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pii-pile-chunk3-300000-350000-tagged

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[ "Geeks To Go is a helpful hub, where thousands of volunteer geeks quickly serve friendly answers and support. ", "Check out the forums and get free advice from the experts. ", "Register now to gain access to all of our features, it's FREE and only takes one minute. ", "Once registered and logged in, you will be able to create topics, post replies to existing threads, give reputation to your fellow members, get your own private messenger, post status updates, manage your profile and so much more.", "\n\nTrojanDownloader.", "XS [RESOLVED]\n\naozy\n\nPosted 26 March 2008 - 04:19 AM\n\naozy\n\nNew Member\n\nMember\n\n9 posts\n\nHi, my com recently have been getting various popups which notify me tt it has been infected with spyware and stuff. ", "Sometimes my wallpaper is replaced by a message saying my com has been infected. ", "A yellow warning triangle also keeps popping up and stuff. ", "I have norton internet security and spybot on my com. ", "I hope to get some assistance regarding this issue and fix up my com cuz im not really tt good with handling all these technical stuff. ", "Thanks in advance.", "\n\nAdvertisements\n\nRorschach112\n\nPosted 30 March 2008 - 02:13 PM\n\nRorschach112\n\nRalphie\n\nRetired Staff\n\n47,710 posts\n\nHello\n\nBefore we begin, you should save these instructions in Notepad to your desktop, or print them, for easy reference. ", "Much of our fix will be done in Safe mode, and you will be unable to access this thread at that time. ", "If you have questions at any point, or are unsure of the instructions, feel free to post here and ask for clarification before proceeding.", "\n\nYou will be prompted : \"Registry cleaning - Do you want to clean the registry ?\"; ", "answer \"Yes\" by typing Y and press \"Enter\" in order to remove the Desktop background and clean registry keys associated with the infection.", "\n\nThe tool will now check if wininet.dll is infected. ", "You may be prompted to replace the infected file (if found); answer \"Yes\" by typing Y and press \"Enter\".", "\n\nThe tool may need to restart your computer to finish the cleaning process; if it doesn't, please restart it into Normal Windows.", "A text file will appear onscreen, with results from the cleaning process; please copy/paste the content of that report into your next reply.", "The report can also be found at the root of the system drive, usually at C:\\rapport.txt\n\nEvent Record #/Type36651 / WarningEvent Submitted/Written: 03/31/2008 01:51:09 AMEvent ID/Source: 1524 / UserenvEvent Description:Windows cannot unload your classes registry file - it is still in use by other applications or services. ", "The file will be unloaded when it is no longer in use.", "\n\nEvent Record #/Type45790 / WarningEvent Submitted/Written: 03/31/2008 10:51:27 PMEvent ID/Source: 3004 / WinDefendEvent Description:%AOZY27 Real-Time Protection agent has detected changes. ", "Microsoft recommends you analyze the software that made these changes for potential risks. ", "You can use information about how these programs operate to choose whether to allow them to run or remove them from your computer. ", "Allow changes only if you trust the program or the software publisher. %", "AOZY27 can't undo changes that you allow.", "\n\nFor more information please see the following:%AOZY275\n\nScan ID: {90ABD979-4B16-4EF5-B1B0-1B710AD532D7}\n\nUser: AOZY\\apples\n\nName: %AOZY271\n\nID: %AOZY272\n\nSeverity: 1.1.1593.05\n\nCategory: 1.1.1593.06\n\nPath Found: %AOZY276\n\nAlert Type: %AOZY278\n\nDetection Type: 1.1.1593.02\n\nEvent Record #/Type45789 / WarningEvent Submitted/Written: 03/31/2008 10:51:27 PMEvent ID/Source: 3004 / WinDefendEvent Description:%AOZY27 Real-Time Protection agent has detected changes. ", "Microsoft recommends you analyze the software that made these changes for potential risks. ", "You can use information about how these programs operate to choose whether to allow them to run or remove them from your computer. ", "Allow changes only if you trust the program or the software publisher. %", "AOZY27 can't undo changes that you allow.", "\n\nFor more information please see the following:%AOZY275\n\nScan ID: {B6F564AB-4C35-4428-A720-8B1A506E0231}\n\nUser: AOZY\\apples\n\nName: %AOZY271\n\nID: %AOZY272\n\nSeverity: 1.1.1593.05\n\nCategory: 1.1.1593.06\n\nPath Found: %AOZY276\n\nAlert Type: %AOZY278\n\nDetection Type: 1.1.1593.02\n\nEvent Record #/Type45788 / WarningEvent Submitted/Written: 03/31/2008 10:51:27 PMEvent ID/Source: 3004 / WinDefendEvent Description:%AOZY27 Real-Time Protection agent has detected changes. ", "Microsoft recommends you analyze the software that made these changes for potential risks. ", "You can use information about how these programs operate to choose whether to allow them to run or remove them from your computer. ", "Allow changes only if you trust the program or the software publisher. %", "AOZY27 can't undo changes that you allow.", "\n\nFor more information please see the following:%AOZY275\n\nScan ID: {58CD38B3-BCE3-48E4-832F-52BC24A0452E}\n\nUser: AOZY\\apples\n\nName: %AOZY271\n\nID: %AOZY272\n\nSeverity: 1.1.1593.05\n\nCategory: 1.1.1593.06\n\nPath Found: %AOZY276\n\nAlert Type: %AOZY278\n\nDetection Type: 1.1.1593.02\n\nEvent Record #/Type45787 / WarningEvent Submitted/Written: 03/31/2008 10:51:24 PMEvent ID/Source: 3004 / WinDefendEvent Description:%AOZY27 Real-Time Protection agent has detected changes. ", "Microsoft recommends you analyze the software that made these changes for potential risks. ", "You can use information about how these programs operate to choose whether to allow them to run or remove them from your computer. ", "Allow changes only if you trust the program or the software publisher. %", "AOZY27 can't undo changes that you allow.", "\n\nFor more information please see the following:%AOZY275\n\nScan ID: {AE549A65-6A7E-46D6-9E29-4D4DA333B86E}\n\nUser: AOZY\\apples\n\nName: %AOZY271\n\nID: %AOZY272\n\nSeverity: 1.1.1593.05\n\nCategory: 1.1.1593.06\n\nPath Found: %AOZY276\n\nAlert Type: %AOZY278\n\nDetection Type: 1.1.1593.02\n\nEvent Record #/Type45786 / WarningEvent Submitted/Written: 03/31/2008 10:51:24 PMEvent ID/Source: 3004 / WinDefendEvent Description:%AOZY27 Real-Time Protection agent has detected changes. ", "Microsoft recommends you analyze the software that made these changes for potential risks. ", "You can use information about how these programs operate to choose whether to allow them to run or remove them from your computer. ", "Allow changes only if you trust the program or the software publisher. %", "AOZY27 can't undo changes that you allow.", "\n\nFor more information please see the following:%AOZY275\n\nScan ID: {640E4F9E-2BEE-49C6-9AAC-A6C769BAEAF0}\n\nUser: AOZY\\apples\n\nName: %AOZY271\n\nID: %AOZY272\n\nSeverity: 1.1.1593.05\n\nCategory: 1.1.1593.06\n\nPath Found: %AOZY276\n\nAlert Type: %AOZY278\n\nDetection Type: 1.1.1593.02\n\n-- End of Deckard's System Scanner: finished at 2008-03-31 22:52:21 ------------\n\n2. ", "Now close all windows other than HiJackThis, including browsers, so that nothing other than HijackThis is open, then click Fix Checked. ", "A box will pop up asking you if you wish to fix the selected items. ", "Please choose YES. ", "Once it has fixed them, please exit/close HijackThis.", "\n\nReturn to OTMoveIt2, right click in the \"Paste List Of Files/Patterns To Search For and Move\" window (under the yellow bar) and choose Paste.", "\n\nClick the red Moveit! ", "button.", "\n\nCopy everything in the Results window (under the green bar) to the clipboard by highlighting ALL of them and pressing CTRL + C (or, after highlighting, right-click and choose copy), and paste it in your next reply.", "\n\nClose OTMoveIt2\n\nIf a file or folder cannot be moved immediately you may be asked to reboot the machine to finish the move process. ", "If you are asked to reboot the machine choose Yes.", "\n\naozy\n\nPosted 31 March 2008 - 10:43 AM\n\nSome files couldn't be moved cuz it stated tt it was not a valid windows image. ", "Will tt pose any problems to the steps tt u have asked me to do?", "\n\nBelow is the results from OTMoveIt2\n\nLoadLibrary failed for C:\\WINDOWS\\userconfig9x.dll\nC:\\WINDOWS\\userconfig9x.dll NOT unregistered.", "\nC:\\WINDOWS\\userconfig9x.dll moved successfully.", "\nC:\\WINDOWS\\a.bat moved successfully.", "\nC:\\WINDOWS\\iTunesMusic.exe moved successfully.", "\nC:\\WINDOWS\\winsystem.exe moved successfully.", "\nC:\\WINDOWS\\bdn.com moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system\\SysSD.dll\nC:\\WINDOWS\\system\\SysSD.dll NOT unregistered.", "\nC:\\WINDOWS\\system\\SysSD.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\9c9af6.dll\nC:\\WINDOWS\\system32\\9c9af6.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\9c9af6.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\5384327.dll\nC:\\WINDOWS\\system32\\5384327.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\5384327.dll moved successfully.", "\nC:\\Documents and Settings\\apples\\Application Data\\PC-Cleaner moved successfully.", "\nC:\\WINDOWS\\system32winlogonpc.exe moved successfully.", "\nC:\\WINDOWS\\system32taack.exe moved successfully.", "\nC:\\WINDOWS\\system32taack.dat moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32ssurf022.dll\nC:\\WINDOWS\\system32ssurf022.dll NOT unregistered.", "\nC:\\WINDOWS\\system32ssurf022.dll moved successfully.", "\nC:\\WINDOWS\\system32sncntr.exe moved successfully.", "\nC:\\WINDOWS\\system32psoft1.exe moved successfully.", "\nC:\\WINDOWS\\system32psof1.exe moved successfully.", "\nC:\\WINDOWS\\system32ps1.exe moved successfully.", "\nC:\\WINDOWS\\system32mwin32.exe moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32msnbho.dll\nC:\\WINDOWS\\system32msnbho.dll NOT unregistered.", "\nC:\\WINDOWS\\system32msnbho.dll moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32medup020.dll\nC:\\WINDOWS\\system32medup020.dll NOT unregistered.", "\nC:\\WINDOWS\\system32medup020.dll moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32medup012.dll\nC:\\WINDOWS\\system32medup012.dll NOT unregistered.", "\nC:\\WINDOWS\\system32medup012.dll moved successfully.", "\nC:\\WINDOWS\\system32hxiwlgpm.exe moved successfully.", "\nC:\\WINDOWS\\system32hxiwlgpm.dat moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32hoproxy.dll\nC:\\WINDOWS\\system32hoproxy.dll NOT unregistered.", "\nC:\\WINDOWS\\system32hoproxy.dll moved successfully.", "\nC:\\WINDOWS\\system32bsva-egihsg52.exe moved successfully.", "\nC:\\WINDOWS\\system32WINWGPX.EXE moved successfully.", "\nC:\\WINDOWS\\system32winsystem.exe moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32vcatchpi.dll\nC:\\WINDOWS\\system32vcatchpi.dll NOT unregistered.", "\nC:\\WINDOWS\\system32vcatchpi.dll moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32vbsys2.dll\nC:\\WINDOWS\\system32vbsys2.dll NOT unregistered.", "\nC:\\WINDOWS\\system32vbsys2.dll moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32thun32.dll\nC:\\WINDOWS\\system32thun32.dll NOT unregistered.", "\nC:\\WINDOWS\\system32thun32.dll moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32thun.dll\nC:\\WINDOWS\\system32thun.dll NOT unregistered.", "\nC:\\WINDOWS\\system32thun.dll moved successfully.", "\nC:\\WINDOWS\\system32temp#01.exe moved successfully.", "\nC:\\WINDOWS\\system32sysreq.exe moved successfully.", "\nC:\\WINDOWS\\system32ssvchost.exe moved successfully.", "\nC:\\WINDOWS\\system32ssvchost.com moved successfully.", "\nC:\\WINDOWS\\system32smp moved successfully.", "\nC:\\WINDOWS\\system32Rundl1.exe moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32regm64.dll\nC:\\WINDOWS\\system32regm64.dll NOT unregistered.", "\nC:\\WINDOWS\\system32regm64.dll moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32regc64.dll\nC:\\WINDOWS\\system32regc64.dll NOT unregistered.", "\nC:\\WINDOWS\\system32regc64.dll moved successfully.", "\nC:\\WINDOWS\\system32newsd32.exe moved successfully.", "\nC:\\WINDOWS\\system32netode.exe moved successfully.", "\nC:\\WINDOWS\\system32mtr2.exe moved successfully.", "\nC:\\WINDOWS\\system32msvchost.exe moved successfully.", "\nC:\\WINDOWS\\system32mssecu.exe moved successfully.", "\nC:\\WINDOWS\\system32msgp.exe moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\[email protected]@@k.dll\nC:\\WINDOWS\\[email protected]@@k.dll NOT unregistered.", "\nC:\\WINDOWS\\[email protected]@@k.dll moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32emesx.dll\nC:\\WINDOWS\\system32emesx.dll NOT unregistered.", "\nC:\\WINDOWS\\system32emesx.dll moved successfully.", "\nC:\\WINDOWS\\system32dpcproxy.exe moved successfully.", "\nC:\\WINDOWS\\system32bdn.com moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32awtoolb.dll\nC:\\WINDOWS\\system32awtoolb.dll NOT unregistered.", "\nC:\\WINDOWS\\system32awtoolb.dll moved successfully.", "\nLoadLibrary failed for C:\\WINDOWS\\system32anticipator.dll\nC:\\WINDOWS\\system32anticipator.dll NOT unregistered.", "\nC:\\WINDOWS\\system32anticipator.dll moved successfully.", "\nC:\\WINDOWS\\system32akttzn.exe moved successfully.", "\nC:\\WINDOWS\\mssecu.exe moved successfully.", "\nC:\\WINDOWS\\system32\\mloahklq.exe moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\15a6644.dll\nC:\\WINDOWS\\system32\\15a6644.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\15a6644.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\247c528.dll\nC:\\WINDOWS\\system32\\247c528.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\247c528.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\2eebd914.dll\nC:\\WINDOWS\\system32\\2eebd914.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\2eebd914.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\16f83ba3.dll\nC:\\WINDOWS\\system32\\16f83ba3.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\16f83ba3.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\4f88424.dll\nC:\\WINDOWS\\system32\\4f88424.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\4f88424.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\26762fe8.dll\nC:\\WINDOWS\\system32\\26762fe8.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\26762fe8.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\f214b3c.dll\nC:\\WINDOWS\\system32\\f214b3c.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\f214b3c.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\18a81d91.dll\nC:\\WINDOWS\\system32\\18a81d91.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\18a81d91.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\1333eaf.dll\nC:\\WINDOWS\\system32\\1333eaf.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\1333eaf.dll moved successfully.", "\nDllUnregisterServer procedure not found in C:\\WINDOWS\\system32\\11e94f4.dll\nC:\\WINDOWS\\system32\\11e94f4.dll NOT unregistered.", "\nC:\\WINDOWS\\system32\\11e94f4.dll moved successfully.", "\nFile/Folder C:\\WINDOWS\\system32\\mloahklq.exe not found.", "\n[Custom Input]\n< purity >\n< HKEY_LOCAL_MACHINE\\software\\microsoft\\shared tools\\msconfig\\startupreg\\mloahklq >\nRegistry key HKEY_LOCAL_MACHINE\\software\\microsoft\\shared tools\\msconfig\\startupreg\\mloahklq\\\\ deleted successfully.", "\n\nPosted 01 April 2008 - 05:12 AM\n\nMake sure a checkmark is placed next to Update Malwarebytes' Anti-Malware and Launch Malwarebytes' Anti-Malware, then click Finish.", "\n\nIf an update is found, it will download and install the latest version.", "\n\nOnce the program has loaded, select \"Perform Full Scan\", then click Scan. ", "Check all the boxes and click Start Scan\n\nThe scan may take some time to finish,so please be patient.", "\n\nWhen the scan is complete, click OK, then Show Results to view the results.", "\n\nMake sure that everything is checked, and click Remove Selected.", "\n\nWhen disinfection is completed, a log will open in Notepad and you may be prompted to Restart.(See Extra Note)\n\nThe log is automatically saved by MBAM and can be viewed by clicking the Logs tab in MBAM.", "\n\nCopy&Paste the entire report in your next reply.", "\n\nExtra Note:If MBAM encounters a file that is difficult to remove,you will be presented with 1 of 2 prompts,click OK to either and let MBAM proceed with the disinfection process,if asked to restart the computer,please do so immediatly.", "\n\nPosted 01 April 2008 - 06:37 AM\n\nA list of tool components used in the Cleanup of malware will be downloaded.", "\n\nIf your Firewall or Real Time protection attempts to block OtMoveit2 to rech the Internet, please allow the application to do so.", "\n\nClick Yes to beging the Cleanup process and remove these components, including this application.", "\n\nYou will be asked to reboot the machine to finish the Cleanup process. ", "If you are asked to reboot the machine choose Yes.", "\n\nNow we need to create a new System Restore point.", "\n\nClick Start Menu > Run > type (or copy and paste)\n\n%SystemRoot%\\System32\\restore\\rstrui.exe\n\nPress OK. ", "Choose Create a Restore Point then click Next. ", "Name it and click Create, when the confirmation screen shows the restore point has been created click Close.", "\n\nNext goto Start Menu > Run > type\n\ncleanmgr\n\nClick OK, Disk Cleanup will open and start calculating the amount of space that can be freed, Once thats finished it will open the Disk Cleanup options screen, click the More Options tab then click Clean up on the system restore area and choose Yes at the confirmation window which will remove all the restore points except the one we just created.", "\n\nTo close Disk Cleanup and remove the Temporary Internet Files detected in the initial scan click OK then choose Yes on the confirmation window.", "\n\nBelow I have included a number of recommendations for how to protect your computer against malware infections.", "\n\n* Keep Windows updated by regularly checking their website at :http://windowsupdate.microsoft.com/This will ensure your computer has always the latest security updates available installed on your computer.", "\n\n* To reduce re-infection for malware in the future, I strongly recommend installing these free programs:SpywareBlaster protects against bad ActiveXIE-SPYAD puts over 5000 sites in your restricted zone so you'll be protected when you visit innocent-looking sites that aren't actually innocent at all Have a look at this tutorial for IE-Spyad here\n\nIn the ActiveX section, set the first two options (\"Download signed and unsigned ActiveX controls) to \"Prompt\", and (\"Initialize and Script ActiveX controls not marked as safe\") to \"Disable\".", "\n\nNext Click OK, then Apply button and then OK to exit the Internet Properties page.", "\n\n* MVPS Hosts file replaces your current HOSTS file with one containing well known ad sites and other bad sites. ", "Basically, this prevents your computer from connecting to those sites by redirecting them to 127.0.0.1 which is your local computer, meaning it will be difficult to infect yourself in the future.", "\n\n* Please consider using an alternate browser. ", "Mozilla's Firefox browser is fantastic; it is much more secure than Internet Explorer, immune to almost all known browser hijackers, and also has the best built-in pop upblocker (as an added benefit!) ", "that I have ever seen. ", "If you are interested, Firefox may be downloaded from Here\n\n* Take a good look at the following suggestions for malware prevention by reading Tony Klein’s article 'How Did I Get Infected In The First Place'Here\n\nThank you for your patience, and performing all of the procedures requested.", "\n\naozy\n\nPosted 01 April 2008 - 07:19 AM\n\naozy\n\nNew Member\n\nTopic Starter\n\nMember\n\n9 posts\n\nHey thanks for ur guidance in regards to solving my problem. ", "I really appreciate ur help and assistance. ", "I'll try my best to keep in mind how to protect my com from now on. ", "It's really great to know that there are ppl out there who will help u with such problems. ", "Continue to do a gd job in helping ppl regarding such issues!" ]

{ "pile_set_name": "Pile-CC" }

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[ { "analysis_explanation": null, "end": 17053, "entity_type": "URL", "recognition_metadata": { "recognizer_identifier": "UrlRecognizer_140094861343568", "recognizer_name": "UrlRecognizer" }, "score": 0.95, "start": 17014 }, { "analysis_explanation": null, "end": 255, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 245 }, { "analysis_explanation": null, "end": 547, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 537 }, { "analysis_explanation": null, "end": 558, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 550 }, { "analysis_explanation": null, "end": 1111, "entity_type": "DATE_TIME", 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[ "“I was just naive enough to think, ‘Oh, I can do this,’” Mr. Griggs said. “", "I look back on it and think, ‘How did I ever decide I could do something like that?’”", "\n\nHis “Sailor Bob” character became much more than simply a host to introduce the next “Popeye” cartoon. ", "He grew into a beloved, even iconic figure for children within reach of the Channel 12 signal. ", "He was a familiar face for kids from the Shenandoah Valley to Southside Virginia at a time when most localities had only three television stations.", "\n\nThe show debuted Monday morning, Jan. 12, 1959. ", "He got through that show, breathed a sigh of relief — and remembered he had another one to do that afternoon. ", "For much of its run, the show was broadcast twice each weekday and performed live with no scripts. ", "Its homespun humor and amusing spontaneity carried the day, as did Mr. Griggs’ genuine kindness.", "\n\nDressed in a sailor’s cap and denim shirt, Mr. Griggs would sit at his drawing board, his marker hovering over his sketch pad as he contemplated his next stroke. ", "He would draw as music played or while he bantered with a puppet named Gilly Gull that poked its head through a porthole and was brought to life by the voice of Dave Davis, a station announcer. ", "They managed to entertain their audience on different levels, leaving children laughing and parents chuckling." ]

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[ "Q:\n\nIs it okay to have one table for storing images against multiple tables - SQL Server 2008 R2\n\nIs it okay to have one table for storing images against multiple tables? ", "Or it is better to have a three separate tables? ", "Only Office can have two images.", "\nSchema\n\nInspectors - InspectorID (PK), InspectorName\nOffices - OfficeID (PK), OfficeName\nStaff - StaffID(PK), StaffName\n\nNew Photo table (storing images in binary form for different table)\nPhotos - PhotoID (PK), PhotoData, InspectorID(FK), OfficeID(FK), StaffID (FK)\n\nNew schema\n\nInspectors - InspectorID (PK), InspectorName, PhotoID(FK) \n or \n\nInspectors - InspectorID (PK), InspectorName, PhotoID_1(FK), PhotoID_2(FK)\nOffices - OfficeID (PK), OfficeName, PhotoID(FK)\nStaff - StaffID(PK), StaffName, PhotoID(FK)\n\nA:\n\nIt's fine but you don't need FKs in both the Photo table and the other tables. ", " Just put the PhotoID FK in the other three tables. ", " \nIf you only have to worry about a second photo for offices, then adding a second PhotoID FK to the office table is fine. ", " \nIf you want a more scalable solution, and/or if a single photo could be used for more than one of the other entities, then a bridge table might be in order.", "\nOR if one photo can only ever belong to one entity, then you have a one-to-many in the opposite direction, and you can put the FK columns in the Photo table, and leave them out of the other entities tables. ", " You might also add an \"Order\" column to the photo table to specify the order the photos appear for the entity, or whatever else the front end might use that information for.", "\n\n" ]

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[ "Q:\n\nCreate symbolic link fails in Docker for Windows, it's not supported yet?", "\n\nI have a docker container running Ubuntu Server. ", "I am running Docker for Windows and I have the following version of Docker and Docker Compose respectively installed:\n> docker-compose -v\ndocker-compose version 1.11.2, build f963d76f\n\n> docker -v\nDocker version 17.03.1-ce-rc1, build 3476dbf\n\nThis is what I have tried so far without success:\n// The dojo linked file exists so I've tried to update it as per this answer (http://stackoverflow.com/a/1951752/719427)\n> docker exec -it dockeramp_webserver_1 ln -sf /var/www/html/externals/dojo /var/www/html/externals/public_html/js/dojo\nln: failed to create symbolic link '/var/www/html/externals/public_html/js/dojo': No such file or directory\n\n// I have deleted the previous linked file and then I tried to create a new one\n> docker exec -it dockeramp_webserver_1 ln -s /var/www/html/externals/dojo /var/www/html/externals/public_html/js/dojo\nln: failed to create symbolic link '/var/www/html/externals/public_html/js/dojo': No such file or directory\n\n// removed the directory name from the link name\n> docker exec -it dockeramp_webserver_1 ln -s /var/www/html/externals/dojo /var/www/html/externals/public_html/js \nln: failed to create symbolic link '/var/www/html/externals/public_html/js': No such file or directory\n\nBecause the error keep saying the directory doesn't exists then I've checked if the error is right or wrong:\n> docker exec -u www-data -it dockeramp_webserver_1 ls -la /var/www/html/externals/dojo\ntotal 80\ndrwxr-xr-x 2 root root 0 Mar 25 15:09 .", "\ndrwxr-xr-x 2 root root 4096 Mar 25 15:09 ..\ndrwxr-xr-x 2 root root 0 Mar 25 15:09 dijit\ndrwxr-xr-x 2 root root 0 Mar 25 15:09 dojo\ndrwxr-xr-x 2 root root 0 Mar 25 15:09 dojox\ndrwxr-xr-x 2 root root 0 Mar 25 15:09 mmi\n-rwxr-xr-x 1 root root 74047 Mar 25 15:09 tundra.css\n\n> docker exec -u www-data -it dockeramp_webserver_1 ls -la /var/www/html/public_html/js\ntotal 24\ndrwxr-xr-x 2 root root 4096 Mar 26 14:40 .", "\ndrwxr-xr-x 2 root root 4096 Mar 25 15:11 ..\n-rwxr-xr-x 1 root root 7123 Mar 25 15:09 jquery.PrintArea.js\n-rwxr-xr-x 1 root root 6141 Mar 25 15:11 quoteit_delegate_search.js\n\nThey both exists so ... what I am missing here? ", "It's not supported in Windows just yet? ", "I have found the development team added something called mfsymlinks in a previous version than mine.", "\n\nA:\n\nThe command is telling you that /var/www/html/externals/public_html does not exist. ", "You only showed that the /var/www/html/externals/dojo and /var/www/html/public_html/js folders exist. ", "I believe this is a simple typo in your commands.", "\n\n" ]

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"recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1584 }, { "analysis_explanation": null, "end": 1611, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1599 }, { "analysis_explanation": null, "end": 1634, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1623 }, { "analysis_explanation": null, "end": 1679, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1673 }, { "analysis_explanation": null, "end": 1727, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1721 }, { "analysis_explanation": null, "end": 1774, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1768 }, { "analysis_explanation": null, "end": 1822, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1816 }, { "analysis_explanation": null, "end": 1868, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1856 }, { "analysis_explanation": null, "end": 1874, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1869 }, { "analysis_explanation": null, "end": 2018, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2007 }, { "analysis_explanation": null, "end": 2039, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2027 }, { "analysis_explanation": null, "end": 2061, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2050 }, { "analysis_explanation": null, "end": 2105, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2094 }, { "analysis_explanation": null, "end": 2111, "entity_type": "DATE_TIME", 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[ "<html>\n<head>\n <script language=\"javascript\" type=\"text/javascript\" src=\"https://cdnjs.cloudflare.com/ajax/libs/p5.js/0.4.21/p5.js\"></script>\n <script language=\"javascript\" type=\"text/javascript\" src=\"sketch.js\"></script>\n <script language=\"javascript\" type=\"text/javascript\" src=\"car.js\"></script>\n\n</head>\n\n<body>\n</body>\n</html>" ]

{ "pile_set_name": "Github" }

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[ "1983 Ms. Olympia\n\nThe 1982 Ms. Olympia contest was an IFBB professional bodybuilding competition was held on October 22, 1983, in Warminster, Pennsylvania. ", "It was the 4th Ms. Olympia competition held.", "\n\nResults\n\nSee also\n 1983 Mr. Olympia\n\nReferences\n\n 1983 Ms Olympia Results\n\nExternal links\n Competitor History of the Ms. Olympia\n\nMs Olympia, 1983\nMs. Olympia\nCategory:Ms. Olympia\nCategory:History of female bodybuilding\n\nes:Ms. Olympia\nit:Ms. Olympia\nhe:גברת אולימפיה\nnl:Ms. Olympia\npl:Ms. Olympia\npt:Ms. Olympia\nsv:Ms. Olympia" ]

{ "pile_set_name": "Wikipedia (en)" }

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[ "Join us in creating a future for sustainable and high-quality real estate.", "\n\nDo you want to be part of a team with resourceful professionals who shape the Dutch skyline? ", "We at RED Company are young, ambitious, open and adventurous. ", "In our field, we are considered ‘The new kid on the block’. ", "Every day we work on projects filled with quality and innovation. ", "We set the bar high for both our projects ánd our people.", "\n\nWe create, we build,\nwe deliver.", "\n\nSenior Development Manager\n\nJoin us in creating the skyline of the\nfuture with high-quality real estate" ]

{ "pile_set_name": "Pile-CC" }

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[ "00 (base 2) to base 9\n-8088\nWhat is a8a8 (base 11) in base 3?", "\n201202012\nWhat is 212 (base 12) in base 16?", "\n12e\nConvert -1000110 (base 2) to base 9.", "\n-77\nConvert -11012 (base 4) to base 9.", "\n-402\n-3354 (base 9) to base 4\n-212233\n13343 (base 5) to base 8\n2112\nWhat is -11101010011010 (base 2) in base 13?", "\n-6aa0\n2000234 (base 5) to base 15\n942e\n423 (base 11) to base 4\n13331\nWhat is 4792 (base 14) in base 8?", "\n30274\nConvert 56745 (base 11) to base 9.", "\n134537\nWhat is 5670 (base 8) in base 6?", "\n21520\nWhat is -1454 (base 8) in base 6?", "\n-3432\nConvert 229 (base 12) to base 13.", "\n1b9\nWhat is 106 (base 16) in base 5?", "\n2022\nConvert 298 (base 13) to base 2.", "\n111001111\nConvert -a7a4 (base 14) to base 12.", "\n-14910\nWhat is -11000000 (base 2) in base 16?", "\n-c0\n169 (base 12) to base 5\n1400\n1510 (base 10) to base 15\n6aa\nConvert -30010 (base 4) to base 8.", "\n-1404\nConvert -2abb4 (base 12) to base 6.", "\n-1143544\nWhat is 895 (base 12) in base 16?", "\n4f1\n10111011110 (base 2) to base 14\n794\nConvert -7187 (base 13) to base 10.", "\n-15659\nWhat is 1305b (base 13) in base 14?", "\ncba4\n-8a8 (base 12) to base 9\n-1672\nConvert -565 (base 9) to base 12.", "\n-328\nWhat is -134450 (base 6) in base 8?", "\n-30636\nConvert 135 (base 13) to base 10.", "\n213\nWhat is -1110100 (base 3) in base 8?", "\n-2046\nWhat is 1377 (base 8) in base 7?", "\n2144\nWhat is 30231220 (base 4) in base 6?", "\n1041024\nConvert -201210 (base 3) to base 4.", "\n-20112\n121441 (base 6) to base 13\n4b82\na05 (base 13) to base 2\n11010011111\nWhat is -d19 (base 15) in base 6?", "\n-21353\n5862 (base 12) to base 11\n745a\n-1071 (base 8) to base 11\n-478\n10505 (base 11) to base 3\n202220212\nConvert 1500 (base 12) to base 4.", "\n212100\nConvert 4807 (base 9) to base 10.", "\n3571\nWhat is -101112 (base 4) in base 5?", "\n-13420\nb2e3 (base 15) to base 7\n215112\n-114054 (base 6) to base 11\n-7544\nConvert 410102 (base 5) to base 15.", "\n3d6c\nConvert 132103 (base 5) to base 8.", "\n12236\n-13528 (base 11) to base 12\n-b199\nWhat is 5b4 (base 13) in base 9?", "\n1322\nConvert 1111010000100 (base 2) to base 15.", "\n24ac\nWhat is 7919 (base 10) in base 11?", "\n5a4a\nWhat is ca90 (base 13) in base 12?", "\n14377\nConvert -101000110111 (base 2) to base 15.", "\n-b95\nConvert -11111011 (base 2) to base 4.", "\n-3323\n8e (base 16) to base 12\nba\n2112022 (base 3) to base 2\n11100110100\n114424 (base 5) to base 10\n4364\nConvert -16645 (base 13) to base 7.", "\n-235552\nConvert -20e (base 15) to base 6.", "\n-2052\nWhat is 10b87 (base 13) in base 11?", "\n20a36\nWhat is 82b (base 12) in base 14?", "\n60b\nWhat is 23403 (base 7) in base 15?", "\n1bc0\n5092 (base 15) to base 16\n4274\nConvert 4704 (base 8) to base 5.", "\n40000\n14702 (base 8) to base 10\n6594\nConvert 1ba9 (base 15) to base 2.", "\n1011101111001\nWhat is -1212230 (base 4) in base 13?", "\n-2cb7\nWhat is 13643 (base 9) in base 6?", "\n110533\n-165 (base 13) to base 12\n-190\n213202 (base 5) to base 4\n1302012\n383 (base 9) to base 7\n633\nWhat is -36045 (base 10) in base 3?", "\n-1211110000\nWhat is -12304 (base 5) in base 4?", "\n-32322\n-11 (base 12) to base 2\n-1101\nWhat is 56290 (base 10) in base 6?", "\n1112334\nConvert 9dd (base 16) to base 11.", "\n1996\nWhat is 2224 (base 6) in base 7?", "\n1342\nConvert -559 (base 16) to base 15.", "\n-614\nConvert 2360 (base 7) to base 15.", "\n3d5\nConvert 1bb8 (base 14) to base 4.", "\n1033012\nConvert 141014 (base 5) to base 14.", "\n2155\nConvert -155e (base 15) to base 3.", "\n-20021222\n119e (base 15) to base 12\n2205\n2111020 (base 3) to base 13\na98\nWhat is 21020 (base 4) in base 9?", "\n718\nWhat is 44b (base 15) in base 9?", "\n1288\nWhat is -103012 (base 4) in base 14?", "\n-634\nConvert -20303 (base 4) to base 13.", "\n-344\nConvert -904 (base 15) to base 8.", "\n-3755\nConvert -623 (base 8) to base 3.", "\n-112221\nConvert 23a (base 11) to base 8.", "\n435\n24e (base 15) to base 8\n1014\nConvert -17e (base 16) to base 13.", "\n-235\nWhat is 5041 (base 12) in base 4?", "\n2013301\n-775 (base 14) to base 7\n-4205\nWhat is 21302 (base 5) in base 11?", "\n1100\nWhat is -1240 (base 5) in base 4?", "\n-3003\nWhat is 834 (base 11) in base 5?", "\n13010\nWhat is 10211230 (base 4) in base 3?", "\n221210011\n4bc0 (base 15) to base 8\n37433\nWhat is -27422 (base 11) in base 4?", "\n-21203003\nConvert -1103321 (base 4) to base 2.", "\n-1010011111001\nConvert 49506 (base 10) to base 2.", "\n1100000101100010\n1003 (base 10) to base 16\n3eb\nWhat is -222a0 (base 13) in base 10?", "\n-61984\nWhat is 20132 (base 7) in base 2?", "\n1001100001010\nConvert -8d (base 16) to base 8.", "\n-215\nConvert 4095 (base 13) to base 15.", "\n2990\n-61478 (base 9) to base 14\n-10a82\n1032123 (base 4) to base 6\n35123\nWhat is -a20 (base 15) in base 5?", "\n-33110\nConvert -b912 (base 15) to base 9.", "\n-58648\nWhat is 8c (base 13) in base 5?", "\n431\n-54433 (base 6) to base 13\n-3558\nConvert d6 (base 16) to base 10.", "\n214\n2312 (base 4) to base 10\n182\n-3312 (base 4) to base 6\n-1050\nConvert -950 (base 12) to base 15.", "\n-606\nConvert 2012 (base 5) to base 7.", "\n515\nd293 (base 15) to base 16\nadaf\nWhat is -13040 (base 15) in base 7?", "\n-342201\nConvert 2a0 (base 12) to base 8.", "\n630\nConvert 72aa (base 13) to base 8.", "\n36761\nConvert -27752 (base 10) to base 12.", "\n-14088\nWhat is 11044 (base 7) in base 4?", "\n223120\nWhat is 2020011 (base 4) in base 10?", "\n8709\nWhat is -100212020 (base 3) in base 11?", "\n-5445\nWhat is 2111212 (base 3) in base 2?", "\n11100101000\n101000001 (base 2) to base 8\n501\n-1a583 (base 11) to base 16\n-6fe7\nWhat is -1717 (base 12) in base 6?", "\n-20431\nConvert -10452 (base 6) to base 9.", "\n-2015\n-1202122011 (base 3) to base 13\n-12a63\nConvert -4671 (base 8) to base 15.", "\n-b0e\n570 (base 15) to base 13\n738\n-301332 (base 6) to base 8\n-56170\n-13758 (base 10) to base 3\n-200212120\nConvert -7a3 (base 16) to base 14.", "\n-9d9\nConvert 20072 (base 10) to base 13.", "\n91a0\n2423 (base 8) to base 9\n1703\n117ba (base 12) to base 3\n1012101121\n-1a6 (base 11) to base 9\n-283\n-11111000111001 (base 2) to base 9\n-23758\n-23 (base 7) to base 8\n-21\n-17606 (base 9) to base 12\n-7050\n-1616 (base 8) to base 4\n-32032\nWhat is -111404 (base 6) in base 13?", "\n-43ab\nConvert 1502 (base 6) to base 12.", "\n292\nWhat is -13307 (base 10) in base 16?", "\n-33fb\n-424 (base 9) to base 5\n-2341\nWhat is 1d59 (base 15) in base 2?", "\n1100011110000\nWhat is 4610 (base 12) in base 4?", "\n1321230\n-55c (base 15) to base 12\n-850\nWhat is -312013 (base 4) in base 2?", "\n-110110000111\n-269 (base 13) to base 6\n-1545\nConvert -1598 (base 13) to base 8.", "\n-6137\nConvert 56622 (base 8) to base 7.", "\n126560\nConvert 57 (base 11) to base 5.", "\n222\nWhat is 1535 (base 13) in base 8?", "\n6016\n-11913 (base 11) to base 3\n-212102102\nWhat is 8418 (base 16) in base 15?", "\na046\nWhat is 51534 (base 6) in base 16?", "\n1af2\nConvert -10b7b (base 12) to base 15.", "\n-6995\nWhat is -1010330 (base 4) in base 11?", "\n-3351\nConvert -3404 (base 11) to base 12.", "\n-2715\nWhat is -1217a (base 11) in base 7?", "\n-102024\nWhat is 5671 (base 9) in base 16?", "\n1063\nWhat is -10212 (base 4) in base 7?", "\n-600\nWhat is -42235 (base 10) in base 5?", "\n-2322420\nWhat is 346 (base 10) in base 7?", "\n1003\nWhat is 2221002 (base 3) in base 7?", "\n6140\nWhat is 1172 (base 9) in base 5?", "\n12000\n1663 (base 7) to base 2\n1010101010\nConvert a0 (base 15) to base 2.", "\n10010110\n4113 (base 11) to base 4\n1111103\nConvert 123001 (base 7) to base 14.", "\n8371\n17999 (base 11) to base 15\n76c0\nConvert -12020 (base 3) to base 4.", "\n-2031\n-7538 (base 9) to base 16\n-15a7\nWhat is 1449 (base 11) in base 12?", "\n10b8\nWhat is -211 (base 7) in base 5?", "\n-411\nWhat is 36304 (base 9) in base 13?", "\nb0a7\nWhat is 213 (base 10) in base 7?", "\n423\nWhat is 3495 (base 10) in base 6?", "\n24103\nWhat is -3a28 (base 11) in base 2?", "\n-1010001110001\nConvert -6bb (base 13) to base 11.", "\n-972\n1457 (base 8) to base 9\n1105\nWhat is 2006 (base 12) in base 3?", "\n11202020\n1b92 (base 16) to base 3\n100200102\nWhat is 5c4 (base 13) in base 14?", "\n51b\n4b0a (base 12) to base 14\n3158\nWhat is -1cb (base 14) in base 7?", "\n-1044\nConvert -57103 (base 9) to base 3.", "\n-1221010010\nWhat is -cd4 (base 15) in base 3?", "\n-10222101\nConvert 30101102 (base 4) to base 12.", "\n25102\nWhat is -30445 (base 6) in base 8?", "\n-7735\n-7403 (base 9) to base 8\n-12466\nConvert -11211 (base 3) to base 10.", "\n-130\nConvert -1556 (base 15) to base 11.", "\n-3495\nConvert -3ca3 (base 15) to base 10.", "\n-12978\nWhat is -1100432 (base 5) in base 11?", "\n-131a2\n-1143 (base 6) to base 5\n-2104\n10765 (base 12) to base 9\n32835\nConvert 1201a (base 12) to base 3.", "\n1020012211\nConvert -11332 (base 6) to base 7.", "\n-4532\n10100111100010 (base 2) to base 7\n43155\nConvert 44371 (base 8) to base 7.", "\n105315\n-22131301 (base 4) to base 7\n-235654\nConvert 1410 (base 7) to base 10.", "\n546\nConvert -235a (base 11) to base 14.", "\n-11aa\n166 (base 14) to base 15\n14" ]

{ "pile_set_name": "DM Mathematics" }

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[ "Q:\n\nR Error in hist.default(Sepal.", "Length ~ Species, data = iris) : 'x' must be numeric\n\nI am trying to plot 2 histograms of a numeric variable by a factor variable in my df.", "\nI searched hist() to do this but why am I getting this error?", "\ndata(iris)\nhist(Sepal.", "Length~Species,data=iris)\nError in hist.default(Sepal.", "Length ~ Species, data = iris) : \n 'x' must be numeric\n\nUPDATE: I am able to get this to work:\nhistogram(~Sepal.", "Length|Species,data=iris,\n type=\"count\",\n xlab=\"Sepal Length\",\n main=\"Iris Dataset\",\n layout=c(1,3))\n\nIt seems there might be a difference between histogram functions?", "\nhttps://www.rforge.net/doc/packages/FSA/hist.formula.html\nand\nhttp://127.0.0.1:27473/library/lattice/html/histogram.html\n\nA:\n\nuse \nlibrary(FSA)\nhist(Sepal.", "Length~Species,data=iris)\n\nIt works\n\n" ]

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[ "Grupo Multimedios\n\nGrupo Multimedios is a Mexican media conglomerate with holdings in broadcast television, radio, publishing and entertainment. ", "The company is headquartered in Monterrey.", "\n\nHistory\n\nMultimedios was founded in 1940 when Jesús Dionisio González acquired Monterrey radio station XEX, where he had formerly worked, for 12,500 pesos. ", "After World War II, the Mexican government requested the XEX callsign to build a national clear-channel station, and González selected the XEAW call letters, which had formerly belonged to a station in Reynosa, Tamaulipas. ", "In the 1950s, the group became known as Organización Estrellas de Oro (\"Gold Stars Organization\"), which in the 1990s changed its name to Multimedios Estrellas de Oro and later Grupo Multimedios.", "\n\nMultimedios entered the television business in 1968 when it launched XHAW-TV channel 12 in Monterrey. ", "Further expansion would come in the 1980s and 1990s when the federal government made available dozens of new radio and TV stations, leading to Multimedios establishing a broadcast presence in cities including Tijuana, Chihuahua, and Tampico.", "\n\nMedia holdings\n\nRadio\n\nMultimedios owns 37 radio stations and operates another five. ", "The station portfolio is primarily concentrated in northeastern Mexico, including 14 stations in Monterrey; through a combination of acquisitions, operating agreements and stations won in the IFT-4 auction of 2017, Multimedios has increased its presence in the state of Veracruz and in western and central Mexico. ", "In addition, Multimedios owns three radio stations in Costa Rica, which it acquired in 2018 in its purchase of Grupo Latino de Radiodifusión from PRISA and Grupo Nación, and Top Radio 97.2 in Madrid.", "\n\nBroadcast television\n\nMultimedios entered the television business in 1968 when it launched XHAW-TV channel 12 in Monterrey. ", "In the 1980s and 1990s, the television network expanded to a regional footprint centered on the states of Coahuila, Nuevo León and Tamaulipas. ", "In the IFT-6 station auction of 2017, Multimedios obtained six additional concessions for television stations in Mexico City, Guadalajara, Puebla, Ciudad Juárez, Durango and Monclova, representing a major expansion into central Mexico.", "\n\nOn July 29, 2017, Multimedios launched a separate television channel in Costa Rica, on channel 44, through a licensing agreement with the Fundación Internacional de las Américas.", "\n\nAdditionally, Multimedios owns cable news channel Milenio Televisión, which shares resources with its Milenio newspaper.", "\n\nPrint\n\nJesús Dionisio González started the Diario de Monterrey newspaper in 1974. ", "On January 1, 2000, the newspaper began publishing in Mexico City and became a national daily, renamed Milenio (Millennium). ", "The company also publishes several magazines.", "\n\nOut-of-home advertising\n\nGrupo Pol is an out-of-home advertising company with a presence in Mexico and other Central American countries.", "\n\nSports\n\nMultimedios entered the sports ownership realm with its acquisition of 50 percent of the Sultanes de Monterrey baseball team in February 2017, with the other half held by Mexican baseball legend José Maiz García. ", "The company grew further in sports in 2018 by buying the Fuerza Regia of the Liga Nacional de Baloncesto Profesional as well as four LNBP expansion franchises and by becoming a majority shareholder of the Bravos de León baseball team, a move that allowed the club to play in 2019.", "\n\nOther holdings\n\nOther Multimedios holdings include real estate company Altea Desarrollos; three Spanish wineries, Lleiroso, Bodega de Sarría and Inversiones Vitivinícolas, with a combined output of 7.5 million bottles of wine a year; the Bosque Mágico (Magic Forest) amusement park in Monterrey;\n\nIn 2015, Comercializadora Jubileo, a Multimedios subsidiary previously dedicated to the creation of toys for amusement parks, obtained a contract with the state government worth 538 million pesos to build a water treatment plant. ", "A new state government rescinded the contract in 2016. ", "The Nuevo León Attorney General's Office later claimed that Jubileo had been awarded the contract despite its lack of prior experience in water treatment and failure to meet bid requirements.", "\n\nFormer holdings\n\nCable television\nMultimedios previously owned 50 percent of Televisión Internacional, S.A. de C.V., which traded as Cablevisión Monterrey. ", "Cablevisión provided cable and internet service to the Monterrey metropolitan area. ", "In 2016, Multimedios sold its stake to the other 50-percent owner, Televisa, and Cablevisión Monterrey was subsumed into Izzi Telecom.", "\n\nMovie theaters\nThe MMCinemas chain of movie theaters was sold in 2008 to Grupo México, which rebranded all of its units as Cinemex.", "\n\nReferences\n\nExternal links \n \n\nCategory:Television broadcasting companies of Mexico" ]

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[ "Neuropsychological impairment and behavioral limitations exhibited within an alcohol treatment program.", "\nThe present study investigated the generalizability of neuropsychological test data to behavioral problems/limitations exhibited by alcoholics within an inpatient treatment program. ", "Ratings supplied by alcohol counselors of problematic behaviors were used to form two groups (N = 40) representing behaviorally impaired (B1) and behaviorally unimpaired (BU) alcoholics. ", "The neuropsychological performance of BI subjects was found to be impaired, relative to BU subjects, on composite measures of motor skill, problem solving, psychomotor speed, and memory. ", "BI subjects, relative to the BU group, were also found to have significantly longer histories of alcoholism, more frequent neurological examination abnormalities, and higher incidences of suboptimal nutrition. ", "Taken as a whole, these data suggest that neuropsychological measures may have some potential for assisting in the generating of valid inferences regarding both underlying cerebral pathology and the behavioral consequences of such as expressed within the alcohol treatment milieu." ]

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[ "Sharad Pawar will appear before the Enforcement Directorate in Mumbai today\n\nHighlights \"Sharad Pawar targeted by vindictive government,\" says Rahul Gandhi\n\n\"Timing of action reeks of political opportunism,\" he said\n\nMr Pawar will appear before Enforcement Directorate today\n\nCongress MP Rahul Gandhi said today that a corruption case naming NCP chief Sharad Pawar just before the Maharashtra election smacked of \"political opportunism\" by a \"vindictive government\".", "\n\nSharad Pawar, whose Nationalist Congress Party (NCP) will contest the October 21 Maharashtra election in alliance with the Congress, has been named by the Enforcement Directorate in a money-laundering case along with his nephew Ajit Pawar.", "\n\n\"Sharad Pawar Ji is the latest Opposition leader to be targeted by a vindictive Government. ", "The timing of this action, a month before elections in Maharashtra, reeks of political opportunism,\" Mr Gandhi tweeted.", "\n\nSharad Pawar Ji is the latest Opposition leader to be targeted by a vindictive Government. ", "The timing of this action, a month before elections in Maharashtra, reeks of political opportunism. ", "https://t.co/XCW0GsdXjj — Rahul Gandhi (@RahulGandhi) September 27, 2019\n\nMr Pawar will appear before the Enforcement Directorate today though he has not been summoned in connection with the case involving loans illegally sanctioned by the Maharashtra State Cooperative Bank. ", "The senior opposition leader said he would appear before the probe agency before he gets busy with the state election.", "\n\nThe Mumbai Police has banned large gatherings near Ballard Estate in south Mumbai, where the Enforcement Directorate's office is located, and also at NCP offices in the city.", "\n\nRahul Gandhi said the \"timing of the action\" against Sharad Pawar \"reeks of political opportunism\"\n\nNCP workers staged protests in Mumbai when Mr Pawar was named in the case.", "\n\nMr Pawar is not listed as an accused in the First Information Report on the alleged Rs 25,000-crore scam, though the complainant calls him a \"kingpin\". ", "While a large number of NCP leaders are allegedly involved in the running of the bank, Mr Pawar was not one of them.", "\n\nThe case involves alleged violation of banking laws and Reserve Bank of India (RBI) guidelines while disbursing loans to the state's sugar factories and spinning mills. ", "Many of those who sanctioned the loans were allegedly linked to the owners of the mill owners.", "\n\nAfter an order from the Delhi High Court, a case was filed last month by the Maharashtra Police. ", "Later, the Enforcement Directorate started an investigation into possible money-laundering.", "\n\nThe Congress and the NCP have questioned the timing of the case as campaigning peaks for the Maharashtra polls, in which they are pitted against the ruling BJP and the Shiv Sena.", "\n\nThe Congress has also accused the government of targeting its leaders with a political agenda, among them former Union Minister P Chidambaram and Karnataka MLA DK Shivakumar, both in Delhi's Tihar jail in connection with corruption cases." ]

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[ "Stratification and segregation features of pulverized electronic waste in flowing film concentration.", "\nGravity separation of metals from plastics in pulverized e-waste using flowing film concentration in a shaking table was investigated. ", "Over 51% rejection of plastics in a single stage operation was achieved under optimum conditions. ", "The shaking table was shown to be suitable for processing ground PCBs. ", "Pulverized e-waste containing 22% metals was enriched to around 40% metals in a single pass. ", "Statistical models for the mass yield of metal-rich stream and its grade were developed by design of experiments. ", "Optimization was carried out to maximize the mass yield at a target product grade and preferred operating regimes were established. ", "Experiments were designed to prevent metal loss and over 95% recovery values were obtained under all conditions. ", "Settling distances of metals and plastics were computed and shown to be good indicators of separation performance. ", "Particle morphology and stratification in the troughs in between the riffles were shown to influence the separation significantly. ", "Water flow-assisted motion of the plastics was captured and its role in determining the effectiveness of separation was described. ", "The efficacy of tabling was well established for treating ground PCBs. ", "The wet process was shown to be environment friendly and sustainable. ", "It is also relatively cheap and has good potential for industrial application. ", "However, rigorous cost estimates will be required before commercial application." ]

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[ "There is an official Pandora app for Windows Phone, but before that came out, we relied on third party applications like MetroRadio. ", "Metro Pandora, the SDK that third party applications have relied on has just been pulled due to infringement notice from Pandora. ", "The complaint will go undisputed.", "\n\nPandora’s DMCA Notice mentions the unauthorized use of their registered trademarks and API. ", "We can’t blame Pandora for protecting their property." ]

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[ "Q:\n\nRemove Duplicates using vba\n\nI want to delete duplicate entries from each column, I am successful in doing it for one column C but I want to do it from A to Column Z. I have tried to change myCol to variable long & wrote column number but it is giving me an error (so that I can run number loop). ", "Here is my code: \nSub test()\nDim myCol As String\n\nmyCol = \"C\"\n\nWith Sheets(\"Union\")\n lastrow = .Range(myCol & .Rows.", "Count).End(xlUp).Row\n .Range(myCol & \"1:\" & myCol & lastrow).RemoveDuplicates Columns:=1, Header:=xlYes\nEnd With\n\nEnd Sub\n\nA:\n\nYou could try creating a For loop accounting for A-Z as integers. ", "I am not sure that this is the most efficient solution, but it could work for you. ", "See below.", "\nOption Explicit\n\nSub test()\n\n Dim myCol As Long\n Dim lastrow As Long\n\n For myCol = 1 To 26\n With Sheets(\"Union\")\n lastrow = .Cells(.Rows.", "Count, myCol).End(xlUp).Row\n\n If lastrow >= 3 Then\n .Range(.Cells(1, myCol), .Cells(lastrow, myCol)).RemoveDuplicates Columns:=1, Header:=xlYes\n End If\n End With\n Next myCol\n\nEnd Sub\n\nEDIT: Tested, and working as required. ", "\nSECOND EDIT: Added in a lastrow check to ensure there is some data in the column before trying to remove duplicates. ", "3 because that would mean at least 2 entries in that column, the minimum for there to be a need to check for duplicates. ", "\n\n" ]

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[ "شركة تنظيف منازل بالدمام\n\nشركة تنظيف منازل بالدمام : عمليه التنظيف لابد ان تكون تحت ايد خبره في مجال التنظيف لان عمليه التنظيف من الامور الصعبه التي تواجه كل ربه منزل لا لذلك لابد من التعامل مع شركة تنظيف بالدمام للحصول علي اعلي جوده في مجال التنظيف فلا داعي للقلق بعد الان فاشركة تنظيف بالدمام سوف تتحمل عنك كل المشاكل التي تواجهك من انتشار حشرات بسبب الاتربه والاوساخ وايضا في التخلص من اصعب البعق التي تواجهك\n\nوفي بعض الاوقات تكون عمليه التنظيف متعبه ومرهقه جدا خاصه اذا كانت مساحه منزلك كبيره وواسعه فقد تحتاج منك عمليه التنظيف وقت طويل هناك من يقوم بعمليه التنظيف بنفسه وهناك من يكون بعمليه التنظيف بالاستعانه باحد الافراد ولكن الحل الامثل هو اللجحواء الي شركه متخصصه وهي شركة تنظيف بالدمام فاشركتنا تتولي عنك كل شئ من تنظيف الي تطهير الي تعقيم وتعطير في الفلل اوالمنزل يوجد كثير من الاثاث الذي يجب علكي تنظيفه بشكل مستمر حتي تقوم بالتخلص من الاتربه والاوساخ العالقه بيه وللحفاظ عليه من تغير الاوان او من تهتك\n\nتقوم شركتنا بتنظيف جميع انواع السجاجيد والموكيت باحداث الاساليب العالميه والنظفات الخاصه بكل نوع من السجاد او الموكيت حتي تظل الالوان ساطعه دون تغيرفي الالوان وايضا الحفاظ علي شكل الموكيت الو السجاد من اي تلف قد يظهؤر من بعض المنظفات التي تكون غاليه الثمن وتعمل علي تلف الانسجه شركتنا تتخصص في العنايه من الانسجه وجعلها خاليه من الاتربه والاوساخ ولان اكثر الاشيا البتي تحتاج الي عنايه فائقه هي الاثاث لانها تعمل علي فا الاثاث بجميع انواعها يحتاج الي عنايه خاصه ونوع معين من النظفات حتي تقةوم بالحفاظ عليه وجعلها دائما يلمع\n\nشركة تنظيف مجالس وكنب بالدمام\n\nالمجالس والكنب من الاشياء التني تظهر جمال منزلك وتقوم بازهار الشكل الاساسي للمنزل لذلك عليك الحفاظ عليها واستعمال مواد مخصصه للحفاظ عليها لذلك تقدم الشركه افضل انواع المنظفات العالميه التي تناسب جميع انواع المجالس والكنب وتعمل علي الحفاظ علي الالوان والانسجه وتقوم بحمايتها من التلف كما ان الشركة تقوم باستخدام مواد ذات فعاليه سريعه في ازاله اصعب انواع البقع التي سوف تواجهك ولا تعمل علي تغير الالوان بلا تعمل علي ثبات الالوان الي اعلي جوده ممكنه كما ان الشركة تقوم بتنظيف المجالس والكنب المصنوعه من الجلد بافضل انواع الزيوت الطبيعيه التي تعمل علي التنظيف والتلمع والتعطير وتجعلها تلمع وكانها جديده\n\nوتقوم بازاله اثار الاحتكاك التي تنتج من الاحتاك الاجسام بها واثار العرق الناتج من الاجسام والذي قد يتسبب في تغير الالوان\n\nشركة تنظيف ارضيات بالدمام\n\nتقوم الشركة بخدمه تنظيف الحوائط والارضيات باعلي جوده فان الشركة تقوم باستخدام معدات عاليه الجوده في تنظيف الارضيات والحوائط باعلي جوده كما ان الشركة تقوم بتنظيف جميع انواع الارضيات مثل البركيه والرخام والجرانيت والبلاط والسراميك كا ان الشركة لديها مواد تقوم بازاله الاثار الجريه التي تنتج من الارضيات كما انها تستخدم مواد تعمل علي الحفاظ علي الارضيا والحفاظ علي الالوان وتقوم بالحفاظ علي الطبقه الخارجيه الامعها وتعمل علي الحفاظ عليها من التلف حتي لا تتغير الالوان ويصبح الالوان الخاصه بالرضيات ليس لها بريق ولان الارضيات من الاشياء التي تظهر ايضا جمال منزلك لذلك يجب عليك استخدام مواد موثوق بها ويجب منك التواصل مع شركه تنظيف بالدمام للحصول علي اعلي جوده في التنظيف وبدقه عاليه ويجب منك التاكد ان هذه المواد التي تستخدمها انت ليس لها ضرر عليك وعلي صحه اسرتك\n\nلماذا عليك التعامل مع شركة تنظيف بالدمام\n\nتقوم شركتنا باستخدام افضل مواد التنظيف التي ليس لهالا ضرر عليك ولا علي صحه اسرتك كما ان هذه المواد حاصله علي موافقه من وزاره الصحه\n\nكما ان الشركة لديها فريق عمل متميز ومدرب علي ايد خبره في مجال التنظيف\n\nتقدم الشركة افضل الاسعار ووافضل العروض والخدمات حتي تنال راحتك واعجابك بنا\n\nلا يوجد لدي شركتنا منافس فاشركتنا رائده في مجال التنظيف\n\nلا تتطلب منك الخدمه مغادره المنزل\n\nتسعي شركتنا الي اصلاح التلف ومحاوله ارجاع كل شئ وكانها جديد\n\nالشركة تسعي دائما ان تكون الاولي في مجال التنظيف" ]

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[ "New money for chip equipment makers?", "\n\nMattAndrejczak\n\nSAN FRANCISCO (MarketWatch) -- When Lam Research Corp. CEO Steve Newberry heads to New York or Boston to talk with prospective investors, he's noticed that value-oriented fund managers are now showing up to size up the chip equipment industry.", "\n\nThat didn't happen before.", "\n\n\"The industry has changed,\" remarks Newberry, alluding to a much shorter timeframe to fill orders, fewer buyers of semiconductor manufacturing machines and less-rambunctious spending sprees by chipmakers.", "\n\nInvestors have already been jumping into the sector, pushing the shares of companies such as Applied Materials and KLA-Tencor up more than 45% over the last 12 months.", "\n\nLam has surged even more, having watched its share price nearly double in that time to reach record-high territory over the last couple of weeks.", "\n\nA common mantra today is \"muted cycles.\" ", "That is, when execs speak about order flows, they expect less of a high in good times and less of a low in bad times. ", "In other words, the industry is riding a new rollercoaster, one whose tracks are shorter and not so steep.", "\n\nSo, should investors modify their strategy?", "\n\nTraditionally, chip-equipment stocks have marched to the drumbeat of order-book flows and capital spending plans by electronics makers, with investors scouring the market for any datapoints about the next possible upturn or downturn in technology spending.", "\n\nIt's typically worked this way: Information suggesting equipment orders would rise was a sign to pump money into the whole sector, regardless of individual company fundamentals. ", "Conversely, data suggesting orders would slow was a sign to bail.", "\n\n\"Ten years ago, these companies made great money during the booms, but when we went into downcycles, these companies lost a ton of money,\" said Patrick Ho, analyst at Stifel Nicolaus. \"", "If you look at these companies today, many have changed their business models.\"", "\n\nIn investment circles, Lam Research Corp.\nLRCX, -3.08%\nand Varian Semiconductor\nVSEA\nare often cited as two prime examples. ", "Also mentioned, but to a lesser extent, is sector leader Applied Materials Inc.\nAMAT, -1.62%\nand KLA-Tencor Corp.\nKLAC, -2.32%\n\nThese companies are now more prepared to absorb the shock that comes when tech spending skids off the tracks, analysts note.", "\n\nChip equipment makers have accomplished this by either outsourcing manufacturing to chop expenses, using new tools to win share in existing markets or restructuring service warranty tool contracts to make more money. ", "And in some cases, they have chosen to enter new markets outside the semiconductor space, such as solar energy.", "\n\nLooking for market share\n\nWhen doing his research, Summers isn't entirely focused on the potential direction of the equipment spending curve. ", "He's trying to identify chip-equipment suppliers who stand to benefit from outsourcing, an emerging trend taking hold in the industry.", "\n\nIn Brooks' case, the company makes the robotic-like arms that move chip wafers around the inside of semiconductor machine and holds vast intellectual property for those designs.", "\n\nApplied and Tokyo Electron Ltd., the world's two largest chip-gear providers, also make robotic arms but Applied has shifted some that business to Brooks. ", "Tokyo Electron plans to take the same approach but hasn't announced who will be the beneficiary, Summers said.", "\n\nHis thinking is Brooks, whose stock has gained 18% so far this year.", "\n\nIn regards to Ultra Clean, which assembles and tests equipment, chip machine makers want more of their equipment installed in Asia, where most of their customers are. ", "This helps cut costs and deliver equipment faster.", "\n\nUltra Clean, based in Menlo Park, Calif., wants to take advantage of that trend with a facility it opened in Shanghai, China in late 2004, Summers said. ", "Its stock is up 14% this year.", "\n\nBenefits of outsourcing\n\nThe outsourcing movement circles back to Lam, the world's No. ", "5 chip-equipment maker based in Fremont, Calif. whose stock has surged 150% the past year years.", "\n\nIt uses Ultra Clean to assemble its equipment as part of a broader outsourcing model that uses outside firms to perform human resource functions, information technology, and facilities management.", "\n\nLam is considered an industry pioneer in this respect. ", "The goal is being able to stay profitable through spending slumps and to be even more profitable during spending booms.", "\n\nIndustrywide, \"this is not a trend that will go on for a few quarters and die out. ", "This is a trend that will take years to play out,\" Summers added.", "\n\nLam's moves have made it an investor favorite. ", "Its shares have soared 140% since August 2004. ", "By comparison, rivals Applied and KLA-Tencor have gained around 40%.", "\n\nThe inevitable cycles\n\nWhen it comes to investing in chip equipment stocks, there is no avoiding the cycles. ", "The cycles will never vanish. ", "Equipment providers cannot fill orders overnight. ", "But investors are looking beyond the cycles and the psychology is evolving, said Stifel's Ho.", "\n\nHe now fields calls from clients asking who the best companies will be three years from now.", "\n\n\"I didn't used to hear that question. ", "That's clearly a different mindset than five years ago,\" Ho said.", "\n\nIntraday Data provided by SIX Financial Information and subject to terms of use.", "\nHistorical and current end-of-day data provided by SIX Financial Information. ", "Intraday data\ndelayed per exchange requirements. ", "S&P/Dow Jones Indices (SM) from Dow Jones & Company, Inc.\nAll quotes are in local exchange time. ", "Real time last sale data provided by NASDAQ. ", "More\ninformation on NASDAQ traded symbols and their current financial status. ", "Intraday\ndata delayed 15 minutes for Nasdaq, and 20 minutes for other exchanges. ", "S&P/Dow Jones Indices (SM)\nfrom Dow Jones & Company, Inc. SEHK intraday data is provided by SIX Financial Information and is\nat least 60-minutes delayed. ", "All quotes are in local exchange time." ]

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[ "Q:\n\nListView checkbox issue after check\n\nMy issue is that when I check Checkbox it turns to checked but it duplicates checked state for next ListView item which isn't on the visible list (e.g. when I can see item on positions 0-5/6 on one screen it is for element on position 7-8)...\nThis is my onClick method:\nviewHolder.messageSelectBox.setOnClickListener(new View.", "OnClickListener() {\n @Override\n public void onClick(View v) {\n if (viewHolder.messageSelectBox.isChecked()) {\n Log.i(\"itemID\", String.valueOf(getItemId(position)));\n Log.i(\"position\", String.valueOf(position));\n mListOfItemsToDelete.add(position);\n Collections.sort(mListOfItemsToDelete);\n Collections.reverse(mListOfItemsToDelete);\n } else {\n for (int i = 0; i < mListOfItemsToDelete.size(); i++) {\n int pos = mListOfItemsToDelete.get(i);\n if (pos == position) {\n mListOfItemsToDelete.remove(i);\n }\n }\n }\n }\n });\n\nsetOnClickListener is in getView() in ListView Adapter...\ngetView() method:\nfinal ViewHolder viewHolder;\n\n if (convertView == null) {\n LayoutInflater inflater = (LayoutInflater) context\n .getSystemService(Context.", "LAYOUT_INFLATER_SERVICE);\n\n convertView = inflater.inflate(R.layout.messages_list_view_single, parent, false);\n }\n\n viewHolder = new ViewHolder(convertView);\n\n viewHolder.messageSelectBox = (CheckBox) convertView.findViewById(R.id.messageSelectBox);\n\nSo guys, have you got any idea what is wrong?", "\n\nA:\n\nIn getView() you have to load the checked state as following before setOnClickListener.", "\nviewHolder.messageSelectBox.setChecked(mListOfItemsToDelete.contains(position))\n\nso the checked state will be maintained in mListOfItemsToDelete and using that state you will be loaded the checked state for the checkbox.", "\n\n" ]

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[ "No. ", "13-1084 – Constellium Rolled Products Ravenswood, LLC and Melvin Lager v.\nSharon Griffith and Lou Ann Wall\n FILED\n June 10, 2015\n RORY L. PERRY II, CLERK\n\n SUPREME COURT OF APPEALS\n\n OF WEST VIRGINIA\n\nKetchum, Justice, concurring in part and dissenting in part:\n\n There was no viable cause of action for either compensatory damages or\n\npunitive damages. ", "In order for a plaintiff to prevail on a claim for gender discrimination\n\nor sexual harassment it must be proven that the alleged wrongful conduct was based on the\n\nplaintiff’s sex. ", "Hanlon v. Chambers, 195 W.Va. ", "99, 464 S.E.2d 741 (1995). ", "In this case,\n\nthe defendant’s alleged wrongful conduct was directed both at men and women.", "\n\n *7 All employees were encouraged to place comments in a suggestion box.", "\n\nThe plant manager would attach his response to every comment. ", "The comments and\n\nresponses were posted on a plant bulletin board. ", "When the comments and responses about\n\nthe plaintiffs were posted, there were also posted approximately thirty nine other\n\ncomments and responses.1 There were postings that had derogatory comments about both\n\nmale and female employees, including a foreman.", "\n\n While it was ill advised to post derogatory comments about any employee,\n\nthese comments were not directed at only the female plaintiffs or female employees. ", "They\n\nwere equal opportunity postings directed at both men and women. ", "Additionally, the\n\ncomments about the plaintiffs were directed at their perceived work ethics.", "\n\n\n\n\n 1At the initial oral argument, it was not disputed that forty two comments and responses were posted at the\nsame time. ", "Three of those comments were about the plaintiffs.", "\n\f There is no cause of action under our sex discrimination laws. ", "Our\n\nanti-discrimination laws are not codes of civility. ", "Our laws are aimed at discrimination\n\ndirected at a protected class, not comments directed at anyone in the work place.", "\n\n Therefore, I dissent.", "\n\n I concur in the striking of the punitive damages only because there can be no\n\npunitive damages when there is no evidence supporting compensatory damages. ", "The\n\nevidence in this case did not support a viable cause of action for compensatory damages,\n\nmuch less, punitive damages to punish the defendant. ", "I do not accept the majority\n\nopinion’s legal reasoning in striking the punitive damages, but agree there can be no\n\npunitive damages awarded.", "\n\f" ]

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[ "[Immune system characteristics in acute pneumonia].", "\nIn 76 patients with acute pneumonia the absolute and relative numbers of T- and B-lymphocytes and their functional activity were determined on the basis of the data on the immunoglobulin level and lymphocyte blast-transformation with phytohemagglutinine. ", "The character of the immune response of the patients was found to depend on the activity of the inflammatory process, its spread and the features of the clinical course of the disease. ", "The most pronounced changes in the immune system of the patients (a sharp decrease in the number and function of T- and B-lymphocytes) were observed in croupous pneumonia and in the prolonged course of local pneumonia, as well as in cases of considerable lesion of the pulmonary tissue (3-6 and more segments)." ]

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[ "Cooking Class from The Nourished Kitchen Cookbook & Wine\n\nCome learn how easy healthy cooking can be from our esteemed farm chef, Melon Corsini, as she cooks and gives you tips you can use at home in your own kitchen. ", "You’ll get to sample from the great dish Melon cooks and see how she incorporates ingredients from our farm every week for our farm menu. ", "Bring a friend and relax with a glass of wine (1 glass included)! ", "Bottles of wine are available for purchase in the farm store. ", "Must be 21 and older to consume alcohol. ", "Space is limited, reservations suggested. ", "Space is limited, reservations required. *", "book is available for purchase" ]

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[ "Q:\n\nHow to put the ArrayList into bundle\n\nI have put some value into arraylist like this : \n private List<InfoProduct> product;\n\n product = new ArrayList<>();\n product.add(new InfoProduct(R.drawable.cloth, Product_title, \"0\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.guitar, Product_title, \"1\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.cloth, Product_title, \"2\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.guitar, Product_title, \"3\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.cloth, Product_title, \"4\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.guitar, Product_title, \"5\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.cloth, Product_title, \"6\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.guitar, Product_title, \"7\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.cloth, Product_title, \"8\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n product.add(new InfoProduct(R.drawable.guitar, Product_title, \"9\", Product_data2, lunch,R.drawable.cardview_circle_corner));\n\nwhen I need to go other Fragment , I want to use Bundle to transfer my ArrayList , so I write some code to comply this \n FragmentTransaction ft = getSupportFragmentManager().beginTransaction();\n ft.replace(R.id.fragment_youtube, new FragmentYoutubeProduct(), \"youtube\");\n ft.addToBackStack(\"youtube\");\n Bundle bundle = new Bundle();\n bundle.putStringArrayList(\"Product\",product);\n ft.commit();\n\nI got error on bundle.putStringArrayList(\"Product\",product); , how can I do to resolve this question ?", "\n\nA:\n\nFirst make InfoProduct Parceble\nCheck this- Link \nThen use `\nbundle.putParcelableArrayList(product)\n\nYou can get arraylist by `\ngetParcelableArrayList(..)\n\nAlso check this\n\n" ]

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[ "The University of Kansas Sexuality and Gender Diversity Faculty Staff Council has expressed \"extreme frustration\" with the university's decision to \"deepen its relationship\" with the popular fast-food chain Chick-fil-A.\n\n\"We, members of the Sexuality & Gender Diversity Faculty and Staff Council, write to express our extreme frustration at the University’s moves over the summer to deepen its relationship with Chick-fil-A,\" the group wrote in a recent letter to university administrators.", "\n\n\"We, members of the Sexuality & Gender Diversity Faculty and Staff Council, write to express our extreme frustration at the University’s moves over the summer to deepen its relationship with Chick-fil-A\"\n\nSpecifically, they took issue with the fact that Chick-fil-A would move to a more prominent location on campus. ", "Their beef with the chicken joint stemmed from the company's perceived stance on LGBTQ issues, particularly its \"history of supporting organizations that are hostile to lesbian, gay, bisexual, transgender, and queer (LGBTQ) people, families, and communities.\"", "\n\nPrevious Campus Reform reporting has indicated:\n\nAccording to the Chick-fil-A Foundation’s website, the company donated $150,000 to the Salvation Army in 2017, funding camps for children, as well as the Atlanta, Ga. Angel Tree program, which provides holiday gifts to poor children. ", "The same year, the foundation donated $1.6 million to the Fellowship of Christian Athletes for school programs and sports camps. ", "As for the Paul Anderson Youth Home, Chick-fil-A donated $6,000 to the group in 2017 for a yearly Christmas dinner theater, as well as a bike ride fundraiser. ", "The three groups have indicated, to varying degrees, that they do not support homosexuality.", "\n\nThe KU council's statement claims that Chick-fil-A has supported Family Research Council, a conservative Christian nonprofit, but the Chick-fil-A Foundation's website, which lists its 2017 donations (the most recent available) does not list FRC as a recipient. ", "The statement also states that Chick-fil-A supported Exodus International, but fails to mention that the organization, which promoted conversion therapy, ceased operations in 2013.", "\n\nThe Chick-fil-A Foundation did not respond in time for publication when asked if a more recent list of its donations is available.", "\n\n[RELATED: Cal Poly faculty call for Chick-fil-A ban; compare chicken chain to porn, Hooters]\n\n\"While we recognize that contractual obligations did not allow the complete removal of the brand from campus, we are outraged that they have been allowed to move from the Wescoe Underground to a new, bigger, more central location on the University of Kansas campus. ", "Despite our denouncements and the university’s own moves to increase the campus’s diversity, equity, and inclusion, KU granted Chick-fil-A, a bastion of bigotry, a prime retail location in the heart of our campus. ", "The Union houses spaces that the KU community designates as safe and accepting—not least of which are the Office of Multicultural Affairs and the Center for Sexual & Gender Diversity,\" the council continued.", "\n\nThe statement comes five years after students and faculty at KU petitioned the university not to renew Chick-fil-A's $60,000 per year contract.", "\n\n“And despite that they went ahead and signed a contract for another 10 years,” Katie Batza, the head of the Sexuality and Gender Diversity Faculty and Staff Council, said, according to the Kansas City Star. ", "That means the university's contract with Chick-fil-A is up again in 2024.", "\n\nHowever, as the Star also reported, “they are not giving us any guarantee that the contact won’t be renewed again,\" Batza said.", "\n\n\"We beseech you to rectify this situation immediately, promoting inclusion and equity instead of hatred and intolerance. ", "At the very least, we demand a guarantee from the Chancellor, KU Athletics, and the Provost that these contracts will not be renewed once expired,\" the council's later stated, later adding, \" we will urge our members and allies to speak with our dollars as well as our words, and boycott the restaurant.\"", "\n\nThe University of Kansas did not return a request for comment but, according to the University Daily Kansas, Interim Provost Carl Lejuez said in an email to faculty and staff, “Moving forward, I believe it is important to have thoughtful discussion and deliberation when we enter into contracts. ", "In the future, we will do so in a manner that is transparent and informed by our commitment to affirm diversity and to be a welcoming and inclusive campus.”", "\n\n[RELATED: EXCLUSIVE: Rider Univ refuses to bring Chick-Fil-A to campus, despite students' demands]\n\nBatza appears to have shared a University Daily Kansan article on the controversy on her personal Facebook page, where she received some criticism. ", "One user commented on the shared link, \"you ought to do some research and perhaps even contact the company before spouting off your misinformed and blatantly false opinions in the media. ", "Describing the company as a ‘bastion of bigotry’ makes you a bastion of idiocy. ", "Oh, wait! ", "I forgot, anyone who does not bow down before your beliefs is a bigoted fascist, right?? ", "Don’t like the food? ", "Don’t eat there. ", "Plenty of people love the food.\"", "\n\nThe KU Center for Sexuality and Gender Diversity official Facebook page also shared the same link, where one user commented, \"Took long enough, but my twin brother and best friend are both gay and love chick-fil-a along with several other gay people i know.\"", "\n\nCampus Reform reached out to Batza but did not hear back in time for publication.", "\n\nThis is the latest example of Chick-fil-A coming under fire on American college campuses. ", "As Campus Reform has reported, students and faculty have grilled Chick-fil-A at colleges from California to Texas to Nebraska to New Jersey.", "\n\nFollow the author of this article on Facebook: @JonStreetDC and Twitter: @JonStreet" ]

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[ "Q:\n\nHow to get Sandcastle to include inherited properties\n\nI have 2 POCO classes for my view model:\npublic class BaseView\n{\n public int Id { get; set; }\n\n public string Name { get; set; }\n}\n\nand \npublic class FullView : BaseView\n{\n public string Reference { get; set; }\n\n public bool IsActive { get; set; }\n}\n\nWhen I generate a CHM help file using Sandcastle (2014.5.31.0) both are included but the FullView only shows it's 2 properties.", "\nHow can I get it to include the BaseView properties that it is inheriting?", "\n\nA:\n\nRight click the Sandcastle project > Properties > Visibility > Inherited Base Class Members\n\n" ]

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[ "Q:\n\nweb.config forms authentication, cookiename\n\nI have a web.config with the following: \n <system.web>\n<customErrors mode=\"Off\"/>\n\n<authentication mode=\"Forms\">\n <forms loginUrl=\"Login.aspx\" name=\"SIPE_ASPXAUTH\">\n <credentials passwordFormat=\"Clear\">\n <user name=\"user1\" password=\"123456\"/>\n <user name=\"user2\" password=\"123456\"/>\n <user name=\"user3\" password=\"123456\"/>\n </credentials>\n\n </forms>\n\n</authentication>\n\n<authorization>\n\n <deny users=\"?\"/>\n</authorization>\n<compilation debug=\"true\"/>\n\nThis web.config always redirects me to the following url\nhttp://localhost:53077/Login.aspx?ReturnUrl=%2fDefault.aspx\n\nMy start page is a Login.aspx and even after entering the correct credentails, it redirects me to the above url.", "\nSo here's what I did. ", "\nI took out the name property in the \n <forms loginUrl=\"Login.aspx\">\n\nand left everything else untouched.", "\nIt works perfectly.", "\nCan anyone pls explain why.", "\nI understand that this is a cookiename and the default is ASPXAUTH. ", "This cookie is used to authenticate a user. ", "Also it is stored in tools..options... \nWhat is the use of setting this cookiename. ", "Is it to allow cross browser functinality.n\nHow would I make this to work by having the name property in the <forms loginUrl=\"Login.aspx\">\nThank u\n\nA:\n\nconfig setting is seems to be OK but you have write some code in your login page's code behainsd also for form authentication. ", "After checking user name & password is corrent you have to write below code :\nFormsAuthentication.", "SetAuthCookie(\n this.", "TextBox_username.", "Text.", "Trim(), flase);\n\n FormsAuthenticationTicket ticket1 = \n new FormsAuthenticationTicket(\n 1, // version\n this.", "TextBox_username.", "Text.", "Trim(), // get username from the form\n DateTime.", "Now, // issue time is now\n DateTime.", "Now.", "AddMinutes(10), // expires in 10 minutes\n false, // cookie is not persistent\n \"HR\" // role assignment is stored\n // in userData\n );\n HttpCookie cookie1 = new HttpCookie(\n FormsAuthentication.", "FormsCookieName, \n FormsAuthentication.", "Encrypt(ticket1) );\n Response.", "Cookies.", "Add(cookie1);\n\nFor more detail on Form Authentication Click Here \n\n" ]

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[ "Tuesday, September 6, 2011\n\nFind and compare the best prices and deals on Asics GEL-DEDICATE OC Womens Tennis Shoes at a reasonable price. ", "The Asics GEL-DEDICATE OC is a stylish omni-court tennis shoe designed with technology that provides comfort, support and durability so you can focus on elevating your game.", "\n\nFeatures a synthetic leather upper with perforations which provide excellent comfort, support and durability. ", "The compression moulded EVA midsole offers enhanced cushioning and stability. ", "The Forefoot Gel Cushioning System provides maximum shock absorption during impact phase. ", "The rubber outsole provides traction on a variety of court surfaces. ", "Outsole wraps up onto the toe for added protection. ", "Also featured is California lasted and a removable compression moulded EVA sockliner which provides comfort and cushioning." ]

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[ "Search\n\nThis is a master class in 3D application development for the new glasses-free 3D mobiles on the market. ", "The class is for anims and Android devs, and will step through the creation of an application specifically for 3D phones. ", "Engineers have a great honor to be the headliners of the event covering the topic of 3D game development.", "\n\nThe very first lecture I gave just a few days ago, “Augmented Reality and 3D”, was very well accepted by the audience and the organizers. ", "I’ve raised some quite challenging propositions that we will be working on over the next weeks and months, such as using worldwide common markers instead of the predefined static ones (car tires, traffic signs, logos, etc…).", "\n\nThe lecture, which is the result of couple of weeks research and development by the Engineers astrophysics-mathematician-developer Damir Burazerovic and myself, is summed up in the slides which I’ve used at the event. ", "As there are quite a few things which I have talked about and are not here, feel free to pop up any questions and start any discussion in this thread.", "\n\nThis is just a short introduction to what I believe are the most interesting bet variations on the market, and is written for the reason of introduction to the further posts for the “Building an online betting solution” series of posts I will write over the next couple of weeks. ", "If enough interest is produced by this post, I’d be happy to write more about what interests you the most.", "\n\nThere are various ways a bet can be placed and interpreted. ", "I will name three most interesting examples:\n\nSport bets\n\nBets before a competition/game has begun\n\nLive betting\n\nAuction bids\n\nPrebids – bids before the auction has began\n\nLive bids\n\nVisual bets\n\nBetting against a credible estimate\n\nSport bets\n\nIn sport bets or any other bets of this type, betters are betting against the final outcome. ", "As the final result is final, the bet is final as well. ", "A bet represents a legally binding contract between the better and the betting company. ", "Further more, betting company must have special licence to operate such business.", "\n\nSport bets which are placed before a game begins are the most common ones. ", "Users are betting on a final outcome of a game in terms of any of it’s parameters (final score, number of final attributes (i.e. sets in tennis, or corners in soccer… the list is infinite).", "\n\nLive betting is referred to an action where users are betting during a game on various outputs/results which occur during the game and mostly within a short time span (i.e. who will score the next goal, or who will foul next… the list is, again, infinite…).", "\n\nAuction bids\n\nAuction bids are an interesting category and is probably rarely spoken about in this context. ", "The main difference from bets is that bids do not present a final contract between a bidder and an auction host, as bid can be overbid at any time. ", "Only the highest (winning) bid is the legally binding one. ", "In this case, bidder is bidding against a final score, where the score represents the highest bid on which the bidder has a direct influence over. ", "A company hosting an auction does not require special licences to operate such business.", "\n\nTwo of the scenarios are the most interesting ones:\n\nAuction hasn’t yet started and bids are being placed which represent a sum one would pay for something that he/she does not know the final cost for yet. ", "These bids are usually hidden until the auction starts. ", "Once the auction begins, the highest prebid is the opening price instead of the opening price initially set by the auctioneer.", "\n\nAuction has started, and bidders are always aware of what is the current highest (winning) bid and they bet in correlation to that one.", "\n\nVisual bets\n\nVisual bets are not amongst the most common ones, but are quite an interesting example. ", "A prime example is company called Best of the Best, a luxury goods competition company where every one someone is guaranteed to win a Supercar.", "\n\nThis is how the “game” is being played:\n\nA sporting picture that has had the ball permanently removed from it is presented to the one betting\n\nUsing best judgment, the individual is to click on the picture where they think the center of that ball should be\n\nThe bid is actually x:y coordinate of where the individual has clicked\n\nWhen the competition is closed on a set date and time, the same picture is presented to a credible panel of Judges who repeat the same process\n\nThe winner is simple the person who is closes to the judges position.", "\n\nThis type of betting does falls under gambling as well as the sport bets, and requires a special licence for the company to operate.", "\n\nCreating a multi-layered background with CSS3 is quite simple – all you need to do is to specify multiple background images for the wrapper class:\n\nHowever, we do need a fall back mechanism for browsers which do not support CSS3 and will never do (&*#*$& !!!). ", "Further more, we’ll implement 3 backgrounds on top of each other in order to produce a result which:\n\nHas a background pattern\n\nIs enriched with another pattern which appears at the top of the page and disappears downwards\n\nHas another visual effect which for examples throw a sunlight effect behind the content\n\nWe start simple by adding background to the .body, which sets our base pattern for the page:\n\nNow that this is set, we go ahead and prepare our page HTML structure:\n\nThe .container element is an independent element laying on the page and has no child elements. ", "We set it’s position to fixed and give it the maximum size:\n\nThe background of this element has the texture we want to apply over the background .body pattern. ", "At this point we are set with two background images, one over another. ", "Note that the position of the element is fixed.", "\n\nThe next step is adding the effect over the body and texture. ", "That would be our “light” element:\n\nAgain, this is an independent element with fixed position and z-index is just one above the container which allows us to create a visual light effect over the container. ", "It’s up to you where you want to position the .light element in the page and you can control it’s position by either CSS or jQuery if you need it specially positioned at certain place while keeping it’s position dynamic in regards to the other elements.", "\n\nThe last but lot least is the .content element where you would place you page content:\n\nThis is the element which will finally has its own child elements (basically, your entire page). ", "Main characteristics of this element are:\n\nz-index is higher than the .light element’s z-index (use small numbers so that you don’t run into problems with modal pop-ups)\n\nQuick intro: “Razor”, a new view-engine for ASP.NET MVC 3 speeds up the development in terms of writing view templates, and what’s more important, puts you in a place that you do not need to interrupt your coding to explicitly denote the start and end of server blocks withing your HTML. ", "The best overview out there is, of course, at Scott Gu’s blog, so go ahead and read it if you need more insight into that.", "\n\nA hidden “Razor” gem that I want to mention today is @helper syntax, which enables you to create reusable helper methods and use them on the go – again, Scott Gu’s post about it, and the solution of how to get an access to the ASP.NET MVC Html helper methods within which is not supported by default.", "\n\nCouple of years ago I spent 2 years working for BWIN.COM, Europe’s largest eGaming provider, as a part of the Sportsbook development team. ", "It was until this year when I met face to face again with a similar project in terms of the back-end system – online live auctioning solution for property rentals – Zumper.com, our new client. ", "Zumper, founded by a highly capable team of Harvard Business School students, is an online real estate market in which students and young professionals can bid on and secure properties in a more efficient and transparent manner. ", "Further more, implementing money flow and virtual currency system (amongst all other systems) into Bloomtrigger.com, brought many things together in terms of algorithm which handles inner and outer transactions.", "\n\nThe series of posts I am about to write are not going to reveal any business secrets or pieces of code used in all these projects, but rather give you an insight of complexity of such systems together with some hidden tricks and tips.", "\n\nHere’s the list of topics I am going to cover (not necessarily in this order, and the list may change as I go along):\n\nBetting scenarios\n\nCurrencies and virtual currencies\n\nBack-end logic vs. database logic\n\nPlacing bids/bets\n\nLive visual result tracking\n\nLogging and history\n\nHandling user errors\n\nHandling system errors\n\nSecurity\n\nMoney flow\n\nI will blog about our first topic, “Types of bets/bids”, in the next couple of days. ", "Watch this space…\n\nBoth events were a success with over 40 participants. ", "We are already planning to repeat the last years success in 2011 and we are open to any suggestions for our events this year. ", "If you’d like to hear us talk on a certain topic, please let us know.", "\n\nAfter so many lines of code in the past decade, we ran onto an issue which should never happen if you follow naming standards… still, a moment of tardiness at 3am after 18 hours long work day you ran onto these as well, and I wanted to share.", "\n\nSimple, ridiculous, but possible, and guess what – IE doesn’t like it:\n\n– here’s my element:<div id=\"DoSomething\"></div>\n\n– here’s my action link:<a href=\"#\">Click here</a>\n\n– here’s my function:function DoSomething() {//whatever}\n\nClicking the link won’t work in IE and Safari. ", "Firefox and Chrome are just fine with it.", "\n\nNote to myself: Follow naming conventions at all times, functions and elements should never have the same name!" ]

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[ "Branko\n\nBranko (Cyrillic script: Бранко; ) is a South Slavic male given name found in all of the former Yugoslavia. ", "It is related to the names Branimir and Branislav, and the female equivalent is Branka.", "\n\nPeople named Branko include:\n\n Branko Babić (born 1947), Serbian football manager\n Branko Baković (born 1981), Serbian footballer\n Branko Baletić (born 1946), Serbian-Montenegrin film director and producer\n Branko Bauer (1921–2002), Croatian film director\n Branko Bokun (1920–2011), Yugoslav-British author and journalist\n Branko Bošković (born 1980), Montenegrin footballer\n Branko Bošnjak (1923–1996), Croatian philosopher\n Branko Bošnjak (born 1955), Yugoslav footballer\n Branko Bošnjaković (born 1939), Dutch-Croatian physicist\n Branko Brnović (born 1967), Montenegrin football manager\n Branko Buljević (born 1947), Croatian-Australian footballer\n Branko Cikatić (born 1954), Croatian martial artist\n Branko Crvenkovski (born 1962), Macedonian politician\n Branko Cvetković (born 1984), Bosnian basketball player\n Branko Ćopić (1915–1984), Yugoslav writer\n Branko Čulina (born 1957), Croatian-Australian football manager\n Branko Đurić (born 1962), Bosnian actor\n Branko Gračanin (born 1943), Croatian footballer\n Branko Grahovac (born 1983), Bosnian footballer\n Branko Grünbaum (1929–2018), Croatian-American mathematician\n Branko Horvat (1928–2003), Croatian economist and politician\n Branko Ilič (born 1983), Slovenian footballer\n Branko Isaković (born 1958), Serbian musician\n Branko Ivanković (born 1954), Croatian football manager\n Branko Jelić (born 1977), Serbian footballer\n Branko Kadija (1921–1942), Albanian communist of Serbian descent, People's Hero of Albania\n Branko Karačić (born 1960), Croatian football manager\n Branko Kostić (born 1939), Montenegrin Serb politician\n Branko Lazarević (born 1984), Serbian footballer\n Branko Lustig (1932–2019), Croatian film producer\n Branko Mamula (born 1921), Yugoslav officer and politician\n Branko Mihaljević (1931–2005), Croatian composer\n Branko Mikša (born 1947), Croatian politician\n Branko Mikulić (1928–1994), Yugoslav politician\n Branko Milanović (born 1953), Serbian-American economist\n Branko Milićević (born 1946), Serbian actor\n Branko Milisavljević (born 1976), Serbian basketball player\n Branko Miljković (1934–1961), Serbian poet\n Branko Miljuš (born 1960), Croatian footballer\n Branko Mladenović (fl. ", "1355), Serbian magnate\n Branko Nuss (born 1976), Basic Element (music group) accordion\n Branko Oblak (born 1947), Slovenian footballer\n Branko Panić (born 1977), Croatian footballer\n Branko Pavlović (born 1960), Serbian politician and lawyer\n Branko Peković (born 1979), Serbian water polo player\n Branko Pleše (1915–1980), Croatian footballer\n Branko Radičević (1924–1953), Serbian poet\n Branko Radivojević (born 1980), Slovak ice hockey player\n Branko Radovanović (born 1981), Serbian footballer\n Branko Rasić (born 1976), Serbian footballer\n Branko Rašović (born 1942), Montenegrin footballer\n Branko Schmidt (born 1957), Croatian film director\n Branko Segota (born 1961), Croatian-Canadian footballer\n Branko Skroče (born 1955), Croatian basketball player\n Branko Smiljanić (born 1957), Serbian football manager\n Branko Stanković (1921–2000), Bosnian Serb football player and manager\n Branko Stanovnik (born 1938), Slovenian chemist\n Branko Strupar (born 1970), Croatian-Belgian footballer\n Branko Štrbac (born 1957), Yugoslav handball player\n Branko Tomović (born 1980), Serbian-German actor\n Branko Tucak (born 1952), Croatian football manager\n Branko Vukelić (1958–2013), Croatian politician\n Branko Zebec (1929–1988), Croatian football player and manager\n\nOther\n Branko's Bridge\n Branko, artist's name of Branko (João Barbosa), Portuguese musician, see Buraka Som Sistema\n\nSee also\n Branislav\n Branković\n Brankovina\n Brankovići (Rogatica)\n\nCategory:Slavic masculine given names\nCategory:Bosnian masculine given names\nCategory:Croatian masculine given names\nCategory:Serbian masculine given names" ]

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[ "WASHINGTON (Reuters) - The United States accounted for more than two-thirds of foreign weapons sales in 2008, a year in which global sales were at a three-year low, The New York Times reported on Sunday.", "\n\nA U.S. Air Force F-15E Strike Eagle aircraft from the 492nd Fighter Squadron, Royal Air Force (RAF) Lakenheath, United Kingdom (UK) releases a GBU-28 \"Bunker Buster\" 5,000-pound Laser-Guided Bomb over the Utah Test and Training Range during a weapons evaluation test hosted by the 86th Fighter Weapons Squadron (FWS) from Eglin Air ForceBase, Florida, in this August 5, 2003 photograph, obtained by Reuters on August 2, 2009. ", "REUTERS/Technical Sgt. ", "Michael Ammons/USAF/Handout\n\nCiting a congressional study released on Friday, the Times said the United States was involved in 68.4 percent of the global sales of arms.", "\n\nU.S. weapons sales jumped nearly 50 percent in 2008 despite the global economic recession to $37.8 billion from $25.4 billion the year before.", "\n\nThe jump defied worldwide trends as global arms sales fell 7.6 percent to $55.2 billion in 2008, the report said. ", "Global weapons agreements were at their lowest level since 2005.", "\n\nItaly, the second ranked country, amassed only $3.7 billion in arms sales, while Russia ranked third with sales falling to $3.5 billion in 2008, down from $10.8 billion in 2007.", "\n\nThe report attributed the increase in U.S. sales to “major new orders from clients in the Near East and in Asia” as well as to continued contracts for equipment and support services with globally based U.S. clients, the Times said.", "\n\nThe United States also led in arms sales to the developing world, signing 70.1 percent of these weapons agreements at a value of $29.6 billion in 2008, the report said.", "\n\nSuch deals with the developing world included a $6.5 billion air defense system for the United Arab Emirates, a $2.1 billion jet fighter for Morocco and a $2 billion attack helicopter for Taiwan.", "\n\nIndia, Iraq, Saudi Arabia, Egypt, South Korea and Brazil also reached weapons deals with the United States, the Times said.", "\n\nThe report revealed the United Arab Emirates was the top buyer of arms in the developing world with $9.7 billion in arms purchases in 2008.", "\n\nSaudi Arabia ranked second with $8.7 billion in weapons agreements, and Morocco was third with $5.4 billion in deals." ]

