGC 43869, UGC 8024, NGC 4789A & 3.7 & \nodata & -14.2 & 1.55 & $0.59 \pm 0.03$ & 0.01 & $-2.50 \pm 0.01$ & $-1.93 \pm 0.01$ & $7.5 \pm 0.09$ & 27 \\
\object{DDO 155} & PGC 44491, UGC 8091, GR 8, LSBC D646-07 & 2.2 & 9 & -12.5 & 0.95 & $0.15 \pm 0.01$ & 0.01 & $-1.44 \pm 0.01$ &\nodata & $7.7 \pm 0.06$ & 29 \\
\object{DDO 165} & PGC 45372, UGC 8201, IIZw 499, Mailyan 82 & 4.6 & 10 & -15.6 & 2.14 & $2.26 \pm 0.08$ & 0.01 & $-3.67 \pm 0.01$ & \nodata & $7.6 \pm0.08$ & 27 \\
\object{DDO 167} & PGC 45939, UGC 8308 & 4.2 & 8 & -13.0 & 0.75 & $0.33 \pm 0.05$ & 0.00 & $-2.36 \pm 0.01$ & $-1.83 \pm 0.01$ & $7.7 \pm 0.2$ & 26 \\
\object{DDO 168} & PGC 46039, UGC 8320 & 4.3 & 8 & -15.7 & 2.32 & $0.82 \pm 0.01$ & 0.00 & $-2.27 \pm 0.01$ &$-2.04 \pm 0.01$ & $8.3 \pm 0.07$ & 25 \\
\object{DDO 187} & PGC 50961, UGC 9128 & 2.2 & 1 & -12.7 & 1.06 & $0.18 \pm 0.01$ & 0.00 & $-2.52 \pm 0.01$ & $-1.98 \pm 0.01$ & $7.7 \pm 0.09$ & 32 \\
\object{DDO 210} & PGC 65367, Aquarius Dwarf & 0.9 & 10 & -10.9 & 1.31 & $0.17 \pm 0.01$ & 0.03 & \nodata & $-2.71 \pm 0.06$ & (7.2) & 28 \\
\object{DDO 216} & PGC 71538, UGC 12613, Peg DIG, Pegasus Dwarf & 1.1 & 11 & -13.7 & 4.00 & $0.54 \pm 0.01$ & 0.02 & $-4.10 \pm 0.07$ & $-3.21 \pm 0.01$ & $7.9 \pm 0.15$ & 33 \\
\object[F564 V3]{F564-V3} & LSBC D564-08 & 8.7 & 4 & -14.0 & \nodata & $0.53 \pm 0.03$ & 0.02 & \nodata & $-2.79 \pm 0.02$ & (7.6) & 28 \\
\object{IC 10} & PGC 1305, UGC 192 & 0.7 & 12 & -16.3 & \nodata & $0.40 \pm 0.01$ & 0.75 & $-1.11 \pm 0.01$ & \nodata & $8.2 \pm 0.12$ & 34 \\
\object{IC 1613} & PGC 3844, UGC 668, DDO 8 & 0.7 & 13 & -14.6 & 9.10 & $0.58 \pm 0.02$ & 0.00 & $-2.56 \pm 0.01$ & $-1.99 \pm 0.01$ & $7.6 \pm 0.05$ & 35 \\
\object{LGS 3} & PGC 3792, Pisces dwarf & 0.7 & 14 & -9.7 & 0.96 & $0.23 \pm 0.02$ & 0.04 & \nodata & $-3.88 \pm 0.06$ & (7.0) & 28 \\
\object[M81 DwA]{M81dwA} & PGC 23521 & 3.5 & 15 & -11.7 & \nodata & $0.26 \pm 0.01$ & 0.02 & \nodata & $-2.26 \pm 0.01$ & (7.3) & 28 \\
\object{NGC 1569} & PGC 15345, UGC 3056, Arp 210, VIIZw 16 & 3.4 & 16 & -18.2 & \nodata & $0.38 \pm 0.02$& 0.51 & $0.19 \pm 0.01$ & $-0.01 \pm 0.01$ & $ 8.2 \pm 0.05$ & 36 \\
\object{NGC 2366} & PGC 21102, UGC 3851, DDO 42 & 3.4 & 17 & -16.8 & 4.72 & $1.36 \pm 0.04$ & 0.04 & $-1.67 \pm 0.01$ & $-1.66 \pm 0.01$ & $7.9 \pm 0.01$ & 37 \\
\object{NGC 3738} & PGC 35856, UGC 6565, Arp 234 & 4.9 & 3 & -17.1 & 2.40 & $0.78 \pm 0.01$ & 0.00 & $-1.66 \pm 0.01$ & $-1.53 \pm 0.01$ & $8.4 \pm 0.01$ & 25 \\
\object{NGC 4163} & PGC 38881, NGC 4167, UGC 7199 & 2.9 & 1 & -14.4 & 1.47 & $0.27 \pm 0.03$ & 0.00 & $-2.28 \pm 0.13$ & $-1.74 \pm 0.01$ & $7.9 \pm 0.2$ & 38 \\
\object{NGC 4214} & PGC 39225, UGC 7278 & 3.0 & 1 & -17.6 & 4.67 & $0.75 \pm 0.01$ & 0.00 & $-1.03 \pm 0.01$ & $-1.08 \pm 0.01$ & $8.2 \pm 0.06$ & 39 \\
\object[Sag DIG]{SagDIG} & PGC 63287, Lowal's Object & 1.1 & 19 & -12.5 & \nodata & $0.23 \pm 0.03$ & 0.14 & $-2.97 \pm 0.04$ & $-2.11 \pm 0.01$ & $7.3 \pm 0.1$ & 35 \\
\object{UGC 8508} & PGC 47495, IZw 60 & 2.6 & 1 & -13.6 & 1.28 & $0.27 \pm 0.01$ & 0.00 & $-2.03 \pm 0.01$ & \nodata & $7.9 \pm 0.2$ & 38 \\
\object{WLM} & PGC 143, UGCA 444, DDO 221, Wolf-Lundmark-Melott & 1.0 & 20 & -14.4 & 5.81 & $0.57 \pm 0.03$ & 0.02 & $-2.77 \pm 0.01$ & $-2.05 \pm 0.01$ & $7.8 \pm 0.06$ & 40 \\
\cutinhead{BCD Galaxies}
\object{Haro 29} & PGC 40665, UGCA 281, Mrk 209, I Zw 36 & 5.8 & 21 & -14.6 & 0.84 & $0.29 \pm 0.01$ & 0.00 & $-0.77 \pm 0.01$ & $-1.07 \pm 0.01$ & $7.9 \pm 0.07$ & 41 \\
\object{Haro 36} & PGC 43124, UGC 7950 & 9.3 & \nodata & -15.9 & \nodata & $0.69 \pm 0.01$ & 0.00 & $-1.86 \pm 0.01$ & $-1.55 \pm 0.01$ & $8.4 \pm 0.08$ & 25 \\
\object{Mrk 178} & PGC 35684, UGC 6541 & 3.9 & 8 & -14.1 & 1.01 & $0.33 \pm 0.01$ & 0.00 & $-1.60 \pm 0.01$ & $-1.66 \pm 0.01$ & $7.7 \pm 0.02 $ & 42 \\
\object[VII Zw 403]{VIIZw 403} & PGC 35286, UGC 6456 & 4.4 & 22,23 & -14.3 & 1.11 & $0.52 \pm 0.02$ & 0.02 & $-1.71 \pm 0.01$ & $-1.67 \pm 0.01$ & $7.7 \pm 0.01$ & 25 \\
\enddata
\tablenotetext{a}{Selected alternate identifications obtained from NED.}
\tablenotetext{b}{Reference for the distance to the galaxy. If no reference is given, the distance was determined from the galaxy's radial velocity, given by de Vaucouleurs et al. (1991), corrected for infall to the Virgo Cluster (Mould et al.\ 2000) and a Hubble constant of 73 km s$^{-1}$ Mpc$^{-1}$.}
\tablenotetext{c}{$R_H$ is the Holmberg radius, the radius of the galaxy at a $B$-band isophote, corrected for reddening, of 26.7 mag arcsec$^{-2}$. $R_D$ is the disk scale length measured from $V$-band images. (Table from Hunter \& Elmegreen 2006).}
\tablenotetext{d}{Foreground reddening from Burstein \& Heiles (1984).}
\tablenotetext{e}{$\Sigma_\mathrm{SFR}\mathrm{(H\alpha)}$ is the Star Formation Rate Density (SFRD) measured from H$\alpha$, calculated over the area $\pi R_D^2$, where $R_D$ is the disk scale length (Hunter \& Elmegreen 2004). $\Sigma_\mathrm{SFR}\mathrm{(FUV)}$ is the SFR density determined from {\it GALEX} FUV fluxes (Hunter et al.\ 2010, with an update of the {\it GALEX} FUV photometry to the GR4/GR5 pipeline reduction).}
\tablenotetext{f}{Values in parentheses were determined from the empirical relationship between oxygen abundance and $M_B$ given by Richer \& McCall (1995) and are particularly uncertain.}
\tablenotetext{g}{Reference for the oxygen abundance.}
\tablerefs{
(1) Dalcanton et al. 2009;
(2) Karachentsev et al. 2004;
(3) Karachentsev et al. 2003a;
(4) Karachentsev et al. 2006;
(5) Dolphin et al. 2002;
(6) Sakai et al. 2004;
(7) Dolphin et al. 2003;
(8) Karachentsev et al. 2003b;
(9) Tolstoy et al. 1995a;
(10) Karachentsev et al. 2002;
(11) Meschin et al. 2009;
(12) Sakai et al. 1999;
(13) Pietrzynski et al. 2006;
(14) Miller et al. 2001;
(15) Freedman et al. 2001;
(16) Grocholski et al. 2008;
(17) Tolstoy et al. 1995b;
(18) Gieren et al. 2006;
(19) Momany et al. 2002;
(20) Gieren et al. 2008;
(21) Schulte-Ladbeck et al. 2001;
(22) Lynds et al. 1998;
(23) M\'endez et al. 2002;
(24) van Zee \& Haynes 2006;
(25) Hunter \& Hoffman 1999;
(26) Skillman, Kennicutt, \& Hodge 1989;
(27) Moustakas et al.\ 2010;
(28) Richer \& McCall 1995;
(29) van Zee et al. 2006;
(30) Kniazev et al. 2005;
(31) Croxall et al. 2009;
(32) Lee et al. 2003b;
(33) Skillman et al. 1997;
(34) Lequex et al.\ 1979;
(35) Lee et al. 2003a;
(36) Kobulnicky \& Skillman 1997;
(37) Gonz\'alez-Delgado et al.\ 1994;
(38) Moustakas \& Kennicutt (2006);
(39) Masegosa et al. 1991;
(40) Lee et al. 2005;
(41) Viallefond \& Thuan 1983;
(42) Gon\'zalez-Riestra et al.\ 1988.
}
\end{deluxetable}
\end{landscape}
\restoregeometry
\section{OBSERVATIONS AND DATA REDUCTION}
\label{section:Paper1sample_and_data_reduction}
\subsection{Observations}
The LITTLE THINGS sample consists of 40 gas-rich dwarf galaxies within 11\,Mpc \cite[cf.][for sample details]{Hunter2012} and is listed in table~\ref{Table:tab-sample}. The sample spans 4\,dex in both SFR and gas mass, and a factor of 50 in metallicity.
Observations of the LITTLE THINGS sample were obtained (project ID: 12A-234) with the VLA at C-band (6\,cm: 4--8\,GHz) and in its C-configuration in 9 observing runs between March and May of 2012. All observing runs included one of four NRAO primary calibrators to calibrate the flux scale, and a calibrator within $10^{\circ}$ of each dwarf galaxy to correct the complex gain on timescales of around ${\rm 10\,minutes}$. For details of the various calibrators used see table~\ref{table:12A-234_Observations}. One of the primary goals of these observations is to resolve the faint low surface brightness emission associated with dwarf galaxies. C-configuration provided the best compromise between resolution and surface brightness sensitivity. We note that IC\,1613 is 0.7\,Mpc away and so has a large angular size. We utilised archival observations taken in D-configuration (project ID: AH1006) to minimise the effect of missing large scale emission for this galaxy. At C-band we expect a roughly equal mix of ${\rm RC_{Th}}$\ and ${\rm RC_{Nth}}$\ emission and sensitivity to spatial scales up to $\sim 4^\prime$. Given that most galaxies have angular sizes smaller than this we do not expect significant loss of large scale flux.
\begin{deluxetable}{ccccccccccc}
\tablewidth{0pt}
\tabletypesize{\tiny}
\tablecolumns{11}
\tablecaption{{\em C-}band\,\,Observations and Imaging Properties of LITTLE THINGS\label{table:12A-234_Observations}}
\tablehead{ & \multicolumn{3}{c}{Observation} & & \multicolumn{6}{c}{Imaging} \\ \\ \cline{2-4} \cline{6-11} \\ \colhead{Galaxy} & \colhead{Date} & \colhead{Flux Cal.} & \colhead{Gain Cal.} & & \multicolumn{2}{c}{Phase Centre} & \colhead{Scale} & \colhead{Res.} & \colhead{Noise} & \colhead{Notes} \\ \\ \cline{6-7} \\ \colhead{Name} & & \colhead{Name} & \colhead{Name} & & \colhead{R.A} & \colhead{Dec.} & \colhead{pc arcsec$^{-1}$} & \colhead{arcsec} & \colhead{$\mu$Jy\,beam$^{-1}$} & \\ (1) & (2) & (3) & (4) & & (5) & (6) & (7) & (8) & (9) & (10) }
\startdata
CVn I dwA & 2012 Mar 17 & 3C286 & J1310+3220& & $12\,38\,40.2$ & $+32\,45\,40$ & 6.3 & $3.0 \times 3.0$ & $4.3$ & N\\
DDO 43 & 2012 Mar 22 & 3C286 & J0818+4222 & & $07\,28\,17.8$ & $+40\,46\,13$ & 8.5 & $2.5 \times 2.3$ & $6.9$ & R,S\\
DDO 46 & 2012 Mar 22 & 3C286 & J0818+4222 & & $07\,41\,26.6$ & $+40\,06\,39$ & 8.5 & $3.0 \times 2.8$ & $5.1$ & N\\
DDO 47 & 2012 Mar 20 & 3C286 & J0738+1742 & & $07\,41\,55.3$ & $+16\,48\,08$ & 8.0 & $3.2 \times 3.0$ & $5.0$ & N\\
DDO 50 & 2012 Mar 17 & 3C147 & J0841+7053 & & $08\,19\,08.7$ & $+70\,43\,25$ & 5.2 & $4.4 \times 3.5$ & $5.5$ & N,S\\
DDO 52 & 2012 Mar 22 & 3C286 & J0818+4222 & & $08\,28\,28.5$ & $+41\,51\,21$ & 9.3 & $2.2 \times 2.0$ & $8.3$ & R,S\\
DDO 53 & 2012 Mar 16 & 3C147 & J0841+7053 & & $08\,34\,08.0$ & $+66\,10\,37$ & 5.6 & $4.9 \times 4.0$ & $5.4$ & N\\
DDO 63 & 2012 Mar 25 & 3C286 & J0841+7053 & & $09\,40\,30.4$ & $+71\,11\,02$ & 5.9 & $6.1 \times 3.4$ & $4.6$ & N\\
DDO 69 & 2012 Mar 20 & 3C286 & J0956+2515 & & $09\,59\,25.0$ & $+30\,44\,42$ & 1.2 & $4.1 \times 3.6$ & $4.0$ & N\\
DDO 70 & 2012 Mar 20 & 3C286 & J0925+0019 & & $10\,00\,00.9$ & $+05\,19\,50$ & 2.0 & $4.5 \times 3.4$ & $5.8$ & N\\
DDO 75 & 2012 Mar 20 & 3C286 & J1024$-$0052 & & $10\,10\,59.2$ & $-04\,41\,56$ & 2.0 & $3.3 \times 2.4$ & $9.7$ & N,S\\
DDO 87 & 2012 Mar 25 & 3C286 & J1048+7143 & & $10\,49\,34.7$ & $+65\,31\,46$ & 10.3 & $3.8 \times 2.2$ & $6.2$ & R\\
DDO 101 & 2012 Mar 17 & 3C286 & J1221+2813 & & $11\,55\,39.4$ & $+31\,31\,08$ & 13.9 & $3.1 \times 3.0$ & $15.1$ & R,S,P\\
DDO 126 & 2012 Apr 05 & 3C286 & J1215+3448 & & $12\,27\,06.5$ & $+37\,08\,23$ & 7.6 & $4.6 \times 4.0$ & $5.4$ & N,S\\
DDO 133 & 2012 Mar 17 & 3C286 & J1310+3220 & & $12\,32\,55.4$ & $+31\,32\,14$ & 9.4 & $3.8 \times 3.7$ & $4.4$ & N,S\\
DDO 154 & 2012 Mar 17 & 3C286 & J1310+3220 & & $12\,54\,06.2$ & $+27\,09\,02$ & 6.6 & $2.2 \times 2.2$ & $7.3$ & R,\\
DDO 155 & 2012 Mar 17 & 3C286 & J1309+1154 & & $12\,58\,39.8$ & $+14\,13\,10$ & 3.4 & $3.8 \times 3.5$ & $4.7$ & N\\
DDO 165 & 2012 Mar 25 & 3C286 & J1313+6735 & & $13\,06\,25.3$ & $+67\,42\,25$ & 7.4 & $3.7 \times 2.8$ & $4.5$ & R\\
DDO 167 & 2012 Apr 20 & 3C286 & J1327+4326 & & $13\,13\,22.9$ & $+46\,19\,11$ & 6.5 & $3.3 \times 3.0$ & $5.1$ & N\\
DDO 168 & 2012 Apr 20 & 3C286 & J1327+4326 & & $13\,14\,27.2$ & $+45\,55\,46$ & 5.4 & $3.9 \times 3.5$ & $4.4$ & N\\
DDO 187 & 2012 Mar 17 & 3C286 & J1407+2827 & & $14\,15\,56.7$ & $+23\,03\,19$ & 3.9 & $2.7 \times 2.5$ & $6.9$ & R,S\\
DDO 210 & 2012 May 19 & 3C48 & J2047$-$1639 & & $20\,46\,52.0$ & $-12\,50\,51$ & 1.4 & $3.1 \times 1.7$ & $4.6$ & R\\
DDO 216 & 2012 Mar 31 & 3C48 & J2253+1608 & & $23\,28\,35.0$ & $+14\,44\,30$ & 1.4 & $3.1 \times 2.9$ & $5.1$ & R\\
F564-V03 & 2012 Mar 20 & 3C286 & J0854+2006 & & $09\,02\,53.9$ & $+20\,04\,29$ & 9.6 & $3.3 \times 3.0$ & $5.4$ & N\\
Haro 29 & 2012 Apr 20 & 3C286 & 1219+484 & & $12\,26\,16.7$ & $+48\,29\,38$ & 8.3 & $3.9 \times 3.6$ & $5.1$ & N\\
Haro 36 & 2012 Apr 20 & 3C286 & 1219+484 & & $12\,46\,56.3$ & $+51\,36\,48$ & 13.9 & $3.9 \times 3.6$ & $5.2$ & N\\
IC 1613 & 2010 Aug 19 & 3C48 & J0108+0135 & & $01\,04\,49.2$ & $+02\,07\,48$ & 1.1 & $9.3 \times 7.8$ & $5.1$ & R\\
IC 10 & 2012 Apr 28 & 3C84 & J0102+5824 & & $00\,20\,17.3$ & $+59\,18\,14$ & 1.5 & $2.6 \times 2.3$ & $7.8$ & R\\
LGS 3 & 2012 Mar 31 & 3C48 & J0112+2244 & & $01\,03\,55.2$ & $+21\,52\,39$ & 0.9 & $3.0 \times 2.8$ & $5.5$ & R\\
M81 dwA & 2012 Mar 17 & 3C147 & J0841+7053 & & $08\,23\,57.2$ & $+71\,01\,51$ & 5.6 & $2.7 \times 1.9$ & $10.8$ & R,S,P\\
Mrk 178 & 2012 Apr 20 & 3C286 & 1219+484 & & $11\,33\,29.0$ & $+49\,14\,24$ & 6.0 & $4.4 \times 4.0$ & $9.3$ & N\\
NGC 1569 & 2012 Mar 16 & 3C147 & J0449+6332 & & $04\,30\,49.8$ & $+64\,50\,51$ & 3.9 & $2.7 \times 2.3$ & $6.8$ & R\\
NGC 2366 & 2012 Mar 16 & 3C147 & J0841+7053 & & $07\,28\,48.8$ & $+69\,12\,22$ & 4.9 & $4.2 \times 3.4$ & $5.1$ & N\\
NGC 3738 & 2012 Apr 20 & 3C286 & J1146+5356 & & $11\,35\,49.0$ & $+54\,31\,23$ & 7.6 & $2.5 \times 2.5$ & $7.6$ & N,S\\
NGC 4163 & 2012 Apr 05 & 3C286 & J1215+3448 & & $12\,12\,09.2$ & $+36\,10\,13$ & 4.3 & $3.3 \times 2.9$ & $4.5$ & N\\
NGC 4214 & 2012 Apr 05 & 3C286 & J1215+3448 & & $12\,15\,39.2$ & $+36\,19\,38$ & 4.5 & $4.5 \times 4.0$ & $6.3$ & N,S\\
Sag DIG & 2012 May 19 & 3C48 & J1911$-$2006 & & $19\,30\,00.6$ & $-17\,40\,56$ & 1.7 & $3.5 \times 1.4$ & $8.2$ & R\\
UGC 8508 & 2012 Apr 20 & 3C286 & J1349+5341 & & $13\,30\,44.9$ & $+54\,54\,29$ & 4.0 & $2.6 \times 2.5$ & $6.0$ & N\\
VIIZw 403 & 2012 Mar 25 & 3C286 & J1153+8058& & $11\,27\,58.2$ & $+78\,59\,39$ & 6.8 & $5.8 \times 3.7$ & $5.8$ & N\\
WLM & 2012 May 19 & 3C48 & J2348$-$1631 & & $00\,01\,59.2$ & $-15\,27\,41$ & 1.5 & $5.0 \times 1.5$ & $5.3$ & R\\
\enddata
\tablecomments{ (Column 1) Name of dwarf galaxy observed;
(Column 2) Date of observation;
(Column 3) Name of primary calibrator;
(Column 4) Name of secondary calibrator;
(Columns 5 \& 6) J$2000$ equatorial coordinate of observation (dwarf galaxy) phase centre;
(Column 7) Physical scale at distance of galaxy;
(Column 8) Resolution of image. Note that some images were made using {\sc robust=0.0} and others using {\sc robust=+2.0} where CASA robust values range between $-2.0$ (uniform weighting) and $+2.0$ (natural weighting);
(Column 9) rms noise;
(Column 10) Comments regarding deviations from the typical imaging process: R signifies that the {\sc clean} algorithm was performed using {\sc robust=0.0} weighting, whereas N signifies an approach closer to natural weighting; S means that the generated image benefited from self-calibration; P refers to those images that were strongly affected by a bright, nearby background source of $\sim 0.1{\rm \,Jy}$ which was located such that it entered the sidelobes of the primary beam. Because of the Alt--Az mounting of the VLA antennas, the primary beam rotates on the sky making the detected signal time varying; self-calibration failed as a result. To minimise the effect of the offending source, only about a quarter of the bandwidth was used, using those spectral windows in which the first null of the primary beam coincides as near as possible to the offending source.}
\end{deluxetable}
\subsection{Radio Continuum Calibration \& Imaging}
We calibrated the data using the Common Astronomy Software Applications ({\sc casa}\footnote{http://casa.nrao.edu/}; \citealt{McMullin2007}) package following standard procedures that we present in the following subsections.
\subsubsection{Flagging}
Before calibration we used the {\sc tflagdata} task to apply two automatic flagging algorithms: {\sc tfcrop} \citep{Rau2003} and {\sc rflag} (based on {\sc aips}; \citealt{Greisen2011}). The {\sc tfcrop} algorithm identifies outliers by splitting each baseline into `chunks' along the frequency--domain (each channel) and time--domain (every $50$ seconds). The amplitude of all visibilities within a given chunk were averaged and then any chunks with an amplitude greater than $4\,\sigma_{\rm pre}$ from the mean were flagged. Here, $\sigma_{\rm pre}$ refers to the pre-calibration dispersion of amplitudes around the mean. We opted for a conservative threshold value as, at this point, we were only concerned with removing extremely high--amplitude data such that subsequent steps in the calibration would not be affected. The {\sc rflag} algorithm detects outliers by using a sliding window in the time and then spectral window domain to determine local statistics and identify data that exceed $4\,\sigma_{\rm pre}$. The algorithm first calculates the local rms within each sliding window. It then calculates the median rms across the time windows, deviations of the local rms from this median, and the median deviation. Data is flagged if the local rms is larger than $4\times(\rm medianRMS + medianDev)$. For a more in depth description of these algorithms see \cite{Rau2003} and \cite{Greisen2011}. Bad baselines, scans and channels, as well as wide--band radio frequency interference (RFI) were generally caught by the algorithms although the measurement sets were manually checked to identify any discrepant visibilities that were missed. This approach typically resulted in the removal of $15$--$20$\% of the observed visibilities.
\subsubsection{Calibration}
The flux scale in our images was set using one of recommended VLA primary flux calibrators given in column\,3 of table~\ref{table:12A-234_Observations} using the task {\sc setjy}. This flux calibrator was also bright enough to be used to correct for the bandpass shape using the task {\sc bandpass}. Calibration of the time-dependant complex gain was achieved by regular observations of a nearby gain calibrator (table~\ref{table:12A-234_Observations}; column\,4) using {\sc gaincal}.
Once calibration was completed, each measurement set was inspected a final time for low--level RFI. First, a manual check was performed to flag baselines, scans, or channels that exhibited deviant amplitudes or phases. In addition to this, a second round of automated flagging was performed (this time designed to catch outliers greater than $3.5\,\sigma_{\rm post}$ from the mean). Here, $\sigma_{\rm post}$ refers to the post--calibration dispersion of amplitudes around the mean. This flagging on the calibrated data often reduced the rms noise in subsequent imaging by a further $\sim 10$\% (compared to when this second round of flagging was omitted).
\subsubsection{Imaging}
\label{Section:paper1_Imaging}
We generated images of our targets using the {\sc casa} {\sc clean} task, using the Multi-Scale, Multi-Frequency Synthesis (MS-MFS) algorithm developed by \cite{Rau2011}. Due to the various angular scales of emission observed in the galaxies, the cleaning scales chosen were unique to each observation to give the optimum {\sc clean} map. At least two scales of $1$ and $3$ times the synthesised beam width were used. In a few cases larger angular scales were added to deal with large--scale emission in the brighter, more extended galaxies such as DDO\,50 and NGC\,1569.
Due to the faint nature of the dwarfs, observations were generally Fourier-transformed using natural weighting ({\sc robust=+2.0}). This ensured we optimised our images for S/N. Some observations were mapped using Brigg's robust imaging method ({\sc robust=0.0}) because either 1) the galaxy was sufficiently bright that a high enough S/N was reached using {\sc robust=0.0} weighting, or 2) the natural weighting {\sc clean} left significant image artefacts throughout the image due to the rather sparse sampling of the ($u,v$) plane. Using the Brigg's {\sc robust=0.0} method ensures that the image is not dominated by visibilities representing the more numerous short baselines. This method increases the resolution, results in a synthesised beam that more closely resembles a Gaussian shape, and improves the image quality but at the expense of a slight (${\rm \sim 20\%}$) increase of the rms noise. Typical rms noise values in these cleaned images fell between $4$ and $8{\rm \,\mu Jy\,beam^{-1}}$ in close agreement with expected values. Table~\ref{table:12A-234_Observations} states whether the image of the galaxy was generated using {\sc robust=0.0} weighting (R) or an approach closer to natural weighting (N).
Self-calibration (phase only) was performed on 11 of our 40 observations to improve the dynamic range across the image; these are marked in table~\ref{table:12A-234_Observations} (S symbol in column 10). In only one case (NGC\,4214) the emission originating from the galaxy itself produced strong enough artefacts to warrant self-calibration; in all other cases, the offending source was an unresolved background object.
Observations of DDO\,101 and M81\,DwA (marked in table~\ref{table:12A-234_Observations}) harboured the strongest background sources in our survey. These sources have a flux density of $> 0.1{\rm \,Jy}$ and are located approximately $9^\prime$ and $6^\prime$ from the observation's phase centre, respectively. Self-calibration was not successful in sufficiently improving the dynamic range for these images. This is due to a combination of both offending sources residing near the edge of the primary beam combined with the VLA antennas operating on an Alt-Az mount. This causes the offending sources to have a time-varying signal due to the source passing through the sidelobes of the primary beam. The result is that the MS--MFS {\sc clean} algorithm cannot successfully remove the sidelobes of the confusing source. Since these sources are not of interest to our project --- they lie beyond the FWHM of the primary beam anyway --- we decided to select solely the spectral windows least affected by the offending background source, i.e., by choosing $2$ or $3$ spectral windows for which the first null of the primary beam fell close to the offending source. In doing this, the rms noise was approximately doubled to $15{\rm \,\mu Jy\,beam^{-1}}$ while the side lobes of the confusing source were considerably suppressed. We note that in an earlier study, \cite{Stil2002} do not list a flux density for DDO\,101 for the same technical reason.
We maintained as much consistency as possible by using the same calibration and imaging pipeline for all observations. Our images prior to primary beam correction had a flat noise background lacking in significant structure. Very few images had artefacts from nearby strong ($>0.5{\rm \,mJy}$) sources. Those that did had the offending regions masked manually. Our residual maps comprise a Gaussian intensity distribution consistent with pure noise, having an average of $0$ and variance of $\sigma$ suggesting that the MS-MFS algorithm successfully modelled all genuine emission present in the ($u$,$v$) data. Only NGC\,1569 and NGC\,4214 showed any indication of sitting in a negative bowl, suggesting they suffer from missing flux on the largest scales (see Section~\ref{Section:MissingStructures} for further discussion). The observations and imaging properties of all LITTLE THINGS targets are summarised in table~\ref{table:12A-234_Observations}. Notes on the data reduction of individual galaxies can be found in Appendix\label{section:Appendix_IndividualNotes}.
\subsection{Ancillary Data}
\label{section:Paper1AncillaryData}
The LITTLE THINGS project has acquired a large collection of multi-wavelength and spatially resolved data on each of the $40$ dwarf galaxies \cite[see][for details]{Hunter2012,Zhang2012}. We make use of the following ancillary data in this study:
\begin{itemize}
\item H${\alpha}$\ line emission: the FWHM of the filter used for the H${\alpha}$\ observations was $30$\,\AA\ centred on $6562.8$\,\AA\ \cite[][]{Hunter2004}, while the FWHM of the point spread function (PSF) was $\sim2^{\prime\prime}$. The maps were continuum subtracted and the fluxes corrected for [NII] contribution. \cite{Hunter2012} used \cite{Burstein1982} values to correct H${\alpha}$\ and FUV maps for foreground reddening. Internal extinction in dwarf galaxies can generally be ignored because they have low--metallicity and consequently a low dust-to-gas ratio with respect to spirals \citep{Ficut2016}. However, internal extinction may be important in some of the more actively star forming dwarfs. We discuss this further in Section~\ref{sect:rccomp};
\item Far-Ultraviolet broadband emission: the FUV data were taken with {\em GALEX} in the $1350$--$1750$ \AA\ band (effective wavelength of $1516$ \AA) with a resolution of $4^{\prime\prime}$ at the FWHM. The data were calibrated with the GR4/5 pipeline except DDO\,165 and NGC\,4214 which were processed with the GR6 pipeline \cite[][]{Zhang2012}. The resulting images have been sky subtracted and geometrically transformed to match the optical {\em V}-band orientation. UGC\,8508 was not observed due to bright foreground stars, and IC\,10 was not observed due to its low Galactic latitude placing it in a region of high extinction. For surface brightness measurements, and hence for extended emission, the estimated uncertainty for the {\em GALEX} FUV maps is $0.15$\,mag \cite[][]{GildePaz2007};
\item Infrared (IR) broadband emission: the IR data were taken with the {\em Spitzer} space telescope using the Multiband Imaging Photometer for Spitzer (MIPS). The two bands used were mid-infrared (MIR), with an effective wavelength of 24\micron\ with a resolution of $6^{\prime\prime}$ at FWHM, and FIR with an effective wavelength of 70\micron\ and a resolution of $17^{\prime\prime}.5$ at FWHM. The {\em Spitzer} $24$ and 70\micron\ maps were taken from either the Local Volume Legacy (LVL) survey \cite[see][for details]{Dale2009} or the {\em Spitzer} Infrared Nearby Galaxies Survey (SINGS). A pixel-dependent background subtraction was performed and images were convolved with a custom kernel to make a near Gaussian PSF. For the Spitzer 24\micron\ maps, the photometric uncertainty is 2\% for both unresolved sources and extended emission \cite[][]{Engelbracht2007}.
\end{itemize}
\section{RESULTS}
\label{section:Paper1Results}
\label{section:Paper1Images}
\label{section:Paper1radio_continuum_images}
\begin{figure*}
\begin{tabular}{ccc}
\includegraphics[width=0.31\linewidth,clip]{f001a_ddo50Cc_Flux.pdf} & \
\includegraphics[width=0.31\linewidth,clip]{{f001b_ddo50Cc_Flux_on_Flux}.pdf} & \
\includegraphics[width=0.31\linewidth,clip]{{f001c_ddo50Cc_Flux_Goodmasked}.pdf} \\
\includegraphics[width=0.31\linewidth,clip]{{f001d_ddo50Cc_Flux_on_Ha}.pdf} & \
\includegraphics[width=0.31\linewidth,clip]{{f001e_ddo50Cc_NT}.pdf} & \
\includegraphics[width=0.31\linewidth,clip]{{f001f_ddo50Cc_Flux_on_FUV}.pdf} \\
\includegraphics[width=0.31\linewidth,clip]{{f001g_ddo50Cc_Flux_on_24um}.pdf} & \
\includegraphics[width=0.31\linewidth,clip]{{f001h_ddo50Cc_Flux_on_70um}.pdf} & \
\includegraphics[width=0.31\linewidth,clip]{{f001i_ddo50Cc_Flux_on_sfrLeroy2012}.pdf} \\
\end{tabular}
\caption{Multi-wavelength coverage of DDO\,50 displaying an $8.0^\prime \times 8.0^\prime$ area. We show total RC flux density at the native resolution (top-left) and again with contours (top-centre). The lowest contour highlights low--surface brightness emission at a S/N level of 3 in the image smoothed to $10''$. The remaining contours are at S/N levels of 3, 6, 9, and then multiples of twice the previous contour level from our native resolution images. These contours are also superposed on ancillary LITTLE THINGS images where possible: H${\alpha}$\ (middle-left); ${\rm RC_{Nth}}$\ (middle-centre); {\em GALEX} FUV (middle-right); {\em Spitzer} 24\micron\ (bottom-left); {\em Spitzer} 70\micron\ (bottom-centre); FUV$+24{\rm \mu m}$--inferred SFRD (bottom-right). We also show the RC that is isolated by the RC--based and disk masking technique (top-right). In this panel the green contours outline the RC mask and includes background and ambiguous sources. The elliptical outline corresponds to the area hence forth referred to as the disk mask.}
\label{figure:example_maps}
\end{figure*}
We present an example of our multi-wavelength data set in Fig.~\ref{figure:example_maps}, which shows our data for DDO\,50. This includes the results of our RC observations and contours overlaid onto the H${\alpha}$, FUV, and 24\micron\ images. Multi-wavelength images for our entire sample can be found in the online electronic version in Appendix~\ref{Section:Appendix_Images}.
\subsection{Identifying Emission unrelated to the Target Object}
\label{section:Paper1background_source_removal}
Contamination by background sources in the RC is an issue since their emission is often brighter than, or similar to, the emission originating from the dwarf galaxy \citep{Padovani2011}. Low resolution observations reported in the literature are predominantly from single dish observations and will have suffered from contamination to varying degrees. Our resolved maps make it possible to remove the effects of contamination by identifying emission unrelated to our galaxies.
We inspected each of our RC images and classified features in a manner similar to \cite{Chomiuk2009}. Flux was attributed as originating from either: %
\begin{itemize}
\item the dwarf galaxy (exactly coincident with a SF tracer); %
\item a background galaxy; %
\item ambiguous emission of unknown origin (i.e., unable to discern between a) background origin, or b) non-thermal emission from unresolved SNRs or diffuse non--thermal emission).
\end{itemize}
\noindent We applied a two step process to classify the RC emission in our images into these three catagories. First, we cross-matched our RC sources with the literature. Following this we applied a procedure designed to isolate RC emission features from background galaxies based on their proximity to H${\alpha}$\ emission. We describe these two steps in more detail below.
\subsubsection{Cross-matching with line-of-sight Optical Counterparts}
We manually cross matched unresolved sources of RC emission with the NASA/IPAC Extragalactic Database\footnote{\scriptsize{\url{http://ned.ipac.caltech.edu/forms/nearposn.html}}} (NED). If an archived galaxy was found within $2^{\prime\prime}$ (approximately half the FWHM of the synthesised beam at the native resolution) of the unresolved RC source, we characterised that source as a background galaxy.
\subsubsection{Isolating obvious Background Galaxies}
RC emission coming from the same line-of-sight as the H${\alpha}$\ emission from H\,{\sc ii}\ regions was assumed to originate from the dwarf galaxy. All galaxies in our sample have heliocentric velocities and rotational speeds \cite[][]{Hunter2012} that ensure all H${\alpha}$\ emission falls within the FWHM of the filter used, which is $30$\,\AA\ wide and centred on $6562.8$\,\AA\ \cite[][]{Hunter2004}. Unresolved background galaxies and SNRs look similar and share broadly similar values for their non--thermal spectral index, with values of $-0.85\pm0.13$ \citep{Niklas1996} and $-0.5 \pm 0.2$ \citep{Green2014}, for background galaxies and SNRs, respectively. SNRs from core--collapse supernovae are expected to be associated with SF regions in our dwarf galaxies. This is because the stellar velocity dispersion in dwarf galaxies is low \citep{Walker2007}, which implies that over the lifetime of a SNR, it will not have strayed very far from its host massive star cluster. Studies of dwarf galaxies have measured velocity dispersions of $\lesssim 10{\rm \,km\,s^{-1}}$ \citep{Walker2007,Mateo1998,Martin2007}, but the stellar velocity dispersion would be yet lower for the sub-population of high mass stars (i.e., the core-collapse supernova progenitors) since these would generally sink to the bottom of the parent cluster's gravitational potential. Based on the above we assume a stellar velocity dispersion of $5{\rm \,km\,s^{-1}}$ for the stars that eventually lead to the injection of \mbox{CR$e$}\ (and the associated ${\rm RC_{Nth}}$\ emission). Given that a SN progenitor may live up to ${\rm 55\,Myr}$ and assuming a typical distance of 5\,Mpc, a SNR can travel a projected distance of $<250$\,pc or $<10^{\prime\prime}$ (for a face-on galaxy). Any significant RC source, unresolved or extended, that had little to no H${\alpha}$\ emission within this projected radius was marked as a background source and was removed by placing a mask over the source. For a Gaussian-like synthesised beam, $99$\% of the power of an unresolved source is contained within $3 \times {\rm FWHM_{\rm native}}$, and so this was the diameter of the mask placed over the background source. Even for a strong background source (e.g., $1{\rm \,m Jy}$), this removal technique leaves at most $10{\rm \,\mu Jy}$ unmasked in the image, whilst not masking out too much of the dwarf galaxy.
\subsubsection{Ambiguous Sources}
After cross matching with NED and isolating ambiguous sources by comparing to H${\alpha}$\ there remained sources that we could not attribute as coming from a background galaxy, but at the same time were not close enough to a SF site to be confidently classified as originating from the target galaxy; we refer to these sources of RC emission as ambiguous. To illustrate our definition of ambiguous RC emission, we present four of our observations that contained such a source in Fig.~\ref{figure:ambiguous_examples}. A strong unresolved source can be seen in DDO\,46 and DDO\,63, whilst DDO\,69 and IC\,1613 demonstrate galaxies with significantly extended sources.
\begin{figure*}
\begin{tabular}{cc}
\includegraphics[width=0.48\linewidth,clip]{{f003a_ddo46Cc_Flux_on_FUV}.pdf} & \
\includegraphics[width=0.48\linewidth,clip]{{f003b_ddo63Cc_Flux_on_FUV}.pdf} \\
\includegraphics[width=0.48\linewidth,clip]{{f003c_ddo69Cc_Flux_on_FUV}.pdf} & \
\includegraphics[width=0.48\linewidth,clip]{{f003d_ic1613C1d1_Flux_on_FUV}.pdf}
\end{tabular}
\caption{\footnotesize{Examples of our definition of ambiguous emission (red dashed circles). We show DDO\,46 and DDO\,63 each of which containing an unresolved source of $1{\rm \,mJy}$ (top-left) and ${\rm 1.4\,mJy}$ (top-right), respectively. We also show DDO\,69 and IC\,1613 which both contain an extended source (bottom panels). The RC emission could not be attributed as definitely coming from a background galaxy, but at the same time was not close enough to a SF site to be confidently classified as originating from the target galaxy either; accordingly, these sources were designated ambiguous.}}
\label{figure:ambiguous_examples}
\end{figure*}
Most of our observations contained at least one ambiguous source; none of these had a non-thermal luminosity that exceeded a reference threshold---that of a known bright SNR ($1 \times 10^{19} {\rm \,W}{\rm \,Hz}^{-1}$ or $3.3 {\rm \,mJy}$ at 5\,Mpc at 6\,GHz). This reference luminosity was based on observations of SNR N4449-12, which resides in the dwarf galaxy NGC\,4449 at a distance of $4.2$\,Mpc. In 2002 this SNR had a luminosity of $S_{\rm 6cm}=4.84{\rm \,mJy}$ with a spectral index of $\alpha=-0.7$ between $20$\,cm and $6$\,cm \cite[][]{Chomiuk2009}. For comparison, this is $10$ times the luminosity of Cassiopeia\,A. Since the luminosity terminally declines for the majority of the SNR's lifetime, we treat the observed luminosity of SNR N4449-12 in 2002 as an approximate empirical upper limit to the luminosity of a supernova remnant. We justify our use of SNR N4449-12 as it was the most luminous from a sample of 43 SNRs from 4 irregular galaxies (35 of which are in galaxies that overlap with our sample, namely: NGC\,1569, NGC\,2366, and NGC\,4214).
Using the method above we are able to classify all of the observed RC emission in our images. As an example, we show DDO\,133 in Fig.~\ref{figure:ddo133_sources} along with the classification attributed to each source of RC emission.
\begin{figure*}
\centering
\includegraphics[width=0.6\linewidth]{{f002a_ddo133_sources}.pdf}
\caption{\footnotesize{{\em GALEX} FUV emission of DDO\,133 overlaid with our RC contours. Following the procedure outlined in the text we attribute RC emission as being from either the galaxy itself (G, green), a background galaxy (B, red), or an unknown or ambiguous source (?, blue). We also overlay the optical disk size (defined by the Holmberg radius; purple dashed ellipse). }}
\label{figure:ddo133_sources}
\end{figure*}
\subsection{Missing Large-scale Structures}
\label{Section:MissingStructures}
Owing to the way that interferometers function, large angular structures in the sky can be completely missed if their corresponding visibilities are not recorded by the interferometer. The largest angular scale ($\theta_{\rm LAS}$) that the VLA is sensitive to in C-configuration (shortest baseline of 35\,m) at 6\,cm is $\sim 4$ arcminutes. This assumes an observation of 12\,hours that is uniformly weighted and untapered. Observations of a shorter duration will have a slightly lower $\theta_{\rm LAS}$ value and for weighting schemes closer to natural weighting the $\theta_{\rm LAS}$ will be larger. In our observations angular scales of $\sim 4$ arcminutes and above may not be adequately sampled leading to a lower than expected flux density; there are only $7$ galaxies with an angular size greater than $4^\prime$ (see column $4$ of table~\ref{table:12A-234_DiskQuantities}). Under the assumption that RC emission coincides with optical emission, it is only these galaxies that are vulnerable to having large angular structures absent in the ($u$,$v$) data. Even so, SF in dwarf galaxies is intermittent on scales of one to a few Gyr, whereas \mbox{CR$e$}\ age over much shorter timescales of tens of Myr; therefore, in the majority of our sample no significant emission is expected from, for example, a \mbox{CR$e$}\ halo. We note that NGC\,1569 was found to have an extended radio halo extending beyond the optical emission when observed between 0.6 and 1.4\,GHz \citep{Israel1988}. This is attributed to the post-starburst nature of the galaxy which is not reflected in the majority of targets in our sample. We do not see any evidence of such a halo in our 6\,GHz image. This may be due to spatial filtering or spectral ageing which has shifted the halo emission below our detection threshold.
\subsection{Disk Integrated Quantities}
With background and ambiguous sources removed (see Section~\ref{section:Paper1background_source_removal}), emission from our RC and ancillary images was integrated within each of the dwarf galaxy's optical disks (hereafter the disk mask; see table~\ref{table:12A-234_DiskQuantities} for the disk parameters). We also extract the integrated properties including the ambiguous sources; these can be found in the online material (Appendix~\ref{Section:Appendix_Tables}). The semi-major axis of the disk was based on optical isophotes: using either the Holmberg radius \cite[defined as the isophote where the {\em B}-band surface brightness drops to a magnitude of 26.66;][]{Hunter2006} or $3$ times the {\em V}-band disk scale length \cite[][]{Hunter2006} if the {\em B}-band radius was not defined. All emission outside this radius was masked.
\begin{deluxetable}{lccccccccccc}
\tablewidth{0pt}
\tabletypesize{\tiny}
\tablecolumns{13}
\rotate
\tablecaption{Integrated emission over the disk of the LITTLE THINGS Galaxies\label{table:12A-234_DiskQuantities}}
\tablehead{
\colhead{Galaxy} & \colhead{Size} & \colhead{P.A.} & \colhead{6\,cm RC} & \colhead{H${\alpha}$} & \colhead{FUV} & \colhead{24\micron\ MIR} & \colhead{70\micron\ FIR} & \colhead{6\,cm ${\rm RC_{Nth}}$} & \colhead{$B_{\rm eq}$} \\
& ($^{\prime}$) & ($^\circ$) & (mJy) & ($10^{-13} $\,ergs\,s$^{-1}$\,cm$^{-2}$) & (mJy) & ($10^{-2}$\,Jy) & ($10^{-2}$\,Jy) & (mJy) & (${\rm \mu G}$) \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10)}
\startdata
CVn I dwA & $1.7 \times 1.4$ & $80$ & $>0.29$ & $1.95\pm 0.03$ & $1.04\pm 0.11$ & $0.15\pm 0.06$ & $2.46\pm 0.04$ & $>0.29$ & $<2$ \\
DDO 43 & $1.8 \times 1.2$ & $6$ & $>0.99$ & $1.28\pm 0.03$ & $1.07\pm 0.11$ & \nodata & \nodata & $>0.99$ & $<2$ \\
DDO 46$^\mathrm{V}$ & $3.8 \times 3.4$ & $84$ & $>1.16$ & $1.08\pm 0.02$ & $1.75\pm 0.17$ & \nodata & \nodata & $>1.16$ & $<2$ \\
DDO 47 & $4.5 \times 2.3$ & $-79$ & $>0.61$ & $3.00\pm 0.03$ & $3.00\pm 0.30$ & \nodata & \nodata & $>0.61$ & $<2$ \\
DDO 50 & $7.9 \times 5.7$ & $18$ & $6.70 \pm 0.60$ & $60.10\pm 0.49$ & $41.95\pm 4.20$ & $17.27\pm 0.01$ & $319.90\pm 0.28$ & $0.99\pm 0.60$ & $<2$ \\
DDO 52 & $2.2 \times 1.4$ & $4$ & $>1.28$ & $0.29\pm 0.01$ & $0.61\pm 0.06$ & $-0.04\pm 0.02$ & $1.81\pm 0.05$ & $>1.28$ & $<1$ \\
DDO 53 & $2.7 \times 1.4$ & $81$ & $0.65 \pm 0.13$ & $4.32\pm 0.04$ & $2.55\pm 0.26$ & $2.32\pm 0.02$ & $24.05\pm 0.03$ & $0.24\pm 0.13$ & $<1$ \\
DDO 63 & $4.3 \times 4.3$ & $0$ & $>0.71$ & $4.39\pm 0.04$ & $5.03\pm 0.50$ & $1.77\pm 0.01$ & $3.74\pm 0.13$ & $>0.71$ & $<1$ \\
DDO 69 & $4.8 \times 2.7$ & $-64$ & $>0.89$ & $1.66\pm 0.01$ & $4.67\pm 0.47$ & $-0.65\pm 0.01$ & $11.08\pm 0.07$ & $>0.89$ & $<1$ \\
DDO 70 & $7.4 \times 4.4$ & $88$ & $>1.48$ & $6.27\pm 0.04$ & $11.53\pm 1.15$ & $0.59\pm 0.01$ & $63.09\pm 0.13$ & $>1.48$ & $<1$ \\
DDO 75 & $6.2 \times 5.2$ & $42$ & $>2.04$ & $40.44\pm 0.10$ & $29.46\pm 2.95$ & $0.20\pm 0.01$ & $77.89\pm 0.20$ & $>2.04$ & $<1$ \\
DDO 87 & $2.3 \times 1.3$ & $76$ & $>0.70$ & $0.68\pm 0.01$ & $0.65\pm 0.06$ & $0.07\pm 0.02$ & $7.03\pm 0.03$ & $>0.70$ & $<2$ \\
DDO 101 & $2.1 \times 1.5$ & $-69$ & $>1.79$ & $0.82\pm 0.01$ & $0.39\pm 0.04$ & $0.24\pm 0.02$ & $-0.54\pm 0.04$ & $>1.79$ & $<2$ \\
DDO 126 & $3.5 \times 1.7$ & $-41$ & $>0.57$ & $3.66\pm 0.08$ & $2.91\pm 0.29$ & $0.32\pm 0.03$ & $14.92\pm 0.10$ & $>0.57$ & $<2$ \\
DDO 133 & $4.7 \times 3.2$ & $-6$ & $>1.17$ & $4.55\pm 0.03$ & $4.09\pm 0.41$ & $0.53\pm 0.01$ & $33.04\pm 0.13$ & $>1.17$ & $<2$ \\
DDO 154 & $3.1 \times 1.6$ & $46$ & $>1.73$ & $2.21\pm 0.02$ & $3.77\pm 0.38$ & $0.28\pm 0.03$ & $3.66\pm 0.04$ & $>1.73$ & $<1$ \\
DDO 155 & $1.9 \times 1.3$ & $51$ & $>0.47$ & $4.85\pm 0.05$ & \nodata & $0.22\pm 0.03$ & $16.15\pm 0.05$ & $>0.47$ & $<2$ \\
DDO 165 & $4.3 \times 2.3$ & $89$ & $>1.19$ & $1.53\pm 0.01$ & \nodata & $0.04\pm 0.01$ & $10.64\pm 0.06$ & $>1.19$ & $<2$ \\
DDO 167 & $1.5 \times 1.0$ & $-24$ & $>0.51$ & $0.80\pm 0.01$ & $1.05\pm 0.11$ & \nodata & \nodata & $>0.51$ & $<3$ \\
DDO 168 & $4.6 \times 2.9$ & $-25$ & $>0.94$ & $5.91\pm 0.03$ & $5.55\pm 0.56$ & $0.67\pm 0.01$ & $41.94\pm 0.10$ & $>0.94$ & $<1$ \\
DDO 187 & $2.1 \times 1.7$ & $37$ & $>1.17$ & $0.57\pm 0.01$ & $1.15\pm 0.12$ & $-0.02\pm 0.03$ & $-1.94\pm 0.09$ & $>1.17$ & $<1$ \\
DDO 210 & $2.6 \times 1.3$ & $-85$ & $>0.87$ & \nodata & $0.80\pm 0.08$ & $-0.16\pm 0.02$ & $5.26\pm 0.04$ & $>0.87$ & $<2$ \\
DDO 216 & $8.0 \times 3.6$ & $-58$ & $>1.28$ & $0.09\pm 0.01$ & $2.00\pm 0.20$ & $-0.12\pm 0.01$ & $9.87\pm 0.08$ & $>1.28$ & $<1$ \\
F564-V03$^\mathrm{V}$ & $1.3 \times 1.0$ & $7$ & $>0.35$ & \nodata & $0.10\pm 0.01$ & \nodata & \nodata & $>0.35$ & $<3$ \\
Haro 29 & $1.7 \times 1.0$ & $85$ & $2.14 \pm 0.11$ & $13.02\pm 0.45$ & $3.02\pm 0.32$ & $5.83\pm 0.05$ & $39.00\pm 0.05$ & $0.91\pm 0.12$ & $6$ \\
Haro 36$^\mathrm{V}$ & $1.5 \times 1.2$ & $90$ & $0.94 \pm 0.09$ & $2.41\pm 0.03$ & $2.84\pm 0.29$ & $0.94\pm 0.04$ & $23.66\pm 0.06$ & $0.71\pm 0.09$ & $5$ \\
IC 1613 & $18.2 \times 14.7$ & $71$ & $4.49 \pm 0.55$ & $55.81\pm 0.87$ & $91.86\pm 9.24$ & $6.85\pm 0.02$ & $408.70\pm 1.73$ & $-0.77\pm 0.55$ & $<1$ \\
IC 10$^\mathrm{V}$ & $11.6 \times 9.1$ & $-38$ & $96.38 \pm 0.81$ & $1191.00\pm 5.73$ & \nodata & $3741.00\pm 4.83$ & $9547.00\pm 12.08$ & $-16.78\pm 0.97$ & $<1$ \\
LGS 3 & $1.9 \times 1.0$ & $-3$ & $>0.57$ & \nodata & $0.08\pm 0.01$ & \nodata & \nodata & $>0.57$ & $<2$ \\
M81 dwA$^\mathrm{V}$ & $1.5 \times 1.1$ & $86$ & $>1.28$ & \nodata & $0.38\pm 0.04$ & \nodata & \nodata & $>1.28$ & $<2$ \\
Mrk 178 & $2.0 \times 0.9$ & $-51$ & $1.01 \pm 0.14$ & $5.38\pm 0.09$ & $2.56\pm 0.27$ & $0.45\pm 0.03$ & $0.45\pm 0.01$ & $0.50\pm 0.14$ & $5$ \\
NGC 1569$^\mathrm{V}$ & $2.3 \times 1.3$ & $-59$ & $149.60 \pm 0.31$ & $486.70\pm 3.02$ & $746.50\pm 75.63$ & $705.50\pm 13.61$ & $3543.00\pm 2.66$ & $71.38\pm 0.57$ & $17$ \\
NGC 2366 & $9.4 \times 4.0$ & $33$ & $9.66 \pm 0.59$ & $96.38\pm 1.11$ & $37.26\pm 3.73$ & $65.47\pm 0.01$ & $506.20\pm 0.30$ & $0.51\pm 0.60$ & $17$ \\
NGC 3738 & $4.8 \times 4.8$ & $0$ & $2.62 \pm 0.48$ & $16.26\pm 0.17$ & $11.22\pm 1.13$ & $11.65\pm 0.03$ & $248.10\pm 0.41$ & $1.07\pm 0.48$ & $17$ \\
NGC 4163 & $2.9 \times 1.9$ & $18$ & $>0.69$ & $1.48\pm 0.02$ & $2.68\pm 0.27$ & $0.43\pm 0.03$ & $10.20\pm 0.11$ & $>0.69$ & $<2$ \\
NGC 4214 & $9.3 \times 8.5$ & $16$ & $27.78 \pm 0.57$ & $178.60\pm 0.92$ & $80.72\pm 8.08$ & $199.60\pm 0.01$ & $2393.00\pm 1.13$ & $10.81\pm 0.57$ & $6$ \\
Sag DIG$^\mathrm{V}$ & $4.3 \times 2.3$ & $88$ & $>2.47$ & $1.28\pm 0.01$ & $4.52\pm 0.45$ & \nodata & \nodata & $>2.47$ & $<1$ \\
UGC 8508 & $2.5 \times 1.4$ & $-60$ & $0.38 \pm 0.13$ & $2.75\pm 0.04$ & \nodata & $0.37\pm 0.03$ & $12.52\pm 0.04$ & $0.12\pm 0.13$ & $<1$ \\
VIIZw 403 & $2.2 \times 1.1$ & $-11$ & $1.37 \pm 0.10$ & $7.48\pm 0.15$ & $3.67\pm 0.38$ & $1.87\pm 15.06$ & $57.05\pm 1.36$ & $0.66\pm 0.10$ & $5$ \\
WLM & $11.6 \times 5.1$ & $-2$ & $>2.51$ & $16.81\pm 0.06$ & $29.53\pm 2.96$ & $4.61\pm 0.01$ & $117.70\pm 0.18$ & $>2.51$ & $<1$ \\
\enddata
\tablecomments{ (Column 1) Name of dwarf galaxy. The superscript V means that disk properties (columns $2$--$5$) are taken from {\em V}--band data;for all others, properties are taken from {\em B}--band;
(Columns 2 \& 3) Size (major and minor axes) and position angle (P.A.) of the optical disk \cite[][]{Hunter2006};
(Column 4) 6\,cm ($\sim 6$\,GHz) radio continuum flux density. This value and those following have ambiguous sources removed. For values where we retain ambiguous sources see Appendix~\ref{Section:Appendix_Tables};
(Column 5) H${\alpha}$\ flux;
(Column 6) {\em GALEX} FUV flux density;
(Column 7) {\em Spitzer} 24\micron\ MIR flux density;
(Column 8) {\em Spitzer} 70\micron\ FIR flux density;
(Column 9) 6\,cm ($\sim 6$\,GHz) radio continuum non-thermal (synchrotron) flux density. All ${\rm RC_{Nth}}$\ emission is assumed to be synchrotron and is inferred by subtracting the ${\rm RC_{Th}}$\ component from the total RC following \cite{Deeg1997}. The quantity in parentheses is the amount that was regarded as ambiguous;
(Column 13) Equipartition magnetic field strength in the plane of the sky \cite[see Equation 3 in][]{Beck2005}. }
\end{deluxetable}
\subsection{Isolating Target RC emission}
\label{section:Paper1RCbasedMask}
The majority of our dwarf galaxy sample only exhibits significant RC emission in isolated regions, which is attributed to both the episodic nature of SF in dwarf galaxies \cite[e.g.,][]{Stinson2007} and the surface brightness sensitivity of our RC observations which limits our RC maps to to detecting SFRDs greater than $\sim5\times10^{-3}$$\rm M_\odot\,yr^{-1}\,kpc^{-2}$. When integrated over the disk, the signal from most galaxies is dominated by the contribution of noise from the individual beams within the integration area. The uncertainty, $\delta N$, is given by $\sigma_{\rm rms} \sqrt{N}$, where $\sigma_{\rm rms}$ is the rms noise level and $N$ is the number of individual beams. This motivates the use of masks to isolate genuine emission from background noise (i.e., reduce the integration area which is proportional to $N$) in order to improve the RC S/N.
\subsubsection{Radio Continuum--based Mask}
\label{section:Paper1masking_techniques}
To characterise the RC emission within our images we first estimate the spatially varying background noise across each image using the {\sc bane} algorithm \citep{Hancock2012}. {\sc bane} works by selecting each pixel in the image on a specified grid and then defines a boxed region. This region is first clipped at $3\sigma$ to remove the contribution of source pixels. The median of the remaining pixels in the box is calculated and used as the background estimate. Linear interpolation is then used to smooth the background across the image. We found that the default options for {\sc bane}, which uses a grid size of four times the beam area and a box size of five times the grid size, produced good estimates of the background noise for the majority of our images. In cases where there is large scale extended emission such as NGC\,1569 and IC\,10 the grid size was increased to the approximate size of the most extended feature in the image, six and nine, respectively, and the default box size was applied. Estimating the background noise allows us to create S/N images that account for local variations in the image background caused by the primary beam sensitivity pattern and any residual low-level artefacts. This results in a robust threshold for our source detection. The average noise towards our galaxies is presented in table~\ref{table:12A-234_Observations}, column\,9.
We apply an automated approach to source identification using the {\sc fellwalker} source finding algorithm \citep{Berry2015} available in the {\sc starlink} distribution {\sc cupid}. {\sc fellwalker} is a thresholding approach to source detection that identifies contiguous features in an image by finding the steepest gradient for each pixel. Starting with the first pixel in an image, above a user defined threshold, each of the surrounding pixels is inspected to locate the pixel with the highest ascending gradient; this process continues until a peak is located (i.e. a pixel surrounded by flat or descending gradients). The pixels along this path are assigned an arbitrary integer to represent their connection along a path. All pixels in the image are inspected in a similar process and the image is segmented into clumps by grouping together all paths that lead to the same peak value. The pixels belonging to paths that lead to the same peak are then defined as belonging to that particular clump. For a full description of this process see \cite{Berry2007}.
Using {\sc fellwalker} we create two masks for each S/N image: the first is at full resolution whilst the second is smoothed to an angular resolution of 10$''$. The former image is used to characterise unresolved point sources whilst the latter is used to define regions of extended emission. We assign a threshold level corresponding to a S/N level of 3 in both cases where the noise levels are derived independently for each image. Fluctuations that are smaller than the beam are excluded; they are identified as noise spikes. We verify the robustness of this approach by comparing our mask to those produced by the {\sc clumpfind} algorithm, which is also available in {\sc cupid}, and by checking each mask by eye to ensure that no spurious emission is included in the maps. An example of the results of this approach can be seen in the top-right panel of Fig.~\ref{section:Paper1Images} and Appendix~\ref{Section:Appendix_Images}.
Using our RC based mask we extract the integrated properties towards our sample of dwarf galaxies excluding background and ambiguous sources and present the results in table~\ref{table:12A-234_MaskQuantities}. A table containing the integrated properties including ambiguous sources can be found in Appendix~\ref{Section:Appendix_Tables}.
\changetext{0.5cm}{}{}{1cm}{}
\begin{deluxetable}{lcccccccccc}
\tablewidth{0pt}
\tabletypesize{\tiny}
\tablecolumns{13}
\rotate
\tablecaption{Integrated emission over the RC mask of the LITTLE THINGS Galaxies\label{table:12A-234_MaskQuantities}}
\tablehead{
\colhead{Galaxy} & \colhead{R.A} & \colhead{Dec.} & \colhead{$f_{\rm disk}$} & \colhead{6\,cm RC} & \colhead{H${\alpha}$} & \colhead{FUV} & \colhead{24\micron\ MIR} & \colhead{70\micron\ FIR} & \colhead{6\,cm ${\rm RC_{Nth}}$} & \colhead{$B_{\rm eq}$} \\
& hh\,mm\,ss.s & dd\,mm\,ss.s & (\%) & (mJy) & ($10^{-13} $\,ergs\,s$^{-1}$\,cm$^{-2}$) & (mJy) & ($10^{-2}$\,Jy) & ($10^{-2}$\,Jy) & (mJy) & (${\rm \mu G}$) \\
(1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11)}
\startdata
DDO 46 & $07\,41\,26.6$ & $+40\,06\,39$ & $0.1$ & $0.02 \pm 0.01$ & $0.16\pm 0.01$ & $0.02\pm 0.01$ & \nodata & \nodata & $0.01\pm 0.01$ & $<1$ \\
DDO 47 & $07\,41\,55.3$ & $+16\,48\,08$ & $0.1$ & $0.03 \pm 0.01$ & $0.15\pm 0.01$ & $0.05\pm 0.01$ & \nodata & \nodata & $0.02\pm 0.01$ & $<1$ \\
DDO 50 & $08\,19\,08.7$ & $+70\,43\,25$ & $2.2$ & $6.27 \pm 0.09$ & $25.28\pm 0.42$ & $7.45\pm 0.76$ & $7.69\pm 0.06$ & $53.17\pm 0.04$ & $3.95\pm 0.10$ & $4$ \\
DDO 53 & $08\,34\,08.0$ & $+66\,10\,37$ & $3.2$ & $0.33 \pm 0.02$ & $1.90\pm 0.04$ & $0.71\pm 0.07$ & $1.32\pm 0.09$ & $5.30\pm 0.01$ & $0.16\pm 0.02$ & $4$ \\
DDO 63 & $09\,40\,30.4$ & $+71\,11\,02$ & $0.1$ & $0.06 \pm 0.01$ & $0.24\pm 0.01$ & $0.14\pm 0.02$ & $0.04\pm 0.34$ & $0.33\pm 0.01$ & $0.04\pm 0.01$ & $2$ \\
DDO 70 & $10\,00\,00.9$ & $+05\,19\,50$ & $0.1$ & $0.07 \pm 0.02$ & $0.29\pm 0.02$ & $0.21\pm 0.03$ & $0.03\pm 0.34$ & $0.34\pm 0.01$ & $0.04\pm 0.02$ & $<1$ \\
DDO 75 & $10\,10\,59.2$ & $-04\,41\,56$ & $0.3$ & $0.24 \pm 0.03$ & $2.87\pm 0.06$ & $0.85\pm 0.09$ & $0.07\pm 0.23$ & $1.61\pm 0.01$ & $0.01\pm 0.01$ & $<1$ \\
DDO 126 & $12\,27\,06.5$ & $+37\,08\,23$ & $2.3$ & $0.35 \pm 0.03$ & $1.46\pm 0.07$ & $0.54\pm 0.06$ & $0.15\pm 0.20$ & $2.11\pm 0.02$ & $0.23\pm 0.03$ & $3$ \\
DDO 155 & $12\,58\,39.8$ & $+14\,13\,10$ & $5.2$ & $0.28 \pm 0.04$ & $2.23\pm 0.04$ & \nodata & $0.15\pm 0.12$ & $2.42\pm 0.01$ & $0.08\pm 0.04$ & $<1$ \\
DDO 168 & $13\,14\,27.2$ & $+45\,55\,46$ & $0.2$ & $0.11 \pm 0.01$ & $0.24\pm 0.01$ & $0.12\pm 0.01$ & $0.04\pm 0.18$ & $0.67\pm 0.01$ & $0.09\pm 0.01$ & $2$ \\
Haro 29 & $12\,26\,16.7$ & $+48\,29\,38$ & $13.4$ & $2.01 \pm 0.04$ & $12.54\pm 0.45$ & $2.65\pm 0.29$ & $4.96\pm 0.14$ & $21.21\pm 0.02$ & $0.82\pm 0.06$ & $6$ \\
Haro 36 & $12\,46\,56.3$ & $+51\,36\,48$ & $9.3$ & $0.37 \pm 0.03$ & $1.17\pm 0.03$ & $1.94\pm 0.21$ & $0.41\pm 0.13$ & $6.88\pm 0.02$ & $0.26\pm 0.03$ & $4$ \\
IC 1613 & $01\,04\,49.2$ & $+02\,07\,48$ & $0.7$ & $2.51 \pm 0.05$ & $10.26\pm 0.43$ & $5.08\pm 0.71$ & $1.69\pm 0.23$ & $23.10\pm 0.12$ & $1.63\pm 0.06$ & $3$ \\
IC 10 & $00\,20\,17.5$ & $+59\,18\,14$ & $22.9$ & $99.33 \pm 0.39$ & $887.90\pm 5.68$ & \nodata & $1369.00\pm 10.10$ & $5482.00\pm 6.68$ & $14.96\pm 0.66$ & $8$ \\
Mrk 178 & $11\,33\,29.0$ & $+49\,14\,24$ & $3.8$ & $0.46 \pm 0.03$ & $2.33\pm 0.08$ & $0.97\pm 0.12$ & $0.16\pm 0.17$ & $0.16\pm 0.01$ & $0.25\pm 0.03$ & $4$ \\
NGC 1569 & $04\,30\,49.8$ & $+64\,50\,51$ & $126.3$ & $155.40 \pm 0.34$ & $503.90\pm 3.03$ & $755.60\pm 76.53$ & $716.20\pm 12.11$ & $3758.00\pm 2.99$ & $74.41\pm 0.60$ & $17$ \\
NGC 2366 & $07\,28\,48.8$ & $+69\,12\,22$ & $2.2$ & $11.98 \pm 0.09$ & $66.97\pm 1.10$ & $12.64\pm 1.28$ & $52.01\pm 0.04$ & $179.50\pm 0.05$ & $5.65\pm 0.14$ & $5$ \\
NGC 3738 & $11\,35\,49.0$ & $+54\,31\,23$ & $6.2$ & $2.98 \pm 0.12$ & $11.83\pm 0.17$ & $7.29\pm 0.75$ & $7.58\pm 0.13$ & $91.12\pm 0.10$ & $1.85\pm 0.12$ & $7$ \\
NGC 4214 & $12\,15\,39.2$ & $+36\,19\,38$ & $2.2$ & $22.58 \pm 0.08$ & $117.20\pm 0.91$ & $32.63\pm 3.29$ & $140.40\pm 0.09$ & $941.10\pm 0.17$ & $11.55\pm 0.12$ & $6$ \\
UGC 8508 & $13\,30\,44.9$ & $+54\,54\,29$ & $3.2$ & $0.16 \pm 0.02$ & $0.65\pm 0.02$ & \nodata & $0.06\pm 0.15$ & $1.18\pm 0.01$ & $0.10\pm 0.02$ & $2$ \\
VIIZw 403 & $11\,27\,58.2$ & $+78\,59\,39$ & $15.8$ & $1.29 \pm 0.04$ & $6.49\pm 0.15$ & $3.21\pm 0.33$ & $2.10\pm 37.85$ & $33.77\pm 0.54$ & $0.68\pm 0.04$ & $5$ \\
WLM & $00\,01\,59.2$ & $-15\,27\,41$ & $0.1$ & $0.16 \pm 0.02$ & $0.79\pm 0.05$ & $0.10\pm 0.01$ & $0.27\pm 0.30$ & $0.31\pm 0.01$ & $0.01\pm 0.01$ & $<1$ \\
\enddata
\tablecomments{ (Column 1) Name of dwarf galaxy;
(Columns 2 \& 3) Equatorial coordinates (J2000) of centre of the galaxy defined by the optical disk;
(Column 4) Fraction of the disk (see table\,\ref{table:12A-234_DiskQuantities}) that has significant RC emission;
(Column 5) 6\,cm ($\sim 6$\,GHz) radio continuum flux density. This value and those following have ambiguous sources removed. For values where we retain ambiguous sources see Appendix~\ref{Section:Appendix_Tables};
(Column 6) H${\alpha}$\ flux;
(Column 7) {\em GALEX} FUV flux density;
(Column 8) {\em Spitzer} 24\micron\ MIR flux density;
(Column 9) {\em Spitzer} 70\micron\ FIR flux density;
(Column 10) 6\,cm ($\sim 6$\,GHz) radio continuum non-thermal (synchrotron) flux density. All ${\rm RC_{Nth}}$\ emission is assumed to be synchrotron and is inferred by subtracting the ${\rm RC_{Th}}$\ component from the total RC following \cite{Deeg1997}. The quantity in parentheses is the amount that was regarded as ambiguous;
(Column 11) Equipartition magnetic field strength in the plane of the sky \cite[see Equation 3 in][]{Beck2005}. }
\end{deluxetable}
In order to compare the RC emission to our ancillary data we first investigate which masks best represent the global emission in our dwarf galaxies. Ideally, we would like to compare the various quantities over the same optically derived disk mask as our ancillary data in general present emission over a large fraction of the disk leading. However, if we integrate the RC emission over the disk we find that only 11 of our 40 observations have significant integrated RC flux density measurements. Using instead our RC mask we identify RC emission associated with 22 out of the 40 LITTLE THINGS galaxies (excluding ambiguous sources); $8$ are new RC detections. It is for this reason that in the course of the analysis of our data we will present results integrated over both the RC and disk based masks.
\subsection{Radio Continuum Source Counts}
\begin{figure}[t!]
\centering
\includegraphics[width=1.0\linewidth]{sourcecounts.pdf}
\caption{\footnotesize{Corrected and normalised source counts recovered from our images. Sources are separated based on our source identification approach into: all sources (black squares), background sources (blue triangles), background and ambiguous sources (green pentagon). We compare these results to those of \cite{Huynh2012} (red circles).}}
\label{figure:sourcecounts}
\end{figure}
\begin{deluxetable}{c|ccc|ccc|ccc|ccc}
\tablewidth{0pt}
\tabletypesize{\tiny}
\tablecolumns{5}
\tablecaption{6\,cm Source Counts\label{Table:SourceCounts}}
\tablehead{
\colhead{$\Delta S$} & \multicolumn{3}{|c}{$N$} & \multicolumn{3}{|c}{$N_{\rm c}$} & \multicolumn{3}{|c}{${\rm d}N_{\rm c}/{\rm d}S$} & \multicolumn{3}{|c}{$N_{\rm c}$ / $N_{\rm exp}$} \\ \
(${\rm \mu Jy}$) & & & & & & & &(${\rm sr^{-1}\,Jy^{-1}}$) & & && \\ \
& all & bg & amb & all & bg & amb & all & bg & amb & all & bg & amb }
\startdata
$ 46 $ -- $ 73 $ & $ 60 $ & $ 50 $ & $ 52 $ & $ 180.18 $ & $ 150.15 $ & $ 156.15 $ & $ 1983.58 $ & $ 1652.99 $ & $ 1719.11 $ & $ 0.44 \pm 0.03 $ & $ 0.37 \pm 0.03 $ & $ 0.38 \pm 0.03 $ \\
$ 73 $ -- $ 116 $ & $ 52 $ & $ 40 $ & $ 42 $ & $ 125.43 $ & $ 96.48 $ & $ 101.31 $ & $ 785.19 $ & $ 603.99 $ & $ 634.19 $ & $ 0.60 \pm 0.05 $ & $ 0.46 \pm 0.05 $ & $ 0.49 \pm 0.05 $ \\
$ 116 $ -- $ 183 $ & $ 55 $ & $ 37 $ & $ 43 $ & $ 124.68 $ & $ 83.87 $ & $ 97.47 $ & $ 485.42 $ & $ 326.55 $ & $ 379.51 $ & $ 1.23 \pm 0.11 $ & $ 0.83 \pm 0.09 $ & $ 0.96 \pm 0.10 $ \\
$ 183 $ -- $ 290 $ & $ 25 $ & $ 15 $ & $ 18 $ & $ 55.52 $ & $ 33.31 $ & $ 39.98 $ & $ 132.29 $ & $ 79.37 $ & $ 95.25 $ & $ 1.08 \pm 0.15 $ & $ 0.65 \pm 0.11 $ & $ 0.78 \pm 0.12 $ \\
$ 290 $ -- $ 460 $ & $ 24 $ & $ 15 $ & $ 16 $ & $ 52.78 $ & $ 32.99 $ & $ 35.19 $ & $ 78.56 $ & $ 49.10 $ & $ 52.37 $ & $ 2.04 \pm 0.28 $ & $ 1.27 \pm 0.22 $ & $ 1.36 \pm 0.23 $ \\
$ 460 $ -- $ 728 $ & $ 26 $ & $ 17 $ & $ 17 $ & $ 56.74 $ & $ 37.10 $ & $ 37.10 $ & $ 55.06 $ & $ 36.00 $ & $ 36.00 $ & $ 4.39 \pm 0.58 $ & $ 2.87 \pm 0.47 $ & $ 2.87 \pm 0.47 $ \\
$ 728 $ -- $ 1155 $ & $ 10 $ & $ 3 $ & $ 5 $ & $ 21.65 $ & $ 6.50 $ & $ 10.83 $ & $ 12.93 $ & $ 3.88 $ & $ 6.47 $ & $ 3.34 \pm 0.72 $ & $ 1.00 \pm 0.39 $ & $ 1.67 \pm 0.51 $ \\
$ 1155 $ -- $ 1831 $ & $ 13 $ & $ 3 $ & $ 5 $ & $ 27.96 $ & $ 6.45 $ & $ 10.75 $ & $ 10.68 $ & $ 2.47 $ & $ 4.11 $ & $ 8.61 \pm 1.63 $ & $ 1.99 \pm 0.78 $ & $ 3.31 \pm 1.01 $ \\
$ 1831 $ -- $ 2901 $ & $ 6 $ & $ 1 $ & $ 1 $ & $ 12.86 $ & $ 2.14 $ & $ 2.14 $ & $ 3.74 $ & $ 0.62 $ & $ 0.62 $ & $ 7.91 \pm 2.20 $ & $ 1.32 \pm 0.90 $ & $ 1.32 \pm 0.90 $ \\
$ 2901 $ -- $ 4598 $ & $ 7 $ & $ 0 $ & $ 1 $ & $ 14.90 $ & $ 0.00 $ & $ 2.13 $ & $ 2.53 $ & $ 0.00 $ & $ 0.36 $ & $ 18.27 \pm 4.73 $ & $ 0.00 \pm 0.00 $ & $ 2.61 \pm 1.79 $ \\
$ 4598 $ -- $ 11478 $ & $ 9 $ & $ 1 $ & $ 1 $ & $ 18.98 $ & $ 2.11 $ & $ 2.11 $ & $ 1.29 $ & $ 0.14 $ & $ 0.14 $ & $ 31.03 \pm 7.12 $ & $ 3.45 \pm 2.37 $ & $ 3.45 \pm 2.37 $ \\
$ 11478 $ -- $ 28653 $ & $ 11 $ & $ 0 $ & $ 0 $ & $ 23.03 $ & $ 0.00 $ & $ 0.00 $ & $ 0.63 $ & $ 0.00 $ & $ 0.00 $ & $ 148.48 \pm 30.94 $ & $ 0.00 \pm 0.00 $ & $ 0.00 \pm 0.00 $ \\
\enddata
\tablecomments{6\,cm ($6.2$\,GHz) source counts.
(Column 1) flux density bins taken from \cite{Huynh2012} converted to $6.2$\,GHz assuming a spectral index of $-0.7$;
(Column 2) number of $>5\,\sigma_{\rm rms}$ RC source counts. We count all sources in the images (all), sources identified as background (bg), sources identified as background or ambiguous (amb);
(Column 3) the completeness and resolution corrected RC source counts;
(Column 4) the corrected RC source count rate---the number of sources found per steradian normalised to the mid–point of the flux density bin.
(Column 5) corrected source counts normalised by the expected number from a non evolving Euclidean model.}
\end{deluxetable}
To test the robustness of our source identification and extraction approach we determine the radio continuum source counts from our images. We compare these to \cite{Huynh2012} who performed $5.5$\,GHz observations with the Australia Telescope Compact Array of a $900$\,arcmin$^2$ region with a restoring beam of $4.9^{\prime\prime}\times2.0^{\prime\prime}$ and an rms noise of $12 {\rm \,\mu Jy\,beam^{-1}}$. After correcting for incompleteness and resolution bias, they present normalised source counts in $10$ flux density bins ranging between $50$ and $5000 {\rm \,\mu Jy}$ (see their table\,2).
Our images were generated using a restoring beam of approximately $3^{\prime\prime}$ and attained an rms noise of $\sim6 {\rm \,\mu Jy\,beam^{-1}}$. Therefore, the sensitivity per beam in our data is comparable to that from \cite{Huynh2012}. We scale the \cite{Huynh2012} bins to $6.2$\,GHz, the effective frequency for most of our images, assuming a spectral index of $-0.7 \pm 0.2$. This assumption is supported by various studies that show the average spectral index of star forming galaxies is narrowly concentrated around $\sim -0.7$ with a small dispersion of $\lesssim 0.2$ \citep{Condon1992,Lisenfeld2000,Niklas1997}. For each bin, we cycled through our images counting all sources with flux densities in the range $\Delta S$. We count sources only from within a $4^{\prime}$ circular aperture centred on the image pointing reference to avoid regions where the primary beam response leads to higher noise levels. Sources are assigned to three different groups following our source classification approach described in Section~\ref{section:Paper1background_source_removal}. The first group includes all sources in the field including the galaxy emission, the second counts only sources we are confident are background sources, and the final group consists of both background and ambiguous sources. Sources were not counted if, in the given bin, the low end of the bin was less than $5$ times the rms noise from the image (this only affected the two lowest bins because of a few high rms images). No attempt was made to count resolved sources as originating from the same source (e.g., radio lobes, multiple SF regions from a dwarf, etc.).
To estimate the completeness of our source catalogue we follow a similar approach to \cite{Huynh2012} and perform a Monte-Carlo simulation. We inject a synthetic Gaussian source with a randomly generated position and brightness from 30 to 3000\,${\rm \,\mu Jy}$ into our image and then apply the {\sc fellwalker} source detection algorithm following the same approach as described in Section~\ref{section:Paper1RCbasedMask} to see if the source is recovered. We do this 8000 times and find that sources with flux densities of $5\,\sigma_{\rm rms}$ ($\sim50\,{\rm \mu\,Jy}$) have a detection rate of 50\%, where $\sigma_{\rm rms}$ is the rms noise in the image. The detection rate rises steeply to 90\% at 120$\rm \mu\,Jy$. We also correct for the resolution bias following the same approach as \cite{Huynh2012}. This correction accounts for sources with weak extended emission and large total integrated flux densities that have peaks which fall below the detection threshold. Given our slightly higher sensitivity and resolution we find lower resolution correction factors than \cite{Huynh2012} with values of $1.24$ in our lowest bin and $1.03$ in our highest bin.
We present the results of our source counts in table~\ref{Table:SourceCounts}. For each bin we present the raw source counts ($N$) and the counts corrected for completeness and resolution bias ($N_{\rm c}$). We determine the RC source count rate (${\rm d}N_{\rm c}/{\rm d}S$), which corresponds to the number of sources found per steradian normalised to the mid point of the flux bin. Finally, we normalise our corrected source counts by dividing by the expected number of sources ($N_{\rm exp}$) derived from a non evolving Euclidean model using the relation $N(>S_{\rm 6\,cm}) = 60 * S_{\rm 6\,cm}^{-1.5}$. The Poissonian errors are presented for the normalised and corrected counts with the resolution and completeness correction uncertainties ($10\%$ and $2$--$5\%$, respectively) added in quadrature.
In Fig.~\ref{figure:sourcecounts} we present a comparison of our source counts using all sources (black squares), only background sources (blue triangles), both background and ambiguous sources (green pentagons). We compare our results to the corrected and normalised source counts of \cite{Huynh2012} (red circles). This plot clearly shows that our counts are consistent with \cite{Huynh2012} until $\sim 10^3\,{\rm \mu\,Jy}$. Beyond this flux we see that including galaxy emission in our source counts leads to higher counts than those found in \cite{Huynh2012}, particularly at flux densities above 8.6\,mJy. Ideally, we would like to use the source counts to test the reliability of our source identification approach, in particular we would like to test whether sources we define as ambiguous are background sources or associated with the galaxy emission. If we assume that our source identification approach has reliably identified the galaxy emission and background sources and that the bulk of our ambiguous sources are associated with one of these groups then we should see a signature of this in our source counts. If the ambiguous sources belong to the background sources group we would expect that including them in the source counts whilst excluding the galaxy emission would lead to source counts that are similar to \cite{Huynh2012}. Conversely, if the ambiguous sources are background sources and we do not count them whilst also excluding the galaxy emission we would expect to see lower source counts than expected. In Fig.~\ref{figure:sourcecounts} we do see some tentative evidence that suggests the ambiguous sources are background sources with the background only source counts (blue triangles) tending to be lower than the source counts including both the background and ambiguous sources (green pentagons). However, due to the small number of sources in each bin and the associated errors we are prevented from stating that, statistically, the ambiguous sources belong to the population of background sources.
\section{DISCUSSION}
\label{section:discussion}
\subsection{The Radio Continuum}
\subsubsection{Comparison with Literature Flux Densities}
\label{section:Paper1Discussion_ComparisonFluxDensity}
There are few significant RC detections of dwarf galaxies in the literature. Of the galaxies that overlap with our sample, the literature is dominated by non-detections \cite[e.g.,][]{Altschuler1984,Wynn-Williams1986,Klein1992,Hoeppe1994}. On closer inspection, the seemingly high detection rate of $40$\% in \cite{Klein1986} is actually dominated by $1$--$3\,\sigma$ detections which are likely influenced by the inclusion of background galaxies in the large Effelsberg 100-m single dish beam. We are therefore limited by the number of dwarf galaxies with flux densities in the literature which we can confidently compare our results against\footnote{We note that the flux densities for sources found in the literature may be derived from a range of absolute flux density scales. Commonly used absolute flux scales include \citet{Baars1977}, \citet{Perley2013}, and \citet{Scaife2012}. Variations of the absolute flux scale between these different standards are on the order of 5\% \citep{Perley2016}.}. Reliable RC detections in the literature mostly come from deeper case studies of individual dwarf galaxies. Below we compare our RC flux density integrated over the RC mask that includes ambiguous sources (table~\ref{table:12A-234_MaskQuantities_ambig}) to the few studies available in the literature:
\paragraph{NGC\,1569:} %
\cite{Lisenfeld2004} find a VLA $8.415$\,GHz flux density of $125\pm12$\,mJy and spectral index of $-0.47$. The same spectral index was found by \cite{Kepley2010} (see their Fig.~\,3). Scaling the $8.415$\,GHz flux density we find an equivalent $6.2$\,GHz flux density of $144\pm14$\,mJy which agrees with our measurement of $157.30 \pm 0.35$\,mJy. Single dish observations performed by the Green Bank telescope at 4.85\,GHz \cite{Gregory1991} found a flux density of 202\,mJy. If we scale this to $6.2$\,GHz, assuming a spectral index of $-0.47$, we find a flux density of 180.0\,mJy. This suggests that we may be missing approximately 12.8\,mJy ($\sim 9$\%) of the flux in our image.
\paragraph{NGC\,4214:} %
\cite{Kepley2011} find a VLA 4.86\,GHz flux density of $34.0\pm6.8$\,mJy (D-array) and spectral index of $-0.43$. The equivalent $6.2$\,GHz flux density is $30\pm6$\,mJy whilst we find $23.16 \pm 0.09$\,mJy. We compare our flux density to that of \cite{Gregory1991} and find that our measured flux density is 3.8\,mJy ($\sim 14\%$) lower. We note that this suggests that we have missed large scale emission.
\paragraph{DDO\,50:} %
\cite{Tongue1995} find a VLA 6\,cm flux density of $11.7 \pm 0.1$\,mJy (D-array) which is higher than the $6.81\pm0.09$\,mJy at $6.2$\,GHz that we measured. Again, we note that there is the possibility that we have missed large scale emission.
\paragraph{NGC\,2366:} %
In the absence of a literature flux density at 6\,cm, we resort to a comparison with an {\em L}--band value. \cite{Condon2002} find a 1.4\,GHz flux density of $19.9$\,mJy whilst we report a $6.2$\,GHz flux density of $12.05 \pm 0.09$\,mJy. This implies a spectral index of $-0.34 \pm 0.10$ which is plausible. In light of this, it is unlikely that we have missed large scale emission which would flatten the spectral index and would imply emission even more dominated by ${\rm RC_{Th}}$\ emission than derived here.
\paragraph{NGC\,3738:} %
\cite{Stil2002} find a 1.4\,GHz flux density of $13\pm2$\,mJy and we find a $6.2$\,GHz flux density of $2.62\pm0.0.48$\,mJy. This implies a spectral index of $-1.08 \pm 0.04$ which is quite steep. Our image is affected by artefacts from a nearby bright source which may be influencing our flux density measurement.
\paragraph{Haro\,29:} %
\cite{Condon1998} find a 1.4\,GHz flux density of $4.5\pm0.5$\,mJy wheras we find a $6.2$\,GHz flux density of $2.18 \pm 0.11$\,mJy. This implies a spectral index of $-0.49 \pm 0.08$ which is plausible.
\paragraph{Others:} %
\cite{Klein1986} find a number of $\sim 4\,\sigma$ detections at $4.75$\,GHz: $3.5\pm1.0$\,mJy for DDO\,126; $4\pm1$\,mJy for DDO\,133; $9\pm2$\,mJy for DDO\,52. However, we observe less than a mJy for each of these. In all cases, we find nearby background galaxies that will have entered their $2^{\prime}30^{\prime\prime}$ single dish beam and contributed to their flux density to some degree.
\subsubsection{Composition of the Radio Continuum: Thermal and Non--thermal contributions}
\label{sect:rccomp}
The total RC emission is comprised of two contributions: ${\rm RC_{Th}}$\ and ${\rm RC_{Nth}}$. Since H${\alpha}$\ and the ${\rm RC_{Th}}$\ both have their origins in hot ($\sim 10^4$\,K) plasma associated with HII regions, a tight spatial and temporal correlation between the two is expected \cite[e.g.,][]{Deeg1997,Murphy2011}. The H${\alpha}$--${\rm RC_{Th}}$\ relation taken from \cite{Deeg1997} assumes the form:
\begin{eqnarray}
\frac{{\rm RC_{Th}}}{{\rm W\,m^{-2}}} & = & 1.14 \times 10^{-25} \, \Big( \frac{\nu}{{\rm GHz}} \Big)^{-0.1}\nonumber \\
& & \times\ \Big(\frac{T_{\rm e}}{{\rm 10^4\,K}} \Big)^{0.34} \, \frac{{F_{{\rm H\alpha}}}}{{\rm ergs\,s^{-1}\,cm^{-2}}}.
\label{Equation:Deeg1997}
\end{eqnarray}%
\noindent where $\nu$ is the observed frequency in GHz, ${T_{\rm e}}$ is the electron temperature, which is assumed to be $10^4$\,K, and $F_{\rm H\alpha}$ is the H${\alpha}$\ luminosity. On a spatially resolved basis, the ${\rm RC_{Th}}$\ flux density can be subtracted from the total RC, yielding the ${\rm RC_{Nth}}$\ flux density distribution.
We do not correct our H${\alpha}$\ estimates for internal extinction, following the same approach as \cite{Heesen2014}. As our later analysis utilises the SFR derived by combining the 24\micron\ and FUV emission, we wish to avoid using the 24\micron\ to correct for internal extinction so as not to introduce a spurious correlation. Dwarf galaxies are expected to have low internal extinction due to their low metallicity and therefore this is thought to generally not have a significant impact on our results. To verify this assertion we estimate the internal extinction in our H${\alpha}$\ maps following the method of \cite{Kennicutt2009}:
\begin{equation}
I_{\rm H\alpha,corr} = I_{\rm H\alpha,obs}+0.02\nu_{\rm 24\mu m}I_{\rm 24\mu m}
\label{Equation:extinction}
\end{equation}
\noindent where $I_{\rm H\alpha,obs}$ is the observed H${\alpha}$\ intensity, which has been corrected for foreground reddening, $I_{\rm H\alpha,corr}$ is the H${\alpha}$\ intensity corrected for internal extinction, and $I_{\rm 24\mu m}$ is the 24$\mu$m intensity. Our most intensely star forming galaxies are IC\,10 and NGC\,1569. We calculate the average internal extinction towards these galaxies and find values of 38\% and 35\%, respectively. We have explored the extinction towards NGC\,1569 in \cite{Westcott2017} using a Bayesian approach to separate the RC emission. We were able to estimate an average internal extinction of $\sim 20\%$, slightly lower than our estimate above. Galaxies with lower SFR, $<0.1$$\rm M_\odot\,yr^{-1}$\, that make up the bulk of our sample have much lower internal extinctions of $<10\%$ as derived from the 24$\mu$m intensity. For example, VIIZw\,403 and DDO\,50 both have an internal extinction of $\sim 8\%$. In light of these results we caution that in our subsequent analysis the ${\rm RC_{Th}}$\ flux estimates in galaxies with higher SFRs may be underestimated.
The uncertainty in our estimate of the ${\rm RC_{Th}}$\ emission is dominated by the foreground Galactic extinction correction and $T_{\rm e}$. The uncertainty in the Galactic extinction correction for our sample is $\pm 0.015$\,mag for values of $E(B-V)\leq 0.015$ and $\sim 10$\% for $E(B-V)> 0.015$ \cite[][]{Burstein1982}. We assume a single value for the foreground extinction across each galaxy. The foreground extinction may vary considerably across each galaxy, particular for those galaxies in close proximity to the Milky Way such as IC\,10 where the foreground extinction has been shown to vary across the face of the galaxy from $-60\%$ to $+25\%$ of our assumed value \citep{Basu2017}.
The value of $T_{\rm e}$ is assumed to be the standard value of $10^4$\,K but the electron temperature in HII regions has been shown to vary considerably. For example a sample of 61 Galactic HII regions where found to have values of $T_{\rm e}$ ranging from $0.25\times10^{4}$\,K to $1.16\times10^{4}$\,K \citep{Hindson2016}. In a study by \cite{Nicholls2014} the mean electron temperature of 17 HII regions in 14 dwarf irregular galaxies was $T_{\rm e} = 1.4\times 10^4$\,K. Variations in the electron temperature from our assumed value could give rise to up to $\sim 20$\% error in the estimated thermal emission.
After the removal of known background galaxies and ambiguous sources, we apply our RC and disk masks to isolate the ${\rm RC_{Th}}$\ (scaled H${\alpha}$) emission. When integrating over the RC mask we find that the average thermal fraction for our sample is $\sim 50 \pm 10$\% (upper limit). When integrating over the entire disk we find a higher thermal fraction of $70 \pm 10$\%. For comparison we scale thermal fractions reported for dwarf galaxies in the literature to $6.2$\,GHz assuming a spectral index of $-0.1$ and $-0.7$ for thermal and non-thermal components, respectively. The scaled thermal fractions in dwarf galaxies have been quoted as $51$\% for a sample of stacked faint dwarfs \cite[][]{Roychowdhury2012}, $53$\% in IC\,10 \cite[][]{Heesen2011}, $41$\% in NGC\,1569 \cite[][]{Lisenfeld2004}, and $41$\% in NGC\,4449\cite[][]{Niklas1997}. Our estimate of the thermal fraction integrated over the RC mask are consistent with these literature values. The thermal fraction integrated over the disk mask is significantly greater. We neglect internal extinction in our estimate of the ${\rm RC_{Th}}$\ which may lead to slightly lower values of the thermal fraction in the high SFR galaxies such as NGC\,1569 and IC\,10. It is also possible that on the scale of the disk we are missing some flux associated with large-scale RC emission which would lead to higher thermal fractions in the most extended galaxies. A more robust measure of the ${\rm RC_{Th}}$\ emission may be obtained using a Bayesian approach \citep{Tabatabaei2017, Westcott2017}, however this requires a large number of observations across the radio SED.
To estimate the ${\rm RC_{Nth}}$\ emission we subtract the ${\rm RC_{Th}}$\ emission from the total RC. We caution that the ${\rm RC_{Nth}}$\ emission may in some cases turn out to be rather an upper limit because of the previous points.
\subsection{The RC--SFR Relation}
\label{section:Paper1rc--sfr_relation}
We estimate the SFR following the approach of \cite{Leroy2012}. This corrects the FUV-inferred SFR for internal extinction, which is only relevant for our more actively star forming dwarfs. The FUV has been proven to be a reliable SF indicator at low SFR in comparison to H${\alpha}$--inferred SFRs (e.g., \citealp{Lee2009}; \citealp{Ficut2016}), and the timescale of ${\rm RC_{Nth}}$\ emission is closer to the FUV--inferred SF timescales than to, e.g., H${\alpha}$--inferred SF timescales. Galactic foreground extinction is taken into account separately \cite[see][for details]{Hunter2012}. To correct for internal extinction, \cite{Bigiel2008} and \cite{Leroy2012} use {\em Spitzer} 24\micron\ dust emission to empirically correct {\em GALEX} FUV fluxes for the fraction of dust-obscured SF on the assumption that a proportion of energy absorbed by internal dust is reradiated at 24\micron\ \cite[this is based on the original idea by][who use H${\alpha}$\ instead of FUV]{Calzetti2007}. We use:
\begin{align}
\frac{\Sigma_{{\rm SFR}}}{{\rm M_\odot\,yr^{-1}\,kpc^{-2}}} & = 0.081\frac{I_{{\rm FUV}}}{{\rm MJy\,sr^{-1}}} \nonumber\\
&\qquad + \ 0.0032\frac{I_{{\rm 24\mu m}}}{{\rm MJy\,sr^{-1}}}
\end{align}
\noindent where the FUV and 24\micron\ intensity are in units of $\rm MJy\,sr^{-1}$ and $\Sigma_{{\rm SFR}}$ represents the Star Formation Rate Density (SFRD). We show a map of the SFRD for DDO\,50 in Fig.~\ref{figure:example_maps}. For those galaxies where {\em Spitzer} 24\micron\ data was not available (see table~\ref{table:12A-234_DiskQuantities} and \ref{table:12A-234_MaskQuantities}, column\,7), we used the FUV--inferred SFR without any correction. Due to the low dust content of the majority of our sample the FUV dominates the SFR estimates. The error associated with our SFR estimates is $\sim 20$\%. When compared to other methods of deriving the SFR this approach was found the have a scatter of $\sim 50$\% down to a $\Sigma_{{\rm SFR}}$ of $10^{-4}$$\rm M_\odot\,yr^{-1}$\ \citep{Leroy2012}.
\begin{figure*}[t!]
\centering
\begin{tabular}{cc}
\includegraphics[width=0.48\linewidth,clip]{f007a_radio_F_disk-sfrleroy2012_diskComparison_retained_new.pdf} &\
\includegraphics[width=0.48\linewidth,clip]{f007b_radio_F_disk-sfrleroy2012_diskComparison_removed_new.pdf}\\
\includegraphics[width=0.48\linewidth,clip]{f007c_radio_F_mask-sfrleroy2012_maskComparison_retained_new.pdf} &\
\includegraphics[width=0.48\linewidth,clip]{f007d_radio_F_mask-sfrleroy2012_maskComparison_removed_new.pdf}
\end{tabular}
\caption{\footnotesize{Total 6\,cm luminosity as a function of SFR over our disk (top-panels) and RC (bottom-panels) masks. Definite background sources have been removed, whilst the ambiguous sources have been retained (left) and removed (right). The solid line is the best-fit power law to our sample. For reference we show the \cite{Murphy2011} RC--SFR relation as a shaded grey band. The errors introduced by our conversion are reflected by the grey shaded band, and the $3\,\sigma$ upper limits of RC emission are shown by grey arrows.}}
\label{figure:sfr_v_Clumin}
\end{figure*}
\begin{figure}[t!]
\centering
\includegraphics[width=0.99\linewidth,clip]{f004a_radio_F_disk-sfrleroy2012_diskComparison_new.pdf}
\includegraphics[width=0.99\linewidth,clip]{f004b_radio_F_mask-sfrleroy2012_maskComparison_new.pdf}
\caption{\footnotesize{Comparison of our disk (top) and mask (bottom) integrated RC and SFR properties with that of \cite{Heesen2014} (blue points). Obvious background and ambiguous sources were removed. The WSRT $22$\,cm data were corrected to $6$\,GHz assuming a spectral index of $-0.7$. The LITTLE THINGS galaxies have been coloured according to their metallicity. The solid black line is the best-fit power law to the LITTLE THINGS sample whilst the shaded band shows the \cite{Murphy2011} relation. The dashed black line shows the fit excluding NGC\,1569.}}
\label{Figure:Heesen2014Comparison}
\end{figure}
\begin{figure*}[h!]
\centering
\begin{tabular}{cc}
\includegraphics[width=0.48\linewidth,clip]{f008a_T_F_disk-sfrleroy2012_diskComparison_removed_new.pdf} &\
\includegraphics[width=0.48\linewidth,clip]{f008b_NT_F_disk-sfrleroy2012_diskComparison_removed_new.pdf} \\
\includegraphics[width=0.48\linewidth,clip]{f008c_T_F_mask-sfrleroy2012_maskComparison_removed_new.pdf} &\
\includegraphics[width=0.48\linewidth,clip]{f008d_NT_F_mask-sfrleroy2012_maskComparison_removed_new.pdf}
\end{tabular}
\caption{\footnotesize{Total 6\,cm ${\rm RC_{Th}}$\ (left) and ${\rm RC_{Nth}}$\ (right) luminosity as a function of SFR integrated over our disk (top) and RC mask (bottom). Both definite background sources and ambiguous sources have been removed. The solid line is the best-fit power law to our sample. We show the \cite{Murphy2011} ${\rm RC_{Th}}$--SFR and ${\rm RC_{Nth}}$--SFR relations for reference as a shaded, grey band; $3\,\sigma$ upper limits of RC emission are shown by the grey symbols with downward arrows.}}
\label{Figure:rcnt_sfr}
\end{figure*}
In Fig.~\ref{figure:sfr_v_Clumin} we present the RC--SFR relation of our sample when considering the optical disk mask (top) and RC based mask (bottom). We are able to determine the RC and SFR for 11 and 19 galaxies in the disk and RC based masks, respectively. The left panels of Fig.~\ref{figure:sfr_v_Clumin} shows the relation when we include the ambiguous RC sources, whereas the right panel shows the relation with ambiguous sources removed. If we do not remove the ambiguous sources we find a significant flattening and increase in scatter of the fit to the data particularly in the case of the RC based mask results. The most likely cause for this is that these ambiguous sources are background radio galaxies. We therefore continue our analysis focusing only on the results where ambiguous sources are removed. In doing so we may remove at most $10$\% of genuine RC emission in the form of SNRs as according to \citet{Chomiuk2009}, RC emission from SNRs contribute $< 10$\% of the total RC in dwarf galaxies
The data points of our sample of galaxies in Figs.~\ref{figure:sfr_v_Clumin} -- \ref{Figure:FIR_v_RC} are colour coded based on the galaxy's metallicity. This was done to investigate if there are any trends with metallicity. We find that in general the lowest metallicity objects congregate toward the low--radio continuum, low--SFR end of the plot whereas the high end is populated by the higher metallicity galaxies. This is a direct consequence of the metallicity--luminosity relation \citep{Skillman1989} and the fact that more luminous, hence more massive galaxies tend to have a higher SFR.
We compare our data points with the RC--SFR relation presented by \cite{Murphy2011}. They derive an expression for the ${\rm RC_{Th}}$\ and ${\rm RC_{Nth}}$\ emission and combine these to determine the total RC in a galaxy. The thermal component is derived from the ionising photon rate, which is directly proportional to the thermal spectral luminosity assuming an optically thin plasma giving:
\begin{align}
\left ( \frac{{\rm SFR}_{\nu}^{\rm Th}}{\rm {M_{\odot} yr^{-1} }} \right ) &= 4.6\times10^{-21}\left ( \frac{T_{\rm e}}{10^4{\rm K}} \right )^{-0.45} \nonumber\\
&\qquad . \left ( \frac{\nu}{{\rm GHz}} \right )^{0.1}\left ( \frac{L_{\nu}^{\rm Th}}{{\rm W\,Hz^{-1}}} \right )
\end{align}
\noindent Where $T_{\rm e}$ is the electron temperature and $L_{\nu}^{\rm Th}$ is the thermal radio luminosity. This equation assumes solar metallicity, continuous SF, and a Kroupa IMF. Using a Kroupa IMF results in SFR estimates that are $\sim 2.5$ times larger than those found by \cite{Condon1992}. We assume an electron temperature of $10^4$\,K. As mentioned previously this value may vary considerably. A value of $T_{\rm e} = 1.4\times 10^4$\,K \cite{Nicholls2014} would lead to a 14\% decrease in the SFR. The expected ${\rm RC_{Nth}}$\ is derived using:
\begin{align}
\left ( \frac{{\rm SFR}_{\nu}^{\rm Nth}}{\rm {M_{\odot} yr^{-1} }} \right ) &= 6.64\times10^{-22} \left ( \frac{\nu}{{\rm GHz}} \right )^{\alpha_{\rm Nth}} \nonumber\\
&\qquad . \left ( \frac{L_{\nu}^{\rm Nth}}{{\rm W\,Hz^{-1}}} \right )
\end{align}
\noindent This relationship is derived using the {\sc starburst99} population synthesis code \citep{Leitherer1999} and the empirical relationship between the supernova rate and non-thermal spectral luminosity of the Milky Way. We assume a value for the non-thermal spectral index of $\alpha_{\rm Nth} = -0.7 \pm 0.2$. Finally, the total RC is the combination of the ${\rm RC_{Th}}$\ and ${\rm RC_{Nth}}$\ leading to:
\begin{align}
&\left ( \frac{{\rm SFR}_{\nu}}{\rm {M_{\odot} yr^{-1} }} \right ) = 10^{-20} \left [ 2.18 \left ( \frac{T_{\rm e}}{10^4{\rm K}} \right )^{-0.45} \right.\nonumber\\
&\qquad \left. {} \left ( \frac{\nu}{{\rm GHz}} \right )^{0.1} + 15.1 \left ( \frac{\nu}{{\rm GHz}} \right )^{\alpha_{\rm Nth}} \right ] \left ( \frac{L_{\nu}}{{\rm W\,Hz^{-1}}} \right )
\end{align}
\noindent where we use a frequency $\nu$ of 6.2\,GHz. These expected relations are plotted as a grey shaded area in Fig.~\ref{figure:sfr_v_Clumin}. The width of the band reflects the overall uncertainty based on a typical error in the spectral index of $0.2$ and a canonical factor of 2 uncertainty in the SFR.
We performed a bivariate linear regression to quantify the relation between the RC luminosity and SFR, assuming the data follow a power law function of the form $y=Ax^n$ or $\log(y) = n \log(x) + c$, where $c = \log(A)$. We used the {\sc odr}\footnote{\scriptsize{\url{www.scipy.org/doc/api\_docs/SciPy.odr.odrpack.html}}} module from {\sc scipy}, which accepts four arrays of data points ($\log{x}$ and $\log{y}$, and the $1\,\sigma$ errors in log--space: $\frac{\delta x}{x}$ and $\frac{\delta y}{y}$) and the model function, and works to minimise the squares of the orthogonal distance between data points and the model, ultimately returning best-fit values and their standard deviations.
We find that the disk mask RC--SFR relation (Fig.~\ref{figure:sfr_v_Clumin} top-right panel) results are consistent with a linear relationship with $n = 0.93 \pm 0.14$ but the RC luminosity is lower than expected based on the observed SFR by approximately a factor of $\sim 5$. We note that IC\,1613 falls below the relation we find. If we exclude this galaxy we find that the average offset is a factor of $\sim 3$. We find that the RC mask integrated RC--SFR relation in Fig.~\ref{figure:sfr_v_Clumin} (bottom-right panel), where the RC mask is applied to both the RC as well as the SFR map, is marginally shallower than the \cite{Murphy2011} relation with a gradient of $n = 0.86 \pm 0.04$ with a scatter of $0.17$\,dex. If we perform the fit excluding NGC\,1569 (Fig.~\ref{figure:sfr_v_Clumin}, dashed black line) we find a value of $n = 0.91 \pm 0.04$. In Fig.~\ref{Figure:Heesen2014Comparison} we compare the results of our disk integrated and mask integrated RC--SFR to the study of 18 spiral galaxies at 20\,cm by \cite{Heesen2014}. We extend their parameter space by $2$\,dex, down to SFRs of $10^{-4}{\rm \,M_\odot\,yr^{-1}}$. At 20\,cm the \cite{Heesen2014} study found a slope of to the RC--SFR relation of $n = 1.24 \pm 0.04$ which is significantly steeper than our results.
\begin{figure}[t!]
\centering
\includegraphics[width=1.0\linewidth,clip]{f009a_radio_S_disk-sfrleroy2012_diskComparison_removed_new.pdf}
\includegraphics[width=1.0\linewidth,clip]{f009b_radio_S_mask-sfrleroy2012_maskComparison_removed_new.pdf}
\caption{\footnotesize{Galaxy-wide total 6\,cm surface brightness as a function of the FUV-inferred SFRD corrected for internal extinction from dust based on their 24\micron\ emission. Background and ambiguous sources have been removed. The solid line is the best-fit power law to our sample. We show the predicted \cite{Murphy2011} RC--SFR relation for reference as a shaded, grey band; $3\,\sigma$ upper limits of RC emission are shown by the grey symbols with downward arrows.}}
\label{Figure:SFRD_v_RCSurfaceBrightness}
\end{figure}
The relationship between the ${\rm RC_{Th}}$\ and ${\rm RC_{Nth}}$\ emission and SFR integrated over the disk and RC mask is shown in Fig.~\ref{Figure:rcnt_sfr}. When integrating the two components over the optical disk mask we find slopes of $n = 1.20 \pm 0.09$ and $n = 0.82 \pm 0.06$ for ${\rm RC_{Th}}$\ and ${\rm RC_{Nth}}$, respectively. We find a slope of $n = 0.82 \pm 0.05$ and $n = 0.79 \pm 0.06$ for ${\rm RC_{Th}}$\ and ${\rm RC_{Nth}}$\ emission integrated over the RC mask, respectively. If we exclude NGC\,1569 from the fit we find marginally steeper slopes. Our results for the ${\rm RC_{Th}}$\ agree with those of \cite{Murphy2011} when integrating over the RC mask but appear to diverge at the low SFR levels ($<10^{-2}$ \,$\rm M_\odot\,yr^{-1}$) in the disk mask. This may be due to the stochastic nature of SF particularly in the faintest galaxies. It is important to note that the ${\rm RC_{Th}}$\ plot is essentially an H${\alpha}$-FUV plot. The ${\rm RC_{Th}}$\ values are based on the H${\alpha}$\ emission and are thus not independently determined, in turn, the SFR relies heavily on the FUV. The scatter, especially for the least active dwarf galaxies (SFR$\,\lesssim 10^{-2} \, \mathrm{\mbox{${M_\odot}$} \,yr^{-1}}$), is likely due to the H${\alpha}$\ emission underestimating the SFR in comparison to that from FUV by a factor of up to $10$ \cite[][]{Lee2009}. These authors argue that as only the highest mass stars ($M \gtrsim 18\,M_{\odot}$) produce a significant number of photons to ionise the surrounding H\,{\sc i}, having a deficit of these stars significantly reduces the amount of H${\alpha}$\ emission, while the FUV emission is not affected as much since a larger fraction of the stellar population contributes to the FUV. On the other hand, \cite{Koda2012} find O stars in stellar clusters as small as $100-1000\,{\rm M_\odot}$ coming to the conclusion that the stellar IMF is not necessarily truncated; it could be stochastically populated at the high mass end, accounting for the observed variations in Fig.~\ref{Figure:rcnt_sfr}. We discuss this further in Section~\ref{sect:interplay}.
The ${\rm RC_{Nth}}$\ results are shallower than expected based on the predictions of \cite{Murphy2011} in both masking cases. Not only is the slope more shallow, we also see that when using the disk mask the ${\rm RC_{Nth}}$\ emission falls below the expected SFR by a factor of 2--4. This agrees with \cite{Bell2003} who finds that the radio emission of low-luminosity galaxies must be suppressed by at least a factor of two to account for the RC--FIR relation at low luminosity. Our results also agree with the findings of \cite{Price1992} who find that the power-law dependence of the synchrotron luminosities and SFR has a slope of $n=0.8$. Using the same method applied here but observing at $20$\,cm, \cite{Heesen2014} found a slope of the ${\rm RC_{Nth}}$\ component for spiral galaxies to be $n = 1.16 \pm 0.08$, significantly steeper than our results (Fig.~\ref{Figure:Heesen2014Comparison}). We note that the ${\rm RC_{Nth}}$\ may be underestimated particularly for large-scale galaxies that have high SFRs such as NGC\,1569. This would lead to the ${\rm RC_{Nth}}$--SFR relation being steeper than we see in Fig.~\ref{Figure:rcnt_sfr}. However, when we remove NGC\,1569 from our fitting our results remain consistent with those with NGC\,1569 included.
The RC surface brightness--SFRD relation is presented in Fig.~\ref{Figure:SFRD_v_RCSurfaceBrightness} where the SFRD is derived over the extent of the galaxy. We find a tight, linear RC--SFRD relation with a slope of $n = 0.99 \pm 0.11$ and $n = 0.88 \pm 0.02$ for the disk and RC based masks, respectively. Within the errors, these slopes are the same as those found for the relations plotted in Fig.~\ref{figure:sfr_v_Clumin}. Unlike the luminosity plots in Fig.~\ref{figure:sfr_v_Clumin}, though, this is independent of distance and so errors introduced by distance uncertainties forcing a linear relation due to flux-to-luminosity scaling are avoided. Figure~\ref{Figure:SFRD_v_RCSurfaceBrightness} could thus be used as a baseline for future studies of normal star forming galaxies---especially those studies that do not have reliable distance measurements (e.g., only photometric redshifts of optical counterparts).
\subsection{The FIR--SFR Relation}
\label{section:Paper1fir--sfr_relation}
\begin{figure*}
\centering
\begin{tabular}{cc}
\includegraphics[width=0.48\linewidth,clip]{dust70_F_disk-sfrleroy2012_diskComparison_removed_new.pdf} &\
\includegraphics[width=0.48\linewidth,clip]{dust70_F_mask-sfrleroy2012_maskComparison_removed_new.pdf}\\
\end{tabular}
\caption{\footnotesize{Total 70\micron\ luminosity as a function of SFR over our disk and RC masks. The solid line is the best-fit power law to our sample. For reference we show the \cite{Calzetti2010} 70\micron--SFR relation assuming a factor of two uncertainty (shaded grey band). Upper limits of 70\micron\ emission are shown by grey symbols with downward arrows.}}
\label{figure:sfr_v_dust}
\end{figure*}
The FIR is often used as a proxy for SFR in studies of unresolved galaxies it is therefore instructive to examine the relationship between the FIR and SFR integrated within the disk and RC masks in Fig.~\ref{figure:sfr_v_dust} of our sample. We compare our estimate to the monochromatic 70\micron\ calibration of \cite{Calzetti2010} using:
\begin{align}
\left ( \frac{{\rm SFR}_{\rm 70\mu m}}{\rm {M_{\odot} yr^{-1} }} \right ) = \left (\frac{L_{\rm 70\mu m}}{{\rm W\,Hz^{-1}}} \right ) \cdot 2.52\times10^{-24}
\end{align}
\noindent where ${L_{\rm 70\mu m}}$ is the $70$\micron\ luminosity in ${\rm W\,Hz^{-1}}$. We find that our best-fit line is the same within the errors for both the disk and RC based masks ($n=1.07\pm0.09$ and $1.05\pm0.06$, respectively) and runs parallel to the \cite{Calzetti2010} relationship. However, for any given SFR we find that our measurement of the integrated 70\,\micron\ emissions is underestimated compared to the expected 70\,\micron\ luminosity by a factor of $\sim 10$. Given the fact that dwarf galaxies have low metallicity this is not surprising. The metallicity of all our galaxies falls below a value of $12+\rm{log(O/H)}\sim 8.1$, below which \cite{Calzetti2010} found the FIR to be an unreliable tracer of the SFR. At these low metallicities the galaxies become basically optically thin and FUV photons can escape before being reprocessed by dust and reemitted in the FIR. This was also suggested as the cause of the ratio between total IR and FUV being $<1$ in low luminosity galaxies in a study by \cite{Bell2003}.
\subsection{The RC--FIR Relation}
\label{section:Paper1rc--fir_relation}
\begin{figure*}
\centering
\begin{tabular}{cc}
\includegraphics[width=0.48\linewidth,clip]{f010a_radio_F_disk-dust70_F_diskComparison_Yun_removed_new.pdf} &\ \includegraphics[width=0.48\linewidth,clip]{f010b_radio_F_mask-dust70_F_maskComparison_Yun_removed_new.pdf}
\end{tabular}
\caption{\footnotesize{Comparison of RC and FIR luminosities from this study to those from \cite{Yun2001} (their VLA $1.4$\,GHz data have been extrapolated to $6$\,GHz and the {\em IRAS} 60\micron\ data corrected to {\em Spitzer} 70\micron). Both definite background and ambiguous RC sources have been removed from the LITTLE THINGS galaxies. Integrated quantities were taken from regions of significant RC emission (i.e., the RC-based mask; right-panel) and from over the whole optically defined disk (left). The LITTLE THINGS galaxies that remain undetected are represented by their $3\,\sigma$ upper limits (grey plus symbols with downward arrow). The uncertainties introduced by our conversion of the relation found by \citet{Yun2001} are reflected by the grey shaded band (see text for details). }}
\label{Figure:Yun2001Comparison}
\end{figure*}
\begin{figure*}
\centering
\begin{tabular}{cc}
\includegraphics[width=0.48\linewidth,clip]{f0011a_radio_F_disk-dust70_F_diskComparison_removed_new.pdf} &\
\includegraphics[width=0.48\linewidth,clip]{f0011b_radio_F_mask-dust70_F_maskComparison_removed_new.pdf} \\
\includegraphics[width=0.48\linewidth,clip]{f012b_radio_F_disk-dust70_F_diskComparison_Jy_removed_new.pdf} &\
\includegraphics[width=0.48\linewidth,clip]{f012d_radio_F_mask-dust70_F_maskComparison_Jy_removed_new.pdf}
\end{tabular}
\caption{\footnotesize{6\,cm luminosity as a function of {\em Spitzer} 70\micron\ FIR integrated over the disk mask (left) and RC mask (right). The top panels show the luminosity relation whilst the bottom panels have not been corrected for the distance and show the flux-density. Definite and ambiguous background sources have been removed. The solid line is the best-fit power law to our sample. We draw the \cite{Yun2001} RC--FIR relation as described in Equation~\ref{Equation:Yun2001_RC-FIR} (dotted line). The uncertainties introduced by our conversion are reflected by the grey shaded band (see text for details). The LITTLE THINGS galaxies that remain undetected are represented by their $3\,\sigma$ upper limits (grey plus symbols with downward arrow) }}
\label{Figure:FIR_v_RC}
\end{figure*}
The RC--FIR relation based on 1809 galaxies culled from the NRAO VLA Sky Survey (NVSS: \citealt{Condon1998}) catalog and the 1.2\,Jy IRAS Redshift Survey catalog \citep{Strauss1992} was investigated by \cite{Yun2001}. They related the integrated $1.4$\,GHz RC of an unresolved galaxy to the {\em IRAS} $60{\rm \mu m}$ luminosity and found:
\begin{equation}
{\rm \frac{L_{6GHz}}{W\,Hz^{-1}}} = (2.24 \pm 0.67) \times 10^{-3} \Bigg( {\rm \frac{L_{70\mu m}}{W\,Hz^{-1}}} \Bigg)^{0.99}
\label{Equation:Yun2001_RC-FIR}
\end{equation}
\noindent where we converted the {\em IRAS} $60{\rm \mu m}$ luminosity to a `luminosity density' (i.e., from ${\rm W}$ to ${\rm W\,Hz^{-1}}$) by noting that the response from the {\em IRAS} $60{\rm \mu m}$ filter is equivalent to a perfectly transmitting filter with a bandwidth of $2.6 \times 10^{12}$\,Hz. The {\em IRAS} $60{\rm \mu m}$ `luminosity density' was further converted to the equivalent {\em Spitzer} 70\micron\ luminosity by scaling it up by a factor of $1.27$. This value is based on a grey body model for dust emission with $\beta=1.82$ and $T_{\rm dust}=35$\,K; this assumes the \citet{Yun2001} galaxies are in a quiescent mode of star formation, and that there is no significant emission from warm dust. The \cite{Yun2001} VLA $1.4$\,GHz RC data were reduced by a factor of $2.83$, to derive predicted equivalent VLA $6$\,GHz flux densities assuming a constant spectral index of $-0.7\pm0.2$ between 20 and 6\,cm for the galaxies in their sample.
In Fig.~\ref{Figure:Yun2001Comparison} we show the RC--FIR relation for our dwarf galaxies and compare this to the results of \cite{Yun2001}. The RC--FIR relation traditionally samples the parameter space above FIR luminosities of $\sim 10^{22} {\rm \,W Hz^{-1}}$; we extend this to lower luminosities by $3$\,dex. The uncertainty presented in Fig.~\ref{Figure:Yun2001Comparison} takes into account an uncertainty in the spectral index of $0.2$ and $15$\,K in dust temperature. We show the RC--FIR relation for our dwarf sample where emission is integrated over the entire disk (Fig.~\ref{Figure:Yun2001Comparison}: left) and from the significant regions of RC emission only (i.e., the RC-based mask, Fig.~\ref{Figure:Yun2001Comparison}: right). In Fig.~\ref{Figure:FIR_v_RC} we show the RC--FIR relation for just our dwarf galaxy sample integrated over the disk mask (left) and RC mask (right). The top-panels of this figure show the luminosity and the bottom-panels the flux density, to illustrate any dependence on distance. We find that when integrated over the disk our results for the luminosity match those found by \cite{Yun2001} with a slope if $1.02 \pm 0.10$. The flux density derived slope is slightly shallower at $0.87\pm0.07$. However, when we integrate the RC and 70\micron\ emission using our RC mask we find that our results diverge from the \cite{Yun2001} relation in both the luminosity and flux density plots with a flatter slope of $0.81 \pm 0.03$ and $0.80\pm0.03$ for the luminosity and flux density, respectively. We discuss the possible reasons behind this in Section~\ref{sect:interplay}.
\subsection{$q$-parameter}
\begin{figure*}
\centering
\begin{tabular}{cc}
\includegraphics[width=0.49\linewidth,clip]{{f013a_q-value.Disk.new}.pdf} &\
\includegraphics[width=0.49\linewidth,clip]{{f013b_q-value.Good.new}.pdf}
\end{tabular}
\caption{\footnotesize{$q_{70:6}$ parameter as a function of 70\micron\ luminosity. Both obvious and ambiguous background sources have been removed. We also show the \cite{Yun2001} data points (purple) and their $q$-parameter appropriately corrected to our observing bands (dashed line). The errors introduced by our conversion are reflected by the grey shaded band.}}
\label{Figure:q70}
\end{figure*}
An alternative way of exploring the RC--FIR relation described by \cite{Yun2001} is the $q$ parameter. This is the natural logarithm of the ratio of the {\em IRAS} FIR (a weighted combination of $60$ and $100{\rm \mu m}$ flux) to VLA $1.4$\,GHz flux densities of the \cite{Yun2001} sample and is described by:
\begin{equation}
q_{\rm FIR:1.4} = \log \Bigg( {\frac{{\rm FIR\ [Jy]}}{{\rm RC\ [Jy]}}} \Bigg) ,
\label{Equation:Yun2001_RCFlux-FIR}
\end{equation}
\noindent the average $q_{\rm FIR:1.4}$ parameter was found to be $2.34 \pm 0.01$. Since our RC and FIR measurements were made in different bands to those used by \cite{Yun2001}, we convert their $q_{\rm FIR:1.4}$ to $q_{\rm 70:6} = 2.68 \pm 0.12$, where the subscript $70$ and $6$ refer to the 70\micron\ FIR and $6$\,GHz RC, respectively. As before, the uncertainty is calculated by assuming an $0.2$ uncertainty in the spectral index between 20 and 6\,cm, and $15$\,K uncertainty in dust temperature.
We plot $q_{\rm 70:6}$ values as a function of 70\micron\ FIR luminosity in Fig.~\ref{Figure:q70}. The LITTLE THINGS dwarfs are consistent with the \cite{Yun2001} sample when integrated over the disk (Fig.~\ref{Figure:q70}; left). This reveals that the RC--FIR `conspiracy' continues in our dwarf galaxy sample. However, we see in the right panel of Fig.~\ref{Figure:q70} that when we integrate the emission over the RC mask there is a considerable excess of RC emission compared to the 70\micron\ for sources that have a low radio luminosity, as was already evident in Figs.~\ref{Figure:Yun2001Comparison} and \ref{Figure:FIR_v_RC} (right hand panels).
\subsection{The Interplay Between SF, RC and FIR}
\label{sect:interplay}
The relationship between the RC, FIR, and SFR can be summarised by three equations. The RC--SFR and FUV-- SFR relations can be expressed as:
\begin{equation}
{\rm \frac{L_{RC}}{W\,Hz^{-1}}} = 10^{A} \Bigg( {\rm \frac{SFR}{M_\odot\,yr^{-1}}} \Bigg)^{n}
\label{Equation:RC-SFR}
\end{equation}
\noindent and:
\begin{equation}
{\rm \frac{L_{FIR}}{W\,Hz^{-1}}} = 10^{A} \Bigg( {\rm \frac{SFR}{M_\odot\,yr^{-1}}} \Bigg)^{n}
\label{Equation:RC-SFR}
\end{equation}
\noindent whilst the RC--FIR relation can be described by:
\begin{equation}
{\rm \frac{RC}{W\,Hz^{-1}}} = 10^{A} \Bigg( {\rm \frac{70\mu m\ FIR}{10^{20} W\,Hz^{-1}}} \Bigg)^{n}
\label{Equation:RC-FIR}
\end{equation}
\noindent We summarise the results for the various fits for these relations over the disk and RC masks in table~\ref{tab:fits}.
We use the Pearson (P) and Spearman (S) coefficients to describe the strength and direction of the correlation in our relationships, where a value of $-1.0$ indicates a strong anti-correlation, $0.0$ indicates the relationship is random or non-existent, and $+1.0$ indicates a strong, positive correlation. The Pearson coefficient assumes a purely linear relationship and so will approach $0.0$ if there is an inconsistent relationship whilst the Spearman coefficient evaluates the monotonic relationship between two variables and so will remain high. Thus a strong relationship that deviates from linearity will have a lower Pearson than Spearman score. Both the Pearson and Spearman coefficients indicate a strong correlation between all components of the RC and SFR, with values ranging from 0.77 to 1.00 depending on the relation and type of mask used.
The fitted parameters for $A$ and $n$ for each relation in table~\ref{tab:fits} vary significantly based on the type of mask used except in the case of the FIR--SFR relation. The FIR--SFR relation has lower Pearson and Spearman scores compared to the RC based relations suggesting a weaker relationship and deviation from linearity and shows a larger scatter. Since the RC based mask is able to probe significantly lower SFR galaxies this suggests that the physical processes responsible for the FIR--SFR relation operate in the same way regardless of the level of SFR in our sample. The varying parameters that fit the various RC--SFR relations in the disk and RC masks indicate that there may be some change in the physical processes operating within regions on the scale of the entire disk and resolved scales traced by the RC based masks.
One of the most striking results of this study is the divergence we see in the RC--FIR relation at low luminosities when integrating over the RC mask (Fig.~\ref{Figure:FIR_v_RC}: right). This appears to be caused by the FIR emission being underestimated in the RC mask relative to the expected \cite{Calzetti2010} SFR (Fig.~\ref{figure:sfr_v_dust}) whereas the RC emission continues to follow the SFR down to low values (Fig.~\ref{figure:sfr_v_Clumin}). Our disk masked results on the other hand, both underestimate the RC and FIR luminosity compared to the predicted SFR leading to the linear slope that continues the RC--FIR `conspiracy' seen in the left panel of Fig.~\ref{Figure:FIR_v_RC}. In the case of the RC emission excess we find evidence that it is the ${\rm RC_{Nth}}$\ component that is responsible for the suppression of the RC on the scale of the disk (Fig.~\ref{Figure:rcnt_sfr}).
We propose two possible scenarios that may be responsible for the relations we observe. The first is that dwarf galaxies do not act as calorimeters and \mbox{CR$e$}\ and dust heating photons are able to escape the galaxy before they are able to generate the total ${\rm RC_{Nth}}$\ and FIR emission associated with their host SF. The second possibility is that we are witnessing the effect of stochastic SF resulting in a partially sampled and/or truncated IMF. This may lead to the ${\rm RC_{Nth}}$\ and FIR underestimating the SFR compared to studies of larger galaxies. It is possible that some combination of these scenarios is responsible for our results.
\begin{table*}
\centering
\caption{The best-fit parameters for the RC--SFR, FIR--SFR, and RC--FUV relation for the total RC, ${\rm RC_{Th}}$, and ${\rm RC_{Nth}}$\ components integrated over the entire disk and only over the RC masks. (1) RC component and mask type; (2 \& 3) Fit parameters; (4) Scatter of the data; (5) Number of galaxies used in the fit; (6 \& 7) The Pearson (P) and Spearman (S) coefficients.}
\label{tab:fits}
\begin{tabular}{lccccccc}
\hline
Mask & \multicolumn{3}{c}{RC Luminosity--SFR Relation} & N & P & S\\
& $A$ & $n$ & $\sigma$ & & & \\
\hline
RC$_{\rm Disk}$--SFR & $20.05 \pm 0.22$ & $0.93 \pm 0.14$ & $0.23$ & $11$ & $0.87$ & $0.93$ \\
RC$_{\rm Mask}$--SFR & $20.16 \pm 0.12$ & $0.86 \pm 0.04$ & $0.17$ & $19$ & $0.92$ & $0.96$ \\
\hline
${\rm RC_{Th}}$$_{\rm , Disk}$--SFR & $20.21 \pm 0.19$ & $1.20 \pm 0.09$ & $0.23$ & $32$ & $0.95$ & $0.88$ \\
${\rm RC_{Th}}$$_{\rm , Mask}$--SFR & $19.75 \pm 0.16$ & $0.82 \pm 0.05$ & $0.22$ & $19$ & $0.92$ & $0.90$ \\
\hline
${\rm RC_{Nth}}$$_{\rm , Disk}$--SFR & $19.72 \pm 0.08$ & $0.82 \pm 0.06$ & $0.08$ & $6$ & $0.99$ & $1.00$ \\
${\rm RC_{Nth}}$$_{\rm , Mask}$--SFR & $19.78 \pm 0.14$ & $0.79 \pm 0.06$ & $0.17$ & $14$ & $0.89$ & $0.91$ \\
\hline
FIR$_{\rm Disk}$--SFR & $22.74 \pm 0.20$ & $1.07 \pm 0.09$ & $0.26$ & $24$ & $0.80$ & $0.88$ \\
FIR$_{\rm Mask}$--SFR & $22.68 \pm 0.16$ & $1.05 \pm 0.06$ & $0.20$ & $15$ & $0.77$ & $0.93$ \\
\hline
RC$_{\rm Disk}$--FIR & $17.31 \pm 0.16$ & $1.02 \pm 0.10$ & $0.18$ & $12$ & $0.93$ & $0.80$ \\
RC$_{\rm Mask}$--FIR & $17.94 \pm 0.04$ & $0.81 \pm 0.03$ & $0.14$ & $18$ & $0.89$ & $0.94$ \\
\end{tabular}
\end{table*}
\subsubsection{Calorimeter breakdown}
Given their low metallicity and dust content it is possible that the mean free path of dust heating photons is less than the galaxy scale height. This would mean that dust heating photons are not completely absorbed and reradiated into the FIR and instead escape the galaxy. This would result in the observed suppression of the FIR relative to the expected SFR from \cite{Calzetti2010} in both the RC and disk mask. Given the low optical depth of dwarf galaxies \citep{Bell2003} this is one plausible explanation for our observed FIR--SFR relation.
The low gravitational potential wells of dwarf galaxies make them particularly susceptible to outflows where material including \mbox{CR$e$}\ can escape the galaxy. In addition \mbox{CR$e$}\ may diffuse out of the galaxy before they are able to emit all their radiation if the magnetic field strength is low. Both these processes would lead to a suppression of the ${\rm RC_{Nth}}$\ emission relative to the SFR (Fig.~\ref{Figure:rcnt_sfr}: right). The ${\rm RC_{Th}}$\ emission is expected to be consistent with theoretical predictions because it is directly associated with ongoing massive star formation \citep{Murphy2011}. This indeed seems to be the case in our study, except at low SFRs of $<10^{-2}$$\rm M_\odot\,yr^{-1}$\ where we see evidence of suppression and an increased scatter of ${\rm RC_{Th}}$\ (and therefore H${\alpha}$) relative to the SFR. The suppression of the ${\rm RC_{Nth}}$\ emission relative to expected SFR is only observed in our results when integrated over the disk mask. This may suggest that on the scales of concentrated SF traced by our RC mask magnetic fields are strong enough to act as a local calorimeter. Therefore, \mbox{CR$e$}\ expend their energy and age to lower frequencies before they have a chance to diffuse into the wider ISM. We explore this possibility further in Section~\ref{Section:Paper1MagneticFields}.
\subsubsection{Stochastic star formation}
An alternative explanation for our observed trends in the RC, FIR, and SFR could be due to the effects of stochastic SF within our dwarf galaxy sample. Synthesis models used to calibrate SFR indicators assume a sufficient number of stars to fully populate the IMF. In the case of dwarf galaxies with low SFRs the short lived high-mass stars may be under represented invalidating this assumption. Simulations of dwarf galaxies undergoing stochastic SF have found that FUV inferred SFRs may be biased at the $\sim 0.5$\,dex level for SFRs of $\sim 10^{-4}$$\rm M_\odot\,yr^{-1}$\ \citep{daSilva2012,daSilva2014}. Moderate variations in the SFR have also been observed in the star formation histories of nearby dwarf galaxies \cite{Dohm1998, Weisz2008}. We would also expect stochasiticity to impact the generation of the FIR, RC, and H${\alpha}$\ emission because these are all sensitive to the high-mass end of the IMF. These effects will have complicated spatial and temporal dependancies that vary for each type of emission mechanism. If the high-mass end of the IMF is underpopulated we would expect H${\alpha}$\ emission to be suppressed or even absent \citep{Lee2009} resulting in an increase in scatter around SFRs of $10^{-2}$$\rm M_\odot\,yr^{-1}$\ and a suppression of the H${\alpha}$\ emission below $10^{-3}$$\rm M_\odot\,yr^{-1}$. We see this behaviour in our ${\rm RC_{Th}}$--SFR relation in the disk mask results (Fig.~\ref{Figure:rcnt_sfr}: top left). This agrees with the simple calculation of \cite{Lee2009} who find that the H${\alpha}$\ flux is only a robust tracer of SFR above $1.4\times10^{-3}$$\rm M_\odot\,yr^{-1}$. However, \cite{Lee2009} argue that the stochastic SF alone is not sufficient to explain the suppression of H${\alpha}$\ emission. In any case the suppression of the RC and FIR we see in our disk masks are both evident at SFRs greater than $10^{-2}$$\rm M_\odot\,yr^{-1}$.
From our current data set it is unclear which of the scenarios we discuss above is responsible for our observed relations. Further work is required to investigate the impact of stochastic SF and a possible breakdown of the calorimeter model in these galaxies and the impact on our RC, FIR, and SFR measurements. In order to establish the origin of the observed suppression of the RC relative to SFR we require further information on the spectral and spatial variation of the RC--SFR relation in these galaxies so we may explore the effects of cosmic ray ageing and transport \citep{Heesen2016}. In order to explore the impact of stochastic SF we require detailed Monte-Carlo simulations of the underlying stellar populations or observations of the resolved stellar populations.
\subsection{Cosmic Ray Electrons and Magnetic Fields}
\label{Section:Paper1MagneticFields}
Our results suggest that it is the suppression of the ${\rm RC_{Nth}}$\ emission that is responsible for the RC--FIR relation remaining consistent at low SFRs. To explore the source of the ${\rm RC_{Nth}}$\ emission, we investigate the synchrotron emissivity in an optically thin region:
\begin{equation}
\epsilon_{\rm NTh} \propto n_{\rm CR} B_{\perp}^{\frac{\gamma + 1}{2}},
\end{equation}
\noindent where $n_{\rm CR}$ is the number density of \mbox{CR$e$}\ present in the dwarf's galactic magnetic field, $B_{\perp}$ is the strength of the transverse magnetic field, and $\gamma$ is the power--law slope of the \mbox{CR$e$}\ injection spectrum.
The ${\rm RC_{Nth}}$\ emission depends both on the energy density contained within the magnetic field and that of the population of \mbox{CR$e$}. The combined energy density associated with the magnetic field and \mbox{CR$e$}\ is usually assumed to be at a minimum \cite[see Section 16.5 of][]{Longair1981}. In galaxies, this is a reasonable assumption. If the energy densities are not equal, they will tend to balance: for example, if the energy density is dominated by the \mbox{CR$e$}, then they will rise out of the galactic disk in Parker lobes due to their buoyancy, expand, and escape thus reducing their energy density until it is balanced with that in the magnetic field.
It is, however, conceivable that dwarf galaxies in particular deviate from equipartition. This would lead to a reduction in synchrotron emission (see Fig.~\ref{Figure:rcnt_sfr}) in two different ways:
\begin{itemize}
\item[1)] a low number density of \mbox{CR$e$}\ ($n_{\rm CR}$) present in the dwarf's galactic magnetic field. Dwarf galaxies in particular are prone to galactic outflows since they have low masses and correspondingly shallow gravitational potentials, and winds can advect plasma and resident \mbox{CR$e$}\ away from the galaxy;
\item[2)] the magnetic field strength ($B$) being lower than the equipartition value at which the energy density of the magnetic field is equal to that of the cosmic rays (electrons and protons combined). In the standard paradigm of a mean field $\alpha$--$\Omega$ dynamo, the key ingredients are turbulence and shear. Dwarf galaxies may be sites of weak, large-scale, ordered magnetic fields, so magnetic field amplification may be less efficient. Studies by \cite{Chyzy2011,Roychowdhury2012} found global magnetic field strengths on the order of $<5{\rm \mu G}$ towards dwarf galaxies. However, the turbulent field in and around the SF regions may not necessarily be weaker than that found in spirals \cite[e.g.,][]{Tabatabaei2013b} as $30{\rm \mu G}$ is observed across some $100$\,pc regions.