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[ "1. ", "Introduction\n===============\n\nIn orthodox seeds, metabolic activity is interrupted during desiccation of maturation and achieves a physiologically relatively quiescent status in which the embryonic cell viability can extend over centuries \\[[@B1-ijms-15-13461]\\]. ", "Following simple imbibition, the non-dormant seeds will initiate the germination process, restart metabolic activity, mobilize the reserves, biosynthesize new proteins, regenerate organelles and cell membranes, eventually protrude the radicle and enter into seedling establishment \\[[@B2-ijms-15-13461]\\].", "\n\nSeed germination is a complex regulation system. ", "Numerous exogenous and endogenous factors can affect the germination process, including seed vigor, water, temperature, oxygen and phytohormones \\[[@B3-ijms-15-13461],[@B4-ijms-15-13461]\\]. ", "Exploration of the functional genes that respond to those factors is an ongoing routine work for seed biologists to elucidate the complex molecular mechanisms underlying seed germination. ", "Forward and reverse genetic methods have been adopted to scan the functional genes. ", "Using retrotransposon Tos17 as an endogenous insertion mutagen, the *Osaba1* gene that controls seed viviparous by improving ABA levels was cloned in rice \\[[@B5-ijms-15-13461]\\]. ", "Bentsink *et al.* ", "had cloned the quantitative trait locus controlling dormancy (*DOG1*) in *Arabidopsis* \\[[@B6-ijms-15-13461]\\]. ", "Recently, through screening the rice T-DNA insertion mutant library, a *gd1* mutant that is characterized by seed germination defects and reduction of GA biosynthesis was obtained \\[[@B7-ijms-15-13461]\\]. ", "Various developed \"-omics\" approaches have greatly expanded the investigation on the mechanism of seed germination \\[[@B8-ijms-15-13461],[@B9-ijms-15-13461],[@B10-ijms-15-13461],[@B11-ijms-15-13461]\\]. ", "A series of genes that manifest vital functions during seed germination are identified, especially for gene response to gibberellin (GA) and abscisic acid (ABA), two antagonistic phytohormones regulating seed germination \\[[@B12-ijms-15-13461]\\]. ", "In farming conditions, environmental stresses constrain crop seed germination; seeds have established the intensive molecular mechanism to resist those stresses. ", "For example, protein RAP2.6, an *Arabidopsis* AP2/ERF family member, can function in multiple abiotic stresses during seed germination, including salt, osmotic, and cold stress \\[[@B13-ijms-15-13461]\\]. ", "Additionally, multiple functional genes can play roles in orchestra to resist stresses. ", "Direct seeding of rice seeds in paddy fields will subject seeds to waterlogged or flooding stress which will expose seeds to hypoxia or even anoxia \\[[@B14-ijms-15-13461]\\]. ", "Under hypoxia, α-amylase (*Amy1A* and *Amy3D*) and sucrose synthase (*Sus3*) genes were activated to degrade starch and sucrose, pyruvate decarboxylase (*Pdc1* and *Pdc2*) and alcohol dehydrogenase (*Adh1* and *Adh2*) genes were induced to adjust the low-oxygen stress by enhanced ethanol fermentation, and ethylene biosynthesis-related genes were greatly increased and then initiated a cascade of reactions to promote the coleoptile elongation \\[[@B15-ijms-15-13461],[@B16-ijms-15-13461],[@B17-ijms-15-13461],[@B18-ijms-15-13461]\\].", "\n\nAs the alive tissues in the cereal dry seed, the aleurone layer and the embryo share several characteristics, including synthesis and accumulation of lipid bodies and special protein bodies, desiccation tolerance, dormancy, and response to GA by inducing synthesis of hydrolytic enzymes to degrade the storage and promote seed germination \\[[@B19-ijms-15-13461]\\]. ", "The characteristic transcripts of aleurone and embryo have been investigated by differential screening of a cDNA library from barley alleurone \\[[@B20-ijms-15-13461]\\], two main groups of clones, *Bal* (Barley aleurone) and *Balem* (Barley aleurone and embryo) were screened. ", "In the *Balem* group, one subgroup of genes, including *Per1*, *Ole1* and *Ole2* having a *Lea*-like expression pattern, were up-regulated by ABA and mannitol and contributed to the desiccation tolerance and dormancy maintenance of mature seeds \\[[@B19-ijms-15-13461],[@B21-ijms-15-13461]\\]. ", "However, another subgroup, including B12D and B22E, had the opposite expression and stress response patterns. ", "B12D and B22E were preferentially expressed in the aleurone layer and embryo of developing seeds and germinating seeds while disappearing in mature seeds \\[[@B19-ijms-15-13461],[@B22-ijms-15-13461],[@B23-ijms-15-13461]\\]. ", "Both of them were inhibited by ABA and mannitol in germinating seeds, but were differentially responsive to GA~3~: B12D could be induced by GA~3~ while B22E was insensitive to GA~3~. The function of the second subgroup remains unknown.", "\n\nIn our previous work on proteomics analysis of rice seed germination \\[[@B11-ijms-15-13461]\\], we identified a B12D-like protein encoded by LOC_Os7g41350 (named *OsB12D1*). ", "In the present study, we systematically analyzed the gene evolution, structure, expressional patterns, function, and protein subcellular localization of *OsB12D1*. ", "Our data demonstrated that *OsB12D1* is a functional gene to enhance rice seedling establishment under flooded condition.", "\n\n2. ", "Results\n==========\n\n2.1. ", "OsB12D1 Pertains to an Ancient Protein Family\n--------------------------------------------------\n\nUsing the full-length sequence of OsB12D1 protein sequence as the query to search against NCBI (The National Center for Biotechnology Information) database, 55 close homologs were obtained from 30 different species in addition to rice, belonging to moss, gymnosperm to angiosperms ([Supplemental Dataset 1](#ijms-15-13461-s001){ref-type=\"supplementary-material\"}). ", "All of these homologs were low-molecular proteins with the number of amino acids ranging from 76 to 134. ", "Transmembrane region analysis using TMHMM software showed that each protein has a hydrophobic *N*-terminal \\[[@B24-ijms-15-13461]\\], which indicated B12Ds might be membrane-anchored proteins.", "\n\nOsB12D1 and its 29 closest homologs from the other species were used for phylogenetic analysis with the neighbor-joining method ([Figure 1](#ijms-15-13461-f001){ref-type=\"fig\"}A). ", "All these B12D proteins were significantly clustered into two clades. ", "Both clades consisted of B12Ds from monocotyledons and dicotyledons, which indicated that the main characteristics of the B12D family formed before the genetic split of monocotyledons and dicotyledons in plants. ", "OsB12D1 was closely grouped with monocot counterpart proteins from brachypodium, maize and sorghum, while it diverged from the HvB12Dg1, sharing only 46% identity.", "\n\n2.2. ", "Gene Structure and Expressional Patterns of OsB12Ds\n--------------------------------------------------------\n\nFrom the RGAP (Rice Genome Annotation Project) database, six OsB12D paralogs were obtained, including two pairs of tandem duplicates (LOC_Os07g17310 and LOC_Os07g17330; LOC_Os07g41340 and LOC_Os07g41350). ", "Gene structure analysis showed that all *OsB12D* genes harbored only two or three exons, and although they have similar CDS size, the intron fragments' size varied greatly ([Figure 1](#ijms-15-13461-f001){ref-type=\"fig\"}B). ", "The six OsB12Ds proteins shared two conserved motifs, including the N-terminal transmembrane region ([Figure 1](#ijms-15-13461-f001){ref-type=\"fig\"}C).", "\n\n{#ijms-15-13461-f001}\n\nQuantitative RT-PCR method was used to examine the expression pattern of the *OsB12Ds* in the embryo of germinating seed at different stages and various tissues from a 60-day-old rice plant. ", "Four *OsB12Ds* were detected in most tissues and had a relatively high expression level in germination seed but low in dry seeds, stems and leaves ([Figure 2](#ijms-15-13461-f002){ref-type=\"fig\"}A). ", "The expression of LOC_Os03g40440 was only detected in the spikelets. ", "For *OsB12D1*, the mRNA level achieved the peak in the seed embryo at 24 h after imbibition (HAI). ", "In addition to the germinating seeds, *OsB12D1* was also highly expressed in root. ", "LOC_Os07g41340, the tandem duplicate of *OsB12D1*, obtained similar expression style. ", "Generally consistent with RT-PCR results, the digital expression patterns indicated the OsB12Ds were highly expressed in germinating seed and low in dry seeds, stems and leaves ([Figure 2](#ijms-15-13461-f002){ref-type=\"fig\"}B). ", "The two pairs of tandem duplicates had similar expression patterns, while the LOC_Os07g17330 and *OsB12D1* were the major transcripts with a higher expression level over their corresponding tandem duplicates. ", "Differing from the RT-PCR result, LOC_Os07g17330 was also detected highly expressed in root ([Figure 2](#ijms-15-13461-f002){ref-type=\"fig\"}B).", "\n\nTo obtain the gene regulation information about *OsB12D*s, gene responses to different factors that influence seed germination were detected. ", "Those factors were phytohormones GA~3~ and ABA, osmotic reagent mannitol, salt, temperature, H~2~O~2~, respiration inhibitors NaN~3~ and SHAM (salicyl-hydroxamic acid), and flooding. ", "Except for being significantly inhibited by mannitol and insensitive to the low concentration of H~2~O~2~ uniformly, four *OsB12Ds* were differentially responsive to the other factors. ", "GA~3~ and high temperature pre-treatment could promote seed germination and impose positive effects on the *OsB12D* expression to some extent. ", "However, although the NaCl and NaN~3~ entailed remarkably germination viability decline, some *OsB12D*s still could be induced by them, especially for Os07g17330. *", "OsB12D1* was not significantly induced by any detected factors; it was inhibited by ABA, mannitol, SHAM, high concentration of H~2~O~2~ and flooding, and insensitive to the other factors ([Figure 2](#ijms-15-13461-f002){ref-type=\"fig\"}C,D). ", "Similar responses occurred on its tandem duplicate LOC_Os07g41340.", "\n\n*Cis-*elements analysis was performed based on the 1 kb promoter sequence upstream of the translation start point of the *OsB12D*s ([Table S1](#ijms-15-13461-s001){ref-type=\"supplementary-material\"}). ", "The pOs07g17330 had various *cis*-elements including stress responsiveness G-box, ABRE, GARE, TCA-element and GC-motif, which indicated LOC_Os07g17330 could respond to multiple germinating impact factors, this is consistent with the RT-PCR result. ", "Unlike *HvB12Dg1*, *OsB12D1* harbored no GA response element within the promoter, which indicated it might not be regulated by GA. ", "In addition to the G-box and ABRE, *OsB12D1* also harbored the anaerobic induction element within the promoter region, which implied *OsB12D1* could be induced by the anaerobia.", "\n\n![", "Expression analyses of *OsB12Ds*. (**", "A**) qRT-PCR analysis of the *OsB12Ds* expressional pattern in different stages of rice seed germination and various tissues. ", "The RNA was extracted from embryos of the dehulled rice seeds at 0, 24, 48, and 72 h after imbibition (HAI) under normal condition and tissues of root, stem, leaf and spikelet of 60 day-old rice plant; (**B**) Digital expression patterns of *OsB12Ds.* ", "Five OsB12Ds were obtained from the ricearray database using meta-analysis tool \\[[@B25-ijms-15-13461]\\]; (**C**) Rice seeds germinating under multiple treatments for 24 h. From left to right: CK, control; GA, 200 µM GA3; ABA, 50 mM ABA; NaCl, 200 mM NaCl; Mannitol, 20% Mannitol; Low Tem, seeds were imbibed at 4 °C for three days in the dark before being transferred to germinate under benign condition; High Tem, seeds pretreated at 40 °C and 100% relative humidity for three days; NaN~3~, 1 mM NaN~3~; SHAM, 15 mM SHAM; 5 mM H~2~O~2~; 20 mM H~2~O~2~; Flooding, seeds were directly submerged in 8 cm deep of distilled water; (**D**) qRT-PCR analysis of the *OsB12D* expression under multiple treatments. ", "The embryos of 24 HAI rice seeds under multiple treatments were excised manually and used for RNA extraction. ", "The expression of *OsB12D1* was normalized to the expression of rice 18 S rRNA. ", "The values are the means with the standard deviations (*n* = 3), asterisks (**\\*** *p* \\< 0.01, Student's *t*-test) represent significant differences from the expression level in 24 HAI seed embryo under normal conditions.](ijms-15-13461-g002){#ijms-15-13461-f002}\n\n2.3. ", "OsB12D1 Positively Responds to the Anoxia, Submergence and Flooding\n------------------------------------------------------------------------\n\nThe potential genes that are coexpressed with *OsB12D1* were searched on the ricearray database \\[[@B25-ijms-15-13461]\\]. ", "Many biotic or abiotic stress-related genes were obtained; including some stress-related, miscellaneous, redox, transport, amino acids metabolism and signaling-related genes ([Figure 3](#ijms-15-13461-f003){ref-type=\"fig\"}A). ", "Notably, four anoxic or anaerobic stress-related proteins were included, that are ethylene-responsive element-binding protein (EREBP-1), alcohol dehydrogenase (ADH) and two non-symbiotic hemoglobin 2 proteins (rHb2), which suggested that *OsB12D1* might respond to the anoxic or anaerobic stress.", "\n\nTo obtain the general view of *OsB12D1* response to stress, the ricearray results related to various stress conditions were retrieved \\[[@B25-ijms-15-13461]\\]. ", "These stress conditions included: subjected 14-day-old light-grown rice seedlings to 42 °C heat shock for 10 h (GSE14275); subjected seven-day-old light-grown rice seedlings to drought, salt and cold stress for 3 h (GSE6901); treated two-week-old rice plants with *Magnaporthe grisea* (virulent isolate FR13) (GSE7256); rice seed germinated under oxygen-free (anoxia) environment in the dark at 28 °C for four days (GSE 6908); submerged 14-day-old rice plants of submergence tolerant M202(*Sub1*) and intolerant M202 for 24 h (GSE18930). ", "The results showed that the OsB12D1 was insensitive to the heat shock, drought, salt, cold and *Magnaporthe grisea* infection, but was significantly induced in the anoxic coleoptiles and submerged seedlings \\[[@B26-ijms-15-13461]\\], which implied that OsB12D1 might function in anoxia and submergence resistance ([Figure 3](#ijms-15-13461-f003){ref-type=\"fig\"}B).", "\n\n{ref-type=\"supplementary-material\"}; (**B**) Heat maps of *OsB12D1* response to different stresses. *", "OsB12D1* was insensitive to the heat shock (GSE14275), drought, salt, cold (GSE6901) and *Magnaporthe grisea* (GSE7256), but was induced by anoxia (GSE 6908), submergence (GSE18930) and Fe deficiency (GSE17245). ", "Data were obtained from the Rice Oligonucleotide Array Database \\[[@B25-ijms-15-13461]\\]; (**C**) qRT-PCR analysis of the *OsB12D1* expression in response to flooding stress. ", "The dehulled seeds were germinated in normal conditions \"N\" for three days, and then switched to the flooded condition \"F\" for two days; the coleoptiles and roots were collected for RNA extraction. ", "The coleoptiles and roots from three- or five days of normal growth and flooding-stressed seedlings also were collected. ", "Embryos from 24 HAI seeds, 24H-CK, under normal conditions were used as internal reference; 3dN-R/-C or 5dN-R/-C, roots \"R\" or coleoptiles \"C\" of 3 or 5 days germinating seeds under normal condition; 3dN+2dF-R/-C, roots or coleoptiles of seedlings switched from 3 days normal germination to flooding for two days; 3dF-C or 5dF-C, coleoptiles from 3 or 5 days germinating seeds under flooding. ", "The expression of *OsB12D1* was normalized to the expression of the rice 18S rRNA. ", "The values are the means with the standard deviations (*n* = 3), asterisks (**\\*** *p* \\< 0.01, Student's *t*-test) represent significant differences from the 24 H-CK expression level.](ijms-15-13461-g003){#ijms-15-13461-f003}\n\nWhile in the seed embryos of 24 HAI under flooding, the expression of *OsB12D1* was very low ([Figure 2](#ijms-15-13461-f002){ref-type=\"fig\"}A). ", "To further check the *OsB12D1* response to the submergence, its expression under flooding during the seed germination and early seedling growth was detected. ", "After germinating under normal conditions for three days when the visible radicles emerged, the rice seedlings were transferred to grow under the flooded condition for two days, and then the coleoptiles and roots (not including hypocotyl) were collected to evaluate the mRNA accumulation of *OsB12D1*. ", "A lower *OsB12D1* expression level was detected in the coleoptiles and roots under normal conditions. ", "After two days of flooding, the expression of *OsB12D1* was increased greatly both in the coleoptiles and roots, especially in the coleoptiles ([Figure 3](#ijms-15-13461-f003){ref-type=\"fig\"}C). ", "Meanwhile, although there was no radicle protrusion, the *OsB12D1* could be induced greatly in the coleoptiles of the three or five-day-old seedlings under sequential flooding ([Figure 3](#ijms-15-13461-f003){ref-type=\"fig\"}C). ", "These results confirmed that the *OsB12D1* is a flooding-responsive gene.", "\n\n2.4. ", "Over Expressing of OsB12D1 Enhances Rice Flooding Tolerance during Seed Germination and Early Seedling Growth\n------------------------------------------------------------------------------------------------------------------\n\nTo investigate the function of *OsB12D1*, an over expression construct of *pUbi*-*OsB12D1-FLAG* was transformed into rice cultivar Zhonghua11 ([Figure 4](#ijms-15-13461-f004){ref-type=\"fig\"}A). ", "Ten independent positive T0 transformants were confirmed by genomic DNA PCR with primer pair pUbi/OsB12D1-R. Three transgenic lines of the T2 generation with the high expression level of *OsB12D1* were used for further study. ", "The gene over expression was detected at the mRNA and protein level, and the transcripts were accumulated more than 300-fold higher than that in the wild type ([Figure 4](#ijms-15-13461-f004){ref-type=\"fig\"}B,C).", "\n\nThe seed of all three *OsB12D1*-OE transgenic lines germinated well under normal growth conditions; there was no significant difference from the wild type ([Figure S1](#ijms-15-13461-s001){ref-type=\"supplementary-material\"}), and no visible phenotypes were found throughout the whole plant's life.", "\n\nConsidering the above analyses, *OsB12D1*-OE seedlings response to flooding was investigated. ", "The dehulled seeds of *OsB12D1*-OE lines and the wild type Zhonghua11 were submerged in 8 cm of distilled water and grown under normal conditions. ", "In the first three days, the coleoptiles of all seeds were elongated and no significant differences were observed between the mutant and wild type. ", "After five days of submergence, visible radicles appeared in the *OsB12D1*-OE seeds. ", "After seven days, all three *OsB12D1*-OE seeds protruded radicles successfully, although they had cracked coleoptiles and outgrew their primary leaves. ", "Notably, line OE-F6 could extend both of the seed roots and adventitious roots under the flooded condition ([Figure 4](#ijms-15-13461-f004){ref-type=\"fig\"}D,E). ", "When the submergence time was prolonged to 10 days, the root could grow quickly, and the transgenic seedling could grow continuously and emerge from the water. ", "However, for the wild type, no radicle protruded and the coleoptiles would bend as the submergence time was prolonged ([Figure S2](#ijms-15-13461-s001){ref-type=\"supplementary-material\"}). ", "Upon being transferred to the mud, all *OsB12D1*-OE seedlings could survive and grow better than the wild type.", "\n\n{#ijms-15-13461-f004}\n\nGA and ethylene are two important regulators for plant flooding escaping \\[[@B27-ijms-15-13461]\\]. ", "The seedling phenotype of OsB12D1-OE lines under flooding containing GA and ethylene biosynthesis inhibitors were detected. ", "The GA biosynthesis inhibitor paclobutrazol (PBZ) retarded seed germination under flooding, while after five days of submergence, the visible radicles emerged in the mutant seedlings but not in the wild type ([Figure S3](#ijms-15-13461-s001){ref-type=\"supplementary-material\"}), which suggested that OsB12D1-OE seeds could enhance radicle protrusion without GA biosynthesis under flooding. ", "Ethylene biosynthesis inhibitors CoCl~2~ could retard the coleoptiles elongation, as well. ", "After five days of submergence with CoCl~2~, all seedlings including the wild type could be observed with radicle protrusion, while there was no significant difference between the wild type and the mutant, thus implying that OsB12D1 could promote radicle protrusion under flooding in correlation to the ethylene.", "\n\n2.5. ", "OsB12D1 Is Mainly Located in the Mitochondrion and Might Enhance Electron Transfer\n---------------------------------------------------------------------------------------\n\nAccording to the Pfam prediction, B12D might be a mitochondrion-located protein \\[[@B28-ijms-15-13461]\\]. ", "To validate this prediction, a construct of p35S*-OsB12D1-gfp* was introduced into the transient expression system of the *Arabidopsis* protoplast to investigate the subcellular localization of OsB12D1. ", "The florescence signal of OsB12D1-GFP was observed to well match the RFP signal of MitoTracker Red but not overlap the chlorophyll ([Figure 5](#ijms-15-13461-f005){ref-type=\"fig\"}A), which indicated that the OsB12D1 is mainly located in the mitochondrion.", "\n\nTo confirm the transient expression result, Western blot analyses were performed on the purified mitochondria. ", "Firstly, the OE-F8 seeds were germinated under about 1 cm water in the dark for seven days to obtain etiolated *OsB12D1-FLAG*-OE seedling for mitochondrial isolation. ", "Consistent with the result of flooding stress, OE-F8 seeds extended the seed roots and adventitious roots more rapidly than the control under waterlogging. ", "Western blot results showed that the highest signal of anti-FLAG and anti-VDAC coexisted in the seventh and eight lanes where the mitochondria-enriched fractions are located, thereby supporting the transient expression result ([Figure 5](#ijms-15-13461-f005){ref-type=\"fig\"}B).", "\n\n{#ijms-15-13461-f005}\n\nFrom the Pfam annotation, B12D is a potential constituent of NADH--ubiquinone reductase of the electron transport chain complex I \\[[@B28-ijms-15-13461]\\]. ", "Except for response to the submergence and anoxia, the *OsB12D1* was also found to be induced by iron (Fe) deficiency ([Figure 3](#ijms-15-13461-f003){ref-type=\"fig\"}B; GSE17425; \\[[@B29-ijms-15-13461]\\]). ", "Fe is important for mitochondrial electron transport since all related enzymes contain Fe. ", "Meanwhile, OsB12D1 is highly coexpressed with two non-symbiotic hemoglobin-2 proteins (Hb2; correlation coefficient are 0.7084 and 0.6848), the Fe and oxygen binding proteins. ", "All those observations suggested that *OsB12D1* might be involved in mitochondrial electron transport. ", "To validate this hypothesis, we selected three related genes to detect their expression in the germinating seeds of *OsB12D1*-OE lines under normal and flooding conditions. ", "Those genes are the mitochondrial electron transport-related gene *Cytc1*, the non-symbiotic hemoglobin-2 gene *OsHb2,* and the Fe transport-related gene *OsNAS3*. ", "For the wild type, *Cytc1* and *OsNAS3* were significantly repressed by flooding, whereas in the *OsB12D1*-OE lines, the repressions were not remarkable, especially for OE-F6, the *Cytc1* was increased. *", "OsHb2* had relatively high expression in the three *OsB12D1*-OE lines over the wild type under normal conditions ([Figure 5](#ijms-15-13461-f005){ref-type=\"fig\"}C). ", "Under flooding, the *OsHb2* could be induced in various lines, and the expression level in OE-F6 was up to 37 times higher than that in the wild type ([Figure 5](#ijms-15-13461-f005){ref-type=\"fig\"}C). ", "These results suggested that OsB12D1 might enhance the electron transfer through coordinating the expression of related genes.", "\n\n3. ", "Discussion\n=============\n\nThe phylogenetic analyses revealed that the amino acid sequence characteristic of OsB12D1 protein is highly conserved from moss to angiosperms. ", "In rice, six *OsB12D*s shared similar gene sizes and protein sequences, while having different exon numbers and intron sizes. ", "This indicated that the long evolutionary history entailed huge variation on the gene structure, which might silence or change the gene function \\[[@B30-ijms-15-13461]\\]. ", "The two pairs of tandem duplicates shared a similar expression pattern; LOC_Os07g17330 and LOC_Os07g41350 were the major transcripts. ", "For lower expression level, LOC_Os07g17310 and LOC_Os07g41340 would tend to lose its function in the future \\[[@B31-ijms-15-13461]\\]. ", "Similar phenomena existed in barley, at least eight to nine B12D copies had been detected by primer extending experiments, while only one or two major transcripts presented in all detected tissues \\[[@B23-ijms-15-13461]\\]. ", "As a *Balem*-like gene, *OsB12D*s were mainly expressed in the germinating seed and developing seed \\[[@B18-ijms-15-13461]\\], while they were also differentially presented in other tissues, especially in the root. ", "RT-PCR showed both germination promoter and inhibitor could drive the transcription of certain *OsB12D*s. ", "Differential expression pattern indicated that functional divergence of *OsB12D*s appears along with evolution, and the multiple gene copies remaining in the genome will favor the species environment adaptation.", "\n\n*Balem* genes can respond to various cereal seed germination signals \\[[@B19-ijms-15-13461],[@B22-ijms-15-13461],[@B23-ijms-15-13461]\\]. ", "The expression of the barley *Balem* gene HvB12Dg1 was suppressed by germinating inhibitor ABA and osmotic agent mannitol, but induced by GA in germinating seeds for carrying the gibberellic acid response complex (GARC)-like element in the promoter region \\[[@B23-ijms-15-13461],[@B32-ijms-15-13461]\\], which implied the B12D might promote seed germination through a GA-dependent way. ", "In this study, *OsB12D1* was greatly inhibited by ABA and mannitol, while weakly improved by GA~3~. None of the other eight detected factors that affected seed germination could induce the *OsB12D1* expression significantly. ", "Meanwhile, overexpression of *OsB12D1* showed no significant difference in germination ability under normal conditions. ", "Since *OsB12D1* was also highly expressed in the root, these observations suggested that *OsB12D1* could not only respond to some seed germination-related signals, but also was regulated by other factors.", "\n\nThe coexpression prediction showed that *OsB12D1* might participate in the stress response, especially for anoxic or anaerobic stress. ", "The microarray data supported this prediction. *", "OsB12D1* was probed to be greatly induced in the four-day-old anoxic coleoptiles and in both of the tolerant or intolerant 14-day-old rice plants submerged for 24 h \\[[@B26-ijms-15-13461],[@B33-ijms-15-13461]\\]. ", "Consistently, the promoter of *OsB12D1* harbored two *cis*-elements of anaerobic induction motif. ", "However, from the transcriptome data of germinating seeds, in the first 30 h under anaerobic stress, the *OsB12D1* was induced very slowly in the rice embryos, and the expression of *OsB12D1* was down-regulated when germinating seeds were switched from the aerobic to anaerobic conditions \\[[@B9-ijms-15-13461]\\]. ", "Anoxia or hypoxia is the primary signal triggered by flooding stress \\[[@B34-ijms-15-13461]\\]. ", "To understand the above seemingly contradictory results, we investigated the expression of *OsB12D1* in response to the flooding in the geminating seeds and seedlings. ", "RT-PCR displayed that the expression level of *OsB12D1* was very low at the first 24 h of flooding, but increased significantly along with the prolonged flooding time ([Figure 2](#ijms-15-13461-f002){ref-type=\"fig\"}D and [Figure 3](#ijms-15-13461-f003){ref-type=\"fig\"}C), and the expression was induced both in the roots and coleoptiles when the three-day-old normally grown seedlings were transferred to flooded conditions for two days. ", "This result also explained why *OsB12D1* was abundant in the root. ", "Because rice is a semiaquatic crop, the roots are always submerged in mud. ", "From the above results, it was deduced that *OsB12D1* was sensitive to oxygen deficiency, while at an early stage of seed germination, the gene expression could be delayed by anoxic or anaerobic stress.", "\n\nUnder flooded conditions, subjected to the stresses of hypoxia and mechanical damage, the rice seed failed to protrude the radicle during germination \\[[@B14-ijms-15-13461]\\]. ", "The phenotype of germinating seeds under multi-treatments showed that the radicle is sensitive to various stresses ([Figure 2](#ijms-15-13461-f002){ref-type=\"fig\"}C). ", "Radicle emergence is the physiological indicator of the seed germination \\[[@B35-ijms-15-13461]\\]. ", "In this study, *OsB12D1-*OE seed radicles protruded and there was also an establishment of adventitious roots under flooded conditions. ", "Additionally, the transgenic seedlings grew continuously and emerged from the water. ", "After transplanting, the *OsB12D1-*OE seedlings grew better than the control with roots to adapt to the environment. ", "The roots of the *OsB12D1*-OE etiolated seedling grew more quickly than the control under waterlogging, too. ", "These results confirmed that the *OsB12D1* can enhance flooding or waterlogging tolerance during seed germination and early seedling growth. ", "The direct crop seeding in farming practice is low cost and simple in comparison to transplanting. ", "However, its large-scale adoption is restrained. ", "One of the major obstacles for rice direct seeding is poor seedling establishment by waterlogging or flooding stress in the uneven land \\[[@B36-ijms-15-13461]\\]. ", "Therefore, fine regulation of the expression of *OsB12D1* could contribute to the spread of direct seeding practices. ", "Because of the high conservation of OsB12D1 sequence across plants, this effect of flooding tolerance possibly exists in other crops.", "\n\nAccording to the Pfam annotation, B12D is analogous to the bovine mitochondrial MLRQ protein, a potential constituent of NADH-ubiquinone reductase of the electron transport chain complex I \\[[@B37-ijms-15-13461]\\]. ", "The subcellular localization results validated that OsB12D1 is mainly localized in mitochondria. ", "During seed germination, along with the function recovery of electron transport chain, the ATP content increased at the first 24 HAI, and then decreased \\[[@B38-ijms-15-13461]\\]. ", "Although the qRT-PCR result showed that the transcript of *OsB12D1* under normal conditions had a similar accumulation style with ATP, however, without consensus phosphorylation sites and cysteine-rich motifs like MLRQ, OsB12D1 is unlikely to participate in the electron transport and ATP biosynthesis directly \\[[@B39-ijms-15-13461]\\]. ", "Under flooding, mitochondrial electron transport-related gene *Cytc1* and Fe transport-related gene *OsNAS3* still maintained certain expression activity in the *OsB12D1-*OE lines, while the Fe and oxygen binding-related gene *OsHb2* was significantly induced in the *OsB12D1-*OE lines. ", "Nonsymbiotic hemoglobinsc can sequester oxygen under hypoxia and promote the NADH oxidization to provide ATP for cell growth and development \\[[@B40-ijms-15-13461]\\]. ", "In *Arabidopsis*, overexpression of *AHb2* can improve oxygen availability within developing seeds \\[[@B41-ijms-15-13461]\\]. ", "Therefore, OsB12D1 might enhance electron transport in mitochondrion through mediating Fe and oxygen availability, and then contribute to ATP biosynthesis under flooded conditions.", "\n\nRice is the only cereal plant that can germinate under flooded conditions through a rapid elongation of coleoptile. ", "This process is inhibited by ABA but promoted by ethylene and GA, associated with carbohydrate consumption \\[[@B15-ijms-15-13461],[@B27-ijms-15-13461]\\]. ", "In this study, RT-PCR indicated that GA~3~ exerted a weak effect on the expression of *OsB12D*1, while the radicle protrusion of *OsB12D1*-OE lines under flooding was not affected by the GA inhibitor PBZ. ", "Ethylene had been detected increasing quickly in the seedlings after three days of germination under flooding \\[[@B15-ijms-15-13461]\\]; the *OsB12D1* transcript also had a similar accumulation style, and ethylene-responsive transcription factor coding gene AP2/EREBP was highly coexpressed with *OsB12D1* ([Table S2](#ijms-15-13461-s001){ref-type=\"supplementary-material\"}; correlation coefficient is 0.662). ", "Ethylene is a power inhibitor of the root growth \\[[@B42-ijms-15-13461]\\]. ", "In this study, the ethylene biosynthesis inhibitor CoCl~2~ exhibited consistent promoting effects on the radicle protrusion of the wild type and *OsB12D1*-OE lines under flooding. ", "These results indicated that the *OsB12D1* gene might have a functional correlation with the ethylene while remaining independent of GA signaling.", "\n\n4. ", "Materials and Methods\n========================\n\n4.1. ", "Rice Seed Imbibition and Germinating Conditions\n----------------------------------------------------\n\nThe dehulled rice (*Oryza sativa* L. japonica. ", "cv. ", "Nipponbare) seeds were washed with distilled water three times and then imbibed in distilled water under 26 °C, 100 mmol·m^−2^ s^−1^ white light with a 16 h light/8 h dark cycle. ", "The embryos of seeds were collected at intervals of 0, 24, 48 and 72 h after imbibition, respectively. ", "For multiple germination factors' treatment analyses, the seeds were treated at 11 different conditions as follows: imbibed in water incorporated with 200 µM GA~3~, 50 mM ABA, 200 mM NaCl, 20 mM H~2~O~2~, 1 mM NaN~3~, 20% Mannitol and 15 mM SHAM, respectively; flooding with seeds directly submerged in 8 cm deep distilled water, and high- or low-temperature treatment with seeds pretreated at 40 °C and 100% relative humidity or 4 °C imbibition in the dark for three days before being transferred to germinate in benign conditions. ", "After 24 h of imbibition, the embryos of treated seeds were sliced for RNA extraction. ", "For an overexpression test, the mutant seeds were imbibed for 24 h and the embryos collected to extract RNA and protein for RT-PCR and Western blot analysis. ", "For the flooding response experiment, the seeds were geminated at normal conditions for three days, and then switched to the flooded conditions for two days; subsequently, the coleoptiles and roots were collected for RNA extraction. ", "For GA or ethylene biosynthesis inhibitor response detection, the seeds were germinated in 8 cm of water incorporated with 200 µM paclobutrazol (PBZ) and 60 µM CoCl~2~, respectively.", "\n\n4.2. ", "RNA Extraction and Quantitative Real-Time PCR\n--------------------------------------------------\n\nTotal RNA was extracted using Trizol reagent (TOYOBO, Kyoto, Japan) from the above samples and 60-day-old rice plant tissues including root, leaf, stem and spikelets. ", "The quality of RNA was checked by agarose gel electrophoresis. ", "High-quality total RNA (1 μg) treated with DNase I (Fermentas, Waltham, MA, USA) was reverse-transcribed using a First Strand cDNA synthesis kit (ReverTra Ace, TOYOBO, Kyoto, Japan), 10-fold diluted cDNA samples were used for qRT-PCR with SYBR Green Real-time PCR Mix (Bio-Rad, Hercules, CA, USA), two biological and three technical replicates analysis were performed on CFX96 Real-time system (Bio-Rad, Hercules, CA, USA). ", "PCR amplification programs was: 95 °C for 3 min, then 40 cycles of 95 °C for 10 s, 60 °C for 15 s, and 72 °C for 15 s, followed by 72 °C for 10 min. ", "The mRNA levels were normalized to the amplication of the rice 18S rRNA according to the 2^−ΔΔt^ method \\[[@B43-ijms-15-13461]\\]. ", "The relative expression level was referred to the mRNA level in 24 HAI seed embryos under normal conditions. ", "Special primers were designed with the sequence information from the RGAP database ([Table S3](#ijms-15-13461-s001){ref-type=\"supplementary-material\"}).", "\n\n4.3. ", "Generation of OsB12D1 Transgenic Rice\n------------------------------------------\n\nThe full-length cDNA of *OsB12D1* was amplified using primer pair OE-F/OE-R and inserted into the modified PUC1301 vector, resulting in an *OsB12D1* overexpression vector fused with FLAG-tag driven by the maize ubiquitin promoter. ", "The construct was transformed into *Oryza sativa* cv. ", "Zhonghua 11 using the *Agrobacterium tumefaciens*-mediated method \\[[@B44-ijms-15-13461]\\]. ", "All seeds were harvested from plants grown simultaneously in the greenhouse of Wuhan Botanic Garden and then stored for four weeks before usage.", "\n\n4.4. ", "Protoplast Transient Expression Assay\n------------------------------------------\n\nThe full-length cDNA of *OsB12D1* was amplified using primer pair Sub-F/Sub-R and inserted into vector pM999GFP (kindly provided by Dr. Jian Xu, Huazhong Agricultural University, China), resulting in a *C*-terminal fusion with GFP driven by CaMV 35S promoter. ", "The transient expression in *Arabidopsis* protoplasts was performed by PEG/calcium-mediated transformation \\[[@B45-ijms-15-13461]\\]. ", "Fluorescent signals were examined at 24 h after transformation using confocal laser microscope (Lecia SP2, Dresden, Germany). ", "GFP green images were obtained at 488 nm argon laser. ", "Mitochondria were stained with MitoTracker Red (Invitrogen, Carlsbad, CA, USA) according to the manufacturer's protocol. ", "The red fluorescence was obtained at 543 nm HeNe laser. ", "All subcellular analyses were performed at least three times in independent experiments.", "\n\n4.5. ", "Mitochondrial Isolation\n----------------------------\n\nThe Percoll gradient method was used for mitochondrial isolation from *OSB12D1-FLAG-OE* etiolated seedling \\[[@B46-ijms-15-13461]\\]. ", "After ultracentrifugation, the Percoll gradient was fractionated into nine 1 mL fractions from top to bottom, after being diluted with washing buffer five times, and the fractions were spun at 22,000 *g* for 15 min at 4 °C to collect the pellets. ", "The pellets were then dissolved with loading buffer and used for Western blot analysis.", "\n\n4.6. ", "Western Blot\n-----------------\n\nProteins were separated by 15% SDS-PAGE and electro-blotted onto PVDF. ", "The blot was probed with Anti-FLAG (Sigma, San Diego, CA, USA) or anti-VDAC (Sigma; mitochondrial membrane voltage-dependent anion channel, a mitochondrial mark protein) followed by alkaline phosphatase conjugated secondary antibody (Sigma, San Diego, CA, USA).", "\n\n4.7. ", "Database Screening and Bioinformatics Analyses\n---------------------------------------------------\n\nHomologs of the OsB12D1 protein sequence in different species were searched using the BLASTP program of NCBI. ", "For rice-conserved homologs, the key word ''B12D'' was used as query to search against the MSU-RGAP Database. ", "Multiple alignments were performed by MUSCLE software \\[[@B47-ijms-15-13461]\\]. ", "MEGA software (version 4.0) was used to perform the phylogenetic analysis. ", "The coexpression prediction, stress microarray data and heat map of the anatomical expression patterns of *OsB12D* genes in different tissues/organs were analyzed on the Rice Oligonucleotide Array Database \\[[@B25-ijms-15-13461]\\]. ", "Gene structure was analyzed by GSDS \\[[@B48-ijms-15-13461]\\]. ", "The sequence conservation of amino acids was analyzed by DNAMAN software \\[[@B49-ijms-15-13461]\\]. ", "The conserved motifs and transmembrane domains were annotated according to MEME \\[[@B50-ijms-15-13461]\\] and TMHMM \\[[@B24-ijms-15-13461]\\], respectively.", "\n\n5. ", "Conclusions\n==============\n\nIn this study, we firstly uncovered the evolution, structure, expressional pattern, function, and protein subcellular localization of a new *Balem*-like gene *OsB12D1* systematically. *", "OsB12D1* belongs to an ancient gene family and was mainly expressed in the germinating rice seed and root. *", "OsB12D1* could be significantly induced by flooding stress, and overexpression of *OsB12D1* could enhance rice flooding tolerance during seed germination by promoting seedling establishment. ", "OsB12D1 is mainly located in the mitochondrion and might be involved in Fe and oxygen availability under flooded condition. ", "The function of *OsB12D1* could be regulated by a variety of signal factors, including oxygen, ABA, ethylene, and Fe deficiency. ", "How can it be regulated by orchestra signals under flooding and contribute to the radicle protrusion? ", "The interaction protein or gene regulatory factor isolation will help to resolve these questions in the future.", "\n\nWe appreciate Rebecca Njeri's help in English editing. ", "This work was supported by grants from the National Natural Science Foundation of China (31101213).", "\n\n###### \n\nClick here for additional data file.", "\n\nPingfang Yang designed experiments and revised the manuscript; Dongli He performed the subcellular location, gene transformation and data analysis; Hui Zhang conducted qRT-PCR.", "\n\nThe authors declare no conflict of interest.", "\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "Q:\n\nWhen does an analytic function grow faster than a polynomial?", "\n\nSuppose $f$ is an analytic function with power series expansion $f(z)=\\sum_{n=0}^{\\infty} a_nz^n$, and $p = \\sum_{n=0}^{d}b_nz^n$ is a polynomial. ", "If $f$ is a polynomial of degree larger than $d$, then $|f|$ grows faster than $|p|$, but the situation is not so clear when the expansion of $f$ has infinitely many nonzero coefficients. ", "I would expect the growth of the function $f$ then to be faster than that of $p$, as with the function $e^z = \\sum_{n=0}^{\\infty}\\frac{z^n}{n!}$. However the function $\\frac{1}{1-z} = \\sum_{n=0}^{\\infty}z^n$ also has infinitely many nonzero coefficients and grows slower than any polynomial (as $|z|\\to\\infty$). ", "I realize this is related to the failure of the power series to converge outside a disk of radius $1$. Also, $log(z)$ grows slower than any polynomial, but any power series representation cannot converge on an infinite radius (The function itself cannot be well-defined everywhere in the complex plane simultaneously).", "\nUnder what conditions can we say that a power series with infinitely many nonzero coefficients represents a function that grows faster than any polynomial? ", "Is this true for any power series with infinite radius of convergence? ", "Are there such power series which grow at the rate $z^\\alpha$, for any $\\alpha\\in(0,\\infty)$?", "\nI have in mind the case where $f$ is complex-analytic, but I would also be interested to hear about the case where $f$ is real-analytic, if the cases differ.", "\n\nA:\n\nSuppose a non-polynomial function $f$ has a power series\n$$\nf(z) = \\sum_{n=0}^{\\infty} a_n z^n\n$$\nwhich converges on all of $\\mathbb{C}$. Then for each integer $n \\geq 0$ and all $r > 0$ we have\n$$\n\\begin{align}\n|a_n| &= \\left|\\frac{f^{(n)}(0)}{n!}\\right| \\\\\n&= \\left| \\frac{1}{2\\pi} \\int_{|z| = r} \\frac{f(z)}{z^{n+1}}\\,dz \\right| \\\\\n&\\leq \\frac{M(r)}{r^n}\n\\end{align}\n$$\nby Cauchy's integral theorem, where $M(r) = \\max\\limits_{|z| = r} |f(z)|$. Since there are infinitely many nonzero coefficients $a_n$ we may conclude from this that $M(r)$ grows faster than any polynomial as $r \\to \\infty$.\n\n" ]

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[ "Revascularization in left main coronary artery disease: comparison of off-pump coronary artery bypass grafting vs percutaneous coronary intervention.", "\nThere is no evidence for the increasing use of percutaneous coronary intervention (PCI) compared with surgery in patients with left main coronary artery (LMCA) disease. ", "We compared the clinical outcomes of patients with LMCA disease who had undergone PCI with those of patients who had off-pump coronary artery bypass (OPCAB) grafting. ", "From January 2001 to December 2009, 899 patients with LMCA disease were treated with OPCAB (n = 553) or PCI (n = 346). ", "Analyses using propensity-score matching were performed to minimize the selection bias. ", "We compared major adverse cardiac and cerebrovascular events (MACCE) including death, stroke, acute myocardial infarction and target-vessel revascularization. ", "The median follow-up was 55.9 months. ", "For the 159 propensity-matched pairs, the early mortality in the OPCAB group was lower than in the PCI group (0 vs 5%, the PCI group; P < 0.001). ", "Overall survival at 8 years was similar between groups (88.6 ± 3.5%, the OPCAB group vs 85.8 ± 5.3%, the PCI group; P = 0.394). ", "Freedom from MACCE at 8 years was significantly higher in the OPCAB than in the PCI group (83.9 ± 5.1 vs 60.2 ± 6.9%, P < 0.001). ", "Although there was no intergroup difference in the risk of death [hazard ratio (HR) for the PCI group, 1.435; 95% confidence interval (CI), 0.62-3.31; P = 0.396], a significant difference was found in the risk of MACCE (HR for the PCI group, 4.193; 95% CI, 2.165-8.121; P < 0.001). ", "This difference was primarily due to a higher risk of acute myocardial infarction (HR for the PCI group, 4.730; 95% CI, 0.99-22.63; P = 0.049) and higher rates of target-vessel revascularization (HR for the PCI group, 5.508; 95% CI, 1.87-16.22; P = 0.002). ", "Compared with PCI, OPCAB is associated with a lower incidence of MACCE in patients with LMCA disease, determined mainly by the lower incidences of acute myocardial infarction and target-vessel revascularization. ", "The incidence of stroke in the OPCAB group was similar to the PCI group." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Q:\n\nhow an object can obtain a pointer to the class object it belongs to c++\n\nPenelope object will need to access the getKey() method in the GameWorld class (which is the base class for your StudentWorld class), Penelope object (or more likely, one of its base classes)\nwill need a way to obtain a pointer to the StudentWorld object it belongs to. ", "If you look at code example, you’ll see how Penelope’s doSomething() method first gets a pointer to its world via a call to\ngetWorld() (a method in one of its base classes that returns a pointer to a StudentWorld), and then uses this\npointer to call the getKey() method.", "\nvoid Penelope::doSomething()\n{\n int ch;\n if (getWorld()->getKey(ch))\n {\n // user hit a key during this tick!", "\n switch (ch)\n {\n case KEY_PRESS_LEFT:\n ... move Penelope to the left ...;\n break;\n case KEY_PRESS_RIGHT:\n ... move Penelope to the right ...;\n break;\n case KEY_PRESS_SPACE:\n ... add flames in front of Penelope...;\n break;\n // etc…\n }\n}\n...\n}\n\ncode for getWorld() is actually required\n\nA:\n\nA minimal example compatible with your question\n#include <iostream>\n\nclass GameWorld {\n public:\n int getKey(int & k) const { k = 123; }\n};\n\nclass StudentWorld : public GameWorld {\n};\n\nclass Student {\n public:\n Student(StudentWorld * w) : world_(w) {}\n\n StudentWorld * getWorld() const { return world_; }\n\n private:\n StudentWorld * world_;\n};\n\nclass Penelope : public Student {\n public:\n Penelope(StudentWorld * w) : Student(w) {}\n void doSomething();\n};\n\nvoid Penelope::doSomething()\n{\n int ch;\n\n getWorld()->getKey(ch);\n std::cout << ch << std::endl;\n}\n\nint main()\n{\n StudentWorld sw;\n Penelope pe(&sw);\n\n pe.doSomething();\n}\n\nI give/memorize the world through a pointer rather than a reference/weak_ptr because strangely getWorld visibly returns a pointer\nI do a direct inheritance between Penelope and the owner of getWorld() even the question says it may not be direct, and I name that owner Student just because seem consistent\nIn the question Penelope object is strange and must be Penelope's object or Penelope instance because Penelope is a class rather than an instance\n\nNew version because of your remark where the Penelope instance is created by StudentWorld but you have to understand like that StudentWorld knows Penelope class and this bad, a fabric or something like that have to be used. ", "May be StudentWorld known Student to memorize all of their instances but certainly not a child class like Penelope\n#include <iostream>\n\nclass GameWorld {\n public:\n int getKey(int & k) const { k = 123; }\n};\n\nclass Penelope;\n\nclass StudentWorld : public GameWorld {\n public:\n Penelope * createPenelope();\n};\n\nclass Student {\n public:\n Student(StudentWorld * w) : world_(w) {}\n\n StudentWorld * getWorld() const { return world_; } \n\n private:\n StudentWorld * world_;\n};\n\nclass Penelope : public Student {\n public:\n Penelope(StudentWorld * w) : Student(w) {}\n void doSomething();\n};\n\nPenelope * StudentWorld::createPenelope()\n{\n // probably the instance is not just returned\n // but also memorized to save all the students\n return new Penelope(this);\n}\n\nvoid Penelope::doSomething()\n{\n int ch;\n\n getWorld()->getKey(ch);\n std::cout << ch << std::endl;\n}\n\nint main()\n{\n StudentWorld sw;\n Penelope * pe = sw.createPenelope();\n\n pe->doSomething();\n}\n\nCompilation and execution :\npi@raspberrypi:/tmp $ g++ -pedantic -Wextra -g w.cc\npi@raspberrypi:/tmp $ ./a.out\n123\n\n" ]

{ "pile_set_name": "StackExchange" }

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"end": 2165, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2157 }, { "analysis_explanation": null, "end": 2255, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2247 }, { "analysis_explanation": null, "end": 2356, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2348 }, { "analysis_explanation": null, "end": 2429, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_140094861343280", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2426 }, { "analysis_explanation": null, "end": 2540, "entity_type": "PERSON", "recognition_metadata": { 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"SpacyRecognizer" }, "score": 0.85, "start": 3352 }, { "analysis_explanation": null, "end": 634, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_140094861343856", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 632 }, { "analysis_explanation": null, "end": 1586, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_140094861343856", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1584 }, { "analysis_explanation": null, "end": 1646, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_140094861343856", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1644 }, { "analysis_explanation": null, "end": 1665, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_140094861343856", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1663 }, { "analysis_explanation": null, "end": 3056, 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"UrlRecognizer_140094861343568", "recognizer_name": "UrlRecognizer" }, "score": 0.5, "start": 1729 }, { "analysis_explanation": null, "end": 3362, "entity_type": "URL", "recognition_metadata": { "recognizer_identifier": "UrlRecognizer_140094861343568", "recognizer_name": "UrlRecognizer" }, "score": 0.5, "start": 3357 }, { "analysis_explanation": null, "end": 3482, "entity_type": "URL", "recognition_metadata": { "recognizer_identifier": "UrlRecognizer_140094861343568", "recognizer_name": "UrlRecognizer" }, "score": 0.5, "start": 3478 } ]

[ "Vibrational spectroscopic (FT-IR, FT-Raman, SERS) and quantum chemical calculations of 3-(10,10-dimethyl-anthracen-9-ylidene)-N,N,N-trimethylpropanaminiium chloride (Melitracenium chloride).", "\nFT-IR, FT-Raman spectra of Melitracenium chloride were recorded and analyzed. ", "SERS spectrum was recorded in silver colloid. ", "The vibrational wavenumbers were computed using DFT quantum chemical calculations. ", "The data obtained from wavenumber calculations are used to assign vibrational bands obtained in infrared and Raman spectra as well as in SERS of the studied molecule. ", "Potential energy distribution was done using GAR2PED program. ", "The geometrical parameters (SDD) of the title compound are in agreement with the XRD results. ", "The presence anthracene ring modes in the SERS spectrum suggest a tilted orientation with respect to the metal surface. ", "The methyl groups in the title molecule are also close to the metal surface. ", "The first hyperpolarizability, NBO analysis and molecular electrostatic potential results are also reported." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.005263157894736842, 0, 0.021739130434782608, 0.012048192771084338, 0.005988023952095809, 0, 0.02127659574468085, 0, 0, 0.009259259259259259 ]

[]

[ "import os\nfrom testing.testcases import LiveTornadoTestCase\nfrom testing.selenium_helper import SeleniumHelper\nfrom selenium.webdriver.support.ui import WebDriverWait\nfrom selenium.webdriver.common.keys import Keys\nfrom selenium.webdriver.common.by import By\nfrom selenium.webdriver.support import expected_conditions as EC\n\nfrom django.conf import settings\n\n\nclass UsermediaOverviewTest(LiveTornadoTestCase, SeleniumHelper):\n\n @classmethod\n def setUpClass(cls):\n super(UsermediaOverviewTest, cls).setUpClass()\n cls.base_url = cls.live_server_url\n driver_data = cls.get_drivers(1)\n cls.driver = driver_data[\"drivers\"][0]\n cls.client = driver_data[\"clients\"][0]\n cls.driver.implicitly_wait(driver_data[\"wait_time\"])\n cls.wait_time = driver_data[\"wait_time\"]\n\n @classmethod\n def tearDownClass(cls):\n cls.driver.quit()\n super(UsermediaOverviewTest, cls).tearDownClass()\n\n def setUp(self):\n self.verificationErrors = []\n self.accept_next_alert = True\n self.user = self.create_user(\n username='Yeti',\n email='yeti@snowman.com',\n passtext='otter1'\n )\n self.login_user(self.user, self.driver, self.client)\n\n def test_overview(self):\n driver = self.driver\n driver.get(self.base_url + \"/usermedia/\")\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'All categories'])[1]/following::button[1]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[1]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[1]\").clear()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[1]\"\n ).send_keys(\"landscape\")\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::span[3]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[2]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[2]\"\n ).clear()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[2]\"\n ).send_keys(\"people\")\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::span[4]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[3]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[3]\"\n ).clear()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::input[3]\"\n ).send_keys(\"scientific\")\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit Categories'])[1]/following::button[2]\"\n ).click()\n driver.refresh()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'All categories'])[1]/following::button[1]\"\n ).click()\n self.assertEqual(\"landscape\", driver.find_element_by_id(\n \"categoryTitle_1\").get_attribute(\"value\"))\n self.assertEqual(\"people\", driver.find_element_by_id(\n \"categoryTitle_2\").get_attribute(\"value\"))\n self.assertEqual(\"scientific\", driver.find_element_by_id(\n \"categoryTitle_3\").get_attribute(\"value\"))\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Submit'])[1]/following::button[1]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Edit categories'])[1]/following::button[1]\"\n ).click()\n driver.find_element_by_name(\"title\").click()\n driver.find_element_by_name(\"title\").send_keys(\"An image\")\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Select categories'])[1]/following::label[1]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'landscape'])[1]/following::label[1]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'people'])[1]/following::label[1]\"\n ).click()\n # image path\n imagePath = os.path.join(\n settings.", "PROJECT_PATH,\n 'usermedia/tests/uploads/image.png'\n )\n driver.find_element_by_name(\"image\").send_keys(imagePath)\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'scientific'])[1]/following::button[1]\"\n ).click()\n image_title = WebDriverWait(driver, self.wait_time).until(\n EC.presence_of_element_located((By.", "CLASS_NAME, \"edit-image\"))\n )\n self.assertEqual(\"An image\", image_title.text)\n search_input = driver.find_element_by_css_selector(\n \".fw-overview-menu-item .fw-button input[type=text]\")\n search_input.click()\n search_input.send_keys(\"fish\")\n self.assertEqual(\"No images available\", driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Size (px)'])[1]/following::td[1]\"\n ).text)\n search_input.send_keys(Keys.", "BACKSPACE)\n search_input.send_keys(Keys.", "BACKSPACE)\n search_input.send_keys(Keys.", "BACKSPACE)\n search_input.send_keys(Keys.", "BACKSPACE)\n self.assertEqual(\"An image\", driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Size (px)'])[1]/following::span[3]\"\n ).text)\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'PNG'])[1]/following::i[1]\"\n ).click()\n driver.find_element_by_xpath(\n \"(.//*[normalize-space(text()) and normalize-space(.)=\"\n \"'Confirm deletion'])[1]/following::button[2]\"\n ).click()\n image_placeholder = WebDriverWait(driver, self.wait_time).until(\n EC.presence_of_element_located((By.", "CLASS_NAME, \"dataTables-empty\"))\n )\n self.assertEqual(\"No images available\", image_placeholder.text)\n\n def tearDown(self):\n self.driver.quit()\n self.assertEqual([], self.verificationErrors)\n" ]

{ "pile_set_name": "Github" }

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[ "Integration of gross anatomy in an organ system-based medical curriculum: strategies and challenges.", "\nThe University of Alabama School of Medicine (UASOM) instituted a fully integrated, organ system-based preclinical curriculum in 2007. ", "Gross anatomy and embryology were integrated with other basic science disciplines throughout the first two years of undergraduate medical education. ", "Here we describe the methods of instruction and integration of gross anatomy and embryology in this curriculum as well as challenges faced along the way. ", "Gross anatomy and embryology are taught through a combination of didactic lectures, team-based learning activities, and cadaveric dissection laboratories. ", "Vertical integration occurs through third- and fourth-year anatomy and embryology elective courses. ", "Radiology is integrated with anatomy instruction through self-study modules and hands-on ultrasound sessions. ", "Our model of anatomy instruction is time efficient, clinically relevant, and effective as demonstrated by student performance on the United States Medical Licensing Examination(®) (USMLE(®) ) Step 1 examination. ", "We recommend that medical schools considering full integration of gross anatomy and embryology (1) carefully consider the sequencing of organ system modules, (2) be willing to sacrifice anatomical detail for clinical application, (3) provide additional electives to third- and fourth-year students, and (4) integrate radiology with anatomical education." ]

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[ "It is widely accepted that a cornerstone of effective breast cancer chemotherapy is to maximise the appropriate dose while minimising the often unpleasant and debilitating side effects. ", "A recent study in women receiving chemotherapy in the first 12 months after diagnosis for breast cancer showed that the incidence of serious effects requiring emergency intervention in hospital (61%) is likely to be higher than that predicted from clinical trial data ([Hassett *et al*, 2006](#bib6){ref-type=\"other\"}). ", "While support medication strategies have improved over the years, it is not uncommon for patients to become reluctant to continue with further cycles of treatment if they have already experienced side effects from initial cycles of chemotherapy ([Craig and Powell, 1987](#bib5){ref-type=\"other\"}; [Atkins and Fallowfield, 2006](#bib1){ref-type=\"other\"}). ", "Chemotherapy support medication is co-prescribed with the intention of minimising side effects with the hope that this will improve chemotherapy concordance, which in turn will assist the success of chemotherapy.", "\n\nResearch has indicated that cancer patients who concord with oral chemotherapy regimens have a higher survival rate than those who do not ([Porzsolt *et al*, 1989](#bib11){ref-type=\"other\"}; [Spiegel, 1997](#bib13){ref-type=\"other\"}).", "\n\nConcordance can be described as a process of prescribing and medicine taking in a prescriber -- patient partnership ([Stevenson, 2001](#bib14){ref-type=\"other\"}). ", "This is particularly important in situations like chemotherapy support medication, where the patient must first recognise the side effect of the chemotherapy, then select the correct drug and self-administer the right dose for the correct period, remote from her immediate healthcare team. ", "All members in the healthcare team have a responsibility to foster concordant relationships with patients. ", "Prescribing physicians may not be able to do this for a variety of reasons ([Stevenson *et al*, 2000](#bib15){ref-type=\"other\"}). ", "These include lack of time to discuss individual medication issues such as potential side effects (what to look out for and what to do about them) and because the prescribing setting may not lend itself to effective counselling.", "\n\nCancer patients face the challenges of understanding often complex and protracted chemotherapy regimens, their side effects and management, while at the same time coming to terms with a potentially life-threatening diagnosis. ", "Acceptance of treatment is largely based on the reality of a terminal condition without it and patient understanding of how chemotherapy can be made less debilitating with support medication is fundamental to building a concordant relationship.", "\n\nPharmacists and more recently, pharmacy technicians counsel patients on their medications in a variety of settings as part of routine clinical pharmacy practice. ", "Patients may have good access to staff on the ward where they receive their chemotherapy, but a busy ward frequently is not conducive to effective information transfer. ", "Studies conducted by pharmacists in other disciplines, such as anticoagulation ([Radley and Hall, 1994](#bib12){ref-type=\"other\"}; [Boddy, 2001](#bib4){ref-type=\"other\"}), dermatology ([Tucker, 2004](#bib16){ref-type=\"other\"}) and palliative care ([Austwick *et al*, 2002](#bib2){ref-type=\"other\"}) which showed improved quality of care, patient understanding and use of resources, suggest that the outpatient clinic may be a suitable alternative setting.", "\n\nLike many breast cancer clinics, patients are seen at Worthing Hospital under a shared care agreement with another local NHS Trust. ", "A co-ordinated, multi-disciplinary team approach relies for its success on good communication between clinicians, chemotherapy nurses on the Medical Day Case Unit (MDCU) and pharmacists and pharmacy technicians working in aseptic services. ", "Prior to this study, any pharmaceutical issues surrounding their support medication could only be resolved post-clinic, when the physician had departed. ", "It was suggested that the service, which was under increasing capacity pressures, could be improved by direct pharmacy involvement at clinic level, when the patient and all healthcare team members were present.", "\n\nA pharmacy technician who has successfully completed an accredited medicines management course is deemed to be competent in routine medication review and drug history taking. ", "These are useful attributes when educating patients on their chemotherapy support medication and assessing their ability to cope with this. ", "This then frees the pharmacist to deal with more complex pharmaceutical care issues raised by the latter, such as drug interactions and side effects, thus making best use of pharmacy resources.", "\n\nAs a result, a pharmacy technician-led outpatient clinic for breast cancer patients being treated on MDCU at Worthing Hospital was proposed. ", "This was considered a potentially useful setting in which to perform a complete medication review and research its effect, through a controlled study on a range of features of patient care.", "\n\nMETHODS\n=======\n\nApproval for the study including all data collection forms and methods, was obtained from the West Sussex Local Research Ethics Committee (04/Q1911/45) and the Sussex NHS Research Consortium (0457/WASH/2004) on 23/11/04 and 6/1/05 respectively, prior to commencement of the study.", "\n\nTechnician training and accreditation\n-------------------------------------\n\nThe research technician (BR) underwent the South East Medicines Management Education and Development Team\\'s accredited medicines management course. ", "The course consists of private study, supplemented with study days and is assessed by demonstration of competence in work-based activities in a written portfolio and observed structured clinical examination. ", "This provided a knowledge and skills framework that was supplemented by additional directed study on patient counselling, chemotherapy regimens for breast cancer and relevant support medication, identification of side effects and drug interactions. ", "Assessment of the pharmacy technician\\'s knowledge of chemotherapy support medication was conducted by formal written examination. ", "Assessment of the technician\\'s counselling skills was undertaken by in-practice observation following completion of a Trust in-house counselling course.", "\n\nAll assessment and training was undertaken during one year (February 2004 to January 2005). ", "Following assessment, the technician was established within the outpatient clinic in a dedicated consulting office. ", "Approval for this was obtained from the consultant oncologist treating breast cancer patents at Worthing Hospital and the senior nursing staff on MDCU and in the Outpatient Department.", "\n\nStudy design\n------------\n\nThe research took the form of a randomised, controlled study, outlined in [Figure 1](#fig1){ref-type=\"fig\"}. ", "The project lasted 12 months including a 1-week pilot study consisting of ten patients to assess applicability of procedures and data collection forms. ", "The pilot indicated that no appreciable changes to protocol or data collection procedures were required and the ten pilot patients were included in the overall analysis.", "\n\nPatient recruitment\n-------------------\n\nPatients with a diagnosis of breast cancer and on course 2, 3 or 4 of their chemotherapy, as identified from their records, were approached by the chief investigator (HR) on attending MDCU. ", "Each patient was provided with verbal and written information about the research and asked to provide written consent. ", "Patients receiving treatment for either adjuvant or metastatic disease receiving a variety of regimens, were included. ", "Patients under 18 years old were excluded.", "\n\nConsenting participants were informed that on their next MDCU visit, they would be asked a series of questions testing their understanding of their support medication.", "\n\nPatient randomisation\n---------------------\n\nPatients were randomised to either the control arm, where they received conventional care, including routine ward counselling from a nurse on the use of their support medication prior to discharge, or to the experimental arm where they attended the pharmacy technician-led outpatient clinic. ", "Randomisation was by a computer-generated random number table produced in Microsoft Excel. ", "Each patient received an information sheet explaining which study arm they had been allocated to and what this involved.", "\n\nPatient assessment at follow-up\n-------------------------------\n\nPatients were interviewed by the chief investigator at their next outpatient appointment after a further chemotherapy cycle (usually of 3 weeks\\' duration) had been completed.", "\n\nControl arm\n-----------\n\nPrior to their next visit, subjects were sent a letter inviting them to arrive early at the clinic and to bring a copy of their GP repeat medication list with them. ", "At the clinic and prior to their scheduled consultant appointment, they were also interviewed about this list and any other medications they were taking in addition to their chemotherapy. ", "The information was used to compile an accurate drug history and to highlight any potential drug interactions with the patient\\'s chemotherapy or chemotherapy support medication. ", "Any problems so identified were forwarded to the consultant to discuss with the patient when they saw them at the allocated time.", "\n\nThe prescription for the patient\\'s next cycle of chemotherapy resulting from the consultation was tracked via the pharmacy aseptic department. ", "Any issues that arose from this prescription were resolved by that department\\'s personnel and recorded as part of the study. ", "This was primarily to document the time taken to resolve prescription problems by contacting the consultant after the clinic.", "\n\nAt their subsequent clinic appointment, patient understanding of their support medication was re-assessed as at baseline.", "\n\nResearch arm\n------------\n\nPatients were asked to attend the pharmacy technician-led outpatient clinic prior to seeing the consultant oncologist at their next outpatient appointment clinic. ", "At the pharmacy technician-led clinic, the following issues were recorded: A full drug historyPotential drug interactionsWhether supplies of support medications were requiredThe patient\\'s perception of the clinic and whether they found it beneficial or not.", "\n\nInformation from items 2 and 3 was noted and attached to the patient\\'s notes so that the consultant could make use of it when consulting with the patient.", "\n\nAfter the consultation, the resulting prescription was tracked as in the control arm.", "\n\nPatients were interviewed again by the chief investigator prior to their next consultant appointment, to assess their knowledge of support medication. ", "As with the control arm, this took place after two chemotherapy cycles had elapsed since enrolment. ", "The chief investigator remained unaware of which arm of the trial each patient was in.", "\n\nPrimary outcome measure -- baseline assessment of patient understanding of support medication\n---------------------------------------------------------------------------------------------\n\nThe chief investigator (HR) interviewed each consented patient using a standard question set, asking the patient to explain what each of their support medications was for and how they used it. ", "Assessments were recorded as an overall rating of the subject\\'s understanding on a Likert scale from 1=very poor to 5=very good, plus a drug-specific score derived from marks awarded for various pieces of information: drug name (+2); indication (+2); dose frequency (+2); dose duration (+1); dose (+1). ", "Thus the maximum score per drug was 8 and the minimum 0. ", "The average score per drug was also calculated. ", "Assessments were conducted prior to randomisation; the chief investigator was blind during subsequent, post-randomisation assessments.", "\n\nSecondary outcome measures\n--------------------------\n\nThere were a number of secondary outcomes of interest. ", "All secondary outcome measures were compared between control and clinic arms directly. ", "The numbers of patients experiencing delays in receiving their chemotherapy.", "The numbers of patients requiring chemotherapy dose reductions.", "Numbers of patients having potential drug interactions between GP prescribed medication and chemotherapy or chemotherapy support medication.", "The number of chemotherapy support medication items supplied per patient.", "The average cost of chemotherapy support medication supplied per patient.", "The numbers and costs of chemotherapy support medication not supplied.", "The average amount of pharmacy time per patient spent resolving medication issues.", "The numbers of patients requiring a prescription intervention at the point of dispensing.", "\n\nAll medication costs were calculated using hospital prices prevailing at the time of the study.", "\n\nData analysis\n-------------\n\nAll statistical analyses were conducted using Minitab version 13 (Minitab Inc., State College, PA, USA), taking *P*\\<0.05 as an acceptable level of probability indicating statistical significance.", "\n\nFor the primary outcome measure (patient knowledge score) mean scores were compared before and after clinic attendance in both the control and clinic arms using Student\\'s *t*-test.", "\n\nFor the secondary outcome measures, the proportions of patients experiencing chemotherapy delays and reductions were compared using the *χ*^2^ test.", "\n\nThe numbers of chemotherapy support medications supplied for each patient were compared using the Mann--Whitney *U*-test and the mean costs of items supplied were compared using a two-sample *t*-test. ", "The mean times spent resolving prescription issues in the two study arms were compared using a two-sample *t*-test.", "\n\nRESULTS\n=======\n\nAll the chemotherapy regimens encountered in this study were prescribed against standard proformas, used on a day to day basis across the Sussex Cancer Network; these had been checked and verified across the whole cancer network, and were last scrutinised as part of the National Cancer Peer Review Programme in 2005/6. ", "Antiemetics were also prescribed according to the cancer network guidelines on the prevention and treatment of nausea and vomiting in adults receiving chemotherapy. ", "The prescribing of support medication was absolutely consistent across the two arms of the trial as the same standard network chemotherapy proformas were used.", "\n\nChemotherapy regimens varied between patients according to disease stage and comorbidity. ", "Patients were not stratified during randomisation for the nature of the chemotherapy regimen used or cycle of therapy. ", "Actual regimens and cycle numbers for control and clinic arms are shown in [Table 1](#tbl1){ref-type=\"table\"}; there was a significantly higher proportion of patients receiving adjuvant therapy in the clinical arm compared to the control (*P*=0.003, *χ*^2^=9.074). ", "There were no differences in cycle numbers. ", "The imbalance between the two arms of the trial, in the numbers of patients receiving trastuzumab monotherapy, is discussed below.", "\n\nOne patient withdrew from each arm of the study, so the base in each was reduced to 69. ", "Key results are summarised in [Table 2](#tbl2){ref-type=\"table\"}.", "\n\nPrimary outcome: level of patient understanding about support medication\n------------------------------------------------------------------------\n\nThere were no statistically significant differences between the mean baseline scores in the control and clinic arms (*P*=0.942) or between second measurement and baseline in the control arm (*P*=0.822). ", "In contrast, the difference from baseline in the clinic arm was very highly significant (*P*\\<0.001).", "\n\nSecondary outcome measures\n--------------------------\n\nSignificantly fewer patients experienced chemotherapy delays after attending the pharmacy technician-led clinic (*P*=0.001) and significantly fewer patients also experienced chemotherapy dose reductions (*P*=0.003).", "\n\nForty-seven (33.8%) of the 139 patients eligible for baseline evaluation had potential drug interactions highlighted. ", "The difference between the control and clinic arms was not statistically significant (*P*=0.188); these data suggest that the pharmacy technician-led clinic detected more potential drug interactions but this hypothesis is unproven. ", "Most drug interactions were between GP prescribed medication and chemotherapy support medication rather than the chemotherapy itself. ", "The most common interactions were between corticosteroids and non-steroidal anti-inflammatory drugs, antidiabetic agents, antiepileptic agents and antihypertensive medication. ", "In the majority of cases it was accepted that a short course of corticosteroids would not lead to a clinically significant interaction with these other agents; however, it would be unwise to assume that this would be the case in all patients where polypharmacy and comorbidities may mitigate.", "\n\nThere were significantly fewer chemotherapy support items supplied per patient in the clinic arm compared to the control (*P*\\<0.001); this cross-correlated with additional data from the pharmacy technician-led clinic where the median number of items not supplied was also three. ", "The bulk of unnecessary prescribing consisted of antiemetics and mouth care products; G-CSF was also prescribed unnecessarily in a small number of patients. ", "A pilot study had shown that it took an average of 3.6 min for a pharmacy technician to dispense and a pharmacist to check an item of chemotherapy support medication; this represented a time saving of approximately 10.8 min per breast cancer patient in this study. ", "If the over-prescription at the first cycle was perpetuated over the full five courses of therapy, then a total of 54 min of pharmacy time would be wasted. ", "In terms of dispensary time saved, this would amount to approximately 146 h per annum.", "\n\nThere was a highly significant reduction in mean cost of items supplied to control patients compared to clinic patients (*t*=3.34, point estimate for difference=16.49, CI=6.72--26.26, *P*\\<0.001). ", "Information collected in the research arm allowed calculation of a mean cost of medication not supplied of £17.54 per patient. ", "Again, if over-prescription was perpetuated over five courses, this would be a waste of £87.70 and projecting over a typical year involving 162 patients, a saving of £14207.40 could be made.", "\n\nTechnician time invested overall in the clinic amounted to 24.7 h per annum, costing £305.29 (based on current salary scales). ", "This input was calculated by subtracting the time saved not having to resolve prescription-related problems post-clinic from the actual time expended in the clinic. ", "In addition, the technician time saved by not dispensing unnecessary items was 146 h per annum, costing £1804.56. ", "Therefore, the total time saved was 146--24.7=121.3 h per annum, saving £1499.27.", "\n\nThe above savings should be set against the cost of the initial technician training in medicines management (approximately £1800); but this is a one-off investment paid for by the Strategic Health Authority and a mandatory requirement of standard post-qualification training for all pharmacy technicians in the Trust. ", "The additional costs incurred in preparing the technician for the cancer clinic role were £155 -- again a one-off investment.", "\n\nThe mean cost of items wasted from previous supplies returned to the pharmacy by patients in the clinic arm of the study and subsequently destroyed was £26.70. ", "As an indication of unnecessary wastage this would amount to an annual saving of £4325.40, based on the throughput of breast cancer patients at Worthing Hospital. ", "This is probably a minimum, as patients do not always return unwanted or unused medicines to the pharmacy.", "\n\nThere was a highly significant reduction in the amount of pharmacy time per patient spent resolving prescription issues in the clinic arm compared to the control arm of this study (*t*=5.31, point estimate for the difference=8.0, 95%CI=5.05--11.04, *P*\\<0.001); fewer patients required a prescription intervention at the point of dispensing in the clinic arm compared to the control arm (30 *vs* 45.7%) but the difference did not reach statistical significance (df=1, *χ*^2^=3.439, *P*=0.064); but together, these results suggest that those interventions required in the clinic patients were of a more complex nature.", "\n\nDISCUSSION\n==========\n\nThe pharmacy technician-led clinic for breast cancer patients could easily be developed for other cancer specialities where routine chemotherapy support medications are used. ", "The hospital clinic is a suitable environment for such exercises. ", "While no other similar published reports could be found, the benefits of medication review clinics in other specialities have been noted. [", "Morlidge (2001)](#bib10){ref-type=\"other\"} reported upon the introduction of a renal medication review clinic that showed similar benefits, such as identification and withdrawal of unnecessary drugs, avoidance of unnecessary repeat medication, improved concordance with therapy, better drug history taking and reductions in wastage of drugs and pharmacy time. ", "Running the clinic alongside the consultant clinic facilitated prompt liaison and ensured medication problems were promptly resolved. [", "Austwick *et al* (2002)](#bib2){ref-type=\"other\"} reported the results of a study in palliative care, where drug regimens can be as complex as those in cancer chemotherapy; it was shown that the pharmacist\\'s input into the outpatient clinic proved invaluable. ", "In general, patients left the pharmacy clinic with a better understanding of their medication as well as knowing how to combat unpleasant side effects. ", "Supply of medication was more efficient, drug histories were kept up to date and medication problems were better addressed.", "\n\nPatient knowledge\n-----------------\n\nAfter their initial diagnosis, breast cancer patients at Worthing Hospital receive an explanation of their chemotherapy treatment and its potential side effects from specialist nursing staff on MDCU. ", "Patients then receive their first cycle of chemotherapy after which they are given their chemotherapy support medication with a one-off explanation of how, when and why each item should be taken. ", "This study has shown that patients who attend the pharmacy technician-led clinic had a significantly better level of understanding of their chemotherapy support medication compared to control patients receiving best standard care.", "\n\nPharmacy and nursing staff play key roles in educating patients about their medicines; both are equipped with specialist knowledge needed to relay important treatment information to patients. ", "Exploration of the factors that may have influenced the success of the pharmacy technician-led clinic is worthwhile.", "\n\nChemotherapy is complex. ", "The stigma surrounding cancer and its treatment can understandably be very disheartening for patients who after diagnosis, receive a plethora of important information about their new (to them) condition. ", "Some of this is re-emphasised, often at the patient\\'s request, during the first chemotherapy session on the ward. ", "Apprehension and the chemotherapy itself can often leave the patient feeling very tired and confused. ", "Anecdotally, patients at the pharmacy technician-led clinic voiced the opinion that an environment away from the ward was more relaxing and that in the ward environment, their concentration had declined significantly before they received information on their chemotherapy support medication. ", "In contrast, the pharmacy technician-led clinic provided an atmosphere where they felt able to ask questions about their support medication and absorb the information. ", "The co-ordination of pharmacy and nursing input may therefore be a crucial step in improving this aspect of care.", "\n\nMany different aides memoir or treatment prompts were observed to be used by patients in this study. ", "These ranged from handwritten notes on the outer cartons to complete computer spreadsheets allowing dose administration records to be kept. ", "Patients with more support medications relied heavily on these treatment prompts and it was observed that in general, those without prompts, particularly those taking larger numbers of support medications, knew the least about their medications. ", "These patients scored poorly on the knowledge rating scale; this was undoubtedly exacerbated by the fact that their mean score was computed from a high number of treatments.", "\n\nThe scoring system used in this study was subjective but applied consistently by one person (the chief investigator). ", "Its application in practice allowed simple rules to be used to assist consistency. ", "The scale was designed to allow weighting of parameters depending on their importance to the patient\\'s understanding of their treatment with more emphasis on drug name, indication and frequency than strength and duration. ", "Interestingly, the most common information omitted by patients during interview was indication and strength. ", "These two pieces of information are very useful, but for different reasons. ", "While the former is obviously important when the patient has to select the appropriate support medication for symptom relief from a range of medicines, the strength is of importance when supplying the information to a healthcare professional so that a further supply or appropriate substitute can be organised. ", "The scale also demonstrated consistency over time. ", "In the control arm, there was little variation in baseline and follow-up scores (see [Table 2](#tbl2){ref-type=\"table\"}).", "\n\nIn general, patients tended to rate their level of understanding of support medication higher than the investigator at both stages of the study. ", "This was the first question they were asked during the interview. ", "Following the assessment questions, many were surprised at how little they knew. ", "Self rating may have been lower if the initial question had been asked at the end.", "\n\nWhatever the patient\\'s initial level of understanding about their support medication the study has demonstrated that the pharmacy technician-led clinic produced significant improvements. ", "Work from a wide range of disciplines and clinical settings, indicates that improved knowledge about their medications is linked to improved patient concordance with therapy; although it seems difficult to demonstrate beyond doubt. [", "Horne (1998a)](#bib7){ref-type=\"other\"} cites evidence for a direct link between adherence to medication and perceived symptomatic benefit; in our case, improved control of the side effects of cancer chemotherapy. ", "Clearly the pharmacy technician-led clinic is an excellent opportunity to impart benefit information.", "\n\n[Horne (1998b)](#bib8){ref-type=\"other\"} undertook an extensive review of the literature surrounding the factors affecting adherence. ", "He found that although a basic awareness of how and when to take medicines was one pre-requisite for adherence it was insufficient on its own; other factors such as the patient\\'s general health beliefs and specific beliefs about medicines also played an important part; furthermore, patients who were more satisfied with their care were more likely to adhere to their treatment regimen. ", "More specifically, [Craig and Powell (1987)](#bib5){ref-type=\"other\"} observed that effective management of chemotherapy-induced emesis improved overall patient adherence and enhanced the effectiveness of patients\\' chemotherapy. ", "The pharmacy technician-led clinic in our study provided the opportunity for a full discussion on the support medication in the context of the patient\\'s primary cancer chemotherapy, both in terms of symptom recognition, choice of support medication and clarification of dosage instructions. ", "Patients were also given the opportunity to ask questions about their management.", "\n\nBreast cancer and its treatments involve many different facets for the patient to get to grips with. [", "Horne (1998b)](#bib8){ref-type=\"other\"} has suggested that in complex diseases, a patient who receives the information over time in a variety of appropriate settings is likely to absorb more and be a more concordant, happier and hopefully healthier patient. ", "A one-off session at the start of treatment is unlikely to be as effective as successive encounters, where the patient can discuss progress and have new enquiries dealt with ([Horne, 2000](#bib9){ref-type=\"other\"}). ", "This supports the repeat use of the pharmacy technician-led clinic on each visit to the breast cancer clinic.", "\n\nFor most cancer patients, acceptance of chemotherapy is based on the reality of a potentially terminal condition without it. ", "Once this initial step has been taken, information on how to modify the debilitating effects of chemotherapy is fundamental to building a successful concordant relationship based around the patient\\'s needs. ", "The healthcare team need to work on this concordant relationship with the patient by providing excellent support that engages in activities that maximise benefit from the patient\\'s perspective.", "\n\nIt has been demonstrated that more active listening by healthcare professionals is needed to avoid missing important verbal and non-verbal signals that need to be followed up with the patient ([Blenkinsopp, 2001](#bib3){ref-type=\"other\"}). ", "The successful delivery of information must include an interactive discussion with the patient. ", "It has been suggested that non-concordance may stem not from lack of understanding but rather a conscious decision by a patient not to take his/her medication as directed. ", "The reasons for this are undoubtedly multifactorial but must surely include the fear of medication side effects. ", "Once they have accepted their diagnosis and the need for chemotherapy and have recognised the side effects of the latter, cancer patients with a better understanding of how those effects may be minimised with additional medicines may be expected to concord with their support medication. ", "This decision might be reinforced by the knowledge that poor tolerance of chemotherapy might lead to dose reductions, treatment delays and possible disease progression or recurrence.", "\n\nWhilst the association between the patient\\'s level of understanding and treatment concordance cannot be assumed from this research, it is clear that the connection between the two concepts is becoming increasingly important to understand.", "\n\nThis study highlighted that further work needs to carried out on the association between level of patient understanding of therapy and treatment concordance. ", "This is particularly important where the patient is being empowered to recognise the side effects of one set of medications (the chemotherapy) and self-treat by selection from a range of other medications (chemotherapy support medication). ", "At this stage, it is sufficient to conclude that pharmacy input achieves greater understanding of these aspects in breast cancer patients.", "\n\nChemotherapy delays and dose reductions\n---------------------------------------\n\nThe pharmacy technician-led clinic produced significantly fewer treatment delays and dose reductions in this study. ", "In most cases, delay was due to poor tolerance, which resulted in a dose reduction. ", "The most common reason for delay was uncontrolled nausea and vomiting and there were notably more patients in the control arm (17) compared to the clinic arm (6). ", "This is one area where the clinic appeared to be making an impact in terms of proper use of support medication, particularly with regard to use of appropriate antiemetic medication. ", "Patients receiving adjuvant therapy might be expected to suffer from nausea and vomiting to a greater extent than patients receiving therapy for metastases and there were more of the latter in the clinic arm of the trial. ", "In some cases, nausea and vomiting had been so severe that hospital admission was necessary to allow resultant dehydration to be resolved before administration of further chemotherapy. ", "There were also more patients on regimens with greater emtogenicity in the clinic arm, notably FEC combinations (see [Table 1](#tbl1){ref-type=\"table\"}).", "\n\nMore patients receiving trastuzumab monotherapy were randomised into the control rather than the clinic arm of the trial (13 *vs* two patients). ", "Although this is a monoclonal antibody, emesis has been observed in our clinics and indeed is featured in the Summary of Product Characteristics. ", "The Sussex Cancer Network (referred to above) advises in its standard treatment proforma for the drug that metoclopramide should be provided for all patients and that treatment should be subject to the same scrutiny as other drugs used in cancer chemotherapy. ", "This was the case in our clinic where all therapies requiring support medication were included. ", "Only one drug is recommended for support medication in this case, compared to greater numbers for other chemotherapy regimens encountered, reducing the potential for confusion. ", "It is likely that the imbalance of trastuzumab numbers would decrease the impact of the pharmacy technician-led clinic rather than enhancing it if the numbers were the other way round. ", "The imbalance is an artefact of strict randomisation.", "\n\nModern antiemetics, if used correctly, should result in fewer cases of delayed nausea and vomiting, but if patients do not know or cannot remember which ones to use and when, then their value is compromised. ", "The efficacy of other oral treatments that patients may be taking may also be diminished due to impaired absorption and consequent sub therapeutic levels; for example in our study there were cases of neutropenic sepsis that may have been prevented had the oral antibiotic patients were taking been absorbed adequately. ", "This study did not assess whether the antibiotic had actually been taken or mistaken for another support medication. ", "A more in-depth study would be needed to determine the contribution of non-compliance with support medication to hospital admission of breast cancer patients for serious sequellae such as these.", "\n\nDrug interactions\n-----------------\n\nHighlighting potential and existing drug interactions is an important part of any patient -- carer interaction and a primary outcome of many studies of pharmacy and pharmacy technician drug history taking conducted in hospital settings.", "\n\nDue to the shared care agreement that currently exists for oncology patients in the study area, drug histories are not taken routinely for cancer patients; this study has highlighted the difference the systematic taking of drug histories can make. ", "Forty-seven of the 139 patients who participated in the study had potential drug interactions highlighted compared to none before the study began.", "\n\nMost potential drug interactions were reported between GP prescribed medication and chemotherapy support medication rather than chemotherapy itself. ", "The majority of these involved dexamethasone with NSAIDs, antidiabetic agents, anticonvulsants and antihypertensive agents.", "\n\nChemotherapy support medication supplies\n----------------------------------------\n\nEffective medicines management is an important contributor to the quality of healthcare, which provides patient-focussed care based on need. ", "In recent years, the Government has invested millions of pounds in developing medicines management across the NHS. ", "Research has shown this strategy to produce financial and other benefits such as improved quality of patient care, more efficient dispensing, patient self-administration, medicines review and continual patient education. ", "It has been shown that the concept of medicines management can be applied successfully to most areas and intuitively, should be of particular benefit when standard treatment regimens that require repeat dispensing are used.", "\n\nIn this study, medicines management and medication review in the pharmacy technician-led clinic reduced significantly the number of support medications required. ", "This in turn equated to marked cost savings and a reduction in pharmacy dispensing time.", "\n\nPrescription interventions\n--------------------------\n\nThe nature of a shared care agreement between two NHS Trusts does not always allow for efficient communication; for example in this case, two discrete sites are involved and the oncologist provides a visiting service from his base at one site to the other. ", "Prescription issues often occur during periods when it is most difficult to resolve them quickly, for example when workload is high and after busy outpatient clinics when the oncologist is elsewhere. ", "In this study, the pharmacy technician-led clinic led to a significant reduction in pharmacy time spent resolving prescription issues at the outpatient clinic.", "\n\nIn both study arms, the most common reported problem was that additions to chemotherapy support medication were unclear to staff. ", "Clarification in the clinic when all healthcare team members are present (oncologist, nurse, and pharmacy staff) is of clear benefit to achieving the right patient prescription.", "\n\nOverall costs of the scheme\n---------------------------\n\nCost analysis of the scheme (see results above) indicates that the initial, one-off payments for technician training (£1955.00) are more than covered by a projected annual saving of £15706.67 in terms of technician time saved (£1499.27) and reductions in dispensing unnecessary medicines (£14207.4). ", "Clearly the actual annual amount will depend on patient throughput and complexity of their regimens, but this result does provide another indication that the approach is worthwhile.", "\n\nCONCLUSION\n==========\n\nThis study has demonstrated that breast cancer patients at Worthing Hospital had a significantly better understanding of their chemotherapy support medication after attending the pharmacy technician-led clinic compared to those patients who did not.", "\n\nIn addition, the study showed that for these patients there were highly significant reductions in the number of chemotherapy delays and dose reductions and the amount of repeat dispensing of chemotherapy support medication, resulting in a significant reduction in dispensary time and expenditure on medicines. ", "There was also a highly significant reduction in pharmacy time spent resolving prescription issues at the point of dispensing.", "\n\nWe propose to extend the clinic to all breast cancer patients at Worthing Hospital and investigate its application to other specialities. ", "A refinement to the process could include the amalgamation of the initial nursing assessment of the patient with the pharmacy technician-led clinic.", "\n\nChemotherapy support medications are commonly standard treatments employed for standard regimens with standard directions. ", "Pre-labelled TTO packs could be available from the pre-assessment clinic under a Patient Group Direction after the pharmacy technician has taken a drug history and conducted a medication review to establish what is required, thus saving valuable dispensary time. ", "The availability of a suitably qualified and accredited pharmacist supplementary prescriber in the pharmacy technician-led clinic could mean that a full service on chemotherapy support medication could be provided in the clinic without recourse to the dispensary. ", "This is an attractive area for future research.", "\n\nThis study showed that as well as providing a better understanding of drug treatments, pharmacy technician-led clinics are also a prime opportunity to apply effective medicines management and medication review.", "\n\n{#fig1}\n\n###### \n\nNature of the chemotherapy regimes and treatment modes used in the control and clinic arms of the study\n\n **Regimen** **Control arm (no. ", "of patients)** **Clinic arm (no. ", "of patients)**\n -------------------------------------- ----------------------------------- ----------------------------------\n Adjuvant FEC 60 mg m^−2^ 8 15\n Adjuvant EC 60 6 5\n Adjuvant paclitaxel 5 ---\n Adjuvant docetaxel --- 2\n Adjuvant FEC 75 mg m^−2^ 17 26\n Adjuvant AC --- 1\n Adjuvant EC 75 --- 3\n Neo-adjuvant FEC 75 1 2\n Metastatic epirubicin+docetaxel 2 ---\n Metastatic docetaxel 10 10\n Metastatic trastuzumab 13 2\n Metastatic vinorelbine 3 2\n Metastatic EC 60 3 ---\n Metastatic capecitabine 2 ---\n Metastatic docetaxel and trastuzumab --- 2\n      \n\n **Chemotherapy cycle number** **Control arm** **Clinic arm**\n ------------------------------- ----------------- ----------------\n 2 53 53\n 3 15 13\n 4 2 4\n\nA=Adriamycin (doxorubicin); C=cyclophosphamide; E=epirubicin; F=fluorouracil.", "\n\n###### \n\nMain outcome measures to demonstrating the impact of the pharmacy-led clinic (clinic arm) compared to control\n\n **Feature** **Control arm *n* (%)** **Clinic arm *n* (%)** **Statistical inference**\n ------------------------------------------------------------------------------- ------------------------- ------------------------ --------------------------------------------------\n *Primary outcome measure: patients\\' understanding of their medication* \n  Number of patients (*n*) 69 69  \n  Mean baseline score 2.942 2.922  \n  Mean follow-up data score 2.965 5.417  \n  Difference between mean baseline and follow-up scores (95%CI) 0.023 (−0.228--0.182) 2.495 (2.165--2.826)  \n  *P* 0.822 \\<0.001  \n        \n *Secondary outcome measures* \n  Number of patients having chemotherapy delays 25 (36.2) 8 (11.6) *χ*^2^=11.51, *P*=0.001\n  Number of patients having chemotherapy dose reductions 21 (30.4) 7 (10.1) *χ*^2^=8.78, *P*=0.003\n  Total number of patients with drug interactions recorded 20 (28.6)^a^ 27 (39.1) *χ*^2^=1.731, *P*=0.188\n  Median number of items of support medication supplied per patient per course 5^a^ 2 *P*\\<0.001, 95%CI=1--3\n  Mean cost of items supplied per patient per course (+/− s.e.) ", " £26.7 (+/−4.7)^a^ £10.2 (+/−1.5) *t*=3.34, *P*\\<0.001\n  Number of patient prescriptions requiring intervention 32 (45.7) 21 (30.4) *χ*^2^=3.439, *P*=0.064\n  Mean time per patient spent resolving prescription issues (minutes) 9.9 1.8 Difference (95%CI)=8.1 (5.05--11.04), *P*\\<0.001\n\nOne control subject was included at baseline, making *n*=70 for this calculation.", "\n" ]

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[ "Q:\n\nIgnoring case sensitive in c#\n\nI have 2 string that I am comparing but I need to avoid problem if I use upper case or lower case.", "\nThere's any way to achieve this?", "\nThanks\nHere's my code:\nif (userID >= 0 && fnIndex >= 0 && lnIndex >= 0)\n{\nfor (int i = 1; i < userDataId.", "Length; i++)\n {\n var userData = userDataId[i].List;\n if (userData[fnIndex].ToString() == \"FIRSTNAME1\" &&\n userData[lnIndex].ToString() == \"LASTNAME1\")\n {\n userId = userData[userID].ToString();\n break;\n }\n }\n}\n\nA:\n\nYou can (and should always) do this to compare strings instead of using ==:\nif (userData[fnIndex].ToString().Equals(\n \"FIRSTNAME1\", StringComparison.", "CurrentCultureIgnoreCase))\n\nAlso, \"FIRSTNAME1\" and \"LASTNAME1\" should be made into constants.", "\n\n" ]

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[ "[Application of European Model of Quality in Oncology].", "\nTo assess a Medical Oncology Service using a healthcare setting version of the European Foundation for Quality Management (EFQM). ", "To use this tool as training, an opportunity for participation and the base for checking the strategic planning. ", "We use the EFQM Model adapted to healthcare centers EFQM as the evaluation instrument. ", "It maintains scores and weights, only modifying vocabulary and simplifying that not relevant to the healthcare setting. ", "Exercise was done with the \"proform\" system. ", "Its advantage is that it uses standard formulas combined with open areas for discussion and presentation of ideas. ", "It uses group sessions for agreement. ", "2001 Management. ", "Evaluation was performed in the second term of 2002. ", "58 strengths and 37 areas of improvement were identified. ", "These elements were used to create a strategic document, which served as the basis for future improvement. ", "The score reached was used as an internal reference to monitor service quality evolution. ", "The EFQM model is applicable in a Medical Oncology Service, although it would be desirable to have standardized quality indicators that permit a more objective and specific evaluation." ]

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[ "Q:\n\nJavascript why isnt this simple counter working in my loop\n\nI have a function that is called button and it appends m table using a loop. ", "I have modified the loop so that it assigns an ID to each <td> it makes. ", "However, it does not seem to be working right.", "\nHere it is in action, follow the use case below to test it: http://jsfiddle.net/JEAkX/19/\nHere is a simple use case I use to test it:\n\nChange the letter in a cell\nPress \"More\"\nChange the letter in one of the new cells\n\nIt should function the same as the original cells if the ID was getting assigned properly.", "\nThe counter is: var n = 13;\nand it is inserted into the appended cell as such: \ncell.innerHTML = \"<input type='text' id='r\"+ (n) +\"' size='1' onChange='getPos('r\"+ (n++) +\"'), modifyCells('alphabetTable')' value='\" + subset[i++] + \"' />\"`\n\nThis is the DOM source I am getting:\n<td><input id=\"r13\" size=\"1\" onchange=\"getPos(\" r14=\"\" ),=\"\" modifycells(=\"\" alphabettable=\"\" )=\"\" value=\"q\" type=\"text\"></td>\n<td><input id=\"r14\" size=\"1\" onchange=\"getPos(\" r15=\"\" ),=\"\" modifycells(=\"\" alphabettable=\"\" )=\"\" value=\"r\" type=\"text\"></td>\n\nI suspect it has to do with cramming everything into 1 line like @zzzzBov said but I dont know how else to do it.", "\n\nA:\n\nBesides the n++, there's a quoting issue in your HTML. ", "There are nested single quotes in the onchange attribute, like so:\n<input type='text' id='r19' size='1' onChange='getPos('r20'), modifyCells('alphabetTable')' value='p' />\nQuick fix for the syntax is to use escaped double quotes, so you can get going:\ncell.innerHTML = \"<input type='text' id='r\"+ n +\"' size='1' onChange='getPos(\\\"r\"+ (n++) +\"\\\"), modifyCells(\\\"alphabetTable\\\")' value='\" + subset[i++] + \"' />\"\n\n" ]

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[ "Stinson 108\n\nThe Stinson 108 was a popular general aviation aircraft produced by the Stinson division of the American airplane company Consolidated Vultee, from immediately after World War II to 1950. ", "It was developed from the prewar Model 10A Voyager. ", "Stinson was bought by Piper Aircraft in 1949. ", "All Stinson model 108, 108-1, 108-2, 108-3 and 108-4 aircraft were built by Stinson at Wayne, Michigan. ", " When Stinson sold the type certificate to Piper in 1949, approximately 325 airplanes of the 5,260 model 108s built by Stinson were complete but unsold. ", "These 325 model 108s went to Piper as part of the sale. ", " Piper then sold that inventory as the Piper-Stinson over the next few years.", "\n\nDesign and development\nThe fuselage was of fabric-covered steel tube. ", "Aftermarket modifiers have obtained supplemental type certificates (STC) allowing conversion to an aluminum covering. ", "Many different engines have been installed in the 108 by STC such as the Lycoming O-360, Franklin O-350, Continental O-470.", "\n\nOne distinctive feature was the partial leading edge slot installed on the wings and aligned with the ailerons on the trailing edge, ensuring that the portion of the wing containing the aileron remains unstalled at higher angles of attack, thus contributing to docile stall behavior.", "\n\nTotal new production of the Stinson Model 108, by Stinson, was 5,260; this total does not include the two converted prototypes. ", "Stinson delivered approximately 4,935 aircraft and Piper delivered approximately 325 aircraft. ", " Piper later sold the type certificate to Univair Aircraft Corporation. ", "Univair built and certified the model 108-5, but built only one example. ", " Total new model production by Stinson and Univair was 5,261 aircraft.", "\n\nVariants\n\nThe 108 variants closely resemble each other but can be visually distinguished by their design changes:\nPrototype 108\nTwo prototype model 108s were converted from Stinson model 10A airframes. ", "FAA records show NX31519 was model 108 serial number 1, and NX31532 is model 108 serial number 2. ", " Both registrations later changed to NC. ", "The production model straight 108 would also use serial number 1 and 2, so there was for a short period 2 duplicate serial numbers;\n108 Voyager 125\nPowered by a Lycoming O-235 piston engine.", "\n108 Voyager 150\nPowered by a Franklin 6A4-150-B31, B3 or B4 piston engine. ", "742 built in 1946.", "\n108-1\nSlightly modified version with external baggage door. ", "1508 built 1947–1948.", "\n108-2\nPowered by Franklin 6A4-165-B3 or -B5. ", "1250 built from May 1948. ", "There was a conversion kit to add the rudder trim to the earlier airplanes advertised.", "\n\n108-3\nThe 108-3 introduced a taller vertical fin with a rudder featuring a straight trailing edge. ", "Larger fuel tanks ( versus ) were also fitted. ", "The -3 has a higher gross weight than its predecessors of . ", "1760 built by Stinson and Piper.", "\n108-4\nThe 108-4 was a higher powered model 108, sn 108-4693, NX149C, not certified, flown experimentally by Stinson, later by Piper, 1 built.", "\nFlying Station Wagon\nThe \"Flying Station Wagon\" version was an option available with the -1, -2 and -3 models, had a utility interior incorporated wood paneling and a reinforced floor, allowing of baggage in the passenger compartment. ", "The aircraft could be fitted with wheel, float or ski landing gear. ", "The single 108-4 built was a Flying Station Wagon.", "\n108-5\nA single 108-5 was built by Univair, who purchased the Stinson 108 type certificate from Piper, in 1964. ", "The 108-5 used a Franklin 6A-335-B1 engine. ", "Univair offered kits to convert earlier aircraft to this standard. ", "The 108-5 brought total model 108 production to 5,261, of which 5,135 were built by Stinson, 125 by Piper, and 1 by Univair.", "\n\nOperators\n\nSpanish Air Force operated eighteen 108-3 aircraft, with the designation L.2.", "\n\nSpecifications (108 Voyager 150)\n\nSee also\n\nReferences\n\nFurther reading\n\nExternal links\n\nCategory:High-wing aircraft\nCategory:1940s United States civil utility aircraft\nModel 108\nCategory:Single-engined tractor aircraft" ]

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[ "Nicki Minaj’s promotional onslaught continues. ", "After taping “106 & Park” on Monday, the green-haired diva rose bright and early on her album release day to pay a visit to SiriusXM Radio’s “Sway in the Morning,” where she discussed her evolution, newfound confidence, “Beez in the Trap” video with 2 Chainz, M.I.A.’s Super Bowl stunt, and her controversial Grammy performance.", "\n\nOn her evolution: “I think I went from being a caricature in people’s eyes to someone with a lot of layers. ", "You just gotta realize that I’m never gonna be one dimensional. ", "Even my core fans at times thought I was one dimensional when I was doing the mixtapes. ", "However, even on the mixtapes, I was singing and I was doing songs like ‘Can Anybody Hear Me.'” … ", "When mainstream got a hold of Nicki Minaj, they turned her into a girl that wears wigs and has funny voices. ", "So then we had to get past that. ", "And then I had to reel it in and say, ‘Hey, actually I’m a businesswoman.'”", "\n\nOn her newfound confidence: “I am not nervous, I am not fearful. ", "All of those emotions have left. ", "The stuff that I felt from the first album, I no longer care.”", "\n\nOn 2 Chainz: “He’s an incredible person. ", "He’s a hard worker and I love seeing hard-working people that’s like, by any means necessary. ", "That makes me passionate because that’s how I was.”", "\n\nOn the video for “Beez in the Trap”: “That video is very sexy, a lot of big booty girls in that video. ", "We actually had to do a clean and a dirty.”", "\n\nOn M.I.A.’s Super Bowl incident: “I don’t think M.I.A. should have done it. ", "It’s possible that she didn’t even plan to do it. ", "Sometimes when you are nervous, you do things that you normally don’t do. ", "I feel that may have been a defense mechanism at that time out of nervousness. ", "I was kind of disappointed because it was on Madonna’s set. ", "We were her guests and so if it was something planned, I think it was corny. ", "I wouldn’t have done it, but M.I.A. is still cool with me.”", "\n\nOn her polarizing Grammy performance: “It was my favorite performance that I’ve ever done in my life. ", "When I watched it back, I was jumping for joy. ", "I wish I could watch that performance over and over like a fan.”" ]

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[ "@echo off\nrem batch file to start Vim with less.vim.", "\nrem Read stdin if no arguments were given.", "\nrem Written by Ken Takata.", "\n\nif \"%1\"==\"\" (\n vim --cmd \"let no_plugin_maps = 1\" -c \"runtime! ", "macros/less.vim\" -\n) else (\n vim --cmd \"let no_plugin_maps = 1\" -c \"runtime! ", "macros/less.vim\" %*\n)\n" ]

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[ "It's an Honour\n\nThe It's an Honour website is the Australian Government database of honours and awards.", "\n\nThe website is maintained by the Department of the Prime Minister and Cabinet.", "\n\nReferences\n\nExternal links\nwebsite\n\nCategory:Orders, decorations, and medals of Australia" ]

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[ "The present invention relates to a method and controller for transferring data by direct memory access, more particularly to a method and controller employing a restricted block transfer mode.", "\nDirect memory access has long been used to transfer data at high speed over data buses in computing and communication equipment, bypassing the equipment's central processing unit (CPU). ", "In the restricted block transfer mode, the data can be transferred in blocks, but the block size is restricted to certain values. ", "After the transfer of each block, direct memory access pauses to allow memory access by the CPU or another device. ", "The restricted block transfer mode is useful when, for example, the memory structure permits rapid access to blocks of data that do not cross certain forbidden address boundaries.", "\nOne way to avoid crossing such address boundaries is to restrict the starting and stopping addresses of data transfers to certain address values. ", "Such restrictions are undesirable, however, because they often force unnecessary data to be transferred.", "\nIf the starting and stopping addresses are not restricted, then to avoid crossing forbidden address boundaries, a data transfer may have to be divided into a plurality of sections, and a different block size employed in each section. ", "Conventional direct memory access controllers are not adapted to do this, however; normally, the block size must be set and changed by the CPU. ", "CPU interrupts must accordingly be generated during the course of the transfer, which slows the transfer and causes undesirable CPU overhead." ]

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[ "The reporting on Donald Trump, Jr.’s treatment in the Mueller report has been woefully inaccurate.", "\n\nThe president’s eldest son, an outspoken and unapologetic conservative, is a favorite punching bag of the left. ", "For more than two years, liberal journalists and shrieking “#resistance” activists have salivated over the thought of seeing Don Jr. carted off in handcuffs.", "\n\nTo their dismay, there is only one crucial takeaway from the Mueller report’s conclusions about the utterly inconsequential “Trump Tower meeting” between Don Jr., several Russians, and others: neither Don Jr. nor anyone else involved in the meeting was charged with any crime.", "\n\nJOE DIGENOVA: WITH FULL MUELLER REPORT OUT, TIME TO GO AFTER THE REAL CONSPIRATORS\n\nThe reasons are clear. ", "The entire theory about what was potentially illegal about the meeting was speculative and untested. ", "What’s more, even if it were illegal, the report concluded that Don Jr. didn’t have the “willful” intent to break the law that would be necessary to make it a crime.", "\n\nIn their disappointment, Don Jr.’s detractors have latched on to a new theory: that he was simply “too stupid” to be charged with a crime because he didn’t know that his conduct was illegal.", "\n\nThey hang this blatant misconstruction on these words from the report: “the Office did not obtain admissible evidence likely to meet the government’s burden to prove beyond a reasonable doubt that these individuals acted ‘willfully,’ i.e. with general knowledge of the illegality of their conduct.”", "\n\nThat’s not just some minor technicality, absent which Robert Mueller’s prosecutors would have had Don Jr. in shackles while revelers in cat-eared pink hats danced in the streets. ", "It’s a central element of the offense they were investigating, and they decided to clear Don Jr. because without it there is no crime.", "\n\nOne often-used definition of “willful” intent states that it “requires proof beyond a reasonable doubt that the defendant knew his or her conduct was unlawful and intended to do something that the law forbids; that the defendant acted with a purpose to disobey or disregard the law.”", "\n\nIn essence, in order to be charged with conspiring to cheat, you have to have been actually meaning to cheat. ", "That’s the law. ", "Without intent, there is no crime. ", "And Mueller’s team, even his hand-picked Democrat attack dog Andrew Weissmann, knew they didn’t have evidence to convince a jury that Don Jr. meant to circumvent election laws when he typed “I love it” in response to a tangentially-related British publicist’s suggestion the Russian government might have “information that would incriminate Hillary.” ", "Don Jr. even voluntarily released his email correspondence related to that meeting.", "\n\nBut even if there were the requisite intent, the Mueller report still exonerates Don Jr., stating that “the government would likely encounter difficulty proving beyond a reasonable doubt that the value of the promised information exceeded the threshold for a criminal violation.”", "\n\nDid you catch that?", "\n\nFor the English speakers among you, let me translate that from Weissmann-speak: “This ‘crime’ we thought up as a way to nail Don Jr. is so speculative and unprecedented, we don’t think there’s a court in the land that would let this fly.”", "\n\nThe entire notion of a criminal conspiracy is predicated on the idea that the federal election law’s ban on campaigns taking “contributions” or “things of value” from foreign nationals also applies to “dirt” on opposing candidates.", "\n\nThat’s hardly an established interpretation of the law. ", "In fact, no one has ever been convicted of something similar. ", "If “dirt” is a “thing of value” for campaign finance purposes, that is a dangerously radical innovation with huge potential First Amendment implications.", "\n\nPersonally, I think it’s a completely untenable interpretation, but don’t take my word it. ", "Mueller and his team considered it, as well — and then rejected it as too “difficult to prove” in their report.", "\n\nI wonder how many of the journalists calling Don Jr. stupid were so certain about this far-fetched legal theory. ", "I further wonder how many of them felt the same way when foreign national Christopher Steele handed the Hillary Clinton campaign a whole dossier of “dirt” on President Trump — at a hefty, agreed-upon price, no less.", "\n\nCLICK HERE TO GET THE FOX NEWS APP\n\nThe whole thing is pure “#resistance” fantasy.", "\n\nIt was reckless for the media to promote the Trump Tower meeting as a crime, and it was irresponsible for Mueller’s report to discuss the matter using language that allows people who hate Don Jr. to continue in that delusion.", "\n\nCLICK HERE TO READ MORE FROM JOE DIGENOVA" ]

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[ "As much as the internet collectively enjoys the furry spectacle of cats, especially kittens, there's also a very real trend of wariness surrounding the feline.", "\n\nCats are often painted as unloving, murderous, disease-carrying moochers who manipulate us into a decidedly one-sided relationship — a description that especially becomes popular when they're compared to dogs (and which I fully confess to having engaged in from time to time).", "\n\nBut my dog favoritism aside, the truth is that cats, for all their supposed frigidness, have long been a trusted ally and supportive comrade to humankind. ", "One sterling example of this is in the benefits cats confer to those with socially crippling autism spectrum disorder (ASD).", "\n\nCoaxing Them Out Of The Shell\n\nIn 2012, French researchers published a study in PLOS One in which they took a look at whether pets could help people with autism, characterized previously by Medical Daily as an inability to connect to other people and engaging in repetitive, often unusual behaviors. ", "The \"spectrum\" in ASD denotes the varying degrees of severity with which these symptoms can present themselves.", "\n\nInterviewing the parents in 260 families with an autistic individual, they found that a certain subset of pet-owning households was associated with an improvement of prosocial behaviors — homes that had welcomed a pet after the autistic child had turned 5, which the researchers noted is a \"key age\" in any evaluation of the behavioral disorder.", "\n\n\"The arrival of a pet in a family has been shown to increase the level of interactions between family members: they spend more time together and share joint attention on the new family member,” the authors wrote. \"", "The new arrival of a pet potentially elicits more attention in individuals with autism, thus leading to a greater chance of bonding with the pet.\"", "\n\nSpecifically, they found that children with autism who had a pet after the age of 5 were more likely to be better at offering to share and offering comfort to others when compared to similarly impaired children. ", "This trend became more significant as the reported bond became stronger between child and pet — whether it was playing or taking care of it. ", "These pets included cats, but also dogs and a hamster.", "\n\n\"Playing with a pet is a complex behavior, sometimes involving object manipulation as a means for practice and mastery of action schemas (i.e. sensorimotor play) or a child’s ability for mental representation,\" they explained. \"", "Thus, it provides a child with means of practicing and understanding the events of his or her social world.\"", "\n\nThough children with autism are often overwhelmed by new stimuli, the authors theorized that the pet’s arrival was seen as a subtle enough shift in the environment that it didn’t frighten them, and the relatively fewer demands that come with a pet-human relationship allowed these children to better acclimate to social interactions — the pet may have also tightened the family dynamic.", "\n\nAnother PLOS One study in 2013 lent support to that theory by studying the peer interactions of 99 children — a third of whom had ASD — as they either spent time with two guinea pigs or a series of toys in the same room.", "\n\n\"Participants with ASD demonstrated more social approach behaviors (including talking, looking at faces, and making tactile contact) and received more social approaches from their peers in the presence of animals compared to toys,\" the authors concluded. \"", "They also displayed more prosocial behaviors and positive effect (i.e. smiling and laughing) as well as less self-focused behaviors and negative effect.\"", "\n\nMore recently, this April, several of the authors published a follow-up study in the journal Development Psychobiology in which they measured children's physiological arousal in different classroom settings, finding that they were more stressed out than their non-autistic peers, except when they got to play with the guinea pigs. ", "The pets acted as a sort-of \"social buffer\" for the children — a furry nonthreatening bridge to improve communication with those around them.", "\n\nBut it’s not just in the controlled environments of a study or two that we can find evidence for the benefits of a pet, specifically cats. ", "in dealing with autism, There are plenty of heartwarming personal stories out there too.", "\n\nPhoto Courtesy of Shutterstock\n\n'Cats Are Like Me'\n\nFor father and neuroscientist J. Manerling, it had been a tumultuous time in his family: his wife had recently died and he was left alone with a 9-year-old daughter and a 4-year-old son with autism whose name was Richard, and who was largely unable to communicate verbally. ", "The family's situation took a turn for the better, however, once they met a new friend — eventually named Clover — at the local animal shelter.", "\n\n\"As we walked past the cages, there in a corner was a black and white tuxedo cat. ", "Suddenly my four-year old non-verbal son pointed to the cage and said, 'Cat!' ", "That was it,\" Manerling said in a 2011 article on Cats.About.com. \"", "From day one, we heard Richard having conversations with Clover when no one was looking. ", "He had language. ", "He needed someone with the patience to listen and who did not ask him to repeat himself or explain what he meant. ", "Clover had all those qualities.\"", "\n\nThough Clover would pass away by the time Richard entered college, other cats, Linus and Melody, would step in to quietly soothe him as he completed his algebra assignments or worked on his art projects. “", "Cats are like me,\" Manerling recalled Richard telling him once. \"", "They look at everything and think about it when everyone thinks they're not paying attention and they only talk when they have something to say.\"", "\n\nMore recently, there’s the beautiful tale of 5-year-old Iris and her art assistant Thula the cat.", "\n\nIris Grace Halmshaw, of the UK, had been diagnosed with ASD in 2011. ", "But while she is also mostly non-verbal, from the age of 3 onward, Iris began to communicate in her own special way through expressive, impressionist-like paintings.", "\n\nIn February of 2014, she took on an apprentice, a Maine Coon breed by the name of Thula, and the two have been inseparable ever since. \"", "She will ride in a basket on our bikes, go for rides in the car, and bathe with Iris,\" Iris’s mother, Arabella Carter Johnson, told Medical Daily in an email, \"She helps Iris through the many challenges she faces on a daily basis.\"", "\n\nIn return, Iris has begun to incorporate Thula into her artwork as Thula sits patiently nearby, never too clingy or rambunctious. ", "Through her art and Thula, Iris is steadily learning how to reach out to the outside world better than ever before. \"", "Thula has certainly allowed us to see cats in a different light and I now feel that many cats would be perfect companions for a child on the spectrum,\" Carter-Johnson said. \"", "They can be incredibly loyal, loving, and courageous.\"", "\n\nA Place In The Heart\n\nMuch like how no two cats are perfectly alike, no two people on the spectrum are either. ", "The idea of a pet, whenever it’s introduced to the home, may not be recommended for everyone with ASD.", "\n\nFor some, it will be a therapy dog that brings them out of their shell; for others, a cat or guinea pig — Carter-Johnson notes that Maine Coons like Thula are known for being particularly people-friendly. ", "But pets, even when they fit perfectly for someone on the spectrum, shouldn’t be seen as a wonder treatment; they’re a companion that can help someone with ASD cope through the added stresses of the disorder. ", "And there still needs to be more research conducted to determine the best ways to utilize the beneficial effects of pet ownership when it’s appropriate.", "\n\nBut, though we’ve mostly touched upon ASD, the simple truth is that pets, including and especially cats, are known to ease the burdens of most everyone who owns them.", "\n\nSo sure cats can be temperamental. ", "Or fussy. ", "Or bossy. ", "But they can also be our best friends. (", "They’re basically the college roommates of the animal world). ", "And for some lucky people, they can be lifesaving.", "\n\n\"Obviously not all cats are like this and maybe Thula’s incredibly special — she certainly is to us — but I don’t believe she will be the only one,\" Carter-Johnson said, \"There will be others that if given the opportunity can help their buddies in similar ways and surprise us all.\"", "\n\n(More of Iris’ paintings, which are partly intended to raise awareness about ASD, and Thula can be seen on her website. ", "Carter-Johnson is currently working on a book about Iris and Thula due to be released in 2016.)" ]

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[ "On February 27 the U.S. Supreme Court will hear arguments in the case Shelby County v. Holder, a challenge to the constitutionality of Section 5 of the Voting Rights Act of 1965. ", "This landmark law outlawed discriminatory voting practices by ending the disfranchisement of minority voters and preventing vote dilution through racial gerrymandering and other techniques that negate the minority vote when the white majority votes as a block.", "\n\nSection 5 furthers these goals by requiring nine full states and parts of seven other states with a history of racial discrimination in voting to ask either the Department of Justice or a three-judge court in Washington, D.C., for approval before making any changes to voting laws—a process known as preclearance. ", "Congress determined the jurisdictions originally covered under Section 5 by using a plan laid out in the Voting Rights Act and also created a scheme for states to “bail out” of coverage if they have complied with the Voting Rights Act for 10 years.", "\n\nFor more on this topic, please see:" ]

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[ "Due September 10th, 2018 -\nSardinia Queer Short Film Festival 2018 is a short movies contest addressed to gay, lesbian, bisexual, transgender and queer themed works, both released and unreleased ones. ", "Contents can be artistically performed in all its possible meanings, interpretations and realities.", "\n\nUSNFestival is a film competition sponsored by ARC, a cultural association from Cagliari, by ARCinema, a member of the Italian Federation of Cinema Societies, and by the students’ association universitARC.", "\n\nUSNFestival is part of a wider project of activities related to Uno Sguardo Normale Expo, a queer culture festival, organized by ARC, the LGBTQ association of Cagliari, ARCinema and unviersitARC. ", "These associations aim, once again this year, to raise awareness towards society, thanks to the universal language of art, on natural forms of sexual orientation, gender identity and equality in terms of civil rights. ", "In addition, through the Festival the associations aims are: to enhance and promote young and independent movie productions, especially the small ones, that are connected to queer culture; to foster dialogue and cultural exchange among productions of different countries; to offer to the city of Cagliari the opportunity to learn more about this still unknown movie niche.", "\n\nAny genre of works will be accepted (documentary, fiction, classic and/or digital animation, video clips, video art) as long as they have been released after January 2016. ", "Application is open to all works without any constraint concerning genre, format and technique. ", "Both distributed (in Italy or abroad) and undistributed films will be accepted too.", "\n\nEntries must be no longer than 25 minutes in length (opening and closing credits included).", "\n\nClick the link below for Official Rules and more details.", "\n\nPrizes\n\nBest Short Film Award:€ 2,000 (Approx. ", "$2,300 USD)\n\nAudience Award:€ 500 (Approx. ", "$600 USD)\n\nBest Original Short Film that speaks about the LGBT situation in Sardinia:€ 300 (Approx. ", "$600 USD)\n\nPhotoSquared Editing ProjectPhotoSquared is an app that frees your photos from your phone, and gets them on your walls with a few simple clicks. ", "Editors, use the given assets to create a :15 video that will drive viewers to place an order." ]