\end{itemize}
In the following, the magnetic field strength in our sample of dwarf galaxies is estimated under the assumption of equipartition; this is the only practical way of estimating the field strengths given our current data set. We apply the equipartition formula for the total magnetic field following equation\,3 from \cite{Beck2005}. We made the standard assumptions of a spectral index of $-0.7\pm0.2$, proton--to--electron number density ratio {\textbf K} is $100 \pm 50$ \cite[][]{Beck2005, Murphy2011}, and that the dwarf galaxy has a scale height of $400 \pm 200$\,pc independent of distance from the galaxy centre \cite[][]{Banerjee2011,Elmegreen2015}. We note that both these assumptions are prone to significant uncertainty. The value of {\textbf K} depends on the acceleration process, propagation and the energy losses of the protons and electrons. As \mbox{CR$e$}\ propagate away from their sites of acceleration they rapidly lose energy leading to values of {\textbf K}$>100$. If this is the case in our dwarf galaxies and if \mbox{CR$e$}\ are escaping the galaxy altogether this will lead to an underestimate of the equipartition magnetic field. The scale height of dwarf galaxies is also prone to large variation due to their low mass and the potential for outflows. Typical scale heights have values ranging from 200-400\,pc in the inner regions and to 600-1000\,pc in the outer regions.
The average transverse magnetic field strength of our sample is $5.2 \pm 2.6{\rm \,\mu G}$ and $7.5 \pm 3.3{\rm \,\mu G}$ when integrated over the RC and disk masks, respectively (table~\ref{table:12A-234_DiskQuantities} and \ref{table:12A-234_MaskQuantities} for galaxy specific values). These values are greater than the $\sim 2 {\rm \mu G}$ found in $\sim 50$ faint dwarf galaxies from the NVSS catalogue \cite[][]{Roychowdhury2012} and within the errors they are consistent with the $4.2{\rm \mu G}$ found towards 12 local group dwarf galaxies reported in \cite{Chyzy2011}.The transverse field strength we measure in both masks is lower than the $9.7{\rm \,\mu G}$ found in larger spiral galaxies in the WSRT SINGS sample \cite[][]{Heesen2014}. The disk integrated magnetic field strength is greater than the mask integrated value because only the brightest galaxies can be integrated over the entire optical disk.
Our data allow the magnetic field strength to be measured on a resolved basis. In a few dwarf galaxies (e.g., NGC 1569, NGC\,2366, NGC\, 4214), we find numerous regions where the magnetic field strength was measured to be as high as $30$--$50{\rm \,\mu G}$ in localised $100$\,pc regions (approximate area of the synthesised beam). In fact, the brightest ${\rm RC_{Nth}}$\ flux density in our sample comes from a $\sim 100$\,pc region in NGC\,1569---the flux density from this unresolved region implied a magnetic field strength of $\sim 50{\rm \,\mu G}$. \citet{Heesen2015} analysed in detail the ${\rm RC_{Nth}}$\ spectrum of the non--thermal super bubble in IC\,10, deriving a magnetic field strength of $44{\rm \,\mu G}$. These are all strong magnetic fields akin to those found in the SF regions of larger spirals \cite[e.g., the turbulent magnetic fields in NGC\,6946's SF regions;][]{Tabatabaei2013b}. With such high magnetic field strengths, \mbox{CR$e$}\ could lose all their energy before diffusing into the ISM (rendering the region a local calorimeter). In IC\,10, for example, \citet{Heesen2015} find that at 6.3\,GHz the \mbox{CR$e$}\ lifetime in the non--thermal super bubble is only 0.9\,Myr, comparable with the age of 1\,Myr derived from the observed curvature of the spectrum. For less intense SF regions, such as DDO\,168, DDO\,47, and DDO\,53 we find peak local magnetic field strengths of 10--15${\rm \,\mu G}$ where \mbox{CR$e$}\ may have sufficient time to escape into the ISM. Once there:
\begin{itemize}
\item 1) the \mbox{CR$e$}, now losing energy through synchrotron radiation at a much slower rate, diffuse or are advected into the intergalactic medium (IGM) before they have the time to radiate all their energy---this is the `non-calorimetric' situation that leads to the RC--FIR `conspiracy' \cite[e.g.,][]{Bell2003,Dale2009,Lacki2010}, or
\item 2) the \mbox{CR$e$}\ continue to diffuse to $1$\,kpc but, because they continue to radiate and lose energy, the frequency of synchrotron emission shifts gradually to lower frequencies to the extent that emission falls outside of the 6\,cm window.
\end{itemize}
Exploring these possibilities and their impact on the ${\rm RC_{Nth}}$--SFR relation requires further information regarding the spectral index of the RC emission so that we can explore the \mbox{CR$e$}\ transport and ageing timescales.
\section{SUMMARY}
\label{section:Paper1Summary}
We used the VLA in C--configuration to make 6\,cm ($\nu = 6.2$\,GHz) observations of 40 dwarf galaxies taken from LITTLE THINGS \cite[][]{Hunter2012}. Our images have a resolution of $3$--$8^{\prime \prime}$ and an rms noise of $3$--$15 {\rm \mu Jy\,beam^{-1}}$. We summarise our findings as follows:
\begin{itemize}
\item Contamination from background sources is a prominent issue in earlier, low resolution observations. Even at the high resolution of the current survey, it is not trivial to reliably remove the contribution from all unrelated background sources;
\item After removing background and ambiguous sources, a total of $22$ out of the $40$ LITTLE THINGS galaxies are associated with significant RC emission; $8$ are new detections. Where reliable flux densities of our sample exist in the literature, we find that our observations are in general good agreement;
\item We find that the average thermal fraction in our sample is $50 \pm 10$\% and $70 \pm 10$\% at $6.2$\,GHz when integrating over the RC and disk based mask, respectively;
\item We present fits for the RC--SFR and FIR--SFR between SFRs of $\sim 10^{-4}$ and 1\,M$_\odot$\,yr$^{-1}$ integrated over the RC mask and disk mask;
\item We find that the RC--SFR is broadly consistent with theoretical predictions when considering the RC mask but we find that the ${\rm RC_{Nth}}$\ is suppressed when integrating over the disk;
\item The FIR emission in our sample is suppressed in both the RC and disk masks given the measured SFR;
\item When integrating the galaxy properties within the optical disk we find that the dwarf galaxies are consistent with the linear \cite{Yun2001} RC--FIR relation. The `conspiracy' invoked to explain the relation continues to hold for our sample of dwarf galaxies (see Fig.~\ref{Figure:FIR_v_RC}). The RC--FIR relation based on our RC mask integrated results shows that our dwarf galaxies diverge from the the linear \cite{Yun2001} relation with a RC excess at low luminosity;
\item In a few dwarf galaxies, the equipartition magnetic field strength reaches as high as $30{\rm \,\mu G}$ in several $100$\,pc regions, and in one case, $50{\rm \,\mu G}$;
\item The average strength of the transverse magnetic field, based on equipartition, is $\sim 5.2{\rm \mu G}$ (RC mask) and $\sim 7.5{\rm \mu G}$ (disk averaged). This value is slightly lower than larger galaxies \cite[e.g., $9.7{\rm \mu G}$ in WSRT SINGS;][]{Heesen2014} but consistent with other studies of dwarf galaxies.
\end{itemize}
\acknowledgments
We thank Dan Smith for valuable discussions on the RC--FIR relation, and his help with FIR--related work. We also appreciate Min Yun's readiness to provide us with his {\em IRAS} and VLA data from the \cite{Yun2001} study. The manuscript has benefitted from constructive comments on an earlier version by the referee. GK acknowledges support from the UK Science and Technology Facilities Council [grant number ST/J501050/1]. Likewise EB and LH acknowledge support from the UK Science and Technology Facilities Council [grant number ST/M001008/1]. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
Facilities: \facility{VLA}; \facility{\em GALEX}; \facility{\em Spitzer}.
|
{
"redpajama_set_name": "RedPajamaArXiv"
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Demonic Screen Part 1
English translation of the German titles and and of the voice-over narration
by K. Wyborny and Marcia Bronstein
made for a screening in Anthology Filmarchive New York in 1978,
where the text was handed out before the screening
DÄMONISCHE LEINWAND TEIL 1
(Demonic Screen Part 1)
contains (in this sequence):
A CROWD IN THE FACE
AUF ZU DEN STERNEN
(Up to the stars)
CHIMNEY PIECE
DAS ABENTEUERLICHE ABER GLÜCKLOSE LEBEN DES WILLIAM PARMAGINO
(The adventurous but luckless life of William Parmagino)
Filmmakers Cooperative shows
c copyright 1968 by Wyborny
Y - Production shows
Klaus Wyborny and Christian Willig in
A film by Klaus Wyborny, camera Rainhild Lüders
dedicated to Wenzel Lüdecke
(5 minutes of dialogue from the German dubbed version of Elia Kazan's "A Face in the Crowd" )
(the film has a mumbled narration of which only few words are understandable)
Y-Production presents
Rainhild Lüders, Sybnille Nabel, Helmut N. und Helmuth Gertig in "Home Sweet home"
a film by Klaus Wyborny, music Antonio Vivaldi
When it had come that far, I set out for the green hills of my homeland. The first obstacles I took without difficulties, later it became strained. Finally after many efforts, I made it, exhausted but not without expectations.
(12 minutes of images)
What I had seen was enough. I decided to try it again, again and again. For some time, however, I had other things to do. In Spain. Border controls lay ahead, and a wide field of tasks. Like someone escaping I left the place of my first memories and somehow I was glad.
And finally … after some … decades … it was … achieved … and … an ancient … dream of mankind … was … fulfilled … Reaching for the satrs … became … reality … The participants of the expedition wer selected with great diligence and everything was…
(next word not understandable because of starting music)
Sybille and Susanne Nabel, Joachim Wolf, Joern Voss, Elna Douce and Peter Flak in
"Up to the Stars"
a film by Klaus Wyborny, assisted by Christian Willig.
Dedicated to the Soviet-Astronauts
This was John.
This was Joel.
And this was Frank.
John fell in love with Janine, and Janine fell in love with Frank. Frank was not sure if he should give preference to Joel or Joanna.
After a few months they stopped talking to each other and after a few weeks they started conversing again.
Nothing was to be seen. just stars, an infinite number of stars.
They were lonely but they didn't become quiet.
After half a year Frank couldn't stand the situation any longer, he wanted to castrate himself.
The ship's cinema played a film by Christian Willig made at a time when one rarely shot in cinema scope. They all found it funny.
At night Frank died of wound-fever, and Maria was now alone. John had pity for her. He comforted her, and Joel comforted the abondoned Janine. Joana felt treated unjustly somehow, and after half a year they landed on Mars.
It was a planet of infinite beauty, with mercilessly burning radiation. The sand of the wide deserts penetrated through the joints of their spaceship way into their wristwatches.
On the one hudred and fortieth day of their stay on Mars, John made a dreadful discovery. But Joel could prove that he was mistaken.
On their way back there were many complications, basically, however, they were in agreement with each other. And that they knew.
And so they prepared themselves for rearrival on Earth.
They were received with jubilation, and by the time the monuments of them stood, new expeditions made for the long trip. And soon the solar system was conquered by man.
New objectives lay ahead.
Chimney Piece c copyright 1969/71 by Klaus Wyborny
Musik: Anthony Moore
(30 minutes of images with music by Anthony Moore)
William Parmagino's
At a time which is not ours, this film was found on a heap of scrap metal, close to Nanterre. It tells of the desparate attempt of a group of people to adjust to the rules others have imposed upon them. E. P.
Janine was born, but she entered at a time in which live seemed hopeless. It was not her fault.
Her parents mediated to her the knowledge of their culture and Janine understood. And when the first day of her short life was over she knew that she would have to die after five more days, and a slight air of mourning signed her face.
In a meadow in a park she met Martin, and Janine fell in love with him. But when Ann appeared, Martin left her, and Janine decided to return home to her parents. On her way home, she nearly ran over John. He told her that he had no place to stay and she took him along.
When they woke up in the morning, Janine's mother was dead; and when they had breakfeast, her father disappeared.
John showed Janine the palaces of the mighty and Janine was wondering about his wrath. After a while she had a feeling as if time was slipping away from her. She told John. He understood her but he carried on. And then she told him that he had already occupied one day of her life and then she went away.
John waited long for Janine, till late at night, but in vain, she had left him.
In the morning he left the place of remembrance. He wanted to forget Janine and visited Joana who loved him.
When his eyes rested on Joana he could feel her face decaying, and he sensed that his soul was dissolving.
John's last day had begun. He said goodbye to Joana and thought of Janine.
In the moment of death he had a vision. He saw a wide grain field and ears bending in the wind, under a sun that was burning unmercilessly. He saw a rainbow floating through the skies, and he knew that he would see Janine never again.
Joana died at night, and in the next morning Janine died, and five days later died their son, and John was forgotten and Janine was forgotten.
When I was still a very small boy there was a dreadful idleness. The ducks were quacking, the cocks were crowing and the church bells were ringing. The war was over and they were about to rebuild it all over again.
William Parmagino's "William"
A film giving joy, a film that tells stories, a film full of poetry, which until now we have only dreamed.
A film about love and death, and full of the mourning we carry within us.
Rosered the sun arose above the Grand Canyon, and William was full of love for Janine, and around evening her hidden smile dissolved into fever.
Effortlessly they had survived on the sinking ship, and he found the separation from Miriam as hard as it had been in Kathmandu. A monk was passing.
Small intellectual essays in the style of Voltaire he wanted to write then, but the Nazis wanted it differently. They put him into a leading position, and forced him to become decisive initiator of those ideas which even today drive the flush of shame into our lips.
A film …
A film giving joy, a film that tells stories, a film full of poetry which until now we have only dreamed.
Albie Thoms about "William Parmagino" (Afterimage No 2, London, fall 1970)
|
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|
package gpio4s
import akka.actor._
import com.typesafe.config.Config
import gpio4s.Device.{DeviceInstallFailed, DeviceInstalled, InstallDevice}
import gpio4s.PiModels.PiModel
import gpio4s.gpiocfg.CfgIO.RichPins
import scala.collection.mutable
/**
* Interface to a Pi
* @author wassj
*/
class Pi(m: PiModel, pp: PinProducer) extends Actor {
import Pi._
val gpios: PinAllocation = produceGpios(m, pp)
val subscribers: SubscriberList = subscriberList()
//\\ WARNING do not forward events - outsiders cannot touch PinRefs WARNING //\\
def receive: Receive = {
case Configure(c) => configure(gpios, c)
case Subscribe(p) => subscribers.addBinding(p, sender())
case Unsubscribe(p) => subscribers.removeBinding(p, sender())
case m @ DigitalRead(p) => gpios(p) ! m
case m @ DigitalWrite(p, _) => gpios(p) ! m
case e @ DigitalEvent(p, v) => subscribers(p).foreach(_ ! e)
case m @ InstallDevice(info) => sender() ! installDevice(info)
case _ =>
}
// todo validate the requested pin exists
// todo validate the pins are not locked
// todo - a locked pin has restricted config
// todo - an unlocked pin can have its config changed
def installDevice(info: DeviceInfo) = {
try {
configure(gpios, info.conf)
val dev = context.actorOf(info.props(gpios))
DeviceInstalled(info.id, dev)
}
catch {
case t: Throwable =>
DeviceInstallFailed(info.id, t)
}
}
}
object Pi {
def apply(m: PiModel, f: PinProducer)(implicit sys: ActorSystem): ActorRef = sys.actorOf(Props(new Pi(m, f)))
def produceGpios(model: PiModel, pp: PinProducer)(implicit ctx: ActorContext): PinAllocation = model.pins.map { p => p -> pp.get(p) }.toMap
def configure(gpios: PinAllocation, conf: Config, reset: Boolean = false) = conf.pins().foreach(p => gpios(p.num) ! Setup(p))
private type SubscriberList = mutable.HashMap[Int, mutable.Set[PinRef]] with mutable.MultiMap[Int, PinRef]
private def subscriberList() = new mutable.HashMap[Int, mutable.Set[PinRef]] with mutable.MultiMap[Int, PinRef]
}
|
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{"url":"https:\/\/github.com\/GENIE-MC\/Generator\/pull\/92","text":"\/ Generator Public\n\n# add -T option to gevgen_atmo to specify livetime instead of number of events#92\n\nMerged\nmerged 1 commit into from Oct 9, 2020\nMerged\n\n# add -T option to gevgen_atmo to specify livetime instead of number of events #92\n\nmerged 1 commit into from Oct 9, 2020\n\n## Conversation\n\nThis file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode characters\n\n### tlatorre-uchicago commented Feb 19, 2020 \u2022 edited\n\nThis commit adds the -T command line option to gevgen_atmo to specify a\nlivetime in seconds instead of a total number of events using the -n option.\n\nTo implement this gevgen_atmo first integrates the 3D flux histogram and\nmultiplies it by the livetime to get the total number of neutrinos that should\nbe simulated per square meter. This number is then multiplied by the area of\nthe flux surface to determine the total number of neutrinos that should be\nsimulated.\n\nInstead of looping over a fixed number of events, gevgen_atmo then continues\nthrowing neutrinos until the number of neutrinos thrown divided by the global\nprobability scale is greater than the total number of neutrinos that should be\nsimulated.\n\nSome potential issues that should be considered before merging:\n\n1. The method I'm using definitely is dimensionally correct and I verified that it behaves as expected using a very simple Monte Carlo I wrote in python, however the actual flux driver and GMCJDriver are a bit more complicated and so I'm not 100% sure that there is something I'm missing and whether it is OK to simply scale the number of flux neutrinos thrown by the global probability scale to get the effective total number of neutrinos simulated.\n\n2. Technically the code in the flux driver allows one to do a scheme whereby the neutrinos are thrown not according to a global probability rescaling but by rescaling each bin and then assigning weights. The whole method I use in this pull request will not work if this method is activated. Currently in gevgen_atmo it's not activated and I added a comment explaining that if it is ever activated then the exposure time method I use will not work.\n\n3. This pull request has not gone through extensive testing. I did some very basic testing with a similar commit applied to version 2.12.8 which is what I'm currently using, and I just build tested it against master. But it probably needs much more testing before being applied.\n\nrequested a review from nusense Feb 26, 2020\n\n### candreop commented Feb 26, 2020\n\n Without thinking too deeply about it, it seems correct. It is broadly equivalent with what we do for accelerator neutrinos. There, each flux ray thrown incremements a POT counter. The rate of increase of the POT counter per flux ray is determined by the flux simulation. Here, each flux ray thrown increments a time counter. The rate of increase is determined by the input flux histograms. The input flux is given in terms of number of flux neutrinos per unit energy per unit solid angle and per unit time. If you integrate over \\theta, \\phi and E, that histogram tells you, for each neutrino species, how many neutrinos we have per unit time. As for acceleator neutrinos, the probability scale affects that exposure unit (at each turn we don't simulate single POTs or single seconds, but rather larger chunks that are more likely to yield an interaction).\n\n### candreop commented Feb 26, 2020\n\n I agree this will not work with the option to produce weighted events, but it seems to be that it can be made to work with that option too. Another thing that needs attention is that gevgen_app allows a user to specify energy limits (in which case, I guess, the input flux simulation will need to be integrated within that specified range in order to yield the appropriate time increment per flux ray)\n\n### tlatorre-uchicago commented Mar 4, 2020\n\n Thanks for the review! I will update this to take into account the energy bounds, but I'm still not sure how it can be made to work with weighted events. Also, to be clear, currently the gevgen_atmo script does not allow one to use weighted events, although this might have been something planned for the future. Or am I misunderstanding what you were saying?\n\n### tlatorre-uchicago commented Apr 1, 2020\n\n I've updated this to hopefully take into account the energy range. I also added two very simple tests to make sure that the integration routines match what we expect. You can run them by doing: $cd src\/contrib\/test$ make gtestGAtmoFlux $cd ..\/..\/$ .\/bin\/gtestGAtmoFlux which will output: \\$ .\/bin\/gtestGAtmoFlux ... [ok] testGetTotalFlux [ok] testGetTotalFluxInEnergyRange I'd like to add a more comprehensive test to test the whole scheme, but haven't come up with a clean way to do that yet.\n\nforce-pushed the exposure-squashed branch 2 times, most recently from 0fd7c45 to 5bb353e Apr 14, 2020\n add -T option to gevgen_atmo to specify livetime instead of number of\u2026 \n d4c796e \n\u2026 events\n\nThis commit adds the -T command line option to gevgen_atmo to specify a\nlivetime in seconds instead of a total number of events using the -n option.\n\nTo implement this gevgen_atmo first integrates the 3D flux histogram and\nmultiplies it by the livetime to get the total number of neutrinos that should\nbe simulated per square meter. This number is then multiplied by the area of\nthe flux surface to determine the total number of neutrinos that should be\nsimulated.\n\nInstead of looping over a fixed number of events, gevgen_atmo then continues\nthrowing neutrinos until the number of neutrinos thrown divided by the global\nprobability scale is greater than the total number of neutrinos that should be\nsimulated.\napproved these changes\n \/\/ event loop for(int iev = 0; iev < gOptNev; iev++) { for(int iev = 0; gOptNev > 0 ? iev < gOptNev : 1; iev++) {\n\n### nusense Apr 21, 2020\n\nI suggest some ()'s here to help with readability:\n\n for (int iev = 0; ( (gOptNev > 0) ? (iev < gOptNev) : true) ; iev++)\n\n\n### tlatorre-uchicago Apr 22, 2020\n\nWhat do you think about just turning it into a while loop to make things easier to understand? I originally thought about doing that but didn't want to change too much, but now that you mention it I think it would be much easier to understand that way.\n\n atmo_flux_driver = GetFlux(); \/\/ Cast to GFluxI, the generic flux driver interface GFluxI *flux_driver = dynamic_cast(atmo_flux_driver);\n\n### nusense Apr 21, 2020\n\npedantically I'm not sure this is ever necessary to down(?) cast to a base class unless the derived class hides some base class method. You should be able to just call those base class methods on the derived class or pass derived object pointer to methods that expect the base class. But that was an issue with the original code, so not a required change here.\n\n### tlatorre-uchicago Apr 22, 2020\n\nGood point, I will update this and push a new set of changes.\n\n \/* Note: For the method of calculating the total number of events using a * livetime we *need* to force a single probability scale. So if you change * the next line you need to make sure that the user didn't specify the -T * option. *\/ mcj_driver->ForceSingleProbScale();\n\n### nusense Apr 21, 2020\n\nI presume it's thus safe to call ForceSingleProbScale() in all cases, but unsafe to not call it if -T was specified. Am I reading that right?\n\n### tlatorre-uchicago Apr 22, 2020\n\nYes that's right. Do you have any suggestions on how I can update that comment or if it belongs somewhere else? I added that just as kind of a future warning to anyone editing it that they shouldn't change that without adding a guard to check against the -T option.\n\nadded this to the 3.2.0 release milestone Jul 6, 2020\nmerged commit f4d15d7 into GENIE-MC:master Oct 9, 2020","date":"2022-11-26 11:39:44","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\": 0.5609599947929382, \"perplexity\": 1491.0543614245892}, \"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\/1669446706291.88\/warc\/CC-MAIN-20221126112341-20221126142341-00744.warc.gz\"}"}
| null | null |
Eleanor Roosevelt's Cold War Dilemma
Carol Anderson discusses Eleanor Roosevelt's struggle to balance her support of civil and human rights with domestic and international politics and policy during the Cold War.
Human & Civil Rights
When you've got an absolutely revered former First Lady who has moved her chair into the middle of an aisle because she refuses to sit with Jim Crow, who has worked to have Marian Anderson sing at the Lincoln Memorial, who is on the board of directors of the NAACP, it's sending the signal that this struggle for civil rights is absolutely grounded in Americana. That it is not foreign. It is in fact as basic and as American as apple pie.
Whereas I think Eleanor was absolutely powerful as a symbol for this struggle for equality in the United States, I think we need to be very clear that we don't mythologize her. One of the pieces of Eleanor is that she's a cold warrior. I mean, this is fighting this struggle for equality within the Cold War.
And there are times when she's sitting in her position as the Chair of the Commission on Human Rights, where she's making decisions, where she's prioritizing, is the priority going to be fighting the struggle against the Soviet Union or fighting the struggle for Black equality? And when it became that discussion, the Soviet Union won out.
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Students examine the strategies of three key civil rights leaders, Martin Luther King Jr., Malcolm X, and Stokely Carmichael.
Resources for Civic Education in Massachusetts
Explore resources that meet the Massachusetts History and Social Science Framework.
The Equal Rights Amendment: A 97-Year Struggle
This teaching idea provides an overview of the ERA and a look at the history behind the struggle to ratify the amendment that would formally guarantee women equal rights to men under the US Constitution.
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Explore resources that meet the California History–Social Science Framework standards.
Explore classroom resources for making connections between current events and your curriculum, including activities and discussion strategies for high school and middle school students.
Standing Up to Hatred and Intolerance
Address today's global challenges with lesson plans focused on current events including the refugee crisis and contemporary antisemitism.
Analysing Gerald's Character
Students develop their understanding of the character Gerald, exploring the differences between his treatment of Eva/Daisy and Sheila, whilst reflecting on Edwardian gender expectations.
Bearing Witness to Eva Smith
Students reflect on Priestley's portrayal of Eva Smith and consider the symbolism of having a character who only appears in the narrative second-hand.
The Cost of Labour
Students explore the moral codes of the world of the play, before being introduced to the concept of a universe of obligation and participating in a debate on workers' rights.
Persuasive Writing: A Letter to Parliament
Students write a persuasive letter to Parliament concerning the gig economy, having reviewed persuasive devices, generated claims and content, and read a model letter.
Persuasive Writing: A Speech about Consent
Students write a persuasive speech for sixth-form students on the importance of consent, having reviewed persuasive devices, generated claims and content, and read a model paragraph.
Analytical Writing: A Character Paragraph
Students write an analytical paragraph on character having generated claims, selected evidence and read a model paragraph.
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|
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"redpajama_set_name": "RedPajamaCommonCrawl"
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| 7,145
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Provided that you picked the right phone contract plan, you'll be enjoying a range of advantages with this type of phone deal in the long run. And as long as you have good credit, you can choose practically any phone contract deal you want. It's a different story if you have a poor credit history.
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If you want a larger storage memory for your iPhone, EE has another attractive offer you'd want to check out. Like most iPhone 6S deals, this particular contract plan comes with a free phone and a generous phone tariff. The phone is available in gold color with 64GB of storage. It is available in a 24-month 4G contract term at £44.99 per month. Included in the phone tariff are unlimited minutes, unlimited texts and 10Gb data. If you want an extra home broadband feature, just add £2.50 per month to enjoy unlimited broadband for 12 months.
|
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|
José Maria Vasconcelos, känd under pseudonym Taur Matan Ruak (Tetum för "Två skarpa ögon"), född den 10 oktober 1956, är en östtimoriansk politiker. Han var landets president mellan 2012 och 2017 då han efterträddes på posten av Francisco Guterres. Den 22 juni 2018 blev Ruak premiärminister.
Ruak fick drygt 61 % av rösterna i presidentvalets andra omgång, i april 2012. Han var, i likhet med huvudmotståndaren Francisco Guterres, gerillaledare under Östtimors 24-åriga befrielsekamp mot Indonesien.
Källor
Ruak ny president i Östtimor Dagens Nyheter, 24 april 2012
Noter
Externa länkar
Östtimoresiska politiker
Födda 1956
Levande personer
Män
|
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| 3,529
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{"url":"https:\/\/math.stackexchange.com\/questions\/1513945\/is-a-regular-point-of-a-smooth-function-also-a-regular-point-for-the-restriction","text":"# Is a regular point of a smooth function also a regular point for the restriction to a submanifold?\n\nSuppose I have a smooth map $F \\colon M \\rightarrow N$ and an embedded submanifold $S \\subset M$. Suppose that the differential of $F$ is non-singular at a point $z \\in M$.\n\nIf $z$ also happens to lie in $S$, is it true that the differential of $F\\vert_S$ (as a smooth map from $S$ to $N$) is non-singular at $z$?\n\n$\\textbf{Edit}$\n\nSo it seems this was a bad question to ask. What I'm trying to do is the following:\n\nI have a smooth vector field $\\widetilde{V} \\colon \\Bbb R^3 \\rightarrow T\\Bbb R^3$ which sends $$(x,y,z) \\mapsto (-y,x,x^2+y^2+z^2-1).$$\n\nIts restriction to $\\Bbb S^2$ is then a smooth vector field $V$.\n\nI want to somehow see that $dV_p$ is non-singular at the points $p =(0,0,\\pm1)$.\n\n\u2022 No, of course not. Take $S=z$. If $F^{-1}(F(z)) \\subset S$, then it's true. (Why?) \u2013\u00a0user98602 Nov 5 '15 at 4:14\n\u2022 Sorry I'm confused, what would be the tangent space $T_zS$ in this case? \u2013\u00a0Open Season Nov 5 '15 at 4:19\n\u2022 It would be trivial in the case $S=z$. \u2013\u00a0user98602 Nov 5 '15 at 4:29","date":"2019-08-25 14:28:02","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\": 0.9676624536514282, \"perplexity\": 164.56004021625708}, \"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-2019-35\/segments\/1566027330233.1\/warc\/CC-MAIN-20190825130849-20190825152849-00555.warc.gz\"}"}
| null | null |
\section{Introduction}\label{Section1}
As urbanization accelerates around the globe, cities increasingly struggle to provide affordable and adequate housing for their growing population. This has forced many people seeking opportunities and employment in the cities into informal settlements, also referred to as 'slums'. These informal settlements are often highly deprived and their populations face various problems, e.g. the lack of healthcare access \citep{VandeVijver2015} or basic infrastructure \citep{Castells-Quintana2017}. The poor living conditions in informal settlements in combination with their continuous growth have led the United Nations (UN) to specifically mention "slums" as a challenge to their sustainable development goals (SDG) \citep{UnitedNations2018}. It is thus crucial to understand informal settlements and their development. In order to optimize humanitarian aid, precise "slum" detection and population estimates are of particular interest. Deep learning approaches built atop satellite image data have recently become more and more popular for this task \citep{Jean2016}, as they scale well on high-dimensional data and outperform traditional methods of remote sensing \citep{Persello2017}. However, these approaches mostly originate from the remote sensing, geographic information science (GIS) and human geography communities \citep{Kuffer2016}. We believe that the machine learning community should assume a more active role tackling these problems, especially since it is at the forefront of computer vision, pattern recognition and scalable deep learning methods. But while image classification is one of the most successful applications of machine learning, it often struggles to generalise to real-life cases such as multi-label images and poor-resolution images. In remote sensing and satellite image classification, we see this effect demonstrated in competitions such as Deep Globe \cite{Demir2018} in which building detection for Las Vegas was 85\% whereas detection for Khartoum was only 54\%. This also highlights another problem: current methods work better on cities in the Western world, while cities in the Global South, which may benefit especially from these applications, remain neglected.
In this study, we propose a flexible framework for estimating the population of informal settlements. Our proposed method builds on high-resolution satellite imagery and utilizes equitable ground-truth: Building-level shapes and labels are mapped and curated in collaboration with local universities and communities. Through this cooperative approach, the local population takes agency over mapping their own neighborhood; furthermore leveraging their unique domain knowledge to generate high-quality data. While satellite images have previously been used to map informal settlements, our equitable ground-truth data presents a novel approach to population mapping. We further comment on the differences with existing population mapping approaches. Our proposed pipeline is based on a gridded population estimation model with adaptable spatial resolution. Methodologically, we have to overcome a lack of training data, stemming from the expensive ground-truth generation process, and resulting proneness to overfitting. We experiment with fine-tuned versions of pre-trained computer vision algorithms like \textit{ResNet50} and \textit{MobileNetV2} to tackle this issue. However, we find a surprising lack of capability of these powerful networks. We use these preliminary finding as a starting point to discuss the challenges of successfully implementing our approach in terms of (1) the ethical and qualitative data requirements and (2) the methodological requirements in the light of inadequate, existing benchmark models. Lastly, we outline a research agenda to address these issues.
\section{Related Work}\label{Section2}
\begin{table}[]
\centering
\scalebox{0.8}{
\begin{tabular}{l|llllll}
Publication & Data (input) & Data (labels) & Output res. & Valid. res. & Method & Eq. GT \\ \hline
\hline
\citealt{Wardrop2018} & census data & - & \textit{flex. grid} & - & Spatial & - \\
& soc.-ec. covariates & & & & Disaggregation & \\
& built environment & & & & & \\
\hline
\citealt{Zong2019} & coarse labels & cellular data & \textit{flex. grid} & cell-tower & Deep & - \\
& POI data & & & & Learning & \\
\hline
\citealt{Weber2018} & high-res & survey data & \textit{flex. grid} & - & Image & - \\
& satellite image & & & & Segmentation & \\
& microcensus & & & & & \\
\hline
\citealt{Hu2019} & high-res & census data & \textit{flex. grid} & village & Deep & - \\
& satellite image & & & & Learning & \\
\hline
\citealt{Xie2015} & nighttime & poverty index & \textit{flex. grid} & household & Deep & - \\
& light & & & group & Learning & \\
& satellite image & & & & & \\
\hline
\textbf{Ours} & high-res & building mask & \textit{flex. grid} & building & Deep & {\color{green}\checkmark} \\
& satellite image & & & & Learning &
\end{tabular}}
\caption{Comparing recent population estimation methods: the \textit{Data} columns describe input and validation labels (if present), \textit{Output res.} and \textit{Validation res.} provide the spatial units of the estimation output and the validation labels respectively, \textit{Method} gives the quantitative approach for population estimation and \textit{Eq. GT} indicates, if the validation labels constitute equitable ground-truth.}
\label{table:1}
\end{table}
Informal settlement mapping is an increasingly prominent research objective \citep{Hofmann2015}, but poses distinct challenges, as the morphology and structure of informal settlements varies substantially--across different cultural spaces and even within cities \citep{Taubenbock2018}. As of recent, machine learning approaches provide promising solutions to account for these complexities \citep{Maiya2018,Wurm2019}. Yet, few studies are built around active community engagement, such as participatory mapping of informal settlements \citep{Yuan2018}. We believe integrating local communities into work such as ours is not only helpful for leveraging the locals' expertise, but also provides them with agency over their data, enables further conversation on the equitability and performance of resulting applications and prevents model bias stemming from poor-quality ground-truth. Informal settlements can be seen as self-contained systems, including their own places of worship, entertainment and trade. Many structures are not inhabited, but rather being used for other purposes (e.g. shops or religious buildings). Precise population estimates are thus often hard to obtain. Recently, Wardrop et al (\citeyear{Wardrop2018}) highlighted the need for better and more granular population estimates in informal settings. Traditionally, spatial disaggregation approaches utilizing auxiliary information such as road networks or vegetation have been used \citep{Wardrop2018}, while more recent machine learning focused work has proposed disaggregation using points-of-interest \citep{Zong2019} or combining satellite images with existing census data \citep{Weber2018,Hu2019}. A further, methodological challenge is that few deep learning methods tailored to satellite imagery exist. Together with the fact that applicable training data and reliable ground-truth can be sparse and expensive to produce, building models which can be trained on limited data but perform well on a global scale are the "holy grail" of informal settlement analysis. So far, this task has been proven to be exceptionally challenging: Wurm et al. (\citeyear{Wurm2019}) point out that data quality and resolution differences are a substantial problem in their transfer learning task on informal settlement satellite imagery. However, Xie et al. (\citeyear{Xie2015}) find that rather simple data such as nighttime lights can be used for successful transfer learning and poverty mapping. They also note that pre-training on standard datasets such as \textit{ImageNet} can be useful. Table 1 provides an overview on data requirements, spatial resolution, methods and equitability of existing approaches, as compared to our proposed approach.
\section{Data \& Equitable ground-truth}\label{Section3}
\begin{figure}
\centering
\includegraphics[scale=0.5]{fig1_v2.pdf}
\caption{\label{fig:fig1}Proposed population estimation framework with equitable ground-truth through participatory online digital mapping with on-site validation; Figure partially adapted from Porto de Albuquerque et al. (\citeyear{PortoDeAlbuquerque2019}).}
\vspace{-4mm}
\end{figure}
Our experiments are conducted using data from three sites: two settlements in Ibadan, Nigeria (Sasa, Idikan) provide training data and one in Lagos, Nigeria (Bariga) test data. Our data can broadly be split into two categories: Satellite image data (\textit{input}) and ground-truth maps (\textit{labels}):
\textbf{Input}: We acquire very high-resolution (VHR) satellite image data with RGB channels and a pixel length of 0.02 meters for each of the three test sites from two major mapping services via the \textit{SAS Planet} software \footnote{Accessible here: \url{http://www.sasgis.org/}}, obtaining two images per informal settlement. Nevertheless, this sub-meter resolution is not indicative of quality; rather we find the images to be quite noisy, especially compared to VHR images of high-income cities such as New York. Satellite data was collected in 2019, the ground-truth labels were mapped in 2018 (note that the images used to create the ground-truth-maps are different from the images we use for model training). We find that the temporal difference in accessing the respective data does not affect the match between both datasets. This implies that all three informal settlements did not change substantially during the period between community-mapping and accessing satellite data. Nevertheless, informal settlements are inherently dynamic and if different imagery is used for mapping and modeling, the overlap between them should always be assessed to guarantee consistent results.
\textbf{Labels}: Active community engagement is essential for avoiding biased or misinformed labels which might transfer into biased models. We use data from the University of Warwick's \textit{Improving Health in Slums Collaborative} (IHSC, \citeyear{IHSC2019}), which is derived from a participatory community mapping framework that aims to achieve equitable, empowering community engagement while at the same time conforming to rigorous, reliable and generalizable data standards \citep{PortoDeAlbuquerque2019}. This framework is based on the premise that the generation of data by citizens can also be an opportunity for mutual learning and to develop a new critical consciousness on the local realities that are being mapped in the data \citep{AlbuquerqueAlmeida2020}. While the \textit{IHSC} paper should be consulted for details, we want to outline the key steps of this approach briefly (also, see Figure 1): In preparation for the mapping, local stakeholders are consulted to identify key local partners. These partners are essential for understanding the complexities of the physical and social environments in informal settlements. The next step involves the creation of a base map from high-resolution satellite imagery. This mapping process can be conducted by locals and remote participants using open-source collaborative software such as the \textit{HOT Tasking Manager} (see: \url{https://tasks.hotosm.org/}). Lastly, "ground-truthing" is conducted at the site using participatory mapping by specially trained local citizens. This validates and enriches the data gathered in the previous step. The final map can then be contributed as open geographic data to volunteered geographic information (VGI) services like \textit{OpenStreetMap}. OpenStreetMap is a "wikipedia of maps"; a collaborative project aim at creating a free editable map of the world. Consequently, our definition of "equitable ground-truth" (and how we compare it to existing work, as in Table \ref{table:1} entails all the principles outlined above: \textit{pre-assessment \& local partners}, \textit{community participation \& education}, \textit{double validation (remote and on-site)} and \textit{transparency \& accessibility}.
\section{Discussion}\label{Section4}
In order to explore how we may learn differently with this community data, we decided to look at the process of classifying buildings into inhabited vs non-inhabited from satellite images. This is a difficult but important question: Building an understanding of where people live is crucial for estimating needs in emergency scenarios and for general public service provision and planning. Below we give some of the steps and results of our preliminary analysis.
First we split the satellite images into a grid of 36x36 meter tiles. We then rescale each image from 1600x1600 pixels to 224x224 pixels - given how noisy the images are there was not much loss of information with this compression. For one of the settlements--Lagos-Bariga--we also removed images with cloud cover, calculating the ratio of white pixels as a proxy - we set threshold at 5\%, which gives us as many images as possible. After creating the grid, each image is assigned a respective residential occupancy level (see Figure 1), calculated as the percentage of pixels occupied by residential buildings. We transform this into a classification problem by declaring images with 30\% or more residential occupancy level as residential ($=1$) and less than that as non-residential ($=0$). We chose this threshold through a preceding analysis, comparing each image to its respective building masks and assessing visual cues in the images, while avoiding further class imbalances. Even though this might seem a fairly low residential occupancy level, this threshold corresponds to the true ratio of occupied versus non-occupied buildings, which we observe to be very similar in all three sites. About $1/3$ of the data are assigned a "residential" label and $2/3$ a "non-residential" label.
\begin{figure}
\centering
\includegraphics[scale=0.35]{residency.png}
\caption{\label{fig:test} Random sample of training data. Highlighted on the lower right is an exemplary image for high residency}
\vspace{-4mm}
\end{figure}
For our baseline analysis, we trained a \textit{ResNet50} model (150 epochs) \citep{He2016} and a \textit{MobileNetV2} (30 epochs) \citep{Sandler2018} using data from Ibadan-Sasa and Ibadan-Idikan for training- which gave us a total of 1056 training examples - and from Lagos-Bariga for validation - 646 validation examples. We found that \textit{MobileNetV2}, trained with only our dataset performed better than both \textit{MobileNetV2} with pre-trained weights from the \textit{Imagenet} dataset. Validation performance converged after running 30/50 epochs. In this set up we got a training accuracy of 75\% and validation accuracy of 63\%. In several studies in machine learning, transfer learning has proven to be a great tool to learn under constrained resources \cite{Zoph_2016,alex2019large}. In our case we find that in questions as complex as that of building separability, standard methods of pre-training with benchmark datasets does not help us much and in fact harms accuracy. This is not a novel finding \cite{ngiam2018domain}, but it once again underlines the importance of curating relevant datasets, especially for applied work. While our preliminary results may suggest that we are not close to a practicable solution, we gained crucial insights to guide future research directions. Further they allow us to comment on lessons-learned and best-practices when working with equitable ground-truth data:
\begin{itemize}
\item During the data preparation, we realised that there were spatial cues in images such as how square a roof is or how square neighbouring roofs are, that help the classification task. However, we have learned automating this separation is a lot more complex. That said, this might just be a function of the limited dataset.
\item Ethical considerations regarding the detachment between the "analysts" (e.g. researchers) and "subjects" (informal settlement population) need to take a more central role in machine learning based population mapping tasks. Although different organisations are increasingly discussing issues around bias and adopting frameworks based on principles for ``responsible AI'', there is still a lack of clear processes for engaging with the local communities that are represented in the data used in machine learning systems. We hope that by having the local community as part of the annotators, we have provided the community with hitherto unavailable data to understand their contexts, while simultaneously generating a more representative training dataset. However, we also conclude that deeper analyses of the informal and often undocumented implications of machine learning systems are needed. Failing to do so would not only exclude or misrepresent large population parts \footnote{In Nigeria, for example, the informal sector accounts for 50-65\% of GDP. IMF 2017 working paper: \url{https://www.imf.org/en/Publications/WP/Issues/2017/07/10/The-Informal-Economy-in-Sub-Saharan-Africa-Size-and-Determinants-45017}}, but also may lead to severe problems with downstream tasks. It is hence crucial that the machine learning community actively works with practitioners and local stakeholders. Further, best-practice guidelines for generating and working with equitable ground-truth data should be developed, both in general and domain-specific, such as the recent proposal of an integrated deprived area mapping system \citep{Kuffer2020}.
\item We observe a certain lack of transferability of existing, pre-trained vision models to our task. In particular, we see that larger--and presumably more powerful--models perform worse than smaller models. This raises the question of how much real-world relevance existing benchmarks hold. This also serves as a call-to-action for developing tailored methodologies and domain-specific benchmarks for common applications of machine learning in the development context.
\end{itemize}
\section{Conclusion}\label{Section5}
Government authorities and NGOs require precise population estimates for informal settlements to optimize their services and health interventions. Often the subject of these estimates, the population, is excluded from the data gathering process. In this paper we discuss the merits and difficulties of deploying machine learning for population estimation in informal settlements, building on equitable ground-truth data, gathered in collaboration with local population and stakeholders. This approach aims at empowering local communities to take agency over their own data and at eliminating potential root causes of biases further down the modelling pipeline. We argue that this method is not only more ethical, but also leads to a higher data quality, as local knowledge is explicitly leveraged throughout the annotation process.
We run experiments using pre-trained and fine-tuned vision models. Interestingly, we observe that pre-trained models don't fare as well as may be expected, and smaller models such as \textit{MobileNetV2} perform best. This raises concerns on the value ascribed to common computer vision benchmark models and their transferability to real world tasks. We hope our findings encourage further investigations in this area within the ML for development community.
\subsubsection*{Acknowledgments}
First, we wish to that thank Nyalleng Moorosi for her guidance and contribution to this project. The authors also gratefully acknowledge funding from the UK Engineering and Physical Sciences Research Council, the EPSRC Centre for Doctoral Training in Urban Science (EPSRC grant no. EP/L016400/1); The Alan Turing Institute (EPSRC grant no. EP/N510129/1). The authors would like to express gratitude to all project members of the NIHR Improving Health in Slums Collaborative for their invaluable input, to informal settlement residents and to the mappers of the OpenStreetMap community who were active locally and remotely to create the data used in this paper.
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Policies force some who rely on social housing to choose between a pet and a home
UCalgary research highlights potential benefits of companion animals from a public health perspective
O'Brien Institute for Public Health Staff
A recent study by UCalgary and UAlberta looks at policies, decision-making around companion animals. Colourbox
People who own pets often consider them to be a part of their family — but for those who are precariously housed that can often mean making tough decisions.
The benefits of having an animal companion for seniors, or for those living with low income, a disability or who are precariously housed, are significant.
A recent study by University of Calgary and University of Alberta researchers published in the journal Housing and Society looks at policies and decision-making around companion animals in social housing in Edmonton and examines the potential benefits of pets.
People's bonds to their companion animals are a positive contributor to their well-being, which isn't often reflected in social housing policies, says Dr. Eloise Carr, RN, PhD, a member of the O'Brien Institute for Public Health at the Cumming School of Medicine (CSM) and one of the article's authors.
"I think it's a really important consideration from a public health perspective. When we look at some of the impacts out there that we're grappling with, loneliness is one of the biggest issues," says Carr, a professor in the Faculty of Nursing at the University of Calgary, whose research areas include exploring how living with a dog can enhance the quality of life for people with chronic pain.
Researchers looked at 16 social housing organizations in Edmonton, and out of those, four organizations allow dogs, cats and other small companion animals, while three organizations only allow fish or birds.
When social housing policies do not allow people to have their pets, it can mean that some people will choose not to go, and instead choose unsafe or substandard housing.
"They may remain homeless, or they may remain in a situation that isn't positive for them in any way; therefore, it's presenting an enormous barrier to them," Carr continues.
Carr says 57 per cent of households in Canada have a companion animal, which represents a large number of people for whom policies banning companion animals would be a barrier.
There is a great deal of evidence that living with a pet has a positive impact on quality of life and well-being, as human-animal relationships lead to reduced loneliness, improved social connectedness, reduced risk of depression, improved ability to be active in the community and, for some, a sense of safety and security. Despite this evidence, making policy about allowing pets in social housing can be complicated," says fellow researcher Dr. Cary Brown, PhD.
Eloise Carr, left, and Cary Brown.
Brown says when people aren't allowed to bring their pets with them into social housing it can lead to rule-breaking and smuggling.
"For a large number of people living with their pets, many consider them to be family members," says Brown, a professor of occupational therapy in the Faculty of Rehabilitation Medicine at the University of Alberta.
"We would never consider telling someone, 'I'm sorry, you can move in, but you can't bring your child, or your grandchild,' but we have not made that move yet to families with a companion animal."
Brown says research like this is important to address evidence gaps and possible misunderstanding that can be reflected in policy, and to give organizations across Canada the best information possible.
Policies can vary widely between organizations and are often not evidence-based, Brown says. Due to this lack of evidence, policies can be based on assumptions that companion animals will cost more due to damage, so more investigation in this area is needed, she adds.
"Until we have that kind of economic data, it's going to be really hard to change this, because policy-makers are forced to rely on belief- and values-based decision-making," she says.
"This is not a new problem, but it's a growing issue, accelerating with financial problems and COVID, and we shouldn't be making decisions based solely on values and beliefs. We need to have access to better information to make decisions."
Read the full article: Does fido have a foot in the door? Social housing companion animal policies and policy decision-making in a Canadian city
The researchers collaborating on the article are Erin McCabe, Cary A. Brown, Maria C. Tan, Douglas P. Gross, Donna M. Wilson, Eloise Carr, Jean E. Wallace, and Maxi Miciak.
Cary Brown is a professor in the Department of Occupational Therapy at the University of Alberta and a member of the O'Brien Institute for Public Health.
Eloise Carr is a member of the O'Brien Institute for Public Health at the Cumming School of Medicine (CSM), the McCaig Institute for Bone and Joint Health, and the Hotchkiss Brain Institute. She is a professor in the Faculty of Nursing and the Department of Community Health Sciences.
UCalgary researchers show living with a dog helps patients with chronic pain
As COVID-19 threatened vulnerable Calgarians, this UCalgary network did something about it
Puppies and burnout: The impact of the coronavirus on veterinarians
Solemn ceremony commemorates those who die on city streets while experiencing homelessness
Who will be left behind when the 'new normal' begins?
O'Brien Institute researchers address health inequities through social innovation
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Q: java sub image display I write a game with cards. And I'm able to output with String. However, I'd like to change the display of String into images. I'm able to use JFrame and GridLayout to show four cards in 2*2 image.
My question is that I have a .png for the deck of cards, how can I get individual cards accordingly?
Class Card
package Chapter7;
public class Card {
Suit suit;
Rank rank;
public Card(Suit suit, Rank rank) {
this.suit = suit;
this.rank = rank;
}
public Rank getRank() {
return this.rank;
}
public Suit getSuit() {
return this.suit;
}
public String toString() {
return this.rank + " of " + this.suit;
}
public enum Suit {
CLUBS(1), SPADE(2), HEARTS(3), DIAMONDS(4);
int value;
Suit(int v) {
this.value = v;
}
int getSuit() {
return this.value;
}
}
public enum Rank {
ACE(1), DEUCE(2), THREE(3), FOUR(4), FIVE(5), SIX(6), SEVEN(7), EIGHT(8), NINE(9), TEN(10), JACK(11), QUEEN(12), KING(13);
int rank;
Rank(int num) {
this.rank = num;
}
int getNumber() {
return this.rank;
}
}
}
Class Deck
package Chapter7;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import Chapter7.Card.Rank;
import Chapter7.Card.Suit;
public class Deck {
List <Card> deck = new ArrayList <Card> ();
Deck() {
for(Suit s : Suit.values()) {
for(Rank r : Rank.values()) {
deck.add(new Card(s, r));
}
}
// System.out.println("A new deck created!!!");
// for(Card c : this.deck) {
// System.out.println(c.toString());
// }
}
public void shuffle(){
this.deck.clear();
Deck ret = new Deck();
for(int i = 0; i < 52; i++) {
int j = (int) (Math.random() * (52-i));
deck.add(ret.deck.remove(j));
}
// System.out.println("After shuffle!!!");
// for(Card c : this.deck) {
// System.out.println(c.toString());
// }
}
}
package Chapter7;
import java.io.IOException;
public class Game {
public static void main(String args[]) throws IOException {
Deck deck = new Deck();
deck.shuffle();
int aGame = 4;
for(int i = 0; i < 52; i++) {
if(aGame == 1) {
System.out.println(deck.deck.get(i).toString());
System.out.println("Start!!!");
while (true) {
char c = (char) System.in.read();
if (c == '\n') {
break;
}
}
aGame = 4;
// if(i == 51) {
// deck.shuffle();
// i = -1;
// }
}
else if(aGame == 4) {
System.out.println("Calculate based on the following four cards!");
System.out.println(deck.deck.get(i).toString());
aGame --;
}
else {
System.out.println(deck.deck.get(i).toString());
aGame --;
}
}
}
}
Class LoadImageApp
Class to load image in 2*2 GridLayout.
package Chapter7;
import java.awt.*;
import java.awt.event.*;
import java.awt.image.*;
import java.io.*;
import javax.imageio.*;
import javax.swing.*;
/**
* This class demonstrates how to load an Image from an external file
*/
public class LoadImageApp extends Component {
BufferedImage img;
public void paint(Graphics g) {
g.drawImage(img, 0, 0, null);
}
public LoadImageApp(String s) {
try {
img = ImageIO.read(new File(s));
} catch (IOException e) {
}
}
public Dimension getPreferredSize() {
if (img == null) {
return new Dimension(100,100);
} else {
return new Dimension(img.getWidth(null), img.getHeight(null));
}
}
public static void main(String[] args) {
JFrame f = new JFrame("Load Image Sample");
GridLayout grid = new GridLayout(2, 2);
f.setLayout(grid);
f.addWindowListener(new WindowAdapter(){
public void windowClosing(WindowEvent e) {
System.exit(0);
}
});
f.add(new LoadImageApp("27.jpg"));
f.add(new LoadImageApp("hw6.jpg"));
f.add(new LoadImageApp("27.jpg"));
f.add(new LoadImageApp("hw6.jpg"));
f.pack();
f.setVisible(true);
}
}
How should I change these two classes to display?
The .png with deck of cards is here.
http://math.hws.edu/javanotes/c13/s1.html
A:
I have a .png for the deck of cards, how can I get individual cards accordingly?
Use the subImage(..) method as detailed in this answer.
That is a single image broken into 9 sub-images. 4 are used for the buttons (with an alternate 'red bordered' icon for the pressed state) and 5 for labels.
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{"url":"https:\/\/zbmath.org\/?q=an:0568.05025","text":"# zbMATH \u2014 the first resource for mathematics\n\nGraph minors - a survey. (English) Zbl\u00a00568.05025\nSurveys in combinatorics 1985, Pap. 10th Br. Combin. Conf., Glasgow\/Scotl. 1985, Lond. Math. Soc. Lect. Note Ser. 103, 153-171 (1985).\n[For the entire collection see Zbl 0561.00003.]\nThis paper is a survey of the results recently obtained by the authors the details of which are to be found in 9 papers, only three of which have yet been published, and apparently more are forthcoming. Most of these results concern the following two problems:\nThe conjecture of Wagner, stating that in any infinite sequence of graphs, at least one is isomorphic to a minor of another. Here a graph H is a minor of a graph G if G topologically contains a copy of H, i.e. H can be obtained from a subgraph of G by contraction of edges.\nThe disjoint connecting paths problem, asking for a polynomial algorithm to decide whether in a graph there exist k vertex-disjoint paths connecting given k origins to given k endpoints. The authors claim to have proven affirmatively both problems, although the details have yet to be checked. This paper gives an outline of the steps the authors went through in the process. The most well-known result concerning minors is the theorem of Kuratowski-Wagner, that there are exactly two minor- minimal nonplanar graphs: the complete graph $$K_ 5$$, and the complete bipartite graph $$K_{3,3}$$. It has now been shown that for any surface the list of minor-minimal not embeddable graphs is finite. Also both problems cited above have been proven right for graphs with given maximum genus. The techniques used are structure theorems, i.e. results stating that graphs without some \u201duseful\u201d minor have a very restrictive nature, which is qualified. Several such structure theorems are cited and it is shown how these have direct consequences on both problems.\nReviewer:\u00a0F.Plastria\n\n##### MSC:\n 05C10 Planar graphs; geometric and topological aspects of graph theory 05C38 Paths and cycles 05-02 Research exposition (monographs, survey articles) pertaining to combinatorics 68R10 Graph theory (including graph drawing) in computer science 68Q25 Analysis of algorithms and problem complexity\n##### Keywords:\ngraph minors; topological graphs; disjoint connecting paths","date":"2021-07-27 14:45:45","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\": 0.637530505657196, \"perplexity\": 835.6455607191324}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046153392.43\/warc\/CC-MAIN-20210727135323-20210727165323-00434.warc.gz\"}"}
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_Life and Ideas: The Anarchist Writings of Errico Malatesta_
Edited and translated by Vernon Richards
ISBN: 978-1-62963-032-8
LCCN: 2014908067
© Vernon Richards
Foreword © Carl Levy
This edition copyright ©2015 PM Press
All Rights Reserved
PM Press
PO Box 23912
Oakland, CA 94623
www.pmpress.org
Originally published by
Freedom Press
Angel Alley
84b Whitechapel High Street
London E1 7QX
www.freedompress.org.uk
Cover by John Yates/stealworks.com
Layout by Jonathan Rowland
10 9 8 7 6 5 4 3 2 1
Printed by the Employee Owners of Thomson-Shore in Dexter, Michigan.
www.thomsonshore.com
# CONTENTS
Foreword by Carl Levy
Editor's Introduction to the First Edition
Editor's Introduction to the Third Edition (1984)
**PART ONE**
Introduction: Anarchy and Anarchism
I
1. Anarchist Schools of Thought
2. Anarchist—Communism
3. Anarchism and Science
4. Anarchism and Freedom
5. Anarchism and Violence
6. Attentats
II
7. Ends and Means
8. Majorities and Minorities
9. Mutual Aid
10. Reformism
11. Organisation
III
12. Production and Distribution
13. The Land
14. Money and Banks
15. Property
16. Crime and Punishment
IV
17. Anarchists and the Working Class Movements
18. The Occupation of the Factories
19. Workers and Intellectuals
20. Anarchism, Socialism, and Communism
21. Anarchists and the Limits of Political Co-Existence
V
22. The Anarchist Revolution
23. The Insurrection
24. Expropriation
25. Defence of the Revolution
VI
26. Anarchist Propaganda
27. An Anarchist Programme
**PART TWO**
Notes for a Biography
Appendix I
Appendix II
Appendix III
Appendix IV
**PART THREE**
Malatesta's Relevance for Anarchists Today
Notes
Index
# **F OREWORD**
# **by C ARL LEVY**
ERRICO MALATESTA (1853–1932) WAS BORN IN SANTA MARIA CAPUA Vetere near to Naples. His family were middle-class tannery owners, and he was not, as the press would have it, a count who conspired with other aristocrats such as Peter Kropotkin and Mikhail Bakunin. Malatesta lived between the era of the Paris Commune and Russian Revolution and the establishment of the Fascist dictatorship of Benito Mussolini. He knew Bakunin and Mussolini and was known and appreciated as a revolutionary (at least initially) by Vladimir Lenin. Although the young Malatesta was a key figure in the First International in Italy and elsewhere, his presence in Italy was mainly between 1885 and 1919, when his reappearances occurred during periods of popular unrest: the 1893–94 _Fasci Siciliani,_ the risings of 1897–98, _La Settimana Rossa_ (The Red Week) of 1914, and finally the _Biennio Rosso_ (Red Biennium) of 1919–20.1
For a large part of his adult life, Malatesta was an exile and spent nearly thirty years in London, then the "capital" of the capitalist world.2 He is an exemplar of the cosmopolitan nomadic radical who circulated through the circuits of world imperialism, transporting an alternative modernity to that of the Gatling gun, the Holy Bible, and the imperialist iron regime of the mine, the plantation and the factory. Malatesta lived, organized, and fought in Egypt, the Levant, the Balkans, Spain, Argentina, the United States, Cuba, Switzerland, and France. The most exciting recent work on anarchism and syndicalism before 1914 is now focused on the dissemination and reception of anarchist and syndicalist repertoires of action, thought, and culture in the Global South as well as the tracing of transnational networks of libertarian diasporas in port cities and elsewhere.3 Malatesta's life is emblematic of this process that allowed anarchists and syndicalist currents to have far greater influence on the global Left than mere numbers would suggest. A sociology of these networks reveals several generations of intellectuals like Carlo Cafiero,4 Francesco Saverio Merlino,5 and Luigi Fabbri,6 who were ideological comrades and sounding boards for his ideas, and several generations of self-taught workers and artisans from the anarchist seedbeds of Liguria, Tuscany, Umbria, the Marches, and Rome who kept his presence alive in Italy even if he rarely set foot in his native land.7 And one of these self-taught anarchists was Emidio Recchioni, the father of Vernon Richards, the author and editor of this very book.8 Malatesta never finished his medical degree at the University of Naples and became an artisan: he trained as a gas-fitter and electrician, and between his stints as an organizer and radical newspaper editor he always returned to his trades, even in old age in Rome during the 1920s. Like the Russian populists he sought to declass himself and go to the people, and he feared and detested the development of a class of left-wing professional journalists, orators, and politicians who fed off the social movements and betrayed their principles.
Malatesta lived in a modern, globalized world of the steamship, the railroad, the telegraph, and dynamite.9 And although he fought a brave battle against the anarchist terrorism and expropriation inspired by Ravachol and Henry in the 1890s or in the new century of Parisian tragic bandits and Latvian revolutionaries turned robbers consumed in the fires of the Siege of Sidney Street, he never endorsed pacifism, wrote long articles against the followers of Tolstoy, and remained a revolutionary inspired by, though critical of, the followers of Mazzini during the Risorgimento. Like many Italian anarchists of his generation, his political apprenticeship was forged in the disappointing aftermath of the Italian struggle for unification and independence.10 Although he renounced Mazzini and the Republicans when the old nationalist revolutionary disavowed the Paris Commune for its atheism and promotion of class war, Malatesta always retained deep ethical and voluntarist strains in his thought and political action, maintained a fruitful dialogue with the Italian Republicans, and indeed formed an alliance through a mutual struggle against the Savoy dynasty. Thus in 1914 this alliance of anarchists, anti-militarists, syndicalists, republicans, and maverick socialists nearly brought the regime to a crisis before the First World War rearranged the political field. But even after the war, during the _Biennio Rosso_ and the years leading to the creation of Mussolini's dictatorship (1922–26), Malatesta sought alliances with the maverick left and the republicans to prevent or overthrow the growing power of the new Fascist movement and its installation in power with the support of the Savoyard king in Rome.11
Malatesta advocated the establishment of a national federation of anarchist groupings—internationalists, anarchist socialists, and then plain anarchists—in Italy from the 1870s to the 1920s, and for this he received strong criticism and indeed abuse from the individualists, Stirnerites, and the affinity group anarcho-communist anarchists associated with his old comrade Luigi Galleani.12 But he was not an advocate of an anarchist revolution as such. The social revolution would be guided by small-'a' anarchist methods but an anarchist party would not be the invisible pilot behind its success. That is why he later looked back on the quarrels between Marxists and Bakuninists in the First International and felt them both to be in the wrong. He argued with Mahkno and the Platformists in the 1920s because they seemed to be advocating an anarchist form of Leninism. The denouement of the Bolshevik Revolution did not surprise him. Like Bakunin, he predicted that a Marxist revolution would result in a dictatorship of a New Class of ex-workers, intellectuals, and politicos. All social organisations might be prey to an "iron law of oligarchy," as German sociologist Robert Michels termed it. Albeit, Malatesta took exception to the concept of "iron laws" in political and social life; thus he objected to his fellow London exile Kropotkin's marriage of biological concepts of mutual aid with the open-ended business of human politics. He fought all determinisms and indeed foreshadowed the critique of many recent post-anarchists who have lambasted "classical anarchism" for its determinism, essentialism, and Whiggish teleology. Nevertheless, Malatesta argued that anarchist or syndicalist trade unions would be prey to the same maladies as the moderate, socialist, or communist ones. The only remedy was for anarchists to work in "ginger groups" in all trade unions and promote libertarian methods: rank and file control, circulation of leadership, and low salaries for these temporary leaders.13
Trade unions were important for Malatesta. Although he never renounced the role of insurrection in making the revolution, by the 1880s and 1890s, with the massive London Dock Strike of 1889 in mind, he advocated a syndicalist strategy to the first generation syndicalist French anarchist exiles in London during the 1890s. When syndicalism grew worldwide in the early twentieth century he pointed out the theoretical and practical weaknesses of its workerism (the revolution was broader than that) and the fact that a peaceful general strike would merely result in the starvation of the urban working classes and the collapse of the strike if it wasn't brought to a quicker termination by the State's armed forces and vigilante groups. When the factories of northern Italy were occupied in September 1920, Malatesta suggested that the workers recommence production and distribution links and not await events or negotiations. The modern city had to be restarted by the revolutionaries on their own initiative if the occupation was not to falter and lead to an inconsequential negotiated settlement.14
But Malatesta did not ignore the countryside and, like Bakunin, saw the tremendous revolutionary potential in the peasantry, and some of his most widely read pamphlets were aimed at landless laborers and smallholders. Unlike the Italian Socialists in 1919–20, he warned against the promotion of the rapid socialisation of the land which drove the smallholders into the hands of the Fascists. A class war between the landless laborers and the smallholders was a war between the poor and the poorest and allowed Fascism to sweep away the Red Zones around Bologna and Ferrara in the spring of 1921; starting a rapid process to allow the former and largely discredited radical socialist Benito Mussolini in 1919, ascend to prime minister by the autumn of 1922.15
Malatesta also argued that small-'a' anarchism was the only method by which the reformists had won their dubious victories: the expansion of the suffrage to the male British working class or the struggle for female suffrage in early twentieth century Britain, which Malatesta witnessed and had known many of the key personalities in the fight, had been won from the ruling classes through direct action not peaceful petition and rallies, he argued, over and over again. But he was not averse on occasion to forming alliances with moderate socialists, anti-clericals, and even liberals if the State threatened the space of civil society in which the anarchists could organize and make their case. Thus he endorsed such broad alliances in Italy when civil liberties were threatened during the 1890s,16 during the road to Fascism in the early 1920s, and under the Fascist regime from his condition of near-house arrest in Rome from 1926 to his death in 1932. But Malatesta would under no conditions stand as a protest electoral candidate as suggested by the former anarchist intellectual and activist Saverio Merlino, who by the turn of the century endorsed a maverick form of libertarian social democracy. Of course Malatesta was not naive: he was no admirer of liberal politicians, such as Lloyd George, whom he termed a hypocrite. He understood the realities of the republican United States in the Gilded Age: industrial welfare, lynch law, nativism, and the unbridled racist jingoism of the Spanish- American war were commented on by Malatesta, who had spent 1900–1901 in the Italian anarchist colony of Paterson, New Jersey, and in U.S. occupied Havana. He knew full well that his near-deportation from London in 1912 was prevented by a united front stretching from MPs such as Ramsay MacDonald and Keir Hardie in the British Labour Party, trade unionists both moderate and syndicalist, Radical Liberals and less radical liberals of the broadsheet press, and even his neighbourhood Islington's "free-born Englishman" (sic) Fair-Trade Unionist (Tory) newspaper. But a united front which involved a careful calibration of direct action when the British government was threatened by industrial unrest, the troubles in Ireland and the suffragettes as well as the pressure of radical and liberal elite networks (indeed one might add "old boy's networks"), which worked to Malatesta's advantage.17
The First World War brought a major split among the most famous personages of international anarchism, especially a fierce debate against Kropotkin, who not only endorsed the Entente and Allies but became a bitter-ender and demanded a continuation of the war in 1916, even when some senior British Tories were demanding a truce and a negotiated settlement. Malatesta remained opposed to the war and witnessed how the war reactivated the industrial radicalism of pre-war syndicalism in the factory council movements and free soviets of Italy and the wider world.18 He felt in 1917 that the expelled anti-parliamentary socialists and anarchists of the London congress of the Second International in 1896,19 in which he fought on the anarchist side, had been vindicated as wartime and (later) post-war socialist and industrial radicalism seemed to be adopting or perhaps adapting pre-war anarchist and syndicalist positions. But by the 1920s and the triumph of Fascism and Bolshevism and the decline of anarchism in many of its former strongholds, Malatesta returned to the basics and engaged in some of his most penetrating journalism on themes of the essence of anarchism, anarchism and violence, and the role of liberalism and spaces for anarchism in civil society. When classical insurrectional anarchism faded after 1945, Malatesta's legacy of an open-ended and non-scientistic anarchism was adapted by "reformist" anarchists such as Colin Ward.20 One of Ward's closest comrades in the post-1945 British anarchist movement was Vernon Richards.
Vero Benevento Constantino Recchioni was born in London in 1915 and later anglicized his name to Vernon Richards.21 As previously mentioned, Emidio Recchioni had been an active anarchist mainly in Ancona before his arrival in London in 1899, which had been preceded by his imprisonment on the penal island of Pantelleria where he made the acquaintance of Luigi Galleani, a fellow prisoner. During the 1890s Emidio had been employed with the Italian railroads, and this facilitated easy access to other comrades throughout the anarchist seedbeds of central Italy. During the 1890s he may have been involved in an attempt on the life of the authoritarian prime minister Francesco Crispi. In London he quickly opened a noted Italian delicatessen, King Bomba, which became a meeting place for two generations of anarchists and radicals, including Malatesta's inner circle when they visited London and the local Malatestan anarchists, and later in the 1920s and 1930s Sylvia Pankhurst, whose partner, Silvio Corio, was another Italian anarchist exile in London, and Emma Goldman and George Orwell. The financial success of the shop allowed Recchioni to help finance Malatesta's major newspapers in Italy in 1913–15 ( _Volontà_ ), 1919–22 ( _Umanità nova_ ), 1924–26 ( _Pensiero e Volontà_ ), and later funded several attempts on Mussolini's life.22 Under the pen-name "Nemo," Recchioni was an avid contributor to the Italian anarchist press and to _Freedom,_ the newspaper founded by Kropotkin in London in 1886. His contributions to the newspaper are still of great interest, especially an article in 1915 in which he predicted a new form of radicalism in a post-war Europe, rather close to the council communism and militant factory shop stewards movements of the period 1917–20 before they were undermined by the rise of Leninist communism and suppressed by the restoration of the bourgeois order.23 He died in 1934, but his son Vero carried on the family politics.
Vernon Richards received his education at Emmanuel school in Wandsworth and then graduated in civil engineering from King's College London in 1939. In his youth he was an accomplished violinist but later let this lapse. In 1934 he became active in the struggle against the Fascist regime of Mussolini and was deported from France where he fell in love with the daughter of the anarchist Camillo Berneri, Marie-Louise. Camillo Berneri was from the next generation of Italian anarchists after Luigi Fabbri and helped modernize its scope with important works on inter-war anti-Semitism, a critique of "worker-worship" and the adaption of the concepts of mass society, psychoanalysis, and totalitarianism for understanding the rise and strength of Fascism and Stalinism in the 1930s. He was murdered in Spain during the May Days of 1937 in Barcelona, most probably by Stalinist agents disguised as Spanish Republican Guards. Berneri had criticised the policies of the CNT-FAI: the joining of the Popular Front government, the lack of a guerrilla war, the sacrifice of the social revolution for a militarised war effort and the lack of a campaign to undermine Morocco, the original base of the Nationalists and the Army of Africa, by engaging in anti-imperialist agitation in the Spanish-controlled portion of that country.24 These critiques would reappear in one of Vernon Richards's most cited works, _The Lessons of the Spanish Revolution,_ first published in 1953.25 Before his death Emidio had helped Berneri's various plots against Fascist and Royal luminaries. Vero/Vernon was deported from France in 1935 but not before a joint collaboration with Camillo Berneri and Marie-Louise Berneri on the anti-Fascist, newspaper, _Free Italy/Italia Libera._ When the Spanish Civil War began in 1936, he collaborated with veterans of _Freedom,_ which had ceased effective publication in 1932, with the new fortnightly, _Spain and the World,_ which then became _Revolt!_ , before becoming the rather popular _War Commentary_ during the Second World War: in 1945 the title reverted to _Freedom._
In 1945 Vernon, Marie-Louise, Philip Sansom, and John Hewetson were charged with trying to disaffect members of the armed forces and were defended by a campaign which included George Orwell, Michael Tippett, T.S. Eliot, and Benjamin Britten. Vernon, Samson, and Hewetson were convicted and served nine months in jail, whereas Marie was acquitted on a technicality. After serving his sentence, instead of pursuing a career as a civil engineer, he ran the family business, which was sold in the 1950s. He then worked as a freelance photographer, which included a series of famous early photographs of Orwell in his Islington flat.26 Later he became an organic gardener and a travel courier. For the last thirty years of his life he lived in a smallholding in Suffolk. In the late 1940s the small but dynamic Freedom group included the likes of Colin Ward, George Woodcock, and Alex Comfort. At the height of his fame, one the founders of the Institute of Contemporary Arts and the guide to the great British and American public on Surrealism, Cubism, and all things modern in art, Herbert Read, was a major contributor to Freedom's publication house, which over the decades published a formidable array of books and pamphlets.27 Marie-Louise died of a viral infection in 1949 shortly after losing a child at birth,28 but she left behind a literary legacy, most notably a fine study of utopias, which is still a wonderful read.29
From 1951 Vernon edited _Freedom_ as a weekly but quit as editor in 1964 only to resume the editorship sporadically for many years to come. He stopped writing for the newspaper in the 1990s. He was a difficult person to work with: most of his closest colleagues such as Sansom, Hewetson, and Woodcock were not on speaking terms at their deaths, and his famous longstanding quarrel with the former contributor to _Freedom,_ Albert Meltzer, was legendary. Although endorsed by _Freedom,_ Colin Ward's 1960s _Anarchy_ tried to make anarchism and its method relevant to the newer generation of the welfare/warfare state, engaging with social scientists, architects, and designers and opening up to university students who would be involved in the social and radical currents of 1968's New Left.30
Although one might assume that Emidio was the key influence in Vero's politics, it was in fact Malatesta who was the central figure in his political life. Vero knew him personally and told me that as a tiny child he sat on Malatesta's shoulders watching the "zepps" (the German zeppelins) bombing London.31 Malatesta never wrote a book or memoir. His written work consisted of journalism and important pamphlets. Richards translated several of the pamphlets and most importantly two collections of his newspaper articles.32 The second collection focussed on his writings from 1924 to 1931.33 The collection here is compiled not in a chronological sense but under twenty-seven topics derived from translated sections of articles taken from throughout his life such as "Anarchism and Anarchy," "Ends and Means," "The Anarchist Revolution," "Anarchists and the Working Class Movements," "Workers and Intellectuals," "Anarchism and Science," etc. This is followed by notes on a biography and Malatesta's relevance for anarchists today. Now surely much of the introductory and concluding material is rather old hat, with an annoying sectarian point-settling air to proceedings, including a rather uncharitable dig at my teacher James Joll,34 and a rather curious, dated museum-piece polemic with George Woodcock over whether or not anarchism was dead as he had announced in the first edition of his history of anarchism of 1962. Woodcock's timing was poor: small-'a' anarchism informed much of the early participatory democratic Anglo-American New Left and Civil Rights movements, and nearly destroyed the Gallic Gaullist State in a few heady weeks in May 1968, something Woodcock admitted in later editions of his popular history.35
The value of this collection is the pithy overview of Malatesta's thought and also the appendices, which reproduce among other things, Malatesta's longish essay of assessment and memories of Kropotkin written a year just before the death of the Italian anarchist. In this collection, one gets an excellent feel for the non-sectarian, open-ended, and thoughtful consistency of Malatesta's anarchism. But this volume can be supplemented with the volume of Malatesta's writing edited by Davide Turcato, _The Method of Freedom_ (2014), which reproduces a selection of articles in a chronological fashion within the various phases of his political militancy. Richards's edition gives the reader a sense of Malatesta's political ideas, whereas Turcato's volume is an English overview of his major project to reproduce all his writing, interviews, and correspondence in ten volumes, of which three have been published in Italian.36 With Richards's pioneering efforts and with Turcato's overview of his ongoing massive, definitive, scholarly, and historically contextual project, the English reader will now appreciate the Malatestan "method of freedom" in all its clarity and good sense.
# **Endnotes**
1. The most extensive biography of Malatesta is in Italian. See Giampietro Berti, _Errico Malatesta e il movimento anarchico italiano e internazionale 1872–1932_ (Milan: FrancoAngeli, 2003). See also Errico Malatesta, _Autobiografia mai scritta. Ricordi (1853–1932),_ Piero Brunello and Pietro Di Paola, eds. (Santa Maria Capua Vetere: Edizioni Spartaco, 2003); and Davide Turcato, _Making Sense of Anarchism: Errico Malatesta's Experiments with Revolution, 1889–1900_ (New York: Palgrave Macmillan, 2012).
2. On Malatesta in London, see Carl Levy, "Malatesta in Exile," _Annali della Fondazione Luigi Einaudi_ 15 (1981): 245–70; Carl Levy, "Malatesta in London: The Era of Dynamite," in _A Century of Italian Emigration to Britain 1880–1980s,_ eds. Lucia Sponza and Arturo Tosi, special supplement of _The Italianist_ 13 (1993), 25–42; Carl Levy, "Da Bresci a Wormwood Scrubs: Il 'Capo' dell'anarchismo mondiale a Londra," in _"Lo sciopero generale armato": Il lungo esilio londinese, 1900–1913_ (vol. 5 of _Errico Malatesta, Opere complete),_ ed. Davide Turcato (Milan: Zero in Condotta, 2014). On Malatesta and the Italian colony of anarchists in London, see Pietro Di Paola, _The Knights Errant of Anarchy: London and the Italian Anarchist Diaspora (1880–1917)_ (Liverpool: Liverpool University Press, 2013).
3. Carl Levy, "Anarchism and Cosmopolitanism," _Journal of Political Ideologies_ 16, no. 3 (2011): 265–78; David Berry and Constance Bantman, _New Perspectives on Anarchism, Labour and Syndicalism: The Individual, the National and the Transnational_ (Newcastle upon Tyne: Cambridge Scholars Publications, 2010); Steven Hirsch and Lucien van der Walt, eds., _Anarchism and Syndicalism in the Colonial and Postcolonial World, 1870–1940: The Praxis of National Liberation, Internationalism, and Social Revolution_ (Leiden: Brill, 2010); Constance Bantman and Bert Altena, eds., _Reassessing the Transnational Turn: Scales of Analysis in Anarchist and Syndicalist Studies_ (London: Routledge, 2015).
4. Pier Carlo Masini, _Cafiero_ (Milan: Rizzoli, 1974).
5. Giampietro Berti, _Francesco Saverio Merlino: dall'anarchismo socialista al socialismo liberale (1856–1930)_ (Milano: FrancoAngeli, 1993).
6. Maurizio Antonioli and Roberto Giulianelli, eds., _Da Fabriano a Montevideo. Luigi Fabbri: vita e idee di un intellettuale anarchico e antifascista_ (Pisa: BFS, 2006).
7. Levy, _Malatesta in Exile,_ 258–59.
8. For accounts of Emidio Recchioni's life, see Pietro Di Paola, "Recchioni, Emidio," in _Dizionario biografico degli anarchici italiani,_ eds. Maurizio Antonioli, Giampietro Berti, Santi Fedele, and Pasquale Iuso (Pisa: BFS, 2004), 418–20; Erika Diemoz, _A morte il tiranno. Anarchia e violenza da Crispi a Mussolini_ (Turin: Giulio Einaudi, 2011).
9. Richard Bach Jensen, _The Battle against Anarchist Terrorism: An International History, 1878–1934_ (Cambridge: Cambridge University Press, 2014).
10. Misato Toda, _Errico Malatesta da Mazzini a Bakunin_ (Naples: Guida, 1988).
11. Carl Levy, "Charisma and Social Movements: Errico Malatesta and Italian Anarchism," _Modern Italian_ 3, no. 2 (1998): 205–17.
12. Ugo Fedeli, _Luigi Galleani: Quarant'anni di lotte rivoluzionarie 1891–1931_ (Cesena: AntiStato, 1956); Paul Avrich, _Sacco and Vanzetti: The Anarchist Background_ (Princeton: Princeton University Press, 1991).
13. Carl Levy, "The Rooted Cosmopolitan: Errico Malatesta, Syndicalism, Transnationalism and the International Labour Movement," in _New Perspectives on Anarchism, Labour and Syndicalism,_ eds. Berry and Bantman, 61–79.
14. Levy, _Charisma and Social Movements,_ 214.
15. Levy, _The Rooted Cosmopolitan,_ 69.
16. Levy, "Malatesta in London," 37–39.
17. Levy, _Da Bresci a Wormwood Scrubs._
18. Carl Levy, "Errico Malatesta and the War Interventionist Debate: 1914–1917," in _Anarchism 1914–1918,_ eds. Matthew Adams and Ruth Kinna (Manchester: Manchester University Press, forthcoming).
19. Carl Levy, _Malatesta in London;_ Davide Turcato, "European Anarchism in the 1890s: Why Labor Matters in Categorizing Anarchism," _Working USA: The Journal of Labor and Society_ 12 (2009): 459–62; and "The 1896 London Congress: Epilogue or Prologue?," in _New Perspectives on Anarchism, Labour and Syndicalism,_ eds. Berry and Bantman, 110–25.
20. Carl Levy, ed., _Colin Ward. Life, Times and Thought_ (London: Lawrence and Wishart, 2013).
21. The details of Vernon Richard's life in the next paragraphs can be found in Colin Ward, "Vernon Richards," _The Guardian,_ 4 February 2002.
22. Di Paola, _Recchioni, Emidio,_ 419; Diemoz, _A morte il tiranno,_ 277–81, 297–332.
23. "Between Ourselves," _Freedom,_ September, 1915.
24. Berneri needs an English language biography, but see: Carlo De Maria, _Camillo Berneri: tra anarchism e liberalism_ (Milan: FrancoAngeli, 2004); Massimo Granchi, _Camillo Berneri e i totalitarismi_ (Reggio Calabria: Cittanova, 2006).
25. _Lessons of the Spanish Revolution_ (London: Freedom Press, 1953).
26. Vernon Richards, _George Orwell at Home (and among the Anarchists): Essays and Photographs_ (London: Freedom Press, 1998).
27. For the trial in 1945 and the Freedom Group in the 1940s see, Pietro Di Paola, "'The man who knows his village': Colin Ward and Freedom Press," in Levy, _Colin Ward,_ 28–52.
28. Pietro Di Paola, "Marie Louise Berneri e il gruppo di Freedom Press,' in Carlo De Maria, _Maria Luisa Berneri e l'anarchismo inglese_ (Reggio Emilia: Biblioteca Panizzi/Archivio famiglia Berneri-Aurelio Chessa, 2013), 133–57.
29. Marie Louise Berneri, _Journey through Utopia_ (London: Freedom Press, 1950).
30. David Goodway, "Colin Ward and the New Left," in Levy, _Colin Ward,_ 53–71.
31. For a recent account of the "zepps" see Jerry White, _Zeppelin Nights: London in the First World War_ (London: The Bodley Head, 2014).
32. For example, _Anarchy_ (London: Freedom Press, 1974).
33. _The Anarchist Revolution: Polemical Articles 1924–1931_ (London: Freedom Press, 1995).
34. James Joll wrote a letter to Margaret Cole, the wife of historian G.D.H. Cole, who had taught at Nuffield College, Oxford, and was a maverick Fabian and former Guild Socialist, and whose immense multi-volume history of socialism was quite sympathetic to the anarchists, indeed concluding with a plea for libertarian socialism in an era of nuclear terror. The letter is dated 5 January 1965 from St Anthony's College Oxford, just after the publication of Joll's book _The Anarchists_ and, as we will see, just after a damning review in Ward's _Anarchy_ by Vernon Richards:
"Your letter came at a most opportune moment, when _Anarchy_ had devoted two long articles to demolishing me and the book, so that it was very encouraging to know that a serious historian of the working-class movement had not thought that that I was unsympathetic to the ideas I was describing!" (Papers of Margaret Cole, Archive collections of Nuffield College, Oxford: MIC/E4/3/1).
On Cole's relationship to anarchism, see Leonie Holthaus, "G.D.H. Cole's International Thought: The Dilemmas of Justifying Socialism in the Twentieth Century," _The International History Review_ 36, no. 5 (2014): 858–75.
35. George Woodcock, _Anarchism: A History of Libertarian Ideas and Movements_ (Harmondsworth: Penguin, 1962).
36. Davide Turcato, ed., _The Method of Freedom: An Errico Malatesta Reader_ (Oakland: AK Press, 2014). Besides the fifth volume of Zero in Condotta's complete works of Malatesta mentioned in endnote 2, two other volumes have been published: Vol. 3, _"Un Lavoro Lungo e Paziente": Il socialism anarchico dell'Agitazione 1897–1898,_ introductory essay by Roberto Giulianelli (2011); and Vol. 4, _"Verso l'Anarchia": Malatesta in America 1899–1900,_ introductory essay by Nunzio Pernicone (2012).
# **E DITOR'S INTRODUCTION TO THE FIRST EDITION**
SINCE THE END OF WORLD WAR II THE NUMBER OF MAJOR WORKS ON anarchism and anarchists published in English is impressive. I will not attempt to list them all, but we have George Woodcock's biographies of Godwin, Proudhon and Kropotkin and Richard Drinnon's biography of Emma Goldman; then there is Maximoff's huge volume of Bakunin's selected writings, Eltzbacher's _Anarchism,_ Stirner's _Ego and His Own_ and Kropotkin's _Memoirs of a Revolutionist_ (edited), and Irving Horowitz's 600-page anthology on and by _The Anarchists;_ and finally there are the histories: G.D.H. Cole's second volume in his "History of Socialist Thought," which deals with _Marxism and Anarchism_ (1850–1890), Woodcock's _Anarchism: A History of Libertarian Ideas and Movements,_ and James Joll's _The Anarchists._ To this list one must add the literature on the Spanish Civil War, at least that part of it which recognises the anarchist contribution to the struggle, and at the top of this list I would put Burnett Bolloten's _Grand Camouflage,_ Orwell's _Homage to Catalonia_ and Brenan's _Spanish Labyrinth_ (the latter two being post-war reprints). One has only to look up at one's bookshelves to realise that I should have mentioned Herbert Read's _Anarchy and Order,_ Marie-Louise Berneri's _Journey through Utopia,_ Rudolf Rocker's _London Years,_ etc., etc.!
And the longer the list becomes the greater is my surprise that no one should have long ago thought that Errico Malatesta deserved a place in that distinguished company, for he is acclaimed by the historians I have mentioned as one of the "giants" in the giant-studded 19th century revolutionary movement. The fact that he is seen by the historians more as a revolutionary agitator than as a thinker, explains in part their superficial treatment of his role in what they call the "historic anarchist movement." Then there is the question of language. It is noteworthy that English social historians are not linguists, and Italian is not an international language (and neither are Italians good linguists) and so, in spite of the fact that the Italian anarchist movement has produced probably more valuable and thought-provoking writers than any other movement, their names, let alone their ideas, are virtually unknown outside their country (the exception being the Spanish speaking movement).
However, the principal disadvantage with which Malatesta has had to "contend" is that he did not conform to the pattern set by 19th century revolutionary thinkers and revolutionary leaders which would have ensured him his place among the historians' "great men." He was, first of all, too good a revolutionary, to even think of keeping a diary; and he was too active to be allowed to live the kind of settled life that would have allowed him carefully to file away his correspondence for posterity and the convenience of historians. Furthermore, though he was in his 79th year when he died he had never found the time (nor, I suspect, felt the inclination) to write his memoirs, which his closest friends, as well as publishers with an eye on a best seller, had, for their different reasons, been urging him to do for many years. And last, but not least, he earned his living as a skilled worker and not as a writer. If it is thought that I exaggerate the disadvantages, I would refer the reader to Cole's valuable History (Vol. II), to the "Principal Characters" a list of more than 60 names with which he prefaced his text, and invite him to apply the various "tests" I have suggested.
Now let me enumerate some of the reasons why I think it high time not only that historians should accord to Malatesta his proper place in the movement (obviously I cannot oblige them to agree with me, but I hope the publication of this volume of his writings will now make it virtually impossible for them to ignore him as a thinker) but more important, that anarchists in the English speaking world should have something more than a pamphlet by which to study his ideas.
For nearly sixty years Malatesta was active in the anarchist movement as an agitator and as a propagandist. He was, as a glance through the files of the anarchist press will show, one of the movement's most respected members as well as remaining to the end one of its most controversial. He was active in many parts of the world, as well as the editor of a number of Italian anarchist journals including the daily _Umanità Nova_ (1920–22). Half his life was spent in exile and the respect he was accorded by governments is surely evidenced by the fact that he spent more than ten years in prison, mainly awaiting trial. Juries, by contrast, showed a different respect, in almost always acquitting him, recognising that the only _galantuomo,_ that the only honest man, was the one facing them in the prisoners' cage!
I have, in this volume, purposely soft-pedalled the man in order to emphasise his ideas, because everybody recognises Malatesta as _the man of action_ but few realise how valuable, and original, and realistic were his _ideas._ Yet if there is merit in his ideas, the principal source is his experience in the day-to-day struggle and his identification with the working people _as one of them._ In my opinion Bakunin and Kropotkin, in spite of their prison experiences, remained aristocrats to the end. What George Woodcock refers to as Kropotkin's "weakness for oversimplification in almost all the issues he discussed" are the attributes not of the saint but of the aristocrat. And indeed even he suggests that one should not "be content with the impression of Kropotkin as a saint. Obstinacy and intolerance had their place in his character...."
Malatesta had no illusions about the "historic role of the masses" because he shared and understood their lives and reactions. But because he also understood how their oppressors "reasoned," and how the "in-betweeners" preached what they were too privileged, socially and materially, to practice, he expected more from the organised workers, but nevertheless he directed his propaganda to _all_ men of good-will.
This volume is divided into three parts. The first consists of selections from his writings, the second, Notes for a Biography of Malatesta, and the third part is an attempt to make an assessment of Malatesta's ideas and tactics in the light of present-day experience.
It is obvious that even the most scrupulous editor cannot avoid reflecting his own preferences in making a selection. But I have done my best to limit this intrusion by attempting to present a "complete" picture of Malatesta's most important ideas and arguments, rather than selecting a limited number of articles from his extensive Writings. And I arrived at the 27 sections in which the ideas have been grouped by the simple process of reading his articles and classifying the subject matter within each article under as many headings as seemed appropriate. The next stage was to condense the material within each classification and then to reduce the number of headings, either by combining some, or by deciding that the material in others was not sufficient or especially interesting to justify inclusion. The picture that emerged was one of Anarchist Ends and Means, and I therefore grouped the sections accordingly, and ending with the complete text of the Anarchist Programme which Malatesta drafted and which was accepted by the Italian anarchist Congress in Bologna in 1920, for it seems to me to synthesise Malatesta's ideas and his commonsense approach to anarchist tactics.
If Malatesta has been badly served by the English speaking movement, quite apart from the historians, the same cannot be said of the Italian movement. After his death all his writings from 1919 to 1932 were collected and published in three volumes (totalling more than 1,000 pages). And after the War two large volumes compiled by the late Cesare Zaccaria and Giovanna Berneri appeared in Naples, containing as well as much of the material that appeared in the first three, many of Malatesta's articles from the _Volontà_ (1913–14) period as well as from _l'Agitazione_ (1897). I have been able to supplement these with a file of _Volontà_ , as well as with odd copies of Bertoni's _Risveglio_ (Geneva) and Fabbri's _Studi Sociali_ (Montevideo) and the magazine _Volontà_ (Naples) in which a number of the earlier articles were reprinted. So though conscious of not having read all Malatesta's writings, I have read enough to feel sure that I have not missed some major aspect of his thought.
Some readers may think that in presenting extracts rather than selections one is presenting Malatesta out of context as well as doing him an injustice as a writer. The latter point seems to me to be a valid one, for in spite of being a reluctant writer, the lucidity of the language and the construction of his articles make them worth reading as literature, and as a propagandist and polemicist he was a master of his craft. Perhaps one of these days it will be possible to make good this "injustice."
As to the extracts being out of their context and needing copious footnotes giving the background in which the articles from which they have been taken, were written, I have resisted doing this partly because this volume would have then appeared to be a work for scholars instead of the undisguised anarchist propaganda it aims at being, but also because it seems to me that the reader himself or herself can easily put these extracts in their context by a quick glance at the foot of the page. For apart from his writings after 1924, one can say that whenever Malatesta took up his pen it was either because the situation was ripe for revolutionary action, or that he saw possibilities, for effective anarchist propaganda. The critics will reply that the fact that Malatesta's writings referred to particular historical situations means the arguments cannot be relevant to, or that they have no bearing on, economic conditions or the political situation today. I take the opposite point of view because I find the ideas of the practical anarchists of the past more stimulating, as well as being able to relate much of what they say to the present, than their starry-eyed contemporaries whose ideal futures had no practical basis even in the present from which they were launched.
Much more than the political background, what should commend Malatesta to our consideration today is his way of thinking. Irving Horowitz in the long Introduction to his above mentioned anthology, seems to have discovered the place Malatesta's ideas should rightly occupy, apparently on the strength of his pamphlet _Anarchy,_ when he describes him as "the great Italian anarchist who bridges 19th- and 20th-century European thought as few of his peers did." To determinism Malatesta opposed free will; to "scientism" he opposed the scientific approach. I feel that Malatesta, who when he was over 70 declared that: "to be told that I have a scientific mind does not displease me at all; I would be glad to deserve the term; for the scientific mind is one which seeks the truth by using positive, rational and experimental methods..." would have been happy to read the remarks with which Dr. Alex Comfort, in 1948, prefaced a long extract from an article he wrote in 1884 on the subject of "Love": "Malatesta, though not a social psychologist, gives a statement of the anarchist case [on marriage] which is possibly more balanced than any since Godwin"; or that a political scientist in an article on "Anarchism and Trade Unionism" written in 1957, considers that not only were Malatesta's writings on the subject "a useful starting point" but that he should also conclude that his "main contentions still hold good."
Malatesta was a propagandist not a professional writer. Enzo Santarelli, the Italian Marxist historian contemptuously refers (1959) to the limitations of Malatesta as a thinker and writes him off as a revolutionary agitator, but in the process Malatesta emerges as the central character and thinker in Santarelli's 300-page volume. What a glorious "failure"!
Part Two of this volume: "Notes for a Biography" is even more modest than its title could imply. It reflects in the main the questions I asked myself about Malatesta's life in the course of reading him and the extravaganzas by the historians. Again most of the answers were to be found in the biographies and the articles published by his friends. Acknowledgement is made in the Source Notes, but I would like to mention specially three invaluable biographers and interpreters, Luigi Fabbri, Max Nettlau, and Armando Borghi (the latter still with us, and the octogenarian editor of the Italian anarchist weekly, _Umanità Nova)_ who have done all the hard work. I have only selected, and if I have not retailed the human anecdotes and have presented Malatesta's Life in some twenty-odd unconnected bits, it is that while I think Malatesta's life illumines his ideas, the neglect he has suffered as a man of ideas in the English speaking world is, in part, due to the emphasis laid on his political notoriety by the historians and some of the anarchists. It seemed to me that what was required was to seek to debunk the popular "image" of the man and his background, as well as to situate him in the political picture of his time.
The Notes are followed by the Appendices. The first two in reply to Kropotkin's first world war attitude (which were written specially for _Freedom_ and are, with the letter to that journal and Malatesta's account of the "Red Week" in Ancona the only texts by Malatesta which have not been translated from the Italian original for this volume) have been included in this part for convenience since they are referred to in the Notes. The article on Kropotkin, as well as being an important document for anarchists also belongs to this part of the book.
Part Three, the last forty pages, is not what I had hoped to write, which was an _Assessment_ of Malatesta's ideas in terms of present-day realities. What I have produced is a rambling piece which ideally I would have wished to hold back to expand and clarify. I have not done so for a number of reasons.
Firstly because it does try to relate Malatesta's ideas to the problems of today; secondly because it deals with his ideas on the General Strike as a revolutionary tactic and in the process gives me, thirdly, the opportunity to question the thoroughness with which we anarchists study the efficacy of the tactical weapons we advocate in our propaganda. And lastly, I have included this piece aware as I am of its structural defects, because if this volume meets with the success I want it to have, it will be reflected in growing activity in the groups, a more efficient use of their energies, more coordination between groups nationally (as distinct from the organisational mania). For, even more than in the 19th century (when the anarchist movement was truly Internationalist) to survive and develop we must explore how to coordinate all our activities internationally, not by the show of internationalism—Congresses and telegrams soon evaporate—but by actions which prove our resolve beyond any shadow of doubt. Part Three, then, is not directed to the "outsiders" who may chance on this volume, but to all revolutionists, and in particular to anarchist comrades and friends wherever they may be.
It is not a criticism of the "Idea," about which the historians write their learned tomes, but an attempt to get those of us who think anarchism a wonderful way of life and also want to do something to try and change things, to take stock and seek to make the best use of our resources. The necessary decisions and action must stem from us. And Malatesta, I am convinced, is the most realistic of guides.
_London, February 1965_
V.R.
Malatesta outside Bow Street Police Court London (1912) where he appeared on a criminal libel charge. He was awarded a three month prison sentence and recommended for deportation. The deportation order was quashed as a result of an energetic campaign in the radical press (notably Lansbury's _Daily Herald_ and the _Manchester Guardian)_ and by the workers' organisations culminating in mass demonstrations in Trafalgar Square.
# **E DITOR'S INTRODUCTION TO THE THIRD EDITION (1984)**
NEARLY TWENTY YEARS HAVE PASSED SINCE I WROTE THE Introduction to the first edition of this book. The May 1968 days have come and gone as have also the Gurus from the other side of the Atlantic such as Reich and Marcuse. Murray Bookchin and Emma Goldman still have their followers while the Germaine Greers are apparently recanting in middle age. Malatesta fortunately has not become a cult figure but his ideas are being slowly recognised by a new generation of anarchists and libertarian socialists in many parts of the world.
This Freedom Press publication has made a modest contribution to a better understanding of Malatesta's ideas in that there have been editions in Italian (Pistoia, 1968 and long out of print), in Dutch (Baarn, 1980—not a success), in Spanish (Barcelona, 1975—more than 6,000 have been sold and it is still in print), in French, as a series of pamphlets (Annecy, 1982).
The most notable effort to make Malatesta's writings available has been made in Italy where the three-volume edition of _Scritti_ (first published in 1934–36) was at last reprinted in 1975 by the Movimento Anarchico Italiano, and is an invaluable source work. The late Gino Cerrito contributed a short introduction to this edition while retaining the important original introductions to each of the volumes written by Malatesta's closest friend and biographer Luigi Fabbri. Two volumes of Selections edited by Cerrito have also been published in Italian: _Scritti Scelti_ (Rome, 1970) and _Rivoluzione e Lotta Quotidiana_ (Revolution and Daily Struggle) (Milan, 1982). And a third volume of anti-militarist writings _Scritti Anti-Militaristi_ (Milan, 1982). The _Selected Writings_ have also appeared in a German edition (Berlin, 1977 and 1980).
The French group published two other volumes of selections: one of 400 pages with the title _Anarchistes, socialistes et communistes_ the other of 128 pages _Pour ou Contre les Elections_ (For or against voting). In all 800 pages of Malatesta's writings in French—an achievement without parallel. In addition the French paperback publishers _10/18_ issued (in 1979) a 400-page volume _Articles Politiques_ selected, translated and introduced by Israel Renof.
In 1982 the fiftieth anniversary of Malatesta's death was commemorated in Italy with special issues of anarchist journals, public meetings in Ancona, and a week-end Seminar organised by the Centro Studi Libertari "G. Pinelli" of Milan.
The growing awareness even among some academics that Malatesta was a considerable exponent of anarchist ideas as well as a man of action can be seen in the inclusion of extracts from his writings in recent anthologies, and such volumes as Professor Woodcock's _Anarchist Reader_ (1977). But more importantly Malatesta's analysis of the political situation in the Western world and his realistic approach to the role that anarchists could play in changing that society are as valid today as ever they were.
_Colchester February 1984_
V.R.
# **PART ONE**
For anarchy to succeed or simply to advance towards its success it must be conceived not only as a lighthouse which illuminates and attracts, but as something possible and attainable, not in centuries to come, but in a relatively short time and without relying on miracles.
Now, we anarchists have much concerned ourselves with the ideal; we have criticised all the moral lies and institutions which corrupt and oppress humanity, and have described, with all the eloquence and poetry each of us possessed, a longed-for harmonious society, based on goodness and on love; but, it must be admitted that we have shown very little concern with the ways and means for the achievement of our ideals.
**( _Pensiero e Volontà,_ 1924)**
# **I NTRODUCTION**
# **A NARCHY AND ANARCHISM**
ANARCHISM IN ITS ORIGINS, ITS ASPIRATIONS, AND ITS METHODS of struggle, is not necessarily linked to any philosophical system. Anarchism was born of a moral revolt against social injustice. When men were to be found who felt as if suffocated by the social climate in which they were obliged to live; who felt the pain of others as if it were their own; who were also convinced that a large part of human suffering is not the inevitable consequence of inexorable natural or supernatural laws, but instead, stems from social realities dependent on human will and can be eliminated through human effort—the way was open that had to lead to anarchism.
The specific causes of social ills and the right means to destroy them had to be found. When some thought that the fundamental cause of the disease was the struggle between men which resulted in domination by the conquerors and the oppression and exploitation of the vanquished, and observed that the domination by the former and this subjection of the latter had given rise to capitalistic property and the State, and when they sought to overthrow both State and property—then it was that anarchism was born.
I prefer to discount uncertain philosophy and stick to the common definitions which tell us that _Anarchy_ is a form of social life in which men live as brothers, where nobody is in a position to oppress or exploit anyone else, and in which all the means to achieve maximum moral and material development are available to everyone; and _Anarchism_ is the method by which to achieve anarchy through freedom and without government, that is without authoritarian organisms which, by using force, even, possibly for good ends, impose their will on others.
Anarchy is _society organised without authority,_ meaning by authority the power to _impose_ one's own will and not the inevitable and beneficial fact that he who has greater understanding of, as well as ability to carry out, a task succeeds more easily in having his opinion accepted, and of acting as a guide on the particular question, for those less able than himself.
In our opinion authority not only is not necessary for social organisation but, far from benefitting it, lives on it parasitically, hampers its development, and uses its advantages for the special benefit of a particular class which exploits and oppresses the others. So long as in a community there is harmony of interests, and no one has either the desire or the means to exploit his fellow beings, there is no trace of authority; when, instead, there are internal struggles and the community is divided into conquerors and conquered, then authority appears and is of course used for the advantage of the strongest and serves to confirm, perpetuate and strengthen their victory.
Because we think in this way, we are anarchists; were we to believe that organisation was not possible without authority we would be authoritarians, because we would still prefer authority, which fetters and impoverishes life, to disorganisation which makes life impossible.
How often must we repeat that we do not wish to impose anything on anybody; that we do not believe it either possible or desirable to do good by the people through force, and that all we want is that no one should impose their will on us, that no one should be in a position to impose on others a form of social life which is not freely accepted.
Socialism (and it is even more true of anarchism) cannot be imposed, both on moral grounds in regard to freedom, as well as because it is impossible to apply "willy-nilly" a regime of justice for all. It cannot be imposed on a minority by a majority. Neither can it be imposed by a majority on one or more minorities.
And it is for this reason that we are anarchists, that is we want everybody to possess the "effective" freedom to live as they wish. This is not possible without expropriating the present holders of social wealth and placing the means of production at the disposal of everybody.
The fundamental basis of the anarchist method is freedom, and we therefore combat, and will go on combating, all that which violates freedom (the equal freedom for all) whatever the dominant regime: monarchist, republican, or any other.
We do not boast that we possess absolute truth; on the contrary, we believe that _social truth_ is not a fixed quantity, good for all times, universally applicable, or determinable in advance, but that instead, once freedom has been secured, mankind will go forward discovering and acting gradually with the least number of upheavals and with a minimum of friction. Thus our solutions always leave the door open to different and, one hopes, better solutions.
The factors of history are too numerous and too complex and human wills are so uncertain and indeterminable, that no one could seriously undertake to prophesy the future. But we do not want to harden our anarchism into dogma, nor impose it by force; it will be what it can be, and will develop, to the extent that men and institutions will become more favourable to integral freedom and justice....
We aim at the good of all, the elimination of all suffering and the extension of all the joys that can depend on human actions; we aim at the attainment of peace and love among all human beings; we aim at a new and better society, at a worthier and happier mankind. But we believe that the good of all cannot be really attained except by the conscious participation of everybody; we believe there are no magic formulae capable of solving the difficulties; that there are no universal and infallible doctrines applicable to all men and to all situations; that there do not exist providential parties and individuals, who can usefully substitute their will for that of the rest of humanity and do good by force; we believe that social life always assumes forms that result from contrasting the ideal and material interests of those who think and who make demands. And therefore we call on everybody to think and to want.
By definition an anarchist is he who does not wish to be oppressed _nor wishes to be himself an oppressor;_ who wants the greatest well-being, freedom and development for _all_ human beings. His ideas, his wishes have their origin in a feeling of sympathy, love and respect for humanity: a feeling which must be sufficiently strong to induce him to want the well-being of others as much as his own, and to renounce those personal advantages, the achievement of which, would involve the sacrifice of others. If it were not so, why would he be the enemy of oppression and not seek to become himself an oppressor?
The anarchist knows that the individual cannot live outside society, indeed he would not exist as a human being but for the fact that he carries within him the sum total of the work of numberless generations, and profits during the whole of his life from the participation of his contemporaries.
He knows that the activity of each individual influences, directly or indirectly, the lives of every other being, and therefore recognizes the great law of solidarity, which predominates in society as in nature. And since he wants freedom for everyone, he must desire that the operation of this essential solidarity instead of being imposed and undergone, unconsciously and involuntarily, instead of being left to chance, and exploited for the advantage of a few to the detriment of the majority, should become conscious, and voluntary, and be applied for the equal benefit of all. The only possible alternative to being either the oppressed or the oppressor is voluntary cooperation for the greatest good of all; and anarchists are, of course, and they cannot but be, for cooperation which is free and desired.
We hope no one will want to "philosophise" and start hair-splitting about egoism and altruism. We agree: we are all egoists, we all seek our own satisfaction. But the anarchist finds his greatest satisfaction in struggling for the good of all, for the achievement of a society in which he can be a brother among brothers, and among healthy, intelligent, educated, happy people. But he who is adaptable, who is satisfied to live among slaves and draw profit from the labour of slaves, is not, and cannot be, an anarchist.
To be an anarchist it is not enough to recognise that anarchism is a beautiful ideal—in theory everyone would agree, including sovereigns, leaders, capitalists, police and, I imagine, even Mussolini himself—but one must want to struggle to achieve anarchism, or at least to approximate to it, by seeking to reduce the power of the State and of privilege, and by demanding always greater freedom, greater justice.
Why are we anarchists?
Apart from our ideas about the political State and government, that is on the coercive organisation of society, which are our specific characteristic, and those on the best way to ensure for everybody free access to the means of production and enjoyment of the good things of life, we are anarchists because of a feeling which is the driving force for all sincere social reformers, and without which our anarchism would be either a lie or just nonsense.
This feeling is the love of mankind, and the fact of sharing the sufferings of others. If I... eat I cannot enjoy what I am eating if I think that there are people dying of hunger; if I buy a toy for my child and am made happy by her pleasure, my happiness is soon embittered at seeing wide-eyed children standing by the shop window who could be made happy with a cheap toy but who cannot have it; if I am enjoying myself, my spirit is saddened as soon as I recall that there are unfortunate fellow beings languishing in jail; if I study, or do a job I enjoy doing, I feel remorse at the thought that there are so many brighter than I who are obliged to waste their lives on exhausting, often useless, or harmful tasks.
Clearly, pure egoism; others call it altruism, call it what you like; but without it, it is not possible to be real anarchists. Intolerance of oppression, the desire to be free and to be able to develop one's personality to its full limits, is not enough to make one an anarchist. That aspiration towards unlimited freedom, if not tempered by a love for mankind and by the desire that all should enjoy equal freedom, may well create rebels who, if they are strong enough, soon become exploiters and tyrants, but never anarchists.
There are strong, intelligent, passionate individuals, with strong material or intellectual needs, who finding themselves, by chance, among the oppressed, seek, at all costs to emancipate themselves and do not resent becoming oppressors: individuals who, feeling imprisoned in existing society, come to despise and hate every society, and realising that it would be absurd to want to live isolated from the human community, seek to subject society and all men to their will and to the satisfaction of their desires. Sometimes, when they are well read, they think of themselves as _supermen._ They are unhampered by scruples; they want "to live their lives"; they poke fun at the revolution and at every forward-looking aspiration, they want to enjoy life in the present at any cost and at everybody's expense; they would sacrifice the whole of mankind for one hour's "intensive living" (there are those who have used these very words).
They are rebels, but not anarchists. They have the mentality and the feelings of unsuccessful bourgeois, and when they do succeed they not only become bourgeois in fact, but are not the least unpleasant among them.
We can sometimes, in the ever-changing circumstances of the struggle, find them alongside us; but we cannot, we must not, and we do not wish to be confused with them. And they know it only too well. But many of them like to call themselves anarchists. It is true—as well as deplorable.
We cannot prevent anyone from calling himself by whatever name he likes, nor can we, on the other hand, abandon the name that succinctly expresses our ideas and which, logically as well as historically, belongs to us. All we can do is to try to prevent any confusion, or at least seek to reduce it to a minimum.
I am an anarchist because it seems to me that anarchy would correspond better than any other way of social life, to my desire for the good of all, to my aspirations towards a society which reconciles the liberty of everyone with cooperation and love among men, and not because anarchism is a scientific truth and a natural law. It is enough for me that it should not contradict any known law of nature to consider it possible and to struggle to win the support needed to achieve it.
I am a communist (libertarian of course); I am for agreement and I believe that through an intelligent decentralisation, and a continuous exchange of ideas, it would be possible to arrive at the organisation of the necessary exchange of goods and satisfy the needs of all without having recourse to the money symbol, which is certainly fraught with problems and dangers. As every good communist does, I aspire to the abolition of money; and, as every good revolutionary, I believe that it will be necessary to strip the bourgeoisie, invalidating all the symbols of wealth which permit people to live without working.
We often find ourselves saying: "anarchism is the abolition of the _gendarme"_ meaning by _gendarme_ any armed force, any material force in the service of a man or of a class, to oblige others to do what they would otherwise not do voluntarily. Of course, that definition does not give even an approximate idea of what is meant by anarchy, which is a society founded on free agreement, in which every individual can achieve the maximum development, material and moral, as well as intellectual; in which he finds in social solidarity the guarantee for his freedom and well-being. The removal of physical constriction is not enough in itself to ensure that he will acquire the dignity of a free man, or learn to love his fellow men and to respect in them those rights which he wants others to respect for him, and to refuse both to command as well as to be commanded. One can be a willing slave for reasons of moral deficiency and a lack of faith in oneself, just as one can be a tyrant through wickedness or a lack of conscience when one does not meet adequate resistance. But this is not to say that "the abolition of the _gendarme_ ," that is the abolition of violence in social relations is not the basis, the indispensable condition without which anarchy could not flourish, and, indeed, could not be conceived.
Since all the present ills of society have their origin in the struggle between men, in the seeking after well-being through one's own efforts and for oneself and against everybody, we want to make amends, replacing hatred by love, competition by solidarity, the individual search for personal well-being by the fraternal cooperation for the well-being of all, oppression and imposition by liberty, the religious and pseudo-scientific lie by truth, therefore:
1. Abolition of private property in land, in raw materials and the instruments of labour, so that no one shall have the means of living by the exploitation of the labour of others, and that everybody, being assured of the means to produce and to live, shall be truly independent and in a position to unite freely among themselves for a common objective and according to their personal sympathies.
2. Abolition of government and of every power which makes the law and imposes it on others: therefore abolition of monarchies, republics, parliaments, armies, police forces, magistratures, and any institution whatsoever endowed with coercive powers.
3. Organisation of social life by means of free association and federations of producers and consumers, created and modified according to the wishes of their members, guided by science and experience, and free from any kind of imposition which does not spring from natural needs, to which everyone, convinced by a feeling of overriding necessity, voluntarily submits.
4. The means of life, for development and well-being, will be guaranteed to children and all who are prevented from providing for themselves.
5. War on religions and all lies, even if they shelter under the cloak of science. Scientific instruction for all to advanced level.
6. War on rivalries and patriotic prejudices. Abolition of frontiers; brotherhood among all peoples.
7. Reconstruction of the family, as will emerge from the practice of love, freed from every legal tie, from every economic and physical oppression, from every religious prejudice.
What we want, therefore, is the complete destruction of the domination and exploitation of man by man; we want men united as brothers by a conscious and desired solidarity, all cooperating voluntarily for the well-being of all; we want society to be constituted for the purpose of supplying everybody with the means for achieving the maximum well-being, the maximum possible moral and spiritual development; we want bread, freedom, love, and science—for everybody.
# I
# **1. A NARCHIST SCHOOLS OF THOUGHT**
ONE CAN BE AN ANARCHIST IRRESPECTIVE OF THE PHILOSOPHIC system one prefers. There are materialist-anarchists as there are others, like myself, who without prejudicing future developments of the human mind, prefer simply to declare their ignorance in these matters.
Certainly it is difficult to understand how certain theories can be reconciled with the practical aspects of life.
The mechanistic theory, no less than the theistic and pantheistic theories, would logically lead to indifference and inaction, to the supine acceptance of all that exists both in the moral and material fields.
Fortunately philosophic concepts have little influence on conduct. And materialists and "mechanicists" in the teeth of logic, often sacrifice themselves for an ideal. Just as, incidentally, do religious people, who believe in the eternal joys of paradise, but take good care to live as well as possible in this world, and when ill are afraid of dying and call in the doctor.
There are those among the anarchists who like to call themselves communists, or collectivists, or individualists or what have you. Often it is a question of different interpretations of words which obscure and hide a fundamental identity of objectives; sometimes it is only a question of theories, hypotheses with which each person explains and justifies in different ways identical practical conclusions.
Among the anarchists there are the revolutionists, who believe that the force which maintains the existing order must be overthrown by force in order to create a political climate in which the free development of individuals and of the community will be possible; and there are the educationists who think that social transformation can be achieved only by first changing people by means of education and propaganda. There are, too, the partisans of non-resistance, or of passive resistance who repudiate violence even when it serves to repel violence; and there are those who recognise the necessity for violence who, in their turn, are divided as to the nature, the extent and the limits of such violence. There are disagreements as to the anarchist attitude to the Trades Unions; disagreements on the need or otherwise of a specific anarchist organisation; permanent or temporary disagreement as to the relationship between anarchists and opposition parties.
And on these and other similar questions one must seek ways of reaching agreement; or if, as seems to be the case, agreement is not possible, we must know how to tolerate each other; by working together when in agreement and, leaving each one to do as he thinks fit without hampering each other when not. For, come to think about it, nobody can be absolutely certain of being in the right, and nobody is always right.
Morally, anarchism is sufficient unto itself; but to be translated into facts it needs concrete forms of material life, and it is the preference for one or other form which differentiates the various anarchist schools of thought.
In the anarchist milieu, communism, individualism, collectivism, mutualism, and all the intermediate and eclectic programmes are simply the ways considered best for achieving freedom and solidarity in economic life; the ways believed to correspond most closely with justice and freedom for the distribution of the means of production and the products of labour among men.
Bakunin was an anarchist, and he was a collectivist, an outspoken enemy of communism because he saw in it the negation of freedom and, therefore, of human dignity. And with Bakunin, and for a long time after him, almost all the Spanish anarchists were collectivists, and yet they were among the most conscious and consistent anarchists.
Others for the same reason of defence and guarantee of liberty declare themselves to be individualists and they want each person to have as individual property the part that is due to him of the means of production and therefore the free disposal of the products of his labour.
Others invent more or less complicated systems of mutuality. But in the long run it is always the searching for a more secure guarantee of freedom which is the common factor among anarchists, and which divides them into different schools.
The individualists assume, or speak as if they assumed, that (anarchist) communists want to impose communism, which of course would put them right outside the ranks of anarchism.
The communists assume, or speak as if they assumed, that the (anarchist) individualists reject every idea of association, want the struggle between men, the domination of the strongest—and this would put them not only outside the anarchist movement but outside humanity.
In reality those who are communists are such because they see in communism freely accepted the realisation of brotherhood, and the best guarantee for individual freedom. And individualists, those that are really anarchists, are anticommunist because they fear that communism would subject individuals nominally to the tyranny of the collectivity and in fact to that of the party or caste, which, with the excuse of administering things, would succeed in taking possession of the power to dispose of material things and thus of the people who need them. Therefore they want each individual, or each group, to be in a position to enjoy freely the product of their labour in conditions of equality with other individuals and groups, with whom they would maintain relations of justice and equity.
In which case it is clear that there is no basic difference between us. But, according to the communists, justice and equity are, under natural conditions, impossible of attainment in an individualistic society, and thus freedom too would not be attained.
If climatic conditions throughout the world were the same, if the land was everywhere equally fertile, if raw materials were evenly distributed and within reach of all who needed them, if social development were the same everywhere in the world, if the work of past generations had benefitted all countries to the same extent, if population were evenly distributed over the whole habitable area of the globe—then one could conceive of everyone (individuals or groups) finding the land, tools and raw materials needed to work and produce independently, without exploiting or being exploited. But natural and historical conditions being what they are, how is it possible to establish equality and justice between he who by chance finds himself with a piece of arid land which demands much labour for small returns with him who has a piece of fertile and well sited land? Or between the inhabitants of a village lost in the mountains or in the middle of a marshy area, with the inhabitant of a city which hundreds of generations of man have enriched with all the skill of human genius and labour?
I warmly recommend Armand's book _l'Iniziazione individualista anarchica_ which is a conscientious piece of work by one of the ablest individualist anarchists and which has received general approval among the individualists. But, in reading this book one asks oneself why on earth Armand continually talks of "anarchist individualism" as a body of doctrine when in general all he does is to expound principles common to anarchists of all tendencies. In fact Armand, who likes to call himself an amoralist, has actually produced a kind of manual or anarchist morality—not "individualist anarchist"—but anarchist in general, indeed more than anarchist, a deeply human morality, because it is based on those human feelings which make anarchy desirable and possible.
Nettlau is mistaken, in my opinion, in believing that the differences between the anarchists who call themselves communists and those who call themselves individualists stem from their respective views on what forms economic life (production and distribution of goods) will take in an anarchist society. These after all are questions which concern the distant future; and if it is true that the ideal, the final aim, is the light that guides or should guide, man's behaviour, it is also even more true that what determines, above all else, agreement or disagreement is not what one aspires to do in the future, but what one does or wants to do in the present. In general, one reaches understanding, and there is a greater incentive to do so with those who are taking the same road as ourselves though they may be going somewhere else, than with those who, though declaring that their destination is the same as ours, take a road which runs in the opposite direction! Thus it has happened for anarchists of the different tendencies, in spite of the fact that fundamentally they wanted the same thing to find themselves, in fierce opposition on the practical questions of life and propaganda.
Admitted the basic principle of anarchism—which is that no-one should wish or have the opportunity to reduce others to a state of subjection and oblige them to work for him—it is clear that all, and only, those ways of life which respect freedom, and recognise that each individual has an equal right to the means of production and to the full enjoyment of the product of his own labour, have anything in common with anarchism.
# **2. A NARCHIST—COMMUNISM**
In 1876 we were, as we are still, anarchist communists; but this does not mean that we use communism as a panacea or dogma, and fail to see that to achieve communism certain moral and material conditions are needed which we must create.
Luigi Galleani's "La Fine dell'Anarchismo"... is in essence a clear, serene, eloquent account of _anarchist communism_ according to the Kropotkinian conception; a conception which I personally find too optimistic, too easy-going, too trusting in _natural harmonies,_ but for all that, his is the most important contribution to anarchist propaganda that has been made so far.
We too aspire to communism as the most perfect achievement of human solidarity, but it must be anarchist communism, that is, freely desired and accepted, and the means by which the freedom of everyone is guaranteed and can expand; for these reasons we maintain that State communism, which is authoritarian and imposed, is the most hateful tyranny that has ever afflicted, tormented and handicapped mankind.
THOSE ANARCHISTS WHO CALL THEMSELVES COMMUNISTS (AND I am one of them) do so not because they wish to impose their particular way of seeing things on others or because they believe that outside communism there can be no salvation, but because they are convinced, until proved wrong, that the more human beings are joined in brotherhood, and the more closely they cooperate in their efforts for the benefit of all concerned, the greater is the well-being and freedom which each can enjoy. They believe that Man, even if freed from oppression by his fellow men, still remains exposed to the hostile forces of Nature, which he cannot overcome alone, but which, in association with others, can be harnessed and transformed into the means for his own well-being. The man who would wish to provide for his material needs by working alone is a slave to his work... as well as not being always sure of producing enough to keep alive. It would be fantastic to think that some anarchists, who call themselves, and indeed are, communists, should desire to live as in a convent, subjected to common rules, uniform meals and clothes, etc.; but it would be equally absurd to think that they should want to do just as they like without taking into account the needs of others or of the right all have to equal freedom. Everybody knows that Kropotkin, for instance, who was one of the most active and eloquent anarchist propagandists of the communist idea was at the same time a staunch defender of the independence of the individual, and passionately desired that everybody should be able to develop and satisfy freely their artistic talents, engage in scientific research, and succeed in establishing a harmonious unity between manual and intellectual activity in order to become human beings in the noblest sense of the word. Furthermore communist-anarchists believe that because of the natural differences in fertility, salubrity, and location of the land masses, it would be impossible to ensure equal working conditions for everyone individually and so achieve, if not solidarity, at least, justice. But at the same time they are aware of the immense difficulties in the way of putting into practice that world wide, free-communism, which they look upon as the ultimate objective of a humanity emancipated and united, without a long period of free development. And for this reason they arrive at conclusions which could be perhaps expressed in the following formula: The achievement of the greatest measures of individualism is in direct ratio to the amount of communism that is possible; that is to say, a maximum of solidarity in order to enjoy a maximum of freedom.
In theory communism is the ideal system which, so far as human relationships are concerned, would replace struggle by solidarity and would utilise natural energies and human labour to the best possible advantage and transform humanity into one big brotherhood intent on mutual aid and love.
But is this practical in the existing spiritual and material state of human affairs? And if so, within what limits?
Worldwide communism, that is a single community among all mankind, is an aspiration, an ideal goal at which one must aim, but which certainly could not be a possible form of economic organisation at present. We are, of course, speaking for our times and probably for some time to come; so far as the distant future is concerned we leave it to future generations to think about that.
For the present one can only think of multiple communities among people who are kindred spirits, and who would, besides, have dealings with each other of various kinds, communistic or commercial; and even within these limits there is always the problem of a possible antagonism between communism and freedom. Assuming the feeling exists that draws men towards brotherhood and a conscious and desired solidarity, and which will encourage us to propagate and put into effect as much communism as possible, I believe that, just as complete individualism would be uneconomic as well as impossible, so would complete communism be impossible as well as anti-libertarian, more so if applied over a large territory.
To organise a communist society on a large scale it would be necessary to transform all economic life radically, such as methods of production, of exchange and consumption; and this could not be achieved other than gradually, as the objective circumstances permitted and to the extent that the masses understood what advantages could be gained and were able to act for themselves. If, on the other hand, one wanted, and could, carry out in one sweep the wishes and the ambitions of a party, the masses, accustomed to obey and serve, would accept the new way of life as a new law imposed on them by a new government, and would wait for a new supreme power to tell them how to produce, and determine for them what they should consume. And the new power, not knowing, and being unable to satisfy a huge variety of often contradictory needs and desires, and not wanting to declare itself useless by leaving to the interested parties the freedom to act as they wish or as best they can, would reconstitute the State, based, as all States are, on military and police forces which, assuming it survived, would simply replace the old set of rules by new, and more fanatical ones. Under the pretext, and even perhaps with the honest and sincere intention of regenerating the world with a new Gospel, a new single rule would be imposed on everybody; all freedom would be suppressed and free initiative made impossible; and as a result there would be disillusionment, a paralyzing of production, black markets, and smuggling, increased power and corruption in the civil service, widespread misery and finally a more or less complete return to those conditions of oppression and exploitation which it was the aim of the revolution to abolish.
The Russian experiment must not have been in vain.
In conclusion, it seems to me, that no system can be vital and really serve to free mankind from the slavery of the remote past, if it is not the result of free development.
Human societies, if they are to be communities of free men working together for the greatest good of all, and no longer convents or despotisms held together by religious superstition or brute force, cannot be the artificial creation of an individual or of a sect. They must be the resultant of the needs and the competitive or divergent wills of all their members who by trial and error find the institutions which at any given time are the best possible, and who develop and change them as circumstances and wills change.
One may, therefore, prefer communism, or individualism or collectivism, or any other system, and work by example and propaganda for the achievement of one's personal preferences; but one must beware, at the risk of certain disaster, of supposing that one's own system is the only, and infallible one, good for all men, everywhere and for all times, and that its success must be ensured at all costs, by means other than those which depend on persuasion, which spring from the evidence of facts.
What is important and indispensable, the point of departure, is to ensure for everybody the means to be free.
# **3. A NARCHISM AND SCIENCE**
Science is a weapon which can be used for good or bad ends; but science ignores completely the idea of good and evil. We are therefore anarchists not because science tells us to be but because, among other reasons, we want everybody to be in a position to enjoy the advantages and pleasures which science procures.
IN SCIENCE, THEORIES ARE ALWAYS HYPOTHETICAL AND PROVISIONAL and are a convenient method for grouping and linking known facts, as well as a useful instrument for research, for the discovery and interpretation of new facts; but they are not the truth. In life—I mean social life—theories are for some people only the scientific guise in which they clothe their desires and their wills. The scientism (I am not saying science) which was prevalent in the second half of the 19th century produced that tendency to consider as scientific truth (namely, natural laws and therefore necessary and predestined) that which was no more than the concept, corresponding to different interests and to the various aspirations that each individual created for himself, of justice, progress, etc. "Scientific socialism," as well as "scientific anarchism," were derived from this concept and, though professed by the most eminent among us, have always seemed to me grotesque concepts, a mixing up of things and concepts which are by their very nature quite distinct.
I may be right or wrong, but in any case I am pleased that I avoided the fashion of the period, and was therefore free of dogmatism and of any pretension of possessing the absolute "social truth."
I do not believe in the infallibility of Science, neither in its ability to explain everything nor in its mission of regulating the conduct of Man, just as I do not believe in the infallibility of the Pope, in revealed Morality and the divine origins of the Holy Scriptures.
I only believe those things which can be proved; but I know full well that _proofs_ are relative and can be, and are in fact, continually superseded and cancelled out by other proved facts; and therefore I believe that doubt should be the mental approach of all who aspire to get ever closer to the truth, or at least to that much of truth that it is possible to establish....
To the _will to believe,_ which cannot be other than the desire to invalidate one's own reason, I oppose the _will to know,_ which leaves the immense field of research and discovery open to us. As I have already stated, I admit only that which can be proved in a way that satisfies my reason—and I admit it only _provisionally, relatively,_ always in the expectation of new truths which are more true than those so far discovered. No _faith_ then, in the religious sense of the word.
I sometimes say that faith is needed, or that in the struggle for the good, men of sure faith are needed. And there is even an anarchist newspaper which, presumably inspired by this need, bears the title _Fede!_ (Faith). But in these cases the word is used in the sense of _determination, great hopes,_ and has nothing in common with the blind belief in things which appear to be either incomprehensible or absurd.
But how, then, do I reconcile this incredulity in religion, and this, what I would call systematic doubt in the definitive results of science, with a moral rule and the determined will and hope of achieving my ideal of freedom, justice and human brotherhood? The fact is that I do not introduce science where science does not belong. The function of science is to discover and to state the fact and the conditions under which fact invariably is produced and is repeated; that is, to state that which is and which inevitably must be, and not that which men desire and want.
Science stops where inevitability ends and freedom begins. It serves man because it prevents him from getting lost in fanciful conceptions, and also supplies him with the means to increase the time available for the exercise of free will: a capacity of willing which distinguishes men, and perhaps to a different degree all animals, from inert matter and unconscious forces.
And it is in this ability to exercise willpower that one must seek for the sources of morality and the rules of behaviour.
I protest against the charge of dogmatism, because, though I am unflinching and definite as to what I _want,_ I am always doubtful about what I know, and I think that, in spite of all the efforts made to understand and explain the Universe, we have so far achieved neither certainty nor even the probability of certainty—and I wonder whether human intelligence will ever get there.
On the other hand to be told that I have a scientific mind does not displease me at all; I would be glad to deserve the term; for the scientific mind is one which seeks the truth by using positive, rational and experimental methods; which never cherishes illusions of having found the absolute Truth and is content with painstakingly approaching it, discovering partial truths, which it considers always as provisional and revisable. In my opinion, the scientist is he who examines facts and draws from them logical conclusions whatever they may be, as opposed to those who form a system for themselves and then seek confirmation in facts, and in so doing unconsciously select the facts which fit into their system and overlook the others; and perhaps even force and distort the facts to squeeze them into the framework of their concepts. The scientist makes use of hypotheses to work on, that is to say he makes certain assumptions which serve him as a guide and as a spur in his research, but he is not the victim of his imagination, nor does he allow familiarity with his assumptions to be hardened into a demonstrated truth, raising to a law, with arbitrary induction, every individual fact which serves his thesis.
The _scientism_ which I reject and which, provoked and encouraged by the enthusiasm which followed the really marvellous discoveries made at that time in the fields of physical-chemistry and of natural history, dominated minds in the second half of the last century, is the belief that science is everything and is capable of everything; it is the acceptance as definitive truths, as dogmas, every partial discovery; it is the confusion of Science with Morals; of Force, in the mechanical sense of the word, with Thought; of natural Law with Will. Scientism logically leads to fatalism, that is, to the denial of free will and of freedom.
In his attempt to fix the "place of Anarchism in Modern Science" Kropotkin finds that "Anarchism is a concept of the universe based on the mechanical interpretation of the phenomena which embrace all nature, not excluding the life of society."
This is philosophy, more or less acceptable, but it is certainly neither science nor Anarchism.
Science is the collection and systematisation of what we know or believe we know: it states the fact and seeks to discover the law of the fact, that is the conditions in which the fact inevitably occurs and repeats itself. It satisfies certain intellectual needs and is at the same time a most valid instrument of power. While, on the one hand, it indicates the limits of human power over natural laws, on the other it adds to the effective freedom of Man by giving him the means to turn these laws to his advantage. Science does not discriminate between men, and serves for good or evil, to liberate as well as to oppress.
Philosophy can be a hypothetical explanation of what is known, or an attempt to guess what is not known. It poses questions which, so far at least, go beyond the competence of science, and suggests answers which, in the present state of our knowledge, cannot be subjected to proof. Thus different philosophers offer divergent, and contradictory solutions. When philosophy is not simply a play on words and an illusionist's trick, it can be a spur and a guide to science, but it is not science.
Anarchy instead, is a human aspiration, which is not founded on any real or imagined natural necessity, but which can be achieved through the exercise of the human will. It takes advantage of the means that science offers to Man in his struggle against nature and between contrasting wills; it can profit from advances in philosophic thought when they serve to teach men to develop their reasoning powers and distinguish more clearly between reality and fantasy; but one leaves oneself open to ridicule by trying to confuse Anarchy with science or any given philosophical system. But let us see if "the mechanical conception of the universe" really explains known facts.
We will then see if it can at least be reconciled, and logically co-exist with anarchism or with any aspiration towards a state of things different from that which exists today.
The fundamental principle of mechanics is the conservation of energy: nothing is created and nothing can be destroyed.
A body cannot give up heat to another without cooling by a similar amount; one form of energy cannot be transformed into another (transference of heat, heat into electric current or vice versa, etc.) without that which is acquired in one way being lost by the other. Indeed, in all physical nature, the very common fact is verified that if someone has ten coppers and spends five, he is left with exactly five, neither more nor less.
Instead, if one has an idea it can be communicated to a million people without losing anything, and the more the idea is propagated the more it gains in strength and effectiveness. A teacher transmits to others what he knows, and does not, as a result become less knowledgeable; on the contrary in teaching others he learns new things and enriches his own mind. If a lead pellet released by a murderous hand cuts short the life of a man of genius, science may be able to explain what happens to all the material elements, (the physical energy of the man of genius when he was killed) and demonstrate that nothing remains of his physical characteristics once his corpse has decomposed, but that at the same time nothing has been lost materially because every atom of that corpse can be traced with all its energy in other combinations. But the ideas which that genius gave to the world, his inventions, remain and grow and can become a potent force; whereas, on the other hand, those ideas which were still developing in him and could have come to fruition, had he not been killed, are lost and cannot ever be found again.
Can mechanics explain this power, this specific quality of the products of the mind?
Please, do not ask me to explain in another way the fact which mechanics does not manage to explain.
I am not a philosopher; but one does not need to be a philosopher in order to see certain problems which more or less torment all thinking minds. And the fact of not knowing how to solve a problem does not oblige one to accept unconvincing solutions... the more so since the solutions the philosophers offer are so numerous as well as mutually contradictory.
And now let us see if "mechanicism" can be reconciled with anarchism.
In the mechanical concept (as, after all, in the theistic concept) everything is determined, inevitable, nothing can be other than what it is. Indeed if nothing is created and nothing is destroyed, if matter and energy (whatever they may be) are fixed quantities, subjected to mechanical laws, all phenomena are inalterably related.
Kropotkin says: Since man is a part of nature, since his personal and social life is also a phenomenon of nature—in the same way as in the growth of a flower, or in the evolution of life in the community of ants and bees—there is no reason why in passing from the flower to Man and from a colony of beavers to a human city, we should abandon the system which had hitherto served us so well, to seek another in the arsenal of metaphysics. And already at the end of the 18th century the great mathematician Laplace had said, "Given the forces animating nature and the respective situations of the beings that compose it, a sufficiently broad human intelligence would be able to know the past and the future as well as the present."
This is the purely mechanical concept; all that has been had to be, all that will be, must be _perforce,_ inevitably, in every minute detail of time, place, and degree.
In such a concept, what meaning can the words "will, freedom, responsibility" have? And of what use would education, propaganda, revolt be? One can no more transform the predestined course of human affairs than one can change the course of the stars. What then?
What has Anarchy to do with this?
Our desk is cluttered with manuscripts from good comrades who want to give "a scientific basis" to anarchism... and whose confused writings are accompanied by notes apologising for not being able to do better because... they have not had the opportunity to study.
But why then bother with the things one doesn't know about instead of doing good propaganda, based on needs and on human aspirations?
It is certainly not necessary to be a doctor to be a good and effective anarchist—indeed sometimes it is a disadvantage. But when it comes to talking about science perhaps it would not be a bad idea to know something about the subject!
And let no one accuse us, as one comrade did recently, of holding science in scant regard. On the contrary, we know what a beautiful, great, powerful and useful thing is science; we know how much it serves the emancipation of thought and the triumph of man in the struggle against adverse forces of nature, and for these reasons wish we all had the possibility of obtaining a general idea of _Science_ as well as probing more deeply at least one of its innumerable branches.
In our programme it says not only "bread for all" but also "science for all." But it seems to us that to discuss science usefully it is first necessary to have clear ideas as to its scope and function. Science, like bread is not a free gift of Nature. It must be won by effort, and we struggle to create the conditions whereby all are in a position to make that effort.
The aim of scientific research is to study nature, to discover the facts and the "laws" that govern it, that is the conditions in which the fact _invariably_ occurs and _invariably_ recurs. A science is established when it can foretell what will happen, whether it can or not explain why; if the prediction does not materialise, it means that there was error and it is needful to proceed further and do more thorough research. Chance, free-will, the exception, are concepts alien to science, which seeks that which is predestined, that which cannot be otherwise, that which is determined. That determination which interlinks in time and space all natural phenomena, and which it is the task of science to investigate and discover, does it embrace all that happens in the Universe, including psychic and social phenomena? The mechanists say it does, and think that everything is subjected to the same mechanical laws, everything is predetermined by physico-chemical antecedents: from the course of the stars, and the opening of a flower, to the heart throb of a lover and the unfolding of human history. And I concur willingly that the system appears grandiose and beautiful, and if it could be demonstrated to be true, would completely satisfy the spirit. But then, in spite of all the pseudo-logical efforts of the determinists to reconcile the System with life and moral sentiment, there just is no room, either conditioned or unconditioned, for will and for freedom. Our lives and the life of human society would all be predestined and foreseeable, _ab eterno_ and for eternity, in each and every minute detail just as is every mechanical fact, and our will would be simply an illusion as in the case of the stone Spinoza talks about which when it falls is conscious of descent and believes that it falls because it wants to.
If this is admitted, which mechanists, cannot but admit without contradicting themselves, it becomes an absurdity to want to regulate one's own life, to want to educate oneself and others, to want to change, in one way or another, social organisation. All this bustle and activity to secure a better future, then, becomes the sterile fruit of an illusion, and could not last once one had discovered that it was an illusion. It is true that illusion and absurdity would be determined products of the mechanical functioning of the brain, and as such would be part of the system. But, once again, we ask what place is left for will and for freedom, for the effectiveness of human action on life and on the future of mankind? If Man is to have confidence, or at least the possibility of useful action, one must admit a creative force, a first cause, or first causes, independent of the physical world and the mechanical laws, and this force is what is called will.
To admit the existence of such a force, means of course, denying the general application of the principle of causality, and our logic is in difficulty. But is this not always the case when we try to seek the origins of things? We do not know what will is; but do we perhaps know what matter, or energy are? We know the facts, but not the reason for them, and however much we try we always arrive at an effect without a cause, to a first cause—and if to explain facts we need first causes to be ever present and ever active, we will accept their existence as a necessary, or at least convenient, hypothesis.
Viewed in this light, the function of science is to discover that which is determined (natural laws) and establish the limits where inevitability ends and freedom begins; and its great usefulness consists in freeing Man from the illusion of believing that he can do anything he likes and can always extend the radius of his effective freedom. So long as the forces which subject all bodies to the laws of gravitation were not known, Man might have thought it possible to fly at will, but remained on the ground; when science discovered the conditions required to float and to move in the atmosphere Man really acquired the freedom to fly.
In conclusion, all I am maintaining is that the existence of wills capable of producing new effects, independent of mechanical laws of nature, is _a necessary presupposition_ for those who believe in the possibility of changing society.
# **4. A NARCHISM AND FREEDOM**
IN NATURE, OUTSIDE HUMAN NATURE, FORCE ONLY RULES, THAT IS, brute force, ruthless, and limitless, because there does not yet exist that new force to which mankind owes its differentiation, and its superiority: the force of conscious will.
All specifically human life is a struggle against outside nature, and every forward step is adaptation, is the overcoming of a natural law.
Natural law is struggle, general slaughter, destruction, or oppression of the vanquished; and on the social plane the greater the tyranny the closer is one to the state of nature.
The concept of freedom for all, which inevitably involves the precept that one's freedom is limited by the equal freedom of others, is a human concept; it is probably mankind's greatest achievement and victory over nature.
It is only too true that the interests, the passions and tastes of Man are not naturally harmonious, and that having to live together in society it is necessary that each individual should seek to adapt himself and reconcile his desires with those of others, in order to arrive at a _modus vivendi_ which satisfies him as well as others. This involves a limitation on freedom, and shows that _freedom,_ in its absolute sense, could not solve the question of a happy and voluntary co-existence.
The question can only be resolved by solidarity, brotherhood and love, as a result of which the sacrificing of desires which are irreconcilable with those of others, is voluntarily and willingly made.
But when one talks of freedom politically, and not philosophically, nobody thinks of the metaphysical bogy of abstract man who exists outside the cosmic and social environment and who, like some god, _could do what he wishes_ in the absolute sense of the word.
When one talks of freedom one is speaking of a society in which no one could constrain his fellow beings without meeting with vigorous resistance, in which, above all, nobody could seize and use the collective force to impose his own wishes on others and on the very groups which are the source of power.
Man is not perfect, agreed. But this is one reason more, perhaps the strongest reason, for not giving anyone the means to "put the brakes on individual freedom."
Man is not perfect. But then where will one also find men who are not only good enough to live at peace with others, but also capable of controlling the lives of others in an authoritarian way? And assuming that there were, who would appoint them? Would they impose themselves? But who would protect them from the resistance and the violence of the "criminals"? Or would they be chosen by the "sovereign people," which is considered too ignorant and too wicked to live in peace, but which suddenly acquires all the necessary good qualities when it is a question of asking it to choose its rulers?...
The harmonious society cannot arise other than from free wills cooperating freely under the pressure of the necessities of life and in order to satisfy that need for brotherhood and love, which always flourishes among men once they are freed from the fear of being imposed upon and of lacking the necessities of life for themselves and their dependents.
We pride ourselves with being, first and foremost, advocates of freedom; freedom not for us alone, but for everybody; freedom not only for that which seems to us to be the truth, but also for that which might be or appears to be error....
Our demand is simply for what could be called social freedom, which is equal freedom for all, an equality of conditions such as to allow everybody to do as they wish, with the only limitation, imposed by inevitable natural necessities and the equal freedom of others....
The freedom we want is not the abstract right, but the power, to do as one wishes; it therefore presupposes that everybody has the means to live and to act without being subjected to the wishes of others. And since to maintain life it is essential to produce, the prerequisite of freedom is that all land, raw materials and the means of production should be at the free disposal of all.
Indeed it is not a question of right or wrong; it is a question of freedom for everybody, freedom for each individual so long as he respects the equal freedom of others.
None can judge with certainty who is right and who is wrong, who is nearest to the truth, or which is the best way to achieve the greatest good for each and everyone. Freedom coupled with experience, is the only way of discovering the truth and what is best; and there can be no freedom if there is a denial of the freedom to err.
Who, in any case, is to tell us what is truth and what error? Shall we have to establish a ministry of public education with its qualified teachers, recognised textbooks, school inspectors, etc.? And all this in the name of the "people," just as with the social democrats, who want to get power in the name of the "proletariat"? And the corruption that is exercised by power, that is, the fact of thinking that one has the right, and is in a position, to impose one's own wishes on others?
With good reason we say that when the social democrats go to Parliament they virtually cease to be socialists. But this, surely, does not stem from the material action of taking a seat in an Assembly which is called Parliament; it is the power which goes with the title of member of parliament [which corrupts].
If we, in any way, dominate the lives of others and prevent them from doing what they wish to do, then for all practical purposes we cease to be anarchists.
By all means let them go on calling us pure sentimentalists as long as they like but we cannot do otherwise than protest loudly against the reactionary, authoritarian, destructive theory which states that freedom is a good principle for a future society but not for the present. It is in the name of this theory that existing tyrannies have been established, and will be established, if the people allow themselves to be taken in.
Louis Blanc, the historian of the Great French Revolution, wanting to explain and justify the contradictions between the alleged humanitarian and liberal aspirations of the Jacobins, and the fierce tyranny they imposed once they were in power, in fact drew a distinction between the "republic" which was then an institution still to come, in which principles would be applied in full measure, with the "revolution" which was the present, and served to justify all tyrannies as a means to achieve the triumph of freedom and justice. What followed was the use of the guillotine upon the best revolutionaries as well as upon a vast number of unfortunates, consolidation of the bourgeois power, the Empire and the Restoration....
To fight our enemies effectively, we do not need to deny the principle of freedom, not even for one moment: it is sufficient for us to want real freedom and to want it for all, for ourselves as well as for others.
We want to expropriate the property-owning class, and with violence, since it is with violence that they hold on to social wealth and use it to exploit the working class. Not because freedom is a good thing for the future, but because it is, at all times, a good thing, today as well as tomorrow, and the property owners by denying us the means for exercising our freedom, in effect, take it away from us.
We want to overthrow the government, all governments—and overthrow them with violence since it is by the use of violence that they force us into obeying—and once again, not because we sneer at freedom when it does not serve our interests but because governments are the negation of freedom and it is not possible to be free without being rid of them.
By force we want to deprive the priests of their privileges, because with these privileges, secured by the power of the State, they deny others the right, that is, the means, of equal freedom to propagate their ideas and beliefs.
The freedom to oppress, to exploit, to oblige people to take up arms, to pay taxes, etc., is the denial of freedom; and the fact that our enemies make irrelevant and hypocritical use of the word freedom is not enough to make us deny the principle of freedom which is the outstanding characteristic of our movement and a permanent, constant and necessary factor in the life and progress of humanity.
Equal freedom for all and the right, therefore, to resist every violation of freedom, and resist with brute force when the violation is maintained by brute force and there is no better way to oppose it successfully.
And this principle is true today and remains true at all times, since in any future society if anyone wished to oppress another human being, the latter would have the right to resist and to use force to resist force.
And furthermore, when does the present society cease to exist and the future society begin? When will it be possible to say that the revolution has definitely ended and the unopposed triumph of a free and equalitarian society started? If some people will have assumed the right to violate anybody's freedom on the pretext of preparing the triumph of freedom, they will always find that the people are not yet sufficiently mature, that the dangers of reaction are ever-present, that the education of the people has not yet been completed. And with these excuses they will seek to perpetuate their own power—which could begin as the strength of a people up in arms, but which, if not controlled by a profound feeling for the freedom of all, would soon become a real government, no different from the governments of today.
But, we shall be told, you therefore want the priests to go on brainwashing the young with their lies?
No, we believe it is necessary, and urgent, to destroy the harmful influence of the priest, but we also believe that the only means to achieve success is freedom—freedom for ourselves and for them. By the use of force we want to deprive the priests of all the privileges and advantages which they owe to the protection they receive from the State and to the conditions of poverty and subjection under which the workers live; but once this has been achieved, we rely and can only rely on the power of truth, that is, on argument. We are anarchists because we believe that no good comes from authority, or if some relative good could come from it, the consequent harm done would be a hundred times greater.
Some talk of the right to prevent the dissemination of error. But with which means?
If the strongest current of opinion supports the priests, then it is the priests who will obstruct our propaganda; and if, instead, opinion is on our side, what need is there to deny freedom in order to combat an influence on the wane, and run the risk that people will feel sympathy for it because it is being persecuted? All other considerations apart, it is in our interest always to be on the side of freedom, because, as a minority proclaiming freedom for all, we would be in a stronger position to demand that others should respect our freedom; and if we are a majority we will have no reason, if we really do not aspire to dominate, to violate the freedom of others.... So freedom for everybody and in everything, with the only limit of the equal freedom for others; which does _not_ mean—it is almost ridiculous to have to point this out—that we recognise, and wish to respect, the "freedom" to exploit, to oppress, to command, which is oppression and certainly not freedom.
# **5. A NARCHISM AND VIOLENCE**
ANARCHISTS ARE OPPOSED TO VIOLENCE; EVERYONE KNOWS THAT. The main plank of anarchism is the removal of violence from human relations. It is life based on the freedom of the individual, without the intervention of the _gendarme._ For this reason we are enemies of capitalism which depends on the protection of the _gendarme_ to oblige workers to allow themselves to be exploited—or even to remain idle and go hungry when it is not in the interest of the bosses to exploit them. We are therefore enemies of the State which is the coercive, violent organisation of society.
But if a man of honour declares that he believes it stupid and barbarous to argue with a stick in his hand and that it is unjust and evil to oblige a person to obey the will of another at pistol point, is it, perhaps, reasonable to deduce that that gentleman intends to allow himself to be beaten up and be made to submit to the will of another without having recourse to more extreme means for his defence?
Violence is justifiable only when it is necessary to defend oneself and others from violence. It is where necessity ceases that crime begins....
The slave is always in a state of legitimate defence and consequently, his violence against the boss, against the oppressor, is always morally justifiable, and must be controlled only by such considerations as that the best and most economical use is being made of human effort and human sufferings.
There are certainly other men, other parties and schools of thought which are as sincerely motivated by the general good as are the best among us. But what distinguishes the anarchists from all the others is in fact their horror of violence, their desire and intention to eliminate physical violence from human relations.... But why, then, it may be asked, have anarchists in the present struggle [against Fascism] advocated and used violence when it is in contradiction with their declared ends? So much so that many critics, some in good faith, and all who are in bad faith, have come to believe that the distinguishing characteristic of anarchism is, in fact, violence. The question may seem embarrassing, but it can be answered in a few words. For two people to live in peace they must both want peace; if one of them insists on using force to oblige the other to work for him and serve him, then the other, if he wishes to retain his dignity as a man and not be reduced to abject slavery, will be obliged, in spite of his love of peace, to resist force with adequate means.
The struggle against government is, in the last analysis, physical, material.
Governments make the law. They must therefore dispose of the material forces (police and army) to impose the law, for otherwise only those who wanted to would obey it, and it would no longer be the law, but a simple series of suggestions which all would be free to accept or reject. Governments have this power, however, and use it through the law, to strengthen their power, as well as to serve the interests of the ruling classes, by oppressing and exploiting the workers.
The only limit to the oppression of government is the power with which the people show themselves capable of opposing it.
Conflict may be open or latent; but it always exists since the government does not pay attention to discontent and popular resistance except when it is faced with the danger of insurrection.
When the people meekly submit to the law, or their protests are feeble and confined to words, the government studies its own interests and ignores the needs of the people; when the protests are lively, insistent, threatening, the government, depending on whether it is more or less understanding, gives way or resorts to repression. But one always comes back to insurrection, for if the government does not give way, the people will end by rebelling; and if the government does give way, then the people gain confidence in themselves and make ever increasing demands, until such time as the incompatibility between freedom and authority becomes clear and the violent struggle is engaged.
It is therefore necessary to be prepared, morally and materially, so that when this does happen the people will emerge victorious.
This revolution must of necessity be violent, even though violence is in itself an evil. It must be violent because it would be folly to hope that the privileged classes will recognise the injustice of, and harm caused by, their privileged status, and voluntarily renounce it. It must be violent because a transitional, revolutionary, violence is the only way to put an end to the far greater, and permanent, violence which keeps the majority of mankind in servitude.
The bourgeoisie will not allow itself to be expropriated without a struggle, and one will always have to resort to the _coup de force,_ to the violation of legal order by illegal means.
We too are deeply unhappy at this need for violent struggle. We who preach love, and who struggle to achieve a state of society in which agreement and love are possible among men, suffer more than anybody by the necessity with which we are confronted of having to defend ourselves with violence against the violence of the ruling classes. However, to renounce a liberating violence, when it is the only way to end the daily sufferings and the savage carnage which afflict mankind, would be to connive at the class antagonisms we deplore and at the evils which arise from them.
We neither seek to impose anything by force nor do we wish to submit to a violent imposition.
We intend to use force against government, because it is by force that we are kept in subjection by government.
We intend to expropriate the owners of property because it is by force that they withhold the raw materials and wealth, which is the fruit of human labour, and use it to oblige others to work in their interest.
We shall resist with force whoever would wish by force, to retain or regain the means to impose his will and exploit the labour of others.
We would resist with force any "dictatorship" or "constituent" which attempted to impose itself on the masses in revolt. And we will fight the republic as we fight the monarchy, if by republic is meant a government, however it may have come to power, which makes laws and disposes of military and penal powers to oblige the people to obey.
With the exception of these cases, in which the use of force is justified as a defence against force, we are always against violence, and for self-determination.
I have repeated a thousand times that I believe that not to "actively" resist evil, adequately and by every possible way is, in theory absurd, because it is in contradiction with the aim of avoiding and destroying evil, and in practice immoral because it is a denial of human solidarity and the duty that stems from it to defend the weak and the oppressed I think that a regime which is born of violence and which continues to exist by violence cannot be overthrown except by a corresponding and proportionate violence, and that one is therefore either stupid or deceived in relying on legality where the oppressors can change the law to suit their own ends. But I believe that violence is, for us who aim at peace among men, and justice and freedom for all, an unpleasant necessity, which must cease the moment liberation is achieved—that is, at the point where defence and security are no longer threatened—or become a crime against humanity, and the harbinger of new oppression and injustice
We are on principle opposed to violence and for this reason wish that the social struggle should be conducted as humanely as possible. But this does not mean that we would wish it to be less determined, less thoroughgoing; indeed we are of the opinion that in the long run half measures only indefinitely prolong the struggle, neutralising it as well as encouraging more of the kind of violence which one wishes to avoid. Neither does it mean that we limit the right of self-defence to resistance against actual or imminent attack. For us the oppressed are always in a state of legitimate defence and are fully justified in rising without waiting to be actually fired on; and we are fully aware of the fact that attack is often the best means of defence....
Revenge, persistent hatred, cruelty to the vanquished when they have been overcome, are understandable reactions and can even be forgiven, in the heat of the struggle, in those whose dignity has been cruelly offended, and whose most intimate feelings have been outraged. But to condone ferocious anti-human feelings and raise them to the level of a principle, advocating them as a tactic for a movement, is both evil and counter-revolutionary.
For us revolution must not mean the substitution of one oppressor for another, of our domination for that of others. We want the material and spiritual elevation of man; the disappearance of every distinction between vanquished and conquerors; sincere brotherhood among all mankind—without which history would continue, as in the past, to be an alternation between oppression and rebellion, at the expense of real progress, and in the long term to the disadvantage of everybody, the conquerors no less than the vanquished.
It is abundantly clear that violence is needed to resist the violence of the adversary, and we must advocate and prepare it, if we do not wish the present situation of slavery in disguise, in which most of humanity finds itself, to continue and worsen. But violence contains within itself the danger of transforming the revolution into a brutal struggle without the light of an ideal and without possibilities of a beneficial outcome; and for this reason one must stress the moral aims of the movement, and the need, and the duty, to contain violence within the limits of strict necessity.
We do not say that violence is good when we use it and harmful when others use it against us. We say that violence is justifiable, good and "moral," as well as a duty when it is used in one's own defence and that of others, against the demands of those who believe in violence; it is evil and "immoral" if it serves to violate the freedom of others....
We are not "pacifists" because peace is not possible unless it is desired by both sides.
We consider violence a necessity and a duty for defence, but only for defence. And we mean not only for defence against direct, sudden, physical attack, but against all those institutions which use force to keep the people in a state of servitude.
We are against fascism and we would wish that it were weakened by opposing to its violence a greater violence. And we are, above all, against government, which is permanent violence.
To my mind if violence is justifiable even beyond the needs of self-defence, then it is justified when it is used against us, and we would have no grounds for protest.
To the alleged incapacity of the people we do not offer a solution by putting ourselves in the place of the former oppressors. Only freedom or the struggle for freedom can be the school for freedom.
But, you will say, to start a revolution and bring it to its conclusion one needs a force which is also armed. And who denies this? But this armed force, or rather the numerous armed revolutionary groups, will be performing a revolutionary task if they serve to free the people and prevent the reemergence of an authoritarian government. But they will be tools of reaction and destroy their own achievements if they are prepared to be used to impose a particular kind of social organisation or the programme of a particular party....
Revolution being, by the necessity of things, violent action, tends to develop, rather than remove, the spirit of violence. But the revolution as conceived by anarchists is the least violent of all and seeks to halt all violence as soon as the need to use force to oppose that of the government and the bourgeoisie, ceases.
Anarchists recognise violence only as a means of legitimate defence; and if today they are in favour of violence it is because they maintain that slaves are always in a state of legitimate defence. But the anarchist ideal is for a society in which the factor of violence has been eliminated, and their ideal serves to restrain, correct and destroy the spirit of revenge which revolution, as a physical act, would tend to develop.
In any case, the remedy would never be the organisation and consolidation of violence in the hands of a government or dictatorship, which cannot be founded on anything but brute force and recognition of the authority of police—and military—forces.
... An error, the opposite of the one which the terrorists make, threatens the anarchist movement. Partly as a reaction to the abuse of violence during recent years, partly as a result of the survival of Christian ideas, and above all, as a result of the mystical preaching of Tolstoy, which owe their popularity and prestige to the genius and high moral qualities of their author, anarchists are beginning to pay serious attention to the party of passive resistance, whose basic principle is that the individual must allow himself and others to be persecuted and despised rather than harm the aggressor. It is what has been called _passive anarchy._
Since there are some, upset by my aversion to useless and harmful violence, who have been suggesting that I displayed tolstoyanist tendencies, I take the opportunity to declare that, in my opinion, this doctrine however sublimely altruistic it may appear to be, is, in fact the negation of instinct and social duties. A man may, if he is a very good... Christian, suffer every kind of provocation without defending himself with every weapon at his disposal, and still remain a moral man. But would he not, in practice, even unconsciously, be a supreme egoist were he to allow others to be persecuted without making any effort to defend them? If, for instance, he were to prefer that a class should be reduced to abject misery, that a people should be downtrodden by an invader, that a man's life or liberty should be abused, rather than bruise the flesh of the oppressor?
There can be cases where passive resistance is an effective weapon, and it would then obviously be the best of weapons, since it would be the most economic in human suffering. But more often than not, to profess passive resistance only serves to reassure the oppressors against their fear of rebellion, and thus it betrays the cause of the oppressed.
It is interesting to observe how both the _terrorists_ and the _tolstoyans,_ just because both are mystics, arrive at practical results which are more or less similar. The former would not hesitate to destroy half mankind so long as the idea triumphed; the latter would be prepared to let all mankind remain under the yoke of great suffering rather than violate a principle.
For myself, I would violate every principle in the world in order to save a man: which would in fact be a question of respecting principle, since, in my opinion, all moral and sociological principles are reduced to this one principle: the good of mankind, the good of all mankind.
# **6. A TTENTATS**
I remember that on the occasion of a much publicised anarchist _attentat_ a socialist of the first rank just back from fighting in the Greco-Turkish war, shouted from the housetops with the approval of his comrades, that human life is always sacred and must not be threatened, not even in the cause of freedom. It appeared that he accepted the lives of Turks and the cause of Greek independence. Illogicality, or hypocrisy?
ANARCHIST VIOLENCE IS THE ONLY VIOLENCE THAT IS JUSTIFIABLE, which is not criminal. I am of course speaking of violence which has truly anarchist characteristics, and not of this or that case of blind and unreasoning violence which has been attributed to anarchists, or which perhaps has been committed by real anarchists driven to fury by abominable persecutions, or blinded by oversensitiveness, uncontrolled by reason, at the sight of social injustices, of suffering for the sufferings of others.
Real anarchist violence is that which ceases when the necessity of defence and liberation ends. It is tempered by the awareness that individuals in isolation are hardly, if at all, responsible for the position they occupy through heredity and environment; real anarchist violence is not motivated by hatred but by love; and is noble because it aims at the liberation of all and not at the substitution of one's own domination for that of others.
There is a political party in Italy which, aiming at highly civilised ends, set itself the task of extinguishing all confidence in violence among the masses... and has succeeded in rendering them incapable of any resistance against the rise of fascism. It seemed to me that Turati himself more or less clearly recognised and lamented the fact in his speech in Paris commemorating Jaurès.
The anarchists are without hypocrisy. Force must be resisted by force: today against the oppression of today; tomorrow against those who might replace that of today.
McKinley, head of North American oligarchy, the instrument and defender of the capitalist giants, the betrayer of the Cubans and the Filipinos, the man who authorised the massacre of the strikers of Hazleton, the torturer of the workers in the "model republic"; McKinley who incarnated the militaristic, expansionist and imperialist policies on which the fat American bourgeoisie have embarked, has fallen foul of an anarchist's revolver.
If we feel at all distressed it is for the fate in store for the generous-hearted man, who opportunely or inopportunely, for good or tactically bad reasons, gave himself in wholesale sacrifice to the cause of equality and liberty....
[It might be argued by those who have condemned Czolgosz's act] that the workers' cause and that of the revolution have not been advanced; that McKinley is succeeded by his equal, Roosevelt, and everything remains unchanged except that the situation for anarchists has become a little more difficult than before. And they may be right; indeed, from what I know of the American scene, this will most likely be the case.
What it means is that [as] in war there are brilliant as well as false moves, there are cautious combatants as well as others who are easily carried away by enthusiasm and allow themselves to be an easy target for the enemy, and may even compromise the position of their comrades. This means that each one must advise, defend and practice the methods which he thinks most suitable to achieve victory in the shortest time and with the least sacrifice possible; but it does not alter the fundamental and obvious fact that he who struggles, well or badly, against the common enemy and towards the same goal as us, is our friend and has a right to expect our warm sympathy even if we cannot accord him our unconditional approval.
Whether the fighting unit is a collectivity or a single individual cannot change the moral aspect of the problem. An armed insurrection carried out inopportunely can produce real or apparent harm to the social war we are fighting, just as an individual attentat which antagonises popular feeling; but if the insurrection was made to conquer freedom, no one will dare deny the socio-political characteristics of the defeated insurrectionists. Why should it be any different when the insurrectionist is a single individual?...
It is not a question of discussing tactics. If it were, I would say that in general I prefer collective action to individual action, also because collective action demands qualities which are fairly common and makes the allocation of tasks more or less possible, whereas one cannot count on heroism, which is exceptional and by its nature sporadic, calling for individual sacrifice. The problem here is of a higher order; it is a question of the revolutionary spirit, of that almost instinctive feeling of hatred of oppression, without which programmes remain dead letters however libertarian are the proposals they embody; it is a question of that combative spirit, without which even anarchists become domesticated and end up, by one road or another, in the slough of legalitarianism....
Gaetano Bresci, worker and anarchist, has killed Humbert, king. Two men: one dead prematurely, the other condemned to a life of torment which is a thousand times worse than death! Two families plunged into sadness!
Whose fault is it?...
It is true that if one takes into consideration such factors as heredity, education and social background, the personal responsibility of those in power is much reduced and perhaps even non-existent. But then if the king is not responsible for his commissions and omissions; if in spite of the oppression, the dispossession, and the massacre of the people carried out in his name, he should have continued to occupy the highest place in the country, why ever then should Bresci have to pay with a life of indescribable suffering, for an act which, however mistaken some may judge it, no one can deny was inspired by altruistic intentions?
But this business of seeking to place the responsibility where it belongs is only of secondary interest to us.
We do not believe in the right to punish; we reject the idea of revenge as a barbarous sentiment. We have no intention of being either executioners or avengers. It seems to us that the role of liberators and peacemakers is more noble and positive. To kings, oppressors and exploiters we would willingly extend our hand, if only they wished to become men among other men, equals among equals. But so long as they insist on profiting from the situation as it exists and to defend it with force, thus causing the martyrdom, the wretchedness and the death through hardships of millions of human beings, we are obliged, we have a duty to oppose force with force....
We know that these attentats, with the people insufficiently prepared for them, are sterile and often, by provoking reactions which one is unable to control, produce much sorrow, and harm the very cause they were intended to serve.
We know that what is essential and undoubtedly useful is not just to kill a king, the man, but to kill all kings—those of the Courts, of parliaments and of the factories—in the hearts and minds of the people; that is, to uproot faith in the principle of authority to which most people owe allegiance.
I do not need to repeat my disapproval and horror for attentats such as that of the Diana, which besides being bad in themselves are also stupid, because they inevitably harm the cause they would wish to serve. And I have never failed to protest strongly, whenever similar acts have taken place and especially when it has turned out that they have been committed by authentic anarchists. I have protested when it would have been better for me to remain silent, because my protest was inspired by superior reasons of principles and tactics, and because I had a duty to do so, since there are people gifted with little personal critical sense, who allow themselves to be guided by what I say. But now it is not a case of judging the fact, and discussing whether it was a good or bad thing to have done, or whether similar actions should or should not be repeated. Now it is a question of judging men threatened with a punishment a thousand times worse than the death penalty; and so one must examine who these men are, what were their intentions and the circumstances in which they acted.
... I said that those assassins are _also_ saints and heroes; and those of my friends who protest against my statement do so in homage to those whom they call the real saints and heroes, who, it would seem, never make mistakes.
I can do no more than confirm what I said. When I think of all that I have learned about Mariani and Aguggini; when I think what good sons and brothers they were, and what affectionate and devoted comrades they were in everyday life, always ready to take risks and to make sacrifices when there was urgent need, I bemoan their fate, I bemoan the destiny that has turned those fine and noble beings into assassins.
I said that one day they will be praised—I did not say that I would praise them; and they will be praised because, as has happened with so many others, the brutal action, the passion that misled them will be forgotten, and only the idea which inspired them and the martyrdom which made them sacrosanct will be remembered.
I don't want to get involved in historical examples; but I could if I wished find in the history of all conspiracies and revolutions, in that of the Italian Risorgimento as well as in our own, a thousand examples of men who have committed actions as bad and as stupid as that of the Diana and yet who are praised by their respective parties, because in fact one forgets the action and remembers the intention, and the individual becomes a symbol and the event is transformed into a legend.
Yes, there are saints and heroes who are assassins; there are assassins who are saints and heroes.
The human mind is really most complicated, and there is a disequilibrium between what one calls heart and what is called brain, between affective qualities and the intellectual faculties, which produces the most unpredictable results and makes possible the most striking contradictions in human behaviour. The war volunteer inebriated by patriotic propaganda, convinced of serving the cause of justice and civilisation, and prepared for the supreme sacrifice, who raged against the "enemy"—Italian against Austrian, or vice versa—and died in the act of killing, was undoubtedly a hero, but a hero who was unconsciously an assassin.
Torquemada who tortured others as well as himself to serve God and to save souls, was both a saint and an assassin....
It could easily be argued that the saint and the hero are almost always unbalanced individuals. But then everything would be reduced to a question of words, to a question of definition. What is a saint? What is a hero?
Enough of hair-splitting.
What is important is to avoid confusing the act with the intentions, and in condemning the bad actions not to overlook doing justice to the good intentions. And not only on the grounds of respect for the truth, or human pity, but also for reasons of propaganda, for the practical repercussions that our judgment may have.
There are, and, so long as present conditions and the environment of violence in which we live last, there will always be generous men, who are rebellious and oversensitive, but who lack sufficient powers of reflection and who in certain situations allow themselves to be carried away by passion and strike out blindly. If we do not openly recognise the goodness of their intentions, if we do not distinguish between error and wickedness, we lose any moral influence over them and abandon them to their blind impulses. If instead, we pay homage to their goodness, their courage and sense of sacrifice, we can reach their minds through their hearts, and ensure that those valuable storehouses of energy shall be used in an intelligent and good, as well as useful, way in the interests of the [common] cause.
# **II**
# **7. E NDS AND MEANS**
THE END JUSTIFIES THE MEANS. THIS SAYING HAS BEEN MUCH abused; yet it is in fact the universal guide to conduct. It would, however, be better to say: every end needs its means. Since morality must be sought in the aims, the means is determined.
Once the goal one is aiming at has been established, consciously or through necessity, the big problem of life is to find the means which, in the circumstances, leads to that end most surely and economically. In the way this problem is solved will depend, so far as it can depend on human will, whether the individual (or party) reaches or fails to achieve his ends, whether he is useful to his cause or unwittingly serves that of the enemy. To have found the right means, herein lies the whole secret of great men and parties that have left their mark on history.
For mystics, the aim of the Jesuits is the glory of God; for others it is the power of the Company of Jesus. They must therefore make every effort to brutalise, terrorise, and subject the masses.
The aim of the Jacobins, and all authoritarian parties who believe themselves to be in possession of absolute truth, is to impose their ideas on the ignorant masses. They must therefore make every effort to seize power, subject the masses, and fit humanity to the Procrustean bed of their concepts.
The problem for us is a different one; because our aims are so different, so also must be our means.
We do not carry on our struggle in order to put ourselves in the place of the exploiters and oppressors of today, nor do we even struggle for the triumph of an empty abstraction. We have nothing in common with that Italian patriot who declared: "What does it matter if all Italians die of hunger so long as Italy is great and glorious!"; nor even with that comrade who confessed to being indifferent to whether three quarters of humanity perished in making the world free and happy....
In our opinion all action which is directed towards the destruction of economic and political oppression; which serves to raise the moral and intellectual level of the people; which gives them an awareness of their individual rights and their power, and persuades them themselves to act on their own behalf; [in a word] all activity that encourages a hatred of oppression and awakens love among Man, brings us closer to our ends and therefore is a good thing (subject only to a quantitative consideration: of obtaining the best results from the available forces at our disposal). On the other hand, all activity that tends to preserve the present state of affairs, that tends to sacrifice man against his will for the triumph of a principle, is bad because it is a denial of our ends. We seek the triumph of freedom and of love.
Should we, for this reason, renounce the use of violent means? Not at all. Our means are those that circumstances allow and impose.
Of course we do not wish to lay a finger on anyone; we would wish to dry all the tears of humanity and not be responsible for more tears. But we must either struggle in the world as it is or remain helpless dreamers. The day will come, we are convinced of this, when it will be possible to serve the cause of Mankind without hurting either oneself or others; but today this is not possible. Even the purest and gentlest of martyrs, those who would allow themselves to be dragged to the gallows for the triumph of good, without resisting, blessing their persecutors, as did the Christ of the legend, would be doing harm. Besides the harm to their own persons, which after all must be reckoned with too, they would cause bitter tears to be shed by all those who loved them. In all actions in life it is, therefore always a question of seeking to cause the least harm to achieve the greatest possible good....
Obviously the revolution will be the cause of many tragedies and much suffering; but even if it produced a hundred times more, it would always be a blessing compared with the sufferings which now exist in the world as a result of the evil organisation of society.
There are, and there always have been in all socio-political struggles, two kinds of hypnotisers.
There are those who consider that we are never mature enough, that we expect too much, that we must wait, and be satisfied to advance a little at a time with the aid of small reforms... which are periodically won and lost without ever solving anything. And there are those who affect contempt for the small things, and advocate all or nothing, and in putting forward schemes, probably excellent ones which cannot however be realised through lack of sufficient support, prevent, or seek to prevent, others from doing the little that can be done.
For us what is most important is not what we achieve... but how we achieve it.
If in order to secure an improvement in the situation one abandons one's basic programme and stops propagating it or struggling to realise it; if one induces the masses to pin their hopes on laws and the good-will of the rulers rather than in their own direct action; if one suffocates the revolutionary spirit, and ceases to foment discontent and resistance—then every advantage will prove illusory and ephemeral, and in all cases will bar the roads to the future society.
But if instead, one does not forget one's final objectives, and encourages the popular forces, as well as inciting to direct action and insurrection, very little may be achieved at the time, but one has made a step forward in the moral preparation of the mass of the people, and in the achievement of a more favourable social climate.
"The optimum is enemy of the good," says the proverb: let us do what we can, assuming we cannot do all we would wish; but do something we must.
Another damaging argument sincerely advanced by many, but which for others is an excuse for doing nothing, is that the present social environment does not make morality possible; and that consequently it is useless to make efforts which cannot succeed, and it is therefore best to get all one can for oneself without bothering about others, except to change one's way of life when the social organisation will be changed. Obviously all anarchists and socialists understand the economic facts of life which today oblige man to struggle against man, and any observer will see the importance of a personal struggle against the overwhelming power of the present social environment. But it is also obvious that without revolt by the individual, who joins with others of like mind to offer resistance to the environment in order to change it, it will never change.
All of us, without exception, are obliged to live, more or less, in contradiction with our ideals; but we are anarchists and socialists because, and in so far as, we suffer by this contradiction, and seek to make it as small as possible. In the event of adapting ourselves to the environment, we would of course also lose the desire to change it, and would become ordinary bourgeois; bourgeois without money perhaps, but for all that bourgeois in our actions and intentions.
# **8. M AJORITIES AND MINORITIES**
WE DO NOT RECOGNISE THE RIGHT OF THE MAJORITY TO IMPOSE the law on the minority, even if the will of the majority in somewhat complicated issues could really be ascertained. The fact of having the majority on one's side does not in any way prove that one must be right. Indeed, humanity has always advanced through the initiative and efforts of individuals and minorities, whereas the majority, by its very nature, is slow, conservative, and submissive to superior force and to established privileges.
But if we do not for one moment recognise the right of majorities to dominate minorities, we are even more opposed to domination of the majority by a minority. It would be absurd to maintain that one is right because one is in a minority. If at all times there have been advanced and enlightened minorities, so too have there been minorities which were backward and reactionary; if there are human beings who are exceptional, and ahead of their times, there are also psychopaths, and especially are there apathetic individuals who allow themselves to be unconsciously carried on the tide of events.
In any case it is not a question of being right or wrong; it is a question of freedom, freedom for all, freedom for each individual so long as he does not violate the equal freedom of others. No one can judge with certainty who is right and who is wrong, who is closer to the truth and which is the best road to the greatest good for each and everyone. Experience through freedom is the only means to arrive at the truth and the best solutions; and there is no freedom if there is not the freedom to be wrong.
In our opinion, therefore, it is necessary that majority and minority should succeed in living together peacefully and profitably by mutual agreement and compromise, by the intelligent recognition of the practical necessities of communal life and of the usefulness of concessions which circumstances make necessary.
As well as their reason and experience telling them that in spite of using all the alchemy of elections and parliament one always ends up by having laws which represent everything but the will of the majority, anarchists do not recognise that the majority as such, even if it were possible to establish beyond all doubt what it wanted, has the right to impose itself on the dissident minorities by the use of force.
Apart from these considerations, there always exists the fact that in a capitalist regime, in which society is divided into rich and poor, into employers and employees whose next meal depends on the absolute power of the boss, there cannot be really free elections.
# **9. M UTUAL AID**
SINCE IT IS A FACT THAT MAN IS A SOCIAL ANIMAL WHOSE EXISTENCE depends on the continued physical and spiritual relations between human beings, these relations must be based either on affinity, solidarity and love, or on hostility and struggle. If each individual thinks only of his well-being, or perhaps that of his small consanguinary or territorial group, he will obviously find himself in conflict with others, and will emerge as victor or vanquished; as the oppressor if he wins, as the oppressed if he loses. Natural harmony, the natural marriage of the good of each with that of all, is the invention of human laziness, which rather than struggle to achieve what it wants assumes that it will be achieved spontaneously, by natural law. In reality, however, natural Man is in a state of continuous conflict with his fellows in his quest for the best, and healthiest site, the most fertile land, and in time, to exploit the many and varied opportunities that social life creates for some or for others. For this reason human history is full of violence, wars, carnage (besides the ruthless exploitation of the labour of others) and innumerable tyrannies and slavery.
If in the human spirit there had only existed this harsh instinct of wanting to predominate and to profit at the expense of others, humanity would have remained in its barbarous state and the development of order as recorded in history, or in our own times, would not have been possible. This order even at its worst, always represents a kind of tempering of the tyrannical spirit with a minimum of social solidarity, indispensable for a more civilised and progressive life.
But fortunately there exists in Man another feeling which draws him closer to his neighbour, the feeling of sympathy, tolerance, of love, and, thanks to it, mankind became more civilised, and from it grew our idea which aims at making society a true gathering of brothers and friends all working for the common good.
How the feeling arose which is expressed by the so-called moral precepts and which, as it develops, denies the existing morality and substitutes a higher morality, is a subject for research which may interest philosophers and sociologists, but it does not detract from the fact that it exists, independently of the explanations which may be advanced. It is of no importance that it may stem from the primitive, physiological fact of the sex act to perpetuate the human species; or the satisfaction to be derived from the company of one's fellow beings; or the advantages to be derived from union in the struggle against the common enemy and in revolt against the common tyrant; or from the desire for leisure, peace and security that even the victors feel a need for; or perhaps for these and a hundred other reasons combined. It _exists_ and it is on its development and growth that we base our hopes for the future of humanity.
"The will of God," "natural laws," "moral laws," the "categorical imperative" of the Kantians, even the "interest clearly understood" of the Utilitarians are all metaphysical fantasies which get one nowhere. They represent the commendable desire of the human mind to want to explain everything, to want to get to the bottom of things, and could be accepted as provisional hypotheses for further research, were they not, in most cases, the human tendency of never wanting to admit ignorance and preferring wordy explanations devoid of factual content to simply saying "I don't know."
Whatever the explanations anyone may or may not choose to give, the problem remains intact: one must choose between love and hate, between brotherly cooperation and fratricidal struggle, between "altruism" and "egoism."
The needs, tastes, aspirations, and interests of mankind are neither similar nor naturally harmonious; often they are diametrically opposed and antagonistic. On the other hand, the life of each individual is so conditioned by the life of others that it would be impossible, even assuming it were convenient to do so, to isolate oneself and live one's own life. Social solidarity is a fact from which no one can escape: it can be freely and consciously accepted and in consequence benefit all concerned, or it can be accepted willy-nilly, consciously or otherwise, in which case it manifests itself by the subjection of one to another, by the exploitation of some by others.
A whole host of practical problems arise in our day-to-day lives which can be solved in different ways, but not by all ways at the same time; yet each individual may prefer one solution to another. If an individual or group have the power to impose their preference on others, they will choose the solution which best suits their interests and tastes; the others will have to submit and sacrifice their wishes. But if no one has the possibility of obliging others to act against their will then, always assuming that it is not possible or considered convenient to adopt more than one solution, one must arrive by mutual concessions at an agreement which best suits everyone and least offends individual interests, tastes and wishes.
History teaches us, daily observation of life around us teaches, that where violence has no place [in human relations] everything is settled in the best possible way, in the best interests of all concerned. But where violence intervenes, injustice, oppression and exploitation invariably triumph.
The fact is that human life is not possible without profiting by the labour of others, and that there are only two ways in which this can be done: either through a fraternal, equalitarian and libertarian association, in which solidarity, consciously and freely expressed unites all mankind; or the struggle of each against the other in which the victors overrule, oppress and exploit the rest....
We want to bring about a society in which men will consider each other as brothers and by mutual support will achieve the greatest well-being and freedom as well as physical and intellectual development for all....
The strongest man is the one who is the least isolated; the most independent is the one who has most contacts and friendships and thereby a wider field for choosing his close collaborators; the most developed man is he who best can, and knows how to, utilise Man's common inheritance as well as the achievements of his contemporaries.
In spite of the rivers of human blood; in spite of the indescribable sufferings and humiliations inflicted; in spite of exploitation and tyranny at the expense of the weakest (by reason of personal, or social, inferiority); in a word, in spite of the struggle and all its consequences, that which in human society represents its vital and progressive characteristics, is the feeling of sympathy, the sense of a common humanity which in normal times, places a limit on the struggle beyond which one cannot venture without rousing deep disgust and widespread disapproval. For what intervenes is morality.
The professional historian of the old school may prefer to present the fruits of his research as sensational events, large-scale conflicts between nations and classes, wars, revolutions, the ins and outs of diplomacy and conspiracies; but what is really much more significant are the innumerable daily contacts between individuals and between groups which are the true substance of social life. And if one closely examines what happens deep down, in the intimate daily lives of the mass of humanity, one finds that as well as the struggle to snatch better working conditions, the thirst for domination, rivalry, envy and all the unhealthy passions which set man against man, is also valuable work, mutual aid, unceasing and voluntary exchange of services, affection, love, friendship and all that which draws people closer together in brotherhood. And human collectivities advance or decay, live or die, depending on whether solidarity and love, or hatred and struggle, predominate in the community's affairs; indeed, the very existence of any community would not be possible if the social feelings, which I would call the _good_ passions, were not stronger than the bad.
The existence of sentiments of affection and sympathy among mankind, and the experience and awareness of the individual and social advantages which stem from the development of these sentiments, have produced and go on producing concepts of "justice" and "right" and "Morality" which, in spite of a thousand contradictions, lies and hypocrisy serving base interests, constitute a goal, an ideal towards which humanity advances.
This "morality" is fickle and relative; it varies with the times, with different peoples, classes and individuals; people use it to serve their own personal interests and that of their families, class or country. But discarding what, in official "morality," serves to defend the privilege and violence of the ruling class, there is always something left which is in the general interest and is the common achievement of all mankind, irrespective of class and race.
The bourgeoisie in its heroic period, when it still felt itself a part of the people and fought for emancipation, had sublime gestures of love and self-abnegation; and the best among its thinkers and martyrs had the almost prophetic vision of that future of peace, brotherhood and well-being which socialists are struggling for today [1909]. But if altruism and solidarity were among the feelings of the best of them, the germ of individualism (in the sense of struggle between individuals), the principle of struggle (as opposed to solidarity) and the exploitation of man by man, were in the programme of the bourgeoisie and could not but give rise to baneful consequences. Individual property and the principle of authority, in the new disguises of capitalism and parliamentarism, were in that programme and had to lead, as has always been the case, to oppression, misery and the dehumanisation of the masses.
And now that the development of capitalism and parliamentarism has borne its fruits, and the bourgeoisie has exhausted every generous sentiment and progressive élan by the practice of political and economic competition, it is reduced to having to defend its privileges with force and deceit, while its philosophers cannot defend it against the socialist attacks except by bringing up, inopportunely, the law of vital competition.
# **10. R EFORMISM**
THE FUNDAMENTAL ERROR OF THE REFORMISTS IS THAT OF dreaming of solidarity, a sincere collaboration, between masters and servants, between proprietors and workers which even if it might have existed here and there in periods of profound unconsciousness of the masses and of ingenuous faith in religion and rewards, is utterly impossible today.
Those who envisage a society of well stuffed pigs which waddle contentedly under the fertile of a small number of swineherd; who do not take into account the need for freedom and the sentiment of human dignity; who really believe in a God that orders, for his abstruse ends, the poor to be submissive and the rich to be good and charitable—can also imagine and aspire to a technical organisation of production which assures abundance to all and is at the same time materially advantageous both to the bosses and to the workers. But in reality "social peace" based on abundance for all will remain a dream, so long as society is divided into antagonistic classes, that is employers and employees. And there will be neither peace nor abundance.
The antagonism is spiritual rather than material. There will never be a sincere understanding between bosses and workers for the better exploitation of the forces of nature in the interests of mankind, because the bosses above all want to remain bosses and secure always more power at the expense of the workers, as well as by competition with other bosses, whereas the workers have had their fill of bosses and don't want more
[Our good friends] are wasting their time when they tell us that a little freedom is better than a brutal and unbridled tyranny; that a reasonable working day, a wage that allows people to live better than animals, and protection of women and children, are preferable to the exploitation of human labour to the point of human exhaustion; or that the State school, bad as it is, is always better, from the point of view of the child's moral development, than schools run by priests and monks... for we are in complete agreement. And we also agree that there may be circumstances in which the Election results, national or local, can have good or bad consequences and that this vote might be determined by the anarchists' votes if the strength of the rival parties were equally balanced.
In most cases it is an illusion; when elections are tolerably free, the only value they have is symbolic: they indicate the state of public opinion, which would have imposed itself by more efficacious means, and with more far reaching results, if it had not been offered the outlet of elections. But no matter; even if some minor advances were the direct result of an electoral victory, anarchists should not flock to the polling booths or cease to preach their methods of struggle.
Since no one can do everything in this world, one must choose one's own line of conduct.
There is always an element of contradiction between minor improvements, the satisfaction of immediate needs and the struggle for a society which is really better than the existing one. Those who want to devote themselves to the erection of public lavatories and drinking fountains where there is a need for them, or who use their energies for the construction of a road, or the establishment of a municipal school, or for the passing of some minor law to protect workers or to get rid of a brutal policeman, do well, perhaps, to use their ballot paper in favour of this or that influential personage. But then—since one wants to be "practical" one must go the whole hog—so, rather than wait for the victory of the opposition party, rather than vote for the more kindred party, it is worth taking a short cut and support the dominant party, and serve the government already in office, and become the agent of the Prefect or the Mayor. And in fact the neo-converts we have in mind did not in fact propose voting for the most "progressive" party, but for the one that had the greater chance of being elected.... But in that case where does it all end?...
In the course of human history it is generally the case that the malcontents, the oppressed, and the rebels, before being able to conceive and desire a radical change in the political and social institutions, restrict their demands to partial changes, to concessions by the rulers, and to improvements. Hopes of obtaining reforms as well as in their efficacy, precede the conviction that in order to destroy the power of a government or of a class, it is necessary to deny the reasons for that power, and therefore to make a revolution.
In the order of things, reforms are then introduced or they are not, and once introduced either consolidate the existing regime or undermine it; assist the advent of revolution or hamper it and benefit or harm progress in general, depending on their specific characteristic, the spirit in which they have been granted, and above all, the spirit in which they are asked for, claimed or seized by the people.
Governments and the privileged classes are naturally always guided by instincts of self-preservation, of consolidation and the development of their powers and privileges; and when they consent to reforms it is either because they consider that they will serve their ends or because they do not feel strong enough to resist, and give in, fearing what might otherwise be a worse alternative.
The oppressed, either ask for and welcome improvements as a benefit graciously conceded, recognise the legitimacy of the power which is over them, and so do more harm than good by helping to slow down, or divert and perhaps even stop the processes of emancipation. Or instead they demand and impose improvements by their action, and welcome them as partial victories over the class enemy, using them as a spur to greater achievements, and thus they are a valid help and a preparation to the total overthrow of privilege, that is, for the revolution. A point is reached when the demands of the dominated class cannot be acceded to by the ruling class without compromising their power. Then the violent conflict inevitably occurs.
It is not true to say therefore, that revolutionaries are systematically opposed to improvements, to reforms. They oppose the reformists on the one hand because their methods are less effective for securing reforms from governments and employers, who only give in through fear, and on the other hand because very often the reforms they prefer are those which not only bring doubtful immediate benefits, but also serve to consolidate the existing regime and to give the workers a vested interest in its continued existence. Thus, for instance, State pensions, insurance schemes, as well as profit sharing schemes in agricultural and industrial enterprises, etc.
Apart from the unpleasantness of the word which has been abused and discredited by politicians, anarchism has always been, and can never be anything but, reformist. We prefer to say _reformative_ in order to avoid any possible confusion with those who are officially classified as "reformists" and seek by means of small and often ephemeral improvements to make the present system more bearable (and as a result help to consolidate it); or who instead believe in good faith that it is possible to eliminate the existing social evils by recognising and respecting, in practice if not in theory, the basic political and economic institutions which are the cause of, as well as the prop that supports these evils. But in any case it is always a question of reforms, and the essential difference lies in the kind of reform one wants and the way one thinks of being able to achieve it. Revolution means, in the historical sense of the word, the radical reform of institutions, achieved rapidly by the violent insurrection of the people against existing power and privileges; and we are revolutionaries and insurrectionists because we do not just want to improve existing institutions but to destroy them completely, abolishing every form of domination by man over man, and every kind of parasitism on human labour; and because we want to achieve this as quickly as possible, and because we believe that institutions born of violence are maintained by violence and will not give way except to an equivalent violence. But the revolution cannot be made just when one likes. Should we remain inactive, waiting for the situation to mature with time?
And even after a successful insurrection, could we overnight realise all our desires and pass from a governmental and capitalist hell to a libertarian-communist heaven which is the complete freedom of man within the wished-for community of interests with all men?
These are illusions which can take root among authoritarians who look upon the masses as the raw material which those who have power can, by decrees, supported by bullets and handcuffs, mould to their will. But these illusions have not taken among anarchists. We need the people's consensus, and therefore we must persuade by means of propaganda and example, we must educate and seek to change the environment in such a way that this education may reach an ever increasing number of people....
We are reformers today in so far as we seek to create the most favourable conditions and as large a body of enlightened militants so that an insurrection by the people would be brought to a satisfactory conclusion. We shall be reformers tomorrow, after a triumphant insurrection, and the achievement of freedom, in that we will seek with all the means that freedom permits, that is by propaganda, example and even violent resistance against anyone who should wish to restrict our freedom in order to win over to our ideas an ever greater number of people.
But we will never recognise the institutions; we will take or win all possible reforms with the same spirit that one tears occupied territory from the enemy's grasp in order to go on advancing, and we will always remain enemies of every government, whether it be that of the monarchy today, or the republican or Bolshevik governments of tomorrow.
# **11. O RGANISATION**
ORGANISATION WHICH IS, AFTER ALL, ONLY THE PRACTICE OF cooperation and solidarity, is a natural and necessary condition of social life; it is an inescapable fact which forces itself on everybody, as much on human society in general as on any group of people who are working towards a common objective. Since man neither wishes to, nor can, live in isolation—indeed being unable to develop his personality, and satisfy his physical and moral needs outside society and without the cooperation of his fellow beings—it is inevitable that those people who have neither the means nor a sufficiently developed social conscience to permit them to associate freely with those of a like mind and with common interests, are subjected to organisation by others, generally constituted in a class or as a ruling group, with the aim of exploiting the labour of others for their personal advantage. And the age-long oppression of the masses by a small privileged group has always been the result of the inability of most workers to agree among themselves to organise with others for production, for enjoyment and for the possible needs of defence against whoever might wish to exploit and oppress them. Anarchism exists to remedy this state of affairs....
There are two factions among those who call themselves anarchists, with or without adjectives: supporters and opponents of organisation. If we cannot succeed in agreeing, let us, at least, try to understand each other.
And first of all let us be clear about the distinctions, since the question is a triple one: organisation in general as a principle and condition of social life today and in a future society; the organisation of the anarchist movement; and the organisation of the popular forces and especially of the working masses for resistance to government and capitalism....
The basic error committed by those opposed to organisation is in believing that organisation is not possible without authority.
Now, it seems to us that organisation, that is to say, association for a specific purpose and with the structure and means required to attain it, is a necessary aspect of social life. A man in isolation cannot even live the life of a beast, for he is unable to obtain nourishment for himself except in tropical regions or when the population is exceptionally sparse; and he is, without exception, unable to rise much above the level of the animals. Having therefore to join with other humans, or more accurately, finding himself united to them as a consequence of the evolutionary antecedents of the species, he must submit to the will of others (be enslaved) or subject others to his will (be in authority) or live with others in fraternal agreement in the interests of the greatest good of all (be an associate). Nobody can escape from this necessity; and the most extreme anti-organisers not only are subject to the general organisation of the society they live in, but also in the voluntary actions in their lives, and in their rebellion against organisation, they unite among themselves, they share out their tasks, they _organise_ with whom they are in agreement, and use the means that society puts at their disposal....
Admitting as a possibility the existence of a community organised without authority, that is without compulsion—and anarchists must admit the possibility, or anarchy would have no meaning—let us pass on to discuss the organisation of the anarchist movement.
In this case too, organisation seems useful and necessary. If movement means the whole—individuals with a common objective which they exert themselves to attain—it is natural that they should agree among themselves, join forces, share out the tasks and take all those steps which they think will lead to the achievement of those objectives. To remain isolated, each individual acting or seeking to act on his own without coordination, without preparation, without joining his modest efforts to a strong group, means condemning oneself to impotence, wasting one's efforts in small ineffectual action, and to lose faith very soon in one's aims and possibly being reduced to complete inactivity....
A mathematician, a chemist, a psychologist or a sociologist may say they have no programme or are concerned only with establishing the truth. They seek knowledge, they are not seeking _to do_ something. But anarchy and socialism are not sciences; they are proposals, projects, that anarchists and socialists seek to realise and which, therefore need to be formulated as definite programmes....
If it is true that [organisation creates leaders]; if it is true that anarchists are unable to come together and arrive at agreement without submitting themselves to an authority, this means that they are not yet very good anarchists, and before thinking of establishing anarchy in the world they must think of making themselves able to live anarchistically. The remedy does not lie in the abolition of organisation but in the growing consciousness of each individual member.... In small as well as large societies, apart from brute force, of which it cannot be a question for us, the origin and justification for authority lies in social disorganisation.
When a community has needs and its members do not know how to organise spontaneously to provide them, someone comes forward, an authority who satisfies those needs by utilising the services of all and directing them to his liking. If the roads are unsafe and the people do not know what measures to take, a police force emerges which in return for whatever services it renders expects to be supported and paid, as well as imposing itself and throwing its weight around; if some article is needed, and the community does not know how to arrange with the distant producers to supply it in exchange for goods produced locally, the merchant will appear who will profit by dealing with the needs of one section to sell and of the other to buy, and impose his own prices both on the producer and the consumer. This is what has happened in our midst; the less organised we have been the more prone are we to be imposed on by a few individuals. And this is understandable....
So much so that organisation, far from creating authority, is the only cure for it and the only means whereby each one of us will get used to taking an active and conscious part in collective work, and cease being passive instruments in the hands of leaders....
But an organisation, it is argued, presupposes an obligation to coordinate one's own activities with those of others; thus it violates liberty and fetters initiative. As we see it, what really takes away liberty and makes initiative impossible is the isolation which renders one powerless. Freedom is not an abstract right but the possibility of acting: this is true among ourselves as well as in society as a whole. And it is by cooperation with his fellows that man finds the means to express his activity and his power of initiative.
An anarchist organisation must, in my opinion [allow for] complete autonomy, and independence, and therefore full responsibility, to individuals and groups; free agreement between those who think it useful to come together for cooperative action, for common aims; a moral duty to fulfil one's pledges and to take no action which is contrary to the accepted programme. On such bases one then introduces practical forms and the suitable instruments to give real life to the organisation. Thus the groups, the federation of groups, the federations of federations, meetings, congresses, correspondence committees, and so on. But this also must be done freely, in such a way as not to restrict the thought and the initiative of individual members, but only to give greater scope to the efforts which in isolation would be impossible or ineffective. Thus for an anarchist organisation congresses, in spite of all the disadvantages from which they suffer as representative bodies... are free from authoritarianism in any shape or form because they do not legislate and do not impose their deliberations on others. They serve to maintain and increase personal contacts among the most active comrades, to summarise and encourage programmatic studies on the ways and means for action; to acquaint everybody with the situation in the regions and the kind of action most urgently needed; to summarise the various currents of anarchist opinions at the time and to prepare some kind of statistics therefrom. And their decisions are not binding but simply suggestions, advice and proposals to submit to all concerned, and they do not become binding and executive except for those who accept them and for as long as they accept them. The administrative organs they nominate—Correspondence Commissions, etc.—have no directive powers, do not take initiatives except for those who specifically solicit and approve of them, and have no authority to impose their own views, which they can certainly hold and propagate as groups of comrades, but which cannot be presented as the official views of the organisation. They publish the resolutions of the congresses and the opinions and proposals communicated to them by groups and individuals; and they act for those who want to make use of them, to facilitate relations between groups, and cooperation between those who are in agreement on various initiatives; each is free to correspond with whoever he likes direct, or to make use of other committees nominated by specific groupings.
In an anarchist organisation individual members can express any opinion and use every tactic which is not in contradiction with the accepted principles and does not interfere with the activities of others. In every case a particular organisation lasts so long as the reasons for union are superior to those for dissension: otherwise it disbands and makes way for other, more homogenous groupings.
Certainly the life and permanence of an organisation is a condition for success in the long struggle before us, and besides, it is natural that every institution should by instinct aim at lasting indefinitely. But the duration of a libertarian organisation must be the result of the spiritual affinity of its members and of the adaptability of its constitution to the continually changing circumstances. When it can no longer serve a useful purpose it is better that it should die.
We would certainly be happy if we could all get along well together and unite all the forces of anarchism in a strong movement; but we do not believe in the solidity of organisations which are built up on concessions and assumptions and in which there is no real agreement and sympathy between members.
Better disunited than badly united. But we would wish that each individual joined his friends and that there should be no isolated forces, or lost forces.
It remains for us to speak of the organisation of the working masses for resistance against both the government and the employers.
...Workers will never be able to emancipate themselves so long as they do not find in union the moral, economic and physical strength that is needed to subdue the organised might of the oppressors.
There have been anarchists, and there are still some, who while recognising the need to organise today for propaganda and action, are hostile to all organisations which do not have anarchism as their goal or which do not follow anarchist methods of struggle.... To those comrades it seemed that all organised forces for an objective less than radically revolutionary, were forces that the revolution was being deprived of. It seems to us instead, and experience has surely already confirmed our view, that their approach would condemn the anarchist movement to a state of perpetual sterility. To make propaganda we must be among the people, and it is in the workers' associations that workers find their comrades and especially those who are most disposed to understand and accept our ideas. But even when it were possible to do as much propaganda as we wished outside the associations, this could not have a noticeable effect on the working masses. Apart from a small number of individuals more educated and capable of abstract thought and theoretical enthusiasms, the worker cannot arrive at anarchism in one leap. To become a convinced anarchist, and not in name only, he must begin to feel the solidarity that joins him to his comrades, and to learn to cooperate with others in the defence of common interests and that, by struggling against the bosses and against the government which supports them, should realise that bosses and governments are useless parasites and that the workers could manage the domestic economy by their own efforts. And when the worker has understood this, he is an anarchist even if he does not call himself such.
Furthermore, to encourage popular organisations of all kinds is the logical consequence of our basic ideas, and should therefore be an integral part of our programme.
An authoritarian party, which aims at capturing power to impose its ideas, has an interest in the people remaining an amorphous mass, unable to act for themselves and therefore always easily dominated. And it follows, logically, that it cannot desire more than that much organisation, and of the kind it needs to attain power: Electoral organisations if it hopes to achieve it by legal means; Military organisation if it relies on violent action.
But we anarchists do not want to _emancipate_ the people; we want the people to _emancipate themselves._ We do not believe in the good that comes from above and imposed by force; we want the new way of life to emerge from the body of the people and correspond to the state of their development and advance as they advance. It matters to us therefore that all interests and opinions should find their expression in a conscious organisation and should influence communal life in proportion to their importance.
We have undertaken the task of struggling against existing social organisation, and of overcoming the obstacles to the advent of a new society in which freedom and well-being would be assured to everybody. To achieve this objective we organise ourselves in a party and seek to become as numerous and as strong as possible. But if it were only our party that was organised; if the workers were to remain isolated like so many units unconcerned about each other and only linked by the common chain; if we ourselves besides being organised as anarchists in a party, were not as workers organised with other workers, we could achieve nothing at all, or at most, we might be able to impose ourselves... and then it would not be the triumph of anarchy but our triumph. We could then go on calling ourselves anarchists, but in reality we should simply be rulers, and as impotent as all rulers are where the general good is concerned.
# **III**
# **12. P RODUCTION AND DISTRIBUTION**
ONE MUST PRODUCE, SAY THE GOVERNMENT AND THE BOURGEOISIE.
One must produce, say the reformists.
One must produce, we (anarchists) also say.
But produce for whom? Produce what? And what are the reasons that not enough is produced?
They say, the revolution cannot take place because production is insufficient, and that we would run the risk of dying of hunger.
We say, the revolution must take place so as to be able to produce and stop the greater part of the population from living in a state of chronic hunger.
... Arturo Labriola, the well known Italian intransigent socialist, maintained at a public meeting some time ago that "the urgent problem which needs solving is not that of the distribution of wealth, but the rational organisation of production."
This is a major error which should be examined, because it compromises the very bases of socialist doctrine, and leads to conclusions which are anything but socialist.
From Malthus onwards, the conservatives of all schools have maintained that poverty does not result from unjust distribution of wealth, but from limited productivity or deficient human industry.
Socialism, in its historic origins and in its basic essence, is the negation of this thesis; it is a clear statement that the social problem is above all a matter of social justice, a question of distribution.
If the thesis sustained by Labriola were true, it would be false to maintain that the antagonisms between bosses and workers cannot be solved, since the workers would find a solution by reason of the interest both bosses and salaried classes have in increasing the quantity of goods; socialism would therefore be false, at least as a practical means for solving the social problem.
Our comrade and friend, Rudolf Rocker says: "The internationalization of raw materials (coal, minerals, oil, etc.) is one of the most important conditions for the realization of socialism and the freeing of humanity from economic, political and social bondage."
In my opinion this is a mistake, a grave error which could serve the enemies of the revolution to paralyze popular movements in those countries which, while lacking particular raw materials, can find themselves, in a given historical situation, better able than others to overthrow the capitalist system.
Such was the case in Italy in 1920. The happy concourse of circumstances made a revolution of a socialist character (using socialist in its widest sense) possible as well as relatively easy. We anarchists and the syndicalists of the Unione Sindacale, strained every nerve to push the masses to act for themselves; but the socialist party, which was then led by the communists, and the General Confederation of labour, (much stronger numerically, organisationally and materially than we were), were determined to prevent any kind of action, and made great use of the argument that we lacked raw materials in Italy. I remember that in Milan, during a heated discussion, a socialist, secretary of the Chemical workers, exclaimed: "How do you expect to make a revolution; don't you know that there are no stocks of rubber in Italy and that in the event of a revolution none would reach us from abroad?" Obviously that good socialist wanted to postpone the advent of socialism until either rubber plantations had been established in Italy or foreign governments had given an undertaking to send us rubber in spite of the revolution!
These raw materials are obviously very useful but they are certainly not indispensable. Humanity lived for innumerable centuries without carbonised vegetable matter, without oil, without rubber, without such an abundance of minerals—and _could_ live without all this stuff in conditions of justice and liberty, that is under socialism, given human understanding and a desire for them.
The question of the distribution of raw materials has assumed such large proportions because of capitalist interests which have been built up around them. It is the capitalists of the various countries who get rich by the exploitation of raw materials and who fight among themselves for the rights; and rival governments find the means of power and revenue in the monopolies enjoyed by their co-nationals.
For the workers, the availability of materials which make work lighter and satisfy certain special needs is as important as you like, but comes after the overriding question of equality and freedom.
Certainly, as Rocker says, the earth will have to be an economic domain available to everybody, the riches of which will be enjoyed by all human beings. But this will happen after, not before, socialism has triumphed everywhere. For the time being, governments, in their own interests and on behalf of their respective financiers and capitalists, defend the monopolies which they have secured in the struggle, and will probably go to war rather than give them up. Briefly then, the internationalisation of natural wealth is not the condition for, but the consequence of, socialism.
The artificial scarcity of goods is a characteristic of the capitalist system and it is the task of the revolution to make rational use of the land and the tools of production in order to increase production to the point where it amply satisfies the needs of all.
Since the means of production (land, tools, etc.) belong to a small number of people who use them to make others work for their profit, it follows that production increases so long as the employers' profits increase, and is artificially held back, when increased production results in smaller profits. In other words, the employer limits production to what he can sell at a profit, and halts production as soon as he stops making profits, or when the prospects of so doing seem remote. And thus, the whole economic life of society, stems not from the necessity of satisfying the needs of everybody, but from the interests of the employers and by the competition in which they are engaged among themselves. Hence limited production to keep prices high; hence the phenomenon of unemployment even when the needs are urgent; hence uncultivated or badly cultivated land; hence poverty and the subjection of the majority of workers.
Under such conditions, how is it possible to produce in abundance for everybody?
There have been many anarchists, and among them some of the most eminent, who have propagated the idea that the quantity of goods produced and stored in the warehouses and granaries is so over-abundant that it would only be necessary to draw on these stores to fully satisfy the needs and wishes of all without having to worry ourselves about the problems of work and production for a long time to come. And, of course, they found people who were willing to believe them. Human beings are only too liable to succumb to a tendency to avoid toil and dangers. Just as the social democrats found a considerable measure of support among the masses when they tried to make out that it was sufficient to put a piece of paper in the ballot box in order to emancipate oneself, so some anarchists attracted other masses by assuring them all that was needed was a one-day epic struggle in order to enjoy, without effort, or with a minimum of effort, the paradise of abundance in a state of freedom.
Now, this is precisely the contrary of the truth. Capitalists make others produce to sell for profit, and therefore stop production as soon as they see that profits would diminish or disappear. They generally find it more advantageous to keep markets in a situation of relative shortage; and this is shown by the fact that one bad harvest can result in goods being in short supply or even not available at all. It can be said therefore, that the greatest harm wrought by the capitalist system is not so much the army of parasites that it feeds, as the obstacles it places in the way of the production of useful commodities. The hungry and the badly clothed are dazzled when they pass shops bulging with goods of every kind; but try to distribute this wealth among all the needy and you will see how small would be each one's share!
Socialism, the aspiration to socialism, in the broad sense of the word, appears as a problem of distribution in so far as it is the spectacle of the poverty of workers compared with the comfort and luxury of the parasites, and the moral revolt against the blatant social injustices which have driven the victims, and all men of feeling, to seek and to advocate better ways of living together in society. But the achievement of socialism—be it anarchist or authoritarian, mutualist or individualist, etc.—is above all a problem of production. When the goods do not exist, it is useless to seek the best way of distributing them, and if men are reduced to fighting over their crust of bread, the sentiments of love and brotherhood are in danger of being overwhelmed by the brutal struggle for existence.
Fortunately today the means of production abound. Mechanisation, science, and technology have centupled the productive potential of human labour. But one has to work, and to do so usefully one must have the know-how: how to do the work and how to organise it in the most economical way.
If anarchists want to act effectively in competition with the various political parties, they must study in depth—each one the branch with which he is most familiar—all the theoretical and practical problems related to useful work.
We must bear in mind that on the morrow of the revolution we shall be faced with the danger of hunger. This is not a reason for delaying the revolution, because the state of production will, with minor variations, remain the same, so long as the capitalist system lasts.
But it is a reason for us to pay attention to the problem and of how in a revolutionary situation, to avoid all waste, to preach the need for reducing consumption to a minimum, and to take immediate steps to increase production, especially of food.
At the very moment of the revolution, as soon as the defeat of bourgeois military power makes it possible, we should put into effect, by means of the free initiative of all workers' organisations, by all militant groups, and all volunteers of the revolutionary movement, the expropriation and the placing of all existing wealth in common and, without delay, proceed to the organisation of distribution and the reorganisation of production according to the needs and wishes of the different regions, communes, and groups, and thus arrive, under the impetus of the idea and of needs, at the understandings, agreements, and decisions needed to carry on the life of society.
Production and distribution must be controlled, that is one must ascertain which commodities are needed and in what quantities; where they are needed and what means are available to produce them and distribute them. Colomer says that "under anarchy it is the individual who determines production and consumption in relation to his needs and his capabilities"; but a moment's reflection should make him realise that he is talking nonsense. Since an individual cannot alone produce all he needs and must exchange his products with those of others, it is necessary that each should know not only what he can produce and what he requires, but be aware of the needs and capabilities of others as well.
Liberty and labour are the prerequisites of socialism (anarchist, communist, etc.) just as they also are the prerequisites of all human progress.
# **13. T HE LAND**
THE PROBLEM OF THE LAND IS PERHAPS THE MOST SERIOUS, AND dangerous problem which the revolution will have to solve. In justice (abstract justice which is contained in the saying _to each his own)_ the land belongs to everybody and must be at the disposal of whoever wants to work it, by whatever means he prefers, whether individually, or in small or large groups, for his own benefit or on behalf of the community.
But justice does not suffice to ensure civilised life, and if it is not tempered, almost cancelled out, by the spirit of brotherhood, by the consciousness of human solidarity, it leads, through the struggle of each against all, to subjection and the exploitation of the vanquished, and that is, to injustice in all social relations.
_To each his own._ The _own_ of each should be the part share due to him of the natural wealth and the accumulated wealth of past generations on top of what he produces by his own efforts. But how to divide justly the natural wealth, and determine in the complexity of civilised life and in the complex process of production, what is an individual's production? And how is one to measure the value of the products for the purposes of exchange?
If one starts from the principle, of each for himself, it is utopian to hope for justice, and to claim it, is hypocrisy, maybe unconscious, which serves to cover up the meanest egoism, the desire for domination and the avidity of each individual.
Communism then appears to be the only possible solution; the only system, based on natural solidarity, which links all mankind; and only a desired solidarity linking them in brotherhood, can reconcile the interests of all and serve as the basis for a society in which everyone is guaranteed the greatest possible well-being and freedom.
On the question of possession and utilisation of the land it is even clearer. If all the cultivable landmasses were equally fertile, equally healthy, and equally well situated for the purpose of barter, one could visualise a division of the land in equal parts among all the workers, who would then work, in association if they wished, and how they wished, in the interests of production.
But the conditions of fertility, the health and situation of the land are so different that it is impossible to think in terms of an equable distribution. A government by nationalising the land and renting it to land workers could, in theory, resolve the problem by a tax, which would go to the State, what economists call the economic return (that is, whatever a piece of land, given equal work, produces in excess over the worse piece). It is the system advocated by the American Henry George. But one sees immediately that such a system presupposes the continuation of the bourgeois order, apart from the growing power of the State and the governmental and bureaucratic powers with which one would have to contend. So, for us, who neither want government nor believe that individual possession of agricultural land is possible or desirable—economically or morally—the only solution is communism. And for this reason we are communists.
But communism must be voluntary, freely desired, and accepted; for were it instead to be imposed, it would produce the most monstrous tyranny which would result in a return to bourgeois individualism.
Now, while waiting for communism to demonstrate, by the example of the collectives so organised from the outset, its advantages and be desired by all, what is our practical agrarian programme, to be put into operation as soon as the revolution takes place?
Once legal protection has been removed from property, the workers will have to take possession of all land which is not being directly cultivated, by existing owners with their own hands; they will have to establish themselves into associations and organise production, making use of the ability and all the technical skills of those who have always been workers, as well as of the former bourgeoisie who having been expropriated and, being no longer able to live by the work of others, will by the necessity of things have become workers as well. Agreements will be promptly reached with the associations of industrial workers for the exchange of goods, either on a communistic basis or in accordance with the different criteria prevailing in different localities.
Meanwhile all food stocks would be expropriated by the people in revolt and distribution to the different localities and individuals organised through the initiative of the revolutionary groups. Seeds, fertilisers and farm machinery, and working animals will be supplied to the land workers; free access to the land for whoever wants to work it.
There remains the question of peasant proprietors. Should they refuse to join forces with the others there would be no reason to harass them so long as they do the work themselves and do not exploit the labour of others.... The disadvantages, the virtual impossibility of isolated work, would soon attract them into the orbit of the collectivity....
# **14. M ONEY AND BANKS**
IT IS A MISTAKE TO BELIEVE AS SOME DO THAT THE BANKS ARE, OR ARE in the main, a means to facilitate exchange; they are a means to speculate on exchange and currencies, to invest capital and make it produce interest, and to fulfil other typically capitalist operations, which will disappear as soon as the principle that no one has the right or the possibility of exploiting the labour of others, triumphs.
That in the post-revolutionary period, in the period of reorganisation and transition, there might be "offices for the concentration and distribution of the capital of collective enterprises," that there might or not be titles recording the work done and the quantity of goods to which one is entitled, is something we shall have to wait and see about, or rather, it is a problem which will have many and varied solutions according to the system of production and distribution which will prevail in the different localities and among the many natural and artificial groupings that will exist. What seems essential to me is that all money actually in circulation, industrial shares, title deeds, government securities, and all other securities which represent the right and the means for living on the labour of others should immediately be considered valueless and also, in so far as it is possible to do so, destroyed.
It is customary in [anarchist] circles to offer a simplicist solution to the problem [of money] by saying that it must be abolished. And this would be the solution if it were a question of an anarchist society, or of a hypothetical revolution to take place in the next hundred years, always assuming that the masses could become anarchist and communist before the conditions under which we live had been radically changed by a revolution.
But today the problem is complicated in quite a different way. Money is a powerful means of exploitation and oppression; but it is also the only means (apart from the most tyrannical dictatorship or the most idyllic accord) so far devised by human intelligence to regulate production and distribution automatically.
For the moment, rather than concerning oneself with the abolition of money one should seek a way to ensure that money truly represents the useful work performed by its possessors....
Let us assume that a successful insurrection takes place tomorrow. Anarchy or no anarchy, the people must go on eating and providing for all their basic needs. The large cities must be supplied with necessities more or less as usual.
If the peasants and carriers, etc. refuse to supply goods and services for nothing, and demand payment in money which they are accustomed to considering as real wealth, what does one do? Oblige them by force? In which case we might as well wave goodbye to anarchism and to any possible change for the better. Let the Russian experience serve as a lesson.
And so?
The comrades generally reply: But the peasants will understand the advantages of communism or at least of the direct exchange of goods for goods.
This is all very well; but certainly not in a day, and the people cannot stay without eating for even a day. I did not mean to propose solutions [at the Bienne meeting]. What I do want to do is to draw the comrades' attention to the most important questions which we shall be faced with in the reality of a revolutionary morrow.
# **15. P ROPERTY**
OUR OPPONENTS, INTERESTED DEFENDERS OF THE EXISTING system are in the habit of saying, to justify the right to private property, that it is the condition and guarantee of freedom.
And we agree with them. Are we not always repeating that he who is poor is a slave? Then why are they our opponents?
The reason is clear and is that in fact the property they defend is capitalist property, that is, property which allows some to live by the work of others and which therefore presupposes a class of dispossessed, propertyless people, obliged to sell their labour power to the property-owners for less than its value....
The principal reason for the bad exploitation of nature, and of the miseries of the workers, of the antagonisms and the social struggles, is the _right to property_ which confers on the owners of the land, the raw materials and of all the means of production, the possibility to exploit the labour of others, and to organise production not for the well-being of all, but in order to guarantee a maximum profit for the owners of property. It is necessary therefore to abolish property.
The principle for which we must fight and on which we cannot compromise, whether we win or lose is that all should possess the means of production in order to work without subjection to capitalist exploitation, large or small. The abolition of individual property, in the literal sense of the word, will come, if it comes, by the force of circumstances, by the demonstrable advantages of communistic management, and by the growing spirit of brotherhood. But what has to be destroyed at once, even with violence if necessary, is _capitalistic property,_ that is, the fact that a few control the natural wealth and the instruments of production and can thus oblige others to work for them.
Imposed communism would be the most detestable tyranny that the human mind could conceive. And free and voluntary communism is ironical if one has not the right and the possibility to live in a different regime, collectivist, mutualist, individualist—as one wishes, always on condition that there is no oppression or exploitation of others.
Free then is the peasant to cultivate his piece of land, alone if he wishes; free is the shoe maker to remain at his last, or the blacksmith in his small forge. It remains to be seen whether not being able to obtain assistance or people to exploit—and he would find none because nobody, having a right to the means of production and being free to work on his own or as an equal with others in the large organisations of production would want to be exploited by a small employer—I was saying, it remains to be seen whether these isolated workers would not find it more convenient to combine with others and voluntarily join one of the existing communities.
The destruction of title deeds would not harm the independent worker whose real title is possession and the work done.
What we are concerned with is the destruction of the titles of the proprietors who exploit the labour of others and, above all, of expropriating them in fact in order to put the land, houses, factories, and all the means of production at the disposal of those who do the work.
It goes without saying that former owners would only have to take part in production in whatever way they can, to be considered equals with all other workers.
Will property [in the revolutionary period] have to be individual or collective? And will the collective holding the undivided goods be the local group, the functional group, the group based on political affinity, the family group—will it comprise all the inhabitants of a nation _en bloc_ and eventually all humanity?
What forms will production and exchange assume? Will it be the triumph of _communism_ (production in association and free consumption for all) or _collectivism_ (production in common and the distribution of goods on the basis of the work done by each individual), or _individualism_ (to each the individual ownership of the means of production and the enjoyment of the full product of his labour), or other composite forms that individual interest and social instinct, illuminated by experience, will suggest?
Probably every possible form of possession and utilisation of the means of production and all ways of distribution of produce will be tried out at the same time in one or many regions, and they will combine and be modified in various ways until experience will indicate which form, or forms, is or are, the most suitable.
In the meantime... the need for not interrupting production, and the impossibility of suspending consumption of the necessities of life, will make it necessary to take decisions for the continuation of daily life at the same time as expropriation proceeds. One will have to do the best one can, and so long as one prevents the constitution and consolidation of new privilege, there will be time to find the best solutions.
But what is the solution that seems best to me and to which one should try to approximate?
I call myself a communist, because communism, it seems to me, is the ideal to which mankind will aspire as love between men, and an abundance of production, will free them from the fear of hunger and will thus destroy the major obstacle to brotherhood between them. But really, even more than the practical forms of organisation which must inevitably be adjusted according to the circumstances, and will always be in a constant state of change, what is important is the spirit which informs those organisations, and the method used to bring them about; what I believe important is that they should be guided by the spirit of justice and the desire of the general good, and that they should always achieve their objectives through freedom, and voluntarily. If freedom and a spirit of brotherhood truly exist, all solutions aim at the same objective of emancipation and human enlightenment and will end by being reconciled by fusion. If, on the contrary, there is no freedom and the desire for the good of all is lacking, all forms of organisation can result in injustice, exploitation, and despotism.
# **16. C RIME AND PUNISHMENT**
EVERY ANARCHIST PROPAGANDIST IS FAMILIAR WITH THE KEY objections: who will keep criminals in check [in the anarchist society]? To my mind their concern is exaggerated since delinquency is a phenomenon of little importance compared with the vastness of ever present and general social realities. And one can believe in its automatic disappearance as a result of an increase in material well-being and education, not to mention advances in pedagogy and medicine. But however optimistic may be our hopes, and rosy the future, the fact remains that delinquency and the fear of crime today prevents peaceful social relations, and it will certainly not disappear from one moment to the next following a revolution, however radical and thoroughgoing it may turn out to be. It could even be the cause of upheaval and disintegration in a society of free men, just as an insignificant grain of sand can stop the most perfect machine.
It is worthwhile and indeed necessary that anarchists should consider the problem in greater detail than they normally do, not only in order the better to deal with a popular "objection" but in order not to expose themselves to unpleasant surprises and dangerous contradictions.
Naturally the crimes we are talking about are anti-social acts, that is those which offend human feelings and which infringe the right of others to equality in freedom, and not the many actions which the penal code punishes simply because they offend against the privileges of the dominant classes.
Crime, in our opinion, is any action which tends to consciously increase human suffering; it is the violation of the right of all to equal freedom and to the greatest possible enjoyment of material and moral well-being.
We know that having thus defined delinquency, it is always difficult even for those who accept the definition, to determine in fact what actions are criminal and which are not; for Man's views differ as to what causes pain or happiness, what is good and what is bad, except in those bestial crimes which offend fundamental human feelings and are therefore universally condemned.
I imagine that no one would be prepared, theoretically, to deny that freedom understood in the sense of reciprocity, is the basic prerequisite of any civilisation, of "humanity"; but only anarchy represents its logical and complete realisation. On this assumption, he is a criminal—not against nature or the result of a metaphysical law, but against his fellow men and because the interests and feelings of others have been offended—whoever violates the equal freedom of others. And so long as such people exist, we must defend ourselves.
This necessary defence against those who violate not the _status quo_ but the deepest feelings which distinguish men from beasts, is one of the pretexts by which governments justify their existence. One must eliminate all the social causes of crime, one must develop in man brotherly feelings, and mutual respect; one must, as Fourier put it, seek useful alternatives to crime. But if, and so long as, there are criminals, either the people will find the means, and have the energy, to directly defend themselves against them, or the police and the magistrature will reappear and with them, government.
It is not by denying a problem that one solves it.
One can, with justification, fear that this necessary defence against crime could be the beginning of and the pretext for, a new system of oppression and privilege. It is the anarchists' mission to see that this does not happen. By seeking the causes of each crime and making every effort to eliminate them; by making it impossible for anybody to derive personal advantage out of the detection of crime, and leaving it to the interested groups themselves to take whatever steps they deem necessary for their defence; by accustoming oneself to consider criminals as brothers who have strayed, as sick people needing loving treatment, as one would for any hydrophobe or dangerous lunatic—it will be possible to reconcile the complete freedom of all with defence against those who obviously and dangerously threaten it.
Obviously this is possible, when crime will be reduced to sporadic, individual, and truly pathological cases. If it were a fact that criminals were too numerous and powerful; if, for example, they were what the bourgeoisie and fascism are today [1922], then it is not a question of discussing what we will do in an anarchist society.
With the growth of civilisation, and of social relations; with the growing awareness of human solidarity which unites mankind; with the development of intelligence and a refinement of feelings there is certainly a corresponding growth of social duties, and many actions which were considered as strictly individual rights and independent of any collective control will be considered, indeed they already are, matters affecting everybody, and must therefore be carried out in conformity with the general interest. For instance, even in our times parents are not allowed to keep their children in ignorance and bring them up in a way which is harmful to their development and future well-being. A person is not allowed to live in filthy conditions and neglect those rules of hygiene which can affect the health of others; one is not allowed to have an infectious disease and not have it treated. In a future society it will be considered a duty to seek to ensure the good of all, just as it will be considered blameworthy to procreate if there are reasons to believe that the progeny will be unhealthy and unhappy. But this sense of our duties to others, and of theirs to us must, according to our social concepts, develop without any other outside sanction than the esteem or the disapproval of our fellow citizens. Respect, the desire for the well-being of others, must enter into the customs, and manifest themselves not as duties but as a normal satisfaction of social instincts.
There are those who would improve the morality of people by force, who would wish to introduce an Article into the penal code for every possible human action, who would place a _gendarme_ alongside every nuptial bed and by every table. But these people if they lack the coercive powers to impose their ideas, only succeed in making a mockery of the best things; and if they have the power to command, make what is good hateful, and encourage reaction.... For us the carrying out of social duties must be a voluntary act, and one has the right to intervene with material force only against those who offend against others _violently_ and prevent them from living in peace. Force, physical restraint, must only be used against attacks of violence and for no other reason than that of self-defence.
But who will judge? Who will provide the necessary defence? Who will establish what measures of restraint are to be used? We do not see any other way than that of leaving it to the interested parties, to the people, that is the mass of citizens, who will act in different ways according to the circumstances and according to their different degrees of social development. One must, above all, avoid the creation of bodies specialising in police work; perhaps something will be lost in repressive efficiency but one will also avoid the creation of the instrument of every tyranny.
We do not believe in the infallibility, nor even in the general goodness of the masses; on the contrary. But we believe even less in the infallibility and goodness of those who seize power and legislate, who consolidate and perpetuate the ideas and interests which prevail at any given moment.
In every respect the injustice, and transitory violence of the people is preferable to the leaden-rule, the legalised State violence of the judiciary and police.
We are, in any case, only one of the forces acting in society, and history will advance, as always, in the direction of the resultant of all the [social] forces.
We must reckon with a residue of delinquency... which we hope will be eliminated more or less rapidly, but which in the meantime will oblige the mass of workers to take defensive action. Discarding every concept of punishment and revenge, which still dominate penal law, and guided only by the need for self-defence and the desire to rehabilitate, we must seek the means to achieve our goal, without falling into the dangers of authoritarianism and consequently finding ourselves in contradiction with the system of liberty and free-will on which we seek to build the new society.
For authoritarians and statesmen, the question is a simple one: a legislative body to list the crimes and prescribe the punishments; a police force to hunt out the delinquents; a magistrature to judge them; and a prison service to make them suffer. And, as is understandable, the legislative body seeks through its penal laws to defend, above all, established interest, which it represents, and to protect the State from those who seek to "subvert" it. The police force exists to suppress crime, and having therefore an interest in the continued existence of crime becomes provocative, and develops in its officers aggressive and perverse instincts; the magistrature also lives and prospers thanks to crime and delinquents, and serves the interests of the government and the ruling classes, and acquires, in the course of exercising its function, a special way of reasoning, which makes it into a machine for awarding a maximum number of people the longest sentences it can. The warders are, or become, insensitive to the suffering of prisoners and at best, passively observe the rules without a spark of human feeling. One sees the results in statistics on delinquency. The penal laws are changed, the police force and the magistrature are reorganised, the prison system is reformed... and delinquency persists and resists all attempts to destroy, or reduce it. It is true of the past and the present, and we think it will apply in the future too, if the whole concept of crime is not changed, and all the organisms which live on the prevention and repression of delinquency are not abolished.
There are in France stringent laws against the traffic in drugs and against those who take them. And as always happens, the scourge grows and spreads in spite, and perhaps because of, the laws. The same is happening in the rest of Europe and in America. Doctor Courtois-Suffit, of the French Academy of Medicine, who, already last year [1921], had sounded the alarm against the dangers of cocaine, noting the failure of penal legislation, now demands... new and more stringent laws.
It is the old mistake of legislators, in spite of experience invariably showing that laws, however barbarous they may be, have never served to suppress vice or to discourage delinquency. The more severe the penalties imposed on the consumers and traffickers of cocaine, the greater will be the attraction of forbidden fruits and the fascination of the risks incurred by the consumer, and the greater will be the profits made by the speculators, avid for money.
It is useless, therefore to hope for anything from the law. We must suggest another solution. Make the use and sale of cocaine free [from restrictions], and open kiosks where it would be sold at cost price or even under cost. And then launch a great propaganda campaign to explain to the public, and let them see for themselves, the evils of cocaine; no one would engage in counter-propaganda because nobody could exploit the misfortunes of cocaine addicts.
Certainly the harmful use of cocaine would not disappear completely, because the social causes which create and drive those poor devils to the use of drugs would still exist. But in any case the evil would decrease, because nobody could make profits out of its sale, and nobody could speculate on the hunt for speculators. And for this reason our suggestion either will not be taken into account, or it will be considered impractical and mad.
Yet intelligent and disinterested people might say to themselves: Since the penal laws have proved to be impotent, would it not be a good thing, as an experiment, to try out the anarchist method?
We will not repeat the classical arguments against the death penalty. They seem lies, when we hear them used by those who then come out in favour of life imprisonment and other inhuman substitutes for the death penalty. Nor will we speak of the "sanctity of life" which all affirm but violate when it suits them, either by actually taking life or treating others in such a way as to torment or shorten their lives.
Fortunately only few men are born, or become, moral bloodthirsty and sadistic monsters whose death we would not know how to mourn. If these poor devils were to be a continuous threat to everybody and there were no other way of defending ourselves other than by killing them, one could also admit the death penalty.
But the trouble is that in order to carry out the death penalty one needs an executioner. The executioner is, or becomes, a monster; and on balance it is better to let the monsters that there are go on living, rather than to create others.
And this applies to real delinquents, anti-social beings who arouse no sympathy and provoke no commiseration. When it comes to the death penalty as a means of political struggle, then... well history teaches us what can be the consequences.
# **IV**
# **17. A NARCHISTS AND THE WORKING CLASS MOVEMENTS**
TODAY THE MOST POWERFUL FORCE FOR SOCIAL TRANSFORMATION is the working-class movement (the trade-union movement), and on its intentions depends to a large degree the course that events will take and the objectives of any future revolution. Through the organisations established for the defence of their interests, workers acquire an awareness of the oppression under which they live and of the antagonisms which divide them from their employers, and so begin to aspire to a better life, get used to collective struggle and to solidarity, and can succeed in winning those improvements which are compatible with the continued existence of the capitalist and statist regime. Later, when the conflict is beyond solution, there is either revolution or reaction.
Anarchists must recognise the usefulness and the importance of the workers' movement, must favour its development, and make it one of the levers for their action, doing all they can so that it, in conjunction with all existing progressive forces, will culminate in a social revolution which leads to the suppression of classes and to complete freedom, equality, peace, and solidarity among all human beings. But it would be a great and fatal illusion to believe, as many do, that the workers' movement can and must on its own, by its very nature, lead to such a revolution. On the contrary, all movements founded on material and immediate interests (and a mass working-class movement cannot be founded on anything else), if the ferment, the drive and the unremitting efforts of men of ideas struggling and making sacrifices for an ideal future are lacking, tend to adapt themselves to circumstances, foster a conservative spirit, and the fear of change in those who manage to improve their conditions, and often end up by creating new privileged classes and serving to support and consolidate the system which one would want to destroy.
Hence the impelling need for strictly anarchist organisations which struggle both inside and outside the trade unions for the achievement of anarchism and which seek to sterilise all the germs of degeneration and reaction.
But it is obvious that to achieve their ends anarchist organisations must be, in their constitution and in their operation, in harmony with anarchist principles, that is, they must not in any way be marked by an authoritarian spirit, and that they should know how to reconcile the free action of individuals with the need for, and the pleasures to be derived from, cooperation, which serve to develop the consciences of their members as well as their abilities to take initiative. Anarchist organisations should also be an educative force in the circle in which they operate and a moral and material preparation for the future we desire.
The task of anarchists is to work to strengthen the revolutionary conscience of organised workers and to remain in the Unions as anarchists.
It is true that the Unions, for pressing reasons, are often obliged to engage in negotiations and accept compromises. I do not criticise them for that, but it is for this very reason that I have to consider the Unions as essentially reformist.
The Unions perform a function of bringing together the proletarian masses and of eliminating conflicts which could otherwise arise between worker and worker. While the Unions must engage in the struggle to obtain immediate benefits, and after all it is just and only human that workers should demand better conditions, revolutionaries go beyond this. They struggle for the revolution which will expropriate capital and destroy the State, every State by whatever name it is called.
Since economic slavery is the product of political servitude, to eliminate one it is necessary to eliminate the other, even if Marx said otherwise.
Why does the peasant bring the corn to the boss?
Because the gendarme is there to oblige him to do so. Thus, Trade Unionism cannot be an end in itself, since the struggle must also be waged at a political level to distinguish the role of the State.
The anarchists do not want to dominate the U.S.I. (Unione Sindacale Italiana); they would not wish to even if all the workers in its ranks were anarchists, neither do they wish to assume the responsibility for its negotiations. We who do not seek power, only want the consciences of men; only those whose wish is to dominate prefer sheep the better to lead them.
We prefer intelligent workers, even if they are our opponents, to anarchists who are such only in order to follow us like sheep. We want freedom for everybody; we want the masses to make the revolution for the masses.
The person who thinks with his own brain is to be preferred to the one who blindly approves everything. For this reason, as anarchists, we support the U.S.I. because this organisation does develop the consciences of the masses. Better an error consciously committed and in good faith, than a good action performed in a servile manner.
Just because I am convinced that the Unions can and must play a most useful, and perhaps necessary, role in the transition from present society to the equalitarian society, I would wish them to be judged at their true worth and by never forgetting that they have a natural tendency to become closed corporations limited to making narrow, sectional demands, or worse still, for their members only; we will thus be in a better position to combat this tendency and prevent them from becoming conservative organisms. Just as, in fact, I recognise the extreme usefulness that cooperatives, by accustoming workers to manage their own affairs, the organisation of their work and other activities, can have at the beginning of a revolution as experienced organisations capable of dealing with the distribution of goods and serving as nerve centres for the mass of the population, I combat the shopkeeper spirit which seems to develop naturally in their midst. I would wish that they were open to all, that they conferred no privileges on their members and, above all, that they did not transform themselves, as often happens, into real capitalistic Liability Companies, which employ and exploit wage earners as well as speculating on the needs of the public.
In my opinion, cooperatives and Trades Unions, under the capitalist regime, do not naturally, or by reason of their intrinsic value, lead to human emancipation (and this is the controversial point), but can be producers of good and evil, today organs of conservation or social transformation, tomorrow, serving the forces of reaction or revolution. All depends on whether they limit themselves to their real function as defenders of the immediate interests of their members or are animated and influenced by the anarchist spirit, which makes the ideals stronger than sectional interests. And by anarchist spirit I mean that deeply human sentiment, which aims at the good of all, freedom and justice for all, solidarity and love among the people; which is not an exclusive characteristic only of self-declared anarchists, but inspires all people who have a generous heart and an open mind....
The working class movement, in spite of all its merits and its potentialities, cannot be, in itself, a revolutionary movement in the sense of being a negation of the juridical and moral bases of present society.
It can, every new organisation can, in the spirit of its founders and according to the letter of its rules, have the highest aspirations and the most radical intentions, but if it wants to exercise its function as a workers' Union, that is, the present defence of its members' interests, it must recognise _de facto_ the institutions which it has denied in theory, adapt itself to circumstances, and attempt to obtain, step by step, as much as it can, by negotiating and compromising with the bosses and the government.
In a word, the Trade Unions are, by their very nature reformist and never revolutionary. The revolutionary spirit must be introduced, developed, and maintained by the constant actions of revolutionaries who work from within their ranks as well as from outside, but it cannot be the normal, natural definition of the Trade Unions function. On the contrary, the real and immediate interests of organised workers, which it is the Unions' role to defend, are very often in conflict with their ideals and forward-looking objectives; and the Union can only act in a revolutionary way if permeated by a spirit of sacrifice and to the extent that the ideal is given precedence over the interest, that is, only if, and to the extent that, it ceases to be an economic Union and becomes a political and idealistic group. And this is not possible in the large Trade Unions which in order to act need the approval of the masses always more or less egotistic, timorous, and backward.
Nor is this the worst aspect of the situation.
Capitalist society is so constituted that, generally speaking, the interests of each class, of each category, of each individual are in conflict with those of all other classes, categories, and individuals. And in daily life one sees the most complicated alignments of harmony and clashes of interests between classes and between individuals who, from the point of view of social justice should always be friends or always enemies. And it often happens, in spite of the much vaunted solidarity of the proletariat, that the interests of one category of workers are antagonistic to those of others and favourable to those of a category of employers; as also happens, that in spite of the desired international brotherhood, the present interests of the workers of any one country ties them to their native capitalists and puts them in a position of hostility to foreign workers. As an example we would refer to the situation of the various workers' organisations to the question of Tariffs, and Customs barriers, and the voluntary role played by the working masses in wars between capitalist States.
The list is unending—antagonism between employed and unemployed, between men and women, between native workers and foreign workers in their midst, between workers who use a public service and those who work in that service, between those who have a trade and those who want to learn it. But I would here draw special attention to the interest that workers engaged in the luxury trades have in the prosperity of the wealthy classes and that of a whole number of categories of workers in different localities that "business" should come their way, even if at the expense of other localities and to the detriment of production which is useful to the community as a whole. And what should be said of those who work in industries harmful to society and to individuals, when they have no other way of earning a living? In normal times, when there is no faith in an imminent revolution, just go and try to persuade workers at the Arsenals who are threatened with unemployment not to demand that the government should build new battleships! And try, with Trade Union means, and doing justice to all, to solve the conflicts between dock labourers, who have no other way of ensuring the means of livelihood for themselves than by monopolising all the available work for those who have been working there a long time, and the new arrivals, the "casuals" who demand their right to work and life! All this, and much else that could be said, shows that the workers' movement, in itself, without the ferment of revolutionary imagination contrasting with the short term interests of the workers, without the criticism and the impulse of the revolutionaries, far from leading to the transformation of society to the advantage of all, tends to encourage group egoism and to create a class of privileged workers living on the backs of the great mass of the "disinherited."
And this explains the general phenomenon that in all countries workers' organisations as they have grown and become strong, have become conservative and reactionary, and those who have served the workers' movement honestly and with dreams of a society based on well-being and justice for all, are condemned, like Sisyphus, to having to start all over again every so often.
This need not happen if there is a spirit of rebellion among the masses, and if idealism inspires and influences those more skillful and favoured by circumstances, who are in a position to constitute the new privileged class. But there is no doubt that if we remain at the level of the defence of present-day interests, which is that of the Trade Unions (and since there is no harmony of interests, nor can they be harmonised in a capitalistic regime), the struggle between workers is a normal occurrence which can, in certain circumstances, and among certain sections become more bitter than the struggle between workers and exploiters.
To convince oneself, one only needs to observe what are the largest workers' organisations in the countries in which there is much organisation and little propaganda or revolutionary tradition. Let us take the American Federation of labour in the United States. It does not carry on a struggle against the bosses except in the sense that two business men struggle when they are discussing the details of a contract. The real struggle is conducted against the newcomers, the foreigners, or natives who seek to be allowed to work in any industrial job; against the forced blacklegs who cannot obtain work in the factories recognised by the Federation because the members are against them, and are obliged to offer their services to the "open shops"... Those American Unions when they have reached the membership which they think sufficient to be able to deal with the employers as equals, immediately seek to prevent the admission of new members by imposing prohibitive entrance fees or quite blatantly simply refusing all new applications for membership. They impose rigorous limitations on the work that members in each Union can undertake, and prohibit workers in one Union from invading the territory "of the others." Skilled workers look down on manual workers; whites despise and oppress blacks; the "real Americans" consider Chinese, Italians, and other foreign workers as inferiors. If a revolution were to come in the United States, the strong and wealthy Unions would inevitably be against the Movement, because they would be worried about their investments and the privileged position they have assured for themselves. And the same would probably happen in Britain and elsewhere.
This is not Trade Unionism, I know; and trade unionists who unceasingly fight this tendency of the Unions to become the instrument of base egoism, are performing a most useful task. But the tendency is there and cannot be corrected except by transcending trade union methods.
The Unions will be most valuable in a revolutionary situation, but on condition that they are... as little like Trade Unions as possible.
It is not true, whatever the syndicalists may say, that the workers' organisations of today will serve as the framework for the future society and will facilitate the transition from the bourgeois to the equalitarian regime. This is an idea which met with favour among the members of the First International; and if I am not mistaken, one will find in Bakunin's writings that the new society would be achieved by all workers joining the Sections of the International.
To my mind this is a mistake.
The structure of existing workers' organisations corresponds to present-day conditions of economic life, which is the result of historic developments and capitalist domination. And the new society cannot be achieved without breaking up those structures and creating new organisms corresponding to the new conditions and the new social objectives.
Workers today are grouped according to the trades they practice, the industries in which they work, the employers against whom they must struggle, or the business to which they are tied. What will be the use of these groupings when, without the employers and with business relations turned upside down, a large number of existing trades and industries will have to disappear, some permanently because they are useless and harmful, others temporarily because, though useful in the future, will have no _raison d'être_ or possibility of existence in the period of social upheaval? Of what use, just to quote one of a thousand examples that come to mind, will be the organisations of the marble quarrymen of Carrara when what will be needed is that they should go and cultivate the land and increase the production of foodstuffs, leaving to the future the construction of monuments and marble palaces?
Certainly workers' organisations, especially in their cooperative forms (which incidentally, under the capitalist system, tend to curb workers' resistance) can serve to develop among workers technical and administrative capacities, but in a revolutionary period and for social reorganisation they must disappear and be absorbed in the new popular groupings as circumstances demand. And it is the task of revolutionaries to seek to prevent the development of an _esprit de corps_ in these existing organisations which would be an obstacle to satisfying the new Social needs.
Therefore, in my opinion, the workers' movement is an instrument to be used today for raising and educating, the masses, and tomorrow for the inevitable official clash. But it is an instrument which has its disadvantages and its dangers. And we anarchists must make every effort to neutralise the disadvantages, parry the dangers, and use the movement as much as we can for our ends. This does not mean, as has been suggested, that we would wish the workers' movement to be the tool of the anarchists. Of course we would be happy if _all_ workers, if everybody were anarchists... but in that case anarchy would be a fact and there would be no need for such discussions.
In the present state of affairs, what we would wish is that the workers' movements were open to all forward-looking, imaginative propaganda and that they participated in all the economic, political, and moral activities of society, living and developing free from all outside control, from us no less than from the political parties.
There are many comrades who aim at making the working class movement and the anarchist movement all one, and where they can, as for example in Spain, Argentina, and to a lesser extent in Italy, France, Germany, etc., they try to give the workers' organisations a frankly anarchist programme. There are those who call themselves "anarcho-syndicalists"; or when they link up with others who are really not anarchists, they take the name of "revolutionary syndicalists." It is necessary to explain what is meant by "syndicalism."
If it is a question of the sought-after future, if, that is, by syndicalism is meant the form of social organisation which should replace the capitalistic and statal organisation, then either it is the same as anarchy, and is therefore a term which only serves to confuse matters, or it is different from anarchy and cannot therefore be accepted by anarchists. Indeed, among the ideas and plans for the future put forward by this or that syndicalist, there are some which are genuinely anarchist, but there are others which present, under different names, and in different guises, the authoritarian structure which is the cause of the evils which today we complain of, and therefore can have nothing in common with anarchy. But it is not syndicalism as a social system that I wish to deal with, since it is not this which can determine the present activity of anarchists in regard to the working-class movement. What we are interested in are all workers' organisations, all the Unions constituted to resist the oppression of the employers and to reduce or destroy the exploitation of human labour by those who control the sources of wealth and the means of production.
Now I say that these cannot be anarchist organisations, and it is not a good thing to wish that they should be, because if they were they would neither manage to do their job nor serve the ends which anarchists aim at in joining them.
The Unions are created to defend today the present interests of workers and improve their conditions as much as possible until such time as they are in a position to carry through a revolution which will make the existing wage earners into free workers, freely associated for the benefit of all.
For the Union to serve its own end and at the same time be a means for education and the terrain for propaganda aimed at a future radical social transformation, it is necessary that it should bring together all workers, or at least all those workers who aim at improving their conditions and whom one succeeds in rendering capable of some kind of resistance against the bosses. Does one perhaps want to wait for workers to be anarchists before inviting them to organise themselves and before admitting them to the organisations of resistance, when it would no longer be required because the masses would already be capable of making the revolution? In this case the Trade Union would be duplicating the role of the anarchist group and would remain impotent both in obtaining improvements and in making the revolution. Alternatively one has an anarchist programme on paper and is satisfied with formal, unconscious support, and so brings together people who follow the organisers sheep like, and who will disappear, or go over to the enemy, at the first opportunity in which it is really necessary to act as anarchists.
Trade Unionism is in its nature reformist. All that can be hoped from it is that the reforms which it demands and pursues are such and obtained in ways which serve revolutionary education and preparation and leave the way free to ever greater demands.
Every fusion or confusion between the anarchist movement and the trade union movement ends, either in rendering the latter unable to carry out its specific task or by weakening, distorting, or extinguishing the anarchist spirit.
The Union can emerge with a socialist, revolutionary, or anarchist programme, and indeed it is with such programmes that many workers' organisations were originally launched. But they remain faithful to the programme so long as they are weak and impotent, that is so long as they are propaganda groups, initiated and sustained by a few enthusiastic and convinced individuals rather than organisms capable of effective action; but then as they manage to attract the masses to their ranks, and acquire the strength to demand and impose improvements, the original programme becomes an empty slogan which no one bothers about, tactics are readjusted to contingent needs, and the enthusiasts of the first hour either adapt themselves or must make way for the "practical" men, who pay attention to the present without worrying about the future.
There certainly are comrades who in spite of being in the front rank of the trade union movement remain sincere and enthusiastic anarchists, as there are workers' groupings which seek their inspiration in anarchist ideas. But it would be a too easy way of criticising, to seek the thousand examples in which these men and these groups in the reality of their day to day actions are in contradiction with anarchist ideas. I agree that these are the hard facts of life.
One cannot act in an anarchist way when one is obliged to deal with employers and the authorities; one cannot let the masses act for themselves when they refuse to act and ask for, or demand, leaders. But why confuse anarchism with what anarchism is not, and why should we, as anarchists, shoulder the responsibility for transactions and compromises made necessary because the masses are not anarchist, not even if they belong to an organisation which has written the anarchist programme into its Constitution?
In my opinion anarchists must not want the Trade Unions to be anarchist, but they must act within their ranks in favour of anarchist aims, as individuals, as groups and as federations of groups. Just as there are, or there should be, study and discussion groups, propaganda groups working among the public with the written and spoken word, cooperative groups, factory groups, groups among the land workers, in the barracks as well as the schools, so special groups should be formed in the different organisations which engage in the class struggle.
Of course, it would be ideal if everyone was anarchist and that organisations functioned in an anarchist way; but in that case, it is clear that there would be no need to organise for the struggle against the employers, for there would no longer be bosses. But in the situation as it is, and recognising that the social development of one's workmates is what it is, the anarchist groups should not expect the workers' organisations to act as if they were anarchist, but should make every effort to induce them to approximate as much as possible to the anarchist method. If for the life of the organisation and for the needs and wishes of its members it is absolutely necessary to negotiate, to compromise, and establish doubtful contacts with the authorities, so be it; but this must be done by others, not by anarchists whose role is that of pointing to the insufficiency and precariousness of all improvements which can be obtained under a capitalist regime, and of pushing the struggle always towards more radical solutions. Anarchists in the Unions should struggle for them to be open to all workers whatever their views or party affiliations on the one condition: of solidarity in the struggle against the bosses; they should be opposed to the corporative spirit and any ambitions to a monopoly of organisation or work. They should prevent the Unions from serving as an instrument to be manipulated by politicians for electoral or other authoritarian ends; they should advocate and practice direct action, decentralisation, autonomy, and individual initiative; they should make special efforts to help members learn how to participate directly in the life of the organisation and to dispense with leaders and full-time functionaries.
In other words, they should remain anarchists, always in close touch with anarchists, and remembering that the workers' organisation is not the end, but just one of the means, however important, in preparing the way for the achievement of anarchism.
One must not confuse "syndicalism," which is intended to be a doctrine and a method for solving the social problem, with the promotion, the existence and the activities of the workers' Unions....
For us it is not all that important that the workers should want more or less; what is important is that they should try to get what they want, by their own efforts, by their _direct action_ against the capitalists and the government.
A small improvement achieved by one's own effort is worth more, in its effect on morale—materially too, in the long term—than a large scale reform granted by government or capitalists for doubtful ends or even out of the "kindness of their hearts."
We have always understood the vital importance of the workers' movement and the need for anarchists to play an active and forceful part in it. And often it has been as a result of the initiative of our comrades that workers' groups have been formed which are more lively and more progressive. We have always thought that the Trade Union is, today, a means whereby workers can begin to understand their position as slaves, to want their emancipation and to accustom themselves to the solidarity of all the oppressed in the struggle against the oppressors—and that tomorrow it will serve as the first necessary nucleus for the continuation of social life and the reorganisation of production without bosses and parasites.
But we have always discussed, and often disagreed, on the ways anarchist action had to be carried out in relation to the workers' organisation.
Should one join the Unions or stay out though taking part in all the struggles, seeking to make them as radical as possible, and always remaining in the forefront of action and danger?
And above all, whether anarchists should accept executive posts within the Unions, and thus lend themselves to those negotiations, compromises, adjustments, and contacts with the authorities and the employers, which the workers themselves demand of them and which are part and parcel of the day to day demands for better conditions or for the defence of concessions already won?
In the two years that followed the peace and up to the eve of the triumph of fascist reaction we found ourselves in a unique situation.
The revolution seemed imminent, and the material and spiritual conditions were, in fact, present to make a revolution possible as well as necessary.
But we anarchists lacked by a long chalk the necessary strength to make the revolution with our methods and relying exclusively on our numbers; we needed the masses, and they were quite prepared to take action, but they were not anarchist. In any case, a revolution without the support of the masses, even had it been possible, could have only resulted in a new domination, which even if exercised by anarchists would have always been the negation of anarchism, would have corrupted the new rulers and would have ended in the return of the Statist, capitalistic order.
To have withdrawn from the struggle, and abstained because we could not do just what we would have wished to do, would have been a renunciation of every present or future possibility, of every hope of developing the movement in the direction we wished it to go. It would have been renunciation for all time because there will never be anarchist masses until society has been economically and politically transformed, and the same problem will present itself each time circumstances create a situation with revolutionary possibilities.
It will therefore be necessary at all costs to win the confidence of the masses, and be in a position to "push" them when they are in the mood for action, and for this it seemed useful to secure executive posts in the workers' organisations. All the dangers of reformism, corruption were pushed into the background, and in any case it was assumed that there wouldn't be time for them to take effect.
So it was decided to leave everybody free to act according to the circumstances and as they thought best, conditional on their not forgetting that they were anarchists guided at all times by the overriding interest of the anarchist cause.
But now bearing in mind recent experience, and in view of the present situation... it seems to me that it would be useful to return to the question and see whether it is a case of modifying our tactic on this most important aspect of our activity.
In my opinion, we must join the Unions, because by remaining outside we appear inimical to them, our criticisms are viewed with suspicion and at a time of agitation we shall appear as intruders and our participation coldly received....
And so far as soliciting and accepting posts as leaders I believe that in general, and in calm periods, it is better to avoid doing so. But I believe that the damage and the danger lie not so much in the fact of occupying an executive post—which in certain circumstances can be useful and also necessary—but where the post becomes a permanent one. In my opinion, the executive personnel should be renewed as often as possible, both in order to give as many workers as possible experience of administrative jobs, as well as to prevent organisational work from becoming a profession and inducing those who do it from introducing into the workers' struggle concern about losing their jobs.
And all this not only in the interests of the present struggle and the education of the workers, but also, and what is more important, with an eye on the development of the revolution once it has started.
Anarchists are justifiably opposed to authoritarian communism, which presupposes a government wanting to direct every aspect of social life, and placing the organisation of production and the distribution of wealth under the orders of its nominees, which cannot but create the most hateful tyranny and the crippling of all the living forces in society.
The Unions, apparently in agreement with the anarchists in their aversion for State centralisation, want to dispense with the government putting the Unions in its place; and they say that it is the Unions which must take over the wealth, requisition all foodstuffs, and be responsible for their distribution as well as organise production and barter. And I would see nothing to object to in this if the Unions opened their doors wide to all the population, and left the dissidents free to act and to have their share.
But in practice this expropriation and this distribution cannot be effected impulsively, by the mass, even if in possession of a Union card, without producing a harmful waste of natural wealth and the sacrificing of the weaker to the stronger; and even more difficult would it be to establish by mass meetings, agreements between the different regions, and the barter arrangements between the various corporations of producers. Provision therefore would have to be made through decisions taken at popular assemblies and carried out by groups and individuals who have volunteered or are duly delegated.
Now, if there are a limited number of people who through long tenure of office are considered trade union leaders; if there are permanent secretaries and official organisers, it will be they who will automatically find themselves charged with organising the revolution, and they will tend to consider as intruders and irresponsible elements, those who want to take independent action, and will want to impose their will, even with the best of intentions—even by the use of force.
And then the "syndicalist regime" would soon become the same lie, the same tyranny which the so-called "dictatorship of the proletariat" has become. The remedy for this danger and the condition for the success of the revolution as a progressive force, is the "formation" of a large number of individuals with initiative and the ability to tackle practical tasks: by accustoming the masses not to leave the common cause in the hands of a few, and to delegate, when delegation is necessary, only for specific missions and for limited duration. And the syndicate, if organised and acting in a truly libertarian manner, is the most effective means to create just such a situation and just such a spirit.
The workers' Union was born out of the necessity to provide for present needs, out of the desire to improve personal conditions, and to protect oneself from a possible worsening of conditions, and is the Union of those who, deprived of the means of production and thus obliged by the exigencies of life to allow themselves to be exploited by those who possess the means, seek, through solidarity with their companions in misery, the strength to struggle against the exploiters. And at this level of the economic struggle, that is, against capitalist exploitation, it would have been possible and easy to achieve the unity of the working class against the owning class.
It was not achieved because the political parties, which incidentally have often been the founders and the first animators of the Trade Union movement, wished to use the workers' associations as a recruiting centre as well as weapons for their particular ends, whether of revolution or conservatism. Hence the divisions within the working class, organised into many groupings under the influence of the political parties, and the concern, of those who want workers' unity, to remove the Unions from the tutelage of political parties. Buried under these intentions is an error and a lie.
If by politics is meant that which concerns the organisation of human relations, and more specifically, the free or limited relations between people and the existence or nonexistence of a "government" which assumes public powers and uses force to impose its will and defend its own interests and those of the class from which it springs, it is clear that politics enters into every expression of social existence, and that a workers' organisation cannot be truly independent of the parties except by itself becoming a party....
It is idle to hope, and in my opinion it would be a bad thing to wish, that politics should be excluded from the Unions, since every economic question of some importance automatically becomes a political question, and it is in the political field, that is, by the struggle between governors and governed, that the question of the emancipation of the workers and of human liberty will have to be finally resolved.
And it is natural, and clear, that it should be so....
The capitalists can maintain the struggle in the economic field so long as workers demand small, and generally illusory improvements; but as soon as they see their profits seriously diminished and the very existence of their privileges threatened, they appeal to government and if it is not sufficiently understanding and not strong enough to defend them, as in the recent cases of Italy and Spain, they use their own wealth to finance new repressive forces and to set up a new government which will serve them better.
Workers' organisations must therefore, of necessity, adopt a line of action in face of present as well as possible future government action.
One can accept the _status quo,_ recognise the legitimacy of economic privilege and the government that defends it, and be content to manoeuvre between the different bourgeois factions and obtain some improvements—as happens with the huge organisations which are inspired by no ideal, such as the American Federation of labour and a large part of the British Unions—and then one becomes in practice the tool of the oppressors and gives up the task of freeing oneself from servitude.
But if one aspires to complete emancipation or even if one only wants specific improvements which do not depend on the will of the boss or the whims of the Markets, there are but two ways of freeing oneself from the threat of government. Either by seizing the reins of government and using the public powers, and the collective force captured and held down by the rulers, to get rid of the capitalist system—or by weakening and destroying government by leaving to the workers and to all who in one way or another, by manual and intellectual work, cooperate in keeping social life going, the freedom to provide for individual and social needs in the way they consider best, but without the right or the possibility of imposing their will on others by the use of force. Now, how is it possible to maintain unity when there are some who would wish to use the strength of the organisation to get a seat in the government, while others believe that every government is of necessity oppressive and iniquitous, and would therefore wish to lead the organisation in the direction of struggle against every authoritarian institution now or in the future? How can social democrats, State communists and anarchists be held together?
This is the problem, and one which can be overlooked at certain moments, such as in a clearly defined struggle, when all are unanimous, but which always reemerges and is not easy to solve so long as conditions of violence, and a diversity of opinion as to the means for resisting violence, exist. The democratic method, that is, of leaving the majority to decide and of "maintaining discipline" does not solve the question, since it too is a lie and is not sincerely supported except by those who have or believe they have the majority on their side. Apart from the fact that the "majority" always means a majority among the leaders and not of the masses, one cannot expect, or even wish, that someone who is firmly convinced that the course taken by the majority leads to disaster, should sacrifice his own convictions and passively look on, or even worse, support a policy he considers wrong.
To say: let the others get on with it and you try in your turn to win over the majority to your point of view is rather similar to the argument used in the, army: "accept your punishment and then put in your complaint"—and it is an unacceptable system when what one does today destroys the possibility of doing otherwise tomorrow. There are matters over which it is worth accepting the will of the majority because the damage caused by a split would be greater than that caused by the error; there are circumstances in which discipline becomes a duty because to fail in it would be to fail in the solidarity between the oppressed and would mean betrayal in face of the enemy. But when one is convinced that the organisation is pursuing a course which threatens the future and makes it difficult to remedy the harm done, then it is a duty to rebel and to resist even at the risk of providing a split.
But then, what is the way out of this difficulty, and what should be the conduct of anarchists in the circumstances?
In my view the solution would be: general agreement and solidarity in the purely economic struggle; complete autonomy of individuals and groups in the political struggle.
But is it possible to see in time where the economic struggle becomes a political struggle? And are there any important economic struggles which do not become political right from the start as a result of government intervention?
In any case we anarchists should extend our activities into all organisations to preach unity among all workers, decentralisation, freedom of initiative, within the common framework of solidarity and not worry over much if the mania for centralisation and authoritarianism of some, or the intolerance to all, even reasonable, discipline by others, leads to new splits. For, if organisation of the workers is a fundamental necessity in the struggles of today and for the achievements of tomorrow, the existence, or the longevity of this or that particular organisation is not all that important. What is essential is that individuals should develop a sense of organisation and solidarity, and the conviction that fraternal cooperation is necessary to fight oppression and to achieve a society in which everybody will be able to enjoy his own life.
# **18. T HE OCCUPATION OF THE FACTORIES**
GENERAL STRIKES OF PROTEST NO LONGER UPSET ANYBODY; neither those who take part in them nor those against whom they are directed. If only the police had the intelligence to avoid being provocative, they would pass off as any public holiday.
One must seek something else. We put forward an idea: the take-over of factories. For the first attempt probably only a few will take part and the effect will be slight; but the method certainly has a future, because it corresponds to the ultimate ends of the workers' movement and constitutes an exercise preparing one for the ultimate general act of expropriation.
The metal workers started the movement over wage rates. It was a strike of a new kind. Instead of abandoning the factories, the idea was to remain inside without working, and maintain a night and day guard to ensure that the bosses could not operate the night shift. But this was in 1920. Throughout Italy there was revolutionary fervour among the workers and soon the demands changed their character. Workers thought that the moment was ripe to take possession once for all of the means of production. They armed themselves for defence, they transformed many factories into veritable fortresses, and began to organise production on their own. Bosses were either thrown out or held in a state of arrest.... It was the right of property abolished in fact, and the law violated in so far as it served to defend capitalist exploitation; it was a new regime, a new form of social life which was being ushered in. And the government stood by because it felt impotent to offer opposition: it admitted it later when apologising to Parliament for its failure to take repressive action.
The movement grew and showed signs of drawing in other categories of workers; here and there peasants occupied the land. It was the beginning of a revolution which was developing, I would say, almost in an ideal way.
The reformists naturally frowned on the movement, and sought to bring it down. The [socialist daily] _Avanti!_ not knowing which way to turn, tried to make out that we were pacifists, because in _Umanità Nova_ we had said that if the movement spread to all sectors of industry, that if workers and peasants had followed the example of the metallurgists, of getting rid of the bosses and taking over the means of production, the revolution would succeed without shedding a single drop of blood.
But this was of no avail. The masses were with us; we were called to the factories to speak, to encourage, and to advise the workers, and would have needed to be in a thousand places at once to satisfy all their requests. Wherever we went it was the anarchists' speeches which were applauded while the reformists had to withdraw or make themselves scarce.
The masses were with us because we were the best interpreters of their instincts, their needs, and interests.
Yet, the underhand work of the CGL and the agreements entered into with the Giolitti government to create the impression of a kind of victory through the sham of _workers control_ was sufficient to induce the workers to abandon the factories, at the very moment when their chances of success were greatest.
The occupation of the factories and the land suited perfectly our programme of action.
We did all we could, through our paper ( _Umanità Nova_ daily, and the various anarchist and syndicalist weeklies) and by personal action in the factories, for the movement to grow and spread. We warned the workers of what would happen to them if they abandoned the factories; we helped in the preparation of armed resistance, and explored the possibilities of making the revolution without hardly a shot being fired if only the decision had been taken to use the arms that had been accumulated.
We did not succeed, and the movement collapsed because there were too few of us and the masses were insufficiently prepared.
When D'Aragona [the secretary of the CGL] and Giolitti [the Prime Minister] concocted the farce of workers control with the acquiescence of the socialist party, which was at the time under communist leadership, we put the workers on their guard against the wicked betrayal. But as soon as the order to leave the factories was issued by the CGL, the workers, who though they had always received us and called for us with enthusiasm and who had applauded our incitement to all-out resistance, docilely obeyed the order, though they disposed of powerful military means for resistance.
The fear in each factory of remaining alone in the struggle, as well as the difficulty of laying-in food supplies for the various strong points induced everybody to give in, in spite of the opposition of individual anarchists dispersed among the factories.
The movement could not last and triumph without growing and spreading, and in the circumstances it could not grow without the support of the leaders of the CGL and the Socialist Party which disposed of the large majority of organised workers. Both Confederation and Socialist Party (including the communists) lined up against the movement and it all had to end in a victory for the bosses.
# **19. W ORKERS AND INTELLECTUALS**
THE ORIGIN OF THIS DIVISION OF MEN INTO "INTELLECTUALS" (who often are simply idle people without any intellectuality) and "workers" can be found in the fact that at times and in circumstances when to produce enough to amply satisfy one's needs demanded excessive and unpleasant effort, and when one ignored the advantages of solidarity and cooperation, the strongest or the more fortunate, found a way of obliging others to work for them. This manual work, apart from being more or less exhausting, also became a symbol of social inferiority; and thus the seigneurs willingly tired themselves and killed each other in equestrian exercises, dangerous and exhausting hunts, and wore themselves out in competitions, but would feel dishonoured at having to dirty their hands doing even the lightest productive job. Work was something for slaves to do; and such is still the case today in spite of greater knowledge and the advances in applied mechanics and science, which make it easy to provide in abundance for the needs of all by pleasant work, reasonable in its duration and in the physical effort demanded.
When everybody will have the free use of the means of production and no man will be able to oblige others to work for him, then it will be in the interests of all to organise work so that it is as productive and pleasant as possible—and then everybody will be able to pursue their studies, useful or useless, without thereby becoming parasites. There would be no parasites, firstly because no one would want to keep parasites and then because everybody would find that by giving their share of manual labour towards production they would at the same time satisfy their body's need for physical activity.
All would work, including the poets and the transcendental philosophers, without any ill effects to poetry or philosophy. On the contrary....
We have no "working class" prejudices, no preferences for the manual worker because he is a manual worker, and above all no admiration for the uneducated and the illiterates, who, nevertheless, have the valid excuse, that their condition is not their fault.
We are revolutionaries, and know that a revolution made without the participation of forces and values which cannot be acquired without an intellectual background, could well appear to be radical, but in fact would be no more than an explosion of anger without significance and without a future. And for this reason we always welcome with open arms the support of writers, artists, scientists, engineers, technicians, and others who can offer the concourse of intellects rich in ideas and informed by facts.
But on the other hand we know that most of the so-called intellectuals are, by reason of their education, their family background, their class prejudices, tied to the Establishment, and tend to want the subjection of the mass of the people to their will. Whereas the mass of workers, even if they are ignorant or illiterate, constitute, because of their needs and their passion for justice which comes to them from the injustice to which they are subjected, the principal force behind the revolution and the guarantee that it will not resolve itself into a simple change of masters.
Therefore we accept the intellectuals with pleasure and without suspicion when they fuse with the working class, when they join the people without pretensions to command; without a patronising air of condescension, but with the open mind of someone who comes in the midst of brothers to repay them the debt he has contracted in educating himself and cultivating his intellect which, in most cases, is at the expense of the children of those whose manual work has produced the means.
Emma Goldman [in "My further Disillusionment in Russia"] gives as among the main causes for the failure of the Russian revolution the hostility, the hatred that workers felt for the intellectuals, and their contempt for science and the things of the mind.
This doesn't seem to me to be quite correct.
Workers have even too much respect and admiration for educated people... who very often have very little education. And this attitude is both a good thing as well as bad. For there are all kinds of intellectuals, revolutionary and reactionary, good ones and bad ones, and above all harmful ones as well as useful ones, depending on the subject to which they have directed their studies and their activities. There are scientists, doctors, engineers, artists, and teachers, but there are also priests, lawyers, politicians, and militarists.
Thus it is in Italy, and I imagine it must be the same in Russia, since one observes that all, or at least almost all, the leaders of the Russian revolution, are intellectuals; indeed one can say that the struggle has taken place between intellectuals while the mass, as is usual, has served as the instrument [in their struggle].
Surely so long as science and higher education will be a privilege of the few (and it will be so so long as existing economic conditions prevail) it is inevitable that those who have knowledge will predominate over those who haven't; but to prevent this preponderance from being a reason and a means to perpetuate present evils or to create new privileges and new tyrannies, one must at the same time stress the glory of science and the usefulness and the need for technical direction, and inspire those who are ignorant with the desire to educate and raise themselves, but one must also make them feel and understand that ignorance is not a reason for being oppressed and ill-treated, but rather gives one a right to greater consideration by way of compensation for being deprived of those things that are among the best in human civilisation.
And "intellectuals," who have had the good fortune of receiving an education, if they take part in a revolution through a sincere love for the good of others, must put themselves at the level of the least fortunate to help them to raise themselves, and not look upon the mass as a flock to lead... and to fleece, depriving them thereby of the chance of educating themselves in responsibility and freedom, and even worse, obliging them to obedience by recourse to the _gendarmes. 3_
What we would call the natural tendency of intellectuals, is to keep apart from the people, and to form themselves into coteries; to give themselves airs and end up by believing themselves protectors and saviours who the masses should worship... and maintain. To separate them from the masses, to give them the illusion of fighting for the general good while they enjoy advantages and different standards of life, will encourage just what the drafters of the Appeal [for an International of Intellectuals] so rightly deprecate: the formation of "a harmful and dangerous caste" inside the working-class movement.
And in any case, what could be the activity and the mission of this special International?
If it were a question of an association, such as already exist, to help in the study of science, history and literature, or in order to disseminate a general culture among the people, the project might be possible and useful. And all enlightened people irrespective of party and class could play a part in such a venture. The truth, science, is neither bourgeois nor proletarian, neither revolutionary nor conservative, and everybody can feel interested in its progress.
But what is proposed is an organisation for struggle, an organisation which wants to take its place in the social struggle. And in that case how could men be held together and work usefully, who, even if they more or less share equal final objectives, pursue different means, belong to rival political parties and who in every practical issue would find themselves lined up against each other? How can pacifists and war supporters, revolutionaries and legalitarians, democrats and totalitarians, authoritarians and anarchists be made to agree?
In practice this is what must happen to every Intellectual International, which is neither a purely scientific and a political institution nor an organisation closely linked to one party. A few pompous manifestoes, the decorative support of a few "big names," of those who through vanity or laziness always say yes... followed by a fictitious, rickety and useless existence. And even this mere preteens of life would not continue without creating a bureaucracy interested in the continuation of the organisation... and in its salaries. This bureaucracy, once the founders tire and withdraw, would manage for a long time to fill the members lists with the names of thousands who knowing how to read and write more or less well, enjoy giving themselves airs of being writers.
But in what way would this be useful to the cause?
For these reasons I believe that our friends who have got caught up in this venture would do well to repeat, at a distance of fifty years, Michael Bakunin's gesture when having declared at a Congress of the Association for Peace and Liberty, that peace and liberty could not be secured except by struggle among the workers for social justice, he abandoned that Association, which was also a kind of International of intellectuals, and, with the revolutionary socialist minority attending the Congress, joined the International Workers' Association....
# **20. A NARCHISM, SOCIALISM, AND COMMUNISM**
IT IS TRUE THAT ANARCHISTS AND SOCIALISTS HAVE ALWAYS profoundly disagreed in their concepts of historic evolution and the revolutionary crises that this evolution creates, and consequently they have hardly ever been in agreement on the means to adopt, or the opportunities that have existed from time to time to open up the way towards human emancipation.
But this is only an incidental and minor disagreement.
There have always been socialists who have been in a hurry, just as there are also anarchists who want to advance with leaden feet, and even some who do not believe at all in revolution. The important, fundamental dissension is quite another: socialists are authoritarians, anarchists are libertarians.
Socialists want power, whether by peaceful means or by force is of no consequence to them, and once in office, wish to impose their programme on the people by dictatorial or democratic means. Anarchists instead maintain, that government cannot be other than harmful, and by its nature it defends either an existing privileged class or creates a new one; and instead of aspiring to take the place of the existing government anarchists seek to destroy every organism which empowers some to impose their own ideas and interests on others, for they want to free the way for development towards better forms of human fellowship which will emerge from experience, by everybody being free and, having, of course, the economic means to make freedom possible as well as a reality.
It seems unbelievable that even today, after what has happened and is happening in Russia [1921], there are still people who imagine that the differences between socialists and anarchists is only that of wanting the revolution slowly or in a hurry.
The democratic socialist party... was born in Italy as a consequence of our mistakes and of the degeneration of the revolutionary spirit among the people; and it will fall, or be reduced to a party of mere politicians, when we, having learned from past failures, are able to be active among the masses, and create a revolutionary spirit in the Italian people.
In any case the democratic socialists would be wrong if they were to seek to draw profit from these "confessions of an anarchist," since we owe our mistakes, common to all the old revolutionary schools, in large measure to Marxist theories, which we anarchists have all shared at some time, in a more logical if less orthodox manner than those professing to be Marxists (not excluding Marx himself possibly) but we have been shedding these theories as we have freed ourselves from the errors of Marxism.
From 1871, when we began our propaganda in Italy, we have always been, and have always called ourselves _socialist-anarchists._ In conversation, we would also call ourselves just anarchists, because it was understood that the anarchists were socialists, just as in earlier days, when we were the only socialists in Italy, we often called ourselves simply socialists, since it was generally understood that socialists were also anarchists. We have always been of the opinion that socialism and anarchy are two words which basically have the same meaning, since it is not possible to have economic emancipation (abolition of property) without political emancipation (abolition of government) and vice versa.
Social democrats start off from the principle that the State, government, is none other than the political organ of the dominant class. In a capitalistic society, they say, the State necessarily serves the interests of the capitalists and ensures for them the right to exploit the workers; but that in a socialist society, when private property were to be abolished, and with the destruction of economic privilege class distinctions would disappear, then the State would represent everybody and become the impartial organ representing the social interests of all members of society.
Here a difficulty immediately arises. If it be true that Government is necessarily, and always, the instrument of those who possess the means of production, how can this miracle of a socialist government arising in the middle of a capitalist regime with the aim of abolishing capitalism, come about? Will it be as Marx and Blanqui wished by means of a dictatorship imposed by revolutionary means, by a _coup de force,_ which by revolution decrees and imposes the confiscation of private property in favour of the state, as representative of the interests of the collectivity? Or will it be, as apparently all Marxists, and most modern Blanquists believe, by means of a socialist majority elected to Parliament by universal suffrage? Will one proceed in one step to the expropriation of the ruling class by the economically subjected class, or will one proceed gradually in obliging property owners and capitalists to allow themselves to be deprived of all their privileges a bit at a time?
All this seems strangely in contradiction with the theory of "historic materialism" which is a fundamental dogma for Marxists....
"Communism is the road that leads in the direction of anarchism." This is the theory of the Bolsheviks; the theory of Marxists and authoritarian socialists of all schools. All recognise that anarchy is a sublime ideal, that it is the goal towards which mankind is, or should, be moving, but they all want to become the government, to oblige the people to take the right road. Anarchists say instead, that anarchy is the way that leads to communism... or elsewhere.
To achieve communism before anarchy, that is before having conquered complete political and economic liberty, would mean (as it has meant in Russia) stabilising the most hateful tyranny, to the point where people long for the bourgeois regime, and to return later (as will happen in Russia) to a capitalistic system as a result of the impossibility of organising a social life which is bearable and as a reaction of the spirit of liberty which is not a privilege of the "latin spirit" as the _Communist_ foolishly accuses me of saying, but a necessity of the human spirit for action in Russia no less than in Italy.
However much we detest the democratic lie, which in the name of the "people" oppresses the people in the interests of a class, we detest even more, if that is possible, the dictatorship which, in the name of the "proletariat" places all the strength and the very lives of the workers in the hands of the creatures of a so-called communist party, who will perpetuate their power and in the end reconstruct the capitalist system for their own advantage.
When F. Engels, perhaps to counter anarchist criticisms, said that once classes disappear the State as such has no _raison d'être_ and transforms itself from a government over men into an administration of things, he was merely playing with words. Whoever has power over things has power over men; whoever governs production also governs the producers; who determines consumption is master over the consumer.
This is the question; either things are administered on the basis of free agreement among the interested parties, and this is anarchy; or they are administered according to laws made by administrators and this is government, it is the State, and inevitably it turns out to be tyrannical.
It is not a question of the good intentions or the good will of this or that man, but of the inevitability of the situation, and of the tendencies which man generally develops in given circumstances.
What is the true basis of the differences between anarchists and State communists? We are for freedom, for the widest and most complete freedom of thought, organisation, and action. We are for the freedom of all, and it is therefore obvious, and not necessary to continually say so, that everyone in exercising his right to freedom must respect the equal freedom of everybody else: otherwise there is oppression on one side and the right to resist and to rebel on the other.
But State communists, to an even greater extent than all other authoritarians, are incapable of conceiving freedom and of respecting for all human beings the dignity that they expect, or should expect, from others. If one speaks to them of freedom they immediately accuse one of wanting to respect, or at least tolerate, the freedom to oppress and exploit one's fellow beings. And if you say that you reject violence when it exceeds the limits imposed by the needs of defence, they accuse you of... pacifism, without understanding that violence is the whole essence of authoritarianism, just as the repudiation of violence is the whole essence of anarchism.
Monarchy is the most suitable political form to impose respect for the privileges of a closed caste; and thus every aristocracy, whatever the circumstance by which it has come into being, tends to establish a monarchical regime, openly or disguised; just as every monarchy, tends to create and perpetuate an all-powerful aristocracy. The Parliamentary system, that is the republic (since constitutional monarchy is in fact only a half-way system in which the function of parliament is still cluttered up with monarchical and aristocratic hangovers) is the most convenient system for the bourgeoisie; and every republic tends in the direction of the constitution of a bourgeois class, just as, on the other hand, at heart, if not in appearances, the bourgeoisie is always republican.
But which is the political form most readily adaptable to the realisation of the principle of solidarity in human relations? What is the method which most surely can lead us to the complete and definite triumph of socialism?
Of course it is not possible to answer this question with absolute certainty because one is dealing with things that have not yet taken place, and logical deductions necessarily lack the evidence of experience. One must therefore be satisfied with the solution which seems to offer the greatest possibilities of success. But that element of doubt, which always remains in the human spirit when it is a question of historical prediction, and which is like a door which has been left open in the human brain to receive new truths, must make us more tolerant and more disposed to be cordially sympathetic towards those who seek the same goals but by other roads, without, however, paralyzing our action or preventing us from choosing our way and following it resolutely.
The basic characteristic of socialism is its equal application to all members of society. For this reason no one must be in a position to exploit the labour of another by capturing the means of production, and no one must be able to impose his will on others by means of brute force, or, which is the same thing, by capturing political power: economic exploitation and political domination being two continually interacting aspects of the same thing—the subjection of man by man.
To attain to, and consolidate socialism it would seem that a means is needed which cannot at the same time be a source of exploitation and domination and lead to a form of organisation which is most readily adaptable to the different and varied interests and preferences of individuals and human groups. This means it cannot be _dictatorship (monarchy, caesarism, etc.)_ since it replaces the will and intelligence of all by that of one or a few; it tends to impose on everybody universal rules in spite of a difference in conditions; it creates the necessity for an armed force to impose obedience on recalcitrants; it gives rise to rival interests among the masses and those who are closest to power; and it ends either with successful rebellion or in the consolidation of a ruling class, which, of course, also becomes the owning class. Neither does _parliamentarism (democracy, republic)_ appear to be a good means since it too substitutes the will of a few for that of all, and if on the one hand it allows a little more freedom than dictatorship, on the other it creates greater illusions, and in the name of a fictitious collective interest, rides roughshod over every real interest, and by means of elections and the vote, disregards the wishes of each and everyone.
There remains free organisation, from below upwards, from the simple to the complex, through free agreement and the federation of associations of production and consumption, that is _anarchy._ And this is the means we prefer.
For us, then, _socialism_ and anarchy are neither antagonistic nor equivalent terms; but they are terms which are closely linked, just as the ends is linked to its necessary means, just as the substance is linked to the form it embodies.
Socialism without anarchy, that is State socialism, seems impossible to us, since it would be destroyed by the very organism destined to support it. Anarchy without socialism seems equally impossible to us, for in such a case it could not be other than the domination of the strongest, and would therefore set in motion right away the organisation and consolidation of this dominion, that is to the constitution of government.
# **21. A NARCHISTS AND THE LIMITS OF POLITICAL CO-EXISTENCE**
**"E** VERYWHERE AND AT ALL TIMES, ESPECIALLY SINCE MY RETURN to Italy [1919] I have repeatedly stated that a union of intent is possible, in spite of our disagreements, to bring about real and lasting results which will really allow the workers to conquer well-being and freedom. Not only have I repeatedly declared that it is possible; I also believe it to be necessary."
"You mean to say that it is necessary for the revolution..."
"Certainly! If we anarchists could achieve the revolution on our own, or if the socialists could on their own, we could enjoy the luxury of each acting independently and of perhaps quarrelling. But the revolution will be made by all the proletariat, all the people, whereas the socialists and anarchists are a numerical minority, though they appear to enjoy the sympathy of the people as a whole. For us to be divided even where there are grounds for unity, would mean dividing the workers, or rather, cooling off their sympathies, as well as making them less likely to follow the socialistic line common to both socialists and anarchists and which is at the heart of the revolution. It is up to the revolutionaries, especially the anarchists and socialists, to see to this by not exaggerating the differences and paying attention above all to the realities and objectives which can unite us and assist us to draw the greatest possible revolutionary advantage from the [present] situation."
Sandomirsky is for the United Front. I am too when it can be achieved in the interests of a liberating revolution.
Meantime, though having no faith left in the revolutionary capacity of the Bolsheviks, I again urge and hope that they will not descend to the level of, or even lower than, the American executioner, the Spanish torturer or the Italian jailer, and will understand that the least they can do is to put an end to the persecutions and set free anarchists and other political prisoners.
Alone we cannot subdue fascism, even less destroy existing institutions. So either we must unite with those who, though not anarchists, share short term, common objectives with us, or allow that the fascists, with the connivance of the government, should be free to terrorise the country, or that the monarchy should go on ruling undisturbed.
But in "revolutionary alliances" one is always "betrayed." Possibly one is. But we prefer to run the risk of being betrayed by others, than betray ourselves to the point of extinction through inaction.
Even the betrayals will not be entirely useless, since they will show the workers who is on their side, and show the revolutionaries who among them really wants to make the revolution.
In recent years we have approached the different avant-garde parties with a view to joint action, and we have always been disappointed. Must we for this reason isolate ourselves, or take refuge from "impure" contacts and stand still trying to move only when we have the necessary strength and in the name of our complete programme? I think not.
Since we cannot make the revolution by ourselves... we should be prepared to support those who are prepared to act, even if it carries with it the risk of later finding ourselves alone and betrayed.
But in giving others our support, that is, in always trying to use the forces at the disposal of others, and taking advantage of every opportunity for action, we must always be ourselves and seek to be in a position to make our influence felt and count at least in direct proportion to our strength.
To this end it is necessary that we should be agreed among ourselves and seek to coordinate and organise our efforts as effectively as possible.
Certainly, it is very difficult to distinguish clearly in practice where useful cooperation against the common enemy ends and where a fusion begins which would lead the weakest party to renounce its specific aims....
We should find ourselves on the one hand alongside the republicans in the revolutionary act and on the other in agreement with the communists in expropriating the bourgeoisie, assuming they were prepared to carry it out in a revolutionary way without first waiting to establish their state, their dictatorship. But not for these reasons would we become republicans or State communists.