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[ "Pandora FMS\n\nPandora FMS (for Pandora Flexible Monitoring System) is software for monitoring computer networks . ", "Pandora FMS allows monitoring in a visual way the status and performance of several parameters from different operating systems, servers, applications and hardware systems such as firewalls, proxies, databases, web servers or routers. ", "\n\nPandora FMS can be deployed in almost any operating system. ", "It features remote monitoring (WMI, SNMP, TCP, UDP, ICMP, HTTP...) and it can also use agents. ", "An agent is available for each platform. ", "It can also monitor hardware systems with a TCP/IP stack, such as load balancers, routers, network switches, printers or firewalls.", "\n\nPandora FMS has several servers that process and get information from different sources, using WMI for gathering remote Windows information, a predictive server, a plug-in server which makes complex user-defined network tests, an advanced export server to replicate data between different sites of Pandora FMS, a network discovery server, and an SNMP Trap console.", "\n\nReleased under the terms of the GNU General Public License, Pandora FMS is free software. ", "At first the project was hosted on SourceForge.net, from where it has been downloaded over one million times, and selected the “Staff Pick” Project of the Month, June 2016, and elected “Community Choice” Project of the Month, November 2017.", "\n\nComponents\n\nPandora Server \n\nIn Pandora FMS architecture, servers are the core of the system because they are the recipients of bundles of information. ", "They also generate monitoring alerts. ", "It is possible to have different modular configurations for the servers: several servers for very big systems, or just a single server. ", "Servers are also responsible for inserting the gathered data into Pandora's database. ", "It is possible to have several Pandora Servers connected to a single Database. ", "Different servers are used for different kind of monitoring: remote monitoring, WMI monitoring, SNMP and other network monitoring, inventory recollection, etc. ", "Highly scalable (up to 2000 nodes with one single server), completely web-driven and a multitenant interface. ", "It has a very flexible ACL system and a lot of graphical reports and user-defined control screens.", "\n\nServers are developed in Perl and work on any platform that has the required modules. ", "Pandora was originally developed for Linux.", "\n\nWeb console \n\nPandora's user interface allows people to operate and manage the monitoring system. ", "It is developed in PHP and depends on a database and a web server. ", "It can work in a wide range of platforms: Linux, Solaris, Windows, AIX and others. ", "Several web consoles can be deployed in the same system if required. ", "Web Console has multiples choices, in example SNMP monitoring.", "\n\nAgents \n\nAgents are daemons or services that can monitor any numeric parameter, Boolean status, string or numerical incremental data and/or condition. ", "They can be developed in any language (as Shellscript, WSH, Perl or C). ", "They run on any type of platform (Microsoft, AIX, Solaris, Linux, IPSO, Mac OS or FreeBSD), also SAP, because the agents can communicate with the Pandora FMS Servers to send data in XML using SSH, FTP, NFS, Tentacle (protocol) or any data transfer means.", "\n\nDatabase \n\nThe database module is the core module of Pandora. ", "All the information of the system resides here. ", "For example, all data gathered by agents, configuration defined by administrator, events, incidents, audit info, etc. ", "are stored in the database. ", "At present, MySQL database and MariaDB database is supported. ", "Oracle support has been added in 6.0 release.", "\n\nTimeline of releases\n\nSoftware appliances \n\nPandora FMS has a software appliance based on a customized CentOS Linux, installable on CD, comes ready to use (including a live CD) or ready to install to hard disk.", "\n\nIt have also an AMI Appliance based on Amazon AWS.", "\n\nA Docker image is also available at Docker Hub.", "\n\nSee also \n\n Comparison of network monitoring systems\n Data logging\n\nReferences\n\nExternal links \n \n\nCategory:Free network-related software\nCategory:Free software programmed in Perl\nCategory:Multi-agent systems\nCategory:Free network management software\nCategory:System monitors" ]

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[ "Q:\n\nHow do I detect QTMovie stop playing?", "\n\nI have done the following - once played a QTMovie (on Mountain Lion) and wanted to get notification when a movie ended. ", "But the notification never got called! ", "Can anybody tell me what have I done wrong?", "\n- (void)playMovie:(QTMovie *)movie {\n [self.movieView.movie stop];\n\n if (movie) {\n self.movieView.movie = movie;\n [movie gotoBeginning];\n [movie play];\n\n [[NSNotificationCenter defaultCenter] addObserver:self selector:@selector(stopMovie:) name:QTMovieDidEndNotification object:self];\n }\n}\n\n- (void)stopMovie:(NSNotification *)notification {\n NSLog(@\"stop movie!\");", "\n [[NSNotificationCenter defaultCenter] removeObserver:self name:QTMovieDidEndNotification object:nil];\n}\n\nA:\n\nTry changing to the following (note the object parameter):\n[[NSNotificationCenter defaultCenter] addObserver:self\n selector:@selector(stopMovie:)\n name:QTMovieDidEndNotification\n object:movie];\n\n" ]

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[ "\n74 S.E.2d 596 (1953)\nWEST VIRGINIA SANITARY ENGINEERING CORP.", "\nv.\nKURISH.", "\nNo. ", "CC801.", "\nSupreme Court of Appeals of West Virginia.", "\nSubmitted January 27, 1953.", "\nDecided March 3, 1953.", "\n*597 Wysong & Wysong, Webster Springs, for plaintiff.", "\nHoover, Hoover & Bickel, Webster Springs, Wolverton & Callaghan, Richwood, for defendant.", "\nBROWNING, Judge.", "\nThe West Virginia Sanitary Engineering Corporation instituted in the Circuit Court of Webster County an action of assumpsit against Bessie E. Kurish, seeking recovery of an amount alleged to be due under the terms of a contract executed between plaintiff and defendant, whereby plaintiff was to construct a certain building upon land owned by defendant. ", "Defendant filed a plea of res judicata and the trial court, having sustained a demurrer to the plea, certified to this Court the following questions:\n\"1. ", "Does the Amended Plea of Res Judicata state a good defense in bar to the plaintiff's declaration?", "\n\"2. ", "Does the decision in the chancery cause referred to and formerly decided operate as res judicata of the issues presented in this law action of assumpsit?", "\n\"3. ", "Does the Statute (Code 38-2-19, Michie 3740), and in particular the language, `shall release such owner from all responsibility and his property from all lien' operate to discharge the debt as well as the lien, when the lien-claimant fails to furnish the itemized statement therein required?\"", "\nThe plea alleges: That after completing certain work and furnishing certain materials, in accordance with the terms of the contract and within the time allowed by the statute, plaintiff filed a mechanic's lien against Bessie E. Kurish and, within six months from the filing thereof, instituted a chancery cause for the enforcement of the lien; that after the institution of the chancery cause, the owner, pursuant to provisions of Code, 38-2-19, demanded of the contractor an itemized account of the work done and materials furnished; that in a special plea filed in the chancery cause, the owner alleged that the contractor failed to comply with the requirement of the statute, in that the itemized account was not furnished within ten days from the time of receipt of notice of the demand; that the trial court overruled a demurrer to the special plea and certified to the Supreme Court of Appeals certain questions arising upon the *598 pleadings; that the Supreme Court of Appeals refused to docket the case; and that subsequently the trial court adjudged the mechanic's lien invalid because of the failure of the contractor to furnish the notice, and dismissed the chancery cause.", "\nCode, 38-2-19, reads: \"The owner may, at any time, by notice in writing, require such subcontractor, laborer, mechanic, workman or other person doing, or causing to be done, work or labor upon such building or other structure or improvement appurtenant thereto, or any such materialman or other person furnishing materials, machinery or other necessary equipment for such work, to file with such owner an itemized account of the work done or caused to be done by such laborer or other person, or of the materials or machinery or other equipment furnished by such materialman or other person for such work, which account shall show the dates upon which such work was done, or such materials were furnished, the price charged therefor, and the nature of such work or materials, and the neglect or failure of any such laborer, mechanic or other person furnishing materials, machinery or other necessary equipment for the doing of the same, so to file such itemized statement with such owner, within ten days after the receipt by him of such written notice so to do, shall release such owner from all responsibility and his property from all lien or charge for all labor done and for all materials furnished by the person so failing to file such required itemized statement, prior to the giving of such notice.\"", "\nThe controlling question raised by the plea of res judicata, filed in the assumpsit action, relates to the effect of the provisions of the quoted statute declaring that failure of the contractor to furnish the itemized statement within ten days after receipt of demand therefor \"shall release such owner from all responsibility and his property from all lien or charge for all labor done and for all materials furnished by the person so failing to file such required itemized statement, prior to the giving of such notice.\" ", "It is the contention of defendant that the provisions have the effect of releasing the owner from all liability, while plaintiff contends that the effect thereof is to release the owner only as to liability created by the mechanics' liens statute, and not as to liability existing by virtue of the building contract. ", "Defendant also contends that, whether or not the statute be interpreted as wholly releasing the owner upon failure to furnish the itemized statement, as required, the question was adjudicated in the chancery proceeding.", "\nArticle 2 of Chapter 38 of the Code, as amended, contains the statutory law relating to the creation, perfecting, preserving and enforcement of mechanics' liens. ", "Section 1 thereof provides that a general contractor shall have the right to a mechanic's lien upon a structure erected by him, and upon the interest of the owner in the land upon which the structure is erected, while Section 2 grants such right to a subcontractor. ", "Section 3 grants such right to a materialman who furnishes any materials to the owner, and Section 4 grants such right to a materialman who furnishes materials to a general contractor or subcontractor. ", "Section 5 grants such right to a laborer who performs work for the owner, and Section 6 grants such right to a person who performs labor for a general contractor or a subcontractor. ", "Different methods are provided for the perfecting and preserving of the respective liens. ", "Any lien perfected attaches only against a building or other structure erected, \"and upon the interest of the owner thereof in the lot of land whereon the same stands * * *.\" ", "Section 35 empowers the court having jurisdiction, after proper proceedings, to order the sale of the property upon which such lien is found to exist, and to enter a \"personal decree in favor of such creditors for the amount of their claims against any party against whom they may be established, and such decree shall have the effect of, and be enforced as, other decrees for money.\"", "\nWith these general principles in mind, we may better understand and apply the provisions of Section 19, quoted above. ", "It will be observed that Section 19 expressly includes a subcontractor, laborer, mechanic, workman and materialman, and expressly requires them to furnish an itemized statement *599 on demand of the owner, while a general contractor is not expressly required to furnish such statement. ", "Though the statute uses, following the specific designations, the words, \"other persons\", it is observed that those words include only persons doing work or furnishing materials of the class designated. ", "Had the Legislature intended that a general contractor be required to furnish such statement, it would have specifically included the words \"general contractor\" within the express terms of the language of the section, as it did the word \"subcontractor\". ", "This meaning seems to be clearly indicated by the Note of the Revisers appended to Section 19, which says: \"The word `subcontractor' is inserted near the beginning of the section. ", "The purpose of the section would seem to apply to such a person as well as to the persons named in § 6, c. 75, Code 1923. ", "The words `or causing to be done' and `or caused to be done' are inserted, being made necessary by the insertion of the word `subcontractor.' \" ", "In 17 M.J., Statutes, Section 45, we find this statement: \"A statute, limiting a thing to be done in a particular manner, or by a prescribed person or tribunal, implies that it shall not be done otherwise, or by a different person or tribunal. ", "Expressio unius est exclusio alterius.\" ", "See Douglass v. Koontz, W.Va., ", "71 S.E.2d 319; Taylor v. Taylor, 66 W.Va. ", "238, 66 S.E. 690, 19 Ann.", "Cas. ", "414; Tate v. Ogg, 170 Va. 95, 195 S.E. 496; Blue v. Baltimore & O. R. Co., 78 W.Va. ", "526, 89 S.E. 288, L.R.A. 1916F, 1001. ", "It seems clear, therefore, that the requirement of the section as to the furnishing of an itemized statement does not apply as between a general contractor and an owner. ", "The reason for the difference readily appears. ", "The contract between the owner and the contractor governs, and affords the owner ample information concerning his liability to the contractor, while he would have no such information as to work done or materials furnished by a subcontractor, or those who worked for or furnished materials to a subcontractor.", "\nDefendant contends, however, that the rights of plaintiff were decreed in the chancery cause, and that the rule res judicata applies. ", "We agree that as to the right of plaintiff to enforce the claimed mechanic's lien, the final decree entered in the chancery cause precludes any further litigation, whether that decree be right or wrong. ", "But did that decree foreclose the right of plaintiff to prosecute an action in assumpsit arising out of the alleged breach of the building contract? ", "Or, to state the question in another way, does the statute, by creating a right to the lien and a method of enforcing it, extinguish the cause of action arising out of the contract? ", "The statute does not expressly attempt to do so. ", "Neither do we find any basis for holding that it impliedly does so. ", "The remedy afforded the contractor by the statute is not the equivalent of the prior remedy. ", "Neither is it the same type of remedy. ", "The new remedy is in equity, the old in assumpit. ", "The lien afforded by the statute, and which can only be enforced if perfected and preserved as required by the statute, can be enforced only as to the particular property, while the lien of a judgment obtained under the old remedy could be enforced as to any personal or real property. ", "The lien afforded a general contractor by the statute is not of equal dignity with liens afforded others by the statute. ", "Code, 38-2-18. ", "While Code, 38-2-35, empowers the court having jurisdiction of a mechanic's lien suit to enter a money decree as to any creditor, against any person liable, as to any portion of a claim not satisfied by a sale of the particular property, the enforcement of such a decree as to real estate would necessitate further drawn-out proceedings in the mechanic's lien suit, or the prosecution of a second suit in chancery.", "\nIn 57 C.J.S., Mechanics' Liens, § 266, it is stated: \"The lien given by the statute to mechanics and materialmen is but a cumulative remedy to enforce their respective contracts, and independently of the lien such parties may resort to the ordinary common-law remedies to enforce their contracts, as by action to recover personal judgment. ", "The two remedies may be pursued simultaneously, although there can be but one satisfaction. * * *\"", "\nIn 36 Am.", "Jur., ", "Mechanics' Liens, Section 234, it is stated:\n*600 \"The enforcement of the lien is a cumulative remedy provided by statute, and an incidental accompaniment of the contract, which may be pursued in connection with ordinary remedies. ", "The lienor may proceed to enforce his lien and simultaneously bring an action to recover a personal judgment for the amount due. ", "While there can only be one satisfaction thereof, the recovery of a judgment against the debtor in a suit at law does not waive the right to a lien, or bar an equitable action to enforce the same. ", "The institution of an attachment suit and levy of the writ to secure a demand for which a mechanic's lien is held does not waive the lien, particularly if the suit is dismissed and the attachment realizes nothing. ", "This is true although the levy is made on the identical property covered by the lien.", "\n\"An action to foreclose a mechanic's lien is not abated by the pendency of a prior suit brought by its property owner against the plaintiff (lien claimant) to recover on a breach of the contract, wherein the plaintiff, as defendant, could have counterclaimed; because, while the plaintiff could have interposed his claim in the former action as a counterclaim, he was not obliged to do so, especially since it appeared that the former action being in law, he would have been restricted to a judgment for money damages, and could not have foreclosed his lien.\"", "\nThe texts are fully supported by the authorities cited therein.", "\nIn the circumstances detailed, can the former decree be said to constitute an adjudication of the matters involved in the action in assumpsit? ", "We recognize, of course, the general principle that not only matters actually litigated in a proceeding, but also such matters as could have been litigated under the pleadings therein, can not be relitigated in a subsequent proceeding. ", "State ex rel. ", "Connellsville By-Product Coal Co. v. Continental Coal Co., 117 W.Va. ", "447, 186 S.E. 119, 106 A.L.R. 83; Marguerite Coal Co. v. Meadow River Lumber Co., 98 W.Va. ", "698, 127 S.E. 644; Choate v. Calhoun, 153 Va. 52, 149 S.E. 470; 50 C.J.S., Judgments, § 598. ", "The rule, however, has limitations. ", "In Pridemore v. Lucas, 131 W.Va. ", "1, 47 S.E.2d 839, Point 1, syllabus, this Court held: \"Where a material question in a pending suit has been put in issue in a former suit, and there judicially determined such question is conclusively settled by a decree rendered therein, and cannot be reasserted in a subsequent suit between the same parties and involving the same claim, demand or cause; but where the pending suit is upon a different claim, demand or cause, the decree in the first suit operates as a bar only as to questions actually litigated and determined in the former suit.\"", "\nIn State ex rel. ", "Connellsville By-Product Coal Co. v. Continental Coal Co., supra, Point 1, syllabus, it is held: \"For a second action to be a second vexation which the law will forbid, the two actions must have (1) substantially the same parties who sue and defend in each case in the same respective character, (2) the same cause of action, and (3) the same object.\" ", "See Eiland v. Powell, W.Va., ", "65 S.E.2d 737; Smith v. Haymond, W.Va., ", "64 S.E.2d 105, 26 A.L.R.2d 437; Hannah v. Beasley, 132 W.Va. ", "814, 53 S.E.2d 729; Central Banking & Security Co. v. U. S. Fidelity & Guaranty Co., 73 W.Va. ", "197, 80 S.E. 121, 51 L.R.A.,N.S., 797; Doonan v. Glynn, 28 W.Va. ", "715.", "\nHaving previously determined that the cause of action declared upon in the assumpsit proceeding is not the same as the cause of action involved in the suit to enforce the mechanic's lien, it becomes clear, from the authorities cited, that the trial court ruled correctly in sustaining the demurrer to the plea of res judicata. ", "Failure to perfect or preserve the mechanic's lien did not have the effect of destroying the rights growing out of the contract.", "\nFor another reason, the action of the trial court in sustaining the demurrer to the plea of res judicata must be affirmed. ", "In the final decree entered in the suit brought to enforce the mechanic's lien, on the 13th day of February, 1950, we find this language: \"To which action of the court in refusing to enter the decree as tendered which contained the above stricken out words `all responsibility upon', the defendant *601 Bessie E. Kurish objects and excepts.\" ", "From this language we think it clear that the court intended to reserve, and did reserve for future determination, the question herein involved relating to the rights growing out of the contract, as distinguished from the mechanic's lien liability created by the statute. ", "Also indicating that the question was reserved for future determination is the fact that the certificate of the chancery court, certifying the cause to this Court, mentioned no such question. ", "In New River & Pocahontas Consolidated Coal Company v. Eary, 115 W.Va. ", "46, 174 S.E. 573, Point 6, syllabus, this Court held: \"An issue held to be not properly before the court and left expressly undetermined may be raised in further proceedings between the parties.\" ", "To the same effect is the holding in Crawford v. Crawford, 111 W.Va. ", "58, 160 S.E. 307.", "\nFrom the conclusions reached, it necessarily follows that the ruling of the Circuit Court of Webster County must be affirmed.", "\nRuling affirmed.", "\n" ]

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[ "Top 10 Best Web Hosting provider For your WordPress Blogs\n\nWordPress is an open source content management platform where you can create a number of useful websites and edit their content whenever needed. ", "To activate the website made on wordpress, it is very important to choose a reliable and powerful web hosting service. ", "There are a huge number of companies who acts as Web Hosting provider For your WordPress Blogs services through whole world. ", "Web hosting companies provides different plans on the basis of speed reliability and security. ", "You can buy these plans on monthly or yearly basis to continue the flow of your website. ", "We have selected 10 best web hosting providers from some of the world top web hosting companies. ", "The most reliable, feature-rich, well known web hosts that offer affordable hosting services at the lowest prices possible.", "\n\nA web hosting service is a type of Internet hosting service that allows individuals and organizations to make their own website accessible via the World Wide Web. ", "Web Hosting provider For your WordPress Blogs server their own or lease for use by their clients as well as providing Internet connectivity, typically in a data center. ", "Web hosts can also provide data center space and connectivity to the Internet for servers they do not own to be located in their data center.", "\n\nThis web hosting service is trusted by over millions of domain owners.", "Best web hosting to pay monthly, Unlimited hosting plans And it offers you Free site transfer, mysql transfer, script transfer and 4500 free web templates. ", "You can trust both the reliability and performance of the hostgator hosting plan and that’s why it tops our list .", "\n\nIt is relatively new to the web hosting market, but it has quickly become one of top web hosting companies by offering an affordable plan are dedicated to providing their customers with the most reliable web hosting service possible at the best possible price ,Only $4.95 per month – save 20% if you buy from us!Monthly billing cycle available @ $7.95 and transfer rate is also good i.e. 400 Gigabits transfer/sec .", "\n\nMonster host is probably the Best Web Hosting provider For your WordPress Blogs which is serving since 1999. ", "it has Easy to use upgraded cCPanel 11.At HostMonster, you get 300 GB of space and 3,000 GB of bandwidth for about $7.95 a month if you pay yearly. ", "The pricing is hidden well within the signup form.", "\n\nThis Top rated web hosting provider – Free 1 click installs For blogs, shopping carts, and more.they provide reliable hosting since 1996 with probably the best customer support around, offering Web Hosting provider For your WordPress Blogs with advanced features like SSH support, Ruby (RoR), Python, etc.", "There’s a limited number of databases (100 each for MySQL and Postgre) and more FTP and email accounts than you could ever use (1,000 and 2500, respectively).", "\n\nThe ixwebhosting is providing Linux web hosting services, has been founded in 2003 and now it’s seven years in business.", "IX Web Hosting offers affordable business website hosting with advenced features reqired for eCommerce such as several (2-15) dedicated IP addresses . ", "Search for “ixwebhosting.com” on 3 biggest search engines returns average of 40333 results so company name popularity rank is #124.", "\n\nLunar pages offers reliable web hosting on Linux-based servers that support few regular for Windows web hosting features such as ASP and JSP, as well as PHP, CGI, Ruby on Rails, Python, etc. ", "This Web Hosting provider For your WordPress Blogs has been founded in 2001 and now it’s nine years in business.", "Search for “lunarpages.com” on 3 biggest search engines returns average of 375333 results so company name popularity rank is #26.", "\n\nThis web hosting company provides 300% green energy web hosting with each hosting plan. ", "All the Sales and support is done by Americans.", "Whether you are new to web hosting or if you want to move your existing web site to the green hosting service, Green Geeks are here to help you every step of the way.", "\n\nYahoo is Friendly and has got Toll Free 24-hour support so you never have to go it alone.it comes with Free Yahoo! ", "site builder and 100 Free Subdomain.", "Yahoo! ", "Small Biz is a Well known reliable hosting. ", "You can get free live insights iPhone app with every web hosting account provided by yahoo. ", "Web Hosting provider For your WordPress Blogs provides three plans according to your usage which are- basic, advanced and premier plans.", "\n\nThis web host is providing Windows web hosting services, has been founded in 1999 and now it’s eleven years in business.", "It offers top notch web hosting, domain names, and email services. ", "Our quality hosting is affordable for either a small business website or a personal web site. ", "Many web hosting review sites rank us as the best web hosting provider. ", "They provide you free domain name after choosing ine of the following extensions:-\n\nA successful blog takes time and effort to create and manage.", "\nDepending on your blog’s theme, you will need a certain set of tool from your\nhosting company. ", "They ought to hold the right skills to create your\nbusiness to the peak as well as the most significant of\nall you’ll need good hosting service.", "\n\nMark SmiithhAugust 9, 2011\n\nThe Web hosting in India services free you from the hassle related with Web hosting. ", "By choosing the reseller hosting plan, you are capable to offer an inadequate server space to your clients with no distressing about other aspects of the military such as server security, hardware operating expense or power efficiency.", "\n\nhost costJuly 25, 2011\n\nI wonder where godaddy went. ", "I’m already familiar with Hostgator and Bluehost. ", "Been using it since in the beginning.", "\n\nshiluJune 27, 2011\n\nAll are talk about web hosting sites for wordpress blogs. ", "Many sites are refer this type of web hosting. ", "I didn’t understand. ", "What is the importance web hosting with wordpress? ", "Any one can give reply please." ]

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[ "Lost Engliah BullDog\n\nHer Name is BEBE. ", "She is a Tan English Bulldog With black circles around her eyes. ", "She has a couple scares on her ears from an infection a couple years ago. ", "And a large scar on her stomach from a CSection. ", "She is 4 years Very gentle. ", "She went missing during the rain storm on Friday morning. ", "She is Spayed and Chipped. ", "If you have any information about My baby Please let me know." ]

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[ "Editor's note: Julian E. Zelizer is a professor of history and public affairs at Princeton University's Woodrow Wilson School. ", "His new book is \"Arsenal of Democracy: The Politics of National Security: From World War II to the War on Terrorism,\" published by Basic Books. ", "Zelizer writes widely about current events.", "\n\n(CNN) -- Responding to President Obama's State of the Union comments about the \"deep and corrosive doubts about how Washington works,\" House Speaker Nancy Pelosi said that \"the American people don't care about process.\"", "\n\nYet Americans have indicated that they are quite unhappy with how their government is working. ", "According to a recent NBC News/Wall Street Journal poll, only 28 percent of those polled believe that the federal government is \"working well,\" while seven out of 10 believe that the \"unhealthy\" government is in need of reform. ", "Almost 93 percent said there was too much partisanship; 84 percent said special interests had excessive power.", "\n\nWe must always take these kinds of poll numbers with a grain of salt. ", "Polls frequently show that Americans do not like how their government works, especially Congress. ", "The U.S. is a country that has always expressed strong distrust of government.", "\n\nThere have been a few exceptional periods, like the progressive era or the 1960s and 1970s, when this frustration turns into a concerted movement for government reform.", "\n\nDuring the 1960s and 1970s, liberal Democrats and Republicans concluded that much of their policy agenda would be impossible to achieve if the political process did not change. ", "They perceived Vietnam and then Watergate as the outgrowth of deep flaws in how our government worked.", "\n\nDuring the 1970s, they were able to pass a series of significant reforms, such as a campaign finance system that included public funds for presidential campaigns and contribution limits. ", "Reforms opened up more of the political process through sunshine laws and retrenched the power of the senior committee chairmen in Congress who had usually done as they pleased, ignoring the will of the majority.", "\n\nEthics laws regulated the behavior of executive and legislative branch. ", "Even the sacrosanct filibuster underwent an overhaul in 1975: The Senate lowered the number of required to end a filibuster from two-thirds of the Senate, 67; to three-fifths, 60.", "\n\nMany of the reforms did not work, some had unintended consequences, and others were gradually unraveled. ", "But substantive reform was possible and, for a moment, changed the way that politics as usual worked.", "\n\nIn addition to diminishing citizens' trust in government, the flaws of the political process constrain and limit what kinds of policies are even possible.", "\n\nIf President Obama, Democrats and Republicans are serious about building trust among citizens and creating a more productive political process, they should work together to do something about it. ", "If Washington is serious about reforming the political process, three specific areas deserve immediate attention.", "\n\nFilibuster reform: The 60-vote supermajority Senate has become dysfunctional. ", "Both parties have expressed frustration with their inability to move legislation through the process. ", "Both parties have used the filibuster as a normal tool of procedural warfare. ", "Because of the rampant use of the filibuster since the 1960s, senators expect that 60 votes are now required on almost every piece of legislation.", "\n\nReform can happen again. ", "One option would be to switch to a majority-based system in which 51 votes can end debate. ", "Another, more feasible, option would lower the number of senators required for cloture to 55. ", "To improve the political prospects for any change, some observers have suggested that any reform would not take effect until after the 2012 election.", "\n\nMaking it easier to end a filibuster is one of the most important concrete steps that Congress could take to actually diminish partisanship. ", "The sources of partisanship are deep-rooted and hard to change. ", "But filibuster reform would disarm both parties by weakening or removing one of their most powerful weapons.", "\n\nCampaign finance reform: A recent Supreme Court decision eliminated many of the barriers to corporate donations and third-party advertising.", "\n\nThe power of private money in campaigns has been a huge political issue for over a century. ", "Because politicians depend on interest group support to obtain funds for their campaigns, they constantly find themselves constrained when it comes to making policy. ", "The influence of private money also diminishes public trust in government. ", "Every story about another lobbyist like Jack Abramoff confirms their worst fears about corruption.", "\n\nIt is not difficult to understand why Congress has crafted a health care bill that avoids making any huge changes to the basic infrastructure of the health care industry. ", "According to The New York Times, citing the Center for Responsive Politics, the health care and insurance industry spent at least $648 million on lobbying in 2009 -- and 20 percent of the year-end reports were not in yet. ", "Pharmaceutical companies spent about $245 million, which the Times said was more than any other single industry has ever spent lobbying on behalf of any issue.", "\n\nSeveral changes have been discussed in recent years. ", "The administration has talked about placing certain kinds of fund-raising restrictions on companies that do business with the government.", "\n\nA second proposal is to build on local and state reforms by providing matching public funds to candidates who raise a certain minimum of private donations. ", "In the end, offering an alternative source of funds to candidates and parties is the only way to change the system, or candidates will be forced to keep going back to the well of interest group money.", "\n\nCongressional earmarks and tax breaks: Pork-barrel politics is as American as apple pie. ", "But in recent decades, the system by which legislators pass appropriations targeted to key interests has become pervasive. ", "Legislators are comfortable putting provisions that are tailor-made for lobbyists or particular interests into bills. ", "These earmarks are not subject to hearings or oversight. ", "The use of earmarks by Senate Democrats to close the health care legislation that passed last month made the public uneasy.", "\n\nThe other way in which Congress distributes hidden benefits is through tax breaks. ", "During the 1960s, reformers named these \"tax expenditures\" to convey the point that the government essentially spends money by forgiving certain groups of their obligation.", "\n\nWe have not had a major tax reform initiative since 1986. ", "The time has come to clean out the tax code once again and reduce the number of provisions that are in the law. ", "There is also bipartisan support for reforms that would limit the use of earmarks by legislators and make certain that they are fully disclosed upon being requested.", "\n\nAlthough voters tend to be more interested in bread-and-butter issues, as well as questions about war and peace, there are a few exceptional moments when public anger about the political system becomes so intense that we enter into a period of substantive reform. ", "We might be reaching one of those points, but in the end it will require the initiative of the president and congressional leaders to make sure that calls for reform are not just empty rhetoric.", "\n\nThe opinions expressed in this commentary are solely those of Julian Zelizer." ]

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[ "[An experimental study of the effect of severed ocular recti on anterior segment circulation].", "\nThe effect of recti tenotomy on the blood flow in iris-ciliary body was studied in 30 anaesthetized dogs with 51Cr labelled RBC of the frog as biological microspheres. ", "The quantitative determinations showed that the blood flow in eyes with 2, 3, and 4 recti detached were 4.47%, 20.80%, and 26.15% less respectively than that of the sham-operation controls, indicating that tenotomy of more than 3 recti compromised the anterior segment circulation seriously. ", "The development of ischemia depended on the number of vertical recti severed when the regional circulation was in a critical situation with the detachment of 2 recti." ]

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[ "\n114 B.R. 1 (1990)\nIn re JAIMALITO'S CANTINA ASSOCIATES LIMITED PARTNERSHIP t/a Jaimalito's, Debtor.", "\nBankruptcy No. ", "89-00946.", "\nUnited States Bankruptcy Court, District of Columbia.", "\nFebruary 26, 1990.", "\nRichard Gins, Washington, D.C., for debtor.", "\nDECISION DENYING APPLICATION TO RETAIN REBECCA J. HABBERT, ATTORNEY AT LAW\nS. MARTIN TEEL, Jr., Bankruptcy Judge.", "\nThe debtor, Jaimalito's Cantina Associates Limited Partnership, applies to employ and appoint Rebecca J. Habbert for purpose of general representation of the debtor. ", "Ms. Habbert is a pre-petition creditor of the debtor, holding a claim of unspecified amount for representing the debtor on matters unrelated to assisting in filing the bankruptcy petition. ", "She was representing the debtor on certain ongoing matters when the petition was filed, but the debtor does not seek appointment under 11 U.S.C. § 327(e) limited to those matters. ", "The application for employment for general representation of the debtor must be denied because, as a creditor, Ms. Habbert is not a \"disinterested person\" as defined in 11 U.S.C. § 101(13) and as required by 11 U.S.C. § 327(a)[1] in order to be eligible for employment. ", "See In re Pierce, 809 F.2d 1356, 1362-63 (8th Cir.1987); In re Gire, 107 B.R. 739, 745-46, 748 (Bankr.", "E.D. Cal.1989); In re Estes, 57 B.R. 158, 162-63 (Bankr.", "N.D.Ala.1986). ", "This result is not altered by 11 U.S.C. § 1107(b).[2]In re Roberts, 75 B.R. 402, 407-09 (D.Utah 1987) (en banc); In re Watervliet Paper Co., Inc., 96 B.R. 768, 771-74 (Bankr.", "W.D.Mich.1989); Matter of Patterson, 53 B.R. 366 (Bankr.", "D. Neb.1985); In re Anver Corp., 44 B.R. 615 (Bankr.", "D.Mass.1984). ", "Contra, In re Heatron, 5 B.R. 703, 705 (Bankr.", "W.D.Mo.1980); accord, In re Viking Ranches, Inc., 89 B.R. 113, 115-16 (Bankr.", "C.D.Cal.1988); In re Best Western Heritage Inn Partnership, 79 B.R. 736, 740 (Bankr.", "E.D.Tenn. ", "1987). ", "Congress could have specified that a claim as a creditor for prior legal representation *2 of the debtor does not disqualify an attorney from representing the debtor-in-possession. ", "It did not. ", "Prior employment or representation as counsel raises disqualification issues distinct from the issue of holding a claim. ", "See, e.g., 11 U.S.C. § 101(13)(D) dealing with lack of disinterestedness based on prior employment notwithstanding absence of any claim. ", "If § 1107(b) eliminates creditor status as a basis of disqualification under § 327(a) for lack of disinterestedness, it logically follows that § 1107(b) also eliminates creditor status as a basis of disqualification under § 327(a) for holding an adverse interest. ", "Heatron and its progeny recognize that § 1107(b) ought not prevent disqualification when the claim results in an adverse interest, but does otherwise prevent disqualification. ", "With all due respect, the logical reading of the statute does not permit that inconsistency. ", "Plainly both requirements of disinterestedness and lack of adverse interest still apply when the attorney occupies the status of a creditor, a status that is unaltered by the relative size of the claim.", "\nAn Order in accordance with this decision shall be entered.", "\nNOTES\n[1] § 327(a) provides:\n\nExcept as otherwise provided in this section, the trustee, with the court's approval, may employ one or more attorneys, accountants, appraisers, auctioneers, or other professional persons, that do not hold or represent an interest adverse to the estate, and that are disinterested persons, to represent or assist the trustee in carrying out the trustee's duties under this title.", "\n[2] § 1107 provides:\n\nNotwithstanding section 327(a) of this title, a person is not disqualified for employment under Section 327 of this title by a debtor in possession solely because of such person's employment by or representation of the debtor before the commencement of the case.", "\n" ]

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[ "SENT FOR MARY COOK:\n\nThe Structured Finance Transactions lunch meeting being held on Wednesday, \nDecember 6, 2000 from 11:30 a.m. to 1:00 p.m. will be in conference room \nEB35C1. ", " If you have not already done so, please remember to RSVP to me via \nemail by Noon on Monday, December 4, 2000.", "\n\nThank you.", "\n\nChaundra Woods\nEnron North America Corp.\n713/345-7621 (office)\n713/646-3490 (fax)\nchaundra.woods@enron.com (email)" ]

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[ "Q:\n\nVertically center one of many div inside a container\n\nA section consists of a navigation group with elements floated to the sides, a center text group, and a background image. ", "The section height was not manually set to fit the background image.", "\nHow do I go about vertically centering the text group? ", "It is div.h1-container.", "\nPlunkr: https://plnkr.co/edit/rSWgdfPQEbIeXbPh4wO1?p=preview\n\nbody {\r\n font: 15px/1.5 Arial, Helvetica, sans-serif;\r\n padding: 0;\r\n margin: 0;\r\n background-color: #f4f4f4;\r\n}\r\n\r\n\r\n/* Global */\r\n\r\n.container {\r\n width: 80%;\r\n margin: auto;\r\n overflow: hidden;\r\n}\r\n\r\n.clear {\r\n clear: both;\r\n}\r\n\r\nul {\r\n margin: 0;\r\n padding: 0;\r\n}\r\n\r\nsection h2 {\r\n line-height: 1.0;\r\n}\r\n\r\n.button_1 {\r\n height: 34px;\r\n background: tomato;\r\n border: 0;\r\n padding-left: 20px;\r\n padding-right: 20px;\r\n color: #ffffff;\r\n width: 200px;\r\n}\r\n\r\n.showcase-nav a {\r\n color: #ffffff;\r\n text-decoration: none;\r\n text-transform: uppercase;\r\n font-size: 16px;\r\n}\r\n\r\n.showcase-nav {\r\n padding-top: 30px;\r\n margin-top: 10px;\r\n float: right;\r\n}\r\n\r\n.showcase-nav li.social i {\r\n padding: 0 4px;\r\n}\r\n\r\n.showcase-nav li {\r\n display: inline;\r\n padding: 0 20px 0 20px;\r\n}\r\n\r\n.showcase-branding {\r\n float: left;\r\n}\r\n\r\n.showcase-branding h1 {\r\n font-size: 26px;\r\n margin: 0;\r\n padding-top: 30px;\r\n color: #fff;\r\n}\r\n\r\n.showcase-branding .highlight {\r\n color: #e8491d;\r\n font-weight: bold;\r\n}\r\n\r\n.showcase-nav a:hover {\r\n color: #cccccc;\r\n font-weight: bold;\r\n}\r\n\r\n.h1-container {\r\n width: 70%;\r\n margin: auto;\r\n}\r\n\r\n.h1-container h1 {\r\n text-transform: uppercase;\r\n text-align: center;\r\n color: #fff;\r\n}\r\n\r\n.h1-container p {\r\n width: 81%;\r\n background: tomato;\r\n margin: auto;\r\n border-radius: 10px;\r\n text-align: center;\r\n color: #fff;\r\n}\r\n\r\n\r\n/* Showcase */\r\n\r\n#showcase {\r\n background: url('http://i68.tinypic.com/2j5jho4.png') no-repeat;\r\n background-size: contain;\r\n width: 100%;\r\n display: inline-block;\r\n position: relative;\r\n margin: 0 auto;\r\n}\r\n\r\n#showcase:after {\r\n padding-top: 51.46%;\r\n display: block;\r\n content: '';\r\n}\r\n\r\n#showcase .container {\r\n position: absolute;\r\n top: 0;\r\n bottom: 0;\r\n right: 0;\r\n left: 0;\r\n}\r\n\r\n#showcase .h1-container h1 {\r\n font-size: 55px;\r\n margin-bottom: 10px;\r\n}\r\n\r\n#showcase p {\r\n font-size: 20px;\r\n padding: 5px;\r\n}\n<link href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.7.0/css/font-awesome.min.css\" rel=\"stylesheet\" />\r\n\r\n<section id=\"showcase\">\r\n <div class=\"container\">\r\n <div class=\"showcase-branding\">\r\n <h1>Title</h1>\r\n </div>\r\n <nav class=\"showcase-nav\">\r\n <ul>\r\n <li class=\"current\"><a href=\"about.html\">About</a></li>\r\n <li><a href=\"contact.html\">Contact</a></li>\r\n <li class=\"social\"><a href=\"\"><i class=\"fa fa-linkedin-square\"></i></a><a href=\"\"><i class=\"fa fa-facebook-official\"></i></a><a href=\"\"><i class=\"fa fa-twitter\"></i></a></li>\r\n </ul>\r\n </nav>\r\n <div class=\"clear\"></div>\r\n <div class=\"h1-container\">\r\n <h1>Text on line 1<br>text on line 2</h1>\r\n <p>lorem ipsum lorem ipsum lorem ipsum lorem ipsum <i class=\"fa fa-caret-right\"></i></p>\r\n </div>\r\n </div>\r\n</section>\n\nA:\n\nGiven the current context there are two simple ways to go about this.", "\nOne way would be to give .h1-container display: flex, flex-direction: column, and justify-content: center.", "\nHere is a jsfiddle.", "\nHowever, if you were to do it this way, each element and every new element placed in .h1-container will end up being stacked vertically and centered vertically in relation to .h1-container, so it will appear as if the children elements are not centered if .h1-container is not properly centered.", "\nAlso remember that justify-content always positions the children elements relative to the direction of the flex-box. ", "Therefore, if your flex-box direction is not explicitly set, and since the default is flex-direction: row, justify-content would position the children horizontally. ", "align-items will always be the opposite of the flex-box's direction property.", "\n\nbody {\r\n font: 15px/1.5 Arial, Helvetica, sans-serif;\r\n padding: 0;\r\n margin: 0;\r\n background-color: #f4f4f4;\r\n}\r\n\r\n\r\n/* Global */\r\n\r\n.container {\r\n width: 80%;\r\n margin: auto;\r\n overflow: hidden;\r\n}\r\n\r\n.clear {\r\n clear: both;\r\n}\r\n\r\nul {\r\n margin: 0;\r\n padding: 0;\r\n}\r\n\r\nsection h2 {\r\n line-height: 1.0;\r\n}\r\n\r\n.button_1 {\r\n height: 34px;\r\n background: tomato;\r\n border: 0;\r\n padding-left: 20px;\r\n padding-right: 20px;\r\n color: #ffffff;\r\n width: 200px;\r\n}\r\n\r\n.showcase-nav a {\r\n color: #ffffff;\r\n text-decoration: none;\r\n text-transform: uppercase;\r\n font-size: 16px;\r\n}\r\n\r\n.showcase-nav {\r\n padding-top: 30px;\r\n margin-top: 10px;\r\n float: right;\r\n}\r\n\r\n.showcase-nav li.social i {\r\n padding: 0 4px;\r\n}\r\n\r\n.showcase-nav li {\r\n display: inline;\r\n padding: 0 20px 0 20px;\r\n}\r\n\r\n.showcase-branding {\r\n float: left;\r\n}\r\n\r\n.showcase-branding h1 {\r\n font-size: 26px;\r\n margin: 0;\r\n padding-top: 30px;\r\n color: #fff;\r\n}\r\n\r\n.showcase-branding .highlight {\r\n color: #e8491d;\r\n font-weight: bold;\r\n}\r\n\r\n.showcase-nav a:hover {\r\n color: #cccccc;\r\n font-weight: bold;\r\n}\r\n\r\n.h1-container {\r\n width: 70%;\r\n margin: auto;\r\n display: flex;\r\n flex-direction: column;\r\n justify-content: center;\r\n}\r\n\r\n.h1-container h1 {\r\n text-transform: uppercase;\r\n text-align: center;\r\n color: #fff;\r\n}\r\n\r\n.h1-container p {\r\n width: 81%;\r\n background: tomato;\r\n margin: auto;\r\n border-radius: 10px;\r\n text-align: center;\r\n color: #fff;\r\n}\r\n\r\n\r\n/* Showcase */\r\n\r\n#showcase {\r\n background: url('http://i68.tinypic.com/2j5jho4.png') no-repeat;\r\n background-size: contain;\r\n width: 100%;\r\n display: inline-block;\r\n position: relative;\r\n margin: 0 auto;\r\n}\r\n\r\n#showcase:after {\r\n padding-top: 51.46%;\r\n display: block;\r\n content: '';\r\n}\r\n\r\n#showcase .container {\r\n position: absolute;\r\n top: 0;\r\n bottom: 0;\r\n right: 0;\r\n left: 0;\r\n}\r\n\r\n#showcase .h1-container h1 {\r\n font-size: 55px;\r\n margin-bottom: 10px;\r\n}\r\n\r\n#showcase p {\r\n font-size: 20px;\r\n padding: 5px;\r\n}\n <body>\r\n <section id=\"showcase\">\r\n <div class=\"container\">\r\n <div class=\"showcase-branding\">\r\n <h1>Title</h1>\r\n </div>\r\n <nav class=\"showcase-nav\">\r\n <ul>\r\n <li class=\"current\"><a href=\"about.html\">About</a></li>\r\n <li><a href=\"contact.html\">Contact</a></li>\r\n <li class=\"social\"><a href=\"\"><i class=\"fa fa-linkedin-square\"></i></a><a href=\"\"><i class=\"fa fa-facebook-official\"></i></a><a href=\"\"><i class=\"fa fa-twitter\"></i></a></li>\r\n </ul>\r\n </nav>\r\n <div class=\"clear\"></div>\r\n <div class=\"h1-container\">\r\n <h1>Text on line 1<br>text on line 2</h1>\r\n <p>lorem ipsum lorem ipsum lorem ipsum lorem ipsum <i class=\"fa fa-caret-right\"></i></p>\r\n </div>\r\n </div>\r\n </section>\r\n </body>\n\nThe other way would be to give .container position: relative, and then give .h1-container position: absolute, top: 50%, and transform: translateY(-50%).", "\nPositioning .container as relative allows you to absolutely position .h1-container in relation to .container as opposed to the entire document.", "\n.container {\n position: relative;\n}\n\n.h1-container {\n position: absolute;\n top: 50%;\n transform: translateY(-50%);\n}\n\nHere is a jsfiddle.", "\nThe following is an inline version which won't display properly due to the dimensions of everything, but it has at least centered the .h1-container.", "\n\nbody {\r\n font: 15px/1.5 Arial, Helvetica, sans-serif;\r\n padding: 0;\r\n margin: 0;\r\n background-color: #f4f4f4;\r\n}\r\n\r\n\r\n/* Global */\r\n\r\n.container {\r\n width: 80%;\r\n margin: auto;\r\n overflow: hidden;\r\n position: relative;\r\n}\r\n\r\n.clear {\r\n clear: both;\r\n}\r\n\r\nul {\r\n margin: 0;\r\n padding: 0;\r\n}\r\n\r\nsection h2 {\r\n line-height: 1.0;\r\n}\r\n\r\n.button_1 {\r\n height: 34px;\r\n background: tomato;\r\n border: 0;\r\n padding-left: 20px;\r\n padding-right: 20px;\r\n color: #ffffff;\r\n width: 200px;\r\n}\r\n\r\n.showcase-nav a {\r\n color: #ffffff;\r\n text-decoration: none;\r\n text-transform: uppercase;\r\n font-size: 16px;\r\n}\r\n\r\n.showcase-nav {\r\n padding-top: 30px;\r\n margin-top: 10px;\r\n float: right;\r\n}\r\n\r\n.showcase-nav li.social i {\r\n padding: 0 4px;\r\n}\r\n\r\n.showcase-nav li {\r\n display: inline;\r\n padding: 0 20px 0 20px;\r\n}\r\n\r\n.showcase-branding {\r\n float: left;\r\n}\r\n\r\n.showcase-branding h1 {\r\n font-size: 26px;\r\n margin: 0;\r\n padding-top: 30px;\r\n color: #fff;\r\n}\r\n\r\n.showcase-branding .highlight {\r\n color: #e8491d;\r\n font-weight: bold;\r\n}\r\n\r\n.showcase-nav a:hover {\r\n color: #cccccc;\r\n font-weight: bold;\r\n}\r\n\r\n.h1-container {\r\n width: 70%;\r\n margin: auto;\r\n position: absolute;\r\n top: 50%;\r\n transform: translateY(-50%);\r\n}\r\n\r\n.h1-container h1 {\r\n text-transform: uppercase;\r\n text-align: center;\r\n color: #fff;\r\n}\r\n\r\n.h1-container p {\r\n width: 81%;\r\n background: tomato;\r\n margin: auto;\r\n border-radius: 10px;\r\n text-align: center;\r\n color: #fff;\r\n}\r\n\r\n\r\n/* Showcase */\r\n\r\n#showcase {\r\n background: url('http://i68.tinypic.com/2j5jho4.png') no-repeat;\r\n background-size: contain;\r\n width: 100%;\r\n display: inline-block;\r\n position: relative;\r\n margin: 0 auto;\r\n}\r\n\r\n#showcase:after {\r\n padding-top: 51.46%;\r\n display: block;\r\n content: '';\r\n}\r\n\r\n#showcase .container {\r\n position: absolute;\r\n top: 0;\r\n bottom: 0;\r\n right: 0;\r\n left: 0;\r\n}\r\n\r\n#showcase .h1-container h1 {\r\n font-size: 55px;\r\n margin-bottom: 10px;\r\n}\r\n\r\n#showcase p {\r\n font-size: 20px;\r\n padding: 5px;\r\n}\n<body>\r\n <section id=\"showcase\">\r\n <div class=\"container\">\r\n <div class=\"showcase-branding\">\r\n <h1>Title</h1>\r\n </div>\r\n <nav class=\"showcase-nav\">\r\n <ul>\r\n <li class=\"current\"><a href=\"about.html\">About</a></li>\r\n <li><a href=\"contact.html\">Contact</a></li>\r\n <li class=\"social\"><a href=\"\"><i class=\"fa fa-linkedin-square\"></i></a><a href=\"\"><i class=\"fa fa-facebook-official\"></i></a><a href=\"\"><i class=\"fa fa-twitter\"></i></a></li>\r\n </ul>\r\n </nav>\r\n <div class=\"clear\"></div>\r\n <div class=\"h1-container\">\r\n <h1>Text on line 1<br>text on line 2</h1>\r\n <p>lorem ipsum lorem ipsum lorem ipsum lorem ipsum <i class=\"fa fa-caret-right\"></i></p>\r\n </div>\r\n </div>\r\n </section>\r\n </body>\n\n" ]

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[ "Social Sustainability\n\nSocial Sustainability\n\nAnother dimension to sustainability is social sustainability, which places emphasis\non the people and the communities in which they live.", "\n\nConsider the following definition:\n\n“Social sustainability occurs when the formal and informal processes, systems, structures,\nrelationships actively support the capacity of current and future generations to create\nhealthy and livable communities . . . ", "Socially sustainable communities are equitable,\ndiverse, connected and democratic and provide a good quality of life” (Hodgson 2008).", "\n\nThe University of West Georgia’s strategic plan makes a commitment to lead “in the\nfield of environmental and social sustainability”.", "\n\nOne aspect of social responsibility mentioned in the strategic plan is creating a\ncampus that is “emotionally and physically safe”. ", "Yet there is much more entailed\nin the broader UWG core values of caring, inclusiveness, and wisdom that can be applied\nto social sustainability. ", "The Center for Sustainability hopes to support and advertise\nsocial sustainability initiatives – check for events on the homepage. ", "Yet, it must\nalso be understood that there are a host of resources and departments that have significant\noverlap with the aims of social sustainability. ", "First and foremost check out UWG's\nCenter for Diversity and Inclusion." ]

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[ "This invention relates generally to devices having keyboards, such as personal-digital-assistant (PDA) devices having soft keyboards as well as desktop and laptop computers having real, physical keyboards, and more particularly to determining in conjunction with such keyboards a most likely intended-to-be-typed keystroke or sequence of keystrokes.", "\nSmall computerized devices that fit into the palm of one\"\"s hand, generally referred to as personal-digital-assistant (PDA) devices, have become increasingly popular. ", "They allow users to look up and record information where computer access is inconvenient, such as when in one\"\"s car, while shopping at the mall, during a business meeting, etc. ", "Unlike a typical desktop or laptop computer, which has an actual physical, or xe2x80x9creal,xe2x80x9d keyboard for text and data entry, a PDA device usually only has a small number of buttons, and a small touch-sensitive area on which a pen-like implement called a stylus can be used. ", "For text entry on such a device, the user is able to write letters or symbols corresponding to letters on the touch-sensitive area with the stylus, which the device attempts to recognize.", "\nHowever, for a variety of reasons, some users prefer not to input text into these devices in this manner. ", "Therefore, most PDA devices also permit a second form of text and data entry. ", "An image of a regular keyboard is displayed on the small display of a PDA device, such that a user is able to select which key to xe2x80x9ctypexe2x80x9d next by tapping the stylus on the part of the image of the keyboard corresponding to the desired key. ", "Such an image of a keyboard being displayed on the display of a device such as a PDA device, to provide for text and data entry on the part of the user by tapping the parts of the image corresponding to keys of the keyboard, is known as a xe2x80x9csoftxe2x80x9d keyboard.", "\nA disadvantage with such soft keyboards is, however, that the displayed keys of the keyboard on the display of the PDA device are very small, since the display of the device as well as the device itself are small. ", "This means that users are apt to tap incorrect keys, especially when xe2x80x9ctypingxe2x80x9d quickly, and also that users are apt to type more slowly using soft keyboards, because of the dexterity required in order to achieve a high accuracy rate when typing. ", "This limits the usefulness of these PDA devices, since they cannot very conveniently be used for quick and/or large amounts of text and data entry. ", "For this and other reasons, there is a need for the present invention.", "\nThe invention relates to fuzzy keyboards, to determine a most likely intended-to-be-typed keystroke or keystrokes. ", "In one embodiment, a computer-implemented method adds each of one or more keys to each of a current list of key sequence xe2x80x9chypotheses,xe2x80x9d to create a new list of key sequence hypotheses, upon a key press event. ", "For a soft keyboard, for example, a key press event may be the actuation of a location within the soft keyboard rendered on a touch-sensitive display. ", "For a hard keyboard, for example, a key press event may be the actuation of an actual key on the keyboard. ", "The method determines a likelihood probability for each hypothesis in the new list, and then removes any hypothesis that fails to satisfy any of one or more thresholds. ", "In one embodiment, the most likely key sequence of the new list is displayed.", "\nIn another embodiment specifically relating to soft keyboards, a computerized system includes a touch-sensitive display, a soft keyboard rendered thereon, and a computer program. ", "The computer program detects actuation of a location on the soft keyboard, and based at least thereon determines a most likely intended-to-be-typed key on the soft keyboard. ", "In another embodiment specifically relating to hard keyboards, a computerized system includes a keyboard and a computer program. ", "The computer program detects actuation of a key on the keyboard, and determines a most likely intended-to-be-typed key of the keyboard, based on at least the key actuated and either a key sequence of keys already determined to have been typed, a list of key sequence hypotheses, or both.", "\nEmbodiments of the invention provide for advantages not found within the prior art. ", "With respect to hard keyboards, the user may be typing fast, for example, and press the xe2x80x9cdxe2x80x9d key instead of the xe2x80x9cexe2x80x9d key. ", "However, the most likely key sequence hypothesis may be such that the typing of the xe2x80x9cexe2x80x9d key is much more probable than the typing of the xe2x80x9cdxe2x80x9d key. ", "As an example, the user may have initially typed xe2x80x9cThxe2x80x9d prior to the xe2x80x9cdxe2x80x9d key. ", "Because the xe2x80x9cdxe2x80x9d key is close to the xe2x80x9cexe2x80x9d key, and few words begin xe2x80x9cThdxe2x80x9d while many words begin xe2x80x9cThe,xe2x80x9d and also because the user was typing fast, the key sequence xe2x80x9cThexe2x80x9d may be displayed instead of xe2x80x9cThd.xe2x80x9d\nWith respect to soft keyboards, keys that are determined as more likely to be entered by the user have a greater probability that they are intended to be typed when the user actuates a location close to those keys. ", "For example, if the user actuates the soft keyboard in the vicinity between the xe2x80x9cdxe2x80x9d and the xe2x80x9cfxe2x80x9d keys, and the most likely key sequence hypothesis is such that the xe2x80x9cdxe2x80x9d key is more likely than the xe2x80x9cfxe2x80x9d key to have been typed by the user, then the xe2x80x9cdxe2x80x9d key may be displayed. ", "In some embodiments of the invention, past keystrokes may also be changed, up to a predetermined number of keystrokes before the current keystroke.", "\nFurthermore, it is noted that in one embodiment of the invention, the fuzzy keyboard as described herein can be implemented in conjunction with the predictive keyboard described in the copending, coassigned, and cofiled application entitled xe2x80x9cPredictive Keyboardxe2x80x9d having U.S. patent application Ser. ", "No. ", "09/484,079. ", "However, the invention itself is not so limited.", "\nThe invention includes computer-implemented methods, machine-readable media, computerized devices, computerized systems, and computers of varying scopes. ", "Other aspects, embodiments and advantages of the invention, beyond those described here, will become apparent by reading the detailed description and with reference to the drawings." ]

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[ "Hello and thank you for visiting AikiWeb, the\nworld's most active online Aikido community! ", "This site is home to\nover 22,000 aikido practitioners from around the world and covers a\nwide range of aikido topics including techniques, philosophy, history,\nhumor, beginner issues, the marketplace, and more.", "\n\nIf you wish to join in the discussions or use the other advanced\nfeatures available, you will need to register first. ", "Registration is\nabsolutely free and takes only a few minutes to complete so sign up today!", "\n\nNOTE: Though to some extent speculative and without the space to quote or cite sources and secondary references, these columns are really intended as a sort of preliminary sketch for a history of aikido as a martial art. ", "No such history has ever been published, though I know that at least one...\n\nMr. Ledyard, could I get you to elaborate on this? ", "I feel this is at odds with my own experience here on the ground in Japan, but you are obviously seeing things from a very different perspective.", "\n\nFor example, I'm a sumo fan. ", "A big sumo fan. ", "And thus, when I talk to a typical Japanese person about sumo, my knowledge far outstrips theirs. ", "The typical (practically scripted) reaction to this is for the self-deprecating Japanese person to say something like, \"Wow, you are more Japanese than I am!\" ", "Which of course is a very silly idea. ", "I simply possess a cache of specialized knowledge that reflects an interest of mine. ", "The typical Japanese person still knows far more about sumo than the typical American, and more to the point, even as an avid sumo enthusiast, when it comes to sumo knowledge I get my clock routinely cleaned by Japanese sumo enthusiasts. ", "And of course this goes both ways, as there are Japanese enthusiasts of certain American cultural aspects who know far more about baseball, jazz, etc. ", "than the average American.", "\n\nThis seems to be my experience here with other aspects of traditional Japanese culture. ", "The average non-Japanese practioner certainly falls to the right of the mean on an average distribution, but your statement \"many if not most of the senior students are foreigners\" seems somewhat hyperbolic. ", "I understand this to be the situation in Toda-ha Buko-ryu, and that Katori Shinto Ryu is experiencing a heavy influx of non-Japanese, but in most other classical arts it seems to me that for every dedicated-more-than-average foreign student, there are a number of dedicated-more-than-average Japanese students.", "\n\nOTOH, the budo world that I know on the English language internet is certainly different from the budo world that I know in real life. ", "So I'm very interested in your perspective.", "\n\nHi Josh,\nOf course, I only get to see a slice of the various arts, martial and otherwise, and that slice is based on my conversations with friends and acquaintances who have lived in Japan and trained or have done certain arts here. ", "There's no question I'm painting with a very broad brush here.", "\n\nOne of my good friends has lived over there for 20 years now, I believe. ", "She went over initially to do Aikido at Honbu and trained with Mitsuzuka Sensei in Iaido as well. ", "Eventually, she drifted away from the martial arts in favor of studying various non-martial arts. ", "Last i talked to her she studying traditional indigo dying and was heavily into the art of paper dolls. ", "What she told me was that, whereas there were certainly Japanese women in the classes, they tended to have a different perspective on things. ", "For them the classes were a culturally relevant hobby. ", "The teachers came from a generation which considered these art to be Michi, paths that one pursued as a form of personal development. ", "The younger generation didn't seem to have the same feeling and therefore were not as serious. ", "Her paper doll teacher actually asked her to take the instructor class because she seemed to have a deeper commitment. ", "This is not surprising as she gave up everything in her homeland to move to Japan and live. ", "She went there specifically to study.", "\n\nI know several people who are either senior or close to senior in some of the martial arts. ", "Ellis Amdur is technically the top parctitioner of the Toda Ha Buko Ryu Naginata style. ", "A number of the other menkyo kaidens are Americans and French. ", "I believe they outnumber the Japanese instructors. ", "There is a Japanese Soke because they felt that it wouldn't be appropriate to have the Soke not living in Japan. ", "But on technical matters Ellis is senior.", "\n\nEllis is also one of only a handful, Japanese or foreign to have studied the Araki Ryu. ", "It's obscure even in Japan and is in danger of passing away I believe as I am not sure there is a generation of instructors in the pipeline. ", "Ellis has trained one person to take over from him here and a couple other fellows have also trained with him for many years now. ", "It could easily come to pass that one or more lines of the Araki Ryu in Japan (I think there are three?) ", "could simply fade away leaving an American based line as crucial the art's preservation.", "\n\nKatori Shinto Ryu is another example... Otake Sensei has a son who will succeed him and by all accounts he his quite capable. ", "But after him it's Relnick Sensei, if I'm not mistaken.", "\n\nJodo also has some very high ranking foreigners with Quentin Chambers and Phil Relnick Senseis being the senior Americans as far as I know. ", "Relnick Sensei travels all over the world teaching Jodo, quite an unusual thing compared to the attitude shown by the folks at Aikido headquarters who would never, as far as I can see, have a foreigner acting on their behalf. ", "if someone contacts the aikikai for an instructor, they are not getting a referral to a non-Japanese teacher.", "\n\nOther than Ellis, the only other case with which I am directly familiar is Angier Sensei, Soke of the Yanagi Ryu. ", "By historical happenstance he ended up as the legitimate Soke of the style. ", "The family wasn't happy about it. ", "His visit to Japan wasn't satisfactory as he was not treated well by the other Japanese martial arts teachers. ", "Apparently they had a hard time with the idea that a foreigner could get to be a Soke.", "\n\nI have another friend who is a blade maker. ", "He is quite skilled and is known for his beautiful tantos. ", "He's had a couple on the cover of Knife Magazine. ", "We are talking about $6000 tantos here... Anyway, he also makes swords, I have one of his live blades. ", "He has two Japanese teachers that he goes back to train with periodically.", "\n\nThe saya on for my live blade has a special lacquer that my friend made a trip to Japan just to learn the technique. ", "That entails a level of commitment that is unusual. ", "But if you consider that there are actually quite a few people like my friend in the states and then other countries also have their equivalents, you can start to see that it's quite possible to have more serious exponents of an art outside the country than in. ", "I'm not saying that there won't be a Japanese Head of whatever style we are talking about but it's quite possible that the number of serious practitioners may outnumber the Japanese. ", "Or there may be foreign students who have been taught specific techniques which all or most of the Japanese students haven't been taught...\n\nRev. Koichi Barrish was the first American to bee certified as a Shrine Shinto Priest. ", "He trained under the head of the Grand Tsubaki Shrine. ", "He was taught the same Chinkon exercises which O-Sensei did daily, probably because of his connection with Aikido. ", "These are not generally taught to the young Priests in training these days. ", "Rev Barrish has found himself in the position of having young Japanese Priests ask him to teach them these exercises because there are so few Japanese Priests who know them.", "\n\nThese are just examples; I am sure that there are more. ", "Collectively, given the fact that there are students from all over the world who journey to train in Japan, the pure numbers can outbalance the number of serious practitioners in Japan itself. ", "I hear from virtually every quarter that the young people in Japan are increasingly less interested in many of their traditional arts, martial and otherwise. ", "If the Japanese can handle this well, as in the case of arts like KSR, then it will only benefit the arts. ", "But Aikido has not yet come to terms with this I believe, at least not the Aikikai. ", "They ar happy to have folks overseas do their art but I don't see them accepting foreign teachers at par with their Japanese peers.", "\n\n... I suggest that the transformation is evident, not just among the students, but among those who teach them, especially in Japan's high schools. ", "The 'cultural intensity' began much earlier that World War II and is the result of a large number of factors. ", "I think that hikikomori, parasaito shinguru and otaku are different manifestations of a certain cultural mania, as are bosozoku, kyouiku mama, ijime, and study groups that teach earnest participants how to sing karaoke songs correctly.", "\n\nThey are trying to find something they have lost and do not even know, really, how to identify so as to know when they have found it. ", "They are trying to rebuild something they have never actually seen.", "\n\nIse-Jinja is rebuilt every twenty years for more than one reason. ", "It is not merely the renewing of the structure, but the renewing and evolution of the process and the mentality that generates the structure from the foundation up. ", "Saotome, I think, understands this. ", "Saito understood it. ", "While different, they seem to have the same essential purpose -- to oppose the determinant of truth as pretense (whether as hierarchical validation, feel-goodism or many, many others, East and West) and keep the sense of real instantaneous encounter in the art.", "\n\nWhether, overgeneralizing, the art as a physical form is taught as form-preserves-principle (Saito) or principle-generates-form (Saotome) the intensity that drives a true encounter must be present or nothing will be gained in those -- or any other -- training paradigm. ", "It is that aspect, more so than any \"lost\" quantum of \"art,\" that is the problem. ", "It is the engine that both preserves and generates anew. ", "Musubi, I think, is the correct word here.", "\n\nThe clarity of true encounter is unmistakable -- and it is the antidote. ", "It does not require the competitive contest, although I understand why those who seek it verge into that territory. ", "It is the reason for training, in my opinion.", "\n\nI will not try to hold forth on my own technical art, as I well know its flaws, and its place. ", "But I know when I feel a true encounter. ", "I know when it is absent, and I know that even the most meager art in that true spirit will defeat the false one, however technically \"advanced.\" ", "When my art fails me, it is generally because I first failed the art, and this is why.", "\n\nIt will not be regained in Japan the manner that it was created. ", "Though not wholly different, they are also not the same. ", "It will not be regained here in the same manner as it was gained there, because we are also not the same. ", "The forms are there. ", "The principles are there. ", "They work. ", "I see them, and make them steadily work better in my own practice. ", "For this I deeply thank my teachers, of every lineage. ", "But what has extended my art, and built upon their foundation of both form and principle has been attending to them in true encounters in practice. ", "Without that it is just dead repetition -- with it, everything is both tantalizingly new and yet increasingly familiar.", "\n\nWe rebuild the shrine. ", "We remake, in every life and every generation, something both continuous and yet new with only pieces of what preceded. ", "It is true in every katachi, in the instant of one cut and in the passing of generations. ", "We always build new with broken or raw parts. ", "It is the way our bodies re-structure and restore themselves -- it is the way we stay in dynamic balance -- always one step from falling down. ", "And when we stop building new, we die, literally and figuratively, whether in the instant of attack or in the history of an art.", "\n\nVery few, East or West are comfortable with this precarious perch we all occupy. ", "Far more are comforted by carefully maintained illusions of security or \"unbroken\" continuity, whether social or individual. ", "The breaking of these illusions is a cause for anger, despair or hope, depending on one's approach. ", "The radical reality and immediacy of the true encounter -- what Levinas described as the irreducible Other -- is a thing of awe, and awe is a source of both wonder and fear. ", "Little in modern society prepares us to meet it, and much that did prepare us has in varying degrees been discarded, abused or perverted.", "\n\nWe cannot usefully mourn \"lost\" master carpenters (though they well deserve our remembrance), or their sketch notes, who did the rebuilding twenty years ago. ", "They, like us started where we are. ", "They, like us all, turned out to be ultimately frail, and notes fade and rot. ", "We cannot pack up their knowledge complete and unpack it again, every twenty years. ", "The most we can hope is to keep seeds, sprout them new again, and give faithful tending.", "\n\nResponding to awe in wonder and invitation, radically accepting the Other is Aikido. ", "Refusing true encounter, or accepting it in less than complete terms, leads to many pathologies, some we have mentioned, and many others besides, individually and collectively. ", "And none of us are immune to that, at any moment, except through diligently developed habits of better response. ", "That is not lost, but each of us can lose it.", "\n\nIf I may request that the truck be put in reverse for a moment, I fear some unnecessarily broad cultural generalizations are being made here. ..", "\n\"Hikikomori\", ... It's prevalence in Japan has been distinctly overstated, ... \"Parasite singles\" are, IMO, a tempest in a teapot, ...\n\nBosozoku, ijime, and to a lesser extent kyoiku mama, I see as definite social issues that Japan faces these days. ... ", "There's a tendency, I think, to make the fundamental attribution error on a cultural scale.", "\n\nIt's all too easy to look at some ephemeral social phenomenon and believe it says something about the culture in which it was born.", "\n\nI come from a tradition where \"the least of these\" are important in their own right, regardless of their absolute or relative number. ", "But the pace and scale of spreading anomie is quite beyond historical precedent, especially in societies as unprecedentedly prosperous as ours are.", "\n\nIt is a problem larger than one culture, although the effects of the problems are felt differently according to culture -- and aikido lives in both of them. ", "The margins of the nonadaptive are growing -- not shrinking. ", "Thomas Sowell said it best: \"Each new generation born is in effect an invasion of civilization by little barbarians, who must be civilized before it is too late.\" ", "The work of civilizing has been falling down on the job, around the world, for some time now. ", "The canaries are not the miners but the miners had best value the health of the canaries -- as they value their own.", "\n\nIt is a very tough thing to let go of one's ancestry, one's heritage, one's sense of ... place.", "\n\nTake, for example, the American Civil War. ", "We have thousands of Americans who delve deeply into reenactments of that period. ", "Some of them have very close ties with those who fought and died. ", "These reenactments are not just idle time killers. ", "Some people put in long hours of sweat and blood to try to get things as close to real as possible. ", "While it is also a social activity and brings people closer together.", "\n\nNow, imagine, someplace in Japan studying these reenactments and putting on their very own Civil War Reenactment involving only Japanese. ", "While they could get very nearly to perfection in details, history, clothing, and sense of the Civil War, they, nor their ancestors had anything to do with the Civil War.", "\n\nIt isn't a great example/analogy/whatever, but it gives food for thought.", "\n\nWhile I understand that non-Japanese can delve just as deeply into Budo as Japanese, Aikido is still relatively new enough to have the kinds of hurdles I illustrated above. ", "This up and coming generation of Aikido teachers are going to have their work cut out for them. ", "Not only are they removed from founder and first generation, but they are going to have to stand on their own without the myriad of support from Japanese instructors as we have now, all the while having to deal with Japan hombu dojos and the Japanese view that the source/center/base of aikido is there.", "\n\nReally, the one thing I find hopeful about this is that Americans can do what the Japanese choose not to -- Americans can build bridges between organizations, no matter what level of difference (The Aiki Expos are prime examples of this). ", "As long as politics do not interfere. ", "We have an opportunity with the next gen of teachers to bring things together rather than fracture them more. ", "But, will we?", "\n\nBosozoku, ijime, and to a lesser extent kyoiku mama, I see as definite social issues that Japan faces these days. ", "However, if I may take up the (much trodden on) banner of cultural relativity, I don't know if I can agree with Professor Goldsbury's characterization of this as \"cultural mania\". (", "Although I suspect we are actually close together in our views, and this more a quibble over semantics.)", "\n\nHello Josh,\n\nI spent much of my time explaining to my students here the grave perils involved in making supposedly 'objective' cultural comparisons. ", "My working hypotheses concerning culture come from Hofstede (Culture's Consequences, Culture and Organizations: Software of the Mind) and the research on which these works are based. ", "I have very little time for the usual run of books on 'Japanese' 'culture'.", "\n\nHi Peter\nSome how I missed addressing you directly in the post above. ", "My apologies. ", "Of course I was directing my comments to you, and would be delighted in any views you care to share.", "\nBTW Outside of the obvious and well documented \"vision of peace\" after the war and influence of Omoto-are you going to consider covering how Ueshiba's vision might have been birthed and given substance by his growing internal skills having the ability to manage aggression without having to attack back? ", "How the generation of internal power became the embodiment of a truly defensive and peaceful art?", "\n\nWere you considering this-any thoughts as to which of these realizations might have been the real prime motivator? ", "The body skills awakened a new vision, or the vision made him change his approach to the Martial arts?", "\nCheers\nDan\n\nHello Dan,\n\nVery interesting questions. ", "I will keep these and your earlier comments / questions in mind as I write further columns.", "\n\nI think the Oomoto 'vision of peace' was clearly prewar and though M Ueshiba virtually stopped contact with Deguchi after the 2nd Oomoto Incident, I do not think he abandoned his beliefs or changed his 'vision'. ", "I do not know, for example, whether he did chinkon kishin training before he met Deguchi (it does not seem Takeda's style somehow), but from the material I have read in Japanese, meeting Deguchi was an important spur to his own private training.", "\n\nI plan to discuss this more when I consider Kisshomaru Ueshiba's ideas about personal training.", "\n\nVery interesting questions. ", "I will keep these and your earlier comments / questions in mind as I write further columns.", "\n\nI think the Oomoto 'vision of peace' was clearly prewar and though M Ueshiba virtually stopped contact with Deguchi after the 2nd Oomoto Incident, I do not think he abandoned his beliefs or changed his 'vision'. ", "I do not know, for example, whether he did chinkon kishin training before he met Deguchi (it does not seem Takeda's style somehow), but from the material I have read in Japanese, meeting Deguchi was an important spur to his own private training.", "\n\nI plan to discuss this more when I consider Kisshomaru Ueshiba's ideas about personal training.", "\n\nBest wishes,\n\nPAG\n\nHello Peter\nI guess the flip side of the coin is whether the solo tanren that exists in Daito ryu were meant for strictly martial purposes and developed the power that Ueshiba had, and where his later chinkon kishin came into play to either blend, morph, or actually -in the end-to do nothing to add to his physical powers.", "\nI've long held a view that it was Ushiba's realization that he could use the internal power-to control and cast away rather than use the associated DR jujutsu waza to draw-in, immobilize and kill, that opened a window into his new vision of peace. ", "That it was this match of the spiritual and physical expression that created *his* Aikido. ", "And it was this that gave Aikido its true testament of power. ", "What Aikido was meant to be all along.", "\n\nAs for Takeda- lest it be ignored- he stated many times that the power of Daito ryu was always meant for defense. ", "Even stating how terrible it would be for this knowldege to be passed into the hands of the wrong type of people.", "\n\nWhy consider Takeda?", "\nWhile much is made of Ueshiba's personal journey and morphing of Takeda's teachings- it is worth considering that NONE of the schools of Daito ryu look the same either. ", "There were what, five of them who founded schools? ", "Four of the five stated that *they* had seen past Takeda's work and changed themselves. ", "It was their understanding of Daito ryus true power, power that Sagawa openly stated that Takeda told him never to reveal, that was the catalyst for *their* personal expressions. ", "Personally, I think it is the nature of the work itself. ", "That it is so highly individual in nature that it can join a mans personal nature and pursuits to his waza. ", "At any rate IMO it places Ueshiba's work in a more revealing light-to see it along side his peers. ", "That each of them ended up with a powerful, yet highly personalized expression of what was supposed to be a single art- bears testament to this idea.", "\nIn the end Ueshiba's journey may not have been as *unique* as previously thought, just more well known, and more attractive to the populace at that time.", "\n\nI do think \"the rot\" set in to Aikido long ago, but I have born witness to it being reversed. ", "All that is needed is a begginers mind and a firm belief in change. ", "Were good teachers, good men with a caring and honest soul to learn these skills, then there is no way to lose. ", "These skills, simply work.", "\n\nRe George's post above:\nIn Toda-ha Buko-ryu, we have four shihan. ", "I am \"first\" among equals only in the sense that I'm first to be made shihan, but I'm not even senior among us. ", "None of us does the kata exactly the same, and that's fine. ", "There will be a next generation soke as well, and it will not be a Westerner, about which all of us, to my knowledge are very happy. ", "A Westerner could not fulfill that post. ", "I do not want to go any further into this, as that would drift the thread.", "\n\nRe George's post above:\nIn Toda-ha Buko-ryu, we have four shihan. ", "I am \"first\" among equals only in the sense that I'm first to be made shihan, but I'm not even senior among us. ", "None of us does the kata exactly the same, and that's fine. ", "There will be a next generation soke as well, and it will not be a Westerner, about which all of us, to my knowledge are very happy. ", "A Westerner could not fulfill that post. ", "I do not want to go any further into this, as that would drift the thread.", "\n\nBest\nEllis\n\nThanks Ellis,\nMy memory on these things gets a bit murky at times. ", "Are any / all of the Shihan Westerners? ", "I'd be interested...\n- George\n\nHello Peter\nI guess the flip side of the coin is whether the solo tanren that exists in Daito ryu were meant for strictly martial purposes and developed the power that Ueshiba had, and where his later chinkon kishin came into play to either blend, morph, or actually -in the end-to do nothing to add to his physical powers.", "\nI've long held a view that it was Ushiba's realization that he could use the internal power-to control and cast away rather than use the associated DR jujutsu waza to draw-in, immobilize and kill, that opened a window into his new vision of peace. ", "That it was this match of the spiritual and physical expression that created *his* Aikido. ", "And it was this that gave Aikido its true testament of power. ", "What Aikido was meant to be all along.", "\n\nPAG. ", "This is a very attractive view. ", "In the two biographies we have of Ueshiba (Kisshomaru Ueshiba's and Kanemoto Sunadomari's), there is constant emphasis placed on Ueshiba's own personal training regime, which was there right from the very beginning and which was refined as he went along. ", "However, and I have heard this from Kisshomaru directly, he appears never to have systematized this for teaching purposes and thus his students 'got' it, only to the extent that they were able to realize for themselves the importance of what he was doing: what lay behind the waza he was constantly showing.", "\n\nQuote:\n\nDan Harden wrote:\n\nAs for Takeda- lest it be ignored- he stated many times that the power of Daito ryu was always meant for defense. ", "Even stating how terrible it would be for this knowldege to be passed into the hands of the wrong type of people.", "\n\nPAG. ", "Yes. ", "Ueshiba is also alleged to have stated that aikido should not be taught to the 'wrong' people: most people assume that he simply meant the waza.", "\n\nQuote:\n\nDan Harden wrote:\n\nWhy consider Takeda?", "\nWhile much is made of Ueshiba's personal journey and morphing of Takeda's teachings- it is worth considering that NONE of the schools of Daito ryu look the same either. ", "There were what, five of them who founded schools? ", "Four of the five stated that *they* had seen past Takeda's work and changed themselves. ", "It was their understanding of Daito ryus true power, power that Sagawa openly stated that Takeda told him never to reveal, that was the catalyst for *their* personal expressions. ", "Personally, I think it is the nature of the work itself. ", "That it is so highly individual in nature that it can join a mans personal nature and pursuits to his waza. ", "At any rate IMO it places Ueshiba's work in a more revealing light-to see it along side his peers. ", "That each of them ended up with a powerful, yet highly personalized expression of what was supposed to be a single art- bears testament to this idea.", "\nIn the end Ueshiba's journey may not have been as *unique* as previously thought, just more well known, and more attractive to the populace at that time.", "\n\nPAG. ", "Did you know that that a new book has come out on Sagawa? ", "It is much more detailed than Kimura's material and is by another of Sagawa's students, Masaru Takahashi. ", "The title is Sagawa Yukiyoshi Sensei-den: Daito-ryu Aiki no Shinshitsu. ", "It is worth having just for the photographs and the diagrams.", "\n\nQuote:\n\nDan Harden wrote:\n\nI do think \"the rot\" set in to Aikido long ago, but I have born witness to it being reversed. ", "All that is needed is a begginers mind and a firm belief in change. ", "Were good teachers, good men with a caring and honest soul to learn these skills, then there is no way to lose. ", "These skills, simply work.", "\n\nCheers\nDan\n\nPAG. ", "I have read everything I can about Ueshiba and asked questions of those surviving deshi I know. ", "I do not think his life followed a fixed course, in the sense that he found a vision in his youth and consistently followed it. ", "Then there is the fact of the war. ", "I have often wondered what would have happened if he had not moved to Iwama in 1942.", "\n\nPAG. ", "This is a very attractive view. ", "In the two biographies we have of Ueshiba (Kisshomaru Ueshiba's and Kanemoto Sunadomari's), there is constant emphasis placed on Ueshiba's own personal training regime, which was there right from the very beginning and which was refined as he went along. ", "However, and I have heard this from Kisshomaru directly, he appears never to have systematized this for teaching purposes and thus his students 'got' it, only to the extent that they were able to realize for themselves the importance of what he was doing: what lay behind the waza he was constantly showing.", "\n\nBest wishes,\n\nPAG\n\nI've read a similar thing elsewhere, but can't remember where or who wrote it (Most likely it was either you or Ellis). ", "And although we know that Ueshiba had his own personal regime, I don't think I've ever seen anyone state what it was. ", "Does anyone know what that personal regime was?", "\n\nI think he exposed a little of his praying routines in a text titled Accord with the totality of the Universe (Aikidojournal aritcle). ", "And Hikitsuchi sensei definitely stated that chinkonkishin no ho ( http://www.cs.ualberta.ca/~mckellar/aiki/1999/0.html ) was transmitted to him by O Sensei and was a daily practice of his.", "\n\nIt may well be that the bona fide uchideshi (pre-war) were the ones who were able to witness the personal training. ", "Same for Ueshiba in the time spent with Takeda Sensei in Hokkaido. ", "I wonder how, without that live in, bath, take care of experience, you would pick those personal training regimes up.", "\n\nBest,\nRon\n\nRon Tisdale\n-----------------------\n\"The higher a monkey climbs, the more you see of his behind.\"", "\nSt. Bonaventure (ca. ", "1221-1274)\n\nIt may well be that the bona fide uchideshi (pre-war) were the ones who were able to witness the personal training. ", "Same for Ueshiba in the time spent with Takeda Sensei in Hokkaido. ", "I wonder how, without that live in, bath, take care of experience, you would pick those personal training regimes up.", "\n\nBest,\nRon\n\nThats another good question Ron and feeds directly into the transmission question. ", "If we put aside who got what where, we are left with a very obvious outcome. ", "Somebody, somewhere, was able to show and teach or nobody would have \"gotten\" anything. ", "But why the live in, take a bath, eat the same food idea? ", "Obviously that didn't work either. ", "I think in the end it was always there to be had if someone either knew how to teach it or even wanted to. ", "IMO it is, and always was, best pursued as a separate study from kata.", "\n\nIf we say that Tohei went elsewhere- then he most certainly got it?", "\nWe know Shioda stepped outside and he got it as well.", "\nNow Ikeda is looking and researching and he is getting it.", "\n\nSo it is there to be gotten. ", "So why isn't it being taught-in Aikido? ", "George makes interesting points with his teacher. ", "That maybe Saotome doesn't know how to transfer or convey the internal information or what he knows of it into a teachable model. ", "Knowing a thing and being able to teach it amidst all the other stuff you are trying to teach might be VERY distracting. ", "And it will not draw most people to it. ", "It is not immediate, and requires an intuitive, creative and obsessive mindset. ", "Maybe Ellis is right you either were an oddduck to pursue it or you became one in the end.", "\n\nSince a series of Aikidoka are now looking elsewhere; at DR methods, Ushiro's methods, etc, why would their bring-back information be seen as anything different than what these earlier men have been doing all along. ", "Including keeping Mum about it (which is what I tell them to do) till -they- become the new seniors.", "\nThen viola...fixed.", "\nBy a series of oddducks.", "\nBut here's the rub. ", "Ask them about it. ", "It certainly seems they have found some things that they are convinced are worth having and training...too bring back, but they can't yet. ", "They are getting all obsessive and odd about \"getting it\" first.", "\nCheers\nDan\n\nAs noted by PAG (roughly paraphrased by me), those that got it figured it out for themselves.", "\n\nHi John:\n\nThe way I would phrase it is that everyone grabs as much information wherever they can and then the rest depends on how hard they work at it and how well they can figure out the gaps.", "\n\nThere is a broad spectrum of abilities and understanding and there is a broad spectrum of specialized ways to apply these skills. ", "To give an example of what I'm trying to say, even though they all understood \"aiki\", Shioda, Ueshiba, and Tohei (to grab examples), those three still had varying degrees of the other things they could do with those skills. ", "If it comes to \"aiki\" itself, the one that I see on film having the widest repertoire of aiki applications seems to be Shioda.... he apparently revelled in that part of it. ", "Ueshiba appears (to my eyes) to have something about power-release skills that Tohei and Shioda didn't have. ", "And so on.", "\n\n\"Figure it out\" is certainly part of it. ", "My opinion is that these are the early days of western Aikido people beginning to acquire and apply these skills into Aikido and it should be interesting to watch the developments by some of the up and coming crowd. ", "Good times.", "\n\nKnowledge is a product of both ones experience and what is inherited from those who have gone before. ", "The depth of knowledge attained by earlier teachers was not simply the result of their personal effort. ", "They were given the basic material and ran with it. ", "That's why lineage and transmission are so important. ", "Their kind of knowledge is like and endangered species. ", "Once it is lost, it will not evolve again. ", "The Japanese Koryu have recognized this and have developed a systematic method for the transmission of the core elements of the style across generations. ", "While there are isolated pockets of Aikido being taught in this manner, most Aikido is not.", "\n\nI think and feel George, you have summed this up here in one paragraph as something fundamental and that which is missing in most of today's aikido..... It reflects my feelings accurately...." ]

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[ "Systematic review of resource utilization in the hospital management of deliberate self-harm.", "\nDeliberate self-harm (DSH) is a significant public health problem, representing a major burden in terms of morbidity to the individual and health-service utilization. ", "While clinical guidelines suggest good practice for the short-term hospital management of DSH, there remains considerable variability in the way that services are provided. ", "A systematic review of the literature was undertaken to examine the current evidence on hospital resource use and costs involved in the short-term hospital management of adults following DSH and to elucidate the factors that influence these differences, in terms of clinical characteristics and service provision. ", "Twenty-one papers reporting on 17 studies met the inclusion criteria for review. ", "Clinical characteristics associated with an increase in resource use included overdose with tricyclic antidepressants (TCAs) compared with selective serotonin re-uptake inhibitors (SSRIs) (weighted ratio 2.6:1) and co-ingestion of alcohol with SSRIs. ", "Variations in service provision, including medical admissions policy and provision of a specialist liaison service, affected resource utilization independently of the clinical needs of patients. ", "Overdoses of TCAs incur substantially greater hospital costs than overdoses of SSRIs. ", "Variations in the medical seriousness of DSH, and in the structure of service provision, affect the resources used in its short-term hospital management, with little evidence about the impact these differences have on clinical outcome. ", "Research is needed to evaluate the impact of different styles of service provision on outcome, and to incorporate these factors into the trial design of future cost-effectiveness studies of interventions following DSH." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Jesus also, that he might sanctify the people with his own blood, suffered outside the gate. ", "Therefore, let us go forth to him outside the camp, bearing his reproach. ", "For we have no continuing city here, but we seek one to come.", "\n\nNahum\n\nChapter 1\n\n¶1. ", "The burden of Nineveh. ", "The book of the vision of Nahum the Elkoshite.", "\n\n2. ", "God is jealous, and theLord takes vengeance. ", "The Lord avenges and is the Master of wrath. ", "The Lord takes vengeance on his adversaries and reserves it for His enemies.", "\n\n3. ", "Though great in power, the Lord is slow to anger, but He will never leave the wicked unpunished. ", "His way is in the whirlwind and the storm, and the clouds are the dust of his feet.", "\n\n4. ", "Rebuking the sea, He made it dry, and He dried up all the rivers. ", "Bashan and Carmel withered, and theblossom of Lebanon languished.", "\n\n5. ", "Because of Him, mountains quake and the hills melt away. ", "The earth heaves at His presence, both the world and all its inhabitants.", "\n\n6. ", "Who can stand before His indignation? ", "Who can withstand the fury of His anger? ", "His wrath is poured out like fire, and the rocks are thrown down by Him.", "\n\n7. ", "The Lord is good, a stronghold in the day of trouble, and He knows those who take refuge in Him,\n\n8.but with an overflowing flood will He utterly destroy this place, and darkness shall pursue His enemies.", "\n\n9. ", "What will you devise against the Lord? ", "He will make an utter end. ", "Trouble will not rise up a second time.", "\n\n10. ", "For while entwined like briars and drunk like drunkards, they will be completely consumed like dry stubble.", "\n\n11. ", "There is one come out from you who plots evil against the Lord, a wicked counsellor.", "\n\n¶12. ", "Thus says the Lord, “Though they be powerful and very many, yet they shall still be cut off and pass away. ", "Though I have afflicted you, I will humble you no more.", "\n\n13.And now I will break his yoke from off you, and I will break off your bonds.”", "\n\n14. ", "And the Lord commands concerning you, “There shall be no seed for your name anymore. ", "I will cut off the graven and molten image from the house of your gods. ", "I will make your grave, for you are worthless.”", "\n\nChapter 2 [Hebrew text]\n\n¶15/1. ", "Behold! ", "Upon the mountains! ", "The feet of the one bringing good news, proclaiming peace. ", "Keep your feast, Judah! ", "Fulfill your vows! ", "For never again will the destroyer pass through you. ", "He has been cut off completely.", "\n\nChapter 2\n\n2/3. ", "For the Lord is restoring majesty to Jacob like the majesty of Israel, though the plunderers wasted them and spoiled their branches.", "\n\n3/4. ", "The shield of his mighty ones are dyed red. ", "The valiant men, clad in scarlet, come with flashing iron chariots in the day of his preparation. ", "And the fir trees are made to quiver.", "\n\n4/5. ", "The chariots rage through the streets. ", "They rush back and forth through the plazas. ", "They look like torches. ", "They dart about like lightning.", "\n\n5/6. ", "He will remember its nobles. ", "They will stumble as they go. ", "They will hurry her wall, and a defense will be prepared.", "\n\n6/7. ", "The gates of the rivers were opened, and the palace was melted away.", "\n\n7/8. ", "It is determined. ", "She is stripped; she is carried away, and her maidservants lament like the sound of doves, beating on their breasts.", "\n\n8/9. ", "Though Nineveh was like a pool of water throughout her days, now they are fleeing. “", "Stop! ", "Stop!” ", "But no one turns back.", "\n\n9/10. ", "Plunder the silver! ", "Plunder the gold! ", "There isno end to the stores; there is an abundance of every precious thing.", "\n\n10/11. ", "Empty! ", "Laid waste and devastated! ", "The heart melts, knees buckle, searing pain is in all loins, and their faces have all turned ashen!", "\n\n11/12. ", "Where is the lions’ den and the pasture for the young lions, where the lion and lioness and the young lion walked? ", "Nothing made them afraid.", "\n\n12/13. ", "The lion tears enough for his cubs and strangles for his lionesses, and he fills his caves with prey and his dens with torn flesh.", "\n\n13/14. “", "Behold, I am against you!” ", "says the Lord of hosts. “", "I will burn up her chariot in smoke, and a sword shall devour your young lions. ", "I will cut off your prey from the earth, and the voice of your messengers will no longer be heard.”", "\n\nChapter 3\n\n¶1. ", "Woe to the bloody city! ", "She is filled with lying and robbery — endless prey!", "\n\n2. ", "The sound of a whip, and the noise of rumbling wheels, and the galloping of horse, and the bounding of chariot,\n\n3.mounted horseman, and flashing sword, and glittering spear, and a multitude of slain, a mass of corpses. ", "There is no end of dead bodies; they will stumble over their corpses,\n\n4.all because of the multitude of whoredoms of the harlot, the beautiful, well-favored mistress of sorceries, who sells nations with her whoredoms and families with her sorceries.", "\n\n5. “", "Behold, I am against you,” says the Lord of hosts, “and I will take off your robes that are on your body and expose your nakedness to the nations, and your shame to the kingdoms.", "\n\n6.I will cast abominations upon you! ", "I will disgrace you and make you a spectacle!", "\n\n7.It shall come to pass that everyone who sees you will flee from you, saying, ‘Nineveh is devastated!’ ", "Who will weep for her? ", "Where will I find comforters for you?", "\n\n8.Are you better than No-Amon, who was situated with the Nile waters surrounding her,whose rampart was the sea, her protective wall, water?", "\n\n9.Cush and Egypt were her might, and it was limitless. ", "Put and Lubim have been your helpers.", "\n\n10.Yet she became an exile; she went into captivity. ", "Her children were dashed to pieces at the head of all the streets, and they cast lots for her nobles, and all her mighty men were bound in fetters.", "\n\n11.You will also be drunk. ", "You will hide yourself. ", "You will seek protection from the enemy.", "\n\n12.All your strongholds are fig trees with ripe fruits. ", "When they are shaken, they will fall into the mouth of the eater.", "\n\n13.Behold, your people in your midst are women. ", "The gates of your land are opened to your enemies. ", "Fire consumes the bars of your city gates.", "\n\n14.Draw water for yourself for the siege! ", "Strengthen your fortresses! ", "Go to the mire and tread the mortar! ", "Make the brick firm!", "\n\n15.There will the fire devour you. ", "A sword will cut you off. ", "It will devour you like the devouring locust. ", "Multiply yourself like the devouring locust! ", "Multiply yourself like the young locust!", "\n\n16.You have made your merchants more numerous than the stars of heaven. ", "The devouring locust raids and flies away.", "\n\n17.Your princes are like the young locust, and your marshals are like a swarm of locust that settles on stone walls on a cold day. ", "The sun rises, and it flees away, but the place where it goes is unknown.", "\n\n18.Your shepherds slumber, O King of Assyria. ", "Your nobles sleep. ", "Your people are scattered on the mountains, and they do not gather together.", "\n\n19.There is no help for your affliction; your wound is incurable. ", "All that hear your report clap the hands over you, for over whom has not your wickedness continually passed?”" ]