We can have relations of cooperation with non-anarchist parties so long as we share a need to fight a common enemy and are unable to destroy him unaided; but as soon as a party takes power and becomes the government, the only relations we can have with it are those between enemies.
Of course it is in our interest that so long as government exists it should be as unoppressive as possible, the less it is a government the better.
But freedom, even a relative freedom, is not won by helping government but by making it feel the danger of squeezing the people too far.
We have always sought to achieve the alliance of all who want to make a revolution in order to destroy the material power of the common enemy, but we have always made it crystal clear that such an affiance should last only for the duration of the insurrectionary act itself, and that immediately after and, if possible or necessary, during the insurrection itself, we would seek to realise our ideas by resisting the formation of a new government or of any centralised authority, and by seeking to urge the masses to take immediate possession of all the means of production and the social wealth, and themselves organise the day to day affairs of the community on the basis of its state of development and the wishes of the people in the different regions.
For my part, I do not believe there is "one solution" to the social problems, but a thousand different and changing solutions in the same way as social existence is different and varied in time and space.
After all, every institution, project or utopia would be equally good to solve the problem of human contentedness, if everybody had the same needs, the same opinions or lived under the same conditions. But since such unanimity of thought and identical conditions are impossible (as well as, in my opinion, undesirable) we must in our daily conduct as well as in our projects for the future, always bear in mind that we are not, and will not in the foreseeable future, be living in a world populated only by anarchists. For a long time to come we shall be a relatively small minority. To isolate ourselves is virtually impossible, but even if we could it would be at the expense of the social task we have undertaken, as well as of our own personal well-being. One must therefore find ways of living among non-anarchists, as anarchistically as possible, and which will further our propaganda and offer possibilities of applying our ideas.
# **V**
# **22. T HE ANARCHIST REVOLUTION**
THE REVOLUTION IS THE CREATION OF NEW LIVING INSTITUTIONS, new groupings, new social relationships; it is the destruction of privileges and monopolies; it is the new spirit of justice, of brotherhood, of freedom which must renew the whole of social life, raise the moral level and the material conditions of the masses by calling on them to provide, through their direct and conscious action, for their own futures. Revolution is the organisation of all public services by those who work in them in their own interest as well as the public's; Revolution is the destruction of all coercive ties; it is the autonomy of groups, of communes, of regions; Revolution is the free federation brought about by a desire for brotherhood, by individual and collective interests, by the needs of production and defence; Revolution is the constitution of innumerable free groupings based on ideas, wishes, and tastes of all kinds that exist among the people; Revolution is the forming and disbanding of thousands of representative, district, communal, regional, national bodies which, without having any legislative power, serve to make known and to coordinate the desires and interests of people near and far and which act through information, advice and example. Revolution is freedom proved in the crucible of facts—and lasts so long as freedom lasts, that is until others, taking advantage of the weariness that overtakes the masses, of the inevitable disappointments that follow exaggerated hopes, of the probable errors and human faults, succeed in constituting a power, which supported by an army of conscripts or mercenaries, lays down the law, arrests the movement at the point it has reached, and then begins the reaction.
The great majority of anarchists, if I am not mistaken, hold the view that human perfectibility and anarchy would not be achieved even in a few thousand years, if first one did not create by the revolution, made by a conscious minority, the necessary environment for freedom and well-being. For this reason we want to make the revolution as soon as possible, and to do so we need to take advantage of all positive forces and every favourable situation that arises.
The task of the conscious minority is to profit from every situation to change the environment in a way that will make possible the education and spiritual elevation of the people, without which there is no real way out.
And since the environment today, which obliges the masses to live in misery, is maintained by violence, we advocate and prepare for violence. That is why we are revolutionaries, and not because "we are desperate men, thirsting for revenge and filled with hate."
We are revolutionaries because we believe that only the revolution, the violent revolution, can solve the social question.... We believe furthermore that the revolution is an act of will—the will of individuals and of the masses; that it needs for its success certain objective conditions, but that it does not happen of necessity, inevitably, through the single action of economic and political forces.
I told the jury [at my trial] in Milan that I am a revolutionary not only in the philosophical meaning of the word but also in the popular and insurrectionalist sense; and I said so in order to clearly distinguish between my views and those of others who call themselves revolutionaries, but who interpret the world even astronomically so as not to have to bring in the fact of violence, the insurrection, which must open the way to revolutionary achievements. I declared that I had not sought to provoke revolution because at the time there was no need to provoke it; what was urgently needed instead was to bend all our efforts for the generally desired revolution to succeed and not lead to new tyrannies; but I insisted that I would have provoked it if the situation demanded then, just as I would in a similar situation in the future.
I had said "we want to make the revolution as soon as possible"; Colomer replies that it would be wiser to say "We want to make anarchy as soon as possible." A poor polemical expedient! Since we are convinced that anarchy cannot be achieved until after the revolution which will sweep away the first material obstacles, it is clear that our efforts must in the first instance be directed to making the revolution and in such a way that it is in the direction of anarchy.... I have repeated thousands of times that we would have to provoke the revolution with all the means at our disposal and act in it as anarchists, that is to say, opposing the constitution of any authoritarian regime and putting into operation as much as we can of our programme. And I would wish that, to take advantage of the increased freedom that we would have won, anarchists were morally and technically prepared to realise within the limits of their numbers, those forms of social life and cooperation which they consider best and most suitable for paving the way for the future.
We do not want to "wait for the masses to become anarchist before making the revolution," the more so since we are convinced that they will never become anarchist if the institutions which keep them enslaved are not first violently destroyed. And since we need the support of the masses to build up a force of sufficient strength and to achieve our specific task of radical change of the social organism by the direct action of the masses, we must get closer to them, accept them as they are, and from within their ranks seek to "push" them forward as much as possible. That is, of course, if we really intend to work for the practical achievement of our ideals, and are not content with preaching in the desert for the simple satisfaction of our intellectual pride.
We are accused of a "reconstructive mania"; we are told that to speak of the "morrow of the revolution" as we do, is a meaningless phrase because the revolution is a profound change in the whole of social life, which has already started and will go on for centuries to come.
All this is simply a misuse of words. If one takes revolution in that sense, it is synonymous with progress, with a historic view of life, which through a thousand and one vicissitudes will end, if our wishes come true, in the total triumph of anarchy throughout the world. In that sense all kinds of people are revolutionary. When you introduce the centuries into the argument, everyone will agree with everything you say.
But when we speak of revolution, when the masses speak of it, as when one refers to it in history, one simply means the _insurrection triumphant._ Insurrections will be necessary as long as there are power groups which use their material force to exact obedience from the masses. And it is only too clear that there will be many more insurrections before the people win that minimum of indispensable conditions for free and peaceful development, when humanity will be able to advance towards its noblest objectives without cruel struggles and useless suffering.
By revolution we do not mean just the insurrectionary act, which is nevertheless indispensable (except in the most unlikely event that the existing regime collapses without the need for a push from outside), but would be sterile if it served to replace one state of coercion by another.
One must clearly distinguish between the revolutionary act which destroys as much as it can of the old regime and puts in its place new institutions, and government which comes afterwards to halt the revolution and suppress as many of the revolutionary conquests as it can.
History teaches us that all advances that are the result of revolutions were secured in the period of popular enthusiasm, when either a recognised government did not exist or was too weak to make a stand against the revolution. But once the government was formed, so reaction started which served the interest of the old and the new privileged classes and took back from the masses all that it could.
Our task then is to make, and to help others make, the revolution by taking advantage of every opportunity and all available forces: advancing the revolution as much as possible in its constructive as well as destructive role, and always remaining opposed to the formation of any government, either ignoring it or combating it to the limits of our capacities.
We will no more recognise a republican Constituent than we now recognise the parliamentary monarchy. We cannot stop it if the people want it; we might even occasionally be with them in fighting attempts to bring about a restoration [of the monarchy]; but we will want and will demand complete freedom for those who think as we do and who wish to live outside the tutelage and oppression of the State, to propagate their ideas by word and deed. Revolutionaries, yes; but above all anarchists.
1. Destruction of all political power is the first duty of the proletariat.
2. Any organisation of an allegedly provisional revolutionary political power to achieve this destruction cannot be other than one trick more, and would be as dangerous to the proletariat as are all present governments.
3. In refusing every compromise for the achievement of the social revolution, workers of the world must establish solidarity in revolutionary action outside the framework of bourgeois politics.
These [anarchist] principles [as formulated in 1872 at the Congress of St. Imier under the inspiration of Bakunin] continue to point to the right road for us. Those who have tried to act in contradiction to them have disappeared, because however defined, State, dictatorship, and parliament can only lead the masses back to slavery. All experience so far bears this out. Needless to say, for the delegates of St. Imier as for us and all anarchists, the abolition of political power is not possible without the simultaneous destruction of economic privilege.
The conviction, which I share, of those who see the need for a revolution to eliminate the material forces which exist to defend privilege and to prevent every real social progress, has led many of them to believe that the only important thing is the insurrection, and to overlook what has to be done to prevent an insurrection from remaining a sterile act of violence against which an act of reactionary violence would be the eventual reply. For these comrades all practical questions, of organisation, of how to make provisions for the distribution of food, are today idle questions: for them these are matters which will solve themselves, or will be solved by those who come after us.... Yet the conclusion we come to is: Social reorganisation is something we must all think about right now, and as the old is destroyed we shall have a more human and just society as well as one more receptive to future advances. The alternative is that "the leaders" will think about these problems, and we shall have a new government, which will do exactly as all previous governments have done, in making the people pay for the scant and poor services they render, by taking away their freedom and allowing them to be oppressed by every kind of parasite and exploiter.
I say that in order to abolish the "gendarme" and all the harmful social institutions we must know what to put in their place, not in a more or less distant future but immediately, the very day we start demolishing. One only destroys, effectively and permanently, that which one replaces by something else; and to put off to a later date the solution of problems which present themselves with the urgency of necessity, would be to give time to the institutions one is intending to abolish to recover from the shock and reassert themselves, perhaps under other names, but certainly with the same structure.
Our solutions may be accepted by a sufficiently large section of the population and we shall have achieved anarchy, or taken a step towards anarchy; or they may not be understood or accepted and then our efforts will serve as propaganda and place before the public at large the programme for a not distant future. But in any case we must have our solutions: provisional, subject to correction and revision in the light of experience, but we must have our solutions if we do not wish to submit passively to those of others, and limit ourselves to the unprofitable role of useless and impotent grumblers.
I believe that we anarchists, convinced of the validity of our programme, must make special efforts to acquire a predominating influence in order to be able to swing the movement towards the realisation of our ideals; but we must acquire this influence by being more active and more effective than the others. Only in this way will it be worth acquiring. Today, we must examine thoroughly, develop and propagate our ideas and coordinate our efforts for common action. We must act inside the workers' movement to prevent it from limiting itself to, and being corrupted by, the exclusive demand for the small improvements possible under the capitalist system, and seek to make it serve for the preparation of the complete social transformation. We must work among the mass of unorganised, and possibly unorganisable, workers, to awaken in them the spirit of revolt and the desire and hope for a free and happy existence. We must initiate and support every possible kind of movement which tends to weaken the power of the State and of the capitalists and to raise the moral level and material conditions of the workers. We must, in a word, get ready and prepare, morally and materially, for the revolutionary act which has to open the way to the future.
And tomorrow, in the revolution, we must play an active part (if possible before, and more effectively, than the others) in the necessary physical struggle, seeking to make it as radical as possible, in order to destroy all the repressive forces of the State and to induce the workers to take possession of the means of production (land, mines, factories, transport, etc.) and of all existing goods, and themselves organise, immediately, a just distribution of food products. At the same time we must arrange for the exchange of goods between communes and regions and continue and intensify production and all those services which are of use to the public.
We must, in every way possible, and in accord with local conditions and possibilities, encourage action by workers' associations, cooperatives, groups of volunteers—in order to prevent the emergence of new authoritarian groups, new governments, combating them with violence if necessary, but above all, by rendering them useless.
And if there were not sufficient support among the people to prevent the reconstitution of the State, its authoritarian institutions and its organs of repression, we should refuse to cooperate or recognise it, and rebel against its demands, claiming full autonomy for ourselves and for all dissident minorities. In short we should remain in a state of open rebellion if possible, and prepare the way to convert present defeat into a future success....
I do not think that what matters is the triumph of our plans, our projects and our utopias, which in any case will need the confirmation of experiment, and may as a result have to be modified, developed or adapted to the true moral and material conditions in time and place. What matters most of all is that the people, all people, should lose their sheeplike instincts and habits with which their minds have been inculcated by an age-long slavery, and that they should learn to think and act freely. It is to this great task of spiritual liberation that anarchists must especially devote their attention.
Once the government has been overthrown, or at least neutralised, it will be the task of the people, and especially of those among them who have initiative and organising ability, to provide for the satisfaction of immediate needs and to prepare for the future by destroying privileges and harmful institutions and in the meantime seeing to it that those useful institutions which today serve the ruling class either exclusively or principally, shall operate in favour of all.
Anarchists will have the special mission of being the vigilant custodians of freedom, against all aspirants to power and against the possible tyranny of the majority.
We are agreed in thinking that apart from the problem of assuring victory against the material forces of the adversary there is also the problem of giving life to the revolution after victory.
We are in agreement that a revolution which were to result in chaos would not be a vital revolution.
But one must not exaggerate; it should not be thought that we must, and can, find, here and now, a perfect solution for every possible problem. One should not want to foresee and determine too much, because instead of preparing for anarchy we might find ourselves indulging in unattainable dreams or even becoming authoritarians, and consciously or otherwise, proposing to act like a government which in the name of freedom and the popular will subject people to its domination.... The fact is that one cannot educate the masses if they are not in a position, or obliged by necessity, to act for themselves, and that the revolutionary organisation of the workers, useful and necessary as it is, cannot be stretched indefinitely: at a certain point if it does not erupt in revolutionary action, either the government strangles it or the organisation itself degenerates and breaks up—and one has to start all over again from the beginning.
I would be unable to accept the view that all past revolutions though they were not anarchist revolutions were useless, nor that future ones which will still not be anarchist will be useless. Indeed, I incline to the view that the complete triumph of anarchy will come by evolution, gradually, rather than by violent revolution: when an earlier or several earlier revolutions will have destroyed the major military and economic obstacles which are opposed to the spiritual development of the people, to increasing production to the level of needs and desires, and to the harmonising of contrasting interests.
In any case, if we take into account our sparse numbers and the prevalent attitudes among the masses, and if we do not wish to confuse our wishes with the reality, we must expect that the next revolution will not be an anarchist one, and therefore what is more pressing, is to think of what we can and must do in a revolution in which we will be a relatively small and badly armed minority.... But we must, however, beware of ourselves becoming less anarchist because the masses are not ready for anarchy. If they want a government, it is unlikely that we will be able to prevent a new government being formed, but this is no reason for our not trying to persuade the people that government is useless and harmful or of preventing the government from also imposing on us and others like us who don't want it. We will have to exert ourselves to ensure that social life and especially economic standards improve without the intervention of government, and thus we must be as ready as possible to deal with the practical problems of production and distribution, remembering, incidentally, that those most suited to organise work are those who now do it, each in his own trade.... If we are unable to prevent the constitution of a new government, if we are unable to destroy it immediately, we should in either case refuse to support it in any shape or form. We should reject military conscription and refuse to pay taxes. Disobedience on principle, resistance to the bitter end against every imposition by the authorities, and an absolute refusal to accept any position of command.
If we are unable to overthrow capitalism, we shall have to demand for ourselves and for all who want it, the right of free access to the necessary means of production to maintain an independent existence.
Advise when we have suggestions to offer; teach if we know more than others; set the example for a life based on free agreement between individuals; defend even with force if necessary and possible, our autonomy against any government provocation... but command—never.
In this way we shall not achieve anarchy, which cannot be imposed against the wishes of the people, but at least we shall be preparing the way for it.
# **23. T HE INSURRECTION**
BUT HOW WILL THIS REVOLUTION BE ACHIEVED?
Naturally one must begin with the insurrectionary act which sweeps away the material obstacles, the armed forces of the government which are opposed to any social transformation.
For the insurrection it is desirable, and it may well be indispensable, that all the anti-monarchical forces, since we are living under a monarchist regime, should be united. It is necessary to be as prepared as possible, morally and materially; and it is above all necessary to profit by all agitations and to seek to extend them and transform them into resolutive movements, to avoid the danger that while the organisations are getting ready the popular forces exhaust themselves in isolated actions.
The masses will make the insurrection, but cannot prepare it technically. Men, groups, and parties are needed who are joined by free agreement, under oath of secrecy, and provided with the necessary means to create the network of speedy communications to keep those concerned informed of all incidents likely to provoke a widespread popular movement.
And when we say that the specific task of organisation must be carried outside the official parties it is because the latter have other tasks which exclude the secrecy needed for the preparation of illegal activities; but it is above all because we have no faith in the revolutionary fervour of the progressive parties as constituted today.
Every new idea and institution, all progress and every revolution have always been the work of minorities. It is our aspiration and our aim that everybody should become socially conscious and effective; but to achieve this end, it is necessary to provide all with the means of life and for development, and it is therefore necessary to destroy with violence, since one cannot do otherwise, the violence which denies these means to the workers.
Naturally, the "small numbers," the minority, must be sufficient, and those who imagine that we want to have an insurrection a day without taking into account the forces opposing us, or whether circumstances are in our favour or against us, misjudge us. In the, now remote, past, we were able, and did, carry out a number of minute insurrectionary acts which had no probability of success. But in those days we were indeed only a handful, and wanted the public to talk about us, and our attempts were simply means of propaganda.
Now it is no longer a question of uprisings to make propaganda; now we can win, and so we want to win, and only take such action when we think we can win. Of course we can be mistaken, and on the grounds of temperament may be led into believing that the fruit is ripe when it is still green; but we must confess our preference for those who err on the side of haste as opposed to those who always play a waiting game and let the best opportunities slip through their fingers for they, through fear of picking a green fruit then let the whole crop go rotten
We must seek to play an active, and if possible a preponderant role in the insurrectionary act. But with the defeat of the forces of repression which serve to keep the people in slavery; with the demobilisation of the army, the dissolution of the police and the magistrature, etc.; having armed the people so that it can resist any armed attempt by reaction to reestablish itself; having called on willing hands to undertake the organisation of public services and to provide, with concepts of just distribution, for the most urgent needs, using with care existing stocks in the various localities—having done all this, we shall have to see to it that there must be no wasted effort and that those institutions, those traditions and habits, those methods of production, exchange and aid should be respected and utilised, if they perform, even insufficiently or badly, necessary services, seeking by all means to destroy every trace of privilege, but being chary of destroying anything that cannot be replaced by something which serves the general good more effectively. We must push the workers to take possession of the factories, to federate among themselves and work for the community, and similarly the peasants should take over the land and the produce usurped by the landlords, and come to an agreement with the industrial workers on the necessary exchange of goods.
We will see to it that all empty and under-occupied houses are used so that no one will be without a roof over his head. We will hasten to abolish banks and destroy title deeds and all that represents and guarantees the power of the State and capitalist privilege. And we will try to reorganise things in such a way that it will be impossible for bourgeois society to be reconstituted. And all this, and whatever else would be required to satisfy public needs and the development of the revolution would be the task of volunteers, by all kinds of committees, local, intercommunal, regional, and national congresses which would attend to the coordination of social activity; would take necessary decisions, advising and carrying out what they considered useful, but without having any right, or the means, to impose their wishes by force, and relying for approval only on the services they rendered and on the demands of the situation as recognised by all concerned. Above all no _gendarmes,_ by whatever name they might be called. The creation of voluntary militia, without powers to interfere as militia in the life of the community, but only to deal with any armed attacks by the forces of reaction to reestablish themselves, or to resist outside intervention by countries as yet not in a state of revolution.
A successful insurrection is the most potent factor in the emancipation of the people, for once the yoke has been shaken off, the people are free to provide themselves with those institutions which they think best, and the time lag between passing the law and the degree of civilisation which the mass of the population has attained, is breached in one leap. The insurrection determines the revolution, that is, the speedy emergence of the latent forces built up during the "evolutionary" period.
Everything depends on what the people are capable of wanting. In past insurrections the people unaware of the real reasons for their misery, have always wanted very little, and have achieved very little. What will they want from the next insurrection?
The answer in part, depends on our propaganda and what efforts we put into it.
# **24. E XPROPRIATION**
TO DESTROY RADICALLY THIS OPPRESSION WITHOUT ANY DANGER of it reemerging, all people must be convinced of their right to the means of production, and be prepared to exercise this basic right by expropriating the landowners, the industrialists and financiers, and putting all social wealth at the disposal of the people.
[In Teramo] at a meeting of peasants the local secretary of the Trade Unions, the president of the socialist cooperative and two socialist MPs told the peasants: "Keep yourselves ready; when your leaders will tell you to strike, abandon the fields, and if on the other hand they tell you to gather in only your share, obey them and leave the other half unharvested."
This is the advice of good reformists. For in fact when the crop is lost one can more easily tell the people that the revolution cannot be made because one would die of hunger.
When will these bad shepherds make up their minds to tell the peasants: "harvest everything and give nothing to the bosses? And after the harvest get the land ready and sow for the coming year with the firm conviction that the bosses must never get anything again."
If one really wants to change the system in fact and not just superficially, it will be necessary to destroy capitalism de facto, expropriating those who now control all social wealth, and immediately set about organising, on a local basis, and without passing through legal channels, a new social life. Which means to say that in order to create the "social republic" one must first bring about... Anarchy
One of the basic tenets of anarchism is the abolition of monopoly, whether of the land, raw materials, or the means of production, and consequently the abolition of exploitation of the labour of others by those who possess the means of production. The appropriation of the labour of others, of all that permits a man to live without contributing his share to society, is from the anarchist and socialist point of view, theft.
Landowners, capitalists have robbed the people, with violence and dishonesty, of the land and all the means of production, and in consequence of this initial theft can each day take away from the workers the product of their labour. But they have been lucky thieves, they have become strong, have made laws to legitimate their situation, and have organised a whole system of repression to defend themselves both from the demands of the workers as well as from those who would want to replace them by the same means. And now the theft of the former is called property, commerce, industry, etc.; whereas the term robbers in common parlance, is reserved for those who would wish to follow the example of capitalists but who, having arrived too late, and in unfavourable circumstances, cannot do so without rebelling against the law.
But a difference in the names by which they are usually referred to, cannot cancel out the moral and social identity of the two situations. The capitalist is a thief who has succeeded through his efforts or those of his ancestors; the common thief is a would-be capitalist, who is simply waiting to become one in fact, to live, without working, on the proceeds of his hauls, that is on the work of others.
As enemies of the capitalists, we cannot have sympathy for the thief who aspires to become a capitalist. As partisans of expropriation by the people for the benefit of everybody, we cannot, as anarchists, have anything in common with actions, the purpose of which, is simply to transfer wealth from the hands of one boss into the hands of another.
Of course I am speaking of the professional thief, the person who does not want to work and seeks the means to live parasitically on the work of others.
It is quite another matter when a man denied the means of working robs in order that he or his family shall not die of hunger. In such a case, theft (if it can thus be called) is a revolt against social injustice, and can become the most sacred right and also the most urgent of duties....
It is true that the professional thief is also a victim of the social environment. The example set by his superiors, his educational background, and the disgusting conditions in which many people are obliged to work, easily explain why some men, who are not morally better than their contemporaries, finding themselves with the choice of being exploiters or exploited choose to be the former and seek to become exploiters with the means they are capable of. But these extenuating circumstances could equally be applied to the capitalists, but in so doing one only demonstrates more clearly the basic identity between the two professions.
Since anarchist ideas cannot be used to push people into becoming capitalists, neither can they be used to make people into thieves. On the contrary, by giving discontented people ideas about a better life and the hope of general emancipation, anarchist ideas if anything advocate withdrawal from all legal or illegal actions which encourage adaptation to the capitalist system and tend to perpetuate it.
In spite of all this, the social environment is so powerful and personal temperaments so diverse, that there is no reason why some anarchists should not become thieves, just as there are some who become business men or industrialists; but in that case both the former and the latter act not because of any anarchist ideas but in spite of them.
# **25. D EFENCE OF THE REVOLUTION**
THE REVOLUTION WE WANT CONSISTS IN DEPRIVING THE PRESENT holders of their power and wealth and in putting the land and the means of production and all existing wealth at the disposal of the workers, that is of everybody, since those who are not, will have to become, workers. And the revolutionaries must defend this revolution by seeing to it that no individual, party or class finds the means to constitute a government and restore privilege in favour of new or old bosses....
To defend, to save the revolution there is only one means: that of pushing the revolution as far as it will go. So long as there are those who will be in a position to oblige others to work for them; so long as there are those who are in a position to violate the freedom of others, the revolution will not be complete, and we will be still in a state of legitimate defence and to the violence which oppresses we will oppose the violence that liberates.
Do you fear that the dispossessed bourgeoisie may hire soldiers of fortune to restore the old regime? Dispossess them completely and you will see that without money you can employ no one.
Do you fear a military coup? Arm all the population, ensure that they really are in possession of all wealth so that every person will have to defend his own freedom and the means which can ensure his well-being, and you will see whether the generals seeking adventures will find who to follow them. But if after that, the people in arms, in possession of the land, the factories, and all the natural wealth were incapable of defending themselves, and allowed themselves once again to be brought under the yoke, it would mean that they were still not capable of enjoying freedom. The revolution would have failed and the work of education and preparation would have to be resumed for another attempt which would have greater chances of success because it would benefit from the seeds that had been sown at the previous attempt.
The dangers with which a revolution is faced do not come solely or principally from the reactionaries conspiring for a restoration and calling for foreign intervention; they also come from the possibility of degeneration of the revolution itself; and from the _arrivistes_ who, though revolutionaries, nevertheless retain a mentality and sympathies which are bourgeois and seek to direct the revolution towards ends which are anything but equalitarian and libertarian.
Once the situation is reached whereby no one could impose his wishes on others by force, nor take away from any man the product of his labour, anarchists could then only act through propaganda and by example.
Destroy the institutions and the machinery of existing social organisations? Yes, certainly, if it is a question of repressive institutions; but these are, after all, only a small part of the complex of social life. The police, the army, the prisons, and the judiciary are potent institutions for evil, which exercise a parasitic function. Other institutions and organisations manage, for better or for worse, to guarantee life to mankind; and these institutions cannot be usefully destroyed without replacing them by something better.
The exchange of raw materials and goods, the distribution of foodstuffs, the railways, postal services, and all public services administered by the State or by private companies, have been organised to serve monopolistic and capitalist interests, but they also serve real needs of the population. We cannot disrupt them (and in any case the people would not in their own interests allow us to) without reorganising them in a better way. And this cannot be achieved in a day; nor as things stand, have we the necessary abilities to do so. We are delighted therefore if in the meantime, others act, even with different criteria from our own.
Social life does not admit of interruptions, and the people want to live on the day of the revolution, on the morrow, and always.
There are still many people who are fascinated by the idea of "terror." For them it seems that the guillotine, firing squads, massacres, deportations, and jails are powerful and indispensable arms of the revolution, and observe that if so many revolutions have been defeated and have not produced the results hoped for, it is the fault of the goodness, and "weakness" of the revolutionaries, who have not persecuted, repressed and killed on a large enough scale.
It is a prejudice current in some revolutionary circles which had its origins in the rhetoric and historic falsification of the apologists of the Great French Revolution and has been revived in recent years by the Bolsheviks in their propaganda. But the truth is just the opposite; Terror has always been the instrument of tyranny. In France it served the grim tyranny of Robespierre and paved the way for Napoleon and the subsequent reaction. In Russia it persecuted and killed anarchists and socialists, and massacred rebellious workers and peasants, and has halted the development of a revolution which really might have ushered in a new era for mankind. Those who believe in the liberating and revolutionary efficacy of repression and savagery have the same kind of backward mentality as the jurists who believe that crimes can be prevented and the world morally improved by the imposition of stiff punishments.
The Terror, like war, awakens atavistic and bellicose sentiments, still barely covered by a cloak of civilisation, and raises to the highest posts the worse elements of the population. And far from serving to defend the revolution it discredits it, makes it repellent to the masses and after a period of fierce struggles, gives rise, of necessity, to what they would today call "a return to normality," that is, to the legalisation and perpetuation of tyranny. Whichever side wins, one always arrives at the creation of a strong government, which assures peace to some at the price of freedom, and to others domination without too many risks....
Certainly the revolution must be defended and developed with an inexorable logic; but one must not and cannot defend it with means which contradict its ends.
The most powerful means for defending the revolution remains always that of taking away from the bourgeoisie the economic means on which their power is based, and of arming everybody (until such time as one will have managed to persuade everybody to throw away their arms as useless and dangerous toys), and of interesting the mass of the population in the victory of the revolution.
If in order to win it were necessary to erect the gallows in the public square, then I would prefer to lose.
And after the revolution, that is, after the defeat of the existing powers and the overwhelming victory of the forces of insurrection, what then?
It is then that gradualism really comes into operation. We shall have to study all the practical problems of life: production, exchange, the means of communication, relations between anarchist groupings and those living under some kind of authority, between communist collectives and those living in an individualistic way; relations between town and country, the utilisation for the benefit of everybody of all natural sources of power and of raw materials; distribution of industries and, cultivation according to the natural resources of the different regions; public education, care of children and the aged, health services, protection against common criminals and the more dangerous ones who might again try to suppress the freedom of others for the benefit of individuals or parties—and so on. And in every problem [anarchists] should prefer the solutions which not only are economically superior but which satisfy the need for justice and freedom and leave the way open for future improvements, which other solutions might not.
In the event justice, liberty and solidarity should override economic advantages. One must not think of destroying everything in the belief that later things will look after themselves. Present civilisation is the result of development extending over thousands of years, and has solved, in a way, the problem of large concentrations of population, often crowded into small territories, and of satisfying their ever-increasing and complex needs. Its benefits have decreased—because development has been taking place under the pressure of authority in the interests of the ruling classes; but even if one takes away authority and privilege, the advantages acquired, the triumphs of man over the adverse forces of nature, the accumulated experience of past generations, sociability learned through cohabitation throughout the ages and by the proven benefits of mutual aid—all these advantages will remain, and it would be foolish, and in any case impossible, to give up all these things.
We must therefore fight authority and privilege, but take advantage of all the benefits of civilisation; and nothing must be destroyed which satisfies, even badly, a human need until we have something better to put in its place. We must be intransigent in our opposition to all capitalist imposition and exploitation, and tolerant of all social concepts which prevail in different human groupings, so long as they do not threaten the equal rights and freedom of others; and content ourselves with advancing gradually in step with the moral development of the people and as the available material and intellectual means increase—doing all we can, of course, by study, work, and propaganda to hasten the development towards ever more advanced ideals.
But after the successful insurrection, when the government has fallen, what must be done?
We anarchists would wish that in every district the workers, or, more accurately, those among them who are more socially conscious and have a spirit of initiative, should take possession of all the means of production, of all the wealth—land, raw materials, houses, machines, food stocks, etc., and to the best of their ability, initiate new forms of social life. We would wish that the land workers who today work for masters should no longer recognise the landowners' property rights but continue and intensify production on their own account, establishing direct contacts with workers in industry and transport for the exchange of goods and services; that industrial workers, including engineers and technicians, should take possession of the factories and continue and intensify production for their own benefit and that of the whole community; immediately switching production in those factories which today turn out useless or harmful goods to supplying the articles most urgently required to satisfy the needs of the public; that the railwaymen should continue to operate the railways but in the service of the community; that committees composed of volunteers or elected by the people should take over, under the direct control of the population, all available accommodation to house, as well as is possible in the circumstances, those most in need; that other committees, always under the direct control of the people, should deal with provisioning and the distribution of consumer goods; that all the members of the bourgeoisie should of necessity have to "muck in" with those who were the proletarian masses and work like everybody else in order to enjoy the same benefits as everybody else. And all this must be done immediately, on the very day, or the morrow of the successful insurrection, without waiting for orders from central committees or from any other kind of authority.
This is what the anarchists want, and it is in fact what would naturally happen if the revolution were to be a truly social revolution and not just a political change, which after a few convulsions would lead things back to what they were formerly. For, if one did not deprive the bourgeoisie of its economic power at once, it would in a short time recapture the political power which the insurrection had torn from its grasp. And in order to take away economic power from the bourgeoisie, it is necessary to organise immediately a new economic structure based on justice and equality. Economic needs, at least the most essential ones, cannot be interrupted; they must be satisfied immediately. "Central Committees" either do nothing or act when their services are no longer required.
# VI
# **26. A NARCHIST PROPAGANDA**
IT MUST BE ADMITTED THAT WE ANARCHISTS, IN OUTLINING WHAT we would like the future society to be—a society without bosses and without gendarmes—have, in general, made everything look a bit too easy.
While on the one hand we reproach our adversaries for being unable to think beyond present conditions and of finding communism and anarchy unattainable, because they imagine that man must remain as he is today, with all his meanness, his vices and his fears, even when their causes have been eliminated, on the other hand we skate over the difficulties and the doubts, assuming that the morally positive effects which will result from the abolition of economic privilege and the triumph of liberty have already been achieved.
So, when we are told that some people won't want to work, we immediately have a string of excellent reasons to show that work, that is the exercise of our faculties and the pleasure to produce, is at the root of man's well-being, and that it is therefore ridiculous to think that healthy people would wish to withdraw from the need to produce for the community when work would not be oppressive, exploited, and despised, as it is today.
And if they bring up the inclinations to, or the anti-social, criminal ways of, a section, however small, of the population, we reply that, except in rare and questionable cases of congenital sickness which it is the task of alienists to deal with, crimes are of social origin and would change with a change of institutions.
Perhaps this exaggerated optimism, this simplification of the problems had its _raison d'être_ when anarchism was a beautiful dream, a hurried anticipation, and what was needed was to push forward to the highest ideal and inspire enthusiasm by stressing the contrast between the present hell and the desired paradise of tomorrow.
But times have changed. Statal and capitalist society is in a state of crisis, of dissolution, or reconstruction depending on whether revolutionaries are able, and know how, to influence with their concepts and their strength, and perhaps we are on the eve of the first attempts at realisation.
It is necessary therefore to leave a little on one side the idyllic descriptions and visions of future and distant perfection and face things as they are today and as they will be in what one can assume to be the foreseeable future.
When anarchist ideas were a novelty which amazed and shocked, and it was only possible to make propaganda for a distant future (and even the attempts at insurrection, and the prosecutions we freely invited and accepted, only served the purpose of drawing the public's attention to our propaganda), it could be enough to criticise existing society and present an exposition of the ideal to which we aspire. Even the questions of tactics were, in fact, simply questions of deciding which were the best ways of propagating one's ideas and preparing individuals and masses for the desired social transformation.
But today the situation is more mature, circumstances have changed... and we must be able to show not only that we have more reason on our side than have the parties because of the nobility of our ideal of freedom, but also that our ideas and methods are the most practical for the achievement of the greatest measure of freedom and well-being that is possible in the present state of our civilisation.
Our task is that of "pushing" the people to demand and to seize all the freedom they can and to make themselves responsible for providing their own needs without waiting for orders from any kind of authority. Our task is that of demonstrating the uselessness and harmfulness of government, provoking and encouraging by propaganda and action, all kinds of individual and collective initiatives.
It is in fact a question of education for freedom, of making people who are accustomed to obedience and passivity consciously aware of their real power and capabilities. One must encourage people to do things for themselves, or to think they are doing so by their own initiative and inspiration even when in fact their actions have been suggested by others, just as the good school teacher when he sets a problem his pupil cannot solve immediately, helps him in such a way that the pupil imagines that he has found the solution unaided, thus acquiring courage and confidence in his own abilities.
This is what we should do in our propaganda. If our critic has ever made propaganda among those who we, with too much disdain, call politically "unconscious," it will have occurred to him to find himself making an effort not to appear to be expounding and forcing on them a well-known and universally accepted truth; he will have tried to stimulate their thought and get them to arrive with their own reason at conclusions which he could have served up ready-made, much more easily so far as he was concerned, but with less profit for the "beginner" in politics. And if he ever found himself in a position of having to act as leader or teacher in some action or in propaganda, when the others were passive he would have tried to avoid making the situation obvious so as to stimulate them to think, to take the initiative, and gain confidence in themselves.
The daily paper _[Umanità Nova]_ is but one of our means of action. If instead of awakening new forces, and encouraging more ambitions and enthusiastic activity, it were to absorb all our forces and stifle all other initiatives, it would be a misfortune rather than an affirmation of vigour, and witness to our strength, vitality, and boldness.
Furthermore there are activities which cannot by definition, be carried out by the paper or by the press. Since the paper has to address itself to the public it must of necessity speak in the presence of the enemy, and there are situations in which the enemy must not be informed. The comrades must make other arrangements for these situations... elsewhere
Must organisation be secret or public?
In general terms the answer is obviously that one must carry out in public what it is convenient that everybody should know and in secret what it is agreed should be withheld from the public at large.
It is obvious that for us who carry on our propaganda to raise the moral level of the masses and induce them to win their emancipation by their own efforts and who have no personal or sectarian ambitions to dominate, it is an advantage where possible to give our activities a maximum of publicity to thereby reach and influence with our propaganda as many people as we can.
But this does not depend only on our wishes; it is clear that if, for example, a government were to prohibit us from speaking, publishing, or meeting and we had not the strength to openly defy the ban, we should seek to do all these things clandestinely.
One must, however, always aim to act in the full light of day, and struggle to win our freedoms, bearing in mind that the best way to obtain a freedom is that of taking it, facing necessary risks; whereas very often a freedom is lost, through one's own fault, either through not exercising it or using it timidly, giving the impression that one has not the right to be doing what one is doing.
Therefore, as a general rule we prefer always to act publicly... also because the revolutionaries of today have qualities, some good and others bad, which reduce their conspiratorial capacities in which the revolutionaries of fifty or a hundred years ago excelled. But certainly there can be circumstances and actions which demand secrecy, and in which case one must act accordingly.
In any case, let us be wary of those "secret" affairs which everybody knows about, and first among them, the police.
Isolated, sporadic propaganda which is often a way of easing a troubled conscience or is simply an outlet for someone who has a passion for argument, serves little or no purpose. In the conditions of unawareness and misery in which the masses live, and with so many forces against us, such propaganda is forgotten and lost before its effect can grow and bear fruit. The soil is too ungrateful for seeds sown haphazardly to germinate and make roots.
What is needed is continuity of effort, patience, coordination, and adaptability to different surroundings and circumstances.
Each one of us must be able to count on the cooperation of everybody else; and that wherever a seed is sown it will not lack the loving care of the cultivator, who tends it and protects it until it has become a plant capable of looking after itself, and in its turn, of sowing new, fruitful, seeds.
# **27. A N ANARCHIST PROGRAMME**
# **1. Aims and Objectives**
We believe that most of the ills that afflict mankind stem from a bad social organisation; and that Man could destroy them if he wished and knew how.
Present society is the result of age-long struggles of man against man. Not understanding the advantages that could accrue for all by cooperation and solidarity; seeing in every other man (with the possible exception of those closest to them by blood ties) a competitor and an enemy, each one of them sought to secure for himself, the greatest number of advantages possible without giving a thought to the interests of others.
In such a struggle, obviously the strongest or more fortunate were bound to win, and in one way or another subject and oppress the losers.
So long as Man was unable to produce more than was strictly needed to keep alive, the conquerors could do no more than put to flight or massacre their victims, and seize the food they had gathered.
Then when with the discovery of grazing and agriculture a man could produce more than what he needed to live, the conquerors found it more profitable to reduce the conquered to a state of slavery, and put them to work for their advantage.
Later, the conquerors realised that it was more convenient, more profitable and certain to exploit the labour of others by other means: to retain for themselves the exclusive right to the land and working implements, and set free the disinherited who, finding themselves without the means of life, were obliged to have recourse to the landowners and work for them, on their terms.
Thus, step by step through a most complicated series of struggles of every description, of invasions, wars, rebellions, repressions, concessions won by struggle, associations of the oppressed united for defence, and of the conquerors for attack, we have arrived at the present state of society, in which some have inherited the land and all social wealth, while the mass of the people, disinherited in all respects, is exploited and oppressed by a small possessing class.
From all this stems the misery in which most workers live today, and which in turn creates the evils such as ignorance, crime, prostitution, diseases due to malnutrition, mental depression, and premature death. From all this arises a special class (government) which, provided with the necessary means of repression, exists to legalise and protect the owning class from the demands of the workers; and then it uses the powers at its disposal to create privileges for itself and to subject, if it can, the owning class itself as well. From this the creation of another privileged class (the clergy), which by a series of fables about the will of God, and about an after-life etc., seeks to persuade the oppressed to accept oppression meekly, and (just as the government does), as well as serving the interest of the owning class, serves its own. From this the creation of an official science which, in all those matters serving the interests of the ruling class, is the negation of true science. From this the patriotic spirit, race hatred, wars, and armed peace, sometimes more disastrous than wars themselves. From this the transformation of love into torment or sordid commerce. From this hatred, more or less disguised, rivalry, suspicion among all men, insecurity, and universal fear.
We want to change radically such a state of affairs. And since all these ills have their origin in the struggle between men, in the seeking after well-being through one's own efforts and for oneself and against everybody, we want to make amends, replacing hatred by love, competition by solidarity, the individual search for personal well-being by the fraternal cooperation for the well-being of all, oppression and imposition by liberty, the religious and pseudo-scientific lie by truth.
Therefore:
1. Abolition of private property in land, in raw materials, and the instruments of labour, so that no one shall have the means of living by the exploitation of the labour of others, and that everybody, being assured of the means to produce and to live, shall be truly independent and in a position to unite freely among themselves for a common objective and according to their personal sympathies.
2. Abolition of government and of every power which makes the law and imposes it on others: therefore abolition of monarchies, republics, parliaments, armies, police forces, magistratures, and any institution whatsoever endowed with coercive powers.
3. Organisation of social life by means of free association and federations of producers and consumers, created and modified according to the wishes of their members, guided by science and experience, and free from any kind of imposition which does not spring from natural needs, to which everyone, convinced by a feeling of overriding necessity, voluntarily submits.
4. The means of life, for development and well-being, will be guaranteed to children and all who are prevented from providing for themselves.
5. War on religions and all lies, even if they shelter under the cloak of science. Scientific instruction for all to advanced level.
6. War on rivalries and patriotic prejudices. Abolition of frontiers; brotherhood among all peoples.
7. Reconstruction of the family, as will emerge from the practice of love, freed from every legal tie, from every economic and physical oppression, from every religious prejudice.
This is our ideal.
# **2. Ways and Means**
We have outlined under a number of headings our objectives and the ideal for which we struggle.
But it is not enough to desire something; if one really wants it adequate means must be used to secure it. And these means are not arbitrary, but instead cannot but be conditioned by the ends we aspire to and by the circumstances in which the struggle takes place, for if we ignore the choice of means we would achieve other ends, possibly diametrically opposed to those we aspire to, and this would be the obvious and inevitable consequence of our choice of means. Whoever sets out on the highroad and takes a wrong turning does not go where be intends to go but where the road leads him.
It is therefore necessary to state what are the means which in our opinion lead to our desired ends, and which we propose to adopt.
Our ideal is not one which depends for its success on the individual considered in isolation. The question is of changing the way of life of society as a whole; of establishing among men relationships based on love and solidarity; of achieving the full material, moral and intellectual development not for isolated individuals, or members of one class or of a particular political party, but for all mankind—and this is not something that can be imposed by force, but must emerge through the enlightened consciences of each one of us and be achieved with the free consent of all.
Our first task therefore must be to persuade people.
We must make people aware of the misfortunes they suffer and of their chances to destroy them. We must awaken sympathy in everybody for the misfortunes of others and a warm desire for the good of all people.
To those who are cold and hungry we will demonstrate how possible and easy it could be to assure to everybody their material needs. To those who are oppressed and despised we shall show how it is possible to live happily in a world of people who are free and equal; to those who are tormented by hatred and bitterness we will point to the road that leads to peace and human warmth that comes through learning to love one's fellow beings.
And when we will have succeeded in arousing the sentiment of rebellion in the minds of men against the avoidable and unjust evils from which we suffer in society today, and in getting them to understand how they are caused and how it depends on human will to rid ourselves of them; and when we will have created a lively and strong desire in men to transform society for the good of all, then those who are convinced, will by their own efforts as well as by the example of those already convinced, unite and want to as well as be able to act for their common ideals.
As we have already pointed out, it would be ridiculous and contrary to our objectives to seek to impose freedom, love among men and the radical development of human faculties, by means of force. One must therefore rely on the free will of others, and all we can do is to provoke the development and the expression of the will of the people. But it would be equally absurd and contrary to our aims to admit that those who do not share our views should prevent us from expressing our will, so long as it does not deny them the same freedom.
Freedom for all, therefore, to propagate and to experiment with their ideas, with no other limitation than that which arises naturally from the equal liberty of everybody.
But to this are opposed—and with brute force—those who benefit from existing privileges and who today dominate and control all social life.
In their hands they have all the means of production; and thus they suppress not only the possibility of free experimentation in new ways of communal living, and the right of workers to live freely by their own efforts, but also the right to life itself; and they oblige whoever is not a boss to have to allow himself to be exploited and oppressed if he does not wish to die of hunger.
They have police forces, a judiciary, and armies created for the express purpose of defending their privileges; and they persecute, imprison and massacre those who would want to abolish those privileges and who claim the means of life and liberty for everyone.
Jealous of their present and immediate interests, corrupted by the spirit of domination, fearful of the future, they, the privileged class, are, generally speaking incapable of a generous gesture; are equally incapable of a wider concept of their interests. And it would be foolish to hope that they should freely give up property and power and adapt themselves to living as equals and with those who today they keep in subjection.
Leaving aside the lessons of history (which demonstrates that never has a privileged class divested itself of all or some of its privileges, and never has a government abandoned its power unless obliged to do so by force or the fear of force), there is enough contemporary evidence to convince anyone that the bourgeoisie and governments intend to use armed force to defend themselves, not only against complete expropriation, but equally against the smallest popular demands, and are always ready to engage in the most atrocious persecutions and the bloodiest massacres.
For those people who want to emancipate themselves, only one course is open: that of opposing force with force.
It follows from what we have said that we have to work to awaken in the oppressed the conscious desire for a radical social transformation, and to persuade them that by uniting they have the strength to win; we must propagate our ideal and prepare the required material and moral forces to overcome those of the enemy, and to organise the new society, and when we will have the strength needed we must, by taking advantage of favourable circumstances as they arise, or which we can ourselves create, to make the social revolution, using force to destroy the government and to expropriate the owners of wealth, and by putting in common the means of life and production, and by preventing the setting up of new governments which would impose their will and to hamper the reorganisation of society by the people themselves.
All this is however less simple than it might appear at first sight. We have to deal with people as they are in society today, in the most miserable moral and material condition; and we would be deluding ourselves in thinking that propaganda is enough to raise them to that level of intellectual development which is needed to put our ideas into effect.
Between man and his social environment there is a reciprocal action. Men make society what it is and society makes men what they are, and the result is therefore a kind of vicious circle. To transform society men must be changed, and to transform men, society must be changed.
Poverty brutalises man, and to abolish poverty men must have a social conscience and determination. Slavery teaches men to be slaves, and to free oneself from slavery there is a need for men who aspire to liberty. Ignorance has the effect of making men unaware of the causes of their misfortunes as well as the means of overcoming them, and to do away with ignorance people must have the time and the means to educate themselves.
Governments accustom people to submit to the Law and to believe that Law is essential to society; and to abolish government men must be convinced of the uselessness and the harmfulness of government.
How does one escape from this vicious circle?
Fortunately existing society has not been created by the inspired will of a dominating class, which has succeeded in reducing all its subjects to passive and unconscious instruments of its interests. It is the result of a thousand internecine struggles, of a thousand human and natural factors acting indifferently, without directive criteria; and thus there are no clear-cut divisions either between individuals or between classes.
Innumerable are the variations in material conditions; innumerable are the degrees of moral and intellectual development; and not always—we would almost say very rarely, does the place of any individual in society correspond with his abilities and his aspirations. Very often individuals accustomed to conditions of comfort fall on hard times and others, through exceptionally favourable circumstances succeed in raising themselves above the conditions into which they were born. A large proportion of the working class has already succeeded either in emerging from a state of abject poverty, or was never in such a situation; no worker to speak of finds himself in a state of complete social unawareness, of complete acquiescence to the conditions imposed on him by the bosses. And the same institutions, such as have been produced by history, contain organic contradictions and are like the germs of death, which as they develop result in the dissolution of institutions and the need for transformation.
From this the possibility of progress—but not the possibility of bringing all men to the necessary level to want, and to achieve, anarchy, by means of propaganda, without a previous gradual transformation of the environment.
Progress must advance contemporaneously and along parallel lines between men and their environment. We must take advantage of all the means, all the possibilities and the opportunities that the present environment allows us to act on our fellow men and to develop their consciences and their demands; we must use all advance in human consciences to induce them to claim and to impose those major social transformations which are possible and which effectively serve to open the way to further advances later.
We must not wait to achieve anarchy, in the meantime limiting ourselves to simple propaganda. Were we to do so we would soon exhaust our field of action; that is, we would have converted all those who in the existing environment are susceptible to understand and accept our ideas, and our subsequent propaganda would fall on sterile ground; or if environmental transformations brought out new popular groupings capable of receiving new ideas, this would happen without our participation, and thus would prejudice our ideas.
We must seek to get all the people, or different sections of the people, to make demands, and impose itself and take for itself all the improvements and freedoms that it desires as and when it reaches the state of wanting them, and the power to demand them; and in always propagating all aspects of our programme, and always struggling for its complete realisation, we must push the people to want always more and to increase its pressures, until it has achieved complete emancipation.
# **3. The Economic Struggle**
The oppression which today impinges most directly on the workers and which is the main cause of the moral and material frustrations under which they labour, is economic oppression, that is the exploitation to which bosses and business men subject them, thanks to their monopoly of all the most important means of production and distribution.
To destroy radically this oppression without any danger of it reemerging, all people must be convinced of their right to the means of production, and be prepared to exercise this basic right by expropriating the land owners, the industrialists and financiers, and putting all social wealth at the disposal of the people.
But can this expropriation be put into effect today? Can we today pass directly, without intermediate steps, from the hell in which the workers now find themselves to the paradise of common property?
Facts demonstrate what the workers are capable of today.
Our task is the moral and material preparation of the people for this essential expropriation; and to attempt it again and again, every time a revolutionary upheaval offers us the chance to, until the final triumph. But in what way can we prepare the people? In what way must one prepare the conditions which make possible not only the material fact of expropriation, but the utilisation to everybody's advantage of the common wealth?
We have already said that spoken and written propaganda alone cannot win over to our ideas the mass of the people. A practical education is needed, which must be alternately cause and effect in a gradual transformation of the environment. Parallel with the workers developing a sense of rebellion against the injustices and useless sufferings of which they are the victims, and the desire to better their conditions, they must be united and mutually dependent in the struggle to achieve their demands.
And we as anarchists and workers, must incite and encourage them to struggle, and join them in their struggle.
But are these improvements possible in a capitalist regime? Are they useful from the point of view of a future complete emancipation of the workers?
Whatever may be the practical results of the struggle for immediate gains, the greatest value lies in the struggle itself. For thereby workers learn that the bosses interests are opposed to theirs and that they cannot improve their conditions, and much less emancipate themselves, except by uniting and becoming stronger than the bosses. If they succeed in getting what they demand, they will be better off: they will earn more, work fewer hours and will have more time and energy to reflect on the things that matter to them, and will immediately make greater demands and have greater needs. If they do not succeed they will be led to study the causes of their failure and recognise the need for closer unity and greater activity and they will in the end understand that to make their victory secure and definitive, it is necessary to destroy capitalism. The revolutionary cause, the cause of the moral elevation and emancipation of the workers must benefit by the fact that workers unite and struggle for their interests.
But, once again, can the workers succeed in really improving their conditions in the present state of society?
This depends on the confluence of a great number of circumstances.
In spite of what some say, there exists no natural law (law of wages) which determines what part of a worker's labour should go to him; or if one wants to formulate a law, it could not be but that: wages cannot normally be less than what is needed to maintain life, nor can they normally rise such that no profit margin is left to the boss.
It is clear that in the first case workers would die, and therefore would stop drawing any wages, and in the second the bosses would stop employing labour and so would pay no more wages. But between these two impossible extremes there is an infinite scale of degrees ranging from the miserable conditions of many land workers to the almost respectable conditions of skilled workers in the large cities.
Wages, hours, and other conditions of employment are the result of the struggle between bosses and workers. The former try to give the workers as little as possible and get them to work themselves to the bone; the latter try, or should try to work as little, and earn as much, as possible. Where workers accept any conditions, or even being discontented, do not know how to put up effective resistance to the bosses demands, they are soon reduced to bestial conditions of life. Where, instead, they have ideas as to how human beings should live and know how to join forces, and through refusal to work or the latent and open threat of rebellion, to win the bosses respect, in such cases, they are treated in a relatively decent way. One can therefore say that within certain limits, the wages he gets are what the worker (not as an individual, of course, but as a class) demands.
Through struggle, by resistance against the bosses, therefore, workers can up to a certain point, prevent a worsening of their conditions as well as obtaining real improvement. And the history of the workers' movement has already demonstrated this truth.
One must not however exaggerate the importance of this struggle between workers and bosses conducted exclusively in the economic field. Bosses can give in, and often they do in face of forcefully expressed demands so long as the demands are not too great; but if workers were to make demands (and it is imperative that they should) which would absorb all the bosses profits and be in effect an indirect form of expropriation, it is certain that the bosses would appeal to the government and would seek to use force to oblige the workers to remain in their state of wage slavery.
And even before, long before workers can expect to receive the full product of their labour, the economic struggle becomes impotent as a means of producing the improvements in living standards.
Workers produce everything and without them life would be impossible; therefore it would seem that by refusing to work they could demand whatever they wanted. But the union of all workers, even in one particular trade, and in one country is difficult to achieve, and opposing the union of workers are the bosses organisations. Workers live from day to day, and if they do not work they soon find themselves without food; whereas the bosses, because they have money, have access to all the goods in stock and can therefore sit back and wait until hunger reduces their employees to a more amenable frame of mind. The invention or the introduction of new machinery makes workers redundant and adds to the large army of unemployed, who are driven by hunger to sell their labour at any price. Immigration immediately creates problems in the countries where better working conditions exist, for the hordes of hungry workers, willy-nilly, offer the bosses an opportunity to depress wages all round. And all these facts, which necessarily derive from the capitalist system, conspire in counteracting and often destroying advances made in working class consciousness and solidarity. And in every case the overriding fact remains that production under capitalism is organised by each capitalist for his personal profit and not, as would be natural, to satisfy the needs of the workers in the best possible way. Hence the chaos, the waste of human effort, the organised scarcity of goods, useless and harmful occupations, unemployment, abandoned land, under-use of plant, and so on, all evils which cannot be avoided except by depriving the capitalists of the means of production and, it follows, the organisation of production.
Soon then, those workers who want to free themselves, or even only to effectively improve their conditions, will be faced with the need to defend themselves from the government, with the need to attack the government, which by legalising the right to property and protecting it with brute force, constitutes a barrier to human progress, which must be beaten down with force if one does not wish to remain indefinitely under present conditions or even worse.
From the economic struggle one must pass to the political struggle, that is to the struggle against government; and instead of opposing the capitalist millions with the workers' few pennies scraped together with difficulty, one must oppose the rifles and guns which defend property with the more effective means that the people will be able to find to defeat force by force.
# **4. The Political Struggle**
By the political struggle we mean the struggle against government. Government is the _ensemble_ of all those individuals who hold the reins of power, however acquired, to make the law and to impose it on the governed, that is the public.
Government is the consequence of the spirit of domination and violence with which some men have imposed themselves on other, and is at the same time the creature as well as the creator of privilege and its natural defender.
It is wrongly said that today government performs the function of defender of capitalism but that once capitalism is abolished it would become the representative and administrator of the general interest. In the first place capitalism will not be destroyed until the workers, having rid themselves of government, take possession of all social wealth and themselves organise production and consumption in the interests of everybody without waiting for the initiative to come from government which, however willing to comply, would be incapable of doing so.
But there is a further question: if capitalism were to be destroyed and a government were to be left in office, the government, through the concession of all kinds of privileges, would create capitalism anew for, being unable to please everybody it would need an economically powerful class to support it in return for the legal and material protection it would receive.
Consequently privilege cannot be abolished and freedom and equality established firmly and definitely without abolishing government—not this or that government but the very institution of government.
As in all questions of general interest, and especially this one, the consent of the people as a whole is needed, and therefore we must strain every nerve to persuade the people that government is useless as well as harmful, and that we can live better lives without government.
But, as we have repeated more than once, propaganda alone is impotent to convince everybody—and if we were to want to limit ourselves to preaching against government, and in the meantime waiting supinely for the day when the public will be convinced of the possibility and value of radically destroying every kind of government, then that day would never come.
While preaching against every kind of government, and demanding complete freedom, we must support all struggles for partial freedom, because we are convinced that one learns through struggle, and that once one begins to enjoy a little freedom one ends by wanting it all. We must always be with the people, and when we do not succeed in getting them to demand a lot we must still seek to get them to want something; and we must make every effort to get them to understand that however much or little they may demand should be obtained by their own efforts and that they should despise and detest whoever is part of, or aspires to, government.
Since government today has the power, through the legal system, to regulate daily life and to broaden or restrict the liberty of the citizen, and because we are still unable to tear this power from its grasp, we must seek to reduce its power and oblige governments to use it in the least harmful ways possible. But this we must do always remaining outside, and against, government, putting pressure on it through agitation in the streets, by threatening to take by force what we demand. Never must we accept any kind of legislative position, be it national or local, for in so doing we will neutralise the effectiveness of our activity as well as betraying the future of our cause.
The struggle against government in the last analysis, is physical, material.
Governments make the law. They must therefore dispose of the material forces (police and army) to impose the law, for otherwise only those who wanted to would obey it, and it would no longer be the law, but a simple series of suggestions which all would be free to accept or reject. Governments have this power, however, and use it through the law, to strengthen their power, as well as to serve the interests of the ruling classes, by oppressing and exploiting the workers.
The only limit to the oppression of government is the power with which the people show themselves capable of opposing it. Conflict may be open or latent; but it always exists since the government does not pay attention to discontent and popular resistance except when it is faced with the danger of insurrection.
When the people meekly submit to the law, or their protests are feeble and confined to words, the government studies its own interests and ignores the needs of the people; when the protests are lively, insistent, threatening, the government, depending on whether it is more or less understanding, gives way or resorts to repression. But one always comes back to insurrection, for if the government does not give way, the people will end by rebelling; and if the government does give way, then the people gain confidence in themselves and make ever increasing demands, until such time as the incompatibility between freedom and authority becomes clear and the violent struggle is engaged.
It is therefore necessary to be prepared, morally and materially, so that when this does happen the people will emerge victorious.
A successful insurrection is the most potent factor in the emancipation of the people, for once the yoke has been shaken off, the people are free to provide themselves with those institutions which they think best, and the time lag between passing the law and the degree of civilisation which the mass of the population has attained, is breached in one leap. The insurrection determines the revolution, that is, the speedy emergence of the latent forces built up during the "evolutionary" period.
Everything depends on what the people are capable of wanting.
In past insurrections unaware of the real reasons for their misfortunes, they have always wanted very little, and have obtained very little.
What will they want in the next insurrection?
The answer, in part, depends on our propaganda and what efforts we put into it.
We shall have to push the people to expropriate the bosses and put all goods in common and organise their daily lives themselves, through freely constituted associations, without waiting for orders from outside and refusing to nominate or recognise any government or constituted body in whatever guise (constituent, dictatorship, etc.) even in a provisional capacity, which ascribes to itself the right to lay down the law and impose with force its will on others.
And if the mass of the population will not respond to our appeal we must—in the name of the right we have to be free even if others wish to remain slaves and because of the force of example—put into effect as many of our ideas as we can, refuse to recognise the new government and keep alive resistance and seek that those localities where our ideas are received with sympathy should constitute themselves into anarchist communities, rejecting all governmental interference and establishing free agreements with other communities which want to live their own lives.
We shall have to, above all, oppose with every means the reestablishment of the police and the armed forces, and use any opportunity to incite workers in non anarchist localities to take advantage of the absence of repressive forces to implement the most far reaching demands that we can induce them to make.
And however things may go, to continue the struggle against the possessing class and the rulers without respite, having always in mind the complete economic, political and moral emancipation of all mankind.
# **5. Conclusion**
What we want, therefore, is the complete destruction of the domination and exploitation of man by man; we want men united as brothers by a conscious and desired solidarity, all cooperating voluntarily for the well-being of all; we want society to be constituted for the purpose of supplying everybody with the means for achieving the maximum well-being, the maximum possible moral and spiritual development; we want bread, freedom, love, and science for everybody.
And in order to achieve these all-important ends, it is necessary in our opinion that the means of production should be at the disposal of everybody and that no man, or groups of men, should be in a position to oblige others to submit to their will or to exercise their influence other than through the power of reason and by example.
Therefore: expropriation of landowners and capitalists for the benefit of all; and abolition of government.
And while waiting for the day when this can be achieved: the propagation of our ideas; unceasing struggle, violent or non-violent depending on the circumstances, against government and against the boss class to conquer as much freedom and well-being as we can for the benefit of everybody.
# **PART TWO**
We follow ideas and not men, and rebel against this habit of embodying a principle in a man.
—Malatesta speaking at the Berne Congress of the International, 1876
Some of us, and Max Nettlau and Luigi Bertoni in particular, often suggested to Malatesta that he should write his Memoirs which would have been such a great contribution to contemporary history as well as to a better understanding of the events in which he was directly involved; and he would reply: "Yes, one day... but there is no hurry; I will think about it when there aren't more important things to do, when I'm an old man." But as he always found more important things to do, and never admitted to being old, he never wrote his Memoirs.
—Luigi Fabbri in his biography **_Malatesta_** (Buenos Aires, 1945)
# **N OTES FOR A BIOGRAPHY**
# **1**
... So I left for Switzerland with Cafiero. At the time I was sickly, I spat blood and was said to be consumptive, more or less.... While crossing the Gothard during the night (at that time there was no tunnel and one had to cross the snowy mountain in a diligence) I had caught cold, and arrived at the house where Bakunin was staying in Zurich, with a feverish cough.
After the first greetings. Bakunin made up a camp bed, and invited me—he almost forced me—to lie on it, covered me with all the blankets he could lay hands on and urged me to stay there quietly and sleep. And all this was accompanied by attention, and motherly tenderness, which gripped my heart.
While I was wrapped up in bed, and all present imagined that I was sleeping, I heard Bakunin whispering nice things about me and then adding sadly: "What a shame that he should be so sick; we shall lose him very soon; he won't last more than six months."
That touching description of his first meeting with Bakunin in 1872 was written by Malatesta in 1926 when he was in his 73rd year and Bakunin had been fifty years in his grave.
Others at the time referred to Malatesta's ill-health. Cafiero (in a letter 1875) spoke of "poor Malatesta is sick with consumption" and thought that no doubt the intentions of their persecutors was "to stifle a life so young and noble, within the stinking and silent walls of a prison cell." Borghi points out that Malatesta's "respiratory system remained his weak point throughout his life" and adds "I will never forget the crises provoked by the bronchial attacks he suffered in the stinking cell in Milan during the cold winter of 1920–21."
His companion during the last years of his life, Elena Melli, in a letter to Damiani (July 28, 1932) describes the last weeks of his life: "He had got over the bronchial-pneumonia, as well as the relapse he suffered a few weeks ago. It seemed as if he was better, and out of danger, but he was getting weaker all the time; one could see it from one day to the next. Even he did not believe that he was dying but another attack on the left side suffocated him.... During those last few days he could hardly breathe, he was suffocating in spite of all the oxygen he took—1,500 litres in five hours.... He died on Friday, the 22nd [July 1932] at 12:20 p.m.
# **2**
George Woodcock in his recent history of Anarchism writes:
In the middle of 1871, however a new group of militants appeared, different in character from those veterans of earlier struggles who had first gathered around Bakunin. The leaders among them, Carlo Cafiero, Errico Malatesta, and Carmelo Palladino, were all young men in their early twenties, the educated sons of Southern Italian landowners; all of them came from regions where peasant poverty was endemic...; they were in fact the Italian equivalent of the conscience-stricken Russian noblemen who in the same decade felt the burning urge to "go to the people."
At least so far as Malatesta is concerned, the comparison does not fit the facts that are available.
(Of Palladino not a great deal is known other than that he was a young lawyer who had been very active in the Naples section of the International from 1869–1871; that he visited Bakunin in company with Cafiero towards the end of 1872 and went to Locarno in 1874 after the failure of the Italian insurrectionary movement of that year but eventually returned to Cagnamo Varamo "where he died many years later in tragic circumstances."
Carlo Cafiero (born in Barletta in 1846 of a "rich and reactionary family") was a member of the London International whom Marx intended should be used to help convert Italy and Spain to Marxism. On his return to Italy it was he who was converted instead, and in part by Malatesta's efforts. Bakunin completed the "conversion" the following year. He remained active until 1882, when he championed the social democratic cause. A year later Cafiero suffered a mental breakdown from which he never recovered. He died in a mental home in 1892.
Errico Malatesta was born in Santa Maria Capua Vetere (a garrison town with a population of 10,000 in the province of Caserta) on December 14, 1853. We know very little about his family's background. The popular view that he was descended from nobility is baseless. Fabbri describes Malatesta's father as "a man of moderately liberal ideas" as well as "a rich landowner." According to Nettlau the family came from the "petit bourgeoisie and engaged in commerce," and this description is confirmed by Borghi who recounts that Malatesta was always highly amused by his alleged descent from Sigismundo Malatesta "the famous tyrant of Rimini" who in the 15th century erected a temple to God and his mistress Isotta. No noble blood coursed through his veins. "His mother and father were retiring and modest landowners."
From Malatesta's own account of his first meeting with Bakunin in 1872 we learn that by then his mother and father as well as a brother and sister had died from "chest complaints," and in another article of political reminiscences, of Giuseppe Fanelli, he mentions that at the time (1871) "I was a student and lived with my brother and an old aunt who was mother to us after the death of our parents."
The International had been introduced in Italy by bourgeois who in their love for justice, had deserted their class, and in 1872 and also later in many places, the majority, at least the leadership and active elements were not workers but young people from the middle- and lower-middle-class.
# **3**
In the middle of 1871 Malatesta was not in his "early twenties" but just over 17 years old, and already active in the political struggle.
When he was fourteen he protested over a local injustice by addressing to King Victor Emmanuel II what Fabbri describes as an "insolent and threatening letter" which Authority took sufficiently seriously to order his arrest (March 25, 1868). With the help of friends his father secured his release from prison and as well as from the threat of being sent to a special school "in view of the fact that his family had so neglected his education as a loyal subject of the Crown."
At supper on the night of his release his father tried to reproach his son or at least warn him to be more prudent in future. But Fabbri tells us that the young Malatesta's reply was so intransigent that all his father could say, with tears in his eyes was "My poor boy, it displeases me to tell you, but at this rate you will end up on the gallows."
Two years later (1870) according to Angiolini he was arrested and sentenced in Naples following a demonstration and "sent down" from the University of Naples (where he was studying medicine) for a year.
Malatesta's schooling started in the _lycée_ of Santa Maria but he was soon to move with his parents to Naples where he attended the Scolopian school (a religious order devoted to education) and studied the classics.
I was then (1868) a youth dedicated to the study of rhetoric, Roman History and Gioberti's philosophy. My teachers did not succeed in stifling in me the forces of nature, so that I was able to preserve in the stupid and corrupting environment of a modern school my intellectual sanity and the purity of my heart.
From the Scolopians he went to the Medical School at the University of Naples. He can have at most completed three years of his medical studies before joining the International and the years following that momentous decision were so packed with political and revolutionary activity that it is unlikely that he ever completed his medical studies.
# 4
At the age of 14 he was a budding Republican and in due course applied for membership of the "Universal Republican Alliance," but Mazzini turned down the application on the grounds that his tendencies were too socialistic and that he would soon have gone over to the International. Malatesta had not heard of the International until then. His insatiable curiosity had to be satisfied and he set about finding out more; in the course of his search he met a number of members of the Italian section of the International and came under the influence of Fanelli and Palladino. He joined the International in 1871, a few months after the "inspiring" events of the Paris Commune. His entry into the Naples section was the beginning of a new phase of activity within the section. As well as a group of workers, many of Malatesta's student friends followed him. He was also indicating not only a great capacity for work but an ability to inspire those around him, a gift he retained throughout his life.
Many years later he was to describe the life of a militant in those days of "enthusiasm" when the Internationalists were "ever ready for any sacrifice for the cause and were inspired by the rosiest hopes."
Everyone gave to propaganda all they could, as well as what they could not afford; and when money was short we gladly sold household objects, facing, in a resigned way, the reprimands from our respective families. For propaganda we neglected our work and our studies. In any case the revolution was to take place at any moment and would put all matters to rights! Often one went to prison, but came out with more energy than before; persecutions only awakened our enthusiasm. It is true that the persecutions at that time were jokes compared with what took place later. At that time the regime had emerged from a series of revolutions; and the authorities, from the beginning stern so far as the workers, especially in the country, were concerned, showed a certain respect for freedom in the political struggle, a kind of embarrassment at being similar to the Bourbon and Austrian rulers, which however disappeared as the regime became consolidated and the struggle for national independence receded into the background.
But he also does not hesitate to point to all the false political assumptions with which, at the time, they fed their enthusiasms.
We believed in the general discontent, and since the poverty that afflicted the mass of the people was truly insupportable, we thought it would be enough to set an example, and with weapons in our hands, launch the slogan "down with the gentlefolk," for the working masses to set about the bourgeoisie and take possession of the land, the factories and all they had produced by their efforts and that had been taken away from them. And then of course we had a mystical faith in the virtues of the people, in its abilities, in its equalitarian and libertarian instincts.
Facts demonstrated then and later (and they had before as well) how far we were from the truth. It was only too clear that hunger, when there is no awareness of individual rights and a guiding idea to action, does not result in revolutions; at most it creates sporadic risings which the _signori,_ if they have any sense, can much more easily control by distributing bread and throwing a few coppers to the clamouring mob from their balconies, than by ordering the carabineers to fire on them. And if our wishes had not blinded our powers of observation, we could easily have noted the depressing, and therefore counter-revolutionary effect of hunger, and the fact that our propaganda was most effective in the least depressed regions and among those workers, mostly artisans, who were in less difficult financial straits.
Unlike many revolutionaries who never saw the wood of reality for the trees of their dreams, Malatesta was at an early stage in his political life subjecting all the hopes and theories of his contemporaries and teachers to the critical test of reality. It is important to stress however that whereas as so often happens, the starry-eyed missionary-type of revolutionary and the action-above-all-else activist who despises those who dare to stop to think, soon lose their missionary zeal, and turn their activism to more mundane pursuits, Malatesta never abandoned his revolutionary activity nor did he lose his optimism, an optimism which must be seen much more as confidence in himself and his closest friends than as blind faith in some anarchist or socialist millennium.
In a rare autobiographical article written in 1884, when he was thirty, and intended both as a warning and an incitement to the youth at that time, he describes his own feelings as a teenager, his dreams of "an ideal world" and his faith in the "republic"—in the cause of which he had seen the inside of a royal prison for the first time—only to be aware as be entered the world of reality what problems had to be surmounted to achieve his ideal world, and the fact that the republic was a government like any other—and sometimes even worse.
# **5**
Early in life Malatesta understood the dangers of the cult of the personality without, nevertheless, ever under-estimating any man's worth, or failing to recognise exceptional qualities in others, or the influences they exerted on his own development. The fact that in his early youth he had to choose between a galaxy of "great men"—Garibaldi, Mazzini, Marx, and Bakunin—may have given him an early insight into the dangers that stemmed from associating ideas with personalities. Indeed at the eighth Congress of the International Working Men's Association held in Berne in October 1876 Malatesta (who was one of the Italian delegates) protested against the habit of calling themselves or of being known as Bakuninists, "since we are not, seeing that we do not share all Bakunin's theoretical and practical ideas, and because above all, we follow ideas and not men, and rebel against this habit of embodying a principle in a man."
And of Mazzini he refers to the way "possibly irritated at being deprived of that kind of pontificate that he had exercised for many years over the revolutionary movement, violently attacked the Commune and the International and held back his followers from the steps that they were about to take." And he writes of Garibaldi's followers and "their _duce" 28_ (Mussolini had himself referred to as "il _duce_ ," and since Malatesta's reference to Garibaldi was written in 1928, at the height of Mussolini's power, his use of the term for Garibaldi can hardly be considered flattering!)
Yet presumably because he combated the idea of superman, he was as generous in pointing to the qualities and achievements of those of his contemporaries and "mentors," as he was uncompromising in his criticism of their personal weaknesses and what he considered their political mistakes. This approach is well illustrated by Malatesta's article of recollections of Kropotkin which is included at the end of these Notes, and in his short but generous defence of Mazzini (1922):
We were against Mazzini for his way of understanding the social struggle, for the providential mission that he attributed to Italy and to Rome, for his religious dogmatism.
There were always, as happens in the heat of the struggle, excesses and misunderstanding on both sides; but in the spirit of objectivity we recognise that at the bottom of our hearts and in the sentiments that inspired us: we were Mazzinians just as Mazzini was an Internationalist.
Fundamental differences of method existed and remain, just as there were and still are basic differences in philosophical concepts; but the animating spirit was the same. Love among men, brotherhood among peoples, social justice and solidarity, the spirit of sacrifice, of duty. And furthermore the decisive and unreconcilable hatred of the institution of monarchy.
# **6**
Of the influences in his own development Bakunin takes pride of place. Malatesta referred to him as "the great revolutionary, he who we all look upon as our spiritual father." His greatest quality was his ability to "communicate faith, the desire for action and sacrifice to all those who had the opportunity of meeting him. He would say that one needed to have _le diable au corps;_ and he certainly had it in him and in his spirit.
I was a Bakuninist, as were all my comrades of those far off days. Today—and for very many years—I would no longer describe myself as such.
Ideas have developed and been modified. Today I find that Bakunin in political economy and in the interpretation of history, was too Marxist; I find that his philosophy was conducted without possible issue in the contradiction between the mechanical concept of the universe and the faith in will over the fate of mankind. But all this of no great importance. Theories are uncertain and changing concepts; and philosophy, consisting of hypotheses inhabiting the clouds, has little or no influence on life. And Bakunin always remains, in spite of all possible disagreements, our great master and inspiration.
What is living is his radical criticism of the principle of authority and of the State that embodies it; living is always the struggle against the two lies, the two guises, in which the masses are oppressed and exploited: democratic and dictatorial; and living is his masterly denunciation of that false socialism he called soporific, and which aims, consciously or unconsciously at consolidating the dominion of the bourgeoisie lulling workers to inactivity with useless reforms. And living are, above all, the intense hatred against all that degrades and humiliates man and the unlimited love of liberty for all.
# **7**
But as he himself wrote of that period "though none of us had read Marx, we were still too Marxist." Fabbri considered that the period of transition between the anarchism of the First International and the anarchism that he expounded to the end of his life occurred during the seven or eight years from the publication of the _l'Associazione_ (London, 1890) to _l'Agitazione_ (Ancona, 1897). Nevertheless, the same writer observes that already in _La Questione Sociale_ (Florence, 1884) "certain fundamental aspects of his evolution are fairly clearly revealed." It was in _l'Agitazione_ that Malatesta published six articles on "Individualism in Anarchism," "Harmony and Organisation" in which, without polemicising openly with Kropotkin, he gives an interpretation of anarchism which is in open contradiction with the Kropotkinian view expressed in the _Conquest of Bread_ and his other writings of the time.
He describes his "evolution" in a letter to Fabbri in which he confirmed the latter's view that since 1897 he had modified his views on small details only. At the time "I had more faith, more hope in syndicalism—or rather, in the syndicates—than I have now; and communism seemed then a more simple and an easier solution than it appears now." And he goes on to point out that there was a greater difference between his ideas of 1897 and those of 1872–73-74. "Then we were 'kropotkinians' even before Kropotkin (in fact Kropotkin found those ideas which he made his own, already widely held by us before he entered the 'bakuninist' wing of the international movement)." He refers to this at greater length in an article on the Question of Revisionism (1927) and also in his Kropotkin "Recollections" appended to these Notes.
# **8**
Malatesta was the "complete" anarchist propagandist. Early in his political life he lost any illusions he might have had about historical inevitability and realised that only if people could be shaken out of their apathy and "pushed" ("spingere" is a favourite word of his which one constantly meets in his writings) to think and act for themselves, would things change. He was therefore an indefatigable propagandist of the written and spoken word. But also because he was aware of the limits of propaganda as such he was also an activist, viewing direct action, intelligently conceived, as a vital aspect of the task of preparing the environment for revolution. The third ingredient in this "complete" anarchist propagandist was that he began as an Internationalist and remained one to the end of his days.
(Unlike our intellectual expatriates who denounce everything English and live like puckasahibs in countries which, apart from the climate and the low cost of living and cheap labour, are still a century behind perfidious Albion in their way of life and their laws, Malatesta was truly the Internationalist because he loved mankind without ceasing to love Italy:
"Is it not absurd"—he once wrote in answer to a shocked comrade—"to believe that he who loves all countries, who looks on the world as his ideal country and seeks to make it the effective country for all men, linked in brotherhood in work and for mutual well-being, should make an exception of the country in which he was born and the people with whom he has greater affinities and links?... _Long Live Italy,_ yes, a thousand times yes: And _Long live all the countries of the world._ And, it is understood, not the political States, all of which we want to see destroyed, but the people, emancipated from all political and economic oppression."
If Malatesta devoted much of his activity and thought to the Italian political scene it was because he felt more able to make an effective contribution to the struggle in a country and among people with whom he shared—among other things—a common language. But as he put it:
For us, our country is the whole world; for us every human achievement is ours just as is every human shame. Italy is part of the world, and though for its liberation we specially devote our efforts, it is only because here our activity can be more effective because here we have relatives, friends and comrades who we specially love.... But all this is so obvious, so elementary, so common-place and has so often been said that one has to make an effort to repeat it.
# **9**
Because of the special attention he was accorded by government and police in Italy, Malatesta spent nearly half his life in exile. His first period of exile in 1878 began when he was twenty-five. He returned to Italy in 1883 only to leave for South America the following year; he did not return until 1897 when he edited _l'Agitazione_ but by 1899 was again in exile. He returned to Italy in 1913–14 for barely a year, and did not manage to set foot in his country again until 1919 where he spent the next 13 years until his death in 1932 (except for a brief visit to Switzerland in 1922 on the occasion of the 50th anniversary of the St. Imier conference of the International which he had attended as the delegate for the Naples Section is his youth). Thus Malatesta spent thirty-five years of his life in exile—much of it filled with activity but also much of it frustrated by inactivity. What is clear however, is that even in exile he never lost touch with the Italian political situation.
At the time of writing these lines the _Sunday Telegraph_ (25.10.64) illustrates a review of Mr. Joll's work on _The Anarchists 36_ with a reproduction of the photograph of Malatesta used on the cover of this volume and captioned "Dangerous Type." Professor George Woodcock in his _History_ perpetuates instead the romantic picture of the "knight errant" ranging through Europe and the Levant "in search of revolutionary adventure." Others accused Malatesta in his time, of being a coward who never stopped to face the music—that is the consequences of his actions. Malatesta _was_ a "dangerous type" but not in the sense clearly implied by the _Sunday Telegraph_ which titles its review "Futile Gang." He was dangerous so far as governments were concerned, but admired and respected as a man of integrity and vision by people from all walks of life throughout the world. His life was full of those incidents which are "romantic" when viewed in retrospect and by those literati who in a lifetime have never said boo to a goose even in anger, but it was quite clear that after the early years when Malatesta and his friends courted arrest and imprisonment as part of their propaganda activities, he did not consider that his effectiveness as a propagandist was greater in prison than at liberty even in exile. On the other hand this did not prevent him from taking big risks, but they were what could be called calculated risks.
Malatesta, as I see him, was neither a romantic nor a martyr type. But neither did he lack a sense of humour, or underestimate his worth as a political thinker and personality; but he was never an exhibitionist, nor a poseur. He obviously sought approval and a following but always on the strength of his arguments and never by compromising them or by encouraging the cult of _his personality._ The fact is that Malatesta's ideas and activities provoked heated discussion not only among the Italian Left but within the anarchist movement itself. It is only since his death that his ideas have ceased to be the centre of heated discussion in the Italian anarchist movement. Perhaps now the discussion will be taken up in the English speaking movement!
# **10**
That Malatesta was far from being the revolutionary in search of adventure is surely illustrated by the relatively inactive years—1900 to 1919—spent in London which were interrupted only by his participation in the Anarchist International Congress in Amsterdam (1907) and that period of less than a year (1913–14) in Italy. His contribution to the Congress is noteworthy for its practical suggestions and approach. I refer to Malatesta's contributions to it in the concluding section of this volume.
Malatesta's return to Italy (1913–14) is a model of the thoroughness and the energy with which he set about any task, or assignment he undertook (and one must bear in mind that by then he was sixty, an age when many other revolutionaries were dead, or resting on their laurels and writing their memoirs).
His decision was prompted by a number of considerations principal among them the political "hunch" that the Italian situation, following the unpopular Tripolitanian war was ripe for some "practical" initiative. At the time the Italian anarchist movement was torn by internal and personal polemics, largely the work of a handful of "comrades" who in due course transferred their activities to the bourgeois parties, as generally is the case, and it was with a view to once again bringing together the movement that Cesare Agostinelli the Ancona hatter and Malatesta's old comrade in arms approached him in London, and Fabbri who was, at the time, doing a teaching job in a village in Emilia, about his idea of starting an anarchist paper in Ancona. Both responded enthusiastically. Fabbri was detailed to draft a circular announcing the forthcoming publication which Malatesta suggested should be called _Volontà._ The first issue appeared in Ancona, June 1913, and edited by Malatesta from London, WC1. Fabbri writes that "right from the start the new periodical bore the imprint of earlier Malatestian newspapers." But so far as the presentation went, Malatesta, from London was writing to his friend (June 13): "What do you think of the first issue of _Volontà_? Typographically its horrible. The quality of the paper makes me shudder. Light inking on grey paper—type too crammed etc. Still... we will improve." On the 16th June he writes to Agostinelli "The 2nd issue has arrived. Much better, well done! If we go on improving we shall end up by doing something really good. Tonight I will send you the editorial. It should reach you by Thursday. Try to keep space for it. I am late—and I am expecting a telling-off. But in future I hope I will make amends and not deserve your strictures..." I quote this extract because it seems to me to shed more light on Malatesta's character, his simplicity, and human warmth and comradeship than anything a third party could write on the subject.
And in the course of his letter to Fabbri, Malatesta lets him onto a secret "which will please you: I have decided to come to Italy." And to Luigi Bertoni editor of the bilingual anarchist fortnightly _Le Réveil/Il Risveglio,_ published for many years in Geneva, he wrote (July 3, 1913) "I have decided to leave for Italy towards the end of the month. Frankly I find it impossible to produce a paper from this distance to meet the needs of the present situation; and furthermore I am loath to spur others on to act while I am safely tucked away [in London]."
Malatesta's activity as an organiser, a propagandist and revolutionary agitator during that period of less than a year can be given in some detail thanks to the fact that in the course of an allied bombardment of Ancona, during the last war, a police station was destroyed. Two anarchists, searching among the debris, found the police dossier on Malatesta which Borghi published as an appendix to the post-war edition of his biography of Malatesta. The material printed comes from the diary of the Captain of the Carabineers of Ancona.
"Malatesta's return from London was the signal for a reawakening of the anarchist movement in Ancona," which had been reduced to a number of "disorganised and inactive groups" without resources. "Malatesta immediately set about reorganising it. He made revolutionary propaganda at meetings and gatherings; by leaflets and through articles in the weekly journal _Volontà_ of which he is the editor and which is the organ of the party."
"In November 1913 after having drawn together all the anarchist elements in Ancona he successfully started a Circle of Social Studies where members and sympathisers meet for readings on social subjects, discussions, and propaganda meetings, which are frequently presided over by Malatesta himself. In a short time in Ancona anarchists and sympathisers number some 600 individuals consisting predominantly of dock porters, workers, and criminal elements of the town." A list of the most prominent anarchists in the town apart from Malatesta "who is the undisputed leader" follows. "They number 33, and to judge from their trades and professions, and their ages are clearly a representative cross section of the working community. They include shoemakers, carpenters, dockworkers, street traders, barbers, shop assistants, and one student. Their ages range from the early twenties, predominate in the thirties."
The Captain also notes in his diary that Malatesta had a season ticket which allowed him to travel anywhere on State railway networks, and "he very frequently travels keeping in contact with the more prominent leaders and in constant touch with the other anarchist groups." And one feels that the next entry is made with a mixture of fear and admiration for the man:
His qualities as an intelligent, combative speaker who seeks to persuade with calm, and never with violent, language, are used to the full to revive the already spent forces of the party and to win converts and sympathisers, never losing sight of his principal goal which is to draw together the forces of the party and undermine the bases of the State, by hindering its workings, paralyze its services, and doing anti-militarist propaganda, until the favourable occasion arises to overturn and destroy the existing State.
Those who underestimate the perception of the police must surely make an exception here! But then Malatesta was always pointing out to those who sought to put words into his mouth which he had never uttered, in order to launch their attacks on him, that what he had to say was crystal clear and could not be misunderstood. And, one can now add, that not even a policeman could miss the points he made!
From August 1913 to May 1914 the Captain lists 37 noteworthy "anarchist demonstrations" in the province at 21 of which Malatesta took part either as the speaker or one of a panel of speakers.
How many private meetings he attended during those months, even the Captain cannot tell for as he notes: "The organisational work of Malatesta is difficult to penetrate, by reason of the prudence with which he acts, and the discretion of his trusted friends, and the circumspection with which he acts."
And his comrade in arms and biographer, Fabbri, recounts that during his short return to Italy Malatesta also lectured and spoke at meetings in the principal cities of Italy: Rome, Milan, Florence, Turin, Leghorn etc., and in his capacity as journalist attended the conferences of the various parties and workers' organisations of the Left which interested him above all in order to assess what part they might be expected to play in the revolutionary upheaval he pinned his hopes on.
# **11**
It was at the end of Malatesta's brief return to Italy that the "Red Week" (June 1914) exploded. _Freedom_ published the following report of "The General Strike and the Insurrection in Italy" by Malatesta himself, who was back in London having only just managed to escape arrest.
The events which have taken place recently are of the greatest importance, not so much in themselves, but as an indication of the disposition of the Italian people and of what we can anticipate in the near future.
The immediate cause of the outbreak was a massacre of unarmed demonstrators by the gendarmes of the town of Ancona.
For a year the revolutionary and labour organisations of all political shades had been carrying on an agitation in favour of several victims of military despotism and for the abolition of _disciplinary battalions,_ to which are sent all young soldiers known to hold anti-monarchical and anti-bourgeois opinions. The treatment is barbarous, and the unhappy young men are submitted to all kinds of moral and physical tortures.
As the meetings and demonstrations were held all over Italy, but on different dates, they seemed to make but little impression on the Government; and the Trades Council of Ancona proposed, therefore to organise manifestations in the whole country on the same day, that day to be the date of the official celebration of the establishment of Italian unity and Monarchy. As on these occasions great military reviews are always held, the comrades thought that the Government would be obliged to postpone the review in order to hold the troops to preserve "order" and the attention of the whole public would be drawn to the object of the demonstration.
The idea put forward by the Ancona comrades was everywhere received with enthusiasm by all the opposition parties. The Minister ordered the police to prevent any public demonstrations. Of course, that did not deter us. In fact, we had counted on the police prohibition to give more publicity to the demonstration and to instigate the masses to resistance.
To stop the people who were leaving a meeting-hall from going to the central square to demonstrate, the gendarmes fired on the unarmed crowd, killing three workers, and wounding twenty more. After this massacre, the gendarmes, frightened, rushed to the barracks for shelter, and the people were left masters of the town. Without anybody mentioning the word, a general strike was soon complete, and workers collected at the Trades Council to hold a meeting.
The Government tried to prevent the events of Ancona from being telegraphed to other parts of the country; but nevertheless by-and-by the news became known, and strikes broke out in all the towns of Italy. The two Federal labour organisations of Italy, the General Confederation of labour, which is reformist, and the _Unione Sindacale,_ with revolutionary tendencies, proclaimed a general strike, and the same was done by the Railwaymen's Union.
These strikes and demonstrations in several towns provoked new conflicts with police, and new massacres. At once, without any common understanding, one place ignorant of what the other was doing, as communications were broken off, the movement assumed everywhere an insurrectional character, and in many places the Republic, which meant for the people the autonomous Commune, was proclaimed.
All was going splendidly; the movement was developing, and the railway strike, spreading on all lines, paralyzed the Government; the workers were beginning to take measures of practical Communism in view of reorganising social life on a new basis; when suddenly the Confederation of labour, by an act which has been qualified as treachery, ordered the strike off, thereby throwing the workers into confusion and discouraging them.
The Government was not slow to profit by this condition, and began to restore "order."
If it had not been for the betrayal of the Confederation, though we could not yet have the revolution for the lack of necessary preparation and understanding, the movement would certainly have assumed larger proportions and a much greater importance.
In every way these events have proved that the mass of the people hate the present order; that the workers are disposed to make use of all opportunities to overthrow the. Government; and that when the fight is directed against the common enemy—that is to say, the Government and the bourgeoisie—all are brothers, though the names of Socialist, Anarchist, Syndicalist, or Republican may seem to divide them.
Now it is up to revolutionaries to profit by these good dispositions.
# **12**
Shortly after his return to London war broke out (August 1914) and not only was any anarchist activity made more difficult by the physical restrictions it imposed, but the fact that the anarchist movement itself was divided in its attitude to the conflagration meant that much of its activity would be neutralised by internal polemics. In _Freedom,_ November 1914 we find articles by Kropotkin, Jean Grave, Tcherkessoff, and a letter by the Belgian anarchist Verbelen all putting forward arguments why anarchists should support the Allied cause. And to rebut their rationalisations was Malatesta's contribution: "Anarchists have forgotten their Principles" (see Appendix I). The title was unfortunate since, as Malatesta notes in the first paragraph it applied to a minority of anarchists, even if among them were "comrades whom we love and respect most," yet the author of the recent study of _The Anarchists_ has used the title, to imply that Malatesta was a lone voice in a pro-war anarchist wilderness:
He [Malatesta] quarrelled with Kropotkin over Kropotkin's support for the war; and he remained a voice of the anarchist conscience constantly declaring that—to quote the title of one of his English articles of 1914—"The Anarchists have forgotten their principles."
As Mr. Joll notes later: "in 1919] Malatesta returned to Italy in triumph" ([p.179) and that Kropotkin's "position" when he returned to Russia in the summer of 1917 "was a curious one, for his support of the war had alienated him from nearly all the revolutionaries on the left" (p.180).
Indeed, but for the fact that the then editor of _Freedom,_ Thomas Keell, who was as opposed to the war as Malatesta and the overwhelming majority of the anarchist movement, was concerned as editor of an anarchist journal to give the "pro-war anarchists" more than a fair hearing, Kropotkin and his supporters would have found themselves in the political wilderness sooner than they did.
When Italy joined the allies Malatesta reiterated his opposition to war in an article headed _Italy Also! (Freedom,_ June 1915). In it he laments that in spite of "the fact that the great majority of Socialists and Syndicalists, and all the Anarchists (except a very few) were solid against war" which "gave us the hope that Italy would escape the massacre and keep all her forces for the works of peace and civilisation," Italy "has been dragged into the slaughter." And he adds:
We do not know, for want of reliable information, the present situation in Italy, and what are the true factors that have determined so quick a change in her attitude. But one redeeming feature is revealed by the news received in London.
The Italian government has felt that it was not safe to make war without suppressing every liberty, and putting in prison a great number of Anarchists.
This means that the Anarchists remain loyal to their flag to the last, and what is more important, that the Government fears their influence on the masses.
This gives us the assurance that as soon as the war fever has calmed down we will be able to begin again our own war—the war for human liberty, equality, and brotherhood—and in better conditions than before, because the people will have had another experience, and what a terrible one!...
And in 1916 Malatesta replies to the pro-war Manifesto signed by Kropotkin, Jean Grave, Malato, and thirteen other "old comrades" in the editorial columns of _Freedom 44_ in which he recognises the "good faith and good intentions" of the signatories as being "beyond all question," but must dissociate himself from "comrades who consider themselves able to reconcile anarchist ideas and cooperation with the Governments and capitalist classes of certain countries in their strife against the capitalists and Governments of certain other countries."
But this he had already done in a letter to _Freedom 45_ in the first months of the war in answer to Kropotkin's article in which he argued that "an anti-militarist propagandist ought never to join the anti-militarist agitation without taking in his inner self a solemn vow that in case a war breaks out, notwithstanding all efforts to prevent it, he will give the full support of his action to the country that will be invaded by a neighbour, whosoever the neighbour may be. Because, if the anti-militarists remain mere onlookers on the war, they support by their inaction the invaders; they help them to make slaves of the conquered populations; they aid them to become still stronger, and thus to be a still stronger obstacle to the Social Revolution in the future."
Malatesta's reply was couched in conciliatory terms though it must have been obviously clear to him that there was no possibility of Kropotkin "seeing his error" in view of the known fact that he had been for ten years "preaching against the 'German danger.'"
Dear Comrade—Allow me to say a few words on Kropotkin's article on Anti-militarism published in your last issue. In my opinion, anti-militarism is the doctrine which affirms that military service is an abominable and murderous trade, and that a man ought never to consent to take up arms at the command of the masters, and never fight except for the Social Revolution.
Is this to misunderstand anti-militarism?
Kropotkin seems to have forgotten the antagonism of the classes, the necessity of economic emancipation, and all the Anarchist teachings; and says that an anti-militarist ought always to be ready, in case a war breaks out, to take arms in support of the "country that will be invaded"; which considering the impossibility, at least for the ordinary workman, of verifying in time who is the real aggressor, practically means that Kropotkin's "anti-militarist" ought always to obey the orders of his government. What remains after that of anti-militarism, and, indeed, of Anarchism too?
As a matter of fact, Kropotkin renounces anti-militarism because he thinks that the national questions must be solved before the social question. For us, national rivalries and hatreds are among the best means the masters have for perpetuating the slavery of the workers, and we must oppose them with all our strength. And so to the right of the small nationalities to preserve, if you like, their language and their customs, that is simply a question of liberty, and will have a real and final solution only when, the States being destroyed, every human group, nay, every individual, will have the right to associate with, and separate from, every other group.
It is very painful for me to oppose a beloved friend like Kropotkin, who has done so much for the cause of Anarchism. But for the very reason that Kropotkin is so much esteemed and loved by us all, it is necessary to make known that we do not follow him in his utterances on the war.
I know that this attitude of Kropotkin is not quite new, and that for more than ten years he has been preaching against the "German danger"; and I confess that we were in the wrong in not giving importance to his Franco-Russian patriotism, and in not foreseeing where his anti-German prejudices would land him. It was because we understood that he meant to invite the French workers to answer a possible German invasion by making a Social Revolution—that is, by taking possession of the French soil, and trying to induce the German workers to fraternise with them in the struggle against French and German oppressors. Certainly we should never have dreamt that Kropotkin could invite the workers to make common cause with governments and masters.
I hope he will see his error, and be again on the side of the workers against all the Governments and all the bourgeois: German, English, French, Russian, Belgian, etc.
Yours fraternally,
E. Malatesta
# **13**
Malatesta spent many, years of his exile in London. When he arrived in 1900 he was forty-seven and at the height of his intellectual powers, and apart from the period 1913–14 spent so actively in Italy, remained in London until the end of 1919. Why did the old Internationalist apparently remain relatively inactive for so many years? It is significant that even Nettlau in his detailed biography of Malatesta has nothing to say about those years other than references to his anti-war stand and the criminal libel case against Malatesta (in 1913) which earned him a three month's prison sentence and a recommendation for deportation, which was not however proceeded with by the Home Secretary thanks to widespread demonstrations and protests which had made clear in what high esteem Malatesta was held by a wide public in this country.
One knows that Keell, for most of those years closely connected with _Freedom,_ as printer and later as editor too had a high regard for him, and in the _Freedom Bulletin_ of December 1932 which was a Malatesta Memorial number, Keell recounts that "if he were asked to write an article he would at first refuse, saying we should get English comrades to write for an English paper; but in the end he usually agreed." Judging by the number of his articles one finds in the files of _Freedom_ for those years one can only conclude that he was not often asked! To what extent was Malatesta inhibited from working with the English movement and contributing to _Freedom_ because of his differences with Kropotkin (with whom he was always careful to avoid engaging in public polemic—though this did not prevent him from pursuing his own line of thought in all his Italian writings)? Nettlau in an important series of articles on Malatesta after his death explains that his reluctance to join issue with Kropotkin was not for "reasons of friendship, but because he thought that the position Kropotkin had established for himself in the public mind in the large countries, by his personality, his intelligence and prestige, was an asset of great importance to the anarchist movement" and that only when Kropotkin sought to use it in favour of the Allies in the First World War did Malatesta feel obliged to challenge his old friend and comrade.
# **14**
As well as contributing to a large number of journals during his lifetime, (and of course many of his articles were translated and published in journals throughout the world) Malatesta was the editor of a number, never however for a long time, mainly because of police attention or government suppression. The list includes _Questione Sociale_ (Florence, 1883–84; Buenos Aires 1885; Paterson, NJ, 1899–1900), _l'Associazione_ (Ancona, 1889–90), _l'Agitazione_ (Ancona, 1897–98), _Volontà_ (Ancona, 1913–14), _Umanità Nova_ (1920–22), _Pensiero e Volontà_ (1924–26). Malatesta never wrote a full scale work on his ideas, and the means by which he thought they could be achieved, even though one finds him hinting in a letter to Fabbri that he might do something to please Fabbri in this respect, just as he never wrote his memoirs in spite of all kinds of attractive offers by publishers to do so. His pamphlets mostly written at the end of the last century include _Anarchy_ (1891) and those famous dialogues _Fra Contadini_ (1884), _Al Caffè_ (1902), _In Tempo di Elezioni_ (1890) which had an immense success at the time though we are all too sophisticated today to have our propaganda in this form (it's now done "live" on Television!).
# **15**
After the years of frustration in London during the 1914–18 War, Malatesta after much difficulty managed to return to Italy at the end of 1919 and the next three years (apart from a period of ten months in prison) were probably among the most active and rewarding in his long lifetime even though once again the hoped-for insurrection did not materialise, and the defeat of the working-class movement in Italy was to be marked by Mussolini's "march" to power. As well as editing the daily anarchist paper _Umanità Nova,_ Malatesta addressed meetings all over Italy, and was engaged in seeking to bring together all the revolutionary elements in the Socialist and republican parties, and in the Trade Union movement. A detailed study of this period would be a rewarding task for it would not only give a clear picture of Malatesta at work and his method of working, but also show to what extent a movement without large resources, and including in its ranks all shades of anarchism, including anti-organisers and believers in organisation, could work together for a common cause.
One would, of course, see the shortcomings, and the weaknesses, but one would also find, in my opinion, even greater shortcomings in the other antifascist, and revolutionary movements in spite of (or perhaps because of?) their authoritarian structure. The anarchists failed to stop Mussolini, but so too did the Socialist and Communist parties as well as the Trades Union organisations.
_Umanità Nova_ managed to survive for over two years, against all kinds of physical difficulties, from paper rationing to the destruction of the printing works and offices by gangs of young fascist thugs, and at its peak had a daily circulation of 50,000 copies. At the height of the agitation among the industrial workers, Malatesta, Borghi (who was then secretary of the Unione Sindacale Italiana, the revolutionary syndicalist Union which had sprung into life after the war and had a membership of more than 500,000), and some 80 other anarchists were arrested (October 1920) and were held in prison awaiting trial until the following July. At their trial which lasted four days, and which Malatesta used to great effect to plead his political cause, they were acquitted by the jury and set free. He moved to Rome where _Umanità Nova_ had been transferred in May 1921, and resumed his activity on the paper "giving it an orientation more in keeping with the situation" (Fabbri) and at the same time "seeking to draw together all the revolutionary and libertarian forces of resistance." His task was made more difficult because he now not only had to combat the opposition and sabotage of the reformist union leadership but also the hostility of the newly created Communist Party, which was trying to destroy and discredit all the working class forces which were not its creatures.
There was too, Fabbri points out, the beginnings of an internal crisis within the anarchist movement itself, (which, in certain parts of Italy because of fascist gangsterism was being reduced to impotence) and Malatesta used all his tact and experience to keep the movement together. During this period, as well as participating in the internal activities of the movement, he played a large part in the creation of the "Workers' Alliance" which sought to bring together the anti-fascist forces and which included all the workers organisations. Faced with the growing provocation of the fascists, the Alliance played its last card: the general strike. At the end of July the general strike took place and—according to Fabbri—"was successful throughout the country, at least where circumstances still permitted; but the desperate attempt nevertheless did not achieve its objective and was drowned in blood by the fascist hordes and the official police."
So far as propaganda activities were concerned the situation rapidly worsened. By now it was virtually impossible to distribute _Umanità Nova_ outside Rome and district, for parcels were either seized, by the postal authorities or at news agents kiosks and burnt, a fate suffered not only by the anarchist press but by all anti-fascist journals. In the circumstances _Umanità Nova_ ceased its daily publications in August 1922 and appeared as a weekly until the end of the year when Malatesta and a number of anarchists connected with the paper were arrested and charged. But it was obviously only a pretext to destroy the paper, for they were shortly afterwards released without trial. (Mussolini's "March" on Rome took place in October 1922.)
# **16**
Seeing no immediate possibility of continuing his activities as a propagandist, Malatesta put his pen to one side and took up his tool bag and, at the age of seventy started work again as an electrician-mechanic. He occasionally wrote however in two other anarchist journals which continued intermittently for a little while longer: _Il Libero Accordo_ an old anarchist journal edited by Temistocle Monticelli, and _Fede!_ a weekly started by Gigi Damiani.
Malatesta's 70th birthday (December 1923) was the occasion for public meetings in Paris, Buenos Aires, and elsewhere, and even in Rome and other parts of Italy it was celebrated but only at private meetings in view of the political repression. But equally important was the decision of many of his friends to give him the opportunity to continue to contribute to anarchist ideas, free from the day-to-day need to earn his living at his trade. And in fact at the beginning of 1924 he issued the first number of the bi-monthly magazine _Pensiero e Volontà_. In the first year of publication Press censorship was introduced after the murder (June 1924) of Matteotti, the socialist deputy (whose death caused such widespread revulsion as to threaten the fascist regime) and the magazine appeared regularly (24 issues) but its existence became more and more difficult. Only 16 issues appeared in 1925, and the feature "news of the fortnight" was forbidden by the authorities. In due course even theoretical articles were banned by the Censor and in 1926 16 issues appeared as well as five others heavily censored. The last issue was dated October 10, 1926. Before the next issue was due to appear, the anarchist, Anteo Zamboni, had made his unsuccessful attempt on Mussolini's life, and this was a pretext for the fascist government to suppress the whole anti-fascist, as well as the simply independent, press in Italy. Nettlau considers that Malatesta published in _Pensiero e Volontà_ "many of his most mature writings" (and readers of this volume have an opportunity to judge for themselves since I have drawn heavily on them) and Fabbri adds that through it Malatesta had been able "to remain in contact with comrades in all parts of Italy and abroad, and continue to participate, within the limits of what was possible, in the active movement."
With the suppression of _Pensiero e Volontà_ Malatesta's voice in Italy was silenced "forever," though he contributed a number of important articles to the international anarchist press, and which Nettlau, rightly I think, considers as "invaluable and the most notable production of modern Anarchist literature, something based upon an experience and keen reflection..." The quality of these writings can be judged by his Recollections on Kropotkin which was probably the last of these occasional writings penned during the last five years of his life. Notable too is his long introductory piece to Nettlau's thoroughgoing study of the International in Italy 1928 and his serene, uncompromising polemic with the Revisionists (Makhno and others) in 1927.
It was not new for Malatesta to have his steps dogged by policemen, and his movements noted by the police of the world. From the end of 1926 until he died in 1932 he lived in Rome under house arrest. A permanent police post was established in the porch of the house where he lived with his companion and her daughter, as well as a police guard day and night outside his flat. Whoever came to see him was arrested; and when he went out anybody approaching him was arrested. His mail was opened and not always delivered to him. Fabbri and other comrades in Paris and Switzerland tried to persuade him to leave Italy but he insisted that if he were capable of doing anything it would be by remaining in Italy and not in exile. By 1930 when he seems to have lost hope of any early change of regime and was prepared to leave, it was then too late.
# **17**
Malatesta must have met a great many of the most active as well as the "eminent" anarchists in the international movement, for there were periods in his lifetime when he travelled extensively, often taking part in the struggles in the countries he visited, and one feels that the absence of dogmatism from his approach to anarchism and the struggle was impressed on him by his experiences of the different problems and revolutionary possibilities that distinguished one country from another. Nettlau has briefly summarised Malatesta's activities outside Italy.
His travels and temporary residence provided him with new local experience, and he helped on his side the local comrades.
In Switzerland he knew Locarno and Lugano at various times; Bakunin's Russian friends in 1872, 1873, up to 1875; James Guillaume and the Jurassians, Zürich and Berne, Geneva when the _Révolté_ was founded (February, 1879), and on other occasions, for the last time in 1914 on his flight from Italy.
He was in Paris for many months, 1879, 1880, and beginning of 1881; very active in the first Anarchist groups there, soon expelled, returning again, arrested, imprisoned for returning. He nevertheless started in 1889 _L'Associazione_ in Nice, but had soon to leave; he was in Paris to observe the May Day movement of 1890, and no doubt on other occasions, but never resident, passing through there in 1914 on his hurried return to London.
In the autumn of 1875 he travelled to Spain; visited Madrid, Cadiz, and Barcelona, and saw the militants of the then proscribed, 1891 and secretly continued, International. He made an open journey, a great lecturing tour, from November, 1891, to January, 1892; but the intimate purpose was the preparation of Revolutionary Days in May, 1892. The tragic Jerez (Andalusia) revolt intervened, and he had to break his journey and leave quickly, reaching London via Lisbon this time.
In Egypt, 1878 and 1882, and in Rumania, 1879, he lived in the Italian _milieu,_ though he came to Egypt in 1882 for a revolutionary purpose connected with the natives' revolt in the days of Arabi Pasha. He intended, for romantic reasons (rivalry in combativeness of the young Internationalists with the young Garibaldians), to join the Serbians in their war against Turkey, 1876, but was twice stopped in Austria-Hungary and sent back to Italy.
He passed some time in Belgium in 1880 and a few days in 1881. He visited the country in 1893 during the political general strike, also 1907 during the violent Antwerp dock strike. Holland he knew at the time of the Amsterdam Anarchist Congress, 1907.
In London he saw the early days of the Socialist movement and knew Joseph Lane and Frank Kitz very well. Returning in October 1889, one of his first visits was to the Socialist League, where he saw William Morris. My acquaintance with him dates from that same evening and lasted until a letter of his to me of May 31, 1932, was the last one I got from him.
He lectured in New York and most of the Eastern industrial towns in the United States where Italian workers live (1899–1900). To Cuba, 1900, for Spanish lectures.
In the Argentine Republic, his activities from 1885 to the first half of 1889, mark the beginning of a more intense and coordinated movement there.
After the Russian revolution of 1917—I do not know at what stage of the ensuing events—he wished to go to Russia, to see things with his own eyes, but the British Government refused to let him depart.
This covers about all his known movement, though I do not pretend that I can retrace all his steps.
His last journey abroad was made in September, 1922, when a Jessinese comrade led him across the high mountains on smuggler paths in Switzerland, where he met the Italian Anarchists residing there in Biel, and the local and international comrades in St. Imier, at a private conference in commemoration of the St. Imier Congress of 1872, of which he was the sole survivor. When the meeting was over, the Swiss police with their order of expulsion of 1879 wanted to get hold of him, but he had just that moment been spirited away and returned to Italy.
# **18**
One other aspect of Malatesta's political life which deserves to be studied in some detail but to which I must be content with only a brief reference, is his attitude to police officials and to imprisonment.
In his time the ordinary policeman in Italy was more often than not some "poor devil"—as he would say—from the hungry South, less interested in protecting the State or of satisfying his personal lust for power, than in ensuring that he and his family could afford a square meal once a day. So Malatesta never missed an opportunity to "seduce" his captors by pointing out to them the relationship between the anarchist struggle and their struggle to live, and there are dozens of delightful anecdotes which illustrate Malatesta's successful technique with policemen and jailers. I would say that the times have changed, that the proportion of "poor devils" engaged in these jobs has considerably decreased in the past forty years, and that Malatesta who was a pragmatist, would today probably adopt quite another tactic. (Even the cover picture to this volume would indicate that the "rapport" with the British "bobby" in 1912 was not flowing with brotherly love even in one so experienced in handling policemen!)
In his youth, as he has already told us earlier in these Notes, being arrested and going to prison were part of the young revolutionaries' apprenticeship: "persecution only awakened our enthusiasm." But he also pointed out that in those days police persecution was a "joke compared with what took place later." It seems clear that during the 16 months he spent in prison awaiting trial for his part in the abortive attempt at insurrection in Benevento in 1877 (which resulted in the acquittal of all concerned) Malatesta had decided that he could better serve his ideas outside than behind prison bars and whenever, therefore, he knew that his activities were about to be curtailed by the authorities, he generally chose the road of exile rather than long months in prison awaiting trial.
Some of the most vulgar and vocal of his political enemies accused him of cowardice, of running away when he should be facing the music; on one occasion in the early twenties, they accused him of cowardice because he took shelter in a doorway during an exchange of shots between police and demonstrators. Malatesta in spite of his rhetorical sortie to the jury at his trial in 1922 "though I am a man with a cause ( _un uomo di fede_ ) I am not a hero. 'The spirit is willing, the flesh is weak' say the mystics. I love life, I love many people who love me..." was playing his cards for one end only, acquittal in order to resume the struggle for revolution as the only answer to the threat of fascism. Had Malatesta and Borghi been free to continue their propaganda during those 10 vital months awaiting trial who knows how the political situation might have developed. It might well have ended in the way it did. But can anyone say that their imprisonment _furthered the revolutionary cause?_
Malatesta was neither a coward nor a hero; he was a courageous and determined man who used these qualities with intelligence. As it was this did not prevent him from spending more time in prison than he would have liked! To the jury at his trial in 1922 he said: "Though I have only served seven months of the sentences imposed on me—all the other sentences were either quashed or annulled by amnesties—yet Authority has managed to make me spend, in bits and pieces, more than ten years of my life in prison." That is, _awaiting_ trial, which more often than not ended in acquittal. Those of us accustomed to British penal procedure will find it difficult to understand how, for instance Malatesta, should have been kept in prison in Italy in 1883 from May to November, awaiting trial and then when found guilty and sentenced to three years imprisonment, released pending appeal, during which time he edited an anarchist paper in Florence (and also tended the sick in the cholera epidemic in Naples). And then managing to escape in the nick of time when he learned that his appeal had failed! Instead of three years in an Italian prison Malatesta spent them in Argentina (1885–89) where he did much to help build up the anarchist and syndicalist movement in that country (the only one, apart from Italy, Spain, and Russia in very exceptional circumstances, which in later years managed to publish a daily anarchist paper for a number of years).
Malatesta, the mature revolutionary, took "calculated" risks, that is, he was prepared to face imprisonment if he felt the revolutionary possibilities justified the risk and he had a chance of fulfilling his assignment before being arrested. Thus in 1897 after the fall of the Crispi government there were possibilities of doing anarchist propaganda openly in Italy, and though his three year sentence of 1883 could be executed until November of that year when it would then automatically lapse, Malatesta thought it worth taking the risk and returned secretly to Ancona in March where he lived in a room from which he edited the weekly anarchist journal _l'Agitazione._ To avoid capture by the Italian police who had been alerted of his disappearance from London he had to refrain from any public activities or appearance at propaganda meetings; the fact that the police suspected that he might be in Ancona also meant that all his contacts with the local comrades, many of them known to, or watched by, the police, had to be conducted with the utmost circumspection. Because he could not by force of circumstances be distracted from his editorial functions by meetings and demonstrations, Fabbri considers _l'Agitazione_ "historically and theoretically," the most important publication edited by Malatesta. (I have unfortunately been unable to see a single copy of this journal though many of Malatesta's articles have been included in the two volumes of selections published in Naples in the post-War years.)
Malatesta would have continued to live clandestinely even after his earlier sentence had automatically expired because he feared that the police would arrest him on any pretext just to keep him from his propaganda which was producing results, and was obviously not to the liking of the then Italian government. Through no indiscretion on his part the police came to know of his hideout and he was arrested but set free the same day. That was in November. Between then and January Malatesta now free to take part in public activities intensified his work, but, as he had expected, the authorities did not leave him alone for long. On the 18th January 1898, during a public demonstration he and eight other comrades including the manager of the weekly were arrested in the street and charged with "criminal association."
One of the interesting aspects of this trial was that whereas in past trials most anarchists denied the charge on the grounds that they were opposed to organisation, Malatesta and his friends not only declared that they were organised, but also demanded the right of anarchists to join a formal organisation. This gave rise to agitation throughout Italy for "the freedom to organise," promoted by the Anarchist Socialist Federation of Romagna, and supported energetically from the columns of _l'Agitazione,_ which continued publication in spite of further arrests of those who had taken Malatesta's place on the paper (among them Fabbri, a young man of 20). By the time the trial took place, four months later, over 3,000 anarchists, in the name of many groups and clubs had signed a public manifesto in which they declared their political beliefs, and affirmed that they were members of a "party," and in complete agreement with the accused. More support came from all parts of the world.
Thus the trial, writes Fabbri, was converted into a battle for public rights, as well as being, as many others were, an excellent medium for anarchist propaganda. It lasted a whole week, at the end of which Malatesta was given a seven month sentence, seven other comrades received six months and one was acquitted. Nevertheless this was a victory in that from then on the right of anarchists to organise themselves was recognised, and though this did not prevent them from being arrested and charged with "subversive" activities, the penalties were less severe and the powers of arrest were less arbitrary. Or were they?
A month after Malatesta's trial widespread popular riots in Milan took place which were violently put down with many dead and wounded among the demonstrators. _l'Agitazione_ was banned and most of the members of the publishing group, who were still free, were arrested. Parliament approved emergency laws, and _domicilio coatto_ (banishment to the penal islands) was reintroduced under worse conditions than before. So when Malatesta's sentence expired in August (and his seven comrades, a month earlier) instead of being released they were held in prison and sentenced to five years _domicilio coatto._
# **19**
Malatesta was sent to Ustica and he soon decided that he would not willingly spend five years on this inhospitable island, and began laying his plans for escape. The Government having also guessed his intentions, had Malatesta transferred to the island of Lampedusa, a more difficult island from which to escape! What the government had overlooked was the sympathetic "governor" on Lampedusa who was so impressed by Malatesta and the other "politicals" that he gave them a free hand, "and closed his eyes to what was going on." Malatesta made his plans for escape carefully and unhurriedly. Not only did he find a way of establishing contact with those on the mainland, but Fabbri recounts that even the socialist Oddino Morgari, who visited the island, in his capacity of Parliamentary deputy, was privy to his plans. On the night of May 9, 1899, Malatesta, Vivoli, a comrade from Florence, and a civil detainee swam to a fishing boat anchored some way out (with a Sicilian socialist Lovetere aboard) boarded her and set sail for Malta. Their escape was discovered the next day because of the unexpected visit to the island of a government inspector sent to investigate rumours circulating in Rome about Malatesta's escape plans! But they were too late. Malatesta reached Malta where he remained a week awaiting a ship to take him to England. A few days later he was back with the Defendi family in Islington. But within a matter of a few weeks he was on his way to Paterson, New Jersey, at the invitation of the Italian comrades there who wanted him to take over the editorship of their periodical _La Questione Sociale._ However, he remained in the United States only a few months, during which time as well as editing the paper he addressed many public meetings, in Italian and Spanish, throughout the continent. Before returning to London he spent ten days in Cuba where he had been invited to address a number of meetings. In spite of difficulties by the police who at first prohibited his meetings and then agreed to their being held so long as he didn't use the word anarchy, Malatesta managed to address four meetings but then decided that it was not worth going on with the tour and returned to New York in March. In April he was back in London.
Fabbri writes that "personal reasons determined his decision to return to London" but gives no indication whether these were political or domestic. There was obviously no political reason for returning to London, but there might well have been for leaving the United States. Nettlau writes that Malatesta's support for organisation always met with strong opposition from the individualist anarchists. His invitation to edit the anarchist journal in Paterson coincided with the announcement that the former editor Giuseppe Ciancabilla was starting another paper, _Aurora,_ with the support of "all" the comrades. Though I, and readers of these notes, may see no point now in establishing the facts of Malatesta's activities during those months, in detail, I referred to it in the first place in ordering to illustrate Malatesta's practical attitude to the propaganda value of imprisonment. His arrest, trial and imprisonment in 1898, was in his opinion good propaganda, the culmination of long months of clandestine activity as editor of _l'Agitazione._ The prospect of five years in the penal islands was not. Hence his determination to escape at all costs. Perhaps those five years, with the exception of the months in the Americas, were not as rewarding as he might have wished, but I suggest that they were better spent both so far as he was concerned and the anarchist movement, than if he had served his five years in _domicilio coatto._
The other reason for referring to the months in the States is to state the facts concerning an incident in which Malatesta was the central figure. At a meeting he was addressing in West Hoboken (now Union City, New Jersey) heated discussion followed in which one member of the audience challenged the speaker, and when Malatesta "put him in his place" he was obviously so incensed that he drew out a revolver and fired at him hitting him in the leg. He was disarmed by a man "one of the most tolerant you could find, and a member of Malatesta's group" the man, who months later was to return to Italy to assassinate King Humbert: Gaetano Bresci.
The false rumour was circulated that Malatesta's assailant was another anarchist, and one can understand with what relish this tit-bit of political scandal was repeated by the anarchists' detractors on every possible occasion. Some thirty years after the shooting it was revived with the publication of Max Nomad's _Rebels and Renegades_ and the anarchists in the United States through their journals had to repeat the true facts, but they could never delete the falsehoods committed to print in Nomad's book. Indeed thirty years after Nomad, George Woodcock (who should have known better than to rely on Nomad for source material) in his history of anarchism (American edition) repeats the lie, naming Ciancabilla as Malatesta's would-be assassin.
In itself the shooting incident is a minor incident in a long and full life and it is as such that it is treated in these Notes. But from the point of view of anarchist propaganda the Nomad-Woodcock version could do great harm even now, and for this reason the facts of the shooting incident are presented as an Appendix, because I hope that English historians who may want to include Malatesta in their magnus opus, and are barred from consulting the original sources by language problems, will at least consult this work rather than Nomad's concoction of half-truths and pure invention!
# **20**
At the beginning of these notes I quoted a passage from Woodcock's History in which he describes Malatesta and other young Internationalists as "the Italian equivalent of the conscience-stricken Russian noblemen" who in the same decade felt the burning urge to go to the people, and produced evidence to try to show that the analogy was not a correct one. I return to it now because Malatesta's character was so unlike this generalisation, and his approach to the social problems so different, that only by fully appreciating this can one put his sixty years militancy in proper perspective.
All the evidence points to the fact that Malatesta did not have a sheltered youth, even though it is clear that his family had the means to allow him to pursue his studies without having to worry about his next meal. His entry into politics was typical of a normal, impulsive "teenager" and just as so many young people in this country were drawn into some kind of political commitment by the enthusiasm that surrounded the first Aldermaston March, so many in Malatesta's time must have felt the same way as a result of the daring exploits of Garibaldi and his "liberators." (And according to Nettlau it is possible that Malatesta as a young boy actually witnessed the liberators in action when Santa Maria and Capua were the centres of fierce struggles.) But what is surely significant in Malatesta's case is that in a matter of three or four years he had "seen through," as well as sympathised with, the Garibaldians and the Mazzinians, and also "discovered" Bakunin and the International. And his mental development took place in the course of political activities of all kinds which gave him an early taste of Authority and government. By contrast both Bakunin and Kropotkin entered the struggle following a relatively long intellectual preparation. Kropotkin was in his 30th year when he made his "first journey abroad" and began reading all the "socialistic literature" he could lay hands on. In his Memoirs he writes:
I spent days and nights in reading, and received a deep impression which nothing will efface.... The more I read the more I saw that there was before me a new world, unknown to me, and totally unknown to the learned makers of sociological theories—a world that I could know only by living in the Workingmen's Association and by meeting the workers in their everyday life. I decided accordingly to spend a couple of months in such a life....
For Bakunin it was in Dresden in 1842—when he was 28—that, to quote Carr, he "was ready to proclaim to the world his conversion to the cause of revolution."
The winter of 1841–42 which he spent alone in Berlin seems to have been the decisive period of Bakunin's conversion. He devoured greedily the mass of pamphlets and dissertations with which the young Hegelians under the very nose of the censors, were flooding Germany.... By the time he settled again in Dresden in the summer of 1842, Bakunin was a full-blown young Hegelian. Ruge discovered that he had "outstripped all the old donkeys in Berlin."
For Malatesta, "going to the people" involved total identification with the working people _as one of them._ And this he did early in life. As soon as he came into his inheritance he handed the properties to his working tenants and what money came to him was used for propaganda. In his early twenties he learned the trade of mechanic in the workshop of a friend and Internationalist, one Agenore Natta of Florence. Throughout his long life Malatesta earned his living as a mechanic-electrician, except when the political situation demanded, and the anarchist movement could afford to keep him, while he devoted his activities full time to the political struggle. Just as he was always opposed to permanent Union officials and organisers, so was he opposed to revolutionaries, being "kept" by the movement. It was not only a matter of principle, that is a rule based on experience, of the harmful effects that inevitably accrued from full-time officials, but also an expression of his own independent spirit, which could not be free unless he were also financially independent of the anarchist movement.
This is why it is wrong to portray Malatesta as the professional agitator and revolutionary, in fact, as well as in the interest of the anarchist movement. For if his life is as important to the anarchist movement as are his ideas, it is just because he was neither the professional revolutionary nor "the saint," neither the "prophet" nor the "man of destiny." Malatesta was always a comrade among comrades, ever seeking to forward his point of view but never seeking to dominate an argument with the weight of his personality. In this connection it is significant that as a speaker he never used oratorical tricks, just as in his writings he was always concerned with convincing readers by the clarity, the logic, and sheer commonsense of his arguments. And because of this approach, rather than in spite of it, all his writings, and I am sure his speeches too, are full of real human warmth for they are based on understanding of the problems (as well as the difficulties in overcoming them) that face all those who are willing and anxious to do something to radically change society.
Malatesta was fully aware of the dangers, as well as the advantages, that the "eminence" or "notoriety" he and a few others enjoyed in the international anarchist movement and in the world of Left politics. It is probably true to say that he went out of his way to underestimate his worth so far as the anarchist movement was concerned, but to exploit his standing in the working class movement whenever he thought it imperative to bring together all the movements and parties of the so-called revolutionary Left to accept an _Entente_ on specific issues. Malatesta was always very "politically conscious," without ever becoming, however, a politician. He explored every political opening—as some of his political enemies were to remind him years later, without however adding the important point, that Malatesta the anarchist emerged unscathed from his excursions along "the paths of political evil"! His anarchism was not in his head but in his heart, or to quote his words "This feeling is the love of mankind, and the fact of sharing the sufferings of others...." But in order to achieve his ends he was always guided by his "head"—that is by his observation and understanding of the human and material problems to be overcome.
# **21**
In a much publicised recent work on _The Anarchists,_ the author, from his cloistered university outpost pronounces sentence on "a disappointed life" when he declares that at the end of Malatesta's life (1932) "The Italian State was... a stronger and more formidable adversary than it had ever been." But surely, Malatesta's life was full, and rich, and satisfying; his ideas still stimulating, and informed by the kind of common sense and humanity millions of our fellow beings have yet to discover.
And is there no lesson to be learned about what _matters_ in our lives, as individuals, and as a civilisation, when, more than thirty years after his death, Malatesta the man and his ideas, are being presented to the English speaking public more or less for the first time, while at the same time the world is desperately trying to forget that Mussolini and the other sordid actors in that "age of disgrace" ever existed? A thought surely, which those historians who are now so busily writing the obituary notices of anarchism might do well to ponder over!
V.R.
# **A PPENDIX I**
# **Anarchists Have Forgotten Their Principles**
# **by E. MALATESTA ( _Freedom,_ November 1914)**
AT THE RISK OF PASSING AS A SIMPLETON, I CONFESS THAT I would never have believed it possible that Socialists—even Social Democrats—would applaud and voluntarily take part, either on the side of the Germans or on that of the Allies, in a war like the one that is at present devastating Europe. But what is there to say when the same is done by Anarchists—not numerous, it is true, but having among them comrades whom we love and respect most?
It is said that the present situation shows the bankruptcy of "our formulas"—i.e., of our principles—and that it will be necessary to revise them.
Generally speaking, every formula must be revised whenever it shows itself insufficient when coming into contact with fact; but it is not the case today, when the bankruptcy is not derived from the shortcoming of our formulas, but from the fact that these have been forgotten and betrayed.
Let us return to our principles.
I am not a "pacifist." I fight, as we all do, for the triumph of peace and of fraternity among all human beings; but I know that a desire not to fight can only be fulfilled when neither side wants to, and that so long as men will be found who want to violate the liberties of others, it is incumbent on these others to defend themselves if they do not wish to be eternally beaten; and I also know that to attack is often the best, or the only, effective means of defending oneself. Besides, I think that the oppressed are always in a state of legitimate self-defence, and have always the right to attack the oppressors. I admit, therefore, that there are wars that are necessary, holy wars: and these are wars of liberation, such as are generally "civil wars"—i.e., revolutions.
But what has the present war in common with human emancipation, which is our cause?
Today we hear Socialists speak, just like any bourgeois, of "France," or "Germany," and of other political and national agglomerations—results of historical struggles—as of homogeneous ethnographic units, each having its proper interests, aspirations, and mission, in opposition to the interests, aspirations, and mission of rival units. This may be true relatively, so long as the oppressed, and chiefly the workers, have no self-consciousness, fail to recognise the injustice of their inferior position, and make themselves the docile tools of the oppressors. There is, then, the dominating class only that counts; and this class, owing to its desire to conserve and to enlarge its power, even its prejudices and its own ideas, may find it convenient to excite racial ambitions and hatred, and send its nation, its flock, against "foreign" countries, with a view to releasing them from their present oppressors, and submitting them to its own political and economical domination.
But the mission of those who, like us, wish the end of all oppression and of all exploitation of man by man, is to awaken a consciousness of the antagonism of interests between dominators and dominated, between exploiters and workers, and to develop the class struggle inside each country, and the solidarity among all workers across the frontiers, as against any prejudice and any passion of either race or nationality.
And this we have always done. We have always preached that the workers of all countries are brothers, and that the enemy—the "foreigner"—is the exploiter, whether born near us or in a far-off country, whether speaking the same language or any other. We have always chosen our friends, our companions-in-arms, as well as our enemies, because of the ideas they profess and of the position they occupy in the social struggle, and never for reasons of race or nationality. We have always fought against patriotism, which is a survival of the past, and serves well the interests of the oppressors; and we were proud of being internationalists, not only in words, but by the deep feelings of our souls.
And now that the most atrocious consequences of capitalist and State domination should indicate, even to the blind, that we were in the right, most of the Socialists and many Anarchists in the belligerent countries associate themselves with the Governments and the bourgeoisie of their respective countries, forgetting Socialism, the class struggle, international fraternity, and the rest.
What a downfall!
It is possible that present events may have shown that national feelings are more alive, while feelings of international brotherhood are less rooted, than we thought; but this should be one more reason for intensifying, not abandoning, our anti-patriotic propaganda. These events also show that in France, for example, religious sentiment is stronger, and the priests have a greater influence than we imagined. Is this a reason for our conversion to Roman Catholicism?
I understand that circumstances may arise owing to which the help of all is necessary for the general well-being: such as an epidemic, an earthquake, an invasion of barbarians, who kill and destroy all that comes under their hands. In such a case the class struggle, the differences of social standing must be forgotten, and common cause must be made against the common danger; but on the condition that these differences are forgotten on both sides. If any one is in prison during an earthquake, and there is a danger of his being crushed to death, it is our duty to save everybody, even the gaolers—on condition that the gaolers begin by opening the prison doors. But if the gaolers take all precautions for the safe custody of the prisoners during and after the catastrophe, it is then the duty of the prisoners towards themselves as well as towards their comrades in captivity to leave the gaolers to their troubles, and profit by the occasion to save themselves.
If, when foreign soldiers invade the _sacred soil of the Fatherland,_ the privileged class were to renounce their privileges, and would act so that the "Fatherland" really became the common property of all the inhabitants, it would then be right that all should fight against the invaders. But if kings wish to remain kings, and the landlords wish to take care of _their_ lands and of _their_ houses, and the merchants wish to take care of _their_ goods, and even sell them at a higher price, then the workers, the Socialists and Anarchists, should leave them to their own devices, while being themselves on the look-out for an opportunity to get rid of the oppressors inside the country, as well as of those coming from outside.
In all circumstances, it is the duty of the Socialists, and especially of the Anarchists, to do everything that can weaken the State and the capitalist class, and to take as the only guide to their conduct the interests of Socialism; or, if they are materially powerless to act efficaciously for their own cause, at least to refuse any voluntary help to the cause of the enemy, and stand aside to save at least their principles—which means to save the future.
All I have just said is theory, and perhaps it is accepted, in theory, by most of those who, in practice, do just the reverse. How, then, could it be applied to the present situation? What should we do, what should we wish, in the interests of our cause?
It is said, on this side of the Rhine, that the victory of the Allies would be the end of militarism, the triumph of civilisation, international justice, etc. The same is said on the other side of the frontier about a German victory.
Personally, judging at their true value the "mad dog" of Berlin and the "old hangman" of Vienna, I have no greater confidence in the bloody Tsar, nor in the English diplomatists who oppress India, who betrayed Persia, who crushed the Boer Republics; nor in the French bourgeoisie, who massacred the natives of Morocco; nor in those of Belgium, who have allowed the Congo atrocities and have largely profited by them—and I only recall some of their misdeeds, taken at random, not to mention what all Governments and all capitalist classes do against the workers and the rebels in their own countries.
In my opinion, the victory of Germany would certainly mean the triumph of militarism and of reaction; but the triumph of the Allies would mean a Russo-English (i.e., a knouto-capitalist) domination in Europe and in Asia, conscription and the development of the militarist spirit in England, and a Clerical and perhaps Monarchist reaction in France.
Besides, in my opinion, it is most probable that there will be no definite victory on either side. After a long war, an enormous loss of life and wealth, both sides being exhausted, some kind of peace will be patched up, leaving all questions open, thus preparing for a new war more murderous than the present.
The only hope is revolution; and as I think that it is from vanquished Germany that in all probability, owing to the present state of things, the revolution would break out, it is for this reason—and for this reason only—that I wish the defeat of Germany.
I may, of course, be mistaken in appreciating the true position. But what seems to me elementary and fundamental for all Socialists (Anarchists, or others) is that it is necessary to keep outside every kind of compromise with the Governments and the governing classes, so as to be able to profit by any opportunity that may present itself, and, in any case, to be able to restart and continue our revolutionary preparations and propaganda.
A young Errico Malatesta
# **A PPENDIX II**
# **Pro-Government Anarchists**
# **by E. MALATESTA ( _Freedom,_ April 1916)**
A MANIFESTO HAS JUST APPEARED, SIGNED BY KROPOTKIN, GRAVE, Malato, and a dozen other old comrades, in which, echoing the supporters of the Entente Governments who are demanding a fight to a finish and the crushing of Germany, they take their stand against any idea of "premature peace."
The capitalist Press publishes, with natural satisfaction, extracts from the manifesto, and announces it as the work of "leaders of the International Anarchist Movement."
Anarchists, almost all of whom have remained faithful to their convictions, owe it to themselves to protest against this attempt to implicate Anarchism in the continuance of a ferocious slaughter that has never held promise of any benefit to the cause of Justice and Liberty, and which now shows itself to be absolutely barren and resultless even from the standpoint of the rulers on either side.
The good faith and good intentions of those who have signed the manifesto are beyond all question. But, however painful it may be to disagree with old friends who have rendered so many services to that which in the past was our common cause, one cannot—having regard to sincerity, and in the interest of our movement for emancipation—fail to dissociate oneself from comrades who consider themselves able to reconcile Anarchist ideas and cooperation with the Governments and capitalist classes of certain countries in their strife against the capitalists and Governments of certain other countries.
During the present war we have seen Republicans placing themselves at the service of kings, Socialists making common cause with the ruling class, labourists serving the interests of capitalists; but in reality all these people are, in varying degrees, Conservatives—believers in the mission of the State, and their hesitation can be understood when the only remedy lay in the destruction of every Governmental chain and the unloosing of the Social Revolution. But such hesitation is incomprehensible in the case of Anarchists.
We hold that the State is incapable of good. In the field of international as well as of individual relations it can only combat aggression by making itself the aggressor; it can only hinder crime by organising and committing still greater crime.
Even on the supposition—which is far from being the truth—that Germany alone was responsible for the present war, it is proved that, as long as governmental methods are adhered to, Germany can only be resisted by suppressing all liberty and reviving the power of all the forces of reaction. Except the popular Revolution, there is no other way of resisting the menace of a disciplined Army but to try and have a stronger and more disciplined Army; so that the sternest anti-militarists, if they are not Anarchists, and if they are afraid of the destruction of the State, are inevitably led to become ardent militarists.
In fact, in the problematical hope of crushing Prussian Militarism, they have renounced all the spirit and all the traditions of Liberty; they have Prussianised England and France; they have submitted themselves to Tsarism; they have restored the prestige of the tottering throne of Italy.
Can Anarchists accept this state of things for a single moment without renouncing all right to call themselves Anarchists? To me, even foreign domination suffered by force and leading to revolt, is preferable to domestic oppression meekly, almost gratefully, accepted, in the belief that by this means we are preserved from a greater evil.
It is useless to say that this is a question of an exceptional time, and that after having contributed to the victory of the Entente in "this war," we shall return, each into his own camp, to the struggle for his own ideal.
If it is necessary today to work in harmony with the Government and the capitalist to defend ourselves against "the German menace," it will be necessary afterwards, as well as during the war.
However great may be the defeat of the German Army—if it is true that it will be defeated—it will never be possible to prevent the German patriots thinking of, and preparing for, revenge; and the patriots of the other countries, very reasonably from their own point of view, will want to hold themselves in readiness so that they may not again be taken unawares. This means that Prussian Militarism will become a permanent and regular institution in all countries.
What will then be said by the self-styled Anarchists who today desire the victory of one of the warring affiances? Will they go on calling themselves anti-militarists and preaching disarmament, refusal to do military service, and sabotage against National Defence, only to become, at the first threat of war, recruiting-sergeants for the Governments that they have attempted to disarm and paralyze?
It will be said that these things will come to an end when the German people have rid themselves of their tyrants and ceased to be a menace to Europe by destroying militarism in their own country. But, if that is the case, the Germans who think, and rightly so, that English and French domination (to say nothing of Tsarist Russia) would be no more delightful to the Germans than German domination to the French and English, will desire first to wait for the Russians and the others to destroy their own militarism, and will meanwhile continue to increase their own country's Army.
And then, how long will the Revolution be delayed? How long Anarchy? Must we always wait for the others to begin?
The line of conduct for Anarchists is clearly marked out by the very logic of their aspirations.
The war ought to have been prevented by bringing about the Revolution, or at least by making the Government afraid of the Revolution. Either the strength or the skill necessary for this has been lacking.
Peace ought to be imposed by bringing about the Revolution, or at least by threatening to do so. To the present time, the strength or the skill is wanting.
Well! there is only one remedy: to do better in future. More than ever we must avoid compromise; deepen the chasm between capitalists and wage-slaves, between rulers and ruled; preach expropriation of private property and the destruction of States as the only means of guaranteeing fraternity between the peoples and Justice and Liberty for all; and we must prepare to accomplish these things.
Meanwhile it seems to me that it is criminal to do anything that tends to prolong the war, that slaughters men destroys wealth, and hinders all resumption of the struggle for emancipation. It appears to me that preaching "war to the end" is really playing the game of the German rulers, who are deceiving their subjects and inflaming their ardour for fighting by persuading them that their opponents desire to crush and enslave the German people.
Today, as ever, let this be our slogan: Down with Capitalists and Governments, all Capitalists and all Governments!
Long live the peoples, all the peoples!
# **A PPENDIX III**
# **Fact and Fiction on the Shooting Incident at a Meeting Addressed by Malatesta in West Hoboken in 1899**
THIS MINOR INCIDENT IN A VERY FULL LIFE WOULD HAVE BEEN put in its proper perspective but for the exaggerated importance attributed to it, as well as the falsification of the facts, by writers more concerned with satisfying their publishers' interest and with entertaining the reading public, than with establishing the facts as well as getting them in their proper perspective.
"Max Nomad"—described in the publisher's blurb of the original American edition of his book _Rebels and Renegades 1_ as "the pen-name of a political emigrant from prewar [1914–18] Europe who has been either a sympathetic observer of, or an active participant in the extreme left-wing revolutionary movements" in some European countries as well as in the United States since—devotes the first of his "sketches of persons still living, who have been prominently identified with revolutionary or labour movements," to Malatesta. The sketch, nearly fifty pages long is a combination of the kind of concoction of half truths one would expect from a newspaper hack and the anti-libertarian hysteria of one who at the time [1932], at least, was a revolutionary of the authoritarian school, an admirer of Lenin and Trotsky as well as Stalin and William Z. Foster. Suffice it to say, that in the mid-twentieth century Max Nomad's name crops up in the columns of the American _Socialist Call_ and in the _New Leader_ peddling anti-Communism and still as anti-anarchist as ever!