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[ "---\nabstract: 'For a polygonal linkage, we produce a fast navigation algorithm on its configuration space. ", "The basic idea is to approximate $M(L)$ by the vertex-edge graph of the cell decomposition of the configuration space discovered by the first author. ", "The algorithm has three aspects: (1) the number of navigation steps does not exceed 14 (independent on the number of edges), (2) each step is a disguised flex of a quadrilateral from one triangular configuration to another, which can be ranged as well understood type of flexes, and (3) each step can be performed in a mechanical way.'", "\naddress: '\\* Institute for Informatics and Automation, St. Petersburg, Russia, Saint-Petersburg State University, St. Petersburg, Russia, e-mail:gaiane-panina@rambler.ru. ", "$^\\dag$ University of Utrecht, Mathematisch Instituut, Utrecht, The Netherlands, e-mail: D.Siersma@uu.nl. '", "\nauthor:\n- 'Gaiane Panina\\*, Dirk Siersma$^\\dag$'\ntitle: Motion planning and control of a planar polygonal linkage\n---\n\nIntroduction\n============\n\nIn the paper we work with a polygonal linkage (equivalently, with a flexible polygon), that is, with a collection of rigid bars connected consecutively in a closed chain. ", "We allow any number of edges and any lengths assignments, (under a necessary assumption of the triangle inequality, which guarantees the closing possibility). ", "The flexible polygon lives in the plane and admits different shapes, with allowed self-intersections. ", "Taken together, they form the moduli space of the linkage. ", "In the paper, we produce a motion planning algorithm (equivalently, a navigation algorithm) which explicitly reconfigures one shape to another via some continuous motion. ", "In the language of the moduli space this means that we present a path leading from one prescribed configuration to another. ", "We not only indicate the path, but also present a way of forcing the linkage to follow the path.", "\n\nAlthough the problem looks not much complicated (since the more edges we have, the more freedom degree we have), the navigation is not an easy issue because of the (possible) topological complexity of the moduli space.", "\n\nOur reconfiguring algorithm is based on a stratification of the moduli space into a cell complex, introduced in [@Pan]. ", "More precisely, we treat the one-skeleton of the complex as an appropriate approximation of the moduli space. ", "In other words, we have an embedded graph, and we mostly navigate along the graph. ", "More precisely, the navigation goes as follows: from a given configuration of the linkage, we first reach an appropriate vertex of the graph, then navigate along the graph until we are close to the target configuration, and next, we pass to the target configuration. ", "There are three important aspects about the algorithm:\n\n1. ", " The number of steps (i.e., the number of edges of the connecting path) never exceeds 13. ", "That is, we have a finite time algorithm with at most 14 steps (rather than $n$ or even $log \\ n$ complexity).", "\n\n2. ", " Each of the steps (that is, going along an edge of the graph is a disguised flex of a quadrilateral polygonal linkage, which is both simple and well-understood.", "\n\n3. ", " Each of the steps can be performed in a mechanical way.", "\n\nThe paper is organized as follows. ", "Section \\[SecPrelim\\] gives precise definitions and explains the cell structure on the configuration space. ", "Besides, we present introductory examples and give a formula for the number of vertices of the graph $\\Gamma$. The navigation on the graph is in Section \\[SecNavigationOnGraph\\]. ", "We show that a vertex-to vertex navigation requires at most 13 steps.", "\n\nOur next goal is to control the prescribed motions. ", "We work under assumption that we have a full control of convex configurations. ", "There are different approaches how to do this: by using Coulomb potential, as in [@KHPS], by mechanically controlling the angles, or in some other way, not to be discussed in the paper. ", "However we stress that for navigating over edges of the graph, is suffices to control just quadrilaterals, which is a much easier task, and which is well understood in all respects.", "\n\nFor a navigation from arbitrary point of the moduli space to a vertex requires one more step: we need to connect the starting point to the graph. ", "There are two different ways to initiate the algorithm in a mechanical way are described in Section \\[SecNavigationOnModuli\\].", "\n\nThe results presented in this paper arose as a natural continuation of the research on Morse functions on moduli spaces of polygonal linkages started in [@khim2010], [@khipan], [@KHPS]. ", "Several approaches to navigation and control of mechanical linkages have previously been discussed, in particular, in [@hausmann], [@hausmannrodriguez], [@khim2010] and [@KHPS]. ", "It seems worthy of noting that some complications related to non-trivial topology of moduli space prevented complete solution to navigation and control problem and served as a main motivation for our research.", "\n\n**Acknowledgments** The authors acknowledge useful discussions with George Khimshiashvili and hospitality of CIRM, Luminy, where this research was completed in framework of “Research in Pairs” program in January of 2014.", "\n\n Moduli spaces of planar polygonal linkages {#SecPrelim}\n===========================================\n\nWe start by a short review of some results on polygonal linkages and their moduli spaces.", "\n\nA *polygonal $n$-linkage* is a sequence of positive numbers $L=(l_1,\\dots ,l_n)$. It should be interpreted as a collection of rigid bars of lengths $l_i$ joined consecutively in a chain by revolving joints. ", "In the literature, it is sometimes called *bar-and-joint mechanism*.", "\n\nWe assume that $L$ satisfies the triangle inequality.", "\n\n*A configuration* of $L$ in the Euclidean plane $ \\mathbb{R}^2$ is a sequence of points $R=(p_1,\\dots,p_{n}), \\ p_i \\in \\mathbb{R}^2$ with $l_i=|p_i,p_{i+1}|$, and $l_n=|p_n,p_{1}|$.\n\nThe set $M(L)$ of all configurations modulo orientation preserving isometries of $\\mathbb{R}^2$ is *the moduli space, or the configuration space* of the linkage $L$.\n\nThe length vector $L$ is called [*generic*]{}, if there is no subset $J\\subset [n]$ such that $$\\sum_{i \\in J} l_i = \\sum_{i\\notin J} l_i.$$ (Here and in the sequel, $[n]$ denotes the set $\\{1,...,n\\}$.)\n\nThe hyperplanes $$\\sum_{i \\in J} l_i = \\sum_{i\\notin J} l_i,$$ called *walls,* decompose $\\mathbb{R}^n$ into a collection of [*chambers*]{}.", "\n\nHere is a (far from complete) summary of facts about $M(L)$:\n\n- If no configuration of $L$ fits a straight line, then $M(L)$ is a smooth $(n-3)$-dimensional manifold. ", "In this case, the linkage is called *generic* [@KapovichMillson]. ", "Throughout the paper we consider only generic linkages.", "\n\n- The topological type of $M(L)$ depends only on the chamber of $L$ [@KapovichMillson].", "\n\n- As it was shown in [@Pan], $M(L)$ admits a structure of a regular cell complex. ", "The combinatorics is very much related (but not identical) to the combinatorics of the permutahedron. ", "The construction is explained later in this section.", "\n\n\\[dfn:short\\] A set $I\\subset [n]$ is called [*long*]{}, if $$|I|=\\sum_{i \\in I} l_i > \\sum_{i\\notin I} l_i.$$ Equivalently, for a long set $I$, $$|I|>\\frac{|L|}{2}.$$\n\nOtherwise $I$ is called [*short*]{}.", "\n\nNote that because the genericity assumption, we never have $|I|=\\frac{|L|}{2}.$\n\n- Homology groups of $M(L)$ are free abelian groups. ", "For a generic length vector $L$, the rank of the homology group $H_k(M(L))$ equals $a_k+a_{n-3-k}$, where $a_i$ is the number of short sets of cardinality $i+1$ containing the longest edge (see [@faS]).", "\n\nWe stress that the manifold $M(L)$ (considered either as a topological manifold, or as a cell complex) is uniquely defined by the collection of short subsets of $[n]$.\n\nA partition of the set $\\{l_1,\\dots ,l_n\\}$ is called *admissible* if all the parts are non-empty and short.", "\n\nInstead of partitions of $\\{l_1,\\dots ,l_n\\}$ we shall speak of partitions of the set $[n]$, keeping in mind the lengths $l_i$.\n\nAssume that for an $n$-linkage $L$, we have the following: $$\\forall \\ i=1,2,...,(n-1), \\hbox{ the set } \\{n,i\\} \\hbox{ is long.}$$ Loosely speaking, we have “one long edge”. ", "Such a linkage we call an $n$-bow.", "\n\nIts moduli space is a sphere (see [@faS]).", "\n\nNow we sketch the cell complex stratification of the moduli space $M(L)$ (see [@Pan])\n\nIn the paper we make use of the vertex-edge graph of the cell complex, that is, we take into account only zero- and one-dimensional cells. ", "We treat is as a (combinatorial) graph, keeping also in mind its embedding in the $M(L)$.\n\nThis allows us to view the graph as a discrete approximation of the moduli space.", "\n\nA more detailed description of the cell complex {#a-more-detailed-description-of-the-cell-complex .unnumbered}\n-----------------------------------------------\n\nBelow we sketch in some more details the construction and properties of the cell decomposition of $M(L)$, referring the reader to even more details and all the proofs to [@Pan].", "\n\nGiven a configuration $P$ of $L$ **without parallel edges**, there exists a unique convex polygon $Conv(P)$ which we call *the convexification of* $P$ such that\n\n1. ", " The edges of $P$ are in one-to-one correspondence with the edges of $Conv(P)$ . ", "The bijection preserves the directions of the vectors.", "\n\n2. ", " The induced orientations of the edges of $Conv(P)$ give the counterclockwise orientation of $Conv(P)$ .", "\n\nIn other words, the edges of $Conv(P)$ are the edges of $P$ ordered by the slope (see Fig. ", "\\[rearrangment1\\]). ", "Obviously, $Conv(P) \\in M(\\lambda L)$ for some permutation $\\lambda\n \\in S_n$. The permutation is defined up to some power of the cyclic permutation $(2,3,4,...,n,1)$. We consider $\\lambda$ as a cyclic ordering on the set $[n]$.\n\n![", "Labeling of a polygon with no parallel edges[]{data-label=\"rearrangment1\"}](rearrangment1.eps){width=\"10\"}\n\n![", "Labeling of a polygon with parallel edges[]{data-label=\"rearrangment2\"}](rearrangment2.eps){width=\"8\"}\n\nConversely, each convex polygon from $ M(\\lambda L)$ is the image of some element of $M(L)$ under the above rearranging map.", "\n\nOur construction assigns to $P\\in M(L)$ the *label* $\\lambda$, considered as a cyclic ordering on the set $[n]$. Or, equivalently, a label of a configuration without parallel edges is a cyclically ordered partition of the set $[n]$ into $n$ singletons.", "\n\nIf $P$ **has parallel edges**, a permutation which makes $P$ convex is not unique. ", "Indeed, one can choose any ordering on the set of parallel edges.", "\n\nThe *label* assigned to $P$ is a cyclically ordered partition of the set $[n]$. Fig. ", "\\[rearrangment2\\] gives an example with one two-element set and three one-element sets.", "\n\nWe stress once again that there is no ordering inside a set, that is, we identify two labels whenever they differ on permutations of the elements inside the parts. ", "For instance, $$(\\{1\\} \\{3 \\} \\{4 2 56\\})\\neq(\\{3 \\}\\{1\\} \\{4 2 56\\})= ( \\{3 \\}\\{1\\}\\{ 24 56\\}).$$\n\nBy the triangle inequality, all labels are admissible partitions.", "\n\nTwo points from $M(L)$ (that is, two configurations) are said to be *equivalent* if they have one and the same label. ", "Equivalence classes of $M(L)$ we call the *open cells*. ", "The closure of an open cell in $M(L)$ is called a *closed cell*. ", "For a cell $C$, either closed or open, its label $\\lambda (C)$ is defined as the label of its interior point.", "\n\n\\[MainThm\\][@Pan] The above described collection of open cells yields a structure of a regular CW-complex $CWM(L)$ on the moduli space $M(L)$. Its complete combinatorial description reads as follows:\n\n1. ", " $k$-cells of the complex $CWM(L)$ are labeled by cyclically ordered admissible partitions of the set $[n]$ into $k+3$ non-empty parts.", "\n\n In particular, the facets of the complex (that is, the cells of maximal dimension $n-3$) are labeled by cyclic orderings of the set $[n]$.\n\n2. ", " A closed cell $C$ belongs to the boundary of some other closed cell $C'$ iff the partition $\\lambda(C')$ is finer than $\\lambda(C)$.\n\n3. ", " The complex is regular, which means that each $k$-cell is attached to the $(k-1)$-skeleton by an injective mapping. ", "All closed cells are ball-homeomorphic.", "\n\n\\[ExTwoVertices\\] The vertex labeled by $$(\\{1,2,5,6,\\},\\{3,4\\},\\{7,8\\})$$ and the vertex labeled by $$(\\{1,2\\},\\{3,4,5,6\\},\\{7,8\\})$$ are connected by an edge labeled by $$(\\{1,2\\},\\{5,6\\},\\{3,4\\},\\{7,8\\}).$$\n\nLet $n=4; \\ \\ l_1=l_2=l_3=1,\\ l_4=1/2.$ The moduli space $M(L)$ is known to be a disjoint union of two circles (see [@faS]). ", "The cell complex $CWM(L)$ is as depicted in Fig. ", "\\[4gon1\\].", "\n\n![", "$CWM(L)$ for the 4-gonal linkage $(1,1,1,1/2)$[]{data-label=\"4gon1\"}](4gon1.eps){width=\"6\"}\n\n\\[ExHexagon\\] Assume that for a $4$-linkage $L$, the sets $\\{2,3\\}$, $\\{4,3\\}$, and $\\{2,4\\}$ are short. ", "An example of such a length assignement is $$l_4=l_2=l_3=1,\\ l_1=2,5.$$\n\nThe moduli space $M(L)$ is homeomorphic to a circle. ", "The cell complex is combinatorially a hexagon, that is, there are six vertices connected by six edges into a circle. ", "The (cyclic) order of the labels of the six vertices is: $$(\\{1\\}\\{2,3\\}\\{4\\})$$ $$(\\{1\\}\\{2\\}\\{4,3\\})$$ $$(\\{1\\}\\{2,4\\}\\{3\\})$$ $$(\\{1\\}\\{4\\}\\{2,3\\})$$ $$(\\{1\\}\\{4,3\\}\\{2\\})$$ $$(\\{1\\}\\{3\\}\\{4,2\\}).$$\n\nFor the equilateral pentagonal linkage $L=(1,1,1,1,1)$, the complex $CWM(L)$ has $30$ vertices, $60$ edges, and $24$ pentagonal $2$-cells. ", "Each vertex is incident to exactly four edges.", "\n\n**We first describe combinatorics of the vertex-edge graph:**\n\nAs a particular case of Theorem \\[MainThm\\], vertices are labeled by cyclically ordered partitions of $[n]$ into three non-empty short sets, and the edges are labeled by cyclically ordered partition of $[n]$ into short non-empty short sets. ", "Two vertices labeled by $\\lambda$ and $\\lambda'$ are joined by an edge whenever the label $\\lambda$ can be obtained from $\\lambda'$ by shifting some amount of entries from one set to another.", "\n\n**Now we describe embedding:**\n\nAssume that a linkage $L$ is fixed. ", "Given a label $\\lambda=(I,J,K)$, it labels some point $P$ of the $M(L)$, that is, some configuration of $L$. The polygon $P$ can be constructed via the following algorithm.", "\n\n**Retrieving a vertex (viewed as a polygon) by its label**\n\n1. ", " Take a positively oriented triangle with edgelengths $$\\sum_Il_i,\\ \\sum_Jl_i, \\hbox{ and }\\sum_Kl_i.$$\n\n2. ", " Assume that each edge is constituted of (short) edges $l_i$. For instance, we decompose the first edge into segments of lengths $\\{l_i\\}_{i\\in I}.$ Their order does not matter.", "\n\n3. ", " Now take all the edges apart, keeping their directions, and rearrange them according to the ordering $1,2,...,n$. We get a closed polygonal chain $P$, see Figure \\[FigVertex\\].", "\n\n![", "Retrieving a vertex from its label. ", "Each vertex is a disguised triangle[]{data-label=\"FigVertex\"}](Vertex.eps){width=\"10\"}\n\nTaken together, all labels give all configurations that have exactly 3 directions of the edges. ", "They form the vertex set of the embedded graph $G(L)$.\n\nNow let us explain the way how the edges are embedded,\n\n**Retrieving an edge by its label**\n\nGiven a label $\\lambda=(I,J,K, N)$, it labels an embedded edge of $\\Gamma(L)$, that is, a one-parametric family of configurations. ", "They are retrieved as follows.", "\n\n1. ", " Take a positively oriented convex quadrilateral with consecutive edgelengths $$\\sum_Il_i,\\ \\sum_Jl_i\\ \\sum_Kl_i, \\hbox{ and } \\sum_Nl_i.$$ The set of such quadrilaterals forms a path in $M(L)$ starting from one triangle to another, see Figure \\[FigEdge\\].", "\n\n2. ", " As in Algorithm 1, decompose each edge into (short) edges $l_i$.\n\n3. ", " Exactly as in algorithm 1, take all the edges apart, keeping their directions, and rearrange them according to the ordering $1,2,...,n$. This gives a one-parametric family of closed polygonal chains.", "\n\n![", "Retrieving an edge from the label $(\\{5\\}\\{1,3\\}\\{2\\}\\{4,6\\})$. Each edge is a disguised flex of a convex quadrilateral from one convex triangular configuration to another []{data-label=\"FigEdge\"}](Edge.eps){width=\"14\"}\n\nIn other words, each embedded edge of the graph $\\Gamma(L)$ corresponds to a flex of some quadrilateral, which connects two triangular configurations. ", "One can perform such a flex (for instance) by compressing one of the diagonals.", "\n\n1. ", " The number of vertices of $\\Gamma(L)$ equals $$\\sum_{k=1}^n N_k2^{n-k} -2\\cdot3^{n-1}+2^n,$$ where $N_k$ is the number of short k-sets.", "\n\n2. ", " For the $n$-bow, $\\Gamma(L)$ has the minimal possible number of vertices among all $n$-linkages. ", "In this case, it equals $2^{n-1}-2$.\n\nProof. ", "Crossing a wall means that exactly one short $k$-set $I$ becomes long, and exaclly one long $(n-k)$-set $\\overline{I}$ becomes short, where the number $k$ depends on the wall. ", "Observe that any proper subset of $\\overline{I}$ is short both before and after crossing a wall. ", "A vertex dies whenever its label contains $I$. A vertex arises whenever its label contains $\\overline{I}$. This means that the number of vertices changes by adding $(2^k-2)-(2^{n-k}-2)=2^k-2^{n-k}$.\n\nTherefore, $$|Vert(\\Gamma)|=\\sum_{k=1}^{n}N_k2^{n-k}+X_n,$$ where $X_n$ depends solely on $n$. Our second observation is that for a bow linkage, labels of the vertices are of type $$(\\{\\hbox{any non-empty proper set } I\\subsetneq [n-1]\\}, \\{\\hbox{ the complement } \\overline{I}\\}, \\{n\\}).$$ Therefore, $|Vert(\\Gamma(n\\hbox{-bow}))|=2^{n-1}-2$. This is a kind of a base of induction.", "\n\nFrom the chamber that corresponds to the bow, we can reach any other camera by crossing walls.", "\n\nFor the $n$-bow,$$N_k=\\left\\{\n \\begin{array}{ll}\n 0=C_{n-1}^0-1, & \\hbox{if } k=0; \\\\\n n=C_{n-1}^1+1, & \\hbox{if } k=1; \\\\\n 0=C_{n-1}^{n-1}-1, & \\hbox{if } k=n-1 \\\\\n C_{n-1}^k, & \\hbox{ otherwise.}", "\n \\end{array}\n \\right.$$\n\n$$2^{n-1}-2=\\sum_{k=0}^{n}C_{n-1}^k2^{n-k}+ 2^{n-1}-2^n-2+X_n$$ $$X_n=2^n-2\\cdot3^{n-1},$$ which yields the final formula.", "\n\nAs we see, the number of vertices of the graph $\\Gamma$ depends exponentially on $n$. However, the valence of the vertices also depends on $n$ exponentially, so one can expect a small diameter (in the graph-theoretic sense, that is, the maximal length of the shortest path between two vertices), and a fast navigating algorithm.", "\n\nA vertex of the graph $\\Gamma$ labeled by $(IJK)$ has exactly $$2^{i}+2^{j}+2^{k}-6$$ incident edges, where $i,\\ j, $ and $k$ are the numbers of elements in $I,\\ J,$ and $K$ respectively.", "\n\n Motion planning on the graph $\\Gamma(L)$ {#SecNavigationOnGraph}\n=========================================\n\nHere we describe a finite-step algorithm of motion planning (or, equivalently, navigation) from an arbitrary vertex of $\\Gamma(L)$ to any arbitrary prescribed vertex.", "\n\nA *path* means a graph-theoretical path, that is, a consecutive collection of edges. ", "Its *length*, or *the number of steps* we mean just the number of edges in the path.", "\n\nWe start with an example demonstrating that we can navigate in a really fast way.", "\n\n\\[AlgBow\\] **(Navigation for the bow linkage)** For any $n$-bow linkage, any two vertices are connected by a path whose length is at most 3. ", "The path is explicitly described as follows.", "\n\n1. ", " We start with a vertex labeled by $$(I,J,\\{n\\}).$$ Assume that the target vertex is labeled by $$(\\{1,2,...,k\\},\\{k+1,k+2,...,n-1\\},\\{n\\}).$$ We also can assume that $|J|>1$. If $1 \\in I$, then go to the step 2. ", "If not, shift the entry $1$ to the set $I$ and go to step 2.", "\n\n2. ", " Shift the subset $I \\setminus \\{1\\}$ to the set $J$. We arrive at the vertex labeled by $$(\\{1\\},\\{2,3,...,n-1\\},\\{n\\}).$$\n\n3. ", " There remains (at most) one step to the target vertex: shift the subset $\\{2,3,...,k\\}$ to the set $I$.\n\nOne could expect an easy navigation for the bow linkage in advance, since the configuration space is just a sphere. ", "However, for more complicated topological types, it still suffices 13 steps.", "\n\nWe first learn how to turn polygons inside out.", "\n\n\\[alg5\\]**(Turning a pentagon inside out)** Assume that a $5$-linkage $L$ satisfies the following conditions:\n\n1. ", " The set $\\{1,2\\}$ is long,\n\n2. ", " The set $\\{1,5\\}$ is long,\n\n3. ", " $\\forall \\ i\\neq1, \\ j\\neq1 ,$ the set $\\{i,j\\}$ is short.", "\n\nThen there exists a 4-steps path which turns the configuration $(\\{4,5\\}\\{1\\}\\{2,3\\})$ inside out. ", "Here is the path: $$(\\{4,5\\}\\{1\\}\\{2,3\\})$$ $$(\\{4,5,3\\}\\{1\\}\\{2\\})$$ $$(\\{4,3\\}\\{1\\}\\{2,5\\})$$ $$(\\{4,3,2\\}\\{1\\}\\{5\\})$$ $$(\\{3,2\\}\\{1\\}\\{4,5\\})$$\n\n\\[AlgINsideOut\\] **(Turning a polygon inside out)** Assume that a linkage $L$ is fixed.", "\n\n1. ", " If the configuration space $M(L)$ is connected, then from each vertex $V$  (labeled, say, by $(I,J,K)$) there are at most 6 step to its mirror image $(J,I,K)$.\n\n2. ", " If the $M(L)$ is disconnected, then the vertex $(I,J,K)$ and its mirror image $(J,I,K)$ lie in different connected components, and no connecting path exists.", "\n\nThe idea is to imitate a pentagon which satisfies the three conditions of the Algorithm \\[alg5\\] by freezing some of the entries in (this requires 4 more steps). ", "Here and in the sequel, “freezing” means putting the entries into one separate set and after that, manipulating with the set as with a single entry.", "\n\nAssume that $l_1\\geq l_k\\geq l_m$ are the longest edges of $L$. It is known from [@KapovichMillson] that $M(L)$ is connected if and only if $$l_k+l_m< \\frac{|L|}{2}.$$\n\nOur starting point is a vertex labeled by $(I,J,K)$, where $1 \\in J$. We also can assume that the entries are ordered counterclockwise, that is, $$(I,J,K)= (\\{r+1,r+2,...,p\\}\\{p+1,p+2,...,n,1,2,...,q\\}\\{q+1,q+2,...,r\\}).$$ Maintaining the ordering, we shift to the middle set as many entries from the first and the last set sets as is possible. ", "This means that we first decide what entries do we shift from $I$, and what entries do we shift from $K$. Then we make two shifts, which means two steps.", "\n\nNote that the choice is not uniquely defined. ", "However, any choice is good for us.", "\n\nSo we can assume that the sets $$\\{p,p+1,p+2,...,n,1,2,...,q\\} \\hbox{ and }\\{p+1,p+2,...,n,1,2,...,q, q+1\\} \\hbox{ are long. }", "$$\n\nObserve that the set $\\{p,q+1\\}$ is short. ", "Indeed, $l_p+l_{q+1}\\leq l_k+l_m < \\frac{|L|}{2}.$ Therefore the set $$A=\\{q+2,q+3,..,r,r+1,...,p-2,p-1\\}$$ is not empty. ", "Now the algorithm splits depending on the number of entries of $A$ which equals $(p-1)-(q+2)+1=p-q-2$.\n\n1. ", " Assume that $p-q-2=1$, which means that $A$ is a one-element set. ", "Then we freeze the set $\\{p+1,p+2,...,n,1,2,...,q\\}.$ After renumbering $$4:= \\{p\\}, \\ 1:=\\{p+1,p+2,...,n,1,2,...,q\\},$$$$\\ 2:=\\{q+1\\}, \\hbox{ and } 3:=A,$$ we arrive at a quadrilateral from Example \\[ExHexagon\\] which can be turned inside out in three steps.", "\n\n2. ", " Assume that $p-q-2>1$. We divide the set $A$ into two non-empty subsets and freeze the two subsets. ", "We also freeze the set $\\{p+1,p+2,...,n,1,2,...,q\\}.$ That is, for instance, we freeze the following three sets of entries: $$\\{r+1,r+2,...,p-1\\},\\ \\{p+1,p+2,...,n,1,2,...,q\\}, \\ \\hbox{ and } \\{q+2,...,r\\}.$$ After renumbering $$4:=\\{r+1,r+2,...,p-1\\},\\ 5:= \\{p\\}, \\ 1:=\\{p+1,p+2,...,n,1,2,...,q\\},$$$$\\ 2:=\\{q+1\\}, \\hbox{ and } 3:=\\{q+2,...,r\\},$$ we arrive at a pentagon which satisfies the properties from the Algorithm \\[alg5\\], and therefore can be turned inside out in four steps.", "\n\n\\[PropEitherOr\\] For any $n$-linkage $L$, and any two vertices $V$ and $V$’ of the graph $\\Gamma(L)$, $V$ is connected either to $V'$ or to the mirror image of $V'$ by a path whose length is at most 7. ", "The path is explicitly described as follows. ", "Assume that the target vertex $V'$ is labeled by $$(\\{1,2,...,k\\},\\{k+1,k+2,...,m\\},\\{m+1,m+2,...,n\\}).$$ Assume also that $l_1$ is the longest edge.", "\n\n1. ", " In two steps we get from $V$ to a vertex labeled by $$(I,\\{1\\},J)$$ for some $I$ and $J$. This is always possible:\n\n 1. ", " Assume that $V$ is labeled by $(A,B,C)$, and $1\\in B$. Start shifting the entries from $B\\setminus \\{1\\}$ to the set $C$ as many as possible, that is, stop one step before $C$ gets long. ", "The order in which we treat the entries does not matter. ", "We can shift all the entries by one step, that is, first decide what entries are to be shifted, and next, shift them as a one subset.", "\n\n 2. ", " Shift the rest of $B\\setminus \\{1\\}$ to the set $A$.", "\n\n2. ", " If one of the sets $I$ or $J$ contains two consecutive entries, we can freeze them. ", "We freeze all possible pairs of consecutive entries and renumber the edges (preserving the ordering), which gives us a linkage with a smaller number of edges.", "\n\n In any case we have a vertex labeled either by $$(\\{3,5,7,...\\}, \\{1\\},\\{2,4,6,8,...\\}),$$ or by the symmetric image $$(\\{2,4,6,8,...\\}, \\{1\\},\\{3,5,7,...\\}).$$\n\n3. ", " Pull $2,3,4,...k$ and $3,5,7,...,k\\pm 1$ to the middle set for the largest $k$ which is possible. (", "This requires 2 steps more). ", "Thus we arrive at $$(\\{k+1,k+3,...\\}, \\{1,2,3,4,...,k\\},\\{k+2,k+4,...\\}),$$ or to the symmetric image. ", "So the first entry that we cannot shift to the middle set is $k+1$.\n\n4. ", " Shift $k+3,k+5,...$ to the third set. ", "It is possible because $\\{1,2,3,4,...,k,k+1\\}$ is long. (", "One step more.) ", "We arrive at $$(\\{k+1\\}, \\{1,2,3,...,k\\},\\{k+2,k+3,....,n\\})=$$$$= (\\{k+1\\}, \\{k,k-1,...,2,1\\},\\{n,n-1,...,k+2,k+3\\}),$$ (or to the symmetric image). ", "Now we have either clockwise or counterclockwise ordering on the entries.", "\n\n5. ", " There are two steps either to the target, or to the mirror image of the target vertex.", "\n\nCombining the two above algorithms, we immediately have the theorem:\n\n1. ", " For any $n$-linkage $L$ with a connected moduli space, any two vertices $V$ and $V$’ of the graph $\\Gamma(L)$ are connected by a path whose length is at most 13.", "\n\n2. ", " For any $n$-linkage $L$ with a disconnected moduli space, and any two vertices $V$ and $V$’ of the graph $\\Gamma(L)$ lying in the same connected component, $V$ and $V$’ are connected by a path whose length is at most 7.", "\n\nThe path is constructed explicitly basing on the above propositions. ", "That is we have the following algorithm:\n\n**Algorithm A**\n\n1. ", " Starting with a vertex $V$, follow algorithm from Algorithm \\[PropEitherOr\\]. ", "It may bring us to the target point, and then we are done.", "\n\n2. ", " If on the first step we get the mirror image of the target point, turn it inside out via Algorithm \\[AlgINsideOut\\].", "\n\nBelow we exemplify the steps of the algorithm for one particular heptagonal configuration.", "\n\nAssume we have a heptagonal linkage with edge lengths $$l_1=10, \\ l_2=1, \\ l_3=9, \\ l_4=4, \\ l_5=9, \\ l_6=2, \\ \\hbox{ and } l_7= 4.$$\n\nAssume that our starting point is $V_1=(\\{3,6\\}\\{1,4,7\\}\\{2,5\\})$, and that the target vertex is $V'=(\\{5,6,7\\}\\{1, 2\\}\\{3,4\\})$. Then Algorithm A runs as is described below and as is depicted in Figure \\[FigHeptagon\\].", "\n\n1. ", " The starting point is the vertex of the graph $$V_1=(\\{3,6\\}\\{1,4,7\\}\\{2,5\\}).$$ According to Algorithm \\[PropEitherOr\\], we go to the point $$V_2=(\\{3,6\\}\\{1,4\\}\\{2,5,7\\}),$$ which is connected with $V_1$ by an edge labeled by $(\\{3,6\\}\\{1,4\\}\\{7\\}\\{2,5\\})$. Next come the vertices $$V_3=(\\{3,4,6\\}\\{1\\}\\{2,5,7\\})$$ $$\\hbox{ and } V_4=(\\{3,4,6\\}\\{1,\n 2\\}\\{5,7\\}).$$ Then comes the vertex $$V_5=(\\{3,4\\}\\{1, 2\\}\\{5,7,6\\})=(\\{4,3\\}\\{2,1\\}\\{7,6,5\\}),$$ which is the mirror image of the target point.", "\n\n Now we start turning the configuration inside out, as is prescribed in Algorithm \\[AlgINsideOut\\].", "\n\n2. ", " The next point is $$V_6=(\\{3,4\\}\\{1, 2,7,6\\}\\{5\\}).$$ After freezing the middle set, we get a triangular configuration of a quadrilateral to be turned inside out in three steps: $$V_7=(\\{3\\}\\{1, 2,7,6\\}\\{5,4\\}),$$ $$V_8=(\\{5,3\\}\\{1, 2,7,6\\}\\{4\\}),$$ $$V_9=(\\{5\\}\\{1, 2,7,6\\}\\{3,4\\})=(\\{5\\}\\{6,7,1, 2\\}\\{3,4\\}).$$ One more edge brings us to the target point $$V_{10}=(\\{5,6,7\\}\\{1, 2\\}\\{3,4\\})=V'.$$\n\n![", "The first part of Algorithm A applied to a heptagonal configuration []{data-label=\"FigHeptagon\"}](heptagon.eps){width=\"14\"}\n\n Navigation and control on the moduli space {#SecNavigationOnModuli}\n===========================================\n\nHere we describe a finite-step algorithm of navigation from an arbitrary (which is not necessarily a vertex of $\\Gamma(L)$) point of the moduli space $M(L)$ to an arbitrary prescribed point.", "\n\nWe work under assumption that we can somehow control the shape of a convex configuration. ", "At the same time, we explain how to realize the flex mechanically. ", "As in the previous section, we assume that $l_1$ is the biggest edgelength.", "\n\n Algorithm B {#algorithm-b .unnumbered}\n------------\n\n1. ", " Given a starting configuration $S$ and a target configuration $T$, we take the $(n-3)$-cells of the complex $CWM(L)$ containing $S$ and $T$. We choose $V_S=(I,\\{1\\},J),$ and $V_T$ to be some vertices of these two cells. ", "Starting from now, we keep in mind Algorithm A applied for the vertices $V_S$ and $V_T$.\n\n2. ", " We navigate from $S$ to $V_S=(I,\\{1\\},J)$. In particular, this means that we spare one step in comparison with Algorithm \\[PropEitherOr\\].", "\n\n We realize both $P$ and the convexification $Conv(P)$ as two bar-and-joint mechanisms. ", "By construction, there is a natural bijection between edges of the two polygons, and the corresponding edges are parallel. ", "For each pair of parallel edges (one edge from $P$, and the other one from $Conv(P)$), we plug in a pair of parallelograms as is shown in Figure \\[FigParall\\].", "\n\n ![", "Connecting parallelograms[]{data-label=\"FigParall\"}](parallelograms.eps){width=\"8\"}\n\n To prevent turning inside out, we add one extra edge inside each of the parallelograms (here we follow [@KM]).", "\n\n Each (convex) flex of $Conv(P)$ uniquely induces a flex of $P$ in such a way that the first polygon remains the convexification of the second one. ", "Therefore, the task is to bring the convex polygon $Conv(P)$ to a triangular configuration. ", "By assumption, we can control $Conv(P)$, and therefore, we have a controlled way of bringing $P$ to the vertex $(I,\\{1\\},J).$\n\n3. ", " On this step, we navigate according to Algorithm A by prescribed edges from one vertex $V$ to some another vertex $V'$.\n\n We realize the motion mechanically almost in the same way as above: Take any point $P$ lying on the edge connecting $V$ and $V'$ and again realize both $P$ and the convexification $Conv(P)$ as bar-and-joint mechanisms. ", "Now the polygon $Conv(P)$ is a quadrilateral. ", "Each of its edge we decompose into small edges of lengths $l_i$. Thus we again have a natural bijection between edges of the two polygons, and the corresponding edges are parallel. ", "For each pair of parallel edges (one edge from $P$, and the other one from $Conv(P)$), we plug in parallelograms in the same way as we did above.", "\n\n We can assume that the edges of the quadrilateral are frozen, that is, the quadrilateral can flex only at the four vertices.", "\n\n Each (convex) flex of $Conv(P)$ uniquely induces a flex of $P$ in such a way that the first polygon remains the convexification of the second one. ", "Therefore, the task is to bring the convex polygon $Conv(P)$ from one triangular configuration to another triangular configuration, see Figure \\[FigEdge\\]. ", "This can be controlled in many ways, since the control of a quadrilateral is well-understood, see [@KHPS].", "\n\n Important is that every next edge needs a separate collection of auxiliary parallelograms.", "\n\n4. ", " Once we arrive at the point $V_T$, we go to the target point $T$ as on the very first step.", "\n\nIn our second approach, we again add axillary bars to the polygonal linkage, but now we have one and the same bar-and-joint mechanism which is not rearranged during the desired flex.", "\n\nThe key observation is that the projection of the 1-skeleton of hypercube can serve as a universal permuting machine: together with any configuration $P$, it contains all other configurations obtained from $P$ by permuting the order of edges, see Figure \\[FigHypercube\\].", "\n\nOn the one hand, an obvious advantage of this approach is that we do not remove and add bars at each step. ", "On the other hand, a disadvantage is that we need much more extra bars to be added. ", "Therefore, the choice between the two ways of control depends on the particular practical task.", "\n\n**Algorithm C**\n\n1. ", " We assume that the starting and the target points are $S, \\ T\\in M(L)$ . ", "We find the vertices $V_S$ and $V_T$ exactly as in Algorithm B.\n\n2. ", " Interpret the edges of $S$ numbered $1,2,...,(n-1)$ as projections of edges of the hypercube $[0,1]^{n-1}$. The edge numbered by $n$ is then the projection of the diagonal of the hypercube. ", "Add extra bars to incorporate $S$ to the entire projection of the hypercube, which is now treated as a bar-and-joint mechanism, see Figure \\[FigHypercube\\].", "\n\n3. ", " The new mechanism includes also $Conv(S)$. Now we can manipulate by $Conv(P)$ following Algorithm A. As in Algorithm B, we first bring $Conv(S)$ to the configuration labeled by $V_S=(I,\\{1\\},J).$\n\n4. ", " Next, we follow the path on the graph $\\Gamma$ prescribed by Algorithm A. For each step, we manipulate with the convex configuration $Conv(P)$ which degenerates to a convex quadrilateral.", "\n\n5. ", " The last step from $V_T$ to $T$ is the same as the very firs step.", "\n\n![", "Projection of the hypercube includes both $P$ (blue) and $Conv(P)$ (red). []{", "data-label=\"FigHypercube\"}](hypercube.eps){width=\"8\"}\n\n[7]{}\n\nM. Farber and D. Schütz, *Homology of planar polygon spaces,* Geom. ", "Dedicata, 125 (2007), 75-92.", "\n\nM. Kapovich and J. Millson, *Universality theorems for configuration spaces of planar linkages,* Topology, 41 (2002), 1051–1107.", "\n\nM. Kapovich and J. Millson, *On the moduli space of polygons in the Euclidean plane*, J. Diff. ", "Geom., ", "42 (1995), 430-464.", "\n\nG. Panina, *Moduli space of planar polygonal linkage: a combinatorial description*, arXiv:1209.3241 I. Streinu, *Pseudo-triangulations, rigidity and motion planning*, Discrete and Computational Geometry, 34 (2005), 587–635.", "\n\nJ.-C. Hausmann, *Control of robot arms and Moebius transformations,* arXiv:1304.6214 J.-C. Hausmann and E. Rodriguez, *Holonomy orbits of the snake charmer algorithm*, Geometry and Topology of Manifolds, Banach Center Publications, 76 (2007)\n\nG. Khimshiashvili, *Maxwell problem for polygonal linkages*, Bull. ", "Georgian Natl. ", "Acad. ", "Sci. ", "6, 2012, No.2, 17-22.", "\n\nG. Panina, G. Khimshiashvili, *On the area of a polygonal linkage*, Doklady Akademii Nauk, Mathematics, 85, No. ", "1 (2012), 120–121. *", "Coulomb control of polygonal linkages,* arXiv:1304.6214, to appear in J. of Dynamical and Control Systems. , *", "Cyclic polygons are critical points of area*, Zap.", "Nauchn. ", "Semin. ", "POMI, 360, (2008), 238–245. ", "G.M. Ziegler, *Lectures on polytopes,* Graduate Texts in Mathematics. (", "Springer, Berlin 1995).", "\n" ]

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[ "Eloisa James had me hooked once again – it has been a while since I have read Regency RomanceReview Originally Posted at: Book Freak\n\nRating: 4.5 Stars\n\nEloisa James had me hooked once again – it has been a while since I have read Regency Romance novels, and I didn’t know I missed it that much until I have read this one.", "\n\nThorn Dautry is a powerful bastard son of a duke. ", "He had now made a fortune, and is as rich as Midas. ", "He could have anything he wanted without really lifting a finger, he could have any woman, but he wanted one thing that had been missing from his life – he wanted a wife. ", "He wanted to marry a lady – but before he could, he needed first to get a country estate, and well, polish his ways. ", "He had acquire an estate, but it was inhabitable, he needed the help of someone to organize his household, and who better employ but the best?", "\n\nLady Xenobia India is beautiful, headstrong and independent. ", "If anyone can do it – it was her. ", "But all she have is three weeks – can she do it? ", "She had to transform his estate, and she had to make him marriageable.", "\n\nWhat they didn’t expect is for flames to ignite, and for their attraction to unleash. ", "Much as he wanted to make her his, he was already sort-of betrothed. ", "But he couldn’t just give India up – she was his perfect match. ", "She can carry a conversation, make him think, make him squirm, and make him crazy all at the same time. ", "He wanted her – and he will do anything to have her. ", "He was careful with his heart, and this time, it might be in grave danger.", "\n\nI liked Lady X, her strong personality, her steadfastness, except for her aunt, she had literally on her own. ", "Being left an orphan at an early age, she was left penniless by her parents and she did all she could to make it through life, build her own dowry and doing things she loved to do despite her title.", "\n\nI enjoyed their correspondence, and it felt like their written foreplay. ", "I got entertained with their banters, Thorn broke my heart when he broke hers, and I shed some tears over some scenes. ", "Awww. ", "There was a time when I wished so hard that he would man up, and offer what she wanted from him. ", "Some men could be just oblivious to what women want. ", "But everything was forgiven with his grand gesture at the end of the novel. ", "WOW. ", "Risking his life to give her something she held dear was really something. ", "I didn’t expect him to do it, and to pull all efforts for it. ", "Nevertheless, he had my heart by then.", "\n\nI’m sure readers will enjoy this installment of Desperate Duchess much as I enjoyed it and the rest of the series. ", "You will fall in love with the characters, pin for them and wish for their HEA. ", "I loved it. ", "I was totally hooked and it had kept me awake all night, I was unable to tear myself from it.", "\n\n✪Complimentary Copy was given in exchange for an honest review.✪...more\n\nSabrina Jeffries had me reading till the wee hours of the morning. ", "The Duke's Men is another series to truly watch out for.", "\n\nWhat The Duke Desires revolSabrina Jeffries had me reading till the wee hours of the morning. ", "The Duke's Men is another series to truly watch out for.", "\n\nWhat The Duke Desires revolves around the search of the brothers of the main characters. ", "Travelling from London to the streets of Paris, Max and Lisette searched to get into the bottom of the mysterious note received by the Duke of Lyons.", "\n\nThe lofty, imperious Duke of Lyons will never, ever marry especially the woman who will catch his heart. ", "Oh he will marry, but it will only be to a lady who will agree to a practical marriage and can give him an heir. ", "After receiving a note telling him that Tristan found his long-lost brother after being kidnapped for several years, he immediately went to Manton's Investigations and demanded that they produce Mr. Bonnaud or he will call the authorities.", "\n\nLisette grown up wanting to be independent and would never want to be in a mercy of a man. ", "She had seen how her mother had suffered after their father suddenly died and left them with nothing. ", "They have lived in poverty and her mother was forced to go back on stage. ", "Marriage was also far from her mind since her birth would make it almost impossible for her to find a suitable husband. ", "She was resigned to her ambition of becoming a lady agent. ", "But first, she had to convince her brothers to allow her. ", "But when an arrogant duke suddenly barge into her brother's office - she saw a chance.", "\n\nI like their characters as individuals and I adore them even more when they are together. ", "They prove to be an entertaining couple. ", "Lisette is not afraid of the duke and doesn't really care about his position in the society. ", "As for Max, he had never found anyone as refreshing as Lisette - she was unlike any other woman he encountered. ", "She was not afraid to speak her mind. ", "However, both of them should be careful not to fall in love with each other. ", "Lisette knew Max would never marry her because of the difference of their station and Max has his own dark secrets he's not yet ready to divulge.", "\n\nCan they stop themselves from falling in love when they could hardly keep their hands off each other? ", "Can the lofty duke fell in love with the bastard daughter of a viscount?", "\n\nSabrina Jeffries will once again awe you and make you fall in love in this first book of her brand new series. ", "Just like the Hellions of Halstead Hall (by the way, some characters were mentioned in this book as well!!), ", "I think the Duke's Men will be on my list of my favorite Regency Series. ", "Looking forward in reading the rest of the books!!...more\n\nWithout a doubt, the Bridgertons has always been my favorite regency family and series. ", "I have followed the romReview Originally Posted at: Book Freak\n\nWithout a doubt, the Bridgertons has always been my favorite regency family and series. ", "I have followed the romantic tales of every siblings from Daphne's story (which is undoubtedly my favorite not just from these series but my favorite regency novel) to Gregory's and each time, Julia Quinn left me wanting for more. ", "It was a bittersweet emotion when the final novel came in print.", "\n\nSo when the news came a new book will be out compiling all second epilogues from each book plus a bonus material: Violet & Edmund's love story - I was like:\n\nThen...\n\nand when I got a copy:\n\n(Excitement was an understatement of the year)\n\nI missed all of them, and it would do me good if I can just read them all one more time. ", "Finally The Bridgertons: Happily Ever After came. ", "It was nice to see them all back together. ", "Although I have read some of the epilogues previously, it was nice of her to just compile it in a single book for convenience. ", "Not to mention, she offered a bonus material no Bridgerton fan could not refuse, Violet's story.", "\n\nIt tells the reader the love story of Violet and Edmund, and her life after losing the man she loved the most. ", "I have always loved and adored Violet Bridgerton on how she have raised eight amazing children on her own. ", "She was a great mother, an even greater and indulgent grand mother. ", "But to live alone after losing Edmund - is it worth it? ", "Can she find another love of her life? ", "Or will she live her life alone? ", "These were the questions I had in mind when I have read Ms. Quinn is about to write her story. ", "And short as it was, it was simply amazing. ", "I would have wanted a longer story for Violet, but the novella was enough for me. ", "It was touching, heartbreaking, and enlightening. ", "I simply love it.", "\n\nThank you Ms. Quinn for sharing the Bridgertons one more time and for allowing us to know Violet & most especially Edmund more....more\n\nBecause I love Eloisa James and I fell in love with the two amazing parents Grace had in With This Kiss, I just knew I have to read how these two loveBecause I love Eloisa James and I fell in love with the two amazing parents Grace had in With This Kiss, I just knew I have to read how these two lovers came to be.", "\n\nAnd there were no regrets reading The Ugly Duchess. ", "Theo and James grew up together. ", "After Theo's father died, she taken under the Duke's care. ", "When the duke was suddenly having problems with finances, he forced James to marry Theo.", "\n\nTheo, or Daisy to James wasn't the belle of the ball. ", "She knew she wasn't pretty, so when James suddenly propose to her in front of the prince himself, she was astounded. ", "She didn't expect James has feelings for her and was contemplating on marrying her. ", "After all, a lot of mama's and debutantes were running after him.", "\n\nEveryone wasn't convinced and every tabloid in town was giving their marriage an expiry date. ", "They referred to Theo as the Ugly Duchess .", "\n\nJames, on the other hand, didn't really want to marry Theo. ", "Oh, he loved her as a sister, and he would forever wallow in guilt for his deception. ", "Everything was going smoothly, James was finally giving their marriage a chance - Theo was an amazing person and they both deserve happiness. ", "Until Theo finally found out that he was only after her dowry, and then he was kicked out of the house.", "\n\nNo one had ever taught him - and he had never imagined the necessity of learning - how to betray the one person whom you truly cared for in life. ", "The only person who genuinely loved you. ", "How to break that person's heart, whether it be tomorrow, or five years or ten years in the future.", "\n\nWhile Theo spent her years transforming from an Ugly Duchess into a Swan, James spent his years at sea. ", "Both of them lived their lives, placing their marriage at the back of their minds. ", "James became an infamous pirate (or privateer), according to the rumors, he has his way with women. ", "Theo, on the other hand, worked hard to flourish whatever was left with her dowry. ", "They had both become successful in their own ways.", "\n\nJames think it was a bad idea to go home, since it was Daisy who threw him out of their house. ", "But something happened that made him rethink of the idea. ", "He decided to go home - to his wife. ", "It has been years, and no news has been heard from him. ", "James was about to be declared dead in front of the peers, and suddenly he appears and shocked everyone, most especially Theo.", "\n\nYou’re the only one for me. ", "I came back from the dead for you, Daisy. ", "Twice.", "\n\nThis is one of those regency romance I'm sure I'd reread... The pacing was great, characters were simply amazing and the scenes - were awesome. ", "It will make you fall in love, break your heart and allow you to forgive and fall in love once more. ...", "more\n\nHistorical Romances have always been one of my favorite genres. ", "This is my first time to read Cecilia Grant, and I wasn’t expecting much but left satiHistorical Romances have always been one of my favorite genres. ", "This is my first time to read Cecilia Grant, and I wasn’t expecting much but left satisfied by the time I reach the end of the page. ", "Admittedly, it was refreshing to read a new (as for me) voice in this genre.", "\n\nI simply love Nick because of his pragmatic sense. ", "He gallantly accepted Kate’s refusal at the beginning of the novel. ", "He carried a torch for her that long, but opted to remain a friend of the family and try to forget his feelings for her. ", "He couldn’t really offer her anything, not when a scandal looms over his head because of what his brother did.", "\n\nMeanwhile Kate, the ambitious Kate, I would have hated her mercenary thoughts if not for the fact that she just wanted to offer her siblings a better future. ", "Descending from a family of nobleman, Kate’s father was shunned from society because he married an actress. ", "While her father was contented with their lives, Kate wanted to be what she thought she (and her sisters) deserved – to be one of the ton.", "\n\nI like A Woman Entangled because it revolves around ordinary people. ", "No royalty or nobleman. ", "The story about the importance of family, forgiveness, and how love can sprout out of nowhere, just when you least expect it. ", "Love means sometimes giving up and allowing the person to be happy. ", "Love can make everything okay.", "\n\nCecilia Grant makes an amazing novel – her pacing was just right. ", "I couldn’t help but get captivated by her characters and plot. ", "Yes, I would read more of her novels, and yes, I would recommend to all Historical Romance lovers out there to read this one!!!...more\n\nThe Wilde cousins are back! ", "After their successful matchmaking scheme in Princess Charming, Kathe and Skye areReview Originally Posted at: Book Freak\n\nThe Wilde cousins are back! ", "After their successful matchmaking scheme in Princess Charming, Kathe and Skye are back. ", "This time, Jack is the center of their project and he's about to portray Romeo in his love tale.", "\n\nTwo households, both alike in dignity, In fair Verona, where we lay our scene, From ancient grudge break to new mutiny, Where civil blood makes civil hands unclean.", "\n\nTheir family has been locked in a 3-generation blood feud when a member of the Wilde household dueled with one of the Fortins which resulted in a blood shed that made Sophie's father, Oliver lost the barony.", "\n\n[image error]\n\nJack Wilde A.K.A RomeoHe's a lovechild of a noblewoman and a prince of a foreign land. ", "His mother died early and at very young age and he was left to fend for himself. ", "His father, the prince has already fled the country. ", "His childhood, after the death of his mother was inconceivable until he was saved by his uncles and brought him to London and adopted them as their own.", "\n\nHe's a rake of the first order, and he eats like his stomach is an empty pit. (", "Yes, orally fixated as a result of his childhood days). ", "He has fears he wasn't really proud of. ", "He also has secrets, secrets that he haven't shared with anyone not even his family.", "\n\nAfter Kaye & Skye's successful matchmaking with Ash & Maura, they were relentless in finding him a suitable bride. ", "To stop his female relations from hounding him - he finally decided to meet Sophie Fortin for himself. ", "What he didn't expect is to find someone who could knock the air out of his lungs.", "\n\nHe still wasn't convinced he was his match, yet he's willing to give it a try.", "\n\nBut Sophie isn't hearing any of his pleas until he bares his soul to her. ", "The thing is, Jack is a close book and like to keep his personal feelings to himself.", "\n\n[image error]If this one kiss would determine his fate, he intended to make it unforgettable.", "\n\nSophie Fortin A.K.A. JulietBut I am supposed to turn my back on my family simply because you have a whim to test a fantastical theory about legendary lovers?", "\n\nSophie is about to get a proposal from the Duke of Dunmore, and she was going to accept it, for her parent's sake. ", "They weren't nobility, and they were just relying on the generosity of Mrs. Pennant, Sophie's Aunt. ", "Sophie felt she owed this to her parents, especially that her father was denied with the barony. ", "Marrying the duke would make her a duchess, thus elevating their social standing in the society.", "\n\nAnd here comes Jack - who was willing to marry her - to the extent of accepting the offer of being the sole heir of his father. ", "But Sophie wanted more. ", "She didn't like being his damsel in distress to his knight-in-shining armor syndrome. ", "If she is likely to go into a loveless marriage, she'd wed Dunmore.", "\n\nMrs Pennant, The AccompliceShe's the character besides the Wilde cousins that had caught my attention in this novel. ", "She's Sophie's loving aunt and I loved her too. ", "Yep, she's the cool aunt - the one that wants what's the best for you and would gladly give it to you even if your parents wouldn't like it.", "\n\nShe wanted Sophie's happiness, and she believed Jack can give it to her. ", "So, she gladly helped Jack with his plans.", "\n\nLegendary Lovers?I spent half of the novel thinking: why in the world would these people forced the \"legendary lovers\" to be the theme of their love stories? ", "And oh, it's Romeo and Juliet - maybe they forgot that this tale ended in a tragedy?", "\n\nAt first, I didn't like the idea that Jack was relentlessly wooing her because of the legendary lovers thing. ", "When an idea is pushed towards your direction and is often reiterated to you - you seem to think that this could be a good idea and you will act upon it on your own. ", "It's a good thing that there was an attraction between the two when they met - or else it would be just weird.", "\n\nFinally, I was relieved when the Romeo-Juliet thing was nowhere to be found in the chapters that followed. ", "Rather, Nicole Jordan worked her magic on romance as two star-crossed lovers found their way into each other's hearts. ", "Jack wins her heart by finally making amends with his past and moving on, being honest about his emotions and finally opening up to her. ", "Good thing our Juliet isn't willing to quit that easy, even if Romeo tried to drive her away....more\n\nA debut novel from Ms. Ashlyn Macnamara: a story of two sisters finding love in the most unusual circumstances.", "Review Originally Posted at: Book Freak\n\nA debut novel from Ms. Ashlyn Macnamara: a story of two sisters finding love in the most unusual circumstances.", "\n\nThe GirlsJulia St.ClaireShe's the youngest among the two sisters. ", "She was also the practical and sensible one. ", "Her reputation is pristine. ", "Unlike girls her age, she haven't really dreamed of falling in love. ", "After knowing what love can do to a person, she had lost fate in love. ", "That's why Ludlowe had chosen her to be his bride. ", "I liked her character because she loved her sister, and she didn't want her to get hurt. ", "Julia tried to dissuade Ludlowe as much as possible. ", "But her parents got other ideas. ", "To escape her fate, she offered her dearest friend, Benedict, a scandalous proposal he couldn't refuse.", "\n\nSophia St. ClaireThe oldest among the St. Claire siblings. ", "She nurses a tendre for Ludlowe for more than five years. ", "Although she's a stunning beauty compared to her sisters, she had refused several offers and had patiently waited for the man she had set her eyes on. ", "Yet, she remained non-existent to him - every time they met, it feels like her heart is breaking inch by inch. ", "Little did she realize that her heart is about to get crushed when Ludlowe asked for her sister's, Julia, hand in marriage. ", "I hated her. ", "As the older sister, she should be the one with more sense. ", "How can she remain blind to Ludlowe's shortcomings when she had witnessed one right before her eyes?", "\n\nThe BoysRufus, The Earl of HighgateLove the name. ", "It's very - ancient. ", "Anyway, he's our tortured brokenhearted hero who had suffered so much not only from the ton's idle gossip but as well as from his previous wife's indiscretions. ", "He preferred the solitude of the country side. ", "But due to his sister's insistence - he came to town in search of a wife. ", "Another looming scandal is hanging over his head when he and Sophia were discovered alone.", "\n\nBenedictJulia's childhood friend. ", "He's your typical prince charming-slash-older brother. ", "Someone who was always there to listen and be with Julia during the times that she needed him the most. ", "Their lands are adjacent to each other in the countryside and they spent a lot of time playing together as children. ", "But all grown up - Benedict never really have feelings for Julia, if ever he has, he hasn't acknowledge it until that night at a certain ball where they danced a waltz. ", "Suddenly, he saw Julia no longer as a friend, but a lady to be desired.", "\n\nUppertonI fell in love with him - his humor, wit and plain old happy-go-lucky charm. ", "No page is left dull if he's on it. ", "He's Benedict's trusted and loyal friend. ", "Upperton is the one who encouraged Benedict not only in pursuing Julia but in other aspects as well. ", "If the next book is about him - I'd gladly grab a copy.", "\n\nLudlowe, The Earl of ClivesdenSince gaining the earldom (or even before it), he wanted to find a suitable bride to be his countess - and among all women in the ton, one caught his attention: Julia. ", "But is it her who really caught his attention, or is there something more to his choice of bride? ", "He may look like he's a gift from God - with his looks, charms and soon-to-have-riches, but what lies beneath is soon to surface when all his dark secrets will finally unveil.", "\n\nCliche Plot: What could be more sweeter than two childhood friends finally realizing that they are meant for each other?", "\n\nA Debut Novel: I have been a fan of regency romance since my mother allowed me to touch her Lindsey collection. ", "I was really excited to receive a copy from Netgalley, especially from a first-time author. ", "With two love tales in one book - there were literally a band of characters to get to know. ", "Nevertheless, she made sure that two couple are given the same attention and no one was left behind. ", "But for a first novel, A Most Scandalous Proposal went well (so yes, you can easily breath now Ms. Ashlyn): nice plot, great group of characters and sizzling romance. ", "I enjoyed reading this book and will look forward for your future writings!", "\n\nFans of regency romances will surely let her into their hearts as well as into their shelves. ", "Great work!...more\n\n“I’m suggesting that you let someone inside that empty room you call a heart. ", "Whether you make her your wife or your mistress, a man’s bed is decided“I’m suggesting that you let someone inside that empty room you call a heart. ", "Whether you make her your wife or your mistress, a man’s bed is decidedly warmer if there’s a fire burning in something other than his cock.”", "\n\nI really loved the Hellions of Halstead Hall Series by Sabrina Jeffries, and for those who haven't read it yet, no worries. '", "Twas the Night After Christmas works well as stand alone. ", "But of course, reading the whole series can be worthwhile.", "\n\nWhy do I love this book?", "\n\n1. ", "Pierce. ", "I wanted to give him a soft, tight hug. ", "He deserves one or a hundred more after what he had been through as a little boy.", "\n\nThe little boy who felt no body wanted him at all. ", "His asthma made him a little weak and his father hated weak. ", "Saying that he has a poor relationship with his father would be an understatement. ", "But his mother, at first I didn't know what went wrong with the relationship because I can feel that his mother loved him to a fault. ", "She was the buffer that he needed with all the shenanigans that his father threw him at an early age. ", "The moment he was sent off to school, he never saw his parents again. ", "He was forced to spend his vacation with the cousins he barely knew. ", "And when he reached his age of majority- he went back to his parents and finally confront them, only to be sent away.", "\n\nI couldn't blame him if he hated both his mother and father. ", "I couldn't blame him if he wanted the truth out- something his mother wanted to forget. ", "I think he deserved to know the truth from the moment he reached his majority...\n\nWhen the truth came out, oh well, it wasn't as dramatic as I hope it could be. ", "But at least the story ended every cards placed on the table. ", "The little boy finally had his needed truth and happy ending.", "\n\n2. ", "Camilla had worked for the countess for a while and saw the great love for her son and her son's subtle rejection for it. ", "Since the old lady has been kind to her and her little boy, she decided to repay the kindness by meddling with her affairs. ", "She sent a missive to the earl that his mother was at death's door. ", "When the earl finally knew that he was tricked, he refuses to stay unless Camilla agreed to a compromise.", "\n\nI love the dedication Camilla has given her work and to the countess. ", "Even though she learned the truth, and could not fathom how the countess could have done it, she never left her. ", "But most of all, I really adore her because she was a great mother. ", "That no matter what her feelings are, or how those feelings run deep for Pierce, she would still chose her son.", "\n\nSabrina Jeffries once again made a beautiful story, not just a love story shared between the opposite sex. ", "But it's a wonderful story of forgiveness, moving on and the extent of a mother's love for her children. '", "Twas a Night After Christmas is a perfect season read for all the regency book lovers out there.", "\n\n“Sometimes people fall in love with those who do not return the same strength of feelings. ", "It is as it is,” he said with a quiet intensity. “", "What I g“Sometimes people fall in love with those who do not return the same strength of feelings. ", "It is as it is,” he said with a quiet intensity. “", "What I give, I give freely. ", "You owe me nothing, not love, not friendship, not even obligation.”", "\n\nSherry Thomas is one of my favorite romance author and this is the story I've been dying to read since I started the series - and my expectations were met. ", "Ms. Thomas made an amazing love story of a man who can't say the right words to the woman he wanted for a long time, and a woman who is deeply in love with another and is willing to risk everything.", "\n\nI don't know whether I'd fall in love with David or not. ", "He can be annoying at times and lovable the next. ", "His tactics are so high school - trying to get the attention of the girl he likes through teasing and not-so-amusing bantering. ", "I wish he can just be honest with Helena and tell her what he really feels for her. ", "On the other hand, he is an amazing father to his illegitimate daughter. ", "He's very patient, kind and just. ", "He didn't want to shun his daughter away like any noble man would do to children who were born outside the blanket. ", "Instead, he took her in his roof, and be the best father that a special child needs.", "\n\nHelena - the perfect epitome of the woman who is blinded by love. ", "She was in love with Andrew for a long time, and when an opportunity knocked, she took it - without looking at the consequences of her actions. ", "Good thing David was there to save her reputation.", "\n\nThe clean slot David wanted came when Helena lost her memory, and despite that - he tried to come clean. ", "But what happens when Helena regains her memory and remember that she loved another?", "\n\nDespite the familiar plot that I'm not really fond of (amnesia), I fell in love with this book and its characters and would gladly recommend it to friends. ", "Especially for those people who look too far for love, not noticing what is in front of them....more\n\nI have never seen a more ambitious lady in all my regency readings than Minerva Montrose - she can be annoying most of the times. ", "Probably, I grew upI have never seen a more ambitious lady in all my regency readings than Minerva Montrose - she can be annoying most of the times. ", "Probably, I grew up reading these Old-London tales with brave women (mostly) rather than radical ones.", "\n\nMy heart goes to Blake - granting, he was an a** in the first chapters, but when all cards were put on the table, my opinion changed. ", "I understand why he would like to keep these secrets to himself and the extend of what he can do to have it that way. ", "The circumstances did not favor when he married a girl who loves to do what he can't.", "\n\nNevertheless, I enjoyed reading the story, I had some laughs and near-heartbreak moments: an ambitious young bride who can be naive at times and annoying the next and her reluctant husband with a heavy secret to divulge. ", "I was wondering how can their marriage work without trust? ", "And the sex! ", "The pooling of excitement that was ignited due to their unconsummated wedding night was quickly extinguished with what happened on their first night in bed together! ...", "more\n\nEverything started with a bracelet Sophie wanted to have back into her possession. ", "It was stolen by a boy while she was strolling. ", "Out of desperation,Everything started with a bracelet Sophie wanted to have back into her possession. ", "It was stolen by a boy while she was strolling. ", "Out of desperation, she went into a place where no respectable ladies should be found in.", "\n\nHere comes Simon, an old friend, the one that she has been in love forever, saving her from any trouble that she gets herself into. ", "Although he asked her to marry him, Sophie knew there was more to the proposal than he was letting on - and she needed to know what it was.", "\n\nSophie is a social burden to Simon. ", "I was not sure whether to like her - because she has a nagging conscience that she acts upon or to hate her because she can be VERY reckless up to a point that she had endangered not only her life, but the life of her servant in doing what she thinks is best at that time. ", "So, you must understand this ambivalence - because I'm sure most readers felt the same way. ", "It was quite exasperating.", "\n\nSimon wants to marry his friend because he wanted her lands - lands that're filled with coal and he couldn't tell her because? ", "He might hurt her feelings - cliche much? ", "And when she found out about it? ", "When do these people realize that truth will come out no matter what?", "\n\nI don't know why these two end up lying to each other, especially with something important. ", "Trust becomes an issue, Sophie loses her trust with Simon because of what he did, yet, he gains it almost immediately. ", "She's very much in love with him that she can turn blind into his machinations and manipulations. ", "But anyway, it all ended nicely, after a heart-wrenching pain and in the heat of the scandal - Sophie's family still supported her and of course, Simon made a moved to atone for his sins, confessing his love for Sophie. ", "But this time, for real. ...", "more\n\nThe story went well, thank God. ", "I could never handle another tragedy to happen to the family in that magnitude. ", "Desperation could indeed drive someoneThe story went well, thank God. ", "I could never handle another tragedy to happen to the family in that magnitude. ", "Desperation could indeed drive someone into thinking the impossible. ", "I love how Caroline took the responsibility head on. ", "It was admirable how she swallowed her pride to keep her family together and keep them out of poverty, securing their futures even it would mean that her future would be bleak. ...", "more\n\nI rarely make reviews for historical romance novels, but I'm making Ravishing the Heiress an exception. ", "I haven't read the first one and felt the urI rarely make reviews for historical romance novels, but I'm making Ravishing the Heiress an exception. ", "I haven't read the first one and felt the urge to jump on the second book.", "\n\nIf you asked me why I liked it - I would have said I adore Millie so much. ", "Her character was more of a strong woman rather than a martyr. ", "I love the courage and the perseverance she has.", "\n\nAnd well, there's Fitz. ", "Who had annoyed me at some point with his insensitive notions and foolishness, but thank God, Millie's mother had been right with her prediction and he'd seen some light at the end.", "\n\nReading the teaser - I guess the book would likely have me in tears by the end part of the novel. ", "And dear me - Sherry Thomas delivered! ", "I was in tears at the end part of the novel. ", "I love the part when he finally realized how he felt for her, and how he came to tell her about what he felt.", "\n\nBut\n\nIt was quite a task in reading all those flashbacks, I think it slowed down the momentum of the whole story. ", "I would have been glad that all the things of the past will be placed on the first part of the novel, and everything else would be in chronological order." ]

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[ "@KatieK I didn't downvote, but questions about the implementation details of Apple's software (in this case, how iTunes matches artwork) are usually a poor fit for StackExchange, because real information about those details is rarely available; as a result, the answers to such questions tend to be subjective / prone to conjecture.", "\n–\nDan JMar 26 '12 at 18:26\n\n6 Answers\n6\n\nClearly, the database being polled either has errors or the mix of the data used to determine the track listing isn't uniquely specified which leads to the errors.", "\n\nHere is what you have in your control:\n\nManually override these artworks by hand or by using a competing service. ", "There are many and I've never found them to be worthwhile for the music I have issues with. ", "YMMV of course and I know several people really love these iTunes add-on programs and cleaners.", "\n\nThe metadata - you can edit the title or the author or any of the other music tag information on the problematic tracks to better match what Apple sells the music. ", "If you have a Jimmy Buffet album labeled \"stoner rock\" for genre - perhaps changing it to \"Rock\" would be the difference in retrieving the correct artwork.", "\n\nAs you can see, the details aren't public, so some trial and error may be needed. ", "If you have the actual CD and can re-encode them, usually this gets the data correct for matching with artwork.", "\n\niTunes uses an external site to search for album art. ", "I don't remember exactly which site it is, but I do remember that it was crowdsourced, so there's a high likelihood that, especially with relatively rare music, it will get the wrong thing.", "\n\nThis seems to be an ongoing problem with iTunes and MP3s. ", "It'll get better for awhile, then suddenly a ton of threads on it will pop up on apple's support boards. ", "It might improve a little, but many will still report problems.", "\n\nEven when the ID3 tags match exactly with the information for the same album in the iTunes store people indicate they are still getting mismatches or missing artwork. ", "Others have complained that after going through and painstakingly attaching artwork manually to all the songs that had missing artwork, a later iTunes upgrade has removed some or all of the artwork they added.", "\n\nThe problem is so pervasive that there are apparently several programs intended to do the work that iTunes should be doing itself:\n\nYes, it could be a problem for songs not puchased from the Store. ", "I advise to store a covers with all full albums / compilations you have. ", "I do so and haven't these situations because I add the covers when I edit meta info of the files (using The Tagger utility).", "\n\nitunes just gets confused sometimes i guess, an easy solution is to go to google, copy the album art you want and go to the album you want to change in itunes. ", "click on advanced and add album art (top left hand corner). ", "then you go to album art i believe and control and copy/paste the picture into the album art space. ", "this allows you to get custom art work!" ]

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[ "FILE PHOTO: Noe Sanchez shows off the Remitly app that he uses to send money to his family in Mexico in this photo taken in San Francisco, California March 30, 2016. ", "REUTERS/Beck Diefenbach\n\nLONDON (Reuters) - U.S. payments startup Remitly has launched services in Britain, expanding its international footprint to a third country from which users can send money abroad, the Seattle-based firm told Reuters on Tuesday.", "\n\nThe digital money transfer service, backed by Amazon.com founder Jeff Bezos, sends more than $2 billion in remittances annually to India, the Phillipines, Mexico and other Latin American countries for users based in the United States and Canada.", "\n\nCustomers in Britain will be able to use Remitly’s desktop and mobile app, and will initially be able to send money to India and the Philippines.", "\n\nRemitly’s UK launch will see it join local competitors such as Transferwise and Azimo in the digital remittance industry, which is quickly eating into the businesses of costlier, traditional services typically offered by banks and “bricks-and-mortar” organizations such as Western Union and Moneygram.", "\n\n“Europe as a continent is the second largest remittance-sending geography, so there’s a lot of opportunity around here,” Remitly CEO Matt Oppenheimer told Reuters.", "\n\n“Over 19 billion pounds in remittances are sent from the UK and launching here is a natural next step for us as we expand across the globe,” he said." ]

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[ "Eustace Percy, 1st Baron Percy of Newcastle\n\nEustace Sutherland Campbell Percy, 1st Baron Percy of Newcastle, PC (21 March 1887 – 3 April 1958), styled Lord Eustace Percy between 1899 and 1953, was a British diplomat, Conservative politician and public servant. ", "He most notably served as President of the Board of Education under Stanley Baldwin between 1924 and 1929.", "\n\nBackground and education\nPercy was born into a noble family: he was the seventh son of Henry Percy, 7th Duke of Northumberland, and Lady Edith, daughter of George Campbell, 8th Duke of Argyll. ", "Henry Percy, Earl Percy, and Alan Percy, 8th Duke of Northumberland, were his elder brothers. ", "His uncle, the ninth Duke of Argyll, was married to HRH Princess Louise, daughter of Queen Victoria. ", "A niece later married the sixth Duke of Sutherland. ", "He was educated at Eton and Christ Church, Oxford.", "\n\nPolitical career\nPercy served in the Diplomatic Service between 1911 and 1919. ", "From 1919-22 he represented Holborn on the London County Council as a Municipal Reform Party councillor. ", "In 1921 he was elected Member of Parliament (MP) for Hastings, a seat he held until 1937. ", "In March 1923 he was appointed Parliamentary Secretary to the Board of Education by Bonar Law. ", "When Stanley Baldwin became Prime Minister in May of the same year, Percy was moved to the post of Parliamentary Secretary to the Ministry of Health, which he remained until the fall of the government in January 1924. ", "When the Conservatives returned to power in November 1924, he was appointed President of the Board of Education by Baldwin, with a seat in the cabinet, and sworn of the Privy Council. ", "He continued as head of the Board of Education until the government fell in June 1929.", "\n\nPercy did not serve in the National Government of Ramsay MacDonald between 1931 and 1935, but when Baldwin returned as Prime Minister in June 1935 he again became a member of the cabinet as Minister without Portfolio, a post he held until 1936. ", "Given charge of policy direction for the government in the latter role, he was often dubbed the \"Minister for Thought\" by the Press. ", "In the 1930s he called for regional government for the North East of England, specifically wishing to be the minister for the region.", "\n\nIn his 1944 Riddell Lecture Percy made a call for the law to be changed radically to recognise companies as associations of productive employees, rather than as associations of shareholders. ", "These were his words: \"Here is the most important challenge to political invention ever offered to the jurist or the statesman. ", "The human association which in fact produces and distributes wealth, the association of workmen, managers, technicians and directors is not an association recognised by law. ", "The association which the law does recognise - the association of shareholders, creditors and directors - is incapable of producing and distributing and is not expected to perform these functions. ", "We have to give law to the real association and withdraw meaningless privilege from the imaginary one.\"", "\n\nIn 1945, Percy chaired the committee on Higher Technological Education that resulted in the Percy report. ", "He also chaired a Royal Commission that reviewed mental health legislation in the 1950s and was Rector of King's College, Durham (now Newcastle University) between 1937 and 1951, in which role he also alternated in the post of Vice-Chancellor of Durham University. ", "In 1953 he was raised to the peerage as Baron Percy of Newcastle, of Etchingham in the County of Sussex.", "\n\nFamily\nPercy married Stella Katherine, daughter of Major-General Laurence George Drummond, in 1918. ", "They had two daughters. ", "He died in April 1958, aged 71. ", "As he had no sons the barony became extinct on his death.", "\n\nReferences\n\nExternal links \n \n\n \n\n \n\nCategory:1887 births\nCategory:1958 deaths\nCategory:Barons in the Peerage of the United Kingdom\nCategory:Barons Percy of Newcastle\nCategory:Conservative Party (UK) MPs for English constituencies\nCategory:Members of the Privy Council of the United Kingdom\nCategory:UK MPs 1918–1922\nCategory:UK MPs 1922–1923\nCategory:UK MPs 1923–1924\nCategory:UK MPs 1924–1929\nCategory:UK MPs 1929–1931\nCategory:UK MPs 1931–1935\nCategory:UK MPs 1935–1945\nCategory:British Secretaries of State\nCategory:British Secretaries of State for Education\nCategory:Younger sons of dukes\nEustace Percy, 01st Baron Percy of Newcastle\nCategory:Members of London County Council\nCategory:Municipal Reform Party politicians\nCategory:James Tait Black Memorial Prize recipients\nCategory:People educated at Eton College" ]

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[ "Scott's phony outrage\n\nApparently it doesn't take much to shock Republican gubernatorial candidate Rick Scott, who is attempting to turn himself into a hand-wringing, whining Wee Willie Winkie of the hustings. • ", "It makes you wonder if Scott would get his debentures into a wad after being confronted by a testy Bichon Frise. • ", "The Lurch of the stump was supposedly flabbergasted, bumfuddled and completely discombobulated the other night during his debate with Democrat Alex Sink when he noticed during a commercial break that the candidate had glanced at a cell phone text message handed to her by a makeup artist in violation of the agreed-upon rules.", "\n\nRelated News/Archive\n\nWas this a boo-boo? ", "Sure. ", "Should Sink have looked at the message from a campaign aide essentially reminding her to be tougher in responding to the Luca Brasi of health care? ", "Absolutely not. ", "It was wrong, shouldn't have done it. ", "Bad, bad Alex. ", "You naughty girl, you.", "\n\nAnd let's all throw in a clucking harrumph for good measure, too.", "\n\nBut among all the Sturm und Drang over Sink's momentary use of a cyber crib sheet, could just a pinch of perspective prevail? ", "Good grief, it is not as if someone slipped Sink the nuclear codes. ", "This wasn't a Wikileaks document dump. ", "This wasn't a Cold War dead drop of secret CIA papers to be collected by Soviet spies.", "\n\nThis was simply a campaign aide urging Sink to stop acting like Aunt Bea and more aggressively attack Scott, the Pancho Villa of bedpans.", "\n\nFor breaching the debate rules, Sink dispatched the offending aide, insurance lobbyist Brian May, from the inner sanctum of her campaign. ", "That means the poor man must now return to his original job making gobs of money schmoozing Tallahassee pols.", "\n\nIf we lived in the real world of adults, Sink's misstep would be simply dismissed as an unfortunate gaffe, which in the end had zero effect on the debate and will have even less impact by Election Day.", "\n\nAlas, this is a political campaign for governor of Florida, which probably explains why Scott is trying to turn the cell phone kerfuffle into the stump's version of a war crime meets Watergate.", "\n\nFor all his feigned indignity, Scott does shock and appall with all the sincerity of my goldendoodle pretending she's contrite after she's been caught raiding the garbage.", "\n\nAfter all, while Scott is acting as if Sink had given him a hot foot, short-sheeted his bed and stolen his lunch money, this is same guy who presided over a company that was indicted in the largest Medicare fraud scheme in United States history, which led to $1.7 billion in fines.", "\n\nAnd while Scott blithely dismisses his association with a corrupt corporation with the alibi he should have hired more bean-counters, the candidate gets all lathered up over a momentary glitch.", "\n\nScott certainly has expressed zero shock when the company he ran was engaged in a massive rip-off of American taxpayers. ", "Good grief, Scott can't even work up a pinch of chagrin.", "\n\nNor has Scott demonstrated even a little appall — just a tad, not too much, not too little — over the fact that he has taken the Fifth in legal depositions more often than Tony Soprano.", "\n\nAnd yet, Scott is getting all huffy that Sink, at best, bent a cockamamie debate rule?", "\n\nThis is a bit like scruples-challenged Afghan President Hamid Karzai getting on his moral high horse because a Kabul traffic cop took a $50 bribe to fix a parking ticket.", "\n\nIf Scott is going to whimper about how shocked and appalled he is because Sink may have committed the political equivalent crime of removing a mattress tag, should he get elected to the Governor's Mansion next week imagine how he'll react to the legislative Sodom and Gomorrah that awaits him in the vomitory of Tallahassee?", "\n\nIn the end, whether Sink received some prohibited counsel from a campaign gofer hardly changed the quality of the discourse in the face-off between the two candidates. ", "These so-called \"debates\" have pretty much been reduced to Sink raising her opponent's association with the Columbia/HCA Medicare fraud, while Scott has remained true to his talking points to accuse Sink of being more liberal than Jane Fonda, Barney Frank and the entire Cal Berkeley faculty.", "\n\nThe Lincoln-Douglas debates these exchanges are not. ", "For that matter Abbott and Costello's \"Who's on first?\" ", "shtick qualifies as higher civic discourse than for what passes for political dialogue these days.", "\n\nOnly a few days to go. ", "But still enough time for Scott to become suitably shocked and appalled that Sink once maliciously double-parked. ", "Oh the scandal of it all!" ]

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[ "Job crafting towards strengths and interests: The effects of a job crafting intervention on person-job fit and the role of age.", "\nWe introduce 2 novel types of job crafting-crafting toward strengths and crafting toward interests-that aim to improve the fit between one's job and personal strengths and interests. ", "Based on Berg, Dutton, and Wrzesniewski (2013), we hypothesized that participating in a job crafting intervention aimed at adjusting the job to personal strengths and interests leads to higher levels of job crafting, which in turn will promote person-job fit. ", "Moreover, we hypothesized that this indirect effect would be stronger for older workers compared with younger workers. ", "Results of an experimental field study indicated that participating in the job crafting intervention leads to strengths crafting, but only among older workers. ", "Strengths crafting was, in turn, positively associated with demands-abilities and needs-supplies fit. ", "Unexpectedly, participating in the job crafting intervention did not influence job crafting toward interests and had a negative effect on crafting toward strengths among younger workers. ", "However, our findings suggest that some types of job crafting interventions can indeed be an effective tool for increasing person-job fit of older workers. (", "PsycINFO Database Record" ]

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[ "Trump derides protections for immigrants from ‘shithole’ countries\n\nPresident Trump grew frustrated with lawmakers Thursday in the Oval Office when they discussed protecting immigrants from Haiti, El Salvador and African countries as part of a bipartisan immigration deal, according to several people briefed on the meeting.", "\n\n\"Why are we having all these people from shithole countries come here?\" ", "Trump said, according to these people, referring to countries mentioned by the lawmakers.", "\n\nTrump then suggested that the United States should instead bring more people from countries such as Norway, whose prime minister he met with Wednesday. ", "The president, according to a White House official, also suggested he would be open to more immigrants from Asian countries because he felt that they help the United States economically.", "\n\nIn addition, the president singled out Haiti, telling lawmakers that immigrants from that country must be left out of any deal, these people said.", "\n\n\"Why do we need more Haitians?\" ", "Trump said, according to people familiar with the meeting. \"", "Take them out.\"", "\n\nIn November, the Trump administration rescinded deportation protection granted to nearly 60,000 Haitians after the 2010 earthquake and told them to return home by July 2019.", "\n\nLawmakers were taken aback by the comments, according to people familiar with their reactions. ", "Sens. ", "Lindsey O. Graham (R-S.C.) and Richard J. Durbin (D-Ill.) had proposed cutting the visa lottery program by 50 percent and then prioritizing countries already in the system, a White House official said.", "\n\nA White House spokesman defended Trump's position on immigration without directly addressing his remarks. ", "White House officials did not dispute the account.", "\n\n\"Certain Washington politicians choose to fight for foreign countries, but President Trump will always fight for the American people,\" spokesman Raj Shah said in a statement issued after The Washington Post first reported Trump's remarks. \". . . ", "Like other nations that have merit-based immigration, President Trump is fighting for permanent solutions that make our country stronger by welcoming those who can contribute to our society, grow our economy and assimilate into our great nation.\"", "\n\nTrump built his candidacy and presidency around hard stances on immigration, vowing to build a wall along the Mexican border and cut legal immigration by half, among other positions. ", "Officials at the Department of Homeland Security have increased immigration raids, including dozens this week at convenience stores across the country.", "\n\nTrump's comments Thursday also put further scrutiny on his long-standing tendency to make racially charged remarks — including attacks on protesting black athletes and his claim that there were fine people \"on both sides\" after neo-Nazis rioted in Charlottesville, Va. Trump falsely claimed for years that Barack Obama was not born in the United States and took out advertisements calling for the death penalty for members of the Central Park Five — four black youths and a Hispanic youth who were accused of a brutal rape in New York and later exonerated.", "\n\nThe president's remarks were quickly met with scorn from Demo­crats and some Republicans and could throw another wrench into bipartisan discussions on immigration, which had shown promise in recent days, according to legislators.", "\n\nRep. Luis Gutiérrez (D-Ill.) said the comments \"will shake the confidence that people have\" in the ongoing immigration policy talks.", "\n\n\"Democrats and Republicans in the Senate made a proposal. ", "The answer is this racist outburst of the president. ", "How can you take him seriously?\" ", "Gutiérrez said. \"", "They [Republicans] don't believe in immigration — it's always been about people of color and keeping them out of this country.\"", "\n\nRep. Cedric L. Richmond (D-La.), chairman of the Congressional Black Caucus, said on Twitter that Trump's remarks \"are further proof that his Make America Great Again Agenda is really a Make America White Again agenda.\"", "\n\nSome Republicans also raised objections. ", "Rep. Mia Love (R-Utah), whose family is from Haiti, said in a statement that Trump's remarks were \"unkind, divisive, elitist, and fly in the face of our nation's values. ", "This behavior is unacceptable from the leader of our nation.\"", "\n\n\"My grandmother used to say, 'Digame con quién caminas, y te diré quién eres.' '", "Tell me who you walk with, and I'll tell you who you are,' \" said Rep. Adriano Espaillat (D-N.Y.), who represents most of Harlem and is an immigrant from the Dominican Republic, which shares the island of Hispaniola with Haiti. \"", "If he's walking around with white supremacists and supporting them, this kind of talk doesn't surprise me.\"", "\n\nThe New York Times also reported last year that Trump said immigrants from Haiti have AIDS. ", "The White House denied that report.", "\n\nIn a statement condemning Thursday's remarks by Trump, Haiti's ambassador to the United States, Paul G. Altidor, said that \"the president was either misinformed or miseducated about Haiti and its people.\" ", "He said the Haitian Embassy was inundated with emails from Americans apologizing for what the president said.", "\n\nDemocrats were quick to note that Trump employs Haitians at his Mar-a-Lago resort in Florida and that he praised Haitian Americans during a roundtable in Miami in September.", "\n\n\"Whether you vote for me or don't vote for me, I really want to be your greatest champion, and I will be your champion,\" Trump said at the roundtable.", "\n\nAlix Desulme, a city council member in North Miami, home to thousands of Haitian Americans, said the president's latest remarks were \"disgusting.\"", "\n\n\"This is very alarming. ", "We know he's not presidential, but this is a low,\" he said. \"", "It's disheartening that someone who is the leader of the free world would use such demeaning language to talk about other folks, referring to folks of color.\"", "\n\nTrump's critics also said racially incendiary language could damage relationships with foreign allies.", "\n\nFor many of Trump's supporters, however, the comments may not prove to be particularly damaging. ", "Trump came under fire from conservatives this week for seeming to suggest that he would be open to a comprehensive immigration reform deal without money for a border wall, before he quickly backtracked.", "\n\n\"He's trying to win me back,\" conservative author Ann Coulter, who has called for harsh limits on immigration, wrote on Twitter.", "\n\nOutlining a potential bipartisan deal, the lawmakers discussed restoring protections for countries that have been removed from the temporary protected status (TPS) program while committing $1.5 billion for a border wall and making changes to the visa lottery system. ", "Lawmakers mentioned that members of the Congressional Black Caucus had requested that some African countries be included in a deal, according to a White House official, who spoke on the condition of anonymity to describe a private conversation.", "\n\nThe exchange was \"salty\" on all sides, this person said, with the president growing profane and animated while discussing immigrants from other countries. \"", "It did not go well,\" this person said.", "\n\nThe administration announced this week that it was removing TPS status for citizens of El Salvador. ", "Haitians were added to the TPS program because of a strong earthquake that devastated Haiti eight years ago.", "\n\nTrump had seemed amenable to a deal earlier in the day during phone calls with lawmakers, aides said, but shifted his position in the meeting and did not seem interested in the bipartisan compromise.", "\n\nThe scene played out hurriedly in the morning. ", "Graham and Durbin thought they would be meeting with Trump alone and were surprised to find immigration hard-liners such as Rep. Bob Goodlatte (R-Va.) and Sen. Tom Cotton (R-Ark.) at the meeting. ", "White House and Capitol Hill aides say Stephen Miller, the president's top immigration official, was concerned there could be a deal proposed that was too liberal and made sure conservative lawmakers were present.", "\n\nAfter the meeting, Marc Short, Trump's director of legislative affairs, said the White House was nowhere near a bipartisan agreement on immigration.", "\n\n\"We still think we can get there,\" White House press secretary Sarah Huckabee Sanders said at the daily White House news briefing." ]

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[ "Wir stellen unsere Artikel und Faktenchecks kostenlos für alle zur Verfügung.", "\n\nHilf uns dabei, dass das so bleiben kann.", "\n\n6.650\n\nDas Wahlprogramm der AfD sachsen\n\nDas Verhältnis der AfD Sachsen zu Kindern und Jugendlichen ist äußerst eigenartig. ", "Der Entwurf des “Regierungsprogramms” der AfD Sachsen benötigt viel Analyse und Einordnung, doch einen Vorgeschmack dessen, was diese Partei umsetzen möchte, sollte sie an die Regierung kommen, sieht man allein daran, wie sie mit Kindern umgehen möchte. ", "Und anscheinend gibt es für sie zwei Sorten Kinder. ", "Hier (nur) 12 Auszüge aus ihrem Wahlprogramm.*", "\n\n\n\n\n\n\n\n1. “", "Toleranz statt akzeptanz”?", "\n\nIn Punkt 5.3. ", "zeigt die AfD ein seltsames Verständnis dieser Begriffe. ", "Sie erklärt offen, dass sie LGBTQ-Personen nicht akzeptiert und dass das auch öffentlich so gehandhabt werden soll. ", "Sie möchte im öffentlich Raum die Existenz von LGBTQ-Personen totschweigen und ein erzkonservatives Familienbild propagieren. ", "Denn Liebe und Sexualität lassen sich nicht einfach ausklammern.", "\n\nWenn eine heterosexuelle Partnerschaft als normal dargestellt wird, eine homosexuelle aber als “Frühsexualisierung” behandelt wird, handelt es sich um eine geheuchelte Diskriminierung. ", "Kinder sollen “behütet” aufwachsen, aber das gilt nicht für Kinder, deren Sexualität nicht heterosexuell ist. ", "Denen wird deutlich erklärt: Ihr werdet nicht akzeptiert.", "\n\n2. ", "Kein Geld für Russlanddeutsche?", "\n\nDie AfD fordert, dass Landeserziehungsgeld nur diejenigen Personen erhalten sollen, deren Eltern mehr als 10 Jahre ALLEINIG die deutsche Staatsbürgerschaft haben. ", "Menschen mit doppelter Staatsbürgerschaft und deren Kinder, selbst wenn diese hier geboren und aufgewachsen sind, werden als Familien zweiter Klasse behandelt. ", "Besonders hart trifft das Russlanddeutsche und Polen, welche gleichzeitig die größten Gruppen der Doppelstaatler ausmachen und überproportional oft die AfD wählen. ", "Diese sollten sich ihre Stimme vielleicht noch einmal überlegen, wenn sie Kinder haben oder haben wollen.", "\n\n3. ", "Maximal 10% nichtdeutsche Kinder? ", "Und der Rest?", "\n\nDie AfD Sachsen möchte den Anteil nichtdeutschsprachiger Kinder in Kitas auf maximal 10% begrenzen. ", "Abgesehen davon, dass Sachsen eines der Bundesländer mit dem geringsten Anteil fremdsprachiger Kinder in Kitas ist, stellt sich doch die Frage: Wohin mit den Kindern? ", "Bekommen diese keinen Kita-Platz?", "\n\nNicht nur werden wieder Kinder nichtdeutscher Herkunft wie Kinder zweiter Klasse behandelt, diesen Kindern wird effektiv auch die Möglichkeit genommen, Deutsch erst zu erlernen. ", "Eben an Kitas und den Schulen können sie diese Sprachkenntnisse erwerben, wenn schon nicht aus dem Elternhaus. ", "Dann wird das Problem doch nur eine Stufe weiterverschoben: Dann kommen die Kinder ohne Kita und ohne Sprachkenntnisse in die Schule. ", "Und noch ein Denkfehler der AfD: Was machen internationale Schulen mit dieser Regelung?", "\n\n4. ", "Einkommensschwache Haushalte weiter schwächen\n\nSie möchten die Schülerbeförderung fördern, jedoch für die Hilfe einen Eigenanteil fordern. ", "Das führt die ganze Idee der kostenlosen Schülerbeförderung ad absurdum. ", "Denn die einkommensschwächsten Haushalte trifft dieser Anteil am stärksten, und es sind doch gerade diejenigen, die ihn am nötigsten hätten. ", "Einkommensschwache Haushalte mit Kindern sollten sich überlegen, ob ihnen das ihre Stimme für diese Partei wert ist.", "\n\n5. ", "Behinderte kinder sollen ausgeschlossen werden\n\nDie AfD behauptet gleichzeitig, die Teilhabe der Kinder am Bildungssystem sei erfüllt und wehrt sich gleichzeitig gegen eben jene Inklusion. ", "Eine Segregation von Kindern mit Behinderung ist eben genau keine Teilhabe. ", "Besonders absurd: Was ist denn mit “ideologisch” gemeint? ", "Ein Hinweis gibt eine AfD-Anfrage, die jüngst gestellt wurde, die fragte, wie viele Behinderte es in Deutschland gebe und welche Rolle Inzucht und Eheschließungen unter Migranten spielen. ", "Dutzende Sozialverbände waren entsetzt, erinnert es doch an die Ideologie des dritten Reiches.", "\n\n6. ", "Flüchtlingskinder sollen ausgeschlossen werden\n\nWieder einmal begeht die AfD Sachsen einen Grundfehler und setzt Flucht mit Migration gleich, dabei sind das zwei völlig verschiedene Dinge. ", "Erneut sollen Kinder mit Fluchterfahrung nicht nur von der Bildung sondern vom Leben ausgeschlossen werden. ", "Soll es “Sonderschulen” für Kinder von Asylbewerbern geben? ", "Oder wird diesen Kindern pauschal der Zugang zu Bildung verweigert? ", "Niemand weiß, wie lange Fliehende hier leben müssen, sie sollten doch Zugang zur Sprache und Arbeitsmarkt erhalten, um hier leben und arbeiten zu können, so lange ihre Heimat bedroht ist.", "\n\nDie AfD möchte also fördern, dass die Flüchtlingskinder kein Deutsch lernen, eigentlich gar nichts lernen (“Zeit bis zur Rückkehr […] überbrücken”). ", "Wenn sie dann aber kein Deutsch können oder nicht arbeiten, werden sie als Last für den deutschen Steuerzahler porträtiert? ", "Das ist absurd und widersprüchlich. ", "Was spricht dagegen, Kinder auszubilden und sie später in die Sozialkassen einzahlen zu lassen, selbst wenn sie eines Tages wieder in ihre Heimat zurückkehren können?", "\n\n7. ", "AfD für rassismus an schulen?", "\n\nSehr bezeichnend ist, dass sich die AfD bei den Schulprojekten “Schule ohne Rassismus” angesprochen fühlt, wenn sie es als “Kampf gegen die AfD und ihre politischen Positionen” bezeichnet. ", "Ok, offenbar ist die AfD damit schamlos offen rassistisch. ", "Denn das Projekt gibt es viel länger, als es die AfD gibt. ", "Und die Frage bleibt auch: Wenn die Kinder nicht lernen sollen, dass Rassismus gefährlich und schlecht ist, will die AfD damit Rassismus fördern? ", "Eine erschreckend ehrliche Passage.", "\n\n8. ", "Absurde Nahrungspläne\n\nOhne auf die Absurdität einzugehen, eine ganze Religion als “unserer Kultur feindlich” darzustellen – dazu ein anderes Mal mehr – ist der große Widerspruch doch: Wenn der Islam nicht von staatlich geprüften Lehrer*innen unterrichtet wird, dann lernen die Kinder doch nur vom Elternhaus und von den Imamen in den Moscheen. ", "Wenn man ehrlich einen toleranten Glauben unterrichten wollen würde, wäre ein staatlicher Religionsunterricht das beste Werkzeug dafür. ", "Die AfD macht das Problem, das sie bekämpfen möchte durch ihre ideologische Verblendung nur schlimmer.", "\n\nUnd zum “Halelen Essen”: Wenn die AfD jedwedes Essen verbieten möchte, das halal ist, dann wird es wohl fortan kein Obst, kein Gemüse, keinen Reis oder kein Wasser mehr geben. ", "Es ist natürlich absurd, weil die AfD das nicht meint. ", "Aber das wäre eine Folge der verblendeten Einstellung gegenüber einer Religion: Dass Kinder ausschließlich Schweinefleisch zu essen bekommen müssten oder dergleichen. ", "Man kann auch ganz normales Essen anbieten, das ist oft halt einfach halal.", "\n\n9. ", "Sinnlose forderung für universitäten\n\nHier wieder der große Widerspruch bei Nationalismus: Durch die Abschaffung des international anerkannten Bachelor- und Mastersystems würde Sachsen ihre AkademikerInnen auf internationaler Bühne entwerten. ", "Das Erhalten der Sprache Deutsch als “Lehr- und Wissenschaftssprache” ist gleichzeitig unglaublich vage, sinnlos und kontraproduktiv. ", "Für internationale Firmen, Studiengänge und Lehreinrichtungen wäre das fatal. ", "Und die Frage bleibt: Wo ist Deutsch nicht mehr relevant, wo Relevanz von Nöten wäre? ", "Dieser Punkt ist nichtssagend.", "\n\n10. ", "Minderjährige Abschieben\n\nEs ist erneut ein absurder Punkt: Die AfD möchte Minderjährige abschieben? ", "Dabei ignoriert sie die Realität, denn wenn sie aus Ländern fliehen, aus welchen Schutzsuchende angenommen wären kann man sie nicht in ihre Heimatländer abschieben. ", "Und häufig ist ja das Problem, dass man nicht weiß, wo sich die Eltern befinden. ", "Diese Forderung scheitert am Grundgesetz und an den Menschenrechten und ist gleichermaßen sinnlos wie grausam. ", "Und nochmal: Hier geht es um Kinder und Babies!", "\n\n11. ", "Einführung von flüchtlingsghettos\n\nNur noch Sachleistungen, eine Residenzpflicht , Ausgangskontrollen und Ausganssperren. ", "Und das dezidiert auch für Kinder und Jugendliche, die nicht nur auf die Nacht begrenzt sind. ", "Zusammen mit der obigen Erklärung für eigene Schuleinrichtungen gewinnt man den Eindruck, die AfD möchte Flüchtlingsghettos einrichten und diese Menschen vom sozialen Leben vollkommen abschneiden. ", "Erneut sieht man, dass keine Integration gewollt ist. ", "Während man sich gleichzeitig über eben jene Fehlende Integration echauffiert.", "\n\n12. ", "Ausschluss aus dem Leben als “Eigeninitiative” verkaufen\n\nDieser Punkt fasst es noch einmal gut zusammen: Schutzsuchende sollen dezidiert nicht integriert werden. ", "Es soll keine Möglichkeit geben, sich zu integrieren oder die Sprache zu lernen, aber es wird erwartet, dass das in “Eigeninitiative” geschieht. ", "Menschen ohne Sprachkenntnisse und oft ohne finanzielle Mittel (Sachleistungen) sollen komplett abgeschnitten werden und es wird erwartet, dass sie sich selbstständig um alles kümmern. ", "Gleichzeitig wird mit deren Hilflosigkeit Stimmungsmache betrieben. ", "Es ist absurd.", "\n\nBesonders leiden darunter die Kinder, die buchstäblich allein gelassen werden, keine Hilfen erhalten sollen, besonders gilt das für unbegleitete Minderjährige, denen der Zugang zu Bildung, Deutschunterricht und Hilfen völlig abgeschnitten werden soll. ", "Und von denen erwartet wird, dass sie sich selbstständig Deutsch beibringen? ", "Die AfD lebt in einer Fantasiewelt.", "\n\nFazit\n\nWer Kinder mag, darf die AfD Sachsen nicht wählen. ", "Für die AfD gibt es zwei Arten von Kindern: Deutsche (Sprich: Nur mit deutscher Staatsbürgerschaft), nicht behinderte Kinder reicher Eltern und alle anderen, deren der Zugang zu Bildung und Teilhabe erschwert und unmöglich gemacht werden soll. ", "Das Verdrängen von Kindern mit Migrationshintergrund oder einkommenschwacher Haushalte ist deutlich und wird auch teilweise explizit als Ziel erklärt. ", "Und ich möchte daran erinnern: Hier geht es um Kinder!", "\n\nDie AfD will Kindern kein Deutsch beibringen, sie will nicht dass sie Bildung erhalten können, oder demokratische Werte wie Toleranz im Religionsunterricht gelehrt bekommen, Kinder von Eltern mit doppelter Staatsbürgerschaft (und ohne deutsche) werden aktiv finanziell benachteiligt. ", "Das trifft vor allem Menschen mit polnischer und russischer doppelter Staatsbürgerschaft. ", "Behinderte Kinder sollen ebenfalls ausgeschlossen werden, ebenso wie die Kinder von Schutzsuchenden.", "\n\nDie Politik der AfD Sachsen ist realitätsfern, widersprüchlich, sinnlos, grausam, rassistisch und erreicht teilweise das Gegenteil dessen, was sie will. ", "Und die absurdeste Wählertäuschung: Für die meisten Punkte ist das Land Sachsen nicht einmal zuständig. ", "Diese Politik, sofern sie überhaupt umsetzbar ist, wird erst zu einer Benachteiligung vieler Kinder und Jugendliche führen, die der AfD mehr Munition für Hetze bietet. ", "Die AfD würde an der Regierung auf dem Rücken von Kindern ihre ideologische Verblendung ausleben. ", "Es wären Kinder, die besonders unter der Politik der AfD zu leiden hätten.", "\n\n*Ergänzung: Diese Punkte haben auch Eingang in das endgültige Wahlprogramm gefunden, stehen aber teilweise an anderen Stellen. ", "Danke an Marianna Henning für die Recherche! ", "Artikelbild: pixabay.com, CC0" ]

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[ "Q:\n\nSet DataGridView arrow to the selected row\n\nHow do I set the arrow to the selected row. ", "I'm programatically selecting the rows based on the value of a combo box. ", "Currently, only the row is highlighted and the arrow doesn't follow\nforeach (DataGridViewRow row in dgv.", "Rows)\n{\n if ((int)row.", "Tag == ma.", "ID)//ma.", "ID is the selected combo box value\n {\n row.", "Selected = true;\n }\n}\n\nA:\n\nYou have to change CurrentCell like this. ", "\n(This will also change CurrentRow)\nforeach (DataGridViewRow row in dgv.", "Rows)\n{\n if ((int)row.", "Tag == ma.", "ID)//ma.", "ID is the selected combo box value\n {\n row.", "Selected = true;\n dgv.", "CurrentCell = row.", "Cells[0];\n }\n}\n\n" ]

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[ "Noemi Garza\n\nKALAMAZOO, MI - A Calhoun County sheriff's deputy pleaded not guilty Friday to charges that she tried to resist police who arrested her on suspicion of drunken driving and leaving the scene of crash near downtown Kalamazoo.", "\n\nNoemi Garza, 32, entered her plea as she appeared in Kalamazoo County District Court where Magistrate Nicholas Schaberg arraigned her on one count each of attempted resisting and obstructing police, operating a motor vehicle while intoxicated, failure to stop at the scene of a collision and possession of a firearm while under the influence.", "\n\nEach charge is a misdemeanor, the most serious of which is the attempted resisting and obstructing. ", "That charge is punishable by up to one year in jail.", "\n\nThe other charges are punishable by a maximum sentence ranging between three months and 93 days in jail.", "\n\nThe charges stem from a June 13 crash near the corner of Douglas Avenue and Forbes Street.", "\n\nA Kalamazoo Public Safety report obtained by the Kalamazoo Gazette through the Michigan Freedom of Information Act said that following the crash, Garza admitted to drinking shots of Fireball whiskey, but refused to complete sobriety tests or take a preliminary breathalyzer test.", "\n\nA blood draw obtained by police later revealed Garza had a blood-alcohol level of 0.17 percent, more than double the legal limit of 0.08 percent for driving in Michigan.", "\n\nIn court Friday, Garza spoke quietly as she told Schaberg she understood the charges against her and the potential penalties. ", "Garza, of Hastings, appeared in court with Attorney Kellie Podolsky, who entered the not guilty plea on her Garza's behalf.", "\n\nIn the June 13 incident, Kalamazoo Public Safety officers found Garza after responding just after midnight to a report of a crash near Douglas and Forbes.", "\n\nAt the scene, a driver told officers he was driving south on Douglas near Kalamazoo Avenue when he was struck by another vehicle that failed to negotiate the curve from Kalamazoo Avenue onto Douglas, according to the KDPS report.", "\n\nThe report said that when police approached Garza at her car, she ran onto the porch of a house on Forbes. ", "She later told officers she had been involved in an accident.", "\n\nPrior to the crash, Garza told police she was driving from a house party in Richland where she had a \"couple of shots\" of Fireball whiskey. ", "When police asked her if the whiskey affected her ability to drive, Garza responded, \"A little bit but not too much.", "\n\nHowever, police said in the report that Garza smelled of alcohol, had trouble keeping her balance, had bloodshot eyes and spoke with a slur.", "\n\nThe report said that when officers arrested Garza, she resisted and told them not to touch her. ", "She also initially refused to get into a police cruiser.", "\n\nOnce inside the cruiser, police said Garza kicked a door of the cruiser and tried to slip her handcuffs off her wrists. ", "She also called an officer offensive names, according to the report.", "\n\nAfter being taken to a holding cell, police said Garza refused a breath test and pretended to be asleep on a bench. ", "The report said Garza later apologized to an officer for calling her names and said she was \"intoxicated.\"", "\n\nOfficers found a .40-caliber Glock handgun in Garza's purse at the scene, according to the report.", "\n\nPodolsky declined to comment following Garza's arraignment Friday. ", "Garza is scheduled to be back in district court July 6 for a pretrial conference.", "\n\nGarza is free on a $200 cash bond.", "\n\nRex Hall Jr. is a public safety reporter for the Kalamazoo Gazette. ", "You can reach him at rhall2@mlive.com. ", "Follow him on Twitter." ]

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[ "Consuelo Vanderbilt\n\nConsuelo Vanderbilt Balsan (formerly Consuelo Spencer-Churchill, Duchess of Marlborough; born Consuelo Vanderbilt; 2 March 1877 – 6 December 1964) was a member of the prominent American Vanderbilt family. ", "Her marriage to the ninth Duke of Marlborough has become known as one of the socially advantageous, but loveless, marriages common during the Gilded Age.", "\n\nLife\n\nEarly life\n\nBorn in New York City, she was the only daughter and eldest child of William Kissam Vanderbilt, a New York railroad millionaire, and his first wife, a Mobile, Alabama, belle and budding suffragist, Alva Erskine Smith (1853–1933, who later married Oliver Belmont). ", "Her Spanish name was in honor of her godmother, Consuelo Yznaga (1853–1909), a half-Cuban, half-American socialite who created a social stir a year earlier when she married the fortune-hunting George, Viscount Mandeville, a union of Old World aristocracy and New World money that caused the groom's father, the 7th Duke of Manchester, to openly wonder if his son and heir had married a \"Red Indian\". ", "Consuelo and her friends were the inspiration for Edith Wharton's unfinished novel The Buccaneers.", "\n\nConsuelo Vanderbilt was largely dominated by her mother, who was determined that her daughter would make a great marriage like that of her famous eponym. ", "In her autobiography, Consuelo Vanderbilt described how she was required to wear a steel rod, which ran down her spine and fastened around her waist and over her shoulders, to improve her posture. ", "She was educated entirely at home by governesses and tutors, and learned foreign languages at an early age. ", "Her mother was abusive and whipped her with a riding crop for minor infractions. ", "When, as a teenager, Consuelo objected to the clothing her mother had selected for her, Alva told her that \"I do the thinking, you do as you are told.\"", "\n\n \nLike her godmother, Consuelo Vanderbilt attracted numerous title-bearing suitors anxious to trade social position for cash. ", "Her mother reportedly received at least five proposals for her hand. ", "Consuelo was allowed to consider the proposal of just one of the men, Prince Francis Joseph of Battenberg, but she developed an instant aversion to him. ", "None of the others, however, was good enough for Alva Vanderbilt, herself the daughter of a cotton factor. ", "Consuelo Vanderbilt was considered a great beauty, with a face compelling enough to cause the playwright Sir James Barrie, author of Peter Pan, to write, \"I would stand all day in the street to see Consuelo Marlborough get into her carriage.\" ", "Oxford undergraduate Guy Fortescue later described how he and his friends were captivated by her \"piquante oval face perched upon a long slender neck, her enormous dark eyes fringed with curling lashes, her dimples, and her tiny teeth when she smiled.\" ", "She came to embody the \"slim, tight look\" that was in vogue during the Edwardian era.", "\n\nFirst marriage \n\nDetermined to secure the highest-ranking mate possible for her only daughter, a union that would emphasize the preeminence of the Vanderbilt family in New York society, Alva Vanderbilt engineered a meeting between Consuelo and the indebted, titled Charles Spencer-Churchill, 9th Duke of Marlborough, chatelain of Blenheim Palace. ", "The matchmaker was a minor American heiress turned major English hostess, Lady Paget, the wife of Sir Arthur Paget. ", "Née Mary \"Minnie\" Stevens, Lady Paget was the daughter of Paran Stevens, the socially ambitious widow of an American hotel entrepreneur who had successfully obtained admittance to the exclusive New York society of the fabled \"Four Hundred\". ", "Lady Paget, always short of money, soon became a sort of international marital agent, introducing eligible American heiresses to British noblemen.", "\n\nUnfortunately, Consuelo Vanderbilt had no interest in the duke, being secretly engaged to an American, Winthrop Rutherfurd. ", "Her mother cajoled, wheedled, begged, and then, ultimately, ordered her daughter to marry Marlborough. ", "When Consuelo – a docile teenager whose only notable characteristic at the time was abject obedience to her fearsome mother – made plans to elope, she was locked in her room as Alva threatened to murder Rutherfurd. ", "Still she refused. ", "It was only when Alva Vanderbilt claimed that her health was being seriously and irretrievably undermined by Consuelo's stubbornness and appeared to be at death's door that the malleable girl acquiesced. ", "Alva made an astonishing recovery from her entirely phantom illness, and when the wedding took place, Consuelo stood at the altar reportedly weeping behind her veil. ", "The duke, for his part, gave up the woman he reportedly loved back in England and collected US$2.5 million (approximately US$75.2 million in 2019 dollars) in railroad stock as a marriage settlement. ", "Consuelo's father built a mansion for her in London, Sunderland House in Curzon Street.", "\n\nConsuelo Vanderbilt married His Grace The 9th Duke of Marlborough at St. Thomas Episcopal Church, New York City, on 6 November 1895. ", "They had two sons, John Albert William Spencer-Churchill, Marquess of Blandford (who became 10th Duke of Marlborough) and Lord Ivor Spencer-Churchill.", "\n\nThe new duchess was adored by the poor and less fortunate tenants on her husband's estate, whom she visited and to whom she provided assistance. ", "She later became involved with other philanthropic projects and was particularly interested in those that affected mothers and children. ", "She was also a social success with royalty and the aristocracy of Britain. ", "However, given the ill-fitting match between the duke and his wife, it was only a matter of time before their marriage was in name only. ", "The duchess eventually was smitten by her husband's cousin, the Hon. ", "Reginald Fellowes (the liaison did not last, to the relief of Fellowes's parents), while the duke fell under the spell of Gladys Marie Deacon, an eccentric American of little money but, like Consuelo, dazzling to look at and of considerable intellect. ", "The Marlboroughs separated in 1906, divorced in 1921, and the marriage was annulled, at the duke's request and with Consuelo's assent, on 19 August 1926.", "\n\nThough largely embarked upon as a way to facilitate the Anglican duke's desire to convert to Roman Catholicism, the annulment, to the surprise of many, also was fully supported by the former duchess's mother, who testified that the Vanderbilt–Marlborough marriage had been an act of unmistakable coercion. \"", "I forced my daughter to marry the duke\", Alva Belmont told an investigator, adding: \"I have always had absolute power over my daughter.\" ", "In later years, Consuelo and her mother enjoyed a closer, easier relationship.", "\n\nSecond marriage and later life\n\nConsuelo's second marriage, on 4 July 1921, was to Lt. ", "Col. ", "Jacques Balsan, a record-breaking pioneer French balloon, aircraft, and hydroplane pilot who once worked with the Wright Brothers. ", "Also a textile manufacturing heir, Balsan was a younger brother of Etienne Balsan, who was an early lover of Coco Chanel. ", "Jacques Balsan died in 1956 at the age of 88.", "\n\nAfter the annulment with the Duke of Marlborough, she still maintained ties with favorite Churchill relatives, particularly Winston Churchill. ", "He was a frequent visitor to her château, in St. Georges Motel, a small commune near Dreux about 50 miles from Paris, in the 1920s and 1930s, where he completed his last painting before the war.", "\n\nRecords in Florida show that in 1932 Consuelo Vanderbilt Balsan built a home in Manalapan, Florida, just south of Palm Beach. ", "It was designed as a love nest by Maurice Fatio. ", "The dream home of 26,000 square feet is called Casa Alva, in honor of her mother. ", " Although Consuelo sold her home in 1957, it still exists. ", " Many believe that Churchill polished his famous Iron Curtain Speech in that house as he visited his cousin's wife on his way to Fulton, Missouri, to deliver an address at Westminster College.", "\n\nConsuelo Balsan published her insightful but not entirely candid autobiography, The Glitter and the Gold, in 1953. ", " It was ghostwritten by Stuart Preston, an American writer who was an art critic for The New York Times. ", "A reviewer in the same paper called it \"an ideal epitaph of the age of elegance.\"", "\n\nConsuelo Balsan died at Southampton, Long Island, New York, on 6 December 1964. ", " She was buried alongside her younger son, Lord Ivor Spencer-Churchill, in the churchyard at St Martin's Church, Bladon, Oxfordshire, England, near her former home, Blenheim Palace.", "\n\nPublic service \nDuring World War I, Consuelo Vanderbilt worked as the chair of the Economic Relief Committee for the American Women's War Relief Fund.", "\n\nDuring the inter-war period, she and Winaretta Singer-Polignac (the Princess de Polignac and Singer Sewing Machine heiress) worked together in the construction of a 360-bed hospital destined to provide medical care to middle class workers. ", "The result of this effort is the Foch Hospital, located in Suresnes, a suburb of Paris, France. ", "The hospital also includes a school of nursing and is one of the top ranked hospitals in France, especially for renal transplants. ", "It has remained true to its origins and stayed a private not-for-profit institution that still serves the Paris community. ", "It is managed by the Fondation médicale Franco-américaine du Mont-Valérien, commonly called Foundation Foch.", "\n\nNotes\n\nExternal links\n\nA Message to the Diocese on the Action of the Vatican Court upon the Marlborough Marriage, by William Thomas Manning, 1926\nThe marriage of Consuelo Vanderbilt\nVideo footage of Consuelo Vanderbilt\n\nConsuelo\nCategory:Spencer-Churchill family\nMarlborough\nCategory:American people of Dutch descent\nCategory:1877 births\nCategory:1964 deaths\nCategory:Burials at St Martin's Church, Bladon\nCategory:Gilded Age\nCategory:People from Manhattan" ]

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[ "This invention relates generally to microwave ovens and more particularly to a microwave oven having a griddle.", "\nAs is known in the art, some microwave ovens include a griddle, alternatively referred to as a grill or hot bottom. ", "Such a feature is desirable since it provides browning to the food product otherwise not achieved with microwave cooking. ", "In one such oven, the griddle is disposed in an aperture in the floor of the cooking cavity.", "\nIn designing such an oven, various factors should be considered. ", "First, a microwave seal should be provided between the griddle and the adjacent cooking cavity floor to prevent microwave energy from leaking.", "\nSecondly, provisions should be made for relative movement occurring between the griddle and the cooking cavity floor. ", "More particularly, such movement may result from the griddle having a different thermal coefficient of expansion than the cavity floor in which it is mounted. ", "Furthermore, this problem may be aggravated by the relatively high temperatures to which the griddle is heated. ", "For example, where the griddle is comprised of aluminum and the cooking cavity floor is stainless steel, buckling in the cooking cavity floor could occur if the floor is rigidly attached to the griddle. ", "This is because aluminum has a higher thermal coefficient of expansion than stainless steel and further because of the relatively high temperature to which the griddle is subjected.", "\nA third factor to be considered when providing a microwave/griddle oven is that water and/or soap is likely to be used in the oven to clean the griddle and food may spill from the griddle onto the adjacent cooking cavity floor. ", "Thus, a liquid seal should be provided at the junction between the griddle and the cooking cavity floor.", "\nFinally, due to the relatively high temperature to which the griddle heats, the adjacent cooking cavity floor and the cooking cavity walls may be excessively heated. ", "This condition is undesirable since the outer housing of the oven may be concomitantly heated rendering it dangerously hot. ", "One solution to this problem is to provide insulation between the outer housing and the cooking cavity. ", "However, this solution may be undesirable due to the additional space required for the insulation and its cost. ", "Another solution is to increase the air circulation within the oven. ", "However, this solution may require additional blowers or fans, thereby reducing the power available for cooking." ]

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[ "Microsoft's Movies & TV app for Windows 10 and Xbox now supports the Movies Anywhere service. ", "And for a limited time, if you add your Microsoft account to the Movies Anywhere app, you'll get a free film.", "\n\nMovies Anywhere, originally launched by Disney in 2014, brings together movies you've bought from a wide range of content providers, including Amazon Video, Google Play, iTunes, and Vudu. ", "Rather than having to hunt through different apps (and even different devices) to figure out which service you bought a given film from, Movies Anywhere means all your films will show up in one app, and the app can run on a wide range of devices. ", "The Movies Anywhere app also supports buying from any service that you've connected.", "\n\nMovies Anywhere movies will show up within Microsoft's Movies & TV apps, even if they were bought on competing platforms. ", "At least, so long as you live in the US, because \"anywhere\" does not actually mean \"anywhere.\"", "\n\nTo sweeten the deal, anyone who connects their Microsoft account to the Movies Anywhere service will receive X-Men: Days of Future Past, which is to say, the last mainline, ensemble X-Men movie that was worth a damn." ]

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[ "<!", "DOCTYPE html>\n<html lang=\"en\">\n <head>\n <title>CGSize Extension Reference</title>\n <link rel=\"stylesheet\" type=\"text/css\" href=\"../css/jazzy.css\" />\n <link rel=\"stylesheet\" type=\"text/css\" href=\"../css/highlight.css\" />\n <meta charset='utf-8'>\n <script src=\"../js/jquery.min.js\" defer></script>\n <script src=\"../js/jazzy.js\" defer></script>\n \n </head>\n <body>\n <a name=\"//apple_ref/swift/Extension/CGSize\" class=\"dashAnchor\"></a>\n <a title=\"CGSize Extension Reference\"></a>\n <header>\n <div class=\"content-wrapper\">\n <p><a href=\"../index.html\">Katana Docs</a> (99% documented)</p>\n <p class=\"header-right\"><a href=\"https://github.com/BendingSpoons/katana-swift\"><img src=\"../img/gh.png\"/>View on GitHub</a></p>\n </div>\n </header>\n <div class=\"content-wrapper\">\n <p id=\"breadcrumbs\">\n <a href=\"../index.html\">Katana Reference</a>\n <img id=\"carat\" src=\"../img/carat.png\" />\n CGSize Extension Reference\n </p>\n </div>\n <div 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href=\"../Structs/Animation.html\">Animation</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/AnimationContainer.html\">AnimationContainer</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/AnimationOptions.html\">AnimationOptions</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/AnimationProps.html\">AnimationProps</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/ChildrenAnimations.html\">ChildrenAnimations</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/EdgeInsets.html\">EdgeInsets</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/EmptyProps.html\">EmptyProps</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/EmptyState.html\">EmptyState</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/Size.html\">Size</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Structs/Value.html\">Value</a>\n </li>\n </ul>\n </li>\n <li class=\"nav-group-name\">\n <a href=\"../Typealiases.html\">Typealiases</a>\n <ul class=\"nav-group-tasks\">\n <li class=\"nav-group-task\">\n <a href=\"../Typealiases.html#/s:6Katana25AnimationPropsTransformer\">AnimationPropsTransformer</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Typealiases.html#/s:6Katana21AnyRefCallbackClosure\">AnyRefCallbackClosure</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Typealiases.html#/s:6Katana20NodeUpdateCompletion\">NodeUpdateCompletion</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Typealiases.html#/s:6Katana18RefCallbackClosure\">RefCallbackClosure</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Typealiases.html#/s:6Katana13StoreDispatch\">StoreDispatch</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Typealiases.html#/s:6Katana13StoreListener\">StoreListener</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Typealiases.html#/s:6Katana15StoreMiddleware\">StoreMiddleware</a>\n </li>\n <li class=\"nav-group-task\">\n <a href=\"../Typealiases.html#/s:6Katana16StoreUnsubscribe\">StoreUnsubscribe</a>\n </li>\n </ul>\n </li>\n <li class=\"nav-group-name\">\n <a href=\"../Associated Types.html\">Associated Types</a>\n <ul class=\"nav-group-tasks\">\n <li class=\"nav-group-task\">\n <a href=\"../Associated Types.html#/s:P6Katana27NodeDescriptionWithChildren9PropsType\">PropsType</a>\n </li>\n </ul>\n </li>\n </ul>\n </nav>\n <article class=\"main-content\">\n <section>\n <section class=\"section\">\n <h1>CGSize</h1>\n <p>Undocumented</p>\n\n </section>\n <section class=\"section task-group-section\">\n <div class=\"task-group\">\n <ul>\n <li class=\"item\">\n <div>\n <code>\n <a name=\"/s:vPs8Hashable9hashValueSi\"></a>\n <a name=\"//apple_ref/swift/Property/hashValue\" class=\"dashAnchor\"></a>\n <a class=\"token\" href=\"#/s:vPs8Hashable9hashValueSi\">hashValue</a>\n </code>\n </div>\n <div class=\"height-container\">\n <div class=\"pointer-container\"></div>\n <section class=\"section\">\n <div class=\"pointer\"></div>\n <div class=\"abstract\">\n <p><code>CGSize</code> extension that makes it hashable</p>\n\n </div>\n <div class=\"declaration\">\n <h4>Declaration</h4>\n <div class=\"language\">\n <p class=\"aside-title\">Swift</p>\n <pre class=\"highlight\"><code><span class=\"kd\">public</span> <span class=\"k\">var</span> <span class=\"nv\">hashValue</span><span class=\"p\">:</span> <span class=\"kt\">Int</span></code></pre>\n\n </div>\n </div>\n <div class=\"slightly-smaller\">\n <a href=\"https://github.com/BendingSpoons/katana-swift/tree/0.8.3/Katana/Plastic/LayoutsCache.swift#L14-L18\">Show on GitHub</a>\n </div>\n </section>\n </div>\n </li>\n </ul>\n </div>\n </section>\n </section>\n <section id=\"footer\">\n <p>&copy; 2017 <a class=\"link\" href=\"http://bendingspoons.com\" target=\"_blank\" rel=\"external\">Bending Spoons Team</a>. ", "All rights reserved. (", "Last updated: 2017-05-11)</p>\n <p>Generated by <a class=\"link\" href=\"https://github.com/realm/jazzy\" target=\"_blank\" rel=\"external\">jazzy ♪♫ v0.7.4</a>, a <a class=\"link\" href=\"http://realm.io\" target=\"_blank\" rel=\"external\">Realm</a> project.</p>\n </section>\n </article>\n </div>\n </body>\n</div>\n</html>\n" ]