In _Rebels and Renegades,_ Nomad writes of Malatesta's stay in America:
The inevitable discussions as to the merits or demerits of organisation now began again, and this time almost cost him his life. During one of these disputes G. Ciancabilla, the leader of the "anti-organizzatori" seeing that the majority were siding with the old champion, emphasised his own argument by emptying his revolver into the body of his opponent. The hero escaped, and Malatesta, unable to leave the place on account of his wound, was arrested. He refused to name his assailant, although the police left him for a time without any treatment in the hope of forcing him to give the desired information. Ciancabilla remained a prophet among the guardians of the Holy Grail of unrestrained individual liberty, and died a few years later in California where he edited a paper with the fitting title _La Protesta Umana._
It was an easy matter to demolish Nomad's fantasy: Ciancabilla was not at the meeting at which Malatesta was shot at; and his assailant was one Domenico Pazzaglia, a barber, "unknown to most of the comrades and ignored by the few who knew him." The anarchist monthly _man!_ (March 1933) further points out that Ciancabilla disapproved of Pazzaglia's act. The July number of that journal published a letter from Nomad in which he apologised for confusing Ciancabilla with Pazzaglia, but asserts that the latter was a follower of Ciancabilla that is, presumably an "anti-organizzatore." Was Ciancabilla such?
In 1897 he was editor of the socialist paper _Avanti!_ (Forward) and published a most interesting interview with Malatesta which took place in "a small railway station, in between trains, and we talked for about an hour, arm in arm, walking up and down the platform under the very noses of two carbineers and a plain clothes detective, detailed to keep a watch on stations."
Apart from the relationship between the two men, which was to become more intimate when Ciancabilla became an anarchist, what is interesting about the preamble to this interview is that this was the period when Malatesta was living incognito in Ancona and the object of a nation-wide police hunt! Was Ciancabilla's preamble one of the many attempts to put the police off the scent, or did he really meet Malatesta in "a small railway station"? I must confess that I am curious to know the answer! Anyway, it was during this period that Ciancabilla as well as a number of other socialists, among them Mamolo Zamboni (father of the Zamboni who years later—in 1926—made the unsuccessful attempt on Mussolini's life) joined the anarchists under the influence of Malatesta. I find it surprising therefore that in so short a time Ciancabilla should have become the spokesman of the individualist section of the Italo-American anarchist movement. Not only was he the Italian translator of Kropotkin's _Conquest of Bread_ (we know, Mussolini also translated Kropotkin!) but even in September 1899 he was expressing the view in _Questione Sociale_ that he could not conceive individual or collective well-being without order, social services, and "a harmonious society based on associations and collectivities functioning organically."
Thirty years after his libel on Ciancabilla and on Malatesta (for Nomad's potted historical sketch can be faulted factually on every page—irrespective of his sneers and guffaws) George Woodcock's history of anarchism was published in the United States as a paperback, and because Professor Woodcock was content to rely on Nomad rather than Nettlau, Fabbri, Borghi, or even his erstwhile comrades in the English speaking world, for his references to Malatesta, he repeated the Nomad libel, presumably unaware of Nomad's subsequent rectification. Not only must one charge Woodcock with not having checked his sources, especially when they are Marx Nomad; but when he was politely informed of his error by anarchists in the United States, he felt it sufficient to change two words in the passage complained of when his _History_ appeared in an English edition to put the record right. I must reproduce the whole paragraph from the American edition in order also to illustrate the slapdash way these professionals of the written word happily churn out the words by the thousand:
As a result of the tense atmosphere which followed the 1898 rising, Malatesta was not released at the end of his prison term, but instead, with a number of other leaders of the movement, was sent to exile for five years on the island of Lampedusa. He did not stay there long. One stormy day he and three of his comrades seized a boat and put out to sea in defiance of the high waves. They were lucky enough to be picked up by a ship on its way to Malta, whence Malatesta sailed to the United States. There his life once again took a sensational turn, which this time almost brought it to an end. He became involved in a dispute with the individualist anarchists of Paterson, who insisted that anarchism implied no organisation at all, and that every man must act solely on his impulses. At last, in one noisy debate, the individual impulse of a certain Ciancabilla directed him to shoot Malatesta who was badly wounded but who obstinately refused to name his assailant. Ciancabilla fled to California, and Malatesta eventually recovered; in 1900 he set sail for London which by now had become his favourite place of exile.
In the Pelican edition, Professor Woodcock deletes the two references to Ciancabilla by name and in place of the first substitutes "a Comrade" and for the second "the would-be assailant." Thus is serious history written: a named comrade becomes "a Comrade" (with a capital C) and "Ciancabilla" becomes the "would-be-assailant" and in Professor Woodcock's two editions both "fled to California." Not in the interests of history but in order to debunk the Woodcocks and the army of self-appointed historians who have neither the love of their _métier_ nor a sense of responsibility towards their readers, I have quoted the paragraph from Woodcock's history in full. I do not propose to analyze the paragraph for factual errors, the reader can do this for himself by comparing it with my brief account of this period. I cannot resist however, underlining what I think is the prize sentence from Professor Woodcock's paragraph: "One stormy day he and three of his comrades seized a boat and put out to sea in defiance of the high waves!"
# **A PPENDIX IV**
# **Pietro Kropotkin—Ricordi E Critiche Di Un Vecchio Amico (Peter Kropotkin—Recollections and Criticisms of an Old Friend)**
# **by E. Malatesta ( _Studi Sociali,_ April 15, 1931)**
PETER KROPOTKIN IS WITHOUT DOUBT ONE OF THOSE WHO HAVE contributed perhaps most—perhaps more even than Bakunin and Elisée Reclus—to the elaboration and propagation of anarchist ideas. And he has therefore well deserved the recognition and the admiration that all anarchists feel for him.
But in homage to the truth and in the greater interest of the cause, one must recognise that his activity has not all been wholly beneficial. It was not his fault; on the contrary, it was the very eminence of his qualities which gave rise to the ills I am proposing to discuss.
Naturally, Kropotkin being a mortal among mortals could not always avoid error and embrace the whole truth. One should have therefore profited by his invaluable contribution and continued the search which would lead to further advances. But his literary talents, the importance and volume of his output, his indefatigable activity, the prestige that came to him from his reputation as a great scientist, the fact that he had given up a highly privileged position to defend, at the cost of suffering and danger, the popular cause, and furthermore the fascination of his personality which held the attention of those who had the good fortune to meet him, all made him acquire a notoriety and an influence such that he appeared, and to a great extent he really was, the recognised master for most anarchists.
As a result of which, criticism was discouraged and the development of the anarchist idea was arrested. For many years, in spite of the iconoclastic and progressive spirit of anarchists, most of them so far as theory and propaganda were concerned, did no more than study and quote Kropotkin. To express oneself other than the way he did was considered by many comrades almost as heresy.
It would therefore be opportune to subject Kropotkin's teachings to close and critical analysis in order to separate that which is ever real and alive from that which more recent thought and experience will have shown to be mistaken. A matter which would concern not only Kropotkin, for the errors that one can blame him for having committed were already being professed by anarchists before Kropotkin acquired his eminent place in the movement: he confirmed them and made them last by adding the weight of his talent and his prestige; but all us old militants, or almost all of us, have our share of responsibility.
In writing now about Kropotkin I do not intend to examine his teachings. I only wish to record a few impressions and recollections, which may I believe, serve to make better known his moral and intellectual stature as well as understanding more clearly his qualities and his faults.
But first of all I will say a few words which come from the heart because I cannot think of Kropotkin without being moved by the recollection of his immense goodness. I remember what he did in Geneva in the winter of 1879 to help a group of Italian refugees in dire straits, among them myself; I remember the small attentions, I would call maternal, which he bestowed on me when one night in London having been the victim of an accident I went and knocked on his door; I recall the innumerable kind actions towards all sorts of people; I remember the cordial atmosphere with which he was surrounded. Because he was a really good person, of that goodness which is almost unconscious and needs to relieve all suffering and be surrounded by smiles and happiness. One would have in fact said that he was good without knowing it; in any case he didn't like one saying so, and he was offended when I wrote in an article on the occasion of his 70th birthday that his goodness was the first of his qualities. He would rather boast of his energy and courage—perhaps because these latter qualities had been developed in, and for, the struggle, whereas goodness was the spontaneous expression of his intimate nature.
I had the honour and good fortune of being for many years linked to Kropotkin by the warmest friendship.
We loved each other because we were inspired by the same passion, by the same hopes... and also by the same illusions.
Both of us were optimistic by temperament (I believe nevertheless that Kropotkin's optimism surpassed mine by a long chalk and possibly sprung from a different source) and we saw things with rose tinted spectacles—alas! everything was too rosy—we then hoped, and it is more than fifty years ago, in a revolution to be made in the immediate future which was to have ushered in our ideal society. During these long years there were certainly periods of doubt and discouragement. I remember Kropotkin once telling me: "My dear Errico, I fear we are alone, you and I, in believing a revolution to be near at hand." But they were passing moods; very soon confidence returned; we explained away the existing difficulties and the scepticism of the comrades and went on working and hoping.
Nevertheless it must not be imagined that on all questions we shared the same views. On the contrary, on many fundamentals we were far from being in agreement, and almost every time we met we would have noisy and heated discussions; but as Kropotkin always felt sure that right was on his side, and could not calmly suffer to be contradicted, and on the other hand, had great respect for his erudition and deep concern for his uncertain health, these discussions always ended by changing the subject to avoid undue excitement.
But this did not in any way harm the intimacy of our relationship, because we loved each other and because we collaborated for sentimental rather than intellectual reasons. Whatever may have been our differences of interpretation of the facts, or the arguments by which we justified our actions, in practice we wanted the same things and were motivated by the same intense feeling for freedom, justice and the well-being of all mankind. We could therefore get on together.
And in fact there was never serious disagreement between us until that day in 1914 when we were faced with a question of practical conduct of capital importance to both of us: that of the attitude to be adopted by anarchists to the [First World] War. On that occasion Kropotkin's old preferences for all that which is Russian and French were reawakened and exacerbated in him, and he declared himself an enthusiastic supporter of the _Entente._ He seemed to forget that he was an Internationalist, a socialist, and an anarchist; he forgot what he himself had written only a short time before about the war that the Capitalists were preparing, and began expressing admiration for the worst Allied statesmen and Generals, and at the same time treated as cowards the anarchists who refused to join the _Union Sacré,_ regretting that his age and his poor health prevented him from taking up a rifle and marching against the Germans. It was impossible therefore to see eye to eye: for me he was a truly pathological case. All the same it was one of the saddest, most painful moments of my life (and, I dare to suggest, for him too) when, after a more than acrimonious discussion, we parted like adversaries, almost as enemies.
Great was my sorrow at the loss of the friend and for the harm done to the cause as a result of the confusion that would be created among the comrades by his defection. But in spite of everything the love and esteem which I felt for the man were unimpaired, just as the hope that once the moment of euphoria had passed and the foreseeable consequences of the war were viewed in their proper perspective, he would admit his mistake and return to the movement, the Kropotkin of old.
Kropotkin was at the same time a scientist and a social reformer. He was inspired by two passions: the desire for knowledge and the desire to act for the good of humanity, two noble passions which can be mutually useful and which one would like to see in all men, without being, for all this, one and the same thing. But Kropotkin was an eminently systematic personality and he wanted to explain everything with one principle, and reduce everything to unity and often, did so, in my opinion, at the expense of logic.
Thus he used science to support his social aspirations, because in his opinion, they were simply rigorous scientific deductions.
I have no special competence to judge Kropotkin as a scientist. I know that he had in his early youth rendered notable services to geography and geology, and I appreciate the great importance of his book on Mutual Aid, and I am convinced that with his vast culture and noble intelligence, could have made a greater contribution to the advancement of the sciences had his thoughts and activity not been absorbed in the social struggle. Nevertheless it seems to me that he lacked that something which goes to make a true man of science; the capacity to forget one's aspirations and preconceptions and observe facts with cold objectivity. He seemed to me to be what I would gladly call, a poet of science. By an original intuition, he might have succeeded in foreseeing new truths, but these truths would have needed to be verified by others with less, or no imagination, but who were better equipped with what is called the scientific spirit. Kropotkin was too passionate to be an accurate observer.
His normal procedure was to start with a hypothesis and then look for the facts that would confirm it—which may be a good method for discovering new things; but what happened, and quite unintentionally, was that he did not see the ones which invalidated his hypothesis.
He could not bring himself to admit a fact, and often not even to consider it, if he had not first managed to explain it, that is to fit it into his system.
As an example I will recount an episode in which I played a part.
When I was in the Argentinian Pampas (in the years 1885 to 1889), I happened to read something about the experiments in hypnosis by the School of Nancy, which was new to me. I was very interested in the subject but had no opportunity at the time to find out more. When I was back again in Europe, I saw Kropotkin in London, and asked him if he could give me some information on hypnosis. Kropotkin flatly denied that there was any truth in it; that it was either all a fake or a question of hallucinations. Some time later I saw him again, and the conversation turned once more onto the subject. To my great surprise I found that his opinion had completely changed; hypnotic phenomena had become a subject of interest deserving to be studied. What had happened then? Had he learned new facts or had he had convincing proofs of those he had previously denied? Not at all. He had, quite simply, read in a book, by I don't know which German physiologist, a theory on the relationship between the two hemispheres of the brain which could serve to explain, well or badly, the phenomena of hypnosis.
In view of this mental predisposition which allowed him to accommodate things to suit himself in questions of pure science, in which there are no reasons why passion should obfuscate the intellect, one could foresee what would happen over those questions which intimately concerned his deepest wishes and his most cherished hopes.
Kropotkin adhered to the materialist philosophy that prevailed among scientists in the second half of the 19th century, the philosophy of Moleschott, Buchner, Vogt, and others; and consequently his concept of the Universe was rigorously mechanistic.
According to his system, Will (a creative power whose source and nature we cannot comprehend, just as, likewise, we do not understand the nature and source of "matter" or of any of the other "first principles")—I was saying, Will which contributes much or little in determining the conduct of individuals—and of society, does not exist and is a mere illusion. All that has been, that is and will be, from the path of the stars to the birth and decline of a civilisation, from the perfume of a rose to the smile on a mother's lips, from an earthquake to the thoughts of a Newton, from a tyrant's cruelty to a saint's goodness, everything had to, must, and will occur as a result of an inevitable sequence of causes and effects of mechanical origin, which leaves no possibility of variety. The illusion of Will is itself a mechanical fact.
Naturally if Will has no power, if everything is necessary and cannot be otherwise, then ideas of freedom, justice and responsibility have no meaning, and have no bearing on reality.
Thus logically all we can do is to contemplate what is happening in the world, with indifference, pleasure or pain, depending on one's personal feelings, without hope and without the possibility of changing anything.
So Kropotkin, who was very critical of the fatalism of the Marxists, was, himself the victim of mechanistic fatalism which is far more inhibiting.
But philosophy could not kill the powerful Will that was in Kropotkin. He was too strongly convinced of the truth of his system to abandon it or stand by passively while others cast doubt on it; he was too passionate, and too desirous of liberty and justice to be halted by the difficulty of a logical contradiction, and give up the struggle. He got round the dilemma by introducing anarchism into his system and making it into a scientific truth.
He would seek confirmation for his view by maintaining that all recent discoveries in all the sciences, from astronomy right through to biology and sociology coincided in demonstrating always more clearly that anarchy is the form of social organisation which is imposed by natural laws.
One could have pointed out that whatever are the conclusions that can be drawn from contemporary science, it was a fact that if new discoveries were to destroy present scientific beliefs, he would have remained an anarchist in spite of science, just as he was an anarchist in spite of logic. But Kropotkin would not have been able to admit the possibility of a conflict between science and his social aspirations and would have always thought up a means, no matter whether it was logical or not, to reconcile his mechanistic philosophy with his anarchism.
Thus, after having said that "anarchy is a concept of the Universe based on the mechanical interpretation of phenomena which embrace the whole of nature including the life of societies" (I _confess I have never succeeded in understanding what this might mean)_ Kropotkin would forget his mechanistic concept as a matter of no importance, and throw himself into the struggle with the fire, enthusiasm, and confidence of one who believes in the efficacy of his Will and who hopes by his activity to obtain or contribute to the achievement of the things he wants.
In point of fact Kropotkin's anarchism and communism were much more the consequence of his sensibility than of reason. In him the heart spoke first and then reason followed to justify and reinforce the impulses of the heart.
What constituted the true essence of his character was his love of mankind, the sympathy he had for the poor and the oppressed. He truly suffered for others, and found injustice intolerable even if it operated in his favour.
At the time when I frequented him in London, he earned his living by collaborating to scientific magazines and other publications, and lived in relatively comfortable circumstances; but he felt a kind of remorse at being better off than most manual workers and always seemed to want to excuse himself for the small comforts he could afford. He often said, when speaking of himself and of those in similar circumstances: "If we have been able to educate ourselves and develop our faculties; if we have access to intellectual satisfactions and live in not too bad material circumstances, it is because we have benefited, through an accident of birth, by the exploitation to which the workers are subjected; and therefore the struggle for the emancipation of the workers is a duty, a debt which we must repay."
It was for his love of justice, and as if by way of expiating the privileges that he had enjoyed, that he had given up his position, neglected the studies he so enjoyed, to devote himself to the education of the workers of St. Petersburg and the struggle against the despotism of the Tsars. Urged on by these same feelings he had subsequently joined the International and accepted anarchist ideas. Finally, among the different interpretations of anarchism he chose and made his own the communist-anarchist programme which, being based on solidarity and on love, goes beyond justice itself.
But as was obviously foreseeable, his philosophy was not without influence on the way he conceived the future and on the form the struggle for its achievement should take.
Since, according to his philosophy that which occurs must necessarily occur, so also the communist-anarchism he desired, must inevitably triumph as if by a law of Nature.
And this freed him from any doubt and removed all difficulties from his path. The bourgeois world was destined to crumble; it was already breaking up and revolutionary action only served to hasten the process.
His immense influence as a propagandist as well as stemming from his great talents, rested on the fact that he showed things to be so simple, so easy, so inevitable, that those who heard him speak or read his articles were immediately fired with enthusiasm.
Moral problems vanished because he attributed to the "people," the working masses, great abilities and all the virtues. With reason he praised the moral influence of work, but did not sufficiently clearly see the depressing and corrupting effects of misery and subjection. And he thought that it would be sufficient to abolish the capitalists' privileges and the rulers' power for all men immediately to start loving each other as brothers and to care for the interests of others as they would for their own.
In the same way he did not see the material difficulties, or he easily dismissed them. He had accepted the idea, widely held among the anarchists at the time, that the accumulated stocks of food and manufactured goods, were so abundant that for a long time to come it would not be necessary to worry about production; and he always declared that the immediate problem was one of consumption, that for the triumph of the revolution it was necessary to satisfy the needs of everyone immediately as well as abundantly, and that production would follow the rhythm of consumption. From this idea came that of "taking from the storehouses" ("presa nel mucchio"), which he popularised and which is certainly the simplest way of conceiving communism and the most likely to please the masses, but which is also the most primitive, as well as truly utopian, way. And when he was made to observe that this accumulation of products could not possibly exist, because the bosses normally only allow for the production of what they can sell at a profit, and that possibly at the beginning of a revolution it would be necessary to organise a system of rationing, and press for an intensification of production rather than call upon [the people] to help themselves from a storehouse which in the event would be nonexistent, Kropotkin set about studying the problem at first hand and arrived at the conclusion that in fact such abundance did not exist and that some countries were continually threatened by shortages. But he recovered [his optimism] by thinking of the great potentialities of agriculture aided by science. He took as examples the results obtained by a few cultivators and gifted agronomists over limited areas and drew the most encouraging conclusions, without thinking of the difficulties that would be put in the way by the ignorance and aversion of peasants to what is change, and in any case to the time that would be needed to achieve general acceptance of the new forms of cultivation and of distribution.
As always, Kropotkin saw things as he would have wished them to be and as we all hope they will be one day; he considered as existing or immediately realizable that which must be won through long and bitter struggle.
At bottom Kropotkin conceived nature as a kind of Providence, thanks to which there had to be harmony in all things, including human societies.
And this has led many anarchists to repeat _that "Anarchy is Natural Order,"_ a phrase with an exquisite Kropotkinian flavour.
If it is true that the law of Nature is Harmony, I suggest one would be entitled to ask why Nature has waited for anarchists to be born, and goes on waiting for them to triumph, in order to destroy the terrible and destructive conflicts from which mankind has always suffered.
Would one not be closer to the truth in saying that anarchy is the struggle, in human society, against the disharmonies of Nature?
I have stressed the two errors which, in my opinion, Kropotkin committed—his theory of fatalism and his excessive optimism, because I believe I have observed the harmful results they have produced on our movement.
There were comrades who took the fatalist theory—which they euphemistically referred to as determinism—seriously and as a result lost all revolutionary spirit. The revolution, they said, is not made; it will come when the time is ripe for it, and it is useless, unscientific and even ridiculous to try to provoke it. And armed with such sound reasons, they withdrew from the movement and went about their own business. But it would be wrong to believe that this was a convenient excuse to withdraw from the struggle. I have known many comrades of great courage and worth, who have exposed themselves to great dangers and who have sacrificed their freedom and even their lives in the name of anarchy while being convinced of the uselessness of their actions. They have acted out of disgust for present society, in a spirit of revenge, out of desperation, or the love of the grand gesture, but without thinking thereby of serving the cause of revolution, and consequently without selecting the target and the opportune moment, or without bothering to coordinate their action with that of others.
On the other hand, those who without troubling themselves with philosophy have wanted to work towards, and for, the revolution, have imagined the problems as much simpler than they are in reality, did not foresee the difficulties, and prepare for them... and because of this we have found ourselves impotent even when there was perhaps a chance of effective action.
May the errors of the past serve to teach us to do better in the future.
I have said what I had to say.
I do not think my strictures on him can diminish Kropotkin, the person, who remains, in spite of everything one of the shining lights of our movement.
If they are just, they will serve to show that no man is free from error, not even when he is gifted with the great intelligence and the generous heart of a Kropotkin.
In any case anarchists will always find in his writings a treasury of fertile ideas and in his life an example and an incentive in the struggle for all that is good.
Police photographs of Malatesta, 1898.
# **PART THREE**
No, I would not like to return to the old times... simply to follow the same road and find ourselves back to where we are now. To want to, one should also be able to take with one the results of fifty years activity and all the experience acquired in that time. And in that case it would be the "good old days."
—From Malatesta's preface to Nettlau's **_Bakunin e l'Internazionale in Italia dal 1864 al 1872_** (1928)
We do not boast that we possess absolute truth; on the contrary, we believe that social truth is not a fixed quantity, good for all times, universally applicable or determinable in advance.... Our solutions always leave the door open to different and, one hopes, better solutions.
**_—Umanità Nova,_** 1921
# **M ALATESTA'S RELEVANCE FOR ANARCHISTS TODAY**
# **An Assessment**
# **I**
Malatesta's critical essay of recollections of Kropotkin was one of the last things he wrote, and that was thirty-four years ago; and some of his writings selected for this volume go back to the '90s. There have been tremendous social upheavals and economic developments in these thirty years which Malatesta, were he writing these concluding lines for me, would be the first to recognise and take into account in formulating anarchist tactics in the '60s of the twentieth century. But we should be wary of confusing technological and scientific discoveries and advancement with political progress and social awareness. Obviously in the past thirty years in the fields of technology and science mankind has made strides which only fifty years ago might have been considered impossible. On the other hand the growth of radical political thought and awareness during the latter half of the 19th century is a phenomenon not experienced since. Indeed the characteristic of our age is that though we have developed the new sciences to the point where we know more about ourselves, about our motivations, our behaviour patterns, our unconscious thoughts; where we know more about the workings of the ruling groups; and of the economic and financial system; where as a result of mass communications secret diplomacy and political scandals, cannot remain uncovered, as easily as in the past, revolutionary avant-garde movements are at their lowest ebb, and Western Man seems unable to project, let alone realise a way of life that combines the full satisfaction of material needs with individual fulfilment and happiness.
It is significant that in the affluent nations of the world, where at last the material conditions for the realisation of socialism have been achieved, there is no longer a socialist movement worthy of the name. And that in the hungry half of the world the movements of "liberation" are nationalistic and intensely hierarchical and political, and rarely influenced by radical revolutionary ideas of social and economic justice.
The temptation is to conclude that the age of classical revolution is passed. As one sociologist put it
Modern revolutionary theory was conceived at an early stage of Capitalism, in a world of scarcity and ruthless exploitation, when one could think only of a life and death struggle between rich and poor in which the poor had nothing to lose but his chains. Since then a situation has developed in advanced industrialist countries where there are too many people who could lose only by revolution. They would therefore prefer to see a peaceful transformation toward a more enlightened social organisation.
It is undoubtedly true that the power structure at the top has undergone very considerable change in the past thirty years, and that a growing proportion of the population, by reason of its economic and/or social status, now has a stake in capitalist society and will resist any attempt at radical change. But because the revolutionary theory, as quoted by Mannheim, has been shown to be fallacious anyway, (the poor being more concerned with their next meal than with their chains, are thus prepared to _follow_ any demagogue who promises them a square meal every day in return for their political servitude) and revolutionary movements, at all times, a small section of the community, the chances of a revolutionary upheaval in this respect have not been made all that much more difficult by the "managerial revolution" on the other side.
To assume that these elements in themselves represent a formidable physical obstacle, which daily grows larger, is to ignore the lessons of Algeria and Kenya for instance and to exaggerate white militancy in Southern Rhodesia and South Africa. In the former, the withdrawal of the military might of the respective Metropolitan powers revealed the bankruptcy of the militant boasting of the "colons." We have yet to see how militant they will be in S. Rhodesia and South Africa if and when they are resisted by armed Africans, and not by moral arguments and the Luthuli tactics of non-violence, which it could be argued, have been shown to be inadequate in dealing with these two situations of injustice.
Mannheim, in his observations on dictatorship, points out that "given modern social techniques, a minority will never hand over power to an unarmed majority." He follows this eminently Malatestian and anarchist remark with "Revolution against any totalitarian power, once entrenched, is nearly hopeless. No established totalitarian regime, whatever its political creed, can be broken from within; it takes an external war to unseat it." From which, in his opinion, "it follows that the utopian hopes of the Communists that their dictatorship would gradually fade away are even more visionary than many of their other over-optimistic expectations."
While agreeing with Mannheim that the "withering away" of the State theory of the Marxists is "visionary," assuming that it was ever expressed by them in good faith, one cannot allow Mannheim's equally utopian faith in the positive role of "external war to unseat" totalitarian power to pass unchallenged. His simplifications hardly stand up to examination. The last war (1) unseated the Hitler and Mussolini gangs (2) aided Franco's regime—at a time when according to Mannheim's arguments it could have destroyed it (3) consolidated the power of the Stalin regime in Russia (4) and as a result of its possession of the Atomic Bomb and the financial advantages resulting from its late entry in the War, the United States emerged as the dominating world Power, politically and economically.
Thus if it can be shown that "external war" has unseated dictatorship it has also consolidated others, as well as creating new ones in the process! So that on balance, considering the price mankind pays in death and destruction, any advantages that can be enjoyed by the survivors are not political but if anything economic ones. The characteristic of modern war is the technological progress that it stimulates and subsidises at all costs.
Most of us welcome the labour-saving gadgets that are now within the reach of our purses, but without considering the terrible price at which this technological breakthrough has been bought nor the price our children and future generations will have to pay to liquidate our debt of folly. Some of us do, and that minority in the affluent society is the guarantee that human values will survive in an environment of milk and gadgets just as they emerged in one of abject poverty lorded over by an aristocracy of undisguised wealth and privilege.
Malatesta's analysis of Capitalism is still valid; mass production needs, and even creates, mass markets. Yet the _raison d'être_ of capitalist economics is still _profits,_ and therefore the "artificial scarcity of goods" which Malatesta referred to in the 1920s as "a characteristic" of that system, still obtains, and in that case it is reasonable to suppose that the "affluence" we enjoy in the West is not the result of a change of heart among capitalists, but the chance effect of a cause serving at the same time other interests.
Have the capitalists then, in serving their interests at the same time silenced popular opposition by dangling the carrot of full employment and "affluence" in front of the working people? They haven't, and not only are they unable to guarantee full employment (assuming that they considered it to be good business) but neither can they control their employees' demands, for as Malatesta pointed out, the more successful they are in pressing their demands the more will they demand.
In other words, general prosperity, which also means more education as well as more material things, does not result in a passive or contented acceptance of a class structure and a privileged society. Just as the intentions of mass communications (apart from being profitable business) which are to condition the mass-reading public, also produce the opposite effect on large numbers of people, so prosperity (more education) produces growing feelings of resentment among wage earners at having to be ordered about by another, simply because he disposes of the means of production. There is a growing cynicism about the alleged superior qualities of those who control our political life, as well as less acceptance than in the past of the ostentatious ways of life of the wealthy parasites in our midst. State funerals for politicians are obvious attempts to rehabilitate the former, and football pools, with the occasional huge prize winnings, an open sesame to the millionaires' club for the man in the street. But the dilemma of capitalism cannot be solved by these obvious tricks, whatever they may do in the short term to distract attention from the major issues.
Even assuming that the problems of world hunger and poverty can and will be satisfactorily solved in the next twenty years, and I make the assumption only in order to argue for the validity of anarchy in a world in which the basic material needs of life _have_ been satisfied, the fact is, if the capitalist, or state-socialist, systems succeed in solving the problems of production and distribution in a way that ensures the basic necessities to maintain health for every individual in the world, they will still not have touched the problem of Authority.
Having filled the empty bellies they are, willy-nilly feeding minds, until then exclusively obsessed by food, with ideas, with ambitions, dreams, power, love. Thus having solved the problem of hunger the ruling elite would surround itself with doting followers, but also in a short time have to contend with the pressures from those hungry for the fruits of power as well as from those simply desirous of running their own lives without being bossed around from above.
Malatesta, speaking for the latter, did not make the mistake of confusing them with those he described as "strong, intelligent, passionate individuals, with strong material or intellectual needs, who finding themselves by chance, among the oppressed, seek, at all costs to emancipate themselves, and do not resent becoming oppressors.... "They are rebels but not anarchists," he concluded, because they had both the feelings and mentality of "unsuccessful bourgeois" and when they do succeed they not only become bourgeois "in fact" but are "not the least unpleasant among them." The anarchist movement has to this day been unable to protect itself from the Colin Wilsons and other "rebels" of this world who were never anarchists. Since we cannot prevent anyone from calling himself by whatever name he likes, all we can do, declared Malatesta, is to "try to prevent any confusion, or at least seek to reduce it to a minimum," even if there may be circumstances in which we "find them alongside us." This, it seems to me is a positive reaction; the alternatives lead to sectarianism, isolation, and in anarchist terms, to an extreme form of individualism.
Malatesta also avoided the mistake, not uncommon in anarchist movements, of seeking to counteract the ill-effects, or the failure, of one extreme by opting for another. The answer to the excesses of "propaganda by the deed" was not Tolstoyan "passive anarchy" any more than organisation with party discipline was the answer to uncoordinated actions, or faith in the inevitability of anarchy. Similarly the failure of insurrectionary attempts in the early days of the movement led to the excessive faith, of some, in the powers of the "general strike," while others concerned by the insufficient influence exerted by anarchists in the workers' organisations and revolutionary parties, either sought to contract out of society (by starting isolated communities) or became so involved in Trades Union and party activities, that many ended up by being _their_ spokesmen.
In steering a middle course, Malatesta was undoubtedly guided by a long experience and observation of the fate of these extreme attitudes and groupings, no less than by his clear image of the role of anarchists in the social struggle. Far from this middle course implying compromise and reformism, Malatesta sought to ensure that the anarchist movement should always retain its fundamental characteristics but without thereby being condemned to sterility and the role of passive observers of the world political scene.
Apart from the early years, when he too was carried away by the bakuninist ideas of successful local insurrections setting the world on fire, Malatesta was only too aware of the improbability of achieving the anarchist revolution in a foreseeable future, and one can therefore understand why he should have steered clear of both kinds of anarchist extremists: those who were convinced of the impossibility of ever achieving anarchism (such as the individualists) no less than those who thought it could be ushered in overnight by toppling a few heads of State, by a successful General Strike, or by a mass syndicalist organisation.
For these reasons he avoided dogmatic postures and refused to win applause by oratorical flourishes. He could not, for instance, conceive of a world or even a community in which _absolute_ freedom reigned. "Mutual Aid" is not "a Law of Nature"—"natural Man is in a state of continuous conflict with his fellows...." He was an anarchist because it corresponded "better than any other way of social life" to the kind of life _he_ wished to live, which for him included, "the good of all" a consideration, in Malatesta's case, free from sentimental or oratorical overtones in view of his realistic appraisal of human problems.
In 1920 when he was editor of the anarchist daily, _Umanità Nova_ and inciting, as well as, hoping for far-reaching popular action, he was never tempted to write-down or simplify the problems of social revolution: "The needs, tastes, aspirations, and interests of mankind"—he wrote—"are neither similar nor naturally harmonious; often they are diametrically opposed and antagonistic. On the other hand, the life of each individual is so conditioned by the life of others that it would be impossible, even assuming it were convenient to do so, to isolate oneself, and live one's own life. Social solidarity is a fact from which no one can escape."
Having presented what is, in his opinion a realistic picture of the human situation Malatesta suggests that
[Social Solidarity] can be freely and consciously accepted and in consequence benefit all concerned, or it can be accepted willy-nilly, consciously or otherwise, in which case it manifests itself by the subjection of one to another, by the exploitation of some by others.
Organisation is surely one of the basic manifestations of human solidarity and one is not surprised to find Malatesta in 1897 defining anarchy as "society _organised_ without authority". To say, as Joll condescendingly does, that he "had always accepted some degree of organisation," in order to conclude that in the polemic between Malatesta and the then anarcho-syndicalist, Monatte, it was the latter "who was right," is to distort the questions at issue between the two militants at the Amsterdam Congress of 1907. Indeed Malatesta went so far as to point out in that same piece of 1897 that
were we to believe that organisation was not possible without authority we would be authoritarians because we would still _prefer_ authority, which fetters and impoverishes life, to _disorganisation_ which makes life impossible (my italics)
and everything he wrote subsequently emphasised the need for, without making a cult out of, organisation. Organisation is "a necessary aspect of social life" from which nobody can escape
and even the most extreme anti-organisers not only are subject to the general organisation of the society they live in, but in the voluntary actions in their lives, and in their rebellion against organisation, they unite among themselves, they share out their tasks, they _organise_ with whom they are in agreement, and use the means that society puts at their disposal.
As to organisation of the anarchist movement, not only did he consider it "useful and necessary." In his view activity in isolation, when possibilities existed to coordinate, or join it, with the activities of a strong group condemned one to impotence, and to wasting one's efforts in small ineffectual action.
Here again, Malatesta's approach was anything but dogmatic. For his experience on the daily anarchist paper made him question, in retrospect, the wisdom (and I assume this to mean the effectiveness, from the point of view of propaganda) of seeking to reconcile all the anarchist currents of thought in one paper, in a period of political ferment such as Italy was passing through in the immediate post-war years. If one juxtaposes these with the following observations
Isolated, sporadic propaganda... serves little or no purpose. In the conditions of awareness and misery in which the masses live, and with so many forces against us, such propaganda is forgotten and lost before its efforts can grow and bear fruit. The soil is too ungrateful for seeds sown haphazardly to germinate and make roots
one is probably justified in concluding that Malatesta felt that when propaganda was at a low ebb it was time for anarchists of all shades to sink their tactical differences, and seek to combine in propagating the ideas, the ends, they held in common, but that when the movement was strong, and the political environment promising from a revolutionary point of view, they should unite where possible but not hesitate to have their respective organs of expression.
A critical study of the international anarchist press—not just simply a bibliography—would not only be revealing, but important in an attempt to further anarchist ideas. In the past fifty years the whole economics of printing and publishing have radically changed—and unfavourably from the point of view of the minority press. Equally the voice of mass communications has centupled in that time, and relatively therefore the difficulties of getting a hearing for anarchist ideas ever greater. Yet throughout the world the anarchist groups and movements each go on struggling to produce their papers and their journals without any attempt at coordinating their efforts or even establishing the most elementary kind of information service which would help to provide factual background material on political and other events of topical interest, while leaving each journal free to contribute its own interpretation.
Far from suggesting that the anarchist press should be centralised (such an attempt was made in Spain by the CNT-FAI Committees in 1938 with disastrous consequences). I am suggesting that internationally its resources could be used more effectively if they were coordinated. I am also suggesting that such coordination would not only improve the topical content of the various journals, but would also result in the discussion of anarchist ideas and tactics by anarchists internationally. In Malatesta's time there was a ferment of ideas singularly lacking today in the anarchist movement.
Do we really know all the answers? Have we restated anarchism in current terms with all the wealth of sociological research at our disposal? Have we reexamined anarchist tactics in the light of the momentous events technological and political that have taken place in the past thirty years? Have we understood the developments in the capitalist system, and in government in these post-war years and have we made an analysis of their significance in anarchist terms? I think not, and I say this as an assiduous reader of anarchist literature of all kinds in four languages, as well as in all humility, in view of my close association with the publishing activities of Freedom Press over many years.
In the course of compiling this volume I have been made only too aware of the inadequacies of anarchist propaganda in dealing with the means which we believe will lead a universally authoritarian society in, at least, a _libertarian_ direction. And as I was pointing out earlier our choice of panaceas is determined by circumstances, with the tendency to veer from one extreme to another. My political education included, for instance, unquestioning "faith" in the efficacy of the "General Strike" as the answer to every anarchist's prayer, and in the course of the years, like many of my comrades, I have called on the "general strike" to put things right, just as socialists have appealed to "revolutionary government" to solve all the problems stemming from "bad" governments!
It was only because I intended to include in the Selections a section on the "general strike" that I discovered that Malatesta had written very little on the subject and that when he did it was generally to warn against placing too high hopes in the general strike as a weapon of social change. This led me to reread some of the literature on the subject including Berkman's valuable _ABC of Anarchism_ (recently reissued by Freedom Press) I append the results of my own somewhat cursory reading, more as an illustration of the extremism (one way or the other) of anarchist positions and the unquestioning acceptance of _our_ panaceas, than as confirmation of Malatesta's thesis or his way of summing up the problems, and of evaluating which, in the circumstances are the best tactics, though I feel that we have something to learn in these directions too.
# **II**
In the early '20s Malatesta was writing of the general strike that it was a powerful weapon of struggle in the hands of the workers and "is, or could be, a way and the occasion to determine a radical social revolution." The situation was analogous to that in Spain fourteen years later, a weak government unable to impose its authority; the workers on the verge of revolution; the Right using the socialist renegade Mussolini to reestablish the rule of "Law and Order." The obvious and vital difference was that whereas in Spain the revolutionary elements captured the imagination of the reformists and indifferents, and swept them forward, in Italy the dead hand of the socialist politicians and Trade Union leaders killed the revolutionary potentialities of the situation. Obviously in such a situation the General Strike as Malatesta put it, "if understood and used differently from the way the old advocates of this weapon used it" could have been a "really effective means for social transformation." Nevertheless in general terms he asked himself whether "the idea of the general strike has not done more harm than good to the revolutionary cause."
It was some years earlier, at the Anarchist Congress in Amsterdam in 1907, that Malatesta expressed his reasons which were that: Firstly, many syndicalists were advocating the general strike as a substitute for the insurrection, and secondly that they overlooked the limitations of the general strike as a weapon in the struggle against the capitalist regime.
Without having any illusions about their past achievements, Malatesta saw that at least steady progress had been made in the right direction by the insurrectionary socialist movement, before it was halted by the emergence of Marxism, "with its dogmas and fatalism" and "unfortunately, with its scientific pretences (we were in a period of full, _scientifist_ euphoria), Marxism gave false hopes and also attracted or diverted most of the anarchists." They began by saying that "the revolution comes but is not made" that socialism would "inevitably come about" in the order of things, and that the political factor (which Malatesta points out is "after all simply violence in the service of economic interests") is of no importance because the economic question determines every aspect of social life. "And so insurrectionary preparation was neglected and practically abandoned. Far from despising the political struggle, the anti-insurrectional Marxists later decided that politics was the principal and almost the only means to bring about the triumph of socialism that is, once they saw the possibility of entering Parliament and of giving to the political struggle the restricted meaning of electoral struggle, and with this means they sought to extinguish in the masses all enthusiasm for insurrectional action."
It was in this atmosphere, writes Malatesta, that the idea of the general strike was launched, and "welcomed enthusiastically by those who had no faith in parliamentary action, and saw in it a new and promising road leading to popular action." The trouble was however, that most of them viewed the general strike "not as a means of drawing the masses towards insurrection, that is, of the violent destruction of the political power, and to the seizure of the land, the means of production and of all social wealth, but as a substitute for the insurrection, a way of 'starving the bourgeoisie' and obliging it to capitulate without a blow being struck." Far from starving the bourgeoisie, "we should starve ourselves first," was his cryptic comment.
That Malatesta was not exaggerating when he referred to the General Strike as a panacea and as a substitute for the insurrection is to be found in a whole number of pamphlets published at the time. In this country, for instance, the anarchist press issued Arnold Roller's well-known essay on "The Social General Strike" (Freedom Press, London, 1912) in which one reads that, "The heroic times of the battle on the barricades have gone by." The "winding lanes" in which a barricade could easily be erected and defended have been replaced in large cities by "broad long streets, in which the columns of an army can easily operate and take the barricades," and even the paving stones have been replaced by wooden blocks and asphalt "and such material is not fit for building barricades." Therefore, Roller concludes "it would be foolish for the people to begin a revolution, relying upon such insufficient means of defence." An excellent argument against barricades in Bond Street but not necessarily against insurrection!
Roller also deals with the problem of feeding the population during a general strike:
As soon as the bakers and butchers quit working, the General Strike will be felt much more intensely, and it will be probably the first time that the ruling classes will understand and feel what it means to be hungry.... The proletarians can stop production, but they cannot stop consumption. In this way they would during the transition do the same thing as the ruling classes have done uninterruptedly for thousands of years—that is, "consume without producing." This action of the ruling classes the working class calls "exploitation"; and if the proletarians do it, the possessing classes call it "plundering," and Socialists call it "expropriation."
In 1907 Malatesta was telling his fellow delegates in Amsterdam: "Some of the enthusiasts of the general strike go so far as to admit that the General Strike involves expropriation. But then the soldiers come. Are we to let ourselves be shot down? Of course not. We should stand up to them, and that would mean Revolution. So why not say Revolution at once, instead of General Strike?
This was not simply a question of words for in Malatesta's view it went deeper than that:
The advocates of the General Strike make people think they can do things without fighting, and thus actually spoil the revolutionary spirit of the people. It was propaganda of this kind that brought about such illogical positions as that taken up by the strikers recently at Barcelona, where they did fight the soldiers, but at the same time treated with the State. This was because they were under the delusion that it was only an economic question.
Again the idea expressed by such writers as Roller that "when the bakers and butchers quit working" the ruling classes will "probably for the first time understand what it means to be hungry" is not only doubtful, but even if it were true, the fact is that they would be no more worse off than the rest of the population and that short of everybody starving to death something must give, and it is inevitable that it will be the workers, for they and not the employers are the producers of the necessities of life. Malatesta argued thus because he was far from convinced that under capitalism there was ever over-production or that the granaries and the warehouses were stuffed with surplus food. Unlike Roller who believed that
the crisis of over-production is the best guarantee for the success of the Social General Strike, because the products on hand permit the satisfaction of all needs before the complete reorganisation; namely, by a general "Help yourself" on the part of the workers.
Malatesta always pointed out that the characteristic of capitalism is under-rather than over-production (see Section 12 "Production & Distribution") and that it was a mistake to believe that the stocks of food and essential goods in the large cities was sufficient to feed the people for more than a few days. When pressed by Malatesta to investigate the true position, Kropotkin who, in all his writings on the subject, had been a partisan of the _prise au tas_ (taking from the storehouses) view, discovered that if the imports of food into England were stopped for four weeks everybody in the country would die of starvation; and that in spite of all the warehouses in London, the capital city was never provisioned for much more than three days. Is the situation much different today in London and in all the large cities of the world?
Malatesta offered the Congress of 1907 what he called "a more or less novel conception" of the General Strike: namely "that in dealing with this question we must _begin_ by considering the necessity of food." And in which case
A peasant strike, for instance, appeared to him as the greatest absurdity. Their only tactics were immediate expropriation, and wherever we find them setting to work on those lines it is our business to go and help them against the soldiers. And then he had read somewhere that we ought to go and smash the railway bridges! He wondered whether the advocates of such foolishness ever realised that corn has to come the same way the cannons come. To adopt the policy of neither cannons nor corn is to make all revolutionists the enemies of the people. We must face the cannons if we want the corn.
"We must face the cannons if we want the corn" symbolises the commonsense which informed all Malatesta's, counsels and his own actions in the long years of his political maturity. It is his approach which even in this new scientific age in which we live, should commend itself to us today. It is not only about "cannons and corn" that his arguments have that ring of realism. I suggest that throughout the Selections this approach is applied to every major problem. For sixty years Malatesta was an anarchist because it "would correspond better than any other way of social life, to my desire for the good of all, to my aspirations towards a society which reconciles the liberty of everyone with cooperation and love among men, and not because anarchism is a scientific truth and a natural law." And for most of those sixty years without ever abandoning these feelings his feet remained firmly planted on the ground. Insurrection, General strikes, Revolution, Anarchy—yes, but the ever-recurring warning in all his theoretical and agitational writings is that the community has to go on eating every day whatever the political upheavals.
He may well have been stating the obvious but so long as it is overlooked it needs to be repeated again and again.
Monatte's taunt, after hearing Malatesta's view at the 1907 Congress was
In listening tonight to Malatesta bitterly criticising the new revolutionary concepts, I felt that I was listening to the arguments of a distant past. To these new concepts, the brutal reality of which frightens him, Malatesta has simply offered the old Blanquist ideas which fondly imagined that it was possible to reinvigorate the world by means of a triumphant armed insurrection.
Furthermore, the revolutionary syndicalists present tonight, have been reproached for having deliberately sacrificed anarchism and the revolution to syndicalism and the general strike. Well, I wish to declare, that our anarchism is as good as yours and we have no more intention than you have _de mettre notre drapeau dans notre poche_ (of hiding our true colours). As everybody here, anarchy is our final object. But because times have changed, we have also modified our concept of the movement and of the revolution. The latter cannot be achieved in the meld of 1848. As to syndicalism, if in some countries in practice it has given rise to some errors and deviations, the experience is there which will prevent us from repeating them. If instead of criticising from above the past, present or even future shortcomings of syndicalism, anarchists were to become more closely involved in its activity, the hidden dangers that might be contained in syndicalism would once for all be exorcised!
Monatte exaggerated the differences between syndicalists and anarchists because he did not or for tactical reasons was not willing to take into account the opening sentences in Malatesta's exposé which made it quite clear that he would only deal with those aspects of his ideas in which "he was _in disagreement_ with earlier speakers and in particular with Monatte" for to do otherwise would simply mean burdening delegates with the kind of repetitions which are permissible at meetings when one is addressing a hostile or indifferent audience. But here—he went on to add—"we are among comrades and none of you hearing me criticise what can be criticised in syndicalism will surely be tempted to take me for an enemy of workers' organisation and action; anyone who does obviously doesn't know me very well!"
Without wishing to be unkind to Monatte, who remained devoted to the cause of revolutionary syndicalism to the end of a long life, but in the interests of truth, it must be mentioned that whereas Monatte succumbed to the temptations of the Bolshevik Revolution a few years later (though he soon left them), Malatesta not only exposed the dangers from the beginning but received the announcement of Lenin's death with what was, for the revolutionary Left, no less than for some anarchists, the shocking remark "Lenin is dead. Long Live the Revolution!"
I have only apparently diverged from the subject of the pros and cons of the General Strike as a revolutionary weapon, because it seems to me that from the foregoing one can the better judge whether Malatesta's criticisms were the "arguments of the distant past" or those of a man who refused to be deflected from the realities of the present and, in the circumstances, of the foreseeable future.
It is interesting to note that French syndicalists, such as Pierre Besnard, in the '30s were defining the general strike as "la grève generale insurrectionelle et expropriatrice." The general strike he explained as "a specifically syndicalist weapon" which can deal "in a _decisive_ manner with all revolutionary situations whatever the initial factors of the movements set in motion. It is directly opposed to _insurrection,_ the only weapon of the political parties." And he adds that it is
by far more complete than [insurrection]. In fact whereas the latter only makes it possible to take power, the general strike not only provides the possibility of destroying that power, of getting rid of those who enjoy it, of preventing any party from capturing it, it deprives capitalism and the State of all means of defence, while at the same time _abolishing_ individual property, replacing it by collective property.
In a word, the general strike has a power of _immediate_ transformation, and this power is exercised for the sole benefit of the proletariat, to whom the possession of the apparatus of production and exchange offers the means of _radically_ transforming the social order.
The expropriatory general strike, with violence which the proletariat will invariably be obliged to use, will be, moreover, clearly _insurrectional._
Its effect will be felt at the same time politically and economically, whereas insurrection permits a party to act only in the political field.
Surely Malatesta would be justified in rising from his grave in anger and demanding that we call a spade a spade! And he would need do no more than point to the fact that the syndicalists were now embellishing the term "general strike" with "insurrectionelle et expropriatrice" and that Besnard, syndicalist, in his interesting "programme" shares the same preoccupations as Malatesta, anarchist, when he writes
Let us, now, examine what are the characteristics of the general strike. I have said that it signified in the first place and above all, the cessation of production, and work, under capitalism.
This means that workers, then the peasants, must simultaneously stop work. Does this mean they must quit their place of work and abandon the means of production to the bosses? No. Unlike what happens during a strike, workers will have to at the same time _stop_ work, _occupy_ the place of production, _get rid_ of the boss, _expropriate_ him, and _get ready_ to get production moving again, but in the interests of the revolution.
The cessation of work and production will mark the end of a regime, the expropriation of the possessors of the means of production and exchange and at the same time the overthrow of State power.
"On the duration of this stoppage will depend the future of the revolutionary movement," writes Besnard. Malatesta in 1907 seeing clearly this danger declared that "rather than calling on workers to stop working we must get them to work on their own account. Failing which the general strike will become a general famine even if we had been able from the outset to seize all the goods stored in the warehouses." And again in 1920 we find him advocating the taking-over of factories as the answer to general strikes of protest (see Section 18).
To this day for syndicalists and many anarchists the general strike remains the battle cry, the short cut to the free society "if only the workers would make up their minds." As far as I know no objective study on the subject of the general strike has been made by anarchists or syndicalists since Malatesta expressed his doubts at the Anarchist Congress in 1907 and again in 1920. It is significant that the major work on the subject should be by an American professor, Wilfrid Crook, and is packed with valuable material though marred by the author's obsession with the Communist bogey. A work which is more objective and valuable, though it only deals briefly with the problem, is Lady Chorley's _Armies and the Art of Revolution, 4_ a war-time publication which was presumably justified by the publishers as a work of "national interest" in so far as it would assist those engaged in "political warfare" in dealing with revolutionary situations among the defeated nations. Be that as it may, Lady Chorley has done the kind of research anarchists should have long ago engaged in. Her conclusions are of considerable interest and bear out the arguments advanced by Malatesta from his own experience. The author is "summing up"
the rather heterogeneous evidence [of the preceding pages and trying] to arrive at some conclusions as to the value of the general strike as a revolutionary weapon. In particular, an attempt must be made to answer the question whether a general strike can in any circumstances provide conditions which will indirectly weaken the fighting power of the forces of the _status quo_ government, so that an insurrection may succeed even against their opposition.
It seems clear that the general strike has certain inherent weaknesses that cannot be overcome. Its object is to hold a government to ransom by the dislocation of all economic life. If the middle classes are against the strike, this dislocation cannot be completely effected since they are competent to run skeleton necessary services. When the dislocation is complete, after a few days the strains put upon the strike organisation will probably be beyond its resources on a vast and probably quite impossible scale. Moreover, the structure of modern community life cannot survive such a dislocation for more than a few days. And if the whole structure crumbles, the resulting chaos will be a crushing liability rather than an asset. History shows that successful revolutions have invariably taken off from a springboard of properly organised community life. Whether, the community life is organised in the interests of this or that class is of no moment. The point is that it is organised. _It is a fallacy to suppose that revolutions are ever the offspring of chaos and foul night._ Relative economic chaos may ensue for a time after a successful revolution. This may be inevitable. But no leader can afford to make the production of general chaos an instrument of revolutionary policy. During a revolution, the more smoothly the machinery runs for the neutral population, the better....
A general strike, then, must succeed in its objective within the first few days. If this does not happen, it will probably collapse under the weight of the dislocation it has itself brought about before that dislocation actually brings down the whole social structure. There is a third alternative: that it should transform itself into armed revolt. Granted the opposition of the armed forces of the government, such a revolt can only be successful if the conditions created by the strike prevent the troops from exerting their full strength.... Taking it by and large, the general strike is not a good revolutionary weapon. Its main revolutionary value is as an expression of working-class solidarity. It can sometimes be used to create artificially a revolutionary situation, _but unless such a situation can be used as the taking-off point for an already planned insurrection, whose chances have been calculated, it is a useless expenditure of enormous energy. As an actual instrument of policy it is more wasteful of energy than a straight insurrection, and its failure is more likely to set back a working-class movement than the failure of an insurrection._
The passages I have italicised in Lady Chorley's conclusions seem to me to be the particularly relevant ones in a piece full of important observations for anarchists and syndicalists, and not least for those who see in the general strike the weapon _par excellence_ of the non-violent revolution.
The point surely is that where the general strike is neither purely economic or political but revolutionary in its objectives, its purpose being to replace government and all the institutions of State by other forms of social and political organisation, it is in effect the insurrection as visualised by Malatesta, and the only difference between his approach and that of any other, what I would call, practical anarchists, such as Alexander Berkman is one of emphasis, but it is crucial to the whole future development of anarchist thinking and propaganda no less than in its possibilities of developing as a movement of radical change. On the subject of "Organisation of labour for the Social Revolution" Berkman writes in the _ABC of Anarchism_
We know that revolution begins with street disturbances, and outbreaks; it is the initial phase which involves force and violence.... This phase of the revolution is of short duration. It is usually followed by the more conscious, yet still spontaneous, destruction of the citadels of authority, the visible symbols of organised violence and brutality; jails, police stations and other government buildings are attacked, the prisoners liberated, legal documents destroyed.... But this stage passes quickly; the people's ire is soon spent. Simultaneously the revolution begins its constructive work.
But then to his imaginary interlocutor who asks whether he really thinks the reconstruction will start so soon, he rightly replies that "it must begin immediately" (the people must eat today and tomorrow warned Malatesta; and this is what the revolutionary workers in Barcelona in 1936 realised when within 48 hours of crushing the military rebellion—and without government authority they reestablished the essential services needed by the community).
But when Berkman's questioner asks "Are you not too hopeful" he replies: "No, I don't think so. I am convinced that the social revolution will not 'just happen.' It will have to be prepared, organised. Yes, indeed, organised—just as a strike is organised. In truth it will be a strike, the strike of the united workers of an entire country— _a general strike."_
And he then goes on to argue that it is obvious unarmed masses and their barricades couldn't in these days of "armoured tanks, poison gas, and military planes" withstand "high power artillery and bombs thrown upon them from flying machines." The whole proposition is "ridiculous" and it is therefore "time to have done with this obsolete idea of revolution"
The strength of labour is not in the field of battle. It is in the shop, in the mine and factory. There lies its power that no army in the world can defeat, no human agency conquer.
In other words the social revolution can take place only by means of the _General Strike._ The General Strike, rightly understood and thoroughly carried out, is the social revolution.
It is most important that we realise that the General Strike is the only possibility of social revolution. In the past the General Strike has been propagated in various countries without sufficient emphasis that its real meaning is revolution, that it is the only practical way to it. It is time for us to learn this, and when we do so the social revolution will cease to be a vague, unknown quantity. It will become an actuality, a definite method and aim, a programme whose first steps is the taking over of the instruments by organised labour.
Berkman's imaginary interlocutor expresses himself satisfied—but about another topic: "that the social revolution means construction rather than destruction"! But in all frankness, Berkman's argument just does not hold water as it stands. "You can shoot people to death but you can't shoot them to work" he declares. But, equally can it be said that without shooting them to death you can starve them back to work.
It is when Berkman implies that a revolutionary social strike will prevent any intervention by the armed forces that he seems to join company with the syndicalists, the "nonviolent" anarchists, and others whom Malatesta roundly criticised, save that Berkman does recognise there must be a "clash" between Authority and the revolutionary workers, which "involves force and violence" but which "will be of short duration." What is this but Malatesta's insurrectionary period? And why assume that the forces opposed to the struggle will not be the full force of the State's armed power?
It seems to me that for those anarchists or revolutionary socialists who cannot honestly see how violence can be avoided in any decisive confrontation between the forces of the under-privileged and those of the State which, after all, they are openly declaring daily, exist to protect privilege by violence (even law can only be enforced by the use or threat of force), it is bad propaganda in the long term to seek to suggest that the struggle to overthrow authoritarian rule as the first step in building a libertarian society will not involve violence, or a series of violent encounters with the entrenched forces of the _status quo._ Not only does one disillusion those who were led to believe that the revolution would all be plain sailing, but one appears as utopians to those practical people whose logic and commonsense are insulted by such "simplicist" arguments.
Arnold Roller in 1912 was not to know that in 1936 the people of Barcelona would defeat a carefully laid plan by the military to seize the city in less than 24 hours, and in spite of the fact that the new part of Barcelona where they met their defeat consisted of wide and straight avenues and "not winding lanes"! Or that in 1944 the Danes would ignore the problems of wood blocks and asphalt and instead "turned over trolley cars for barricades" (see Crook p.302), any more than Berkman was to know in 1929 that the Algerian resistance could successfully wage its war of independence against the cream of French military might—500,000 strong, armed with the latest weapons of horror, both military and psychological, from flame throwers, helicopters, the latest in automatic weapons and heavy armoured transport and offensive weapons, and the ruthless "paras" as well as a militant million white "colons" who certainly did not give up their privileged status without a fight, to torture, refined and crude, terrorism, bombings of civilian populations, starvation... in a word, the French pulled every dirty trick from the militarist-imperialist bag to no avail. Ben Bella in the end was received in the Elysée as spokesmen for the Algerian people, just as in 1936 the anarchists in Catalonia were received in the Generalitat as "masters" of the city, and of the province.
It is surely significant that Malatesta who equally was not to know about these, and other, events that could be enumerated, puts forward arguments which are confirmed—not refuted—by the experience of the past thirty years. What, it seems to me, makes _his_ approach so worthy of serious consideration as contemporary is that it was not only patently honest but was also illumined by an imagination which was _political_ as well as human. Can one, by the same token, concede that he was probably right when he declared that the simplification of the revolutionary problems only served to "spoil the revolutionary spirit of the people"?
# **III**
I have only touched on the subject of the General Strike. Professor Crook's angled work on the subject has probably uncovered all the sources available. What we need is an anarchist eye and imagination to interpret the 400 pages of text and probe the 70 invaluable pages of source notes, and in due course supply us with the findings!
But even a cursory glance at the general strike as a weapon of social revolution leads us to the question of "violence" and "non-violence" one of the three tactical issues over which anarchists have wasted more hours and reams of paper arguing at cross purposes. It will come as something of a shock to some anarchists reading Malatesta to learn that "non-violent revolutionary direct action" was in fact "rediscovered" not _discovered_ by the "Committee of 100" in its meteoric, short-lived, but historically and socially, significant existence. When he referred to "passive anarchy" as "an error the opposite of the one which the terrorists make" he was writing in 1896. Thus it can be said that the Tolstoyan-Gandhist and Bakuninist-Malatestian trends have co-existed in the anarchist movement these past 70 years, and therefore, to present the former as a new departure in anarchist tactics—as anarchism's New Look—is as unconvincing as it is historically false!
If the barricades in Barcelona led to Franco and his vaunted "25 años de paz" ("25 years of peace"—or should it be "repression," or "apathy"?) what did Gandhism lead to in India, and where has it got the blacks in South Africa? Again, to say as the Tolstoyans do, that even assuming the barricades and insurrection had a chance of succeeding in the distant past, the power of the State backed by formidable armed forces, and the entrenched power of industrialists and financiers, today has relegated such tactics to the history books, is an argument which must be examined and appraised in the light of all the evidence from Spain, Cuba, Algeria, Egypt, and Black Africa.
But to say all this without recognising that these same "problems" equally militate against "non-violent" tactics, clearly indicates that for some nonviolence is accepted as an article of faith. It probably explains the sterility of the discussions in the columns of _Freedom_ in recent years. What I propose to do now is not to reopen the discussion, but simply to point out that Malatesta and those of a like mind have never suggested that the anarchist society could be brought about through violence.
What they do say is that the possibility of radical change in society depends on first destroying the entrenched power of the ruling, the privileged, minority or class in present society, seeing that all the evidence on which we can draw indicates that no ruling class abdicates its power except when opposed by a superior force, and anarchists are not alone in drawing such conclusions. But as Malatesta points out again and again, what emerges from such upheavals is not necessarily anarchy but "the resultant" of all the active forces in society. So far as the role of anarchists in such situations is concerned, they must beware of trying, or hoping, to _impose_ anarchy by force, just as they must be prepared to _defend_ their right to live as anarchists, with force if necessary, it being clearly understood however that in living their way of life they do not interfere with the equal freedom of others to live theirs.
Malatesta therefore remained to the end of his life a believer in the need for violent, insurrectionary, action, not for the romantic and sentimental reasons attributed to him by popular historians, but because it was the only way out of the "vicious circle" which he so succinctly defines in these terms:
Between man and his social environment there is a reciprocal action. Men make society what it is and society makes men what they are, and the result is therefore a kind of vicious circle. To transform society men must be changed, and to transform men society must be changed.
Propaganda by the spoken and written word is not the answer. By propaganda we must encourage as many people as possible to make demands on the bosses and State by direct action; this in turn will, open the way to further penetration by anarchist propaganda among larger sections of the community and so on. Malatesta sought to create on the one hand an ever-growing mass-movement of political and social awareness as well as militancy which on the other hand would weaken the power as well as the _raison d'être_ of the State, a situation which ideally would culminate in a violent "confrontation" provoked by the State in a last desperate attempt to stave off the inevitable.
In reality of course, the "confrontation" generally takes place at a much earlier stage, that is when government still feels confident of having the necessary forces to intimidate and curb those of the people who dare to challenge its authority. Russia in 1917, Spain 1936, Italy 1920 were the culminating chapters in long histories of struggle, of challenge and repression, highlights of revolutionary "breakthroughs" followed by "biennia negros," military dictatorships, and the suppression of "elementary rights." That neither in Russia, Italy, or Spain did these struggles lead to anything resembling the libertarian society—indeed they in fact ended in the victory of dictatorships—must obviously make us question the means.
If we dismiss these "failures," as the propagandists of "non-violence" invariably do, with the slogan that "violence begets violence" we shall learn nothing. The very fact that _they_ are proposing to combat the violence of the State and of the privileged class, with non-violence, which they offer as a viable tactic, would indicate that _they_ are not convinced that violence "begets violence." And indeed one has only to look around one to see that State violence more often than not "begets" obedience and servility, as well as bottled-up feelings of revenge which in times of upheaval often manifest themselves in horrible, anti-social acts of violence. And it is these explosions by the politically unconscious victims of the authoritarian society, and not the positive, generous practical actions of the conscious revolutionaries at such moments of history, which are seized upon by reactionary newspapermen in the heat of the struggle and perpetuated by equally reactionary, and cloistered and unimaginative historians.
Malatesta sought to base anarchist tactics on historic realities without nevertheless assuming that the pattern that emerged should or must perforce be slavishly followed. If history teaches us nothing else it is surely that we should seek to avoid repeating the mistakes of our predecessors. Thus there are certain well trodden political paths which from an anarchist point of view invariably lead to disaster. But if anarchists are to count in those social struggles which, albeit, are not anarchist, they must offer practical solutions as well as valuable criticism. It should be emphasised that our practical solutions may well be unattainable in the circumstances and yet still be practical.
Anarchists, as Malatesta was always pointing out, cannot stand on the sidelines waiting for a sign that might indicate society was ripe for anarchy. For, if they do, they will wait forever; in fact they would do better to give up because they would be left behind by events. The anarchist revolution is the culmination of a series of forward and alternating steps by man and his environment, and for them to lead eventually to anarchist ends, demands the participation of anarchists at every stage, _as anarchists._
So long as the life of society is regulated by a privileged minority asserting and protecting itself with the complex machinery of Law and violence, and thus creating a class with a vested interest in the maintenance of the status quo, every serious challenge to its authority be it violent or non-violent will be met with the full force of the Law and legalised violence, the only language with which a privileged minority can address itself to the arguments and pressures of a majority without privileges, in any society. I do not propose to develop the insurrectionary argument here; it has already been clearly put by Malatesta. All I would add is that subsequent events have confirmed his arguments as well as his warnings. From the anarchist point of view obviously the Spanish Revolution of 1936–39 is the most significant social upheaval in our time. Though the anarchists have not yet subjected these events to the exhaustive analysis they deserve, the broad outline contained in the literature available could so easily be used to illustrate these pages of Malatesta's writings, just as his writings, because they foresaw the very problems that faced the anarchists and other revolutionaries in the Spanish struggle, could have served them as a tactical manual, the acceptance and application of which would have in all probability pushed the revolutionary possibilities to their fullest limits resulting either in the complete defeat of Franco's coup d'état in the first weeks of the struggle or in his military victory in the first six months, but without the possibility of lording over the country.
In other words, if the anarchists and syndicalist "leaders" after their spectacular victories of the first days of the military uprising had sought to exploit their richly deserved prestige in the eyes of the workers by directing all their energies and propaganda to the workers, inciting them to enlarge and consolidate the revolutionary gains of the 19th July, rather than seeking to use that prestige to cement a unity at top level with the other organisations and parties (which is what they did with scant success) they would have liberated _all_ the latent and potential revolutionary forces in the country and beyond their frontiers. This may have ended in defeat within a few weeks. But it would have been defeat when the revolutionary feelings and expectations were still high—and therefore when it was possible to continue the struggle by other means. Whereas, in prolonging the struggle by sacrificing the revolution to the war of fronts, not only did the politicians, with the support of the revolutionary organisations, ensure military defeat, but also ensured that a people subjected for more than two years to great material privations as well as growing political dissensions between the parties and workers' organisations, when it did finally concede victory to Franco and his backers, was exhausted, decimated, disillusioned, bitter, and helpless. The great exodus of half a million Spaniards, who preferred exile or French concentration camps, to Spain under Franco, was no guarantee of continuity in the struggle, for they, no less than those left behind, and who escaped the repression were also exhausted, disillusioned, and... _divided._ Franco's proclaimed "25 years of peace" obviously does not accurately describe his years of repressive and corrupt rule. But neither would "25 years of resistance" accurately describe the opposition to his regime. And I say all this not in a critical vein (for if we must be critical, it is of my generation which supported the Spanish people's great struggle only with fine words and medical aid) but in seeking to provoke a dispassionate evaluation of anarchist tactics and principles in the light of anarchist experience in that life-and-death struggle. Spain was not only the military training ground for Hitler's troops and the testing ground for his weapons of destruction, it was also a political crucible for all the parties and movements of the Left. They all failed, not just the anarchists and the revolutionary syndicalists of the CNT, but the Socialists, the Communists, the Catalan Separatists no less than the Basque Nationalists, (and I assume that just as by anarchists I mean all shades from extreme individualists to "reluctant" Ministers, so the reader also takes socialists and communists to include all the shades and factions from Right to Left: from POUM to PSUC)!
We know that fighting a war of fronts resulted in military defeat; we know that the entry of anarchists and the two workers' organisations (UGTCNT) into the government neither safeguarded their particular interests nor helped the armed struggle against Franco; we know that conscription did not produce military victories any more than did Russian military aid. The question Spanish anarchists have not to this day sought to answer is: _from the anarchist point of view_ was the defeat in Spain a defeat of anarchist theory and tactics as distinct from the failure of anarchists to seek to apply their theory and tactics? And from what I have previously said, by "defeat" I am not referring to Franco's military victory but to the defeat of the Revolution with which a section of the Spanish people opposed, and in two thirds of Spain defeated, the military uprising in July 1936. Anarchist tactics might well have led to defeat: this has already been admitted. What we must ask ourselves is whether the alternative course, of playing the government game, produced beneficial results, irrespective of military defeat. The point I am trying to make is that there are "successful" failures; that is, where the seeds of positive future struggles have been sown. This was not only the basis of Malatesta's teachings, but also the conclusions reached by Lady Chorley:
The object of an insurrection is to affect a seizure of power; and this has been shown in the opening chapter that straight insurrections have never been won and probably never can be won against the full strength of a professional army. But insurrections have frequently broken out spontaneously in conditions where any chance of permanent success was impossible and even occasionally have been launched deliberately in the accepted knowledge that they could achieve no positive and direct success. Regarding revolutionary strategy by and large it does not necessarily follow that such insurrections are always unjustifiable. Indirectly, they can sometimes alter the whole political situation so deeply that from a revolutionary standpoint they may be a valuable factor in long-term strategy, even though foredoomed to military failure.
And it is interesting that among the historic examples she quotes to support her conclusions is that of the Asturian Rising in 1934, which was followed by the "biennio negro" (the two black years).
The Asturian Rising was a desperate protest against the failure of the 1931 Revolution to hold its gains and effect any deep alteration in the social system of Spain.... In the Asturias where the UGT was supreme, the working class rose in a revolt as determined and heroic as any in all European working class history. They held out for a fortnight, and were finally subdued by Moorish troops, foreign legionaries, and air bombing. The liquidation of the revolt was particularly cruel—some 30,000 prisoners were kept in gaol for eighteen months apart from bloodier and more spectacular acts of vengeance.... The working classes now had a tradition and a heroic myth. Asturias combined for them "the pride of an army in its previous feats of military glory and the pride of a Church in its religious martyrs." It was a welding iron to fuse the differences of the Left parties into a common aim.... It is not, therefore going too far to say that a direct result of the splendid failure in Asturias was the triumph of the Left in the elections of February 1963, the decisive turning point in the path of the revolution.
For 25 years anarchists the world over have been commemorating the Spanish Revolution. If reading Malatesta convinces us that it is time we started studying the valuable lessons it can teach us, I am convinced that we would learn to waste less of our time and our other slender material resources in sloganising and gesturing; I think some of us would drop out; and I am also convinced that those who do not believe in the Kropotkinian theory of inevitability or in some kind of social spontaneous combustion, will welcome with relief the Malatestian cold-douche of commonsense, pragmatic anarchism, and far from being pessimistic as a result, we too may also discover the argument that for sixty years "captured" such an intelligence who was also, by common consent, the most active and realistic of all anarchists!
# IV
The writers of all the recently published histories of anarchism are unanimous in declaring that the anarchist movement is dead. All that remains is the idea and a few anarchists dotted about the globe. Their conclusions may well be right; what I question are the arguments which lead them to their conclusion, for I find myself wondering whether the Movement they are talking about is the one I have in mind. For as I see it, it is a movement of continuous renewal rather than "an historically determined movement" as the Marxist historian Santarelli views it, and as I suspect Woodcock and Joll also do.
Not only do the historians consider that the anarchist "movement" in the 1880s was numerically stronger than it has even been since, but that it was more active, and as a movement with a popular basis, had greater opportunities of achieving its aims. Furthermore that governmental power and the means of repression were weak by contrast with what they were soon to become. To sustain such a thesis one should also be prepared to accommodate such notable exceptions as the revival of anarchist fortunes in Italy in 1913–14 and in 1919–22, as well as of anarchism as a growing influence in Spanish politics at various periods in the present century, culminating in the revolutionary events of 1936. One has also to bear in mind that the 20th is a century of revolutionary upheavals, whether we approve of them or not, by comparison to which those of the 19th century are almost small fry!
I criticise the modern historians of anarchism because it seems to me that they have either started work with an _idée fixe_ and selected their facts to prove their thesis, or have started with no preconceived ideas but neither with any burning desire to get to the root of the anarchist dilemma, if such it is. They have instead contented themselves with rehashing the considerable material already available on the 19th century revolutionary movements, and seem to have fallen into the trap of assuming that writers and diarists and assiduous correspondents are necessarily the most active revolutionaries and "trend-setters." And because, as I have pointed out in the introduction to this volume, Malatesta was a reluctant writer, and too good a revolutionary and conspirator to keep a diary or file away his letters for posterity, our historians have not even bothered to read what he did write and have as a result failed to realise that not only was he a "dedicated" revolutionary but also a thinker whose ideas were forged in the social struggle and had nothing in common with the rhetorical, the "millenarian," predictions of a world of love and plenty which most of his 19th century contemporaries indulged in. Far from Malatesta being Kropotkin's "collaborator and most famous disciple" as one writer—who declares that he has been "interested in the international anarchist movement since the turn of the century"—recently put it, it is abundantly clear that the personal esteem each had for the other never bridged the fundamental tactical differences which divided them for most of their lives. The fact is that both men went their own ways, neither seeking to join issue with the other (until Kropotkin declared his support for the Allies in the 1914–18 war, and Malatesta publicly disassociated himself from his friend's attitude).
From the point of view of the development of the anarchist movement the Marx-Bakunin struggle could be seen to be less significant than the Kropotkin-Malatesta confrontation that-might-have-been—and from this distance in time, not to have provoked it, seems to this writer to have been a serious tactical mistake on Malatesta's part.
Both men were undoubtedly the major "trend-setters" in the anarchist movements that saw the light in the 20th century. Woodcock succinctly summed up their different approaches in his Biography of Kropotkin when he wrote:
That this quality [Kropotkin's constitutional optimism], with its tendency to expect rapid and painless solutions to vast problems, amounted at times to a fault, was evident not only to hostile critics, but also to some who shared his fundamental ideals, for even his old friend and comrade, Malatesta, _the most realistic of all anarchists,_ said after his death that he had leaned too much towards excessive optimism and theoretical fatalism (p.439)
and again in a footnote he points out that even though the two men were "close personal friends up to the time of the break over the first world war,
they did not always agree on tactics or general ideas. Malatesta was a practical revolutionist, with a tendency towards conspiratorial action. _The most realist of the great anarchists,_ he did not always share Kropotkin's optimism and while he accepted anarchist communism, regarded it in the light of a hypothesis to be revised and reconsidered according to changing circumstances (p.382)
I have italicised Woodcock's two references to Malatesta in order to underline my surprise that in his History, published ten years after the Biography, Malatesta becomes the "knight errant in search of revolutionary adventure" and the subject for the usual anecdotes, but has no place in the first half of his history dealing with the Idea, in which he devotes 30 pages to Godwin, 12 to Stirner, and 39 to Proudhon. That these writers are full of thought-provoking ideas no one who has bothered (or tried) to read them will deny. But what have they, except for Proudhon, to do with the second part of his History—"The Movement"?
Until recent years the names, let alone the writings, of Godwin and Stirner were unknown in the anarchist movement. As Woodcock points out of Godwin's "Political Justice," in spite of the _succès d'estime_ it enjoyed at the time of publication in 1793, a century was to elapse before it was reprinted. And Godwin himself "died in obscurity. His ideas were familiar only to a restricted group of people with literary interests, and his social writings became the gospel of no political group," and he adds "The general neglect of Godwin has persisted. Never, in the nineteenth century, was he among the revered political writers."
Malatesta was for more than fifty years both at the centre of the ferment of ideas, and for most of that time an active militant in various countries. He did not enjoy the same kind of reverent esteem accorded to Kropotkin in the anarchist movement if for no other reason that his writings for the most part published in journals of which he was editor, and which were agitational papers existing to take advantage of a particular political situation (e.g., _l'Agitazione, Volontà, Umanità Nova_ —I can only think of _Pensiero e Volontà_ published after Mussolini's victory, as the exception to this rule) and one of Malatesta's roles in such papers was to seek to create a coordinated movement out of all the anarchist goodwill dispersed and unorganised. As a result he found himself frequently engaged in polemics generally with the extremist elements, between the out and out individualists on the one hand and those who in their concern to do something would almost veer to authoritarianism. As a result Malatesta was always a controversial figure, and not without his detractors within the anarchist circles as well as, of course, in the Left wing authoritarian parties. And one can imagine that he felt that he would do his cause more harm than good by challenging the Kropotkinian "optimism and theoretical fatalism." That it was in his opinion a stumbling block to the full development of the anarchist movement as a revolutionary and political force, emerges only too clearly from his recollections on Kropotkin, which was the last article he wrote, only a year before his death. I cannot understand how an historian of Woodcock's experience and knowledge of the anarchist trends could deliberately disregard this document of fundamental importance to an objective understanding of why the anarchist movement has failed.
I too, think the anarchist movement has failed but not because, to quote Woodcock's conclusions, "in almost a century of effort it has not even approached the fulfilment of its great aim to destroy the state and build Jerusalem in its ruins"—few anarchists would share the view that this has been the aim of the anarchist movement as such—but because most anarchists have seemed unable or have been unwilling, to distinguish between their problems as conscious individuals and the problems of society as a whole. And because they generally manage to find solutions to their basic material needs which permit them to live full lives they assume that what they have done others can also do, and either they conclude that propaganda is unnecessary, in which case they spend the rest of their lives living out their one-man-revolutions; or if they feel an urge to communicate their "discoveries" to their fellow-men tend to express and project their personal experience and solutions as applicable and possible for the community at large. Such propaganda can be shown to have produced valuable results in helping other individuals "discover" a new way of life for themselves, and even make them, in turn, into propagandists. In theory such propaganda will snowball, and in a short time an important minority of the population will be anarchists. In practice the results from such propaganda have been limited because its impact is personal and not social.
By way of illustration I recall the case of a Glasgow factory worker during the last world war who became an anarchist and developed into a brilliant public speaker. At a certain stage he realised that the factory was no place for him, and set out in a caravan to live the free life, earning a living making clothes pegs. He had applied theory to practice, was the conclusion drawn by his anarchist comrades. He has not been heard of since in the anarchist movement—which means nearly twenty years silence. Those who say that he—assuming he is still making and selling clothes pegs from his horse-drawn caravan—is still the best anarchist among us, are right in one sense: he has obviously reduced his personal material needs to a minimum and this he can acquire by making pegs and is left with a great deal of leisure to enjoy life. They are also wrong, because they overlook the equally important fact that our clothes-peg-anarchist depends on other people wanting his pegs and growing the food he and his horse need; and, most important, that very few other people have chosen to share his way of life. For if everybody decided to take to the road and earn a living making pegs, all of us, horses and anarchists would all die of hunger; and the monument to their naiveté—mountains of unwanted clothes pegs!
Woodcock makes a valid point when he writes that while it is true that anarchists are, in theory, revolutionaries
in practice however, organised anarchism in the nineteenth and twentieth centuries was really a movement of rebellion rather than a movement of revolution. It was a protest, a dedicated resistance to the worldwide trend since the middle of the eighteenth century toward political and economic centralisation.
But one cannot share his conclusions that anarchism is a lost—albeit good—cause but that "once lost they are never won again" and that the "heritage that anarchism has left to the modern world" is
in the incitement to return to a moral and natural view of society which we find in the writings of Godwin and Tolstoy, of Proudhon and Kropotkin, and in the stimulation such writers give to that very taste for free choice and free judgment which modern society has so insidiously induced the majority of men to barter for material goods and the illusion of security. The great anarchists call on us to stand on our own moral feet like a generation of princes, to become aware of justice as an inner fire and to learn that the still, small voices of our own hearts speak more truly than the choruses of propaganda that daily assault our outer ears.
For if anarchism is a lost cause then there can be no anarchist "heritage" unless one is satisfied to say that anarchists are an élite, the "princes" in a world of slaves.
Woodcock also fails to see that for a large number of anarchists "the historic anarchist movement" has no meaning. Few people come to accept an idea simply by reading an "authority." Somewhere Malatesta writes that it is action that sets people thinking—and while this is certainly true in his case for he only discovered the existence of the International and Bakunin after he had become an active Mazzinian in his early student days—and while he was not dogmatic on this and would recognise that for some, thought precedes, action, I think it is generally true that people formulate even vague social ideas as a result of their direct experience or observation of the world around them. Writers can help to clarify or develop these vague ideas, if they succeed in relating their writings to realities.
It is in this respect that Malatesta was one of the ablest and most honest of anarchist propagandists, and because the basic problems, which set in motion the vague ideas I refer to, have not in fact changed all that much in the past fifty years there is still a great deal that Malatesta can teach us, not as a prophet, but as somebody who belongs to our time and who worked and lived among the people, and always aware that he would be the last to suggest that anarchists today should blindly accept his ideas, or adopt his "anarchist programme" piecemeal or seek to relive his life as an agitator.
Malatesta has much to teach us, bearing in mind the present situation in the anarchist movements of the world, in his _approach to anarchism,_ both as an idea and a way of life, and in his _political sense and realism._ To ignore _these_ lessons is to condemn the anarchist movement to the political graveyard, mourned by the few dedicated custodians of the "Idea," and to periodic disinterment by historians in search of a subject.
V.R.
# **N OTES**
# **Introduction: Anarchy and Anarchism**
. _Pensiero e Volontà,_ May 16, 1925
. _Pensiero e Volontà,_ September 1, 1925.
. _l'Agitazione,_ June 4, 1897
. _Umanità Nova,_ August 25, 1920
. _Umanità Nova,_ September 2, 1922
. _Umanità Nova,_ April 27, 1922
. _Umanità Nova,_ September 16, 1921
. _Pensiero e Volontà,_ May 15, 1924
. _Pensiero e Volontà,_ January 1, 1924
. _Volontà,_ June 15, 1913
. _Pensiero e Volontà,_ May 16, 1925
. _Umanità Nova,_ September 16, 1922
. _Volontà,_ June 15, 1913
. _Umanità Nova,_ April 27, 1922
. _Il Risveglio,_ December 20, 1922
. _Umanità Nova,_ July 25, 1920
. _Il Programma Anarchico,_ Bologna, 1920, in this volume, pp.173–88
. _Il Programma Anarchico,_ Bologna, 1920, in this volume, pp.173–88
# **1. Anarchist Schools of Thought**
. _Pensiero e Volontà,_ July 1, 1925
. _Umanità Nova,_ February 27, 1920
. _Pensiero e Volontà,_ April 1, 1926
. _Pensiero e Volontà,_ August 8, 1924
. _Pensiero e Volontà,_ July 1, 1924
. _Pensiero e Volontà,_ July 1, 1924
. _Pensiero e Volontà,_ April 1, 1926
# **2. Anarchist—Communism**
. _Pensiero e Volontà,_ August 25, 1926
. _Pensiero e Volontà,_ June 1, 1926
. _Umanità Nova,_ August 31, 1921
. _Pensiero e Volontà,_ April 1, 1926
. _Il Risveglio,_ November 30, 1929
# **3. Anarchism and Science**
. _Volontà,_ December 27, 1913
. _Umanità Nova,_ April 27, 1922
. _Pensiero e Volontà,_ September 15, 1924
. _Pensiero e Volontà,_ November 1, 1924
. _Pensiero e Volontà,_ July 1, 1925
. _Pensiero e Volontà,_ November 16, 1925
. _Pensiero e Volontà,_ February 1, 1926
# **4. Anarchism and Freedom**
. _Umanità Nova,_ September 30, 1922
. _Umanità Nova,_ September 24, 1920
. _Umanità Nova,_ November 24, 1921
. _Umanità Nova,_ September 11, 1920
. _La Questione Sociale,_ November 25, 1899
. _La Questione Sociale,_ November 25, 1899
# **5. Anarchism and Violence**
. _Umanità Nova,_ August 25, 1921
. _Pensiero e Volontà,_ September 1, 1924
. _Il Programma Anarchico,_ Bologna, 1920, in this volume, pp.173–88
. _Umanità Nova,_ August 12, 1920
. _Umanità Nova,_ September 9, 1921
. _Umanità Nova,_ April 27, 1920
. _Umanità Nova,_ May 9, 1920
. _Pensiero e Volontà,_ April 16, 1925
. _Fede!,_ October 28, 1923
. _Umanità Nova,_ October 21, 1922
. _Il Risveglio,_ December 20, 1922
. _Fede!,_ November 25, 1923
. _Umanità,_ Nova July 18, 1920
. _l'Anarchia_ (Numero Unico), August 1896
# **6. Attentats**
. _Pensiero e Volontà,_ September 1, 1924
. _Pensiero e Volontà,_ September 1, 1924
. _l'Agitazione,_ September 22, 1901
. "Causa ed Effetti," September 22, 1900
. _Umanità Nova,_ December 18, 1921
. _Umanità Nova,_ December 24, 1921
# **7. Ends and Means**
. _l'En Dehors,_ August 17, 1892
. _Umanità Nova,_ June 25, 1922
. _l'Anarchia,_ August 1896
# **8. Majorities and Minorities**
. _Umanità Nova,_ August 11, 1922
. _Umanità Nova,_ October 6, 1921
. _Pensiero e Volontà,_ June 15, 1924
# **9. Mutual Aid**
. _Umanità Nova,_ September 16, 1922
. _Umanità Nova,_ July 25, 1920
. _Umanità Nova,_ September 2, 1922
. _Umanità Nova,_ October 21, 1922
. _Il Pensiero,_ June 1, 1909
# **10. Reformism**
. _Umanità Nova,_ May 10, 1922
. _Pensiero e Volontà,_ May 15, 1924
. _Umanità Nova,_ September 10, 1920
. _Pensiero e Volontà,_ March 1, 1924
# **11. Organisation**
. _Il Risveglio,_ October 15, 1927
. _l'Agitazione,_ June 4, 1897
. _l'Agitazione,_ June 11, 1897
. _Il Risveglio,_ October 15, 1927
. _l'Agitazione,_ June 11, 1897
. _l'Agitazione,_ June 18, 1897
# **12. Production and Distribution**
. _Umanità Nova,_ March 7, 1920
. _Il Pensiero,_ May 16, 1905
. _Il Risveglio,_ May 16, 1931
. _Il Risveglio,_ December 30, 1922
. _Umanità Nova,_ March 7, 1920
. _Pensiero e Volontà,_ May 1, 1924
. _Umanità Nova,_ October 4, 1922
. _Umanità Nova,_ May 9, 1920
. _Il Risveglio,_ December 30, 1922
. _Pensiero e Volontà,_ August 25, 1926
# **13. The Land**
. _Umanità Nova,_ May 15, 1920
# **14. Money and Banks**
. _Umanità Nova,_ April 18, 1922
. _Umanità Nova,_ October 7, 1922
# **15. Property**
. _Il Risveglio,_ November 30, 1929
. _Umanità Nova,_ May 10, 1922
. _Umanità Nova,_ April 18, 1922
. _Il Risveglio,_ November 31, 1929
# **16. Crime and Punishment**
. _Umanità Nova,_ August 27, 1920
. _Pensiero e Volontà,_ August 15, 1924
. _Umanità Nova,_ September 30, 1922
. _Umanità Nova,_ August 19, 1922
. _Umanità Nova,_ September 30, 1922
. _Umanità Nova,_ September 2, 1920
. _Umanità Nova,_ September 2, 1920
. _Umanità Nova,_ September 2, 1920
. _Umanità Nova,_ August 10, 1922
. _Il Risveglio,_ February 11, 1933
# **17. Anarchists and the Working Class Movements**
. _Il Risveglio,_ October 1–15, 1927
. _Umanità Nova,_ March 14, 1922
. _Umanità Nova,_ April 13, 1922
. _Umanità Nova,_ April 6, 1922
. _Umanità Nova,_ April 13, 1922
. _Umanità Nova,_ April 6, 1922
. _Pensiero e Volontà,_ April 16, 1925
. _Umanità Nova,_ April 6, 1922
. _Fede!,_ September 30, 1922
. _Pensiero e Volontà,_ February 16, 1925
# **18. The Occupation of the Factories**
. _Umanità Nova,_ March 17, 1920
. Confederazione Generale del Lavoro (the reformist Trade Union organization).
. _Umanità Nova,_ June 28, 1922
. _Pensiero e Volontà,_ April 1, 1924
# **19. Workers and Intellectuals**
. _Umanità Nova,_ August 10, 1922
. _Umanità Nova,_ October 20, 1921
. _Pensiero e Volontà,_ May 16, 1925
. _Umanità Nova,_ October 20, 1921
# **20. Anarchism, Socialism, and Communism**
. _Umanità Nova,_ September 3, 1921
. _l'Agitazione,_ September 23, 1897
. _l'Anarchia,_ August 1896
. _l'Agitazione,_ May 15, 1897
. _Umanità Nova,_ August 31, 1921
. _l'Agitazione,_ May 15, 1897
. _Fede!,_ October 28, 1923
. _l'Anarchia,_ August 1896
# **21. Anarchists and the Limits of Political Co-Existence**
. _Umanità Nova,_ May 1, 1920
. _Umanità Nova,_ May 4, 1922
. _Umanità Nova,_ June 25, 1922
. _Umanità Nova,_ August 26, 1922
. _Pensiero e Volontà,_ June 1, 1924
. _Pensiero e Volontà,_ August 1, 1926
. _Umanità Nova,_ November 25, 1922
. _Pensiero e Volontà,_ May 1, 1924
# **22. The Anarchist Revolution**
. _Pensiero e Volontà,_ June 15, 1924
. _Umanità Nova,_ October 28, 1921
. _Umanità Nova,_ September 30, 1920
. _Umanità Nova,_ April 22, 1920
. _Umanità Nova,_ August 30, 1921
. _Il Risveglio,_ December 30, 1922
. _Umanità Nova,_ November 25, 1922
. _Pensiero e Volontà,_ June 15, 1924
. _Pensiero e Volontà,_ June 1, 1926
. _Pensiero e Volontà,_ July 1, 1926
. _Pensiero e Volontà,_ June 16, 1926
. _Pensiero e Volontà,_ August 1, 1926
. _Il Risveglio,_ December 14, 1929
. _Il Risveglio,_ November 30, 1929
. _Vogliamo,_ June 1930
. _Vogliamo,_ June 1930
# **23. The Insurrection**
. _Umanità Nova,_ August 12, 1920
. _Umanità Nova,_ August 7, 1920
. _Umanità Nova,_ September 6, 1921
. _Vogliamo,_ June 1930
. _Umanità Nova,_ April 7, 1922
. _Il Programma Anarchico,_ Bologna, 1920, in this volume, pp.173–88
# **24. Expropriation**
. _Il Programma Anarchico,_ Bologna, 1920, in this volume, pp.173–88
. _Umanità Nova,_ June 19, 1920
. _Umanità Nova,_ April 1, 1920
# **25. Defence of the Revolution**
. _Fede!,_ November 25, 1923
. _Umanità Nova,_ August 27, 1920
. _Umanità Nova,_ October 7, 1922
. _Pensiero e Volontà,_ October 1, 1924
. _Pensiero e Volontà,_ October 1, 1925
. _Umanità Nova,_ August 12, 1920
# **26. Anarchist Propaganda**
. _Umanità Nova,_ September 2, 1921
. _Pensiero e Volontà,_ April 1, 1924
. _l'Adunata dei Refrattari,_ December 26, 1931
. _Umanità Nova,_ February 27, 1920
. _Pensiero e Volontà,_ January 1, 1925
. _l'Agitazione,_ September 22, 1901
# **27. An Anarchist Programme**
. _Il Programma Anarchico_ was drafted by Malatesta and adopted by the Unione Anarchica Italiana at its Congress in Bologna (1920)
# **Notes for a Biography**
. _Pensiero e Volontà,_ July 1, 1926
. Max Nettlau, _Errico Malatesta—La Vida de un Anarquista_ (Buenos Aires, 1923)
. Armando Borghi, _Errico Malatesta_ (Milan, 1947)
. Errico Malatesta, _Scritti Scelti_ Vol. 2 (Naples, 1954)
. George Woodcock, _Anarchism—A History of Libertarian Ideas and Movements_ (London, 1963)
. Max Nettlau, op. cit.
. Max Nettlau, op. cit.
. Luis Fabbri, _Malatesta_ (Buenos Aires, 1945)
. Max Nettlau, op. cit.
. Armando Borghi, _Mezzo Secolo di Anarchia_ (Naples, 1954)
. _Pensiero e Volontà,_ July 1, 1926
. _Pensiero e Volontà,_ September 16, 1925
. Max Nettlau, _Bakunin e l'Internazionale in Italia dal 1864 al 1872_ (Geneva, 1928) preface by Malatesta
. Luis Fabbri, op. cit.
. Max Nettlau, _Errico Malatesta—El Hombre, el Revolucionario, el Anarquista_ (Barcelona 1933)
. Luis Fabbri, op. cit.
. Angiolini quoted Nettlau, _Errico Malatesta—La Vida de un Anarquista_ (Buenos Aires, 1923)
. Max Nettlau, op. cit.
. _Questione Sociale_ (Florence, 1884) quoted Nettlau op. cit.
. Max Nettlau, op. cit.
. Max Nettlau, op. cit.
. Malatesta in preface to Nettlau op. cit.
. Malatesta in preface to Nettlau op. cit.
. _Questione Sociale,_ quoted Nettlau, _Errico Malatesta_
. _Questione Sociale,_ quoted Nettlau, _Errico Malatesta_
. Max Nettlau, op. cit.
. Max Nettlau, op. cit.
. Malatesta, in preface to Nettlau op. cit.
. _Umanità Nova,_ March 11, 1922
. _Pensiero e Volontà,_ July 1, 1926
. Malatesta in preface to Nettlau, op. cit.
. Luis Fabbri, op. cit.
. Errico Malatesta, _Scritti_ Vol. 3 (Geneva, 1936)
. _Umanità Nova,_ August 24, 1921
. op. cit.
. James Joll, _The Anarchists_ (London, 1964)
. Luis Fabbri, op. cit.
. Errico Malatesta, _Scritti Scelti_ (Naples, 1954)
. op. cit.
. Armando Borghi, _Errico Malatesta_ (Milan, 1947)
. Luis Fabbri, op. cit.
. _Freedom,_ July 1914
. James Joll, op. cit., see Appendix I
. _Freedom,_ April 1916, see Appendix II
. _Freedom,_ December 1914
. _l'Adunata dei Refrattari_ (Newark, NJ, September 3, 10, 17, 24, 1932)
. See Ugo Fedeli, _Errico Malatesta—Bibliografia_ (Naples, 1951)
. Luigi Fabbri, _Malatesta l'Uomo e il Pensiero_ (Naples, 1951)
. Trento Tagliaferri, _Errico Malatesta, Armando Borghi e Compagni davanti ai Giurati di Milano_ (Milan n.d. 1921?)
. _Il Libero Accordo_ (Rome, 1920–1926), _Fede!_ (Rome, 1923–1926)
. _Pensiero e Volontà_ (Rome 1924–1926)
. Max Nettlau, op. cit. (Barcelona, 1933)
. Max Nettlau, in _Freedom Bulletin,_ December 1932
. See Appendix IV
. Max Nettlau, op. cit. (Geneva, 1928)
. _A proposito della Piataforma in Risveglio_ (Geneva, December 14, 1929)
. _Freedom Bulletin,_ December 1932
. See Borghi, Fabbri, Nettlau, op. cit.
. See Nettlau, _Errico Malatesta Vita e Pensiero_ (New York, 1921) Chapter 11
. Only quite recently a Spanish syndicalist of mature years expressed to me his admiration for Malatesta's ideas but repeated as a fact that Malatesta always managed to get away when things were getting "too hot." He was most surprised when I told him that Malatesta had spent some ten years in the various prisons of the world!
. _Umanità Nova_
. Trento Tagliaferri, op. cit.
. op. cit.
. _La Protesta_ was a daily paper for 25 years. See Rocker, _Anarcho-Syndicalism_ (London, 1938)
. Luis Fabbri, op. cit.
. Errico Malatesta, _Scritti Scelti_ Vol. 1 (Naples, 1947), Vol. 2 (Naples, 1954)
. Luis Fabbri, op. cit.
. Max Nettlau, op. cit.
. Armando Borghi, op. cit.
. See Appendix III
. P. Kropotkin, _Memoirs of a Revolutionist_ (London, 1899) Vol. 2, pp.59–60
. E.H. Carr, _Michael Bakunin_ (London, 1937)
. Luis Fabbri, op. cit.
. James Joll, op. cit.
# **Appendix—III**
. MacMillan (New York, 1932)
. Armando Borghi _Errico Malatesta_ (Istituto Editoriale Italiano, Milan, 1947) pp.136–37
. _Man!,_ March, 1933
. _Avanti!_ October 3, 1897. Reprinted in _Scritti Scelti_ (Naples, 1954) p.54
. Borghi op. cit. pp.135–36
. _Anarchism: A History of Libertarian Ideas and Movements_ (Cleveland, 1962)
. Pelican Books (London, 1963)
. See "Anarchism and the Historians" by V.R. in the monthly journal _Anarchy_ 46 (Freedom Press, London, December, 1964) for a detailed analysis of the escape, fact and fiction.
# **Malatesta's Relevance for Anarchists Today**
. Karl Mannheim, _Freedom, Power and Democratic Planning_ (London, 1951)
. Pierre Besnard, _Les Syndicats Ouvriers et la Revolution Sociale_ (Paris, 1930)
. Wilfrid H. Crook, _Communism and the General Strike_ (Connecticut, 1960)
. Katharine Chorley, _Armies and the Art of Revolution_ (London, 1943)
. I do not agree with all the evidence with which Lady Chorley builds up her case. For instance I would consider more significant as a revolutionary portent the weakness of the government, following the repression of the Asturian Rising and the mass imprisonment of the revolutionaries, to assert itself dictatorially, and the more or less free elections (by Spanish standards) which it found itself obliged to hold, than by the results! From an anarchist point of view Lady Chorley's conclusions and observations are so valuable because if anything they stem from personal convictions which at most are orthodox Labour Party, and her Spanish sources, Jellinek, Atholl, et alia, are the kind I spent my time denouncing!
. Max Nomad in _New Leader_ (New York, December, 1964).
. Woodcock and Avakumovic, _The Anarchist Prince_ (London, 1950)
# **I NDEX**
"Passim" (literally "scattered") indicates intermittent discussion of a topic over a cluster of pages. Page numbers in _italic_ refer to illustrations.
_ABC of Anarchism_ (Berkman), , 274–76
Africa, , 256–57, ,
_l'Agitazione_ , , , , , 219–22 passim
Agostinelli, Cesare,
agriculture, 92–93, , ,
Aguggini, Ettore,
Algerian War of Independence,
alliance, political. _See_ political alliance
altruism, , , , , ,
American Federation of Labor, ,
Amsterdam Congress, 1907. _See_ International Anarchist Congress, Amsterdam, 1907
"anarchism" (word), 13–14
_Anarchism: A History of Libertarian Ideas and Movements_ (Woodcock), , , 239–40, 287–89 passim
anarchist communism, , , 27–30,
anarchist congresses. _See_ Bologna anarchist congress of 1920; International Anarchist Congress of Amsterdam, 1907; St. Imier Congress, 1872
anarchist individualists and individualism, 21–24 passim, ,
anarchist organisations, 80–83 passim, , , ,
anarchist press, , , , , 212–16 passim, , , ; dailies, ; repression of, 213–15 passim. See also _l'Agitazione_ ; _Umanità Nova_ ; _Volontà_
_Anarchist Prince, The_ (Woodcock and Avakumovic), 285–86
_Anarchists, The_ ( Joll), , ,
"Anarchists Have Forgotten Their Principles" (Malatesta), 227–31
Anarchist Socialist Federation of Romagna,
anarchist tendencies, 21–25,
anarcho-syndicalism. _See_ syndicalists and syndicalism
"anarchy" (word), 13–14
anarchy, "passive." _See_ "passive anarchy"
Ancona, Italy, , , , 203–6 passim, , 219–20, 238–39
Angiolini, Alfredo,
Argentina, , , . _See also_ Buenos Aires
Armand, Émile: _L'Initiation individualiste anarchiste_ ,
armed forces, , , , 177–78, ,
artificial scarcity of goods, ,
assassinations and attentats, 53–58, ,
associations. _See_ groups, associations, etc.
_l'Associazione_ , ,
Asturian Rising, 1934,
attentats. _See_ assassinations and attentats
_Aurora_ ,
authoritarian communism, , 137–40 passim,
_Avanti!_ , ,
Bakunin, Mikhail, , , , 191–93 passim, , 224–25, , ; as aristocrat, ; First International and, ; Malatesta on, , 198–99; Marx and, ; Russian friends,
Bakuninists and Bakuninism, 197–200 passim, ,
banishment to penal islands. See penal islands
banks and banking, ,
Barcelona, , , , ,
barter, , ,
Belgium, ,
Benevento: insurrection attempt of 1877,
Berkman, Alexander: _ABC of Anarchism_ , , 274–76
Berlin,
Berne Congress, 1876, ,
Berneri, Giovanna,
Bertoni, Luigi, ,
Besnard, Pierre, 270–71
Blanc, Louis,
Blanqui, Louis-Auguste,
Bologna anarchist congress of 1920, ,
Bolshevik Revolution. See Russian Revolution
Borghi, Armando, , , , 203–4, , ,
bourgeoisie, , ,
Bowman, Guy,
Bresci, Gaetano, ,
Britain. _See_ Great Britain
Buenos Aires, ,
Cafiero, Carlo, 191–93 passim
capital punishment. _See_ death penalty
Carr, E.H., 224–25
censorship, , ,
Cerrito, Gino,
children, , , , , ,
Chorley, Katharine, 272–74, 282–83, 298n5
Christianity, 50–51,
Ciancabilla, Giuseppe, , , 238–40 passim
class, , , , , , . _See also_ bourgeoisie; labour movement; workers
CNT (Spain). _See_ Confederación Nacional del Trabajo (CNT) (Spain)
cocaine and cocaine traffic, 105–6
Cole, G.D.H., ,
collective action, 54–55
collectivism,
Colomer, André, ,
Comfort, Alex, 5–6
Communist Party of Italy,
communists and communism, , 91–93, , 137–38, . _See also_ anarchist communism; authoritarian communism
Confederación Nacional del Trabajo (CNT) (Spain), , ,
Confederazione Generale del Lavoro (CGL). _See_ General Confederation of Labour (Italy)
Congress of Amsterdam. _See_ International Anarchist Congress, Amsterdam, 1907
Congress of Berne, 1876. _See_ Berne Congress, 1876
Congress of Bologna, 1920. _See_ Bologna anarchist congress of 1920
Congress of St. Imier, 1872. _See_ St. Imier Congress, 1872
_Conquest of Bread_ (Kropotkin), ,
consumption, ,
cooperatives, , , , ,
Courtois-Suffit, Maurice,
crime and punishment, , 101–6, . _See also_ prison
Crispi, Francesco,
Crook, Wilfrid H., , ,
Cuba, , ,
cult of personality. _See_ personality cult
Cunninghame Graham, R.B.,
Czolgosz, Leon,
Damiani, Gigi, ,
D'Aragona, Ludovico,
death penalty,
Defendi family,
democracy. _See_ parliamentarism
demonstrations. _See_ protests and demonstrations
Denmark,
deportation, ,
determinism, ,
Diana Theatre bombing, Milan, 1921, ,
dictatorship, ,
dictatorship of the proletariat, ,
direct action, , , , , , , , . _See also_ occupation of factories; strikes
distribution of goods. _See_ production and distribution
dogma and dogmatism, , , , , , ; of Marxism, , ; of Mazzini,
Dresden, Germany, ,
drugs and drug traffic, 105–6
education, , , , , ; Malatesta's,
Egypt,
elections and voting, , . _See also_ parliamentarism
employment and unemployment, , , . _See also_ wages
ends and means, , 59–62, 175–76
Engels, Friedrich,
_Enquiry concerning Political Justice_ (Godwin). See _Political Justice_ (Godwin)
escapes, 221–22,
exchange of goods, 95–96, . _See also_ barter
exile, , 202–12 passim, 216–19 passim
expropriation, 180–81, ,
Fabbri, Luigi, , , , , , , 212–16 passim, 220–22 passim; on Malatesta's father, , ; _Studi Sociali_ , ; on urging Malatesta to write memoirs,
factory occupation. _See_ occupation of factories
Fanelli, Giuseppe, ,
farming. _See_ agriculture
fascists, , , , 213–15 passim, ,
fatalism, , , 250–51, , ,
_Fede!_ ,
Federación Anarquista Ibérica (FAI) (Spain),
federations. _See_ groups, associations, etc.
First International, , , , 192–95 passim, , , ; Berne Congress, 1876, ,
Florence, Italy,
food production and distribution, , 92–93, , , , 267–68
Fourier, Charles,
France, , , , , , , ; in Algeria, ; Malatesta publications in, , . _See also_ French Revolution; Paris
Franco, Francisco, , , 280–82 passim
free association, ,
freedom, , 38–44 passim, , , , ; crime as violation of, ; government and, ; organisation and, ; property and, , ; revolution and, . _See also_ free will
_Freedom_ , , 207–12 passim, ; excerpts, 205–7, 210–11, 227–36
freedom to organise, ,
free will, , , , , ,
French Revolution, ,
Galleani, Luigi,
Garibaldi, Giuseppe, , ,
gendarmerie, , , , , ,
General Confederation of Labour (Italy), , , ,
general strikes, 206–7, , , , 264–77 passim
Geneva, , , ,
George, Henry,
Germany, 210–11, 224–37 passim
Giolitti, Giovanni,
Godwin, William, ,
Goldman, Emma, 130–31
goods exchange. _See_ exchange of goods
government, , , , 136–43 passim, , , 174–79 passim, 183–87 passim; "permanent violence," ; self-preservation instinct of, . _See also_ law and laws; parliamentarism
Grave, Jean, 207–9 passim,
Great Britain, , , , . _See also_ London, England
groups, associations, etc., 77–83 passim. _See also_ anarchist organisations; labour union federations
Guillaume, James,
health, public. _See_ public health
historiography, 1–2, 284–89 passim. See also _Anarchism: A History of Libertarian Ideas and Movements_ (Woodcock); _Anarchists, The_ ( Joll); _Rebels and Renegades_ (Nomad)
Horowitz, Irving, ,
human will. _See_ will
Humbert I, King of Italy, ,
hunger, , , , , , ; counterrevolutionary nature of,
hypnosis, 245–46
immigrant workers,
imprisonment. _See_ prison
India, ,
individualists and individualism, , , , , , . _See also_ anarchist individualists and individualism
_l'Iniziazione individualiste anarchica_ (Armand),
insurrection. _See_ revolution
intellectuals, 129–33
International Anarchist Congress, Amsterdam, 1907, , , , 265–69 passim,
internationalism, , , 228–29
internationalization of raw materials, 86–87
International Workingmen's Association. _See_ First International
Italy, , , , , , , , 197–98; anarchist movement, 192–93, , 202–7 passim, 212–20 passim, 238–40 passim, ; fascists, , 213–15 passim, ; general strikes, ; insurrection attempt of 1877, ; Malatesta view, 200–201; occupation of factories, 125–27; Parliament, ; penal islands, 221–22; Red Week, 1914, , 205–7; "Workers' Alliance," ; World War I, 208–9. _See also_ Ancona, Italy; General Confederation of Labour (Italy); Naples; Rome; Union Sindacale Italiana (U.S.I.)
Jaurès, Jean,
Joll, James, , ; _The Anarchists_ , , ,
justice, criminal. _See_ crime and punishment
Keell, Thomas, ,
King Humbert I. _See_ Humbert I, King of Italy
King Victor Emmanuel II. _See_ Victor Emmanuel II, King of Italy
Kitz, Frank,
Kropotkin, Peter, , , , , 197–200 passim, , 267–68, 283–88 passim; _Conquest of Bread_ , ; Malatesta essay on, 197–98, , , 241–51, , ; radicalization, ; reverent esteem for, ; view of natural systems, ; Woodcock on, , ; World War I views, 207–12 passim, , ,
labour. _See_ work
labour movement, 107–24, , ; Italy, , 206–7, ,
labour union federations, , , , , , ,
Labriola, Arturo, ,
Lampedusa, 221–22,
land, 91–93,
Lane, Joseph,
Laplace, Pierre-Simon,
law and laws, , 105–6, , , . _See also_ natural law
League of Peace and Freedom. _See_ Ligue Internationale de la Paix et de la Liberté
legalisation of drugs, 105–6
Lenin, Vladimir,
liberty. _See_ freedom
Ligue Internationale de la Paix et de la Liberté,
Locarno, ,
London, England, , 202–12 passim, , , , 245–46, ,
Lovetere, Filippo,
mail tampering, seizure, etc. _See_ postal repression
majorities and minorities, 63–64
Makhno, Nestor,
Malatesta, Errico: "Anarchists Have Forgotten Their Principles," 227–31; in Ancona, 203–6 passim, 219–20, 238–39; on Bakunin, 198–99; Bakunin meeting, ; in Belgium, ; bibliography, 9–10; birth, ; death, ; as editor, , , , , 219–20, , , ; in Egypt, ; exile, , 202–12 passim, 216–19 passim; in France, ; health, 191–92; house arrest in Rome (1926–32), 215–16; imprisonment, , , , , , , ; inheritance, ; lectures and speeches, , , ; letter to king, ; letters to comrades, , 210–11, ; libel case, , ; in London, , 202–12 passim, , , , 245–46, ; as mechanic-electrician, , ; photos of, , , ; police dossier on, 203–5; "Peter Kropotkin—Recollections and Criticisms," 197–98, , , 241–51, , ; prudence and discretion of, , ; return to Italy, 212–16; schooling, ; shooting of, , 237–40; in South America, , , , , ; trials, , , 218–22 passim; in United States, , , 237–40 passim; World War I views, 207–12 passim; youth, 193–97 passim,
_Malatesta_ (Fabbri),
Malato, Charles, ,
Malta, 221–22
manifestos, , , 220–21,
Mann, Mrs. Tom,
Mannheim, Karl, ,
manual labour, , , ,
Mariani, Giuseppe,
Marx, Karl, , , , ,
Marxists and Marxism, , , , ,
massacres, police, 205–7 passim
Matteotti, Giacomo,
Mazzini, Giuseppe, , 197–98, ,
McKinley, William,
means and ends. _See_ ends and means
"mechanicism," 35–38,
Melli, Elena, , 215–16
middle class. _See_ bourgeoisie
Milan, Italy, , , . _See also_ Diana Theatre bombing, Milan, 1921
military. _See_ armed forces
minorities and majorities. _See_ majorities and minorities
monarchy, , 148–49
Monatte, Pierre, , 269–70
money, 95–96,
Monticelli, Temistocle,
Morgari, Oddino,
Morris, William,
Mussolini, Benito, , , , ,
mutual aid, 65–69,
_Mutual Aid_ (Kropotkin),
Naples, , , ,
Natta, Agenore,
nationalism, , , , , , ,
natural law, , 31–34 passim, , , , , , ,
nature, ,
Netherlands, ,
Nettlau, Max, , , , 211–16 passim, , ; _Bakunin e l'Internazionale in Italia dal 1864 al 1872_ ,
New York City, ,
Nice, France,
Nomad, Max: _Rebels and Renegades_ , , 237–39
non-violent resistance, , , 277–79 passim
occupation of factories, 125–27,
optimism, , , , , , 285–86, ; of Kropotkin, , , , 285–87 passim
organisation, 77–83, , , , , 261–62, . _See also_ freedom to organise
pacifism, ,
Palladino, Carmelo, 192–93,
pamphlets, ,
Paris, , ,
Paris Commune, ,
parliamentarism, , , 136–37, , , ,
Partito Comunista Italiano. _See_ Communist Party of Italy
Partito Socialista Italiano (PSI). _See_ Socialist Party of Italy
"passive anarchy," 50–51, ,
patriotism, , , ,
Paterson, New Jersey, , ,
pay. _See_ wages
Pazzaglia, Domenico,
penal islands, 221–22, 239–40
_Pensiero e Volontà_ , , ,
personality cult, ,
"Peter Kropotkin—Recollections and Criticisms" (Malatesta), 197–98, , , 241–51, ,
police, 104–5, , ; Cuba, ; dossiers on Malatesta, 203–5; London, , ; Malatesta attitude toward, ; Malatesta evasion of, ; Rome, 215–16; during Red Week, 1914, 205–7 passim; Switzerland, . _See also_ gendarmerie
political alliance, 141–44
_Political Justice_ (Godwin),
postal repression, ,
poverty, , ,
predestination, , ,
press. _See_ anarchist press; socialist press
prison, , , , , 211–13 passim, , ; Malatesta attitude toward, , . _See also_ penal islands
private property. _See_ property
production and distribution, 85–90, 120–21, ; agricultural, 92–93
propaganda, 169–72, 176–81 passim, , , , , 276–79 passim, ; imprisonment as medium for, ; inheritance spent on, ; trial as medium for,
propaganda of the deed. _See_ attentats
property, , , , 97–99,
_Protesta Umana_ ,
protests and demonstrations, , , , ; London, ,
Proudhon, Pierre, ,
public health, ,
punishment. _See_ crime and punishment
_Questione Sociale_ , , ,
reading circles,
_Rebels and Renegades_ (Nomad), , 237–39
Reclus, Elisée,
Red Week, 1914, , 205–7
reformism, 71–75, , , ,
religion, , , , , . _See also_ Christianity
representative government. _See_ parliamentarism
revenge, 48–50 passim, 55–56, , , , , ,
_Révolté_ ,
revolution, , , , , 145–58 passim, , 266–67; Berkman view, 274–76; Chorley view, 272–73, ; defence of, 163–68; errors in, ; hunger and, ; intellectuals and, 130–31; land and, ; Mannheim view, 256–57; Marx/Blanqui view, ; Marxist view, ; necessities and, ; production/distribution and, , ; labour movement and, , , , , ; seen as near at hand, ; violence of, , , . _See also_ French Revolution; Russian Revolution; Spanish Revolution
"revolutionary alliances," 141–43
Richards, Vernon,
right to organise. _See_ freedom to organise
riots,
Rocker, Rudolf, ,
Roller, Arnold, ,
Rome, 213–16 passim
Ruge, Arnold,
Russia, , , , , , , ,
Russian Revolution, 130–31, , , , , , ,
St. Imier Congress, 1872, , ,
Sandomirsky, Herman,
Santarelli, Enzo, ,
science, , 31–38, , ,
scientism, , ,
Serbian-Turkish War,
social democracy, , 136–37
"Social General Strike, The" (Roller), ,
socialism, , 85–90 passim, 135–40 passim; "false,"
"socialist-anarchists" (term),
Socialist League,
Socialist Party of Italy, ,
socialist press,
South Africa, ,
South America, , , ,
Spain, , , , 216–19 passim, , , , 274–84 passim
Spanish Revolution, 280–83 passim
Spinoza, Baruch,
state communism. _See_ authoritarian communism
Stirner, Max,
strikes, , 206–7, . _See also_ general strikes
Switzerland, , , , , , , . _See also_ Berne Congress, 1876
syndicalists and syndicalism, , , , , , 269–72 passim,
Tcherkesoff, Warlaam,
terrorism, , , , , ,
Tillett, Ben,
Tolstoy, Leo, 50–51, , ,
trade union movement. _See_ labour movement
trials, , , 218–22 passim
Turati, Filippo,
Turkish-Serbian War. _See_ Serbian-Turkish War
_Umanità Nova_ , , , , , , , ,
Umberto I, King of Italy. _See_ Humbert I, King of Italy
unemployment. _See_ employment and unemployment
Unión General de Trabajadores (UGT) (Spain),
union movement. _See_ labour movement
Union Sindacale Italiana (U.S.I.), , , ,
United Kingdom. _See_ Great Britain
United States, , , , , ;
labour movement, 112–13, ;
shooting of Malatesta in, , 237–40.
_See also_ Paterson, New Jersey
Universal Republican Alliance,
University of Naples,
uprisings, , . _See also_ Red Week, 1914
Ustica,
vengeance. _See_ revenge
Verbelen, Frans, 207–8
Victor Emmanuel II, King of Italy,
violence, 45–51, , , , 276–79 passim. _See also_ attentats
Vivoli, Giorgio,
_Volontà_ , , , , ,
wages, ,
wars. _See_ Algerian War of Independence; Serbian-Turkish War; World War I; World War II
West Hoboken, New Jersey, , 237–40 passim
will, , , . _See also_ free will
Woodcock, George, , , , , 239–40, 284–89 passim
work, , , , , 129–30, ; agricultural, ; exploitation of, , , ; Kropotkin view, . _See also_ employment and unemployment; manual labour
workers, 180–84 passim, ; relationship to intellectuals, 129–33; struggle between, ,
"Workers' Alliance" (Italy),
working-class movement. _See_ labour movement
World War I, 207–11, , 227–37, ,
World War II, ,
Zaccaria, Cesare,
Zamboni, Anteo, ,
Zamboni, Mamolo,
Zurich,
# **V ERNON RICHARDS**
Vernon Richards (born Vero Recchioni) the writer, publisher, translator, photographer, and organic gardener was born July 19, 1915 and died December 10, 2001 at the age of 86.
During his life he was involved in the publishing of many anarchist periodicals. _Italia Libera_ (Free Italy) a collaboration with Italian anarchist Camillo Berneri. _Spain and the World_ published along with veterans of _Freedom_ as an English-language news source for Spanish anarchists during the civil war. At the end of the civil war the paper was renamed _Revolt!_ and by the start of the second world war was known as _War Commentary_ (during which time he served a nine month prison sentence for inciting disaffection in soldiers) before finally returning to the title _Freedom_ in 1945. Richards was editor of _Freedom_ from 1952 until 1964 and continued to write for the paper until the 1990s.
Among his other publications are _Lessons of the Spanish Revolution, 1936–1939; George Orwell at home (and among the Anarchists): essays and photographs; Violence & Anarchism: a polemic;_ as well as several volumes of photographs.
# **C ARL LEVY**
Carl Levy is a professor of politics at Goldsmiths, University of London. He has published extensively on anarchism, comparative history, and politics.
About PM Press
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|
{
"redpajama_set_name": "RedPajamaBook"
}
| 7,348
|
\section{Introduction}
This note is a companion to \cite{Hoare:2011wr}. In \cite{Hoare:2011wr} we considered a certain deformation of the S-matrix for excitations on the superstring worldsheet propagating in $\text{\text{AdS}}_5\times S^5$. This deformed S-matrix theory is based on the fundamental R-matrix of the quantum-deformed Hubbard chain~\cite{Beisert:2008tw,arXiv:1002.1097}. The scattering theory depends on two separate couplings: $g$, the original coupling of the magnon theory that corresponds to the 't~Hooft coupling of the dual gauge theory, and a new quantum deformation parameter $q=e^{i \pi/k}$.
In \cite{Hoare:2011wr} we showed that there are two versions of the scattering theory, one appropriate for the original magnon theory and the other for the so-called mirror theory~\cite{arXiv:0710.1568}. The latter is related to the former by a double Wick rotation and is the appropriate theory for setting up the thermodynamic Bethe Ansatz.\footnote{In fact in \cite{Hoare:2011wr} we constructed four different S-matrices. However, in the present work we are only interested in the two built from the dressing factor $\sigma$ and not the other two built from the alternative dressing factor $\widehat\sigma$.} In a relativistic theory a double Wick rotation leads to the same theory, but for the non-relativistic situation that ensues with general $(g,k)$ these are distinct theories.
The bound state R-matrix of the deformed theory was constructed in \cite{deLeeuw:2011jr} using the underlying infinite dimensional quantum affine symmetry \cite{Beisert:2011wq,deLeeuw:2011fr,deLeeuw:2012jf}. Together with the dressing phase for the fundamental S-matrix constructed in \cite{Hoare:2011wr} one should be able to construct the exact S-matrix. However, due to the non-relativistic nature of the deformed theory, the identification of the bound state spectrum is subtle and depends on the couplings and the momenta of the particles.
The spectrum of the non-relativistic $q$-deformed, or interpolating, theory has some unusual properties that we conceptualize below:
\begin{center}
\begin{tikzpicture}[scale=0.8]
\draw[-,very thick] (0,0) -- (6,0) -- (6,4) -- (0,4) -- (0,0);
\draw[-,very thick] (0,0) -- (6,4);
\node at (0,-0.4) (a1) {$(g,\infty)$};
\node at (6.8,-0.4) (a2) {$(\infty,k)$};
\node at (3,-0.4) (a3) {$(g,k)$};
\node[rotate=90] at (-0.5,2) (a4) {\bf string};
\node[rotate=90] at (6.5,2) (a5) {\bf relativistic};
\node[rotate=90] at (7,2) (a6) {\bf SSSSG};
\node at (1.5,3) (a6) {\bf magnons};
\node at (1.5,2.2) (b1) {$\langle a-1,0\rangle^{\times2}$};
\node at (4.5,1.5) (a7) {\bf solitons};
\node at (4.5,0.7) (b2) {$\langle0,a-1\rangle^{\times2}$};
\draw[->] (3,0.5) -- (3,3.2);
\node at (3,3.5) (a8) {$|p|$};
\begin{scope}[xshift=7.5cm]
\draw[-,very thick] (0,0) -- (6,0) -- (6,4) -- (0,4) -- (0,0);
\node at (6,-0.4) (a1) {$(g,\infty)$};
\node at (3,-0.4) (a3) {$(g,k)$};
\node[rotate=90] at (6.5,2) (a5) {\bf mirror string};
\node at (2.7,3) (a6) {\bf mirror magnons};
\node at (3.5,2.3) (a7) {$=$~~~ {\bf solitons}};
\node at (2.8,1.2) (b1) {$\langle 0,a-1\rangle^{\times2}$};\end{scope}
\draw[<->,very thick] (4,4.3) arc (110:70:8);
\node at (6.75,5.2) (c1) {double Wick rotation};
\end{tikzpicture}
\end{center}
In the theory described by the left-hand side of the diagram, the conventional stringy magnon theory is obtained in the limit $k\to\infty$ with fixed $g$ (see \cite{Beisert:2010jr} and references therein). The limit $g\to\infty$ with fixed $k$ of the same theory gives the relativistic semi-symmetric space sine-Gordon (SSSSG) theory, that is to say the Pohlmeyer reduced theory \cite{Grigoriev:2007bu,Mikhailov:2007xr,Hoare:2009fs,Hoare:2011fj,Hollowood:2011fq,Hoare:2011nd}. On this side of the diagram, at generic $(g,k)$ a state is either a soliton or magnon depending on whether the momentum is $|p|\lessgtr E$, respectively, an occurrence that is peculiar to a non-relativistic theory lacking Lorentz boost symmetry. Here, $a=1,2,\ldots$ labels the bound state which transforms in representation $\langle a-1,0\rangle^{\times2}$ for a magnon and $\langle 0,a-1\rangle^{\times2}$ for a soliton.
The right-hand side of the diagram describes the mirror theory obtained by a double Wick rotation. Such a transformation has no effect on the relativistic SSSSG theory but for generic $(g,k)$ the transformation is physically significant since the change in energy and momentum changes the bound state structure. In this case there is only one set of states, the mirror magnons or solitons which transform in representation $\langle0,a-1\rangle^{\times2}$. The stringy limit $k\to\infty$ with $g$ fixed of the mirror theory gives the theory that is needed to define the thermodynamic Bethe Ansatz of the string moving on $\text{AdS}_5\times S^5$~\cite{arXiv:0901.1417,Bombardelli:2009ns,arXiv:0902.4458,arXiv:0907.2647,arXiv:1012.3995}.
\section{Symmetries, Dispersion Relations and S-Matrix \label{sec2}}
The $q$ deformed theory admits a quantum group deformed version of the centrally-extended Lie super-algebra
\EQ{\label{symalg}
\mathfrak{psu}(2|2) \oplus \mathfrak{psu}(2|2)\ltimes\mathbb{R}^3 \ .
}
This algebra consists of two copies of the triply-extended super-algebra $\mathfrak h=\mathfrak{psu}(2|2)\ltimes\mathbb{R}^3$ with the central extensions of the two factors identified. The fundamental states of the theory transform in the
product of two copies of the short 4-dimensional representation $\langle0,0\rangle$ of $\mathfrak h$. We will denote this 16-dimensional product representation $\langle0,0\rangle^{\times2}$. The representation $\langle0,0\rangle$ has an associated module spanned by the basis $\{|\phi^a\rangle,|\psi^\alpha\rangle\}$, $a,\alpha=1,2$, where $|\phi^a\rangle$ are bosonic and $|\psi^\alpha\rangle$ are fermionic. The basic states of the theory are then the sixteen product states $|\phi^a\phi^b\rangle$, $|\phi^a\psi^\beta\rangle$, $|\psi^\alpha\phi^b\rangle$ and $|\psi^\alpha\psi^\beta\rangle$. Note that for a single representation $\langle0,0\rangle$, the bosonic and fermionic states are distinguished by the fermionic parity $(-1)^F|\phi^a\rangle=|\phi^a\rangle$ and $(-1)^F|\psi^\alpha\rangle=-|\psi^\alpha\rangle$, but the product states are actually invariant under interchanging the fermionic parity of $|\phi^a\rangle$ and $|\psi^\alpha\rangle$ (as is clear from \eqref{sws} below).
Each $\mathfrak{psu}(2|2)$ has two $\mathfrak{su}(2)$ bosonic sub-algebras under which $|\phi^a\rangle$ transforms as a $(1,0)$ and $|\psi^\alpha\rangle$ as a $(0,1)$.\footnote{Here, we label the spin $j$ representations of $\mathfrak{su}(2)$ as $2j$.} Overall, the theory therefore has four $\mathfrak{su}(2)$ bosonic sub-algebras under which the representation $\langle0,0\rangle^{\times2}$ decomposes as
\EQ{\label{sws}
(1,0,1,0)\text{:}&\qquad|\phi^a\phi^b\rangle\qquad (-1)^F=1\ ,\\
(1,0,0,1)\text{:}&\qquad|\phi^a\psi^\beta\rangle\qquad (-1)^F=-1\ ,\\
(0,1,1,0)\text{:}&\qquad|\psi^\alpha\phi^b\rangle\qquad (-1)^F=-1\ ,\\
(0,1,0,1)\text{:}&\qquad|\psi^\alpha\psi^\beta\rangle\qquad (-1)^F=1\ ,
}
with fermionic parity as written.
Bound states are expected to transform in either the product of short representations $\langle a-1,0\rangle^{\times2}$ or $\langle 0,a-1\rangle^{\times2}$ each of dimension $16a^2$. Taken individually the two representations $\langle a-1,0\rangle$ and $\langle 0,a-1\rangle$ are physically distinguished by the fermionic parity of the states. In fact the representations are sometimes called the ``symmetric" and ``anti-symmetric" representations, respectively, although their $\mathfrak{su}(2)\oplus\mathfrak{su}(2)$ are mirrors of each other:
\EQ{
\langle a-1,0\rangle&=(a,0)\oplus(a-1,1)\oplus(a-2,0)\ ,\\
\langle0,a-1\rangle&=(0,a)\oplus(1,a-1)\oplus(0,a-2)\ .
}
However, just as for the fundamental representation, once we take the product the two representations become isomorphic.
Following \cite{Beisert:2011wq}, the fundamental particle states are labelled by two kinematic variables $x^\pm$ which are subject to a dispersion relation
\EQ{\label{p11}
q^{-1}\Big(x^++\frac1{x^+}\Big)-q\Big(x^-+\frac1{x^-}\Big)=(q-q^{-1})\Big(\xi+\frac1\xi\Big)\ ,
}
where
\EQ{\label{couplings}
\xi=-i\tilde g(q-q^{-1})\ ,\qquad
\tilde g^2=\frac{g^2}{1-g^2(q-q^{-1})^2}\ .
}
The deformation parameter $q$ is taken to be the complex phase\footnote{In the relativistic $g \rightarrow \infty$ limit, $k$ is identified with the coupling of the SSSSG or Pohlmeyer reduced theory \cite{Hoare:2011fj,Hollowood:2011fq}.}
\EQ{
q=\exp\Big[\frac{i\pi}k\Big]\ ,\qquad k\in\mathbb R>0\ .
}
With the choice above both $\tilde g$ and $\xi$ are real numbers with $\tilde g>0$ and $0\leq\xi\leq 1$.
In \cite{Hoare:2011wr} it was shown that another useful way to parameterize the kinematic parameters $x^\pm$ is via the map $x(u)$ defined by
\EQ{\label{sqr}
x+\frac1x+\xi+\frac1\xi=\frac1\xi\left(\frac{\tilde g}{g}\right)^2 q^{-2iu}\ .
}
Note that $x(u)$ has two sheets. Given the map $x(u)$, we can then solve \eqref{p11} by taking
\EQ{
x^\pm=x\Big(u\pm \frac i2\Big)\ ,
}
which shows that the kinematic variables define a 4-sheeted branched cover of the $q^{-2iu}$ plane which defines the rapidity torus. The 4-fold cover of the $u$-plane has sheets
\EQ{\label{sheets}
{\cal R}_{\pm2}\,:\qquad |x^+|<1\ ,\quad |x^-|<1\ , \\
{\cal R}_1\,:\qquad |x^+|<1\ ,\quad |x^-|>1\ , \\
{\cal R}_0\,:\qquad |x^+|>1\ ,\quad |x^-|>1\ , \\
{\cal R}_{-1}\,:\qquad |x^+|>1\ ,\quad |x^-|<1\ ,
}
where it is useful to think of the label as defined modulo 4 so that ${\cal R}_{-2}\equiv{\cal R}_2$. In some situations it is useful to introduce yet another coordinate $z$ which is the uniformized coordinate for the torus \cite{Hoare:2011wr}.
The abstract kinematic variables $x^\pm$ encode the energy and momentum of the state. To make this concrete one can define the two quantities \cite{Beisert:2011wq}
\EQ{\label{jww}
U^2=q^{-1}\frac{x^++\xi}{x^-+\xi}=q\frac{\frac1{x^-}+\xi}{\frac1{x^+}+\xi}\ ,\qquad
V^2=q^{-1}\frac{\xi x^++1}{\xi x^-+1}=q\frac{\frac\xi{x^-}+1}{\frac\xi{x^+}+1}\ ,
}
where the equalities follow from the dispersion relation \eqref{p11}. These quantities determine the three central charges $(C,P,K)$ of the symmetry algebra \eqref{symalg} by
\EQ{\label{cch}
q^{2C}=V^2\ ,\qquad P=g\alpha(1-U^2V^2)\ ,\qquad K=g\alpha^{-1}(V^{-2}-U^{-2})\ ,
}
where $\alpha$ is a free normalization constant. The central charges are related via
\EQ{\label{sht}
[C]_q^2-PK=[1/2]_q^2\, ,
}
where $[x]_q=(q^x-q^{-x})/(q-q^{-1})$. This is precisely the shortening condition for the atypical, or short, fundamental 4-dimensional representation of $U_q(\mathfrak h)$ labelled $\langle0,0\rangle$. What is particularly noteworthy is that the Hopf algebra structure ensures that the group-like elements $U$ and $V$ have a trivial co-product on a multi-particle state, e.g.~on a two particle state
\EQ{\label{cop}
\Delta(U)=U\otimes U\ ,\qquad \Delta(V)=V\otimes V\ .
}
The dispersion relation \eqref{p11} can be re-written in terms of $U$ and $V$ as
\EQ{\label{dsr}
V^2+V^{-2}-g^2(q-q^{-1})^2(V^2+V^{-2}-U^2-U^{-2})=q+q^{-1}\ ,
}
or equivalently (see appendix \ref{appa})
\EQ{\label{dit2}
\xi^{-1}\left(V^2 + \frac1{V^{2}} - q - \frac1q\right) = \xi \left(U^2 + \frac1{U^2} - q - \frac1q\right)\ .}
\noindent{\bf Magnon kinematics}
The fact that $U$ and $V$ have a trivial co-product suggest that they should be related in a simple way to energy and momentum. To start with let us take magnon kinematics identified by the behaviour in the string theory limit, that is $k\to\infty$ with $g$ fixed. In this case, the known behaviour suggests that physical states are subject to the reality condition $x^{\pm*}=x^\mp$. This implies that $U^*=U^{-1}$ and $V^*=V^{-1}$. The relation with the energy and momentum (up to some overall re-scaling) is
\EQ{\label{uvr1}
U=e^{ip/2g}\ ,\qquad V=e^{iE/2g}\ .
}
To define a one-to-one map between $p,E$ and the central charges $(C,P,K)$ given by~\eqref{cch}, we restrict the arguments of $U^2$ and $V^2$ to lie in the range $[-\pi,\pi]$, so that the momentum and the energy lie in the region $|p|, |E|\leq \pi g$. It is worth noticing that the coproduct~\eqref{cop} ensures the conservation of energy and momentum only modulo $2\pi g$. This suggests that, for generic finite values of $(g,k)$, the interpolating theory with magnon kinematics could exhibit umklapp type processes, an interesting possibility that will be investigated elsewhere.\footnote{While the periodic dependence of the dispersion relation on $E$ and $p$ is not an issue for finding the solutions to the bound state equations (the subject we address in this paper), a more general question is how to define the energy or momentum of a multi particle state. In particular, defining energy and momentum modulo $2\pi g$ implies that a tensor product of two single particle states with physical values of energy and positive momentum can have a total energy or momentum which is negative. While for momentum this is well-understood in the context of lattice models (giving rise to umklapp type processes), for energy it is not clear how this should be interpreted physically.} Substituting in for $U$ and $V$ the dispersion relation \eqref{dsr} becomes
\EQ{\label{dismag}
\cos(E/g)-\xi^2\cos(p/g)=(1-\xi^2)\cos(\pi/k)\ .
}
Taking $|p|\leq \pi g$, physical values of the energy should correspond to positive solutions of the dispersion relation \eqref{dismag}. This places physical values of the kinematic variables on the sheet ${\cal R}_0$ of the rapidity torus. The left-hand side of Fig.~\ref{f1} shows the dispersion relation.
\begin{figure}[ht]
\begin{minipage}[t]{.49\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.9]
\draw[->] (-3.3,0) -- (3.4,0);
\draw[->] (0,-0.2) -- (0,2.7);
\draw[-] (-3.142,2.25) -- (-3.142,-0.1);
\draw[-] (3.142,2.25) -- (3.142,-0.1);
\draw[-] (-1.5,1.4) -- (-1.5,-0.1);
\draw[-] (1.5,1.4) -- (1.5,-0.1);
\node at (1.5,-0.6) (c1) {$\frac{g\pi}k$};
\node at (-1.5,-0.6) (c2) {$-\frac{g\pi}k$};
\node at (0,-1.9) (b1) {\bf soliton};
\node at (2.4,-2) (b2) {\bf magnon};
\node at (-2.4,-2) (b3) {\bf magnon};
\node at (3.142,-0.6) (a1) {$g\pi$};
\node at (-3.142,-0.6) (a2) {$-g\pi$};
\node at (4,0) (a3) {$p$};
\node at (0,3.2) (a4) {$E$};
\draw[very thick] plot[smooth] coordinates {(-3.142, 2.246) (-2.811, 2.195) (-2.480, 2.057) (-2.150, 1.860) (-1.819, 1.630) (-1.488, 1.383) (-1.157, 1.130) (-0.8267, 0.8854) (-0.4960, 0.6687) (-0.1653, 0.5261) (0.1653, 0.5261) (0.4960, 0.6687) (0.8267, 0.8854) (1.157, 1.130) (1.488, 1.383) (1.819, 1.630) (2.150, 1.860) (2.480, 2.057) (2.811, 2.195) (3.142, 2.246)};
\node at (2,3) (b1) {$\boxed{\text{magnon}}$};
\draw[decoration={brace,amplitude=0.5em},decorate,very thick] (1.4,-1.3) -- (-1.4,-1.3);
\draw[decoration={brace,amplitude=0.5em},decorate,very thick] (3.142,-1.3) -- (1.6,-1.3);
\draw[decoration={brace,amplitude=0.5em},decorate,very thick] (-1.6,-1.3) -- (-3.142,-1.3);
\end{tikzpicture}
\end{center}
\end{minipage}
\hfill
\begin{minipage}[t]{.49\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.9]
\draw[->] (-3.3,0) -- (3.3,0);
\draw[->] (0,-0.2) -- (0,2.7);
\node at (4,0) (a3) {$p$};
\node at (0,3.2) (a4) {$E$};
\node at (0,-2.2) (q1) {};
\draw[very thick] plot[smooth] coordinates {(-3.142, 1.824) (-2.811, 1.656) (-2.480, 1.490) (-2.150, 1.325) (-1.819, 1.164) (-1.488, 1.008) (-1.157, 0.8632) (-0.8267, 0.7347) (-0.4960, 0.6341) (-0.1653, 0.5771) (0.1653, 0.5771) (0.4960, 0.6341) (0.8267, 0.7347) (1.157, 0.8632) (1.488, 1.008) (1.819, 1.164) (2.150, 1.325) (2.480, 1.490) (2.811, 1.656) (3.142, 1.824)};
\node at (2,3) (b1) {$\boxed{\text{mirror}}$};
\end{tikzpicture}
\end{center}
\end{minipage}
\caption{\small Dispersion relation for ``magnon kinematics" (left)---in this case the momentum is restricted to lie in the interval $|p|\leq g\pi$, and ``mirror kinematics" (right)---in this case the momentum takes values along the real line. For the case of magnon kinematics we have shown the two distinct branches labelled ``soliton" and ``magnon" corresponding to $|p|\lessgtr E$, that is $|p|\lessgtr\pi g/k$, respectively.}
\label{f1}
\end{figure}
In the string limit we have $p$ of order $k^0$, $E$ of order $k^{-1}$ and the dispersion relation becomes the familiar \cite{Beisert:2004hm}
\EQ{
E^2=\Big(\frac{\pi g}{2k}\Big)^2\Big(1+16g^2\sin^2\frac{g\,p}2\Big)\ ,
}
up to a simple re-scaling of $E$ and $p$. In the relativistic limit, that is $g\to\infty$ with fixed $k$, the dispersion relation \eqref{dsr} assumes the normal relativistic form
\EQ{
E^2-p^2=\left(2\cos\frac\pi{2k}\right)^{-2}\ .
}
It is interesting to investigate the relation between the physical momentum and the generalized rapidity variable $u$ \eqref{sqr}. In fact one finds that the reality condition $x^{\pm*}=x^\mp$ implies that $q^{-2iu}$ is real but there are two distinct branches depending on whether $q^{-2iu}$ is real and positive or negative. Using the relations
\EQ{\label{xpm}
x^+&=\xi\cdot\frac{1-qU^2}{qV^{-2}-1}=\frac1\xi\cdot\frac{q V^2-1}{1-qU^{-2}}\ ,\\
x^-&=\xi\cdot\frac{U^{-2}-q}{q-V^2}=\frac1\xi\cdot\frac{q-V^{-2}}{U^2-q}\ ,
}
where the equalities are guaranteed by the dispersion relation \eqref{dsr}, we can correlate the momentum $p$ with the coordinate $u$ as
\EQ{\label{claim}
\text{soliton branch:}\qquad& |p|<E\ ,\qquad|p|< \frac{\pi g}k\ ,\qquad q^{-2iu}\in{\mathbb R}<0\ ,\\
\text{magnon branch:}\qquad&|p|>E\ ,\qquad \frac{\pi g}k< |p| \ ,\qquad q^{-2iu}\in{\mathbb R}>0\ .
}
Note that the cross-over is precisely when $|p|=E$. An explicit proof of this claim follows from the relation is provided by the simple on-shell relation \eqref{rr}
\EQ{
q^{-2iu} = \frac{2\sin^2(\frac{E+p}{2g})}{(1-\xi^2)(\cos \frac{\pi}{k}-\cos \frac{p}{g})}
= \frac{\sin(\frac{p+E}{2g})}{\sin(\frac{p-E}{2g})}\ .
}
proved in appendix \ref{appa}. The names soliton and magnon in \eqref{claim} refer to the fact that in the string limit $k\to\infty$ only the magnon branch remains, while in the relativistic limit $g \to \infty$ only the soliton branch remains.
It is worth pausing to appreciate what is going on here. In a relativistic theory, Lorentz transformations can be used to boost the momentum of a state. The intrinsic properties of the state, however, do not change. A remarkable finding of our analysis is that this simple intuition must be abandoned in the non-relativistic interpolating theory: the nature of the state depends on its momentum.
\noindent{\bf Mirror kinematics}
There is an associated theory, the so-called mirror theory, obtained by a double Wick rotation $p\to -iE$ and $E\to -ip$~\cite{arXiv:0710.1568}. In particular, the S-matrix of the mirror theory is just the S-matrix of the original theory with this transformation on the kinematic variables. In the relativistic limit, the mirror theory is identical to the original but in the more general non-relativistic theory, for generic $(g,k)$ including the string theory limit, this is no longer true. With mirror kinematics we have
\EQ{\label{uvr2}
U=e^{E/2g}\ ,\qquad V=e^{p/2g}
}
and physical states satisfy a different reality condition $x^{+*}=1/x^-$ which ensures $U^*=U$ and $V^*=V$. Notice that, in contrast to the case of magnon kinematics, the coproduct~\eqref{cop} is consistent now with the usual conservation of energy and momentum. In the mirror case, the dispersion relation becomes
\EQ{\label{dismirr}
\cosh(p/g)-\xi^2\cosh(E/g)=(1-\xi^2)\cos(\pi/k)\ ,
}
where the momentum $p$ is valued along the real line. The physical values of the energy are the positive solutions of~\eqref{dismirr}, and on the right-hand side of Fig.~\ref{f1} we illustrate this dispersion relation. The corresponding kinematic variables lie on the sheet ${\cal R}_{-1}$ of the rapidity torus.
The relativistic dispersion relation results from taking the limit $g\to\infty$, in which case
\EQ{\label{rlm}
E^2-p^2=\left(2\cos\frac\pi{2k}\right)^{-2}\ .
}
This is identical to the same limit of the magnon theory as expected since the double Wick rotation is a symmetry of the relativistic theory. In the string limit $k\to\infty$, the dispersion relations becomes
\EQ{
E=2g\,\text{arcsinh}\,\Big[ \frac1{4g}\sqrt{1+\Big(\frac{2kgp}\pi\Big)^2}\Big]\ ,
}
which with a simple re-scaling of $E$ and $p$ is the known dispersion relation of the mirror theory \cite{arXiv:0710.1568}.
Concerning the relationship between the physical momentum and the generalized rapidity variable $u$, in the mirror case the reality condition $x^{+*}=1/x^-$ also implies that $q^{-2iu}$ is real. But, compared to the case of magnon kinematics, $q^{-2iu}$ turns out to be always positive, as can be easily checked using eq.~\eqref{rrpre}.
We will not write down the complete S-matrix. However, it is worth writing down two of its elements that play an important r\^ole. The first fact to bear in mind is that when written in terms of the $x_1^\pm$ and $x_2^\pm$ variables the S-matrix for the magnon and mirror theories are identical. It is only the way that $x_1^\pm$ and $x_2^\pm$ are expressed in terms of the energy and momentum that changes. The S-matrix element of the so-called ``$\mathfrak{su}(2)$ sector" corresponding to the particular element $|\phi^a\phi^a;z_1\rangle\otimes\ket{\phi^a\phi^a;z_2}\to|\phi^a\phi^a;z_2\rangle\otimes\ket{\phi^a\phi^a;z_1}$ takes the form
\EQ{\label{xpp}
S_{\mathfrak{su}(2)}(z_1,z_2)=\frac1{\sigma(z_1,z_2)^2}\cdot\frac{x_1^+x_2^-}{x_1^-x_2^+}\cdot\frac{x_1^--x_2^+}{x_1^+-x_2^-}\cdot \frac{1-\frac1{x_1^-x_2^+}}{1-\frac1{x_1^+x_2^-}}\ .
}
In the above, we have written the energy and momentum of the states in terms of the uniformized coordinate $z$ \cite{Hoare:2011wr}. The other S-matrix element of interest is the one of the ``$\mathfrak{sl}(2)$ sector"\footnote{This terminology of $\mathfrak{su}(2)$ and $\mathfrak{sl}(2)$ sectors is not completely appropriate since all states transform in representations of the compact bosonic algebra $\mathfrak{su}(2)^{\oplus4}$. The origin refers to the fact that, in the context of $\text{AdS}_5\times S^5$, the pairs of $\mathfrak{su}(2)$'s under which $|\phi^a\phi^b\rangle$ transforms as $(2,2)$ form a subalgebra of the algebra of the compact $\text{SO(6)}$ arising from the $S^5\simeq\text{SO}(6)/\text{SO}(5)$ part of the geometry whilst the pair of $\mathfrak{su}(2)$'s under which $|\psi^\alpha\psi^\beta\rangle$ transforms as $(2,2)$ are a subalgebra of the algebra of the non-compact group $\text{SO(2,4)}$ arising from the $\text{AdS}_5\simeq\text{SO}(2,4)/\text{SO}(1,4)$ part of the geometry.} that corresponds to the particular element $|\psi^\alpha\psi^\alpha;z_1\rangle\otimes\ket{\psi^\alpha\psi^\alpha;z_2}\to|\psi^\alpha\psi^\alpha;z_2\rangle\otimes\ket{\psi^\alpha\psi^\alpha;z_1}$, which takes the form
\EQ{\label{xpp2}
S_{\mathfrak{sl}(2)}(z_1,z_2)=\frac1{\sigma(z_1,z_2)^2}\cdot\frac{x_1^+-x_2^-}{x_1^--x_2^+}\cdot \frac{1-\frac1{x_1^-x_2^+}}{1-\frac1{x_1^+x_2^-}}\ .
}
In a relativistic theory, the S-matrix is valued on an infinite but unbranched cover of the relative rapidity cylinder. This is simply the relative rapidity complex plane $\theta=\theta_1-\theta_2$. Physical values correspond to real values of $\theta$. The situation in the non-relativistic interpolating theory is much more complex. The S-matrix is a function separately of the rapidity of each of the incoming particles since there is no relativistic invariance or notion of a relative rapidity. Then, for each of the rapidities the S-matrix is actually a function on an infinite but now branched cover of the rapidity torus (the latter with uniformized coordinate $z$). This cover cannot be viewed as the complex $z$ plane, however, it is useful to think of it as extending the sheets ${\cal R}_n$, with $n=-1,0,1,2$, to $n\in{\mathbb Z}$ where now the sheet ${\cal R}_{-2}$ is not identified with ${\cal R}_2$. In this description, we label the sheets for both particles together as ${\cal R}_{m,n}\equiv{\cal R}_m^{(1)}\times{\cal R}_n^{(2)}$. For instance, physical values of the rapidity of the incoming particles lie on sheet ${\cal R}_{0,0}$ for magnon kinematics, and sheet ${\cal R}_{-1,-1}$ for mirror kinematics. But even this description is only partial since there are a plethora of additional cuts that lead to further sheets. The dressing phase $\sigma(z_1,z_2)$ is regular in the region ${\cal R}_{0,0}$ and as a consequence the $\mathfrak{su}(2)$ sector S-matrix \eqref{xpp} has a simple pole at $x_1^+=x_2^-$ while the $\mathfrak{sl}(2)$ sector S-matrix \eqref{xpp2} has a simple pole at $x_1^-=x_2^+$. In the next section we shall investigate which of these poles lies on the analogue of the physical sheet and so is a candidate for a bound state pole. The analytic continuation of the dressing phase to other sheets is complicated but can be deduced from the formulae in~\cite{Hoare:2011wr}.
\section{Bound states}
In a relativistic theory, two-to-two body particle scattering can be described in terms of the familiar $s=(p_1+p_2)^2$, $t=(p_1-p_3)^2$ and $u=(p_1-p_4)^2$ Mandelstam variables. In a 1+1 dimensional integrable theory the individual momenta are conserved, $p_3=p_2$ and $p_4=p_1$, so that $u=0$ and $t=2(m_1^2+m_2^2) -s$. Considering equal mass scattering ($m_1 = m_2 = m$) and introducing the rapidity $p_i=m(\cosh\theta_i,\sinh\theta_i)$ we have
\EQ{
s=4m^2\cosh^2\frac\theta2\ ,
}
where $\theta=\theta_1-\theta_2$. S-matrix theory involves how the S-matrix behaves in the complex $s$-plane. In fact the S-matrix is defined on an infinite cover of the complex plane. One starts on the {\it physical sheet\/} which has branch points at $s=4m^2$, the 2-particle threshold, and $s=0$. The cuts are usually taken to lie along the positive and negative real axis, respectively. In the complex rapidity plane the physical sheet becomes the {\it physical strip\/} $0\leq\operatorname{Im}\theta\leq\pi$. In an integrable theory the infinite set of sheets of $s$ cover the whole complex rapidity plane. In this sense, the rapidity is a uniformizing coordinate for the S-matrix. Physical values correspond to $s=s_0+i0^+$ with $s_0$ real and $\geq4m^2$. This corresponds to $\theta$ being real and positive. The existence of a stable bound state of mass $M$ is signalled by a simple pole at $s=M^2$ lying along the real axis between $s=0$ and $s=4m^2$,\footnote{Other poles can correspond to bound states in the crossed channel or anomalous thresholds.} where the upper bound here is the 2-particle threshold. In terms of the rapidity, this corresponds to imaginary values of $\theta$ between 0 and $\pi$. In terms of the spatial momentum these bound states occur at complex values $p_1=\tilde p+ir$ and $p_2=\tilde p-ir$. Note that the fact that the energy of the bound state is real requires that the real parts of the momenta are equal. The imaginary part of the momentum $r$ is determined by the mass-shell condition for the bound state $s=M^2$. For the case of incoming particles with equal mass $m$ we have
\EQ{\label{bsc}
r^2=\Big(\frac{4m^2}{M^2}-1\Big)\Big(\tilde p^2+\frac{M^2}4\Big)\ .
}
The problem that we face is that it is not obvious how to generalize these aspects of S-matrix theory to the non-relativistic context and in particular how to identify when a pole in the S-matrix corresponds to a bound state, an anomalous threshold, or neither. The conditions under which a bound state can form can most easily be stated in terms of the variables $x_i^\pm$. From the representation theory of the symmetry algebra, bound states can occur when $x_1^+=x_2^-$, corresponding to the product of the short representations $\langle1,0\rangle^{\times2}$, or when $x_1^-=x_2^+$, corresponding to the product of the short representations $\langle0,1\rangle^{\times2}$. More generally we expect that the theory contains states in representations $\langle a-1,0\rangle^{\times2}$ and/or $\langle 0,a-1\rangle^{\times 2}$, with $a=1,2,\ldots$. The general dispersion relation for these states takes the form\footnote{Using the dispersion relation in terms of $x^\pm$ in \cite{deLeeuw:2011jr,Hoare:2011wr}; namely,
\EQ{\label{bsdr}
q^{-a}\Big(x^++\frac1{x^+}\Big)-q^a\Big(x^-+\frac1{x^-}\Big)=(q^a-q^{-a})\Big(\xi+\frac1\xi\Big)
}
and
\EQ{\label{bsuv}
U^2=q^{-a}\frac{x^++\xi}{x^-+\xi}=q^a\frac{\frac1{x^-}+\xi}{\frac1{x^+}+\xi}\ ,\qquad
V^2=q^{-a}\frac{\xi x^++1}{\xi x^-+1}=q^a\frac{\frac\xi{x^-}+1}{\frac\xi{x^+}+1}\ .
}
With magnon and mirror kinematics, the physical values of the kinematic variables of these states also lie on the sheets ${\cal R}_0$ and ${\cal R}_{-1}$, respectively.}
\EQ{\label{dsr2}
V^2+V^{-2}-g^2(q-q^{-1})^2(V^2+V^{-2}-U^2-U^{-2})=q^a+q^{-a}\ ,
}
with $(U,V)$ related to the energy and momentum as in \eqref{uvr1} or \eqref{uvr2}. In particular, in the relativistic limit, one finds
\EQ{\label{rlm2}
E^2-p^2=\Big(\frac{q^{a/2}-q^{-a/2}}{q-q^{-1}}\Big)^{2}=\left[a/2\right]_q^2\ .
}
With magnon kinematics, the situation we found in section \ref{sec2} for the fundamental particle generalizes in an obviously way (see eq.~\eqref{rrbs}). Once again there are two branches, a soliton branch with $|p|<a\pi g/k$ and a magnon branch with $|p|>a\pi g/k$. In a moment we will argue that the bound states in each branch are actually different since they occur at $x_1^-=x_2^+$ on the soliton branch and at $x_1^+=x_2^-$ on the magnon branch. In particular, this means that the bound states transform in representations $\langle0,a-1\rangle^{\times2}$ for $|p|<a\pi g/k$ and $\langle a-1,0\rangle^{\times2}$ for $|p|>a\pi g/k$. We will argue that at the special point $|p|=a\pi g/k$ the states become un-bound. This behaviour, as we have already described for the fundamental particle, clearly could not occur in a relativistic theory due to the principle of special relativity.
In the non-relativistic theory, we can find the generalization of the bound state condition \eqref{bsc} by imposing the dispersion relation \eqref{dsr2} for the bound state $a=2$ on the incoming energy and momenta $U=U_1U_2$ and $V=V_1V_2$, that is $E=E_1+E_2$ and $p=p_1+p_2$ up to the comments made after eq.~\eqref{uvr1} for magnon kinematics. In the non-relativistic theory we do not know a priori the analogue of the physical sheet/strip so it is not entirely obvious how to identify which simple poles of the S-matrix are due to bound states in the direct channel. However, we can proceed in a way that is as close as possible to the relativistic case. The idea is to take an analytic continuation of the incoming momenta away from physical values along the path $p_1=\tilde p_1+ir$ and $p_2=\tilde p_2-ir$ with $r$ increasing from 0, keeping the overall energy $E_1+E_2$ real, until the total energy and momentum hit the on-shell values for the bound state. In a relativistic theory, the condition that the total energy is real, with equal masses for the incoming particles, requires $\tilde p_1=\tilde p_2$ and we shall find the same condition in the non-relativistic case for small enough $\tilde p_1$. As we discuss below, a necessary condition for the formation of a bound state is $r>0$. In the relativistic situation the analytic continuation described above covers the region where $s\in{\mathbb R}$ and $0<s <4m^2$ lying on the physical strip, precisely the region where we expect to find bound state poles. We will assume that bound state poles must be found in the same analytically continued region in the $q$-deformed non-relativistic theory.
The positivity of $r$ follows thinking about scattering in one of the scalar sectors, e.g.~the $\mathfrak{su}(2)$ sector with S-matrix \eqref{xpp}. The argument, taken from \cite{Dorey:2007xn}, is a simple application of quantum mechanical scattering theory (for example, see~\cite{Mussardo:2010} appendix 17B). Labelling the S-matrix by the momenta of the incoming excitations, the wavefunction for the 2 states in the asymptotic regime $x_1\ll x_2$\,\footnote{Note that here $x_{1,2}$ are the spatial coordinates of the two particles being scattered and are not related to $x_{1,2}^\pm$.} can be expressed as
\EQ{
\Psi(x_1,x_2)=e^{ip_1x_1+ip_2x_2}+S(p_1,p_2)e^{ip_1x_2+ip_2x_1}\ .
}
Assuming that $v_1>v_2$,\footnote{The velocities are given by $v=\partial E/\partial p$ up to an overall positive normalization.} the first term represents the incoming two-particle wave and the second term the reflected wave with permuted momenta. We then analytically continue the momenta $p_1=\tilde p_1+ir$ and $p_2=\tilde p_2-ir$. The incoming wavefunction then behaves as $e^{-r(x_1-x_2)}$ and the reflected wavefunction as $e^{r(x_1-x_2)}$ in the region $x_1\ll x_2$. In order that we can give a probabilistic interpretation to the formation of a bound state we require that the reflected wavefunction is small relative to the incoming wavefunction in the region $x_1\ll x_2$ which means that a bound state can only form when the imaginary part of the momentum of the incoming particle from the left is positive: $r>0$.
In the non-relativistic theory there is no a priori reason why the bound state should form with $\tilde p_1=\tilde p_2$. As stated above, the actual condition is determined by requiring that the energy of the bound state is real and positive. In the following analysis we find that this requires $\tilde p_{1,2}$ to have the same sign. Furthermore, restricting the discussion to $\tilde p_{1,2}>0$,\footnote{The analysis is symmetric with respect to $\tilde p_{1,2} \rightarrow - \tilde p_{2,1}$. Care needs to be taken when $\tilde p_1 \neq \tilde p_2$, in which case their r\^oles are interchanged on flipping signs. This is required to preserve $v_1 > v_2$.} we find that for $\tilde p_{1,2}$ both less than a critical value $\tilde p_0$ the reality of the total energy does imply that $\tilde p_1=\tilde p_2$ as in a relativistic theory. However, there exists another branch of solutions with $\tilde p_2> \tilde p_0$, i.e.~above the threshold, such that $\tilde p_1$ and $\tilde p_2$ are not equal and indeed $\tilde p_1<\tilde p_0$.\,\footnote{This is precisely what Arutyunov and Frolov found in \cite{arXiv:0710.1568} for the string theory limit.} Notice that there are other solutions with $\tilde p_1$ and $\tilde p_2$ interchanged but in our convention particle 1 is the one coming in from the left and so we require $v_1\geq v_2$ for consistency, where we identify the velocity with the real part of $\partial E/\partial p$. This picks out the solution with $\tilde p_2>\tilde p_0>\tilde p_1$. The consistency conditions are illustrated in Fig.~\ref{f2}.
\begin{figure}[ht]
\begin{center}
\begin{tikzpicture} [line width=1.5pt,inner sep=2mm,
place/.style={circle,draw=blue!50,fill=blue!20,thick},proj/.style={circle,draw=red!50,fill=red!20,thick}]
\node at (2,2) [proj] (p1) {};
\node at (0,0.4) (i1) {$(\tilde E_1+is,\tilde p_1+ir)$};
\node at (4,0.4) (i2) {$(\tilde E_2-is,\tilde p_2-ir)$};
\node at (2,4) (i3) {$(\tilde E_1+\tilde E_2,\tilde p_1+\tilde p_2)$};
\draw[->] (i1) -- (p1);
\draw[->] (i2) -- (p1);
\draw[<-] (i3) -- (p1);
\end{tikzpicture}
\caption{\small The kinematic conditions required to form a bound state. All particles are on shell but the incoming particles have momenta which are analytically continued $p_1=\tilde p_1+ir$ and $p_2=\tilde p_2-ir$. Additional conditions to form a bound state are that $r>0$, $v_1\geq v_2$ and the bound state has physical (real) momentum and energy. The on-shell requirement implies that either $x_1^+=x_2^-$ or $x_1^-=x_2^+$. In the case of magnon kinematics, $\tilde E_1+\tilde E_2$ and $\tilde p_1+\tilde p_2$ are restricted to be $>0$ and $<\pi g$, and $>-\pi g$ and $<\pi g$, respectively, and have to be understood modulo $2\pi g$.}
\label{f2}
\end{center}
\end{figure}
In order to solve the bound state conditions it is useful to notice that we can solve for $U$ and $V$ in terms of either $x^+$ or $x^-$. Using \eqref{xpm} we find the two equations
\EQ{\label{a11}
\Big(\frac1{x^\pm}+\xi\Big)\, U^{\pm2}+(x^\pm+\xi)\, U^{\mp2} = q^{\mp 1}\Big(x^\pm + \frac1{x^{\pm}} + \xi + \frac1\xi\Big) + q^{\pm 1}\Big(\xi - \frac1\xi\Big)\ ,
}
which can be solved for either $U=U(x^+)$ or $U=U(x^-)$ and then
\EQ{\label{kqq}
V^2= \xi\big(q^{\mp1}-U^{-2}\big)(x^\pm)^{\pm1}+q^{\mp1}
}
\begin{figure}[ht]
\begin{center}
\begin{tikzpicture}[scale=1.2]
\draw[-] (0,0) -- (0,6) -- (6,6) -- (6,0) -- (0,0);
\draw[very thick] (1,0) .. controls (1,1) and (1.5,2) .. (2.5,2);
\draw[very thick,densely dashed] (5.5,0) .. controls (5.5,1) and (3.5,2) .. (2.5,2);
\draw[very thick,red] (2,0) .. controls (2.3,0.3) and (2.5,1) .. (2.5,2);
\draw[very thick,blue] (2,6) .. controls (2,5) and (2.5,3) .. (2.5,2);
\filldraw[black] (2.5,2) circle (1pt);
\draw[-] (0,2) -- (0.1,2);
\node at (-0.4,2) (z1) {$\tilde p_0$};
\node at (3,-0.7) (a1) {$r$};
\node at (-0.8,3) (a2) {$\tilde p$};
\node[blue] at (3.3,3.3) (a3) {$\tilde p_2$};
\node[red] at (3,0.5) (a4) {$\tilde p_1$};
\node at (1,2.5) (d1) {$|x_1^-|=1$};
\node[blue] at (1,4) (d2) {$x_1^-\in{\mathbb R}$};
\draw[->] (d1) -- (1.5,1.7);
\draw[->,blue] (d2) -- (2.1,4);
\node at (4.5,5.7) (b1) {mirror kinematics};
\node at (-0.4,0) (c3) {0};
\draw[->,blue] (a3) -- (2.5,3.3);
\draw[->,red] (a4) -- (2.4,0.5);
\end{tikzpicture}
\end{center}
\caption{\small Schematic plot (values exaggerated for clarity) of the bound-state momenta of the 2 particles $p_1=\tilde p_1+ir$ and $p_2=\tilde p_2-ir$ for mirror kinematics. The solid black and dashed part of the curve corresponds to the branch with $x_1^-=x_2^+$ and $|x_1^-|=1$ on which $\tilde p_1=\tilde p_2\leq\tilde p_0$. The solid blue/red part of the curve corresponds to the branch also with $x_1^-=x_2^+$ but now $x_1^-\in{\mathbb R}$, $\tilde p_2\geq p_0$ (blue) and $\tilde p_1\leq\tilde p_0$ (red).}
\label{f3}
\end{figure}
Bound states can form either when $x_1^- = x_2^+$ or $x_1^+ = x_2^-$. Working with the former and substituting these expressions into $U_1U_2$ and $V_1V_2$ it is clear that the parameters $x_{\!B}^\pm$ labelling the bound state are equal to $(x_1^+, x_2^-)$. As described above, in the fusion procedure the energy and momentum of the bound state should be a real---the reality conditions for the bound state (for both magnon and mirror kinematics) imply the following relation\footnote{This relation encodes both the magnon, $x_{\!B}^{+*} = x_{\!B}^-$, and mirror, $x_{\!B}^{+*} = 1/x_{\!B}^-$, reality conditions.}
\EQ{
\left(x_1^+ + \frac{1}{x_1^+}\right)^* = x_2^- + \frac{1}{x_2^-} \ .
}
This condition along with the dispersion relations for $x_1^\pm$ and $x_2^\pm$ \eqref{p11} imply that
\EQ{
x_1^- + \frac{1}{x_1^-} \in {\mathbb R} \qquad (x_1^- = x_2^+)
}
is a necessary requirement for the formation of a bound state with real energy and momentum. Therefore, in the following discussion we can restrict the search for solutions of the bound state conditions to two cases: $x_1^- \in {\mathbb R}$ and $|x_1^-| = 1$. A similar argument works for the bound states forming when $x_1^+ = x_2^-$; that is either $x_1^+ \in {\mathbb R}$ or $|x_1^+| = 1$.
In addition, in order to be physical, the energy of the bound state has to be positive. In general, the dispersion relations~\eqref{p11} and~\eqref{bsdr} have two different solutions corresponding to positive and negative energy. An efficient way to select the physical one is to require that the kinematic variables of the bound state $x_B^\pm$ lie on the correct sheet of the rapidity torus. Namely, for magnon kinematics $x_B^\pm \in {\cal R}_0$ while for mirror kinematics $x_B^\pm \in {\cal R}_{-1}$.
\noindent{\bf Mirror kinematics}
The equations above, \eqref{a11} and \eqref{kqq}, can be used to solve for the kinematic conditions at a bound state pole. Firstly, we consider the simpler case of mirror kinematics for which we have
\EQ{
&V_1=e^{(\tilde p_1+ir)/2g}\ ,\qquad V_2=e^{(\tilde p_2-ir)/2g}\ ,\\
&U_1=e^{(\tilde E_1+is)/2g}\ ,\qquad U_2=e^{(\tilde E_2-is)/2g}\ ,
}
a parameterization which ensures that the bound state has real momentum and energy. One then finds that the bound state condition $x_1^+=x_2^-$ has no solutions which satisfy the physical requirements. On the other hand for $x_1^-=x_2^+$, which corresponds to the bound state $\langle0,1\rangle^{\times2}$, we find that there are two distinct branches of solutions. On the first branch $|x_1^-|=1$, $\tilde p_1=\tilde p_2$ and $\tilde E_1=\tilde E_2$ whilst on the second $x_1^-\in{\mathbb R}$ and
\EQ{
e^{(\tilde p_1-\tilde p_2)/g}=\frac{\frac\xi{x_1^{-}}+1}{\xi x_1^-+1}\ ,\qquad e^{(\tilde E_1-\tilde E_2)/g}=\frac{\xi+x_1^-}{\xi+\frac1{x_1^-}}\ .
}
It is now a simple matter to map out the bound state momenta and energies using $V_1(x_1^-)$, $U_1(x_1^-)$, $V_2(x_2^+)$ and $U_2(x_2^+)$. Once the physical conditions are imposed, we find the solutions that are illustrated in Fig.~\ref{f3}. For $\tilde p_{1} = \tilde p_2 <\tilde p_0$, where the critical value $\tilde p_0$ corresponds to the point where the two branches meet at $x_1^-=1$, the solution corresponds to the first branch with $|x_1^-|=1$. On this branch $\tilde p_1=\tilde p_2$ and $\tilde E_1=\tilde E_2$. For a given $\tilde p_1$ there are actually two solutions for $r$, shown by the solid and dashed lines, and both are potential bound state poles. We discuss this in more detail below. This branch lies on the intersection of boundaries of the sheets ${\cal R}_{-1,-1}$ and ${\cal R}_{0,-2}$. On the second branch for which $x_1^-\in{\mathbb R}$ the real parts of the momenta are no longer equal $\tilde p_1\neq\tilde p_2$. On this branch there are two possible solutions to the condition $x_1^-=x_2^+$ but only the one with $v_1>v_2$ corresponds to a bound state. This is the solution with $\tilde p_2>\tilde p_0>\tilde p_1$ which lies on the sheet ${\cal R}_{0,-1}$.\footnote{The corresponding branch with negative $\tilde p_{1,2}$ lies on the sheet ${\cal R}_{-1,-2}$.}
We now consider the issue, relevant for the first branch, that there are two solutions with different values of $r$. For this branch (for both solutions) the total momentum $\tilde p_1 + \tilde p_2$ lies between $0$ and $2\tilde p_0$. For the second branch the total momentum is greater than $2 \tilde p_0$, and furthermore, there is only a single bound state solution for a given total momentum greater than $2\tilde p_0$. It therefore seems likely that there should also only be a single solution below this threshold so that there is only a single bound state for each value of the total momentum $\tilde p_1+\tilde p_2$. The likeliest explanation is that only the smaller root, denoted by the solid black line, corresponds to a bound state. The dashed line would then have to correspond instead to an anomalous threshold or the pole must be cancelled by a zero of the dressing phase in this region of parameter space. A definitive statement on this issue could only be made with a detailed investigation of the dressing phase and the kinematics required to produce an anomalous threshold in the form of a simple pole. An example of the latter, where a potential bound-state pole is actually an anomalous threshold, occurs in soliton scattering in the sine-Gordon theory \cite{Dorey:1996gd}.
\noindent{\bf Magnon kinematics}
The case of magnon kinematics is more subtle as we illustrate in Fig.~\ref{f4}. In this case we have the parameterization
\EQ{
&U_1=e^{(i\tilde p_1-r)/2g}\ ,\qquad U_2=e^{(i\tilde p_2+r)/2g}\ ,\\
&V_1=e^{(i\tilde E_1-s)/2g}\ ,\qquad V_2=e^{(i\tilde E_2+s)/2g}\ .
}
There are four distinct branches of solutions. The branches denoted by solid black lines in Fig.~\ref{f4} lie on the sheet ${\cal R}_{0,0}$, while the dashed black line lies on the sheet ${\cal R}_{1,-1}$. The coloured lines lie on the intersection of the boundaries of these two sheets. The first branch has $\tilde p_1 = \tilde p_2<\pi g/k$ and we call it the ``soliton branch" since it corresponds to $x_1^-=x_2^+$ and a bound state in representation $\langle 0,1 \rangle^{\times 2}$. The other three branches have $\tilde p_2>\pi g/k$ and we call them ``magnon branches" since they correspond to $x_1^+=x_2^-$ and a bound state in representation $\langle 1,0 \rangle^{\times 2}$. Recall that with magnon kinematics the momentum of states is restricted to the interval $|p|\leq g\pi$, and that the coproduct~\eqref{cop} ensures the conservation of energy and momentum only modulo $2\pi g$. In fact, in Fig.~\ref{f4}, the states corresponding to the dashed line with $\pi g-\frac{\pi g}{k}<\tilde p_1= \tilde p_2<\pi g$ have energy and momentum\,\footnote{It is not difficult to show that in the limit $r\to\infty$ there are two solutions with
\EQ{
\tilde p_1= \tilde p_2\to \pm \frac{\pi g}{k}\,, \qquad \tilde E_1= \tilde E_2\to \frac{\pi g}{k}
}
and
\EQ{
\tilde p_1= \tilde p_2\to \pm (\pi g-\frac{\pi g}{k})\,, \qquad \tilde E_1= \tilde E_2\to \frac{\pi g}{k}-\pi g
}
that correspond to the asymptotes of the dashed lines in Fig.~\ref{f4}. Notice that for the second solution $\tilde E_1= \tilde E_2$ turn out to be $<0$.
}
\EQ{
E=\tilde E_1+\tilde E_2 +2\pi g\,, \qquad p=\tilde p_1+\tilde p_2 \pm2\pi g\ .
}
\begin{figure}[ht]
\begin{center}
\begin{tikzpicture}[scale=1.2]
\draw[-] (0,0) -- (0,6) -- (6,6) -- (6,0) -- (0,0);
\draw[very thick] (0.6,0) .. controls (0.6,0.3) and (0.8,0.6) .. (0.8,0.9);
\draw[very thick] (0.8,0.9) .. controls (0.8,1.3) and (0.3,1.5) .. (0,1.5);
\filldraw[black] (0,1.5) circle (1pt);
\draw[very thick] (0,1.5) .. controls (0.3,1.8) and (0.6,2.5) .. (1.5,2.5);
\draw[very thick,densely dashed] (6,1.55) .. controls (4,1.7) and (3,2.5) .. (1.5,2.5);
\draw[very thick,densely dashed] (6,4.8) .. controls (4.5,5) and (3.5,5.4) .. (2.5,6);
\filldraw[black] (1.5,2.5) circle (1pt);
\draw[very thick,red] (1,0) .. controls (1,0.3) and (1.5,1) .. (1.5,2.5);
\draw[very thick,blue] (1,6) .. controls (1,5) and (1.5,4) .. (1.5,2.5);
\draw[dashed,black!50] (0,4.5) -- (6,4.5);
\draw[dashed,black!50] (0,1.5) -- (6,1.5);
\node at (3,-0.7) (a1) {$r$};
\node at (-1.2,3) (a2) {$\tilde p$};
\draw[-] (0,2.5) -- (0.1,2.5);
\node at (-0.4,2.5) (z1) {$\tilde p_0$};
\node at (-0.4,0) (c3) {0};
\node at (-0.4,6) (c4) {$\pi g$};
\node at (-0.5,1.5) (a7) {$\dfrac{\pi g}k$};
\node at (-0.8,4.5) (a8) {$\pi g -\dfrac{\pi g}k$};
\node at (3.1,3.1) (c1) {\bf magnon};
\node at (3.3,2.8) (l1) {$x_1^+=x_2^-$, $x_1^+\in{\mathbb R}$};
\node at (3.4,0.6) (c2) {{\bf soliton} $x_1^-=x_2^+$, $x_1^-\in{\mathbb R}$};
\node[blue] at (3.1,4.1) (c3) {\bf magnon};
\node[blue] at (3.3,3.8) (l2) {$x_1^+=x_2^-$, $|x_1^+|=1$};
\node[blue] at (1.9,5.3) (a3) {$\tilde p_2$};
\node[red] at (2.2,2) (a4) {$\tilde p_1$};
\draw[->,blue] (a3) -- (1.2,5.3);
\draw[->,red] (a4) -- (1.6,2);
\draw[->] (c2) -- (0.8,0.6);
\draw[->,blue] (c3) -- (1.5,4.1);
\draw[->] (2.3,3.1) .. controls (2.3,3.1) and (1.6,3) .. (1.1,2.6);
\draw[->] (3.9,3.125) .. controls (5,3.125) and (5.2,4) .. (5.5,4.8);
\draw[->] (3.9,2.5) -- (4.2,2);
\end{tikzpicture}
\end{center}
\caption{\small Schematic plot (values exaggerated for clarity) of the bound-state momenta of the 2 particles $p_1=\tilde p_1+ir$ and $p_2=\tilde p_1-ir$ for magnon kinematics. The solid black part of the curve corresponds to the bound state with $\tilde p_1=\tilde p_2\leq\tilde p_0$. This part of the curve is split into two branches corresponding to the soliton for $\tilde p_1=\tilde p_2<\frac{\pi g}k$ on which $x_1^-=x_2^+\in{\mathbb R}$ and the magnon for $\tilde p_1=\tilde p_2>\frac{\pi g}k$ on which $x_1^+=x_2^-\in{\mathbb R}$. The magnon branch then touches the third branch (also a magnon branch) at $x_1^+=1$ which continues with $x_1^+=x_2^-$ and $|x_1^+|=1$. The real parts of the momenta are no longer equal since $\tilde p_2>\tilde p_0$ (blue) and $\tilde p_1<\tilde p_0$ (red). On the fourth branch (also of magnon type), $\tilde p_1= \tilde p_2$, $\pi g-\frac{\pi g}{k}<\tilde p_1<\pi g$, and $-\pi g<\tilde E_1 =\tilde E_2 <0$.}
\label{f4}
\end{figure}
As $\tilde p_{1}$ and $\tilde p_2$ increase from 0, the bound state corresponds to a soliton with $x_1^-=x_2^+$. On this branch $x_1^-\in{\mathbb R}$, while $\tilde p_1=\tilde p_2$ and $\tilde E_1=\tilde E_2$. However, this branch only exists for $\tilde p_1<\pi g/k$. At the end point $\tilde p_1=\pi g/k$, the imaginary part $r$ goes to zero. This point has an interesting interpretation. If we consider the $a^\text{th}$ bound state then it is easy to see that \eqref{dsr2} has the solution
\EQ{
U^2=V^2=q^a\quad\implies\quad E=p=a\frac{\pi g}k\ .
}
At this point the $a^\text{th}$ bound state is marginally unstable for decay into $a$ fundamental particles with $U=U_1U_2\cdots U_a$ and $V=V_1V_2\cdots V_a$ or equivalently
\EQ{
E_1=E_2=\cdots=E_a=\frac{\pi g}k\ ,\qquad p_1=p_2=\cdots=p_a=\frac{\pi g}k\ .
}
Hence, for 2-body scattering the point $\tilde p_{1,2}=\pi g/k$ is the point at which the bound state of 2 solitons in the representation $\langle0,1\rangle^{\times2}$ becomes un-bound and the bound state of 2 magnons in the representation $\langle1,0\rangle^{\times2}$ becomes bound as $\tilde p_{1,2}$ are increasing, or vice-versa when $\tilde p_{1,2}$ are decreasing. The picture we have established above means that the bound state with $a=2$ has two different branches as we anticipated earlier in section \ref{sec2} based on the dispersion relation. When the bound state momentum $p=\tilde p_1+\tilde p_2$ is less than $2\pi g/k$ the bound state is a soliton transforming in representation $\langle0,1\rangle^{\times2}$. On the contrary when the bound state momentum $p>2\pi g/k$ the bound state is a magnon transforming in representation $\langle1,0\rangle^{\times2}$.
As $\tilde p_1$ and $\tilde p_2$ increase beyond $\pi g/k$ we move onto one of the magnon branches with $x_1^+=x_2^-$. For $\tilde p_2<\tilde p_0$, we have $x_1^+\in{\mathbb R}$ which implies $\tilde p_1=\tilde p_2$ and $\tilde E_1=\tilde E_2$. The critical value $\tilde p_0$ corresponds to the point where the two magnon branches meet at $x_1^+=1$. As in the case of mirror kinematics there are two solutions for $r$ for a given $\tilde p_1$ shown by the solid and dashed lines and the same argument suggests that only the solid line corresponds to a bound state while the dashed line is an anomalous threshold. On the second magnon branch, $|x_1^+|=1$, there are two solutions and we pick the one with $v_1>v_2$ which implies $\tilde p_2>\tilde p_0>\tilde p_1$ with
\EQ{
e^{i(\tilde p_1-\tilde p_2)/g}=\frac{\frac1{x_1^{+*}}+\xi}{\frac1{x_1^+}+\xi}\ ,\qquad e^{i(\tilde E_1-\tilde E_2)/g}=\frac{1+x_1^+\xi}{1+x_1^{+*}\xi}\ .
}
The third magnon branch, with $\tilde p_1= \tilde p_2$ and $\pi g-\frac{\pi g}{k}<|\tilde p_1|<\pi g$, is obtained with $-\xi<x_1^+=x_2^-\in{\mathbb R}<0$. It corresponds to total momentum $0< |p|=2\pi g- 2|\tilde p_1|<\frac{2\pi g}{k}$, which overlaps with the range of momenta of the soliton branch. In this case, $-\pi g<\tilde E_1 =\tilde E_2 <0$ so that the total energy is $0<E=\tilde E_1+ \tilde E_2 + 2\pi g<\pi g$. Again, since we expect a single bound state for each value of the total momentum, we conjecture that this branch, which is the only one where the conservation of energy and momentum is non-standard, also gives rise to anomalous thresholds.
\section{Discussion}
One interesting conclusion of the analysis of \cite{Hoare:2011wr} is that the magnon-like S-matrix did not satisfy the correct crossing symmetry equation in the relativistic limit. However, the subtleties of the magnon case described above show that this conclusion was too hasty. In fact, in the relativistic limit, only the bound state below the threshold at $p=2\pi g/k$ is relevant and survives. Consequently the correct identification of the parameters $x^\pm=x(u\pm\frac i2)$ and the relativistic rapidity is $e^\theta=-q^{-iu}$ (where the sign implies that for real (physical) rapidities $q^{-iu}<0$, as required) and {\it not\/} $e^{-\theta}=q^{-iu}$ as claimed in \cite{Hoare:2011wr}. With this change the magnon S-matrix is consistent with crossing symmetry in the relativistic limit. So in this improved understanding in both the magnon and mirror theories the bound states that survive in the relativistic limit are the anti-symmetric ones $\langle 0,a-1\rangle^{\times2}$ which are identified with the solitons of the SSSSG theory. It is important to bear in mind that from the point-of-view of the SSSSG theory taking the solitons to transform in either $\langle a-1,0\rangle^{\times2}$ or $\langle 0,a-1\rangle^{\times2}$ is simply a matter of convention because the representations are isomorphic.
It is interesting that this assignment of representations implies that the identification of the $\mathfrak{su}(2)^{\oplus4}$ sub-algebras with the $\text{AdS}_5\times S^5$ geometry has to be re-arranged as one interpolates from the string limit to the relativistic limit. To appreciate this notice that in the string limit the states are associated to two of the four $\mathfrak{su}(2)$ symmetries. For instance the representation $ \langle a-1,0\rangle^{\times2}$ includes the states $(a,0,a,0)$, and the two $\mathfrak{su}(2)$'s associated to spin-$\frac a2$ factors are the ones associated to the $S^5$ part of the geometry. In the relativistic limit, the states in the $ \langle 0,a-1\rangle^{\times2}$ includes the states $(0,a,0,a)$. But from the point of view of the SSSSG theory, where the bound states are solitons, the two $\mathfrak{su}(2)$'s associated to spin-$\frac a2$ factors are also associated to the ``$S^5$'' part of the geometry.\footnote{In the SSSSG theory, the phrases ``$S^5$'' and ``$\text{AdS}_5$'' parts of the geometry refer to its origin as the Pohlmeyer reduction of superstring theory on $\text{AdS}_5 \times S^5$ \cite{Grigoriev:2007bu}. Solitons are naturally associated to the ``$S^5$'' part of the SSSSG theory where they are embeddings of the complex sine-Gordon soliton into the symmetric space sine-Gordon theory based on $S^5=\text{SO}(6)/\text{SO}(5)$~\cite{Hollowood:2011fq,Hollowood:2011fm}. If one tries to put a soliton in the ``$\text{AdS}_5$'' part it turns out to have singularities. In this sense it is a relative of a spiky string that goes to the boundary of $\text{AdS}_5$.} Therefore, if the interpolating theory can be given a geometrical setting then it must involve a kind of permutation $\text{AdS}_5\times S^5\leftrightarrow S^5\times \text{AdS}_5$. This is potentially an important clue for the search for a geometrical interpretation of the $q$-deformed theory.
\section*{Acknowledgements}
\noindent
BH is supported by ERC Advanced Grant No.\,290456 and would like to thank Arkady Tseytlin for enjoyable collaborations and useful discussions on related topics.
\noindent
TJH is supported in part by the STFC grant ST/G000506/1.
\noindent
JLM is supported in part by MINECO (FPA2011-22594 and
FPA2008-01177), Xunta de Galicia (Consejer\'\i a de Educaci\'on and INCITE09.296.035PR), the Spanish Consolider-Ingenio 2010
Programme CPAN (CSD2007-00042), and FEDER. He thanks Gleb Arutyunov for valuable discussions about his work.
\vspace{1cm}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
\label{sec:intro}
Knowledge Graph (KG) describes the real-world entities and their internal relations by triples $(head, rel, tail)$, expressing the information on the internet in a form closer to human cognition.
To this day, KGs have facilitated a mount of downstream internet applications (e.g., search engines \cite{DBLP:conf/icde/YangAJTW19} and dialogue systems \cite{DBLP:conf/emnlp/YangZE20}) and become one of the core driving forces in the development of artificial intelligence.
In practice, KGs are usually constructed by various departments with multi-source data.
Therefore, they typically contain complementary knowledge while having overlapping parts.
Integrating these independent KGs could significantly improve the coverage rate, which is especially beneficial to low-resource language users.
\begin{figure}
\centering
\includegraphics[width = 0.95\linewidth]{intro.pdf}
\caption{A toy example of entity alignment.}
\label{fig:intro}
\end{figure}
Entity Alignment (EA) aims to find equivalent entity pairs between KGs (as shown in Figure \ref{fig:intro}), which is the core step of bridging and integrating multi-source KGs.
Therefore, EA attracts enormous attention and progresses rapidly.
Most existing methods regard EA as a graph representation learning task and share the same two-stage architecture: (i) encoding the KGs into low-dimensional spaces via graph encoders (e.g., TransE \cite{DBLP:conf/nips/BordesUGWY13} and GCN \cite{DBLP:journals/corr/KipfW16}) and (ii) mapping the embeddings of equivalent entity pairs into a unified vector space through contrastive losses \cite{DBLP:conf/cvpr/HadsellCL06}.
Recently, \emph{Graph Neural Network} (GNN) has achieved impressive success in many sorts of graph applications.
Following \citet{DBLP:conf/emnlp/WangLLZ18}, who first introduced \emph{Graph Convolutional Network} (GCN) into EA, numerous new fancy mechanisms are proposed and stacked over vanilla GCN for better performance, such as \emph{Graph Matching} \cite{DBLP:conf/iclr/FeyL0MK20}, \emph{Relational Attention} \cite{DBLP:conf/wsdm/MaoWXLW20}, and \emph{Hyperbolic embedding} \cite{DBLP:conf/emnlp/SunCHWDZ20}.
According to an EA paper list \footnote{\url{github.com/THU-KEG/Entity_Alignment_Papers}} on Github, over $90\%$ of EA methods adopted GNNs as their graph encoders in recent three years.
However, there is no such thing as a free lunch.
These increasingly complex GNN-based methods inherit the following inborn defects from their GNN lineage:
(i) \textbf{Weak scalability}.
Since the scales of real-world graphs are usually massive (e.g., YAGO$3$ \cite{DBLP:conf/www/SuchanekKW07} contains $17$ million entities), the scalability of graph algorithms is crucial.
However, as summarized by \citet{9174835}, most advanced EA methods require several hours \cite{DBLP:conf/ijcai/SunHZQ18, DBLP:conf/acl/CaoLLLLC19} or even days \cite{DBLP:conf/acl/XuWYFSWY19} on the DWY$100$K dataset, which only contains $200,000$ nodes.
Although an efficient loss function \cite{DBLP:conf/www/MaoWWL21} or a graph sampler \cite{DBLP:journals/corr/abs-2205-10312} could effectively alleviate this problem, all existing EA methods are still overstretched when facing the real-world KGs.
(ii) \textbf{Poor interpretability}.
Interpreting neural networks is a recognized challenge, and the complex graph structure makes it more difficult.
A few studies try to explain the behaviors of EA methods by showing wrong cases \cite{DBLP:conf/emnlp/YangZSLLS19} or visualizing attention weights \cite{DBLP:conf/acl/WuLFWZ20}.
And most EA studies \cite{DBLP:conf/ijcai/SunHZQ18, DBLP:conf/acl/XuWYFSWY19, DBLP:conf/cikm/MaoWXWL20} do not attempt to give any interpretation, only focusing on improving the performances on evaluation metrics.
An ancient Chinese saying goes, \emph{"drawing new inspiration while reviewing the old."}
A recent study \cite{DBLP:conf/iclr/HuangHSLB21} reinvents the classical graph algorithm --- \emph{Label Propagation} (LP) \cite{Zhu2002LearningFL}, combining it with shallow neural networks.
Surprisingly, this simple method out-performs the current best-known GNNs with more than two orders of magnitude fewer parameters and more than two orders of magnitude less training time.
Inspired by their excellent work, this paper proposes the \emph{Three-view Label Propagation} mechanism that enables the LP algorithm, designed for homogeneous graphs, to effectively run on KGs (a kind of typical heterogeneous graph).
Besides, we further propose two approximation strategies to reduce the computational complexity and enhance the scalability:
\emph{Random Orthogonal Label Generation} and \emph{Sparse Sinkhorn Iteration}.
The above three components constitute the proposed non-neural EA framework --- LightEA.
According to the extensive experiments on four groups of public datasets, LightEA has impressive scalability, robustness, and interpretability:
(1) \textbf{Scalability}:
Unlike GNN-based EA methods that require multiple rounds of forward and backward propagation, LightEA only requires one round of label propagation without any trainable parameters.
After abandoning neural networks, LightEA achieves extremely high parallel computing efficiency.
With a PC that has one RTX$3090$ GPU, LightEA only takes $7$ seconds to obtain the alignment results on DBP$15$K and less than $35$ seconds on DWY$100$K, which is only one-tenth of the state-of-the-art EA method.
LightEA could also easily handle DBP$1$M which contains more than one million entities and nearly ten million triples, while most EA methods even cannot run on it.
Besides running speed, the flexible framework enables LightEA could easily incorporate iterative strategies and literal features (e.g., entity names) to improve performance.
(2) \textbf{Robustness}:
In this paper, we design a thorough robustness examination that evaluates LightEA on four groups of public datasets containing cross-lingual, mono-lingual, sparse, dense, and large-scale subsets.
With a mere tenth of time consumption, LightEA achieves comparable results to state-of-the-art methods across all datasets and even surpasses them on many.
Besides, since LightEA does not have trainable parameters, the performance fluctuation of multiple runs is limited.
(3) \textbf{Interpretability}:
Researchers generally consider linear models (e.g., Linear Regression) have decent interpretability because their outputs are the linear summation of the input features.
Consistent with the LP algorithm, the computational process of LightEA is also entirely linear.
After removing \emph{Random Orthogonal Label}, each dimension of the label vectors will have a clear and realistic meaning.
We could trace the propagation process at each step to clearly explain how the entities are aligned.
In addition to the above contributions, we further design extensive auxiliary experiments to investigate the behaviors of LightEA in various situations.
The source code and datasets are now available in Github (\url{github.com/MaoXinn/LightEA}).
\section{Task Definition}
A KG could be defined as $\mathcal{G} = (\mathcal{E},\mathcal{R},\mathcal{T})$, where $\mathcal{E}$ is the entity set, $\mathcal{R}$ is the relation set, and $\mathcal{T}\subset \mathcal{E}\times \mathcal{R}\times \mathcal{E}$ represents the set of triples.
Given the source graph $\mathcal{G}_s$, the target graph $\mathcal{G}_t$, and the set of pre-aligned entity pairs $\mathcal{P}$, EA aims to find new equivalent entity pairs based on $\mathcal{G}_s$, $\mathcal{G}_t$, and $\mathcal{P}$.
\section{Related Work}
\subsection{Entity Alignment}
Most existing methods regard EA as a graph representation learning task and share the same two-stage architecture: (i) encoding the KGs into low-dimensional spaces via graph encoders and then (ii) mapping the embeddings of equivalent entity pairs into a unified vector space by contrastive losses.
Graph encoder is the most prominent and important part of existing EA methods.
Early methods usually used TransE \cite{DBLP:conf/nips/BordesUGWY13} and its variants as the graph encoder.
However, due to TransE only focusing on optimizing independent triples $\bm h + \bm r \approx \bm t$, it lacks the ability to model the global structure of KGs.
With impressive capability in modeling graph data, GNNs quickly become the mainstream algorithm for almost all graph applications, including entity alignment.
Since \citet{DBLP:conf/emnlp/WangLLZ18} first introduced GCN into EA, numerous GNN-based EA methods have been springing up.
For example, GM-Align \cite{DBLP:conf/acl/XuWYFSWY19} introduces \emph{Graph Matching Networks} to capture the entity interactions across KGs.
RREA \cite{DBLP:conf/cikm/MaoWXWL20} proposes the \emph{Relational Reflection} operation to generate relation-specific entity embeddings.
HyperEA \cite{DBLP:conf/emnlp/SunCHWDZ20} adopts hyperbolic embeddings to reduce the dimension of entities.
Besides the modifications on encoders, some EA methods adopt iterative strategies to generate semi-supervised data due to the lack of labeled entities.
Some EA methods propose that introducing literal information (e.g., entity names) could provide a multi-aspect view for alignment models.
However, it should be noted that not all KGs contain literal information, especially in practical applications.
Table \ref{tabel:rw} categorizes some popular EA methods based on their encoders and whether using iterative strategies or literal information.
\begin{table}
\resizebox{1\linewidth}{!}{
\renewcommand\arraystretch{0.9}
\begin{tabular}{cccc}
\toprule
\textbf{Method}&\textbf{Encoder}&\textbf{Literal}&\textbf{Iterative}\\
\midrule
MtransE\cite{DBLP:conf/ijcai/ChenTYZ17} &Trans&&\\
JAPE \cite{DBLP:conf/semweb/SunHL17}&Trans&&\\
BootEA \cite{DBLP:conf/ijcai/SunHZQ18}&Trans&&\CheckmarkBold\\
KDCoE \cite{DBLP:conf/ijcai/ChenTCSZ18}&Trans&\CheckmarkBold&\CheckmarkBold\\
RSN \cite{DBLP:conf/icml/GuoSH19} &RNN&&\\
TransEdge\cite{DBLP:journals/corr/abs-2004-13579}&Trans&&\CheckmarkBold\\
\midrule
GCN-Align \cite{DBLP:conf/emnlp/WangLLZ18}&GNN&&\\
MuGNN \cite{DBLP:conf/acl/CaoLLLLC19}&GNN&&\\
RDGCN \cite{DBLP:conf/ijcai/WuLF0Y019}&GNN&\CheckmarkBold&\\
GM-Align \cite{DBLP:conf/acl/XuWYFSWY19}&GNN&\CheckmarkBold&\\
HyperKA \cite{DBLP:conf/emnlp/SunCHWDZ20}&GNN&&\\
MRAEA \cite{DBLP:conf/wsdm/MaoWXLW20}&GNN&&\CheckmarkBold\\
RREA \cite{DBLP:conf/cikm/MaoWXWL20}&GNN&&\CheckmarkBold\\
Dual-AMN \cite{DBLP:conf/www/MaoWWL21}&GNN&&\CheckmarkBold\\
EASY \cite{DBLP:conf/sigir/GeLCZG21}&GNN&\CheckmarkBold&\CheckmarkBold\\
ClusterEA \cite{DBLP:journals/corr/abs-2205-10312}&GNN&&\CheckmarkBold\\
\bottomrule
\end{tabular}
}
\caption{Categorization of some popular EA methods.}\label{tabel:rw}
\end{table}
\subsection{Label Propagation and GCN}
\emph{Label Propagation} (LP) \cite{Zhu2002LearningFL} is a classical graph algorithm for node classification and community detection.
It assumes that two connected nodes are likely to have the same label, and thus it propagates labels along the edges.
Let $\bm A \in \mathbb{R}^{|\mathcal{E}|\times |\mathcal{E}|}$ be the graph adjacency matrix, $\bm D \in \mathbb{R}^{|\mathcal{E}|\times |\mathcal{E}|}$ be the diagonal degree matrix of $\bm A$, $\bm L^{(k)} \in \mathbb{R}^{|\mathcal{E}|\times c}$ be the label matrix after $k$ rounds of label propagation, where $c$ is the number of classes.
Each column of $\bm L^{(0)}$ is a one-hot vector, initialized by the input labels of the known nodes, while the label vectors of unknown nodes remain zeros.
The propagation process of the random LP algorithm could be formulated as follow:
\begin{equation}
\bm L^{(k+1)}=\bm D^{-1}\bm A\bm L^{(k)}\\
\end{equation}
\emph{Graph Convolutional Network} (GCN) \cite{DBLP:journals/corr/KipfW16} is a multi-layer neural network that propagates and transforms node features across the graph.
Let $\bm H^{(k)} \in \mathbb{R}^{|\mathcal{E}|\times d_{in}}$ be the input features of layer $k$, and $\bm W^{(k)} \in\mathbb{R}^{d_{in}\times d_{out}}$ be the transformation matrix.
The layer-wise propagation process of GCN could be summarized as follow:
\begin{equation}
\bm H^{(k+1)}=\sigma(\bm D^{-1/2}\bm A\bm D^{-1/2}\bm H^{(k)}\bm W^{(k)})\\
\end{equation}
Equations (1) and (2) indicate that the common intuition behind both LP and GCN is smoothing the labels or features.
\citet{DBLP:journals/corr/abs-2002-06755} notice this kind of inner correlation and unify them into one framework.
\citet{DBLP:conf/iclr/HuangHSLB21} combine shallow neural networks with the LP algorithm, achieving comparable performances to state-of-the-art GNNs, but with a small fraction of the parameters and time consumption.
These excellent works inspire us that the LP algorithm, neglected by the EA community, deserves further investigation.
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{MRW.pdf}
\caption{Illustrations of \emph{Three-view Label Propagation}.}
\label{fig:MRW}
\end{figure*}
\section{The Proposed Method}
LightEA is a non-neural EA framework consisting of three components: (i) \emph{Random Orthogonal Label Generation}, (ii) \emph{Three-view Label Propagation}, and (iii) \emph{Sparse Sinkhorn Iteration}.
We will describe each component of LightEA in this section.
\subsection{Random Orthogonal Label Generation}
Different from the node classification and community detection tasks, the entities in EA do not have explicit class labels.
LightEA borrows a common idea from face recognition \cite{DBLP:journals/spl/WangCLL18,DBLP:conf/cvpr/DengGXZ19} that regards each pair of pre-aligned entities as a independent class.
Assume that $(e_i,e_j)\in \mathcal{P}$ is the $x$-$th$ pre-aligned entity pair, the input label matrix of entities $\bm L^{(0)}_e = \left[\bm l^{(0)}_{e_1},\bm l^{(0)}_{e_2},...,,\bm l^{(0)}_{e_{|\mathcal{E}|}}\right]$ is initialized as follows:
\begin{equation}
\bm l^{(0)}_{e_i}=\bm l^{(0)}_{e_j}=onehot(x)\;\;\;\forall(e_i,e_j)\in \mathcal{P}
\end{equation}
where $onehot(x) \in \mathbb{R}^{|\mathcal{P}|} $ represents the one-hot vector that only the $x$-$th$ element equals one.
The input label vectors of remaining unaligned entities are initialized to all-zero.
Besides, since existing EA datasets do not provide pre-aligned relation pairs, the input label matrix of relations $\bm L^{(0)}_r \in \mathbb{R}^{|\mathcal{R}|\times|\mathcal{P}|}$ is also initialized to all-zero.
However, this initialization strategy will cause the input label matrices of entities and relations overly large and extremely sparse.
To ensure that LightEA runs well on large-scale datasets, we have to seek a solution that could reduce the dimension of input label matrices while the loss of orthogonality is slight.
Fortunately, independent random vectors on the high-dimensional hyper-sphere could satisfy our requirement.
\begin{lemma}
If $\bm x$ and $\bm y$ are independent random unit vectors on the $d$-dimensional hyper-sphere, $\left\langle\cdot\right\rangle$ represents the inner-product operation, then we have:
\begin{equation}
P\left(\langle\bm x,\bm y\rangle > \epsilon\right) \leq (1-\epsilon^2)^{(d+1)/2}
\end{equation}
\label{lemma:1}
\end{lemma}
Lemma \ref{lemma:1} \cite{Ball1997AnEI} states that any two independent random vectors on the high-dimensional hyper-sphere are approximately orthogonal.
For example, when $d>2048$, the probability upper bound of $\left\langle\bm x,\bm y\right\rangle > 0.1$ is less than $3.37\times 10^{-5}$.
Therefore, LightEA independently samples random vectors on the $d$-dimensional hyper-sphere to approximate the one-hot label vectors for better space-time complexity:
\begin{equation}
\bm l^{(0)}_{e_i}=\bm l^{(0)}_{e_j}=random(d)\;\;\;\forall(e_i,e_j)\in \mathcal{P}
\end{equation}
With this approximation strategy, the dimensions of $\bm L^{(0)}_e $ and $\bm L^{(0)}_r$ are reduced to $\mathbb{R}^{|\mathcal{E}|\times d}$ and $\mathbb{R}^{|\mathcal{R}|\times d}$.
One of the significant differences between LP and GCN is that one propagates labels, and the other propagates features.
However, the above discussion indicates that randomly initialized features could be regarded as an approximation to one-hot labels.
From this perspective, the propagation processes of GCN and LP are equivalent.
\subsection{Three-view Label Propagation}
Both LP algorithm and vanilla GCN were originally designed for homogeneous graphs.
However, KG is a kind of typical heterogeneous graph that requires a third-order tensor $\boldsymbol{\mathcal{A}}\in \mathbb{R}^{|\mathcal{E}|\times|\mathcal{E}|\times|\mathcal{R}|}$ to fully describe its adjacency relations.
Some early EA methods \cite{DBLP:conf/emnlp/WangLLZ18,DBLP:conf/acl/XuWYFSWY19} crudely treat all relations as equivalent, resulting in information losses.
Follow-up studies usually address this problem by adopting the relational attention mechanism \cite{DBLP:conf/ijcai/WuLF0Y019,DBLP:conf/wsdm/MaoWXLW20} to learn attention parameters and assign different weights for different relations and triples.
Besides the above methods, an intuitive solution for generalizing LP on KGs is to use the tensor-matrix product to replace the matrix product:
\begin{align}
\bm L^{(k+1)}_e &= \boldsymbol{\mathcal{A}} \times_2 \bm L^{(k)}_e \times_3 \bm L^{(k)}_r\\
\bm L^{(k+1)}_r &= \boldsymbol{\mathcal{A}} \times_1 \bm L^{(k)}_e \times_2 \bm L^{(k)}_e
\end{align}
where $\times_i$ represents the $i$-mode tensor-matrix product (i.e., along the $i$-$th$ axis).
Unfortunately, this solution has two fatal defects:
(i) The tensor-matrix product leads to a squared increase in the dimension after each round of propagation.
(ii) Existing tensor computing frameworks (e.g., Tensorflow) do not provide the tensor-matrix product operator for sparse tensors.
Inspired by the three-view drawing of engineering fields, we propose a \emph{Three-view Label Propagation} mechanism that compresses the adjacency tensor $\boldsymbol{\mathcal{A}}$ along three axes to retain maximum information from the original tensor while reducing computational complexity.
As shown in Figure \ref{fig:MRW}(a), we first separately sum the original tensor $\boldsymbol{\mathcal{A}}$ along three axes to obtain the top view $\bm A^{top}\in\mathbb{R}^{|\mathcal{R}|\times|\mathcal{E}|}$, the side view $\bm A^{side}\in\mathbb{R}^{|\mathcal{E}|\times|\mathcal{E}|}$, and the front view $\bm A^{front}\in\mathbb{R}^{|\mathcal{E}|\times|\mathcal{R}|}$.
From the perspective of inside meaning, $\bm A^{side}$, $\bm A^{front}$, and $\bm A^{top}$ represent the adjacency relations from head entity to tail entity, head entity to relation, and relation to tail entity, respectively.
Then, the labels of entities and relations are propagated according to the three views:
\begin{align}
\bm L^{(k+1)}_e &= \bm A^{side} \bm L^{(k)}_e + \bm A^{front} \bm L^{(k)}_r\\
\bm L^{(k+1)}_r &= \bm A^{top} \bm L^{(k)}_e
\end{align}
Intuitively, LightEA transforms the propagation process on triples into a triangular process, where each side of the triangle represents a different view (as shown in Figure \ref{fig:MRW}(b)).
In this way, labels could be effectively propagated on KGs without any trainable parameters while keeping the complexity consistent with the classical LP algorithm $O(|\mathcal{T}|d)$.
Finally, for each entity $e_i$, we concatenate the label vectors of all time-steps as the outputs:
\begin{equation}
\bm l^{out}_{e_i} = \left[\bm l^{(0)}_{e_i}||\bm l^{(1)}_{e_i}||...||\bm l^{(k-1)}_{e_i}||\bm l^{(k)}_{e_i}\right]
\end{equation}
\subsection{Sparse Sinkhorn Iteration}
Early EA studies \cite{DBLP:conf/emnlp/WangLLZ18,DBLP:conf/semweb/SunHL17} simply calculate the Euclidean distances or cosine similarities of all entity pairs and select the closest one as the alignment result.
In this way, one entity could be aligned to multiple entities simultaneously, which violates the one-to-one constraint of EA.
To address this problem, some studies \cite{DBLP:conf/aaai/XuSFSY20, DBLP:conf/emnlp/MaoWWL21} transform the decoding process of EA into an assignment problem and achieve significant performance improvement:
\begin{equation}
\underset{\bm P\in\mathbb{P}_{|\mathcal{E}|}}{arg\;max}{\;\left\langle \bm P, \bm S\right\rangle}_F
\end{equation}
$\bm S \in \mathbb{R}^{|\mathcal{E}|\times|\mathcal{E}|}$ is the similarity matrix of entities, and $s_{i,j} = cosine(\bm l^{out}_{e_i},\bm l^{out}_{e_j})$ in LightEA.
$\bm P$ is a permutation matrix denoting the alignment plan, where exactly one entry of $1$ in each row and column and $0$s elsewhere.
$\mathbb{P}_{|\mathcal{E}|}$ represents the set of all $|\mathcal{E}|$-dimensional permutation matrices.
$\langle\cdot\rangle_F$ represents the Frobenius inner product.
\begin{figure}
\centering
\includegraphics[width=0.95\linewidth]{Sinkhorn.pdf}
\caption{\emph{Sinkhorn} and \emph{Sparse Sinkhorn Iteration}.}
\label{fig:sink}
\end{figure}
Although the \emph{Hungarian} algorithm \cite{lawler1963quadratic} could solve assignment problems accurately, its high complexity $O(|\mathcal{E}|^3)$ makes it impossible to apply in large-scale datasets.
Therefore, recent studies \cite{DBLP:conf/sigir/GeLCZG21, DBLP:conf/emnlp/MaoWWL21} propose to use the \emph{Sinkhorn iteration} \footnote{The implementation details of the \emph{Sinkhorn iteration} are listed in Appendix \ref{apd:sinkhorn}.} \cite{DBLP:conf/nips/Cuturi13} to obtain an approximate solution:
\begin{align}
\begin{split}
&\underset{\bm P\in\mathbb{P}_{|\mathcal{E}|}}{arg\;max}{\;\left\langle \bm P,\bm S\right\rangle}_F\\
=& \lim_{\tau\rightarrow 0^+}{\rm Sinkhorn}(\bm S/\tau)
\end{split}
\end{align}
The space-time complexity of the \emph{Sinkhorn iteration} is $O(q|\mathcal{E}|^2)$, where $q$ is the number of iteration rounds.
Even though the \emph{Sinkhorn iteration} is significantly faster than the \emph{Hungarian} algorithm, it still becomes the main bottleneck of LightEA.
In LightEA, we adopt the decoding algorithm proposed by \citet{Mao2022AnEA} and utilize \emph{Sparse Sinkhorn Iteration} to reduce the computational complexity.
Specifically, we notice that the exponential normalization of the \emph{Sinkhorn iteration} causes most smaller values in the similarity matrix $\bm S$ to be infinitely close to zero.
Even if these smaller values are removed initially, it does not significantly affect the alignment results.
Therefore, instead of calculating the similarities between all entities, LightEA only retrieves the top-$k$ nearest neighbors for each entity by \emph{Approximate Nearest Neighbor} algorithms \footnote{In LighEA, we use the FAISS framework \cite{johnson2019billion} for approximate vector retrieval.}, such as \emph{Inverted Index System} and \emph{Product Quantizer} \cite{DBLP:journals/pami/JegouDS11}.
As shown in Figure \ref{fig:sink}, the similarity matrix $\bm S$ will become sparse.
There are only $k$ non-zero elements in each row, while the others are set to zeros.
In this way, the complexity of the \emph{Sinkhorn iteration} could be reduced to $O(qk|\mathcal{E}|)$.
\begin{table*}[t]
\begin{center}
\resizebox{1\textwidth}{!}{
\renewcommand\arraystretch{0.95}
\begin{tabular}{c|ccc|ccc|ccc|ccc|ccc}
\toprule
\multicolumn{1}{c}{\multirow{2}{*}{Method}} & \multicolumn{3}{c}{$\rm{DBP_{ZH-EN}}$} & \multicolumn{3}{c}{$\rm{DBP_{JA-EN}}$} & \multicolumn{3}{c}{$\rm{DBP_{FR-EN}}$}& \multicolumn{3}{c}{$\rm{SRPRS_{FR-EN}}$}& \multicolumn{3}{c}{$\rm{SRPRS_{DE-EN}}$} \\
& H@1 & H@10 & MRR & H@1 & H@10 & MRR & H@1 & H@10 & MRR & H@1 & H@10 & MRR & H@1 & H@10 & MRR\\
\hline
MTransE & 0.209 & 0.512 & 0.310 & 0.250 & 0.572 & 0.360 & 0.247 & 0.577 & 0.360 &0.213& 0.447&0.290&0.107&0.248&0.160\\
GCN-Align & 0.434 & 0.762 & 0.550 & 0.427 & 0.762 & 0.540 & 0.411 & 0.772 & 0.530 & 0.243& 0.522&0.340&0.385&0.600& 0.460\\
RSNs&0.508&0.745&0.591&0.507&0.737&0.590&0.516&0.768&0.605&0.350&0.636& 0.440& 0.484& 0.729&0.570\\
HyperKA&0.572&0.865&0.678& 0.564&0.865& 0.673&0.597&0.891& 0.704& -& -& -&- &-& -\\
\textbf{LightEA-B} &\textbf{0.756}&\textbf{0.905}&\textbf{0.811}&\textbf{0.762}&\textbf{0.919}&\textbf{0.819}&\textbf{0.807}&\textbf{0.943}&\textbf{0.857}&\textbf{0.466 }&\textbf{0.746}&\textbf{0.560}&\textbf{0.594}&\textbf{0.814}&\textbf{0.670}\\
\hline
BootEA & 0.629 & 0.847 & 0.703 & 0.622 & 0.853 & 0.701 & 0.653 & 0.874 & 0.731 & 0.365&0.649&0.460&0.503&0.732&0.580\\
TransEdge&0.735&0.919&0.801&0.719&0.932&0.795&0.710&0.941&0.796&0.400&0.675&0.490&0.556&0.753&0.630\\
MRAEA &0.757&0.930&0.827&0.758&0.934&0.826&0.781&0.948&0.849&0.460&0.768&0.559&0.594&0.818&0.666\\
Dual-AMN &0.808&\textbf{0.940}&\textbf{0.857}&0.801&\textbf{0.949}&0.855&0.840&\textbf{0.965}&0.888&0.481&\textbf{0.778}&0.568&0.614&\textbf{0.823}&\textbf{0.687}\\
\textbf{LightEA-I} &\textbf{0.812}&0.915&0.849&\textbf{0.821}&0.933&\textbf{0.864}&\textbf{0.863}&0.959&\textbf{0.900}&\textbf{0.484}&0.769&\textbf{0.570}&\textbf{0.615}&0.817&0.685\\
\hline
GM-Align & 0.679 & 0.785 & - & 0.739 & 0.872 & - & 0.894 & 0.952 & - & 0.574&0.646&0.602&0.681&0.748&0.710\\
RDGCN & 0.697 & 0.842 & 0.750 & 0.763 & 0.897 & 0.810 & 0.873 & 0.950 & 0.901 &0.672&0.767& 0.710&0.779&0.886&0.820 \\
EASY &0.898& 0.979& 0.930 &0.943 &0.990 &0.960 &0.980 &0.998 &0.990 &0.965 &0.989 &0.970 &0.974 &0.992 &0.980\\
SEU &0.900 &0.965 &0.924 &0.956 &0.991 &0.969 &0.988 &\textbf{0.999} &0.992 &0.982 &\textbf{0.995} &0.986 &0.983 &0.996 &0.987\\
\textbf{LightEA-L} &\textbf{0.952}&\textbf{0.984}&\textbf{0.964}&\textbf{0.981}&\textbf{0.997}&\textbf{0.987}&\textbf{0.995}&0.998&\textbf{0.996}&\textbf{0.986}&0.994&\textbf{0.989}&\textbf{0.988 }&\textbf{0.995}&\textbf{0.991}\\
\bottomrule
\end{tabular}
}
\caption{Performances on DBP$15$K and SRPRS. Baselines' results are from original papers or \citet{9174835}.}
\label{table:res1}
\end{center}
\end{table*}
\section{Experiments}
All experiments are conducted on a PC with an Nvidia RTX$3090$ GPU and an EPYC 7452 CPU.
\subsection{Datesets and Metrics}
To comprehensively verify the scalability, robustness, and interpretability of our proposed methods, we conduct experiments on the following four groups of datasets:
(1) \textbf{DBP15K} \cite{DBLP:conf/semweb/SunHL17} is the most commonly used EA dataset, consisting of three small-sized cross-lingual subsets.
Each subset contains $15,000$ pre-aligned entity pairs.
(2) \textbf{SRPRS} \cite{DBLP:conf/icml/GuoSH19} is a sparse dataset that includes two small-sized cross-lingual subsets.
Each subset of SRPRS also contains $15,000$ pre-aligned entity pairs but with much fewer triples.
(3) \textbf{DWY100K} \cite{DBLP:conf/ijcai/SunHZQ18} comprises two medium-sized mono-lingual subsets, each containing $100,000$ pre-aligned entity pairs and nearly one million triples.
(4) \textbf{DBP1M} \cite{DBLP:journals/pvldb/GeLCZG21} is one of the largest EA datasets so far, consisting of two cross-lingual subsets with more than one million entities and nearly ten million triples.
The detailed statistics are listed in Table \ref{table:dataset1}.
Consistent with the previous studies \cite{DBLP:conf/semweb/SunHL17,DBLP:conf/ijcai/WuLF0Y019,DBLP:conf/wsdm/MaoWXLW20}, we randomly split $30\%$ of the pre-aligned entity pairs for training and the remaining $70\%$ for testing.
Following convention \cite{DBLP:conf/ijcai/ChenTYZ17,DBLP:conf/emnlp/WangLLZ18}, we use $Hits@k$ and \emph{Mean Reciprocal Rank} (MRR) as our evaluation metrics.
The reported performances are the average of five independent runs.
\subsection{Baselines}
According to the categorization in Table \ref{tabel:rw}, we compare LightEA against the following three groups of advanced EA methods:
(1) \textbf{Basic}:
MtransE \cite{DBLP:conf/ijcai/ChenTYZ17}, GCN-Align \cite{DBLP:conf/emnlp/WangLLZ18}, RSNs \cite{DBLP:conf/icml/GuoSH19}, HyperKA \cite{DBLP:conf/emnlp/SunCHWDZ20}.
(2) \textbf{Iterative}:
BootEA \cite{DBLP:conf/ijcai/SunHZQ18}, TransEdge \cite{DBLP:journals/corr/abs-2004-13579}, MRAEA \cite{DBLP:conf/wsdm/MaoWXLW20}, Dual-AMN \cite{DBLP:conf/www/MaoWWL21}, LargeEA \cite{DBLP:journals/pvldb/GeLCZG21}, ClusterEA \cite{DBLP:journals/corr/abs-2205-10312}.
(3) \textbf{Literal}:
GM-Align \cite{DBLP:conf/acl/XuWYFSWY19}, RDGCN \cite{DBLP:conf/ijcai/WuLF0Y019}, SEU \cite{DBLP:conf/emnlp/MaoWWL21}, EASY \cite{DBLP:conf/sigir/GeLCZG21}.
To make a fair comparison against the above methods, LightEA also has three corresponding versions:
(1) LightEA-B is the basic version.
(2) LightEA-I adopts the bi-directional iterative strategy proposed by \citet{DBLP:conf/wsdm/MaoWXLW20}.
(3) LightEA-L uses the pre-trained word embeddings of translated entity names \footnote{The name translations and word embeddings are provided by \citet{DBLP:conf/acl/XuWYFSWY19}, which is consistent with follow-up studies.} as the inputs matrix and also adopts the bi-directional iterative strategy.
Same with SEU and EASY, LightEA-L is an unsupervised method that does not require any pre-aligned entity pairs.
\subsection{Hyper-parameters}
\label{sec:hyper}
Except for DBP$1$M, we use the same setting:
the dimension of hyper-sphere $d = 1,024$;
the number of \emph{Three-view Label Propagation} rounds $k = 2$.
We reserve the top-$500$ nearest neighbors for each entity in \emph{Sparse Sinkhorn Iteration}.
Following \citet{DBLP:conf/emnlp/MaoWWL21}, the number of Sinkhorn iteration rounds $q = 10$ and the temperature $\tau = 0.05$.
Due to the limitation of GPU memory, the dimension of hyper-sphere $d$ is reduced to $256$ for DBP$1$M.
\begin{table}[t]
\resizebox{\linewidth}{!}{
\renewcommand\arraystretch{0.9}
\begin{tabular}{ccccccc}
\toprule
\multicolumn{1}{c}{\multirow{2}{*}{Method}} & \multicolumn{3}{c}{$\rm{DWY_{DBP-WD}}$}& \multicolumn{3}{c}{$\rm{DWY_{DBP-YG}}$} \\
\multicolumn{1}{c}{} & H@1 & H@10 & MRR & H@1 & H@10 & MRR\\
\hline
MTransE &0.238&0.507&0.330&0.227&0.414&0.290\\
GCN-Align&0.494&0.756&0.590&0.598&0.829&0.680\\
RSNs&0.607&0.793&0.673&0.689&0.878&0.756\\
MuGNN &0.604&0.894&0.701&0.739&0.937&0.810\\
\textbf{LightEA-B}&\textbf{0.861}&\textbf{0.962}&\textbf{0.898}&\textbf{0.884}&\textbf{0.977}&\textbf{0.918}\\
\hline
BootEA &0.748&0.898&0.801&0.761&0.894&0.808\\
TransEdge&0.788&0.938&0.824&0.792&0.936&0.832\\
MRAEA&0.794&0.930&0.856&0.819&0.951&0.875\\
Dual-AMN&0.869&0.969&0.908&\textbf{0.907}&\textbf{0.981}&\textbf{0.935}\\
\textbf{LightEA-I}&\textbf{0.907}&\textbf{0.978}&\textbf{0.934}&0.902&0.980&0.929\\
\bottomrule
\end{tabular}
}
\caption{Experimental results on DWY$100$K.}
\label{table:res2}
\end{table}
\begin{table}[t]
\resizebox{1\linewidth}{!}{
\renewcommand\arraystretch{0.9}
\begin{tabular}{ccccccc}
\toprule
\multicolumn{1}{c}{\multirow{2}{*}{Method}} & \multicolumn{3}{c}{$\rm{DBP1M_{FR-EN}}$}& \multicolumn{3}{c}{$\rm{DBP1M_{DE-EN}}$} \\
\multicolumn{1}{c}{} & H@1 & H@10 & MRR & H@1 & H@10 & MRR\\
\hline
LargeEA-G &0.051 &0.134& 0.080 & 0.034& 0.095& 0.050 \\
LargeEA-R &0.094& 0.215& 0.130& 0.064 &0.150 &0.090 \\
LargeEA-D &0.105 &0.219 &0.150& 0.066&0.147& 0.090 \\
ClusterEA-G &0.100 &0.245 &0.150 &0.069 &0.177 &0.110 \\
ClusterEA-R &0.260& 0.456& 0.320 & 0.250 &0.450& 0.320 \\
ClusterEA-D &0.281& \textbf{0.474}& \textbf{0.350}& 0.288& \textbf{0.488} &\textbf{0.350} \\
\hline
\textbf{LightEA-B}&0.262&0.450& 0.318&0.258&0.457&0.316\\
\textbf{LightEA-I}&\textbf{0.285}&0.468&0.345&\textbf{0.289}&0.479&0.347\\
\bottomrule
\end{tabular}
}
\caption{Experimental results on DBP$1$M\protect\footnotemark.}
\label{table:res3}
\end{table}
\footnotetext{The results of baselines are from ClusterEA\cite{DBLP:journals/corr/abs-2205-10312}. To solve the name bias issue, ClusterEA removes parts of entities and all literal information while retaining all the triples. Therefore, LightEA-L cannot run on this dataset.}
\subsection{Main Experiments}
Table \ref{table:res1} lists the experimental results of LightEA on DBP$15$K and SRPRS.
Table \ref{table:res2} and Table \ref{table:res3} list the results on DWY$100$K and DBP$1$M, respectively.
\noindent
\textbf{DBP15K}.
Compared to the basic EA baselines, LightEA-B has significant improvements on all metrics.
The main reason is that these basic EA methods were proposed earlier, while most advanced methods adopts iterative strategies for better performance.
For LightEA-I, the bi-directional iterative strategy improves the performance by more than $5\%$ on $Hits@1$ and $4\%$ on MRR.
Compared to Dual-AMN, the state-of-the-art structure-based EA method, LightEA-I achieves comparable results that are slightly better on $Hits@1$ and weaker on $Hits@10$.
Among literal-based EA methods, LightEA-L consistently achieves the best performances.
Especially for $\rm DBP_{ZH-EN}$, LightEA-L beats SEU by more than $5\%$ on $Hits@1$.
\noindent
\textbf{SRPRS}.
The performance rankings on SRPRS are pretty similar to those on DBP$15$K.
LightEA-B and LightEA-L defeat all the competitors, while LightEA-I achieves similar performances to Dual-AMN.
The main difference is that the impact of iterative strategies is significantly weakened on SPRPS, in which the performance gain is less than $2\%$ on $Hits@1$ and $1\%$ on MRR.
That is mainly because the structural information of SRPRS is particularly sparse, causing iterative strategies to fail to generate high-quality semi-supervised data.
\noindent
\textbf{DWY100K}.
For DWY$100$K, LightEA maintains competitive performance.
On $\rm DWY_{DBP-WD}$, LightEA outperforms Dual-AMN by $4\%$ on $Hits@1$ and $3\%$ on MRR while having a comparable result on $\rm DWY_{DBP-YG}$.
According to \citet{9174835}, the names of equivalent entities in DWY$100$K are almost identical, and using the edit distance could easily achieve the ground-truth performance.
Therefore, Table \ref{table:res2} does not list the results of literal methods.
\noindent
\textbf{DBP1M}.
As one of the largest EA datasets so far, DBP1M poses a severe challenge to scalability, and most EA methods cannot directly run on this dataset.
As shown in Table \ref{table:res3}, the experimental results show that LightEA still achieves similar performances to the state-of-the-art method on this challenging dataset.
LargeEA and ClusterEA are two acceleration frameworks for GNN-based EA methods, consisting of mini-batch graph samplers, efficient losses, etc.
"-G," "-R," and "-D" represent using GCN-Align, RREA, and Dual-AMN as the backbone networks, respectively.
\begin{table}
\begin{center}
\resizebox{1\linewidth}{!}{
\renewcommand\arraystretch{0.9}
\begin{tabular}{ccccc}
\toprule
\textbf{Method}&\textbf{DBP15K}&\textbf{SRPRS}&\textbf{DWY100K}&\textbf{DBP1M}\\
\hline
Dual-AMN&69&57&2,237&-\\
LargeEA-D&26&23&227&2,119\\
ClusterEA-D&43&36&389&1,503\\
\hline
LightEA-B&2.8&2.2&15.4&97\\
LightEA-I&7.1&6.5&34.5&228\\
LightEA-L&14.8&11.2&-&-\\
\bottomrule
\end{tabular}
}
\end{center}
\caption{Time costs on all datasets (seconds). }\label{tabel:time}
\end{table}
\noindent
\textbf{Time cost}.
Table \ref{tabel:time} reports the time costs of three variants of LightEA.
Due to the space limitation, we only list out the time costs of Dual-AMN with two acceleration frameworks as the baselines.
For the results of other EA methods, please refer to Table \ref{tabel:timeapp} in Appendix C.
LargeEA and ClusterEA effectively accelerate Dual-AMN, achieving ten times speedups on DBP$1$M.
However, GNN-based methods are still stuck with multiple rounds of forward and backward propagation, while LightEA only requires one round of label propagation and no need for training.
With similar performances, the time consumption of LightEA-B is less than one-seventh of Dual-AMN variants.
Besides, introducing iterative strategies and literal features significantly increases time consumption while also improving performance.
\begin{figure*}
\centering
\includegraphics[width=0.95\textwidth]{hyper.pdf}
\caption{Hyper-parameter experiments of LightEA-I on DBP$15$K.}
\label{fig:hyper}
\end{figure*}
\subsection{Hyper-parameters}
We design extensive hyper-parameter experiments to investigate the behaviors of LightEA in various situations.
Due to the space limitation, Figure \ref{fig:hyper} only shows the results of LightEA-I on DBP$15$K.
Appendix \ref{sec:hyperapp} shows the results on other datasets.
\noindent
\textbf{Dimension}.
To alleviate the problem that one-hot label vectors being over-sparse, LightEA proposes to replace them with independent random vectors on high-dimensional hyper-spheres.
Figure \ref{fig:hyper}(a) shows the $Hits@1$ curves with different dimensions $d$.
Clearly, there are significant diminishing marginal effects on increasing dimensions.
When the dimension $d>1,024$, the performance gain becomes limited.
Actually, the reason behind diminishing marginal effects has been told by Lemma \ref{lemma:1} --- the probability of two random drawn vectors "conflicting" with each other (i.e., $\langle\bm x,\bm y\rangle > \epsilon$) decreases exponentially as the dimension $d$ increases.
\noindent
\textbf{Propagation Round}.
Figure \ref{fig:hyper}(b) shows the performances with different numbers of propagation rounds.
Similar to the network depth of GNNs, more propagation rounds also lead to the over-smoothing problem.
When the number of rounds $q=2$, LightEA-I achieves the best performance and then begins to decline.
This phenomenon indicates a high correlation between label propagation and GNNs from the side.
\noindent
\textbf{Top-K}.
In \emph{Sparse Sinkhorn Iteration}, LightEA only retrieves the top-$k$ nearest neighbors for each entity instead of calculating the distances between all pairs.
As expected, Figure \ref{fig:hyper}(c) shows that removing smaller values from the similarity matrix hardly affects the alignment performances.
The trick of \emph{Sparse Sinkhorn Iteration} could reduce the space-time complexity with limited losses.
Besides hyper-parameters, we further design more auxiliary experiments, such as ablation experiments.
Due to the space limitation, these experiments are listed in Appendix \ref{sec:pre}, \ref{sec:able}, and \ref{sec:openEA}.
\subsection{How to Interpret the Results}
\label{sec:interpret}
Existing GNN-based EA methods inherit poor interpretability from neural networks.
It is hard to explain the inside meaning of each dimension of entity features and why two entities are aligned.
Therefore, the output features are only used to calculate the similarities.
Different from GNN-based methods, we could clearly interpret the alignment results of LightEA by the following steps:
(1) Remove \emph{Random Orthogonal Label}.
After removing this component, the meaning of each dimension of label vectors becomes clear and realistic.
The $x$-$th$ dimension of $\bm l_{e_i}^{(k)}$ represents the relevance score between $e_i$ and the $x$-$th$ pre-aligned entity pair after $k$ rounds of propagation.
If two entities are equivalent, their distributions of relevance scores should also be similar.
(2) Trace the propagation:
Since we have known the meaning of each dimension, we could trace the propagation process at each time-step to investigate why two entities are aligned.
However, removing the \emph{Random Orthogonal Label Generation} will make the label matrices extremely large and sparse, and the \emph{Three-view Label Propagation} can only run on the small-sized sub-graphs.
Therefore, this strategy only fits for interpreting a limited number of entities.
\begin{figure*}[t]
\centering
\includegraphics[width=\textwidth]{wrong_case.pdf}
\caption{An example of tracing the propagation process and interpreting the alignment results.}
\label{fig:wrong}
\end{figure*}
\subsection{An Example of Tracing the Wrong Case}
\label{sec:wrong_case}
Figure \ref{fig:wrong} shows an example of tracing the propagation process and interpreting the alignment results.
In this case, \emph{United\_States\_Armed\_Forces} is incorrectly aligned with \emph{US\_Marine\_Corps}, and the correct answer is \emph{US\_Armed\_Forces}.
As described in last section, we first remove the \emph{Random Orthogonal Label}, run the \emph{Three-view Label Propagation}, and obtain the sparse label matrices $\bm L^{(1)}_e$ and $\bm L^{(2)}_e$.
Then, we separately sort the label vectors $\bm l^{(1)}_{e_i}$ and $\bm l^{(2)}_{e_i}$ of each entity to get the dimension indexes of top-$5$ non-zero elements.
Finally, we look up the corresponding names of dimension indexes in the entity name list and show them in Figure \ref{fig:wrong}.
Apparently, the noise of graph structure causes this wrong case.
Compared to the correct entity, the incorrect entity has a more similar neighborhood structure to \emph{United\_States\_Armed\_Forces}.
There are five common elements between the wrong alignment pair, while only three between the right alignment pair.
\section{Conclusion}
In this paper, we reinvent the \emph{Label Propagation} algorithm to effectively run on KGs and propose a non-neural EA framework --- LightEA.
According to the experiments on public datasets, LightEA has impressive scalability, robustness, and interpretability.
With a mere tenth of time consumption, LightEA achieves comparable results to state-of-the-art methods across all datasets.
\section*{Limitations}
Although we have demonstrated that LightEA has impressive scalability, robustness, and interpretability on multiple public datasets with different scales, there are still three limitations that should be addressed in the future:
(1) In LightEA, good interpretability and high efficiency cannot coexist.
If not removing the \emph{Random Orthogonal Label}, LightEA's interpretability will be significantly weakened.
How to balance the interpretability and efficiency is our future work.
(2) Theoretically, LightEA has high parallel efficiency that could obtain linear speedup with multiple GPUs.
However, we do not have enough devices to verify this advantage, and all the experiments in this paper run with a single RTX3090.
We will purchase more devices to complete these missing experiments in the future.
(3) Currently, we implement LightEA via Tensorflow.
Since LightEA is a non-neural algorithm without any trainable parameters, a complex deep learning framework would be redundant and inefficient.
In the future, we will refactor LightEA with CUDA and C++ to further improve efficiency.
\section*{Ethics Statement}
To the best of our knowledge, this work does not involve any discrimination, social bias, or private data.
All the datasets are open-source and constructed from open-source KGs such as Wikidata, YAGO, and DBpedia.
Therefore, we believe that our study complies with the \href{https://www.aclweb.org/portal/content/acl-code-ethics}{ACL Ethics Policy}.
In addition, introducing literal features may cause concerns about the misuse of user-generated content.
LightEA can avoid this concern by using pure structural information for entity alignment.
\section*{Ethics Statement}
We appreciate the support from National Natural Science Foundation of China with the Research Project on Human Behavior in Human-Machine Collaboration (Project Number: 72192824) and the support from Pudong New Area Science \& Technology Development Fund (Project Number: PKX2021-R05).
\section{Introduction}
\label{sec:intro}
Knowledge Graph (KG) describes the real-world entities and their internal relations by triples $(head, rel, tail)$, expressing the information on the internet in a form closer to human cognition.
To this day, KGs have facilitated a mount of downstream internet applications (e.g., search engines \cite{DBLP:conf/icde/YangAJTW19} and dialogue systems \cite{DBLP:conf/emnlp/YangZE20}) and become one of the core driving forces in the development of artificial intelligence.
In practice, KGs are usually constructed by various departments with multi-source data.
Therefore, they typically contain complementary knowledge while having overlapping parts.
Integrating these independent KGs could significantly improve the coverage rate, which is especially beneficial to low-resource language users.
\begin{figure}
\centering
\includegraphics[width = 0.95\linewidth]{intro.pdf}
\caption{A toy example of entity alignment.}
\label{fig:intro}
\end{figure}
Entity Alignment (EA) aims to find equivalent entity pairs between KGs (as shown in Figure \ref{fig:intro}), which is the core step of bridging and integrating multi-source KGs.
Therefore, EA attracts enormous attention and progresses rapidly.
Most existing methods regard EA as a graph representation learning task and share the same two-stage architecture: (i) encoding the KGs into low-dimensional spaces via graph encoders (e.g., TransE \cite{DBLP:conf/nips/BordesUGWY13} and GCN \cite{DBLP:journals/corr/KipfW16}) and (ii) mapping the embeddings of equivalent entity pairs into a unified vector space through contrastive losses \cite{DBLP:conf/cvpr/HadsellCL06}.
Recently, \emph{Graph Neural Network} (GNN) has achieved impressive success in many sorts of graph applications.
Following \citet{DBLP:conf/emnlp/WangLLZ18}, who first introduced \emph{Graph Convolutional Network} (GCN) into EA, numerous new fancy mechanisms are proposed and stacked over vanilla GCN for better performance, such as \emph{Graph Matching} \cite{DBLP:conf/iclr/FeyL0MK20}, \emph{Relational Attention} \cite{DBLP:conf/wsdm/MaoWXLW20}, and \emph{Hyperbolic embedding} \cite{DBLP:conf/emnlp/SunCHWDZ20}.
According to an EA paper list \footnote{\url{github.com/THU-KEG/Entity_Alignment_Papers}} on Github, over $90\%$ of EA methods adopted GNNs as their graph encoders in recent three years.
However, there is no such thing as a free lunch.
These increasingly complex GNN-based methods inherit the following inborn defects from their GNN lineage:
(i) \textbf{Weak scalability}.
Since the scales of real-world graphs are usually massive (e.g., YAGO$3$ \cite{DBLP:conf/www/SuchanekKW07} contains $17$ million entities), the scalability of graph algorithms is crucial.
However, as summarized by \citet{9174835}, most advanced EA methods require several hours \cite{DBLP:conf/ijcai/SunHZQ18, DBLP:conf/acl/CaoLLLLC19} or even days \cite{DBLP:conf/acl/XuWYFSWY19} on the DWY$100$K dataset, which only contains $200,000$ nodes.
Although an efficient loss function \cite{DBLP:conf/www/MaoWWL21} or a graph sampler \cite{DBLP:journals/corr/abs-2205-10312} could effectively alleviate this problem, all existing EA methods are still overstretched when facing the real-world KGs.
(ii) \textbf{Poor interpretability}.
Interpreting neural networks is a recognized challenge, and the complex graph structure makes it more difficult.
A few studies try to explain the behaviors of EA methods by showing wrong cases \cite{DBLP:conf/emnlp/YangZSLLS19} or visualizing attention weights \cite{DBLP:conf/acl/WuLFWZ20}.
And most EA studies \cite{DBLP:conf/ijcai/SunHZQ18, DBLP:conf/acl/XuWYFSWY19, DBLP:conf/cikm/MaoWXWL20} do not attempt to give any interpretation, only focusing on improving the performances on evaluation metrics.
An ancient Chinese saying goes, \emph{"drawing new inspiration while reviewing the old."}
A recent study \cite{DBLP:conf/iclr/HuangHSLB21} reinvents the classical graph algorithm --- \emph{Label Propagation} (LP) \cite{Zhu2002LearningFL}, combining it with shallow neural networks.
Surprisingly, this simple method out-performs the current best-known GNNs with more than two orders of magnitude fewer parameters and more than two orders of magnitude less training time.
Inspired by their excellent work, this paper proposes the \emph{Three-view Label Propagation} mechanism that enables the LP algorithm, designed for homogeneous graphs, to effectively run on KGs (a kind of typical heterogeneous graph).
Besides, we further propose two approximation strategies to reduce the computational complexity and enhance the scalability:
\emph{Random Orthogonal Label Generation} and \emph{Sparse Sinkhorn Iteration}.
The above three components constitute the proposed non-neural EA framework --- LightEA.
According to the extensive experiments on four groups of public datasets, LightEA has impressive scalability, robustness, and interpretability:
(1) \textbf{Scalability}:
Unlike GNN-based EA methods that require multiple rounds of forward and backward propagation, LightEA only requires one round of label propagation without any trainable parameters.
After abandoning neural networks, LightEA achieves extremely high parallel computing efficiency.
With a PC that has one RTX$3090$ GPU, LightEA only takes $7$ seconds to obtain the alignment results on DBP$15$K and less than $35$ seconds on DWY$100$K, which is only one-tenth of the state-of-the-art EA method.
LightEA could also easily handle DBP$1$M which contains more than one million entities and nearly ten million triples, while most EA methods even cannot run on it.
Besides running speed, the flexible framework enables LightEA could easily incorporate iterative strategies and literal features (e.g., entity names) to improve performance.
(2) \textbf{Robustness}:
In this paper, we design a thorough robustness examination that evaluates LightEA on four groups of public datasets containing cross-lingual, mono-lingual, sparse, dense, and large-scale subsets.
With a mere tenth of time consumption, LightEA achieves comparable results to state-of-the-art methods across all datasets and even surpasses them on many.
Besides, since LightEA does not have trainable parameters, the performance fluctuation of multiple runs is limited.
(3) \textbf{Interpretability}:
Researchers generally consider linear models (e.g., Linear Regression) have decent interpretability because their outputs are the linear summation of the input features.
Consistent with the LP algorithm, the computational process of LightEA is also entirely linear.
After removing \emph{Random Orthogonal Label}, each dimension of the label vectors will have a clear and realistic meaning.
We could trace the propagation process at each step to clearly explain how the entities are aligned.
In addition to the above contributions, we further design extensive auxiliary experiments to investigate the behaviors of LightEA in various situations.
The source code and datasets are now available in Github (\url{github.com/MaoXinn/LightEA}).
\section{Task Definition}
A KG could be defined as $\mathcal{G} = (\mathcal{E},\mathcal{R},\mathcal{T})$, where $\mathcal{E}$ is the entity set, $\mathcal{R}$ is the relation set, and $\mathcal{T}\subset \mathcal{E}\times \mathcal{R}\times \mathcal{E}$ represents the set of triples.
Given the source graph $\mathcal{G}_s$, the target graph $\mathcal{G}_t$, and the set of pre-aligned entity pairs $\mathcal{P}$, EA aims to find new equivalent entity pairs based on $\mathcal{G}_s$, $\mathcal{G}_t$, and $\mathcal{P}$.
\section{Related Work}
\subsection{Entity Alignment}
Most existing methods regard EA as a graph representation learning task and share the same two-stage architecture: (i) encoding the KGs into low-dimensional spaces via graph encoders and then (ii) mapping the embeddings of equivalent entity pairs into a unified vector space by contrastive losses.
Graph encoder is the most prominent and important part of existing EA methods.
Early methods usually used TransE \cite{DBLP:conf/nips/BordesUGWY13} and its variants as the graph encoder.
However, due to TransE only focusing on optimizing independent triples $\bm h + \bm r \approx \bm t$, it lacks the ability to model the global structure of KGs.
With impressive capability in modeling graph data, GNNs quickly become the mainstream algorithm for almost all graph applications, including entity alignment.
Since \citet{DBLP:conf/emnlp/WangLLZ18} first introduced GCN into EA, numerous GNN-based EA methods have been springing up.
For example, GM-Align \cite{DBLP:conf/acl/XuWYFSWY19} introduces \emph{Graph Matching Networks} to capture the entity interactions across KGs.
RREA \cite{DBLP:conf/cikm/MaoWXWL20} proposes the \emph{Relational Reflection} operation to generate relation-specific entity embeddings.
HyperEA \cite{DBLP:conf/emnlp/SunCHWDZ20} adopts hyperbolic embeddings to reduce the dimension of entities.
Besides the modifications on encoders, some EA methods adopt iterative strategies to generate semi-supervised data due to the lack of labeled entities.
Some EA methods propose that introducing literal information (e.g., entity names) could provide a multi-aspect view for alignment models.
However, it should be noted that not all KGs contain literal information, especially in practical applications.
Table \ref{tabel:rw} categorizes some popular EA methods based on their encoders and whether using iterative strategies or literal information.
\begin{table}
\resizebox{1\linewidth}{!}{
\renewcommand\arraystretch{0.9}
\begin{tabular}{cccc}
\toprule
\textbf{Method}&\textbf{Encoder}&\textbf{Literal}&\textbf{Iterative}\\
\midrule
MtransE\cite{DBLP:conf/ijcai/ChenTYZ17} &Trans&&\\
JAPE \cite{DBLP:conf/semweb/SunHL17}&Trans&&\\
BootEA \cite{DBLP:conf/ijcai/SunHZQ18}&Trans&&\CheckmarkBold\\
KDCoE \cite{DBLP:conf/ijcai/ChenTCSZ18}&Trans&\CheckmarkBold&\CheckmarkBold\\
RSN \cite{DBLP:conf/icml/GuoSH19} &RNN&&\\
TransEdge\cite{DBLP:journals/corr/abs-2004-13579}&Trans&&\CheckmarkBold\\
\midrule
GCN-Align \cite{DBLP:conf/emnlp/WangLLZ18}&GNN&&\\
MuGNN \cite{DBLP:conf/acl/CaoLLLLC19}&GNN&&\\
RDGCN \cite{DBLP:conf/ijcai/WuLF0Y019}&GNN&\CheckmarkBold&\\
GM-Align \cite{DBLP:conf/acl/XuWYFSWY19}&GNN&\CheckmarkBold&\\
HyperKA \cite{DBLP:conf/emnlp/SunCHWDZ20}&GNN&&\\
MRAEA \cite{DBLP:conf/wsdm/MaoWXLW20}&GNN&&\CheckmarkBold\\
RREA \cite{DBLP:conf/cikm/MaoWXWL20}&GNN&&\CheckmarkBold\\
Dual-AMN \cite{DBLP:conf/www/MaoWWL21}&GNN&&\CheckmarkBold\\
EASY \cite{DBLP:conf/sigir/GeLCZG21}&GNN&\CheckmarkBold&\CheckmarkBold\\
ClusterEA \cite{DBLP:journals/corr/abs-2205-10312}&GNN&&\CheckmarkBold\\
\bottomrule
\end{tabular}
}
\caption{Categorization of some popular EA methods.}\label{tabel:rw}
\end{table}
\subsection{Label Propagation and GCN}
\emph{Label Propagation} (LP) \cite{Zhu2002LearningFL} is a classical graph algorithm for node classification and community detection.
It assumes that two connected nodes are likely to have the same label, and thus it propagates labels along the edges.
Let $\bm A \in \mathbb{R}^{|\mathcal{E}|\times |\mathcal{E}|}$ be the graph adjacency matrix, $\bm D \in \mathbb{R}^{|\mathcal{E}|\times |\mathcal{E}|}$ be the diagonal degree matrix of $\bm A$, $\bm L^{(k)} \in \mathbb{R}^{|\mathcal{E}|\times c}$ be the label matrix after $k$ rounds of label propagation, where $c$ is the number of classes.
Each column of $\bm L^{(0)}$ is a one-hot vector, initialized by the input labels of the known nodes, while the label vectors of unknown nodes remain zeros.
The propagation process of the random LP algorithm could be formulated as follow:
\begin{equation}
\bm L^{(k+1)}=\bm D^{-1}\bm A\bm L^{(k)}\\
\end{equation}
\emph{Graph Convolutional Network} (GCN) \cite{DBLP:journals/corr/KipfW16} is a multi-layer neural network that propagates and transforms node features across the graph.
Let $\bm H^{(k)} \in \mathbb{R}^{|\mathcal{E}|\times d_{in}}$ be the input features of layer $k$, and $\bm W^{(k)} \in\mathbb{R}^{d_{in}\times d_{out}}$ be the transformation matrix.
The layer-wise propagation process of GCN could be summarized as follow:
\begin{equation}
\bm H^{(k+1)}=\sigma(\bm D^{-1/2}\bm A\bm D^{-1/2}\bm H^{(k)}\bm W^{(k)})\\
\end{equation}
Equations (1) and (2) indicate that the common intuition behind both LP and GCN is smoothing the labels or features.
\citet{DBLP:journals/corr/abs-2002-06755} notice this kind of inner correlation and unify them into one framework.
\citet{DBLP:conf/iclr/HuangHSLB21} combine shallow neural networks with the LP algorithm, achieving comparable performances to state-of-the-art GNNs, but with a small fraction of the parameters and time consumption.
These excellent works inspire us that the LP algorithm, neglected by the EA community, deserves further investigation.
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{MRW.pdf}
\caption{Illustrations of \emph{Three-view Label Propagation}.}
\label{fig:MRW}
\end{figure*}
\section{The Proposed Method}
LightEA is a non-neural EA framework consisting of three components: (i) \emph{Random Orthogonal Label Generation}, (ii) \emph{Three-view Label Propagation}, and (iii) \emph{Sparse Sinkhorn Iteration}.
We will describe each component of LightEA in this section.
\subsection{Random Orthogonal Label Generation}
Different from the node classification and community detection tasks, the entities in EA do not have explicit class labels.
LightEA borrows a common idea from face recognition \cite{DBLP:journals/spl/WangCLL18,DBLP:conf/cvpr/DengGXZ19} that regards each pair of pre-aligned entities as a independent class.
Assume that $(e_i,e_j)\in \mathcal{P}$ is the $x$-$th$ pre-aligned entity pair, the input label matrix of entities $\bm L^{(0)}_e = \left[\bm l^{(0)}_{e_1},\bm l^{(0)}_{e_2},...,,\bm l^{(0)}_{e_{|\mathcal{E}|}}\right]$ is initialized as follows:
\begin{equation}
\bm l^{(0)}_{e_i}=\bm l^{(0)}_{e_j}=onehot(x)\;\;\;\forall(e_i,e_j)\in \mathcal{P}
\end{equation}
where $onehot(x) \in \mathbb{R}^{|\mathcal{P}|} $ represents the one-hot vector that only the $x$-$th$ element equals one.
The input label vectors of remaining unaligned entities are initialized to all-zero.
Besides, since existing EA datasets do not provide pre-aligned relation pairs, the input label matrix of relations $\bm L^{(0)}_r \in \mathbb{R}^{|\mathcal{R}|\times|\mathcal{P}|}$ is also initialized to all-zero.
However, this initialization strategy will cause the input label matrices of entities and relations overly large and extremely sparse.
To ensure that LightEA runs well on large-scale datasets, we have to seek a solution that could reduce the dimension of input label matrices while the loss of orthogonality is slight.
Fortunately, independent random vectors on the high-dimensional hyper-sphere could satisfy our requirement.
\begin{lemma}
If $\bm x$ and $\bm y$ are independent random unit vectors on the $d$-dimensional hyper-sphere, $\left\langle\cdot\right\rangle$ represents the inner-product operation, then we have:
\begin{equation}
P\left(\langle\bm x,\bm y\rangle > \epsilon\right) \leq (1-\epsilon^2)^{(d+1)/2}
\end{equation}
\label{lemma:1}
\end{lemma}
Lemma \ref{lemma:1} \cite{Ball1997AnEI} states that any two independent random vectors on the high-dimensional hyper-sphere are approximately orthogonal.
For example, when $d>2048$, the probability upper bound of $\left\langle\bm x,\bm y\right\rangle > 0.1$ is less than $3.37\times 10^{-5}$.
Therefore, LightEA independently samples random vectors on the $d$-dimensional hyper-sphere to approximate the one-hot label vectors for better space-time complexity:
\begin{equation}
\bm l^{(0)}_{e_i}=\bm l^{(0)}_{e_j}=random(d)\;\;\;\forall(e_i,e_j)\in \mathcal{P}
\end{equation}
With this approximation strategy, the dimensions of $\bm L^{(0)}_e $ and $\bm L^{(0)}_r$ are reduced to $\mathbb{R}^{|\mathcal{E}|\times d}$ and $\mathbb{R}^{|\mathcal{R}|\times d}$.
One of the significant differences between LP and GCN is that one propagates labels, and the other propagates features.
However, the above discussion indicates that randomly initialized features could be regarded as an approximation to one-hot labels.
From this perspective, the propagation processes of GCN and LP are equivalent.
\subsection{Three-view Label Propagation}
Both LP algorithm and vanilla GCN were originally designed for homogeneous graphs.
However, KG is a kind of typical heterogeneous graph that requires a third-order tensor $\boldsymbol{\mathcal{A}}\in \mathbb{R}^{|\mathcal{E}|\times|\mathcal{E}|\times|\mathcal{R}|}$ to fully describe its adjacency relations.
Some early EA methods \cite{DBLP:conf/emnlp/WangLLZ18,DBLP:conf/acl/XuWYFSWY19} crudely treat all relations as equivalent, resulting in information losses.
Follow-up studies usually address this problem by adopting the relational attention mechanism \cite{DBLP:conf/ijcai/WuLF0Y019,DBLP:conf/wsdm/MaoWXLW20} to learn attention parameters and assign different weights for different relations and triples.
Besides the above methods, an intuitive solution for generalizing LP on KGs is to use the tensor-matrix product to replace the matrix product:
\begin{align}
\bm L^{(k+1)}_e &= \boldsymbol{\mathcal{A}} \times_2 \bm L^{(k)}_e \times_3 \bm L^{(k)}_r\\
\bm L^{(k+1)}_r &= \boldsymbol{\mathcal{A}} \times_1 \bm L^{(k)}_e \times_2 \bm L^{(k)}_e
\end{align}
where $\times_i$ represents the $i$-mode tensor-matrix product (i.e., along the $i$-$th$ axis).
Unfortunately, this solution has two fatal defects:
(i) The tensor-matrix product leads to a squared increase in the dimension after each round of propagation.
(ii) Existing tensor computing frameworks (e.g., Tensorflow) do not provide the tensor-matrix product operator for sparse tensors.
Inspired by the three-view drawing of engineering fields, we propose a \emph{Three-view Label Propagation} mechanism that compresses the adjacency tensor $\boldsymbol{\mathcal{A}}$ along three axes to retain maximum information from the original tensor while reducing computational complexity.
As shown in Figure \ref{fig:MRW}(a), we first separately sum the original tensor $\boldsymbol{\mathcal{A}}$ along three axes to obtain the top view $\bm A^{top}\in\mathbb{R}^{|\mathcal{R}|\times|\mathcal{E}|}$, the side view $\bm A^{side}\in\mathbb{R}^{|\mathcal{E}|\times|\mathcal{E}|}$, and the front view $\bm A^{front}\in\mathbb{R}^{|\mathcal{E}|\times|\mathcal{R}|}$.
From the perspective of inside meaning, $\bm A^{side}$, $\bm A^{front}$, and $\bm A^{top}$ represent the adjacency relations from head entity to tail entity, head entity to relation, and relation to tail entity, respectively.
Then, the labels of entities and relations are propagated according to the three views:
\begin{align}
\bm L^{(k+1)}_e &= \bm A^{side} \bm L^{(k)}_e + \bm A^{front} \bm L^{(k)}_r\\
\bm L^{(k+1)}_r &= \bm A^{top} \bm L^{(k)}_e
\end{align}
Intuitively, LightEA transforms the propagation process on triples into a triangular process, where each side of the triangle represents a different view (as shown in Figure \ref{fig:MRW}(b)).
In this way, labels could be effectively propagated on KGs without any trainable parameters while keeping the complexity consistent with the classical LP algorithm $O(|\mathcal{T}|d)$.
Finally, for each entity $e_i$, we concatenate the label vectors of all time-steps as the outputs:
\begin{equation}
\bm l^{out}_{e_i} = \left[\bm l^{(0)}_{e_i}||\bm l^{(1)}_{e_i}||...||\bm l^{(k-1)}_{e_i}||\bm l^{(k)}_{e_i}\right]
\end{equation}
\subsection{Sparse Sinkhorn Iteration}
Early EA studies \cite{DBLP:conf/emnlp/WangLLZ18,DBLP:conf/semweb/SunHL17} simply calculate the Euclidean distances or cosine similarities of all entity pairs and select the closest one as the alignment result.
In this way, one entity could be aligned to multiple entities simultaneously, which violates the one-to-one constraint of EA.
To address this problem, some studies \cite{DBLP:conf/aaai/XuSFSY20, DBLP:conf/emnlp/MaoWWL21} transform the decoding process of EA into an assignment problem and achieve significant performance improvement:
\begin{equation}
\underset{\bm P\in\mathbb{P}_{|\mathcal{E}|}}{arg\;max}{\;\left\langle \bm P, \bm S\right\rangle}_F
\end{equation}
$\bm S \in \mathbb{R}^{|\mathcal{E}|\times|\mathcal{E}|}$ is the similarity matrix of entities, and $s_{i,j} = cosine(\bm l^{out}_{e_i},\bm l^{out}_{e_j})$ in LightEA.
$\bm P$ is a permutation matrix denoting the alignment plan, where exactly one entry of $1$ in each row and column and $0$s elsewhere.
$\mathbb{P}_{|\mathcal{E}|}$ represents the set of all $|\mathcal{E}|$-dimensional permutation matrices.
$\langle\cdot\rangle_F$ represents the Frobenius inner product.
\begin{figure}
\centering
\includegraphics[width=0.95\linewidth]{Sinkhorn.pdf}
\caption{\emph{Sinkhorn} and \emph{Sparse Sinkhorn Iteration}.}
\label{fig:sink}
\end{figure}
Although the \emph{Hungarian} algorithm \cite{lawler1963quadratic} could solve assignment problems accurately, its high complexity $O(|\mathcal{E}|^3)$ makes it impossible to apply in large-scale datasets.
Therefore, recent studies \cite{DBLP:conf/sigir/GeLCZG21, DBLP:conf/emnlp/MaoWWL21} propose to use the \emph{Sinkhorn iteration} \footnote{The implementation details of the \emph{Sinkhorn iteration} are listed in Appendix \ref{apd:sinkhorn}.} \cite{DBLP:conf/nips/Cuturi13} to obtain an approximate solution:
\begin{align}
\begin{split}
&\underset{\bm P\in\mathbb{P}_{|\mathcal{E}|}}{arg\;max}{\;\left\langle \bm P,\bm S\right\rangle}_F\\
=& \lim_{\tau\rightarrow 0^+}{\rm Sinkhorn}(\bm S/\tau)
\end{split}
\end{align}
The space-time complexity of the \emph{Sinkhorn iteration} is $O(q|\mathcal{E}|^2)$, where $q$ is the number of iteration rounds.
Even though the \emph{Sinkhorn iteration} is significantly faster than the \emph{Hungarian} algorithm, it still becomes the main bottleneck of LightEA.
In LightEA, we adopt the decoding algorithm proposed by \citet{Mao2022AnEA} and utilize \emph{Sparse Sinkhorn Iteration} to reduce the computational complexity.
Specifically, we notice that the exponential normalization of the \emph{Sinkhorn iteration} causes most smaller values in the similarity matrix $\bm S$ to be infinitely close to zero.
Even if these smaller values are removed initially, it does not significantly affect the alignment results.
Therefore, instead of calculating the similarities between all entities, LightEA only retrieves the top-$k$ nearest neighbors for each entity by \emph{Approximate Nearest Neighbor} algorithms \footnote{In LighEA, we use the FAISS framework \cite{johnson2019billion} for approximate vector retrieval.}, such as \emph{Inverted Index System} and \emph{Product Quantizer} \cite{DBLP:journals/pami/JegouDS11}.
As shown in Figure \ref{fig:sink}, the similarity matrix $\bm S$ will become sparse.
There are only $k$ non-zero elements in each row, while the others are set to zeros.
In this way, the complexity of the \emph{Sinkhorn iteration} could be reduced to $O(qk|\mathcal{E}|)$.
\begin{table*}[t]
\begin{center}
\resizebox{1\textwidth}{!}{
\renewcommand\arraystretch{0.95}
\begin{tabular}{c|ccc|ccc|ccc|ccc|ccc}
\toprule
\multicolumn{1}{c}{\multirow{2}{*}{Method}} & \multicolumn{3}{c}{$\rm{DBP_{ZH-EN}}$} & \multicolumn{3}{c}{$\rm{DBP_{JA-EN}}$} & \multicolumn{3}{c}{$\rm{DBP_{FR-EN}}$}& \multicolumn{3}{c}{$\rm{SRPRS_{FR-EN}}$}& \multicolumn{3}{c}{$\rm{SRPRS_{DE-EN}}$} \\
& H@1 & H@10 & MRR & H@1 & H@10 & MRR & H@1 & H@10 & MRR & H@1 & H@10 & MRR & H@1 & H@10 & MRR\\
\hline
MTransE & 0.209 & 0.512 & 0.310 & 0.250 & 0.572 & 0.360 & 0.247 & 0.577 & 0.360 &0.213& 0.447&0.290&0.107&0.248&0.160\\
GCN-Align & 0.434 & 0.762 & 0.550 & 0.427 & 0.762 & 0.540 & 0.411 & 0.772 & 0.530 & 0.243& 0.522&0.340&0.385&0.600& 0.460\\
RSNs&0.508&0.745&0.591&0.507&0.737&0.590&0.516&0.768&0.605&0.350&0.636& 0.440& 0.484& 0.729&0.570\\
HyperKA&0.572&0.865&0.678& 0.564&0.865& 0.673&0.597&0.891& 0.704& -& -& -&- &-& -\\
\textbf{LightEA-B} &\textbf{0.756}&\textbf{0.905}&\textbf{0.811}&\textbf{0.762}&\textbf{0.919}&\textbf{0.819}&\textbf{0.807}&\textbf{0.943}&\textbf{0.857}&\textbf{0.466 }&\textbf{0.746}&\textbf{0.560}&\textbf{0.594}&\textbf{0.814}&\textbf{0.670}\\
\hline
BootEA & 0.629 & 0.847 & 0.703 & 0.622 & 0.853 & 0.701 & 0.653 & 0.874 & 0.731 & 0.365&0.649&0.460&0.503&0.732&0.580\\
TransEdge&0.735&0.919&0.801&0.719&0.932&0.795&0.710&0.941&0.796&0.400&0.675&0.490&0.556&0.753&0.630\\
MRAEA &0.757&0.930&0.827&0.758&0.934&0.826&0.781&0.948&0.849&0.460&0.768&0.559&0.594&0.818&0.666\\
Dual-AMN &0.808&\textbf{0.940}&\textbf{0.857}&0.801&\textbf{0.949}&0.855&0.840&\textbf{0.965}&0.888&0.481&\textbf{0.778}&0.568&0.614&\textbf{0.823}&\textbf{0.687}\\
\textbf{LightEA-I} &\textbf{0.812}&0.915&0.849&\textbf{0.821}&0.933&\textbf{0.864}&\textbf{0.863}&0.959&\textbf{0.900}&\textbf{0.484}&0.769&\textbf{0.570}&\textbf{0.615}&0.817&0.685\\
\hline
GM-Align & 0.679 & 0.785 & - & 0.739 & 0.872 & - & 0.894 & 0.952 & - & 0.574&0.646&0.602&0.681&0.748&0.710\\
RDGCN & 0.697 & 0.842 & 0.750 & 0.763 & 0.897 & 0.810 & 0.873 & 0.950 & 0.901 &0.672&0.767& 0.710&0.779&0.886&0.820 \\
EASY &0.898& 0.979& 0.930 &0.943 &0.990 &0.960 &0.980 &0.998 &0.990 &0.965 &0.989 &0.970 &0.974 &0.992 &0.980\\
SEU &0.900 &0.965 &0.924 &0.956 &0.991 &0.969 &0.988 &\textbf{0.999} &0.992 &0.982 &\textbf{0.995} &0.986 &0.983 &0.996 &0.987\\
\textbf{LightEA-L} &\textbf{0.952}&\textbf{0.984}&\textbf{0.964}&\textbf{0.981}&\textbf{0.997}&\textbf{0.987}&\textbf{0.995}&0.998&\textbf{0.996}&\textbf{0.986}&0.994&\textbf{0.989}&\textbf{0.988 }&\textbf{0.995}&\textbf{0.991}\\
\bottomrule
\end{tabular}
}
\caption{Performances on DBP$15$K and SRPRS. Baselines' results are from original papers or \citet{9174835}.}
\label{table:res1}
\end{center}
\end{table*}
\section{Experiments}
All experiments are conducted on a PC with an Nvidia RTX$3090$ GPU and an EPYC 7452 CPU.
\subsection{Datesets and Metrics}
To comprehensively verify the scalability, robustness, and interpretability of our proposed methods, we conduct experiments on the following four groups of datasets:
(1) \textbf{DBP15K} \cite{DBLP:conf/semweb/SunHL17} is the most commonly used EA dataset, consisting of three small-sized cross-lingual subsets.
Each subset contains $15,000$ pre-aligned entity pairs.
(2) \textbf{SRPRS} \cite{DBLP:conf/icml/GuoSH19} is a sparse dataset that includes two small-sized cross-lingual subsets.
Each subset of SRPRS also contains $15,000$ pre-aligned entity pairs but with much fewer triples.
(3) \textbf{DWY100K} \cite{DBLP:conf/ijcai/SunHZQ18} comprises two medium-sized mono-lingual subsets, each containing $100,000$ pre-aligned entity pairs and nearly one million triples.
(4) \textbf{DBP1M} \cite{DBLP:journals/pvldb/GeLCZG21} is one of the largest EA datasets so far, consisting of two cross-lingual subsets with more than one million entities and nearly ten million triples.
The detailed statistics are listed in Table \ref{table:dataset1}.
Consistent with the previous studies \cite{DBLP:conf/semweb/SunHL17,DBLP:conf/ijcai/WuLF0Y019,DBLP:conf/wsdm/MaoWXLW20}, we randomly split $30\%$ of the pre-aligned entity pairs for training and the remaining $70\%$ for testing.
Following convention \cite{DBLP:conf/ijcai/ChenTYZ17,DBLP:conf/emnlp/WangLLZ18}, we use $Hits@k$ and \emph{Mean Reciprocal Rank} (MRR) as our evaluation metrics.
The reported performances are the average of five independent runs.
\subsection{Baselines}
According to the categorization in Table \ref{tabel:rw}, we compare LightEA against the following three groups of advanced EA methods:
(1) \textbf{Basic}:
MtransE \cite{DBLP:conf/ijcai/ChenTYZ17}, GCN-Align \cite{DBLP:conf/emnlp/WangLLZ18}, RSNs \cite{DBLP:conf/icml/GuoSH19}, HyperKA \cite{DBLP:conf/emnlp/SunCHWDZ20}.
(2) \textbf{Iterative}:
BootEA \cite{DBLP:conf/ijcai/SunHZQ18}, TransEdge \cite{DBLP:journals/corr/abs-2004-13579}, MRAEA \cite{DBLP:conf/wsdm/MaoWXLW20}, Dual-AMN \cite{DBLP:conf/www/MaoWWL21}, LargeEA \cite{DBLP:journals/pvldb/GeLCZG21}, ClusterEA \cite{DBLP:journals/corr/abs-2205-10312}.
(3) \textbf{Literal}:
GM-Align \cite{DBLP:conf/acl/XuWYFSWY19}, RDGCN \cite{DBLP:conf/ijcai/WuLF0Y019}, SEU \cite{DBLP:conf/emnlp/MaoWWL21}, EASY \cite{DBLP:conf/sigir/GeLCZG21}.
To make a fair comparison against the above methods, LightEA also has three corresponding versions:
(1) LightEA-B is the basic version.
(2) LightEA-I adopts the bi-directional iterative strategy proposed by \citet{DBLP:conf/wsdm/MaoWXLW20}.
(3) LightEA-L uses the pre-trained word embeddings of translated entity names \footnote{The name translations and word embeddings are provided by \citet{DBLP:conf/acl/XuWYFSWY19}, which is consistent with follow-up studies.} as the inputs matrix and also adopts the bi-directional iterative strategy.
Same with SEU and EASY, LightEA-L is an unsupervised method that does not require any pre-aligned entity pairs.
\subsection{Hyper-parameters}
\label{sec:hyper}
Except for DBP$1$M, we use the same setting:
the dimension of hyper-sphere $d = 1,024$;
the number of \emph{Three-view Label Propagation} rounds $k = 2$.
We reserve the top-$500$ nearest neighbors for each entity in \emph{Sparse Sinkhorn Iteration}.
Following \citet{DBLP:conf/emnlp/MaoWWL21}, the number of Sinkhorn iteration rounds $q = 10$ and the temperature $\tau = 0.05$.
Due to the limitation of GPU memory, the dimension of hyper-sphere $d$ is reduced to $256$ for DBP$1$M.
\begin{table}[t]
\resizebox{\linewidth}{!}{
\renewcommand\arraystretch{0.9}
\begin{tabular}{ccccccc}
\toprule
\multicolumn{1}{c}{\multirow{2}{*}{Method}} & \multicolumn{3}{c}{$\rm{DWY_{DBP-WD}}$}& \multicolumn{3}{c}{$\rm{DWY_{DBP-YG}}$} \\
\multicolumn{1}{c}{} & H@1 & H@10 & MRR & H@1 & H@10 & MRR\\
\hline
MTransE &0.238&0.507&0.330&0.227&0.414&0.290\\
GCN-Align&0.494&0.756&0.590&0.598&0.829&0.680\\
RSNs&0.607&0.793&0.673&0.689&0.878&0.756\\
MuGNN &0.604&0.894&0.701&0.739&0.937&0.810\\
\textbf{LightEA-B}&\textbf{0.861}&\textbf{0.962}&\textbf{0.898}&\textbf{0.884}&\textbf{0.977}&\textbf{0.918}\\
\hline
BootEA &0.748&0.898&0.801&0.761&0.894&0.808\\
TransEdge&0.788&0.938&0.824&0.792&0.936&0.832\\
MRAEA&0.794&0.930&0.856&0.819&0.951&0.875\\
Dual-AMN&0.869&0.969&0.908&\textbf{0.907}&\textbf{0.981}&\textbf{0.935}\\
\textbf{LightEA-I}&\textbf{0.907}&\textbf{0.978}&\textbf{0.934}&0.902&0.980&0.929\\
\bottomrule
\end{tabular}
}
\caption{Experimental results on DWY$100$K.}
\label{table:res2}
\end{table}
\begin{table}[t]
\resizebox{1\linewidth}{!}{
\renewcommand\arraystretch{0.9}
\begin{tabular}{ccccccc}
\toprule
\multicolumn{1}{c}{\multirow{2}{*}{Method}} & \multicolumn{3}{c}{$\rm{DBP1M_{FR-EN}}$}& \multicolumn{3}{c}{$\rm{DBP1M_{DE-EN}}$} \\
\multicolumn{1}{c}{} & H@1 & H@10 & MRR & H@1 & H@10 & MRR\\
\hline
LargeEA-G &0.051 &0.134& 0.080 & 0.034& 0.095& 0.050 \\
LargeEA-R &0.094& 0.215& 0.130& 0.064 &0.150 &0.090 \\
LargeEA-D &0.105 &0.219 &0.150& 0.066&0.147& 0.090 \\
ClusterEA-G &0.100 &0.245 &0.150 &0.069 &0.177 &0.110 \\
ClusterEA-R &0.260& 0.456& 0.320 & 0.250 &0.450& 0.320 \\
ClusterEA-D &0.281& \textbf{0.474}& \textbf{0.350}& 0.288& \textbf{0.488} &\textbf{0.350} \\
\hline
\textbf{LightEA-B}&0.262&0.450& 0.318&0.258&0.457&0.316\\
\textbf{LightEA-I}&\textbf{0.285}&0.468&0.345&\textbf{0.289}&0.479&0.347\\
\bottomrule
\end{tabular}
}
\caption{Experimental results on DBP$1$M\protect\footnotemark.}
\label{table:res3}
\end{table}
\footnotetext{The results of baselines are from ClusterEA\cite{DBLP:journals/corr/abs-2205-10312}. To solve the name bias issue, ClusterEA removes parts of entities and all literal information while retaining all the triples. Therefore, LightEA-L cannot run on this dataset.}
\subsection{Main Experiments}
Table \ref{table:res1} lists the experimental results of LightEA on DBP$15$K and SRPRS.
Table \ref{table:res2} and Table \ref{table:res3} list the results on DWY$100$K and DBP$1$M, respectively.
\noindent
\textbf{DBP15K}.
Compared to the basic EA baselines, LightEA-B has significant improvements on all metrics.
The main reason is that these basic EA methods were proposed earlier, while most advanced methods adopts iterative strategies for better performance.
For LightEA-I, the bi-directional iterative strategy improves the performance by more than $5\%$ on $Hits@1$ and $4\%$ on MRR.
Compared to Dual-AMN, the state-of-the-art structure-based EA method, LightEA-I achieves comparable results that are slightly better on $Hits@1$ and weaker on $Hits@10$.
Among literal-based EA methods, LightEA-L consistently achieves the best performances.
Especially for $\rm DBP_{ZH-EN}$, LightEA-L beats SEU by more than $5\%$ on $Hits@1$.
\noindent
\textbf{SRPRS}.
The performance rankings on SRPRS are pretty similar to those on DBP$15$K.
LightEA-B and LightEA-L defeat all the competitors, while LightEA-I achieves similar performances to Dual-AMN.
The main difference is that the impact of iterative strategies is significantly weakened on SPRPS, in which the performance gain is less than $2\%$ on $Hits@1$ and $1\%$ on MRR.
That is mainly because the structural information of SRPRS is particularly sparse, causing iterative strategies to fail to generate high-quality semi-supervised data.
\noindent
\textbf{DWY100K}.
For DWY$100$K, LightEA maintains competitive performance.
On $\rm DWY_{DBP-WD}$, LightEA outperforms Dual-AMN by $4\%$ on $Hits@1$ and $3\%$ on MRR while having a comparable result on $\rm DWY_{DBP-YG}$.
According to \citet{9174835}, the names of equivalent entities in DWY$100$K are almost identical, and using the edit distance could easily achieve the ground-truth performance.
Therefore, Table \ref{table:res2} does not list the results of literal methods.
\noindent
\textbf{DBP1M}.
As one of the largest EA datasets so far, DBP1M poses a severe challenge to scalability, and most EA methods cannot directly run on this dataset.
As shown in Table \ref{table:res3}, the experimental results show that LightEA still achieves similar performances to the state-of-the-art method on this challenging dataset.
LargeEA and ClusterEA are two acceleration frameworks for GNN-based EA methods, consisting of mini-batch graph samplers, efficient losses, etc.
"-G," "-R," and "-D" represent using GCN-Align, RREA, and Dual-AMN as the backbone networks, respectively.
\begin{table}
\begin{center}
\resizebox{1\linewidth}{!}{
\renewcommand\arraystretch{0.9}
\begin{tabular}{ccccc}
\toprule
\textbf{Method}&\textbf{DBP15K}&\textbf{SRPRS}&\textbf{DWY100K}&\textbf{DBP1M}\\
\hline
Dual-AMN&69&57&2,237&-\\
LargeEA-D&26&23&227&2,119\\
ClusterEA-D&43&36&389&1,503\\
\hline
LightEA-B&2.8&2.2&15.4&97\\
LightEA-I&7.1&6.5&34.5&228\\
LightEA-L&14.8&11.2&-&-\\
\bottomrule
\end{tabular}
}
\end{center}
\caption{Time costs on all datasets (seconds). }\label{tabel:time}
\end{table}
\noindent
\textbf{Time cost}.
Table \ref{tabel:time} reports the time costs of three variants of LightEA.
Due to the space limitation, we only list out the time costs of Dual-AMN with two acceleration frameworks as the baselines.
For the results of other EA methods, please refer to Table \ref{tabel:timeapp} in Appendix C.
LargeEA and ClusterEA effectively accelerate Dual-AMN, achieving ten times speedups on DBP$1$M.
However, GNN-based methods are still stuck with multiple rounds of forward and backward propagation, while LightEA only requires one round of label propagation and no need for training.
With similar performances, the time consumption of LightEA-B is less than one-seventh of Dual-AMN variants.
Besides, introducing iterative strategies and literal features significantly increases time consumption while also improving performance.
\begin{figure*}
\centering
\includegraphics[width=0.95\textwidth]{hyper.pdf}
\caption{Hyper-parameter experiments of LightEA-I on DBP$15$K.}
\label{fig:hyper}
\end{figure*}
\subsection{Hyper-parameters}
We design extensive hyper-parameter experiments to investigate the behaviors of LightEA in various situations.
Due to the space limitation, Figure \ref{fig:hyper} only shows the results of LightEA-I on DBP$15$K.
Appendix \ref{sec:hyperapp} shows the results on other datasets.
\noindent
\textbf{Dimension}.
To alleviate the problem that one-hot label vectors being over-sparse, LightEA proposes to replace them with independent random vectors on high-dimensional hyper-spheres.
Figure \ref{fig:hyper}(a) shows the $Hits@1$ curves with different dimensions $d$.
Clearly, there are significant diminishing marginal effects on increasing dimensions.
When the dimension $d>1,024$, the performance gain becomes limited.
Actually, the reason behind diminishing marginal effects has been told by Lemma \ref{lemma:1} --- the probability of two random drawn vectors "conflicting" with each other (i.e., $\langle\bm x,\bm y\rangle > \epsilon$) decreases exponentially as the dimension $d$ increases.
\noindent
\textbf{Propagation Round}.
Figure \ref{fig:hyper}(b) shows the performances with different numbers of propagation rounds.
Similar to the network depth of GNNs, more propagation rounds also lead to the over-smoothing problem.
When the number of rounds $q=2$, LightEA-I achieves the best performance and then begins to decline.
This phenomenon indicates a high correlation between label propagation and GNNs from the side.
\noindent
\textbf{Top-K}.
In \emph{Sparse Sinkhorn Iteration}, LightEA only retrieves the top-$k$ nearest neighbors for each entity instead of calculating the distances between all pairs.
As expected, Figure \ref{fig:hyper}(c) shows that removing smaller values from the similarity matrix hardly affects the alignment performances.
The trick of \emph{Sparse Sinkhorn Iteration} could reduce the space-time complexity with limited losses.
Besides hyper-parameters, we further design more auxiliary experiments, such as ablation experiments.
Due to the space limitation, these experiments are listed in Appendix \ref{sec:pre}, \ref{sec:able}, and \ref{sec:openEA}.
\subsection{How to Interpret the Results}
\label{sec:interpret}
Existing GNN-based EA methods inherit poor interpretability from neural networks.
It is hard to explain the inside meaning of each dimension of entity features and why two entities are aligned.
Therefore, the output features are only used to calculate the similarities.
Different from GNN-based methods, we could clearly interpret the alignment results of LightEA by the following steps:
(1) Remove \emph{Random Orthogonal Label}.
After removing this component, the meaning of each dimension of label vectors becomes clear and realistic.
The $x$-$th$ dimension of $\bm l_{e_i}^{(k)}$ represents the relevance score between $e_i$ and the $x$-$th$ pre-aligned entity pair after $k$ rounds of propagation.
If two entities are equivalent, their distributions of relevance scores should also be similar.
(2) Trace the propagation:
Since we have known the meaning of each dimension, we could trace the propagation process at each time-step to investigate why two entities are aligned.
However, removing the \emph{Random Orthogonal Label Generation} will make the label matrices extremely large and sparse, and the \emph{Three-view Label Propagation} can only run on the small-sized sub-graphs.
Therefore, this strategy only fits for interpreting a limited number of entities.
\begin{figure*}[t]
\centering
\includegraphics[width=\textwidth]{wrong_case.pdf}
\caption{An example of tracing the propagation process and interpreting the alignment results.}
\label{fig:wrong}
\end{figure*}
\subsection{An Example of Tracing the Wrong Case}
\label{sec:wrong_case}
Figure \ref{fig:wrong} shows an example of tracing the propagation process and interpreting the alignment results.
In this case, \emph{United\_States\_Armed\_Forces} is incorrectly aligned with \emph{US\_Marine\_Corps}, and the correct answer is \emph{US\_Armed\_Forces}.
As described in last section, we first remove the \emph{Random Orthogonal Label}, run the \emph{Three-view Label Propagation}, and obtain the sparse label matrices $\bm L^{(1)}_e$ and $\bm L^{(2)}_e$.
Then, we separately sort the label vectors $\bm l^{(1)}_{e_i}$ and $\bm l^{(2)}_{e_i}$ of each entity to get the dimension indexes of top-$5$ non-zero elements.
Finally, we look up the corresponding names of dimension indexes in the entity name list and show them in Figure \ref{fig:wrong}.
Apparently, the noise of graph structure causes this wrong case.
Compared to the correct entity, the incorrect entity has a more similar neighborhood structure to \emph{United\_States\_Armed\_Forces}.
There are five common elements between the wrong alignment pair, while only three between the right alignment pair.
\section{Conclusion}
In this paper, we reinvent the \emph{Label Propagation} algorithm to effectively run on KGs and propose a non-neural EA framework --- LightEA.
According to the experiments on public datasets, LightEA has impressive scalability, robustness, and interpretability.
With a mere tenth of time consumption, LightEA achieves comparable results to state-of-the-art methods across all datasets.
\section*{Limitations}
Although we have demonstrated that LightEA has impressive scalability, robustness, and interpretability on multiple public datasets with different scales, there are still three limitations that should be addressed in the future:
(1) In LightEA, good interpretability and high efficiency cannot coexist.
If not removing the \emph{Random Orthogonal Label}, LightEA's interpretability will be significantly weakened.
How to balance the interpretability and efficiency is our future work.
(2) Theoretically, LightEA has high parallel efficiency that could obtain linear speedup with multiple GPUs.
However, we do not have enough devices to verify this advantage, and all the experiments in this paper run with a single RTX3090.
We will purchase more devices to complete these missing experiments in the future.