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[ "I am in love with this bra. ", "I've always had a larger cup and smaller band size which is difficult if not impossible to find in stores. ", "I recently stopped breastfeeding and I really needed a bra that would have great support. ", "This is the first bra I have worn in years that fit perfectly and was supportive. ", "So happy I bought this!", "\n\nI'm happy that I purchased this bra. ", "It's very stylish and supportive for running. ", "My one complaint would be that the cups are very thin so if you're wearing the bra with a tight top you will get nipple show through. ", "As for sizing, I'd say that the cups are true to size but the band is on the tight side. ", "I usually am in between a 32 and 34 and in this bra I wear the 34 band on the loosest hook.", "\n\nI ordered this in 30G and 30GG because some reviews said it ran large, but the one in my true size (30G) fit perfectly. ", "This bra gives me the lift and cleavage I desire. ", "I also like the shape it gives me. ", "To those who are considering buying this bra, just note that this is not an everyday bra that can easily be worn under t-shirts.", "\n\nFINALLY! ", "I am now a 36DD and have been on the lookout for a good sports bra (yoga running and regular gym activity). ", "I wanted an underwire one but I really needed something that was lightweight. ", "I did not like the Panache 5021 (felt like armour) and I didn't like the Wacoal one bc I couldn't find a size that fit me perfect. ", "Tried this one - and poof! ", "PERFECTION FOUND.", "\nI love the material and smoothness under my shirts and I can wear this all day if I wanted to. ", "Try this ladies and you will not be disappointed!", "\n\nI'm a Fantasie & Freya girl so trying a different manufacturer made me a bit unsure. ", "While I'm not sure about the longevity of this bra, it is very supportive while still being a little sexy with the lace overlay. ", "I like/don't mind the 3 hooks and while being a little on the heavy side I think it adds to the support I'm receiving (34DDDD) I do wish there was a next cup size larger but DDDD is the largest available.", "\n\nThe material is a bit scratchy, and the cups with or without the included padding, are about a half size bigger than the size listed. ", "it is very supportive but due to fabric less than 4 hour wear from mild skin irritation. ", "The colour and pattern are lovely and i do wear it frequently.", "\n\nThis bra is fun because it's not only comfortable and sexy, but also has a great color. ", "My boyfriend loves the hot pink/orange pop of color to my wardrobe. ", "The bra fits great band wise, but is just a little undersized with the cup due to its shape/seam. ", "I wouldn't go up in a cup size though.", "\n\nI love the Simone Perele line of bras... they are so pretty and feminine and fit me so well. ", "I wear a 32E in this brand and this Revelation bra fits great. ", "I wouldn't really call it a demi cup as it covers a lot and is very supportive and doesn't add any bulk. ", "Highly recommended.", "\n\nI'm a size 14 that wears between a 34H and a 36FF. ", "I got the 36 and might need to go down in band size. ", "I will warn you, the suit is very chesty! ", "The plunge shows a bit of my ribcage under the round of the bottom of my boobs, but I'm okay with that. ", "There isn't a lot of support, due to the deep cut on the suit, so I will be relying on my straps a lot to keep things up. ", "I'm hoping that by exchanging to a 34 band, this will help a bit. ", "I bought the skirted bottoms to go with it and they provide cute coverage, but I don't feel like an old lady. ", "The texture of the suit hides a lot of stuff for us bigger ladies, so that alone makes it a good choice!", "\n\nThis is a great top for support without the padding. ", "I could have used a smaller size but I was in a rush to leave for vacation. ", "I also could probably tie the straps a little tighter to push up the top a bit more to avoid pancake boob.", "\n\nThis top is very supportive and stays up on its own(even without the removable straps). ", "At 7 months pregnant I had a very difficult time finding a top to support my 32FF chest. ", "This bandini top is not only supportive but comfortable as well. ", "It does not dig into your sides as other underwire tops tend to do. ", "I love Freya and love this top!", "\n\nThis suit is great! ", "I read all the online reviews I could find, and everyone else was saying that this top runs a size small due to the padding on the inside. ", "I am a 36 DD, and I ordered a 38 E (38 DDD in American sizing) and it fit wonderfully. ", "High quality fabric, and the removable straps are very comfortable. ", "No digging or uncomfortable feeling from the underwire, either. ", "It held up to the ocean waves and pool dives without shifting. ", "Would definitely recommend this!!", "\n\nShop Confidently\n\nOur apologies...We are experiencing a technical issue with this page. ", "Please call us at 1.877.728.9272, 24 hours a day, 7 days a week and we'll gladly help you complete your order.", "\n\nIf you prefer, you may also email us at info@barenecessities.com. ", "Please include: Your name, where on our site you received the error, any questions you may have, and how and when you'd like us to contact you. ", "Our business hours are Monday-Saturday 8am-6pm EST.", "\n\nOur apologies...We are experiencing a technical issue with this page. ", "Please call us at 1.877.728.9272, 24 hours a day, 7 days a week and we'll gladly help you complete your order.", "\n\nIf you prefer, you may also email us at info@barenecessities.com. ", "Please include: Your name, where on our site you received the error, any questions you may have, and how and when you'd like us to contact you. ", "Our business hours are Monday-Saturday 8am-6pm EST." ]

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[ "Q:\n\nFiltering out top_hits subaggregation based on total documents\n\nI'm doing map clustering using Elasticsearch GeoHash grid aggregation.", "\nThe query returns on average 100-200 buckets. ", "\nEach of the bucket uses the top_hits aggregation which I use to return 3 documents for each aggregated cluster. ", "\nThe problem is that I want to return top_hits only when the parent aggregation (GeoHash) aggregates no more than 3 documents.", "\nIf a cluster aggregates more than 3 documents I don't want ES to return any documents for this cluster (because I'm not gonna use them).", "\nI've tried to use Bucket Selector Aggregation, but didn't manage to construct a correct bucket_path.", "\nI use bucket selector aggregation on the same level as top_hits aggregation.", "\nThe number of total documents for a bucket is available at top_hits.hits.total but what I'm getting is reason=path not supported for [top_hits]: [hits.total].", "\nIs this possible in elasticsearch?", "\nIt's important for me, because in most of the queries only small percentage of buckets will have less than 3 documents. ", "But top hits subaggregation is always returning top 3 documents even for clusters of 1000 documents.", "\nIf a result of a query return 200 buckets and only 5 of them are aggregating <= 3 documents so I want to return only 5*3 documents, not 200*3 (Te response is 10MB in this case).", "\nHere is the aggs part of my query:\n\"clusters\": {\n \"geohash_grid\": {\n \"field\": \"coordinates\",\n \"precision\": 3\n },\n \"aggs\": {\n \"top_hits\": {\n \"top_hits\": {\n \"size\": 3\n }\n },\n \"top_hits_filter\": {\n \"bucket_selector\": {\n \"buckets_path\": {\n \"total_hits\": \"top_hits._count\" // tried top_hits.hits.total\n },\n \"script\": {\n \"inline\": \"total_hits <= 3\"\n }\n }\n }\n }\n}\n\nA:\n\nTry this @ilivewithian :\n \"aggs\": {\n \"clusters\": {\n \"geohash_grid\": {\n \"field\": \"coordinates\",\n \"precision\": 3\n },\n \"aggs\": {\n \"top_hits\": {\n \"top_hits\": {\n \"size\": 3\n }\n },\n \"top_hits_filter\": {\n \"bucket_selector\": {\n \"buckets_path\": {\n \"total_hits\": \"_count\"\n },\n \"script\": {\n \"inline\": \"params.total_hits <= 3\"\n }\n }\n }\n }\n }\n }\n\n" ]

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[ "Tewkesbury\n\nTewkesbury ( ) is a market town and civil parish in Gloucestershire, England. ", "It stands at the confluence of the River Severn and the River Avon, and also minor tributaries the Swilgate and Carrant Brook. ", "It gives its name to the Borough of Tewkesbury, of which the town is the second largest settlement. ", "It lies in the far north of the county, forming part of the border with Worcestershire.", "\n\nThe name Tewkesbury comes from Theoc, the name of a Saxon who founded a hermitage there in the 7th century, and in the Old English language was called . ", "An erroneous derivation from Theotokos (the Greek title of Mary, mother of God) enjoyed currency in the monastic period of the town's history.", "\n\nThe Battle of Tewkesbury, which took place on 4 May 1471, was one of the decisive battles of the Wars of the Roses.", "\n\nGeography\n\nNearby places\n\n Bredon\n Bishop's Cleeve\n Cheltenham\n Evesham\n Gloucester\n Pershore\n Malvern (Great Malvern)\n Upton upon Severn\n Cotswolds\n Forest of Dean\n Malvern Hills\n Winchcombe\n Gretton\n\nDemography\nAt the 2011 UK census the Tewkesbury parish had a population of 10,704. ", "If the neighbouring parishes of Wheatpieces (3,577), Northway (5,080) and Ashchurch Rural (957) are added, the figure rises to 20,318. ", "The Tewkesbury urban area is divided in two by the north-south running M5 motorway, opened in February 1971. ", "However, the town is generally considered as the built-up area to the immediate east and west of the M5 at junction 9, with the town centre, abbey and old town situated to the west. ", "The close proximity of large areas of land that are prone to flooding, as evidenced by the severe floods that struck the region in July 2007, would make further expansion difficult. ", "However, the present Borough of Tewkesbury, created on 1 April 1974, also contains a large portion of rural north Gloucestershire, extending as far as the edges of Gloucester itself and also Cheltenham, and has a present population of 81,943.", "\n\nLandmarks\n\nThe town features many notable Medieval, Tudor buildings, but its major claim to fame is Tewkesbury Abbey, a fine Norman abbey church, originally part of a monastery, which was saved from the Dissolution of the Monasteries by King Henry VIII after being bought by the townspeople for the price of the lead on the roof to use as their parish church. ", "Most of the monastery buildings, as well as the vineyards, were destroyed during this time. ", "The Abbey Mill however still remains, resting upon the Mill Avon, a channel allegedly built by the monks. ", "This channel represents one of the biggest projects in Tewkesbury's history, though the present weir dates only from the 1990s, replacing two sluice gates installed in the 1930s. ", "The Abbey Mill is also sometimes known as \"Abel Fletcher's Mill\", but this is simply the name given to it in Dinah Craik's novel John Halifax, Gentleman, whose setting Norton Bury is based on Tewkesbury (see the Tewkesbury in Literature section below).", "\n\nThe abbey is thought to be the site of the place where the hermit Theoc once lived. ", "The great Romanesque arch on the west front is particularly striking, and the stained glass window at that end has been restored. ", "The monastery was founded by the Despensers as a family mausoleum, and the Despenser and Neville tombs are fine examples of small-scale late medieval stonework.", "\n\nThe tower is believed to be the largest Norman tower still in existence (though that at Norwich Cathedral is another strong contender). ", "The tower once had a wooden spire which may have taken the total height of the building to as much as 260 feet (79 m), but this was blown off in a heavy storm on Easter Monday 1559; the present pinnacles and battlements were added in 1600 to give the tower a more \"finished\" look. ", "The height to the top of the pinnacles is 148 feet (45 m). ", "The abbey is thought to be the third largest church in Britain that is not a cathedral (after Westminster Abbey and Beverley Minster). ", "From end to end it measures 331 feet (101 m), though prior to the destruction of the original Lady Chapel (also at the time of the dissolution), the total length was 375 feet (114 m). ", "The abbey is a parish church, still used for daily services, and is believed to be the second-largest parish church in England, again, after Beverley Minster.", "\n\nTewkesbury claims Gloucestershire's oldest public house, the Black Bear, dating from 1308, although this is currently closed and for sale with its future as a pub in doubt. ", "Other notable buildings are the Royal Hop Pole Hotel in Church Street (which has recently been converted into a part of the Wetherspoons pub chain with the discovery of a former medieval banqueting hall in the structure), mentioned in Charles Dickens' The Pickwick Papers, the Bell Hotel, a large half-timbered structure opposite the Abbey gateway, and the House of the Nodding Gables in the High Street.", "\n\nThe Abbey Cottages, adjacent to Tewkesbury Abbey, were built between 1410 and 1412. ", "They were restored 1967 to 1972 by the Abbey Lawn Trust, a building preservation charity. ", "They house the John Moore Museum, residential homes and commercial offices. ", "The John Moore Museum was established in 1980 in memory of the writer and naturalist, John Moore. ", "The museum consists of three buildings: the main John Moore Museum, home to an extensive Natural History collection; the Merchant's House, restored to its Tudor appearance; and the Old Baptist Chapel. ", "The Old Baptist Chapel, located off Church Street, is a timber-framed building, formally a medieval hall house dating to the 1480s. ", "Sometime in the 17th century, it was converted for use as a Nonconformist meeting house. ", "Including the original baptistery and pastor's room, the building is of significant historic interest. ", "The building was restored to its 1720 appearance in the 1970s by Tewkesbury Borough Council. ", "It was further renovated and interpreted in 2015 by the Abbey Lawn Trust and is used as a venue for a variety of cultural events. ", "Behind the chapel is a small cemetery for those who were members of the congregation. ", "This includes the grave of William Shakespeare-Hart, fifth great grand nephew of William Shakespeare. ", "The cemetery is managed by Tewkesbury Borough Council.", "\n\nJust to the west of the town is Thomas Telford's impressive Mythe Bridge over the River Severn, a cast-iron structure with a 170-foot span, opened in 1826. ", "Tewkesbury's other notable bridge is the stone-built King John's Bridge over the Avon, commissioned by King John in the late 12th century as part of improvements to the main road from Gloucester to Worcester. ", "Original stonework can still be seen on its north side; the bridge was widened in the mid-to-late 1950s to meet traffic requirements.", "\n\nGovernance\n\nModern Governance\n\nThe Town of Tewkesbury is located within the Non-Metropolitan County of Gloucestershire and forms part of the Tewkesbury Urban Area. ", "Civil Parishes of Tewkesbury Town, Wheatpieces and Northway form the Tewkesbury Urban Area. ", "The Tewkesbury Town Civil Parish is the largest Parish within the Urban Area and is the location of the Deveraux Centre, Tewkesbury Community Hospital, Tewkesbury Leisure Centre, Tewkesbury Borough Council Public Services Centre and the main shopping streets.", "\n\nThe Town Council (not to be confused with Tewkesbury Borough, which covers a wider area than Tewkesbury Town) has 16 members from the 4 wards of Town with Mitton, Newtown, Priors Park, and Mythe who are elected every four years. ", "Councillors were last elected in 2015, with all councillors sitting as independents. ", "The Mayor of Tewkesbury Councillor Christine Danter is the civic head of the Council and chairs meetings of the Full Council. ", "The Council also appoints a Deputy Mayor who supports the Mayor in their duties and often succeeds to the office of Mayor in the following civic year. ", "The Council was formally established in 1974 following the dissolution of the municipal borough of Tewkesbury but continues to occupy the same premises and maintains the same civic role within the Town.", "\n\nFollowing the 2019 Local Elections, the Town Council will continue to be formed of 16 members representing 3 wards of Tewkesbury North, Tewkesbury South and Newtown. ", "The boundaries of these new Town Council Wards will mirror the new Tewkesbury Borough Wards of Tewkesbury North with Twyning, Tewkesbury South and Tewkesbury East. ", "The Gloucestershire County Council divisions of Tewkesbury and Tewkesbury East will be unchanged by the new Ward Boundaries at the Town and Borough Councils.", "\n\nTewkesbury is also covered by Tewkesbury Borough Council (district level) and Gloucestershire County Council. ", "Tewkesbury is part of the wider Tewkesbury constituency for elections to the House of Commons and is represented in the European Parliament as part of the South West England constituency in the European Parliament.", "\n\nThrough the provisions of the Local Government Act 1972, a new District Council was created comprising the pre-1974 Tewkesbury Borough, Cheltenham Rural District and parts of Gloucester Rural District. ", "In May 1973 a joint committee of the predecessor Councils recommended that a new Royal Charter be applied for. ", "This Royal Charter conferring Borough Status was granted on 27 February 1973 and took effect on 1 April 1974. ", "By virtue of this Charter the Borough appoint a Mayor and Deputy Mayor which results in there being two Mayors covering Tewkesbury at different level of government. ", "The Borough Mayor being the first citizen of Tewkesbury Borough and the Town Mayor being the first citizen of the Town itself.", "\n\nHistorical Governance and Town Mayoralty\n\nThe following table lists the Mayors of Tewkesbury between 1836 and 1973. ", "After 1973 both Tewkesbury Borough and Tewkesbury Town Council have appointed the Borough Mayor and Town Mayor respectively. ", "The date of the Mayors Election changed from November to May in 1947/48 during the term of office of J.O. Martin JP.", "\n\nRailways\n\nTewkesbury is served by Ashchurch for Tewkesbury railway station. ", "It was the last mainline station in Gloucestershire to be reopened after British Rail was fragmented into Railtrack.", "\n\nThe first station was opened by the Birmingham and Gloucester Railway in 1840 and was sited in the High Street. ", "It was replaced in 1864 by a new station built for the Tewkesbury and Malvern Railway. ", " This closed on 14 August 1961, when the Ashchurch to Upton-on-Severn passenger service was withdrawn by British Railways (through trains to had previously ceased in December 1952). ", " Freight traffic continued until final closure in December 1964.", "\n\nRoad transport\nTewkesbury is served by the M5 and M50 motorways and the A38 and A46 trunk roads. ", "There are frequent direct buses to Ashchurch for Tewkesbury railway station and to Cheltenham. ", "Other direct bus services include Gloucester and Evesham. ", "Congestion on the A46 around Ashchurch and junction 9 of the M5 is being addressed through a series of road works starting in 2014.", "\n\nCycling\nIn Newtown, Tewkesbury 10 per cent of all work trips are made by bicycle.", "\nThere are some bicycle paths in the built up area of Tewkesbury.", "\n\nCulture\nRoses Theatre, combines an arthouse cinema and a live performance venue. ", "The Roses Theatre is where comedian Eric Morecambe collapsed after a charity performance in May 1984. ", "He died hours later in Cheltenham General Hospital. ", "Eric is remembered at the theatre with the naming of a conference/changing room: The Eric Morecambe Room.", "\nBattle of Tewkesbury, mentioned in Shakespeare's play Richard III.", "\nRaymond Priestley, geologist on Robert Falcon Scott's expedition to the South Pole, left one of the sleds, used on that expedition, to the former Tewkesbury Grammar School (c. 1576 – 1972). ", "It is now kept in the Tewkesbury School's Humanities building.", "\nTewkesbury mustard, a blend of mustard and horseradish, made the town famous in the 17th century and is again being manufactured. ", "The mustard was mentioned in some of Shakespeare's works.", "\nSka punk band Spunge are from Tewkesbury.", "\nTewkesbury Camerata, a chamber orchestra, performs regularly in Tewkesbury Methodist Church, drawing musicians from across Tewkesbury, the wider South West, Midlands and across Wales. ", "The musicians of Tewkesbury Camerata perform for no fee, instead donating ticket proceeds to worthy causes. ", "Founded in 2012, it has so far raised over £6,000 for charity.", "\nTewkesbury Town Band (a brass band) plays locally, tours abroad and takes part in competitions.", "\nWednesdays and Saturdays, one of the town centre car parks is the location of Tewkesbury Market. ", "A farmers' market is also held every month close by Tewkesbury Abbey.", "\n\nFestivals and fairs\nIn February Tewkesbury holds a Winter Beer Festival, organised by the Tewkesbury branch of CAMRA.", "\nSince 2005, an annual Food and Drink Festival has been held, in or near the Abbey grounds.", "\nOn the second full weekend of July the town hosts Tewkesbury Medieval Festival, \"Europe's largest battle re-enactment and fair\". ", "Thousands of re-enactors travel to the town from around the world to re-enact the Battle of Tewkesbury near to the original battle site. ", "The festival includes a \"living history\" recreation of a medieval encampment, games, food and a large fair where re-enactment clothing, furniture and weaponry can be purchased. ", "In 2008 the festival celebrated its 25th anniversary.", "\n\nIn July the Water Festival takes place with events on the river and the banks including an evening procession of lit boats ending with a firework display. ", "The festival started in 1996 but its future is now in question due to funding issues and the 2006 event was much reduced in scale. ", "The event was cancelled in 2007 as it coincided with the Summer 2007 Flood (it went ahead later in the year). ", "The event was scheduled for 2008 on Saturday, 20 September, but was again cancelled due to flooding in the weeks prior to the event.", "\nIn October the town holds the annual mop fair. ", "Originally a hiring fair where people came to seek employment, the event is now a large travelling funfair taking over much of the centre of town. ", "The fair itself is also an underlining point of Tewkesbury's industrial past, as Walker Gallopers were produced in the area by Walkers in the early 20th century. ", "The fair is organised by The Showmen's Guild of Great Britain (Western Section)\nEvery year at the end of July and into August the Abbey hosts a festival of liturgical music entitled Musica Deo Sacra (Music Sacred to God).", "\n\nCultural references\nVictorian author Dinah Craik (1826–1887) visited Tewkesbury in 1852, and later set her most famous work John Halifax, Gentleman (pub. ", "1857) in the town, calling it Norton Bury in the book. ", "There is a \"Craik House\" in Church Street, near the Abbey, but Mrs Craik never lived there and had no other connection with Tewkesbury. ", "There is a memorial to her in the Abbey's south transept.", "\nAuthor John Moore (1907–1967) was born and lived in Tewkesbury. ", "He set his novel Portrait of Elmbury (pub. ", "1945) as a \"fictionalised biography\" of Tewkesbury, the town being the \"Elmbury\" of the book. ", "Another of his books, Brensham Village (pub. ", "1946) used nearby Bredon as its basis. ", "A local museum has been named after him.", "\nA.E. Housman's A Shropshire Lad also mentions Tewkesbury, as well as nearby Bredon Hill, even though neither place is in Shropshire.", "\nThe opening scene of the 1995 film version of Richard III takes place at the Field Headquarters of King Henry's army at Tewkesbury.", "\n\nNotable people\nHenry Disston - industrialist - born Tewkesbury 1819.", "\nRobert Harold Compton - South African botanist - born Tewkesbury 1886.", "\n Kathleen Hawkins- poet - born Tewkesbury 1883.", "\nAlfred Jones - cricketer - born Tewkesbury 1900.", "\nHenry Green - author - born Tewkesbury 1905.", "\nAnna Ford - newsreader and TV presenter - born Tewkesbury 1943.", "\nEric Morecambe - British comedian - collapsed backstage at the town's Roses Theatre 1984.", "\nJohn Moore - writer - born Tewkesbury 1907.", "\nRaymond Priestley - scientist, Antarctic explorer, educationalist - born & educated in Tewkesbury.", "\nEunice Spry - sadistic foster mother and subject of a high-profile case - lived in Tewkesbury.", "\nFKA Twigs - singer - was raised in Tewkesbury.", "\nOswald Wardell-Yerburgh – Vicar of Tewkesbury 1899 to 1913.", "\nSimon Goodwin - Footballer, Cheltenham Town, Southampton FC - born 1979 - lives Tewkesbury\n\nSports and recreation\nTewkesbury has one of the 471 King George's Fields as its recreation ground.", "\nThe football club, Tewkesbury Town FC have three men's teams in the Saturday Cheltenham Leagues, two teams in the Evesham Birdseye Sunday Leagues, a Veterans team for ages 35+ in the Gloucestershire North County League and hold weekly training sessions for Ladies in preparation for starting a team in the 2014/15 season. ", "They are holders of the Gloucestershire County Cup as well as the Evesham Bluck cup, Pershore Hospital cup, are Evesham League Division 3 Champions and are the Evesham Leagues Team of the Year 2012/13.", "\nThe cricket team, Tewkesbury Cricket Club 1st XI play in the Glos/wilts Division of the West of England Premier League.", "\nThe rugby team, Tewkesbury RFC, plays Rugby Union in Gloucestershire Division One and has gained promotion to Gloucester Division Premiership\nThe running club, Tewkesbury AC compete in local, national and international running events.", "\nCheltenham College Boathouse is situated at Lower Lode\nFacilities at Tewkesbury School are used as a public sports centre for swimming, gym, squash and other sports.", "\nThe Tewkesbury lawn green Bowling Club plays in the Gloucestershire men's and ladies leagues.", "\n\nTwin town\nTewkesbury Borough is twinned with Miesbach in Bavaria, Germany.", "\nTewkesbury Town has had a sister city relationship twinned with Tewksbury Township, New Jersey, United States of America since 2003.", "\n\nReferences\n\nExternal links\n\nTewkesbury Borough Council\nBBC archive film of Tewkesbury from 1984\nTewkesbury Town Showcase and Events\nTewkesbury's Medieval Festival annual event - United Kingdom\nTewkesbury's annual Medieval Life from the court to the kitchens event - United Kingdom\n\n \nCategory:Populated places on the River Severn\nCategory:Towns in Gloucestershire" ]

{ "pile_set_name": "Wikipedia (en)" }

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[ "Mahmoud Guendouz\n\nMahmoud Guendouz (born February 24, 1953 in El Harrach, Algiers Province) is an Algerian former footballer and coach. ", "\n\nA stalwart of the Algerian national team during its greatest period on the world stage, he appeared at the 1980 Olympics as well as the FIFA World Cups of 1982 and 1986. ", "As a club player he was largely based in his homeland, although he also appeared for FC Martigues in France.", "\n\nCareer\nGuendouz played every minute of Algeria's World Cup finals campaign of 1982 and was solid in a campaign in which les Fennecs won two games out of three and only missed out on the second round due to goal difference. ", "He did blot his copy book, however, with a foul on Patricio Yáñez in the game against Chile, with Miguel Ángel Neira scoring from the resulting penalty. ", "He also featured in every minute of the country's less impressive 1986 finals campaign.", "\n\nAfter retiring from the game, Guendouz entered into football management. ", "He was joint manager of Martigues with Yves Herbet in 1998-99 then sole manager for a spell from 1999 to 2000. ", "Later he would go on to manage Algerian club side US Biskra.", "\n\nReferences\n\nExternal links\n\nCategory:1953 births\nCategory:Living people\nCategory:People from El Harrach\nCategory:Algerian footballers\nCategory:Algerian expatriate footballers\nCategory:Algeria international footballers\nCategory:Algerian football managers\nCategory:1982 FIFA World Cup players\nCategory:1986 FIFA World Cup players\nCategory:Olympic footballers of Algeria\nCategory:Footballers at the 1980 Summer Olympics\nCategory:FC Martigues players\nCategory:NA Hussein Dey players\nCategory:FC Martigues managers\nCategory:Ligue 2 players\nCategory:Expatriate footballers in France\nCategory:Expatriate football managers in France\nCategory:Algerian expatriate sportspeople in France\nCategory:Expatriate football managers in Lebanon\nCategory:1980 African Cup of Nations players\nCategory:1984 African Cup of Nations players\nCategory:1986 African Cup of Nations players\nCategory:Mediterranean Games bronze medalists for Algeria\nCategory:Competitors at the 1979 Mediterranean Games\nCategory:Competitors at the 1983 Mediterranean Games\nCategory:JS El Biar players\nCategory:Lebanese Premier League managers\nCategory:Nejmeh SC managers\nCategory:Association football defenders\nCategory:Mediterranean Games medalists in football" ]

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[ "Film Review: Soul Surfer\n\nBethany (Anna Sophia Robb, pictured right, with the real life Bethany) has the perfect life in Hawaii, loving parents Tom (Dennis Quaid) and Cheri (Helen Hunt), two brothers Noah and Timmy and a best friend Anna, all of who share her love of the water. ", "All she’d ever dreamed of doing was growing up and becoming a pro surfer.", "\n\nBethany and Anna have just been sponsored by Ripcurl and everything is going perfectly to plan. ", "But then one morning when the girls are out training with Anna’s Father Holt (Kevin Sorbo) and brother Byron (Jeremy Sumpter) Bethany is attacked by the 14 foot Tiger Shark.", "\n\nBethany survives but loses an arm and begins to question her purpose in life. ", "Her father has always told her that she can do anything she desires, but if she can’t surf then what is she suppose to do?", "\n\nBethany joins her local youth group leader Sarah Hill (Country Music star Carrie Underwood’s debut film role) on a group mission to help the people in Thailand put their life back together after the 2004 Tsunami.", "\n\nBy helping some people there conquer their fear of the water she finds hope and a new determination to overcome her own limitations to set and example for others to do the same.", "\n\nIt’s a true story, but for me the movie failed to really scratch beneath the surface properly. ", "Well paced, but as is the case with many true story adaptation’s it was all a little bit too sugar coated and lacked that little bit of realism that ironically would make it more believable.", "\n\nDespite this there are some good turns from the cast and Anna Sophia Robb has come a long way from Violet Beauregarde in Tim Burton’s Charlie and the Chocolate Factory. ", "As the lead she gives a motivating performance of Bethany’s fantastic journey through recovery, self discovery and back to the top of her game again.", "\n\n‘Old timers’ Quaid and Hunt help keep the movie from ‘sinking’ totally with believable emotional performances and there are some breathtaking surf scenes to distract you from some of the more ‘cheesier’ moments.", "\n\nDespite its flaws Soul Surfer is still an amazing story and a film that could inspire your own dreams, or to believe with perseverance anything is possible." ]

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[ "\n166 F.Supp.2d 810 (2001)\nEQUAL EMPLOYMENT OPPORTUNITY COMMISSION, Plaintiff,\nv.\nSAFEGUARD CHEMICAL CORPORATION, Defendant.", "\nNo. ", "99 CIV 12411 (SAS).", "\nUnited States District Court, S.D. New York.", "\nApril 18, 2001.", "\n*811 Louis Graziano, Equal Employment Opportunity Commission, New York District Office, New York City, for Plaintiff.", "\nJeffrey C. Slade, Slade & Associates, P.C., New York City, for Defendant.", "\n\nOPINION AND ORDER\nSCHEINDLIN, District Judge.", "\nDefendant Safeguard Chemical Corporation (\"Safeguard\"), the prevailing party in this action, moves for attorneys' fees, costs and expenses pursuant to Title VII of the Civil Rights Act of 1964 (\"Title VII\"), 28 U.S.C. § 1920, Federal Rule of Civil Procedure *812 (\"Rule\") 54(d) and Local Civil Rule 54.1. ", "In particular, Safeguard asserts that plaintiff Equal Employment Opportunity Commission (\"EEOC\") brought suit frivolously, unreasonably and without foundation. ", "For the reasons set forth below, Safeguard's motion for attorneys' fees is denied, but its motion to recover costs is granted.", "\n\nI. BACKGROUND\nOn December 28, 1999, the EEOC brought a lawsuit against Safeguard, a New York corporation, on behalf of complainants Jamilet Colon, Madeline Rios and Angel Lopez (\"complainants\") under Title VII of the Civil Rights Act of 1964 and Title I of the Civil Rights Act of 1991 for alleged \"unlawful discrimination on the basis of national origin discrimination and retaliation\" that occurred in 1993-94. ", "See Complaint (\"Compl.\") ¶¶ ", "8-11. ", "In particular, the EEOC alleged that \"Safeguard [had] engaged in unlawful employment practices at its Bronx, New York facility in violation of section 703(a) of Title VII, 42 U.S.C. § 2000e-2(a).\"[1] Compl. ¶ ", "7. ", "Some of the discriminatory acts alleged by the EEOC included management's repeated use of the word \"spic\" in describing Hispanic employees and calling Colon a \"Spic Aunt Jemima.\" ", "See Compl. ¶ ", "7(1)-(3). ", "The EEOC further alleged that Safeguard violated section 704(a) of Title VII, 42 U.S.C. § 2000e-3(a), by discharging the complainants in retaliation for \"engaging in the protected activity of protesting the national origin harassment.\" ", "Compl. ¶¶ ", "8-10.", "\nPrior to filing suit, the complainants filed charges with the New York State Division of Human Rights (\"NYSDHR\") in accordance with section 706(c) of Title VII, 42 U.S.C. § 2000e-5(c).[2]See 1/5/01 Notice of Motion for Attorneys' Fees, Expenses & Taxable Costs (\"Def.", "Motion\") ¶¶ 3-4. ", "Upon review, the NYSDHR found \"probable cause to believe that there was evidence that Safeguard had engaged in unlawful discrimination\" against Colon based on New York's human rights laws. ", "Id. ¶ 5. ", "However, the NYSDHR did not find similar probable cause as to Rios or Lopez.[3]See id. ¶¶ 6, 7.", "\nAfter the NYSDHR made its conclusions, Lopez began gathering additional information and statements to support his allegation that Safeguard engaged in national origin discrimination. ", "See id. ¶ 8. ", "This newly gathered information contained many allegations of racial and ethnic slurs, including many that were previously undisclosed by Rios and Colon. ", "See Statements *813 by Safeguard Employees and Former Employees, Ex. ", "F. to Def. ", "Motion, at 0-6. ", "This information was presented to the EEOC in November 1997. ", "See id.; see also Def. ", "Motion ¶ 10. ", "Upon receiving the newly gathered information, the EEOC began an investigation to make its own determinations of whether Safeguard had engaged in national origin discrimination. ", "See Def. ", "Motion ¶ 10.", "\nThe EEOC first requested certain documents from Safeguard to better assess the complaints against it. ", "See id. Safeguard did not respond. ", "See id. ¶ 12. ", "The EEOC then issued a subpoena on April 9, 1998, requiring Safeguard to produce the requested documents by April 20, 1998. ", "See id. Although Safeguard received the subpoena on April 13, 1998, it did not reply in a timely manner. ", "See id. ¶¶ 12, 13. ", "The EEOC then filed an order to show cause why the subpoena should not be enforced. ", "See id. On June 10, 1998, Sang K. Lee, Safeguard's then-recently hired controller, wrote to Elizabeth Grossman, a trial attorney for the EEOC. ", "See Safeguard 1998 Letter in Regard to EEOC Charge, Ex. ", "I to Def. ", "Motion, ¶ 1. ", "Lee explained that administrative confusion, caused by a void at the controller position for over a year, had prevented Safeguard from complying with the initial document request and the subsequent subpoena. ", "See id. On June 23, 1998, with Lee's consent, the order to enforce the subpoena was granted and the documents were produced. ", "See Def. ", "Motion ¶ 16.", "\nNearly six months later, on December 22, 1998, the EEOC notified Safeguard, via a letter addressed to Lee, that the documents it provided were deficient and that it was seeking additional documents. ", "See EEOC Letter in Response to Document Production, Ex. ", "L. to Def. ", "Motion, at 2-3. ", "However, Lee was no longer employed at Safeguard and the position of controller was now held by William Rossa. ", "See Def. ", "Motion ¶ 18. ", "Rossa complied with this additional request on January 12, 1999. ", "See id. There was no further correspondence between the EEOC and Safeguard until September 17, 1999, when the EEOC determined that Safeguard had discriminated against Colon, Rios and Lopez on the basis of their national origin. ", "See EEOC Determinations, Ex. ", "O to Def. ", "Motion, at 1, 3, 5.", "\nOn September 20, 1999, the EEOC informed Safeguard that it was prepared to conciliate and offered a proposal to remedy the discriminatory practices. ", "See EEOC Conciliation Letter, Ex. ", "P to Def. ", "Motion, at 1, 3, 5. ", "The EEOC, in turn, asked Safeguard for a response to its proposal by September 28, 1999. ", "See id. at 2, 4, 6. ", "Safeguard did not respond to the EEOC's conciliation effort. ", "See Def. ", "Motion ¶ 20(c). ", "Without any further communication, the EEOC informed Safeguard on September 30, 1999 that\nThe EEOC has determined that efforts to conciliate this charge as required by Title VII, as amended, have been unsuccessful. ", "This letter constitutes the notice required by § 1601.25 of the Commission's Procedural Regulations which provides that the Commission shall notify a respondent in writing when it determines that further conciliation would be futile or non-productive. ", "No further effort to conciliate this case will be made.", "\nEEOC Conciliation Determination Letter, Ex. ", "Q to Def. ", "Motion, at 1.", "\nOn December 20, 1999, the EEOC commenced a Title VII action against Safeguard alleging national origin discrimination and unlawful retaliatory actions in firing the complainants for protesting the alleged discrimination. ", "See Compl. ", "at 1. ", "After attempts at mediation failed, a jury trial commenced on November 28, 2000.[4]*814 After a four-day trial, the jury found in favor of Safeguard. ", "See Def. ", "Motion ¶ 24.", "\nSafeguard has since filed this motion for attorneys' fees[5] and costs[6] pursuant to section 706(k) of Title VII (42 U.S.C. § 2000e-5(k)), 28 U.S.C. § 1920, Rule 54(d) and Local Civil Rule 54.1. ", "See Def. ", "Motion at 1. ", "Safeguard alleges that the EEOC's decision to sue was frivolous, unreasonable, and without foundation, and it should therefore be awarded fees and costs. ", "See 01/29/01 Memorandum of Law in Support of Defendant Safeguard's Motion for Attorneys' Fees, Expenses and Taxable Costs (\"Def.", "Mem.\") ", "at 3.", "\n\nII. ", "DISCUSSION\n\nA. Legal Standards\n\n1. ", "Attorneys' Fees\nGenerally, litigants must pay their own attorneys' fees. ", "See Christiansburg Garment Co. v. EEOC, 434 U.S. 412, 415, 98 S.Ct. ", "694, 54 L.Ed.2d 648 (1978). ", "At times, however, Congress has authorized district courts to use their discretion in awarding attorneys' fees to prevailing litigants. ", "See id. Section 706(k) of Title VII is one such statute. ", "It provides:\nIn any action or proceeding under this subchapter the court, in its discretion, may allow the prevailing party, other than the Commission or the United States, a reasonable attorney's fee (including expert fees) as part of the costs, and the Commission and the United States shall be liable for costs the same as a private person.", "\n42 U.S.C. § 2000e-5(k). ", "In interpreting this statute, the Supreme Court has stated that a prevailing defendant seeking to recover attorneys' fees has a higher burden than does a prevailing plaintiff. ", "See Christiansburg, 434 U.S. at 418-19, 98 S.Ct. ", "694.", "\nCourts routinely award attorneys' fees to prevailing Title VII plaintiffs. ", "In Christiansburg, the Court expounded \"two strong equitable considerations\" for this policy. ", "Id. at 418, 98 S.Ct. ", "694. ", "First, \"the plaintiff is the chosen instrument of Congress to vindicate `a policy that Congress considered of the highest priority.'\" ", "Id. (quoting Newman v. Piggie Park Enter., ", "390 U.S. 400, 402, 88 S.Ct. ", "964, 19 L.Ed.2d 1263 (1968)). \"", "Second, when a district court awards counsel fees to a prevailing plaintiff, it is awarding them against a violator of federal law.\" ", "Christiansburg, 434 U.S. at 418, 98 S.Ct. ", "694.", "\nThese considerations are \"wholly absent\" when a prevailing defendant seeks attorneys' fees. ", "See id. \"In order to avoid chilling the initiation and prosecution of meritorious civil rights actions, fees are not to be awarded to a prevailing defendant unless the plaintiff's action was `frivolous, unreasonable, or groundless ....'\" LeBlanc-Sternberg v. Fletcher, 143 F.3d 765, 770 (2d Cir.1998) (quoting Christiansburg, 434 U.S. at 422, 98 S.Ct. ", "694). ", "In applying the \"frivolous, unreasonable, or groundless\" standard in awarding a defendant attorneys' fees, \"it is important that a district court resist the understandable temptation to engage in post hoc reasoning by concluding that, because a plaintiff did not ultimately prevail, his action must have been unreasonable or without foundation.\" ", "Christiansburg, 434 U.S. at 421-22, 98 S.Ct. ", "694. \"", "`Generally ... where evidence is introduced that, if credited, would suffice to support a judgment' in favor of the plaintiff, a fee award to the defendant *815 is `unjustified.'\" ", "LeBlanc-Sternberg, 143 F.3d at 770 (quoting American Fed'n of State, County and Mun. ", "Employees, AFL-CIO (\"AFSCME\") v. County of Nassau, 96 F.3d 644, 652 (2d Cir.1996)).", "\n\n2. ", "Costs\nRule 54(d)(1) states that \"[e]xcept when express provision therefor is made either in a statute of the United States or in these rules, costs other than attorneys' fees shall be allowed as of course to the prevailing party unless the court otherwise directs ....\" Fed.", "R.Civ.", "P. 54(d)(1). ", "Furthermore, \"[a] judge or clerk of any court of the United States may tax as costs the following: ... (2) Fees of the court reporter for all or any party of the stenographic transcript necessarily obtained for use in the case; (3) Fees and disbursements for printing and witnesses ....\" 28 U.S.C. § 1920.", "\nAssuming that the prevailing party has moved in a timely manner,[7] a court usually \"grants costs to a prevailing party as a matter of course in the absence of countervailing statute or rule, unless the trial judge directs otherwise.\" ", "Cosgrove v. Sears, Roebuck, & Co., 191 F.3d 98, 101 (2d Cir.1999). ", "Unlike attorneys' fees, a court uses the same standard in awarding costs to either a prevailing plaintiff or a prevailing defendant. ", "In Poe v. John Deere Co., 695 F.2d 1103, 1108 (8th Cir. ", "1982), the court reasoned: \"Whereas the magnitude and unpredictability of attorney's fees would deter parties with meritorious claims from litigation, the costs of the suit in the traditional sense are predictable and, compared to the costs of attorneys' fees, small.\" ", "The Second Circuit follows this reasoning and routinely awards costs to the prevailing party, be it plaintiff or defendant, in Title VII actions. ", "See, e.g., Cosgrove, 191 F.3d at 101-02 (quoting Poe, 695 F.2d at 1108).", "\n\nB. Safeguard's Claim for Attorneys' Fees\nSafeguard claims it is entitled to attorneys' fees because the EEOC was \"vexatious\" and brought this action \"in subjective bad faith.\" ", "See 01/29/01 Reply Memorandum of Law in Support of Defendant Safeguard's Motion for Attorneys' Fees, Expenses and Taxable Costs (\"Def.", "Reply\") at 4. ", "Safeguard claims that the EEOC brought this action to teach it a lesson about responding to EEOC subpoenas. ", "See Def. ", "Mem. ", "at 1. ", "Additionally, Safeguard alleges that the EEOC used perjurious statements in its case in chief[8] and that \"no reasonable person who had objectively studied the actual merits of this case would have brought it to Court.\" ", "Id. at 3. ", "Safeguard further states that the NYSDHR findings, the unsuccessful mediation, the expediency of the jury deliberations and the verdict are proof of its allegation that the claim was brought vexatiously and in bad faith. ", "See id. at 10.", "\nThough it may believe that the suit was brought for vindictive purposes, Safeguard offers no objective proof to substantiate this allegation. ", "The following synopsis shows that the EEOC was acting without any vexatious intent. ", "First, the EEOC requested documents in order to determine whether the allegations against Safeguard had merit. ", "See Def. ", "Motion ¶ 10. ", "After some difficulty obtaining the documents, the EEOC made its findings of *816 discrimination after carefully reviewing the documents.[9]See id. ¶ 20(a). ", "Upon making these findings, the EEOC attempted a conciliation with Safeguard. ", "See id. ¶ 20(b). ", "The EEOC brought suit as a last resort. ", "The EEOC used appropriate measures in its investigation, in making its determinations and ultimately in bringing suit. ", "See EEOC v. Bruno's Restaurant, 13 F.3d 285, 288-89 (9th Cir.1993) (EEOC must conduct an investigation, make a reasonable cause determination and attempt conciliation).", "\nSafeguard next points to the NYSDHR findings to strengthen its position that this lawsuit was brought vexatiously. ", "Though the EEOC is required to give substantial weight to state agency findings, it is not bound to follow these findings. ", "See Kremer, 456 U.S. at 469-70, 102 S.Ct. ", "1883. ", "Here, after its investigation and review of all the materials before it, the EEOC determined that Safeguard acted in a discriminatory manner against all three claimants, not just against Colon, as the NYSDHR had determined. ", "See EEOC Determination Letters, Ex. ", "Q to Def. ", "Motion, at 1. ", "Based on its determinations, the EEOC proceeded to bring an action on behalf of all claimants.", "\nSafeguard points to the speed of the jury deliberations, approximately one-and-a-half hours, as further support for its position that this action was frivolous. ", "See Def. ", "Motion ¶ 24. ", "In AFSCME, the Second Circuit stated:\nIn determining whether a valid claim has been established, the assessment of evidence and testimony is of course within the province of the trier of fact. ", "But a claim is not necessarily frivolous because a witness is disbelieved or an item of evidence is discounted, disproved or disregarded at trial.", "\nAFSCME, 96 F.3d at 652. ", "Had the jury credited the EEOC's evidence, then the EEOC would have prevailed. ", "Because the jury did not credit the EEOC's witnesses, its deliberations were swift.", "\nThe Supreme Court has warned against this type of post hoc analysis in Title VII claims. ", "See Christiansburg, 434 U.S. at 421-22, 98 S.Ct. ", "694. ", "The mere fact that the EEOC did not prevail does not necessarily permit a defendant to recover attorneys' fees. ", "See id. Hindsight is disfavored when a clear decision favoring one party can only be rendered after deliberations have concluded. ", "See id. (\"[I]t is important that a district court resist the understandable temptation to engage in post hoc reasoning by concluding that, because a plaintiff did not ultimately prevail, his action must have been unreasonable or without foundation. ", "This kind of hindsight logic could discourage all but the most airtight claims, for seldom can a prospective plaintiff be sure of ultimate success.\").", "\nFinally, Safeguard sets forth its poor financial situation and prays for the instant relief so that the detrimental economic effect of this lawsuit is minimized. ", "See Def. ", "Mem at 11 (stating that the company lost $301,762 and $759,049 in fiscal years 1999 and 2000 respectively). ", "Though \"the fact [is] that many defendants in Title VII claims are small- and moderate-size employers for whom the expense of defending even a frivolous claim may become a strong disincentive to the exercise of their legal rights,\" a prevailing defendant does not necessarily receive attorneys' fees. ", "Christiansburg, 434 U.S. at 422 n. 20, 98 S.Ct. ", "694. ", "Because this action is not frivolous, unreasonable or without foundation, an award of attorneys' fees would be inappropriate. ", "Cf. ", "EEOC v. Bellemar Parts *817 Indus., ", "868 F.2d 199, 200 (6th Cir.1989) (attorneys' fees and costs were awarded when the EEOC filed a groundless action against a company that it knew was unincorporated when the alleged discriminatory action occurred).", "\n\nC. Safeguard's Motion for Costs and Expenses\nSafeguard has also moved to recover its costs which total $2,669.79. ", "Costs are routinely awarded to the prevailing party in Title VII actions regardless of whether it is the plaintiff or defendant. ", "See Cosgrove, 191 F.3d at 101-02. ", "Safeguard seeks recovery of the costs it incurred in bringing a witness to the trial and purchasing deposition transcripts. ", "See Def. ", "Motion ¶ 30. ", "The costs prayed for fall within the bounds of 28 U.S.C. § 1920. ", "See 28 U.S.C. § 1920(2), (3). ", "Accordingly, because the EEOC has offered no reason why Safeguard should not be awarded costs, including a countervailing rule or statute, the entire amount of Safeguard's costs are awarded pursuant to Rule 54(d).", "\n\nIII. ", "Conclusion\nFor the reasons set forth above, Safeguard's motion for attorneys' fees is denied, but its motion for $2,669.79 in costs is granted. ", "The Clerk of the Court is directed to close this motion.", "\nSO ORDERED:\nNOTES\n[1] Section 703(a) states that\n\nIt shall be an unlawful employment practice for an employer —\n(1) to fail or refuse to hire or to discharge any individual, or otherwise to discriminate against any individual with respect to his compensation, terms, conditions, or privileges of employment, because of such individual's race, color, religion, sex, or national origin; or\n(2) to limit, segregate, or classify his employees or applicants for employment in any way which would deprive or tend to deprive any individual of employment opportunities or otherwise adversely affect his status as an employee, because of such individual's race, color, religion, sex, or national origin.", "\n42 U.S.C. § 2000e-2(a) (emphasis added).", "\n[2] Title VII requires that if the action occurs in a state that has already enacted a law prohibiting the alleged discrimination, the EEOC must wait until the state proceedings have ended or at least sixty days after the appropriate state remedy has been invoked before bringing an action. ", "See 42 U.S.C. § 2000e-5(c); see also Kremer v. Chemical Constr. ", "Co., 456 U.S. 461, 469, 102 S.Ct. ", "1883, 72 L.Ed.2d 262 (1982).", "\n[3] Of the three claims submitted to the NYSDHR, only the statement given by Lopez contained racial or ethnic slurs. ", "See Statements by Colon, Rios and Lopez to the NYSDHR, Ex. ", "A to Def. ", "Motion, at 9.", "\n[4] Some time between the mediation and the start of trial, Rios was dismissed from this lawsuit, leaving only the claims against Colon and Lopez.", "\n[5] The attorneys' fees total $63,022.50. ", "See Def. ", "Motion ¶ 26.", "\n[6] The costs and expenses amount to $2,669.79 and include 1) $1,937.20 for six depositions; and, 2) $732.59 for the transportation costs of a defense witness. ", "See Def. ", "Motion ¶ 30.", "\n[7] Safeguard was granted an extension of time in which to file its motion for fees, expenses and costs. ", "See 02/13/01 Endorsed Copy of Notice of Motion for Leave to File Motion for Attorneys' Fees, Expenses & Taxable Costs Out of Time.", "\n[8] Safeguard alleges that Lopez's statements to the EEOC were perjurious because the ethnic slurs contained therein were not alleged in the earlier NYSDHR claim and were fabricated to induce the EEOC to bring this action. ", "See Def. ", "Mem. ", "at 3.", "\n[9] Safeguard believes that the EEOC should have been more discerning in viewing the claimants' statements. ", "See Def. ", "Motion at 14. ", "However, there is no proof that the EEOC acted in bad faith.", "\n" ]

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[ "What is the common thread among the only four U.S. Presidents who have been assassinated - Lincoln, Garfield, McKinley, and Kennedy? ", "They were also the only four presidents to ever to take ... See full summary »" ]

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[ "---\nabstract: 'This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. ", "The subject is presented in a self-contained and pedagogical way. ", "The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). ", "It became essential in condensed matter physics and quantum information (measurement-based quantum computation). ", "Many publications have been devoted to the subject. ", "Recently entanglement was studied in the VBS state. ", "In this review we start with the definition of a general AKLT spin chain and the construction of VBS ground state. ", "In order to study entanglement, a block subsystem is introduced and described by the density matrix. ", "Density matrices of $1$-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Rényi entropy) are calculated. ", "In the large block limit, the entropies also approach finite limits. ", "Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.'", "\naddress:\n- |\n C.N. Yang Institute for Theoretical Physics\\\n State University of New York at Stony Brook\\\n Stony Brook, NY 11794-3840, U.S.\\\n korepin@insti.physics.sunysb.edu\n- |\n Institut für Theoretische Physik, Universität Innsbruck\\\n Institut für Quantenoptik und Quanteninformation\\\n der Österreichischen Akademie der Wissenschaften\\\n Technikerstraße 21a, 6020 Innsbruck, Austria\\\n ying.xu@uibk.ac.at\nauthor:\n- 'VLADIMIR E. KOREPIN'\n- YING XU\ntitle: 'ENTANGLEMENT IN VALENCE-BOND-SOLID STATES'\n---\n\nIntroduction {#sec:intro1}\n============\n\nThe fields of statistical mechanics, condensed matter physics and quantum information theory share a common interest in the study of interacting quantum many body systems. ", "The concept of **entanglement** in quantum mechanics has significant importance in all these areas, it was introduced in [@S]. ", "Roughly speaking, entanglement [@NC] is a phenomenon of quantum mechanical nature in which quantum states of physical systems are linked together so that one system can not be adequately described without full mention of its counterpart, even when the individual systems may be spatially separated. ", "Entanglement becomes particularly interesting in a many body interacting system where a subsystem strongly correlates with its environment (other parts of the system). ", "The correlations may reject the principle of local realism, which states that information about the state of a system can only be mediated by interactions in its immediate surroundings (neighbors). ", "The characteristic length of entanglement may be diverging while the usual correlation length remains finite [@VMC]. ", "Quantum entanglement is a fundamental measure of ‘quantumness’ of a system: how much quantum effects we can observe and use to control one quantum system by another. ", "It is the primary resource in emerging technologies of quantum computation and quantum information processing [@BD; @L]. ", "Entanglement properties play an important role in condensed matter physics, such as phase transitions [@OAFF; @ON] and macroscopic properties of solids [@GRAC]. ", "There is an excellent review [@GT] on entanglement detection, which covers many topics (such as multi-partite entanglement, concurrence, Bell inequalities, entanglement witnesses and experiments) beyond the scope of our present discussion.", "\n\nMuch of current research seeks to elucidate quantum entanglement in a variety of interacting systems. ", "Extensive research has been undertaken to investigate quantum entanglement in strongly correlated states such as spin chains, correlated electrons, interacting bosons as well as other models. (", "See [@AFOV; @ABV; @BH; @CBO; @GDLL; @EC; @FIJK; @FIK; @HZS; @HJPW; @HLW; @IJK; @JK; @JKLPPSW; @KM; @K; @LORV; @LRV; @OL; @P; @PP; @PS; @VMC; @VLRK; @ZR] for reviews and references.) ", "A general approach studies the density matrix of a certain subsystem of a strongly entangled state. ", "The concept of the reduced density matrix was first introduced by P. A. M. Dirac in [@D]. ", "Following C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schumacher [@BBPS], the entropy (derived from the spectrum of the density matrix) of a subsystem serves as the measure of entanglement for a **pure state**. ", "The von Neumann entropy and its generalization (the Rényi entropy) are typical quantifications of entanglement. ", "These characteristic functions may depend on the physical parameters (size, coupling constants, external fields, *etc*.) ", "in various different ways. ", "An area law for the von Neumann entropy in harmonic lattice systems has been extensively studied [@CEP; @CEPD; @Has]. ", "The area law states that the entropy scales proportional to the size (area) of the boundary of the subsystem (this statement was strictly proved for gapped models only). ", "The entropy of the whole system vanishes if the system is in a pure state (usually the unique ground state), but it can be positive for a subsystem (this means entanglement). ", "This is in contrast with a classical system in which if the entropy is equal to zero for the whole system, then it also vanishes for any subsystem. ", "In quantum mechanics, when the whole system is in a pure state, a subsystem can be in a mixed state. *", "e.g.* The Bell pair (or the Einstein-Podolsky-Rosen state) $(|\\uparrow\\downarrow\\rangle-|\\downarrow\\uparrow\\rangle)/\\sqrt{2}$ is a pure state. ", "A single spin subsystem is in a completely mixed state. ", "The density matrix of one spin in an EPR state is proportional to identity matrix: $\\boldsymbol{\\rho}=(|\\uparrow\\rangle\\langle\\uparrow|+|\\downarrow\\rangle\\langle\\downarrow|)/2$, which has entropy $\\ln 2$. In a more general case, we shall consider a pure system consisting of two subsystems $B$ (Block) and $E$ (Environment) with two different Hilbert spaces $\\mathbf{H}_{B}$ and $\\mathbf{H}_{E}$ of dimensions $dim_{B}$ and $dim_{E}$, respectively (assuming that $dim_{B}\\leq dim_{E}$). ", "So the entropy of the whole system $B\\cup E$ is zero. ", "If the entropy of a subsystem ($B$) is positive then the wave function of the whole system does not factorize: $$\\begin{aligned}\n|B\\cup E\\rangle\\neq|B\\rangle\\otimes|E\\rangle.\\end{aligned}$$ Let $\\{|b_{j}\\rangle\\}$ and $\\{|e_{k}\\rangle\\}$ be any fixed orthonormal bases for subsystems $B$ and $E$, respectively. ", "Then the wave function of the whole system can be written as $$\\begin{aligned}\n |B\\cup E\\rangle=\\sum_{jk}A_{jk}|b_{j}\\rangle\\otimes|e_{k}\\rangle,\\end{aligned}$$ for some matrix $A$ of complex elements $A_{jk}$. Then by the singular value decomposition (see §$\\,2.1.10\\,$ of [@NC]), $A=U\\mathcal{D}V$, where $\\mathcal{D}$ is a diagonal matrix with non-negative elements, and $U$ and $V$ are unitary matrices ($A$ is a rectangular matrix if $dim_{B}\\neq dim_{E}$, in that case $U$ and $V$ have different dimensions). ", "Define $|B_{i}\\rangle\\equiv\\sum_{j}U_{ji}|b_{j}\\rangle$, $|E_{i}\\rangle\\equiv\\sum_{k}V_{ik}|e_{k}\\rangle$, and $\\sqrt{\\lambda_{i}}\\equiv \\mathcal{D}_{ii}$. With such a choice of bases, we find that the wave function can be put in the following form: $$\\begin{aligned}\n |B\\cup E\\rangle=\\sum^{D}_{j=1}\\sqrt{\\lambda_{j}}\\,|B_{j}\\rangle\\otimes|E_{j}\\rangle\\end{aligned}$$ where $\\{|B_{j}\\rangle\\}$, as well as $\\{|E_{j}\\rangle\\}$, are orthonormal bases. ", "The coefficients $0<\\sqrt{\\lambda_{j}}<1$ satisfy $$\\begin{aligned}\n \\sum^{D}_{j=1}\\lambda_{j}=1.\\end{aligned}$$ Once again, if the entropy of the subsystem $S[B]>0$ then $D>1$ ($D\\leq dim_{B}$). ", "In this case we can control one subsystem by the other. ", "Indeed if we measure subsystem $B$ (in $|B_{j}\\rangle$ basis), then the wave function of the whole system will change (collapse) into $$\\begin{aligned}\n |B_{j_{0}}\\rangle\\otimes|E_{j_{0}}\\rangle\\end{aligned}$$ with probability $\\lambda_{j_{0}}$ for some $j_{0}$. So that a measurement of $B$ changes the state of $E$ and this is quantum control. ", "This is an important resource for quantum device building (and maybe even quantum computation). ", "Much insight in understanding entanglement of quantum systems has been obtained by studying exactly solvable models in statistical mechanics, in which it is possible to solve the subsystem density matrix and calculate the entropy exactly. ", "This review is devoted to one particular set of models – the AKLT models.", "\n\nIn 1987, I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki proposed a spin interacting model known as the AKLT model [@AKLT1; @AKLT2]. ", "The model consists of spins on lattice sites and the Hamiltonian describes interactions between nearest neighbors. ", "The Hamiltonian density is a linear combination of projectors. ", "Each projector is written as a polynomial of the inner product of a pair of interacting spin vectors. ", "The authors (AKLT) of [@AKLT1; @AKLT2] found the exact ground state, which has an exponentially-decaying correlation function and a finite energy gap. ", "In their early works, authors discussed the $1$-dimensional AKLT lattices with open and periodic boundary conditions and $2$-dimensional models such as the hexagonal lattice. ", "D. A. Arovas, A. Auerbach and F. D. M. Haldane studied the model [@AAH] in the Schwinger boson representation (see §$\\,\\ref{sec:vbssch}\\,$ below) and calculated the correlation functions using the coherent state basis (see §$\\,\\ref{sec:cohe}\\,$ below). ", "In their work [@AAH], it was shown that the quantum spins in the AKLT model is equivalent to classical spins. ", "This model has been attracting enormous research interests since then [@AAH; @FM; @KHH; @KLT; @KK; @KSZ; @RB]. ", "It can be defined and solved in higher dimensional lattices [@AKLT2; @FKR2; @KLT; @RB]. ", "It is generalizable to the inhomogeneous (non-translational invariant) case (spins at different lattice sites may take different values) and an arbitrary graph [@AKLT1; @AKLT2; @KK; @XK]. ", "The AKLT model has also been generalized to the $SU(n)$ version [@GR; @GRS; @KHK; @RSSTG; @RTFSG]. ", "Given certain conditions (see §$\\,\\ref{sec:unique}\\,$), the ground state has proven to be unique [@AKLT1; @AKLT2; @KLT; @KK]. ", "It is known as the Valence-Bond-Solid (VBS) state. ", "The VBS state is interesting to different research fields. ", "The Schwinger boson representation of the VBS state (see (\\[generalizedvbs\\])) relates to the Laughlin ansatz of the fractional quantum Hall effect [@AAH; @HZS; @ILO]. ", "The Laughlin wave function of the fractional quantum Hall effect is the VBS state on the complete graph [@HR0]. ", "The VBS state illustrates ground state properties of anti-ferromagnetic integer-spin chains with a Haldane gap [@H]. ", "In $1$-dimension, the VBS state is related to the matrix product state discovered by A. Klümper, A. Schadschneider and J. Zittartzand, see [@KSZ1; @KSZ] where a ‘q–deformed’ VBS-model (a generalized anisotropic version) was studied. ", "The geometric entanglement for a $1$-dimensional spin-$1$ VBS state was studied in [@O]. ", "The VBS state can be used as a resource state in measurement-based quantum computation invented by R. Raussendorf and H. Briegel [@RB1]. ", "VBS state allows universal quantum computation [@VC] . ", "Many people developed these ideas [@BM; @GESG]. ", "AKLT Hamiltonian can be implemented in optical lattices [@GMC]. [", "^1]\n\nThis review introduces some of the main results on quantum entanglement in VBS states defined on a lattice or a graph. ", "We take a pedagogical approach, starting with the basics of the AKLT model, the construction of VBS states and measures of entanglement (special attention being paid to the uniqueness of the ground state for a finite lattice or graph). ", "We shall consider a part (subsystem) of the ground state, *i.e.* a block of spins. ", "It is described completely by the reduced density matrix of the block, which we call *the density matrix* later for short. ", "The density matrix has been studied extensively. ", "It contains information of all correlation functions [@AAH; @JK; @KHH; @XKHK]. ", "The entanglement properties of the VBS states has been studied by means of the density matrix as in [@FK; @FKR; @FKR2; @FM; @KHH; @VMC; @XKHK; @XKHK2; @XK]. ", "Note that throughout the review we are considering **zero temperature** so that the AKLT spin system lies in the VBS ground state.", "\n\nThe review is divided into eight sections including a complete treatment of $1$-dimensional models with open boundary conditions:\n\n1. ", " A brief introduction to the topic. (§", "$\\,\\ref{sec:intro1}\\,$)\n\n2. ", " The construction of the general AKLT Hamiltonian. ", "Introduction of the VBS ground state. ", "Definition of different versions of the AKLT model: 1) The *basic* model; 2) The *generalized* (including the inhomogeneous) model. ", "Proof of the uniqueness of the VBS ground state on a finite graph. ", "In this and the next sections, we consider the AKLT model on an arbitrary connected finite graph. ", "This includes all lattices in any dimension. (§", "$\\,\\ref{sec:general}\\,$)\n\n3. ", " In order to study entanglement, the graph (or lattice) is divided into two subsystems (the *block* and the *environment*). ", "Different measures of entanglement, namely, the *von Neumann Entropy* and the *Rényi entropy* are defined. ", "We define anther Hamiltonian called the *block Hamiltonian*. ", "The block Hamiltonian is the AKLT Hamiltonian for the block, but the uniqueness condition is violated. ", "The block Hamiltonian is used to describe general properties of the block density matrix. ", "We discuss the relation between the spectrum of the density matrix and the degenerate ground states of the block Hamiltonian. (§", "$\\,\\ref{sec:subandmeas}\\,$)\n\n4. ", " The simplest $1$-dimensional AKLT model with spin-$1$. Calculation and diagonalization of the density matrix (in an algebraic approach). ", "Calculation of the **entanglement entropies**. (§", "$\\,\\ref{sec:1dspin1}\\,$)\n\n5. ", " The $1$-dimensional AKLT model with spin-$S$. Calculation and diagonalization of the density matrix using the Schwinger boson representation. ", "Discussion of the entanglement entropies. ", "Derivation of the relation between the density matrix and correlation functions. (§", "$\\,\\ref{sec:1dssh}\\,$)\n\n6. ", " The $1$-dimensional inhomogeneous model (spins at different lattice sites can be different). ", "Discussion of entanglement entropies. (§", "$\\,\\ref{sec:1dinhom}\\,$)\n\n7. ", " The $1$-dimensional $SU(n)$ model (in the adjoint representation). ", "Calculation of entanglement entropies. (§", "$\\,\\ref{sec:su(n)}\\,$)\n\n8. ", " A summary including open problems and conjectures. (§", "$\\,\\ref{sec:sum1}\\,$)\n\nThe General AKLT Model {#sec:general}\n======================\n\nIn the following we give the most general AKLT Hamiltonian and VBS states. ", "The definition applies to both graphs and arbitrary lattices.", "\n\nThe Hamiltonian {#sec:hamil}\n---------------\n\nThe original AKLT Hamiltonian describes a spin interacting system, in which spins sitting at lattice sites interact with nearest neighbors. ", "One of the most simple versions is an ($1$-dimensional) open chain of $N$ sites with spin-$1$ at each site, and the Hamiltonian is given by [@AKLT1] $$\\begin{aligned}\nH=\\frac{1}{2}\\sum^{N-1}_{j=0}\\left(\\boldsymbol{S}_{j}\\cdot\\boldsymbol{S}_{j+1}+\\frac{1}{3}(\\boldsymbol{S}_{j}\\cdot\\boldsymbol{S}_{j+1})^{2}+\\frac{2}{3}\\right), \\label{simphami}\\end{aligned}$$ in which $\\boldsymbol{S}_{j}$ denotes the quantum operator for a spin vector $\\boldsymbol{S}_{j}=\\left(S^{x}_{j}, S^{y}_{j}, S^{z}_{j}\\right)$ at site $j$. This Hamiltonian (\\[simphami\\]) looks like the Heisenberg Hamiltonian with an extra quadratic term (the proportionality factor $1/2$ and the additive constant $2/3$ are sometimes neglected which only shifts and scales the energy spectrum as a whole), but the physical system behaves quite differently. ", "It was later generalized: 1) The spin $\\boldsymbol{S}_{j}$ at each site can take higher values; 2) Different lattice sites can have different spins; 3) Different boundary conditions (*e.g.* an open boundary condition) can be applied. ", "An arbitrary boundary condition or distribution of spin values over sites may not yield a unique ground state (*e.g.* Hamiltonian (\\[simphami\\]) has $4$-fold degenerate ground states). ", "We could find the condition for the uniqueness of the ground state (see §$\\,\\ref{sec:unique}\\,$ and [@KK]). ", "The Hamiltonian can be defined on higher dimensional lattices (*e.g.* $2$-dimensional square or hexagonal lattice [@AKLT1; @AKLT2]) or an arbitrary graph (A graph consists of two types of elements, namely *vertices* and *edges*. ", "Every edge connects two vertices. ", "Spins locate on vertices and two vertices connected by an edge are nearest neighbors. ", "An edge is also called a *bond* physically. ", "In our considerations only nearest neighbors are present in the Hamiltonian. ", "More formal and detailed explanation of a graph is given in §$\\,\\ref{sec:basichamil}\\,$). ", "These different versions of the AKLT Hamiltonian under consideration share two common features:\n\n1. ", " The Hamiltonian is a sum of terms with only nearest neighbor interactions. *", "i.e.* $$\\begin{aligned}\n H=\\sum_{\\langle kl\\rangle}H(k,l), \\qquad \\langle kl\\rangle\\in\\{\\mathrm{edges}\\}. ", "\\label{hamisum}\n \\end{aligned}$$ Here the Hamiltonian density $H(k,l)$ describes the interaction between two spins at vertices $k$ and $l$ for a connected graph. ", "The construction for a lattice is similar. ", "Only spins at nearest neighbor pairs $\\langle kl \\rangle$’s called *bonds* (edges of a graph) interact.", "\n\n2. ", " The Hamiltonian density $H(k,l)$ is a sum of several terms. ", "Each term is proportional to a projector. ", "The proportionality coefficients are all positive numbers. *", "i.e.* $$\\begin{aligned}\n H(k,l)=\\sum_{J}C_{J}(k,l)\\,\\pi_{J}(k,l). ", "\\label{hamiden}\n \\end{aligned}$$ Here $\\pi_{J}(k,l)$’s are projectors and $C_{J}(k,l)$’s are positive coefficients. ", "Note that the coefficients may depend on the bond $\\langle kl\\rangle$ and the projector $\\pi_{J}(k,l)$. The projector $\\pi_{J}(k,l)$ projects $\\boldsymbol{S}_{k}$ and $\\boldsymbol{S}_{l}$ on the joint value $J$ of the bond spin $\\boldsymbol{J}_{kl}=\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l}$. (We also call the joint spin value $J$ the *bond spin* value). ", "The meaning is this: The spin $\\boldsymbol{S}_{k}$ with spin value $S_{k}$ at site (or vertex) $k$ is a $(2S_{k}+1)$-dimensional representation of the $SU(2)$ Lie algebra, while $\\boldsymbol{S}_{l}$ is a $(2S_{l}+1)$-dimensional representation. ", "The direct product of these two representations is reducible to a direct sum of irreducible representations with dimensions $2J+1$ and $J$ runs from $|S_{k}-S_{l}|$ to $S_{k}+S_{l}$. The Hilbert space ‘splits’ into these invariant subspaces labeled by $J$ which is called the *bond spin* value of $\\boldsymbol{S}_{k}$ and $\\boldsymbol{S}_{l}$. (The eigenvalues of the Casimir operator – the square of the bond spin $(\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l})^{2}$ is $J(J+1)$.) The projector $\\pi_{J}(k,l)$ projects on the invariant subspace with bond spin $J$. If we choose an orthonormal basis $\\{|J,m\\rangle\\ |\\ m=-J,\\ldots,J\\}$ for the subspace, such that $(\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l})^{2}|J,m\\rangle=J(J+1)|J,m\\rangle$ and $(S^{z}_{k}+S^{z}_{l})|J,m\\rangle=m|J,m\\rangle$, then the projector could be written as $$\\begin{aligned}\n \\pi_{J}(k,l)=\\sum^{J}_{m=-J}|J,m\\rangle\\langle J,m|. ", "\\label{projstates}\n \\end{aligned}$$ This form (\\[projstates\\]) is cumbersome in practical use and it is preferred to express the projector $\\pi_{J}(k,l)$ explicitly in terms of spin operators $\\boldsymbol{S}_{k}$ and $\\boldsymbol{S}_{l}$. We shall do that in the next section (§$\\,\\ref{sec:proj}\\,$).", "\n\nEven without an explicit form of the projectors, an immediate consequence of these two properties is that the Hamiltonian is *positive semi-definite*. [", "^2] Furthermore, because of this, if we could construct a state $|\\psi\\rangle$ which has no projection on any of the specified bond spin-$J$ states appearing in (\\[hamiden\\]) for each bond, *i.e.* $\\pi_{J}(k,l)|\\psi\\rangle=0$, $\\forall\\ \\langle kl\\rangle$, then it has to be a ground state (with energy equal to zero) regardless of the specific values of the coefficients. [", "^3] The uniqueness condition of the ground state will be discussed later in §$\\,\\ref{sec:unique}\\,$.\n\nThe Projector {#sec:proj}\n-------------\n\nIn order to complete the definition of the general AKLT Hamiltonian (\\[hamisum\\]) and Hamiltonian density (\\[hamiden\\]), we have to give an explicit expression of the projector $\\pi_{J}(k,l)$ in terms of spin operators $\\boldsymbol{S}_{k}$ and $\\boldsymbol{S}_{l}$. We derive the expression in two steps. ", "The forms of $\\pi_{J}(k,l)$ for a specific model such as the expression (\\[simphami\\]) or those for $1$-dimensional models in §$\\,\\ref{sec:1dspin1}\\,$, §$\\,\\ref{sec:1dssh}\\,$ and §$\\,\\ref{sec:1dinhom}\\,$ can all be obtained through this approach as follows. (", "An explicit construction of the projector was given in [@KK].)", "\n\n1. ", " Consider the following two sets of operators: the projectors $$\\begin{aligned}\n \\{\\pi_{J}(k,l)\\ |\\ J=|S_{k}-S_{l}|,\\ldots,S_{k}+S_{l}\\}\n \\end{aligned}$$ and the powers of the inner product $(\\boldsymbol{S}_{k}\\cdot\\boldsymbol{S}_{l})$ $$\\begin{aligned}\n \\{(\\boldsymbol{S}_{k}\\cdot\\boldsymbol{S}_{l})^{n}\\ |\\ n=0,\\ldots,2S_{<}\\}, \\qquad S_{<}\\equiv \\mathrm{min}\\{S_{k}, S_{l}\\}.", "\n \\end{aligned}$$ One set is expressible in terms of the other. ", "They are related by a linear transformation: $$\\begin{aligned}\n &&(\\boldsymbol{S}_{k}\\cdot\\boldsymbol{S}_{l})^{n} \\nonumber\\\\\n &=&\\left(\\frac{1}{2}\\right)^{n}\\left[(\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l})^{2}-S_{k}(S_{k}+1)-S_{l}(S_{l}+1)\\right]^{n}\\sum^{S_{k}+S_{l}}_{J=|S_{k}-S_{l}|}\\pi_{J}(k,l) \\nonumber\\\\\n &=&\\sum^{S_{k}+S_{l}}_{J=|S_{k}-S_{l}|}\\left(\\frac{1}{2}\\right)^{n}\\left[J(J+1)-S_{k}(S_{k}+1)-S_{l}(S_{l}+1)\\right]^{n}\\pi_{J}(k,l) \\nonumber\\\\\n \\label{lineartr}\n \\end{aligned}$$ for $n=0,\\ldots,2S_{<}$. In (\\[lineartr\\]) we have used $$\\begin{aligned}\n \\sum^{S_{k}+S_{l}}_{J=|S_{k}-S_{l}|}\\pi_{J}(k,l)=I\n \\end{aligned}$$ being the identity. ", "This set of $2S_{<}+1$ linear equations (\\[lineartr\\]) can be inverted, which express the projector $\\pi_{J}(k,l)$ as a polynomial of the inner product $(\\boldsymbol{S}_{k}\\cdot\\boldsymbol{S}_{l})$. We shall not pursue with the inversion of (\\[lineartr\\]) but to construct the projector in the next step.", "\n\n2. ", " The next step is to realize that if an operator $\\mathcal{P}(k,l)$ satisfies the following conditions $$\\begin{aligned}\n \\mathcal{P}(k,l)\\pi_{J'}(k,l)=\\delta_{JJ'}\\pi_{J}(k,l), \\qquad \\forall \\ J' \\label{cond}\n \\end{aligned}$$ then the operator $\\mathcal{P}(k,l)$ is identified with $\\pi_{J}(k,l)$ because $$\\begin{aligned}\n \\mathcal{P}(k,l)&=&\\mathcal{P}(k,l)\\sum^{S_{k}+S_{l}}_{J'=|S_{k}-S_{l}|}\\pi_{J'}(k,l) \\nonumber\\\\\n &=&\\left(\\sum^{S_{k}+S_{l}}_{J'=|S_{k}-S_{l}|}\\delta_{JJ'}\\right)\\pi_{J}(k,l)=\\pi_{J}(k,l).", "\n \\end{aligned}$$ Therefore we could construct an operator satisfying the condition (\\[cond\\]): $$\\begin{aligned}\n \\mathcal{P}(k,l)=\\prod^{j\\neq J}_{|S_{k}-S_{l}|\\leq j\\leq S_{k}+S_{l}}\\frac{(\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l})^{2}-j(j+1)}{J(J+1)-j(j+1)}. ", "\\label{piproj}\n \\end{aligned}$$ When $\\mathcal{P}(k,l)$ acting on $\\pi_{J'}(k,l)$, we have:\n\n 1. ", " If $J'\\neq J$, then the numerator of one factor in the product vanishes, so that $\\mathcal{P}$ vanishes. *", "i.e.* $\\mathcal{P}(k,l)\\pi_{J'}(k,l)=0$, if $J'\\neq J$;\n\n 2. ", " If $J'=J$, all factors in the product become equal to $1$, so as the expression $\\mathcal{P}$. *i.e.* $\\mathcal{P}(k,l)\\pi_{J}(k,l)=\\pi_{J}(k,l)$.\n\n So that (\\[piproj\\]) is the projector $\\pi_{J}(k,l)$, *i.e.* $\\pi_{J}(k,l)=\\mathcal{P}(k,l)$. Operator $$\\begin{aligned}\n \\pi_{J}(k,l)=\\prod^{j\\neq J}_{|S_{k}-S_{l}|\\leq j\\leq S_{k}+S_{l}}\\frac{(\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l})^{2}-j(j+1)}{J(J+1)-j(j+1)} \\label{pi}\\end{aligned}$$ projects the bond spin $\\boldsymbol{J}_{kl}\\equiv\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l}$ on the subspace with fixed total spin value $J$ and $|S_{k}-S_{l}|\\leq J\\leq S_{k}+S_{l}$. Note that we could expand $(\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l})^{2}=2\\boldsymbol{S}_{k}\\cdot\\boldsymbol{S}_{l}+S_{k}(S_{k}+1)+S_{l}(S_{l}+1)$. Therefore projector $\\pi_{J}(k,l)$ in (\\[pi\\]) is a polynomial in the scalar product $(\\boldsymbol{S}_{k}\\cdot\\boldsymbol{S}_{l})$ of degree $2S_{<}$, where $S_{<}\\equiv \\mathrm{min}\\{S_{k}, S_{l}\\}$ is the minimum of the two spin values of the same bond $\\langle kl\\rangle$. For example with $S_{k}=S_{l}=1$, we may have a quadratic polynomial as in (\\[simphami\\]): $$\\begin{aligned}\n \\pi_{2}(k,l)=\\frac{1}{6}(\\boldsymbol{S}_{k}\\cdot\\boldsymbol{S}_{l})^{2}+\\frac{1}{2}(\\boldsymbol{S}_{k}\\cdot\\boldsymbol{S}_{l})+\\frac{1}{3}. ", "\\label{examplepi2}\\end{aligned}$$\n\nThe Basic AKLT Model {#sec:basic}\n--------------------\n\n### The Hamiltonian {#sec:basichamil}\n\nOnce we have the building blocks for the Hamiltonian from §$\\,\\ref{sec:hamil}\\,$ and §$\\,\\ref{sec:proj}\\,$, various types of the AKLT model can be constructed. ", "Let us start with the definition of the *basic* AKLT model on a connected graph or lattice. (", "Any lattice is a special graph with periodic structure; our notations and definitions refer to the most general). ", "A *graph* consists of two types of elements, namely *vertices* and *edges*. ", "Every edge *connects* two vertices. ", "As in Figure (\\[figure1\\]), a vertex is drawn as a (large) circle and an edge is drawn as a solid line connecting two vertices. ", "For every pair of vertices in the *connected* graph, there is a *walk* [^4] from one to the other. ", "Vertices can also be called *sites* and edges sometimes called *links* or *bonds*. ", "In a graph, a pair of vertices connected by an edge is regarded nearest neighbors, *i.e.* the terms edge, bond and nearest neighbor are equivalent and interchangeable. (", "For a lattice, vertices become sites and bonds become lattice vectors connecting nearest neighboring sites.) ", "In the case of a disconnected graph, the Hamiltonian (\\[hamisum\\]) is a direct sum with respect to connected components and the ground state is a direct product. ", "Therefore we shall need only to study a connected graph. ", "Also, assuming that the graph consists of more than one vertices to avoid the trivial case where there would be no interaction at all.", "\n\nLet us introduce mathematical notations. ", "By $\\boldsymbol{S}_{l}$ we shall denote the spin operator located at vertex $l$ with spin value $S_{l}$. In the *basic* model we require that $S_{l}=z_{l}/2$, where $z_{l}$ is the number of incident edges connected to vertex $l$, also known as the *valence* or *coordination number* (the number of nearest neighbors of the vertex $l$). ", "The relation between the spin value and coordination number must be true for any vertex $l$, including boundaries. ", "This will guarantee the uniqueness of the ground state, see §$\\,\\ref{sec:unique}\\,$. For a lattice, this condition would also yield that bulk spins (spins not on the boundary) take the same value $z/2$ because the number of nearest neighbors $z$ is a constant.", "\n\nIn the *basic* model we define the Hamiltonian density $H(k,l)$ for bond (edge) $\\langle kl\\rangle$ as $$\\begin{aligned}\n H(k,l)=C(k,l)\\,\\pi_{S_{k}+S_{l}}(k,l), \\qquad H(k,l)\\geq 0 \\label{basichd}\\end{aligned}$$ with $C(k,l)$ an arbitrary positive real coefficient (it may depend on the bond $\\langle kl\\rangle$). ", "So that the Hamiltonian density for each bond (edge) is proportional to the projector on the subspace with the highest possible bond spin value $(S_{k}+S_{l})$. The physical meaning is that interacting spins do not form the highest possible bond spin (this will increase the energy) in the ground state. ", "Then the basic AKLT Hamiltonian on an arbitrary connected graph according to (\\[hamisum\\]) is $$\\begin{aligned}\n H=\\sum_{\\langle kl\\rangle}H(k,l)=\\sum_{\\langle kl\\rangle}C(k,l)\\,\\pi_{S_{k}+S_{l}}(k,l). ", "\\label{basich}\\end{aligned}$$ Here we sum over all bonds (edges) $\\langle kl\\rangle$. Note that for a lattice all the highest bond spin values for bulk spins are the same and equal to the coordination number $z$. For example, the basic model defined on a $2$-dimensional square lattice must have spin-$2$ in each bulk vertex and $\\pi_{4}$ in the Hamiltonian; also, the Hexagonal lattice has spin-$3/2$ in each vertex and $\\pi_{3}$ in the Hamiltonian.", "\n\n### The VBS State – Pictorial Method {#sec:graphvbs}\n\nIn this section we consider the Hamiltonian (\\[basich\\]) and construct a ground state which is denoted by $|\\mathrm{VBS}\\rangle$. Later we shall see in §$\\,\\ref{sec:unique}\\,$ that it is the unique ground state.", "\n\nThe Hamiltonian (\\[basich\\]) with condition $$\\begin{aligned}\n S_{l}=\\frac{1}{2}z_{l} \\label{basiccond}\\end{aligned}$$ has a unique ground state [@AKLT1; @AKLT2; @AAH; @KK] known as the Valence-Bond-Solid (VBS) state. ", "It can be constructed in a Pictorial way as follows (see Figure \\[figure1\\]).", "\n\n![", "Example of a part of the graph including vertex $k$ with $z_{k}=3$ and vertex $l$ with $z_{l}=4$. Black dots represent spin-$1/2$ states, which are enclosed by large circles representing vertices and symmetrization of the product of spin-$1/2$’s at each vertex. ", "Solid lines represent edges (bonds) which anti-symmetrize the pair of connected spin-$1/2$’s.[]{data-label=\"figure1\"}](figure1.eps){width=\"4in\"}\n\nEach vertex $l$ is represented by $z_{l}$ spin-$1/2$’s. ", "We associate each spin-$1/2$ with an incident edge. ", "In such a way each edge has two spin-$1/2$’s at its ends. ", "We anti-symmetrize the spin states of these two spin-$1/2$’s. ", "So that anti-symmetrization is done along each edge. ", "These anti-symmetrizations ensure that there is no projection on the highest bond spin states for every bond. ", "Then we also symmetrize the product of spin-$1/2$’s at each vertex (each large circle in Figure \\[figure1\\]). ", "These symmetrizations preserve the correct spin value at each vertex.", "\n\nLet us write down the VBS ground state algebraically following this approach. ", "We label the particular dot from vertex $l$ connected with some dot from vertex $k$ by $l_{k}$ (correspondingly, that dot from vertex $k$ is labeled by $k_{l}$). ", "In this way we have specified a unique prescription of indices with dots. ", "Then the anti-symmetrization results in the singlet state $$\\begin{aligned}\n |\\Phi\\rangle_{kl}=\\frac{1}{\\sqrt{2}}\\left(|\\uparrow\\rangle_{l_{k}}|\\downarrow\\rangle_{k_{l}}-|\\downarrow\\rangle_{l_{k}}|\\uparrow\\rangle_{k_{l}}\\right), \\label{antisymm}\\end{aligned}$$ where $|\\uparrow\\rangle$ (or $\\downarrow\\rangle$) denotes spin up (or down) states referring to a basis. ", "The direct product of all these $|\\Phi\\rangle$ singlet states corresponds to all edges (bonds) in our Figure \\[figure1\\]: $$\\begin{aligned}\n \\prod_{\\langle kl\\rangle}|\\Phi\\rangle_{kl}. ", "\\label{prodsing}\\end{aligned}$$ We still have to complete the symmetrization (circles) at each vertex. ", "We denote the symmetrization operator of $z_{l}$ black dots in vertex $l$ by $\\mathbf{P}(l)$. The action of $\\mathbf{P}(l)$ on any product of $z_{l}$ spin-$1/2$’s is $$\\begin{aligned}\n &&\\mathbf{P}(l)|\\chi_{l_{k_{1}}}\\rangle_{l_{k_{1}}}|\\chi_{l_{k_{2}}}\\rangle_{l_{k_{2}}}\\cdots|\\chi_{l_{k_{z_{l}}}}\\rangle_{l_{k_{z_{l}}}} \\label{symmtri}\\\\\n&=&\\sum^{z_{l}!\\ \\mathrm{terms}}_{\\sigma}|\\chi_{l_{k_{\\sigma(1)}}}\\rangle_{l_{k_{1}}}|\\chi_{l_{k_{\\sigma(2)}}}\\rangle_{l_{k_{2}}}\\cdots|\\chi_{l_{k_{\\sigma(z_{l})}}}\\rangle_{l_{k_{z_{l}}}}, \\qquad \\chi=\\uparrow \\mathrm{or} \\downarrow \\nonumber\\end{aligned}$$ where $k_{1}, k_{2}, \\ldots, k_{z_{l}}$ are the $z_{l}$ spin-$1/2$’s (block dots) belonging to vertex $l$ (the index also refers to the $z_{l}$ vertices connected to vertex $l$ by an edge) and $\\sigma$ is a permutation of the indices: $$\\begin{aligned}\n \\sigma=\\left(\\begin{array}{cccc} 1 & 2 & \\cdots & z_{l} \\\\ \\sigma(1) & \\sigma(2) & \\cdots & \\sigma(z_{l})\\end{array}\\right).\\end{aligned}$$ All permutations are summed up in (\\[symmtri\\]). ", "Then the symmetrization at each vertex is carried out by taking the product $\\prod_{l}\\mathbf{P}(l)$ of all vertices. ", "Finally, the unique VBS ground state can be written as $$\\begin{aligned}\n |\\mathrm{VBS}\\rangle=\\prod_{l}\\mathbf{P}(l)\\prod_{\\langle kl\\rangle}|\\Phi\\rangle_{kl}. ", "\\label{basicvbs}\\end{aligned}$$ Here the first product runs over all vertices and the second over all edges (bonds). ", "So that we have constructed a ground state of the AKLT Hamiltonian (\\[basich\\]) such that $$\\begin{aligned}\n H|\\mathrm{VBS}\\rangle=0, \\qquad \\pi_{S_{k}+S_{l}}(k,l)|\\mathrm{VBS}\\rangle=0, \\qquad \\forall\\ \\langle kl\\rangle. ", "\\label{hvbs=0}\\end{aligned}$$ Note that the VBS state in (\\[basicvbs\\]) is not normalized in general. ", "If the coordination number $z_{l}$ is a constant over all vertices in the graph except for boundaries (such as in the case of a lattice), then we would have the same spin value at each bulk vertex. ", "In that case the *basic* model is also referred to as the *homogeneous* model.", "\n\nThe Generalized AKLT Model {#sec:generalized}\n--------------------------\n\n### The Hamiltonian {#sec:generalhamil}\n\nIn the *generalized* AKLT model, relation (\\[basiccond\\]) is generalized. ", "We associate a positive integer $M_{kl}$ ($M_{kl}\\equiv M_{lk}$) to each edge $\\langle kl\\rangle$ of the graph (or each bond of a lattice). ", "We shall call $M_{kl}$ *multiplicity numbers*. ", "Similar to the basic model, the AKLT Hamiltonian describes interactions between nearest neighbors (vertices connected by an edge): $$\\begin{aligned}\n H=\\sum_{\\langle kl\\rangle}H(k,l). ", "\\label{generalizedh}\\end{aligned}$$ However, the Hamiltonian density is no longer proportional to a single projector as in (\\[basichd\\]) in general. ", "Instead, it is a linear combination of projectors $$\\begin{aligned}\n H(k,l)=\\sum^{S_{k}+S_{l}}_{J=S_{k}+S_{l}-M_{kl}+1}C_{J}(k,l)\\,\\pi_{J}(k,l), \\label{generalizedhd} \\\\\n 1\\leq M_{kl}\\leq 2S_{<}, \\qquad S_{<}\\equiv \\mathrm{min}\\{S_{k}, S_{l}\\}. ", "\\nonumber \\end{aligned}$$ Projector $\\pi_{J}(k,l)$ is given by (\\[pi\\]), and $C_{J}(k,l)$’s are arbitrary positive coefficients. ", "So that $H(k,l)$ projects the bond spin on the subspace with bond spin value $J$ greater than $S_{k}+S_{l}-M_{kl}$. Physically formation of any bond spin higher than $S_{k}+S_{l}-M_{kl}$ would increase the energy.", "\n\nThe condition of uniqueness of the ground state was introduced by Kirillov and Korepin in [@KK]: $$\\begin{aligned}\n 2S_{l}=\\sum_{k}M_{kl}, \\qquad \\forall \\ l. \\label{condition1}\\end{aligned}$$ Here $S_{l}$ is the spin value at vertex $l$ and we sum over all edges incident to vertex $l$ (connected to vertex $l$). *", "i.e.* $k$ are nearest neighbors. ", "The Hamiltonian (\\[generalizedh\\]) has a unique ground state if (\\[condition1\\]) is valid, see §$\\,\\ref{sec:unique}\\,$. The relation $2S_{l}=z_{l}$ for the *basic* model is a special case when all $M_{kl}=1$. Also, when $M_{kl}=1$, the Hamiltonian density (\\[generalizedhd\\]) reduces to that of the basic model (\\[basichd\\]). ", "The condition (\\[condition1\\]) can be put into an invariant form. ", "Let us define a column vector $\\mathbf{S}$, the $l^{\\mathrm{th}}$ component of which is associated with vertex $l$ of the graph and equal to $S_{l}$. The number of components is equal to the number of vertices $N$ in the whole graph. ", "Next, we define another column vector $\\mathbf{M}$ with its dimension equal to the number of edges $M$ in the graph. ", "The $k^{\\mathrm{th}}$ and $l^{\\mathrm{th}}$ components of this vector are associated with edge $\\langle kl\\rangle$ and both equal to $M_{kl}$. The most important geometrical characteristic of the graph is the vertex-edge incidence matrix $\\hat{\\mathbf{I}}$ (see [@Har]). ", "This is a rectangular matrix with $N$ rows and $M$ columns. ", "Each row is associated with the vertex and each column is associated with the edge. ", "If the vertex belongs to the edge the corresponding matrix element is equal to one, otherwise zero. ", "Then the condition (\\[condition1\\]) of uniqueness can be re-written as $$\\begin{aligned}\n 2\\,\\mathbf{S}=\\hat{\\mathbf{I}}\\cdot\\mathbf{M}. ", "\\label{condition2} \\end{aligned}$$ For more details we refer to [@KK].", "\n\n### The VBS State – Schwinger Boson Representation {#sec:vbssch}\n\nUnder condition (\\[condition1\\]) or (\\[condition2\\]), the unique ground state of Hamiltonian (\\[generalizedh\\]) is referred to as the generalized VBS state. ", "It is constructed by introducing the Schwinger boson representation [@AAH; @FM; @KK; @KHH; @XKHK; @XKHK2; @XK]. ", "This method uses a pair of bosonic creation and annihilation operators (similar to the treatment of the harmonic oscillator problem) to realize the $SU(2)$ Lie algebra.", "\n\nDefine a pair of independent canonical bosonic operators $a_{l}$ and $b_{l}$ for each vertex (or site) $l$: $$\\begin{aligned}\n [\\,a_{k}\\,,\\,a^{\\dagger}_{l}\\,]=[\\,b_{k}\\,,\\,b^{\\dagger}_{l}\\,]=\\delta_{kl} \\label{commutator}\\end{aligned}$$ with all other commutators vanishing: $$\\begin{aligned}\n [\\,a_{k}\\,,\\,a_{l}\\,]=[\\,b_{k}\\,,\\,b_{l}\\,]=[\\,a_{k}\\,,\\,b_{l}\\,]=[\\,a_{k}\\,,\\,b^{\\dagger}_{l}\\,]=0, \\qquad \\forall\\ k, l. \\label{commvani}\\end{aligned}$$ Spin operators are represented as $$\\begin{aligned}\n S^{+}_{l}=a^{\\dagger}_{l}b_{l}, \\qquad S^{-}_{l}=b^{\\dagger}_{l}a_{l}, \\qquad S^{z}_{l}=\\frac{1}{2}(a^{\\dagger}_{l}a_{l}-b^{\\dagger}_{l}b_{l}). ", "\\label{spinrep}\\end{aligned}$$ It is straightforward to verify that the $SU(2)$ Lie algebra is realized. ", "To reproduce the dimension of the spin-$S_{l}$ Hilbert space at vertex $l$, a constraint on the total boson occupation number is required: $$\\begin{aligned}\n \\hat{S}_{l}\\equiv\\frac{1}{2}(a^{\\dagger}_{l}a_{l}+b^{\\dagger}_{l}b_{l})=S_{l}. ", "\\label{constraintspin}\\end{aligned}$$ *i.e.* any physical spin state $|\\psi\\rangle_{l}$ at vertex $l$ must satisfy $\\hat{S}_{l}|\\psi\\rangle_{l}=S_{l}|\\psi\\rangle_{l}$. In this framework the spin state $|S_{l},m_{l}\\rangle_{l}$ such that $\\boldsymbol{S}^{2}_{l}|S_{l},m_{l}\\rangle_{l}=S_{l}(S_{l}+1)|S_{l},m_{l}\\rangle_{l}$ and $S^{z}_{l}|S_{l},m_{l}\\rangle_{l}=m_{l}|S_{l},m_{l}\\rangle_{l}$ is represented by $$\\begin{aligned}\n |S_{l},m_{l}\\rangle_{l}=\\frac{(a^{\\dagger}_{l})^{S_{l}+m_{l}}(b^{\\dagger}_{l})^{S_{l}-m_{l}}}{\\sqrt{(S_{l}+m_{l})!(S_{l}-m_{l})!}}\\,|\\mathrm{vac}\\rangle_{l}, \\label{spinstatesch}\\end{aligned}$$ where the *vacuum* $\\left|\\mathrm{vac}\\right\\rangle_{l}$ is annihilated by any of the annihilation operators: $$\\begin{aligned}\n a_{l}\\left|\\mathrm{vac}\\right\\rangle_{l}=b_{l}\\left|\\mathrm{vac}\\right\\rangle_{l}=0. ", "\\label{vacuum}\\end{aligned}$$ As a result, the VBS ground state in the Schwinger representation is constructed as $$\\begin{aligned}\n |\\mathrm{VBS}\\rangle=\n \\prod_{\\langle kl\\rangle}\n\\left(a^{\\dagger}_{k}b^{\\dagger}_{l}-b^{\\dagger}_{k}a^{\\dagger}_{l}\\right)^{M_{kl}}|\\mathrm{vac}\\rangle. ", "\\label{generalizedvbs}\\end{aligned}$$ It worth mentioning that this representation shows that for a full graph (each vertex is connected to every other vertex by definition) the VBS state coincides with the Laughlin wave function [@AAH; @HR0; @HZS]. ", "In (\\[generalizedvbs\\]) the product runs over all bonds (edges) and the vacuum $|\\mathrm{vac}\\rangle$ is the direct product of vacuums of each vertex $$\\begin{aligned}\n |\\mathrm{vac}\\rangle=\\bigotimes_{l}|\\mathrm{vac}\\rangle_{l},\\end{aligned}$$ which is destroyed by any annihilation operators $a_{l}$ or $b_{l}$, $\\forall\\ l$. (Note that $[\\,a^{\\dagger}_{k}\\,,\\,b^{\\dagger}_{l}\\,]=0$, $\\forall\\ k,l$.)\n\nTo prove that (\\[generalizedvbs\\]) is the ground state we need only to verify for any vertex $l$ and bond (edge) $\\langle kl\\rangle$:\n\n1. ", " The total power of $a^{\\dagger}_{l}$ and $b^{\\dagger}_{l}$ is $2S_{l}$, so that we have spin-$S_{l}$ at vertex $l$;\n\n2. ", " The $z$-component of the bond spin satisfies $$\\begin{aligned}\n -\\frac{1}{2}(\\sum_{l^{\\prime}\\neq l}M_{l^{\\prime}k}+\\sum_{k^{\\prime}\\neq k}M_{k^{\\prime}l})\\leq J^{z}_{kl}\\equiv S^{z}_{k}+S^{z}_{l}\\leq \\frac{1}{2}(\\sum_{l^{\\prime}\\neq l}M_{l^{\\prime}k}+\\sum_{k^{\\prime}\\neq k}M_{k^{\\prime}l})\\nonumber\\\\\n \\end{aligned}$$ by a binomial expansion. ", "Consequently, the maximum value of the bond spin $J_{kl}$ is $(\\sum_{l^{\\prime}\\neq l}M_{l^{\\prime}k}+\\sum_{k^{\\prime}\\neq k}M_{k^{\\prime}l})/2=S_{k}+S_{l}-M_{kl}$ (from $SU(2)$ invariance, see §$\\,\\ref{sec:larges}\\,$ and [@AAH]).", "\n\nTherefore, the state $|\\mathrm{VBS}\\rangle$ defined in (\\[generalizedvbs\\]) has spin-$S_{l}$ at vertex $l$ and no projection onto the $J_{kl}>S_{k}+S_{l}-M_{kl}$ subspace for any bond (edge). ", "As a consequence, $$\\begin{aligned}\n H|\\mathrm{VBS}\\rangle=0, \\qquad \\pi_{J}(k,l)|\\mathrm{VBS}\\rangle=0,\\nonumber\\\\\n S_{k}+S_{l}-M_{kl}+1\\leq J\\leq S_{k}+S_{l}, \\qquad \\forall\\ \\langle kl\\rangle. ", "\\label{hgvbs=0}\\end{aligned}$$ The introduction of Schwinger bosons can be used to construct a spin coherent state basis (as expected due to the similarity with the harmonic oscillator) in which spins at each vertex behave as classical unit vectors, see §$\\,\\ref{sec:cohe}\\,$ and [@AAH; @FM; @KK; @KHH; @XKHK; @XKHK2]. ", "The coherent state basis converts algebraic computations into classical integrals which becomes extremely useful in later sections.", "\n\nThe Uniqueness Condition {#sec:unique}\n------------------------\n\nAs stated in previous sections, the condition for the existence of a unique VBS ground state is $2S_{l}=z_{l}$ for the basic model and $2S_{l}=\\sum_{k}M_{kl}$ for the generalized model (the former being a special case of the latter). ", "This uniqueness condition for the AKLT model defined on a finite graph or lattice was proved in [@KK].", "\n\nNow let us turn to the proof of the uniqueness condition $2S_{l}=\\sum_{k}M_{kl}$ , *i.e.* the equation $$\\begin{aligned}\n H|\\Psi\\rangle=0 \\label{condgrou}\\end{aligned}$$ with $H$ the AKLT Hamiltonian (\\[generalizedh\\]) has exactly one solution under the condition (\\[condition1\\]) or (\\[condition2\\]). ", "Note that this expression (\\[condgrou\\]) is equivalent to $$\\begin{aligned}\n \\pi_{J}(k,l)|\\Psi\\rangle=0, \\qquad \\forall\\ \\langle k,l\\rangle, \\qquad S_{k}+S_{l}-M_{kl}+1\\leq J\\leq S_{k}+S_{l} \\label{condgrou1}\\end{aligned}$$ because of the positive semi-definiteness of every projector $\\pi_{J}$ and the positive coefficients $C_{J}$. In order to prove the uniqueness condition, we first prove the following lemma.", "\n\n\\[lemma1\\] All solutions of the equation $$\\begin{aligned}\n \\pi_{J}(k,l)|\\psi\\rangle=0, \\qquad S_{k}+S_{l}-M_{kl}+1\\leq J\\leq S_{k}+S_{l} \\label{pipsi0}\\end{aligned}$$ for fixed $k$ and $l$ can be represented in the following form $$\\begin{aligned}\n |\\psi\\rangle=f(a^{\\dagger},b^{\\dagger})(a^{\\dagger}_{k}b^{\\dagger}_{l}-a^{\\dagger}_{l}b^{\\dagger}_{k})^{M_{kl}}|\\mathrm{vac}\\rangle. ", "\\label{psicom}\\end{aligned}$$ Here $f(a^{\\dagger},b^{\\dagger})$ is some polynomial in $a^{\\dagger}_{k}$, $b^{\\dagger}_{k}$ and $a^{\\dagger}_{l}$, $b^{\\dagger}_{l}$.\n\nFor convenience, let us apply the Weyl representation of the $SU(2)$ Lie algebra. ", "Consider the space of polynomials in pairs of variables $x_{l}$ and $y_{l}$ with coefficients in $\\mathbf{C}$. We represent operator $a^{\\dagger}_{l}$ as multiplication on $x_{l}$ and $b^{\\dagger}_{l}$ as multiplication on $y_{l}$. At site $l$ we have $$\\begin{aligned}\n S^{+}_{l}=x_{l}\\frac{\\partial}{\\partial y_{l}}, \\qquad\\qquad\\qquad S^{-}_{l}=y_{l}\\frac{\\partial}{\\partial x_{l}} \\nonumber\\\\\n 2S^{z}_{l}=x_{l}\\frac{\\partial}{\\partial x_{l}}-y_{l}\\frac{\\partial}{\\partial y_{l}}, \\qquad 2\\hat{S}_{l}=x_{l}\\frac{\\partial}{\\partial x_{l}}+y_{l}\\frac{\\partial}{\\partial y_{l}}.\\end{aligned}$$ A basis of the $(2S_{l}+1)$-dimensional irreducible representation of spin-$S_{l}$ can be chosen in such a way: $$\\begin{aligned}\n \\mathbf{V}_{S_{l}}=\\{x^{S_{l}+m_{l}}_{l}y^{S_{l}-m_{l}}_{l}\\ |\\ m=-S,\\ldots,S\\}.\\end{aligned}$$ These monomials with total power $2S_{l}$ are clearly eigenvectors of $S^{z}_{l}$ and $\\hat{S}_{l}$. Now let us consider the tensor product of two irreducible representations $\\mathbf{V}_{S_{l}}\\otimes\\mathbf{V}_{S_{k}}$. Define the bond spin $\\boldsymbol{J}_{kl}\\equiv\\boldsymbol{S}_{k}+\\boldsymbol{S}_{l}$, then $$\\begin{aligned}\n J^{+}_{kl}&=&x_{k}\\frac{\\partial}{\\partial y_{k}}+x_{l}\\frac{\\partial}{\\partial y_{l}}, \\nonumber\\\\\n J^{-}_{kl}&=&y_{k}\\frac{\\partial}{\\partial x_{k}}+y_{l}\\frac{\\partial}{\\partial x_{l}}, \\nonumber\\\\\n 2J^{z}_{kl}&=&x_{k}\\frac{\\partial}{\\partial x_{k}}+x_{l}\\frac{\\partial}{\\partial x_{l}}-y_{k}\\frac{\\partial}{\\partial y_{k}}-y_{l}\\frac{\\partial}{\\partial y_{l}}, \\nonumber\\\\\n 2\\hat{J}_{kl}&=&x_{k}\\frac{\\partial}{\\partial x_{k}}+x_{l}\\frac{\\partial}{\\partial x_{l}}+y_{k}\\frac{\\partial}{\\partial y_{k}}+y_{l}\\frac{\\partial}{\\partial y_{l}}.\\end{aligned}$$ The tensor product of irreducible representation can be reduced to a direct sum of irreducible representations $$\\begin{aligned}\n \\mathbf{V}_{S_{k}}\\otimes\\mathbf{V}_{S_{l}}=\\bigoplus^{S_{k}+S_{l}}_{J=|S_{k}-S_{l}|}\\mathbf{V}_{J}.\\end{aligned}$$ Now we construct the highest vector (polynomial) $v_{J}$ of irreducible representation $\\mathbf{V}_{J}$ with fixed $J$: $$\\begin{aligned}\n J^{+}_{kl}v_{J}=0, \\qquad J^{z}_{kl}v_{J}=Jv_{J}, \\qquad \\hat{J}_{kl}v_{J}=(S_{k}+S_{l})v_{J}. ", "\\label{sativj}\\end{aligned}$$ It must have a total power $2(S_{k}+S_{l})$, so that the form can be taken as $$\\begin{aligned}\n v_{J}=\\sum_{m_{k}+m_{l}=J}C_{m_{k}m_{l}}x^{S_{l}+m_{l}}_{l}y^{S_{l}-m_{l}}_{l}x^{S_{k}+m_{k}}_{k}y^{S_{k}-m_{k}}_{k}. ", "\\label{vjform}\\end{aligned}$$ This form already satisfies the second and third equations in (\\[sativj\\]). ", "After rearranging terms (relabeling indices), the first equation of (\\[sativj\\]) becomes $$\\begin{aligned}\n J^{+}_{kl}v_{J}&=&\\sum^{J-1}_{m_{k}=0}\\left[(S_{k}-m_{k})C_{m_{k},J-m_{k}}+(S_{l}-J+m_{k}+1)C_{m_{k}+1,J-m_{k}-1}\\right]\n \\nonumber\\\\\n &&\\cdot x^{S_{k}+m_{k}+1}_{k}y^{S_{k}-m_{k}-1}_{k}x^{S_{l}+J-m_{k}}_{l}y^{S_{l}-J+m_{k}}_{l}. ", "\\label{jplusvj}\\end{aligned}$$ Because of the linear independence of the monomials appearing in (\\[jplusvj\\]), the coefficients must vanish, which yields the following recurrence relation $$\\begin{aligned}\n C_{m_{k}+1,J-m_{k}-1}=-\\frac{S_{k}-m_{k}}{S_{l}-J+m_{k}+1}\\,C_{m_{k},J-m_{k}}. ", "\\label{recurcc}\\end{aligned}$$ The solution to (\\[recurcc\\]) in terms of $C_{0,J}$ is $$\\begin{aligned}\n C_{m_{k},J-m_{k}}=\\frac{(-1)^{S_{k}-m_{k}}\\left(\\begin{array}{c} S_{k}+S_{l}-J \\\\ S_{k}-m_{k} \\end{array}\\right)}{(-1)^{S_{k}}\\left(\\begin{array}{c} S_{k}+S_{l}-J \\\\ S_{k} \\end{array}\\right)}\\,C_{0,J}. ", "\\label{solutioncc}\\end{aligned}$$ Therefore by substituting (\\[solutioncc\\]) into (\\[vjform\\]) and recognizing a binomial expansion, the form of $v_{J}$ is found to be $$\\begin{aligned}\n v_{J}&=&\\frac{C_{0,J}}{(-1)^{S_{k}}\\left(\\begin{array}{c} S_{k}+S_{l}-J \\\\ S_{k} \\end{array}\\right)}\\,x^{S_{k}-S_{l}+J}_{k}x^{S_{l}-S_{k}+J}_{l}(x_{k}y_{l}-x_{l}y_{k})^{S_{k}+S_{l}-J} \\nonumber\\\\ \\\\\n &\\propto& x^{2S_{k}-M}_{k}x^{2S_{l}-M}_{l}(x_{k}y_{l}-x_{l}y_{k})^{M}, \\qquad M=S_{k}+S_{l}-J. \\label{vjsolu}\\end{aligned}$$ The over all constant factor is irrelevant. ", "All other vectors of representation $\\mathbf{V}_{J}$ can be obtained from the highest vector $v_{J}$ by applications of operator $J^{-}_{kl}$. Notice that $J^{-}_{kl}$ commutes with the factor $(x_{k}y_{l}-x_{l}y_{k})$ $$\\begin{aligned}\n [\\,J^{-}_{kl}\\,,\\,x_{k}y_{l}-x_{l}y_{k}\\,]=0. ", "\\label{commjminus}\\end{aligned}$$ So that all vectors of representation $\\mathbf{V}_{J}$ are divisible by $$\\begin{aligned}\n (x_{k}y_{l}-x_{l}y_{k})^{M}, \\qquad M=S_{k}+S_{l}-J. \\label{divisor}\\end{aligned}$$ In other words, any vector (polynomial in $x_{k}$, $y_{k}$ and $x_{l}$, $y_{l}$) in the vector space spanned by $\\mathbf{V}_{J}$ has a common factor (\\[divisor\\]). ", "As a consequence, if there is no projection on the states with bond spin values $$\\begin{aligned}\n S_{k}+S_{l}-M_{kl}+1\\leq J\\leq S_{k}+S_{l} \\label{noproj}\\end{aligned}$$ after summation of spins $\\boldsymbol{S}_{k}$ and $\\boldsymbol{S}_{l}$ (*i.e.* no projection on $\\mathbf{V}_{J}$ with $S_{k}+S_{l}-M_{kl}+1\\leq J\\leq S_{k}+S_{l}$), then a factor $$\\begin{aligned}\n (x_{k}y_{l}-x_{l}y_{k})^{M_{kl}} \\label{factorcom}\\end{aligned}$$ can be isolated. *", "i.e.* Any vector in $\\sum^{S_{k}+S_{l}-M_{kl}}_{J=|S_{k}-S_{l}|}\\mathbf{V}_{J}$ would have a common factor (\\[factorcom\\]). ", "Moreover, this fact is independent of whether we are using the Weyl representation or the Schwinger representation of the Lie algebra. ", "Therefore, any solution to (\\[pipsi0\\]) must take the form of (\\[psicom\\]) with the factor $(a^{\\dagger}_{k}b^{\\dagger}_{l}-a^{\\dagger}_{l}b^{\\dagger}_{k})^{M_{kl}}$ isolated. ", "Thus we have proved **Lemma** \\[lemma1\\].", "\n\nNow let us use **Lemma** \\[lemma1\\] to prove the uniqueness condition (\\[condition1\\]) or (\\[condition2\\]). ", "Note that (\\[pipsi0\\]) is valid for each bond $\\langle kl\\rangle$, consequently any ground state $|\\Psi\\rangle$ of the Hamiltonian satisfying (\\[condgrou\\]) and (\\[condgrou1\\]) can be presented in the form $$\\begin{aligned}\n |\\Psi\\rangle=\\prod_{\\langle kl\\rangle}F(a^{\\dagger},b^{\\dagger})(a^{\\dagger}_{k}b^{\\dagger}_{l}-a^{\\dagger}_{l}b^{\\dagger}_{k})^{M_{kl}}|\\mathrm{vac}\\rangle, \\label{groufac}\\end{aligned}$$ where $F(a^{\\dagger},b^{\\dagger})$ is some polynomial in $a^{\\dagger}$’s and $b^{\\dagger}$’s. ", "Now we have to make sure that in (\\[groufac\\]) each vertex (site) should have the correct spin value. ", "By applying $2\\hat{S}_{l}=(a^{\\dagger}_{l}a_{l}+b^{\\dagger}_{l}b_{l})$ to the state $|\\Psi\\rangle$, we realize that the explicit factor in (\\[groufac\\]) contribute to $2S_{l}$ (denoting the eigenvalue of $2\\hat{S}_{l}$) exactly the value $\\sum_{\\langle kl\\rangle}M_{kl}$ which is the sum of powers of $a^{\\dagger}_{l}$ and $b^{\\dagger}_{l}$. A comparison with expression (\\[condition1\\]) or (\\[condition2\\]) shows that if we require this condition $2S_{l}=\\sum_{\\langle kl\\rangle}M_{kl}$, then each site would already have the correct spin value with the presence in (\\[groufac\\]) of the explicit factor only. ", "Therefore the degree of the polynomial in variables $a^{\\dagger}_{l}$ and $b^{\\dagger}_{l}$ is zero. ", "This is true for every site $l$. Therefore the polynomial $F(a^{\\dagger},b^{\\dagger})$ is a constant which can be removed. ", "So that we have proved that the uniqueness condition (\\[condition1\\]) or (\\[condition2\\]) guarantees the existence (through explicit construction in §$\\,\\ref{sec:vbssch}\\,$) and uniqueness of an energy ground state – the VBS state.", "\n\nThe Subsystem and Measures of Entanglement {#sec:subandmeas}\n==========================================\n\nThe VBS states constructed in previous sections §$\\,\\ref{sec:basic}\\,$ and §$\\,\\ref{sec:generalized}\\,$ as ground states of AKLT models are highly entangled states. ", "The quantification of entanglement is our main subject of study.", "\n\nThe Block Density Matrix and the Block Hamiltonian {#sec:block}\n--------------------------------------------------\n\n### The Block Density Matrix and Entropies {#sec:rhoands}\n\nThe VBS state (see (\\[basicvbs\\]) and (\\[generalizedvbs\\])) has non-trivial entanglement properties. ", "The density matrix of the VBS state is a projector (a pure state density matrix): $$\\begin{aligned}\n \\boldsymbol{\\rho}=\\frac{|\\mathrm{VBS}\\rangle\\langle\\mathrm{VBS}|}{\\langle\\mathrm{VBS}|\\mathrm{VBS}\\rangle}. ", "\\label{purematrix}\\end{aligned}$$ In order to analyze the entanglement, let us cut the original graph (lattice) into two subgraphs (sublattices) $B$ and $E$. That is, we cut through some edges (bonds) such that the resulting graph (or lattice) $B\\cup E$ becomes disconnected (no edge between $B$ and $E$). ", "We may call one of them $B$, the *block*, and the other one $E$ the *environment*. ", "The distinction is somewhat arbitrary and the two subsystems are equivalent in measuring entanglement.", "\n\nLet us focus on the block (subsystem $B$). ", "It is described by the density matrix $\\boldsymbol{\\rho}_{B}$ of the block (obtained by tracing out all degrees of freedom of the environment $E$ from the density matrix $\\boldsymbol{\\rho}$ (\\[purematrix\\])): $$\\begin{aligned}\n \\boldsymbol{\\rho}_{B}=\\mathrm{tr}_{E}\\left[\\,\\boldsymbol{\\rho}\\,\\right]. ", "\\label{rhoa}\\end{aligned}$$ In (\\[rhoa\\]) and below we use subscript $B$ for *block* and $E$ for *environment*. ", "After tracing out all degrees of freedom outside the block the density matrix $\\boldsymbol{\\rho}_{B}$ is, in general, a mixed state density matrix (unless the pure state density matrix $\\boldsymbol{\\rho}$ of the whole system projects on a product state, which is obviously not our case of the VBS state). ", "Formula (\\[rhoa\\]) is the definition of the block (subsystem) density matrix and it satisfies all three requirements of a density matrix:\n\n1. ", " The trace $\\mathrm{tr}_{B}\\left[\\,\\boldsymbol\\rho_{B}\\,\\right]=1$ and hermiticity $\\boldsymbol{\\rho}^{\\dagger}_{B}=\\boldsymbol{\\rho}_{B}$ follow immediately from those of $\\boldsymbol{\\rho}$;\n\n2. ", " The positive semi-definiteness is seen by picking up an arbitrary state $|\\psi\\rangle_{B}$ of the block and realizing that $$\\begin{aligned}\n {}_{B}\\langle \\psi|\\boldsymbol{\\rho}_{B}|\\psi\\rangle_{B}&=&\\mathrm{tr}_{B}\\left[\\,\\boldsymbol{\\rho}_{B}|\\psi\\rangle_{B}\\langle\\psi|\\,\\right]\\nonumber\\\\\n &=&\\mathrm{tr}_{B}\\left[\\,(\\mathrm{tr}_{E}\\boldsymbol{\\rho})|\\psi\\rangle_{B}\\langle\\psi|\\,\\right]\\nonumber\\\\\n &=&\\mathrm{tr}\\left[\\,\\boldsymbol{\\rho}\\,|\\psi\\rangle_{B}\\langle \\psi|\\otimes I_{E}\\,\\right]\\geq 0,\\end{aligned}$$ because of the positive semi-definiteness of $\\boldsymbol{\\rho}$ ($I_{E}$ is the identity of the environment).", "\n\nThe density matrix $\\boldsymbol{\\rho}_{B}$ is a central quantity in description of the subsystem (block). ", "It contains all correlation functions in the VBS ground state as matrix entries [@AAH; @JK; @KHH; @XKHK]. (", "The relation between elements of the density matrix and correlation functions is given in §$\\,\\ref{sec:denandcorr}\\,$.) It is essential in measuring the entanglement which is our main subject.", "\n\nThe entanglement can be measured or *quantified* by the von Neumann entropy $$\\begin{aligned}\n S_{\\mathrm{v\\ N}}=-\\mathrm{tr_{B}}\\left[\\,\\boldsymbol{\\rho}_{B}\\ln\\boldsymbol{\\rho}_{B}\\,\\right] =-\\sum_{\\lambda\\neq 0}\\lambda\\ln\\lambda \\label{vnentropy}\\end{aligned}$$ or the Rényi entropy $$\\begin{aligned}\n S_{\\mathrm{R}}(\\alpha)=\\frac{1}{1-\\alpha}\\ln\\left\\{\\mathrm{tr}_{B}\\left[\\,\\boldsymbol{\\rho}^{\\alpha}_{B}\\,\\right]\\right\\}=\\frac{1}{1-\\alpha}\\ln\\left(\\sum_{\\lambda\\neq 0}\\lambda^{\\alpha}\\right), \\qquad \\alpha>0.\\end{aligned}$$ Here $\\lambda$’s are (non-zero) eigenvalues of the density matrix $\\boldsymbol{\\rho}_{B}$. The corresponding eigenvector is denoted by $|\\lambda\\rangle$. *i.e.* $$\\begin{aligned}\n \\boldsymbol{\\rho}_{B}|\\lambda\\rangle=\\lambda|\\lambda\\rangle, \\qquad \\lambda\\neq 0.\\end{aligned}$$ The Rényi entropy depends on an arbitrary parameter $\\alpha$. If we know the Rényi entropy at any $\\alpha$, then we know all eigenvalues of the density matrix. ", "Note that the Rényi entropy can be regarded a generalization of the von Neumann entropy and reduces to the latter in the limit $\\alpha\\to 1$. The von Neumann entropy is a proper extension of the Gibbs entropy (in statistical mechanics) and the Shannon entropy (in information theory) to the quantum case. (", "The Shannon entropy measures the uncertainty associated with a classical probability distribution. ", "Whereas in quantum case a density operator replaces a classical distribution.) ", "It was shown by using the Schmidt decomposition (Section $2.5$ of [@NC]) that non-zero eigenvalues of the density matrix of subsystem $B$ (block) is equal to those of the density matrix of subsystem $E$ (environment). ", "So that the two subsystems are equivalent in measuring entanglement in terms of entanglement entropies, *i.e.* $S_{\\mathrm{v\\ N}}[B]=S_{\\mathrm{v\\ N}}[E]$ and $S_{\\mathrm{R}}[B]=S_{\\mathrm{R}}[E]$. This fact has been used in obtaining entanglement entropies of $1$-dimensional VBS states as in [@FKR; @KHH] instead of diagonalizing the density matrix directly. ", "We will study the entropies in detail in following sections.", "\n\n### The Block Hamiltonian {#sec:blockhamil}\n\nThe AKLT block density matrix $\\boldsymbol{\\rho}_{B}$ possesses certain characteristic properties which distinguish the VBS states from others. ", "We shall show in §$\\,\\ref{sec:den0spec}\\,$ that the spectrum of the density matrix $\\boldsymbol{\\rho}_{B}$ contains a lot of zero eigenvalues. ", "In order to understand this and give the subsystem (block) a more complete description, we first introduce the Hamiltonian of the subsystem (called the *block* Hamiltonian).", "\n\nThe *block* Hamiltonian $H_{B}$ is the sum of Hamiltonian densities $H(k,l)$ with both $k\\in B$ and $l\\in B$, *i.e.* nearest neighbor interactions (bond terms) within the block $B$: $$\\begin{aligned}\n H_{B}=\\sum_{\\langle kl\\rangle\\in B}H(k,l),\\qquad k\\in B, \\quad l\\in B. \\label{subsystemh}\\end{aligned}$$ Here $H(k,l)$ is given in (\\[basichd\\]) for the basic model and (\\[generalizedhd\\]) for the generalized model, for $k$ and $l$ connected by an edge (bond). ", "In (\\[subsystemh\\]) no cut edges are present (boundary edges between subgraphs $B$ and $E$ removed). ", "In other words, the block Hamiltonian is the *internal* interactions of the subsystem $B$. This Hamiltonian has degenerate ground states because uniqueness conditions (\\[basiccond\\]) and (\\[condition1\\]) are no longer valid.", "\n\nLet us discuss the degeneracy of ground states of the block Hamiltonian (\\[subsystemh\\]). ", "Let us denote by $N_{\\partial B}$ the number of vertices on the boundary $\\partial B$ of the block $B$. The boundary consists of vertices (sites) with several incident edges (bonds) being cut, see Figure \\[figure2\\].", "\n\n![", "Example of the cutting for the basic model. ", "The curved double line represents the boundary between the two subgraphs. ", "We have the block $B$ on the left and the environment $E$ on the right. ", "Solid lines represent edges (bonds) while dashed lines represent cut edges (cut bonds). ", "Each dashed line connects two dots. ", "All vertices in the figure belong to the boundary of $B$ or $E$ because of the presence of one or more cut incident edges (dashed lines).[]{data-label=\"figure2\"}](figure2.eps){width=\"2.9in\"}\n\nThe degeneracy of ground states of $H_{B}$ (which is abbreviated by $deg$) is given by the Katsura’s formula $$\\begin{aligned}\n deg=\\prod_{l\\in \\partial B}\\left[\\left(\\sum_{k \\in \\partial E}M_{kl}\\right)+1\\right], \\qquad \\langle kl\\rangle\\in\\{\\mathrm{cut\\ edges}\\}. ", "\\label{generalizeddeg}\\end{aligned}$$ Here $\\partial B$ denotes vertices (sites) on the boundary of the block $B$ and $\\partial E$ are vertices (sites) on the boundary of the environment $E$. In (\\[generalizeddeg\\]) we have $N_{\\partial B}$ terms in the product. ", "Formula (\\[generalizeddeg\\]) is valid for both the basic and the generalized model. ", "For the basic model all $M_{kl}=1$, including those corresponding to cut edges. ", "Take, for example, a particularly simple case that each vertex on the boundary of the block $\\partial B$ was connected to exactly one vertex on the boundary of the environment $\\partial E$. Then the degeneracy $deg=2^{N_{\\partial B}}$. A general proof of formula (\\[generalizeddeg\\]) is given in the next section §$\\,\\ref{sec:deg}\\,$. The subspace spanned by the degenerate ground states is called the *ground space*, with the dimension given by $deg$ in (\\[generalizeddeg\\]). ", "We emphasize at this point that the block $B$ should contain more than one vertices, otherwise we have a trivial case that the block Hamiltonian vanishes $H_{B}=0$ and the whole Hilbert space become the *ground space*. ", "We discuss the density matrix for a single vertex block at the end of §$\\,\\ref{sec:den0spec}\\,$. The spectrum of the density matrix $\\boldsymbol{\\rho}_{B}$ is closely related to the block Hamiltonian. ", "The density matrix is a projector onto the ground space multiplied by another matrix. ", "We shall prove this statement for an arbitrary graph or lattice in §$\\,\\ref{sec:den0spec}\\,$.\n\nThe Degeneracy of Ground States of the Block Hamiltonian {#sec:deg}\n--------------------------------------------------------\n\nWe prove Katsura’s formula (\\[generalizeddeg\\]) for the degeneracy of ground states of the block Hamiltonian. ", "The proof applies to both the basic and the generalized models. ", "The block Hamiltonian is defined in (\\[subsystemh\\]). ", "Let us first look at the uniqueness condition (\\[condition1\\]). (", "The condition (\\[basiccond\\]) for the basic model is a special case of this general one.) ", "For an arbitrary vertex (site) $l$ in the block $B$, the condition can be written as $$\\begin{aligned}\n 2S_{l}=\\sum_{k}M_{kl}=\\sum_{k\\in B}M_{kl}+\\sum_{k\\in \\partial E}M_{kl}, \\qquad l\\in B. \\label{split}\\end{aligned}$$ Note that the sum over vertices $k\\in \\partial E$ is *outside* the block $B$. These terms are only present for boundary vertices $l\\in \\partial B$. Expression (\\[split\\]) is valid for *any* vertex in the block (for a bulk vertex the last summation vanishes). ", "Next we define *the block VBS state* $$\\begin{aligned}\n |\\mathrm{VBS}_{N_{B}}\\rangle=\\prod_{\\langle kl\\rangle\\in B}\n\\left(a^{\\dagger}_{k}b^{\\dagger}_{l}-b^{\\dagger}_{k}a^{\\dagger}_{l}\\right)^{M_{kl}}|\\mathrm{vac}\\rangle, \\qquad k\\in B,\\quad l\\in B. \\label{blockvbs}\\end{aligned}$$ Here edge (bond) $\\langle kl\\rangle$ lies completely inside the block $B$. Now an *arbitrary* ground state of the block Hamiltonian $H_{B}$ takes the following form (see **Lemma** \\[lemma1\\] in §$\\,\\ref{sec:unique}\\,$ which explains the appearance of the factor $(a^{\\dagger}_{k}b^{\\dagger}_{l}-b^{\\dagger}_{k}a^{\\dagger}_{l})^{M_{kl}}$ in (\\[blockvbs\\]) above): $$\\begin{aligned}\n |\\mathrm{G}\\rangle=\\left[\\prod^{N_{\\partial B}\\ \\mathrm{terms}}_{l\\ \\in\\ \\partial B}f(a^{\\dagger}_{l},b^{\\dagger}_{l})\\right]|\\mathrm{VBS}_{N_{B}}\\rangle, \\label{ground}\\end{aligned}$$ where $f(a^{\\dagger}_{l},b^{\\dagger}_{l})$ is a polynomial (it may depend on the vertex $l$) in $a^{\\dagger}_{l}$ and $b^{\\dagger}_{l}$ and the product runs over all boundary vertices (with the total number denoted by $N_{\\partial B}$). ", "The degree of this polynomial is equal to $\\sum_{k\\in \\partial E}M_{kl}$. (Each term in the polynomial must have the same total power $\\sum_{k\\in \\partial E}M_{kl}$ of $a^{\\dagger}_{l}$ and $b^{\\dagger}_{l}$.) It is straightforward to verify that $|\\mathrm{G}\\rangle$ in (\\[ground\\]) is a ground state:\n\n1. ", " The power of $a^{\\dagger}_{l}$ and $b^{\\dagger}_{l}$ in $|\\mathrm{VBS}_{N_{B}}\\rangle$ is $\\sum_{k\\in B}M_{kl}$ (see (\\[blockvbs\\])), so that the total power of $a^{\\dagger}_{l}$ and $b^{\\dagger}_{l}$ in (\\[ground\\]) is $\\sum_{k\\in B}M_{kl}+\\sum_{k\\in \\partial E}M_{kl}=2S_{l}$ according to (\\[split\\]). ", "Therefore, we have the correct power $2S_{l}$ of the bosonic operators $a^{\\dagger}_{l}$ and $b^{\\dagger}_{l}$ for each vertex $l$ in the block $B$ (constraint (\\[constraintspin\\]) is satisfied);\n\n2. ", " There is no projection on any bond (edge) spin value greater than or equal to $S_{k}+S_{l}-M_{kl}+1$ because of the construction of the block VBS state (\\[blockvbs\\]). (", "One could use the same reasoning as in §$\\,\\ref{sec:generalized}\\,$).", "\n\nTherefore the degeneracy $deg$ of the ground states of $H_{B}$ is equal to the number of linearly independent states of the form (\\[ground\\]). ", "Since $a^{\\dagger}_{l}$’s and $b^{\\dagger}_{l}$’s are bosonic and commute, the number of linearly independent polynomials $f(a^{\\dagger}_{l},a^{\\dagger}_{l})$ for an arbitrary $l$ is equal to its degree plus one, *i.e.* $$\\begin{aligned}\n \\left(\\sum_{k\\in \\partial E}M_{kl}\\right)+1,\\qquad \\forall\\ l\\in \\partial B. \\label{degreenum}\\end{aligned}$$ So that the total number of linearly independent polynomials of the form $$\\begin{aligned}\n \\prod^{N_{\\partial B}\\ \\mathrm{terms}}_{l\\ \\in\\ \\partial B}f(a^{\\dagger}_{l},b^{\\dagger}_{l})\\end{aligned}$$ is the product of these numbers (\\[degreenum\\]) for each $l\\in \\partial B$. Finally, the ground state degeneracy of the block Hamiltonian $H_{B}$ is (Katsura’s formula) $$\\begin{aligned}\n deg=\\prod_{l\\in\\partial B}\\left[\\left(\\sum_{k\\in \\partial E}M_{kl}\\right)+1\\right]. ", "\\label{kastura}\\end{aligned}$$ In the case of the basic model all $M_{kl}=1$, formula (\\[kastura\\]) has a graphical illustration, see Figure \\[figure2\\]. ", "We count the number \\# of all cut edges (dashed lines) incident to one boundary vertex of the block, then add one to the number \\#. ", "The degeneracy is the product of these $(\\# +1)$’s for each boundary vertex.", "\n\nGeneral Properties of the Density Matrix {#sec:den0spec}\n----------------------------------------\n\nThe reduced density matrix $\\boldsymbol{\\rho}_{B}$ from a VBS state has important and special spectrum structures which are universal among AKLT models. ", "Let us denote by $N_{B}$ the number of vertices in the block $B$. Then the dimension $dim$ of the Hilbert space of the block $B$ is equal to $\\prod_{l}(2S_{l}+1)$ with $l\\in B$, which is also the dimension of the density matrix $\\boldsymbol{\\rho}_{B}$. The value is $$\\begin{aligned}\n dim=\\prod_{l\\in B}\\left[z_{l}+1\\right], \\label{basicdima}\\end{aligned}$$ for the basic model and $$\\begin{aligned}\n dim=\\prod_{l\\in B}\\left[\\left(\\sum_{k\\in (B\\cup\\partial E)}M_{kl}\\right)+1\\right], \\label{generalizeddima}\\end{aligned}$$ for the generalized model. ", "In both expressions (\\[basicdima\\]) and (\\[generalizeddima\\]) we have $N_{B}$ factors in the product. ", "Take, for example, a particularly simple basic model in which each vertex is connected with the same number $z$ of vertices, including those corresponding to boundary vertices (such as in the case of a lattice). ", "Then the dimension $dim=(z+1)^{N_{B}}$. The density matrix $\\boldsymbol{\\rho}_{B}$ would have $dim$ number of eigenvalues. ", "However, most of the eigenvalues are vanishing and $\\boldsymbol{\\rho}_{B}$ is a projector onto a much smaller subspace multiplied by another matrix. ", "To prove this statement, we define a *support* to be the subspace of the Hilbert space of the block $B$ with non-zero eigenvalues, *i.e.* it is spanned by eigenstates of $\\boldsymbol{\\rho}_{B}$ with non-zero eigenvalues. ", "The dimension of the support is denoted by $D$. Then We have the following theorem on the structure of the density matrix $\\boldsymbol{\\rho}_{B}$ (Assuming that the block have more than one vertices, *i.e.* $N_{B}\\geq 2$, so that $H_{B}$ is not equal to zero identically):\n\n\\[theorem1\\] The *support* of $\\boldsymbol{\\rho}_{B}$ (\\[rhoa\\]) is a subspace of the *ground space* of the block Hamiltonian $H_{B}$ (\\[subsystemh\\]).", "\n\nTo prove the theorem, we recall that $H=\\sum_{\\langle kl\\rangle\\in B}H(k,l)$ and each $H(k,l)$ is a sum of projectors (\\[generalizedhd\\]). ", "We have $H(k,l)\\geq 0$. Then the construction of the VBS ground state (\\[basicvbs\\]) and (\\[generalizedvbs\\]) guarantees that there is no projection onto the subspace with higher bond spins ($J\\geq S_{k}+S_{l}-M_{kl}+1$) for *any* bond (edge). (", "See §$\\,\\ref{sec:unique}\\,$ for the proof.) ", "Therefore, $$\\begin{aligned}\n H(k,l)|\\mathrm{VBS}\\rangle=0, \\qquad \\forall\\ \\langle kl\\rangle. ", "\\label{noprojection}\\end{aligned}$$ In particular, this is true for bonds (edges) *inside* the block $B$, *i.e.* both $k\\in B$ and $l\\in B$. Now, from the definition of $\\boldsymbol{\\rho}_{B}$ in ($\\ref{rhoa}$), we have $$\\begin{aligned}\n H(k,l)\\boldsymbol{\\rho}_{B}&=&H(k,l)\\mathrm{tr}_{E}\\left[\\,\\boldsymbol{\\rho}\\,\\right]\n\\nonumber \\\\\n&=&\\frac{H(k,l)\\mathrm{tr}_{E}\\left[\\,|\\mathrm{VBS}\\rangle\\langle \\mathrm{VBS}|\\,\\right]}{\\langle \\mathrm{VBS}|\\mathrm{VBS}\\rangle}\n\\nonumber \\\\\n&=&\\frac{\\mathrm{tr}_{E}\\left[\\,H(k,l)|\\mathrm{VBS}\\rangle\\langle \\mathrm{VBS}|\\,\\right]}{\\langle \\mathrm{VBS}|\\mathrm{VBS}\\rangle} \\nonumber\\\\\n&=&0, \\qquad k\\in B, \\quad l\\in B. \\label{proof}\\end{aligned}$$ In the last step of (\\[proof\\]) we have used (\\[noprojection\\]) and the fact that bond (edge) $\\langle kl\\rangle$ lies completely inside the block $B$ so that $H(k,l)$ commutes with the tracing operation in the environment $E$. Equation (\\[proof\\]) is true for any bond (edge) in $B$, so that $$\\begin{aligned}\n H_{B}\\boldsymbol{\\rho}_{B}=\\sum_{\\langle kl\\rangle\\in B}H(k,l)\\boldsymbol{\\rho}_{B}=0, \\qquad k\\in B, \\quad l\\in B. \\label{harhoa}\\end{aligned}$$ If we diagonalize the density matrix $\\boldsymbol{\\rho}_{B}$ $$\\begin{aligned}\n \\boldsymbol{\\rho}_{B}=\\sum_{\\lambda\\neq 0}\\lambda\\,|\\lambda\\rangle\\langle \\lambda|, \\label{diag}\\end{aligned}$$ where $|\\lambda\\rangle$ is the eigenstate corresponding to eigenvalue $\\lambda$. Then (\\[harhoa\\]) can be re-written as $$\\begin{aligned}\n H_{B}\\sum_{\\lambda\\neq 0}\\lambda|\\lambda\\rangle\\langle \\lambda|=\\sum_{\\lambda\\neq 0}\\lambda H_{B}|\\lambda\\rangle\\langle \\lambda|=0, \\label{eigenstate}\\end{aligned}$$ Note that $\\{|\\lambda\\rangle\\}$ is a linearly independent set. ", "Therefore the solution of (\\[eigenstate\\]) means that $$\\begin{aligned}\n H_{B}|\\lambda\\rangle=0, \\qquad \\lambda\\neq 0. ", "\\label{solution}\\end{aligned}$$ Expression (\\[solution\\]) states that any eigenstate of $\\boldsymbol{\\rho}_{B}$ (with non-zero eigenvalue) is a ground state of $H_{B}$. As a result, we have proved **Theorem** \\[theorem1\\] that the *support* of $\\boldsymbol{\\rho}_{B}$ is a subspace of the *ground space* of $H_{B}$, so that $D\\leq deg$. The density matrix takes the form of a projector multiplied by another matrix (a constant matrix depending on non-vanishing eigenvalues) and the projector projects on the *ground space*.", "\n\nAlso, it is clear from expressions (\\[generalizeddeg\\]) and (\\[basicdima\\]), (\\[generalizeddima\\]) that $deg \\leq dim$ ($\\partial B\\subseteq B$ so that $N_{\\partial B}\\leq N_{B}$). ", "Usually, $deg$ is much smaller than $dim$ because the former involves only contributions from boundary vertices (sites) of the block while the latter also involves contributions from all bulk vertices (sites). ", "Then as a corollary of **Theorem** \\[theorem1\\], we have $$\\begin{aligned}\n D\\leq deg\\leq dim .\\end{aligned}$$\n\nIf the block $B$ consists of only one vertex with a spin-$S$, then we *conjecture* that it is in the maximally entangled state. ", "The *support* has dimension $D=2S+1$.\n\nThe One–dimensional Spin–1 Model {#sec:1dspin1}\n================================\n\nOne of the most simple models is defined on a $1$-dimensional lattice with spin-$1$’s in the bulk and spin-$1/2$’s at both ends. ", "We shall denote by $\\boldsymbol{S}_{j}$ the vector spin operator at site $j$ ($j=0,1,\\ldots,N+1$). ", "The Hamiltonian is $$\\begin{aligned}\n H=\\frac{1}{2}\\sum^{N-1}_{j=1} \\left(\\boldsymbol{S}_{j}\\cdot\\boldsymbol{S}_{j+1}+\\frac{1}{3}\\left(\\boldsymbol{S}_{j}\\cdot\\boldsymbol{S}_{j+1}\\right)^{2}+\\frac{2}{3}\\right)+\\pi_{\\frac{3}{2}}(0,1)+\\pi_{\\frac{3}{2}}(N,N+1).\\nonumber\\\\ \\label{uniq1}\\end{aligned}$$ Each bulk term is a projector $\\pi_{2}$ onto the states with bond spin-$2$. The boundary terms $\\pi_{3/2}$ describe interactions of a spin-$1/2$ on the boundary and a spin-$1$ in the bulk. ", "Each term is a projector onto the states with bond spin-$3/2$: $$\\begin{aligned}\n \\pi_{\\frac{3}{2}}(0,1)=\\frac{2}{3}\\left(1+\\boldsymbol{S}_{0}\\cdot\\boldsymbol{S}_{1}\\right), \\qquad \\pi_{\\frac{3}{2}}(N,N+1)=\\frac{2}{3}\\left(1+\\boldsymbol{S}_{N}\\cdot\\boldsymbol{S}_{N+1}\\right). ", "\\label{boun1}\\end{aligned}$$ The choice of boundary terms guarantees the uniqueness of the ground state. ", "As mentioned before, if we have spin-$1$ at every site in (\\[uniq1\\]) instead, the ground state would become $4$-fold degenerate.", "\n\nIn this section we study the entanglement of the unique VBS ground state of this $1$-dimensional spin-$1$ model. ", "As to be shown below, the density matrix $\\boldsymbol{\\rho}_{L}$ of a block of $L$ contiguous spins is diagonalizable. ", "It has four non-zero eigenvalues: $$\\begin{aligned}\n \\Lambda_{\\alpha}=\\left\\{ \\begin{array}{cc}\n \\frac{1}{4}(1+3(-\\frac{1}{3})^{L}), & \\alpha=0;\\\\ \\\\\n \\frac{1}{4}(1-(-\\frac{1}{3})^{L}), & \\alpha=1, 2, 3. ", "\\end{array}\\right. ", "\\label{eigval1rep}\\end{aligned}$$ These eigenvalues depend on the length $L$ of the block subsystem and are independent of the size of the whole spin chain. ", "The von Neumann entropy and the Rényi entropy derived from these eigenvalues are $$\\begin{aligned}\n S_{\\mathrm{v\\ N}}&=&\\ln4-\\frac{1}{4}(1+3(-\\frac{1}{3})^{L})\\ln(1+3(-\\frac{1}{3})^{L})\\nonumber\\\\\n &&-\\frac{3}{4}(1-(-\\frac{1}{3})^{L})\\ln(1-(-\\frac{1}{3})^{L})\\nonumber\\\\ \\nonumber\\\\\n S_{\\mathrm{R}}(\\alpha)&=&\\frac{1}{1-\\alpha}\\ln\\left\\{\\left[\\frac{1}{4}(1+3(-\\frac{1}{3})^{L})\\right]^{\\alpha}+3\\left[\\frac{1}{4}(1-(-\\frac{1}{3})^{L})\\right]^{\\alpha}\\right\\}. ", "\n \\label{entropies}\\end{aligned}$$ Note that the parameter $\\alpha$ in the Rényi entropy should not be confused with the label $\\alpha$ for the eigenvalues in (\\[eigval1rep\\]).", "\n\nThe VBS Ground State {#sec:1dspin1VBS}\n--------------------\n\nGiven the Hamiltonian (\\[uniq1\\]), we are going to use the pictorial method (see §$\\,\\ref{sec:graphvbs}\\,$) to construct the unique VBS ground state. ", "In order to represent the state, we first introduce the following notation for convenience [@FKR]: $$\\begin{aligned}\n |\\alpha\\rangle \\equiv (-1)^{1+\\delta_{\\alpha, 0}}I\\otimes\\sigma_{\\alpha}|0\\rangle, \\qquad \\alpha=0, 1, 2, 3 \\label{alph}\\end{aligned}$$ where $\\sigma_{0}\\equiv I$ (2-dimensional identity), $\\sigma_{\\alpha=1, 2, 3}$ are standard Pauli matrices and $|0\\rangle\\equiv -(|\\uparrow\\downarrow\\rangle-|\\downarrow\\uparrow\\rangle)/\\sqrt{2}$ is the singlet state (antisymmetric projection) of two spin-$1/2$’s. (", "It corresponds to the antisymmetrized state $|\\Phi\\rangle$ in §$\\,\\ref{sec:graphvbs}\\,$.) These four states (\\[alph\\]) (called *maximally entangled states*) form an orthonormal basis of the Hilbert space of two spin-$1/2$ operators.", "\n\nThe spin-$1$ state at each site is represented by a symmetric projection of two spin-$1/2$ states given by (\\[alph\\]) for $\\alpha=1, 2, 3$. Let us take the $j^{\\mathrm{th}}$ site for example, see Figure \\[fig:Figure3\\].", "\n\n![", "Graphical representation of the VSB ground state for the $1$-dimensional spin-$1$ model: Each spin-$1$ is realized by a pair of spin-$1/2$’s which are represented by small black dots in the figure. ", "The pair of spin-$1/2$ states at site $j$ are labeled $j$, $\\bar{j}$. The solid lines connecting two neighboring dots ($\\bar{j}$ and $j+1$) represent anti-symmetrization of two spin-$1/2$’s; The large circles enclosing two dots ($j$ and $\\bar{j}$) represent symmetrization at each site. ", "The boundary spin-$1/2$’s are labeled $\\bar{0}$ and $N+1$ in consistency with the prescription.[]{data-label=\"fig:Figure3\"}](figure3.eps){width=\"5in\"}\n\nThe two spin-$1/2$’s are labeled by $(j, \\bar{j})$ (from left to right, respectively). ", "Then the spin-$1$ states are prepared by projecting these two spin-$1/2$’s (4-dimensional space) onto a symmetric 3-dimensional subspace spanned by $$\\begin{aligned}\n |1\\rangle_{j\\bar{j}} &=& \\frac{1}{\\sqrt{2}}(|\\uparrow\\rangle_{j}|\\uparrow\\rangle_{\\bar{j}}-|\\downarrow\\rangle_{j}|\\downarrow\\rangle_{\\bar{j}}), \\nonumber \\\\\n |2\\rangle_{j\\bar{j}} &=& \\frac{-i}{\\sqrt{2}}(|\\uparrow\\rangle_{j}|\\uparrow\\rangle_{\\bar{j}}+|\\downarrow\\rangle_{j}|\\downarrow\\rangle_{\\bar{j}}), \\nonumber \\\\\n |3\\rangle_{j\\bar{j}} &=& \\frac{-1}{\\sqrt{2}}(|\\uparrow\\rangle_{j}|\\downarrow\\rangle_{\\bar{j}}+|\\downarrow\\rangle_{j}|\\uparrow\\rangle_{\\bar{j}}). ", "\\label{3j}\\end{aligned}$$ Thus the two ending spin-$1/2$’s are labeled as site $\\bar{0}$ and $N+1$, consistently (Figure \\[fig:Figure3\\]). ", "The unique VBS ground state in this representation is [@AKLT1; @AKLT2; @FKR] $$\\begin{aligned}\n |\\mathrm{VBS}\\rangle=\\left(\\bigotimes^{N}_{j=1}\\mathbf{P}_{j\\bar{j}}\\right)|0\\rangle_{\\bar{0}1}|0\\rangle_{\\bar{1}2}\\cdots|0\\rangle_{\\bar{N}N+1}. ", "\\label{grou1}\\end{aligned}$$ Here $\\mathbf{P}_{j\\bar{j}}$ projects two spin-$1/2$ states onto a symmetric subspace, which describes spin-$1$. Using basis (\\[alph\\]), we have $$\\begin{aligned}\n \\mathbf{P}_{j\\bar{j}}=\\sum^{3}_{\\alpha=1}|\\alpha\\rangle_{j\\bar{j}}\\langle \\alpha|. ", "\\label{proj}\\end{aligned}$$ This projector $\\mathbf{P}_{j\\bar{j}}$ serves the same purpose as the symmetrization operator $\\mathbf{P}(l)$ in §$\\,\\ref{sec:graphvbs}\\,$ and their results acting on a product state of spin-$1/2$’s only differ by a normalization. ", "We use the projector $\\mathbf{P}_{j\\bar{j}}$ for convenience here.", "\n\nA crucial step (see [@FKR]) is that the ground state (\\[grou1\\]) can be expressed in a different form using the following identity $$\\begin{aligned}\n |0\\rangle_{\\bar{A}B}|0\\rangle_{\\bar{B}C}=\\frac{-1}{2}\\sum^{3}_{\\alpha=0}|\\alpha\\rangle_{B\\bar{B}}\\left[I_{\\bar{A}}\\otimes\\left(\\sigma_{\\alpha}\\right)_{C}\\right]|0\\rangle_{\\bar{A}C} \\label{maxi}\\end{aligned}$$ for arbitrary labels (indices) $A$, $B$ and $C$. ", "This identity (\\[maxi\\]) can be verified by direct calculation and comparison. ", "Repeatedly using relation (\\[maxi\\]), the product of $|0\\rangle$’s in (\\[grou1\\]) can be re-written as $$\\begin{aligned}\n &&|0\\rangle_{\\bar{0}1}|0\\rangle_{\\bar{1}2}\\cdots|0\\rangle_{\\bar{N}N+1} \\label{prod} \\\\\n &=&\\left(\\frac{-1}{2}\\right)^{N}\\sum^{3}_{\\alpha_{1}, \\cdots, \\alpha_{N}=0}|\\alpha_{1}\\rangle\\cdots|\\alpha_{N}\\rangle\\left[ I_{\\bar{0}}\\otimes\\left(\\sigma_{\\alpha_{N}}\\cdots\\sigma_{\\alpha_{1}}\\right)_{N+1}\\right]|0\\rangle_{\\bar{0}N+1}. ", "\\nonumber\\end{aligned}$$ Then by projecting onto the symmetric subspace spanned by $|\\alpha=1, 2, 3\\rangle$, the ground VBS state (\\[grou1\\]) takes the form [@VMC]$$\\begin{aligned}\n |\\mathrm{VBS}\\rangle=\\frac{1}{3^{N/2}}\\sum^{3}_{\\alpha_{1}, \\cdots, \\alpha_{N}=1}|\\alpha_{1}\\rangle\\cdots|\\alpha_{N}\\rangle\\left[I_{\\bar{0}}\\otimes\\left(\\sigma_{\\alpha_{N}}\\cdots\\sigma_{\\alpha_{1}}\\right)_{N+1}\\right]|0\\rangle_{\\bar{0}N+1}. ", "\\label{grou}\\end{aligned}$$ Note that this ground state (\\[grou\\]) is normalized and we have re-written the overall phase for it has no physical content.", "\n\nThe Block Density Matrix {#sec:1ds1den}\n------------------------\n\nGiven the ground state in the form (\\[grou\\]), we obtain the density matrix of a block of $L$ contiguous bulk spins starting at site $k$ by tracing out spin degrees of freedom outside the block using basis (\\[alph\\]): $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}\\equiv \\mathrm{tr}_{\\bar{0}, 1, \\ldots, k-1, k+L, \\ldots, N, N+1}\\left[\\,|\\mathrm{VBS}\\rangle\\langle \\mathrm{VBS}|\\,\\right]. ", "\\label{den1}\\end{aligned}$$ (Note that we use subscript $L$ to emphasize the dependence of the density matrix on the size of the block instead of using the general $B$ as representing ‘block’.) ", "In taking the partial trace, we will encounter the following expression in calculation $$\\begin{aligned}\n I_{n}=\\sum^{3}_{\\sigma_{\\alpha_{1}},\\cdots,\\sigma_{\\alpha_{n}}=1} I\\otimes\\left(\\sigma_{\\alpha_{n}}\\cdots\\sigma_{\\alpha_{1}}\\right)|0\\rangle\\langle 0|\\, I\\otimes\\left(\\sigma_{\\alpha_{1}}\\cdots\\sigma_{\\alpha_{n}}\\right), \\qquad n\\geq1 \\label{itera}\\end{aligned}$$ given $I_{0}=|0\\rangle\\langle0|$. To solve this (\\[itera\\]), we introduce iterative coefficients $A_{n}$ and $B_{n}$ and write $$\\begin{aligned}\n I_{n}=A_{n}|0\\rangle\\langle0|+B_{n}\\sum^{3}_{\\beta=1}|\\beta\\rangle\\langle\\beta|, \\qquad n\\geq1.\\end{aligned}$$ Then from (\\[itera\\]) we could write down the expression of $I_{n+1}$ in terms of $A_{n}$ and $B_{n}$. Comparison of coefficients yields the following iteration relation $$\\begin{aligned}\n A_{n+1}=3B_{n}, \\qquad B_{n+1}=A_{n}+2B_{n}, \\qquad n\\geq1 \\label{anbn}\\end{aligned}$$ with $A_{0}=1$ and $B_{0}=0$. The solution to (\\[anbn\\]) is $$\\begin{aligned}\n A_{n}=\\frac{1}{4}\\left(3^{n}+3(-1)^{n}\\right), \\qquad B_{n}=\\frac{1}{4}\\left(3^{n}-(-1)^{n}\\right).\\end{aligned}$$ As a result, we have found that $$\\begin{aligned}\n I_{n}=\\frac{1}{4}\\left(3^{n}+3(-1)^{n}\\right)|0\\rangle\\langle0|+\\frac{1}{4}\\left(3^{n}-(-1)^{n}\\right)\\sum^{3}_{\\beta=1}|\\beta\\rangle\\langle\\beta|. ", "\\label{inexpp}\\end{aligned}$$ Using (\\[inexpp\\]), it is straightforward to take the partial trace in (\\[den1\\]). ", "The result is independent of the starting site $k$ and the total length $N$ (see [@FKR]). (", "So that the density matrix is translational invariant though the whole spin chain Hamiltonian does not have complete translational invariance because of the boundary conditions.) ", "We choose $k=1$ (*i.e.* re-label the indices of sites for notational convenience) so that the density matrix reads [@FKR] $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L} \\label{matr1}=\n \\frac{1}{3^{L}}\\sum^{3}_{\\alpha, \\alpha^{\\prime}=1}|\\alpha_{1}\\rangle \\langle\\alpha^{\\prime}_{1}|\\cdots|\\alpha_{L}\\rangle \\langle\\alpha^{\\prime}_{L}|\\,\\langle 0|I\\otimes (\\sigma_{\\alpha^{\\prime}_{1}}\\cdots\\sigma_{\\alpha^{\\prime}_{L}})I\\otimes (\\sigma_{\\alpha_{L}}\\cdots\\sigma_{\\alpha_{1}})|0\\rangle.%_{\\bar{0}L+1}. ", "\n\\nonumber\\\\\\end{aligned}$$\n\nGround States of the Block Hamiltonian {#sec:1ds1gsbh}\n--------------------------------------\n\nThe block in $1$-dimension is $L$ contiguous bulk spins. ", "The block Hamiltonian $H_{B}$ by definition (\\[subsystemh\\]) reads $$\\begin{aligned}\n H_{B}=\\frac{1}{2}\\sum^{L-1}_{j=1} \\left(\\boldsymbol{S}_{j}\\cdot\\boldsymbol{S}_{j+1}+\\frac{1}{3}\\left(\\boldsymbol{S}_{j}\\cdot\\boldsymbol{S}_{j+1}\\right)^{2}+\\frac{2}{3}\\right). ", "\\label{degel1}\\end{aligned}$$ Any linear combination of states of the following form $$\\begin{aligned}\n |\\mathrm{G}; \\chi_{1}, \\chi_{\\bar{L}}\\rangle\n\\equiv\\left(\\bigotimes^{L}_{j=1}\\mathbf{P}_{j\\bar{j}}\\right)|\\chi_{1}\\rangle_{1}|0\\rangle_{\\bar{1}2}|0\\rangle_{\\bar{2}3}\\cdots|0\\rangle_{\\overline{L-1}L}|\\chi_{\\bar{L}}\\rangle_{\\bar{L}} \\label{dgini}\\end{aligned}$$ is a ground state of the block Hamiltonian (\\[degel1\\]). ", "In (\\[dgini\\]) we have made notation $|\\chi\\rangle \\equiv |\\uparrow \\mathrm{or} \\downarrow\\rangle$ represents the two spin-$1/2$ states and $\\mathbf{P}_{j\\bar{j}}$ is defined in (\\[proj\\]). ", "Let us make a particular linear combination of these $|\\mathrm{G}; \\chi_{1}, \\chi_{\\bar{L}}\\rangle$ states using (\\[alph\\]) and write the four ($\\alpha=0,1,2,3$) linearly independent ground states of the block Hamiltonian (\\[degel1\\]) as follows $$\\begin{aligned}\n |\\mathrm{VBS}; \\alpha\\rangle\n\\equiv\\left(\\bigotimes^{L}_{j=1}\\mathbf{P}_{j\\bar{j}}\\right)|\\alpha\\rangle_{\\bar{L}1}|0\\rangle_{\\bar{1}2}|0\\rangle_{\\bar{2}3}\\cdots|0\\rangle_{\\overline{L-1}L}. ", "\\label{dgalph}\\end{aligned}$$ Note that we have changed the label G to VBS and these 4 states in (\\[dgalph\\]) are called *degenerate VBS states*. ", "Now we go through the same steps as from (\\[grou1\\]) to (\\[grou\\]), the resultant form of the four ground states ($\\alpha=0, 1, 2, 3$) is $$\\begin{aligned}\n |\\mathrm{VBS}; \\alpha\\rangle=\n \\sum^{3}_{\\alpha_{1}, \\cdots, \\alpha_{L}=1}|\\alpha_{1}\\rangle\\cdots|\\alpha_{L}\\rangle\\,\\langle\\alpha_{L}|\\sigma_{\\alpha}\\otimes\\left(\\sigma_{\\alpha_{L-1}}\\cdots\\sigma_{\\alpha_{1}}\\right)|0\\rangle.", "\n \\label{galph}\\end{aligned}$$ Again we have re-written the overall phase for simplicity. ", "These four states are orthogonal, and the normalization is given by (the calculation is similar to that of $A_{n}$ and $B_{n}$ in (\\[anbn\\])) $$\\begin{aligned}\n \\langle \\mathrm{VBS}; \\alpha|\\mathrm{VBS}; \\alpha\\rangle=\\left\\{ \\begin{array}{cc}\n \\frac{1}{4}(3^{L}+3(-1)^{L}), & \\alpha=0;\\\\ \\\\\n \\frac{1}{4}(3^{L}-(-1)^{L}), & \\alpha=1, 2, 3. ", "\\end{array}\\right. ", "\\label{norm}\\end{aligned}$$\n\nSpectrum of the Density Matrix {#sec:1ds1specden}\n------------------------------\n\nAccording to **Theorem** \\[theorem1\\], the eigenvectors corresponding to non-zero eigenvalues of the density matrix (\\[matr1\\]) are degenerate ground states of the block Hamiltonian (\\[degel1\\]). ", "These are exactly the degenerate VBS states found in (\\[galph\\]). ", "Let us apply $\\boldsymbol{\\rho}_{L}$ to $|\\mathrm{VBS}; \\alpha\\rangle$ and use orthogonality of the $|\\alpha\\rangle$ states. ", "Then we obtain $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}|\\mathrm{VBS}; \\alpha\\rangle=\\frac{1}{3^{L}}\\sum^{3}_{\\alpha_{1}, \\cdots, \\alpha_{L}=1}|\\alpha_{1}\\rangle\\cdots|\\alpha_{L}\\rangle\\,C_{\\alpha_{1}\\cdots\\alpha_{L}} \\label{rhoga}\\end{aligned}$$ with coefficient $$\\begin{aligned}\n C_{\\alpha_{1}\\cdots\\alpha_{L}}&=&\\sum^{3}_{\\alpha^{\\prime}_{1}, \\cdots, \\alpha^{\\prime}_{L}=1}\n\\langle\\alpha^{\\prime}_{L}|\\sigma_{\\alpha}\\otimes(\\sigma_{\\alpha^{\\prime}_{L-1}}\\cdots\\sigma_{\\alpha^{\\prime}_{1}})|0\\rangle \\label{coef} \\\\\n &&\n\\cdot\\langle 0|I\\otimes (\\sigma_{\\alpha^{\\prime}_{1}}\\cdots\\sigma_{\\alpha^{\\prime}_{L}}) \nI\\otimes (\\sigma_{\\alpha_{L}}\\cdots\\sigma_{\\alpha_{1}})|0\\rangle.", "\n\\nonumber\\end{aligned}$$ Using the same method of induction as in obtaining $A_{n}$ and $B_{n}$ in (\\[anbn\\]), we have $$\\begin{aligned}\n \\sum^{3}_{\\alpha^{\\prime}_{1}, \\cdots, \\alpha^{\\prime}_{L-1}=1}\n(I\\otimes\\sigma_{\\alpha^{\\prime}_{L-1}}\\cdots\\sigma_{\\alpha^{\\prime}_{1}})|0\\rangle\n\\langle 0|(I\\otimes \\sigma_{\\alpha^{\\prime}_{1}}\\cdots\\sigma_{\\alpha^{\\prime}_{L-1}})=\n\\sum^{3}_{\\beta=0}A_{\\beta}|\\beta\\rangle\\langle \\beta| \\label{indu}\\end{aligned}$$ with $$\\begin{aligned}\n A_{\\beta}=\\left\\{ \\begin{array}{cc}\n \\frac{1}{4}(3^{L-1}+3(-1)^{L-1}), & \\beta=0;\\\\ \\\\\n \\frac{1}{4}(3^{L-1}-(-1)^{L-1}), & \\beta=1, 2, 3. ", "\\end{array}\\right. ", "\\label{indu2}\\end{aligned}$$ Therefore the coefficient $C_{\\alpha_{1}\\cdots\\alpha_{L}}$ defined in (\\[coef\\]) can be simplified as $$\\begin{aligned}\n C_{\\alpha_{1}\\cdots\\alpha_{L}}\n =\\sum^{3}_{\\alpha^{\\prime}_{L}=1, \\beta=0}\n A_{\\beta}\\langle\\alpha^{\\prime}_{L}|\\sigma_{\\alpha}\\otimes I|\\beta\\rangle\n \\langle \\beta|I\\otimes (\\sigma_{\\alpha^{\\prime}_{L}}\\sigma_{\\alpha_{L}}) \n I\\otimes (\\sigma_{\\alpha_{L-1}}\\cdots\\sigma_{\\alpha_{1}})|0\\rangle. ", "\\nonumber\\\\\n\\label{coefind}\\end{aligned}$$ Straightforward calculation using multiplication rules of Pauli matrices shows that (\\[coefind\\]) can be further simplified as $$\\begin{aligned}\n &&C_{\\alpha_{1}\\cdots\\alpha_{L}}=\n 3A_{1}\\delta_{\\alpha,0}\\langle\\alpha_{L}|I\\otimes (\\sigma_{\\alpha_{L-1}}\\cdots\\sigma_{\\alpha_{1}})|0\\rangle \\label{coefsimp} \\\\\n &&+(A_{0}+2A_{1})(1-\\delta_{\\alpha,0})(\\delta_{\\alpha\\alpha_{L}}\\langle 0|-\\mathrm{i}\\sum^{3}_{\\beta=1}\\epsilon_{\\alpha\\alpha_{L}\\beta}\\langle \\beta|)I\\otimes(\\sigma_{\\alpha_{L-1}}\\cdots\\sigma_{\\alpha_{1}})|0\\rangle \\nonumber\\end{aligned}$$ where $\\epsilon_{\\alpha\\alpha_{L}\\beta}$ is the totally antisymmetric tensor of three indices with $\\epsilon_{123}=1$. By realizing that $$\\begin{aligned}\n \\delta_{\\alpha\\alpha_{L}}\\langle 0|-\\mathrm{i}\\sum^{3}_{\\beta=1}\\epsilon_{\\alpha\\alpha_{L}\\beta}\\langle \\beta|=\\langle 0|\\sigma_{\\alpha_{L}}\\sigma_{\\alpha}\\otimes I=\\langle \\alpha_{L}|\\sigma_{\\alpha}\\otimes I, \\label{real}\\end{aligned}$$ we have reached the final form of the coefficient $C_{\\alpha_{1}\\cdots\\alpha_{L}}$ such that $$\\begin{aligned}\n C_{\\alpha_{1}\\cdots\\alpha_{L}}=\\left[3A_{1}\\delta_{\\alpha,0}+(A_{0}+2A_{1})(1-\\delta_{\\alpha,0})\\right]\\langle\\alpha_{L}|\\sigma_{\\alpha}\\otimes (\\sigma_{\\alpha_{L-1}}\\cdots\\sigma_{\\alpha_{1}})|0\\rangle. ", "\\label{codffin}\\end{aligned}$$ As a result, we plug (\\[codffin\\]) into (\\[rhoga\\]) and find that $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}|\\mathrm{VBS}; \\alpha\\rangle&=&\\frac{3A_{1}\\delta_{\\alpha,0}+(A_{0}+2A_{1})(1-\\delta_{\\alpha,0})}{3^{L}}\\label{eigeqn} \\\\\n &&\\cdot\\sum^{3}_{\\alpha_{1}, \\cdots, \\alpha_{L}=1}|\\alpha_{1}\\rangle\\cdots|\\alpha_{L}\\rangle\\,\\langle\\alpha_{L}|\\sigma_{\\alpha}\\otimes (\\sigma_{\\alpha_{L-1}}\\cdots\\sigma_{\\alpha_{1}})|0\\rangle. ", "\\nonumber\\end{aligned}$$ By comparing with (\\[galph\\]), we find that (\\[eigeqn\\]) is exactly the statement that $|\\mathrm{VBS}; \\alpha\\rangle$ $(\\alpha=0, 1, 2, 3)$ are eigenvectors of the density matrix $\\boldsymbol{\\rho}_{L}$: $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}|\\mathrm{VBS}; \\alpha\\rangle=\\Lambda_{\\alpha}|\\mathrm{VBS}; \\alpha\\rangle, \\qquad \\alpha=0, 1, 2, 3 \\label{eigen}\\end{aligned}$$ with eigenvalues $$\\begin{aligned}\n \\Lambda_{\\alpha}=\\frac{3A_{1}\\delta_{\\alpha,0}+(A_{0}+2A_{1})(1-\\delta_{\\alpha,0})}{3^{L}}\n =\\left\\{ \\begin{array}{cc}\n \\frac{1}{4}(1+3(-\\frac{1}{3})^{L}), & \\alpha=0;\\\\ \\\\\n \\frac{1}{4}(1-(-\\frac{1}{3})^{L}), & \\alpha=1, 2, 3. ", "\\end{array}\\right. ", "\\label{eigval1}\\end{aligned}$$ These numbers obtained in (\\[eigval1\\]) are exactly the eigenvalues found in [@FKR; @KHH] for spin-$1$, and are consistent with our later explicit expression for eigenvalues in the more general case, see (\\[eivaex\\]) in §$\\,\\ref{sec:eigval1}\\,$.\n\nWe can also prove explicitly that any other eigenvectors of $\\boldsymbol{\\rho}_{L}$ orthogonal to the set $\\{|\\mathrm{VBS}; \\alpha\\rangle\\}$ have zero eigenvalue. ", "Note that a complete basis of the Hilbert space $\\mathbf{H}$ of the block of spins can be chosen as $$\\begin{aligned}\n \\{|\\alpha_{1}\\rangle\\cdots|\\alpha_{L}\\rangle\\}, \\qquad \\alpha=1, 2, 3. ", "\\label{hlba}\\end{aligned}$$ The subspace $\\mathbf{H}_{4}$ with non-zero eigenvalues is panned by $\\{|\\mathrm{VBS}; \\alpha\\rangle\\}$, as we have already shown. ", "The Hilbert space can be reduced into a direct sum $$\\begin{aligned}\n \\mathbf{H}=\\mathbf{H}_{4}\\oplus\\mathbf{H}_{\\Phi}. ", "\\label{splithil}\\end{aligned}$$ We will show that the subspace $\\mathbf{H}_{\\Phi}$ orthogonal to $\\mathbf{H}_{4}$ is a subspace of vanishing eigenvalues. ", "Mathematically, this means that for an arbitrary basis vector $|\\beta_{1}\\rangle\\cdots|\\beta_{L}\\rangle$, we shall have $$\\begin{aligned}\n\\boldsymbol{\\rho}_{L}(\\mathbf{I}-\\mathbf{P}_{4})|\\beta_{1}\\rangle\\cdots|\\beta_{L}\\rangle=0, \\label{zero}\\end{aligned}$$ where $\\mathbf{I}$ is the identity of $\\mathbf{H}$ and $\\mathbf{P}_{4}$ is the projector onto $\\mathbf{H}_{4}$: $$\\begin{aligned}\n \\mathbf{I}&\\equiv& \\sum^{3}_{\\alpha_{1},\\cdots,\\alpha_{L}=1}|\\alpha_{1}\\rangle\\cdots|\\alpha_{L}\\rangle\\langle\\alpha_{1}|\\cdots\\langle\\alpha_{L}|, \\nonumber\\\\\n \\mathbf{P}_{4}&\\equiv& \\sum^{3}_{\\alpha=1}\\frac{|\\mathrm{VBS}; \\alpha\\rangle\\langle\\mathrm{VBS}; \\alpha|}{\\langle \\mathrm{VBS}; \\alpha|\\mathrm{VBS}; \\alpha\\rangle}. ", "\\label{ip}\\end{aligned}$$ By taking expressions (\\[matr1\\]), (\\[ip\\]), (\\[eigen\\]), and realizing that $$\\begin{aligned}\n \\sum^{3}_{\\alpha=0}\\frac{3^{L}\\Lambda_{\\alpha}}{\\langle \\mathrm{VBS}; \\alpha|\\mathrm{VBS}; \\alpha\\rangle}\\,|\\alpha\\rangle \\langle \\alpha|=\\sum^{3}_{\\alpha=0}|\\alpha\\rangle \\langle \\alpha|=I\\otimes I \\label{iden},\\end{aligned}$$ we find the left hand side of (\\[zero\\]) being equal to $$\\begin{aligned}\n &&\\boldsymbol{\\rho}_{L}(\\mathbf{I}-\\mathbf{P}_{4})|\\beta_{1}\\rangle\\cdots|\\beta_{L}\\rangle \\label{comm1} \\\\\n &=&\\frac{1}{3^{L}}\\sum^{3}_{\\alpha_{1}\\cdots\\alpha_{L}=1}\n |\\alpha_{1}\\rangle\\cdots|\\alpha_{L}\\rangle\\,\\langle 0|\\,[\\,I\\otimes(\\sigma_{\\beta_{1}}\\cdots\\sigma_{\\beta_{L}})\\,,\\,I\\otimes(\\sigma_{\\alpha_{L}}\\cdots\\sigma_{\\alpha_{1}})\\,]\\,|0\\rangle. ", "\\nonumber\\end{aligned}$$ We use multiplication rules of Pauli matrices to write the two terms within the commutator in (\\[comm1\\]) as $$\\begin{aligned}\n I\\otimes(\\sigma_{\\beta_{1}}\\cdots\\sigma_{\\beta_{L}})=\\mathrm{e}^{\\mathrm{i}\\theta(\\beta)}I\\otimes\\sigma_{\\beta}, \\qquad \\beta=0, 1, 2, 3; \\nonumber \\\\\n I\\otimes(\\sigma_{\\alpha_{L}}\\cdots\\sigma_{\\alpha_{1}})=\\mathrm{e}^{\\mathrm{i}\\theta(\\alpha)}I\\otimes\\sigma_{\\alpha}, \\qquad \\alpha=0, 1, 2, 3. ", "\\label{ab}\\end{aligned}$$ Here $\\mathrm{e}^{\\mathrm{i}\\theta(\\beta)}$ and $\\mathrm{e}^{\\mathrm{i}\\theta(\\alpha)}$ are two phase factors. ", "Then the commutator is $$\\begin{aligned}\n [\\,I\\otimes(\\sigma_{\\beta_{1}}\\cdots\\sigma_{\\beta_{L}})\\,,\\,I\\otimes(\\sigma_{\\alpha_{L}}\\cdots\\sigma_{\\alpha_{1}})\\,]=\\mathrm{e}^{\\mathrm{i}(\\theta(\\beta)+\\theta(\\alpha))}I\\otimes [\\,\\sigma_{\\beta}\\,,\\,\\sigma_{\\alpha}\\,]. ", "\\label{comm2}\\end{aligned}$$ There are two possibilities:\n\n1. ", " $\\alpha=\\beta$ or at least one of the two is equal to zero, then $\\sigma_{\\beta}$ and $\\sigma_{\\alpha}$ commutes;\n\n2. ", " $\\alpha\\neq\\beta\\neq 0$, then $[\\,\\sigma_{\\beta}\\,,\\,\\sigma_{\\alpha}\\,]=2\\mathrm{i}\\sum^{3}_{\\gamma=1}\\epsilon_{\\beta\\alpha\\gamma}\\sigma_{\\gamma}$, but we still have $\\langle 0|I\\otimes\\sigma_{\\gamma}|0\\rangle=\\langle 0|\\gamma\\rangle=0$.\n\nTherefore, the factor $\\langle 0|\\,[I\\,\\otimes(\\sigma_{\\beta_{1}}\\cdots\\sigma_{\\beta_{L}})\\,,\\,I\\otimes(\\sigma_{\\alpha_{L}}\\cdots\\sigma_{\\alpha_{1}})\\,]\\,|0\\rangle$ in (\\[comm1\\]) is identically zero. ", "So that we have proved (\\[zero\\]). ", "Therefore $\\mathbf{H}_{\\Phi}$ is a subspace with only zero eigenvalues.", "\n\nThe Large Block Limit {#sec:1ds1limit}\n---------------------\n\nIt is interesting to study the large block limit that $L\\to\\infty$. We recognized from (\\[eigval1\\]) that all four eigenvalues approach the same limit $$\\begin{aligned}\n \\Lambda_{\\alpha}=\\frac{1}{4}, \\qquad L\\to\\infty.\\end{aligned}$$ As a result, the von Neumann entropy coincides with the Rényi entropy in the numerical value and both equal to $$\\begin{aligned}\n S_{\\mathrm{v\\ N}}=S_{\\mathrm{R}}(\\alpha)=\\ln4, \\qquad L\\to\\infty.\\end{aligned}$$ The limiting density matrix $\\boldsymbol{\\rho}_{\\infty}$ ($\\lim_{L\\to\\infty}\\boldsymbol{\\rho}_{L}\\equiv\\boldsymbol{\\rho}_{\\infty}$) is proportional to the projector $\\mathbf{P}_{4}$ (\\[ip\\]) which projects on the $4$-degenerate ground states (the ground space) of the block Hamiltonian, *i.e.* $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}\\to\\boldsymbol{\\rho}_{\\infty}=\\frac{1}{4}\\,\\mathbf{P}_{4}, \\qquad L\\to\\infty. ", "\\label{1dsirholimit}\\end{aligned}$$\n\nThe One–dimensional Spin-S Homogeneous Model {#sec:1dssh}\n============================================\n\nIn $1$-dimension, if all bulk spins take the same **integer** value $S$, the model is called the *homogeneous* model. ", "The system consists of a linear chain of $N$ spin-$S$’s in the bulk, and two spin-$S/2$’s on the boundaries. ", "Let $\\boldsymbol{S}_{j}$ denotes the vector spin operator at site $j$ ($j=0,1,\\ldots,N+1$). ", "The Hamiltonian is $$\\begin{aligned}\n H=\\sum^{N-1}_{j=1}\\sum^{2S}_{J=S+1} C_{J}(j,j+1)\\,\\pi_{J}(j,j+1)+H(0,1)+H(N, N+1), \\label{uniq}\\end{aligned}$$ where the projector $\\pi_{J}(j,j+1)$ projects the bond spin $\\boldsymbol{J}_{j,j+1}\\equiv\\boldsymbol{S}_{j}+\\boldsymbol{S}_{j+1}$ onto the subspace with total spin $J$ ($J=S+1, \\ldots, 2S$). ", "Physically formation of bond spins with these values would increase energy. ", "The boundary terms describe interactions between a spin-$S/2$ and a spin-$S$: $$\\begin{aligned}\n H(0,1)&=&\\sum^{3S/2}_{J=S/2+1} C_{J}(0,1)\\,\\pi_{J}(0, 1),\\nonumber\\\\ H(N, N+1)&=&\\sum^{3S/2}_{J=S/2+1} C_{J}(N,N+1)\\,\\pi_{J}(N, N+1). ", "\\label{boun}\\end{aligned}$$ Coefficients $C_{J}(j,j+1)$ can take arbitrary positive values. ", "This model is a special case of the generalized model in $1$-dimension with all multiplicity number $M_{j,j+1}=S$.\n\nWe study the entanglement of the unique VBS ground state of the Hamiltonian (\\[uniq\\]) in this section. ", "The density matrix of a block of spins and the entropies were calculated by H. Katsura, T. Hirano, Y. Hatsugai and their collaborators in [@KHH; @XKHK].", "\n\nThe VBS Ground State {#sec:1dsshvbs}\n--------------------\n\n### The Construction of the VBS State {#sec:convbs}\n\nAccording to the general approach in §$\\,\\ref{sec:vbssch}\\,$, the unique VBS ground state of the Hamiltonian (\\[uniq\\]) is constructed in the Schwinger representation as [@AAH] $$\\begin{aligned}\n |\\mathrm{VBS}\\rangle \\equiv\n \\prod^{N}_{j=0}\n\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{S}|\\mathrm{vac}\\rangle, \\label{vbs}\\end{aligned}$$ where $a^{\\dagger}$, $b^{\\dagger}$ are bosonic creation operators and $\\left|\\mathrm{vac}\\right\\rangle$ is destroyed by any of the annihilation operators $a$, $b$. Recall that these operators satisfy $[\\,a_{i}\\,,\\,a^{\\dagger}_{j}\\,]=[\\,b_{i}\\,,\\,b^{\\dagger}_{j}\\,]=\\delta_{ij}$ with all other commutators vanishing. ", "The spin operators are represented as $S^{+}_{j}=a^{\\dagger}_{j}b_{j}$, $S^{-}_{j}=b^{\\dagger}_{j}a_{j}$, $S^{z}_{j}=(a^{\\dagger}_{j}a_{j}-b^{\\dagger}_{j}b_{j})/2$. To reproduce the dimension of the spin-$S$ Hilbert space at each site, an additional constraint on the total boson occupation number is required, namely $(a^{\\dagger}_{j}a_{j}+b^{\\dagger}_{j}b_{j})/2=S$. More details and properties of the VBS state in the Schwinger representation can be found in §$\\,\\ref{sec:vbssch}\\,$ and [@AAH; @A; @KK]. ", "The pure state density matrix of the VBS ground state (\\[vbs\\]) is $$\\begin{aligned}\n \\boldsymbol{\\rho}=\\frac{|\\mathrm{VBS}\\rangle\\langle \\mathrm{VBS}|}{\\langle \\mathrm{VBS}|\\mathrm{VBS}\\rangle}. ", "\\label{pure}\\end{aligned}$$ We will discuss the normalization $\\langle \\mathrm{VBS}|\\mathrm{VBS}\\rangle$ of the VBS state after introducing the coherent state basis.", "\n\n### The Coherent State Basis {#sec:cohe}\n\nIn order to calculate the normalization of the VBS state (\\[vbs\\]) and later the density matrix of the block, it is convenient to introduce a spin coherent state basis. ", "As shown in [@AAH], this basis represents the quantum spins in the model in terms of classical unit vectors. ", "We first introduce spinor coordinates $$\\begin{aligned}\n \\left(u, v\\right)\\equiv\\left(\\cos\\frac{\\theta}{2}\\,\\mathrm{e}^{\\mathrm{i}\\frac{\\phi}{2}}, \\sin\\frac{\\theta}{2}\\,\\mathrm{e}^{-\\mathrm{i}\\frac{\\phi}{2}}\\right), \\qquad 0\\leq\\theta\\leq\\pi, \\quad 0\\leq\\phi\\leq 2\\pi. ", "\\label{spin}\\end{aligned}$$ Then for a point $\\hat{\\Omega}\\equiv (\\sin\\theta\\cos\\phi, \\sin\\theta\\sin\\phi, \\cos\\theta)$ on the unit sphere, the spin-$S$ coherent state is defined as $$\\begin{aligned}\n |\\hat{\\Omega}\\rangle\\equiv\\frac{\\left(ua^{\\dagger}+vb^{\\dagger}\\right)^{2S}}{\\sqrt{\\left(2S\\right)!}}\\,|\\mathrm{vac}\\rangle. ", "\\label{cohebas}\\end{aligned}$$ Here we have fixed the overall phase (a $U(1)$ gauge degree of freedom) since it has no physical content. ", "Note that (\\[cohebas\\]) is covariant under $SU(2)$ transforms (see §$\\,\\ref{sec:larges}\\,$). ", "The set of coherent states is complete (but not orthogonal) such that [@FM] $$\\begin{aligned}\n \\frac{2S+1}{4\\pi}\\int \\mathrm{d}\\hat{\\Omega}\\,|\\hat{\\Omega}\\rangle \\langle \\hat{\\Omega}|=\\sum^{S}_{m=-S}|S, m\\rangle\\langle S, m|=I_{2S+1}, \\label{comp}\\end{aligned}$$ where $|S, m\\rangle$ denote the eigenstate of $\\boldsymbol{S}^{2}$ and $S_{z}$, and $I_{2S+1}$ is the identity of the $(2S+1)$-dimensional Hilbert space for spin-$S$. To prove (\\[comp\\]), we expand the expression (\\[cohebas\\]) (see also (\\[spinstatesch\\])) $$\\begin{aligned}\n |\\hat{\\Omega}\\rangle=\\sum^{S}_{m=-S}\\sqrt{\\frac{(2S)!}{(S+m)!(S-m)!}}\\,\\,u^{S+m}v^{S-m}|S,m\\rangle. ", "\\label{omegaexp}\\end{aligned}$$ Then, by substituting (\\[omegaexp\\]) into (\\[comp\\]) and realizing that $$\\begin{aligned}\n \\int\\mathrm{d}\\hat{\\Omega}\\,u^{S+m}v^{S-m}u^{\\ast S+m'}v^{\\ast S-m'}=\\frac{(S+m)!(S-m)!}{(2S+1)!}\\,4\\pi\\delta_{mm'},\\end{aligned}$$ the completeness relation (\\[comp\\]) is then established. ", "This relation (\\[comp\\]) can be used in taking trace of an arbitrary operator.", "\n\n### Normalization of the VBS State {#sec:norm}\n\nThe VBS state $|\\mathrm{VBS}\\rangle$ defined in (\\[vbs\\]) is not normalized. ", "Using the coherent state formalism (\\[cohebas\\]) and the completeness relation (\\[comp\\]), we express the norm square as $$\\begin{aligned}\n &&\\langle \\mathrm{VBS}|\\mathrm{VBS}\\rangle \\label{norm1}\\\\\n &=&\\left[\\frac{(S+1)!}{4\\pi}\\right]^{2}\\left[\\frac{(2S+1)!}{4\\pi}\\right]^{N}\\int \\left(\\prod^{N+1}_{j=0}\\mathrm{d}\\hat{\\Omega}_{j}\\right)\\prod^{N}_{j=0}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S} \\nonumber\\end{aligned}$$ where we have used $$\\begin{aligned}\n \\langle 0|a^{S+l}b^{S-l}|\\hat{\\Omega}\\rangle=\\sqrt{(2S)!}\\,\\,u^{S+l}v^{S-l}.\\end{aligned}$$ In order to carry out the integral in (\\[norm1\\]), we consider the expansion of the function $\\left[\\frac{1}{2}(1-x)\\right]^{S}$ in terms of Legendre polynomials $$\\begin{aligned}\n P_{l}(x)=\\frac{1}{2^{l}l!}\\left(\\frac{\\mathrm{d}}{\\mathrm{d}x}\\right)^{l}(x^{2}-1)^{l}\\end{aligned}$$ as follows $$\\begin{aligned}\n \\left[\\frac{1}{2}(1-x)\\right]^{S}=\\sum^{S}_{l=0}C_{l}P_{l}(x).\\end{aligned}$$ The coefficient $C_{l}$ is derived by using the orthogonality of $P_{l}$ and repeatedly integrating by parts $$\\begin{aligned}\n C_{l}&=&\\frac{2l+1}{2}\\int^{1}_{-1}\\mathrm{d}x P_{l}(x)\\left[\\frac{1}{2}(1-x)\\right]^{S} \\nonumber\\\\\n &=&\\frac{2l+1}{2}\\int^{1}_{-1}\\mathrm{d}x\\frac{1}{2^{l}l!}\\left(\\frac{\\mathrm{d}}{\\mathrm{d}x}\\right)^{l}(x^{2}-1)^{l}\\left[\\frac{1}{2}(1-x)\\right]^{S} \\nonumber\\\\\n &=&\\frac{(2l+1)S!}{2^{S+l+1}l!(S-l)!}\\int^{1}_{-1}\\mathrm{d}x (x^{2}-1)^{l}(1-x)^{S-l} \\nonumber\\\\\n &=&\\frac{(-1)^{l}(2l+1)S!}{2^{S+l+1}l!(S-l)!}\\int^{1}_{-1}\\mathrm{d}x (1-x)^{S}(1+x)^{l} \\nonumber\\\\\n &=&\\frac{(-1)^{l}(2l+1)S!S!}{(S-l)!(S+l+1)!}. ", "\\label{ccoeff}\\end{aligned}$$ Having expansion coefficients (\\[ccoeff\\]) and by replacing $x$ with $\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1}$, the factor $\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S}$ under the integral of (\\[norm1\\]) can be expanded in terms of Legendre polynomials and further in terms of spherical harmonics by further using $$\\begin{aligned}\n P_{l}(\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})=\\frac{4\\pi}{2l+1}\\sum^{l}_{m=-l}Y_{lm}(\\hat{\\Omega}_{j})Y^{\\ast}_{lm}(\\hat{\\Omega}_{j+1}).\\end{aligned}$$ The final result is [@FM; @KHH] $$\\begin{aligned}\n &&\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S} \\nonumber\\\\\n &=&\\frac{1}{S+1}\\sum^{S}_{l=0}(2l+1)\\lambda(l,S)P_{l}(\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\nonumber \\\\\n &=&\\frac{4\\pi}{S+1}\\sum^{S}_{l=0}\\lambda(l,S)\\sum^{l}_{m=-l}Y_{lm}(\\hat{\\Omega}_{j})Y^{\\ast}_{lm}(\\hat{\\Omega}_{j+1}) \\label{expansion}\\end{aligned}$$ with coefficients $\\lambda(l,S)$ given by $$\\begin{aligned}\n \\lambda(l,S)\\equiv\\frac{(-1)^{l}S!(S+1)!}{(S-l)!(S+l+1)!}. ", "\\label{lamb}\\end{aligned}$$ Now we expand $\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S}$ in terms of spherical harmonics as in (\\[expansion\\]), then integrate from $\\hat{\\Omega}_{0}$ to $\\hat{\\Omega}_{N+1}$. We notice by using the orthogonality of spherical harmonics that each integral contributes a factor of $4\\pi/(S+1)$ except the last one. ", "For example, $$\\begin{aligned}\n &&\\int \\mathrm{d}\\hat{\\Omega}_{0}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{0}\\cdot\\hat{\\Omega}_{1})\\right]^{S} \\nonumber\\\\ &=&\\frac{4\\pi}{S+1}\\sum^{S}_{l=0}\\lambda(l,S)\\sum^{l}_{m=-l}\\sqrt{4\\pi}\\ Y^{\\ast}_{lm}(\\hat{\\Omega}_{1})\\int \\mathrm{d}\\hat{\\Omega}_{0}\\,Y_{lm}(\\hat{\\Omega}_{0})Y^{\\ast}_{00}(\\hat{\\Omega}_{0}) \n\\nonumber \\\\\n &=&\\frac{4\\pi}{S+1}\\sqrt{4\\pi}\\ Y^{\\ast}_{00}(\\hat{\\Omega}_{1})= \\frac{4\\pi}{S+1}. ", "\\label{exam}\\end{aligned}$$ The last integral over $\\hat{\\Omega}_{N+1}$ contributes simply a factor of $4\\pi$. Consequently, the norm square (\\[norm1\\]) is equal to $$\\begin{aligned}\n \\langle \\mathrm{VBS}|\\mathrm{VBS}\\rangle=\\left[\\frac{(2S+1)!}{S+1}\\right]^{N}S!(S+1)!. ", "\\label{normvbs}\\end{aligned}$$\n\nThe Block Density Matrix {#sec:1dssden}\n------------------------\n\nWe take a block of $L$ contiguous bulk spins as a subsystem. ", "Now we calculate the block density matrix in the VBS state (\\[vbs\\]). ", "By definition, this is achieved by taking the pure state density matrix (\\[pure\\]) and tracing out all spin degrees of freedom outside the block: $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}\\equiv \\mathrm{tr}_{0, 1, \\ldots, k-1, k+L, \\ldots, N, N+1}\\ \\left[\\,\\boldsymbol{\\rho}\\,\\right],\\qquad 1\\leq k,\\quad k+L-1\\leq N. \\label{trac}\\end{aligned}$$ Here the block of length $L$ starts from site $k$ and ends at site $k+L-1$. $\\boldsymbol{\\rho}_{L}$ is no longer a pure state density matrix because of entanglement of the block with the environment (sites outside the block of the spin chain). ", "It was shown in [@JK; @XKHK] that entries of the density matrix are multi-point correlation functions in the ground state. ", "We give the proof of this statement for our spin-$S$ case in §$\\,\\ref{sec:denandcorr}\\,$.\n\nUsing the coherent state basis (\\[cohebas\\]) and completeness relation (\\[comp\\]), $\\boldsymbol{\\rho}_{L}$ can be written as [@KHH] $$\\begin{aligned}\n &&\\boldsymbol{\\rho}_{L}=\n \\label{rougs} \\\\\n &&\\frac{\n\\displaystyle\\int\\left[\\prod^{k-1}_{j=0}\\prod^{N+1}_{j=k+L}\\mathrm{d}\\hat{\\Omega}_{j}\\right]\\prod^{k-2}_{j=0}\\prod^{N}_{j=k+L}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S}\n B^{\\dagger}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|B}\n {\\displaystyle\\left[\\frac{(2S+1)!}{4\\pi}\\right]^{L}\n\\int\\left[\\prod^{N+1}_{j=0}\\mathrm{d}\\hat{\\Omega}_{j}\\right]\\prod^{N}_{j=0}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S}}. ", "\\nonumber \\end{aligned}$$ Here the boundary operator $B$ and block VBS state $\\left|\\mathrm{VBS}_{L}\\right\\rangle$ are defined as $$\\begin{aligned}\n &&B\\equiv \\left(u_{k-1}b_{k}-v_{k-1}a_{k}\\right)^{S}\\left(a_{k+L-1}v_{k+L}-b_{k+L-1}u_{k+L}\\right)^{S},\\label{bope} \\\\\n &&|\\mathrm{VBS}_{L}\\rangle \\equiv\n \\prod^{k+L-2}_{j=k}\n\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{S}|\\mathrm{vac}\\rangle, \\label{vbsl}\\end{aligned}$$ respectively. ", "Note that both $B$ and $|\\mathrm{VBS}_{L}\\rangle$ are $SU(2)$ covariant (see §$\\,\\ref{sec:larges}\\,$). ", "The expression (\\[rougs\\]) can be simplified. ", "We can perform the integrals over $\\hat{\\Omega}_{j}$ ($j=0, 1, \\ldots, k-2, k+L+1, \\ldots, N, N+1$) in the numerator and all integrals in the denominator (see §$\\,\\ref{sec:norm}\\,$). ", "After integrating over these variables, the density matrix $\\boldsymbol{\\rho}_{L}$ turns out to be independent of both the starting site $k$ and the total length $N$ of the spin chain. ", "This property has been proved in [@FKR] for spin $S=1$ (using a different representation, namely the maximally entangled states, see §$\\,\\ref{sec:1ds1den}\\,$) and generalized in [@KHH] for generic spin-$S$. Therefore, we can choose $k=1$ (a relabeling for convenience) and the density matrix takes the form $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}=\\left[\\frac{S+1}{(2S+1)!}\\right]^{L}\\frac{(S+1)}{(4\\pi)^{2}}\n \\int \\mathrm{d}\\hat{\\Omega}_{0}\\mathrm{d}\\hat{\\Omega}_{L+1}\\,B^{\\dagger}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|B \\label{matrix}\\end{aligned}$$ with $$\\begin{aligned}\n&&B^{\\dagger}=\\left(u^{\\ast}_{0}b^{\\dagger}_{1}-v^{\\ast}_{0}a^{\\dagger}_{1}\\right)^{S}\\left(a^{\\dagger}_{L}v^{\\ast}_{L+1}-b^{\\dagger}_{L}u^{\\ast}_{L+1}\\right)^{S}, \\label{bope1} \\\\\n &&|\\mathrm{VBS}_{L}\\rangle=\\prod^{L-1}_{j=1}\n\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{S}|\\mathrm{vac}\\rangle. ", "\\label{vbsl1} \\end{aligned}$$ The state $|\\mathrm{VBS}_{L}\\rangle$ is called the block VBS state. ", "The last two integral of (\\[matrix\\]) can be performed, but we keep its present form for later use.", "\n\nGround States of the Block Hamiltonian {#sec:gsbhs}\n--------------------------------------\n\n### Degenerate Ground States\n\nIn order to describe the eigenvectors and spectrum of the density matrix (\\[matrix\\]), we first study the zero-energy ground states of the block Hamiltonian. ", "The block Hamiltonian is a collection of interacting terms within the block, *i.e.* $$\\begin{aligned}\n H_{B}=\\sum^{L-1}_{j=1}\\sum^{2S}_{J=S+1} C_{J}\\pi_{J}(j, j+1). ", "\\label{degels}\\end{aligned}$$ Now we define a set of $S+1$ operators covariant under $SU(2)$ (see §$\\,\\ref{sec:larges}\\,$) $$\\begin{aligned}\n A^{\\dagger}_{J}\\equiv\n\\left(ua^{\\dagger}_{1}+vb^{\\dagger}_{1}\\right)^{J} \\left(a^{\\dagger}_{1}b^{\\dagger}_{L}-b^{\\dagger}_{1}a^{\\dagger}_{L}\\right)^{S-J}\n\\left(ua^{\\dagger}_{L}+vb^{\\dagger}_{L}\\right)^{J}, \\quad 0\\leq J\\leq S. \\label{aope}\\end{aligned}$$ These operators act on the direct product of Hilbert spaces of spins at site $1$ and site $L$. Then the set of ground states of (\\[degels\\]) can be chosen as $$\\begin{aligned}\n |\\mathrm{G}; J, \\hat{\\Omega}\\rangle \\equiv\nA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle, \\qquad J=0, \\ldots, S. \\label{eiges}\\end{aligned}$$ Any state $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ of this set for fixed $J$ and $\\hat{\\Omega}$ is a zero-energy ground state of (\\[degels\\]). ", "To prove this we need only to verify:\n\n1. ", " The total power of $a^{\\dagger}_{1}$ and $b^{\\dagger}_{1}$ is $2S$, so that we have spin-$S$ at the first site;\n\n2. ", " The bond spin value satisfies $-S\\leq J^{z}_{1,2}\\equiv S^{z}_{1}+S^{z}_{2}\\leq S$ by a binomial expansion, so that the maximum value of the bond spin $J_{1,2}$ is $S$ (from $SU(2)$ invariance, see §$\\,\\ref{sec:larges}\\,$ and [@AAH]).", "\n\nThese properties are true for any other site $j$ and bond $\\langle j, j+1\\rangle$, respectively. ", "Therefore, the state $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ defined in (\\[eiges\\]) has spin-$S$ at each site and no projection onto the $J_{j, j+1}>S$ subspace for any bond.", "\n\n### Degenerate VBS States\n\nThe set of states $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ depend on a discrete parameter $J$ as well as a continuous unit vector $\\hat{\\Omega}$. States with the same $J$ value are not mutually orthogonal. ", "It is possible also to introduce an orthogonal basis in description of the degenerate zero-energy ground states. ", "This new basis could be used in determining the rank and the completeness of the set $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$. For notational convenience, we define $$\\begin{aligned}\n X_{JM}\\equiv\\frac{u^{J+M}v^{J-M}}{\\sqrt{(J+M)!(J-M)!}}, ", "\\qquad\n \\psi^{\\dagger}_{Sm}\\equiv\\frac{(a^{\\dagger})^{S+m}(b^{\\dagger})^{S-m}}{\\sqrt{(S+m)!(S-m)!}}. ", "\\label{2def}\\end{aligned}$$ These two variables transform conjugately with respect to one another under $SU(2)$. (See §$\\,\\ref{sec:larges}\\,$ for more details of transformation properties.) ", "Variable $X_{JM}$ has the following orthogonality relation $$\\begin{aligned}\n \\int \\mathrm{d}\\hat{\\Omega}\\,X^{\\ast}_{JM}X_{JM^{\\prime}}=\\frac{4\\pi}{(2J+1)!}\\,\\delta_{MM^{\\prime}}. ", "\\label{orth}\\end{aligned}$$ Operator $\\psi^{\\dagger}_{Sm}$ is a spin state creation operator such that $$\\begin{aligned}\n \\psi^{\\dagger}_{Sm}|\\mathrm{vac}\\rangle=|S, m\\rangle. ", "\\label{crea1}\\end{aligned}$$ With the introduction of these variables (\\[2def\\]), the operator $A^{\\dagger}_{J}$ defined in (\\[aope\\]) can be expanded as (see Chapter $9$ of [@Ha]) $$\\begin{aligned}\n A^{\\dagger}_{J}&=&\\sqrt{\\frac{(S+J+1)!(S-J)!J!J!}{2J+1}} \\label{aexp} \\\\\n &&\\cdot\\sum^{J}_{M=-J}X_{JM}\\sum^{m_{1}+m_{L}=M}_{m_{1}, m_{L}}(S/2, m_{1}; S/2, m_{2}|J, M)\\,\\psi^{\\dagger}_{S/2,m_{1}}\\otimes\\psi^{\\dagger}_{S/2,m_{L}}, \\nonumber\\end{aligned}$$ where $(S/2, m_{1}; S/2, m_{2}|J, M)$ are the Clebsch-Gordan coefficients. ", "Note that $\\psi^{\\dagger}_{S/2,m_{1}}$ and $\\psi^{\\dagger}_{S/2,m_{L}}$ are defined in the Hilbert spaces of spins at site $1$ and site $L$, respectively. ", "We realize that the particular form of the sum over $m_{1}$ and $m_{L}$ in (\\[aexp\\]) can be identified as a single spin state creation operator $$\\begin{aligned}\n \\Psi^{\\dagger}_{JM}\\equiv\\sum^{m_{1}+m_{L}=M}_{m_{1}, m_{L}}(S/2, m_{1}; S/2, m_{2}|J, M)\\,\\psi^{\\dagger}_{S/2,m_{1}}\\otimes\\psi^{\\dagger}_{S/2,m_{L}}. ", "\\label{crea2}\\end{aligned}$$ This operator $\\Psi^{\\dagger}_{JM}$ acts on the direct product of two Hilbert spaces of spins at site $1$ and site $L$. It has the property that $$\\begin{aligned}\n \\Psi^{\\dagger}_{JM}|\\mathrm{vac}\\rangle_{1}\\otimes|\\mathrm{vac}\\rangle_{L}=|J, M\\rangle_{1,L}. ", "\\label{crea3}\\end{aligned}$$ If we define a set of *degenerate VBS states* $\\{|\\mathrm{VBS}_L(J,M)\\rangle\\}$ such that $$\\begin{aligned}\n |\\mathrm{VBS}_L(J,M)\\rangle\\equiv \\Psi^{\\dagger}_{JM}|\\mathrm{VBS}_L\\rangle, \\quad J=0,...,S, \\quad M=-J, ...,J, \\label{devb}\\end{aligned}$$ then these $(S+1)^{2}$ states (\\[devb\\]) are not only linearly independent but also mutually orthogonal.", "\n\n### The Orthogonality\n\nTo show the orthogonality of the degenerate VBS states (\\[devb\\]), it is convenient to introduce the total spin operators of the subsystem (block): $$S^{+}_{\\mathrm{tot}}=\\sum^{L}_{j=1} a^{\\dagger}_{j} b_{j}, \\qquad\nS^{-}_{\\mathrm{tot}}=\\sum^{L}_{j=1} b^{\\dagger}_{j} a_{j}, \\qquad\nS^{z}_{\\mathrm{tot}}=\\frac{1}{2}\\sum^{L}_{j=1} (a^{\\dagger}_{j} a_{j}-b^{\\dagger}_{j} b_{j}).$$ First we show that the set of operators $\\{ S^{+}_{\\mathrm{tot}}, S^{-}_{\\mathrm{tot}}, S^{z}_{\\mathrm{tot}} \\}$ commute with the product of valence bonds, *i.e.* $$[\\,S^{\\pm}_{\\mathrm{tot}}\\,,\\,\\prod_{j=1}^{L-1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]=0, \\quad \n[\\,S^{z}_{\\mathrm{tot}}\\,,\\,\\prod_{j=1}^{L-1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]=0.", "\n\\label{commutere}$$ These commutation relations (\\[commutere\\]) can be shown in similar ways. ", "Take the commutator with $S^{+}_{\\mbox{\\scriptsize{tot}}}$ first. ", "We re-write the commutator as $$\\begin{aligned}\n&&[\\,S^{+}_{\\mathrm{tot}}\\,,\\,\\prod_{j=1}^{L-1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,] \\\\\n&=& \\sum_{j=1}^{L-1} (a^{\\dagger}_{1} b^{\\dagger}_{2}-b^{\\dagger}_{1} a^{\\dagger}_{2})^{S} \\cdots \n[\\,S^{+}_{\\mbox{\\scriptsize{tot}}}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,] \\cdots (a^{\\dagger}_{L-1} b^{\\dagger}_{L}-b^{\\dagger}_{L-1} a^{\\dagger}_{L})^{S} \\nonumber \\\\\n&=& \\sum_{j=1}^{L-1} (a^{\\dagger}_{1} b^{\\dagger}_{2}-b^{\\dagger}_{1} a^{\\dagger}_{2})^{S} \\cdots \n[\\,S^{+}_{j} + S^{+}_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]\n\\cdots\\nonumber\\\\ &&\\cdots(a^{\\dagger}_{L-1} b^{\\dagger}_{L}-b^{\\dagger}_{L-1} a^{\\dagger}_{L})^{S}.", "\n\\nonumber\\end{aligned}$$ Then using commutators $[a_{i}, a^{\\dagger}_{j}]=\\delta_{ij}$ and $[b_{i}, b^{\\dagger}_{j}]=\\delta_{ij}$, we find that $$\\begin{aligned}\n&& [\\,S^{+}_{j} + S^{+}_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]\n\\nonumber \\\\\n&=& [\\,a^{\\dagger}_{j} b_{j}+a^{\\dagger}_{j+1} b_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,] \\nonumber \\\\\n&=& a^{\\dagger}_{j} [\\,b_{j}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]+\n a^{\\dagger}_{j+1} [\\,b_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]\n \\nonumber \\\\\n&=& a^{\\dagger}_{j} (-S)a^{\\dagger}_{j+1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S-1}\n +a^{\\dagger}_{j+1} S a^{\\dagger}_{j} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S-1}\n\\nonumber \\\\\n&=&0. ", "\\label{comm}\\end{aligned}$$ Therefore $[\\,S^{+}_{\\mathrm{tot}}\\,,\\,\\prod_{j=1}^{L-1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]=0$. In (\\[comm\\]) we have used $$\\begin{aligned}\n [\\,b_{j}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]=-S a^{\\dagger}_{j+1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S-1}.\\end{aligned}$$ In a similar way, we find that the commutator with $S^{-}_{\\mathrm{tot}}$ also vanishes. ", "Next we consider the commutator with $S^{z}_{\\mathrm{tot}}$: $$\\begin{aligned}\n&&[\\,S^{z}_{\\mathrm{tot}}\\,,\\,\\prod_{j=1}^{L-1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,] \\label{comSz} \\\\\n&=& \\sum_{j=1}^{L-1} (a^{\\dagger}_{1} b^{\\dagger}_{2}-b^{\\dagger}_{1} a^{\\dagger}_{2})^{S}\n\\cdots [\\,S^{z}_{j} + S^{z}_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]\\cdots\\nonumber\\\\\n&&\\cdots(a^{\\dagger}_{L-1} b^{\\dagger}_{L}-b^{\\dagger}_{L-1} a^{\\dagger}_{L})^{S}.", "\n\\nonumber\\end{aligned}$$ In the right hand side of (\\[comSz\\]), the commutator involved also vanishes because $$\\begin{aligned}\n&&[\\,S^{z}_{j} + S^{z}_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,] \n\\nonumber \\\\\n&=& \\frac{1}{2}[\\,a^{\\dagger}_{j} a_{j} -b^{\\dagger}_{j} b_{j} +a^{\\dagger}_{j+1} a_{j+1} -b^{\\dagger}_{j+1} b_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,] \n\\nonumber \\\\\n&=& \\frac{1}{2}a^{\\dagger}_{j} [\\,a_{j}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]\n -\\frac{1}{2}b^{\\dagger}_{j} [\\,b_{j}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,] \n\\nonumber \\\\\n&&+ \\frac{1}{2}a^{\\dagger}_{j+1} [\\,a_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]\n -\\frac{1}{2}b^{\\dagger}_{j+1} [\\,b_{j+1}\\,,\\,(a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]\n\\nonumber \\\\\n&=& 0 \\label{com1}\\end{aligned}$$ Substituting (\\[com1\\]) into (\\[comSz\\]), we obtain $[\\,S^{z}_{\\mathrm{tot}}\\,,\\,\\prod_{j=1}^{L-1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S}\\,]=0$. Now we shall show that the state $|\\mathrm{VBS}_L(J,M)\\rangle$ is a common eigenstate of $S^{z}_{\\mathrm{tot}}$ and the total spin square $\\boldsymbol{S}^2_{\\mathrm{tot}}=\\frac{1}{2}(S^{+}_{\\mathrm{tot}}S^{-}_{\\mathrm{tot}}+S^{-}_{\\mathrm{tot}}S^{+}_{\\mathrm{tot}}) + (S^{z}_{\\mathrm{tot}})^{2}$ with eigenvalues $M$ and $J(J+1)$, respectively. ", "Using the commutation relations (\\[commutere\\]), we can show that $$\\begin{aligned}\nS^{\\pm}_{\\mathrm{tot}}|\\mathrm{VBS}_L(J,M)\\rangle = \\prod_{j=1}^{L-1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S} (S^{\\pm}_{1} + S^{\\pm}_{L})|J,M \\rangle_{1,L} |\\mathrm{vac}\\rangle_{2, ..., L-1} \\nonumber \\\\\nS^{z}_{\\mathrm{tot}}|\\mathrm{VBS}_L(J,M)\\rangle = \\prod_{j=1}^{L-1} (a^{\\dagger}_{j} b^{\\dagger}_{j+1}-b^{\\dagger}_{j} a^{\\dagger}_{j+1})^{S} (S^{z}_{1} + S^{z}_{L})|J,M \\rangle_{1,L} |\\mathrm{vac}\\rangle_{2,..., L-1}.\\nonumber\\\\\\end{aligned}$$ Then from the definition of the state $|\\mathrm{VBS}_L(J,M)\\rangle$ and the following relations: $$\\begin{aligned}\n(S^{\\pm}_1+S^{\\pm}_{L})|J,M \\rangle_{1,L}&=& \\sqrt{(J \\mp M) (J \\pm M +1)}\\,\\,|J, M\\pm1 \\rangle, \n\\nonumber \\\\\n(S^{z}_{1}+S^{z}_{L})|J,M \\rangle_{1,L} &=& M |J,M \\rangle_{1,L},\\end{aligned}$$ we obtain $$\\begin{aligned}\nS^{\\pm}_{\\mathrm{tot}}|\\mathrm{VBS}_L(J,M)\\rangle &=& \\sqrt{(J \\mp M) (J \\pm M +1)}\\,\\,|\\mathrm{VBS}_L(J,M\\pm1)\\rangle, \\nonumber \\\\\nS^z_{\\mathrm{tot}}|\\mathrm{VBS}_L(J,M)\\rangle &=& M |\\mathrm{VBS}_L(J,M)\\rangle\\end{aligned}$$ and hence $\\boldsymbol{S}^{2}_{\\mathrm{tot}}|\\mathrm{VBS}_L(J,M)\\rangle=J(J+1)|\\mathrm{VBS}_L(J,M)\\rangle$. It is now proved that $|\\mathrm{VBS}_L(J,M)\\rangle$ is a common eigenstate of Hermitian operators $S^{z}_{\\mbox{\\scriptsize{tot}}}$ and $\\boldsymbol{S}^{2}_{\\mbox{\\scriptsize{tot}}}$ with eigenvalues $M$ and $J(J+1)$, respectively. ", "Therefore the states with different eigenvalues $(J, M)$ are orthogonal to each other. ", "Thus we have proved the orthogonality of the set $\\{|\\mathrm{VBS}_L(J,M)\\rangle\\,|\\,J=0,\\ldots,S; \\ M=-J,\\ldots,J\\}$.\n\n### Completeness and Equivalence\n\nIt is obvious from (\\[aexp\\]) that any ground state $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ can be written as a linear superposition over these degenerate VBS states: $$\\begin{aligned}\n |\\mathrm{G};J,\\hat{\\Omega}\\rangle=\\sqrt{\\frac{(S+J+1)!(S-J)!J!J!}{2J+1}}\\sum^{J}_{M=-J}X_{JM}|\\mathrm{VBS}_{L}(J, M)\\rangle, \\label{line}\\end{aligned}$$ and *vice versa*. ", "Now we can derive the completeness relation of the set $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ using (\\[orth\\]), (\\[aexp\\]) and (\\[crea2\\]): $$\\begin{aligned}\n &&\\int \\mathrm{d}\\hat{\\Omega}\\,|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\langle \\mathrm{G}; J, \\hat{\\Omega}| \\label{compga} \\\\\n &=&\\frac{4\\pi}{(2J+1)!}\\frac{(S+J+1)!(S-J)!J!J!}{2J+1}\\sum^{J}_{M=-J}\\Psi^{\\dagger}_{JM}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|\\Psi_{JM}. ", "\\nonumber\\end{aligned}$$ The set of states $\\{\\Psi^{\\dagger}_{JM}|\\mathrm{VBS}_{L}\\rangle\\ |\\ M=-J, \\ldots, J\\}$ are linearly independent. ", "So that the rank of $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ with fixed $J$ value is $2J+1$, which can be obtained from the completeness relation (\\[compga\\]) (see [@Ha]). ", "Thus the total number of linearly independent states of the set $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ is $\\sum^{S}_{J=0}(2J+1)=(S+1)^2$, which is exactly the degeneracy of the ground states of (\\[degels\\]). ", "So that $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ forms a complete set of zero-energy ground states. ", "The set $\\{|\\mathrm{VBS}_L(J,M)\\rangle\\}$ differs from $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ by a change of basis, therefore it also forms a complete set of zero-energy ground states. ", "These two sets (\\[eiges\\]) and (\\[devb\\]) are equivalent in description of the degenerate ground states of the block Hamiltonian (\\[degels\\]). (", "More details such as the expansion (\\[aexp\\]) *etc.* ", "can be found in Chapter $9$ of [@Ha].)", "\n\nEigenvectors of the Density Matrix {#sec:eigvecs}\n----------------------------------\n\nEigenvalues of the density matrix $\\boldsymbol{\\rho}_{L}$ can be derived indirectly, as in [@FKR] for spin-$1$ (see §$\\,\\ref{sec:1ds1specden}\\,$ for comparison) and in [@KHH] for spin-$S$. The basic idea is the following: Because the density matrix is independent of both the total length of the spin chain and the starting site of the block, we can add boundary spins directly to the ends of the block. ", "It was shown in [@FKR; @KHH] by a Schmidt decomposition (see Section $2.5$ of [@NC]) that non-zero eigenvalues of the density matrix (\\[matrix\\]) are equal to those of the density matrix of the two boundary spins. ", "All other eigenvalues of the density matrix (\\[matrix\\]) are zero. ", "This fact reveals the structure of the density matrix as a projector (up to a multiplicative ‘scaling’ matrix) onto a subspace of dimension $(S+1)^{2}$.\n\nNow we propose a theorem on the eigenvectors of the density matrix $\\boldsymbol{\\rho}_{L}$ given by (\\[matrix\\]). ", "The explicit construction of eigenvectors allows us to diagonalize the density matrix directly. ", "The set of eigenvectors also spans the subspace that the density matrix projects onto.", "\n\n\\[theorem2\\] Eigenvectors of the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[matrix\\]) with non-zero eigenvalues are given by the set $\\{\\,|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\,\\}$ (\\[eiges\\]), or, equivalently, by the set $\\{\\,|\\mathrm{VBS}_L(J,M)\\rangle\\,\\}$ (\\[devb\\]). *", "i.e.* They are zero-energy ground states of the block Hamiltonian $H_{B}$ (\\[degels\\]). (", "We shall emphasize that the eigenvectors $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ and $|\\mathrm{VBS}_L(J,M)\\rangle$ correspond to the vectors $|\\lambda\\rangle$ in §$\\,\\ref{sec:rhoands}\\,$ and in **Theorem** \\[theorem1\\] of §$\\,\\ref{sec:den0spec}\\,$.)\n\nWe prove this theorem by showing that the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[matrix\\]) can be written as a projector in diagonal form onto the orthogonal degenerate VBS states $\\{\\,|\\mathrm{VBS}_{L}(J, M)\\rangle\\,\\}$ introduced in (\\[devb\\]). ", "An alternative proof taking a different approach is given in the next section §$\\,\\ref{sec:alterproof}\\,$.\n\nFirst, it is realized from the definition of spinor coordinates (\\[spin\\]) that if we change variables $(u, v)$ to $(\\mathrm{i}v^{\\ast}, -\\mathrm{i}u^{\\ast})$, then the unit vector $\\hat{\\Omega}$ is inverted about the origin to $-\\hat{\\Omega}$. So that we have [@KHH] $$\\begin{aligned}\n (u^{\\ast}b^{\\dagger}-v^{\\ast}a^{\\dagger})^{S}|\\mathrm{vac}\\rangle=\\mathrm{i}^{S}\\sqrt{S!}\\,\\,|-\\hat{\\Omega}\\rangle, \\label{inve}\\end{aligned}$$ where $|-\\hat{\\Omega}\\rangle$ means a spin-$S/2$ coherent state for a point opposite to $\\hat{\\Omega}$ on the unit sphere. ", "Therefore, taking expressions of the boundary operator $B^{\\dagger}$ (\\[bope1\\]) and the block VBS state $|\\mathrm{VBS}_{L}\\rangle$ (\\[vbsl1\\]), we have $$\\begin{aligned}\n &&B^{\\dagger}|\\mathrm{VBS}_{L}\\rangle \\label{bvbs}= \\\\\n &&S!\\prod^{L-1}_{j=1}\n\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{S}|-\\hat{\\Omega}_{0}\\rangle_{1}\\otimes|\\mathrm{vac}\\rangle_{2}\\otimes\\cdots\\otimes|\\mathrm{vac}\\rangle_{L-1}\\otimes|-\\hat{\\Omega}_{L+1}\\rangle_{L}. ", "\\nonumber\\end{aligned}$$ Consequently the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[matrix\\]) can be re-written as $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}&&=\\left[\\frac{S+1}{(2S+1)!}\\right]^{L}\\frac{S!S!}{S+1}\\prod^{L-1}_{j=1}\n\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{S} \\label{rewr} \\\\\n&&\\cdot I^{(1)}_{S+1}\\otimes|\\mathrm{vac}\\rangle_{2}\\langle \\mathrm{vac}|\\otimes\\cdots\\otimes|\\mathrm{vac}\\rangle_{L-1}\\langle \\mathrm{vac}|\\otimes I^{(L)}_{S+1}\\prod^{L-1}_{j=1}\\left(a_{j}b_{j+1}-b_{j}a_{j+1}\\right)^{S}, \\nonumber\\end{aligned}$$ where $I^{(1)}_{S+1}$ and $I^{(L)}_{S+1}$ are $(S+1)$-dimensional identities associated with site $1$ and site $L$, respectively. ", "In obtaining (\\[rewr\\]), we have changed integral variables from $\\hat{\\Omega}_{0}$ , $\\hat{\\Omega}_{L+1}$ to $-\\hat{\\Omega}_{0}$, $-\\hat{\\Omega}_{L+1}$ and performed these two integrals using the completeness relation (\\[comp\\]). ", "Next we notice that (see §$\\,\\ref{sec:gsbhs}\\,$) $$\\begin{aligned}\n I^{(1)}_{S+1}\\otimes I^{(L)}_{S+1}&=&\\sum^{S}_{J=0}\\sum^{J}_{M=-J}|J, M\\rangle_{1,L}\\langle J, M| \\label{iide} \\\\\n&=&\\sum^{S}_{J=0}\\sum^{J}_{M=-J}\\Psi^{\\dagger}_{JM}|\\mathrm{vac}\\rangle_{1}\\langle \\mathrm{vac}|\\otimes|\\mathrm{vac}\\rangle_{L}\\langle \\mathrm{vac}|\\Psi_{JM}. ", "\\nonumber\\end{aligned}$$ As a result, combining (\\[rewr\\]) and (\\[iide\\]), recalling definitions of $|\\mathrm{VBS}_{L}\\rangle$ (\\[vbsl1\\]) and $|\\mathrm{VBS}_{L}(J, M)\\rangle$ (\\[devb\\]), the density matrix $\\boldsymbol{\\rho}_{L}$ takes the following final form $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}&=&\\left[\\frac{S+1}{(2S+1)!}\\right]^{L}\\frac{S!S!}{S+1}\\sum^{S}_{J=0}\\sum^{J}_{M=-J}\\Psi^{\\dagger}_{JM}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|\\Psi_{JM} \\label{fipr} \\\\\n&=&\\left[\\frac{S+1}{(2S+1)!}\\right]^{L}\\frac{S!S!}{S+1}\\sum^{S}_{J=0}\\sum^{J}_{M=-J}|\\mathrm{VBS}_{L}(J, M)\\rangle\\langle \\mathrm{VBS}_{L}(J, M)|. ", "\\nonumber\\end{aligned}$$ The set of degenerate VBS states $\\{|\\mathrm{VBS}_{L}(J, M)\\rangle\\}$ with $J=0,\\ldots,S$ and $M=-J,\\ldots,J$ forms an orthogonal basis (see §$\\,\\ref{sec:gsbhs}\\,$). ", "These $(S+1)^{2}$ states also forms a complete set of zero-energy ground states of the block Hamiltonian (\\[degels\\]) (see §$\\,\\ref{sec:gsbhs}\\,$). ", "So that in expression (\\[fipr\\]) we have put the density matrix as a projector in diagonal form over an orthogonal basis. ", "Each degenerate VBS state $|\\mathrm{VBS}_{L}(J, M)\\rangle$ is an eigenvector of the density matrix, so as any of the state $|\\mbox{G}; J, \\hat{\\Omega}\\rangle$ (because of the degeneracy of corresponding eigenvalues of the density matrix, see §$\\,\\ref{sec:eigval1}\\,$ and §$\\,\\ref{sec:eigval2}\\,$ that the eigenvalues depend only on $J$). ", "Thus we have proved **Theorem** \\[theorem2\\].", "\n\nAn Alternative Proof of **Theorem** \\[theorem2\\] {#sec:alterproof}\n------------------------------------------------\n\nIt was shown in §$\\,\\ref{sec:eigvecs}\\,$ that the density matrix takes a diagonal form in the basis of zero-energy ground states of the block Hamiltonian (\\[degels\\]). ", "In this section, we show the same result by taking a different approach. ", "This alternative proof of **Theorem** \\[theorem2\\] does not involve the coherent state basis.", "\n\nThe proof uses the fact that the density matrix is independent of the starting site and the total length of the chain (see §$\\,\\ref{sec:1dssden}\\,$). ", "So that we could change the configuration of the whole system by adding the two ending spins directly to the block without affecting the form of the block density matrix. ", "The new system now has $L+2$ sites with the block starting at site $1$ and ending at site $L$. Let us start with the ground VBS state of the Hamiltonian (\\[uniq\\]) of the system with $N=L$: $$\\begin{aligned}\n|\\mathrm{VBS}\\rangle&\\equiv&\\prod_{j=0}^{L}\\left(\n a_j^{\\dagger}b_{j+1}^{\\dagger}-b_j^{\\dagger}a_{j+1}^{\\dagger}\\right)^{S}|\\mathrm{vac}\\rangle. ", "\\label{vbsn=l}\\end{aligned}$$ In order to calculate the density matrix $\\boldsymbol{\\rho}_L=\n\\mathrm{tr}_{0,L+1}\\left[\\,\\boldsymbol{\\rho}\\,\\right]$, where $\\boldsymbol{\\rho}$ is defined in (\\[pure\\]), we introduce a useful identity: $$\\begin{aligned}\n{}_{0,L+1}\\langle J,M|\\left(|s\\rangle_{0,1}\\otimes|s\\rangle_{L,L+1}\\right)\n&=&\n\\frac{(-1)^{S-J+M}}{(S+1)}\\,|J,-M\\rangle_{1,L},\\label{EigenTrans}\\end{aligned}$$ where $|J,M\\rangle_{0,L+1}$ is identical to the spin state defined in (\\[crea3\\]) except for site indices. ", "$|s\\rangle_{i,j}$ in (\\[EigenTrans\\]) is the normalized singlet state with $S$ valence bonds defined as $$\\begin{aligned}\n |s\\rangle_{i,j}&=&\\frac{1}{S!\\sqrt{S+1}}\\left(\na^{\\dagger}_{i}b^{\\dagger}_{j}-b^{\\dagger}_{i}a^{\\dagger}_{j}\\right)^{S}|\\mathrm{vac}\\rangle_{i}\\otimes|\\mathrm{vac}\\rangle_{j}\n\\nonumber \\\\ \n&=&\\frac{(-1)^{\\frac{S}{2}}}{\\sqrt{S+1}}\\sum_{m=-S/2}^{S/2}(-1)^{m}|S/2,-m \\rangle_{i}\\otimes|S/2,m \\rangle_{j}. ", "\\label{singlet}\\end{aligned}$$ Identity (\\[EigenTrans\\]) is derived using properties of the singlet state (\\[singlet\\]) and Clebsch-Gordan coefficients as follows: $$\\begin{aligned}\n&&{}_{0,L+1}\\langle J,M|\\left(|s\\rangle_{0,1}\\otimes|s\\rangle_{L,L+1}\\right) \\nonumber\\\\\n&=&\n\\sum^{m_{0}+m_{L+1}=M}_{m_{0},m_{L+1}}(J,M|S/2,m_{0};S/2,m_{L+1})\n{}_{0}\\langle S/2,m_{0}| {}_{L+1}\\langle S/2,m_{L+1}|\n\\nonumber\\\\&&\\cdot\n\\frac{(-1)^{\\frac{S}{2}}}{\\sqrt{S+1}}\\sum_{m_{1}=-S/2}^{S/2}(-1)^{m_{1}}|S/2,-m_{1}\\rangle_{0}|S/2,m_{1}\\rangle_{1}\n\\nonumber\\\\&&\\cdot\n\\frac{(-1)^{\\frac{S}{2}}}{\\sqrt{S+1}}\\sum_{m_{L}=-S/2}^{S/2}(-1)^{m_{L}}|S/2,-m_{L}\\rangle_{L}|S/2,m_{L}\\rangle_{L+1}\n\\nonumber\\\\&=&\n\\frac{1}{S+1}\n\\sum^{m_{0}+m_{L+1}=M}_{m_0,m_{L+1}}(-1)^{m_0+m_{L+1}}\n(J,M|S/2,m_0;S/2,m_{L+1})\n\\nonumber\\\\&&\\cdot\n|S/2,-m_0\\rangle_1\n|S/2,-m_{L+1}\\rangle_L.\\end{aligned}$$ Here the Clebsch-Gordan coefficient is defined by $$(J,M|S/2,m_0;S/2,m_{L+1})= {}_{i,j}\\langle J,M|\\left(|S/2,m_{0} \\rangle_{i}\\otimes|S/2,m_{L+1} \\rangle_{j}\\right).$$ Then using the symmetry property of Clebsch-Gordan coefficients $$\\begin{aligned}\n(J,M|S/2,m_{0};S/2,m_{L+1})\n=(-1)^{S-J}\n(J,-M|S/2,-m_{0};S/2,-m_{L+1})\\nonumber\\\\\\end{aligned}$$ and the completeness of the basis $\\{\\,|S/2,m_{0}\\rangle_{0}\\otimes|S/2,m_{L+1}\\rangle_{L+1}\\,\\}$, we obtain the identity (\\[EigenTrans\\]).", "\n\nWith the help of identity (\\[EigenTrans\\]), we calculate the partial inner product of the VBS state (\\[vbsn=l\\]) with the state $|J,M\\rangle_{0,L+1}$, which is involved in taking trace of boundary spins. ", "The VBS state $|\\mbox{VBS}\\rangle$ is decomposed into the bulk part and boundary parts, then making use of (\\[EigenTrans\\]), we have $$\\begin{aligned}\n&&{}_{0,L+1}\\langle J,M|\\mathrm{VBS}\\rangle\\nonumber\\\\\n&=&\n{}_{0,L+1}\\langle J,M|\n\\prod_{j=0}^{L}\\left(\n a_j^{\\dagger}b_{j+1}^{\\dagger}-b_j^{\\dagger}a_{j+1}^{\\dagger}\\right)^{S}|\\mathrm{vac}\\rangle\n\\nonumber\\\\&=& S! (", "S+1)!", "\n\\prod_{j=1}^{L-1}\\left(\n a_j^{\\dagger}b_{j+1}^{\\dagger}-b_j^{\\dagger}a_{j+1}^{\\dagger}\\right)^{S}\n{}_{0,L+1}\\langle J,M|s\\rangle_{0,1} |s\\rangle_{L,L+1} |\\mathrm{vac}\\rangle_{2\\cdots L-1}\n\\nonumber\\\\\n&=&(S!)^2\n\\prod_{j=1}^{L-1}\\left(\n a_j^{\\dagger}b_{j+1}^{\\dagger}-b_j^{\\dagger}a_{j+1}^{\\dagger}\\right)^{S}\n(-1)^{S-J+M}\n|J,-M\\rangle_{1,L} |\\mathrm{vac}\\rangle_{2\\cdots L-1}\n\\nonumber\\\\\n&=&\n(-1)^{S-J+M}(S!)^2\n|\\mathrm{VBS}_L(J,-M)\\rangle. ", "\\label{partial}\\end{aligned}$$ We see that the $(S+1)^2$ degenerate VBS states $\\{\\,|\\mbox{VBS}_L(J,M)\\rangle\\,\\}$ defined in (\\[devb\\]) appear in the partial inner product (\\[partial\\]). ", "As discussed in §$\\,\\ref{sec:gsbhs}\\,$, they form a complete set of zero-energy ground states of the block Hamiltonian (\\[degels\\]).", "\n\nNow, it is straightforward to evaluate the density matrix as $$\\begin{aligned}\n\\mathrm{tr}_{0,L+1}\\left[\\,\\boldsymbol{\\rho}\\,\\right]\n&=&\n\\sum_{J,M}\n\\frac{{}_{0,L+1}\\langle J,M\n|\\mbox{VBS}\\rangle\\langle\\mbox{VBS}|\n J,M\\rangle_{0,L+1}\n}{\\langle\\mbox{VBS}|\\mbox{VBS}\\rangle}\n\\nonumber\\\\&=&\n\\frac{(S!)^4}{\\langle\\mbox{VBS}|\\mbox{VBS}\\rangle}\n\\sum_{J,M}|\\mbox{VBS}_{L}(J,-M)\\rangle\n\\langle\\mbox{VBS}_{L}(J,-M)|. ", "\\nonumber\\\\\\end{aligned}$$ This expression is identical to (\\[fipr\\]) as we change dummy index from $M$ to $-M$. Therefore, in this approach again we arrive at **Theorem** \\[theorem2\\] that the density matrix is proportional to a projector onto a subspace spanned by the $(S+1)^2$ ground states of the block Hamiltonian (\\[degels\\]). ", "Normalization $\\langle\\mathrm{VBS}|\\mathrm{VBS}\\rangle$ has been obtained in §$\\,\\ref{sec:norm}\\,$. States $|\\mbox{VBS}_{L}(J,M)\\rangle$ have been shown to be mutually orthogonal in §$\\,\\ref{sec:gsbhs}\\,$.\n\nEigenvalues of the Density Matrix (normalization of degenerate VBS states) {#sec:eigval1}\n--------------------------------------------------------------------------\n\nAs the next step in analyzing the spectrum of the density matrix, now we study the eigenvalues. ", "Based on the diagonalized form (\\[fipr\\]), it is clear that eigenvalues of the density matrix $\\boldsymbol{\\rho}_{L}$ can be derived from the normalization of degenerate VBS states. ", "We obtain an explicit expression for eigenvalues in terms of Wigner $3j$-symbols in this section.", "\n\nFirst, the following property is important: Normalization of the degenerate VBS state $|\\mathrm{VBS}_L(J,M)\\rangle$ depends only on $J$ and is independent of $M$. This point is important in proving that any $|\\mathrm{G};J,\\hat{\\Omega}\\rangle$ is an eigenvector of $\\boldsymbol{\\rho}_{L}$ because it can be written as a superposition of $|\\mathrm{VBS}_L(J,M)\\rangle$’s with the same $J$ value (\\[line\\]). ", "With the introduction of total spin operators of the block $S^{\\pm}_{\\mathrm{tot}}$, $S^{z}_{\\mathrm{tot}}$ and $\\boldsymbol{S}^{2}_{\\mathrm{tot}}$ (see §$\\,\\ref{sec:gsbhs}\\,$), we prove the statement as follows: $$\\begin{aligned}\n&& \\langle \\mathrm{VBS}_{L}(J,M\\pm 1)|\\mathrm{VBS}_{L}(J,M\\pm 1)\\rangle\n\\nonumber \\\\\n&=& \\frac{1}{(J\\mp M)(J \\pm M+1)}\\langle\\mathrm{VBS}_{L}(J,M)|S^{\\mp}_{\\mathrm{tot}}S^{\\pm}_{\\mathrm{tot}}|\\mathrm{VBS}_{L}(J,M)\\rangle\n\\nonumber \\\\\n&=& \\frac{1}{(J\\mp M)(J \\pm M+1)}\\langle\\mathrm{VBS}_{L}(J,M)|(\\boldsymbol{S}^{2}_{\\mathrm{tot}}-(S^{z}_{\\mathrm{tot}})^{2}\\mp S^{z}_{\\mathrm{tot}})|\\mathrm{VBS}_{L}(J,M)\\rangle\n\\nonumber \\\\\n&=& \\langle\\mathrm{VBS}_{L}(J,M)|\\mathrm{VBS}_{L}(J,M)\\rangle.\\end{aligned}$$ Here we have used the fact that $|\\mathrm{VBS}_{L}(J,M)\\rangle$ is the common eigenstate of $\\boldsymbol{S}^{2}_{\\mathrm{tot}}$ and $S^{z}_{\\mathrm{tot}}$ with eigenvalues $J(J+1)$ and $M$, respectively (see §$\\,\\ref{sec:gsbhs}\\,$).", "\n\nIt is also realized that the normalization of $|\\mathrm{VBS}_{L}(J,M)\\rangle$ can be calculated from integrating the inner product of $|\\mathrm{G};J,{\\hat\\Omega}\\rangle$ with itself over the unit vector $\\hat{\\Omega}$ such that $$\\begin{aligned}\n&&\\frac{1}{4\\pi}\\int \\mathrm{d}\\hat{\\Omega}\\,\\langle\\mathrm{G};J,\\hat{\\Omega}|\\mathrm{G};J,\\hat{\\Omega}\\rangle \\nonumber\\\\\n&=& \\frac{(S+J+1)!(S-J)!J!J!}{(2J+1)!}\\langle\\mathrm{VBS}_L(J,M)|\\mathrm{VBS}_L(J,M)\\rangle. ", "\\label{novb}\\end{aligned}$$ In obtaining this relation (\\[novb\\]) we have used expansion (\\[line\\]) and orthogonality (\\[orth\\]) in §$\\,\\ref{sec:gsbhs}\\,$.\n\nLet us consider the integral involved in (\\[novb\\]). ", "Using the coherent state basis (\\[cohebas\\]) and completeness relation (\\[comp\\]) as before, we obtain $$\\begin{aligned}\n&&\\frac{1}{4\\pi}\\int \\mathrm{d}\\hat{\\Omega}\\,\\langle\\mathrm{G};J,\\hat{\\Omega}|\\mathrm{G};J,{\\hat\\Omega}\\rangle\n\\label{inne} \\\\\n&=& \\frac{1}{4\\pi}\\left[\\frac{(2S+1)!}{4\\pi}\\right]^{L} \\int \\mathrm{d}\\hat{\\Omega} \\int \\left[\\prod^{L}_{j=1} \\mathrm{d}\\hat{\\Omega}_{j}\\right] \\prod^{L-1}_{j=1}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S} \\nonumber \\\\\n&&\\cdot\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{1}\\cdot\\hat{\\Omega}_{L})\\right]^{S-J}\n\\left[\\frac{1}{2}(1+\\hat{\\Omega}_{1} \\cdot\\hat{\\Omega})\\right]^{J}\n\\left[\\frac{1}{2}(1+\\hat{\\Omega} \\cdot\\hat{\\Omega}_{L})\\right]^{J}. ", "\\nonumber\\end{aligned}$$ Now we expand $\\left[\\frac{1}{2}(1-\\hat{\\Omega}_i \\cdot\\hat{\\Omega}_j)\\right]^{J}$ in terms of spherical harmonics as in (\\[expansion\\]), then integrate over ${\\hat\\Omega}$ and from ${\\hat\\Omega}_2$ to ${\\hat\\Omega}_{L-1}$, the right hand side of (\\[inne\\]) is equal to $$\\begin{aligned}\n&& \\frac{4\\pi ((2S+1)!)^{L}}{(S+1)^{L-1}(S-J+1)(J+1)^{2}}\n\\sum_{l_{1}=0}^{S} \\sum_{l_{L}=0}^{S-J} \\sum_{l=0}^{J}\n\\sum_{m_{1}=-l_{1}}^{l_{1}} \\sum_{m_{L}=-l_{L}}^{l_{L}} \\sum_{m=-l}^{l} \\nonumber \\\\\n&& \\int \\mathrm{d}\\hat{\\Omega}_{1} \\int \\mathrm{d}\\hat{\\Omega}_{L}\\,\n\\lambda^{L-1}(l_{1},S) \\lambda(l_{L},S-J) \\lambda^{2}(l,J) \\nonumber \\\\\n&&\\cdot Y_{l_{1},m_{1}}({\\hat\\Omega}_{1})Y_{l_{L},m_{L}}({\\hat\\Omega}_{1})Y_{l,m}({\\hat\\Omega}_1)\nY^{\\ast}_{l_{1},m_{1}}({\\hat\\Omega}_{L})Y^{\\ast}_{l_{L},m_{L}}({\\hat\\Omega}_{L})Y^{\\ast}_{l,m}({\\hat\\Omega}_{L}).\\label{pre1}\\end{aligned}$$ Here we apply the following useful formula: $$\\begin{aligned}\n&&\\int \\mathrm{d}\\hat{\\Omega}\\, Y_{l_{1},m_{1}}({\\hat\\Omega})Y_{l_{L},m_{L}}({\\hat\\Omega})Y_{l,m}({\\hat\\Omega})\n\\nonumber \\\\\n&=&\\sqrt{\\frac{(2l_1+1)(2l_L+1)(2l+1)}{4\\pi}}\n\\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\n0 & 0 & 0 \n\\end{array}\\right)\n\\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\nm_{1} & m_{L} & m \n\\end{array}\\right), \\nonumber\\\\ \\label{wign}\\end{aligned}$$ where $\\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\nm_{1} & m_{L} & m \n\\end{array}\\right)$ is the Wigner $3j$-symbol. ", "Using formula (\\[wign\\]), we carry out the remaining integrals in (\\[pre1\\]) and obtain $$\\begin{aligned}\n&& \\frac{((2S+1)!)^{L}}{(S+1)^{L-1}(S-J+1)(J+1)^{2}} \\sum_{l_{1}=0}^S \\sum_{l_{L}=0}^{S-J} \\sum_{l=0}^J\n\\sum_{m_{1}=-l_{1}}^{l_{1}} \\sum_{m_{L}=-l_{L}}^{l_{L}} \\sum_{m=-l}^{l} \n\\nonumber \\\\\n&& (2l_{1}+1)(2l_{L}+1)(2l+1)\n\\lambda^{L-1}(l_{1},S) \\lambda(l_{L},S-J) \\lambda^{2}(l,J) \\nonumber \\\\\n&&\\cdot \\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\n0 & 0 & 0 \n\\end{array}\\right)^{2}\n\\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\nm_{1} & m_{L} & m \n\\end{array}\\right)^{2}.", "\n\\label{wigner}\\end{aligned}$$ These $3j$-symbols obey the following orthogonality relation: $$\\begin{aligned}\n \\sum_{m_{1},m_{L}}(2l+1)\n \\left(\\begin{array}{c c c}\n l_{1} & l_{L} & l \\\\\n m_{1} & m_{L} & m \n \\end{array}\\right)\n \\left(\\begin{array}{c c c}\n l_{1} & l_{L} & l^{\\prime} \\\\\n m_{1} & m_{L} & m^{\\prime} \n \\end{array}\\right)=\\delta_{ll^{\\prime}} \\delta_{mm^{\\prime}}. ", "\\label{3jor}\\end{aligned}$$ Using this orthogonality (\\[3jor\\]), we can recast expression (\\[wigner\\]) as $$\\begin{aligned}\n&&\\frac{((2S+1)!)^{L}}{(S+1)^{L-1}(S-J+1)(J+1)^{2}} \\sum_{l_{1}=0}^{S} \\sum_{l_{L}=0}^{S-J} \\sum_{l=0}^{J} \n\\label{pre2} \\\\\n&&(2l_{1}+1)(2l_{L}+1)(2l+1) \\lambda^{L-1}(l_{1},S) \\lambda(l_{L},S-J) \\lambda^{2}(l,J)\n\\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\n0 & 0 & 0 \n\\end{array}\\right)^{2}.\\nonumber\\end{aligned}$$ The explicit value of $\\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\n0 & 0 & 0 \n\\end{array} \\right)$ is given by $$\\begin{aligned}\n&&\\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\n0 & 0 & 0 \n\\end{array} \\right) \\nonumber\\\\\n&=&(-1)^{g} \\sqrt{\\frac{(2g-2l_{1})!(2g-2l_{L})!(2g-2l)!}{(2g+1)!}}\\,\\frac{g!}{(g-l_{1})!(g-l_{L})!(g-l)!},", "\n\\nonumber \\\\ \\label{3jva}\\end{aligned}$$ if $l_{1}+l_{L}+l=2g$ ($g \\in \\mathbf{N}$), otherwise zero. ", "Finally, the normalization of degenerate VBS states $|\\mathrm{VBS}_{L}(J,M)\\rangle$ is obtained as $$\\begin{aligned}\n&&\\langle\\mathrm{VBS}_{L}(J,M)|\\mathrm{VBS}_{L}(J,M)\\rangle \\label{renovb} \\\\\n&=&\\frac{(2J+1)!((2S+1)!)^{L}}{(S+1)^{L-1}(S+J+1)!(S-J+1)!(J+1)!(J+1)!}\\sum_{l_{1}=0}^{S} \\sum_{l_{L}=0}^{S-J} \\sum_{l=0}^{J}\n\\nonumber \\\\\n&&(2l_{1}+1)(2l_{L}+1)(2l+1) \\lambda^{L-1}(l_{1},S) \\lambda(l_{L},S-J) \\lambda^{2}(l,J)\n\\left(\\begin{array}{c c c}\nl_{1} & l_{L} & l \\\\\n0 & 0 & 0 \n\\end{array}\\right)^{2}. ", "\\nonumber\\end{aligned}$$\n\nCombining results of (\\[fipr\\]) and (\\[renovb\\]), we arrive at the following theorem on eigenvalues:\n\n\\[theorem3\\] Eigenvalues $\\Lambda(J)$ $(J=0,\\ldots,S)$ of the density matrix $\\boldsymbol{\\rho}_{L}$ are independent of $\\hat{\\Omega}$ and $M$ in defining eigenvectors (see (\\[eiges\\]) and (\\[devb\\])). ", "An explicit expression is given by the following triple sum $$\\begin{aligned}\n &&\\Lambda(J) \\label{eivaex} \\\\ &=&\\left[\\frac{S+1}{(2S+1)!}\\right]^{L}\\frac{S!S!}{S+1}\\langle\\mathrm{VBS}_{L}(J,M)|\\mathrm{VBS}_{L}(J,M)\\rangle \\nonumber\\\\\n &=&\\frac{(2J+1)!S!S!}{(S+J+1)!(S-J+1)!(J+1)!(J+1)!}\\sum^{S}_{l_{1}=0} \\sum^{S-J}_{l_{L}=0} \\sum^{J}_{l=0}\n \\nonumber \\\\\n &&(2l_{1}+1)(2l_{L}+1)(2l+1) \\lambda^{L-1}(l_{1},S) \\lambda(l_{L},S-J) \\lambda^{2}(l,J)\n \\left(\\begin{array}{ccc}\n l_{1} & l_{L} & l \\\\\n 0 & 0 & 0 \n \\end{array}\\right)^{2}. ", "\\nonumber\n \\end{aligned}$$\n\nAlthough not straightforward to verify, this expression (\\[eivaex\\]) should be consistent with eigenvalues given through the recurrence expression (\\[eiva\\]) in the next section §$\\,\\ref{sec:eigval2}\\,$ and the expression $\\Lambda_{\\alpha}$ in §$\\,\\ref{sec:1ds1specden}\\,$ as a special case. ", "We could check the case when $S=1$ that $$\\begin{aligned}\n&&\\langle\\mathrm{VBS}_{L}(0,0)|\\mathrm{VBS}_{L}(0,0)\\rangle=\\frac{1}{2}(3^{L}+3(-1)^{L}),\n\\nonumber \\\\\n&&\\langle\\mathrm{VBS}_{L}(1,M)|\\mathrm{VBS}_{L}(1,M)\\rangle=\\frac{1}{2}(3^{L}-(-1)^{L}),\\end{aligned}$$ where we have used the selection rule of the Wigner $3j$-symbol. ", "From (\\[normvbs\\]) we find that $\\langle\\mathrm{VBS}|\\mathrm{VBS}\\rangle=2\\cdot 3^{L}$, so that we obtain the correct eigenvalues of the density matrix from the above result (\\[eivaex\\]) (see §$\\,\\ref{sec:1ds1specden}\\,$ for comparison).", "\n\nWe shall emphasize at this point that given eigenvalues (\\[eivaex\\]), both von Neumann entropy $$\\begin{aligned}\n S_{\\mathrm{v\\ N}}=-\\mathrm{tr}\\left[\\,\\boldsymbol{\\rho}_{L}\\ln{\\boldsymbol{\\rho}_{L}}\\,\\right]=-\\sum^{S}_{J=0}(2J+1)\\Lambda(J)\\ln\\Lambda(J) \\label{vonn}\\end{aligned}$$ and Rényi entropy $$\\begin{aligned}\n S_{R}=\\frac{1}{1-\\alpha}\\ln \\left\\{\\mathrm{tr}\\left[\\,\\boldsymbol{\\rho}^{\\alpha}_{L}\\,\\right]\\right\\}=\\frac{1}{1-\\alpha}\\ln\\left\\{\\sum^{S}_{J=0}(2J+1)\\Lambda^{\\alpha}(J)\\right\\} \\label{renyi}\\end{aligned}$$ can be expressed directly.", "\n\nEigenvalues of the Density Matrix (recurrence formula) {#sec:eigval2}\n------------------------------------------------------\n\nHaving constructed eigenvectors, there are more than one way to specify the corresponding eigenvalues. ", "An explicit expression of eigenvalues has been obtained in §$\\,\\ref{sec:eigval1}\\,$. In this section we express eigenvalues through a conjectured recurrence formula as appeared in [@FM; @KHH]. ", "Let us apply the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[matrix\\]) to the state $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ (\\[eiges\\]) and obtain $$\\begin{aligned}\n &&\\boldsymbol{\\rho}_{L}|\\mathrm{G}; J, \\hat{\\Omega}\\rangle \\nonumber\\\\\n &=&\\left[\\frac{S+1}{(2S+1)!}\\right]^{L}\\frac{S+1}{(4\\pi)^{2}}\n \\int \\mathrm{d}\\hat{\\Omega}_{0}\\mathrm{d}\\hat{\\Omega}_{L+1}\\,B^{\\dagger}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|BA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle. ", "\\nonumber\\\\ \\label{appl1}\\end{aligned}$$ Using the coherent state basis (\\[cohebas\\]) and completeness relation (\\[comp\\]), the factor $\\langle \\mathrm{VBS}_{L}|BA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle$ in (\\[appl1\\]) can be re-written as $$\\begin{aligned}\n &&\\langle \\mathrm{VBS}_{L}|BA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle \\label{appl2} \\\\\n &=&\\displaystyle\\left[\\frac{(2S+1)!}{4\\pi}\\right]^{L}\\int \\left(\\prod^{L}_{j=1}\\mathrm{d}\\hat{\\Omega}_{j}\\right)\\prod^{L-1}_{j=1}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S}\n \\left(u_{0}v_{1}-v_{0}u_{1}\\right)^{S} \\nonumber \\\\ &&\\cdot\\left(uu^{\\ast}_{1}+vv^{\\ast}_{1}\\right)^{J}\\left(u^{\\ast}_{1}v^{\\ast}_{L}-v^{\\ast}_{1}u^{\\ast}_{L}\\right)^{S-J}\\left(uu^{\\ast}_{L}+vv^{\\ast}_{L}\\right)^{J}\\left(u_{L}v_{L+1}-v_{L}u_{L+1}\\right)^{S}. ", "\\nonumber\\end{aligned}$$ The factor $\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{S}$ under the integral of (\\[appl2\\]) can be expanded in terms of Legendre polynomials and further in terms of spherical harmonics as discussed in §$\\,\\ref{sec:norm}\\,$ (see also [@FM; @KHH]). ", "Using the expansion (\\[expansion\\]) and orthogonality of spherical harmonics, the integrals over $\\hat{\\Omega}_{j}$ with $j=2, \\ldots, L-1$ in (\\[appl2\\]) can be performed. ", "The result is $$\\begin{aligned}\n \\langle \\mathrm{VBS}_{L}|BA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle &&= \\frac{S+1}{(4\\pi)^{2}}\\left[\\frac{(2S+1)!}{S+1}\\right]^{L}\\sum^{S}_{l=0}(2l+1)\\lambda^{L-1}(l,S) \\nonumber\\\\\n &&\\cdot\\int \\mathrm{d}\\hat{\\Omega}_{1}\\mathrm{d}\\hat{\\Omega}_{L}\\,P_{l}(\\hat{\\Omega}_{1}\\cdot\\hat{\\Omega}_{L})\\left(u_{0}v_{1}-v_{0}u_{1}\\right)^{S}\\left(uu^{\\ast}_{1}+vv^{\\ast}_{1}\\right)^{J} \\nonumber \\\\\n&&\\left(u^{\\ast}_{1}v^{\\ast}_{L}-v^{\\ast}_{1}u^{\\ast}_{L}\\right)^{S-J}\\left(uu^{\\ast}_{L}+vv^{\\ast}_{L}\\right)^{J}\\left(u_{L}v_{L+1}-v_{L}u_{L+1}\\right)^{S}. ", "\\nonumber\\\\ \\label{resu}\\end{aligned}$$ We plug the expression (\\[resu\\]) into (\\[appl1\\]). ", "Using transformation properties under $SU(2)$ and a binomial expansion (see §$\\,\\ref{sec:larges}\\,$), the integral over $\\hat{\\Omega}_{0}$ yields that $$\\begin{aligned}\n \\int \\mathrm{d}\\hat{\\Omega}_{0}\\left(u^{\\ast}_{0}b^{\\dagger}_{1}-v^{\\ast}_{0}a^{\\dagger}_{1}\\right)^{S}\\left(u_{0}v_{1}-v_{0}u_{1}\\right)^{S}=\\frac{4\\pi}{S+1}\\left(u_{1}a^{\\dagger}_{1}+v_{1}b^{\\dagger}_{1}\\right)^{S} \\label{int0}\\end{aligned}$$ Similarly we can perform the integral over $\\hat{\\Omega}_{L+1}$. As a result, the following expression is obtained from (\\[appl1\\]): $$\\begin{aligned}\n\\boldsymbol{\\rho}_{L}|\\mathrm{G}; J, \\hat{\\Omega}\\rangle = \\frac{1}{(4\\pi)^{2}}\\sum^{S}_{l=0}(2l+1)\\lambda^{L-1}(l,S)\nK^{\\dagger}_{l}(\\hat{\\Omega})\n\\left|\\mathrm{VBS}_{L}\\right\\rangle. ", "\\label{sum}\\end{aligned}$$ The operator $K^{\\dagger}_{l}(\\hat{\\Omega})$ involved in (\\[sum\\]) is defined as $$\\begin{aligned}\n K^{\\dagger}_{l}(\\hat{\\Omega})&\\equiv&\\int \\mathrm{d}\\hat{\\Omega}_{1} \\mathrm{d}\\hat{\\Omega}_{L} \n \\left(u_{1}a^{\\dagger}_{1}+v_{1}b^{\\dagger}_{1}\\right)^{S} \\left(uu^{\\ast}_{1}+vv^{\\ast}_{1}\\right)^{J}\n\\left(u^{\\ast}_{1}v^{\\ast}_{L}-v^{\\ast}_{1}u^{\\ast}_{L}\\right)^{S-J} \n\\nonumber \\\\ &&\\cdot\n\\left(uu^{\\ast}_{L}+vv^{\\ast}_{L}\\right)^{J}\n\\left(u_{L}a^{\\dagger}_{L}+v_{L}b^{\\dagger}_{L}\\right)^{S}\nP_{l}(\\hat{\\Omega}_{1} \\cdot \\hat{\\Omega}_{L}). ", "\\label{inte}\\end{aligned}$$ It is expressed as an integral depending on the order $l$ of the Legendre polynomial $P_{l}(\\hat{\\Omega}_{1} \\cdot \\hat{\\Omega}_{L})$. $K^{\\dagger}_{l}(\\hat{\\Omega})$ can be calculated from the lowest few orders (see §$\\,\\ref{sec:larges}\\,$ for example). ", "It becomes increasingly difficult to perform the integral as order $l$ increases. ", "Based on the eigenvalue expressions of the density matrix obtained in [@FKR; @KHH], we make a conjecture on the explicit form of the operator $K^{\\dagger}_{l}(\\hat{\\Omega})$ for generic order $l$:\n\n**Conjecture 1** $$\\begin{aligned}\n K^{\\dagger}_{l}(\\hat{\\Omega})=\\left(\\frac{4\\pi}{S+1}\\right)^{2}I_{l}\\left(\\frac{1}{2}J(J+1)-\\frac{1}{2}S(\\frac{1}{2}S+1)\\right)A^{\\dagger}_{J}. ", "\\label{conj2}\\end{aligned}$$ Here the polynomial $I_{l}\\left(x\\right)$ satisfy the recurrence relation $$\\begin{aligned}\n I_{l+1}(x)=\n \\frac{2l+1}{\\left(S+l+2\\right)^{2}}\\left(\\frac{4x}{l+1}+l\\right)I_{l}\\left(x\\right)\n -\\frac{l}{l+1}\\left(\\frac{S-l+1}{S+l+2}\\right)^{2}I_{l-1}(x)\\nonumber\\\\ \\label{recu}\\end{aligned}$$ with $I_{0}=1$ and $I_{1}=\\frac{x}{(\\frac{S}{2}+1)^{2}}$.\n\nNote that it is important that $K^{\\dagger}_{l}(\\hat{\\Omega})\\propto A^{\\dagger}_{J}$ defined in (\\[aope\\]) and $I_{l}(x)$ has the same order as the Legendre polynomial $P_{l}(x)$. The recurrence relation (\\[recu\\]) was proposed in [@FM] and used in [@KHH] to obtain the eigenvalues of the density matrix. (", "The original definition of $I_l(x)$ differs from our definition in (\\[recu\\]) by a factor of $(2l+1)/4\\pi$.) **Conjecture 1** is an alternative form of **Theorem** \\[theorem2\\] together with **Theorem** \\[theorem3\\], which also gives eigenvalues through the recurrence relation (\\[recu\\]). ", "Indeed, expressions (\\[sum\\]), altogether with (\\[conj2\\]) and (\\[recu\\]) yields that $$\\begin{aligned}\n &&\\boldsymbol{\\rho}_{L}|\\mathrm{G}; J, \\hat{\\Omega}\\rangle \\label{appl} \\\\ &=&\\frac{1}{(S+1)^{2}}\\sum^{S}_{l=0}(2l+1)\\lambda^{L-1}(l,S)\nI_{l}\\left(\\frac{1}{2}J(J+1)-\\frac{1}{2}S(\\frac{1}{2}S+1)\\right)|\\mathrm{G}; J, \\hat{\\Omega}\\rangle. ", "\\nonumber\\end{aligned}$$ Non-zero eigenvalues ($J=0, 1, \\ldots, S$) are seen from (\\[appl\\]) as $$\\begin{aligned}\n \\Lambda(J)\\equiv\\frac{1}{(S+1)^{2}}\\sum^{S}_{l=0}(2l+1)\\lambda^{L-1}(l,S)\nI_{l}\\left(\\frac{1}{2}J(J+1)-\\frac{1}{2}S(\\frac{1}{2}S+1)\\right).\\nonumber\\\\ \\label{eiva}\\end{aligned}$$ Since all other eigenvalues of the density matrix are vanishing, then we conclude again that the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[matrix\\]) is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is spanned by the set of vectors $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ (\\[eiges\\]). (", "The rank of the set is equal to $(S+1)^2$.) Furthermore, we observe from (\\[eiva\\]) again that non-zero eigenvalues $\\Lambda(J)$ depend only on $J$, not on $\\hat{\\Omega}$. Therefore, $\\{|\\mbox{G}; J, \\hat{\\Omega}\\rangle\\}$ with fixed $J$ value spans a degenerate subspace with the same eigenvalue.", "\n\nThe Large Block Limit {#sec:larges}\n---------------------\n\nIn the limit $L\\rightarrow\\infty$, that is when the size of the block becomes large, we learned from [@FKR; @Had; @KHH] that the von Neumann entropy reaches the saturated value $S_{\\mathrm{v\\ N}}=\\ln\\left(S+1\\right)^{2}$. This fact implies that the density matrix (denoted by $\\boldsymbol{\\rho}_{\\infty}$ in the limit) can only take the form (see [@NC] for a general proof) $$\\begin{aligned}\n \\boldsymbol{\\rho}_{\\infty}=\\frac{1}{(S+1)^{2}}I_{(S+1)^{2}}\\oplus \\Phi_{\\infty}, \\label{denl}\\end{aligned}$$ where $I_{(S+1)^{2}}$ is the identity of dimension $(S+1)^{2}$ and $\\Phi_{\\infty}$ is an infinite dimensional matrix with only zero entries. ", "In this section, we give a proof of **Conjecture 1** (\\[conj2\\]) in the limiting case as $L\\rightarrow\\infty$. Then we shall verify the structure of the density matrix (\\[denl\\]) explicitly.", "\n\nWe first realize from (\\[lamb\\]) that as $L\\rightarrow\\infty$, $\\lambda^{L-1}(l,S)\\rightarrow \\delta_{l,0}$. Therefore only the first term with $l=0$ is left in (\\[sum\\]) and contributes to the final result. ", "So that we need only to calculate $K^{\\dagger}_{0}(\\hat{\\Omega})$: $$\\begin{aligned}\n K^{\\dagger}_{0}(\\hat{\\Omega})&=&\\int \\mathrm{d}\\hat{\\Omega}_{1} \\mathrm{d}\\hat{\\Omega}_{L} \n \\left(u_{1}a^{\\dagger}_{1}+v_{1}b^{\\dagger}_{1}\\right)^{S} \\left(uu^{\\ast}_{1}+vv^{\\ast}_{1}\\right)^{J} \\nonumber \\\\ &&\\cdot\n\\left(u^{\\ast}_{1}v^{\\ast}_{L}-v^{\\ast}_{1}u^{\\ast}_{L}\\right)^{S-J}\n\\left(uu^{\\ast}_{L}+vv^{\\ast}_{L}\\right)^{J}\n\\left(u_{L}a^{\\dagger}_{L}+v_{L}b^{\\dagger}_{L}\\right)^{S}. ", "\\label{k0}\\end{aligned}$$\n\nIt is useful to know transformation properties of the integrand in (\\[k0\\]) under $SU(2)$. The pair of variables $(u, v)$ defined in (\\[spin\\]) and bosonic annihilation operators $(a, b)$ in the Schwinger representation both transform as spinors under $SU(2)$. That is to say, if we take an arbitrary element $\\mathbf{D}\\in SU(2)$ (a $2\\times 2$ unitary matrix with determinant $1$), then $(u, v)$, *etc.* ", "transform according to $$\\begin{aligned}\n\\left( \\begin{array}{c}\n u \\\\ v \n\\end{array}\\right)\n\\rightarrow \\mathbf{D}\n\\left( \\begin{array}{c}\n u \\\\ v\n\\end{array} \\right). ", "\\label{tran}\\end{aligned}$$ On the other hand, $(u^{\\ast}, v^{\\ast})$, $(-v, u)$, $(a^{\\dagger}, b^{\\dagger})$ and $(-b, a)$ transform conjugately to $(u, v)$. That is to say $(u^{\\ast}, v^{\\ast})$, *etc.* ", "transform according to $$\\begin{aligned}\n \\left( \\begin{array}{c}\n u^{\\ast} \\\\ v^{\\ast} \n\\end{array}\\right)\n\\rightarrow \\mathbf{D}^{\\ast}\n\\left( \\begin{array}{c}\n u^{\\ast} \\\\ v^{\\ast}\n\\end{array}\\right). ", "\\label{ctra}\\end{aligned}$$ The combinations appeared in $K^{\\dagger}_{0}(\\hat{\\Omega})$ (\\[k0\\]) $$\\begin{aligned}\n u_{1}a^{\\dagger}_{1}+v_{1}b^{\\dagger}_{1},\\ \\ uu^{\\ast}_{1}+vv^{\\ast}_{1},\\ \\ u^{\\ast}_{1}v^{\\ast}_{L}-v^{\\ast}_{1}u^{\\ast}_{L},\\ \\ uu^{\\ast}_{L}+vv^{\\ast}_{L},\\ \\\n u_{L}a^{\\dagger}_{L}+v_{L}b^{\\dagger}_{L} \\label{comb}\\end{aligned}$$ as well as $A^{\\dagger}_{J}$ in (\\[aope\\]), boundary operator $B^{\\dagger}$ in (\\[bope1\\]), *etc.* ", "all transform covariantly under $SU(2)$, *i.e.* those expressions keep their form in the new (transformed) coordinates.", "\n\nThese transformation properties (\\[tran\\]), (\\[ctra\\]) can be used to simplify the $K^{\\dagger}_{0}(\\hat{\\Omega})$ integral. ", "We first make a $SU(2)$ transform $$\\begin{aligned}\n \\mathbf{D}_{u_{L}}=\n\\left( \\begin{array}{cc}\n u^{\\ast}_{L} & v^{\\ast}_{L} \\\\\n -v_{L} & u_{L}\n\\end{array} \\right), \\qquad\n\\mathbf{D}_{u_{L}}\n\\left( \\begin{array}{c}\n u_{L} \\\\ v_{L}\n\\end{array} \\right)=\\left( \\begin{array}{c}\n 1 \\\\ 0\n\\end{array} \\right), \\label{utra}\\end{aligned}$$ under the part of the integral (\\[k0\\]) over $\\hat{\\Omega}_{1}$. Then this part of integral becomes $$\\begin{aligned}\n \\int \\mathrm{d}\\hat{\\Omega}_{1} \n\\left(u_{1}a^{\\dagger}_{1}+v_{1}b^{\\dagger}_{1}\\right)^{S} \\left(uu^{\\ast}_{1}+vv^{\\ast}_{1}\\right)^{J} \\left(-v^{\\ast}_{1}\\right)^{S-J}.\\end{aligned}$$ This can be calculated using binomial expansion and the result is $$\\begin{aligned}\n \\frac{4\\pi}{S+1}\\left(ua^{\\dagger}_{1}+vb^{\\dagger}_{1}\\right)^{J} \\left(-b^{\\dagger}_{1}\\right)^{S-J}. ", "\\label{part1}\\end{aligned}$$ Then we make an inverse transform in (\\[part1\\]) using $\\mathbf{D}^{-1}_{u_{L}}=\\mathbf{D}^{\\dagger}_{u_{L}}$, consequently (\\[k0\\]) is put in a form with a single integral over $\\hat{\\Omega}_{L}$ remaining: $$\\begin{aligned}\nK^{\\dagger}_{0}(\\hat{\\Omega})&=&\\frac{4\\pi}{S+1}\\left(ua^{\\dagger}_{1}+vb^{\\dagger}_{1}\\right)^{J} \\label{rema} \\\\\n&&\\cdot\\int \\mathrm{d}\\hat{\\Omega}_{L} \n\\left(a^{\\dagger}_{1}v^{\\ast}_{L}-b^{\\dagger}_{1}u^{\\ast}_{L}\\right)^{S-J}\n\\left(uu^{\\ast}_{L}+vv^{\\ast}_{L}\\right)^{J} \\left(u_{L}a^{\\dagger}_{L}+v_{L}b^{\\dagger}_{L}\\right)^{S}. ", "\\nonumber\\end{aligned}$$ Now we make another $SU(2)$ transform using $$\\begin{aligned}\n \\mathbf{D}_{u}=\n\\left( \\begin{array}{cc}\n u^{\\ast} & v^{\\ast} \\\\\n -v & u\n\\end{array} \\right), \\qquad\n\\mathbf{D}_{u}\n\\left( \\begin{array}{c}\n u \\\\ v\n\\end{array} \\right)=\\left( \\begin{array}{c}\n 1 \\\\ 0\n\\end{array} \\right),\\end{aligned}$$ then the remaining integral over $\\hat{\\Omega}_{L}$ in (\\[rema\\]) becomes $$\\begin{aligned}\n\\int \\mathrm{d}\\hat{\\Omega}_{L} \n\\left(a^{\\dagger}_{1}v^{\\ast}_{L}-b^{\\dagger}_{1}u^{\\ast}_{L}\\right)^{S-J}\n\\left(u^{\\ast}_{L}\\right)^{J} \\left(u_{L}a^{\\dagger}_{L}+v_{L}b^{\\dagger}_{L}\\right)^{S}. ", "\\label{reml}\\end{aligned}$$ Using again binomial expansion, this integral (\\[reml\\]) yields $$\\begin{aligned}\n\\frac{4\\pi}{S+1}\n\\left(a^{\\dagger}_{1}b^{\\dagger}_{L}-b^{\\dagger}_{1}a^{\\dagger}_{L}\\right)^{S-J}\n\\left(a^{\\dagger}_{L}\\right)^{J}. ", "\\label{part2}\\end{aligned}$$ At last we make an inverse transform in (\\[part2\\]) using $\\mathbf{D}^{-1}_{u}=\\mathbf{D}^{\\dagger}_{u}$ and plug the result into (\\[rema\\]), the final form is $$\\begin{aligned}\nK^{\\dagger}_{0}(\\hat{\\Omega})\n=\\left(\\frac{4\\pi}{S+1}\\right)^{2}A^{\\dagger}_{J}. ", "\\label{fina}\\end{aligned}$$ This expression is consistent with **Conjecture 1** (\\[conj2\\]), which also proves that $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ is a set of eigenvectors of the density matrix as $L\\rightarrow\\infty$. Let us denote the density matrix in the limit by $\\boldsymbol{\\rho}_{\\infty}$. Then (\\[fina\\]) leads to the result (see (\\[appl\\])) $$\\begin{aligned}\n \\boldsymbol{\\rho}_{\\infty}|\\mathrm{G}; J, \\hat{\\Omega}\\rangle=\n \\frac{1}{(S+1)^{2}}\\,|\\mathrm{G}; J, \\hat{\\Omega}\\rangle. ", "\\label{appll}\\end{aligned}$$\n\nWe find from (\\[appll\\]) that the limiting eigenvalue $$\\begin{aligned}\n \\Lambda_{\\infty}=\\frac{1}{(S+1)^{2}}, \\qquad L\\to\\infty\\end{aligned}$$ is independent of $J$. Any vector of the $(S+1)^2$-dimensional subspace spanned by the set $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ is an eigenvector of $\\boldsymbol{\\rho}_{\\infty}$ with the same eigenvalue $1/(S+1)^{2}$. Therefore $\\boldsymbol{\\rho}_{\\infty}$ acts on this subspace as (proportional to) the identity $I_{(S+1)^{2}}$. So that we have proved explicitly that the density matrix takes the form (\\[denl\\]) in the large block limit. ", "The limiting density matrix is proportional to a projector $\\mathbf{P}_{(S+1)^{2}}$ on the degenerate ground states of the block Hamiltonian $H_{B}$ (\\[degels\\]) $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}\\to\\boldsymbol{\\rho}_{\\infty}=\\frac{1}{(S+1)^{2}}\\,\\mathbf{P}_{(S+1)^{2}} , \\qquad L\\to\\infty. ", "\\label{largedens}\\end{aligned}$$ In addition, we also derive from the eigenvalues that the von Neumann entropy $S_{\\mathrm{v\\ N}}=-\\sum^{S}_{J=0}(2J+1)\\Lambda_{\\infty}\\ln\\Lambda_{\\infty}$ coincides with the Rényi entropy $S_{\\mathrm{R}}(\\alpha)=\\frac{1}{1-\\alpha}\\ln\\left\\{\\sum^{S}_{J=0}(2J+1)\\Lambda^{\\alpha}_{\\infty}\\right\\}$ and is equal to the saturated value $$\\begin{aligned}\n S_{\\mathrm{v\\ N}}=S_{\\mathrm{R}}(\\alpha)=\\ln(S+1)^{2} , \\qquad L\\to\\infty.\\end{aligned}$$\n\nThe Density Matrix and Correlation Functions {#sec:denandcorr}\n--------------------------------------------\n\nThe relation between the density matrix and correlation functions was studied in [@AAH; @JK; @KHH; @XKHK]. ", "It was shown in [@JK] that the density matrix contains information of all correlation functions in the ground state. ", "The original proof was for spin $S=1/2$. In this section we generalize the result to generic spin-$S$ as in [@XKHK] and the proof is written in a form applicable but not restricted to the VBS state.", "\n\nThe Hilbert space associated with a spin-$S$ is $(2S+1)$-dimensional. ", "Therefore we could choose a basis of $(2S+1)^{2}$ linearly independent matrices such that an arbitrary operator defined in the Hilbert space can be written as a superposition over the basis. ", "Let us denote the basis by $\\{A_{ab}\\ | \\ a,b=1,\\ldots,2S+1\\}$, in which each matrix $A_{ab}$ is labeled by a pair of indices $a$ and $b$ with totally $(2S+1)^{2}$ possible combinations. ", "The matrix element is defined as $$\\begin{aligned}\n (A_{ab})_{kl}=\\delta_{ak}\\delta_{bl}, \\qquad k,l=1,\\ldots,2S+1. ", "\\label{aab}\\end{aligned}$$ In addition to $\\{A_{ab}\\}$, we introduce an equivalent *conjugate basis* $\\{\\bar{A}_{ab}\\}$ such that $$\\begin{aligned}\n (\\bar{A}_{ab})_{kl}=\\delta_{al}\\delta_{bk}, \\qquad a,b,k,l=1,\\ldots,2S+1. ", "\\label{abar}\\end{aligned}$$ These matrices (\\[aab\\]) and (\\[abar\\]) are actually matrix representation of operators $\\{|S,m\\rangle\\langle S,m^{\\prime}| \\ |\\ m,m^{\\prime}=-S,\\ldots,S\\}$. They are normalized such that $$\\begin{aligned}\n \\mathrm{tr}(\\bar{A}_{ab}A_{cd})=\\sum_{k,l}(\\bar{A}_{ab})_{kl}(A_{cd})_{lk}=\\sum_{k,l}\\delta_{al}\\delta_{bk}\\delta_{cl}\\delta_{dk}=\\delta_{ac}\\delta_{bd}. ", "\\label{traceaa}\\end{aligned}$$ Here ‘$\\mathrm{tr}$’ takes trace at one and the same site. ", "Because of the completeness of $\\{A_{ab}\\}$ at each site, the density matrix of the block ($B$) can be written as (see (\\[den1\\])) $$\\begin{aligned}\n \\boldsymbol{\\rho}_{B}=\\mathrm{tr}_{E}|\\mathrm{G}\\rangle\\langle \\mathrm{G}|=\\sum_{\\{a_{j}b_{j}\\}}\\left(\\bigotimes_{j\\in B}A_{a_{j}b_{j}}\\right)\\mathrm{coeff}\\{a_{j}b_{j}\\}, \\label{rhoblock}\\end{aligned}$$ where $|\\mathrm{G}\\rangle$ denotes the unique ground state (*e.g.* the VBS state), $\\mathrm{tr}_{E}$ takes traces of sites outside the block (*i.e.* sites in the environment $E$) and $\\mathrm{coeff}\\{a_{j}b_{j}\\}$ denotes the coefficient. ", "Using the normalization property (\\[traceaa\\]), the coefficient $\\mathrm{coeff}\\{a_{j}b_{j}\\}$ with label $j$ taking values within the block can be expressed as $$\\begin{aligned}\n \\mathrm{coeff}\\{a_{j}b_{j}\\}&=&\\sum_{\\{c_{j}d_{j}\\}}\\prod_{j\\in B}\\mathrm{tr}(\\bar{A}_{a_{j}b_{j}}A_{c_{j}d_{j}})\\mathrm{coeff}\\{c_{j}d_{j}\\} \\nonumber \\\\\n &=&\\mathrm{tr}_{B}\\left[\\left(\\bigotimes_{j\\in B}\\bar{A}_{a_{j}b_{j}}\\right)\\boldsymbol{\\rho}_{B}\\right] \\nonumber \\\\\n&=&\\mathrm{tr}\\left[\\left(\\bigotimes_{j\\in B}\\bar{A}_{a_{j}b_{j}}\\right)|\\mathrm{G}\\rangle\\langle \\mathrm{G}|\\right]\\nonumber \\\\\n&=&\\langle \\mathrm{G}|\\left(\\bigotimes_{j\\in B}\\bar{A}_{a_{j}b_{j}}\\right)|\\mathrm{G}\\rangle. ", "\\label{coeajbj}\\end{aligned}$$ Here $\\mathrm{tr}_{B}$ takes traces of sites within the block and $\\mathrm{tr}$ takes traces of all lattice sites. ", "Combing (\\[rhoblock\\]) with (\\[coeajbj\\]), we have the final form $$\\begin{aligned}\n \\boldsymbol{\\rho}_{B}=\\sum_{\\{a_{j}b_{j}\\}}\\left(\\bigotimes_{j\\in B}A_{a_{j}b_{j}}\\right)\\langle \\mathrm{G}|\\left(\\bigotimes_{j\\in B}\\bar{A}_{a_{j}b_{j}}\\right)|\\mathrm{G}\\rangle. ", "\\label{rhocorr}\\end{aligned}$$ This is the expression of the density matrix with entries related to multi-point correlation functions $\\langle \\mathrm{G}|\\left(\\bigotimes_{j\\in B}\\bar{A}_{a_{j}b_{j}}\\right)|\\mathrm{G}\\rangle$ in the ground state. ", "All possible combinations $\\{a_{j}b_{j}\\}$ are involved in the summation. ", "Therefore, we have prove for generic spin-$S$ that the density matrix contains information of all correlation functions. ", "The matrix elements are all multi-point correlators.", "\n\nThe One–dimensional Inhomogeneous Model {#sec:1dinhom}\n=======================================\n\nThe most general $1$-dimensional model is the inhomogeneous model in which spins at different lattice site can take different values. ", "As a special case of the generalized model defined in §$\\,\\ref{sec:generalized}\\,$, we associate a positive integer number (called multiplicity numbers, see §$\\,\\ref{sec:generalhamil}\\,$) to each bond of the lattice and denote by $M_{ij}$ ($M_{ij}=M_{ji}$) the multiplicity number between sites $i$ and $j$. They are related to bulk spins by the following relation which ensures the existence of a unique ground state $$\\begin{aligned}\n 2S_{j}=M_{j-1,j}+M_{j,j+1}, \\qquad \\forall\\ j \\label{smrela00}\\end{aligned}$$ with $2S_{0}=M_{01}$ and $2S_{N+1}=M_{N, N+1}$ for ending spins. (", "Equation (\\[smrela00\\]) is a special case of the more general relation (\\[condition1\\]).) ", "The condition for solvability of relation (\\[smrela00\\]) is $$\\begin{aligned}\n \\sum^{N+1}_{j=0}(-1)^{j}S_{j}=0. ", "\\label{condition00}\\end{aligned}$$ Solution to relation (\\[smrela00\\]) under condition (\\[condition00\\]) is $$\\begin{aligned}\n M_{j,j+1}=2\\sum^{j}_{l=0}(-1)^{j-l}S_{l}\\geq 1. ", "\\label{solution00}\\end{aligned}$$ (More details can be found in [@KK].) ", "Now we defined the Hamiltonian of the inhomogeneous AKLT model according to (\\[generalizedh\\]) as $$\\begin{aligned}\n H=\\sum^{N}_{j=0}\\ \\sum^{S_{j}+S_{j+1}}_{J=S_{j}+S_{j+1}-M_{j,j+1}+1} C_{J}(j,j+1)\\,\\pi_{J}(j, j+1). ", "\\label{hami00}\\end{aligned}$$ Here the projector $\\pi_{J}(j, j+1)$ describes interactions between neighboring spins $j$ and $j+1$, which projects the bond spin $\\boldsymbol{J}_{j, j+1}\\equiv\\boldsymbol{S}_{j}+\\boldsymbol{S}_{j+1}$ onto the subspace with total spin $J$ ($J=S_{j}+S_{j+1}-M_{j,j+1}+1, \\ldots, S_{j}+S_{j+1}$). ", "An explicit expression of $\\pi_{J}(j,j+1)$ is given in §$\\,\\ref{sec:proj}\\,$ and [@KK]. ", "The coefficient $C_{J}(j,j+1)$ can take an arbitrary positive value. ", "This Hamiltonian (\\[hami00\\]) has a unique ground state (VBS state, see §$\\,\\ref{sec:unique}\\,$).", "\n\nFollowing [@XKHK2], we study the entanglement of the unique VBS ground state of the inhomogeneous model (\\[hami00\\]) in this section.", "\n\nThe VBS Ground State {#sec:inhomvbs}\n--------------------\n\nThe unique VBS ground state of the Hamiltonian (\\[hami00\\]) is given in the Schwinger representation by [@AAH; @KK] $$\\begin{aligned}\n |\\mathrm{VBS}\\rangle \\equiv\n \\prod^{N}_{j=0}\n\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{M_{j,j+1}}|\\mathrm{vac}\\rangle, \\label{inhomvbs}\\end{aligned}$$ where $a^{\\dagger}$, $b^{\\dagger}$ are bosonic creation operators defined in exactly the same way as in §$\\,\\ref{sec:vbssch}\\,$, the constraint on the total boson occupation number is now $(a^{\\dagger}_{j}a_{j}+b^{\\dagger}_{j}b_{j})/2=S_{j}$. The pure state density matrix of the VBS ground state (\\[inhomvbs\\]) is $$\\begin{aligned}\n \\boldsymbol{\\rho}=\\frac{|\\mathrm{VBS}\\rangle\\langle \\mathrm{VBS}|}{\\langle \\mathrm{VBS}|\\mathrm{VBS}\\rangle}. ", "\\label{pure00}\\end{aligned}$$ Normalization of the VBS state is (calculation similar to those in §$\\,\\ref{sec:norm}\\,$) $$\\begin{aligned}\n \\langle \\mathrm{VBS}|\\mathrm{VBS}\\rangle=\\frac{\\displaystyle\\prod^{N+1}_{j=0}(2S_{j}+1)!}{\\displaystyle\\prod^{N}_{j=0}(M_{j,j+1}+1)}. ", "\\label{normvbs00}\\end{aligned}$$ (See [@XKHK2] for more details.)", "\n\nThe Block Density Matrix {#sec:deninhom}\n------------------------\n\nWe take a block of $L$ contiguous bulk spins as a subsystem, which starts from site $k$ and ends at site $k+L-1$. Using the coherent state basis (\\[cohebas\\]) and completeness relation (\\[comp\\]), tracing out degrees of freedom outside the block, $\\boldsymbol{\\rho}_{L}$ can be written as [@KHH; @XKHK2] $$\\begin{aligned}\n &&\\boldsymbol{\\rho}_{L}=\n \\label{roug00} \\\\\n &&\\frac{\n\\displaystyle\\int\\left[\\prod^{k-1}_{j=0}\\prod^{N+1}_{j=k+L}\\mathrm{d}\\hat{\\Omega}_{j}\\right]\\prod^{k-2}_{j=0}\\prod^{N}_{j=k+L}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{M_{j,j+1}}\n B^{\\dagger}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|B}\n {\\displaystyle\\left[\\prod^{k+L-1}_{j=k}\\frac{(2S_{j}+1)!}{4\\pi}\\right]\n\\int\\left[\\prod^{N+1}_{j=0}\\mathrm{d}\\hat{\\Omega}_{j}\\right]\\prod^{N}_{j=0}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{M_{j,j+1}}}. ", "\\nonumber \\end{aligned}$$ Here the boundary operator $B$ and block VBS state $\\left|\\mathrm{VBS}_{L}\\right\\rangle$ are defined as $$\\begin{aligned}\n &&B\\equiv \\left(u_{k-1}b_{k}-v_{k-1}a_{k}\\right)^{M_{k-1,k}}\\left(a_{k+L-1}v_{k+L}-b_{k+L-1}u_{k+L}\\right)^{M_{k+L-1,k+L}}, \\nonumber \\\\ \\label{bope00} \\\\\n &&|\\mathrm{VBS}_{L}\\rangle \\equiv\n \\prod^{k+L-2}_{j=k}\n\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{M_{j,j+1}}|\\mathrm{vac}\\rangle, \\label{vbsl00}\\end{aligned}$$ respectively. ", "After performing integrals over $\\hat{\\Omega}_{j}$ ($j=0, 1, \\ldots, k-2, k+L+1, \\ldots, N, N+1$) in the numerator and all integrals in the denominator, the density matrix $\\boldsymbol{\\rho}_{L}$ turns out to be independent of spins outside the block. ", "This property has been proved for the homogeneous AKLT model in §$\\,\\ref{sec:1dssden}\\,$ (see also [@FKR; @KHH; @XKHK]). ", "Therefore, we can re-label spins within the block for notational convenience. ", "Let $k=1$ and the density matrix takes the form $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}=\\frac{\\displaystyle\\prod^{L}_{j=0}(M_{j,j+1}+1)}{\\displaystyle\\prod^{L}_{j=1}(2S_{j}+1)!}\\frac{1}{(4\\pi)^{2}}\n \\int \\mathrm{d}\\hat{\\Omega}_{0}\\mathrm{d}\\hat{\\Omega}_{L+1}\\,B^{\\dagger}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|B \\label{matr00}\\end{aligned}$$ with $$\\begin{aligned}\n&&B^{\\dagger}=\\left(u^{\\ast}_{0}b^{\\dagger}_{1}-v^{\\ast}_{0}a^{\\dagger}_{1}\\right)^{M_{0,1}}\\left(a^{\\dagger}_{L}v^{\\ast}_{L+1}-b^{\\dagger}_{L}u^{\\ast}_{L+1}\\right)^{M_{L,L+1}}, \\label{bope100} \\\\\n &&|\\mathrm{VBS}_{L}\\rangle=\\prod^{L-1}_{j=1}\n\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{M_{j,j+1}}|\\mathrm{vac}\\rangle. ", "\\label{vbsl100} \\end{aligned}$$ Again, the remaining two integrals in (\\[matr00\\]) are kept in the present form for later use.", "\n\nGround States of the Block Hamiltonian {#sec:gsbhinhom}\n--------------------------------------\n\nThe block Hamiltonian with the re-labeling $k=1$ reads $$\\begin{aligned}\n H_{B}=\\sum^{L-1}_{j=1}\\ \\sum^{S_{j}+S_{j+1}}_{J=S_{j}+S_{j+1}-M_{j,j+1}+1} C_{J}(j,j+1)P_{J}(j, j+1). ", "\\label{blockhamire00}\\end{aligned}$$ Now the degenerate ground states are constructed in a similar way as in §$\\,\\ref{sec:gsbhs}\\,$. The new $A^{\\dagger}_{J}$ operator is defined as: $$\\begin{aligned}\n A^{\\dagger}_{J}\\equiv\n\\left(ua^{\\dagger}_{1}+vb^{\\dagger}_{1}\\right)^{J_{-}+J} \\left(a^{\\dagger}_{1}b^{\\dagger}_{L}-b^{\\dagger}_{1}a^{\\dagger}_{L}\\right)^{J_{+}-J}\n\\left(ua^{\\dagger}_{L}+vb^{\\dagger}_{L}\\right)^{-J_{-}+J}, \\label{aope00}\\end{aligned}$$ where $J_{-}\\equiv(M_{01}-M_{L,L+1})/2$, $J_{+}\\equiv(M_{01}+M_{L,L+1})/2$ and $|J_{-}|\\leq J\\leq J_{+}$. Then the set of ground states of the block Hamiltonian (\\[blockhamire00\\]) is $$\\begin{aligned}\n |\\mathrm{G}; J, \\hat{\\Omega}\\rangle \\equiv\nA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle, \\qquad J=|J_{-}|, \\ldots, J_{+}. ", "\\label{eigeinhom}\\end{aligned}$$ To prove that any state $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ is a zero-energy ground state of (\\[blockhamire00\\]), we essentially repeat the arguments as in §$\\,\\ref{sec:gsbhs}\\,$ for any site $j$ and bond $(j, j+1)$:\n\n1. ", " The total power of $a^{\\dagger}_{j}$ and $b^{\\dagger}_{j}$ is $2S_{j}$, so that we have spin-$S_{j}$ at site $j$;\n\n2. ", " $-\\frac{1}{2}(M_{j-1,j}+M_{j+1,j+2})\\leq J^{z}_{j,j+1}\\equiv S^{z}_{j}+S^{z}_{j+1}\\leq \\frac{1}{2}(M_{j-1,j}+M_{j+1,j+2})$ by a binomial expansion, so that the maximum value of the bond spin $J_{j,j+1}$ is $\\frac{1}{2}(M_{j-1,j}+M_{j+1,j+2})=S_{j}+S_{j+1}-M_{j,j+1}$ (from $SU(2)$ invariance, see [@AAH]).", "\n\nTherefore, the state $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ defined in (\\[eigeinhom\\]) has spin-$S_{j}$ at site $j$ and no projection onto the $J_{j, j+1}>S_{j}+S_{j+1}-M_{j,j+1}$ subspace for any bond.", "\n\nParallelly, we also introduce an orthogonal basis in description of the degenerate zero-energy ground states of $H_{B}$ (\\[blockhamire00\\]), *i.e.* the degenerate VBS states. ", "Using the same notations as in §$\\,\\ref{sec:gsbhs}\\,$, the operator $A^{\\dagger}_{J}$ defined in (\\[aope00\\]) can be expanded as (see [@Ha; @XKHK2]) $$\\begin{aligned}\n A^{\\dagger}_{J}&=&\\sqrt{\\frac{(J_{+}+J+1)!(J_{-}+J)!(J_{+}-J)!(-J_{-}+J)!}{2J+1}} \n \\sum^{J}_{M=-J}X_{JM} \\label{aexp00} \\\\\n &&\\cdot\\sum^{m_{1}+m_{L}=M}_{m_{1}, m_{L}}(\\frac{1}{2}M_{01}, m_{1}; \\frac{1}{2}M_{L,L+1}, m_{L}|J, M)\\ \\psi^{\\dagger}_{\\frac{1}{2}M_{01},m_{1}}\\otimes\\psi^{\\dagger}_{\\frac{1}{2}M_{L,L+1},m_{L}}, \\nonumber\\end{aligned}$$ where $(\\frac{1}{2}M_{01}, m_{1}; \\frac{1}{2}M_{L,L+1}, m_{L}|J, M)$ is the Clebsch-Gordan coefficient. ", "Again, the particular form of the sum over $m_{1}$ and $m_{L}$ in (\\[aexp00\\]) is identified as a single spin state creation operator $$\\begin{aligned}\n \\Psi^{\\dagger}_{JM}\\equiv\\sum^{m_{1}+m_{L}=M}_{m_{1}, m_{L}}(\\frac{1}{2}M_{01}, m_{1}; \\frac{1}{2}M_{L,L+1}, m_{L}|J, M)\\ \\psi^{\\dagger}_{\\frac{1}{2}M_{01},m_{1}}\\otimes\\psi^{\\dagger}_{\\frac{1}{2}M_{L,L+1},m_{L}}.\\nonumber \\\\ \\label{crea200}\\end{aligned}$$ So that the set of *degenerate VBS states* $\\{|\\mathrm{VBS}_L(J,M)\\rangle\\}$ is defined as $$\\begin{aligned}\n |\\mathrm{VBS}_L(J,M)\\rangle\\equiv \\Psi^{\\dagger}_{JM}|\\mathrm{VBS}_L\\rangle, \\quad J=|J_{-}|,...,J_{+}, \\quad M=-J, ...,J. \\label{devb00}\\end{aligned}$$ Then these $(M_{01}+1)(M_{L,L+1}+1)$ states (\\[devb00\\]) are mutually orthogonal (the proof is exactly the same as in §$\\,\\ref{sec:gsbhs}\\,$). ", "Also, the state $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ written as a linear superposition over these degenerate VBS states reads $$\\begin{aligned}\n |\\mathrm{G};J,\\hat{\\Omega}\\rangle&=&\\sqrt{\\frac{(J_{+}+J+1)!(J_{-}+J)!(J_{+}-J)!(-J_{-}+J)}{2J+1}}\n \\nonumber \\\\\n &&\\cdot\\sum^{J}_{M=-J}X_{JM}|\\mathrm{VBS}_{L}(J, M)\\rangle.", "\n \\label{line00}\\end{aligned}$$\n\nTherefore, as seen from (\\[line00\\]), the rank of set of states $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ with the same $J$ value is $2J+1$ and the total number of linearly independent states of the set $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ is $\\sum^{J_{+}}_{J=|J_{-}|}(2J+1)=(M_{01}+1)(M_{L,L+1}+1)$, which is exactly the degeneracy of the ground states of (\\[blockhamire00\\]). ", "So that $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ forms a complete set of zero-energy ground states. ", "The orthogonal set $\\{|\\mathrm{VBS}_L(J,M)\\rangle\\}$ also forms a complete set of zero-energy ground states, which differs from $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ by a change of basis.", "\n\nDiagonalization of the Density Matrix {#sec:diadeninhom}\n-------------------------------------\n\nThe density matrix is diagonalized in §$\\,\\ref{sec:eigvecs}\\,$ and §$\\,\\ref{sec:alterproof}\\,$ for the homogeneous AKLT model. ", "The analysis can be made in parallel for the inhomogeneous model.", "\n\nThe statement of **Theorem** \\[theorem2\\] is still valid here. *", "i.e.* Eigenvectors of the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[matr00\\]) with non-zero eigenvalues are given by the set $\\{|\\mbox{G}; J, \\hat{\\Omega}\\rangle\\}$ (\\[eigeinhom\\]) or $\\{|\\mathrm{VBS}_L(J,M)\\rangle\\}$ (\\[devb00\\]). ", "This explicit construction of eigenvectors yields a direct diagonalization of the density matrix.", "\n\nAgain, we prove the theorem by re-writing the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[matr00\\]) as a projector in diagonal form onto the orthogonal degenerate VBS states $\\{|\\mathrm{VBS}_{L}(J, M)\\rangle\\}$ introduced in (\\[devb00\\]).", "\n\nTake expression (\\[matr00\\]) and integrate over $\\hat{\\Omega}_{0}$ and $\\hat{\\Omega}_{L+1}$ using binomial expansions and $$\\begin{aligned}\n \\int^{1}_{-1}\\mathrm{d}x (1+x)^{m}(1-x)^{n}=\\frac{m!n!}{(m+n+1)!}2^{m+n+1}.\\end{aligned}$$ Then we have $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}&=& \\frac{\\displaystyle\\prod^{L-1}_{j=1}(M_{j,j+1}+1)}{\\displaystyle\\prod^{L}_{j=1}(2S_{j}+1)!}\\sum^{M_{01}}_{p=0}\\sum^{M_{L,L+1}}_{q=0}\\left(\\begin{array}{c}M_{01}\\\\p\\end{array}\\right)\\left(\\begin{array}{c}M_{L,L+1}\\\\q\\end{array}\\right)\n\\nonumber \\\\\n&&(b^{\\dagger}_{1})^{p}(a^{\\dagger}_{1})^{M_{01}-p}(a^{\\dagger}_{L})^{q}(b^{\\dagger}_{L})^{M_{L,L+1}-q}|\\mathrm{VBS}_{L}\\rangle\n\\nonumber \\\\\n&&\\langle\\mathrm{VBS}_{L}|(b_{L})^{M_{L,L+1}-q}(a_{L})^{q}(a_{1})^{M_{01}-p}(b_{1})^{p}. ", "\\label{treat100}\\end{aligned}$$ The particular combinations of bosonic operators appeared in (\\[treat100\\]) are recognized up to a constant as spin creation operators $\\psi^{\\dagger}_{\\frac{1}{2}M_{01},\\frac{1}{2}M_{01}-p}$ and\\\n$\\psi^{\\dagger}_{\\frac{1}{2}M_{L,L+1},q-\\frac{1}{2}M_{L,L+1}}$ at site $1$ and site $L$, respectively. ", "They commute with all bond operators $\\left(a^{\\dagger}_{j}b^{\\dagger}_{j+1}-b^{\\dagger}_{j}a^{\\dagger}_{j+1}\\right)^{M_{j,j+1}}$, so that we could simplify the right hand side of (\\[treat100\\]) using definition (\\[crea200\\]) and the following identity: $$\\begin{aligned}\n&&\\sum^{M_{01}}_{p=0}\\sum^{M_{L,L+1}}_{q=0}\\psi^{\\dagger}_{\\frac{1}{2}M_{01},\\frac{1}{2}M_{01}-p}\\otimes\\psi^{\\dagger}_{\\frac{1}{2}M_{L,L+1},q-\\frac{1}{2}M_{L,L+1}}|\\mathrm{vac}\\rangle_{1,L}\n\\nonumber \\\\\n&&{}_{1,L}\\langle\\mathrm{vac}|\\psi_{\\frac{1}{2}M_{01},\\frac{1}{2}M_{01}-p}\\otimes\\psi_{\\frac{1}{2}M_{L,L+1},q-\\frac{1}{2}M_{L,L+1}} \\nonumber \\\\\n&=&\\sum^{M_{01}}_{p=0}\\sum^{M_{L,L+1}}_{q=0}|\\frac{1}{2}M_{01},\\frac{1}{2}M_{01}-p\\rangle_{1}\\langle\\frac{1}{2}M_{01},\\frac{1}{2}M_{01}-p| \\nonumber \\\\\n&&\\otimes|\\frac{1}{2}M_{L,L+1},q-\\frac{1}{2}M_{L,L+1}\\rangle_{L}\\langle\\frac{1}{2}M_{L,L+1},q-\\frac{1}{2}M_{L,L+1}| \\nonumber \\\\\n&=&\\sum^{J_{+}}_{J=|J_{-}|}\\sum^{J}_{M=-J}|J,M\\rangle_{1,L}\\langle J,M| \\nonumber \\\\\n&=&\\sum^{J_{+}}_{J=|J_{-}|}\\sum^{J}_{M=-J}\\Psi^{\\dagger}_{JM}|\\mathrm{vac}\\rangle_{1,L}\\langle \\mathrm{vac}|\\Psi_{JM}.\\end{aligned}$$ The resultant final form of density matrix $\\boldsymbol{\\rho}_{L}$ is then $$\\begin{aligned}\n &&\\boldsymbol{\\rho}_{L}=\\frac{\\displaystyle\\prod^{L-1}_{j=1}(M_{j,j+1}+1)}{\\displaystyle\\prod^{L}_{j=1}(2S_{j}+1)!}M_{01}!M_{L,L+1}!\\sum^{J_{+}}_{J=|J_{-}|}\\sum^{J}_{M=-J}\\Psi^{\\dagger}_{JM}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|\\Psi_{JM} \\label{fipr00} \\nonumber \\\\\n&&=\\frac{\\displaystyle\\prod^{L-1}_{j=1}(M_{j,j+1}+1)}{\\displaystyle\\prod^{L}_{j=1}(2S_{j}+1)!}M_{01}!M_{L,L+1}!\\sum^{J_{+}}_{J=|J_{-}|}\\sum^{J}_{M=-J}|\\mathrm{VBS}_{L}(J, M)\\rangle\\langle \\mathrm{VBS}_{L}(J, M)|. ", "\\nonumber \\\\ \\label{finalrho00}\\end{aligned}$$\n\nThe set of degenerate VBS states $\\{|\\mathrm{VBS}_{L}(J, M)\\rangle\\}$ with $J=|J_{-}|,\\ldots,J_{+}$ and $M=-J,\\ldots,J$ forms an orthogonal basis. ", "These $(M_{01}+1)(M_{L,L+1}+1)$ states also forms a complete set of zero-energy ground states of the block Hamiltonian (\\[blockhamire00\\]). ", "So that in expression (\\[finalrho00\\]) we have re-written the density matrix as a projector in diagonal form over an orthogonal basis. ", "Each degenerate VBS state $|\\mathrm{VBS}_{L}(J, M)\\rangle$ is an eigenvector of the density matrix, so as any of the state $|\\mbox{G}; J, \\hat{\\Omega}\\rangle$ (because of the degeneracy of corresponding eigenvalues of the density matrix, see §$\\,\\ref{sec:eigvalinhom}\\,$). ", "Thus we have generalized **Theorem** \\[theorem2\\] to the inhomogeneous case.", "\n\nEigenvalues of the Density Matrix {#sec:eigvalinhom}\n---------------------------------\n\nGiven the diagonalized form (\\[finalrho00\\]), again eigenvalues of the density matrix $\\boldsymbol{\\rho}_{L}$ are derived from normalization of degenerate VBS states with an explicit expression in terms of Wigner $3j$-symbols.", "\n\nSimilarly, we first calculate the integral of the norm square of $|\\mbox{G};J,{\\hat\\Omega}\\rangle$over the unit vector $\\hat{\\Omega}$ $$\\begin{aligned}\n &&\\frac{1}{4\\pi}\\int \\mathrm{d}{\\hat \\Omega}\\,\\langle\\mathrm{G};J,\\hat{\\Omega}|\\mathrm{G};J,\\hat{\\Omega}\\rangle \\label{novb00} \\\\\n&=& \\frac{(J_{+}+J+1)!(J_{-}+J)!(J_{+}-J)!(-J_{-}+J)!}{(2J+1)!}\\,\\langle \\mathrm{VBS}_L(J,M)|\\mathrm{VBS}_L(J,M)\\rangle.\\nonumber\\end{aligned}$$ This expression (\\[novb00\\]) also states that normalization of the degenerate VBS state is independent of $\\hat{\\Omega}$ and/or $M$.\n\nLet us consider the integral involved in (\\[novb00\\]). ", "Using coherent state basis (\\[cohebas\\]) and completeness relation (\\[comp\\]) as before, we obtain $$\\begin{aligned}\n&& \\frac{1}{4\\pi}\\int \\mathrm{d}{\\hat\\Omega}\\,\\langle\\mathrm{G};J,{\\hat\\Omega}|\\mathrm{G};J,{\\hat\\Omega}\\rangle\n\\label{inne00} \\\\\n&=& \\frac{1}{4\\pi}\\left[\\prod^{L}_{j=1}\\frac{(2S_{j}+1)!}{4\\pi}\\right] \\int \\mathrm{d}{\\hat\\Omega} \\int \\left[\\prod^{L}_{j=1} \\mathrm{d}{\\hat\\Omega}_{j}\\right] \\prod^{L-1}_{j=1}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{M_{j,j+1}} \\nonumber \\\\\n&&\\cdot\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{1}\\cdot\\hat{\\Omega}_{L})\\right]^{J_{+}-J}\n\\left[\\frac{1}{2}(1+\\hat{\\Omega}_{1} \\cdot\\hat{\\Omega})\\right]^{J_{-}+J}\n\\left[\\frac{1}{2}(1+\\hat{\\Omega} \\cdot\\hat{\\Omega}_{L})\\right]^{-J_{-}+J}. ", "\\nonumber\\end{aligned}$$ Now we expand $\\left[\\frac{1}{2}(1-\\hat{\\Omega}_i \\cdot\\hat{\\Omega}_j)\\right]^{M_{ij}}$ in terms of spherical harmonics $$\\begin{aligned}\n\\left[\\frac{1}{2}(1-\\hat{\\Omega}_i \\cdot\\hat{\\Omega}_j)\\right]^{M_{ij}}\n=\\frac{4\\pi}{M_{ij}+1}\\sum^{M_{ij}}_{l=0}\\lambda(l,M_{ij})\\sum^{l}_{m=-l} Y_{lm}(\\hat{\\Omega}_{i})\nY^{\\ast}_{lm}(\\hat{\\Omega}_{j}) \\label{expansion00}\\end{aligned}$$ with $$\\lambda(l,M_{ij})=\\frac{(-1)^l M_{ij}!(M_{ij}+1)!}{(M_{ij}-l)!(M_{ij}+l+1)!}. ", "\\label{lambdalm00}$$ Then integrate over ${\\hat\\Omega}$ and from ${\\hat\\Omega}_2$ to ${\\hat\\Omega}_{L-1}$, the right hand side of (\\[inne00\\]) is equal to $$\\begin{aligned}\n&& \\frac{4\\pi \\displaystyle\\prod^{L}_{j=1}(2S_{j}+1)!}{\\left[\\displaystyle\\prod^{L-1}_{j=1}(M_{j,j+1}+1)\\right](J_{-}+J+1)(J_{+}-J+1)(-J_{-}+J+1)} \\nonumber \\\\\n&&\\sum^{M_{<}}_{l} \\sum^{J_{+}-J}_{l_{\\alpha}=0} \\sum^{J_{<}}_{l_{\\beta}=0}\n\\sum^{l}_{m=-l} \\sum^{l_{\\alpha}}_{m_{\\alpha}=-l_{\\alpha}} \\sum^{l_{\\beta}}_{m_{\\beta}=-l_{\\beta}}\n\\left[\\prod^{L-1}_{j=1}\\lambda(l,M_{j,j+1})\\right] \\nonumber \\\\\n&&\\cdot\\lambda(l_{\\alpha},J_{+}-J) \\lambda(l_{\\beta},J_{-}+J) \\lambda(l_{\\beta},-J_{-}+J)\n\\int \\mathrm{d}{\\hat\\Omega}_{1} \\int \\mathrm{d}{\\hat\\Omega}_{L}\n\\nonumber \\\\\n&&\\cdot Y_{l,m}({\\hat\\Omega}_{1})Y_{l_{\\alpha},m_{\\alpha}}({\\hat\\Omega}_{1})Y_{l_{\\beta},m_{\\beta}}({\\hat\\Omega}_1)\nY^{\\ast}_{l,m}({\\hat\\Omega}_{L})Y^{\\ast}_{l_{\\alpha},m_{\\alpha}}({\\hat\\Omega}_{L})Y^{\\ast}_{l_{\\beta},m_{\\beta}}({\\hat\\Omega}_{L}).\\nonumber\\\\\n\\label{pre100}\\end{aligned}$$ Where we have $M_{<}\\equiv \\mathrm{min}\\{M_{j,j+1},j=1,\\ldots,L-1\\}$ and $J_{<}\\equiv \\mathrm{min}\\{J_{-}+J, -J_{-}+J\\}$, both being the minimum of the corresponding set. ", "Now we carry out remaining integrals in (\\[pre100\\]) using $$\\begin{aligned}\n&&\\int \\mathrm{d}{\\hat\\Omega}\\, Y_{l,m}({\\hat\\Omega})Y_{l_{\\alpha},m_{\\alpha}}({\\hat\\Omega})Y_{l_{\\beta},m_{\\beta}}({\\hat\\Omega})\n\\nonumber \\\\\n&=&\\sqrt{\\frac{(2l+1)(2l_{\\alpha}+1)(2l_{\\beta}+1)}{4\\pi}}\n\\left(\\begin{array}{c c c}\nl & l_{\\alpha} & l_{\\beta} \\\\\n0 & 0 & 0 \n\\end{array}\\right)\n\\left(\\begin{array}{c c c}\nl & l_{\\alpha} & l_{\\beta} \\\\\nm & m_{\\alpha} & m_{\\beta} \n\\end{array}\\right). ", "\\nonumber\\\\ \\label{wign00}\\end{aligned}$$ The result after integration can be further simplified by applying the following orthogonality relation $$\\begin{aligned}\n \\sum_{m,m_{\\alpha}}(2l_{\\beta}+1)\n \\left(\\begin{array}{c c c}\n l & l_{\\alpha} & l_{\\beta} \\\\\n m & m_{\\alpha} & m_{\\beta} \n \\end{array}\\right)\n \\left(\\begin{array}{c c c}\n l & l_{\\alpha} & l^{\\prime}_{\\beta} \\\\\n m & m_{\\alpha} & m^{\\prime}_{\\beta} \n \\end{array}\\right)=\\delta_{l_{\\beta}l^{\\prime}_{\\beta}} \\delta_{m_{\\beta}m^{\\prime}_{\\beta}}, \\label{3jor00}\\end{aligned}$$ where $\\left(\\begin{array}{c c c}\nl & l_{\\alpha} & l_{\\beta} \\\\\nm & m_{\\alpha} & m_{\\beta} \n\\end{array}\\right)$, *etc.* ", "are the Wigner $3j$-symbols.", "\n\nSo that finally expression (\\[pre100\\]) is equal to $$\\begin{aligned}\n&&\\frac{\\displaystyle\\prod^{L}_{j=1}(2S_{j}+1)!}{\\left[\\displaystyle\\prod^{L-1}_{j=1}(M_{j,j+1}+1)\\right](J_{-}+J+1)(J_{+}-J+1)(-J_{-}+J+1)} \\nonumber \\\\\n&&\\sum^{M_{<}}_{l} \\sum^{J_{+}-J}_{l_{\\alpha}=0} \\sum^{J_{<}}_{l_{\\beta}=0}\n\\left[\\prod^{L-1}_{j=1}\\lambda(l,M_{j,j+1})\\right]\n\\lambda(l_{\\alpha},J_{+}-J) \\lambda(l_{\\beta},J_{-}+J) \\lambda(l_{\\beta},-J_{-}+J)\n\\nonumber \\\\\n&&\\cdot(2l+1)(2l_{\\alpha}+1)(2l_{\\beta}+1)\n\\left(\\begin{array}{c c c}\nl & l_{\\alpha} & l_{\\beta} \\\\\n0 & 0 & 0 \n\\end{array}\\right)^{2}. ", "\\label{renovb00}\\end{aligned}$$ The explicit value of $\\left(\\begin{array}{c c c}\nl & l_{\\alpha} & l_{\\beta} \\\\\n0 & 0 & 0 \n\\end{array} \\right)$ is given by $$\\begin{aligned}\n&&\\left(\\begin{array}{c c c}\nl & l_{\\alpha} & l_{\\beta} \\\\\n0 & 0 & 0 \n\\end{array} \\right) \\label{3jva00} \\\\\n&=&(-1)^{g} \\sqrt{\\frac{(2g-2l)!(2g-2l_{\\alpha})!(2g-2l_{\\beta})!}{(2g+1)!}}\\frac{g!}{(g-l)!(g-l_{\\alpha})!(g-l_{\\beta})!},", "\n\\nonumber\\end{aligned}$$ if $l+l_{\\alpha}+l_{\\beta}=2g$ ($g \\in \\mathbf{N}$), otherwise zero.", "\n\nCombining results of (\\[fipr00\\]), (\\[novb00\\]) and (\\[renovb00\\]), we arrive at the following result for eigenvalues: Eigenvalues $\\Lambda(J)$ $(J=|J_{-}|,\\ldots,J_{+})$ of the density matrix are independent of $\\hat{\\Omega}$ and/or $M$ in defining eigenvectors (see (\\[eigeinhom\\]) and (\\[devb00\\])). ", "An explicit expression is given by the following triple sum $$\\begin{aligned}\n&&\\Lambda(J) =\\frac{\\displaystyle\\prod^{L-1}_{j=1}(M_{j,j+1}+1)}{\\displaystyle\\prod^{L}_{j=1}(2S_{j}+1)!}{M_{01}!M_{L,L+1}!}\\,\\langle\\mathrm{VBS}_{L}(J,M)|\\mathrm{VBS}_{L}(J,M)\\rangle \\nonumber\\\\\n&&=\\frac{(2J+1)!M_{01}!M_{L,L+1}!}{(J_{+}+J+1)!(J_{-}+J+1)!(J_{+}-J+1)!(-J_{-}+J+1)!} ", "\\nonumber \\\\\n&&\\sum^{M_{<}}_{l} \\sum^{J_{+}-J}_{l_{\\alpha}=0} \\sum^{J_{<}}_{l_{\\beta}=0}\n\\left[\\prod^{L-1}_{j=1}\\lambda(l,M_{j,j+1})\\right]\n\\lambda(l_{\\alpha},J_{+}-J) \\lambda(l_{\\beta},J_{-}+J) \\lambda(l_{\\beta},-J_{-}+J)\n\\nonumber \\\\\n&&\\cdot(2l+1)(2l_{\\alpha}+1)(2l_{\\beta}+1)\n\\left(\\begin{array}{c c c}\nl & l_{\\alpha} & l_{\\beta} \\\\\n0 & 0 & 0 \n\\end{array}\\right)^{2}. ", "\\label{eivaex00}\n \\end{aligned}$$\n\nThe Large Block Limit {#sec:largeinhom}\n---------------------\n\nIn this section, we generalize the characteristic properties (§$\\,\\ref{sec:larges}\\,$) of the limiting density matrix to the inhomogeneous model.", "\n\nLet us apply the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[matr00\\]) to the state $|\\mathrm{G}; J, \\hat{\\Omega}\\rangle$ (\\[eigeinhom\\]) and get $$\\begin{aligned}\n &&\\boldsymbol{\\rho}_{L}|\\mathrm{G}; J, \\hat{\\Omega}\\rangle \\label{appl100} \\\\\n &=&\\frac{\\displaystyle\\prod^{L}_{j=0}(M_{j,j+1}+1)}{\\displaystyle\\prod^{L}_{j=1}(2S_{j}+1)!}\\frac{1}{(4\\pi)^{2}}\n \\int \\mathrm{d}\\hat{\\Omega}_{0}\\mathrm{d}\\hat{\\Omega}_{L+1}\\,B^{\\dagger}|\\mathrm{VBS}_{L}\\rangle\\langle \\mathrm{VBS}_{L}|BA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle. ", "\\nonumber\\end{aligned}$$ Using the coherent state basis (\\[cohebas\\]) and completeness relation (\\[comp\\]), the factor $\\langle \\mathrm{VBS}_{L}|BA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle$ in (\\[appl1\\]) can be re-written as $$\\begin{aligned}\n &&\\langle \\mathrm{VBS}_{L}|BA^{\\dagger}_{J}|\\mathrm{VBS}_{L}\\rangle \\label{appl200} \\\\\n &=&\\displaystyle\\left[\\prod^{L}_{j=1}\\frac{(2S_{j}+1)!}{4\\pi}\\right]\\int \\left(\\prod^{L}_{j=1}\\mathrm{d}\\hat{\\Omega}_{j}\\right)\\prod^{L-1}_{j=1}\\left[\\frac{1}{2}(1-\\hat{\\Omega}_{j}\\cdot\\hat{\\Omega}_{j+1})\\right]^{M_{j,j+1}}\n \\nonumber \\\\\n &&\\cdot\\left(u_{0}v_{1}-v_{0}u_{1}\\right)^{M_{01}} \\left(uu^{\\ast}_{1}+vv^{\\ast}_{1}\\right)^{J_{-}+J}\\left(u^{\\ast}_{1}v^{\\ast}_{L}-v^{\\ast}_{1}u^{\\ast}_{L}\\right)^{J_{+}-J}\n\\nonumber \\\\ &&\\cdot\\left(uu^{\\ast}_{L}+vv^{\\ast}_{L}\\right)^{-J_{-}+J}\\left(u_{L}v_{L+1}-v_{L}u_{L+1}\\right)^{M_{L,L+1}}. ", "\\nonumber\\end{aligned}$$ We plug the expression (\\[appl200\\]) into (\\[appl100\\]). ", "Using transformation properties under $SU(2)$ and a binomial expansion, the integral over $\\hat{\\Omega}_{0}$ yields that $$\\begin{aligned}\n \\int \\mathrm{d}\\hat{\\Omega}_{0}\\left(u^{\\ast}_{0}b^{\\dagger}_{1}-v^{\\ast}_{0}a^{\\dagger}_{1}\\right)^{M_{01}}\\left(u_{0}v_{1}-v_{0}u_{1}\\right)^{M_{01}}\n =\\frac{4\\pi}{M_{01}+1}\\left(u_{1}a^{\\dagger}_{1}+v_{1}b^{\\dagger}_{1}\\right)^{M_{01}}.\\nonumber\\\\ \\label{int000}\\end{aligned}$$ Similarly we can perform the integral over $\\hat{\\Omega}_{L+1}$. Then using expansion (\\[expansion00\\]) and orthogonality of spherical harmonics, other integrals over $\\hat{\\Omega}_{j}$ with $j=2, \\ldots, L-1$ in (\\[appl200\\]) can be performed. ", "As a result, the following expression is obtained from (\\[appl100\\]): $$\\begin{aligned}\n\\boldsymbol{\\rho}_{L}|\\mathrm{G}; J, \\hat{\\Omega}\\rangle = \\frac{1}{(4\\pi)^{2}}\\sum^{M_{<}}_{l=0}(2l+1)\\left[\\prod^{L-1}_{j=1}\\lambda(l,M_{j,j+1})\\right]\nK^{\\dagger}_{l}(\\hat{\\Omega})\n\\left|\\mathrm{VBS}_{L}\\right\\rangle. ", "\\label{sum00}\\end{aligned}$$ The operator $K^{\\dagger}_{l}(\\hat{\\Omega})$ involved in (\\[sum00\\]) is defined as $$\\begin{aligned}\n K^{\\dagger}_{l}(\\hat{\\Omega})&\\equiv&\\int \\mathrm{d}\\hat{\\Omega}_{1} \\mathrm{d}\\hat{\\Omega}_{L}\\, \n P_{l}(\\hat{\\Omega}_{1} \\cdot \\hat{\\Omega}_{L})\n \\left(u_{1}a^{\\dagger}_{1}+v_{1}b^{\\dagger}_{1}\\right)^{M_{01}} \\left(uu^{\\ast}_{1}+vv^{\\ast}_{1}\\right)^{J_{-}+J}\n\\nonumber \\\\ \n&&\\cdot \\left(u^{\\ast}_{1}v^{\\ast}_{L}-v^{\\ast}_{1}u^{\\ast}_{L}\\right)^{J_{+}-J}\n\\left(uu^{\\ast}_{L}+vv^{\\ast}_{L}\\right)^{-J_{-}+J}\n\\left(u_{L}a^{\\dagger}_{L}+v_{L}b^{\\dagger}_{L}\\right)^{M_{L,L+1}}. ", "\\nonumber \\\\ \\label{inte00}\\end{aligned}$$ It is expressed as an integral depending on the order $l$ of the Legendre polynomial $P_{l}(\\hat{\\Omega}_{1} \\cdot \\hat{\\Omega}_{L})$.\n\nThere was no ambiguity in defining the large block limit in the homogeneous AKLT model (see §$\\,\\ref{sec:larges}\\,$). ", "However, in the inhomogeneous model we must specify the behavior of ending spins in the large block limit. ", "So we define the large block limit as when $L\\rightarrow\\infty$, the two ending spins approach definite values, namely, $M_{01}\\rightarrow S_{-}$ and $M_{L,L+1}\\rightarrow S_{+}$. Then we realize from (\\[lambdalm00\\]) that as $L\\rightarrow\\infty$, $\\prod^{L-1}_{j=1}\\lambda(l,M_{j,j+1})\\rightarrow \\delta_{l,0}$. Therefore only the first term with $l=0$ is left in (\\[sum00\\]). ", "So that we need only to calculate the limiting $K^{\\dagger}_{0}(\\hat{\\Omega})$: $$\\begin{aligned}\n K^{\\dagger}_{0}(\\hat{\\Omega})&\\stackrel{L\\rightarrow\\infty}{\\longrightarrow}&\\int \\mathrm{d}\\hat{\\Omega}_{1} \\mathrm{d}\\hat{\\Omega}_{L} \n \\left(u_{1}a^{\\dagger}_{1}+v_{1}b^{\\dagger}_{1}\\right)^{S_{-}} \\left(uu^{\\ast}_{1}+vv^{\\ast}_{1}\\right)^{J_{-}+J} \\nonumber \\\\ &&\\cdot\n\\left(u^{\\ast}_{1}v^{\\ast}_{L}-v^{\\ast}_{1}u^{\\ast}_{L}\\right)^{J_{+}-J}\n\\left(uu^{\\ast}_{L}+vv^{\\ast}_{L}\\right)^{-J_{-}+J}\n\\left(u_{L}a^{\\dagger}_{L}+v_{L}b^{\\dagger}_{L}\\right)^{S_{+}}. ", "\\nonumber\\\\ \\label{k000}\\end{aligned}$$ Here both $J_{-}$ and $J_{+}$ take the limiting values $\\frac{1}{2}(S_{-}-S_{+})$ and $\\frac{1}{2}(S_{-}+S_{+})$, respectively.", "\n\nUsing transformation properties of the integrand in (\\[k000\\]) under $SU(2)$, the $K^{\\dagger}_{0}(\\hat{\\Omega})$ integral is simplified and carried out as $$\\begin{aligned}\nK^{\\dagger}_{0}(\\hat{\\Omega})\n=\\frac{(4\\pi)^{2}}{(S_{-}+1)(S_{+}+1)}\\,A^{\\dagger}_{J}. ", "\\label{fina00}\\end{aligned}$$ This expression states that $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ is a set of eigenvectors of the density matrix as $L\\rightarrow\\infty$. Let us denote the density matrix in the limit by $\\boldsymbol{\\rho}_{\\infty}$. Then (\\[fina00\\]) leads to the result (see (\\[sum00\\])) $$\\begin{aligned}\n \\boldsymbol{\\rho}_{\\infty}|\\mathrm{G}; J, \\hat{\\Omega}\\rangle=\n \\frac{1}{(S_{-}+1)(S_{+}+1)}\\,|\\mathrm{G}; J, \\hat{\\Omega}\\rangle. ", "\\label{appll00}\\end{aligned}$$\n\nWe find from (\\[appll00\\]) that the limiting eigenvalue $$\\begin{aligned}\n \\Lambda_{\\infty}=\\frac{1}{(S_{-}+1)(S_{+}+1)}, \\qquad L\\to\\infty\\end{aligned}$$ is independent of $J$. Any vector of the $(S_{-}+1)(S_{+}+1)$-dimensional subspace spanned by the set $\\{|\\mathrm{G}; J, \\hat{\\Omega}\\rangle\\}$ is an eigenvector of $\\boldsymbol{\\rho}_{\\infty}$ with the same eigenvalue $\\frac{1}{(S_{-}+1)(S_{+}+1)}$. Therefore $\\boldsymbol{\\rho}_{\\infty}$ is proportional to a projector $\\mathbf{P}_{(S_{-}+1)(S_{+}+1)}$: $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}\\to\\boldsymbol{\\rho}_{\\infty}=\\frac{1}{(S_{-}+1)(S_{+}+1)}\\,\\mathbf{P}_{(S_{-}+1)(S_{+}+1)}, \\label{limitrho00}\\end{aligned}$$ which is a generalization of (\\[largedens\\]) to the inhomogeneous model. ", "In the expression (\\[limitrho00\\]) $S_{-}$ and $S_{+}$ denote the limiting spin values at the left and right boundary sites of the block, respectively. ", "In addition, we also derive from the eigenvalues that the von Neumann entropy $S_{\\mathrm{v\\ N}}$ coincides with the Rényi entropy $S_{\\mathrm{R}}$ and is equal to the saturated value $\\ln\\left[(S_{-}+1)(S_{+}+1)\\right]$.\n\nThe One–dimensional SU(n) Model {#sec:su(n)}\n===============================\n\nIn previous sections, we have discussed VBS states with spins in different representations of $SU(2)$. Our discussion essentially exhausted all possible variations of $SU(2)$ VBS states in $1$-dimension with open boundary conditions. ", "The AKLT model and the VBS ground state can be generalized to the $SU(n)$ case as in [@GR; @GRS; @RSSTG; @RTFSG]. ", "In this section we study the entanglement of the VBS state in the $SU(n)$ version with open boundary conditions. ", "Our treatment follows [@KHK].", "\n\nThe Hamiltonian and the SU(n) VBS State {#sec:su(n)hamil}\n---------------------------------------\n\nLet us first define the model. ", "Consider a $1$-dimensional lattice with spins sitting on each site. ", "What we mean by a ‘spin’ in our model is an adjoint representation of $SU(n)$. Our spin chain consists of $N$ adjoint representations of $SU(n)$ in the bulk and fundamental and conjugate representations of $SU(n)$ on the two boundaries. ", "This construction corresponds to the spin-$1$ model in §$\\,\\ref{sec:1dspin1}\\,$ where we have the adjoint representation of $SU(2)$ (*i.e.* spin-$1$) in the bulk and the fundamental representation of $SU(2)$ (*i.e.* spin-$1/2$) at two ends (the fundamental representation $\\square$ and its conjugate representation $\\bar{\\square}$ are equivalent for $SU(2)$). ", "Unlike previous sections, in this section we shall reverse the order of discussion for better understanding. ", "That is, we construct the $SU(n)$ VBS state before writing down the Hamiltonian. ", "The Hamiltonian will be constructed in such a way that the VBS state shall be the ground state.", "\n\nNow let us first construct an $SU(n)$ VBS state which consists of $N$ adjoint representations of $SU(n)$ in the bulk and fundamental and conjugate representations of $SU(n)$ on the boundary. ", "First, we prepare sites $k$ ($k=0, 1, ..., N$) and ${\\bar k}$ ($k=1, 2, ..., N+1$) and arrange $SU(n)$ singlets consisting of a fundamental ($\\square$) and its conjugate ($\\bar {\\square}$) representations as shown in Figure \\[construction\\] (see also [@NO]).", "\n\n![", "Construction of the $SU(n)$ VBS state. ", "White and black dots represent the $SU(n)$ fundamental and its conjugate representations, respectively. ", "A solid line connecting two dots corresponds to the singlet state $|0,0\\rangle$ and a large circle denotes the projection onto the adjoint representation.[]{data-label=\"construction\"}](figure4.eps){width=\"5in\"}\n\nWe assign $|j\\rangle$ $(j=0,1,2, ..., n-1)$ to the fundamental representation, while $|{\\bar{j}}\\rangle$ $(j=0,1,2, ..., n-1)$ to the conjugate representation. ", "$|{\\bar j}\\rangle$ can be represented by the tensor product of $(n-1)$ $|j\\rangle$’s as $$|\\bar{j}\\rangle \\equiv \\frac{1}{\\sqrt{(n-1)!}}\\sum_{\\alpha_2, ..., \\alpha_n} \\epsilon^{j \\alpha_2,...,\\alpha_n}|\\alpha_2,...,\\alpha_n \\rangle\n\\label{conjugate}$$ where $\\epsilon^{j \\alpha_2,...,\\alpha_n}$ is a totally antisymmetric tensor of rank $n$. Using $|j\\rangle$ and $|{\\bar j}\\rangle$, an $SU(n)$ singlet state $|0,0\\rangle$ can be represented as a maximally entangled state: $$|0,0\\rangle = \\frac{1}{\\sqrt{N}}\\sum_{j=0}^{N-1}|j\\rangle |\\bar{j}\\rangle.$$ The above relation can be easily confirmed by inserting the resolution of the identity $I=\\sum_{j=0}^{n-1}|j\\rangle \\langle j|$ and substituting (\\[conjugate\\]). ", "Next, we prepare the adjoint representation of $SU(n)$ by projecting the tensor product $\\square \\otimes {\\bar \\square}$ onto an $(n^2-1)$-dimensional subspace (the dimension of the adjoint representation of $SU(n)$ is equal to the number of generators). ", "This procedure corresponds to large circles in Figure \\[construction\\]. ", "In Figure \\[construction2\\](a) we visualize the decomposition rule $\\square \\otimes \\bar{\\square}=(\\mathrm{singlet}) \\oplus (\\mathrm{adjoint})$. Then we have obtained the $SU(n)$ adjoint representation at each composite site ($k,{\\bar k}$). ", "Henceforth we shall call this composite site $k$. Finally, we can represent the $SU(n)$ generalized VBS state as $$|\\mathrm{VBS}\\rangle = \\left(\\bigotimes_{k=1}^N \\mathbf{P}_{k{\\bar k}}\\right)|0,0\\rangle_{0{\\bar 1}} |0,0\\rangle_{1{\\bar 2}} \\dots |0,0\\rangle_{N\\overline{N+1}},\n\\label{gs}$$ where $\\mathbf{P}_{k{\\bar k}}$ is a projection operator onto an adjoint representation of $SU(n)$.\n\nAfter construction of the VBS state (\\[gs\\]), we now write down the Hamiltonian along the same line as the $SU(2)$ AKLT model: $$\\begin{aligned}\n &&H = \\sum_{k=1}^{N-1} H(k,k+1)+H(0,1)+H(N,N+1), \\nonumber\\\\\n &&H(k,k+1) = \\sum_{Y}C_{Y}(k,k+1)\\,\\pi_{Y}(k,k+1),\n\\label{Ham}\\end{aligned}$$ where $Y$ is a Young tableau which is neither \\[$n, n$\\] nor \\[$n$, $n-1$, 1\\]. ", "Here we have assigned \\[$\\kappa_1, ..., \\kappa_{\\lambda_1}$\\] to the Young tableau $Y$, where $\\kappa_j$ is the number of boxes in the $j^{\\mathrm{th}}$ column and $\\lambda_1$ is the number of boxes in the first row. ", "$\\pi_{Y}(k,k+1)$ is a projection operator which projects $(\\mathrm{adjoint})\\otimes(\\mathrm{adjoint})$ onto a representation characterized by $Y$ and the coefficient $C_Y(k,k+1)$ can be an arbitrary positive number. ", "The reason why \\[$n, n$\\] and \\[$n$, $n-1$, 1\\] are excluded from the sum is the following: Since $\\square$ at site $k$ and $\\bar \\square$ at site $k+1$ have already formed a singlet in the ground state (\\[gs\\]), the possible representations obtained from the decomposition of $(\\mathrm{adjoint})\\otimes(\\mathrm{adjoint})$ are restricted to \\[$n, n$\\] and \\[$n$, $n-1$, 1\\] (as graphically shown in Figure \\[construction2\\](b)).", "\n\n![(", "a)The decomposition rule for the tensor product of $\\square \\otimes {\\bar \\square}$. (b)The Young tableaux corresponding to \\[$n,n$\\] and \\[$n,n-1,1$\\].[]{data-label=\"construction2\"}](figure5.eps){width=\"5in\"}\n\n$H(0,1)$ and $H(N,N+1)$ are boundary terms which assure the uniqueness of the ground state of this Hamiltonian. ", "$H(0,1)$ and $H(N,N+1)$ can be written in terms of the projection operators acting on the tensor products $(\\mathrm{fundamental})\\otimes(\\mathrm{adjoint})$ and $(\\mathrm{conjugate})\\otimes(\\mathrm{adjoint})$, respectively. ", "By construction, the $SU(n)$ VBS state (\\[gs\\]) is a zero-energy ground state of this Hamiltonian (\\[Ham\\]). ", "We note here that another construction of the Hamiltonian by M. Greiter and S. Rachel [@GR] is similar but slightly different from ours.", "\n\nThe Block Density Matrix {#sec:su(n)denmatr}\n------------------------\n\nNext, we consider the density matrix of a block subsystem of the VBS ground state $|\\mathrm{VBS}\\rangle$ (\\[gs\\]). ", "To calculate the density matrix, it is more convenient to recast the chain of singlets $|0,0\\rangle_{0{\\bar 1}} |0,0\\rangle_{1{\\bar 2}} \\dots |0,0\\rangle_{N\\overline{N+1}}$ in (\\[gs\\]) in a different form. ", "Let us first look at a chain of two singlets $|0,0\\rangle_{0{\\bar 1}} |0,0\\rangle_{1{\\bar 2}}$. We can rewrite this product state as $$|0,0\\rangle_{0{\\bar 1}} |0,0\\rangle_{1{\\bar 2}}=\n\\frac{1}{n}\\sum_{l=0}^{n-1}\\sum_{m=0}^{n-1}|l,m\\rangle_{0{\\bar 2}} \n|l,-m\\rangle_{{\\bar 1}1},\n\\label{important_relation}$$ where $|m,n\\rangle$ is a basis of the maximally entangled state defined by $$|l,m\\rangle = (U_{l,m}\\otimes I)|0,0\\rangle.$$ Here $I$ is an $n$-dimensional identity matrix and $U_{l,m}=X^lZ^m$ ($m,n=0, 1, ..., n-1$) are generalized Pauli matrices, where the unitary operators $X$ and $Z$ act on $|j\\rangle$ as $X|j\\rangle=|j+1 ({\\rm mod}.n)\\rangle$ and $Z|j\\rangle=\\omega^j|j\\rangle$ with $\\omega=\\mathrm{e}^{2\\pi \\mathrm{i}/n}$, respectively. ", "One can easily show the relation (\\[important\\_relation\\]) by using the fact that $|0,0\\rangle$ is invariant under the action of $(U_{l,m}\\otimes U_{l,-m})$, see [@F]. ", "This procedure can be regarded as a multi-dimensional generalization of entanglement swapping. (", "The maximally entangled state basis (\\[alph\\]) and a similar relation (\\[maxi\\]) have been used in §$\\,\\ref{sec:1dspin1VBS}\\,$ for the $SU(2)$ spin-$1$ VBS state.) ", "By repeatedly using the relation (\\[important\\_relation\\]), we can generalize in a straightforward way to a chain of singlet states: $$\\begin{aligned}\n&&|0,0\\rangle_{0{\\bar 1}} |0,0\\rangle_{1{\\bar 2}} \\dots |0,0\\rangle_{N\\overline{N+1}}\\nonumber\\\\\n&=&\\frac{1}{n^N}\n\\sum_{(l_1,m_1)}\\cdots \\sum_{(l_N,m_N)}|l_1,-m_1\\rangle_{{\\bar 1}1}\\cdots |l_N,-m_N\\rangle_{{\\bar N}N}\\nonumber\\\\\n&&\\cdot (U_{l_1,m_1}\\cdots U_{l_N,m_N}\\otimes I)|0,0\\rangle_{0\\overline{N+1}},\n\\label{singlet_product}\\end{aligned}$$ where $(m_k,n_k)$ ($k=1, 2, ..., N$) runs from (0,0) to $(n-1,n-1)$. To obtain the ground state $|\\mathrm{VBS}\\rangle$ from (\\[singlet\\_product\\]), we still have to make a projection onto the subspace of adjoint representation at each site $k$. Since the decomposition rule $\\square \\otimes \\bar{\\square}=(\\mathrm{singlet}) \\oplus (\\mathrm{adjoint})$ and the fact that $|0,0\\rangle$ is an $SU(n)$ singlet, the vector space of the adjoint representation is spanned by $|l,-m\\rangle$ ($(l,m)\\ne (0,0)$). ", "Then the only thing to do is to omit the summation over $(l_k,m_k)=(0,0)$ in (\\[singlet\\_product\\]). ", "As a result, the $SU(n)$ generalized VBS state can be re-written as: $$\\begin{aligned}\n|\\mathrm{VBS}\\rangle &=&\\frac{1}{(n^2-1)^{N/2}}\\sum_{\\stackrel{(l_1,m_1)}{\\ne(0,0)}}\\cdots\\sum_{\\stackrel{(l_N,m_N)}{\\ne(0,0)}}|l_1,-m_1\\rangle_{{\\bar 1}1}\\cdots |l_N,-m_N\\rangle_{{\\bar N}N}\\nonumber\\\\\n&&\\cdot (U_{l_1,m_1}\\cdots U_{l_N,m_N}\\otimes I)|0,0\\rangle_{0\\overline{N+1}},\\end{aligned}$$ where we have already normalized $|\\mathrm{VBS}\\rangle$ by the factor $1/(n^2-1)^{N/2}$.\n\nNow we calculate the density matrix of a block of contiguous spins of length $L$. Assume that the block starts from site $k$ and stretches up to $k+L-1$, where $k\\ge 1$ and $k+L-1 \\le N$. The reduced density matrix is obtained by taking the trace over the sites $j=0,1, ..., k-1$ and $j=k+L, ..., N, \\overline{N+1}$ outside the block as $$\\begin{aligned}\n\\boldsymbol{\\rho}_{L} &=& \\mathrm{tr}_{1,...,k-1,k+L,...,N,0,\\overline{N+1}}\\left[\\,|\\mathrm{VBS}\\rangle \\langle \\mathrm{VBS}|\\,\\right] \n\\nonumber \\\\\n&=&\\frac{1}{(n^2-1)^N} \\sum_{\\stackrel{(l_1,m_1)}{\\ne(0,0)}}\\cdots\\sum_{\\stackrel{(l_{k-1},m_{k-1})}{\\ne(0,0)}}\\sum_{\\stackrel{(l_{k+L},m_{k+L})}{\\ne(0,0)}}\\nonumber\\\\\n&&\\cdots\\sum_{\\stackrel{(l_N,m_N)}{\\ne(0,0)}}\n%\\nonumber \\\\\n%&\\times&\n\\sum_{\\stackrel{(l_k,m_k)}{\\ne(0,0)}}\\sum_{\\stackrel{(l_k',m_k')}{\\ne(0,0)}}\\cdots \\sum_{\\stackrel{(l_{L+k-1},m_{L+k-1})}{\\ne(0,0)}}\\sum_{\\stackrel{(l_{L+k-1}',m_{L+k-1}')}{\\ne(0,0)}}\n\\nonumber \\\\\n&& \\cdot|l_k,-m_k\\rangle_{{\\bar k}k}\\langle l_k',-m_k'|\\cdots|l_{L+k-1},-m_{L+k-1}\\rangle_{\\overline{L+k-1}L+k-1}\\langle l_{L+k-1}',-m_{L+k-1}'| \\nonumber \\\\\n&& \\cdot\\mathrm{tr}_{0,\\overline{N+1}}\\left[(U_1 V U_2 \\otimes I)|0,0\\rangle_{0\\overline{N+1}}\\langle 0,0|(U_1 V' U_2 \\otimes I)^\\dagger\\right],\n\\label{RDM1}\\end{aligned}$$ where $U_1=U_{l_1,m_1}\\cdots U_{l_{k-1},m_{k-1}}$, $U_2=U_{l_{L+k},m_{L+k}}\\cdots U_{l_N,m_N}$,\\\n$V=U_{l_k,m_k}\\cdots U_{l_{L+k-1},m_{L+k-1}}$ and $V'=U_{l_k',m_k'}\\cdots U_{l_{L+k-1}',m_{L+k-1}'}$. To rewrite the complicated expression (\\[RDM1\\]), we use the following property of $|0,0\\rangle$: $$(S \\otimes T)|0,0\\rangle =(ST^t\\otimes I)|0,0\\rangle=(I\\otimes TS^t)|0,0\\rangle,$$ where $S$ and $T$ are $n$-dimensional unitary operations acting on $|j\\rangle$ and $|{\\bar j}\\rangle$, respectively, and the superscript $t$ denotes the transposition. ", "Using this property and the cyclic property of the trace, we can simplify the last part of (\\[RDM1\\]) as $$\\begin{aligned}\n&&\\mathrm{tr}_{0,\\overline{N+1}}\\left[(U_1 V U_2 \\otimes I)|0,0\\rangle_{0\\overline{N+1}}\\langle 0,0|(U_1 V' U_2 \\otimes I)^\\dagger\\right] \\nonumber \\\\\n&=&\\mathrm{tr}_{0,\\overline{N+1}}\\left[(U_1\\otimes I)(V \\otimes I)(U_2 \\otimes I)|0,0\\rangle_{0\\overline{N+1}}\\langle 0,0|(U_2 \\otimes I)^\\dagger(V' \\otimes I)^\\dagger(U_1 \\otimes I)^\\dagger\\right] \\nonumber \\\\\n%&=&{\\rm Tr}_{0,\\overline{N+1}}(V \\otimes I)(U_2 \\otimes I)|\\Phi_{0,0}\\rangle_{0\\overline{N+1}}\\langle \\Phi_{0,0}|(U_2 \\otimes I)^\\dagger(V' \\otimes I)^\\dagger \\nonumber \\\\\n&=&\\mathrm{tr}_{0,\\overline{N+1}}\\left[(V \\otimes I)(I \\otimes U_2^t)|0,0\\rangle_{0\\overline{N+1}}\\langle 0,0|(I \\otimes U_2^t)^\\dagger(V' \\otimes I)^\\dagger\\right] \\nonumber \\\\\n&=&\\mathrm{tr}_{0,\\overline{N+1}}\\left[(I \\otimes U_2^t)(V \\otimes I)|0,0\\rangle_{0\\overline{N+1}}\\langle 0,0|(V' \\otimes I)^\\dagger(I \\otimes U_2^t)^\\dagger\\right] \\nonumber \\\\\n&=&\\mathrm{tr}_{0,\\overline{N+1}}\\left[(V \\otimes I)|0,0\\rangle_{0\\overline{N+1}}\\langle 0,0|(V' \\otimes I)^\\dagger\\right].", "\n\\label{trace_relation}\\end{aligned}$$ Since (\\[trace\\_relation\\]) does not depend on $(l_1,m_1), \\cdots, (l_{k-1},m_{k-1})$ and $(l_{k+L},m_{k+L}), \\cdots,\\\\ (l_N,k_N)$, we can rewrite the density matrix (\\[RDM1\\]) as $$\\begin{aligned}\n\\boldsymbol{\\rho}_L\n&=&\\frac{1}{(n^2-1)^L}\n\\sum_{\\stackrel{(l_k,m_k)}{\\ne(0,0)}}\\sum_{\\stackrel{(l_k',m_k')}{\\ne(0,0)}}\\cdots \\sum_{\\stackrel{(l_{L+k-1},m_{L+k-1})}{\\ne(0,0)}}\\sum_{\\stackrel{(l_{L+k-1}',m_{L+k-1}')}{\\ne(0,0)}}\n|l_k,-m_k\\rangle_{{\\bar k}k}\\langle l_k',-m_k'|\\nonumber\\\\\n&&\\cdots|l_{L+k-1},-m_{L+k-1}\\rangle_{\\overline{L+k-1}L+k-1}\\langle l_{L+k-1}',-m_{L+k-1}'|\\nonumber\\\\ \n&&\\cdot\\mathrm{tr}_{0,\\overline{N+1}}\\left[(V \\otimes I)|0,0\\rangle_{0\\overline{N+1}}\\langle 0,0|(V' \\otimes I)^\\dagger\\right].", "\n\\label{RDM2}\\end{aligned}$$ From the form of the density matrix in (\\[RDM2\\]), we immediately notice that the density matrix does not depend on both the starting site $k$ and the total length of the chain $N$. The same property for $SU(2)$ VBS states has been discussed in §$\\,\\ref{sec:1ds1den}\\,$, §$\\,\\ref{sec:1dssden}\\,$ and §$\\,\\ref{sec:deninhom}\\,$ (this property was proved in [@FKR] for spin-$1$, in [@XKHK] for Spin-$S$, and in [@XKHK2] for the inhomogeneous $SU(2)$ models, respectively). ", "We can regard the above result as an $SU(n)$ generalization of those results.", "\n\nSpectrum of the Density Matrix and Entropies {#sec:su(n)spec}\n--------------------------------------------\n\nSince the density matrix $\\boldsymbol{\\rho}_{L}$ (\\[RDM2\\]) is independent of both $k$ and $N$, we can set $N=L$ without loss of generality. ", "We can further reduce the original problem to that of the reduced density matrix of two ending spins ($\\square$ and $\\bar \\square$) using the Schmidt decomposition of a bipartite pure state (see the introduction §$\\,\\ref{sec:intro1}\\,$ for a brief discussion). ", "Suppose that $|B\\cup E\\rangle$ is a bipartite pure state of a total system $B\\cup E$. Then there exists orthonormal states $|B_j\\rangle$ for the subsystem $B$, and orthonormal states $|E_j\\rangle$ for $E$ such that $$|B\\cup E\\rangle=\\sum_j \\sqrt{\\lambda_j}\\ |B_j\\rangle\\otimes |E_j\\rangle,\n\\label{Schmidt}$$ where $\\lambda_j(>0)$ satisfy $\\sum_j \\lambda_j=1$. The proof of the above theorem using the singular value decomposition can be found in §$\\,2.1.10\\,$ and §$\\,2.5\\,$ of [@NC]. ", "From (\\[Schmidt\\]), one can immediately notice that the set of non-vanishing eigenvalues of $\\boldsymbol{\\rho}_B=\\mathrm{tr}_E\\left[\\,|B\\cup E\\rangle\\langle B\\cup E|\\,\\right]$ coincides with that of $\\boldsymbol{\\rho}_E=\\mathrm{tr}_B\\left[\\,|B\\cup E\\rangle\\langle B\\cup E|\\,\\right]$.\n\nNow we can reduce the eigenvalue-problem of $\\boldsymbol{\\rho}_L$ to that of the density matrix for the two ending spins $\\boldsymbol{\\rho}_{\\hat L}$. This density matrix $\\boldsymbol{\\rho}_{\\hat L}$ takes the following form: $$\\boldsymbol{\\rho}_{\\hat L}=\\frac{1}{(n^2-1)^L}\\sum_{\\stackrel{(l_1,m_1)}{\\ne(0,0)}}\\cdots \\sum_{\\stackrel{(l_L,m_L)}{\\ne(0,0)}} (U \\otimes I)|0,0\\rangle_{0,\\overline{L+1}}\\langle 0,0|(U \\otimes I)^\\dagger,\n\\label{edge_RDM}$$ where $U=U_{l_1,m_1}\\cdots U_{l_L,m_L}$. To evaluate the eigenvalues of $\\boldsymbol{\\rho}_{\\hat L}$, it is convenient to formulate the action of $(U_{l,m}\\otimes I)$ as a transfer matrix. ", "Let us first see the action of $(U_{l',m'}\\otimes I)$ on a state $|l,m\\rangle$: $$(U_{l',m'}\\otimes I)|l,m\\rangle\n=(X^{l'}Z^{m'}X^{l}Z^{m}\\otimes I)|0,0\\rangle\n%&=&\\frac{1}{\\sqrt{n}}\\sum_{j=0}^{n-1}(X^{l'}Z^{m'}X^{l}Z^{m})|j\\rangle |\\bar j\\rangle \n%=\\frac{1}{\\sqrt{n}}\\sum_{j=0}^{n-1}\\omega^{mj+m'(j+l)}|j+l+l'\\rangle |\\bar j\\rangle \\nonumber \\\\\n%&=& \\omega^{m'l} \\frac{1}{\\sqrt{n}}\n%\\sum_{j=0}^{n-1}\\omega^{(m+m')j}|j+l+l'\\rangle |\\bar j \\rangle \n%= \\omega^{m'l}(U_{l+l',m+m'}\\otimes I)|\\Phi_{0,0}\\rangle \n=\\omega^{m'l}|l+l',m+m'\\rangle,$$ where we have used the relation $ZX=\\omega XZ$ with $\\omega=\\mathrm{e}^{2\\pi\\mathrm{i}/n}$. Using the above relation, we can prove that $$(U_{l',m'}\\otimes I)|l,m\\rangle\\langle l,m|(U_{l',m'}\\otimes I)^\\dagger =|l+l',m+m'\\rangle\\langle l+l',m+m'|.$$ Next, we assign the vector $(0, ..., 0,1((l,m)^{\\mathrm{th}}$ entry), 0, ..., 0)$^t$ to the state $|l,m\\rangle \\langle l,m|$. This one to one correspondence plays an essential role in our analysis. ", "From this bijection, the operation\\\n$\\sum_{(l',m')\\ne(0,0)}(U_{l',m'}\\otimes I)|l,m\\rangle\\langle l,m|(U_{l',m'}\\otimes I)^\\dagger$ can be written in terms of $(n^2 \\times n^2)$-dimensional matrix as $$T \\equiv\n\\begin{array}{c}\n\\longleftarrow \\hspace{2mm} n^2 \\hspace{2mm} \\longrightarrow \\\\\n\\left(\\begin{array}{ccccc}\n0 & 1 & 1 & \\cdots & 1 \\\\\n1 & 0 & 1 & \\cdots & 1 \\\\\n1 & 1 & 0 & \\cdots & 1 \\\\\n\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n1 & 1 & 1 & \\cdots & 0 \\\\\n\\end{array}\\right).", "\n\\end{array}$$ This transfer matrix can be diagonalized by the following unitary matrix: $$U_c=\\frac{1}{n}\\left(\n\\begin{array}{ccccc}\n1 & 1 & 1 & \\cdots & 1 \\\\\n1 & \\zeta & \\zeta^2 & \\cdots & \\zeta^{n^2-1} \\\\\n1 & \\zeta ^2 & \\zeta^4 & \\cdots & \\zeta^{2(n^2-1)} \\\\\n\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n1 & \\zeta^{n^2-1} & \\zeta^{2(n^2-1)} & \\cdots & \\zeta^{(n^2-1)^2}\\\\\n\\end{array}\\right),$$ where $\\zeta={\\rm exp}(2\\pi \\mathrm{i}/n^2)$. Then we can obtain the explicit form of the reduced density matrix $\\boldsymbol{\\rho}_{\\hat L}$ as $$\\begin{aligned}\n\\boldsymbol{\\rho}_{\\hat L}&=&\\frac{1}{(n^2-1)^L}T^L (1, 0, ..., 0)^t\\nonumber\\\\\n&=&\\frac{1}{(n^2-1)^L} U_c [{\\rm diag}(n^2-1,-1, ..., -1)]^L U_c^\\dagger (1, 0, ..., 0)^t \\nonumber \\\\\n&=& \\frac{1}{n^2}(1+(n^2-1)p_n(L))|0,0\\rangle_{0\\overline{N+1}}\\langle 0,0|\\nonumber\\\\\n &&+ \\frac{1}{n^2}\\sum_{(l,m)\\ne(0,0)}(1-p_n(L))|l,m\\rangle_{0\\overline{N+1}}\\langle l,m|,\n\\label{RDM3}\\end{aligned}$$ where we have used the relation, $1+\\zeta^k+\\zeta^{2k}+\\cdots +\\zeta^{(n^2-1)k}=0$ ($1\\le k \\le n^2-1$) and $p_n(L)=(\\frac{-1}{n^2-1})^L$. Substituting $n=2$ into (\\[RDM3\\]), one can reproduce the result of the $SU(2)$ Spin-$1$ VBS state obtained in §$\\,\\ref{sec:1dspin1}\\,$ (see also [@FKR]).", "\n\nLet us now start the evaluation of the von Neumann and the Rényi entropies of a block of $L$ contiguous spins. ", "First, we shall examine the von Neumann entropy of the block. ", "From the Schmidt decomposition and the definition of the von Neumann entropy $S_{\\mathrm{v\\ N}}\\left[\\boldsymbol{\\rho}_{L}\\right]=S_{\\mathrm{v\\ N}}\\left[\\boldsymbol{\\rho}_{\\hat L}\\right]=-\\mathrm{tr}_{1,2,...,L}(\\boldsymbol{\\rho}_{\\hat L}\\ln \\boldsymbol{\\rho}_{\\hat L})$, we obtain $$\\begin{aligned}\nS_{\\mathrm{v\\ N}}&=& \\ln n^{2} -\\frac{1+(n^2-1)p_n(L)}{n^2}\\ln (1+(n^2-1)p_n(L)) \\nonumber\\\\\n&&-(n^2-1)\\frac{1-p_n(L)}{n^2}\\ln(1-p_n(L))\\end{aligned}$$ with $p_n(L)=(\\frac{-1}{n^2-1})^L$. Similarly to the $SU(2)$ VBS states [@FKR; @KHH; @XKHK; @XKHK2] and the $XY$ spin chains in the gapped regime [@IJK; @IJK2; @FIJK0; @FIJK], $S_{\\mathrm{v\\ N}}[\\boldsymbol{\\rho}_{L}]$ is bounded by $2 \\ln n$ in the limit of large block sizes $L \\to \\infty$ and approaches to this value exponentially fast in $L$. This is a partial proof of the conjecture proposed in [@VLRK], that the von Neumann entropy of a large block of spins in gapped spin chains shows saturation. ", "Next we shall examine the Rényi entropy of our system. ", "From the definition of the Rényi entropy $S_{\\mathrm{R}}(\\alpha)=\\frac{1}{1-\\alpha}\\ln \\left[\\mathrm{tr}(\\boldsymbol{\\rho}_L^{\\alpha})\\right]$ ($\\alpha \\ne 1$ and $\\alpha >0$), $$S_{\\mathrm{R}}(\\alpha)=\\frac{1}{1-\\alpha}\\ln(\\lambda_{0,0}(L)^\\alpha + (n^2-1)\\lambda_{l,m \\ne 0,0}(L)^\\alpha),$$ where $$\\lambda_{l,m}(L) =\\left\\{\n\\begin{array}{cc}\n\\frac{1}{n^2}(1+(n^2-1)p_n(L)), & (l,m)=(0,0)\\\\ \\\\\n\\frac{1}{n^2}(1-p_n(L)) & (l,m)\\ne(0,0).", "\n\\end{array}\\right.", "\n\\label{lambda}$$\n\nThe Density Matrix as a Projector {#projectorsun}\n---------------------------------\n\nWe have obtained the spectrum and derived the entropies of the density matrix in §$\\,\\ref{sec:su(n)spec}\\,$. Our treatment avoided explicit construction of the eigenvectors by reducing the problem to the density matrix of the two ending spins. ", "In this section, we shall show that **Theorem** \\[theorem1\\] in §$\\,\\ref{sec:den0spec}\\,$ is also valid for our $SU(n)$ version VBS state. *", "i.e.* The eigenvectors of $\\boldsymbol{\\rho}_{L}$ with non-zero eigenvalues are degenerate ground states of the block Hamiltonian (The block Hamiltonian is defined similarly as in the $SU(2)$ model, see (\\[blockhsun\\]) below). ", "Indeed, the proof of **Theorem** \\[theorem1\\] is completely applicable in our $SU(n)$ case because it only relies on the definition of the density matrix and the fact that the VBS state has no projection on any of the subspaces specified in the Hamiltonian. ", "The $SU(n)$ block Hamiltonian, defined along the same line as in the $SU(2)$ model, is the sum of interaction terms within the block: $$\\begin{aligned}\nH_{B}=\\sum_{k=1}^{L-1} H(k,k+1). ", "\\label{blockhsun}\\end{aligned}$$ The number of degrees of freedom in the block subsystem can be counted from the von Neumann entropy as $n^2$. This number coincides with the number of degenerate ground states of the block Hamiltonian $H_{B}$. *i.e.* $$\\begin{aligned}\n D=deg=n^{2},\\end{aligned}$$ where $D$ is the number of non-zero eigenvalues (dimension of the *support*) of the density matrix and $deg$ is the number of degenerate ground states of the block Hamiltonian. ", "A basis of the degenerate ground states can be constructed as follows: $$\\begin{aligned}\n|\\mathrm{VBS}; p,q\\rangle &\\equiv& C_{p,q}\\sum_{\\stackrel{(l_1,m_1)}{\\ne(0,0)}}\\cdots \\sum_{\\stackrel{(l_L,m_L)}{\\ne(0,0)}} |l_1,-m_1\\rangle_{\\bar 11}\\cdots|l_{L-1},-m_{L-1}\\rangle_{\\overline{L-1}L-1} \\nonumber \\\\\n&&\\cdot \\mathbf{P}_{L \\bar L}\\left((U_{p,q}U_{l_1,m_1}...U_{l_{L-1},m_{L-1}} \\otimes I)|0,0\\rangle_{L \\bar L}\\right),\n\\label{Edgestate}\\end{aligned}$$ where $C_{p,q}$ is a normalization factor and $\\mathbf{P}_{L \\bar L}$ is a projector onto the adjoint representation of $SU(n)$. This set of states (\\[Edgestate\\]) can be called the *degenerate VBS states*. ", "Any linear combination of (\\[Edgestate\\]) is apparently a ground state of $H_{B}$ (\\[blockhsun\\]). ", "The graphical representation of the construction of this state is shown in Figure \\[construction\\_open\\].", "\n\n![", "Construction of the degenerate VBS states $|\\mathrm{VBS}; p,q\\rangle$ for the block. ", "A white (black) dot represents the $SU(n)$ fundamental (conjugate) representation. ", "A large circle denotes the projection onto the adjoint representation. ", "The dashed line corresponds to the state $|\\mathrm{VBS}; p,q\\rangle$.[]{data-label=\"construction_open\"}](figure6.eps){width=\"5in\"}\n\nThe following orthogonality relation of these generate VBS states (\\[Edgestate\\]) holds: $$\\langle \\mathrm{VBS}; p,q| \\mathrm{VBS}; r,s \\rangle =C_{p,q}^2 (n^2-1)^{L}\\delta_{p,r}\\delta_{q,s}\\lambda_{-p,-q}(L)$$ where the subscripts $-p$ and $-q$ are modulo $n$. This can be shown as follows: $$\\begin{aligned}\n&&\\langle \\mathrm{VBS}; p,q| \\mathrm{VBS}; r,s \\rangle\\nonumber\\\\ \n&=& C_{p,q} C_{r,s} \\sum_{\\stackrel{(l_1,m_1)}{\\ne(0,0)}}\\cdots\\sum_{\\stackrel{(l_{L-1},m_{L-1})}{\\ne(0,0)}} \\nonumber \\\\\n&& {}_{L \\bar L}\\langle 0,0| (U_{p,q}U_{l_1,m_1}...U_{l_{L-1},m_{L-1}})^\\dagger \\mathbf{P}_{L\\bar L}(U_{r,s}U_{l_1,m_1}...U_{l_{L-1},m_{L-1}} \\otimes I)|0,0\\rangle_{L \\bar L} \n\\nonumber \\\\\n&=& C_{p,q} C_{r,s}\\sum_{\\stackrel{(l,m)}{\\ne(0,0)}} \\sum_{\\stackrel{(l_1,m_1)}{\\ne(0,0)}} \\cdots \\sum_{\\stackrel{(l_{L-1},m_{L-1})}{\\ne (0,0)}}\\nonumber\\\\\n&& {}_{L \\bar L}\\langle 0,0| (U_{l_1,m_1}...U_{l_{L-1},m_{L-1}}\\otimes I)^\\dagger (U_{p,q}\\otimes I)^\\dagger |l,m\\rangle_{L\\bar L}\n\\nonumber \\\\\n&&\\cdot {}_{L \\bar L}\\langle l,m|\n(U_{r,s}\\otimes I)(U_{l_1,m_1}...U_{l_{L-1},m_{L-1}} \\otimes I)|0,0\\rangle_{L \\bar L} \n\\nonumber \\\\\n%&=&C_{p,q}C_{r,s}(n^2-1)^{L-1}\\sum_{(l,m)\\atop \\ne(0,0)}\\sum_{(l',m')} \\lambda_{l',m'}(L-1) {}_{L \\bar L}\\langle \\Phi_{l,m}|(U_{r,s}\\otimes I)|\\Phi_{l',m'}\\rangle_{L \\bar L} \\langle \\Phi_{l',m'}|(U_{p,q}\\otimes I)^\\dagger|\\Phi_{l,m}\\rangle_{L \\bar L} \n%\\nonumber \\\\\n&=& C_{p,q}C_{r,s}(n^2-1)^{L-1}\\nonumber\\\\\n&&\\cdot\\sum_{(l',m')} \\lambda_{l',m'}(L-1) {}_{L \\bar L}\\langle p+l',q+m'|(1-|0,0\\rangle_{L \\bar L}\\langle 0,0|)|r+l',s+m'\\rangle_{L \\bar L}\n\\nonumber \\\\\n%&=& C_{p,q}C_{r,s} (n^2-1)^{L-1}\\delta_{p,r}\\delta_{q,s}(1-\\lambda_{-p,-q}(L-1)).", "\n%\\nonumber \\\\\n&=& C_{p,q}^2 (n^2-1)^{L}\\delta_{p,r}\\delta_{q,s}\\lambda_{-p,-q}(L).\\end{aligned}$$ Here we have recalled (\\[edge\\_RDM\\]) and used the relation $$\\begin{aligned}\n&& \\sum_{\\stackrel{(l_1,m_1)}{\\ne(0,0)}} \\cdots \\sum_{\\stackrel{(l_{L-1},m_{L-1})}{\\ne (0,0)}}\\nonumber\\\\\n&&(U_{l_1,m_1}...U_{l_{L-1},m_{L-1}} \\otimes I)|0,0\\rangle_{L \\bar L}\\langle 0,0| (U_{l_1,m_1}...U_{l_{L-1},m_{L-1}}\\otimes I)^{\\dagger}\\nonumber \\\\\n&=&(n^2-1)^{L-1}\\boldsymbol{\\rho}_{\\widehat{L-1}}=(n^2-1)^{L-1}\\sum_{(l,m)}\\lambda_{l,m}(L-1)|l,m\\rangle_{L\\bar L}\\langle l,m|.\\end{aligned}$$ The explicit form of the normalization factors $C_{p,q}$ are given by $C_{p,q}= 1/\\sqrt{(n^2-1)^{L}\\lambda_{-p,-q}(L)}$. Now, we could write $\\boldsymbol{\\rho}_L$ in terms of this basis of degenerate VBS states. ", "By the original definition, $$\\begin{aligned}\n\\boldsymbol{\\rho}_L &=& \\mathrm{tr}_{0,\\overline{L+1}}\\left[\\,|\\mathrm{VBS}\\rangle \\langle \\mathrm{VBS}|\\,\\right] \\nonumber \\\\\n&=& \\frac{1}{(n^2-1)^L}\\sum_{(p,q)}\\sum_{\\stackrel{(l_1,m_1)}{\\ne(0,0)}}\\sum_{\\stackrel{(l'_1,m'_1)}{\\ne(0,0)}}\\cdots \\sum_{\\stackrel{(l_{L-1},m_{L-1})}{\\ne (0,0)}}\\sum_{\\stackrel{(l'_{L-1},m'_{L-1})}{\\ne (0,0)}}\n\\nonumber \\\\\n&& |l_1,-m_1\\rangle \\langle l'_1,-m'_1|\n\\cdots |l_{L-1},-m_{L-1}\\rangle \\langle l'_{L-1},-m'_{L-1}|\n\\nonumber \\\\\n&&\\cdot \\mathbf{P}_{L\\bar L}(U_{p,q}U_{l_1,m_1}...U_{l_{L-1},m_{L-1}} \\otimes I)|0,0\\rangle_{L \\bar L} \\langle 0,0|(U_{p,q}U_{l'_1,m'_1}...U_{l'_{L-1},m'_{L-1}} \\otimes I)^\\dagger \\mathbf{P}_{L \\bar L}.\\nonumber\\\\\\end{aligned}$$ Then by comparing with (\\[Edgestate\\]), we obtain $$\\boldsymbol{\\rho}_L=\\sum_{(p,q)} \\lambda_{-p,-q}(L) |\\mathrm{VBS}; p,q\\rangle \\langle \\mathrm{VBS}; p,q|,$$ where $\\lambda_{-p,-q}(=\\lambda_{n-p,n-q})$ was defined in (\\[lambda\\]). ", "Therefore we conclude that the density matrix $\\boldsymbol{\\rho}_{L}$ of a block of $L$ contiguous spins in the $SU(n)$ VBS state is completely characterized by the degenerate ground states $\\{\\,|\\mathrm{VBS}; p,q \\rangle\\,\\}$ of the block Hamiltonian $H_{B}$ (\\[blockhsun\\]).", "\n\nThe Large Block Limit {#sec:limitsun}\n---------------------\n\nNow we consider the large block limit, *i.e.* $L \\to \\infty$. In this case, $p_{n}(L)\\to 0$ and $\\lambda_{l,m}$ (\\[lambda\\]) become degenerate. ", "So that great simplification occurs in the expressions of entropies as $L\\to\\infty$: $$\\begin{aligned}\nS_{\\mathrm{v\\ N}}&=& \\ln n^{2}, \\nonumber\\\\\nS_{\\mathrm{R}}(\\alpha)&=&\\frac{1}{1-\\alpha}\\ln \\left( \\left(\\frac{1}{n^2}\\right)^\\alpha+(n^2-1)\\left(\\frac{1}{n^2}\\right)^\\alpha \\right) \\nonumber \\\\\n&=& \\frac{1}{1-\\alpha}\\ln(n^2)^{1-\\alpha} \\nonumber \\\\\n&=& \\ln n^{2}. ", "\\label{renyisun}\\end{aligned}$$ We notice that the Rényi entropy is independent of $\\alpha$ and coincides with the von Neumann entropy in the large block limit. ", "The same saturation behavior was observed in all our $SU(2)$ cases in §$\\,\\ref{sec:1ds1limit}\\,$, §$\\,\\ref{sec:larges}\\,$, §$\\,\\ref{sec:largeinhom}\\,$. This means that the density matrix of a large block is proportional to a $n^2$-dimensional identity matrix. ", "In other words, a sufficiently large block of neighboring spins in our $SU(n)$ VBS ground state is maximally entangled with the rest of the chain.", "\n\nIn the limit of large block sizes, *i.e.* $L \\to \\infty$, $\\boldsymbol{\\rho}_{L}$ can be written as $$\\boldsymbol{\\rho}_{L}\\to\\boldsymbol{\\rho}_{\\infty} = \\frac{1}{n^2}\\sum_{(p,q)}|\\mathrm{VBS}; p,q\\rangle \\langle \\mathrm{VBS}; p,q|=\\frac{1}{n^{2}}\\,\\mathbf{P}_{n^{2}}, \\qquad L\\to\\infty. ", "\\label{limitrhosun}$$ The limiting density matrix is proportional to a projector $\\mathbf{P}_{n^{2}}$ which projects on the $n^{2}$-dimensional subspace spanned by the degenerate ground states of the block Hamiltonian. ", "This structure of the limiting density matrix is also a generalization of the corresponding results for $SU(2)$ density matrices in §$\\,\\ref{sec:1ds1limit}\\,$, §$\\,\\ref{sec:larges}\\,$, §$\\,\\ref{sec:largeinhom}\\,$.\n\nSummary {#sec:sum1}\n=======\n\nWe have studied the entanglement in the VBS ground state of the AKLT model in this review. ", "The AKLT model is formulated on an arbitrary connected graph or a lattice. ", "The Hamiltonian (\\[basich\\]), (\\[generalizedh\\]) is a sum of projectors which describe interactions between nearest neighbors. ", "The condition of uniqueness of the ground state relates the spin value at each vertex (site) with multiplicity numbers associated with edges incident to the vertex (bonds connected to the site), see (\\[basiccond\\]), (\\[condition1\\]), (\\[condition2\\]). ", "The unique ground state is known as the Valence-Bond-Solid state (\\[basicvbs\\]), (\\[generalizedvbs\\]).", "\n\nTo study the entanglement, the graph (lattice) is divided into two parts: the *block* and the *environment*. ", "We investigate the density matrix $\\boldsymbol{\\rho}_{B}$ of the block and show that it has many zero eigenvalues. ", "We describe the subspace (called the *support*) of eigenvectors of $\\boldsymbol{\\rho}_{B}$ with non-zero eigenvalues. ", "It has been proved (see **Theorem** \\[theorem1\\] in §$\\,\\ref{sec:den0spec}\\,$) that this subspace is the degenerate *ground space* of some Hamiltonian which is called the *block Hamiltonian* $H_{B}$ (\\[subsystemh\\]). ", "The block Hamiltonian is a part of the original AKLT Hamiltonian describing interactions of spins inside of the block.", "\n\nThe entanglement can be measured by the von Neumann entropy or the Rényi entropy of the density matrix $\\boldsymbol{\\rho}_{B}$. Most eigenvalues of $\\boldsymbol{\\rho}_{B}$ vanish and have no contribution to the entanglement entropies. ", "The density matrix takes the form of a projector on the *ground space* of $H_{B}$ multiplied by another matrix (see also [@XK]).", "\n\n![", "A $2$-dimensional Cayley tree. ", "Each dot represents a spin-$3S/2$ in the bulk and a spin-$S/2$ on the boundary. ", "Each solid line represents the bond connecting a pair of interacting spins. ", "This tree structure has no loop.[]{data-label=\"fig:Cayley\"}](cayley.eps){width=\"3in\"}\n\nA complete analysis of the density matrix for a variety of $1$-dimensional AKLT models (including the $SU(n)$ generalization) has been presented. ", "The block density matrix $\\boldsymbol{\\rho}_{L}$ for a subsystem of $L$ contiguous bulk spins has been diagonalized with non-zero eigenvalues calculated (see also [@FKR; @KHH; @KHK; @XKHK; @XKHK2]). (", "The general notation of the density matrix $\\boldsymbol{\\rho}_{B}$ is changed to $\\boldsymbol{\\rho}_{L}$ for these $1$-dimensional models as emphasizing the dependence on the size $L$ of the block.) ", "We find that in all these cases the *support* coincides with the *ground space*, so their dimensions are equal $D=deg$. In the large block limit $L \\to \\infty$[^5], all non-zero eigenvalues become the same and the density matrix is proportional to a projector (\\[1dsirholimit\\]), (\\[largedens\\]), (\\[limitrho00\\]), (\\[limitrhosun\\]). ", "The von Neumann entropy equals the Rényi entropy and both take the saturated value $S_{\\mathrm{v\\ N}}=S_{\\mathrm{R}}=\\ln D=\\ln (deg)$.\n\nMoreover, it turns out that the block Hamiltonian $H_{B}$ defines the density matrix $\\boldsymbol{\\rho}_{L}$ completely in the large block limit $L\\to\\infty$. The zero-energy ground states of the block Hamiltonian $H_{B}$ span the subspace that the density matrix $\\boldsymbol{\\rho}_{L}$ projects onto. ", "So that $\\boldsymbol{\\rho}_{L}$ can be represented as the zero-temperature limit of the canonical ensemble density matrix defined by $H_{B}$: $$\\begin{aligned}\n \\boldsymbol{\\rho}_{L}=\\lim_{\\beta\\to +\\infty}\\left(\\frac{\\mathrm{e}^{-\\beta H_{B}}}{\\mathrm{tr}\\left[\\ \\mathrm{e}^{-\\beta H_{B}}\\ \\right]}\\right), \\qquad L\\to\\infty. ", "\\label{enlim}\\end{aligned}$$ In the zero-temperature limit, contributions from excited states of $H_{B}$ all vanish and the right hand side of (\\[enlim\\]) turns into a projector onto the ground states of the block Hamiltonian.", "\n\nFor more complicated graphs or lattices, non-zero eigenvalues of the density matrix are still unknown. ", "One open problem is to calculate those eigenvalues. ", "One may start with the Cayley tree (also known as the Bethe tree), see Figure \\[fig:Cayley\\]. ", "The picture shows a Cayley tree with each bulk vertex connected to three edges. ", "The uniqueness condition (\\[condition1\\]) requires that we shall have spin-$3S/2$ in the bulk and spin-$S/2$ on the boundary. ", "A symmetric block subsystem consists of spins enclosed by a circle centered at the center of the tree. ", "The degeneracy of ground states of the block Hamiltonian is $(S+1)^{N_{\\partial B}}$, where $N_{\\partial B}$ is the number of sites on the boundary of the block. ", "An exact explicit expression for the non-zero eigenvalues (finite block) is expected because there is no loop. ", "It is also interesting to study the large block limit. ", "In all known examples [@FKR; @KHK; @XKHK; @XKHK2] where the density matrix of a large block has been calculated, all non-zero eigenvalues approach the same value $1/D=1/deg$. So that the entanglement entropies are saturated, *i.e.* $S_{\\mathrm{v\\ N}}=S_{\\mathrm{R}}=\\ln{D}=\\ln{(deg)}$. Therefore the density matrix of a large block is proportional to a projector on the ground space of the block Hamiltonian, *i.e.* $\\boldsymbol{\\rho}_{B}=\\frac{1}{D}\\,\\mathbf{P}_{D}=\\frac{1}{deg}\\,\\mathbf{P}_{deg}$. However, this might not be the case for the Cayley tree. ", "According to the area law, we expect that in the large block limit (a circular block centered at the center of the tree), the entropy be proportional to the length of the boundary with some coefficient $\\alpha$, *i.e.* $S_{\\mathrm{v\\ N}}=\\alpha N_{\\partial B}$. It is interesting to calculate $\\alpha$ and we expect that it will be smaller than $\\ln(S+1)$. Another open problem is the generalization of the VBS state to other Lie algebras beyond $SU(n)$ and the study of the entanglement.", "\n\nIt is also important to calculate non-zero eigenvalues of $\\boldsymbol{\\rho}_{B}$ for graphs with loops.", "\n\n![", "The basic model on a $2$-dimensional hexagonal lattice. ", "Each spin-$3/2$ in the bulk is represented by three small dots representing spin-$1/2$’s enclosed by a solid circle (a symmetrization). ", "The solid lines antisymmetrize the connected two spin-$1/2$ states. ", "The block is given by a dashed large circle. ", "Each line cut by the dashed circle results in a free spin-$1/2$ on the boundary of the block.[]{data-label=\"fig:Hexagonal\"}](hexagonal.eps){width=\"3.6in\"}\n\nFor example, consider a basic AKLT model defined on the $2$-dimensional hexagonal lattice, see Figure \\[fig:Hexagonal\\]. ", "The basic model has spin-$3/2$ in the bulk and the block is a large circle. ", "Note that each spin on the boundary of the block contributes effectively a free spin-$1/2$. Then according to Kastura’s formula (\\[kastura\\]), the degeneracy of the ground states of the block Hamiltonian is $2^{N_{\\partial B}}$, where $N_{\\partial B}$ denotes the number of site (spins) on the boundary of the block. ", "There is at most $2^{N_{\\partial B}}$ number of non-zero eigenvalues of the density matrix. ", "The entropy takes a saturated value if all these eigenvalues are equal in the large block limit. 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So that for an arbitrary state $|\\psi\\rangle$, we have $\\langle\\psi|\\pi|\\psi\\rangle=\\langle\\psi|\\pi^{2}|\\psi\\rangle\\geq0$ because it is an inner product of $\\pi|\\psi\\rangle$ with itself.", "\n\n[^3]: Some authors add or omit additive constants in the expression of projectors. *", "e.g.* in (\\[simphami\\]) the constant $2/3$ can be dropped. ", "This may shift the ground state energy but does not affect the form of the ground state because the ground state is constructed to have no projection on the specified subspaces for every bond.", "\n\n[^4]: A *walk* is an alternating sequence of vertices and edges, beginning and ending with a vertex, in which each vertex is incident to the two edges that precede and follow it in the sequence, and the vertices that precede and follow an edge are the endvertices of that edge.", "\n\n[^5]: As $L\\to\\infty$, the size of the whole spin chain also goes to infinity.", "\n\n[^6]: If your browser displays an error message for this link, you can get the PDF file using Google search for ‘The valence bond solid in quasicrystals’.", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "Manifest covariance\n\nIn general relativity, a manifestly covariant equation is one in which all expressions are tensors. ", " The operations of addition, tensor multiplication, tensor contraction, raising and lowering indices, and covariant differentiation may appear in the equation. ", " Forbidden terms include but are not restricted to partial derivatives. ", " Tensor densities, especially integrands and variables of integration, may be allowed in manifestly covariant equations if they are clearly weighted by the appropriate power of the determinant of the metric. ", " \n\nWriting an equation in manifestly covariant form is useful because it guarantees general covariance upon quick inspection. ", " If an equation is manifestly covariant, and if it reduces to a correct, corresponding equation in special relativity when evaluated instantaneously in a local inertial frame, then it is usually the correct generalization of the special relativistic equation in general relativity.", "\n\nExample \n\nAn equation may be Lorentz covariant even if it is not manifestly covariant. ", " Consider the electromagnetic field tensor\n\nwhere is the electromagnetic four-potential in the Lorenz gauge. ", " The equation above contains partial derivatives and is therefore not manifestly covariant. ", " Note that the partial derivatives may be written in terms of covariant derivatives and Christoffel symbols as\n\nFor a torsion-free metric assumed in general relativity, we may appeal to the symmetry of the Christoffel symbols\n\nwhich allows the field tensor to be written in manifestly covariant form\n\nSee also\n\nLorentz covariance\nIntroduction to the mathematics of general relativity\nIntroduction to special relativity\n\nReferences\n\n \n \n\nCategory:General relativity\nCategory:Tensors" ]