(3) Currently, we implement LightEA via Tensorflow.
Since LightEA is a non-neural algorithm without any trainable parameters, a complex deep learning framework would be redundant and inefficient.
In the future, we will refactor LightEA with CUDA and C++ to further improve efficiency.
\section*{Ethics Statement}
To the best of our knowledge, this work does not involve any discrimination, social bias, or private data.
All the datasets are open-source and constructed from open-source KGs such as Wikidata, YAGO, and DBpedia.
Therefore, we believe that our study complies with the \href{https://www.aclweb.org/portal/content/acl-code-ethics}{ACL Ethics Policy}.
In addition, introducing literal features may cause concerns about the misuse of user-generated content.
LightEA can avoid this concern by using pure structural information for entity alignment.
\section*{Ethics Statement}
We appreciate the support from National Natural Science Foundation of China with the Research Project on Human Behavior in Human-Machine Collaboration (Project Number: 72192824) and the support from Pudong New Area Science \& Technology Development Fund (Project Number: PKX2021-R05).
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,357
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Aimy Palogiannidou
Seascapes: From Urbanism to Nature
A Voyage with Synergy
Cognitive Cartography
Unveiling
Out of Balance
i d i ό t ē s
A City Within A City
Experiencing A Dark Space
Experiencing Urbanism Through Sounds
Painting the Space – The Aluminium Period
Public Issues #6
Finsbury Square, London. Before the performance.
On Sunday 28th of April 2013, Aimy Palogiannidou organised a group action in a public space in the area of City, a privatized, autonomous and self-governed area in central London with super-contemporary buildings where the offices of the city's biggest companies are hosted. Her aim was the production of a situation, which will challenge (locally and instantly) the established order of the everyday and contribute to the creation of a new local environment. Performing in a space with a background of the majestic skyscrapers of City of London, a group of people with playful attitude and a sense of teamwork will be called to "play", transform and alter a word made of cardboard. This will be the reformed word i d i ό t ē s referring to the English word idiot (=stupid, individual with bad judgment) and derives from the Greek word ιδιώτης (=private, someone who is characterized by self-centeredness and denies to participate in public affairs, person with bad judgment in public and political matters, person lacking professional skill).
London is a big metropolis that represents our modern society and encourages competition and individualism. The dry professionalism of London has led to a sterilization of the world that threatens to wipe out any spontaneity or playfulness. Aimy Palogiannidou explores the urban space using practices like dérive and psychogéography and she is interested in the interaction between urban environment and everyday life. For her, the city street is the essential space of the everyday where life is performed. It is the space between private and public where the everydayness is conceived with what is lived.
Visit the Openshowstudio website
Ropemaker street, London.
The word i d i ό t ē s was firstly set up on Ropemaker street in the City of London, a privatised area in the heart of London. The performance was stopped by the local authorities. The team was moved to Finsbury Square, a public space on the other side of City road where the performance was completed with great success.
During the performance at Finsbury Square.
Hackney E5
Skype name
emmapalo1
emmapalo@gmail.com
This is a Fine Art portfolio of Aimy Palogiannidou since 2009 to date.
Copyright © 2023 Aimy Palogiannidou
Web design by AP Art Studio
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,981
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18 / f, south china ind bldg. , no. 1 chun pin st. , kwai chung. hong kong.
zhangjiagang huayi mechanical & electronic co., ltd.
zhejiang feiying sewing equipment co., ltd.
zhejiang xinsheng sewing equipment co., ltd.
jinjiang city chaojun machine co., ltd.
zhuji zhiyu machinery co., ltd.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,390
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/* @flow */
/* React, browser and server rendering functions. We need the
* first import as JSX compiled to React.createComponent(...) */
import React from 'react';
import { render as renderToDom } from 'react-dom';
import { renderToString } from 'react-dom/server';
import Helmet from 'react-helmet';
/* Hot-module reloading */
import { AppContainer } from 'react-hot-loader'
/* State management with redux */
import { Provider } from 'react-redux';
/* Routing with react-router */
import { StaticRouter } from 'react-router';
import { BrowserRouter } from 'react-router-dom';
import App from './containers/App';
import createStore from './createStore';
/* Client-side rendering. We rehydrate the Redux store and plugin it into the page render.*/
if (typeof window !== 'undefined') {
// Only create the store once!
const store = createStore(window.__INITIAL_STATE__);
const render = Component => {
const app = (
<AppContainer>
<Provider store={store}>
<BrowserRouter>
<Component />
</BrowserRouter>
</Provider>
</AppContainer>
);
renderToDom(app, document.getElementById('root'));
}
render(App);
// Register with Hot Module Replacement API
if (module.hot) {
module.hot.accept('./containers/App', () => { render(App) });
}
}
/**
* Performs server-side rendering. The function is exported because the templating function
* that Spring will call uses this function to perform the meat of the rendering.
*
* @param path the path to the resource requested by the client
* @param state the Redux state supplied by Spring and massaged by the template engine
* @returns string the rendered page
*/
// eslint-disable-next-line import/prefer-default-export
export function renderApp(path : string, state : Object) {
const store = createStore(state);
// 404's will be handled by correct route definitions. Redirects will be handled by Spring.
const markup = renderToString(
<Provider store={ store }>
<StaticRouter
location={ path }
context={ {} }
>
<App/>
</StaticRouter>
</Provider>
)
// Free accumulated object to avoid memory leak and return data to parent renderer
const head = Helmet.rewind();
return { markup, head };
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
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{"url":"https:\/\/elfi.readthedocs.io\/en\/dev\/usage\/BOLFI.html","text":"This tutorial is generated from a Jupyter notebook that can be found here.\n\n# BOLFI\u00b6\n\nIn practice inference problems often have a complicated and computationally heavy simulator, and one simply cannot run it for millions of times. The Bayesian Optimization for Likelihood-Free Inference BOLFI framework is likely to prove useful in such situation: a statistical model (usually Gaussian process, GP) is created for the discrepancy, and its minimum is inferred with Bayesian optimization. This approach typically reduces the number of required simulator calls by several orders of magnitude.\n\nThis tutorial demonstrates how to use BOLFI to do LFI in ELFI.\n\nimport numpy as np\nimport scipy.stats\nimport matplotlib\nimport matplotlib.pyplot as plt\n\n%matplotlib inline\n%precision 2\n\nimport logging\nlogging.basicConfig(level=logging.INFO)\n\n# Set an arbitrary global seed to keep the randomly generated quantities the same\nseed = 1\nnp.random.seed(seed)\n\nimport elfi\n\n\nAlthough BOLFI is best used with complicated simulators, for demonstration purposes we will use the familiar MA2 model introduced in the basic tutorial, and load it from ready-made examples:\n\nfrom elfi.examples import ma2\nmodel = ma2.get_model(seed_obs=seed)\nelfi.draw(model)\n\n\n## Fitting the surrogate model\u00b6\n\nNow we can immediately proceed with the inference. However, when dealing with a Gaussian process, it may be beneficial to take a logarithm of the discrepancies in order to reduce the effect that high discrepancies have on the GP. (Sometimes you may want to add a small constant to avoid very negative or even -Inf distances occurring especially if it is likely that there can be exact matches between simulated and observed data.) In ELFI such transformed node can be created easily:\n\nlog_d = elfi.Operation(np.log, model['d'])\n\n\nAs BOLFI is a more advanced inference method, its interface is also a bit more involved as compared to for example rejection sampling. But not much: Using the same graphical model as earlier, the inference could begin by defining a Gaussian process (GP) model, for which ELFI uses the GPy library. This could be given as an elfi.GPyRegression object via the keyword argument target_model. In this case, we are happy with the default that ELFI creates for us when we just give it each parameter some bounds as a dictionary.\n\nOther notable arguments include the initial_evidence, which gives the number of initialization points sampled straight from the priors before starting to optimize the acquisition of points, update_interval which defines how often the GP hyperparameters are optimized, and acq_noise_var which defines the diagonal covariance of noise added to the acquired points. Note that in general BOLFI does not benefit from a batch_size higher than one, since the acquisition surface is updated after each batch (especially so if the noise is 0!).\n\nbolfi = elfi.BOLFI(log_d, batch_size=1, initial_evidence=20, update_interval=10,\nbounds={'t1':(-2, 2), 't2':(-1, 1)}, acq_noise_var=[0.1, 0.1], seed=seed)\n\n\nSometimes you may have some samples readily available. You could then initialize the GP model with a dictionary of previous results by giving initial_evidence=result.outputs.\n\nThe BOLFI class can now try to fit the surrogate model (the GP) to the relationship between parameter values and the resulting discrepancies. We\u2019ll request only 100 evidence points (including the initial_evidence defined above).\n\n%time post = bolfi.fit(n_evidence=200)\n\nINFO:elfi.methods.parameter_inference:BOLFI: Fitting the surrogate model...\nINFO:elfi.methods.posteriors:Using optimized minimum value (-1.6146) of the GP discrepancy mean function as a threshold\n\nCPU times: user 1min 48s, sys: 1.29 s, total: 1min 50s\nWall time: 1min\n\n\n(More on the returned BolfiPosterior object below.)\n\nNote that in spite of the very few simulator runs, fitting the model took longer than any of the previous methods. Indeed, BOLFI is intended for scenarios where the simulator takes a lot of time to run.\n\nThe fitted target_model uses the GPy library, and can be investigated further:\n\nbolfi.target_model\n\nName : GP regression\nObjective : 151.86636065302943\nNumber of Parameters : 4\nNumber of Optimization Parameters : 4\nParameters:\n\u001b[1mGP_regression. \u001b[0;0m | value | constraints | priors\n\u001b[1msum.rbf.variance \u001b[0;0m | 0.321697451372 | +ve | Ga(0.024, 1)\n\u001b[1msum.rbf.lengthscale \u001b[0;0m | 0.541352150083 | +ve | Ga(1.3, 1)\n\u001b[1msum.bias.variance \u001b[0;0m | 0.021827430988 | +ve | Ga(0.006, 1)\n\u001b[1mGaussian_noise.variance\u001b[0;0m | 0.183562040169 | +ve |\n\nbolfi.plot_state();\n\n<matplotlib.figure.Figure at 0x11b2b2ba8>\n\n\nIt may be useful to see the acquired parameter values and the resulting discrepancies:\n\nbolfi.plot_discrepancy();\n\n\nThere could be an unnecessarily high number of points at parameter bounds. These could probably be decreased by lowering the covariance of the noise added to acquired points, defined by the optional acq_noise_var argument for the BOLFI constructor. Another possibility could be to add virtual derivative observations at the borders, though not yet implemented in ELFI.\n\n## BOLFI Posterior\u00b6\n\nAbove, the fit method returned a BolfiPosterior object representing a BOLFI posterior (please see the paper for details). The fit method accepts a threshold parameter; if none is given, ELFI will use the minimum value of discrepancy estimate mean. Afterwards, one may request for a posterior with a different threshold:\n\npost2 = bolfi.extract_posterior(-1.)\n\n\nOne can visualize a posterior directly (remember that the priors form a triangle):\n\npost.plot(logpdf=True)\n\n\n## Sampling\u00b6\n\nFinally, samples from the posterior can be acquired with an MCMC sampler. By default it runs 4 chains, and half of the requested samples are spent in adaptation\/warmup. Note that depending on the smoothness of the GP approximation, the number of priors, their gradients etc., this may be slow.\n\n%time result_BOLFI = bolfi.sample(1000, info_freq=1000)\n\nINFO:elfi.methods.posteriors:Using optimized minimum value (-1.6146) of the GP discrepancy mean function as a threshold\nINFO:elfi.methods.mcmc:NUTS: Performing 1000 iterations with 500 adaptation steps.\nINFO:elfi.methods.mcmc:NUTS: Acceptance ratio: 0.423. After warmup 68 proposals were outside of the region allowed by priors and rejected, decreasing acceptance ratio.\nINFO:elfi.methods.mcmc:NUTS: Performing 1000 iterations with 500 adaptation steps.\nINFO:elfi.methods.mcmc:NUTS: Acceptance ratio: 0.422. After warmup 71 proposals were outside of the region allowed by priors and rejected, decreasing acceptance ratio.\nINFO:elfi.methods.mcmc:NUTS: Performing 1000 iterations with 500 adaptation steps.\nINFO:elfi.methods.mcmc:NUTS: Acceptance ratio: 0.419. After warmup 65 proposals were outside of the region allowed by priors and rejected, decreasing acceptance ratio.\nINFO:elfi.methods.mcmc:NUTS: Performing 1000 iterations with 500 adaptation steps.\nINFO:elfi.methods.mcmc:NUTS: Acceptance ratio: 0.439. After warmup 66 proposals were outside of the region allowed by priors and rejected, decreasing acceptance ratio.\n\n4 chains of 1000 iterations acquired. Effective sample size and Rhat for each parameter:\nt1 2222.1197791 1.00106816947\nt2 2256.93599184 1.0003364409\nCPU times: user 1min 45s, sys: 1.29 s, total: 1min 47s\nWall time: 55.1 s\n\n\nThe sampling algorithms may be fine-tuned with some parameters. The default No-U-Turn-Sampler is a sophisticated algorithm, and in some cases one may get warnings about diverged proposals, which are signs that something may be wrong and should be investigated. It is good to understand the cause of these warnings although they don\u2019t automatically mean that the results are unreliable. You could try rerunning the sample method with a higher target probability target_prob during adaptation, as its default 0.6 may be inadequate for a non-smooth posteriors, but this will slow down the sampling.\n\nNote also that since MCMC proposals outside the region allowed by either the model priors or GP bounds are rejected, a tight domain may lead to suboptimal overall acceptance ratio. In our MA2 case the prior defines a triangle-shaped uniform support for the posterior, making it a good example of a difficult model for the NUTS algorithm.\n\nNow we finally have a Sample object again, which has several convenience methods:\n\nresult_BOLFI\n\nMethod: BOLFI\nNumber of samples: 2000\nNumber of simulations: 200\nThreshold: -1.61\nSample means: t1: 0.429, t2: 0.0277\n\nresult_BOLFI.plot_traces();\n\n\nThe black vertical lines indicate the end of warmup, which by default is half of the number of iterations.\n\nresult_BOLFI.plot_marginals();","date":"2019-02-17 17:30:28","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.5653047561645508, \"perplexity\": 3013.068658981619}, \"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-2019-09\/segments\/1550247482347.44\/warc\/CC-MAIN-20190217172628-20190217194628-00424.warc.gz\"}"}
| null | null |
775 lucky dogs and cats were spayed and neutered in November.....and the vets and vet techs at Romania Animal Rescue are still working to stop suffering. The photos show dogs and cats at the Center of Hope during the month of November - all spayed and neutered to stop unwanted puppies and kittens from being born to suffer. This is the only humane solution to end the suffering for stray dogs and cats.
Your help is needed to enable us to continue this lifechanging work. Please in this season of giving think of all the dogs and cats that need us to make a difference. We can only do this work with the support of animal lovers like you. Donate today and help us continue to help more dogs and cats in need.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 932
|
\section{Cross-section measurement}\label{sec:cro}
The $pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ cross-section is calculated within the
kinematic region $60 < M_{\tau\tau} < 120~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$, $2.0 \leq \eta^\tau
\leq 4.5$, and $\ensuremath{p_\mathrm{T}}\xspace^\tau > 20~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$ using
\begin{equation}
\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace} = \frac{\sum_{i = 1}^{N} 1 /
\varepsilon_\ensuremath{\mathrm{rec}}\xspace^i - \sum_j N^j_\ensuremath{\mathrm{bkg}}\xspace \langle 1 / \varepsilon_\ensuremath{\mathrm{rec}}\xspace \rangle^j}
{\ensuremath{\mathscr{L}}\xspace \cdot \ensuremath{\mathcal{A}}\xspace \cdot \ensuremath{\mathcal{B}}\xspace \cdot \eff{\ensuremath{\mathrm{sel}}\xspace}}
\label{equ:xs}
\end{equation}
where $N$ is the number of observed candidates and $N_\ensuremath{\mathrm{bkg}}\xspace^j$ is the
estimated background from source $j$. The integrated luminosity is
given by \ensuremath{\mathscr{L}}\xspace, \ensuremath{\mathcal{A}}\xspace is an acceptance and final state radiation
correction factor, \ensuremath{\mathcal{B}}\xspace is the branching fraction for the \ensuremath{\tau}-lepton\xspace pair to
decay to the final state, and \eff{\ensuremath{\mathrm{sel}}\xspace} is the selection
efficiency. A summary of these values for each final state is given in
\tab{\ref{tab:mea}}. The reconstruction efficiency, \eff{\ensuremath{\mathrm{rec}}\xspace}, is
calculated using simulation or data for each event, assuming that it
is signal, and depends on the momentum and pseudorapidity of the \ensuremath{\tau} lepton\xspace
decay product candidates. $\langle 1 / \varepsilon_\ensuremath{\mathrm{rec}}\xspace\rangle^j$
indicates the average value of $1/\eff{\ensuremath{\mathrm{rec}}\xspace}$ for background source
$j$.
\begin{table}
\caption{Acceptance factors, branching fractions, selection
efficiencies, numbers of background and observed events for each
$\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ analysis stream.\label{tab:mea}}
\begin{center}
\small
\begin{tabular}[t]{c|r|r|r|r|r}
\toprule
\multicolumn{1}{c|}{Stream}
& \multicolumn{1}{c|}{\ensuremath{\mathcal{A}}\xspace}
& \multicolumn{1}{c|}{\ensuremath{\mathcal{B}}\xspace $[\%]$}
& \multicolumn{1}{c|}{\eff{\ensuremath{\mathrm{sel}}\xspace}}
& \multicolumn{1}{c|}{$N_\ensuremath{\mathrm{bkg}}\xspace$}
& \multicolumn{1}{c}{$N$} \\
\midrule
\ensuremath{\tau_\mu\tau_\mu}\xspace & $0.405 \pm 0.006$ & $3.031 \pm 0.014$ & $0.138 \pm 0.006$
& $ 41.6 \pm 8.5$ & $124$ \\
\ensuremath{\tau_\mu\tau_e}\xspace & $0.248 \pm 0.004$ & $6.208 \pm 0.020$ & $0.517 \pm 0.012$
& $129.7 \pm 4.9$ & $421$ \\
\ensuremath{\tau_e\tau_\mu}\xspace & $0.152 \pm 0.002$ & $6.208 \pm 0.020$ & $0.344 \pm 0.016$
& $ 56.6 \pm 3.3$ & $155$ \\
\ensuremath{\tau_\mu\tau_\had}\xspace & $0.182 \pm 0.002$ & $16.933 \pm 0.056$ & $0.135 \pm 0.004$
& $ 53.3 \pm 0.8$ & $189$ \\
\ensuremath{\tau_e\tau_\had}\xspace & $0.180 \pm 0.002$ & $17.341 \pm 0.057$ & $0.082 \pm 0.004$
& $ 36.6 \pm 0.9$ & $101$ \\
\bottomrule
\end{tabular}
\end{center}
\end{table}
The integrated luminosity of the datasets for the \ensuremath{\tau_\mu\tau_\mu}\xspace, \ensuremath{\tau_\mu\tau_e}\xspace, and
\ensuremath{\tau_\mu\tau_\had}\xspace samples is $1028 \pm 36~\ensuremath{\mathrm{pb}^{-1}}\xspace$, while the \ensuremath{\tau_e\tau_\mu}\xspace and \ensuremath{\tau_e\tau_\had}\xspace final state
datasets have an integrated luminosity of $955 \pm 33~\ensuremath{\mathrm{pb}^{-1}}\xspace$.
\subsection{Acceptances and branching fractions}\label{sec:cro:acc}
The acceptance factor, \ensuremath{\mathcal{A}}\xspace, is used to correct the kinematics of each
analysis stream to the kinematic region $60 < M_{\tau\tau} <
120~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$, $2.0 \leq \eta^\tau \leq 4.5$, and $\ensuremath{p_\mathrm{T}}\xspace^\tau >
20~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$. This region corresponds to the detector fiducial acceptance
and allows a comparison with the LHCb\xspace $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$
measurement~\cite{lhcb}. The acceptance factor is taken from
simulation and is defined as the number of $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ events
where the generated \ensuremath{\tau} lepton\xspace decay products fulfil the kinematic
requirements described in \sec{\ref{sec:eve}}, divided by the number
of $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ events where the generated \ensuremath{\tau} leptons\xspace lie within the
kinematic region defined above.
For each final state the acceptance factors are calculated at
leading-order using fully modelled hadronic decay currents and spin
correlated \ensuremath{\tau} lepton\xspace decays with final state radiation in {\sc Pythia}\xspace $8$ and
{\sc Herwig++}\xspace, and at next-to-leading-order using the {\sc Powheg}\xspace method
implemented in {\sc Herwig++}\xspace. For {\sc Pythia}\xspace $8$ the {CTEQ$5$L}\xspace leading-order PDF
set~\cite{cteqp} was used, while for {\sc Herwig++}\xspace the {MSTW$08$}\xspace PDF
set~\cite{mstw} was used. The mean of the maximum and minimum values
from the three generators is taken as the acceptance factor and is
given in \tab{\ref{tab:mea}}. The uncertainty is taken as half the
difference between the maximum and minimum values.
The branching fractions are calculated using the world
averages~\cite{pdg} and are given in \tab{\ref{tab:mea}}. The \ensuremath{\tau} lepton\xspace to
single charged-hadron branching fraction is the sum of all \ensuremath{\tau} lepton\xspace decays
containing a single charged hadron. The final states presented in this
analysis account for $44\%$ of all expected $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ decays.
\subsection{Selection efficiency}\label{sec:cro:sel}
The event selection efficiency, $\eff{\ensuremath{\mathrm{sel}}\xspace}$, is the product of the
efficiencies described below. Each efficiency is determined from
either data, or simulation which has been calibrated using data. The
resulting $\eff{\ensuremath{\mathrm{sel}}\xspace}$ for each stream is given in
\tab{\ref{tab:mea}}.
The kinematic efficiency, \eff{\ensuremath{\mathrm{kin}}\xspace}, is obtained from simulation and
is the number of events fulfilling the kinematic requirements of
\sec{\ref{sec:eve}} at both the simulated and reconstructed level
divided by the number of events passing the requirements at the
simulated level. The efficiency is consistent with unity for the \ensuremath{\tau_\mu\tau_\mu}\xspace
and \ensuremath{\tau_\mu\tau_\had}\xspace analysis streams. For streams involving electrons, \eff{\ensuremath{\mathrm{kin}}\xspace}
is significantly lower due to the saturation of the \ensuremath{\mathrm{ECAL}}\xspace. This
results in electrons being reconstructed with lower momenta than their
true momenta due to incomplete bremsstrahlung recovery. In the \ensuremath{\tau_\mu\tau_e}\xspace,
\ensuremath{\tau_e\tau_\mu}\xspace, and \ensuremath{\tau_e\tau_\had}\xspace streams, \eff{\ensuremath{\mathrm{kin}}\xspace} is \prc{99.3 \pm 1.0}, \prc{66.8 \pm
1.9}, and \prc{67.0 \pm 1.3} respectively. The uncertainties come
from the statistical uncertainty of the $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ simulation and
the calibration of the electron momentum scale which has been obtained
by comparing the \ensuremath{p_\mathrm{T}}\xspace spectrum of $\ensuremath{Z}\xspace \to \ensuremath{ee}\xspace$ events in data and
simulation~\cite{zee}.
The efficiency of the isolation requirement, \eff{\ensuremath{{I_{p_\mathrm{T}}}}\xspace}, for each
analysis stream is taken from $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ simulation, and
calibrated to data by multiplying \eff{\ensuremath{{I_{p_\mathrm{T}}}}\xspace} by the ratio of the
efficiency obtained in $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ data to $\ensuremath{Z}\xspace \to \ensuremath{\tau_\mu\tau_\mu}\xspace$
simulation. The systematic uncertainty on \eff{\ensuremath{{I_{p_\mathrm{T}}}}\xspace} is estimated as
the difference between the efficiencies obtained from $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$
simulation and $\ensuremath{Z}\xspace \to \ensuremath{\tau_\mu\tau_\mu}\xspace$ simulation.
The efficiency of the impact parameter significance requirement,
\eff{\ensuremath{{\mathrm{IPS}}}\xspace}, is evaluated from $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ simulation. A comparison
of the \ensuremath{{\mathrm{IPS}}}\xspace distributions in $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ events from data and
simulation show that the impact parameter resolution is underestimated
by \prc{12\pm 1} in simulation, and so the simulated $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$
events are corrected by this factor. The systematic uncertainty on
\eff{\ensuremath{{\mathrm{IPS}}}\xspace} is determined by re-calculating the efficiency in $\ensuremath{Z}\xspace \to
\ensuremath{\tau\tau}\xspace$ simulation with the scale factor varied by its uncertainty.
The efficiency of the azimuthal angle separation requirement,
\eff{\ensuremath{{|\Delta \Phi|}}\xspace}, and \ensuremath{p_\mathrm{T}}\xspace asymmetry efficiency requirement, \eff{\ensuremath{{A_{p_\mathrm{T}}}}\xspace}, are
evaluated from simulation. The systematic uncertainty on each is taken
as the difference in the evaluation of these efficiencies in $\ensuremath{Z}\xspace \to
\ensuremath{\mu\mu}\xspace$ data and simulation, combined in quadrature with the
statistical uncertainty from the $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ simulation.
\subsection{Reconstruction efficiency}\label{sec:cro:rec}
The reconstruction efficiency, \eff{\ensuremath{\mathrm{rec}}\xspace}, is the product of the \ensuremath{\mathrm{GEC}}\xspace,
trigger, and tracking and identification efficiencies for both \ensuremath{\tau} lepton\xspace
decay product candidates. The tracking efficiency is the probability
for reconstructing the track and the identification efficiency is the
probability for the track to be identified by the relevant
sub-detectors. All efficiencies determined from data have been checked
against simulation and found to agree within the percent level.
The \ensuremath{\mathrm{GEC}}\xspace efficiency, \eff{\ensuremath{\mathrm{GEC}}\xspace}, is a correction for the loss due to
the rejection by the hardware trigger of events with an \ensuremath{\mathrm{SPD}}\xspace
multiplicity of greater than $600~\mathrm{hits}$. For muon triggered
events, the efficiency has been evaluated to be \prc{95.5 \pm 0.1}
from $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ data events using a hardware di-muon trigger with
a relaxed \ensuremath{\mathrm{SPD}}\xspace requirement of $900~\mathrm{hits}$. For electron
trigger events, the efficiency is estimated to be \prc{95.1 \pm 0.1}
by comparing the hit multiplicities in $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ and $\ensuremath{Z}\xspace \to
\ensuremath{ee}\xspace$ events.
The muon and electron trigger efficiencies, \eff{\ensuremath{\mathrm{trg}}\xspace}, are evaluated
in bins of momentum using a tag-and-probe method on $\ensuremath{Z}\xspace \to \ensuremath{\lep\lep}\xspace$
data events, which have been selected requiring two reconstructed and
identified muon or electron candidates with an invariant mass
consistent with that of the \ensuremath{Z}\xspace. In the events the triggered lepton is
taken as the tag lepton, and the other as the probe lepton. The event
topologies for $\ensuremath{Z}\xspace \to \ensuremath{\lep\lep}\xspace$ and $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ events are nearly
identical except for the momenta of the final state particles and so
the trigger efficiency is calculated only as a function of the probe
momentum below $500~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$. The trigger efficiency is the fraction of
events where the probe has also triggered, and varies as a function of
probe momentum between $75\%$ and $80\%$ for the muon trigger and
between $62\%$ and $75\%$ for the electron trigger. The trigger
efficiency uncertainty for each bin in momenta is taken as the
statistical uncertainty.
The tracking efficiency, \eff{\ensuremath{\mathrm{trk}}\xspace}, is also evaluated for muons using
a tag-and-probe method on the $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ data. The tag must
satisfy all the muon reconstruction and identification
requirements. The probe is reconstructed from a track segment in the
muon chambers that has been associated to a hit in the \ensuremath{\mathrm{TT}}\xspace
sub-detector, which is not required in the track
reconstruction. Events with a tag and probe mass consistent with the
on-shell \ensuremath{Z}\xspace mass are used. The tracking efficiency is evaluated as the
number of events with a reconstructed probe track over the total
number of events. For lower \ensuremath{p_\mathrm{T}}\xspace tracks, masses consistent with the
\ensuremath{J/\psi}\xspace are used.
The $\ensuremath{J/\psi}\xspace \to \ensuremath{\mu\mu}\xspace$ topology differs from the $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$
topology in both pseudorapidity and momentum, and so the \ensuremath{J/\psi}\xspace muon
tracking efficiencies are evaluated in bins of both variables. The
muon tracking efficiency is found to vary between $85\%$ and
$93\%$. The uncertainty on the tracking efficiency is given by the
statistical precision and the knowledge of the purity of the sample of
$\ensuremath{J/\psi}\xspace \to \ensuremath{\mu\mu}\xspace$ candidates. The purity is estimated by fitting the
di-muon invariant mass distribution of the $\ensuremath{J/\psi}\xspace \to \ensuremath{\mu\mu}\xspace$
candidates with a Crystal Ball function~\cite{crystal} to describe the
signal shape and a linear background. An alternative estimate is
obtained by fitting only the linear background on either side of the
di-muon resonance. The difference in the efficiency evaluated using
the two purity methods is taken as the systematic uncertainty.
All particles pass through approximately $20\%$ of a hadronic
interaction length of material prior to the final tracking station.
Early showering of hadrons reduces the hadron tracking efficiency
compared to the muon tracking efficiency. An additional correction
factor to the muon tracking efficiency of \prc{84.3 \pm 1.5} for
hadrons is applied which has been estimated using the full detector
simulation, where the uncertainty on this correction corresponds to an
uncertainty of $10\%$ in the material budget~\cite{track}.
The electron tracking efficiency uses a tag-and-probe method on $\ensuremath{Z}\xspace
\to \ensuremath{ee}\xspace$ data events. The tag must satisfy all the electron
reconstruction and identification requirements and the probe is
selected as the highest energy \ensuremath{\mathrm{ECAL}}\xspace cluster in the event not
associated with the tag. The purity of the sample is found, from
simulation, to depend on the \ensuremath{p_\mathrm{T}}\xspace of the tag. The dependence of the
purity is fitted with signal and background templates obtained from
same-sign and opposite-sign events from data. No momentum information
is available for the probe, so the tag-and-probe technique only
provides an overall tracking efficiency for the electrons, which is
measured to be \prc{83 \pm 3}. The momentum dependence is taken from
$\ensuremath{Z}\xspace \to \ensuremath{ee}\xspace$ and $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ simulation. The electron tracking
efficiency uncertainty is taken from the fit uncertainty added in
quadrature to the statistical uncertainty.
The identification efficiency, \eff{\ensuremath{\mathrm{id}}\xspace}, is measured for muons with
the tag-and-probe method for the $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ data, using a
reconstructed track as the probe lepton and evaluated as a function of
the probe momentum. For low momenta the efficiency is evaluated using
a $\ensuremath{J/\psi}\xspace \to \ensuremath{\mu\mu}\xspace$ sample as a function of both probe pseudorapidity
and momentum. The muon identification efficiency is found to vary
between $93\%$ and $99\%$ in pseudorapidity and momentum. The muon
\eff{\ensuremath{\mathrm{id}}\xspace} uncertainty is evaluated with the same method used for the
muon \eff{\ensuremath{\mathrm{trk}}\xspace} uncertainty.
The electron identification efficiency is measured as a function of
probe momentum using the tag-and-probe method on $\ensuremath{Z}\xspace \to \ensuremath{ee}\xspace$ data
and simulation events. The isolation requirement introduces a bias of
$1\% - 4\%$ in data and reconstructed simulation and so simulation
without the isolation criteria is used instead. The electron
identification efficiency is found to vary between $85\%$ and $96\%$,
with an uncertainty in each bin estimated as the difference in the
biased efficiencies from data and simulation.
The hadron identification efficiency is determined using events
triggered on a single \ensuremath{\mathrm{VELO}}\xspace track. The highest \ensuremath{p_\mathrm{T}}\xspace track in each
minimum bias event is assumed to be a hadron, as verified by
simulation. The hadron identification efficiency is taken as the
fraction of tracks fulfilling the hadron identification
requirements. Although the minimum bias topology differs significantly
from the $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ topology, an efficiency dependence is
observed only in pseudorapidity and so the efficiency is evaluated as
a function of pseudorapidity and found to vary between $92\%$ and
$95\%$. The uncertainty for each bin of pseudorapidity is estimated as
the statistical uncertainty of the bin. A summary of the systematic
uncertainties is given in \tab{\ref{tab:unc}}.
\section{Conclusions}\label{sec:con}
Measurements of inclusive $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ production in $pp$
collisions at $\sqrt{s} = 7~\ensuremath{\mathrm{Te\kern -0.1em V}}\xspace$ in final states containing two
muons, a muon and an electron, a muon and a hadron, and an electron
and a hadron have been performed using a dataset corresponding to an
integrated luminosity of $1028 \pm 36~\ensuremath{\mathrm{pb}^{-1}}\xspace.$ The cross-sections for
the individual states have been measured in the forward region of $2.0
\leq \eta^\tau \leq 4.5$ with $\ensuremath{p_\mathrm{T}}\xspace^\tau > 20~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$ and $60 <
M_{\tau\tau} < 120~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$, and a combined result calculated. The
results have been compared to Standard Model NNLO theory predictions
and with the LHCb\xspace $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ cross-section measurement. The
individual measurements, the combined result, the $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$
cross-section, and the theory prediction are all in good
agreement. The ratio of the $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ cross-section to the $\ensuremath{Z}\xspace
\to \ensuremath{\tau\tau}\xspace$ cross-section is found to be consistent with lepton
universality.
\section{Event selection}\label{sec:eve}
The signatures for $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ decays considered in this analysis
are two oppositely-charged tracks, consistent with an electron, muon,
or hadron hypothesis, having large impact parameters with respect to
the primary vertex of the event.
Tracks are reconstructed in the \ensuremath{\mathrm{VELO}}\xspace and extrapolated to the
\ensuremath{\mathrm{IT}}\xspace/\ensuremath{\mathrm{OT}}\xspace sub-detectors; any \ensuremath{\mathrm{TT}}\xspace sub-detector hits consistent with
the track are added and a full track fit is performed. Only tracks
with fit probabilities greater than $0.001$ are considered.
Tracks are extrapolated to the calorimeters and matched with
calorimeter clusters. Electron candidates are required to have a \ensuremath{\mathrm{PRS}}\xspace
energy greater than $0.05~\ensuremath{\mathrm{Ge\kern -0.1em V}}\xspace$, a ratio of \ensuremath{\mathrm{ECAL}}\xspace energy to candidate
momentum, $E / pc$, greater than $0.1$, and a ratio of \ensuremath{\mathrm{HCAL}}\xspace energy to
candidate momentum less than $0.05$. Any electron candidate momentum
is corrected using bremsstrahlung photon recovery~\cite{brem}. Since
the \ensuremath{\mathrm{ECAL}}\xspace is designed to register particles from $b$-hadron decays,
calorimeter cells with transverse energy above $10~\ensuremath{\mathrm{Ge\kern -0.1em V}}\xspace$ saturate the
electronics, and lead to degradation in the electron energy
resolution.
Hadron candidates are identified by requiring the ratio of \ensuremath{\mathrm{HCAL}}\xspace
energy to track momentum to be greater than $0.05$. Due to the limited
\ensuremath{\mathrm{HCAL}}\xspace acceptance, the candidate track is required to have a
pseudorapidity of $2.25 \leq \eta \leq 3.75$.
Muon candidates are identified by extrapolating tracks to the muon
system downstream of the calorimeters and matching them with
compatible hits. Muon candidates are required to have a hit in each of
the four stations and consequently will have traversed over $20$
hadronic interaction lengths of material.
The data have been collected using two triggers: a trigger which
selects muon candidates with a \ensuremath{p_\mathrm{T}}\xspace greater than $10~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$; and a
trigger which selects electron candidates with \ensuremath{p_\mathrm{T}}\xspace greater than
$15~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$.
The analysis is divided into five streams, labelled \ensuremath{\tau_\mu\tau_\mu}\xspace, \ensuremath{\tau_\mu\tau_e}\xspace, \ensuremath{\tau_e\tau_\mu}\xspace,
\ensuremath{\tau_\mu\tau_\had}\xspace, and \ensuremath{\tau_e\tau_\had}\xspace, defined such that the streams are exclusive. The first
\ensuremath{\tau} lepton\xspace decay product candidate is required to have $\ensuremath{p_\mathrm{T}}\xspace > 20~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$ and
the second is required to have $\ensuremath{p_\mathrm{T}}\xspace > 5~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$. The following
additional kinematic and particle identification requirements are
specific to each analysis stream:
\begin{itemize}
\item \ensuremath{\tau_\mu\tau_\mu}\xspace requires two oppositely-charged muons where at least one
triggered the event. The muon with the larger \ensuremath{p_\mathrm{T}}\xspace is considered as
the first \ensuremath{\tau} lepton\xspace decay product candidate.
\item \ensuremath{\tau_\mu\tau_e}\xspace requires a muon that triggered the event and an
oppositely-charged electron.
\item \ensuremath{\tau_e\tau_\mu}\xspace requires an electron and an oppositely-charged muon with
$\ensuremath{p_\mathrm{T}}\xspace < 20~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$. Either lepton can trigger the event.
\item \ensuremath{\tau_\mu\tau_\had}\xspace requires a muon that triggered the event and an
oppositely-charged hadron.
\item \ensuremath{\tau_e\tau_\had}\xspace requires an electron that triggered the event and an
oppositely-charged hadron.
\end{itemize}
In $pp$ collisions the cross-section for hadronic QCD processes is
very large. These events can pass the above requirements either due to
semileptonic $c$- or $b$-hadron decays or through the
misidentification of hadrons as leptons.
Signal decays, coming from an on-shell \ensuremath{Z}\xspace, tend to have back-to-back
isolated tracks in the transverse plane with a higher invariant mass
than tracks in QCD events. The absolute difference in azimuthal angle
of the two \ensuremath{\tau} lepton\xspace decay product candidates, \ensuremath{{|\Delta \Phi|}}\xspace, is required to be
greater than $2.7~\mathrm{radians}$ and their invariant mass is
required to be greater than $20~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$.
Tracks in QCD events also tend to be associated with jet activity, in
contrast to signal events where they are isolated. An isolation
variable, \ensuremath{{I_{p_\mathrm{T}}}}\xspace, is defined as the transverse component of the
vectorial sum of all track momenta that satisfy $\sqrt{\Delta \phi^2 +
\Delta \eta^2} < 0.5$, where $\Delta \phi$ and $\Delta \eta$ are the
differences in $\phi$ and $\eta$ between the \ensuremath{\tau} lepton\xspace decay product
candidate and the track. The track of the \ensuremath{\tau} lepton\xspace decay product candidate
is excluded from the sum. Both \ensuremath{\tau} lepton\xspace decay product candidates are
required to have $\ensuremath{{I_{p_\mathrm{T}}}}\xspace < 2~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$ for the \ensuremath{\tau_\mu\tau_\mu}\xspace, \ensuremath{\tau_\mu\tau_e}\xspace, and \ensuremath{\tau_e\tau_\mu}\xspace
analysis streams and $\ensuremath{{I_{p_\mathrm{T}}}}\xspace < 1~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$ for \ensuremath{\tau_\mu\tau_\had}\xspace and \ensuremath{\tau_e\tau_\had}\xspace due to the
larger \ensuremath{\mathrm{QCD}}\xspace backgrounds.
The lifetime of the \ensuremath{\tau} lepton\xspace is used to separate signal from prompt
backgrounds. The signed impact parameter for a track is defined as the
magnitude of the track vector of closest approach to the primary
vertex signed by the $z$-component of the cross product between this
vector and the track momentum. The impact parameter significance,
\ensuremath{{\mathrm{IPS}}}\xspace, is then defined as the absolute sum of the signed impact
parameters of the two \ensuremath{\tau} lepton\xspace decay product candidates, divided by their
combined uncertainty. The \ensuremath{{\mathrm{IPS}}}\xspace is required to be greater than $9$ for
the \ensuremath{\tau_\mu\tau_\mu}\xspace, \ensuremath{\tau_\mu\tau_\had}\xspace, and \ensuremath{\tau_e\tau_\had}\xspace analysis streams while no \ensuremath{{\mathrm{IPS}}}\xspace requirement is
placed on the \ensuremath{\tau_\mu\tau_e}\xspace or \ensuremath{\tau_e\tau_\mu}\xspace streams.
In the \ensuremath{\tau_\mu\tau_\mu}\xspace analysis stream an additional background component arises
from $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ events. This produces two muons with similar \ensuremath{p_\mathrm{T}}\xspace,
most of which also have an invariant mass close to the \ensuremath{Z}\xspace mass. In
contrast, signal events tend to have unbalanced \ensuremath{p_\mathrm{T}}\xspace and a lower
invariant mass due to unreconstructed energy from neutrinos and
neutral hadrons. The \ensuremath{p_\mathrm{T}}\xspace asymmetry, \ensuremath{{A_{p_\mathrm{T}}}}\xspace, is defined as the absolute
difference between the \ensuremath{p_\mathrm{T}}\xspace of the two candidates divided by their
sum. For the \ensuremath{\tau_\mu\tau_\mu}\xspace analysis stream the \ensuremath{{A_{p_\mathrm{T}}}}\xspace is required to be greater
than $0.3$ and the di-muon invariant mass must lie outside the range
$80 < M_{\mu\mu} < 100~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$.
\section{Background estimation}\label{sec:bac}
The invariant mass distributions for the selected $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$
candidates, the simulated signal, and the estimated backgrounds for
the five analysis streams are shown in \fig{\ref{fig:mas}}, where no
candidates are observed with a mass above $120~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$. Five types of
background have been considered: generic QCD; electroweak, where a
high \ensuremath{p_\mathrm{T}}\xspace lepton is produced by a \ensuremath{W}\xspace or \ensuremath{Z}\xspace boson and the second
candidate \ensuremath{\tau} lepton\xspace decay product is misidentified from the underlying
event; \ensuremath{{t\bar{t}}}\xspace, where two hard leptons are produced from top decays;
\ensuremath{{WW}}\xspace, where each \ensuremath{W}\xspace decays to a lepton; and $\ensuremath{Z}\xspace \to \ensuremath{\lep\lep}\xspace$ for the
\ensuremath{\tau_\mu\tau_\mu}\xspace, \ensuremath{\tau_\mu\tau_\had}\xspace, and \ensuremath{\tau_e\tau_\had}\xspace streams, where for the \ensuremath{\tau_\mu\tau_\had}\xspace stream a single muon
is misidentified as a hadron and for the \ensuremath{\tau_e\tau_\had}\xspace stream an electron is
misidentified. The \ensuremath{{t\bar{t}}}\xspace and \ensuremath{{WW}}\xspace backgrounds are estimated using
simulation and found to be small for all final states.
\begin{figure}
\newlength{\plotwidth}
\newlength{\plotsep}
\newlength{\capwidth}
\newlength{\capsep}
\setlength{\plotwidth}{0.5\textwidth}
\setlength{\plotsep}{-0.1cm}
\setlength{\capwidth}{2.4cm}
\setlength{\capsep}{-1.6cm}
\begin{center}
\vspace{-1.9cm}
\centerline{
\begin{tabular}{@{\extracolsep{-0.6cm}}cc}
\subfloat[]{\label{fig:mumu}}\hspace{\capwidth} &
\subfloat[]{\label{fig:mue}}\hspace{\capwidth} \\[\capsep]
\includesvg[width=\plotwidth,name=Fig.\arabic{svgfigure}a]
{Z2TauTau2MuMu.Apt.ZMass} &
\includesvg[width=\plotwidth]{Z2TauTau2MuE.Phi.ZMass}
\\[\plotsep]
\subfloat[]{\label{fig:emu}}\hspace{\capwidth} &
\subfloat[]{\label{fig:muh}}\hspace{\capwidth} \\[\capsep]
\includesvg[width=\plotwidth,name=Fig.\arabic{svgfigure}c]
{Z2TauTau2EMu.Phi.ZMass} &
\includesvg[width=\plotwidth]{Z2TauTau2MuPi.Ips.ZMass}
\\[\plotsep]
\subfloat[]{\label{fig:eh}}\hspace{\capwidth} & \\[\capsep]
\includesvg[width=\plotwidth]{Z2TauTau2EPi.Ips.ZMass} & \\
\end{tabular}}
\end{center}
\vspace{-0.95cm}
\caption{Invariant mass distributions for the
\protect\subref{fig:mumu} \ensuremath{\tau_\mu\tau_\mu}\xspace, \protect\subref{fig:mue} \ensuremath{\tau_\mu\tau_e}\xspace,
\protect\subref{fig:emu} \ensuremath{\tau_e\tau_\mu}\xspace, \protect\subref{fig:muh} \ensuremath{\tau_\mu\tau_\had}\xspace, and
\protect\subref{fig:eh} \ensuremath{\tau_e\tau_\had}\xspace candidates with the excluded mass
range indicated for \ensuremath{\tau_\mu\tau_\mu}\xspace. The $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ simulation (solid
red) is normalised to the number of signal events. The \ensuremath{\mathrm{QCD}}\xspace
(horizontal green), electroweak (vertical blue), and \ensuremath{Z}\xspace (solid
cyan) backgrounds are estimated from data. The \ensuremath{{t\bar{t}}}\xspace (vertical
orange) and \ensuremath{{WW}}\xspace (horizontal magenta) backgrounds are estimated
from simulation and generally not visible.\label{fig:mas}}
\end{figure}
The QCD and electroweak backgrounds are estimated from data. A
signal-depleted control sample is created by applying all selection
criteria but requiring that the \ensuremath{\tau} lepton\xspace decay product candidates have the
same-sign (\ensuremath{\mathrm{SS}}\xspace) charge. The QCD and electroweak background events in
this sample, $N_\ensuremath{\mathrm{QCD}}\xspace^\ensuremath{\mathrm{SS}}\xspace$ and $N_\ensuremath{\mathrm{EWK}}\xspace^\ensuremath{\mathrm{SS}}\xspace$, are obtained by fitting
template shapes to the distribution of the difference between the \ensuremath{p_\mathrm{T}}\xspace
of the first and second \ensuremath{\tau} lepton\xspace decay product candidates. The template
shape for the electroweak background is taken from simulation. To
determine the shape of the QCD contribution, the isolation requirement
is reversed such that $\ensuremath{{I_{p_\mathrm{T}}}}\xspace > 10~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$. The number of candidates for
each background category in the signal sample is then calculated as
$N_\ensuremath{\mathrm{QCD}}\xspace = f_\ensuremath{\mathrm{QCD}}\xspace N^\ensuremath{\mathrm{SS}}\xspace_\ensuremath{\mathrm{QCD}}\xspace$ and $N_\ensuremath{\mathrm{EWK}}\xspace = f_\ensuremath{\mathrm{EWK}}\xspace N^\ensuremath{\mathrm{SS}}\xspace_\ensuremath{\mathrm{EWK}}\xspace$, where
$f_\ensuremath{\mathrm{QCD}}\xspace$ and $f_\ensuremath{\mathrm{EWK}}\xspace$ are the ratio of opposite-sign to same-sign
events for QCD and electroweak events respectively. Both $f_\ensuremath{\mathrm{QCD}}\xspace$ and
$f_\ensuremath{\mathrm{EWK}}\xspace$ are determined as the ratio of opposite-sign to same-sign
events satisfying the template requirements. The uncertainties on the
\ensuremath{\mathrm{QCD}}\xspace and electroweak backgrounds are estimated by combining the
statistical uncertainty on the fraction with the uncertainties from
the fit used to determine $N_\ensuremath{\mathrm{QCD}}\xspace^\ensuremath{\mathrm{SS}}\xspace$ and $N_\ensuremath{\mathrm{EWK}}\xspace^\ensuremath{\mathrm{SS}}\xspace$.
The number of $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ background events for the \ensuremath{\tau_\mu\tau_\mu}\xspace stream is
obtained by applying all selection criteria except for the $80 <
M_{\mu\mu} < 100~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$ requirement. This produces a sample with a
clear peak around the \ensuremath{Z}\xspace mass as shown in \fig{\subref*{fig:mumu}}. A
template for $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ events is obtained from data by applying
the event selection, but requiring prompt events with $\ensuremath{{\mathrm{IPS}}}\xspace < 1$. The
template is normalised to the number of events within the \ensuremath{\tau_\mu\tau_\mu}\xspace sample
with $\ensuremath{{\mathrm{IPS}}}\xspace > 9$ and within the invariant mass range $80 < M_{\mu\mu} <
100~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$. The $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ background is the number of events in
the normalised template outside this mass range. The uncertainty on
this background is estimated from the statistical uncertainty on the
normalisation factor.
The $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ process also contributes a small background to the
\ensuremath{\tau_\mu\tau_\had}\xspace stream when one of the muons is misidentified as a hadron. This
is evaluated by applying the \ensuremath{\tau_\mu\tau_\had}\xspace selection but requiring a second
identified muon rather than a hadron, and scaling this by the
probability for a muon to be misidentified as a hadron. The latter is
found from a sample of $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ events that have been selected
by requiring a single well defined muon and a second isolated track,
which give an invariant mass between $80$ and $100~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$; \prc{0.06
\pm 0.01} of these tracks pass the hadron identification
requirement.
Similarly, a small $\ensuremath{Z}\xspace \to \ensuremath{ee}\xspace$ background can contribute to the \ensuremath{\tau_e\tau_\had}\xspace
stream when one of the electrons is misidentified as a hadron. This
is evaluated by applying the \ensuremath{\tau_e\tau_\had}\xspace selection but requiring a second
identified electron rather than a hadron, and scaling this by the
probability for an electron to be misidentified as a hadron. The
electron mis-identification is found from simulated $\ensuremath{Z}\xspace \to \ensuremath{ee}\xspace$
events to be \prc{0.63 \pm 0.02}.
\section{Introduction}\label{sec:int}
The measurement of the production cross-section for \ensuremath{Z}\xspace
bosons\footnote{Here, the \ensuremath{Z}\xspace is used to indicate production from \ensuremath{Z}\xspace
bosons, photons, and their interference.} in proton-proton ($pp$)
collisions constitutes an important verification of Standard Model
predictions. Since lepton universality in \ensuremath{Z}\xspace decays has been tested to
better than $1\%$ at LEP~\cite{lep}, any deviation observed at the LHC
would be evidence for additional physics effects producing final state
leptons. In particular, \ensuremath{\tau}-lepton\xspace pairs can be important signatures for
supersymmetry, extra gauge bosons, or extra
dimensions~\cite{susy,gauge,extra}. The LHCb experiment has previously
measured the cross-section for $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$~\cite{lhcb} with both
leptons having transverse momentum (\ensuremath{p_\mathrm{T}}\xspace) above $20~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$ and an
invariant mass between $60$ and $120~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c^2}\xspace$. Here a complementary
measurement in the decay mode $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ is presented. This
measurement extends the $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ cross-section measurements
from the central pseudorapidity range covered by ATLAS\xspace
$\left(\abs{\eta} < 2.4\right)$~\cite{atlas} and CMS\xspace
$\left(\abs{\eta} < 2.3\right)$~\cite{cms} into the forward region
covered by the LHCb\xspace experiment $(2 < \eta < 4.5)$.
\section{Detector and datasets}\label{sec:det}
The LHCb\xspace detector~\cite{detector} is a single-arm forward
spectrometer designed for the study of particles containing $b$ or $c$
quarks. The detector includes a high precision tracking system
consisting of a silicon-strip vertex detector (\ensuremath{\mathrm{VELO}}\xspace) surrounding the
$pp$ interaction region, a large-area silicon-strip detector (\ensuremath{\mathrm{TT}}\xspace)
located upstream of a dipole magnet with a bending power of about
$4~\mathrm{Tm}$, and three stations of silicon-strip detectors (\ensuremath{\mathrm{IT}}\xspace)
and straw drift tubes (\ensuremath{\mathrm{OT}}\xspace) placed downstream. The combined tracking
system has a momentum resolution $\Delta p/p$ that varies from $0.4\%$
at $5~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$ to $0.6\%$ at $100~\ensuremath{\mathrm{Ge\kern -0.1em V\!/}c}\xspace$, and an impact parameter
resolution of $20~\mu\mathrm{m}$ for tracks with high \ensuremath{p_\mathrm{T}}\xspace.
Charged hadrons are identified using two ring-imaging Cherenkov
detectors. Photon, electron and hadron candidates are identified by a
calorimeter system consisting of scintillating-pad (\ensuremath{\mathrm{SPD}}\xspace) and
pre-shower detectors (\ensuremath{\mathrm{PRS}}\xspace), an electromagnetic calorimeter (\ensuremath{\mathrm{ECAL}}\xspace)
and a hadronic calorimeter (\ensuremath{\mathrm{HCAL}}\xspace). Muons are identified by a system
composed of alternating layers of iron and multiwire proportional
chambers. The trigger consists of a hardware stage, based on
information from the calorimeter and muon systems, followed by a
software stage that applies a full event reconstruction. The hardware
stage imposes a global event requirement (\ensuremath{\mathrm{GEC}}\xspace) on the hit
multiplicities of most sub-detectors used in the pattern recognition
algorithms to avoid overloading of the software trigger by high
occupancy events.
This analysis uses data, corresponding to an integrated luminosity of
$1028 \pm 36~\ensuremath{\mathrm{pb}^{-1}}\xspace$, taken at a centre-of-mass energy of $7~\ensuremath{\mathrm{Te\kern -0.1em V}}\xspace$. The
absolute luminosity scale was measured periodically throughout the
data taking period using Van der Meer scans~\cite{scan} where the beam
profile is determined by moving the beams transversely across one
another. A beam-gas imaging method was also used where the beam
profile is determined through reconstructing beam-gas interaction
vertices near the beam crossing point~\cite{gas}. Both methods provide
similar results and the integrated luminosity is determined from the
average of the two, with an estimated systematic uncertainty of
$3.5\%$~\cite{lumi}. The primary systematic uncertainty of $2.7\%$ is
due to the beam current measurement, shared between the two methods.
Simulated data samples are used to develop the event selection,
determine efficiencies, and estimate systematic uncertainties. Each
sample was generated using an LHCb\xspace configuration~\cite{tune} of
{\sc Pythia}\xspace $6.4$~\cite{pythia6} with the {CTEQ$6$L$1$}\xspace leading-order PDF
set~\cite{cteq} and passed through a {\sc Geant4}\xspace~\cite{geanta, *geantb}
based simulation of the LHCb\xspace detector~\cite{gauss}. Trigger emulation
and full event reconstruction were performed using the LHCb\xspace
reconstruction software~\cite{brunel}. Additional samples, without
detector simulation or event reconstruction, are used to study the
signal acceptance and were generated using {\sc Pythia}\xspace
$8.1.55$~\cite{pythia8}, {\sc Herwig++}\xspace $2.5.1$~\cite{herwig}, and {\sc Herwig++}\xspace
with the {\sc Powheg}\xspace method~\cite{powheg}.
\section*{Acknowledgements}
\noindent We express our gratitude to our colleagues in the CERN
accelerator departments for the excellent performance of the LHC. We
thank the technical and administrative staff at the LHCb
institutes. We acknowledge support from CERN and from the national
agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China);
CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF and MPG
(Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands);
SCSR (Poland); ANCS/IFA (Romania); MinES, Rosatom, RFBR and NRC
``Kurchatov Institute'' (Russia); MinECo, XuntaGal and GENCAT (Spain);
SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United
Kingdom); NSF (USA). We also acknowledge the support received from the
ERC under FP7. The Tier1 computing centres are supported by IN2P3
(France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The
Netherlands), PIC (Spain), GridPP (United Kingdom). We are thankful
for the computing resources put at our disposal by Yandex LLC
(Russia), as well as to the communities behind the multiple open
source software packages that we depend on.
\section{Results}\label{sec:res}
The cross-sections for each analysis stream are determined using
\equ{\ref{equ:xs}}, the values given in \tab{\ref{tab:mea}}, and the
systematic uncertainties presented in \tab{\ref{tab:unc}}. The results
are
\begin{equation*}
\begin{aligned}
\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace} ~ (\ensuremath{\tau_\mu\tau_\mu}\xspace) ~ &= 77.4 \pm 10.4 \pm 8.6 \pm 2.7 ~\ensuremath{\mathrm{pb}}\xspace \\
\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace} ~ (\ensuremath{\tau_\mu\tau_e}\xspace ) ~ &= 75.2 \pm \phantom{1}5.4 \pm 4.1 \pm 2.6 ~\ensuremath{\mathrm{pb}}\xspace \\
\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace} ~ (\ensuremath{\tau_e\tau_\mu}\xspace ) ~ &= 64.2 \pm \phantom{1}8.2 \pm 4.9 \pm 2.2 ~\ensuremath{\mathrm{pb}}\xspace \\
\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace} ~ (\ensuremath{\tau_\mu\tau_\had}\xspace ) ~ &= 68.3 \pm \phantom{1}7.0 \pm 2.6 \pm 2.4 ~\ensuremath{\mathrm{pb}}\xspace \\
\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace} ~ (\ensuremath{\tau_e\tau_\had}\xspace ) ~ &= 77.9 \pm 12.2 \pm 6.1 \pm 2.7 ~\ensuremath{\mathrm{pb}}\xspace \\
\end{aligned}
\end{equation*}
where the first uncertainty is statistical, the second uncertainty is
systematic, and the third is due to the uncertainty on the integrated
luminosity.
A global fit is performed using a best linear unbiased
estimator~\cite{blue} including correlations between the final states,
and a combined result of
\begin{equation*}
\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace} = 71.4 \pm 3.5 \pm 2.8 \pm 2.5 ~\ensuremath{\mathrm{pb}}\xspace
\end{equation*}
is obtained, with a $\chi^2$ per degree of freedom of $0.43$. The
statistical uncertainties are assumed to be uncorrelated as each
analysis stream contains mutually exclusive datasets. The luminosity
and any shared selection or reconstruction efficiencies are assumed to
be fully correlated.
A graphical summary of the individual final state measurements, the
combined measurement, the $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ measurement of
\rfr{\cite{lhcb}}, and a theory prediction is shown in
\fig{\ref{fig:sum}}. The theory calculation uses {\sc Dynnlo}\xspace~\cite{dynnlo}
with the {MSTW$08$}\xspace next-to-next-leading-order (NNLO) PDF set~\cite{mstw},
and is found to be $74.3^{+1.9}_{-2.1}~\ensuremath{\mathrm{pb}}\xspace$.
The ratio of the combined cross-section to the LHCb\xspace $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$
cross-section measurement~\cite{lhcb} is found to be
\begin{equation*}
\frac{\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace}}{\sigma_{pp \to \ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace}}
= 0.93 \pm 0.09
\end{equation*}
where the uncertainty is the combined statistical, systematic, and
luminosity uncertainties from both measured cross-sections, which are
assumed to be uncorrelated.
\begin{figure}[h]
\begin{center}
\includesvg[width=\columnwidth]{summary}
\end{center}
\caption{Measured cross-sections for the \ensuremath{Z}\xspace decaying to the final
states \ensuremath{\tau_\mu\tau_\mu}\xspace, \ensuremath{\tau_\mu\tau_e}\xspace, \ensuremath{\tau_e\tau_\mu}\xspace, \ensuremath{\tau_\mu\tau_\had}\xspace, and \ensuremath{\tau_e\tau_\had}\xspace (open points) compared
with theory (yellow band) and the combined $\ensuremath{Z}\xspace \to \ensuremath{\tau\tau}\xspace$ and
LHCb\xspace $\ensuremath{Z}\xspace \to \ensuremath{\mu\mu}\xspace$ measurements (closed points) where \ensuremath{p_\mathrm{T}}\xspace and
$\eta$ are the transverse momentum and pseudorapidity of the
leptons, and $M$ is the di-lepton invariant mass. The inner error
bars represent statistical uncertainty while the outer error bars
represent combined statistical, systematic, and luminosity
uncertainties. The central theory value is given by the light
yellow line while the associated uncertainty by the orange
band.\label{fig:sum}}
\end{figure}
\afterpage{\clearpage}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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\section{Introduction}
In his seminal papers \cite{howe1, howe2}, Howe introduced the notion of reductive dual pairs and developed the theory of theta lifting, which has been an important subject in the representation theory of real and $p$-adic reductive groups for more than $40$ years and which has many arithmetic applications to the theory of automorphic forms.
The theta lifting is defined as a correspondence between representations of the two groups in a reductive dual pair in terms of the restriction of the Weil representation \cite{weil1}.
In fact, it is shown that this correspondence is one-to-one by Howe himself \cite{howe2} in the real case and by Gan--Takeda \cite{gt} in the $p$-adic case, following earlier work of Howe \cite{howe1} and Waldspurger \cite{wal} for $p \ne 2$.
For the history and recent development of the theta lifting, the reader can consult the ICM report of Gan \cite{gan}.
In the theory of theta lifting, one of the basic problems is to describe it explicitly.
We consider this problem in the real case, which has been studied by M{\oe}glin \cite{moeglin89}, Li \cite{li90}, Adams--Barbasch \cite{ab1, ab2}, Paul \cite{paul1, paul2, paul3}, Li--Paul--Tan--Zhu \cite{lptz} to mention a few, but which has not been solved in general.
In this paper, we focus on the case of the reductive dual pair $(\U(p,q),\U(r,s))$ consisting of real unitary groups.
Recall the Weil representation $\omega$ of $\Mp_{2l}(\R)$ (relative to a fixed nontrivial character of $\R$), where $l = (p+q)(r+s)$ and $\Mp_{2l}(\R)$ is the metaplectic cover of the symplectic group $\Sp_{2l}(\R)$ of rank $l$.
Via the choice of a lift
\begin{align*}
\U(p,q) \times \U(r,s) & \rightarrow \Mp_{2l}(\R) \\
\shortintertext{of a natural homomorphism}
\U(p,q) \times \U(r,s) & \rightarrow \Sp_{2l}(\R),
\end{align*}
we may regard $\omega$ as a representation of $\U(p,q) \times \U(r,s)$.
Then for any irreducible representation $\pi$ of $\U(p,q)$, its theta lift to $\U(r,s)$ is defined as an irreducible representation $\theta_{r,s}(\pi)$ of $\U(r,s)$ such that
\[
\Hom_{\U(p,q) \times \U(r,s)}(\omega, \pi \boxtimes \theta_{r,s}(\pi)) \ne 0,
\]
which is uniquely determined (if exists) by the Howe duality \cite{howe2}.
If such a representation does not exist, we interpret $\theta_{r,s}(\pi)$ as zero.
When $p+q \le r+s$ and $\pi$ is a discrete series representation with sufficiently regular infinitesimal character, Li \cite{li90} showed that $\theta_{r,s}(\pi)$ is nonzero and expressed it as a cohomologically induced representation in the good range.
When $p+q=r+s$ or $p+q=r+s \pm 1$, Paul \cite{paul1, paul2} generalized his result and completely determined $\theta_{r,s}(\pi)$ for arbitrary $\pi$.
The purpose of this paper is to describe $\theta_{r,s}(\pi)$ explicitly when $\pi$ is tempered but for arbitrary $p,q,r,s$.
For this, we first prove the following generalization of \cite{li90} to the case of (limits of) discrete series representations (see Theorem \ref{t:main-lds} for more details).
\begin{thm}
\label{t:intro}
Let $\pi$ be a (limit of) discrete series representation of $\U(p,q)$.
Assume that its theta lift $\theta_{r,s}(\pi)$ to $\U(r,s)$ is nonzero.
Then we have
\[
\theta_{r,s}(\pi) = A_\q(\lambda),
\]
where the right-hand side is a cohomologically induced representation in the weakly fair range, and $\q$ and $\lambda$ can be described explicitly.
Moreover, if $p+q \ge r+s-1$, then $\theta_{r,s}(\pi)$ is a (limit of) discrete series representation.
\end{thm}
We have stated the result under the assumption that $\theta_{r,s}(\pi)$ is nonzero, but there is a combinatorial criterion for the nonvanishing of $\theta_{r,s}(\pi)$ due to Atobe \cite{atobe} (see also \S \ref{s:atobe}).
Based on this theorem, we can describe $\theta_{r,s}(\pi)$ explicitly for any tempered representation $\pi$ (see Theorem \ref{t:main-temp} for more details).
We now give some details of the proof of Theorem \ref{t:intro}.
Our proof is global and relies on Arthur's endoscopic classification \cite{arthur,mok,kmsw}.
Thus our main result is conditional on Arthur's multiplicity formula for the automorphic discrete spectra of unitary groups announced by Kaletha--M\'inguez--Shin--White \cite{kmsw} (see \eqref{eq:amf} for details), whose proof will be completed in their subsequent work.
We first globalize the given local theta lift for real unitary groups.
Namely, we find a global theta lift such that
\begin{itemize}
\item at one real place, its localization is the theta lift of an arbitrary (limit of) discrete series representation;
\item at another real place, its localization is the theta lift of a discrete series representation with sufficiently regular infinitesimal character, which is determined explicitly by Li \cite{li90};
\item at the other places, its localizations are easy to describe explicitly.
\end{itemize}
Then we use Arthur's multiplicity formula (viewed as a product formula) to transfer the information from the case of sufficiently regular infinitesimal character to the general case.
However, there is a difficulty in this argument: it is not straightforward to globalize a local theta lift for real unitary groups.
More precisely, let $\pi$ be a (limit of) discrete series representation of $\U(p,q)$ and consider its theta lift $\theta_{r,s}(\pi)$ to $\U(r,s)$.
Switching the roles of $\U(p,q)$ and $\U(r,s)$ if necessary, we may assume that $p+q < r+s$.
Let $F \ne \Q$ be a totally real number field with ad\`ele ring of $\A$ and fix a real place $v_0$ of $F$.
Then it is easy to find
\begin{itemize}
\item anisotropic unitary groups $G$ and $H$ over $F$ such that $G_{v_0} = \U(p,q)$ and $H_{v_0} = \U(r,s)$, respectively;
\item an irreducible automorphic representation of $G(\A)$ such that $\varPi_{v_0} = \pi$.
\end{itemize}
But we need $G,H,\varPi$ such that the global theta lift $\theta(\varPi)$ to $H(\A)$ is nonzero.
For this, we proceed as follows.
\begin{enumerate}
\item
\label{item:intro1}
Find $G,H,\varPi$ such that the local theta lift $\theta(\varPi_v)$ to $H_v$ is nonzero for all places $v$ of $F$.
\item
\label{item:intro2}
Show that $\theta(\varPi)$ is nonzero if and only if $\theta(\varPi_v)$ is nonzero for all $v$.
\end{enumerate}
To show that $G,H,\varPi$ as in \eqref{item:intro1} exist, we appeal to Arthur's multiplicity formula.
In fact, we may impose further local conditions on $G,H,\varPi$ to make the global-to-local argument work.
On the other hand, \eqref{item:intro2} is largely but not completely known for unitary groups (see \cite[Theorem 1.3]{gqt}).
Indeed, the standard argument relies on the Rallis inner product formula, which involves the local integral at $v_0$ given by
\[
\int_{\U(p,q)} (\omega(g) \varphi_1, \varphi_2) \overline{(\pi(g)v_1, v_2)} \, dg
\]
for $\varphi_1, \varphi_2 \in \omega$ and $v_1, v_2 \in \pi$.
Here $(\cdot, \cdot)$ denotes an invariant Hermitian inner product.
This integral is absolutely convergent and defines an invariant functional
\[
\ZZ_{r,s}(\pi) : \omega \otimes \bar{\omega} \otimes \bar{\pi} \otimes \pi \rightarrow \C.
\]
Then we have $\theta_{r,s}(\pi) \ne 0$ if $\ZZ_{r,s}(\pi) \ne 0$, and we are reduced to proving the converse.
However, it was previously only known that if $\theta_{r,s}(\pi) \ne 0$, then $\ZZ_{r', s'}(\pi) \ne 0$ for some $r', s'$ such that $r'+s'=r+s$ and $r' \equiv r \bmod 2$ (see \cite[Proposition 11.5]{gqt}).
Thus we need to prove the following (see Proposition \ref{p:key}), which is the key innovation in this paper.
\begin{prop}
\label{p:intro}
We have
\[
\ZZ_{r,s}(\pi) \ne 0 \, \Leftrightarrow \, \theta_{r,s}(\pi) \ne 0.
\]
\end{prop}
To prove this proposition, we modify an inductive argument of Atobe \cite{atobe} for the nonvanishing of $\theta_{r,s}(\pi)$, which relies on the Gan--Gross--Prasad conjecture \cite{ggp1} proved by Xue \cite{xue}.
Indeed, if $\theta_{r,s}(\pi) \ne 0$, then we can deduce that there exists a discrete series representation $\pi'$ of $\U(p+1,q)$ such that $\theta_{r,s}(\pi') \ne 0$ and $\Hom_{\U(p,q)}(\pi',\pi) \ne 0$.
In particular, by a result of Beuzart-Plessis \cite{bp}, we have
\begin{equation}
\label{eq:bp}
\int_{\U(p,q)} (\pi'(g) v'_1, v'_2) \overline{(\pi(g) v_1, v_2)} \,dg \ne 0
\end{equation}
for some $v'_1, v'_2 \in \pi'$ and $v_1, v_2 \in \pi$.
On the other hand, if we write $\omega'$ for the Weil representation of $\U(p+1,q) \times \U(r,s)$, then matrix coefficients of $\omega'$ (regarded as functions on $\U(p+1,q)$) belong to the Harish-Chandra Schwartz space $\CC(\U(p+1,q))$.
Since we may assume that $\ZZ_{r,s}(\pi') \ne 0$ by induction on $(r+s) - (p+q)$, the projection of these matrix coefficients to the $\pi' \boxtimes \bar{\pi}'$-isotypic component of $\CC(\U(p+1,q))$ is nonzero and hence dense.
This combined with \eqref{eq:bp} implies that
\[
\int_{\U(p,q)} (\omega'(g) \varphi'_1, \varphi'_2) \overline{(\pi(g) v_1, v_2)} \,dg \ne 0
\]
for some $\varphi'_1, \varphi'_2 \in \omega'$, from which Proposition \ref{p:intro} follows easily.
We stress that the proof is local and does not rely on Arthur's endoscopic classification, so that Proposition \ref{p:intro} is unconditional.
\subsection*{Acknowledgements}
The author is partially supported by JSPS KAKENHI Grant Number 19H01781.
He would like to thank Hiraku Atobe, Rapha\"el Beuzart-Plessis, Wee Teck Gan, and Hang Xue for useful discussions.
He would also like to thank the referee for helpful comments.
\subsection*{Notation}
For any representation $\pi$, we denote by $\pi^\vee$ the contragredient of $\pi$ and by $\bar{\pi}$ the complex conjugate of $\pi$.
For any real reductive group $G$, we work with the category of $(\g,K)$-modules unless otherwise specified, where $\g$ is the complexified Lie algebra of $G$ and $K$ is a maximal compact subgroup of $G$.
Thus by abuse of terminology, we usually mean a $(\g,K)$-module by a representation of $G$.
\section{Local theta lifting}
In this section, we review the notion of local theta lifting.
We follow the convention in \cite{gi1, gi2}, which is different from that in \cite{kudla,hks}.
\subsection{Hermitian and skew-Hermitian spaces}
\label{ss:herm-spaces}
Let $F$ be a local field of characteristic zero.
Let $E$ be an \'etale quadratic algebra over $F$, so that $E$ is either $F \times F$ or a quadratic extension of $F$.
We denote by $c$ the nontrivial automorphism of $E$ over $F$.
Let $\Tr_{E/F}$ and $\operatorname{N}_{E/F}$ be the trace and norm maps from $E$ to $F$, respectively.
Let $\omega_{E/F}$ be the (possibly trivial) quadratic character of $F^\times$ associated to $E/F$ by local class field theory, so that $\operatorname{Ker}(\omega_{E/F}) = \operatorname{N}_{E/F}(E^\times)$.
Fix an element $\delta \in E^\times$ such that $\Tr_{E/F}(\delta) = 0$.
Fix $\varepsilon = \pm 1$.
Let $V$ be an $n$-dimensional $\varepsilon$-Hermitian space over $E$.
Namely, $V$ is a free $E$-module of rank $n$ equipped with a nondegenerate sesquilinear form $\langle \cdot, \cdot \rangle_V : V \times V \rightarrow E$ satisfying
\[
\langle a v, b w \rangle_V = a b^c \langle v, w \rangle_V, \quad
\langle w, v \rangle_V = \varepsilon \langle v, w \rangle_V^c
\]
for $a, b \in E$ and $v, w \in V$.
Let $\det(V) \in E^\times / \operatorname{N}_{E/F}(E^\times)$ be the determinant of the matrix
\[
(\langle v_i, v_j \rangle_V)_{1 \le i,j \le n},
\]
where $v_1, \dots, v_n$ is a basis of $V$.
Define $\epsilon(V) = \pm 1$ by
\[
\epsilon(V) =
\begin{cases}
\omega_{E/F}((-1)^{\frac{1}{2}n(n-1)} \cdot \det(V)) & \text{if $\varepsilon = +1$;} \\
\omega_{E/F}((-1)^{\frac{1}{2}n(n-1)} \cdot \det(V) \cdot \delta^{-n}) & \text{if $\varepsilon = -1$.}
\end{cases}
\]
Note that $\epsilon(V)$ depends on $\delta$ if $\varepsilon = -1$, $E \ne F \times F$, and $n$ is odd.
We denote by $\U(V)$ the unitary group of $V$, i.e.
\[
\U(V) = \{ g \in \GL(V) \, | \, \text{$\langle gv, gw \rangle_V = \langle v, w \rangle_V$ for all $v, w \in V$} \}.
\]
Recall that given a positive integer $n$, the $n$-dimensional $\varepsilon$-Hermitian spaces over $E$ (up to isometry) are classified as follows.
\begin{itemize}
\item
If $E = F \times F$, then there is a unique such space.
We denote it by $V_n^+$.
Then we have $\epsilon(V_n^+) = +1$ and $V_n^+ = \VV_n \otimes_F E$ for some $n$-dimensional vector space $\VV_n$ over $F$.
Moreover, the first projection $V_n^+ = \VV_n \times \VV_n \rightarrow \VV_n$ induces an isomorphism $\U(V_n^+) \cong \GL(\VV_n)$.
\item
If $F$ is nonarchimedean and $E \ne F \times F$, then there are precisely two such spaces, which are distinguished by their signs.
We denote them by $V_n^+$ and $V_n^-$ so that $\epsilon(V_n^+) = +1$ and $\epsilon(V_n^-) = -1$.
\item
If $F = \R$ and $E = \C$, then there are precisely $n+1$ such spaces, which are distinguished by their signatures.
We denote by $V_{p,q}$ the space of signature $(p,q)$, where $p,q$ are nonnegative integers such that $p+q=n$.
More precisely, we require that $V_{p,q}$ has a basis $v_1, \dots, v_n$ such that
\[
\langle v_i, v_j \rangle_{V_{p,q}} = \zeta \times
\begin{cases}
1 & \text{if $i = j \le p$;} \\
-1 & \text{if $i = j > p$;} \\
0 & \text{if $i \ne j$,}
\end{cases}
\]
where
\[
\zeta =
\begin{cases}
1 & \text{if $\varepsilon = +1$;} \\
\sqrt{-1} & \text{if $\varepsilon = -1$.}
\end{cases}
\]
Then we have
\[
\epsilon(V_{p,q}) = (-1)^{\frac{1}{2}(p-q)(p-q-1)}
\]
if we take $\delta = \sqrt{-1}$.
For uniformity, we write
\[
V_n^+ =
\begin{cases}
V_{\frac{n}{2}, \frac{n}{2}} & \text{if $n$ is even;} \\
V_{\frac{n+1}{2}, \frac{n-1}{2}} & \text{if $n$ is odd.}
\end{cases}
\]
\end{itemize}
Note that $\U(V_n^+)$ is quasi-split over $F$.
\subsection{Theta lifts}
Let $V$ be an $m$-dimensional Hermitian space over $E$ and $W$ an $n$-dimensional skew-Hermitian space over $E$.
We regard $\W = V \otimes_E W$ as a vector space over $F$ and equip it with the symplectic form given by
\[
\langle \hspace{-1mm} \langle v_1 \otimes w_1, v_2 \otimes w_2 \rangle \hspace{-1mm} \rangle = \Tr_{E/F}(\langle v_1, v_2 \rangle_V \langle w_1, w_2 \rangle_W).
\]
Let $\Sp(\W)$ be the symplectic group of $\W$ and $\Mp(\W)$ the metaplectic $\C^1$-cover of $\Sp(\W)$.
Then it follows from \cite{kudla,hks} that the natural homomorphism $\U(V) \times \U(W) \rightarrow \Sp(\W)$ has a lift
\[
\iota_{V,W,\chi_V,\chi_W,\psi} : \U(V) \times \U(W) \rightarrow \Mp(\W)
\]
which depends on the choice of the following datum:
\begin{itemize}
\item two unitary characters $\chi_V, \chi_W$ of $E^\times$ such that
\[
\chi_V|_{F^\times} = \omega_{E/F}^m, \quad
\chi_W|_{F^\times} = \omega_{E/F}^n;
\]
\item a nontrivial additive character $\psi$ of $F$.
\end{itemize}
Composing this with the Weil representation $\omega_\psi$ of $\Mp(\W)$ relative to $\psi$, we obtain a representation
\[
\omega_{V, W, \chi_V, \chi_W, \psi} = \omega_\psi \circ \iota_{V, W, \chi_V, \chi_W, \psi}
\]
of $\U(V) \times \U(W)$.
Note that if we apply the construction to the spaces $W$ and $V$ equipped with the Hermitian form $\delta^{-1} \langle \cdot, \cdot \rangle_W$ and the skew-Hermitian form $\delta \langle \cdot, \cdot \rangle_V$, respectively, then we obtain the representation
\[
\omega_{V, W, \chi_V, \chi_W, \psi} \circ \mathrm{sw},
\]
where $\mathrm{sw}: \U(W) \times \U(V) \rightarrow \U(V) \times \U(W)$ switches factors.
In particular, we can freely switch the roles of $V$ and $W$.
For any irreducible representation $\pi$ of $\U(W)$, we denote by $\theta_{V, W, \chi_V, \chi_W, \psi}(\pi)$ its theta lift to $\U(V)$, i.e.~an irreducible representation of $\U(V)$ such that
\[
\Hom_{\U(V) \times \U(W)}(\omega_{V,W,\chi_V,\chi_W,\psi}, \theta_{V, W, \chi_V, \chi_W, \psi}(\pi) \boxtimes \pi) \ne 0,
\]
which is uniquely determined (if exists) by the Howe duality \cite{howe2,wal,minguez,gt}.
If such a representation does not exist, we interpret $\theta_{V, W, \chi_V, \chi_W, \psi}(\pi)$ as zero.
\section{Representations of real unitary groups}
In this section, we introduce some representations of real unitary groups which will be needed in this paper.
\subsection{Real unitary groups}
\label{ss:real-notation}
Fix $\varepsilon = \pm 1$.
Let $V$ be an $n$-dimensional $\varepsilon$-Hermitian space over $\C$ of signature $(p,q)$, so that $p + q = n$.
Let $G = \U(V)$ be the unitary group of $V$, which we identify with
\[
\U(p,q) = \left\{ g \in \GL_n(\C) \, \left| \, {}^t \bar{g}
\begin{pmatrix}
\1_p & \\
& -\1_q
\end{pmatrix}
g =
\begin{pmatrix}
\1_p & \\
& -\1_q
\end{pmatrix}
\right. \right\}
\]
via the basis as in \S \ref{ss:herm-spaces}
Define a Cartan involution $\theta$ of $G$ by
\[
\theta(g) = {}^t \bar{g}^{-1}
\]
and let $K = \{ g \in G \, | \, \theta(g) = g \}$ be the associated maximal compact subgroup of $G$.
Let $\g_0$ be the Lie algebra of $G$ and $\t_0$ the Cartan subalgebra of $\g_0$ consisting of diagonal matrices.
Let $\g = \g_0 \otimes_\R \C$ and $\t = \t_0 \otimes_\R \C$ be their complexifications.
We identify $\t$ with $\C^n$ via the isomorphism
\[
(x_1, \dots, x_n) \mapsto \diag(x_1, \dots, x_n)
\]
and $\t^*$ with $\C^n$ via the basis $\varepsilon_1,\dots,\varepsilon_n$ given by
\[
\varepsilon_i(\diag(x_1, \dots, x_n)) = x_i.
\]
Define a bilinear form $\langle \cdot, \cdot \rangle : \t^* \times \t^* \rightarrow \C$ by
\[
\langle \alpha, \beta \rangle = \alpha_1 \beta_1 + \dots + \alpha_n \beta_n
\]
for $\alpha = (\alpha_1,\dots,\alpha_n), \beta = (\beta_1,\dots,\beta_n) \in \t^* \cong \C^n$.
Let $\Delta$ be the set of roots of $\t$ in $\g$, so that
\[
\Delta = \{ \pm(\varepsilon_i - \varepsilon_j) \, | \, 1 \le i < j \le n \}.
\]
Let $\Delta_c$ be the set of compact roots in $\Delta$ and take the positive system $\Delta_c^+$ of $\Delta_c$ given by
\[
\Delta_c^+ = \{ \varepsilon_i - \varepsilon_j \, | \, 1 \le i < j \le p \} \cup \{ \varepsilon_i - \varepsilon_j \, | \, p < i < j \le n \}.
\]
For any subspace $\mathfrak{f}$ of $\g$ stable under the adjoint action of $\t$, we denote by $\Delta(\mathfrak{f})$ the set of roots of $\t$ in $\mathfrak{f}$ and put $\rho(\mathfrak{f}) = \frac{1}{2} \sum_{\alpha \in \Delta(\mathfrak{f})} \alpha$.
\subsection{Parabolically induced representations}
\label{ss:parab-ind}
Let $d$ be a nonnegative integer with $d \le \min \{ p, q \}$.
When $d > 0$, we take elements $v'_1, \dots, v'_d, v''_1, \dots, v''_d \in V$ such that
\[
\langle v'_i, v'_j \rangle_V = \langle v''_i, v''_j \rangle_V = 0, \quad
\langle v'_i, v''_j \rangle_V = \delta_{i,j}
\]
and put
\[
X_i = \C v'_i, \quad
X^*_i = \C v''_i.
\]
Let $V_0$ be the orthogonal complement of $X_1 \oplus \dots \oplus X_d \oplus X_1^* \oplus \dots \oplus X_d^*$ in $V$, so that $V_0$ is an $\varepsilon$-Hermitian space over $\C$ of signature $(p-d,q-d)$.
Let $P = MU$ be the parabolic subgroup of $G$ stabilizing the flag
\[
X_1 \subset X_1 \oplus X_2 \subset \dots \subset X_1 \oplus \dots \oplus X_d,
\]
where $M$ is the Levi component of $P$ stabilizing the flag
\[
X^*_1 \subset X^*_1 \oplus X^*_2 \subset \dots \subset X^*_1 \oplus \dots \oplus X^*_d
\]
and $U$ is the unipotent radical of $P$.
As in the previous subsection, we identify $M \cong \GL(X_1) \times \dots \times \GL(X_d) \times \U(V_0)$ with $(\C^\times)^d \times \U(p-d,q-d)$.
For any characters $\chi_1, \dots, \chi_d$ of $\C^\times$ and any representation $\pi_0$ of $\U(p-d,q-d)$, we write
\[
I(\chi_1, \dots, \chi_d, \pi_0) = \Ind^G_P(\chi_1 \boxtimes \dots \boxtimes \chi_d \boxtimes \pi_0)
\]
for the associated normalized parabolically induced representation.
When $d=0$, we interpret $I(\chi_1, \dots, \chi_d, \pi_0)$ as $\pi_0$.
\subsection{(Limits of) discrete series representations}
\label{ss:lds}
Recall that the discrete series representations of $G$ are parametrized by Harish-Chandra parameters (which are dominant for $\Delta_c^+$)
\[
\lambda = (\lambda_1, \dots, \lambda_n) \in \sqrt{-1} \t_0^*,
\]
where
\begin{itemize}
\item $\lambda_i \in \Z + \frac{n-1}{2}$;
\item $\lambda_i \ne \lambda_j$ if $i \ne j$;
\item $\lambda_1 > \dots > \lambda_p$ and $\lambda_{p+1} > \dots > \lambda_n$.
\end{itemize}
More generally, the (limits of) discrete series representations of $G$ are parametrized by pairs $(\lambda,\Psi)$ consisting of $\lambda \in \sqrt{-1} \t_0^*$ of the form
\begin{equation}
\label{eq:lambda}
\lambda = (\underbrace{\lambda_1, \dots, \lambda_1}_{p_1}, \dots, \underbrace{\lambda_k, \dots, \lambda_k}_{p_k}, \underbrace{\lambda_1, \dots, \lambda_1}_{q_1}, \dots, \underbrace{\lambda_k, \dots, \lambda_k}_{q_k}),
\end{equation}
where
\begin{itemize}
\item $\lambda_i \in \Z + \frac{n-1}{2}$;
\item $\lambda_1 > \dots > \lambda_k$;
\item $p_i, q_j \ge 0$;
\item $(p_i,q_i) \ne (0,0)$ and $|p_i - q_i| \le 1$ for all $i$;
\item $p_1 + \dots + p_k = p$ and $q_1 + \dots + q_k = q$,
\end{itemize}
and a positive system $\Psi$ of $\Delta$ such that
\begin{itemize}
\item $\Delta_c^+ \subset \Psi$;
\item $\langle \lambda, \alpha \rangle \ge 0$ for all $\alpha \in \Psi$;
\item if $\alpha$ is a simple root in $\Psi$ such that $\langle \lambda, \alpha \rangle = 0$, then $\alpha$ is noncompact.
\end{itemize}
Note that if $(\lambda, \Psi)$ corresponds to a discrete series representation, then $\Psi$ is uniquely determined by $\lambda$.
\subsection{Tempered representations}
We say that a character $\chi$ of $\C^\times$ is conjugate-selfdual with sign $+1$ (resp.~$-1$) if $\chi|_{\R^\times} = \mathbbm{1}$ (resp.~$\chi|_{\R^\times} = \omega_{\C/\R}$).
Recall that any irreducible tempered representation of $G$ can be realized as a subrepresentation of $I(\chi_1, \dots, \chi_d, \pi_0)$, where
\begin{itemize}
\item $d$ is a nonnegative integer with $d \le \min \{ p, q \}$;
\item $\chi_1, \dots, \chi_d$ are unitary characters of $\C^\times$;
\item $\pi_0$ is a discrete series representation of $\U(p-d,q-d)$.
\end{itemize}
More precisely, we have the following results of Knapp--Zuckerman \cite{kz1, kz2}.
\begin{lem}
Assume that $p,q > 0$.
Let $\chi$ be a conjugate-selfdual character of $\C^\times$ with sign $(-1)^{n-1}$, so that
\[
\chi(z) = \bigg( \frac{z}{\sqrt{z \bar{z}}} \bigg)^{2 \kappa}
\]
for some $\kappa \in \Z + \frac{n-1}{2}$.
Let $\pi_0$ be a (limit of) discrete series representation of $\U(p-1,q-1)$ associated to a pair $(\lambda_0, \Psi_0)$ as in \S \ref{ss:lds}.
\begin{itemize}
\item
If $\kappa = \lambda_{0,i}$ for some $i$, then $I(\chi,\pi_0)$ is irreducible and is a limit of discrete series representation of $G$.
\item
If $\kappa \ne \lambda_{0,i}$ for all $i$, then we have $I(\chi,\pi_0) = \pi \oplus \pi'$, where $\pi$ and $\pi'$ are distinct limits of discrete series representations of $G$.
\end{itemize}
(See \S \ref{sss:packets-real-lds} below for more explicit description.)
\end{lem}
\begin{lem}
\label{l:irred-temp}
Let $d$ be a nonnegative integer with $d \le \min \{ p, q \}$.
Let $\xi_1, \dots, \xi_d$ be unitary characters of $\C^\times$ which are not conjugate-selfdual with sign $(-1)^{n-1}$.
Let $\pi_0$ be a (limit of) discrete series representation of $\U(p-d,q-d)$.
Then $I(\xi_1, \dots, \xi_d, \pi_0)$ is irreducible and tempered.
\end{lem}
In particular, we may write an irreducible tempered representation $\pi$ of $G$ as
\begin{equation}
\label{eq:temp}
\pi = I(\xi_1, \dots, \xi_d, \pi_0),
\end{equation}
where
\begin{itemize}
\item $d$ is a nonnegative integer with $d \le \min \{ p, q \}$;
\item $\xi_1, \dots, \xi_d$ are unitary characters of $\C^\times$ which are not conjugate-selfdual with sign $(-1)^{n-1}$;
\item $\pi_0$ is a (limit of) discrete series representation of $\U(p-d,q-d)$.
\end{itemize}
\subsection{Cohomologically induced representations}
For $x \in \sqrt{-1} \t_0$, let $\l$ (resp.~$\u$) be the sum of zero (resp.~positive) eigenspaces of $\operatorname{ad}(x)$ in $\g$.
Then $\q = \l \oplus \u$ is a $\theta$-stable parabolic subalgebra of $\g$.
We also write
\[
\q = \q(x)
\]
to indicate the dependence on $x$.
Let $L$ be the normalizer of $\q$ in $G$, so that $\l$ is the complexified Lie algebra of $L$.
If $x$ is of the form
\begin{equation}
\label{eq:x}
x = (\underbrace{x_1,\dots,x_1}_{p_1}, \dots, \underbrace{x_k,\dots,x_k}_{p_k}, \underbrace{x_1,\dots,x_1}_{q_1}, \dots, \underbrace{x_k,\dots,x_k}_{q_k}),
\end{equation}
where
\begin{itemize}
\item $x_i \in \R$;
\item $x_1 > \dots > x_k$;
\item $p_i, q_j \ge 0$;
\item $(p_i,q_i) \ne (0,0)$ for all $i$;
\item $p_1 + \dots + p_k = p$ and $q_1 + \dots + q_k = q$,
\end{itemize}
then we have
\[
L \cong \U(p_1,q_1) \times \dots \times \U(p_k,q_k).
\]
Let $\lambda$ be the differential of a character of $L$ and regard it as an element in $\sqrt{-1} \t_0^*$ by restriction.
We consider a cohomologically induced representation
\[
A_\q(\lambda)
\]
defined by \cite[(5.6)]{kv}.
The following summarizes some basic properties of $A_\q(\lambda)$.
\begin{itemize}
\item
The infinitesimal character of $A_\q(\lambda)$ is $\lambda+\rho$.
Here we choose a positive system $\Delta^+$ of $\Delta$ containing $\Delta(\u)$ and put $\rho = \frac{1}{2} \sum_{\alpha \in \Delta^+} \alpha$.
\item
If $\lambda$ is in the good range, i.e.
\[
\langle \lambda + \rho, \alpha \rangle > 0
\]
for all $\alpha \in \Delta(\u)$, then $A_\q(\lambda)$ is nonzero and irreducible.
(Note that this condition does not depend the choice of $\rho$.)
\item
If $\lambda$ is in the weakly fair range, i.e.
\[
\langle \lambda + \rho(\u), \alpha \rangle \ge 0
\]
for all $\alpha \in \Delta(\u)$, then $A_\q(\lambda)$ is unitary (but possibly zero).
\end{itemize}
We also have the following, which is special to unitary groups.
\begin{itemize}
\item
If $\lambda$ is in the weakly fair range and $A_\q(\lambda)$ is nonzero, then it is irreducible by \cite{matumoto, trapa}.
\item
There is an algorithm due to Trapa \cite{trapa} which determines the nonvanishing and the Langlands parameter of $A_\q(\lambda)$ with $\lambda$ in the weakly fair range.
\end{itemize}
Moreover, we have the following irreducibility result of Matumoto \cite[Theorem 3.3.1(2)]{matumoto}.
\begin{lem}
\label{l:irred-cohom}
Let $d$ be a nonnegative integer with $d \le \min \{ p, q \}$.
Let $\xi_1, \dots, \xi_d$ be unitary characters of $\C^\times$ which are not conjugate-selfdual with sign $(-1)^{n-1}$.
Let $\pi_0$ be a cohomologically induced representation of $\U(p-d,q-d)$ which is weakly fair and nonzero.
Then $I(\xi_1, \dots, \xi_d, \pi_0)$ is irreducible.
\end{lem}
In this paper, we will use a normalized version of $A_\q(\lambda)$, which makes the statement of the main theorems cleaner.
Put
\[
{\mathstrut}^n \! A_\q(\lambda) = A_\q(\lambda - \rho(\u)),
\]
where if $x$ is of the form \eqref{eq:x}, then $\lambda \in \sqrt{-1} \t_0^*$ is of the form
\[
\lambda = (\underbrace{\lambda_1,\dots,\lambda_1}_{p_1}, \dots, \underbrace{\lambda_k,\dots,\lambda_k}_{p_k}, \underbrace{\lambda_1,\dots,\lambda_1}_{q_1}, \dots, \underbrace{\lambda_k,\dots,\lambda_k}_{q_k})
\]
with $\lambda_i \in \Z + \frac{1}{2}(n-p_i-q_i)$.
Then
\begin{itemize}
\item
${\mathstrut}^n \! A_\q(\lambda)$ is good if and only if $\lambda_i \ge \lambda_{i+1} + \frac{1}{2}(p_i + q_i + p_{i+1} + q_{i+1})$ for all $i$;
\item
${\mathstrut}^n \! A_\q(\lambda)$ is weakly fair if and only if $\lambda_i \ge \lambda_{i+1}$ for all $i$,
\end{itemize}
noting that
\[
\rho - \rho(\u) = (\alpha^{(1)}_1, \dots, \alpha^{(1)}_{p_1}, \dots, \alpha^{(k)}_1, \dots, \alpha^{(k)}_{p_k}, \beta^{(1)}_1, \dots, \beta^{(1)}_{q_1}, \dots, \beta^{(k)}_1, \dots, \beta^{(k)}_{q_k})
\]
with
\[
\{ \alpha^{(i)}_1, \dots, \alpha^{(i)}_{p_i}, \beta^{(i)}_1, \dots, \beta^{(i)}_{q_i} \}
= \left\{ \left. \frac{p_i+q_i+1}{2} - j \, \right| \, 1 \le j \le p_i+q_i \right\}.
\]
With this normalization, we may write a (limit of) discrete series representation $\pi$ of $G$ associated to a pair $(\lambda, \Psi)$ as in \S \ref{ss:lds} as
\begin{equation}
\label{eq:lds}
\pi = {\mathstrut}^n \! A_{\b}(\lambda),
\end{equation}
where $\b = \t \oplus \mathfrak{n}$ is the $\theta$-stable Borel subalgebra of $\g$ with nilpotent radical $\mathfrak{n}$ such that $\Delta(\mathfrak{n}) = \Psi$ (see \cite[\S XI.8]{kv}).
More explicitly, if $\lambda$ is of the form \eqref{eq:lambda} and $\b = \q(x)$ is associated to
\[
x = (x^{(1)}_1, \dots, x^{(1)}_{p_1}, \dots, x^{(k)}_1, \dots, x^{(k)}_{p_k}, y^{(1)}_1, \dots, y^{(1)}_{q_1}, \dots, y^{(k)}_1, \dots, y^{(k)}_{q_k}),
\]
then the conditions on $\Psi$ in \S \ref{ss:lds} are equivalent to the following conditions on $x$:
\begin{itemize}
\item $x^{(1)}_1 > \dots > x^{(1)}_{p_1} > \dots > x^{(k)}_1 > \dots > x^{(k)}_{p_k}$;
\item $y^{(1)}_1 > \dots > y^{(1)}_{q_1} > \dots > y^{(k)}_1 > \dots > y^{(k)}_{q_k}$;
\item $x^{(i)}_{p_i} > y^{(i+1)}_1$ for all $1 \le i < k$;
\item $y^{(i)}_{q_i} > x^{(i+1)}_1$ for all $1 \le i < k$;
\item if $p_i - q_i = 0$, then either
\[
x^{(i)}_1 > y^{(i)}_1 > x^{(i)}_2 > y^{(i)}_2 > \dots > x^{(i)}_{p_i} > y^{(i)}_{q_i}
\]
or
\[
y^{(i)}_1 > x^{(i)}_1 > y^{(i)}_2 > x^{(i)}_2 > \dots > y^{(i)}_{q_i} > x^{(i)}_{p_i};
\]
\item if $p_i - q_i = 1$, then
\[
x^{(i)}_1 > y^{(i)}_1 > x^{(i)}_2 > y^{(i)}_2 > \dots > x^{(i)}_{q_i} > y^{(i)}_{q_i} > x^{(i)}_{p_i};
\]
\item if $p_i - q_i = -1$, then
\[
y^{(i)}_1 > x^{(i)}_1 > y^{(i)}_2 > x^{(i)}_2 > \dots > y^{(i)}_{p_i} > x^{(i)}_{p_i} > y^{(i)}_{q_i}.
\]
\end{itemize}
Note that if $\pi$ is a discrete series representation, then $\b$ is uniquely determined by $\lambda$.
\section{Statement of the main theorems}
In this section, we state the main theorems of this paper, which describe the theta lifts of tempered representations of real unitary groups explicitly.
\subsection{Setup}
\label{ss:main-theorem-setup}
We consider the theta lifting from $\U(W)$ to $\U(V)$, where $W$ is an $n$-dimensional skew-Hermitian space over $\C$ and $V$ is an $m$-dimensional Hermitian space over $\C$.
Let $(p,q)$ and $(r,s)$ be the signatures of $W$ and $V$, respectively, so that $p+q = n$ and $r+s = m$.
As in \S \ref{ss:real-notation}, we identify $\U(W)$ and $\U(V)$ with $\U(p,q)$ and $\U(r,s)$, respectively.
From now on, we take the characters $\chi_V, \chi_W$ of $\C^\times$ given by
\[
\chi_V(z) = \left( \frac{z}{\sqrt{z \bar{z}}} \right)^{m_0}, \quad
\chi_W(z) = \left( \frac{z}{\sqrt{z \bar{z}}} \right)^{n_0}
\]
for some fixed integers $m_0, n_0$ such that
\[
m_0 \equiv m \bmod 2, \quad
n_0 \equiv n \bmod 2,
\]
and the character $\psi$ of $\R$ given by
\[
\psi(x) = e^{-2 \pi \sqrt{-1} x}.
\]
(We make this choice so that Lemma \ref{l:K-type-corresp} below holds.)
Then we write the theta lift of an irreducible representation $\pi$ of $\U(W) = \U(p,q)$ to $\U(V) = \U(r,s)$ as
\[
\theta_{r,s}(\pi) = \theta_{V, W, \chi_V, \chi_W, \psi}(\pi).
\]
\subsection{Explicit description of theta lifts}
We now state our main theorems.
\begin{thm}
\label{t:main-lds}
Let $\pi$ be a (limit of) discrete series representation of $\U(W) = \U(p,q)$ and write $\pi = {\mathstrut}^n \! A_\b(\lambda)$ as in \eqref{eq:lds}.
Assume that its theta lift $\theta_{r,s}(\pi)$ to $\U(V) = \U(r,s)$ is nonzero.
Then we have
\[
\theta_{r,s}(\pi) = {\mathstrut}^n \! A_\q(\lambda'),
\]
where $\q$ and $\lambda'$ are given as follows.
\begin{enumerate}
\item
\label{main-lds-1}
Assume that $m > n$.
Write
\[
\lambda = (\alpha_1, \dots, \alpha_{p^+}, \beta_1, \dots, \beta_{p^-}, \gamma_1, \dots, \gamma_{q^+}, \delta_1, \dots, \delta_{q^-}) + \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg),
\]
where
\begin{itemize}
\item $\alpha_i, \gamma_j > 0$ and $\beta_i, \delta_j \le 0$;
\item $p^++p^- = p$ and $q^++q^- = q$,
\end{itemize}
and $\b = \q(x)$ with
\[
x = (x^+_1, \dots, x^+_{p^+}, x^-_1, \dots, x^-_{p^-}, y^+_1, \dots, y^+_{q^+}, y^-_1, \dots, y^-_{q^-}).
\]
We assume without loss of generality that
\begin{itemize}
\item $x^+_1 > \dots > x^+_{p^+} > 0 > x^-_1 > \dots > x^-_{p^-}$;
\item $y^+_1 > \dots > y^+_{q^+} > 0 > y^-_1 > \dots > y^-_{q^-}$.
\end{itemize}
Then
\begin{itemize}
\item $p^++q^- \le r$ and $p^-+q^+ \le s$;
\item $\lambda'$ is given by
\[
\lambda' = (\alpha_1, \dots, \alpha_{p^+}, \underbrace{0, \dots, 0}_{r-p^+-q^-}, \delta_1, \dots, \delta_{q^-}, \gamma_1, \dots, \gamma_{q^+}, \underbrace{0, \dots, 0}_{s-p^--q^+}, \beta_1, \dots, \beta_{p^-}) + \bigg(\frac{n_0}{2}, \dots, \frac{n_0}{2}\bigg);
\]
\item $\q = \q(x')$ is associated to
\[
x' = (x^+_1, \dots, x^+_{p^+}, \underbrace{0, \dots, 0}_{r-p^+-q^-}, y^-_1, \dots, y^-_{q^-}, y^+_1, \dots, y^+_{q^+}, \underbrace{0, \dots, 0}_{s-p^--q^+}, x^-_1, \dots, x^-_{p^-}).
\]
\end{itemize}
\item
\label{main-lds-2}
Assume that $m \le n$.
Put $k = n - m$.
Write
\begin{align*}
\lambda & = \bigg( \alpha_1, \dots, \alpha_{p^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{p_1},
\underbrace{\frac{k-3}{2}, \dots, \frac{k-3}{2}}_{p_2}, \dots,
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{p_k},
\beta_1, \dots, \beta_{p^-}, \\
& \phantom{{} = \bigg(}
\gamma_1, \dots, \gamma_{q^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{q_1},
\underbrace{\frac{k-3}{2}, \dots, \frac{k-3}{2}}_{q_2}, \dots,
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{q_k},
\delta_1, \dots, \delta_{q^-} \bigg) \\
& + \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg),
\end{align*}
where
\begin{itemize}
\item $\alpha_i, \gamma_j > \frac{k-1}{2}$ and $\beta_i, \delta_j < -\frac{k-1}{2}$;
\item $p_i, q_j \ge 0$;
\item $|p_i-q_i| \le 1$ for all $i$;
\item $p^++p^-+p_1 + \dots + p_k = p$ and $q^++q^-+q_1 + \dots +q_k = q$,
\end{itemize}
and $\b = \q(x)$ with
\begin{align*}
x & = (x^+_1, \dots, x^+_{p^+}, x^{(1)}_1, \dots, x^{(1)}_{p_1}, x^{(2)}_1, \dots, x^{(2)}_{p_2}, \dots, x^{(k)}_1, \dots, x^{(k)}_{p_k}, x^-_1, \dots, x^-_{p^-}, \\
& \phantom{{} = (} y^+_1, \dots, y^+_{q^+}, y^{(1)}_1, \dots, y^{(1)}_{q_1}, y^{(2)}_1, \dots, y^{(2)}_{q_2}, \dots, y^{(k)}_1, \dots, y^{(k)}_{q_k}, y^-_1, \dots, y^-_{q^-}).
\end{align*}
(When $k=0$, we interpret $\lambda$ and $x$ as
\[
(\alpha_1, \dots, \alpha_{p^+}, \beta_1, \dots, \beta_{p^-},
\gamma_1, \dots, \gamma_{q^+}, \delta_1, \dots, \delta_{q^-})
+ \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg)
\]
and
\[
x = (x^+_1, \dots, x^+_{p^+}, x^-_1, \dots, x^-_{p^-}, y^+_1, \dots, y^+_{q^+}, y^-_1, \dots, y^-_{q^-}),
\]
respectively.)
Then
\begin{itemize}
\item $p_i + q_i >0$ for all $1 \le i \le k$;
\item if $k \ge 2$, then either the conditions
\begin{enumerate}
\item
\label{e+1}
$p_i - q_i = 1$ for all $1 < i < k$;
\item
\label{e+2}
$p_1 - q_1 = 1$ or $0$;
\item
\label{e+3}
$p_k - q_k = 1$ or $0$,
\end{enumerate}
or the conditions
\begin{enumerate}[resume]
\item
\label{e-1}
$p_i - q_i = -1$ for all $1 < i < k$;
\item
\label{e-2}
$p_1 - q_1 = -1$ or $0$;
\item
\label{e-3}
$p_k - q_k = -1$ or $0$
\end{enumerate}
hold;
\item if $k \ge 2$, then
\[
\begin{cases}
y^{(1)}_1 > x^{(1)}_1 > \dots > y^{(1)}_{q_1} > x^{(1)}_{p_1} &
\text{if the conditions \eqref{e+1}, \eqref{e+2}, \eqref{e+3} hold and $p_1 - q_1 = 0$;} \\
x^{(k)}_1 > y^{(k)}_1 > \dots > x^{(k)}_{p_k} > y^{(k)}_{q_k} &
\text{if the conditions \eqref{e+1}, \eqref{e+2}, \eqref{e+3} hold and $p_k - q_k = 0$;} \\
x^{(1)}_1 > y^{(1)}_1 > \dots > x^{(1)}_{p_1} > y^{(1)}_{q_1} &
\text{if the conditions \eqref{e-1}, \eqref{e-2}, \eqref{e-3} hold and $p_1 - q_1 = 0$;} \\
y^{(k)}_1 > x^{(k)}_1 > \dots > y^{(k)}_{q_k} > x^{(k)}_{p_k} &
\text{if the conditions \eqref{e-1}, \eqref{e-2}, \eqref{e-3} hold and $p_k - q_k = 0$;}
\end{cases}
\]
\item
$r = p^+ + q^- + r_1 + \dots + r_k$ and $s = p^- + q^+ + s_1 + \dots + s_k$, where
\[
(r_i, s_i) =
\begin{cases}
(p_i-1, q_i) & \text{if $p_i-q_i = 1$, or $p_i-q_i = 0$ and $y^{(i)}_1 > x^{(i)}_1 > \dots > y^{(i)}_{q_i} > x^{(i)}_{p_i}$;} \\
(p_i, q_i-1) & \text{if $p_i-q_i = -1$, or $p_i-q_i = 0$ and $x^{(i)}_1 > y^{(i)}_1 > \dots > x^{(i)}_{p_i} > y^{(i)}_{q_i}$;}
\end{cases}
\]
\item $\lambda'$ is given by
\begin{align*}
\lambda' & = \bigg( \alpha_1, \dots, \alpha_{p^+}, \underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{r_1}, \underbrace{\frac{k-3}{2}, \dots, \frac{k-3}{2}}_{r_2}, \dots,
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{r_k},
\delta_1, \dots, \delta_{q^-}, \\
& \phantom{{} = \bigg(}
\gamma_1, \dots, \gamma_{q^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{s_1}, \underbrace{\frac{k-3}{2}, \dots, \frac{k-3}{2}}_{s_2}, \dots,
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{s_k},
\beta_1, \dots, \beta_{p^-} \bigg) \\
& + \bigg( \frac{n_0}{2}, \dots, \frac{n_0}{2} \bigg);
\end{align*}
\item
$\q = \q(x')$ is associated to
\begin{align*}
x' & = (x^+_1, \dots, x^+_{p^+}, z^{(1)}_1, \dots, z^{(1)}_{r_1}, z^{(2)}_1, \dots, z^{(2)}_{r_2}, \dots, z^{(k)}_1, \dots, z^{(k)}_{r_k}, y^-_1, \dots, y^-_{q^-}, \\
& \phantom{{} = (} y^+_1, \dots, y^+_{q^+}, w^{(1)}_1, \dots, w^{(1)}_{s_1}, w^{(2)}_1, \dots, w^{(2)}_{s_2}, \dots, w^{(k)}_1, \dots, w^{(k)}_{s_k}, x^-_1, \dots, x^-_{p^-})
\end{align*}
such that
\[
\begin{cases}
z^{(i)}_1 > w^{(i)}_1 > \dots > z^{(i)}_{r_i} > w^{(i)}_{s_i} &
\text{if $p_i - q_i = 1$;} \\
w^{(i)}_1 > z^{(i)}_1 > \dots > w^{(i)}_{s_i} > z^{(i)}_{r_i} &
\text{if $p_i - q_i = -1$.}
\end{cases}
\]
\end{itemize}
\end{enumerate}
\end{thm}
In particular, $\theta_{r,s}(\pi)$ is a (limit of) discrete series representation when $m \le n+1$.
Also, this theorem shows that if $\theta_{r,s}(\pi)$ is nonzero, then the associated cohomologically induced representation ${\mathstrut}^n \! A_\q(\lambda')$ is nonzero, which was not known when $m \ge n+2$ and ${\mathstrut}^n \! A_\q(\lambda')$ is not good.
It is not clear to the author whether this nonvanishing follows directly from a result of Trapa \cite[Theorem 7.9]{trapa}.
\begin{thm}
\label{t:main-temp}
Let $\pi$ be an irreducible tempered representation of $\U(W) = \U(p,q)$ and write $\pi = I(\xi_1, \dots, \xi_d, \pi_0)$ as in \eqref{eq:temp}.
Assume that its theta lift $\theta_{r,s}(\pi)$ to $\U(V) = \U(r,s)$ is nonzero.
Then we have $d \le \min \{ r,s \}$ and
\[
\theta_{r,s}(\pi) = I(\xi_1 \chi_V^{-1} \chi_W, \dots, \xi_d \chi_V^{-1} \chi_W, \theta_{r-d,s-d}(\pi_0)).
\]
\end{thm}
The rest of this paper is devoted to the proof of Theorems \ref{t:main-lds} and \ref{t:main-temp}.
\section{$L$- and $A$-packets}
In this section, we describe the representations in some local $L$- and $A$-packets for unitary groups explicitly.
\subsection{Parameters and packets}
Let $F$ be a local field of characteristic zero and $W_F$ the Weil group of $F$.
Put
\[
L_F =
\begin{cases}
W_F & \text{if $F$ is archimedean;} \\
W_F \times \SL_2(\C) & \text{if $F$ is nonarchimedean.}
\end{cases}
\]
Let $E$ be a quadratic extension of $F$.
Following \cite[\S 8]{ggp1}, we regard an $L$-parameter $\phi : L_F \rightarrow {}^L \U_n$ (resp.~an $A$-parameter $\phi : L_F \times \SL_2(\C) \rightarrow {}^L \U_n$) for $\U_n$ as an $n$-dimensional conjugate-selfdual representation of $L_E$ (resp.~$L_E \times \SL_2(\C)$) with sign $(-1)^{n-1}$.
Here $\U_n$ stands for the unitary group of any $n$-dimensional Hermitian or skew-Hermitian space over $E$ and ${}^L \U_n = \GL_n(\C) \rtimes W_F$ is the $L$-group of $\U_n$.
For any such a parameter $\phi$, we denote by $S_\phi$ the component group of the centralizer of the image of $\phi$ in $\GL_n(\C)$ and by $\widehat{S}_\phi$ the group of characters of $S_\phi$.
Note that $S_\phi$ is a finitely generated free $\Z/2\Z$-module.
For any positive integer $d$, we denote by $S_d$ the unique $d$-dimensional irreducible representation of $\SL_2(\C)$.
Fix $\varepsilon = \pm 1$.
Let $V$ be an $n$-dimensional $\varepsilon$-Hermitian space over $E$ and $\Irr(\U(V))$ the set of equivalence classes of irreducible representations of $\U(V)$.
Then the local Langlands correspondence \cite{mok,kmsw,mr18} gives a partition of $\Irr(\U(V))$ into finite sets called $L$-packets:
\begin{equation}
\label{eq:llc}
\Irr(\U(V)) = \bigsqcup_\phi \Pi_\phi(\U(V)),
\end{equation}
where $\phi$ runs over $L$-parameters for $\U_n$.
Moreover, given the choice of a Whittaker datum, there exists a canonical bijection
\[
\bigsqcup_V \Pi_\phi(\U(V)) \, \leftrightarrow \, \widehat{S}_\phi,
\]
where $V$ runs over isometry classes of $n$-dimensional $\varepsilon$-Hermitian spaces over $E$.
We denote by $\pi(\phi, \eta)$ the irreducible representation associated to $\eta \in \widehat{S}_\phi$.
To any $A$-parameter $\phi$ for $\U_n$, Arthur's endoscopic classification \cite{mok,kmsw} assigns a finite set called an $A$-packet
\[
\Pi_{\phi}(\U(V))
\]
consisting of semisimple representations of $\U(V)$ of finite length, which are indexed by $\widehat{S}_\phi$.
We denote by $\sigma(\phi, \eta)$ the representation associated to $\eta \in \widehat{S}_{\phi}$.
\subsection{Whittaker data}
\label{ss:whit}
To index the representations in $L$- and $A$-packets as in the previous subsection, we take the following Whittaker datum (which is a conjugacy class of pairs $(N,\psi_N)$ consisting of the unipotent radical $N$ of a Borel subgroup of $\U(V_n^+)$ and a generic character $\psi_N$ of $N$) in this paper.
If $n$ is odd, then there is a unique Whittaker datum.
Thus assume that $n$ is even.
Then by \cite[Proposition 12.1]{ggp1}, the Whittaker data are parametrized by $\mathrm{N}_{E/F}(E^\times)$-orbits of nontrivial additive characters of $E/F$ (resp.~$F$) if $\varepsilon = +1$ (resp.~$\varepsilon = -1$).
On the other hand, we have fixed an element $\delta \in E^\times$ such that $\Tr_{E/F}(\delta) = 0$ and a nontrivial additive character $\psi$ of $F$.
Define a nontrivial additive character $\psi^E$ of $E/F$ by $\psi^E(x) = \psi(\frac{1}{2} \Tr_{E/F}(\delta x))$.
Following \cite[\S 2.4]{gi2}, we take the Whittaker datum associated to $\psi^E$ (resp.~$\psi$) if $\varepsilon = +1$ (resp.~$\varepsilon = -1$).
If $F = \R$, we always assume that $\delta = \sqrt{-1}$ and $\psi(x) = e^{- 2 \pi \sqrt{-1} x}$.
Then our Whittaker datum agrees with the Whittaker datum $\mathfrak{w}_+$ as in \cite[\S A.3]{atobe}.
Moreover, by \cite[Theorem A.4]{atobe}, it also agrees with the Whittaker datum as in \cite[Remarque 4.5]{mr19}.
\subsection{The real case}
Suppose that $F = \R$.
For any $\kappa \in \frac{1}{2} \Z$, we define a character $\chi_\kappa$ of $W_\C = \C^\times$ by
\[
\chi_\kappa(z) = \bigg( \frac{z}{\sqrt{z \bar{z}}} \bigg)^{2 \kappa}.
\]
For any character $\xi$ of $\C^\times$, we define another character $\check{\xi}$ of $\C^\times$ by $\check{\xi}(z) = \xi(\bar{z})^{-1}$.
\subsubsection{(Limits of) discrete series $L$-packets}
\label{sss:packets-real-lds}
Let $\Irr_{\mathrm{lds}}(\U(p,q))$ be the set of equivalence classes of (limits of) discrete series representations of $\U(p,q)$.
Then \eqref{eq:llc} restricts to a partition
\[
\Irr_{\mathrm{lds}}(\U(p,q)) = \bigsqcup_\phi \Pi_\phi(\U(p,q)),
\]
where $\phi$ runs over (limits of) discrete series $L$-parameters for $\U_n$ with $n = p+q$.
Here we say that an $L$-parameter $\phi$ for $\U_n$ is (limit of) discrete series if $\phi$ is of the form
\[
\phi = \chi_{\kappa_1} \oplus \dots \oplus \chi_{\kappa_n}
\]
with $\kappa_i \in \Z + \frac{n-1}{2}$.
For such a parameter $\phi$, we assume without loss of generality that $\kappa_1 \ge \dots \ge \kappa_n$ and identify $S_\phi$ with a quotient of a free $\Z/2\Z$-module
\[
\widetilde{S}_\phi = (\Z/2\Z) e_1 \oplus \dots \oplus (\Z/2\Z) e_n,
\]
where $e_i$ corresponds to $\chi_{\kappa_i}$, in such a way that $\widehat{S}_\phi$ consists of the characters $\eta$ of $\widetilde{S}_\phi$ satisfying
\[
\eta(e_i) = \eta(e_j)
\]
for all $i,j$ such that $\kappa_i = \kappa_j$.
Let $\eta \in \widehat{S}_\phi$.
For $1 \le i \le n$, we define a pair of integers $(p_i,q_i)$ by
\[
(p_i, q_i) =
\begin{cases}
(1,0) & \text{if $\eta(e_i) = (-1)^{i-1}$;} \\
(0,1) & \text{if $\eta(e_i) = (-1)^i$.}
\end{cases}
\]
Then by \cite[Th\'eor\`eme 1.1]{mr19}, $\pi(\phi,\eta)$ is a representation of $\U(p,q)$ if and only if
\[
p = p_1 + \dots + p_n, \quad
q = q_1 + \dots + q_n,
\]
in which case we have
\[
\eta(e_1 + \dots + e_n) = (-1)^{\frac{1}{2}(p-q)(p-q-1)}
\]
and
\[
\pi(\phi,\eta) = {\mathstrut}^n \! A_\b(\lambda).
\]
Here $\lambda$ is given by
\[
\lambda = (\underbrace{\kappa_1,\dots,\kappa_1}_{p_1}, \dots, \underbrace{\kappa_n,\dots,\kappa_n}_{p_n}, \underbrace{\kappa_1,\dots,\kappa_1}_{q_1}, \dots, \underbrace{\kappa_n,\dots,\kappa_n}_{q_n})
\]
and $\b = \q(x)$ is associated to
\[
x = (\underbrace{x_1,\dots,x_1}_{p_1}, \dots, \underbrace{x_n,\dots,x_n}_{p_n}, \underbrace{x_1,\dots,x_1}_{q_1}, \dots, \underbrace{x_n,\dots,x_n}_{q_n})
\]
for any $x_1, \dots, x_n \in \R$ such that $x_1 > \dots > x_n$.
Assume that $p,q > 0$.
Let $\chi$ be a conjugate-selfdual character of $\C^\times$ with sign $(-1)^{n-1}$, so that $\chi = \chi_\kappa$ for some $\kappa \in \Z + \frac{n-1}{2}$.
Let $\pi_0$ be a (limit of) discrete series representation of $\U(p-1,q-1)$ and write $\pi_0 = \pi(\phi_0, \eta_0)$, where $\phi_0$ is a (limit of) discrete series $L$-parameter for $\U_{n-2}$ and $\eta_0$ is a character of $S_{\phi_0}$.
Define a (limit of) discrete series $L$-parameter for $\U_n$ by
\[
\phi = 2 \chi \oplus \phi_0.
\]
We may naturally identify $S_{\phi_0}$ with a subgroup of $S_\phi$.
Then we have
\[
I(\chi, \pi_0) = \bigoplus_\eta \pi(\phi, \eta),
\]
where $\eta$ runs over elements in $\widehat{S}_\phi$ such that $\eta|_{S_{\phi_0}} = \eta_0$.
\subsubsection{Tempered $L$-packets}
Let $\Irr_{\mathrm{temp}}(\U(p,q))$ be the set of equivalence classes of irreducible tempered representations of $\U(p,q)$.
Then \eqref{eq:llc} restricts to a partition
\[
\Irr_{\mathrm{temp}}(\U(p,q)) = \bigsqcup_\phi \Pi_\phi(\U(p,q)),
\]
where $\phi$ runs over tempered $L$-parameters for $\U_n$ with $n=p+q$.
Here we say that an $L$-parameter $\phi$ for $\U_n$ is tempered if $\phi$ is of the form
\[
\phi = \chi_{\kappa_1} \oplus \dots \oplus \chi_{\kappa_{n_0}} \oplus \xi_1 \oplus \dots \oplus \xi_d \oplus \check{\xi}_1 \oplus \dots \oplus \check{\xi}_d,
\]
where
\begin{itemize}
\item $\kappa_i \in \Z + \frac{n-1}{2}$;
\item $\xi_i$ is a unitary character of $\C^\times$ which is not conjugate-selfdual with sign $(-1)^{n-1}$;
\item $n_0 + 2d = n$.
\end{itemize}
For such a parameter $\phi$, we define a (limit of) discrete series $L$-parameter $\phi_0$ for $\U_{n_0}$ by
\[
\phi_0 = \chi_{\kappa_1} \oplus \dots \oplus \chi_{\kappa_{n_0}}.
\]
Then $\Pi_{\phi}(\U(p,q))$ consists of the parabolically induced representations
\[
I(\xi_1, \dots, \xi_d, \pi_0)
\]
for all $\pi_0 \in \Pi_{\phi_0}(\U(p-d,q-d))$, which are irreducible by Lemma \ref{l:irred-temp}.
(When $d > \min\{ p, q \}$, we interpret $\Pi_{\phi_0}(\U(p-d,q-d))$ as the empty set.)
Moreover, via the natural identification $S_\phi = S_{\phi_0}$, the character of $S_\phi$ associated to $I(\xi_1, \dots, \xi_d, \pi_0)$ is equal to the character of $S_{\phi_0}$ associated to $\pi_0$.
\subsubsection{Some $A$-packets}
\label{sss:packets-real-coh}
We consider the $A$-packet $\Pi_{\phi'}(\U(r,s))$, where $\phi'$ is an $A$-parameter for $\U_m$ with $m=r+s$ of the form
\[
\phi' = \chi_{\mu_1} \oplus \cdots \oplus \chi_{\mu_n} \oplus (\chi_{\mu_0} \boxtimes S_{m-n}),
\]
where
\begin{itemize}
\item $\mu_i \in \Z + \frac{m-1}{2}$ for $i \ne 0$;
\item $\mu_0 \in \Z + \frac{n}{2}$;
\item $\mu_1 \ge \dots \ge \mu_{i_0-1} > \mu_0 \ge \mu_{i_0} \ge \dots \ge \mu_n$;
\item $n < m$.
\end{itemize}
For such a parameter $\phi'$, we identify $S_{\phi'}$ with a quotient of a free $\Z/2\Z$-module
\[
\widetilde{S}_{\phi'} = (\Z / 2 \Z) e'_1 \oplus \dots \oplus (\Z / 2 \Z) e'_n \oplus (\Z / 2 \Z) e_0',
\]
where $e'_i$ corresponds to $\chi_{\mu_i}$ (resp.~$\chi_{\mu_0} \boxtimes S_{m-n}$) if $i \ne 0$ (resp.~$i=0$), in such a way that $\widehat{S}_{\phi'}$ consists of the characters $\eta'$ of $\widetilde{S}_{\phi'}$ satisfying
\[
\eta'(e_i') = \eta'(e_j')
\]
for all $i,j$ such that $\mu_i = \mu_j$ with either $i, j \ne 0$ or $i \ne 0$, $j = 0$, $m-n=1$.
Let $\eta' \in \widehat{S}_{\phi'}$.
For $1 \le i \le n+1$, we define a pair of integers $(r_i, s_i)$ by
\[
(r_i, s_i) =
\begin{cases}
(1,0) & \text{if $i<i_0$ and $\eta'(e_i') = (-1)^{i-1}$;} \\
(0,1) & \text{if $i<i_0$ and $\eta'(e_i') = (-1)^i$;} \\
(1,0) & \text{if $i>i_0$ and $\eta'(e_{i-1}') = (-1)^{i+m-n-2}$;} \\
(0,1) & \text{if $i>i_0$ and $\eta'(e_{i-1}') = (-1)^{i+m-n-1}$}
\end{cases}
\]
and
\[
(r_{i_0}, s_{i_0}) = (r - r_1 - \dots - r_{i_0-1} - r_{i_0+1} \dots - r_{n+1}, s - s_1 - \dots - s_{i_0-1} - s_{i_0+1} \dots - s_{n+1}).
\]
Note that $r_{i_0} + s_{i_0} = m-n$.
Then by \cite[Th\'eor\`eme 1.1]{mr19}, the representation $\sigma(\phi', \eta')$ of $\U(r,s)$ is nonzero only if
\[
r_{i_0}, s_{i_0} \ge 0
\]
and
\begin{equation}
\label{eq:eta'}
\eta'(e_1' + \dots + e_n' + e_0') = (-1)^{\frac{1}{2}(r-s)(r-s-1)}
\end{equation}
(see also \cite[(1-3)]{mr19} and Lemma \ref{l:eta'} below), in which case we have
\[
\sigma(\phi', \eta') = {\mathstrut}^n \! A_\q(\lambda').
\]
Here $\lambda'$ is given by
\[
\lambda' = (\underbrace{\lambda'_1,\dots,\lambda'_1}_{r_1}, \dots, \underbrace{\lambda'_{n+1},\dots,\lambda'_{n+1}}_{r_{n+1}}, \underbrace{\lambda'_1,\dots,\lambda'_1}_{s_1}, \dots, \underbrace{\lambda'_{n+1},\dots,\lambda'_{n+1}}_{s_{n+1}})
\]
with
\[
\lambda'_i =
\begin{cases}
\mu_i & \text{if $i < i_0$;} \\
\mu_0 & \text{if $i = i_0$;} \\
\mu_{i-1} & \text{if $i > i_0$}
\end{cases}
\]
and $\q = \q(x')$ is associated to
\[
x' = (\underbrace{x'_1,\dots,x'_1}_{r_1}, \dots, \underbrace{x'_{n+1},\dots,x'_{n+1}}_{r_{n+1}}, \underbrace{x'_1,\dots,x'_1}_{s_1}, \dots, \underbrace{x'_{n+1},\dots,x'_{n+1}}_{s_{n+1}})
\]
for any $x'_1, \dots, x'_{n+1} \in \R$ such that $x'_1 > \dots > x'_{n+1}$, so that ${\mathstrut}^n \! A_\q(\lambda')$ is weakly fair.
(Note that there is a typo in \cite[(4-2)]{mr19}: $(t_i+a_i-N)/2 - a_{<i}$ should be $(t_i+a_i-N)/2 + a_{<i}$.)
Moreover, if two representations $\sigma(\phi', \eta_1'), \sigma(\phi', \eta_2')$ with $\eta_1', \eta_2' \in \widehat{S}_{\phi'}$ are nonzero and isomorphic, then we have $\eta_1' = \eta_2'$.
\begin{lem}
\label{l:eta'}
Let $\eta' \in \widehat{S}_{\phi'}$ and define $(r_i,s_i)$ as above.
Then $\eta'$ satisfies \eqref{eq:eta'} if and only if
\[
\eta'(e_0') = (-1)^{r_{i_0}(i_0-1) + s_{i_0} i_0 + \frac{1}{2}(m-n)(m-n-1)}.
\]
\end{lem}
\begin{proof}
It suffices to show that
\[
\eta'(e_1' + \dots + e_n') \cdot (-1)^{r_{i_0}(i_0-1) + s_{i_0} i_0 + \frac{1}{2}(m-n)(m-n-1)} \cdot (-1)^{\frac{1}{2}(r-s)(r-s-1)} = 1.
\]
We may write $\eta'(e_1' + \dots + e_n') = (-1)^j$, where
\begin{align*}
j & = \sum_{i=1}^{i_0-1} (i-1+s_i) + \sum_{i=i_0+1}^{n+1} (i+m-n-2+s_i) \\
& = \frac{1}{2}(i_0-1)(i_0-2) + \frac{1}{2}(n-i_0+1)(2m-n+i_0-2) + s-s_{i_0} \\
& = \frac{1}{2}n(2m-n-1) - (m-n)(i_0-1) + s-s_{i_0} \\
& = \frac{1}{2}n(2m-n-1) - r_{i_0}(i_0-1) - s_{i_0} i_0 + s.
\end{align*}
Then we have
\begin{align*}
& j + r_{i_0}(i_0-1) + s_{i_0} i_0 + \frac{1}{2}(m-n)(m-n-1) + \frac{1}{2}(r-s)(r-s-1) \\
& = \frac{1}{2}n(2m-n-1) + s + \frac{1}{2}(m-n)(m-n-1) + \frac{1}{2}(r-s)(r-s-1) \\
& = \frac{1}{2} m (m-1) + s + \frac{1}{2}(r-s)(r-s-1) \\
& = \frac{1}{2} (r+s) (r+s-1) + s + \frac{1}{2}(r-s)(r-s-1) \\
& = r(r-1) + s(s+1) \\
& \equiv 0 \bmod 2.
\end{align*}
This implies the assertion.
\end{proof}
\subsection{The nonarchimedean case}
Suppose that $F$ is nonarchimedean.
Recall that given a positive integer $n$, there are precisely two $n$-dimensional $\varepsilon$-Hermitian spaces $V_n^+$ and $V_n^-$ over $E$ (up to isometry).
Consider a normalized parabolically induced representation
\[
\Ind^{\U(V_n^+)}_P(\xi_1 \boxtimes \dots \boxtimes \xi_d \boxtimes \pi_0),
\]
where
\begin{itemize}
\item $d$ is a nonnegative integer with $2d \le n$;
\item $P$ is a parabolic subgroup of $\U(V_n^+)$ with Levi component $(E^\times)^d \times \U(V_{n-2d}^+)$ defined as in \S \ref{ss:parab-ind};
\item $\xi_1, \dots, \xi_d$ are characters of $E^\times$;
\item $\pi_0$ is an irreducible tempered representation of $\U(V_{n-2d}^+)$.
\end{itemize}
If this representation is a standard module, we denote its unique irreducible quotient by
\[
J(\xi_1, \dots, \xi_d, \pi_0).
\]
\subsubsection{Some $L$-packets}
We consider the $L$-packet $\Pi_\phi(\U(V_n^+))$, where $\phi$ is an $L$-parameter for $\U_n$ of the form
\[
\phi = \chi_1 \oplus \dots \oplus \chi_n
\]
with (not necessarily distinct) conjugate-selfdual characters $\chi_1, \dots, \chi_n$ of $E^\times$ with sign $(-1)^{n-1}$.
Then $\pi(\phi,\mathbbm{1})$ is an irreducible tempered representation of $\U(V_n^+)$.
For more properties, we refer the reader to \cite[\S 2.5]{gi2}.
\subsubsection{Some $A$-packets}
We consider the $A$-packet $\Pi_{\phi'}(\U(V_m^+))$, where $\phi'$ is an $A$-parameter for $\U_m$ of the form
\[
\phi' = \chi_1 \oplus \dots \oplus \chi_n \oplus (\chi_0 \boxtimes S_{m-n})
\]
with $n < m$ and (not necessarily distinct) conjugate-selfdual characters $\chi_1, \dots, \chi_n,\chi_0$ of $E^\times$ with sign
\[
\begin{cases}
(-1)^{m-1} & \text{if $i \ne 0$;} \\
(-1)^n & \text{if $i=0$.}
\end{cases}
\]
Then by \cite[\S 4.1]{mr18}, the representation $\sigma(\phi', \eta')$ of $\U(V_m^+)$ with $\eta' \in \widehat{S}_{\phi'}$ is either zero or irreducible.
Moreover, if two representations $\sigma(\phi', \eta_1'), \sigma(\phi', \eta_2')$ with $\eta_1', \eta_2' \in \widehat{S}_{\phi'}$ are nonzero and isomorphic, then we have $\eta_1' = \eta_2'$.
\begin{lem}
\label{l:local-Apacket}
\begin{enumerate}
\item
If $m \equiv n \bmod 2$, then we have
\[
\sigma(\phi', \mathbbm{1}) = J(\chi_0 | \cdot |^{\frac{1}{2}(m-n-1)}, \chi_0 | \cdot |^{\frac{1}{2}(m-n-3)}, \dots, \chi_0 | \cdot |^{\frac{1}{2}}, \pi(\phi_0, \mathbbm{1}))
\]
with an $L$-parameter $\phi_0 = \chi_1 \oplus \dots \oplus \chi_n$ for $\U_n$.
\item
If $m \not \equiv n \bmod 2$, then we have
\[
\sigma(\phi', \mathbbm{1}) = J(\chi_0 | \cdot |^{\frac{1}{2}(m-n-1)}, \chi_0 | \cdot |^{\frac{1}{2}(m-n-3)}, \dots, \chi_0 | \cdot |^1, \pi(\phi_1, \mathbbm{1}))
\]
with an $L$-parameter $\phi_1 = \chi_1 \oplus \dots \oplus \chi_n \oplus \chi_0$ for $\U_{n+1}$.
\end{enumerate}
\end{lem}
\begin{proof}
The assertion follows from \cite[Proposition 8.4.1]{mok} and the irreducibility of $\sigma(\phi', \mathbbm{1})$.
\end{proof}
\subsection{The split case}
We also need to consider the case when $F$ is nonarchimedean and $E = F \times F$.
Recall that given a positive integer $n$, there is a unique $n$-dimensional $\varepsilon$-Hermitian space $V_n^+ = \VV_n \otimes_F E$ over $E$ (up to isometry), where $\VV_n$ is an $n$-dimensional vector space over $F$.
Via the isomorphism $\U(V_n^+) \cong \GL(\VV_n)$ induced by the first projection, we may regard an $L$-parameter $\phi : L_F \rightarrow {}^L \U_n$ (resp.~an $A$-parameter $\phi : L_F \times \SL_2(\C) \rightarrow {}^L \U_n$) for $\U_n$ as an $n$-dimensional representation of $L_F$ (resp.~$L_F \times \SL_2(\C)$).
For any such a parameter $\phi$, the component group $S_\phi$ is always trivial.
Let $\phi$ and $\phi'$ be $L$- and $A$-parameters for $\U_n$ and $\U_m$, respectively, of the form
\begin{align*}
\phi & = \chi_1 \oplus \dots \oplus \chi_n, \\
\phi' & = \chi_1 \oplus \dots \oplus \chi_n \oplus (\chi_0 \boxtimes S_{m-n})
\end{align*}
with $n < m$ and (not necessarily distinct) unitary characters $\chi_1, \dots, \chi_n, \chi_0$ of $F^\times$.
We denote by $\pi(\phi, \mathbbm{1})$ and $\sigma(\phi', \mathbbm{1})$ the unique representations of $\U(V_n^+) \cong \GL(\VV_n)$ and $\U(V_m^+) \cong \GL(\VV_m)$ in the $L$- and $A$-packets $\Pi_\phi(\U(V_n^+))$ and $\Pi_{\phi'}(\U(V_m^+))$, respectively.
Then we have
\begin{align*}
\pi(\phi, \mathbbm{1}) & = \Ind^{\GL(\VV_n)}_{\mathcal{B}}(\chi_1 \boxtimes \dots \boxtimes \chi_n), \\
\sigma(\phi', \mathbbm{1}) & = \Ind^{\GL(\VV_m)}_{\mathcal{P}}(\chi_1 \boxtimes \dots \boxtimes \chi_n \boxtimes (\chi_0 \circ \det)),
\end{align*}
where $\mathcal{B}$ is a Borel subgroup of $\GL(\VV_n)$ and $\mathcal{P}$ is a parabolic subgroup of $\GL(\VV_m)$ with Levi component $(F^\times)^n \times \GL_{m-n}(F)$.
Note that the parabolically induced representations on the right-hand side are irreducible by \cite[Theorem 4.2]{zel}.
\section{Nonvanishing of theta lifts}
\label{s:atobe}
In this section, we review a criterion for the nonvanishing of theta lifts due to Atobe \cite{atobe}.
\subsection{Some invariants}
\label{ss:atobe-def}
Let $W$ be an $n$-dimensional skew-Hermitian space over $\C$.
Fix $k_0 = -1$ or $0$.
We consider the theta lifting from $\U(W)$ to $\U(V)$, where $V$ varies over $m$-dimensional Hermitian spaces over $\C$ with
\[
m \equiv n+k_0 \bmod 2.
\]
Fix an integer $m_0$ with $m_0 \equiv n+k_0 \bmod 2$ and take the character $\chi_V$ of $\C^\times$ given by
\[
\chi_V(z) = \bigg( \frac{z}{\sqrt{z \bar{z}}} \bigg)^{m_0}.
\]
Let $\pi$ be an irreducible tempered representation of $\U(W)$.
Following \cite[\S 4.1]{atobe}, we define some invariants of $\pi$ (which depend on $k_0$ and $\chi_V$) as follows.
Write $\pi = \pi(\phi, \eta)$, where $\phi$ is a tempered $L$-parameter for $\U_n$ and $\eta$ is a character of $S_\phi$.
We may write $\phi$ as
\[
\phi = (m_1 \chi_{\kappa_1} \oplus \dots \oplus m_a \chi_{\kappa_a} \oplus n_1 \chi_{\mu_1} \oplus \dots \oplus n_b \chi_{\mu_b} \oplus \xi_1 \oplus \dots \oplus \xi_d \oplus \check{\xi}_1 \oplus \dots \oplus \check{\xi}_d) \otimes \chi_V,
\]
where
\begin{itemize}
\item $\kappa_i, \mu_j \in \Z + \frac{k_0-1}{2}$;
\item $\kappa_i \ne \mu_j$ for all $i,j$;
\item $\kappa_1 > \dots > \kappa_a$ and $\mu_1 > \dots > \mu_b$;
\item $\xi_i$ is a unitary character of $\C^\times$ which is not conjugate-selfdual with sign $(-1)^{n-1}$;
\item $m_i$ and $n_j$ are odd and even positive integers, respectively;
\item $m_1 + \dots + m_a + n_1 + \dots + n_b + 2d = n$.
\end{itemize}
Then $S_\phi$ is a free $\Z/2\Z$-module of the form
\[
S_\phi = (\Z/2\Z) \tilde{e}_{\kappa_1} \oplus \dots \oplus (\Z/2\Z) \tilde{e}_{\kappa_a} \oplus (\Z/2\Z) \tilde{e}_{\mu_1} \oplus \dots \oplus (\Z/2\Z) \tilde{e}_{\mu_b},
\]
where $\tilde{e}_{\kappa_i}$ and $\tilde{e}_{\mu_j}$ correspond to $\chi_{\kappa_i} \chi_V$ and $\chi_{\mu_j} \chi_V$, respectively.