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[ "Toto Wolff says Mercedes will act to prevent the first corner clash between its two drivers at the U.S. Grand Prix flaring up ahead of the final rounds of the season.", "\n\nNico Rosberg was forced wide at Turn 1 after Lewis Hamilton attempted a move on the inside that resulted in the cars colliding. ", "Rosberg made clear he felt Hamilton had gone \"one step too far\" with the move, although the incident had little bearing on the end result, which saw Lewis Hamilton take victory and the title after Nico Rosberg threw away his chance of winning the race with a mistake between Turns 12 and 13.", "\n\nNevertheless, team boss Wolff said the collision would be discussed once the title celebrations die down.", "\n\n\"It is also a crucial moment now to make sure today's race and this incident don't release consequences within the team and splitting the two sides of the garage,\" Wolff said.", "\n\n\"It's very hard. ", "Lewis came on the radio and said it wasn't on purpose, I think it's something that we are going to talk about in a couple of days, but this is the moment to celebrate a world champion who deserves to be a world champion and once the emotions have cooled down we will discuss.\"", "\n\nThe last time Hamilton and Rosberg clashed on track was at the 2014 Belgian Grand Prix, which brought to a head a season of tension and resulted in a series of post-race meetings to diffuse the situation. ", "Wolff admitted Sunday's collision could have similar repercussions if Mercedes does not soothe the relations between its drivers.", "\n\n\"If we don't take any action it has the potential [to be like Spa]. ", "It's never easy and it wasn't easy the first time around. ", "I think we have some experience and we just need to have a calm approach and a firm approach of how we would like them to compete.\"", "\n\nAsked if Rosberg may start treating Hamilton differently, Wolff added: \"That danger is for sure imminent.\"" ]