Put
\[
\epsilon_{\kappa_i} = \eta(\tilde{e}_{\kappa_i}), \quad
\epsilon_{\mu_j} = \eta(\tilde{e}_{\mu_j}).
\]
\begin{enumerate}
\item
Let $k_\pi$ be the largest positive integer such that
\begin{itemize}
\item $k_\pi \equiv k_0 \bmod 2$;
\item $\{ \frac{k_\pi-1}{2}, \frac{k_\pi-3}{2}, \dots, -\frac{k_\pi-1}{2} \} \subset \{ \kappa_1, \dots, \kappa_a \}$;
\item $\epsilon_{\frac{k_\pi+1}{2} - i} \ne \epsilon_{\frac{k_\pi-1}{2} - i}$ for all $1 \le i < k_\pi$.
\end{itemize}
If such an integer does not exist, we put $k_\pi = k_0$.
\item
Put
\begin{align*}
r_\pi & = \# \left\{ 1 \le i \le a \, \left| \, |\kappa_i| \ge \frac{k_\pi+1}{2}, (-1)^{i-1} \epsilon_{\kappa_i} \kappa_i > 0 \right. \right\} + \frac{n-a}{2}, \\
s_\pi & = \# \left\{ 1 \le i \le a \, \left| \, |\kappa_i| \ge \frac{k_\pi+1}{2}, (-1)^{i-1} \epsilon_{\kappa_i} \kappa_i < 0 \right. \right\} + \frac{n-a}{2}.
\end{align*}
\item
Define a finite subset $\XX_\pi$ of $\frac{1}{2} \Z \times \{ \pm 1 \}$ by
\[
\XX_\pi = \{ (\kappa_i, (-1)^{i-1} \epsilon_{\kappa_i}) \, | \, 1 \le i \le a \} \cup \{ (\mu_j, +1), (\mu_j, -1) \, | \, 1 \le j \le b, \, \epsilon_{\mu_j} \ne (-1)^{c_j} \},
\]
where $c_j = \# \{ 1 \le i \le a \, | \, \kappa_i > \mu_j \}$.
\item
Define a sequence
\[
\XX_\pi = \XX_\pi^{(0)} \supset \XX_\pi^{(1)} \supset \dots \supset \XX_\pi^{(j)} \supset \cdots
\]
inductively as follows.
Write the image of $\XX_\pi^{(j)}$ under the projection $\frac{1}{2} \Z \times \{ \pm 1 \} \rightarrow \frac{1}{2} \Z$ as
\[
\{ \nu_1, \nu_2, \dots \}
\]
with $\nu_1 > \nu_2 > \cdots$ and define a subset $\XX_\pi^{(j+1)}$ of $\XX_\pi^{(j)}$ by
\[
\XX_\pi^{(j+1)} = \XX_\pi^{(j)} \smallsetminus
\bigg( \bigcup_i \{ (\nu_i, +1), (\nu_{i+1}, -1) \} \bigg),
\]
where $i$ runs over indices such that
\begin{itemize}
\item $(\nu_i, +1), (\nu_{i+1},-1) \in \XX_\pi^{(j)}$;
\item $\min \{ |\nu_i|, |\nu_{i+1}| \} \ge \frac{k_\pi+1}{2}$;
\item $\nu_i \nu_{i+1} \ge 0$.
\end{itemize}
\item
Put
\[
\XX_\pi^{(\infty)} = \XX_\pi^{(n)} = \XX_\pi^{(n+1)} = \cdots.
\]
\item
For any integer $x$, we define subsets $\CC_\pi^\pm(x)$ of $\XX_\pi^{(\infty)}$ by
\begin{align*}
\CC_\pi^+(x) & = \left\{ (\nu,+1) \in \XX_\pi^{(\infty)} \, \left| \, 0 \le \frac{k_\pi-1}{2} + \nu < x \right. \right\}, \\
\CC_\pi^-(x) & = \left\{ (\nu,-1) \in \XX_\pi^{(\infty)} \, \left| \, 0 \le \frac{k_\pi-1}{2} - \nu < x \right. \right\}.
\end{align*}
\end{enumerate}
\subsection{A result of Atobe}
We have the following criterion for the nonvanishing of $\theta_{r,s}(\pi)$ due to Atobe \cite[Theorem 4.2]{atobe}, which relies on the Gan--Gross--Prasad conjecture \cite{ggp1} for real unitary groups but is now unconditional thanks to a recent result of Xue \cite{xue}.
Note that the choice of $\psi$ in \cite[\S 3.3]{atobe} is not made explicit, but it agrees with our choice (see \cite[Lemma 1.4.5]{paul1} and Lemma \ref{l:K-type-corresp} below).
Note also that \cite[Theorem 4.2(1)]{atobe} is not correct as stated, but the argument in \cite[\S 5]{atobe} in fact proves:
\begin{thm}[Atobe]
\label{t:atobe}
Let $\pi$ be an irreducible tempered representation of $\U(W)$.
Let $l,t$ be integers with $t \ge 1$.
\begin{enumerate}
\item
Assume that $k_\pi = -1$.
(In particular, we have either $(0, +1), (0, -1) \notin \XX_\pi$ or $(0, +1), (0, -1) \in \XX_\pi$.)
Then
\begin{itemize}
\item
$\theta_{r_\pi + l + 2t + 1, s_\pi + l}(\pi)$ is nonzero if and only if
\[
\left\{
\begin{aligned}
l & \ge 0, \, &
\# \CC_\pi^+(l+t) & \le l, \, &
\# \CC_\pi^-(l+t) & \le l \, &
\text{if $(0, +1), (0, -1) \notin \XX_\pi$;} \\
l & \ge 1, \, &
\# \CC_\pi^+(l+t) & \le l-1, \, &
\# \CC_\pi^-(l+t) & \le l-1 \, &
\text{if $(0, +1), (0, -1) \in \XX_\pi$;}
\end{aligned}
\right.
\]
\item
$\theta_{r_\pi + l + 1, s_\pi + l}(\pi)$ is nonzero if and only if
\[
\begin{cases}
l \ge 0 & \text{if $0 \notin \{ \mu_1, \dots, \mu_b \}$;} \\
l \ge -1 & \text{if $0 \in \{ \mu_1, \dots, \mu_b \}$ and $(0, +1), (0, -1) \notin \XX_\pi$;} \\
l \ge 1 & \text{if $0 \in \{ \mu_1, \dots, \mu_b \}$ and $(0,+1), (0,-1) \in \XX_\pi$.}
\end{cases}
\]
\end{itemize}
\item
Assume that $k_\pi \ge 0$.
Then
\begin{itemize}
\item
$\theta_{r_\pi + l + 2t, s_\pi + l}(\pi)$ is nonzero if and only if
\[
l \ge k_\pi, \quad
\# \CC_\pi^+(l+t) \le l, \quad
\# \CC_\pi^-(l+t) \le l;
\]
\item
$\theta_{r_\pi + l, s_\pi + l}(\pi)$ is nonzero if and only if
\[
\begin{cases}
l \ge -1 & \text{if the conditions \eqref{atobe-1}, \eqref{atobe-2}, \eqref{atobe-3} below hold;} \\
l \ge 0 & \text{otherwise,}
\end{cases}
\]
where
\begin{enumerate}
\item
\label{atobe-1}
$\{ \frac{k_\pi+1}{2}, -\frac{k_\pi+1}{2} \} \subset \{ \kappa_1, \dots, \kappa_a, \mu_1, \dots, \mu_b \}$;
\item
\label{atobe-2}
$\{ \frac{k_\pi+1}{2}, -\frac{k_\pi+1}{2} \} \cap \{ \mu_1, \dots, \mu_b \} \ne \varnothing$;
\item
\label{atobe-3}
$\epsilon_{\frac{k_\pi+1}{2} - i} \ne \epsilon_{\frac{k_\pi-1}{2} - i}$ for all $0 \le i \le k_\pi$.
\end{enumerate}
\end{itemize}
\end{enumerate}
\end{thm}
\begin{rem}
\label{r:atobe}
To determine the nonvanishing of $\theta_{r,s}(\pi)$ with $r+s=m$, we may assume that
\[
r-r_\pi \ge s-s_\pi
\]
by replacing $(r,s)$ by $(s,r)$ and $\pi$ by $\tilde{\pi} = \bar{\pi} \otimes (\chi_V \circ \det)$ if necessary.
Indeed, we have $\theta_{r,s}(\pi) \ne 0$ if and only if $\theta_{s,r}(\tilde{\pi}) \ne 0$ by \cite[Proposition 3.9]{atobe}, while we have
\[
k_{\tilde{\pi}} = k_\pi, \quad
(r_{\tilde{\pi}}, s_{\tilde{\pi}}) = (s_\pi, r_\pi)
\]
by \cite[Lemma 4.4]{atobe}.
If $r-r_\pi \ge s-s_\pi$, then since $m - n \equiv k_\pi \bmod 2$ and
\[
n =
\begin{cases}
r_\pi + s_\pi & \text{if $k_\pi = -1$;} \\
r_\pi + s_\pi + k_\pi & \text{if $k_\pi \ge 0$,}
\end{cases}
\]
we have
\[
(r-r_\pi) - (s-s_\pi) =
\begin{cases}
2t+1 & \text{if $k_\pi = -1$;} \\
2t & \text{if $k_\pi \ge 0$}
\end{cases}
\]
for some nonnegative integer $t$.
Thus Theorem \ref{t:atobe} completely determines the nonvanishing of $\theta_{r,s}(\pi)$.
\end{rem}
\subsection{Some corollaries}
In this subsection, we state some corollaries of Theorem \ref{t:atobe} which will be used later.
We consider the theta lifting from $\U(p,q)$ to $\U(r,s)$ with $p+q=n$ and $r+s=m$.
\begin{cor}
\label{c:jacquet}
Assume that $p,q > 0$.
Let $\pi$ be an irreducible tempered representation of $\U(p,q)$ such that $\pi \subset I(\chi, \pi_0)$, where
\begin{itemize}
\item $\chi$ is a unitary character of $\C^\times$;
\item $\pi_0$ is an irreducible tempered representation of $\U(p-1,q-1)$.
\end{itemize}
Assume further that $\theta_{r,s}(\pi) \ne 0$ and that either $m>n$ or $\chi$ satisfies one of the following conditions (with the notation of \S \ref{ss:atobe-def}):
\begin{itemize}
\item $\chi = \chi_{\kappa_i}$ for some $i$ such that $m_i \ge 3$;
\item $\chi = \chi_{\mu_j}$ for some $j$ such that $n_j \ge 4$;
\item $\chi$ is not conjugate-selfdual with sign $(-1)^{n-1}$.
\end{itemize}
Then we have $r,s > 0$ and $\theta_{r-1,s-1}(\pi_0) \ne 0$.
\end{cor}
\begin{proof}
If $m>n$, then the assertion was proved in \cite[Corollary 4.5]{atobe}.
Thus we assume that $\chi$ satisfies one of the conditions above.
We may assume that $r-r_\pi \ge s-s_\pi$.
By Theorem \ref{t:atobe}, we have
\[
\left\{
\begin{aligned}
r & \ge r_\pi -1, \, & s & \ge s_\pi -1 \, & \text{if $b > 0$;} \\
r & \ge r_\pi, \, & s & \ge s_\pi \, & \text{if $b = 0$.}
\end{aligned}
\right.
\]
On the other hand, we have
\[
r_\pi, s_\pi \ge \sum_{i=1}^a \frac{m_i - 1}{2} + \sum_{j=1}^b \frac{n_j}{2} + d.
\]
From this and the assumption on $\chi$, we can deduce that $r, s > 0$.
Moreover, we have
\[
r_{\pi_0} = r_{\pi} -1, \quad
s_{\pi_0} = s_{\pi} -1, \quad
\XX_{\pi_0} = \XX_\pi, \quad
\CC^\pm_{\pi_0}(x) = \CC^\pm_\pi(x).
\]
Hence by Theorem \ref{t:atobe}, we have $\theta_{r-1,s-1}(\pi_0) \ne 0$.
This completes the proof.
\end{proof}
\begin{cor}
\label{c:local-theta-xyzw}
Let $\pi$ be a (limit of) discrete series representation of $\U(p,q)$ and write $\pi = {\mathstrut}^n \! A_\b(\lambda)$ as in \eqref{eq:lds} with
\[
\lambda = (\alpha_1, \dots, \alpha_{p^+}, \beta_1, \dots, \beta_{p^-}, \gamma_1, \dots, \gamma_{q^+}, \delta_1, \dots, \delta_{q^-}) + \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg),
\]
where
\begin{itemize}
\item $\alpha_i, \gamma_j > 0$ and $\beta_i, \delta_j \le 0$;
\item $p^++p^- = p$ and $q^++q^- = q$.
\end{itemize}
Assume that $m \ge n$ and $\theta_{r,s}(\pi) \ne 0$.
Then we have
\[
p^++q^- \le r, \quad
p^-+q^+ \le s.
\]
\end{cor}
\begin{proof}
We may assume that $r - r_\pi \ge s - s_\pi$, so that
\[
(r,s) =
\begin{cases}
(r_\pi + l + 2t + 1, s_\pi + l) & \text{if $k_\pi = -1$;} \\
(r_\pi + l + 2t, s_\pi + l) & \text{if $k_\pi \ge 0$}
\end{cases}
\]
for some integers $l,t$ with $t \ge 0$.
Since $m \ge n$ and $\theta_{r,s}(\pi) \ne 0$, it follows from Theorem \ref{t:atobe} that
\[
\begin{cases}
l \ge 0 & \text{if $k_\pi = -1$;} \\
l \ge \frac{k_\pi}{2} & \text{if $k_\pi \ge 0$.}
\end{cases}
\]
On the other hand, we have
\[
(r_\pi, s_\pi) =
\begin{cases}
(p^++q^-, p^-+q^+) & \text{if $k_\pi = -1$}; \\
(p^++q^--\frac{k_\pi}{2}, p^-+q^+-\frac{k_\pi}{2}) & \text{if $k_\pi \ge 0$ and $k_\pi$ is even}; \\
(p^++q^--\frac{k_\pi \pm 1}{2}, p^-+q^+-\frac{k_\pi \mp 1}{2}) & \text{if $k_\pi \ge 0$ and $k_\pi$ is odd.}
\end{cases}
\]
This implies the assertion.
\end{proof}
\begin{cor}
\label{c:going-down}
Let $\pi$ be a (limit of) discrete series representation of $\U(p,q)$.
Assume that $m \le n-2$ and $\theta_{r,s}(\pi) \ne 0$.
Put $k = n-m$.
Then one of the following holds:
\begin{itemize}
\item
$k_\pi \ge 2$, $2 \le k \le k_\pi$, and
\[
(r,s) = (r_\pi + \tfrac{k_\pi - k}{2}, s_\pi + \tfrac{k_\pi - k}{2});
\]
\item
$k_\pi \ge 0$, $k = k_\pi + 2$,
\[
(r,s) = (r_\pi -1, s_\pi -1),
\]
and the conditions \eqref{atobe-1}, \eqref{atobe-2}, \eqref{atobe-3} in Theorem \ref{t:atobe} hold.
\end{itemize}
\end{cor}
\begin{proof}
We may assume that $r - r_\pi \ge s - s_\pi$, so that
\[
(r,s) =
\begin{cases}
(r_\pi + l + 2t + 1, s_\pi + l) & \text{if $k_\pi = -1$;} \\
(r_\pi + l + 2t, s_\pi + l) & \text{if $k_\pi \ge 0$}
\end{cases}
\]
for some integers $l,t$ with $t \ge 0$.
Since $m \le n-2$ and
\[
n =
\begin{cases}
r_\pi + s_\pi & \text{if $k_\pi = -1$;} \\
r_\pi + s_\pi + k_\pi & \text{if $k_\pi \ge 0$,}
\end{cases}
\]
we have $2l+2t \le k_\pi -2$.
Hence it follows from Theorem \ref{t:atobe} that one of the following holds:
\begin{itemize}
\item $k_\pi \ge 2$, $0 \le l \le \frac{k_\pi}{2} -1$, and $t = 0$;
\item $k_\pi \ge 0$, $l=-1$, $t=0$, and the conditions \eqref{atobe-1}, \eqref{atobe-2}, \eqref{atobe-3} in Theorem \ref{t:atobe} hold.
\end{itemize}
This implies the assertion.
\end{proof}
\begin{cor}
\label{c:going-up}
Let $\pi$ be a (limit of) discrete series representation of $\U(p,q)$ and write $\pi = {\mathstrut}^n \! A_\b(\lambda)$ as in \eqref{eq:lds}.
Assume that $m \ge n+2$.
Put $k = m-n$.
Assume further that $\lambda$ is of the form
\begin{align*}
\lambda & = \bigg( \alpha_1, \dots, \alpha_{p^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{p'},
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{p''},
\beta_1, \dots, \beta_{p^-}, \\
& \phantom{{} = \bigg(} \gamma_1, \dots, \gamma_{q^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{q'},
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{q''},
\delta_1, \dots, \delta_{q^-} \bigg)
+ \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg),
\end{align*}
where
\begin{itemize}
\item $\alpha_i, \gamma_j > \frac{k-1}{2}$ and $\beta_i, \delta_j < -\frac{k-1}{2}$;
\item $p',p'',q',q'' \ge 0$;
\item $|p'-q'|, |p''-q''| \le 1$;
\item $p^++p^-+p'+p'' = p$ and $q^++q^-+q'+q'' = q$,
\end{itemize}
and that $\b = \q(x)$ is associated to
\begin{align*}
x & = (x^+_1, \dots, x^+_{p^+}, x'_1, \dots, x'_{p'}, x''_1, \dots, x''_{p''}, x^-_1, \dots, x^-_{p^-}, \\
& \phantom{{} = (} y^+_1, \dots, y^+_{q^+}, y'_1, \dots, y'_{q'}, y''_1, \dots, y''_{q''}, y^-_1, \dots, y^-_{q^-})
\end{align*}
such that either the conditions
\begin{enumerate}
\item
\label{going-up-1}
$p'-q'=0$ and
\[
x'_1 > y'_1 > \dots > x'_{p'} > y'_{q'},
\]
or $p'-q'=-1$ and
\[
y'_1 > x'_1 > \dots > y'_{p'} > x'_{p'} > y'_{q'};
\]
\item
\label{going-up-2}
$p'' - q'' = 0$ and
\[
x''_1 > y''_1 > \dots > x''_{p''} > y''_{q''},
\]
or $p'' - q'' = 1$ and
\[
x''_1 > y''_1 > \dots > x''_{q''} > y''_{q''} > x''_{p''},
\]
\end{enumerate}
or the conditions
\begin{enumerate}[resume]
\item
\label{going-up-3}
$p'-q'=0$ and
\[
y'_1 > x'_1 > \dots > y'_{q'} > x'_{p'},
\]
or $p'-q'=1$ and
\[
x'_{1} > y'_{1}> \dots > x'_{q'} > y'_{q'} > x'_{p'};
\]
\item
\label{going-up-4}
$p'' - q'' = 0$ and
\[
y''_1 > x''_1 > \dots > y''_{q''} > x''_{p''},
\]
or $p'' - q'' = -1$ and
\[
y''_1 > x''_1 > \dots > y''_{p''} > x''_{p''} > y''_{q''}
\]
\end{enumerate}
hold.
Then we have
\[
\theta_{r,s}(\pi) \ne 0,
\]
where
\[
(r,s) =
\begin{cases}
(p^+ + p' + q^- + q'' + k, p^- + p'' + q^+ + q') & \text{if the conditions \eqref{going-up-1}, \eqref{going-up-2} hold;} \\
(p^+ + p' + q^- + q'', p^- + p'' + q^+ + q' + k) & \text{if the conditions \eqref{going-up-3}, \eqref{going-up-4} hold.}
\end{cases}
\]
\end{cor}
\begin{proof}
Put
\[
m' = p'+q', \quad
m'' = p''+q'', \quad
t = \frac{k+k_0}{2},
\]
where $k_0 = -1$ or $0$ is such that $k_0 \equiv k \bmod 2$.
Write $\pi = \pi(\phi, \eta)$, where $\phi$ is a (limit of) discrete series $L$-parameter for $\U_n$ and $\eta$ is a character of $S_\phi$.
Then we have
\[
\eta(\tilde{e}_{\frac{k-1}{2}}) = \eta(\tilde{e}_{-\frac{k-1}{2}}) = \epsilon_0 \cdot (-1)^{p^+ + q^+ +m'}
\]
with the notation of \S \ref{ss:atobe-def}, where
\[
\epsilon_0 =
\begin{cases}
+1 & \text{if the conditions \eqref{going-up-1}, \eqref{going-up-2} hold;} \\
-1 & \text{if the conditions \eqref{going-up-3}, \eqref{going-up-4} hold.}
\end{cases}
\]
(When $m'=0$ or $m''=0$, we ignore the corresponding identity.)
Replacing $\pi$ by $\bar{\pi} \otimes (\chi_V \circ \det)$ if necessary, we may assume that $\epsilon_0 = +1$.
Then we have $k_\pi = k_0$ and
\[
(r_\pi, s_\pi) = (p^+ + p' + q^- + q'', p^- + p'' + q^++ q').
\]
Moreover, we have the following.
\begin{itemize}
\item If $k_0 = -1$, then we have $(0, +1), (0, -1) \notin \XX_{\pi}$.
\item If $m'$ is even, then we have $(\frac{k-1}{2}, +1), (\frac{k-1}{2}, -1) \notin \XX_{\pi}$, so that $\CC^+_\pi(t) = \varnothing$.
\item If $m'$ is odd, then we have $(\frac{k-1}{2}, -1) \in \XX_{\pi}$ but $(\frac{k-1}{2}, +1) \notin \XX_{\pi}$, so that $\CC^+_\pi(t) = \varnothing$.
\item If $m''$ is even, then we have $(-\frac{k-1}{2}, +1), (-\frac{k-1}{2}, -1) \notin \XX_{\pi}$, so that $\CC^-_\pi(t) = \varnothing$.
\item If $m''$ is odd, then we have $(-\frac{k-1}{2}, +1) \in \XX_{\pi}$ but $(-\frac{k-1}{2}, -1) \notin \XX_{\pi}$, so that $\CC^-_\pi(t) = \varnothing$.
\end{itemize}
Hence by Theorem \ref{t:atobe}, we have
\[
\theta_{r_\pi + k, s_\pi}(\pi) \ne 0.
\]
This completes the proof.
\end{proof}
\section{Nonvanishing of integrals of matrix coefficients}
In this section, we show that the nonvanishing of theta lifts is equivalent to that of the associated integrals of matrix coefficients in some cases, which is a crucial step in the proof of Theorem \ref{t:main-lds}.
\subsection{A key proposition}
\label{ss:key}
Let $V$ be an $m$-dimensional Hermitian space over $\C$ and $W$ an $n$-dimensional skew-Hermitian space over $\C$.
Recall the associated symplectic space $V \otimes_\C W$ over $\R$ and fix a maximal isotropic subspace $\X$ of $V \otimes_\C W$.
We take the datum $(\chi_V, \chi_W, \psi)$ given in \S \ref{ss:main-theorem-setup} and realize the (smooth) Weil representation $\omega = \omega_{V,W,\chi_V,\chi_W,\psi}$ of $\U(V) \times \U(W)$ on the space $\SS(\X)$ of Schwartz functions on $\X$.
Here $\SS(\X)$ is endowed with the usual topology which makes it into a Fr\'echet space.
Let $(\cdot, \cdot)$ be the invariant Hermitian inner product on $\SS(\X)$ given by
\[
(\varphi_1, \varphi_2) = \int_{\X} \varphi_1(x) \overline{\varphi_2(x)} \, dx.
\]
Let $\pi$ be an irreducible tempered representation of $\U(W)$.
Here we work with a smooth representation of moderate growth, so that the space $\VV$ of $\pi$ is a Fr\'echet space.
Let $(\cdot, \cdot)$ be an invariant Hermitian inner product on $\VV$.
If $m \ge n$, then we have a separately continuous map
\[
\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi) : \mathcal{S}(\X) \times \mathcal{S}(\X) \times \VV \times \VV \rightarrow \C
\]
given by
\[
(\varphi_1, \varphi_2, v_1, v_2) \mapsto \int_{\U(W)} (\omega(g) \varphi_1, \varphi_2) \overline{(\pi(g) v_1, v_2)} \, dg,
\]
where the integral above is absolutely convergent (see \S \ref{ss:matcoeff-weil} below).
\begin{prop}
\label{p:key}
Let $\pi$ be an irreducible tempered representation of $\U(W)$.
Assume that $m \ge n$.
Then $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi)$ is nonzero if and only if $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi)$ is nonzero.
\end{prop}
\begin{rem}
Since $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi)$ is separately continuous, we may replace $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi)$ in the proposition above by its restriction to the dense subspace
\[
S(\X) \times S(\X) \times \VV_K \times \VV_K.
\]
Here $S(\X)$ is the subspace of $\SS(\X)$ consisting of functions which correspond to polynomials in the Fock model and $\VV_K$ is the space of $K$-finite vectors in $\VV$, where $K$ is a maximal compact subgroup of $\U(W)$.
Also, we mean $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi)$ by either the smooth version of the theta lift of $\pi$ or the algebraic version of the theta lift of the Harish-Chandra module associated to $\pi$.
In fact, they coincide by \cite{bao-sun}.
\end{rem}
\begin{rem}
\label{r:Z}
As explained in Remark \ref{r:atobe}, we have $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$ if and only if $\theta_{-V,W,\chi_V,\chi_W,\psi}(\tilde{\pi}) \ne 0$, where we write $-V$ for the space $V$ equipped with the Hermitian form $- \langle \cdot, \cdot \rangle_V$ and put $\tilde{\pi} = \bar{\pi} \otimes (\chi_V \circ \det)$.
This is an immediate consequence of the fact that
\[
\overline{\omega_{V,W,\chi_V,\chi_W,\psi}}
= \omega_{-V,W,\chi_V,\chi_W,\psi} \otimes ((\chi_W^{-1} \circ \det) \boxtimes (\chi_V^{-1} \circ \det))
\]
as representations of $\U(V) \times \U(W)$, which in fact induces a natural identification
\[
\overline{\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi)} = \ZZ_{-V,W,\chi_V,\chi_W,\psi}(\tilde{\pi}).
\]
In particular, we also have $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$ if and only if $\ZZ_{-V,W,\chi_V,\chi_W,\psi}(\tilde{\pi}) \ne 0$.
\end{rem}
The rest of this section is devoted to the proof of Proposition \ref{p:key}.
\subsection{Harish-Chandra Schwartz spaces}
Put $G = \U(W)$.
Let $\g$ be the complexified Lie algebra of $G$ and $U(\g)$ the universal enveloping algebra of $\g$.
Let $\Xi = \Xi_G$ and $\sigma = \sigma_G$ be the spherical functions on $G$ as in \cite[p.~329]{va} and \cite[p.~320]{va}, respectively.
For $X, Y \in U(\g)$, $r \in \R$, and a smooth function $f$ on $G$, put
\[
p_{X,Y,r}(f) = \sup_{g \in G} |(L(X)R(Y)f)(g)| \Xi(g)^{-1} (1 + \sigma(g))^r,
\]
where $L$ and $R$ are the left and right translations, respectively.
We denote by $\CC(G)$ the Harish-Chandra Schwartz space, which is defined as the space of smooth functions $f$ on $G$ such that
\[
p_{X,Y,r}(f) < \infty
\]
for all $X, Y \in U(\g)$ and $r > 0$.
We endow $\CC(G)$ with the topology given by seminorms $p_{X,Y,r}$ for all $X, Y \in U(\g)$ and $r>0$, which makes it into a Fr\'echet space.
For $f_1, f_2 \in \CC(G)$, we may define their convolution $f_1 * f_2$ by
\[
(f_1 * f_2)(g) = \int_G f_1(h) f_2(h^{-1} g) \, dh,
\]
where the integral above is absolutely convergent.
Then $f_1 * f_2$ belongs to $\CC(G)$ and the associated map
\[
\CC(G) \times \CC(G) \rightarrow \CC(G)
\]
is continuous (see \cite[p.~357, Theorem 18]{va}).
Let $\pi$ be an irreducible tempered representation of $G$ on a Fr\'echet space $\VV$.
Namely, for any $v_1, v_2 \in \VV$, there exists a constant $C$ such that
\[
|(\pi(g) v_1, v_2)| \le C \Xi(g)
\]
for all $g \in G$.
We may extend the action of $G$ on $\VV$ to an action of $\CC(G)$ by
\begin{equation}
\label{eq:C(G)-action}
(\pi(f) v_1, v_2) = \int_G f(g) (\pi(g) v_1, v_2) \, dg
\end{equation}
for $f \in \CC(G)$ and $v_1, v_2 \in \VV$.
Assume that $\pi$ is a discrete series representation.
Then the function $g \mapsto (\pi(g) v_1, v_2)$ belongs to $\CC(G)$ for all $v_1, v_2 \in \VV$.
Let $\AA(\pi)$ be the closure in $\CC(G)$ of the subspace spanned by these functions, on which the left and right translations define an irreducible representation of $G \times G$ (see \cite[p.~468, Theorem 11 and p.~469, Theorem 13]{va}).
For $f_1 \in \CC(G)$ and $f_2 \in \AA(\pi)$, we have $f_1 * f_2 \in \AA(\pi)$ by \eqref{eq:C(G)-action}.
\subsection{Matrix coefficients of Weil representations}
\label{ss:matcoeff-weil}
Assume that $m \ge n$.
Recall the Weil representation $\omega$ of $G$ on $\SS(\X)$.
\begin{lem}
\label{l:matcoeff-weil}
For $\varphi_1, \varphi_2 \in \SS(\X)$, the function $g \mapsto (\omega(g) \varphi_1, \varphi_2)$ belongs to $\CC(G)$.
\end{lem}
\begin{proof}
The assertion follows from \cite[(25)]{li89} and \cite[p.~330, Proposition 17]{va}.
\end{proof}
Let $\pi$ be an irreducible tempered representation of $G$ on $\VV$.
Then the lemma above implies that the integral defining $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi)$ is absolutely convergent.
Moreover, as in the proof of \cite[Lemma 6.2]{li89}, we can deduce from this and the bounds for matrix coefficients due to Sun \cite{sun} that $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi)$ is separately continuous.
\begin{lem}
\label{l:proj-pi}
Assume that $\pi$ is a discrete series representation and that $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi)$ is nonzero.
Then the functions
\[
g \mapsto \int_G (\omega(gh) \varphi_1, \varphi_2) \overline{(\pi(h) v_1, v_2)} \, dh
\]
for all $\varphi_1, \varphi_2 \in \SS(\X)$ and $v_1, v_2 \in \VV$ span a dense subspace of $\AA(\pi)$.
\end{lem}
\begin{proof}
We may write the integral above as $(f_1 * f_2)(g)$, where
\[
f_1(g) = (\omega(g) \varphi_1, \varphi_2), \quad
f_2(g) = (\pi(g) v_2, v_1).
\]
Since $f_1 \in \CC(G)$ by Lemma \ref{l:matcoeff-weil} and $f_2 \in \AA(\pi)$, we have $f_1 * f_2 \in \AA(\pi)$.
Hence these functions span a $G \times G$-invariant subspace of $\AA(\pi)$.
Since $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$, this subspace is nonzero, so that its closure in $\CC(G)$ agrees with $\AA(\pi)$ by the irreducibility of $\AA(\pi)$.
This completes the proof.
\end{proof}
\subsection{Inductive step}
The only if part of Proposition \ref{p:key} is obvious.
For the if part, we proceed by induction on $\dim V - \dim W$ as in the proof of \cite[Proposition 5.4]{atobe}, where $V$ is fixed but $W$ and $\pi$ vary.
In particular, we use a seesaw diagram
\[
\begin{tikzcd}
\U(W') \arrow[rd,dash] & \U(V) \times \U(V) \arrow[ld,dash] \\
\U(W) \times \U(W^\perp) \arrow[u,dash] & \U(V) \arrow[u,dash]
\end{tikzcd},
\]
where $V$ is an $m$-dimensional Hermitian space over $\C$, $W'$ is an $(n+1)$-dimensional skew-Hermitian space over $\C$, $W$ is an $n$-dimensional skew-Hermitian subspace of $W'$, and $W^\perp$ is the orthogonal complement of $W$ in $W'$.
We take a datum $(\chi_V, \chi_{W'}, \psi)$, where $\chi_V$ and $\psi$ are as above, and $\chi_{W'}$ is a characters of $\C^\times$ given by
\[
\chi_{W'}(z) = \left( \frac{z}{\sqrt{z \bar{z}}} \right)^{n'_0}
\]
for some integer $n'_0$ such that $n'_0 \equiv n+1 \bmod 2$.
\begin{lem}
\label{l:seesaw}
Let $\pi$ be an irreducible tempered representation of $\U(W)$.
Assume that $m > n$ and that there exists a discrete series representation $\pi'$ of $\U(W')$ such that
\begin{enumerate}
\item
\label{seesaw-1}
$\ZZ_{V,W',\chi_V,\chi_{W'},\psi}(\pi') \ne 0$;
\item
\label{seesaw-2}
$\Hom_{\U(W)}(\pi', \pi) \ne 0$.
\end{enumerate}
Then we have $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$.
\end{lem}
\begin{proof}
Put $G = \U(W)$ and $G' = \U(W')$.
Let $\VV$ and $\VV'$ be the spaces of $\pi$ and $\pi'$, respectively.
Define a continuous map
\[
\LL(\pi', \pi) : \VV' \times \VV' \times \VV \times \VV \rightarrow \C
\]
by
\[
(v_1', v_2', v_1, v_2) \mapsto \int_G (\pi'(g) v_1',v_2') \overline{(\pi(g) v_1,v_2)} \, dg,
\]
where the integral above is absolutely convergent (see \cite[Lemma 6.5.1(i)]{bp}).
By \eqref{seesaw-2} and a result of Beuzart-Plessis \cite[Theorem 7.2.1]{bp}, we have $\LL(\pi', \pi) \ne 0$.
Hence by \eqref{seesaw-1} and Lemma \ref{l:proj-pi}, we have
\[
\int_G \bigg( \int_{G'} (\omega'(g g') \varphi_1', \varphi_2') \overline{(\pi'(g')v_1', v_2')} \, dg' \bigg) \overline{(\pi(g) v_1, v_2)} \, dg \ne 0\]
for some $\varphi_1', \varphi_2' \in \SS(\X')$, $v_1', v_2' \in \VV'$, and $v_1, v_2 \in \VV$.
Here $\omega' = \omega_{V,W',\chi_V, \chi_{W'}, \psi}$ is the Weil representation of $G'$ on $\SS(\X')$, where $\X'$ is a maximal isotropic subspace of $V \otimes_\C W'$.
If we formally interchange the order of integration, then we have
\begin{equation}
\label{eq:nonvanish-2}
\int_G (\omega'(g g') \varphi_1', \varphi_2') \overline{(\pi(g) v_1, v_2)} \, dg \ne 0
\end{equation}
for some $g' \in G'$.
To justify the manipulation, we show that the double integral
\[
\int_G \int_{G'} (\omega'(g g') \varphi_1', \varphi_2') \overline{(\pi'(g')v_1', v_2') (\pi(g) v_1, v_2)} \, dg' \, dg
\]
is absolutely convergent.
By Lemma \ref{l:matcoeff-weil}, the integral above is bounded by
\[
C \int_G \int_{G'} \Xi_{G'}(gg') (1 + \sigma_{G'}(gg'))^{-r} \Xi_{G'}(g') \Xi_G(g) \, dg' \, dg
\]
for some $C>0$ and $r \gg 0$.
By \cite[p.~356, Lemma 17]{va}, we have
\[
\int_{G'} \Xi_{G'}(gg') (1 + \sigma_{G'}(gg'))^{-r} \Xi_{G'}(g') \, dg' \le C' \Xi_{G'}(g)
\]
for some $C'>0$.
Hence the absolute convergence follows from \cite[Lemma 6.5.1(i)]{bp}.
We may assume that $\X' = \X \oplus \X^\perp$, where $\X^\perp$ is a maximal isotropic subspace of $V \otimes_\C W^\perp$.
Then we have an identification
\[
\SS(\X') = \SS(\X) \mathbin{\hat{\otimes}} \SS(\X^\perp),
\]
where $\mathbin{\hat{\otimes}}$ denotes the projective tensor product, such that
\[
\omega'(g) (\varphi \otimes \varphi^\perp) = (\omega(g) \varphi) \otimes \varphi^\perp
\]
for $g \in G$, $\varphi \in \SS(\X)$, and $\varphi^\perp \in \SS(\X^\perp)$.
On the other hand, it follows from the argument in the proof of \cite[Lemma 6.2]{li89} that the map
\[
(\varphi', \varphi'') \mapsto
\int_G (\omega'(g) \varphi', \varphi'') \overline{(\pi(g) v_1, v_2)} \, dg
\]
on $\SS(\X') \times \SS(\X')$ is separately continuous.
From this and \eqref{eq:nonvanish-2}, we can deduce that
\[
\int_G (\omega(g) \varphi_1, \varphi_2) \overline{(\pi(g) v_1, v_2)} \, dg \ne 0
\]
for some $\varphi_1, \varphi_2 \in \SS(\X)$, so that $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$.
This completes the proof.
\end{proof}
Fix an $m$-dimensional Hermitian space $V$ over $\C$ and a character $\chi_V$ of $\C^\times$ such that $\chi_V|_{\R^\times} = \omega_{\C/\R}^m$.
Let $(r,s)$ be the signature of $V$.
For any $n$-dimensional skew-Hermitian space $W$ over $\C$ and any irreducible tempered representation $\pi$ of $\U(W)$, we define integers $k_\pi, r_\pi, s_\pi$ as in \S \ref{ss:atobe-def} with respect to $k_0$ and $\chi_V$, where $k_0 = -1$ or $0$ is determined by
\[
m \equiv n + k_0 \bmod 2.
\]
By Remarks \ref{r:atobe} and \ref{r:Z}, we may assume that $r-r_\pi \ge s - s_\pi$, so that
\begin{equation}
\label{eq:(r,s)}
(r,s) =
\begin{cases}
(r_\pi + l + 2t + 1, s_\pi + l) & \text{if $k_\pi = -1$;} \\
(r_\pi + l + 2t, s_\pi + l) & \text{if $k_\pi \ge 0$}
\end{cases}
\end{equation}
for some integers $l,t$ with $t \ge 0$.
\begin{lem}
\label{l:induction-disc}
Let $\pi$ be a discrete series representation of $\U(W)$ such that $k_\pi, r_\pi, s_\pi$ satisfy \eqref{eq:(r,s)} for some integers $l,t$ with
\[
\begin{cases}
l \ge 0, t \ge 0 & \text{if $k_\pi = -1$;} \\
l \ge 0, t \ge 1 & \text{if $k_\pi = 0$;} \\
l \ge k_\pi, t \ge 0 & \text{if $k_\pi \ge 1$}
\end{cases}
\]
(and hence $m>n$).
Assume that $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$.
Then there exist an $(n+1)$-dimensional skew-Hermitian space $W'$ over $\C$ containing $W$ and a discrete series representation $\pi'$ of $\U(W')$ such that
\begin{itemize}
\item $\theta_{V,W',\chi_V,\chi_{W'},\psi}(\pi') \ne 0$;
\item $\Hom_{\U(W)}(\pi', \pi) \ne 0$;
\item $k_{\pi'}, r_{\pi'}, s_{\pi'}$ satisfy the following conditions:
\begin{itemize}
\item
if $k_\pi = -1$, then $k_{\pi'} = 0$ and
\[
(r,s) = (r_{\pi'} + l + 2t, s_{\pi'} + l);
\]
\item
if $k_\pi = 0$, then $k_{\pi'} = -1$ and
\[
\text{$(r,s) = (r_{\pi'} + l + 2(t-1) + 1, s_{\pi'} + l)$ or $(r_{\pi'} + (l-1) + 2t + 1, s_{\pi'} + (l-1))$,}
\]
where the second case happens only if $l \ge 1$;
\item
if $k_\pi \ge 1$, then $k_{\pi'} = k_\pi-1$ and
\[
(r,s) = (r_{\pi'} + (l-1) + 2t, s_{\pi'} + (l-1)).
\]
\end{itemize}
\end{itemize}
\end{lem}
\begin{proof}
The assertion was essentially proved by Atobe (see Lemmas 5.1, 5.2, 5.3 of \cite{atobe} in the cases $k_\pi = -1, k_\pi = 0, k_\pi \ge 1$, respectively).
We only give some details in the case $k_\pi = 0$.
Since $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$, we have $\# \CC_\pi^\pm(l+t) \le l$ by Theorem \ref{t:atobe}.
Let $W'$ be the skew-Hermitian space over $\C$ of signature $(p+1,q)$, where $(p,q)$ is the signature of $W$.
Then by \cite[Lemma 5.2]{atobe}, there exists a discrete series representation $\pi'$ of $\U(W')$ (relative to the choice of integers $l+t \ll \beta_0 < \beta_1 < \cdots$) satisfying the following conditions:
\begin{itemize}
\item $\Hom_{\U(W)}(\pi', \pi) \ne 0$;
\item $k_{\pi'} = -1$;
\item $(r_{\pi'}, s_{\pi'}) =
\begin{cases}
(r_\pi + 1, s_\pi) & \text{if $(\frac{1}{2}, +1)$ and $(-\frac{1}{2}, -1)$ do not belong to $\XX_\pi$;} \\
(r_\pi, s_\pi + 1) & \text{if $(\frac{1}{2}, +1)$ or $(-\frac{1}{2}, -1)$ belongs to $\XX_\pi$;}
\end{cases}
$
\item $\# \CC^\pm_{\pi'}(l+t-1) \le
\begin{cases}
l & \text{if $(\frac{1}{2}, +1)$ and $(-\frac{1}{2}, -1)$ do not belong to $\XX_\pi$;} \\
l-1 & \text{if $(\frac{1}{2}, +1)$ or $(-\frac{1}{2}, -1)$ belongs to $\XX_\pi$.}
\end{cases}
$
\end{itemize}
Note that if $(\frac{\epsilon}{2}, \epsilon) \in \XX_\pi$ for some $\epsilon = \pm 1$, then $(\frac{\epsilon}{2}, \epsilon) \in \XX_\pi^{(\infty)}$.
Since $t \ge 1$, this implies that $\# \CC_\pi^\epsilon(t) \ge 1$ and hence $l \ge 1$.
By Theorem \ref{t:atobe} again, the conditions above imply that $\theta_{V,W',\chi_V,\chi_{W'},\psi}(\pi') \ne 0$.
This completes the proof.
\end{proof}
\begin{lem}
\label{l:induction-temp}
Let $\pi$ be an irreducible tempered representation of $\U(W)$ such that $k_\pi, r_\pi, s_\pi$ satisfy \eqref{eq:(r,s)} for some integers $l,t$ with $t \ge 0$.
Assume that $m>n$ and $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$.
Then there exist an $(n+1)$-dimensional skew-Hermitian space $W'$ over $\C$ containing $W$ and a discrete series representation $\pi'$ of $\U(W')$ such that
\begin{itemize}
\item $\theta_{V,W',\chi_V,\chi_{W'},\psi}(\pi') \ne 0$;
\item $\Hom_{\U(W)}(\pi', \pi) \ne 0$.
\end{itemize}
\end{lem}
\begin{proof}
As in Lemma \ref{l:induction-disc}, we can deduce the assertion from Theorem \ref{t:atobe} and \cite[Lemmas 5.1, 5.2, 5.3]{atobe}.
We omit the details.
\end{proof}
We now prove Proposition \ref{p:key}.
Let $\pi$ be an irreducible tempered representation of $\U(W)$.
If $m=n$ or $n+1$, then Proposition \ref{p:key} was proved in \cite[Proposition B.4.1]{hls}, \cite[Proposition 11.5(ii)]{gqt}.
(Note that these cases were used by Xue \cite{xue} in the proof of the Gan--Gross--Prasad conjecture.)
Thus we assume that $m \ge n+2$.
Then we need to show that if $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$, then $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$.
As above, we may assume that $k_\pi, r_\pi, s_\pi$ satisfy \eqref{eq:(r,s)} for some integers $l,t$ with $t \ge 0$.
By Lemmas \ref{l:seesaw} and \ref{l:induction-temp}, we are reduced to the case when $\pi$ is a discrete series representation.
In this case, it follows from Theorem \ref{t:atobe} that if $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$, then
\[
\begin{cases}
l \ge 0, t \ge 0 & \text{if $k_\pi = -1$;} \\
l \ge 0, t \ge 0 & \text{if $k_\pi = 0$;} \\
\text{$l \ge 0, t = 0$ or $l \ge k_\pi, t \ge 1$} & \text{if $k_\pi \ge 1$.}
\end{cases}
\]
We first consider the case $k_\pi = -1$ or $0$ (and hence $l \ge 0, t \ge 0$).
By Lemmas \ref{l:seesaw} and \ref{l:induction-disc}, and an induction on $l+t$, we are reduced to the case $k_\pi = 0, l \ge 0, t = 0$.
In this case, the assertion will be proved in Lemma \ref{l:base} below.
We next consider the case $k_\pi \ge 1$.
If $t \ge 1$ (and hence $l \ge k_\pi$), then by Lemmas \ref{l:seesaw} and \ref{l:induction-disc}, and an induction on $k_\pi$, we are reduced to the case $k_\pi = 0, l \ge 0, t \ge 1$.
But this case has already been treated above.
If $t = 0$ (and hence $l \ge \frac{k_\pi}{2}$), then the assertion will be proved in Lemma \ref{l:base} below.
\subsection{Base step}
We continue with the setup of the previous subsection.
To finish the proof of Proposition \ref{p:key}, it remains to prove the following.
\begin{lem}
\label{l:base}
Let $\pi$ be a discrete series representation of $\U(W)$.
Assume that $k_\pi \ge 0$ and
\[
(r,s) = (r_\pi + l, s_\pi + l)
\]
for some integer $l \ge \frac{k_\pi}{2}$ (and hence $m \ge n$).
Then we have $\ZZ_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$.
\end{lem}
This lemma is an immediate consequence of a result of Li \cite[Theorem 4.1]{li90}, but we include some details for the convenience of the reader.
Note that by Theorem \ref{t:atobe}, the assumption automatically implies that $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) \ne 0$.
To prove Lemma \ref{l:base}, we need the notion of $K$-types of minimal degrees introduced by Howe \cite{howe2}.
Let $(p,q)$ be the signature of $W$.
We take the maximal compact subgroup $K \cong \U(p) \times \U(q)$ of $\U(W) = \U(p,q)$ as in \S \ref{ss:real-notation} and parametrize the irreducible representations of $K$ by highest weights
\[
(a_1, \dots, a_p; b_1, \dots, b_q),
\]
where
\begin{itemize}
\item $a_i, b_j \in \Z$;
\item $a_1 \ge \dots \ge a_p$ and $b_1 \ge \dots \ge b_q$.
\end{itemize}
Similarly, we take the maximal compact subgroup $K' \cong \U(r) \times \U(s)$ of $\U(V) = \U(r,s)$ and parametrize the irreducible representations of $K'$.
Let $\mathcal{P} = \bigoplus_{d=0}^\infty \mathcal{P}_d$ be the Fock model of the Weil representation $\omega_{V,W,\chi_V,\chi_W,\psi}$ of $\U(W) \times \U(V)$ relative to the datum $(\chi_V,\chi_W,\psi)$ given in \S \ref{ss:main-theorem-setup}, where $\mathcal{P}$ is the space of polynomials in $mn$ variables and $\mathcal{P}_d$ is the subspace of homogeneous polynomials of degree $d$.
Note that $\mathcal{P}_d$ is invariant under the action of $K \times K'$.
For any irreducible representation $\mu$ of $K$ occurring in $\mathcal{P}$, we define the $(r,s)$-degree of $\mu$ as the smallest nonnegative integer $d$ such that the $\mu$-isotypic component of $\mathcal{P}_d$ is nonzero, which depends only on $r-s$ (see \cite[Lemma 1.4.5]{paul1}).
Let $\mathcal{H}$ be the space of joint harmonics, which is a $K \times K'$-invariant subspace of $\mathcal{P}$.
For any irreducible representations $\mu$ and $\mu'$ of $K$ and $K'$, respectively, we say that $\mu$ and $\mu'$ correspond if $\mu \boxtimes \mu'$ occurs in $\mathcal{H}$, in which case $\mu$ and $\mu'$ determine each other.
This correspondence can be described as follows.
\begin{lem}
\label{l:K-type-corresp}
Let $\mu$ and $\mu'$ be irreducible representations of $K$ and $K'$, respectively.
Then $\mu$ and $\mu'$ correspond if and only if $\mu$ and $\mu'$ are of the form
\begin{align*}
\mu & = (a_1, \dots, a_{p^+}, 0, \dots, 0, b_1, \dots, b_{p^-}; c_1, \dots, c_{q^+}, 0, \dots, 0, d_1, \dots, d_{q^-}) \\
& + \bigg( \frac{r-s}{2}, \dots, \frac{r-s}{2}; \frac{s-r}{2}, \dots, \frac{s-r}{2} \bigg) + \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg)
\end{align*}
and
\begin{align*}
\mu' & = (a_1, \dots, a_{p^+}, 0, \dots, 0, d_1, \dots, d_{q^-}; c_1, \dots, c_{q^+}, 0, \dots, 0, b_1, \dots, b_{p^-}) \\
& + \bigg( \frac{p-q}{2}, \dots, \frac{p-q}{2}; \frac{q-p}{2}, \dots, \frac{q-p}{2} \bigg) + \bigg( \frac{n_0}{2}, \dots, \frac{n_0}{2} \bigg),
\end{align*}
where
\begin{itemize}
\item $a_i, b_j, c_k, d_l \in \Z$;
\item $a_1 \ge \dots \ge a_{p^+} > 0 > b_1 \ge \dots \ge b_{p^-}$ and $c_1 \ge \dots \ge c_{q^+} > 0 > d_1 \ge \dots \ge d_{q^-}$;
\item $p^+ + p^- \le p$ and $q^+ + q^- \le q$;
\item $p^+ + q^- \le r$ and $p^- + q^+ \le s$.
\end{itemize}
\end{lem}
\begin{proof}
Given our choice of the datum $(\chi_V, \chi_W, \psi)$, the assertion follows from \cite[Theorem 5.4]{konno}.
We remark that the convention in \cite{konno} is different from ours (see \cite[Lemma 3.1]{konno} and \cite[p.~758]{gi2}).
In particular, to switch the left and right actions of $\U(W)$ on $W$, we need to compose the Weil representation $\omega_{V,W, \underline{\xi}}$ as in \cite[\S 3.3]{konno} relative to the pair $\underline{\xi} = (\chi_W, \chi_V^{-1})$ with the automorphism $g \mapsto {}^t g^{-1}$ of $\U(p,q)$.
\end{proof}
Let $\pi$ be an irreducible representation of $\U(W)$ such that the theta lift $\theta_{V,W,\chi_V,\chi_W,\psi}(\pi)$ to $\U(V)$ is nonzero.
Let $\mu$ be a $K$-type of $\pi$, i.e.~an irreducible representation of $K$ occurring in $\pi|_K$.
We say that $\mu$ is of minimal $(r,s)$-degree in $\pi$ if the $(r,s)$-degree of $\mu$ is minimal among all $K$-types of $\pi$, in which case $\mu$ occurs in $\mathcal{H}$.
\begin{lem}
\label{l:lkt->mindeg}
Let $\pi$ be a discrete series representation of $\U(W)$ satisfying the assumption of Lemma \ref{l:base}.
Let $\mu$ be the lowest $K$-type of $\pi$.
Then $\mu$ is of minimal $(r,s)$-degree in $\pi$.
\end{lem}
\begin{proof}
Put $(r_0, s_0) = (r_\pi + [\frac{k_\pi}{2}], s_\pi + [\frac{k_\pi}{2}])$, so that $r_0+s_0 = n$ or $n-1$.
Let $V_0$ be the Hermitian space over $\C$ of signature $(r_0, s_0)$.
Then by Theorem \ref{t:atobe}, the theta lift $\theta_{V_0,W,\chi_V,\chi_W,\psi}(\pi)$ to $\U(V_0)$ is nonzero.
Moreover, by \cite[Proposition 0.5]{paul1} and \cite[Proposition 1.4]{paul2}, $\mu$ is of minimal $(r_0,s_0)$-degree in $\pi$.
On the other hand, since $r_0-s_0 = r-s$, the $(r_0,s_0)$-degree of any $K$-type $\nu$ of $\pi$ agrees with the $(r,s)$-degree of $\nu$.
Hence $\mu$ is of minimal $(r,s)$-degree in $\pi$.
\end{proof}
We also need a seesaw diagram
\[
\begin{tikzcd}
\U(W) \times \U(W) \arrow[rd,dash] & \U(V) \arrow[ld,dash] \\
\U(W) \arrow[u,dash] & \U(V_1) \times \U(V_2) \arrow[u,dash]
\end{tikzcd},
\]
where $V_1$ and $V_2$ are the Hermitian spaces over $\C$ of signatures $(r,0)$ and $(0,s)$, respectively, such that $V = V_1 \oplus V_2$ and $K' = \U(V_1) \times \U(V_2)$.
Consider the symplectic spaces
\[
\W = V \otimes_E W, \quad
\W_1 = V_1 \otimes_E W, \quad
\W_2 = V_2 \otimes_E W
\]
over $F$, so that $\W = \W_1 \oplus \W_2$.
We may take complete polarizations
\[
\W = \X \oplus \Y, \quad
\W_1 = \X_1 \oplus \Y_1, \quad
\W_2 = \X_2 \oplus \Y_2
\]
such that $\X = \X_1 \oplus \X_2$ and $\Y = \Y_1 \oplus \Y_2$.
Write
\[
\omega = \omega_{V,W,\chi_V,\chi_W,\psi}, \quad
\omega_1 = \omega_{V_1,W,\chi_{V_1},\chi_W,\psi}, \quad
\omega_2 = \omega_{V_2,W,\chi_{V_2},\chi_W,\psi},
\]
where $\chi_{V_1}, \chi_{V_2}$ are characters of $\C^\times$ given by
\[
\chi_{V_1}(z) = \left( \frac{z}{\sqrt{z \bar{z}}} \right)^{m_1}, \quad
\chi_{V_2}(z) = \left( \frac{z}{\sqrt{z \bar{z}}} \right)^{m_2}
\]
for some integers $m_1, m_2$ such that
\[
m_1 \equiv r \bmod 2, \quad
m_2 \equiv s \bmod 2, \quad
m_1 + m_2 = m_0.
\]
Then we have an identification
\[
(\omega, S(\X)) = (\omega_1 \boxtimes \omega_2, S(\X_1) \otimes S(\X_2))
\]
as representations of $\U(W) \times \U(V_1) \times \U(V_2)$.
In particular, we have
\begin{equation}
\label{eq:matcoeff-weil}
(\omega(g) \varphi_1, \varphi_2) =
(\omega_1(g) \varphi_{1,1}, \varphi_{2,1})
(\omega_2(g) \varphi_{1,2}, \varphi_{2,2})
\end{equation}
for $g \in \U(W)$ and $\varphi_1 = \varphi_{1,1} \otimes \varphi_{1,2}, \varphi_2 = \varphi_{2,1} \otimes \varphi_{2,2} \in S(\X)$ with $\varphi_{1,i}, \varphi_{2,i} \in S(\X_i)$.
We now prove Lemma \ref{l:base}.
Let $\pi$ be a discrete series representation of $\U(W)$ satisfying the assumption of Lemma \ref{l:base}.
Let $\mu$ be the lowest $K$-type of $\pi$.
By Lemma \ref{l:lkt->mindeg}, we may write
\begin{align*}
\mu & = (a_1, \dots, a_{p^+}, 0, \dots, 0, b_1, \dots, b_{p^-}; c_1, \dots, c_{q^+}, 0, \dots, 0, d_1, \dots, d_{q^-}) \\
& + \bigg( \frac{r-s}{2}, \dots, \frac{r-s}{2}; \frac{s-r}{2}, \dots, \frac{s-r}{2} \bigg) + \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg)
\end{align*}
as in Lemma \ref{l:K-type-corresp}.
Put
\begin{align*}
\mu_1 & = (a_1, \dots, a_{p^+}, 0, \dots, 0; 0, \dots, 0, d_1, \dots, d_{q^-})
+ \bigg( \frac{r}{2}, \dots, \frac{r}{2}; -\frac{r}{2}, \dots, -\frac{r}{2} \bigg) + \bigg( \frac{m_1}{2}, \dots, \frac{m_1}{2} \bigg), \\
\mu_2 & = (0, \dots, 0, b_1, \dots, b_{p^-}; c_1, \dots, c_{q^+}, 0, \dots, 0)
+ \bigg( {-\frac{s}{2}}, \dots, -\frac{s}{2}; \frac{s}{2}, \dots, \frac{s}{2} \bigg) + \bigg( \frac{m_2}{2}, \dots, \frac{m_2}{2} \bigg),
\end{align*}
so that the tensor product representation $\mu_1 \otimes \mu_2$ contains $\mu$.
Let $\mu'$ be the irreducible representation of $K'$ corresponding to $\mu$.
Let $\mu_1'$ and $\mu_2'$ be the irreducible representations of $\U(V_1)$ and $\U(V_2)$, respectively, given by
\begin{align*}
\mu_1' & = (a_1, \dots, a_{p^+}, 0, \dots, 0, d_1, \dots, d_{q^-})
+ \bigg( \frac{p-q}{2}, \dots, \frac{p-q}{2} \bigg) + \bigg( \frac{n_0}{2}, \dots, \frac{n_0}{2} \bigg), \\
\mu_2' & = (c_1, \dots, c_{q^+}, 0, \dots, 0, b_1, \dots, b_{p^-})
+ \bigg( \frac{q-p}{2}, \dots, \frac{q-p}{2} \bigg) + \bigg( \frac{n_0}{2}, \dots, \frac{n_0}{2} \bigg),
\end{align*}
so that $\mu' = \mu_1' \boxtimes \mu_2'$.
Then the theta lift $\pi_i = \theta_{V_i,W,\chi_{V_i},\chi_W, \psi}(\mu_i')$ to $\U(W)$ is nonzero.
In fact, $\pi_i$ is the unitary highest weight module with lowest $K$-type $\mu_i$ (see \cite{kashiwara-vergne}).
Since $\U(V_i)$ is compact, we may realize the representation $\pi_i \boxtimes \mu_i'$ of $\U(W) \times \U(V_i)$ on the $\mu_i'$-isotypic component $S(\X_i)_{\mu_i'}$ of $S(\X_i)$.
In particular, for $\varphi_{1,i}, \varphi_{2,i} \in S(\X_i)_{\mu_i'}$, the function
\[
g \mapsto (\omega_i(g) \varphi_{1,i}, \varphi_{2,i})
\]
is a matrix coefficient of $\pi_i$.
By \eqref{eq:matcoeff-weil}, it suffices to show that the integral
\begin{equation}
\label{eq:matcoeff-integral}
\int_{\U(W)} (\omega_1(g) \varphi_{1,1}, \varphi_{2,1}) (\omega_2(g) \varphi_{1,2}, \varphi_{2,2}) \overline{(\pi(g) v_1, v_2)} \, dg
\end{equation}
is nonzero for some $\varphi_{1,1}, \varphi_{2,1} \in S(\X_1)_{\mu_1'}$, $\varphi_{1,2}, \varphi_{2,2} \in S(\X_2)_{\mu_2'}$, and $v_1, v_2 \in \pi$.
Let $\Psi$ be the Flensted-Jensen function given by
\[
\Psi(g) = \frac{1}{\dim \mu} \cdot \Tr(P_\mu \pi(g) P_\mu),
\]
where $P_\mu$ is the orthogonal projection to the $\mu$-isotypic component of $\pi$ (see \cite[\S 7]{flensted-jensen}).
Similarly, let $\Psi_i$ be the function given by
\[
\Psi_i(g) = \frac{1}{\dim \mu_i} \cdot \Tr(P_{\mu_i} \pi_i(g) P_{\mu_i}).
\]
Then it follows from the proof of \cite[Theorem 4.1]{li90} that
\[
\int_{\U(W)} \Psi_1(g) \Psi_2(g) \overline{\Psi(g)} \, dg \ne 0.
\]
Since $\Psi_1, \Psi_2, \Psi$ are linear combinations of matrix coefficients of $\pi_1, \pi_2, \pi$, respectively, this integral is a linear combination of integrals of the form \eqref{eq:matcoeff-integral}.
This completes the proof of Lemma \ref{l:base} and hence of Proposition \ref{p:key}.
\section{Proof of Theorem \ref{t:main-lds}\eqref{main-lds-1}}
In this section, we consider the theta lifting from $\U(p,q)$ to $\U(r,s)$ with $p+q=n$ and $r+s=m$ in the case $m>n$ and determine the theta lifts of (limits of) discrete series representations by a global-to-local argument.
\subsection{Local theta lifting}
Let $F$ be a local field of characteristic zero and $E$ an \'etale quadratic algebra over $F$.
We consider the theta lifting from $\U(W)$ to $\U(V)$, where $W$ is an $n$-dimensional skew-Hermitian space over $E$ and $V$ is an $m$-dimensional Hermitian space over $E$ with $m>n$.
\subsubsection{The real case}
\label{sss:local-theta-real}
Suppose that $F=\R$ and $E=\C$.
Let $(p,q)$ and $(r,s)$ be the signatures of $W$ and $V$, respectively.
We take the datum $(\chi_V, \chi_W, \psi)$ given in \S \ref{ss:main-theorem-setup}.
Let $\pi$ be a (limit of) discrete series representation of $\U(p,q)$ and write $\pi = {\mathstrut}^n \! A_\b(\lambda)$ as in \eqref{eq:lds} with
\[
\lambda = (\alpha_1, \dots, \alpha_{p^+}, \beta_1, \dots, \beta_{p^-}, \gamma_1, \dots, \gamma_{q^+}, \delta_1, \dots, \delta_{q^-}) + \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg),
\]
where
\begin{itemize}
\item $\alpha_i, \gamma_j > 0$ and $\beta_i, \delta_j \le 0$;
\item $p^++p^- = p$ and $q^++q^- = q$.
\end{itemize}
Define $L$- and $A$-parameters $\phi$ and $\phi'$ for $\U_n$ and $\U_m$, respectively, by
\begin{align*}
\phi & = \chi_{\kappa_1} \oplus \dots \oplus \chi_{\kappa_n}, \\
\phi' & = \chi_{\kappa_1} \chi_V^{-1} \chi_W \oplus \dots \oplus \chi_{\kappa_n} \chi_V^{-1} \chi_W \oplus (\chi_W \boxtimes S_{m-n}),
\end{align*}
where
\begin{itemize}
\item $\kappa_1 \ge \dots \ge \kappa_{i_0-1} > \frac{m_0}{2} \ge \kappa_{i_0} \ge \dots \ge \kappa_n$;
\item $\{ \kappa_1 - \frac{m_0}{2}, \dots, \kappa_{i_0-1} - \frac{m_0}{2} \} = \{ \alpha_1, \dots, \alpha_{p^+}, \gamma_1, \dots, \gamma_{q^+} \}$ as multi-sets;
\item $\{ \kappa_{i_0} - \frac{m_0}{2}, \dots, \kappa_n - \frac{m_0}{2} \} = \{ \beta_1, \dots, \beta_{p^-}, \delta_1, \dots, \delta_{q^-} \}$ as multi-sets;
\item $i_0 = p^++q^++1$.
\end{itemize}
Then we have
\[
\pi = \pi(\phi, \eta)
\]
for some character $\eta$ of $S_\phi$.
We identify $S_\phi, S_{\phi'}$ with quotients of
\begin{align*}
\widetilde{S}_\phi & = (\Z/2\Z) e_1 \oplus \dots \oplus (\Z/2 \Z) e_n, \\
\widetilde{S}_{\phi'} & = (\Z/2\Z) e'_1 \oplus \dots \oplus (\Z/2 \Z) e'_n \oplus (\Z/2 \Z) e'_0
\end{align*}
as in \S \ref{sss:packets-real-lds}, \S \ref{sss:packets-real-coh}, respectively.
Define a character $\eta'$ of $\widetilde{S}_{\phi'}$ by
\[
\eta'(e_i') = \zeta_i \times
\begin{cases}
\eta(e_i) & \text{if $i \ne 0$;} \\
(-1)^{\frac{1}{2}(p-q)(p-q-1) + \frac{1}{2}(r-s)(r-s-1)} & \text{if $i = 0$,}
\end{cases}
\]
where
\[
\zeta_i =
\begin{cases}
+1 & \text{if $m \equiv n \bmod 2$ and $0 < i < i_0$}; \\
-1 & \text{if $m \equiv n \bmod 2$ and $i \ge i_0$;} \\
+1 & \text{if $m \not \equiv n \bmod 2$ and $i \ne 0$}
\end{cases}
\]
and
\[
\zeta_0 = \zeta_1 \cdots \zeta_n.
\]
\begin{lem}
\label{l:Aq-eta}
Assume that $\theta_{r,s}(\pi) \ne 0$.
Then $\eta'$ descends to a character of $S_{\phi'}$ and the associated representation $\sigma(\phi', \eta')$ of $\U(r,s)$ is equal to ${\mathstrut}^n \! A_\q(\lambda')$, where $\q$ and $\lambda'$ are as in Theorem \ref{t:main-lds}\eqref{main-lds-1}.
\end{lem}
\begin{proof}
Recall that $\b = \q(x)$ is associated to
\[
x = (\underbrace{x_1,\dots,x_1}_{p_1}, \dots, \underbrace{x_n,\dots,x_n}_{p_n}, \underbrace{x_1,\dots,x_1}_{q_1}, \dots, \underbrace{x_n,\dots,x_n}_{q_n})
\]
for any $x_1, \dots, x_n \in \R$ such that $x_1 > \dots > x_n$, where
\begin{equation}
\label{eq:piqi}
(p_i, q_i) =
\begin{cases}
(1,0) & \text{if $\eta(e_i) = (-1)^{i-1}$;} \\
(0,1) & \text{if $\eta(e_i) = (-1)^i$.}
\end{cases}
\end{equation}
In particular, we have
\[
\begin{aligned}
p^+ & = p_1 + \dots + p_{i_0-1}, \, &
p^- & = p_{i_0} + \dots + p_n, \\
q^+ & = q_1 + \dots + q_{i_0-1}, \, &
q^- & = q_{i_0} + \dots + q_n.
\end{aligned}
\]
For the first assertion, it suffices to show that if $m=n+1$ and $\kappa_{i_0} = \frac{m_0}{2}$, then
\begin{equation}
\label{eq:eta(e_{i_0})}
\eta(e_{i_0}) = (-1)^{\frac{1}{2}(p-q)(p-q-1) + \frac{1}{2}(r-s)(r-s-1)}.
\end{equation}
Let $k \ge 1$ be the multiplicity of $\frac{m_0}{2}$ in $\{ \kappa_1, \dots, \kappa_n \}$.
Then we have
\[
\begin{cases}
k_\pi = -1 & \text{if $k$ is even;} \\
k_\pi \ge 1 & \text{if $k$ is odd,}
\end{cases}
\]
and
\[
(r_\pi, s_\pi) =
\begin{cases}
(p^+ + q^-, p^- + q^+) & \text{if $k$ is even;} \\
(p^+ + q^- - \frac{k_\pi - 1}{2}, p^- + q^+ - \frac{k_\pi + 1}{2}) & \text{if $k$ is odd and $\eta(e_{i_0}) = (-1)^{i_0-1}$;} \\
(p^+ + q^- - \frac{k_\pi + 1}{2}, p^- + q^+ - \frac{k_\pi - 1}{2}) & \text{if $k$ is odd and $\eta(e_{i_0}) = (-1)^{i_0}$.}
\end{cases}
\]
Hence by Theorem \ref{t:atobe}, we must have
\[
(r, s) =
\begin{cases}
(p^+ + q^- + 1, p^- + q^+) & \text{if $\eta(e_{i_0}) = (-1)^{i_0-1}$;} \\
(p^+ + q^-, p^- + q^+ + 1) & \text{if $\eta(e_{i_0}) = (-1)^{i_0}$.}
\end{cases}
\]
If $\eta(e_{i_0}) = (-1)^{i_0-1}$, then we have
\begin{align*}
& \frac{1}{2}(p-q)(p-q-1) + \frac{1}{2}(r-s)(r-s-1) \\
& = \frac{1}{2}(p^+ - q^+ + p^- - q^-)(p^+ - q^+ + p^- - q^- -1) \\
& + \frac{1}{2}(p^+ - q^+ - p^- + q^- +1)(p^+ - q^+ - p^- + q^-) \\
& = (p^+ - q^+)^2 + (p^- - q^-)(p^- - q^- -1) \\
& \equiv p^+ + q^+ \bmod 2,
\end{align*}
so that \eqref{eq:eta(e_{i_0})} follows.
If $\eta(e_{i_0}) = (-1)^{i_0}$, then \eqref{eq:eta(e_{i_0})} follows similarly.
For the second assertion, we first note that
\[
p^+ + q^- \le r, \quad
p^- + q^+ \le s
\]
by Corollary \ref{c:local-theta-xyzw}.
For $1 \le i \le n+1$, we define a pair of integers $(r_i, s_i)$ as in \S \ref{sss:packets-real-coh}, so that
\begin{equation}
\label{eq:risi}
(r_i, s_i) =
\begin{cases}
(1,0) & \text{if $i<i_0$ and $\eta(e_i) = (-1)^{i-1}$;} \\
(0,1) & \text{if $i<i_0$ and $\eta(e_i) = (-1)^i$;} \\
(1,0) & \text{if $i>i_0$ and $\eta(e_{i-1}) = (-1)^{i-1}$;} \\
(0,1) & \text{if $i>i_0$ and $\eta(e_{i-1}) = (-1)^i$}
\end{cases}
\end{equation}
and
\[
(r_{i_0}, s_{i_0}) = (r - p^+ - q^-, s - p^- - q^+).
\]
Since $r_{i_0}, s_{i_0} \ge 0$ and
\begin{align*}
\eta'(e_1' + \dots + e_n' + e_0') & = \eta(e_1 + \dots + e_n) \cdot (-1)^{\frac{1}{2}(p-q)(p-q-1) + \frac{1}{2}(r-s)(r-s-1)} \\
& = (-1)^{\frac{1}{2}(r-s)(r-s-1)},
\end{align*}
we have
\[
\sigma(\phi', \eta') = {\mathstrut}^n \! A_{\tilde{\q}}(\tilde{\lambda}'),
\]
where $\tilde{\lambda}'$ is given by
\[
\tilde{\lambda}' = (\underbrace{\tilde{\lambda}'_1,\dots,\tilde{\lambda}'_1}_{r_1}, \dots, \underbrace{\tilde{\lambda}'_{n+1},\dots,\tilde{\lambda}'_{n+1}}_{r_{n+1}}, \underbrace{\tilde{\lambda}'_1,\dots,\tilde{\lambda}'_1}_{s_1}, \dots, \underbrace{\tilde{\lambda}'_{n+1},\dots,\tilde{\lambda}'_{n+1}}_{s_{n+1}})
\]
with
\[
\tilde{\lambda}'_i =
\begin{cases}
\kappa_i - \frac{m_0}{2} + \frac{n_0}{2} & \text{if $i < i_0$;} \\
\frac{n_0}{2} & \text{if $i = i_0$;} \\
\kappa_{i-1} - \frac{m_0}{2} + \frac{n_0}{2} & \text{if $i > i_0$}
\end{cases}
\]
and $\tilde{\q} = \q(\tilde{x})$ is associated to
\[
\tilde{x} = (\underbrace{\tilde{x}_1,\dots,\tilde{x}_1}_{r_1}, \dots, \underbrace{\tilde{x}_{n+1},\dots,\tilde{x}_{n+1}}_{r_{n+1}}, \underbrace{\tilde{x}_1,\dots,\tilde{x}_1}_{s_1}, \dots, \underbrace{\tilde{x}_{n+1},\dots,\tilde{x}_{n+1}}_{s_{n+1}})
\]
for any $\tilde{x}_1, \dots, \tilde{x}_{n+1} \in \R$ such that $\tilde{x}_1 > \dots > \tilde{x}_{n+1}$.
However, we can deduce from \eqref{eq:piqi} and \eqref{eq:risi} that $\tilde{\q} = \q$ and $\tilde{\lambda}' = \lambda'$.
This completes the proof.
\end{proof}
\begin{lem}
\label{l:local-theta-1}
Assume that $\pi$ is a discrete series representation such that
\[
p^+ + q^- \le r, \quad
p^- + q^+ \le s
\]
and
\[
\alpha_i, \gamma_j \ge \frac{m-n+1}{2}, \quad
\beta_i, \delta_j \le -\frac{m-n+1}{2}.
\]
Then we have
\[
\theta_{r,s}(\pi) = \sigma(\phi', \eta').
\]
\end{lem}
\begin{proof}
By a result of Li \cite{li90}, we have $\theta_{r,s}(\pi) \ne 0$ and
\[
\theta_{r,s}(\pi) = {\mathstrut}^n \! A_\q(\lambda'),
\]
where $\q$ and $\lambda'$ are as in Theorem \ref{t:main-lds}\eqref{main-lds-1}.
Hence the assertion follows from Lemma \ref{l:Aq-eta}.
\end{proof}
\subsubsection{The nonarchimedean case}
Suppose that $F$ is nonarchimedean and $E \ne F \times F$.
Let $\phi$ and $\phi'$ be $L$- and $A$-parameters for $\U_n$ and $\U_m$, respectively, of the form
\begin{align*}
\phi & = \chi_1 \oplus \dots \oplus \chi_n, \\
\phi' & = \chi_1 \chi_V^{-1} \chi_W \oplus \dots \oplus \chi_n \chi_V^{-1} \chi_W \oplus (\chi_W \boxtimes S_{m-n})
\end{align*}
with (not necessarily distinct) conjugate-selfdual characters $\chi_1, \dots, \chi_n$ of $E^\times$ with sign $(-1)^{n-1}$.
If $m \equiv n \bmod 2$, we assume further the condition on the $\epsilon$-factor
\begin{equation}
\label{eq:epsilon-assumption}
\epsilon(\tfrac{1}{2}, \chi_i \chi_V^{-1}, \psi^E_2) = 1
\end{equation}
for all $i$, where $\psi^E_2$ is the character of $E$ given by $\psi^E_2(x) = \psi(\Tr_{E/F}(\delta x))$.
\begin{lem}
\label{l:local-theta-2}
Assume that $\epsilon(V) = \epsilon(W) = +1$.
Then we have
\[
\theta_{V,W,\chi_V,\chi_W,\psi}(\pi(\phi, \mathbbm{1})) = \sigma(\phi', \mathbbm{1}).
\]
\end{lem}
\begin{proof}
Write $\pi = \pi(\phi, \mathbbm{1})$ for brevity.
For any $\epsilon = \pm 1$, we define the first occurrence index $m^\epsilon(\pi)$ as the smallest nonnegative integer $m'$ with $m' \equiv m \bmod 2$ such that $\theta_{V_{m'}^\epsilon, W, \chi_V, \chi_W, \psi}(\pi) \ne 0$.
Put
\[
m^\up(\pi) = \max \{ m^+(\pi), m^-(\pi) \}, \quad
m^\down(\pi) = \min \{ m^+(\pi), m^-(\pi) \}.
\]
Assume first that $m \equiv n \bmod 2$.
Then by \cite[Theorem 4.1]{atobe-gan} and \eqref{eq:epsilon-assumption}, we have
\[
m^\up(\pi) = n+2, \quad
m^\down(\pi) = n
\]
with $m^\down(\pi) = m^+(\pi)$.
Moreover, it follows from \cite[Theorem 4.3]{atobe-gan} that
\[
\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) = J(\chi_W|\cdot|^{\frac{1}{2}(m-n-1)}, \chi_W|\cdot|^{\frac{1}{2}(m-n-3)}, \dots, \chi_W|\cdot|^{\frac{1}{2}}, \pi(\phi_0, \mathbbm{1}))
\]
with an $L$-parameter
\[
\phi_0 = \chi_1 \chi_V^{-1} \chi_W \oplus \dots \oplus \chi_n \chi_V^{-1} \chi_W
\]
for $\U_n$.
Hence the assertion follows from Lemma \ref{l:local-Apacket}.
Assume next that $m \not \equiv n \bmod 2$.
Then by \cite[Theorem 4.1]{atobe-gan}, we have
\[
\begin{cases}
m^\up(\pi) = n+1, \quad m^\down(\pi) = n+1 & \text{if $\chi_i \ne \chi_V$ for all $i$;} \\
m^\up(\pi) = n+3, \quad m^\down(\pi) = n-1 & \text{otherwise}
\end{cases}
\]
with $m^\down(\pi) = m^+(\pi)$.
Moreover, it follows from \cite[Theorem 4.3]{atobe-gan} that
\[
\theta_{V,W,\chi_V,\chi_W,\psi}(\pi) = J(\chi_W|\cdot|^{\frac{1}{2}(m-n-1)}, \chi_W|\cdot|^{\frac{1}{2}(m-n-3)}, \dots, \chi_W|\cdot|^1, \pi(\phi_1, \mathbbm{1}))
\]
with an $L$-parameter
\[
\phi_1 = \chi_1 \chi_V^{-1} \chi_W \oplus \dots \oplus \chi_n \chi_V^{-1} \chi_W \oplus \chi_W
\]
for $\U_{n+1}$.
Hence the assertion follows from Lemma \ref{l:local-Apacket}.
\end{proof}
\subsubsection{The split case}
Suppose that $F$ is nonarchimedean and $E = F \times F$.
In this case, we may identify $\chi_V, \chi_W$ with unitary characters of $F^\times$ via the first projection.
Let $\phi$ and $\phi'$ be $L$- and $A$-parameters for $\U_n$ and $\U_m$, respectively, of the form
\begin{align*}
\phi & = \chi_1 \oplus \dots \oplus \chi_n, \\
\phi' & = \chi_1 \chi_V^{-1} \chi_W \oplus \dots \oplus \chi_n \chi_V^{-1} \chi_W \oplus (\chi_W \boxtimes S_{m-n})
\end{align*}
with (not necessarily distinct) unitary characters $\chi_1, \dots, \chi_n$ of $F^\times$.
\begin{lem}
\label{l:local-theta-3}
We have
\[
\theta_{V,W,\chi_V,\chi_W,\psi}(\pi(\phi, \mathbbm{1})) = \sigma(\phi', \mathbbm{1}).
\]
\end{lem}
\begin{proof}
The assertion was proved by M\'inguez \cite{minguez}.
\end{proof}
\subsection{Global theta lifting}
\label{ss:global-theta}
Let $\F$ be a totally real number field with ad\`ele ring $\A = \A_\F$.
Let $\E$ be a totally imaginary quadratic extension of $\F$ and $\omega_{\E/\F}$ the quadratic character of $\A^\times/\F^\times$ associated to $\E/\F$ by global class field theory.
We consider the theta lifting from $\U(\W)$ to $\U(\V)$, where $\W$ is an $n$-dimensional skew-Hermitian space over $\E$ and $\V$ is an $m$-dimensional Hermitian space over $\E$ with $m>n$.
For simplicity, we assume that $\W$ and $\V$ are anisotropic.
Let $\omega_{\V,\W,\chi_\V,\chi_\W,\varPsi}$ be the Weil representation of $\U(\W)(\A) \times \U(\V)(\A)$ relative to $(\chi_\V,\chi_\W,\varPsi)$, where $\chi_\V, \chi_\W$ are characters of $\A_\E^\times / \E^\times$ such that $\chi_\V|_{\A^\times} = \omega_{\E/\F}^m, \chi_\W|_{\A^\times} = \omega_{\E/\F}^n$ and $\varPsi$ is a nontrivial additive character of $\A/\F$.
This is equipped with a natural equivariant map $\varphi \mapsto \theta(\varphi)$ to the space of left $\U(\W)(\F) \times \U(\V)(\F)$-invariant smooth functions on $\U(\W)(\A) \times \U(\V)(\A)$ of moderate growth.
For any irreducible automorphic representation $\varPi$ of $\U(\W)(\A)$, we denote by $\theta_{\V,\W,\chi_\V,\chi_\W,\varPsi}(\varPi)$ the space spanned by automorphic forms on $\U(\V)(\A)$ of the form
\[
\theta(\varphi, f)(h) = \int_{\U(\W)(\F) \backslash \U(\W)(\A)} \theta(\varphi)(g,h) \overline{f(g)} \, dg
\]
for $\varphi \in \omega_{\V,\W,\chi_\V,\chi_\W,\varPsi}$ and $f \in \varPi$.
If $\theta_{\V,\W,\chi_\V,\chi_\W,\varPsi}(\varPi)$ is nonzero, then it follows from the Howe duality that $\theta_{\V,\W,\chi_\V,\chi_\W,\varPsi}(\varPi)$ is irreducible and isomorphic to $\bigotimes_v \theta_{\V_v,\W_v,\chi_{\V,v},\chi_{\W,v},\varPsi_v}(\varPi_v)$ (see \cite[Corollary 7.1.3]{kudla-rallis}).
We now discuss the nonvanishing of $\theta_{\V,\W,\chi_\V,\chi_\W,\varPsi}(\varPi)$.
For simplicity, we assume that $\varPi_v$ is tempered for all $v$ and that the partial standard $L$-function $L^S(s, \varPi, \chi_\V^{-1})$ of $\varPi$ twisted by $\chi_\V^{-1}$ is holomorphic and nonzero at $s = \frac{1}{2}(m-n+1)$, where $S$ is a sufficiently large finite set of places of $\F$.
Then the Rallis inner product formula, which is a consequence of the Siegel--Weil formula in the convergent range \cite{weil2, ichino}, says that
\[
\langle \theta(\varphi_1, f_1), \theta(\varphi_2, f_2) \rangle = \frac{L^S(\frac{1}{2}(m-n+1), \varPi, \chi_\V^{-1})}{d^S(\frac{1}{2}(m-n))} \cdot \prod_{v \in S} \ZZ(\varphi_{1,v}, \varphi_{2,v}, f_{1,v}, f_{2,v})
\]
for $\varphi_1 = \bigotimes_v \varphi_{1,v}, \varphi_2 = \bigotimes_v \varphi_{2,v} \in \omega_{\V,\W,\chi_\V,\chi_\W,\varPsi}$ and $f_1 = \bigotimes_v f_{1,v}, f_2 = \bigotimes_v f_{2,v} \in \varPi$, where
\begin{itemize}
\item $\langle \cdot, \cdot \rangle$ is the Petersson inner product;
\item $d^S(s) = \prod_{i=1}^n L^S(2s+i, \omega_{\E/\F}^{m-n+i})$, which is holomorphic and nonzero at $s = \frac{1}{2}(m-n)$;
\item $\ZZ(\varphi_{1,v}, \varphi_{2,v}, f_{1,v}, f_{2,v})$ is an integral of matrix coefficients defined as in \S \ref{ss:key}, which can be regarded as a doubling zeta integral of Piatetski-Shapiro--Rallis and which is absolutely convergent by \cite[Lemma 9.5]{gi1}, \cite[Lemma 7.2]{yamana}.
\end{itemize}
Hence $\theta_{\V,\W,\chi_\V,\chi_\W,\varPsi}(\varPi)$ is nonzero if and only if there exist $\varphi_{1,v}, \varphi_{2,v} \in \omega_{\V_v,\W_v,\chi_{\V,v},\chi_{\W,v},\varPsi_v}$ and $f_{1,v}, f_{2,v} \in \varPi_v$ such that
\[
\ZZ(\varphi_{1,v}, \varphi_{2,v}, f_{1,v}, f_{2,v}) \ne 0
\]
for all $v$.
\subsection{Arthur's multiplicity formula}
In this subsection, we review Arthur's multiplicity formula for unitary groups \cite{mok,kmsw}, which is a key ingredient in the proof of Theorem \ref{t:main-lds}\eqref{main-lds-1}.
Let $\F$ be a number field and $\E$ a quadratic extension of $\F$.
Let $\overline{\F}$ and $\overline{\F}_v$ be algebraic closures of $\F$ and $\F_v$, respectively, and fix an embedding $\overline{\F} \hookrightarrow \overline{\F}_v$ over $\F$ for each place $v$ of $\F$.
We also fix an embedding $\E \hookrightarrow \overline{\F}$ over $\F$, which determines an embedding $\E \hookrightarrow \overline{\F}_v$ for each place $v$ of $\F$ and hence a distinguished place $\tilde{v}$ of $\E$ above $v$.
If $v$ is split in $\E$, we identify $\E_v$ with $\F_v \times \F_v$ so that $\tilde{v}$ corresponds to the composition of the natural embedding $\E \hookrightarrow \E_v$ with the first projection $\E_v \rightarrow \F_v$.
Let $\V$ be an $n$-dimensional $\varepsilon$-Hermitian space over $\E$.
Then Arthur's endoscopic classification gives a decomposition of the automorphic discrete spectrum into near equivalence classes of representations:
\[
L^2_{\mathrm{disc}}(\U(\V)(\F) \backslash \U(\V)(\A)) = \bigoplus_\varPhi L^2_\varPhi(\U(\V)),
\]
where $\varPhi$ runs over global $A$-parameters for $\U_n$, which is a formal unordered finite direct sum of the form
\[
\varPhi = \bigoplus_i \varPhi_i \boxtimes S_{d_i},
\]
where
\begin{itemize}
\item $\varPhi_i$ is an irreducible conjugate-selfdual cuspidal automorphic representation of $\GL_{n_i}(\A_\E)$ with sign $(-1)^{n-d_i}$;
\item $S_{d_i}$ is the unique $d_i$-dimensional irreducible representation of $\SL_2(\C)$;
\item $(\varPhi_i, d_i) \ne (\varPhi_j, d_j)$ if $i \ne j$;
\item $\sum_i n_i d_i = n$.
\end{itemize}
Moreover, the multiplicity of each irreducible representation in $L^2_\varPhi(\U(\V))$ can be described as follows.
For each place $v$ of $\F$, we regard the localization $\varPhi_v = \bigoplus_i \varPhi_{i,v} \boxtimes S_{d_i}$ of $\varPhi$ at $v$ (where $\varPhi_{i,v}$ is viewed as a representation of $L_{\E_{\tilde{v}}}$ via the local Langlands correspondence) as a local $A$-parameter $\varPhi_v : L_{\F_v} \times \SL_2(\C) \rightarrow {}^L \U_n$ for $\U_n$.
Let $S_{\varPhi_v}$ be the local component group of $\varPhi_v$.
Recall that the local $A$-packet $\Pi_{\varPhi_v}(\U(\V_v))$ consists of semisimple representations of $\U(\V_v)$ of finite length.
We fix a global Whittaker datum, and with respect to its localization at $v$, we denote by $\sigma(\varPhi_v, \eta_v)$ the representation in $\Pi_{\varPhi_v}(\U(\V_v))$ associated to $\eta_v \in \widehat{S}_{\varPhi_v}$.
Let $S_\varPhi$ be the global component group of $\varPhi$, which is defined formally as a free $\Z/2\Z$-module
\[
S_\varPhi = \bigoplus_i (\Z/2 \Z) e_i,
\]
where $e_i$ corresponds to $\varPhi_i \boxtimes S_{d_i}$, and which is equipped with a natural homomorphism $S_\varPhi \rightarrow S_{\varPhi_v}$ for each $v$.
This gives rise to a compact group $S_{\varPhi, \A} = \prod_v S_{\varPhi_v}$ equipped with the diagonal map $\Delta : S_\varPhi \rightarrow S_{\varPhi, \A}$.
We denote by $\widehat{S}_{\varPhi, \A}$ the group of continuous characters of $S_{\varPhi, \A}$.
For any $\eta = \bigotimes_v \eta_v \in \widehat{S}_{\varPhi, \A}$, we may form a representation
\[
\sigma(\varPhi,\eta) = \bigotimes_v \sigma(\varPhi_v,\eta_v)
\]
of $\U(\V)(\A)$.
Finally, let $\epsilon_\varPhi$ be the character of $S_\varPhi$ defined by \cite[(2.5.5)]{mok}.
Then Arthur's multiplicity formula \cite[Theorem* 1.7.1]{kmsw} says that
\begin{equation}
\label{eq:amf}
L^2_\varPhi(\U(\V)) \cong \bigoplus_\eta \sigma(\varPhi,\eta),
\end{equation}
where $\eta$ runs over elements in $\widehat{S}_{\varPhi, \A}$ such that $\eta \circ \Delta = \epsilon_\varPhi$.
We can describe the character $\epsilon_\varPhi$ more explicitly as follows.
\begin{lem}
\label{l:epsilon}
We have
\[
\epsilon_\varPhi(e_i) = \prod_{j \ne i} \epsilon(\tfrac{1}{2}, \varPhi_i \times \varPhi_j^\vee)^{\min\{ d_i, d_j \}},
\]
where $\epsilon(s, \varPhi_i \times \varPhi_j^\vee)$ is the global $\epsilon$-factor of the pair $(\varPhi_i, \varPhi_j^\vee)$.
In particular, $\epsilon_\varPhi$ is trivial if $d_i=1$ for all $i$.
\end{lem}
\begin{proof}
The character $\epsilon_\varPhi$ is explicated in \cite[Proposition-Definition 8.3.7]{chenevier-lannes} in the case of orthogonal and symplectic groups.
We can apply the same argument to the case of unitary groups, noting that $\epsilon(\tfrac{1}{2}, \varPhi_i \times \varPhi_j^\vee) = 1$ if $\varPhi_i$ and $\varPhi_j$ have the same sign (see \cite[Theorem 2.5.4]{mok}).
\end{proof}
\subsection{Conjugate-selfdual characters}
In this subsection, we collect some results on conjugate-selfdual characters which we will use in the proof of Theorem \ref{t:main-lds}\eqref{main-lds-1}.
Let $F$ be a local field of characteristic zero and $E$ an \'etale quadratic algebra over $F$.
Let $\psi$ be a nontrivial additive character of $F$ and define a nontrivial additive character $\psi^E_2$ of $E$ by $\psi^E_2(x) = \psi(\Tr_{E/F}(\delta x))$.
Let $\chi$ be a character of $E^\times$.
Then $\chi$ is conjugate-selfdual if and only if $\chi$ is trivial on $\mathrm{N}_{E/F}(E^\times)$.
Also, if $E \ne F \times F$, then $\chi$ is conjugate-orthogonal (resp.~conjugate-symplectic) if and only if $\chi|_{F^\times} = \mathbbm{1}$ (resp.~$\chi|_{F^\times} =\omega_{E/F}$).
We consider the value of the $\epsilon$-factor $\epsilon(s, \chi, \psi_2^E)$ at $s = \frac{1}{2}$.
\begin{lem}
\label{l:csd-char-epsilon}
Let $\chi$ be a conjugate-selfdual character of $E^\times$.
\begin{enumerate}
\item
\label{item:csd-char-epsilon1}
If $E = F \times F$, then we have
\[
\epsilon(\tfrac{1}{2}, \chi, \psi_2^E) = 1.
\]
\item
\label{item:csd-char-epsilon2}
If $E \ne F \times F$, then we have
\[
\epsilon(\tfrac{1}{2}, \chi, \psi_2^E) = \pm 1.
\]
If further $\chi$ is conjugate-orthogonal, then we have
\[
\epsilon(\tfrac{1}{2}, \chi, \psi_2^E) = 1.
\]
\item
\label{item:csd-char-epsilon3}
Suppose that $F = \R$ and $E = \C$.
Write
\[
\chi(z) = \left( \frac{z}{\sqrt{z \bar{z}}} \right)^{2 \kappa}
\]
for some $\kappa \in \frac{1}{2} \Z$.
Assume further that $\delta = \sqrt{-1}$ and $\psi(x) = e^{- 2 \pi \sqrt{-1} x}$, so that $\psi_2^E(z) = e^{2 \pi (z - \bar{z})}$.
If $\kappa \in \Z$, then we have
\[
\epsilon(\tfrac{1}{2}, \chi, \psi_2^E) = 1.
\]
If $\kappa \notin \Z$, then we have
\[
\epsilon(\tfrac{1}{2}, \chi, \psi_2^E) =
\begin{cases}
+1 & \text{if $\kappa > 0$;} \\
-1 & \text{if $\kappa < 0$.}
\end{cases}
\]
\end{enumerate}
\end{lem}
\begin{proof}
If $F = E \times E$, then we may write $\chi = \chi_0 \boxtimes \chi_0^{-1}$ and $\psi_2^E = \psi_0 \boxtimes \psi_0^{-1}$ for some characters $\chi_0$ and $\psi_0$ of $F^\times$ and $F$, respectively.
Then we have
\[
\epsilon(\tfrac{1}{2}, \chi, \psi_2^E)
= \epsilon(\tfrac{1}{2}, \chi_0, \psi_0) \cdot
\epsilon(\tfrac{1}{2}, \chi_0^{-1}, \psi_0^{-1})
= 1,
\]
so that \eqref{item:csd-char-epsilon1} follows.
For \eqref{item:csd-char-epsilon2} and \eqref{item:csd-char-epsilon3}, see \cite[Propositions 5.1 and 5.2]{ggp1} and \cite[Proposition 2.1]{ggp2}, respectively.
\end{proof}
Let $F$ be a nonarchimedean local field of characteristic zero and $E$ a quadratic extension of $F$.
We prove the existence of a conjugate-symplectic character $\chi$ of $E^\times$ with a prescribed value of $\epsilon(\tfrac{1}{2}, \chi, \psi^E_2)$.
\begin{lem}
\label{l:csd-char-local}
Assume that either
\begin{itemize}
\item $E$ is unramified over $F$; or
\item the residual characteristic of $F$ is odd and $E$ is ramified over $F$.
\end{itemize}
Then there exists a conjugate-symplectic character $\chi$ of $E^\times$ such that
\[
\epsilon(\tfrac{1}{2}, \chi, \psi^E_2) = 1.
\]
\end{lem}
\begin{proof}
If $E$ is unramified over $F$, then the assertion follows from \cite[Proposition 3.1]{ggp2}.
Hence we may assume that the residual characteristic of $F$ is odd and $E$ is ramified over $F$.
Let $\mathfrak{o}_F$ (resp.~$\mathfrak{o}_E$) be the maximal compact subring of $F$ (resp.~$E$), $\mathfrak{p}_F$ (resp.~$\mathfrak{p}_E$) the maximal ideal of $\mathfrak{o}_F$ (resp.~$\mathfrak{o}_E$), and $\varpi_F$ (resp.~$\varpi_E$) a uniformizer of $\mathfrak{o}_F$ (resp.~$\mathfrak{o}_E$).
Then the different of $E/F$ is $\mathfrak{p}_E$ and we may assume that $\varpi_E^2 = \varpi_F$, so that $\Tr_{E/F}(\varpi_E) = 0$ and $\varpi_E^{-1} \delta \in F^\times$.
In particular, there exists an integer $a$ such that $\psi^E_2$ is trivial on $\varpi_E^{-2a} \mathfrak{o}_E$ but nontrivial on $\varpi_E^{-2a-1} \mathfrak{o}_E$.
Since $\omega_{E/F}|_{1 + \mathfrak{p}_F} = \mathbbm{1}$ and $\mathfrak{o}_F^\times / (1 + \mathfrak{p}_F) \cong \mathfrak{o}_E^\times / (1 + \mathfrak{p}_E)$, there are precisely two conjugate-symplectic characters of $E^\times$ of conductor $1$.
Indeed, such a character $\chi$ is given by
\[
\chi|_{F^\times} = \omega_{E/F}, \quad
\chi|_{1 + \mathfrak{p}_E} = \mathbbm{1}, \quad
\chi(\varpi_E) = \zeta
\]
for some square root $\zeta$ of $\omega_{E/F}(\varpi_F)$.
By \cite[(3.6.3)]{tate}, we have
\[
\epsilon(\tfrac{1}{2}, \chi, \psi^E_2) = \chi(\varpi_E^{2a+1}) \cdot \frac{\mathcal{I}}{|\mathcal{I}|},
\]
where
\[
\mathcal{I} = \int_{\mathfrak{o}_E^\times} \chi(x)^{-1} \psi^E_2(\varpi_E^{-2a-1} x) \, dx.
\]
Note that $\chi(\varpi_E^{2a+1}) = \zeta \cdot \omega_{E/F}(\varpi_F^a)$ but that $\mathcal{I}$ does not depend on $\zeta$ since
\begin{align*}
\mathcal{I} & = \operatorname{vol}(1 + \mathfrak{p}_E) \cdot \sum_{x \in \mathfrak{o}_E^\times/ (1 + \mathfrak{p}_E)} \chi(x)^{-1} \psi^E_2(\varpi_E^{-2a-1} x) \\
& = \operatorname{vol}(1 + \mathfrak{p}_E) \cdot \sum_{x \in \mathfrak{o}_F^\times/ (1 + \mathfrak{p}_F)} \omega_{E/F}(x)^{-1} \psi(2 \delta_0 x),
\end{align*}
where $\delta_0 = \varpi_E^{-2a-1} \delta \in F^\times$.
On the other hand, by Lemma \ref{l:csd-char-epsilon}, we have $\epsilon(\tfrac{1}{2}, \chi, \psi_2^E) = \pm 1$.
Hence we can choose $\zeta$ so that $\epsilon(\tfrac{1}{2}, \chi, \psi^E_2) = 1$.
\end{proof}
Let $\F$ be a number field and $\E$ a quadratic extension of $\F$.
Let $\Sigma$ be the set of places $v$ of $\F$ such that $\E_v \ne \F_v \times \F_v$.
We globalize local conjugate-selfdual characters to a global conjugate-selfdual character.
\begin{lem}
\label{l:csd-char-global}
For each $v \in \Sigma$, let $\chi_v$ be a conjugate-orthogonal (resp.~conjugate-symplectic) character of $\E_v^\times$.
Assume that $\chi_v$ is unramified for almost all $v \in \Sigma$.
Then there exists a conjugate-orthogonal (resp.~conjugate-symplectic) character $\chi_0$ of $\A_\E^\times/\E^\times$ such that
\[
\chi_{0,v} = \chi_v
\]
for all $v \in \Sigma$.
\end{lem}
\begin{proof}
We may reduce the conjugate-symplectic case to the conjugate-orthogonal case by taking a conjugate-symplectic character $\chi'$ of $\A_\E^\times / \E^\times$ and applying the lemma to the character $\chi_v \cdot \chi_v'$ of $\E_v^\times$ for $v \in \Sigma$.
To treat the conjugate-orthogonal case, we consider an anisotropic torus
\[
T = {\Res}_{E/F}(\mathbb{G}_m) / \mathbb{G}_m
\]
over $\F$.
For each $v \in \Sigma$, let $\nu_v$ be a character of $T_v$.
Assume that $\nu_v$ is unramified for almost all $v \in \Sigma$.
Then we may form a character $\nu_\Sigma = \bigotimes_{v \in \Sigma} \nu_v$ of $T_\Sigma = \prod_{v \in \Sigma} T_v$.
Since $T_\Sigma$ is compact, the image of the natural continuous embedding
\[
T_\Sigma \hookrightarrow T(\A) / T(\F)
\]
is closed.
Hence we may extend $\nu_\Sigma$ to a character $\nu_0$ of $T(\A) / T(\F)$, so that
\[
\nu_{0,v} = \nu_v
\]
for all $v \in \Sigma$.
This completes the proof.
\end{proof}
\subsection{Global-to-local argument}
We now return to the setup of \S \ref{sss:local-theta-real}, so that $\pi$ is a (limit of) discrete series representation of $\U(p,q)$.
Assume that $\theta_{r,s}(\pi) \ne 0$.
Then by Corollary \ref{c:local-theta-xyzw}, we have
\[
p^+ + q^- \le r, \quad
p^- + q^+ \le s.
\]
To prove Theorem \ref{t:main-lds}\eqref{main-lds-1}, we appeal to a global-to-local argument and derive the information about $\theta_{r,s}(\pi)$ from the knowledge of $\theta_{r,s}(\pi_+)$, where $\pi_+$ is an auxiliary discrete series representation of $\U(p,q)$ with sufficiently regular infinitesimal character.
More precisely, let $\pi_+$ be a discrete series representation $\pi_+$ of $\U(p,q)$ of the form $\pi_+ = {\mathstrut}^n \! A_\b(\lambda_+)$ with
\[
\lambda_+ = (\tilde{\alpha}_1, \dots, \tilde{\alpha}_{p^+}, \tilde{\beta}_1, \dots, \tilde{\beta}_{p^-}, \tilde{\gamma}_1, \dots, \tilde{\gamma}_{q^+}, \tilde{\delta}_1, \dots, \tilde{\delta}_{q^-}) + \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg)
\]
such that
\[
\tilde{\alpha}_i, \tilde{\gamma}_j \ge \frac{m-n+1}{2}, \quad
\tilde{\beta}_i, \tilde{\delta}_j \le -\frac{m-n+1}{2}
\]
and such that the $\theta$-stable Borel subalgebra determined by $\lambda_+$ agrees with $\b$.
As in \S \ref{sss:local-theta-real}, we define $L$- and $A$-parameters $\phi_+$ and $\phi'_+$ for $\U_n$ and $\U_m$ with respect to $\pi_+$, respectively, so that $\phi_+$ is of the form
\[
\phi_+ = \chi_{\tilde{\kappa}_1} \oplus \dots \oplus \chi_{\tilde{\kappa}_n}
\]
with $\tilde{\kappa}_1 > \dots > \tilde{\kappa}_{i_0-1} > \frac{m_0}{2} > \tilde{\kappa}_{i_0} > \dots > \tilde{\kappa}_n$.
Then we have
\[
\pi_+ = \pi(\phi_+, \eta),
\]
where $\eta$ is viewed as a character of $S_{\phi_+}$ via the natural isomorphism $S_{\phi_+} \cong \widetilde{S}_\phi$.
Moreover, by Lemma \ref{l:local-theta-1}, we have $\theta_{r,s}(\pi_+) \ne 0$ and
\begin{equation}
\label{eq:theta(pi+)}
\theta_{r,s}(\pi_+) = \sigma(\phi'_+,\eta'),
\end{equation}
where $\eta'$ is viewed as a character of $S_{\phi'_+}$ via the natural isomorphism $S_{\phi'_+} \cong \widetilde{S}_{\phi'}$.
To simplify the argument, we also need an auxiliary irreducible representation $\pi_0$ of $\U(n,0)$ with Harish-Chandra parameter $(\kappa_{0,1}, \dots, \kappa_{0,n})$ such that
\[
\kappa_{0,1} > \dots > \kappa_{0,n} > \frac{m_0+m-n+1}{2}.
\]
As in \S \ref{sss:local-theta-real}, we define an $L$-parameter $\phi_0$ for $\U_n$ by
\[
\phi_0 = \chi_{\kappa_{0,1}} \oplus \dots \oplus \chi_{\kappa_{0,n}}.
\]
Then we have
\[
\pi_0 = \pi(\phi_0, \eta_0)
\]
for some character $\eta_0$ of $S_{\phi_0}$.
We now globalize everything in sight.
Let $\F$ be a real quartic field and $\E$ a totally imaginary quadratic extension of $\F$ such that $\E_v = \F_v \times \F_v$ for all places $v$ of $\F$ above $2$.
Let $v_0,v_1,v_2,v_3$ be the four real places of $\F$.
Fix an element $\delta \in \E^\times$ with $\Tr_{\E/\F}(\delta) = 0$ and a nontrivial additive character $\varPsi$ of $\A/\F$ such that
\begin{itemize}
\item $\delta$ belongs to the $(\F_{v_i}^\times)^2$-orbit of $\sqrt{-1}$ for $i=0,1,2,3$;
\item $\varPsi_{v_i}$ belongs to the $(\F_{v_i}^\times)^2$-orbit of $\psi$ for $i=0,1,2,3$.
\end{itemize}
We will take the global Whittaker datum determined by $\delta$ and $\varPsi$ as in \S \ref{ss:whit}.
Let $\W$ be the $n$-dimensional anisotropic skew-Hermitian space over $\E$ such that
\begin{itemize}
\item the signature of $\W_{v_i}$ is $(p,q)$ for $i=0,1$;
\item the signature of $\W_{v_i}$ is $(n,0)$ for $i=2,3$;
\item $\epsilon(\W_v) = 1$ for all nonarchimedean places $v$ of $\F$.
\end{itemize}
Similarly, let $\V$ be the $m$-dimensional anisotropic Hermitian space over $\E$ such that
\begin{itemize}
\item the signature of $\V_{v_i}$ is $(r,s)$ for $i=0,1$;
\item the signature of $\V_{v_i}$ is $(m,0)$ for $i=2,3$;
\item $\epsilon(\V_v) = 1$ for all nonarchimedean places $v$ of $\F$.
\end{itemize}
Note that such spaces $\W$ and $\V$ exist since $\prod_v \epsilon(\W_v) = \prod_v \epsilon(\V_v) = 1$.
By Lemma \ref{l:csd-char-global}, we may take two (unitary) characters $\chi_\V, \chi_\W$ of $\A_\E^\times/\E^\times$ such that
\begin{alignat*}{2}
\chi_\V|_{\A^\times} & = \omega_{\E/\F}^m, \quad & \chi_{\V, v_i} & = \chi_V, \\
\chi_\W|_{\A^\times} & = \omega_{\E/\F}^n, \quad & \chi_{\W, v_i} & = \chi_W
\end{alignat*}
for $i=0,1,2,3$.
Similarly, by Lemmas \ref{l:csd-char-local} and \ref{l:csd-char-global}, we may take conjugate-selfdual characters $\chi_1, \dots, \chi_n$ of $\A_\E^\times/\E^\times$ with sign $(-1)^{n-1}$ satisfying the following conditions:
\begin{itemize}
\item $\chi_{i,v_0} = \chi_{\kappa_i}$ for all $i$;
\item $\chi_{i,v_1} = \chi_{\tilde{\kappa}_i}$ for all $i$;
\item $\chi_{i,v_2} = \chi_{i,v_3} = \chi_{\kappa_{0,i}}$ for all $i$;
\item if $m \equiv n \bmod 2$, then
\begin{equation}
\label{eq:assumption-epsilon}
\epsilon(\tfrac{1}{2}, \chi_{i,v} \chi_{\V,v}^{-1}, \varPsi_{2,v}^\E) = 1
\end{equation}
for all nonarchimedean places $v$ of $\F$ such that $\E_v \ne \F_v \times \F_v$, where $\varPsi_{2,v}^\E$ is the character of $\E_v$ given by $\varPsi_{2,v}^\E(x) = \varPsi_v(\Tr_{\E_v/\F_v}(\delta x))$.
\end{itemize}
In particular, $\chi_1, \dots, \chi_n, \chi_\V$ are pairwise distinct.
Define a global $A$-parameter $\varPhi$ for $\U_n$ by
\[
\varPhi = \chi_1 \oplus \dots \oplus \chi_n,
\]
so that
\[
\varPhi_{v_0} = \phi, \quad \varPhi_{v_1} = \phi_+, \quad \varPhi_{v_2} = \varPhi_{v_3} = \phi_0.
\]
Let $S_\varPhi$ be the global component group of $\varPhi$, which is defined formally as a free $\Z/2\Z$-module
\[
S_\varPhi = (\Z/2\Z) e_1 \oplus \dots \oplus (\Z/2 \Z) e_n,
\]
where $e_i$ corresponds to $\chi_i$.
For each place $v$ of $\F$, let $S_{\varPhi_v}$ be the local component group of $\varPhi_v$ equipped with a natural homomorphism $S_\varPhi \rightarrow S_{\varPhi_v}$.
We denote by $e_{i,v}$ the image of $e_i$ in $S_{\varPhi_v}$.
Recall the compact group $S_{\varPhi, \A} = \prod_v S_{\varPhi_v}$ equipped with the diagonal map $\Delta : S_\varPhi \rightarrow S_{\varPhi, \A}$.
Define a continuous character $\eta = \bigotimes_v \eta_v$ of $S_{\varPhi,\A}$ by
\begin{itemize}
\item $\eta_{v_0} = \eta_{v_1} = \eta$;
\item $\eta_{v_2} = \eta_{v_3} = \eta_0$;
\item $\eta_v = \mathbbm{1}$ for all nonarchimedean places $v$ of $\F$.
\end{itemize}
Note that $\eta_v(e_{1,v} + \dots + e_{n,v}) = \epsilon(\W_v)$ for all $v$.
Let
\[
\varPi_v = \pi(\varPhi_v, \eta_v)
\]
be the irreducible tempered representation in the local $L$-packet $\Pi_{\varPhi_v}(\U(\W_v))$ associated to $\eta_v$.
Then we may form an irreducible representation $\varPi = \bigotimes_v \varPi_v$ of $\U(\W)(\A)$.
Since
\[
(\eta \circ \Delta) (e_i) = \prod_v \eta_v(e_{i,v}) = 1
\]
for all $i$, it follows from Arthur's multiplicity formula \eqref{eq:amf} that $\varPi$ is automorphic.
Moreover, since $m>n$ and $\chi_i \chi_{\V}^{-1} \ne \mathbbm{1}$ for all $i$, the partial standard $L$-function
\[
L^S(s, \varPi, \chi_\V^{-1}) = L^S(s, \chi_1 \chi_{\V}^{-1}) \cdots L^S(s, \chi_n \chi_{\V}^{-1})
\]
is holomorphic and nonzero at $s = \frac{1}{2}(m-n+1)$.
We consider the global theta lift $\varSigma = \theta_{\V, \W, \chi_\V, \chi_\W, \varPsi}(\varPi)$ to $\U(\V)(\A)$.
Recall that the local theta lift $\varSigma_v = \theta_{\V_v, \W_v, \chi_{\V,v}, \chi_{\W,v}, \varPsi_v}(\varPi_v)$ to $\U(\V_v)$ is nonzero by assumption if $v = v_0$ and by Lemmas \ref{l:local-theta-1}, \ref{l:local-theta-2}, \ref{l:local-theta-3} if $v \ne v_0$.
Hence there exist $\varphi_{1,v}, \varphi_{2,v} \in \omega_{\V_v,\W_v,\chi_{\V,v},\chi_{\W,v},\varPsi_v}$ and $f_{1,v}, f_{2,v} \in \varPi_v$ such that
\[
\ZZ(\varphi_{1,v}, \varphi_{2,v}, f_{1,v}, f_{2,v}) \ne 0
\]
by Proposition \ref{p:key} if $v$ is real and by \cite[Proposition 11.5]{gqt}, \cite[Lemma 8.6]{yamana} if $v$ is nonarchimedean.
As explained in \S \ref{ss:global-theta}, this implies that $\varSigma$ is nonzero.
Thus we obtain an irreducible automorphic representation $\varSigma = \bigotimes_v \varSigma_v$ of $\U(\V)(\A)$.
Finally, we derive the information about $\varSigma_{v_0} = \theta_{r,s}(\pi)$ from the knowledge of $\varSigma_v$ for $v \ne v_0$ and Arthur's multiplicity formula.
Define a global $A$-parameter $\varPhi'$ for $\U_m$ by
\[
\varPhi' = \chi_1 \chi_\V^{-1} \chi_\W \oplus \dots \oplus \chi_n \chi_\V^{-1} \chi_\W \oplus (\chi_\W \boxtimes S_{m-n}),
\]
so that
\[
\varPhi'_{v_0} = \phi', \quad \varPhi'_{v_1} = \phi_+'.
\]
Let $S_{\varPhi'}$ be the global component group of $\varPhi'$, which is defined formally as a free $\Z/2\Z$-module
\[
S_{\varPhi'} = (\Z/2\Z) e'_1 \oplus \dots \oplus (\Z/2 \Z) e'_n \oplus (\Z/2 \Z) e'_0,
\]
where $e'_i$ corresponds to $\chi_1 \chi_\V^{-1} \chi_\W$ (resp.~$\chi_\W \boxtimes S_{m-n}$) if $i \ne 0$ (resp.~$i=0$).
For each place $v$ of $\F$, let $S_{\varPhi'_v}$ be the local component group of $\varPhi'_v$ equipped with a natural homomorphism $S_{\varPhi'} \rightarrow S_{\varPhi'_v}$.
We denote by $e'_{i,v}$ the image of $e'_i$ in $S_{\varPhi'_v}$.
By Lemmas \ref{l:local-theta-2} and \ref{l:local-theta-3}, $\varSigma$ occurs in the near equivalence class $L^2_{\varPhi'}(\U(\V))$.
Hence $\varSigma_v$ belongs to the local $A$-packet $\Pi_{\varPhi'_v}(\U(\V_v))$ for all $v$.
Since $\Pi_{\varPhi'_v}(\U(\V_v))$ is multiplicity-free, we may associate to $\varSigma_v$ a character $\eta'_v$ of $S_{\varPhi'_v}$.
Then it follows from Arthur's multiplicity formula \eqref{eq:amf} and Lemma \ref{l:epsilon} that
\[
\prod_v \eta_v'(e_{i,v}') =
\begin{cases}
\epsilon(\tfrac{1}{2}, \chi_i \chi_{\V}^{-1}) & \text{if $i \ne 0$;} \\
\epsilon(\tfrac{1}{2}, \varPi, \chi_{\V}^{-1}) & \text{if $i = 0$.}
\end{cases}
\]
However, it follows from Lemma \ref{l:csd-char-epsilon} and \eqref{eq:assumption-epsilon} that
\[
\epsilon(\tfrac{1}{2}, \chi_i \chi_{\V}^{-1}) = \prod_v \epsilon(\tfrac{1}{2}, \chi_{i,v} \chi_{\V,v}^{-1}, \varPsi_{2,v}^\E) = 1,
\]
so that
\[
\epsilon(\tfrac{1}{2}, \varPi, \chi_{\V}^{-1})
= \epsilon(\tfrac{1}{2}, \chi_1 \chi_{\V}^{-1}) \cdots \epsilon(\tfrac{1}{2}, \chi_n \chi_{\V}^{-1}) = 1.
\]
Hence we have
\[
\prod_v \eta_v'(e_{i,v}') = 1
\]
for all $i$.
On the other hand, by Lemmas \ref{l:local-theta-2} and \ref{l:local-theta-3}, we have $\eta_v' = \mathbbm{1}$ for all nonarchimedean places $v$ of $\F$.
Since $\eta_{v_2}' = \eta_{v_3}'$, we conclude that
\[
\eta_{v_0}'(e_{i,v_0}) = \eta_{v_1}'(e_{i,v_1})
\]
for all $i$.
But by \eqref{eq:theta(pi+)}, $\eta_{v_1}'$ agrees with the character $\eta'$ of $S_{\phi'_+} \cong \widetilde{S}_{\phi'}$ as in \S \ref{sss:local-theta-real}, so that
\[
\theta_{r,s}(\pi) = \varSigma_{v_0} = \sigma(\varPhi_{v_0}', \eta_{v_0}') = \sigma(\phi', \eta').
\]
This combined with Lemma \ref{l:Aq-eta} proves Theorem \ref{t:main-lds}\eqref{main-lds-1}.
\section{Proof of Theorem \ref{t:main-lds}\eqref{main-lds-2}}
In this section, we consider the theta lifting from $\U(p,q)$ to $\U(r,s)$ with $p+q=n$ and $r+s=m$ in the case $m \le n$ and determine the theta lifts of (limits of) discrete series representations by switching the roles of $\U(p,q)$ and $\U(r,s)$.
Let $\pi$ be a (limit of) discrete series representation of $\U(p,q)$.
Assume that $\theta_{r,s}(\pi) \ne 0$.
If $m=n$ or $n-1$, then Theorem \ref{t:main-lds} was proved by Paul \cite{paul1, paul2}.
Thus we assume that $m \le n-2$.
Put $k = n-m$.
Write $\pi = \pi(\phi, \eta)$, where $\phi$ is a (limit of) discrete series $L$-parameter for $\U_n$ and $\eta$ is a character of $S_\phi$.
Write
\[
\phi = (m_1 \chi_{\kappa_1} \oplus \dots \oplus m_a \chi_{\kappa_a}) \otimes \chi_V
\]
and
\[
S_\phi = (\Z/2\Z) e_1 \oplus \dots \oplus (\Z/2\Z) e_a,
\]
where
\begin{itemize}
\item $\kappa_i \in \Z + \frac{k-1}{2}$;
\item $\kappa_1 > \dots > \kappa_a$;
\item $m_i$ is a positive integer;
\item $m_1 + \dots + m_a = n$,
\end{itemize}
and $e_i$ corresponds to $\chi_{\kappa_i} \chi_V$.
Put $n_i = m_1 + \dots + m_{i-1}$ and
\[
(p_i, q_i) =
\begin{cases}
(\frac{m_i+1}{2}, \frac{m_i-1}{2}) & \text{if $m_i$ is odd and $\eta(e_i) = (-1)^{n_i}$;} \\
(\frac{m_i-1}{2}, \frac{m_i+1}{2}) & \text{if $m_i$ is odd and $\eta(e_i) = (-1)^{n_i+1}$;} \\
(\frac{m_i}{2}, \frac{m_i}{2}) & \text{if $m_i$ is even.}
\end{cases}
\]
Then by Corollary \ref{c:going-down}, there exist $0 \le i_0 \le a-k$ and $\epsilon_0 = \pm 1$ such that
\begin{itemize}
\item $\kappa_{i_0 + i} = \frac{k+1}{2} - i$ for all $1 \le i \le k$;
\item $m_{i_0 + i}$ is odd for all $1 < i < k$;
\item $\eta(e_{i_0 + 1}) = \epsilon_0 \times
\begin{cases}
(-1)^{n_{i_0 + 1}} & \text{if $m_{i_0 + 1}$ is odd;} \\
(-1)^{n_{i_0 + 1}+1} & \text{if $m_{i_0 + 1}$ is even;}
\end{cases}
$
\item $\eta(e_{i_0 + i}) = \epsilon_0 \cdot (-1)^{n_{{i_0 + i}}}$ for all $1 < i \le k$.
\end{itemize}
In particular, if we write $\pi = {\mathstrut}^n \! A_\b(\lambda)$ as in \eqref{eq:lds}, then $\b$ and $\lambda$ satisfy the conditions in Theorem \ref{t:main-lds}\eqref{main-lds-2}.
Put
\[
\begin{aligned}
p^+ & = p_1 + \dots + p_{i_0}, \, &
p^- & = p_{i_0+k+1} + \dots + p_a, \\
q^+ & = q_1 + \dots + q_{i_0}, \, &
q^- & = q_{i_0+k+1} + \dots + q_a,
\end{aligned}
\]
and
\[
l =
\begin{cases}
q_{i_0 + 1} + \dots + q_{i_0 + k}
& \text{if $\epsilon_0 = +1$;} \\
p_{i_0 + 1} + \dots + p_{i_0 + k}
& \text{if $\epsilon_0 = -1$.}
\end{cases}
\]
Then we have
\begin{align*}
(p,q) & =
\begin{cases}
(p^+ + p^- + l + k, q^+ + q^- + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is odd;} \\
(p^+ + p^- + l + k-1, q^+ + q^- + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is even;} \\
(p^+ + p^- + l + k-1, q^+ + q^- + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is odd;} \\
(p^+ + p^- + l + k-2, q^+ + q^- + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is even;} \\
(p^+ + p^- + l, q^+ + q^- + l + k)
& \text{if $\epsilon_0 = -1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is odd;} \\
(p^+ + p^- + l, q^+ + q^- + l + k-1)
& \text{if $\epsilon_0 = -1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is even;} \\
(p^+ + p^- + l, q^+ + q^- + l + k-1)
& \text{if $\epsilon_0 = -1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is odd;} \\
(p^+ + p^- + l, q^+ + q^- + l + k-2)
& \text{if $\epsilon_0 = -1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is even,}
\end{cases} \\
(r,s) & =
\begin{cases}
(p^+ + q^- + l, p^- + q^+ + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is odd;} \\
(p^+ + q^- + l, p^- + q^+ + l-1)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is even;} \\
(p^+ + q^- + l-1, p^- + q^+ + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is odd;} \\
(p^+ + q^- + l-1, p^- + q^+ + l-1)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is even;} \\
(p^+ + q^- + l, p^- + q^+ + l)
& \text{if $\epsilon_0 = -1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is odd;} \\
(p^+ + q^- + l-1, p^- + q^+ + l)
& \text{if $\epsilon_0 = -1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is even;} \\
(p^+ + q^- + l, p^- + q^+ + l-1)
& \text{if $\epsilon_0 = -1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is odd;} \\
(p^+ + q^- + l-1, p^- + q^+ + l-1)
& \text{if $\epsilon_0 = -1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is even.}
\end{cases}
\end{align*}
Assume first that $m_i = 1$ for all $i_0 + 1 < i < i_0 + k$.
We only consider the case $\epsilon_0 = +1$; the case $\epsilon_0 = -1$ is similar.
Write $\pi = {\mathstrut}^n \! A_\b(\lambda)$ as in \eqref{eq:lds} and put
\[
p' = p_{i_0+1}, \quad
p'' = p_{i_0+k}, \quad
q' = q_{i_0+1}, \quad
q'' = q_{i_0+k}.
\]
Then $\lambda$ is of the form
\begin{align*}
\lambda & = \bigg( \alpha_1, \dots, \alpha_{p^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{p'},
\frac{k-3}{2}, \frac{k-5}{2}, \dots, -\frac{k-3}{2},
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{p''},
\beta_1, \dots, \beta_{p^-}, \\
& \phantom{{} = \bigg(} \gamma_1, \dots, \gamma_{q^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{q'},
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{q''},
\delta_1, \dots, \delta_{q^-} \bigg)
+ \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg),
\end{align*}
where $\alpha_i, \gamma_j > \frac{k-1}{2}$ and $\beta_i, \delta_j < -\frac{k-1}{2}$, and $\b = \q(x)$ is associated to
\begin{align*}
x & = (x^+_1, \dots, x^+_{p^+}, x'_1, \dots, x'_{p'}, z_2, z_3, \dots, z_{k-1}, x''_1, \dots, x''_{p''}, x^-_1, \dots, x^-_{p^-}, \\
& \phantom{{} = (} y^+_1, \dots, y^+_{q^+}, y'_1, \dots, y'_{q'}, y''_1, \dots, y''_{q''}, y^-_1, \dots, y^-_{q^-})
\end{align*}
such that
\begin{align*}
&
\begin{cases}
\mathrlap{x'_1 > y'_1 > \dots > x'_{q'} > y'_{q'} > x'_{p'}}\hphantom{x''_1 > y''_1 > \dots > x''_{q''} > y''_{q''} > x''_{p''}} &
\text{if $m_{i_0+1}$ is odd;} \\
y'_1 > x'_1 > \dots > y'_{q'} > x'_{p'} &
\text{if $m_{i_0+1}$ is even,}
\end{cases} \\
&
\begin{cases}
x''_1 > y''_1 > \dots > x''_{q''} > y''_{q''} > x''_{p''} &
\text{if $m_{i_0+k}$ is odd;} \\
x''_1 > y''_1 > \dots > x''_{p''} > y''_{q''} &
\text{if $m_{i_0+k}$ is even.}
\end{cases}
\end{align*}
We assume without loss of generality that
\[
x'_{p'} > 0 > x''_1.
\]
Put $\sigma = {\mathstrut}^n \! A_{\b'}(\lambda')$, where
\begin{align*}
\lambda' & = \bigg( \alpha_1, \dots, \alpha_{p^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{p'-1},
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{q''},
\delta_1, \dots, \delta_{q^-}, \\
& \phantom{{} = \bigg(} \gamma_1, \dots, \gamma_{q^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{q'},
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{p''-1},
\beta_1, \dots, \beta_{p^-} \bigg)
+ \bigg( \frac{n_0}{2}, \dots, \frac{n_0}{2} \bigg)
\end{align*}
and $\b' = \q(x')$ with
\begin{align*}
x' & = (x^+_1, \dots, x^+_{p^+}, x'_1, \dots, x'_{p'-1}, y''_1, \dots, y''_{q''}, y^-_1, \dots, y^-_{q^-}, \\
& \phantom{{} = (} y^+_1, \dots, y^+_{q^+}, y'_1, \dots, y'_{q'}, x''_2, \dots, x''_{p''}, x^-_1, \dots, x^-_{p^-}).
\end{align*}
Then $\sigma$ is a (limit of) discrete series representation of $\U(r,s)$.
By Corollary \ref{c:going-up}, we have $\theta_{p,q}(\sigma) \ne 0$.
Hence it follows from Theorem \ref{t:main-lds}\eqref{main-lds-1} proved in the previous section that
\[
\theta_{p,q}(\sigma) = {\mathstrut}^n \! A_{\tilde{\q}}(\tilde{\lambda}),
\]
where
\begin{align*}
\tilde{\lambda} & = \bigg( \alpha_1, \dots, \alpha_{p^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{p' - 1},
\underbrace{0, \dots, 0 \vphantom{\frac{k-1}{2}}}_{k},
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{p'' - 1},
\beta_1, \dots, \beta_{p^-}, \\
& \phantom{{} = \bigg(} \gamma_1, \dots, \gamma_{q^+},
\underbrace{\frac{k-1}{2}, \dots, \frac{k-1}{2}}_{q'},
\underbrace{-\frac{k-1}{2}, \dots, -\frac{k-1}{2}}_{q''},
\delta_1, \dots, \delta_{q^-} \bigg) + \bigg( \frac{m_0}{2}, \dots, \frac{m_0}{2} \bigg)
\end{align*}
and $\tilde{\q} = \q(\tilde{x})$ with
\begin{align*}
\tilde{x} & = (x^+_1, \dots, x^+_{p^+}, x'_1, \dots, x'_{p'-1}, \underbrace{0, \dots, 0}_k, x''_2, \dots, x''_{p''}, x^-_1, \dots, x^-_{p^-}, \\
& \phantom{{} = (} y^+_1, \dots, y^+_{q^+}, y'_1, \dots, y'_{q'}, y''_1, \dots, y''_{q''}, y^-_1, \dots, y^-_{q^-}).
\end{align*}
Since $\tilde{\l} \subset \k$ (where $\tilde{\l}$ is the Levi component of $\tilde{\q}$ and $\k$ is the complexified Lie algebra of $K$), we have
\[
{\mathstrut}^n \! A_{\tilde{\q}}(\tilde{\lambda}) = {\mathstrut}^n \! A_{\b}(\lambda)
\]
by induction in stages \cite[Corollary 11.86]{kv}.
Thus we have shown that $\theta_{p,q}(\sigma) = \pi$, so that $\theta_{r,s}(\pi) = \sigma$ as desired.
Assume next that $m_{i_1} \ge 3$ for some $i_0 + 1 < i_1 < i_0 + k$.
In particular, we have $p,q,r,s > 0$.
Define a (limit of) discrete series $L$-parameter $\phi'$ for $\U_m$ by
\[
\phi' = (m'_1 \chi_{\kappa_1} \oplus \dots \oplus m'_a \chi_{\kappa_a}) \otimes \chi_W
\]
and write
\[
S_{\phi'} = (\Z/2\Z) e'_1 \oplus \dots \oplus (\Z/2\Z) e'_a,
\]
where
\[
m'_i =
\begin{cases}
m_i -1 & \text{if $i_0 + 1 \le i \le i_0 + k$;} \\
m_i & \text{if $i \le i_0$ or $i > i_0+k$}
\end{cases}
\]
and $e'_i$ corresponds to $\chi_{\kappa_i} \chi_W$.
(When $m'_i = 0$, we interpret $e'_i$ as zero.)
Define a character $\eta'$ of $S_{\phi'}$ by
\[
\eta'(e'_i) =
\begin{cases}
\epsilon_0 \cdot (-1)^{n_{i_0+2} + 1} & \text{if $i_0 + 1 \le i \le i_0 + k$ and $m'_i > 0$;} \\
\zeta_i \cdot \eta(e_i) & \text{if $i \le i_0$ or $i > i_0+k$,}
\end{cases}
\]
where
\[
\zeta_i =
\begin{cases}
+1 & \text{if $k$ is even and $i \le i_0$;} \\
-1 & \text{if $k$ is even and $i > i_0 + k$;} \\
+1 & \text{if $k$ is odd.}
\end{cases}
\]
Put $\sigma = \pi(\phi', \eta')$, so that $\sigma$ is a (limit of) discrete series representation of $\U(r,s)$.
\begin{lem}
We have $\sigma = {\mathstrut}^n \! A_\q(\lambda')$, where $\q$ and $\lambda'$ are as in Theorem \ref{t:main-lds}\eqref{main-lds-2}.
\end{lem}
\begin{proof}
Put $n_i' = m_1' + \dots + m_{i-1}'$.
Then we have the following.
\begin{itemize}
\item
We have
\begin{align*}
\eta(e_i) & = \epsilon_0 \times
\begin{cases}
(-1)^{n_i} & \text{if $i=i_0+1$ and $m_i$ is odd;} \\
(-1)^{n_i+1} & \text{if $i=i_0+1$ and $m_i$ is even;} \\
(-1)^{n_i} & \text{if $i_0+1 < i \le i_0+k$,}
\end{cases} \\
\eta'(e_i') & = \epsilon_0 \times
\begin{cases}
(-1)^{n_i'} & \text{if $i=i_0+1$ and $m_i$ is odd;} \\
(-1)^{n_i'+1} & \text{if $i=i_0+1$ and $m_i$ is even;} \\
(-1)^{n_i'} & \text{if $i_0+1 < i \le i_0+k$,}
\end{cases}
\end{align*}
noting that $n_{i_0+1}' = n_{i_0+2} - m_{i_0+1}$, $n_{i_0+2}' = n_{i_0+2} - 1$, and $n_i' \equiv n'_{i_0+2} \bmod 2$ for $i_0+1 < i \le i_0+k$.
(When $m_i'=0$, we ignore the corresponding identity.)
\item
If $i \le i_0$, then we have $n_i' = n_i$, so that $\eta'(e_i') = (-1)^{n_i'}$ if and only if $\eta(e_i) = (-1)^{n_i}$.
\item
If $i > i_0 + k$, then we have $n_i' = n_i-k$, so that $\eta'(e_i') = (-1)^{n_i'}$ if and only if $\eta(e_i) = (-1)^{n_i+1}$.
\end{itemize}
This implies the assertion.
\end{proof}
Thus Theorem \ref{t:main-lds} in this case amounts to
\[
\theta_{r,s}(\pi) = \sigma.
\]
We now proceed by induction on $m'_{i_0+2} + \dots + m'_{i_0+k-1}$.
Define (limits of) discrete series $L$-parameters $\phi_0$ and $\phi_0'$ for $\U_{n-2}$ and $\U_{m-2}$, respectively, by
\begin{align*}
\phi_0 & = (m_1 \chi_{\kappa_1} \oplus \cdots \oplus m_{i_1-1} \chi_{\kappa_{i_1-1}} \oplus (m_{i_1} - 2) \chi_{\kappa_{i_1}} \oplus m_{i_1+1} \chi_{\kappa_{i_1+1}} \oplus \cdots \oplus m_a \chi_{\kappa_a}) \otimes \chi_V, \\
\phi'_0 & = (m'_1 \chi_{\kappa_1} \oplus \cdots \oplus m'_{i_1-1} \chi_{\kappa_{i_1-1}} \oplus (m'_{i_1} - 2) \chi_{\kappa_{i_1}} \oplus m'_{i_1+1} \chi_{\kappa_{i_1+1}} \oplus \cdots \oplus m'_a \chi_{\kappa_a}) \otimes \chi_W.
\end{align*}
Then we have a natural isomorphism $S_{\phi_0} \cong S_\phi$ and a natural embedding $S_{\phi'_0} \hookrightarrow S_{\phi'}$, which is an isomorphism if and only if $m_{i_1} \ge 5$.
Put $\pi_0 = \pi(\phi_0, \eta)$ and $\sigma_0 = \pi(\phi'_0, \eta'_0)$, where $\eta$ is viewed as a character of $S_{\phi_0}$ and $\eta_0'$ is the restriction of $\eta'$ to $S_{\phi'_0}$, so that $\pi_0$ and $\sigma_0$ are (limits of) discrete series representations of $\U(p-1, q-1)$ and $\U(r-1, s-1)$, respectively.
Then $\pi$ and $\sigma$ are subrepresentations of $I(\chi, \pi_0)$ and $I(\chi \chi_V^{-1} \chi_W, \sigma_0)$, respectively, where $\chi = \chi_{\kappa_{i_1}} \chi_V$.
In fact, $I(\chi, \pi_0)$ is irreducible and
\[
\pi = I(\chi, \pi_0).
\]
Since $\theta_{r,s}(\pi) \ne 0$, we have $\theta_{r-1,s-1}(\pi_0) \ne 0$ by Corollary \ref{c:jacquet}, so that $\theta_{r-1,s-1}(\pi_0) = \sigma_0$ by the induction hypothesis.
Hence by the induction principle \cite[Theorem 4.5.5]{paul1}, $\theta_{r,s}(\pi)$ is a subquotient of $I(\chi \chi_V^{-1} \chi_W, \sigma_0)$.
If $m_{i_1} \ge 5$, then $I(\chi \chi_V^{-1} \chi_W, \sigma_0)$ is irreducible and
\[
\sigma = I(\chi \chi_V^{-1} \chi_W, \sigma_0),
\]
so that $\theta_{r,s}(\pi) = \sigma$ as desired.
Thus we assume that $m_{i_1} = 3$.
Then we have $S_{\phi'} = S_{\phi'_0} \oplus (\Z/2\Z) e'_{i_1}$ and
\[
I(\chi \chi_V^{-1} \chi_W, \sigma_0) = \sigma \oplus \sigma'
\]
with $\sigma' = \pi(\phi', \eta'')$, where $\eta''$ is the character of $S_{\phi'}$ given by
\[
\eta''|_{S_{\phi_0'}} = \eta_0', \quad
\eta''(e'_{i_1}) = \epsilon_0 \cdot (-1)^{n_{i_0+2}}.
\]
To prove $\theta_{r,s}(\pi) = \sigma$, it suffices to show that
\[
\theta_{p,q}(\sigma') = 0.
\]
We only consider the case $\epsilon_0 = +1$; the case $\epsilon_0 = -1$ is similar.
Let $k_0 = -1$ or $0$ be such that $k_0 \equiv k \bmod 2$ and put
\[
t = \frac{k+k_0}{2}.
\]
As in \S \ref{ss:atobe-def}, we define the invariants of $\sigma'$ (with respect to $k_0$ and $\chi_W$).
Then we have $k_{\sigma'} = k_0$ and
\[
(r_{\sigma'}, s_{\sigma'}) =
\begin{cases}
(p^+ + p^- + l, q^+ + q^- + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is odd;} \\
(p^+ + p^- + l-1, q^+ + q^- + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is odd, $m_{i_0+k}$ is even;} \\
(p^+ + p^- + l-1, q^+ + q^- + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is odd;} \\
(p^+ + p^- + l-2, q^+ + q^- + l)
& \text{if $\epsilon_0 = +1$, $m_{i_0+1}$ is even, $m_{i_0+k}$ is even,}
\end{cases}
\]
so that
\[
(p,q) = (r_{\sigma'} + k, s_{\sigma'}).
\]
Moreover, we have the following.
\begin{itemize}
\item
If $\kappa_{i_1} > 0$, then we have $(\kappa_{i_1}, +1) \in \XX_{\sigma'}$ but $(\kappa_i, -1) \notin \XX_{\sigma'}$ for all $i_1 < i < i_0 + k$.
Hence we have $(\kappa_{i_1}, +1) \in \CC^+_{\sigma'}(t)$.
\item
If $\kappa_{i_1} < 0$, then we have $(\kappa_{i_1}, -1) \in \XX_{\sigma'}$ but $(\kappa_i, +1) \notin \XX_{\sigma'}$ for all $i_0 + 1 < i < i_1$.
Hence we have $(\kappa_{i_1}, -1) \in \CC^-_{\sigma'}(t)$.
\item
If $\kappa_{i_1} = 0$ (so that $k_{\sigma'} = -1$), then we have $(0, +1), (0, -1) \in \XX_{\sigma'}$.
\end{itemize}
Hence by Theorem \ref{t:atobe}, we have $\theta_{p,q}(\sigma') = 0$ as desired.
This completes the proof of Theorem \ref{t:main-lds}\eqref{main-lds-2}.
\section{Proof of Theorem \ref{t:main-temp}}
In this section, we consider the theta lifting from $\U(p,q)$ to $\U(r,s)$ and determine the theta lifts of tempered representations in terms of those of (limits of) discrete series representations.
Let $\pi$ be an irreducible tempered representation of $\U(p,q)$ and write $\pi = I(\xi_1, \dots, \xi_d, \pi_0)$ as in \eqref{eq:temp}.
Assume that $\theta_{r,s}(\pi) \ne 0$.
Then by Corollary \ref{c:jacquet}, we have $d \le \min \{ r, s \}$ and $\theta_{r-d,s-d}(\pi_0) \ne 0$.
Hence by the induction principle \cite[Theorem 4.5.5]{paul1}, $\theta_{r,s}(\pi)$ is a subquotient of
\[
I(\xi_1 \chi_V^{-1} \chi_W, \dots, \xi_d \chi_V^{-1} \chi_W, \theta_{r-d,s-d}(\pi_0)).
\]
However, it follows Lemma \ref{l:irred-cohom} and Theorem \ref{t:main-lds} that the parabolically induced representation above is irreducible.
Thus we conclude that
\[
\theta_{r,s}(\pi) = I(\xi_1 \chi_V^{-1} \chi_W, \dots, \xi_d \chi_V^{-1} \chi_W, \theta_{r-d,s-d}(\pi_0)).
\]
This completes the proof of Theorem \ref{t:main-temp}.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,963
|
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