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[ "Hobbyist photographer back in the '70s and '80s. ", "Took my first photo when I was five years old, got an SLR when I was ten. (", "Film, all manual, handheld light meter, we had a darkroom in the basement.)", "\nShelved the hobby for a couple of decades. ", "Returned recently, this time with digital equipment.", "\n\nJack of many trades (and master of none), but I have a professional background in software development." ]

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[ "With the release of The Fellowship of the Ring in late 2001 came a flood of interest in the Professor's works and a flood of new posters to TORC - the majority of whom joined in 2002.", "\n\nThe result was a significant shift in the messageboard's culture - and I believe we, the Class of 2002, are the shapers of the board we see today.", "\n\nThis thread is a place for the class of 2002 to come and hang out, reminisce and share news.", "\n\nWe've all been through a lot, on the boards and off, since those heady days in 2002 and this thread and this message board is a testament to the magic that is simple, human friendship.", "\n\nThe road goes ever on and on...\n\nEveryone is welcome here. ", "Please join in!", "\n\nIn 2007 the Class of 2002 thread was awarded the prestigious Mellon Award for being a friendly and inviting place.", "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\nSo welcome all especially those with a joining year of 2002.", "\n\nJust post a message here and we will see your name goes on the roster!", "\n\nHonorary Members Always Welcome!", "\n\n(Special invite to those mid-December 2001 Torcers who arrived just before the December Demise of Torc. ", "Torcers like Leoba! )", "\n\n*drops into a comfy chair with a steaming mug of cocoa and hopes to meet some old friends and make a few new ones. *", "\n\n~~~~The 2002 Roll Call~~~~These illustrious Torcers joined in the year 2002:\n\nA caravan of moving vans lumbers along a desolate country lane lined with ancient trees; oaks, ash, even elms for this is a special bit of country where special things endure and grow.", "\n\nThe lane dips down gently, furrowing into a deep nest of tall horse chesnut trees before pulling up again, over a gentle ridge that, once cleared, brings one onto a vast open expance of land that slopes up, ever gradually. ", "It is clear to the left and right that it is, in fact a hill draped with a gentle, rolling sward of green like the train of lady’s dress which ambles and rolls to the hill’s flat pinnacle, which juts out over a verdant plain like the prow of a great ship. ", "Sheer cliffs hold up a castle that shows all the marks of Westernesse (sorry, Scribbles); great masses of expertly hewn rock meshed together to create a magnificent and impenetrable fortress. ", "A moat rings the western side whereas the cliffs protect the castle from the north, east and south and provide the most spectacular views of the surrounding countryside, which, by virtue of the clouds and mists, change - sometimes making it appear the castle was surrounded by a mighty sea, other times by more gentle, rolling plains. ", "At times the clouds show vast mountain ranges nearby; it all depended upon the viewer and the viewed.", "\n\nAs for the rooms inside- there were many and each decorated differently depending entirely, again, on the wishes of occupant.", "\n\nIt was a perfect place for the Class of ’02.", "\n\nThere was one design element that seemed out of place however; once over the drawbridge and through the bridge gate one could see a set of irregular, perhaps even dangerous, stairs leading down to a metal door that led into the lowest level of the castle. ", "Over the door buzzed a neon sign which spelled the word ‘BAR’ - except that not all of the neon in the letter ‘r’ illuminated, resulting in the irregular flashing of the word ‘BAP’.", "\n\nBardhwyn pulled her van to a halt in front of the castle’s dropped drawbridge and shut off the engine. ", "Jumping out, she trotted towards the realtor’s sign that still stood stuck in the soft loam near the castle’s mail box. ", "She smiled at the large SOLD sticker plastered over the sign’s front and pulled it out of the ground. ", "Sticking her arm in the mailbox, she pulled out a huge iron ring with at least fifty different keys dangling from it.", "\n\n‘What is it with me and keys lately,’ she wondered to herself.", "\n\nThe rest of the ’02 caravan had cleared the ridge followed by the pizza delivery guy. ", "It was time to move in.", "WELCOME TO OUR NEW HOME!", "\n\nAs the last of the moving vans were parked in the courtyard of the castle and the pizza van pulled back out headed back to town a bicycle is seen rising and falling with the road over the hills and into the roads valleys as it makes it's way to the castle. ", "Finally a very tired and very grimy cyclist comes over the draw bridge and stops trying hard to catch her breath and looking about the now busy courtyard.", "\n\n*Phew* I made it!", "\n\n**With her legs feeling like rubber Vana places her bike up against a wall and strolls over to one of the moving vans and grabs a box. ", "She then trudges into the castles main entrance and finds herself in the largest foyer she has ever been in. ", "Her mouth falls open as she admires the suits of armor and the tapestries of the finest quality that lined the walls. ", "The floor was made of black marble and a staircase leading to the next level of white marble. ", "The contrast was breathtaking!**", "\n\nWOW!!!!", "\n\n**Her response echoed and startled Bardy just as she was returning into the foyer from depositing a box in another room. ", "When she saw who said it she smiled**\n\nWell look what the cat dragged in??? ", "Its about time you showed up and helped!", "\n\nSorry I fell asleep and had the worst time dragging my sorry bum out of bed this morning. ", "I got to the old place just as you lot were pulling out. ", "I had to chase you all on a bicycle.", "\n\nYou look like you been through the ringer dear!! ", "Why don't you get something cold to drink then come back and go up pick out your room. ", "Then you can help with the unpacking!", "\n\nOkay I don't mind of I do!! ", "OH and the place is gorgeous!!! ", "I love it!!!", "\n\nHappy 7th TORCiversary Impenitent/Novice!!!", "\n\nLast edited by Vanaladiel on Sat Feb 14, 2009 11:25 am, edited 1 time in total.", "\n\nSpring come quickly!!~*Sister of the Twilight*~~*Daughter of the Moon*~\n\nWe mourn the loss of another wonderful man from TORC! ", "Cockrobin has passed away on 02/18/2019 Rest in the arms of Jesus my friend!oldtoby we will always remember you and your wit and smile! ", "Love you my friend! ", "RIP 1/20/18\n\nVanaladiel wrote:Okay I don't mind of I do!! ", "OH and the place is gorgeous!!! ", "I love it!!!", "\n\nBardy grinned as she watched Vana drift towards the smell of pizza where root beer was sure to be found.", "\n\nThat meant one pleased '02er and how many more to go?", "\n\nBardy cast her gaze around the resplendent entry foyer and silently fretted about Scribbles, wondering if there was any sort of allergy medication available for Numenorean hives because she was sure the Peredhel would break out in them.", "\n\nHer cell phone rang. ", "Pulling it free from her pocket she smiled at the little display: Radesh. ", "She silently waved to the newly arrived Rowen just as she opened the phone.", "\n\n\"Hello, Radesh\" she beamed. \"", "Yes, all moved in. .... ", "I miss you, too. ", "When are you coming for a visit?\" ", "Bardhwyn's face fell. \"", "I thought you had a break? ", "All the characters were going to be asleep for two weeks or something? ", "Oh.\" ", "Bardhwyn listened. \" ", "A reunion scene, huh? ", "Ok, that will take, what? ", "Three months to script? ", "Yes, well, no, not angry - disappointed. ", "I miss you - the WCA awards feel like they were years ago. ", "We never did get to finish ... hmm?\" ", "She broke out into a wide smile. \"", "Promise? ", "Ok, then. ", "I can wait. ", "Love you, too. ", "Bye\"\n\nShe put the phone back into her pocket and caught a whiff of the pizza.", "\n\n'I think it is dinner time.'", "\n\n(OOC - sorry to all the non-RP'ers! ", "Come on in and post, no role play required!)", "\n\nVana grabs a nice cold root beer from the kitchen refrigerator and heads up the back stairs to look at the rooms.", "\n\nThe hallways were wide and decorated with elaborate candle sconces and artwork from the masters (Alan Lee, Ted Nasmith, the Hildibrandts and others) but at the end of the hallway was a portrait lit by a simple but elegant wall mounted light. ", "It was the portrait of the Professor underneath a tree. ", "Vana couldn't help but smile. ", "It was one of her favorite pictures of him.", "\n\nVana turned back to the first door on her right and turning the large crystal knob entered a huge room. ", "the wooden floor had a persian rug upon it and the four poster bed was huge. ", "Sheers hung over the windows and a cat rested upon the window ledge. ", "It looked up at her and mewed softly then stretched and jumped down and walked over to the bed and jumped up again. ", "She dropped her back pack off of her shoulders and leaned it against the wall by the doorway then moved over to sit upon the edge of the bed and the kitty nuzzled up to her purring. ", "The cat had beautiful markings, definitely part calico and part Siamese. ", "A petite thing but you could tell it was no longer a kitten. ", "The tips of her toes were white with dark brown socks and her face had a dark mark that came over one eye and ended in the middle of her nose making a straight line break of color down the center of her face. ", "Her ears were both dark as well. ", "But the orange of the calico mixed in and covered her neck.", "\n\nYou are beautiful sweetie!! ", "Do you come with the room??? ", "I sure hope so!", "\n\nSo then the last room on the left as you come up the stairs is mine!!! ", "Well and his!!! ", "I hope he likes you as much as I do!!!", "\n\nSo Vana headed back down the hallway to the main stairway down to the foyer and popped out to grab some of the boxes and help bring things in.", "\n\nHey Bardy did you notice the number of posts we left the last place at??? ", "It was 2002!!!!", "\n\nAlso it was the most looked at or read thread of the entire first page!! ", "Over 47,800 viewings!", "\n\nSpring come quickly!!~*Sister of the Twilight*~~*Daughter of the Moon*~\n\nWe mourn the loss of another wonderful man from TORC! ", "Cockrobin has passed away on 02/18/2019 Rest in the arms of Jesus my friend!oldtoby we will always remember you and your wit and smile! ", "Love you my friend! ", "RIP 1/20/18\n\nSil, whose brain hurt too much to do any decent RPing, followed a suitcase-toting Aramir down a long, airy hallway, eager to get to the pizza that she'd seen being carried in the direction of the bap, erm, bar.", "\n\n\"Hurry up, I'm hungry!\" ", "She came up behind him and poked him repeatedly in the back, which, of course, only made him walk more slowly.", "\n\n\"Maybe if you -oof- did some of the -ouch- work around here instead of -ow, geez, what did you pack in here??\"", "\n\nStarlin stretched her arms and yawned... \"Ouch!\" ", "Something cracked in her back. ", "Rusty bones. ", "Need more exercise. ", "Carrying all that stuff in a backpack was probably not the bestest of ideas... But one has to keep appearances, you know. ", "People still think that you've been traveling around the world these past few years, so darlin, you better have the hugest, the heaviest backpack ever, just to convince them it's true.", "\n\nStarlin looked around. ", "The place was enormous, and she shivered. ", "Could it have any, well, deceased inhabitants? ", "Like... ghosts? ", "Goodness, hope not! \"", "Go find your room!\" ", "someone nudged her, and she lifted her backpack again. \"", "What?\" ", "she didn't like the stares, \"Well me got all me goodies in there, so me carryin them up to me room, whether you like it or not.\"", "\n\nShe trudged up the stairs and found herself in front of a row of doors, all looking different. \"", "Hah. ", "Go find my room, she said,\" Starlin turned to the right and moved along the corridor, peeping into every single room. ", "They all looked nice but none looked like it could be *hers*.", "\n\n\"Wrong way,\" a voice said. ", "Starlin jumped. \"", "Wh-wh-whattt?\" \"", "I said, wrong way. ", "Look to your right. ", "You almost missed it.\" ", "Starlin's heart was jumping up and down. ", "This place *is* haunted after all!", "\n\nWell, at least the ghost wasn't lying. ", "A door, with seven elaborate letters engraved on it: S-t-a-r-l-i-n. She opened the door and looked inside. ", "It looked remarkably cosy, just as she liked. ", "No bed, just a mattress on the floor. ", "A sitting sack, a large table with a comfy chair, a wardrobe, and a small fridge in the corner. ", "Lots of sunlight. ", "Perfect.", "\n\n\"Glad you like it,\" said the voice again. ", "Starlin jumped up. \"", "Who are you?\" ", "she finally managed to open her mouth. \"", "Questions later,\" the ghost chuckled, \"Don't worry, we will meet again. ", "Now, go downstairs and get yourself a pizza. ", "We don't want you to starve to death, do we?\"", "\n\n\"N-n-n-o, I guess... no.\" ", "Starlin stammered and, dropping her backpack on the floor, ran downstairs to the BAP.", "\n\n\"Hey Bardy did you notice the number of posts we left the last place at??? ", "It was 2002!!!! \"", "\n\nYeah and then some darn fool went and ruined the space time continuum.", "\n\n****\n\nMeanwhile, outiside Rholarowyn and Bryttar could be found directing the big rig full of all the archery nessecities for a 28 outdoor field target range, an Olympic range, a practice/warm up range and the ever important 32 bale indoor archery range (for inclement weather of course.)", "\n\n***\n\nBardy, would you mind updating the caption under my screen name in your first post? ", "I'm back from the West now.", "\n\n.", "\n\nSo True the Arrow, So Steady the Hand\n\nNo word in your quiver goes errant, no thought from your bow is misspent, no image falls short of your target, so true are the arrows thus sent. ", "Your heart with a steady compunction pulls the bowstrings few others could ply, your story does more than just function-- your steady hand helps my heart fly!", "\n\nSupervising the pizza uh... why not? ", "She looked at the different boxes: X large pizzas. ", "Needed indeed, some pepperoni, veggie (always crucial to have a veggie handy), Hawaiian, cheese (boring but then again necessary too), salmon. ", "Should have a taste...\n\n~~~~~~~~~~~~~~~~~\n\"Hurry up, I'm hungry!\"", "\n\nEari looked down at the boxes... a call might be in order. ", "What they had told her to supervise the pizzas. ", "The pizzas evaporated before they became cold. ", "That was the nature of pizza.", "\n\nShe had eaten for three really... Some appetite; and she'd be sick by next morning but those pizzas were good.", "\n\nShe picked up the cell phone she had taken while leaving - might have been Joan's come to think of it and not one of the 02ers' but who cared? - ", "and ordered some extra pizzas for the others...\n\n\"Hi, my order is...\"\n\"Hurry up, I smell pizza!\"", "\n\"Your total is 2 silver coins miss.", "\n\"Make it here within 15 minutes and I pay you 4. ", "And tell your guy to pass by the alleyway directly to the kitchens... no going through the main gate. ", "Clear\"\n\"Yes ma'am\"\n\nNow, some diversion so the others wouldn't come to the kitchen... And so she ran to the hall, picked some broom and mop before she left again... crying over her shoulders...\n\n\"The people didn't leave it alright... Dangerous dustbunnies in the kitchen, no one can go there before I'm done. ", "Check the rooms one never knows...\"\n\nWho can say if I've been changed for the better?But because I knew youI have been changed for good.", "\n\nIt's funny how some distanceMakes everything seem smallAnd the fears that once controlled meCan't get to me at allIt's time to see what I can doTo test the limits and break throughNo right, no wrong, no rules for meI'm free\n\nThe rig was a bustle of energy as Bryttar and the other worker buzzed around on fork lifts pulling the 200+ archery bales from the depths of the trailer and placing them in neat stacks under the large oak trees.", "\n\nSoon a delivery truck slowly drove up the drive, stopped, backed up, then pulled forward again. ", "Rholarowyn could see the driver check the scrap of paper and then look back at the castle.", "\n\n“Can I help you?” ", "She inquired once close enough for the man to hear. “", "Wait, pizza…what do you have in there?", "\n\n6 San Diego Pizzas with feta cheese, avocado, red onions, and pesto. ", "Good call, those are always popular…\n\nThen we have 5 vegetarian, 4 pepperoni, 3 with pepperoni and sausage, and 6 with everything on it.”", "\n\n“Great!” ", "replied the shieldmaiden. “", "Give me one San Diego and one with everything on it…”\n\n.", "\n\nSo True the Arrow, So Steady the Hand\n\nNo word in your quiver goes errant, no thought from your bow is misspent, no image falls short of your target, so true are the arrows thus sent. ", "Your heart with a steady compunction pulls the bowstrings few others could ply, your story does more than just function-- your steady hand helps my heart fly!", "\n\nBehind the elf the man coughs loudly. ", "Rolling his eyes, the bartender adjusts the metal lever sticking out of the bar chimney. ", "Several marks already adorn the freshly redone stonework, and after Phil's movement a large cloud of smoke pours out of the fireplace.", "\n\n\"I'd say you're right.\" ", "Anorast turned about and peers through the smoke. \"", "Mark it, and for goodness sakes, let the fire burn clean.\"", "\n\n\"I still can't believe you wanted to do this.\"", "\n\n\"Well, it's got to have the right ambiance, wouldn't you say?\"", "\n\n\"Ambiance is one thing, but I might say this is insanity,\" answered Phil. \"", "Not to mention hazardous working conditions.\"", "\n\n\"Well, it's only for special occasions.\" ", "Anorast carefully made his way across the bar room, barely avoiding tables and chairs hidden in the smoke, and nearly hitting his head several times on the heavy wooden ceiling beams. ", "Finally he found the front door, and thrust it open. ", "On the other side of the room Phil opened the door to the back rooms, letting the smoke blow out several vents through the outer walls.", "\n\nAs a gentle breeze slid past him into the bar Anorast looked about the courtyard, seeing the busy activity of moving a massive community into a new home. ", "Almost immediately one of his fellow '02ers walked down the stairs to the bar entrance.", "\n\n\"I wouldn't go in there yet, Starlin.\"", "\n\n\"Uhh, what's going on?\"", "\n\n\"We were testing the smoke generating mechanism, and it's still pretty thick in there.\"", "\n\n\"Well, have you tested the strobe lights?\"", "\n\n\"Umm, no...those are in the main hall.\" ", "Anorast chuckled, imagining what might happen if the lighting system was moved into the bar. \"", "There's no room for dancing inside the bar, only shadowy drinking and confused games of darts and pool.\"", "\n\n\"No dancing?\"", "\n\n\"No, but there is a hidden staircase straight to the main hall,\" Anorast said with a wink.", "\n\nWarden turns up looking rather tired and dragging behind him an incredibly worn armchair complete with old-lay antimacasser...\n\n\"Hey Guys, I know I wasn't around to help with the move but I was wonderng if it would be okay if I had my own armchair here... it helps me to think/be imaginative/sleep...\"\n\nThis is just a quick post guys as I have to be at choir practice in 10mins...\n\nJust to say a few things:\n\n1) Great to be in a new place !!!!!!!!!! ", "I really like it!", "\n2) Happy Birthday to everyone I missed over the last 5 days or so!!!", "\n3) Sorry I haven't been about again! ", "You'll get a big post, although it may well be tomorrow as I have plans today involving sorting essay topics and watching Ireland thrash Italy in the rugby...\n\nIn true elvish fashion, and eschewing anything modern, a troop of Elves on horseback arrived at the front of the castle. ", "Following was a slow moving cart also driven by elves.", "\n\nBardhwyn rushed out the front door, through the wide courtyard and out the gate, through another passage and gate (it was, after all, a fully defensible castle) then trotted over the drawbridge and bid them all to follow her to the courtyard.", "\n\nOnce in front of the main hall entrance, the elves carefully lifted a very large, very long bundle from the cart and followed the Archer up the wide entry steps.", "\n\nIn the entrance foyer the Elves worked quickly, scaling the scaffolding that stood to the left, hoisting the large object up and fastening either end to elaborate hooks that had been embedded into the stone work.", "\n\nThe elves descended the scaffolding and quickly worked to break it down, piling the pieces onto the waiting cart outside. ", "Once completed the elves returned and joined Bardhwyn who stood looking at the strange item the elves had mounted.", "\n\n\"You need only pull this cord,\" and elf explained. ", "He pointed to a long, golden rope that hung from the right hand end of the mysterious wrapped object.", "\n\n\"No doubt you wish to wait until all are assembled,\" another elf commented.", "\n\nBardhwyn guffawed. \"", "This lot? ", "Assembling in one place? ", "At one time? ", "It will never happen but not out of a lack of want to do so, it is just we're spread all over the globe, live in dozens of time zones. \" ", "She walked up to where the golden cord dangled against the wall and pulled it, unceremoniously.", "\n\nWith a cool hiss of silk unfolding the object unwrapped and unfurled. ", "A cascade of gold, silver and silk rippled down the ancient stonework until, finally, a resplendant, hand embroidered tapestry revealed itself.", "\n\nThe Class of 2002 Roll, hand wrought, with the finest gold and silver threads on a deep maroon field of silk that covered the entire wall.", "\n\nBardhwyn took an quick intake of breath for it was far more beautiful than she could imagine and all the names, shaped so beautifully in gold thread, glittered in the hall's mix of sun and lamplight. ", "Now who ever entered the main castle hall would walk through this entrance foyer and see, to their left, the names of any and all who wish to have their names added and no name would be stricken off.", "\n\n\"I think you will find, Lady Bardhwyn, that when new names are added, there will forever be enough room, for this is silk retrieved from Gondolin ere its fall, and it is marked with magic of old,\" one elf explained. ", "Another walked up and presented an ornately carved mahogany box, rather large. ", "He opened the lid and showed its contents: threads, needles - all that was need to add and amend the tapestry.", "\n\n\"Me? ", "You don't expect me to... \" The Archer's eyes widened with fear. \"", "Oh, no! ", "I never did well with needlepoint! ", "Arrow point, yes.\"", "\n\n\"No, no!\" ", "The elf holding the box said with a smile. \"", "The box will stay here and if you ever require an addition or amendment, send word and we will send a seamstress.\"", "\n\n\"Thank the gods!\" ", "Bardhwyn whispered. \"", "And thank all of you! ", "Please tell your craftsmen and women we are delighted and honored to display this in our new home.\"", "\n\nPleased with the thanks and courtesy the elves bowed and departed, leaving Bardhwyn with the new member's chest, as she named it. ", "She placed it on a high table to the left of the Member Tapestry and stepped back again to admire the it.", "\n\nIt was then she noticed smoke outside... coming from the direction of the bap, er bar... and she ran...\n\nOOC --\n\nPB!! ", "I am sorry, I thought we had you listed there.", "\n\nYou are now!!", "\n\nYou did exactly what was required, you made your request known. ", "I am totally dependent on people posting here and letting me know they want (or need) to be added to the rolls.", "\n\nSo spread the word - to join, all one needs to do is join in and ask!", "\n\nAnd Rho, I changed your listing, too. ", "When I add people I simply copy and paste direct from their signature image as it appears online at that moment. ", "I think your custom title must have had 'Returned from the West' in it, because I wouldn't be so clever as to put that in.", "\n\nAnd no SilverScribe yet. ", "Yup, I think the Numenorean architecture has spooked her.", "\n\n\"There!\" ", "Rholarowyn signed scooting the last archery bale neatly beside the others then turning towards Bryttar who was looking off towards the castle. ", "Quickly the shieldmaiden followed his gaze. ", "A quick glance between them followed and then they took off.", "\n\nThey reached the trail of smoke with its wispy arms stretching up towards the sky and were suprised at the source.", "\n\n\"Did you hear that?\" ", "Bryttar asked.", "\n\n\"I did,\" replied Rholarowyn glancing down into the round cobblestone cistern, trying to peer through the ever increasing gray haze.", "\n\nThe Archer of Dale was suddenly at their sides.", "\n\n\"Bardhwyn,\" Bryttar smiled momentarily and then watched as she peered down the deep smoke filled hole.", "\n\nJust then they heard it again. ", "The faint cry coming from the depths of the darkened hole in the ground.", "\n\n\"Hello...hello...?\"", "\n\n.", "\n\nSo True the Arrow, So Steady the Hand\n\nNo word in your quiver goes errant, no thought from your bow is misspent, no image falls short of your target, so true are the arrows thus sent. ", "Your heart with a steady compunction pulls the bowstrings few others could ply, your story does more than just function-- your steady hand helps my heart fly!", "\n\nScribbles dismounted at the bottom of the hill, just in side the treeline. ", "She scowled, and putting both hands on her hips muttered something that if anyone had been near enough to hear, sounded faintly like \"Westernesse? ", "Why did it have to be Westernesse? . . .", "\n\nShe turned to her big grey (and as yet unamed) warhorse and smiled when he pushed his head into her shoulder, looking for a bit of dried apple or apricot. \"", "Soon, old son, soon. ", "I'm fresh out of dried fruit.\" ", "The big stallion snorted, whether in disgust at the lack of treats or her disgraceful play on words, it was hard to tell.", "\n\nRe-mounting, the Scribe covered the final distance and after making sure her horse was properly stabled, watered, unsaddled and fed, she snuck in a side postern door. ", "Taking a back staircase she discovered a small, closet like room in one of the towers and dumped her pack.", "\n\n\"Hmmm, I smell pizza,\" she mused. \"", "I hope that seedy bar made it into the basement . . .\"", "\n\n*****************\n\nLOL, boy, y'all been busy little posters, eh wot? ", "Sorry, yesterday was taken up with romanticness and this morning by churchliness . . . ", "No matter, the new digs look MAHVELOUS Bardy dahlink, we shall undoubtably have some great times ahead.", "\n\nI'm not sure if I said I'd post links here, or in some other thread, but here's pictures of the Celtic Circle Table Runner I just finished for my sister . . .", "\n\nPiccy 1 ... the accordion fold is just to show the corners as well as the central design.", "\n\nPiccy 2 . . . ", "showing the corner pattern detail (which wasn't on the original but I added because the corners looked too bare and blah.)", "\n\nPiccy 3 . . . ", "a closeup of the underside to show the mitred corners. ", "I had to stitch the mitres by hand since the hem was very narrow . . .)", "\n\nOkay, boring stuff over. ", "I think I'll have my character grab her big ol' Elven longbow and see if we can't punch a few holes in Rho's nice archery butts . . .", "\n\n“Hello…hello?” ", "Fala’s melodic, yet weak and optimistic query floated up like the melody of song-birds in Spring, and seemed to reverberate with gathering energy as it bounced off the rounded, time-worn cobbled stones that lined the cistern. “", "Elves do NOT fall into ditches” her finely tuned upbringing had taught her. ", "However, the Universe had neglected to remember that Elves, like mortals, are subject to the same laws of nature, and a distracted Elf can fall into a cistern just as easily as any mortal.", "\n\nThe nice thing was that this particular cistern had a very mossy, cushiony and fragrant bottom. ", "That established, being stuck at the bottom of a well, however fragrant and green, could enchant even an Elf only temporarily. “", "OK, aside from HOW I got here, the issue is: how do I get OUT? ", "Hmmmmm, considering I have no ruby slippers…”\n\nThe Elf drew a large breath, lengthened up through her spine, inclined her chin, and in a relaxed and elongated exhale, drew her focus to the present moment. ", "Hmmmmmmm… her gaze fell upon a cluster of gemstones and a small pile of dried wood that, in her frustration, she had not noticed before…\n\nWho can say if I've been changed for the better?But because I knew youI have been changed for good.", "\n\nIt's funny how some distanceMakes everything seem smallAnd the fears that once controlled meCan't get to me at allIt's time to see what I can doTo test the limits and break throughNo right, no wrong, no rules for meI'm free\n\nWe mourn the loss of another wonderful man from TORC! ", "Cockrobin has passed away on 02/18/2019 Rest in the arms of Jesus my friend!oldtoby we will always remember you and your wit and smile! ", "Love you my friend! ", "RIP 1/20/18\n\nA very fast, very colourful car is seen speeding up to the castle. ", "The british flag, which adorns it, has seen better days and the license plate, which reads shaguar, incidentally, is slightly crooked. ", "But as strange a sight the car is, it is far superseeded by the temporary inhabiants of the car, i.e. the slightly annoyed Silmarie and five disturbingly handsome elves, in various states of disarray. ", "Although elves never can be said to be in disarray, deshabille is more appropriate.", "\n\nYou'd wreck it, Silmarie replies unceremonously. ", "And besides, I'm a great driver! ", "And don't you smirk back there Ithil, I can see you.", "\n\nThe smirk, however, was well deserved. ", "Various small animals did not litter the streets where Silmarie passed only because they had more sense than her and great reflexes.", "\n\nAnd incidentally, Galathil objected, 'twas I who finally overpowered the former owner of the vehicle.", "\n\nJust because he thought you were female, Dior mumbled from the back seat.", "\n\nOh, stop it. ", "Anyways, we're here. ", "And late, as usual.", "\nThe company disembarked and Celeb went to the back and unlocked the trunk. ", "He gently helped up a very silly looking British gentleman who kept saying Groovy, baby. ", "Celeb was quite confused as he did not see where the grooves are supposed to be. ", "Perhaps he was complaining about the state of his transport? ", "But he looked quite happy with the world. ", "Elven wine can do that to you, he mused. ", "He picked up his pack and followed the others.", "\n\nLet's find our room, hey? ", "Silmarie suggested as she sprinted to the top of the stairs. ", "She turned right and, as luck would have it, she noticed a discreete plate Silmarie and company. ", "The room was just their taste. ", "Basic beds, plenty of room on the floor with various cushions, which almost cried out Lounge and play rummy! ", "And, there in the shadows...Silmarie burst into silent tears...an easel and a box of Sennelier pastels. ", "The world went white for her and then exploded in colour. ", "She sat down and without even noticing, she picked up a pastel and began to draw.", "\n\nThe Silmarils quietly left and shut the door. ", "What say ye we find a bar in this fine establishement? ", "Dior enquiered. ", "A fine suggestion and well worthy of following, Elros replied and led the party down the stairs and outside. ", "They found the blinking sign very amusing, the black cloud rising from the object of their desire not so.", "\n\nShould we help? ", "Mayhap there is someone who is in need of assistance Celeb enquired. ", "Dior rolled his eyes, Yes, yes, poetically put. ", "If there's a fire, let's help put it out. ", "They rushed to the scene and opened the door.", "\n\nBefore she knew it Bardhwyn was flanked by Lady Heather, five very handsome if not disheveled Elves, her old friend Rholarowyn and the Rider Bryttar.", "\n\nShe felt the blood rise in her cheeks. \"", "Hello Bryttar,\" she said shyly. ", "Bardhwyn nodded to Rho with warm smile before her attention was drawn by the faint calling from a dry and abandoned cistern a few paces away.", "\n\n\"Right!\" ", "she said trying her best to take command of this RP situation. \"", "It seems we have smoke pouring out from the bap, uh I mean the bar - we need someone to go check that out. ", "Any volunteers??\" ", "The Archer looked over the elven quintet and felt the blood rise a second time. ", "Lady Heather caught her eye and grinned, causing Bardy to blush all the more but she quickly collected herself with a self-conscious cough.", "\n\n\"It isn't clear if the smoke is dropping down into this hole in the ground or pouring out of it....\" Bardhwyn quickly fell to her knees and scrambled toward the gaping hole,\" ... but there certainly someone down there.\"", "\n\n\"Are you hurt down there!!\" ", "Bardhwyn called out.", "\n\n\"Bardy? ", "Is that you?!\" ", "a voice called up.", "\n\n\"Fala???!!\"", "\n\nLast edited by Bardhwyn on Tue Feb 17, 2009 4:48 pm, edited 1 time in total.", "\n\n\"Eru almighty, the bar is in no state to be drunk in! ", "Tis a tragedy! ", "Ai, fell are the stars...\"\n\n\"Okay, Galathil, how bout you stop and we take a look inside. ", "I'll go in and if I'm not back in five minutes, someone come and get me.\" ", "Elros, as usual had his mind completely focused on business at hand. ", "He half crawled half kicked his way to the bar.", "\n\nAlas! ", "Tis a tragedy after all! ", "his cries were heard not moments later.", "\n\nThe Silmarils cast a worried glance towards the proprietress. ", "They dearly hoped she had no-one dear to her in there, but fortunately she had her hands full with the suspiciously smokey hole.", "\n\nNay, not a tragedy a downright villainry towards all creation! ", "The beer's gone to the ground! ", "Elros cried from the stricken bap.", "\n\nCeleb made a mental note to do something unpleasant to Elros while he sleeps. ", "He helped the distressed workers out of the bar. ", "The Silmarils looked none too pleased. ", "Tis a horrible fate to be stuck between a dishevelled elf and his long-overdue pick-me-up \"What exactly happened here?\" ", "Galathil enquired\n\nAs the smoke makes its way up the back stairwell from the basement bap/bar, Vana walks into the kitchen looking for another piece of pizza. ", "She sniffs the air and makes her way following the scent to the doorway leading down.", "\n\nVana grabs a piece if the pizza out of the box on the counter and heads down the stairwell into the smoke. ", "Slowly making her way down feeling along the cool stone walls.", "\n\nAs she gets closer to the bottom of the stairway she hears some coughing and hears Guru speaking with the unseen character helping him test his machine.", "\n\n\"Um..... I hate to disturb your fun hon but you are smoking up the house!!\" ", "Vana chides at Guru through the smoke still billowing toward the stairwell.", "\n\n\"Sorry sweetheart!!\" ", "Guru coughs, \"I didn't mean for it to be so thick. ", "I promise I will come up and air out the house personally!!\" ", "Guru coughed again and then she could hear him berate the guy helping him. \"", "I told you to only turn it on 3 not 8! ", "Now you got me in trouble with the Mrs.\"\n\nVana laughs to herself, then rolls her eyes.", "\n\n\"You are not in trouble dear I just wanted you to know! ", "I will go open the windows, I suggest you find a way to clear this out some before someone calls the Shire Firehall and gets the fire crew here!\" ", "Vana then turns and feels her way back up the stairs and into the castle where she opens doors and throws open the sashes of the windows to air the place out.", "\n\nSpring come quickly!!~*Sister of the Twilight*~~*Daughter of the Moon*~\n\nWe mourn the loss of another wonderful man from TORC! ", "Cockrobin has passed away on 02/18/2019 Rest in the arms of Jesus my friend!oldtoby we will always remember you and your wit and smile! ", "Love you my friend! ", "RIP 1/20/18" ]

{ "pile_set_name": "Pile-CC" }

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[ "All SEO tips say to use heading tags (h1-h6) to help your site rank better in search engines. ", "Does it affect how well heading tags work with search engines if you use CSS to change their styling, such as their font size and color?", "\n\najetrumpet\n\n11-04-2010, 10:24 AM\n\nI am not an expert at this, but the last article read about meta tags said that they are now even useless. ", "So I seriously doubt that using header tags have any effect on a search engine ranking at all. ", "After all, they're HTML tags, nothing else. ", "aren't they? ", "robots don't search for HTML tags on pages, as far as I know.", "\n\nThe other thing that people never think of when trying to improve their search ranking is the fact that search engines are run by for-profit companies too. ", "They want people to use their engine, and if results comes up that aren't popular and don't have a track record of being click on often, they're not going to show up regardless of what you do.", "\n\nI personally think that search engine ranking is a joke. ", "I'd concentrate your efforts elsewhere until the word of mouth has gotten to the point where the website is garnering a significant amount of traffic.", "\n\nabduraooft\n\n11-04-2010, 11:16 AM\n\nSo I seriously doubt that using header tags have any effect on a search engine ranking at all. ", "After all, they're HTML tags, nothing else. ", "aren't they? ", "robots don't search for HTML tags on pages, as far as I know. ", "That's wrong, I'd say.", "\nRead http://boagworld.com/technology/semantic-code-what-why-how and\nhttp://www.searchenginejournal.com/how-to-analyze-a-page-html-semantic-structure/7515/\n\nI personally think that search engine ranking is a joke. ", "I'd concentrate your efforts elsewhere until the word of mouth has gotten to the point where the website is garnering a significant amount of traffic.", "\nI've a site to which ~62% of the traffic is through search engines.", "\n\n@OP: It won't be an issue to apply styles on the heading tags, to change the color of font-size, though setting display/visibility properties to hide them from the users' view may cause some issues.", "\n\nteedoff\n\n11-04-2010, 03:34 PM\n\nI am not an expert at this, but the last article read about meta tags said that they are now even useless. ", "So I seriously doubt that using header tags have any effect on a search engine ranking at all. ", "After all, they're HTML tags, nothing else. ", "aren't they? ", "robots don't search for HTML tags on pages, as far as I know.", "\n\nDont confuse heading tags with meta tags that are placed inside the head section of your page.", "\n\nAs Abdura pointed out, heading tags DO have a great bearing on SEO. ", "If you do a google search on the top SEO tricks, you will find some good articles and gain some knowledge on your own.", "\n\nI too have a company I work for that is a 100% online based company. ", "I havent looked at the numbers, but I would say that probably at least 75% of our revenue is generated by search engines. ", "Search any product and our site will most always rank in the top 3 if not number 1. ", "And btw, our site rankings are all organic. ", "No pay per click.", "\n\nNow styling your <h1> tags will have no bearing on rankings, to answer the OP. ", "Search engine spiders look at content, not how the content is styled.", "\n\najetrumpet\n\n11-04-2010, 06:41 PM\n\nI stand corrected, so I thought as much!", "\n\nBut then again, I don't do much business online so I don't put much weight on search engines if people are searching for general content." ]

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[ "Lascelles quite happy at Newcastle, says Benitez\n\n15/04/2018\n\nDavid Ospina has been ruled out for two to three weeks with an ankle injury sustained in training on Wednesday.", "\n\nMohamed Elneny is also available after winning an appeal against the red card he received against Southampton. ", "Despite the highly-rated Alexandre Lacazette and Pierre-Emerick Aubameyang being available to play, the 27-year-old England global may be the first name on Arsene Wenger's team sheet to take on the Magpies.", "\n\nWith the Europa League providing the only realistic path to the Champions League, the Premier League may become less of a priority for Arsene Wenger, though he will be able to pick a strong team for this match, with Arsenal having a week to prepare before their next game.", "\n\nNewcastle have shipped only 41 goals this season, a record bettered only by Burnley and the division's top-five sides. ", "The striker has scored in his last four Premier League games for Arsenal and has 6 goals and an assist in seven games with the Gunners. ", "Only against Man City (12, 2009-2015) have they had a longer losing streak in top-flight history. ", "Wins over Southampton, Huddersfield and Leicester in succession leave the Magpies in 10th place.", "\n\nMotorola Moto G6 Play leaked in real life pictures\nIn terms of optics, the G6 Play could be launched with a single 13-megapixel sensor at the rear and a 5-megapixel selfie sensor. ", "Ahead of its April 19 launch, we now have some live images of the Moto G6 Play that further confirms the new design language.", "\n\n\"Cup-tied in Europe, Pierre-Emerick Aubameyang has taken to the Premier League nicely, and could score in a fifth successive game - against a club he almost joined, in a part of the world where he's made his mark before.\" . ", "Nine of their 26 wins against the Magpies in the division have been by a single goal, including the last three.", "\n\nThe centre-back has been a mainstay in Newcastle's starting XI under Benitez and his impressive performances have led to British media reports linking him with a £30 million (S$56.1 million) transfer to Premier League rivals Chelsea.", "\n\n\"United have won their last three league games while the Gunners have actually lost their last four Premier League games on the road\".", "\n\nRelated News:\n\nHowever, comparing the original post and the new one, it looks like a new filter is all that Kim added to the re-upload. ", "To help Khloe relax, the gift basket also contains bath and baby product for a total of $1,000.", "\n\nThe ministry additionally pointed to previous alleged use of chemicals by the rebels in fighting with Syrian government troops. ", "A fact-finding mission from the Organisation for the Prohibition of Chemical Weapons is expected to head to Douma.", "\n\nThe group said this in a statement to mark the fourth year remembrance of the Chibok girls' kidnap which took place in April 2014. ", "It restated its calls for the release of all hostages in Boko Haram custody.", "\n\nOn Thursday, it was Dickinson's turn to tell jurors that Cosby had taken advantage of her after knocking her out with drugs. ", "Defense attorneys noted that there were differences between her testimony and what she wrote about in her 2002 biography.", "\n\nMandela fired her as one of his deputy ministers and her stints as a lawmaker, a post she held until her death, were lackluster. ", "Apartheid security agents have gone on the record revealing the extent of their propaganda campaign against Madikizela-Mandela.", "\n\nThe lengthy memo was released after President Donald Trump announced precision strikes against military targets in Syria . ", "Trump said that the reason for the strike is to \"establish a strong deterrent\" to the use of chemical weapons .", "\n\nHis nationally-syndicated program, \" Coast to Coast AM \", was aired on about 500 stations in North America in the 1990s. ", "He later enlisted in the US Air Force while also starting his own pirate radio station.", "\n\nWe will see the result at the end. \"", "For Burnley Football Club even to be spoken about, it's a long, long way from where we were. ", "It is more than 50 years since the Clarets have been involved in a continental competition.", "\n\nThe Englishman sustained the problem after playing 90 minutes against Stoke , though his absence is not expected to be lengthy. ", "The dominant start was deservedly rewarded with a 22nd-minute lead and it was not out of the usual Manchester City playbook.", "\n\nThis is pretty impressive considering the fact that the Warriors have had to deal with a multitude of injuries this season. ", "Philly's momentum: There is no more intriguing team than the Philadelphia 76ers, who just two seasons ago went 10-72.", "\n\nThe joint operation came one week after a suspected chemical attack outside Damascus left more than 40 people dead. ", "Senator Lindsey Graham who wrote, \"We should apply \"3 strikes , you're out\" to the butcher of Damascus\".", "\n\nThe improved design includes features such as offline support, smart replies and a snooze option to deal with annoying messages. ", "The Verge has published some screenshots of the new Gmail design they have obtained, which is now under testing at Google .", "\n\nTrump's message to Iran, Russia after Syria strikes\nThe statement also accused Syria of providing military bases for Iran, putting its \"territory, forces and leadership in danger\". ", "Russia's Ministry of Defense claimed Syria's air defense systems intercepted 71 missiles launched in the airstrikes.", "\n\nCWG updates: Boxer Gaurav Solanki wins gold, silver for Manish\nIndia's women's hockey team turned in an embarrassing performance in the bronze medal round against England and was thrashed 6-0. ", "In badminton, Saina Nehwal hardly broke a sweat to clinch a 21-8, 21-13 win over Canada's Rachel Honderich, while P.V.\n\nIPL 2018: Warm Mumbai to host MI vs DD match\nHe has made 123 runs in two IPL matches with the highest score of 78 not out with an average of 103.00 to retain the Orange Cap. ", "They brutally punished Boult as 15 runs came in his second over, with Yadav hitting two fours and Lewis striking his first six.", "\n\nMizuho Securities USA LLC Grows Position in ExxonMobil (XOM)\nIt is positive, as 37 investors sold WYNN shares while 149 reduced holdings. ", "123 funds opened positions while 603 raised stakes. ", "The firm owned 243,217 shares of the oil and gas company's stock after buying an additional 73,848 shares during the period.", "\n\nMama Winnie's family to speak today\nMama Winnie was born in Mbizana in the Eastern Cape on 26 September 1936 and passed away in Johannesburg on Monday‚ 2 April 2018. ", "The stadium is on its way to being packed as ANC and EFF supporters can be seen singing together proudly.", "\n\nTurkey welcomes strikes on Syria as 'appropriate'\nErdogan said he had a \"sleepless night\" as he monitored all the developments. \"", "Whoever the perpetrators they should pay a price\". ", "Turkish Deputy Prime Minister Bekir Bozdag said the strikes had not been launched via Turkey's southern Incirlik air base." ]

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[ "Monday, December 21, 2015\n\nSilver Part 222\n\nSilver Wants Corruption Conviction Tossed\n\nSheldon Silver’s lawyers want his corruption conviction tossed (NYP) Lawyers for Sheldon Silver have 12 minutes on Thursday to argue before a three-judge appeals panel that the disgraced ex-Assembly Speaker’s conviction should be tossed — or that he be granted a new trial. ", "The appeal lawyers think Silver deserves another shot because, they argue, the definition of public corruption has changed since he was found guilty in November 2015. ", "They plan to cite the US Supreme Court’s move in June to toss the public corruption conviction of ex-Virginia Gov. Robert McDonnell, who accepted more than $165,000 in loans and gifts from a business executive in exchange for promoting a dietary supplement because there was no proof the McDonnell took the Ferraris, Rolexes and ball gowns in exchange for an “official act” like legislation. ", "The government’s case against Silver also included allegations of corruption that might now be deemed innocent, such as help he provided a co-conspirator’s daughter to land a job interview, Silver’s lawyer Steven Molo said in court filings.* ", "Sheldon Silver Appeal Looks to New Definition of Corruption (NYT)\n\nSilver's Court Where He Picks the Judges, Still Protects Silver's Doctor and Asbestos Racket\n\nSheldon Silver’s doctor pal wins round in battle against Columbia (NYP) The doctor at the center of the corruption case that toppled former Assembly Speaker Sheldon Silver won a round in his lawsuit against Columbia University over his firing after more than 35 years on the job. ", "In three just-released decisions, Manhattan Supreme Court Judge Manuel Mendez reinforced a July court order that protects Dr. Robert Taub by barring Columbia from interfering with his “salary, work, research and staff” until the school goes through the proper motions of terminating him. ", "Mendez also sided with Taub in his motion to hold Columbia in civil contempt for violating the judge’s order by trying to slash Taub’s salary from $300,000 to $105,871 and firing his staff.", "\n\n* The doctor at the center of the corruption case that toppled former Assembly Speaker Sheldon Silver won a round in his lawsuit against Columbia University over his firing after more than 35 years on the job, the Post reports. * ", "New York’s never-ending asbestos racket (NYP Ed) A year after his corruption conviction, ex-Assembly Speaker Sheldon Silver’s influence is still harming our courts. ", "The American Tort Reform Foundation now ranks New York City’s Asbestos Litigation court as its No. ", "3 “Judicial Hellhole,” after St. Louis and the state of California. ", "The ATRF report notes that the court favors plaintiffs even more than it did before Silver’s fall. ", "Defendants continue to face liability beyond their level of responsibility. ", "And the court still favors plaintiffs with excess use of punitive damages and by regularly consolidating multiple cases into a single trial, making it easier to confuse jurors. ", "In part, it’s a legacy of Silver influence over the courts dating from the time he arranged for major asbestos litigator Arthur Luxenberg — the name-partner at Shelly’s old law firm Weitz &amp; Luxenberg — to serve on a key judge-picking committee. ", "Silver also blocked any and all tort-reform measures for decades. ", "The ATRF also faults the state’s highest court, the Court of Appeals, for expanding liability to cover companies that never made nor sold cancer-causing asbestos. ", "The average award for asbestos cases in New York — $16 million per plaintiff between 2010 and 2014 — is at least twice the size granted by courts nationwide, according to Bates White Economic Consulting.", "\n\nDisgraced Silver being used in campaign ads (NYDN) One TV ad paid for by New Yorkers For Independent Action, a Super PAC targeting candidates who oppose the creation of an education investment tax credit, attacks incumbent Assemblywoman Carrie Woerner (D-Saratoga County) for her ties to Silver. ", "The ads, which hits Woerner for backing Silver as speaker, concludes with pictures of the assemblywoman and Silver and the tagline: “It’s hard to stand up for us when she’s standing with them.” ", "Meanwhile, Assemblyman James Tedisco, a Schenectady Republican running for state Senate, has an ad highlighting a public argument he had with Silver over taxes. ", "The ad notes that Silver is gone but Tedisco is still fighting for constituents. * ", "Depending on the outcome of the elections in November, IDC Leader Jeff Klein could become the Senate’s ultimate power broker, especially as his independent caucus grows to an expected six members, the Buffalo News writes.", "\n\nSilver Avoids Jail . . . ", "Did Anyone Expect Him to Be Lock Up?", "\n\nSheldon Silver avoids jail for at least another year (NYP) Crooked former Assembly Speaker Sheldon Silver caught the break of a lifetime Thursday when a judge ruled that he can stay out of prison while he appeals — likely buying him at least another year of freedom. ", "The powerful puppet master, who used his position to swindle $5.4 million in kickbacks and bribes, was supposed to surrender Wednesday to begin serving his 12-year sentence.", "\nBut Manhattan federal Judge Valerie Caproni, who presided over Silver’s trial, instead granted the Manhattan Democrat’s request that he remain free on bail.*", "\n\nCaproni made it clear in her ruling that she thinks Silver, 72, was guilty — even under a new and far narrower definition of “official acts” constituting corruption established by a June 27 Supreme Court ruling. ", "In that case, the court tossed the conviction of ex-Virginia Gov. Bob McDonnell, who had accepted cash, loans and pricey gifts from a rich businessman looking for favors, ruling that simply arranging meetings did not constitute official acts. “", "As stated previously, this case differs from McDonnell because most of the official acts presented to the jury — the provision of state grants, approval of tax-exempt state financing, and voting on legislation — are undoubtedly official acts under McDonnell,” Caproni wrote. ", "She granted Silver bail, however, over concerns that her instructions to the jury may have been inadequate under the new standards set by the high court. * ", "Justice delayed for Shelly Silver(NYP Ed) * Silver, Like Skelos, Can Remain Free While Appealing Graft Conviction (NYT) Sheldon Silver, the former State Assembly speaker, and Dean G. Skelos, the former Senate majority leader, have moved aggressively to stave off the day they had to begin serving their sentences.* ", "In a ruling that appears to bolster Sheldon Silver’s appeal of his public-corruption conviction, a federal judge said that the former Assembly speaker can stay out of prison at least until Oct. 27 while he awaits a decision, The Wall Street Journal reports. * ", "The Times’ Lawrence Downes knocks Silver’s successor for his Assembly seat, Alice Cancel, and writes the quality of new candidates running in the September primary have an opportunity to move beyond Silver’s legacy and bring real change and reform to the district.* ", "Sheldon Silver not allowed to travel outside lower 48 states (NYP)\n\nSilver's Gerrymandering Jealousy Cuts A Romantic Rival Out of His District Silver and Skelos Replacement Special Elections\n\nSheldon Silver has some serious jealousy issues (NYP) Crooked ex-Assembly Speaker Sheldon Silver ended the career of a fellow pol — because the man had an affair with the powerful Manhattan Democrat’s mistress,\nsources told The Post. ", "Silver was so jealous of then-Assemblyman Dan\nBurling carrying on with then-Assemblywoman Janele Hyer-Spencer that he\nforced his romantic rival out of office through a redistricting scheme,\nsources said. ", "He engineered the drawing of new lines around Burling’s\nupstate district in 2012, said well-placed sources on both sides of the\naisle in Albany. ", "The maneuver expanded the Republican’s district into Erie County and exposed him to a potential primary challenge from East Aurora Mayor David DiPietro, sources said.* ", "New York Elections to Replace Silver and Skelos Offer Intrigue and Incivility (NYT)\nThe races to replace the former Assembly speaker and Senate majority\nleader, both removed after being convicted on public corruption charges,\npresents an unprecedented situation and has resulted in races filled\nwith intrigue * Cuomo early on endorsed Kaminsky, the Democrat in the\nrace to replace former Senate Majority Leader Dean Skelos, but has not\ncampaigned once for him in the Nassau County district where the governor remains popular, the Daily News writes:\n* Ex-Assembly Speaker Sheldon Silver ended the career of\nthen-Assemblyman Dan Burling because he had an affair with Silver’s\nmistress, then-Assemblywoman Janele Hyer-Spencer, sources tell the New York Post: * Ex-Assembly Speaker Sheldon Silver ended the career of\na fellow pol, Republican former Assemblyman Dan Burling, by\nredistricting him out of office because Burling had an affair with the\npowerful Manhattan Democrat’s mistress, former Assemblywoman Janele\nHyer-Spencer.", "Special Elections Cuomo\nhas endorsed the Democratic candidate for former Senate Majority Leader\nDean Skelos’ seat, Assemblyman Todd Kaminsky, and maxed out in\ncontributions to his campaign, but has not appeared in person for the candidate in advance of tomorrow’s special election.* ", "Tthe special elections on Long Island and in Lower Manhattan offer voters a chance to\ndo the unprecedented: to replace, in the space of one day, two former\nmembers of New York State’s ruling triumvirate, both of whom are\nscheduled to be sentenced in the coming weeks after being convicted on\ncorruption charges.", "CheepSilver bedded mistresses at cheap Albany hotels (NYP) Sheldon\nSilver was the ultimate cheap date — bedding his “Barbie doll’’\nmistress at budget hotels paid for with his taxpayer-funded per diem,\nsources told The Post on Monday.", "“It was the worst-kept secret in politics. ", "Shelly would stay at [cheap Albany hotels]\nwhen he was up there doing state business. ", "She was seen leaving his\nroom on a number of occasions,’’ a politically connected source said of\nthe convicted ex-Assembly speaker and Janele Hyer-Spencer, one of the women with whom federal authorities say he had affairs. “", "Let’s\nsay it’s $100, and he spends $25 on accommodations and $25 on dining\nfor the night. ", "Then he’d pocket the rest. ", "That’s why he chose’’ cheap\nhotels, such as the Red Carpet Inn, where rooms start as low as $55, the\nsource said.", "\n\nSilver Blocked A Bill to Protect Sexually Abused Kids After Catholic Group Hired Lobbyists the Speaker Was Sleeping With\n\nSheldon Silveraccused of blocking bills to aid sexually abused kids after Catholic group hiredhis longtime aid as a lobbyist (NYDN)\nDisgraced ex-Assembly Speaker Sheldon Silver was all about pay to play\n— and sexually abused kids were the ones to pay the price. ", "Silver\nstopped pushing for a bill to aid victims of predators after the state\nCatholic Conference hired his former long-time aide as a lobbyist, says a\ncontroversial former lawyer who has taken on the Church. ", "John Aretakis,\nof upstate Troy,\nmade the alarming charge in a scathing letter he sent to a judge who in\nMay will sentence Silver on an unrelated federal corruption conviction.", "\nAretakis wrote that he met with Silver each year between 2004 and 2006\nto discuss the bill, which the then-powerful pol “bragged” had passed\nthe Assembly several times with over 100 votes even as it stalled in the\nSenate. ", "That changed after the lobbying firm owned by Patricia Lynch,\nwho previously was a longtime Silver aide, took on the Catholic Church\nas a client, Aretakis wrote. ", "The Church was aggressively lobbying\nagainst the bill. ", "Longtime aide Patricia Lynch was hired to lobby for\nthe Catholic Conference in 2009 — the year after the last time the bill\npassed the Assembly. ", "State records show that Patricia Lynch &amp;\nAssociates was first hired by the state Catholic Conference in 2009 —\nthe same year the Democrats briefly took control of the chamber and had\nconsidered taking up the measure. ", "Then-Senate Codes Committee Chairman\nEric Schneiderman, now the state attorney general, tried to move the\nbill out of committee but the vote fell short and the measure died.", "\n“Once Ms. Lynch lobbied for the Catholic Conference, Mr. Silver’s\nsupport for our bill ended, and the bill did not come out of the\nAssembly’s Codes Committee ... which as speaker, he controlled,”\nAretakis wrote.* ", "The five members of a breakaway group of state Senate Democrats say they will supportnew legislation to help adults who were sexually abused as children seek legal recourse.* ", "Cuomo: Silver’s Alleged Affairs Should Spur Ethics Reform (YNN)\n* According to sources, former Assembly Speaker Sheldon Silver carried\non affairs with two women at Albany-area hotels that were paid for with\nhis taxpayer-funded per diem, the Post reports: *\nGov. Andrew Cuomo said Silver’s alleged affairs should encourage state\nlawmakers to approve new ethics and anti-corruption legislation and\ncalled for legislation to be passed in post-budget portion of the\nlegislative session, State of Politicswrites:\n\nJust Like Ever One Knows About Corruption in Albany Everyone Knew About Silver's Affairs for Years\n\nThe affairs were poorly-kept secrets, Albany\ninsiders said. ", "Lynch and Silver were seen kissing in an elevator at the\n2008 Democratic Convention in LA. ", "Another legislative source said\nSilver and Hyer-Spencer had adjoining rooms during a 2008 Assembly trip\nto Israel. ", "This, even though other lawmakers were also staying in the same hotel.", "Silver\nand Hyer-Spencer were also seen together in the hotel lobby at the\nSomos Uno conference during one of the Assembly’s annual post-election\ntrips to Puerto Rico.", "\n\nThe @NYDailyNews, citing an anonymous source, says Sheldon Silver was having an affair with lobbyist Patricia Lynch.", "\n\nSheldon Silver cheated on his wife with two women\n(NYP) While serving as Assembly speaker, Sheldon Silver was engaged in\nextramarital affairs with two women – one of whom lobbied him on behalf\nof clients who had business before the state and the other for whom he\nused his position to recommend a state job, according to new documents\nfrom his criminal case. ", "The revelation was included in the documents,\nwhich were unsealed Friday morning. ", "The documents redacted the names of\nthe two women, as well as other information about. ", "Prosecutors had\nwanted to introduce the evidence during Silver’s corruption trial last\nyear. ", "At the heart of the secret files is a mysterious “Sealed Party A” –\nan unidentified woman whose name was never mentioned at Silver’s trial.", "\nBut her high-powered attorney Abbe Lowell has been fighting tooth and\nnail to stop the documents from going public. ", "Judge Valerie Caproni said\nthe filings – which pertain to a hearing last October about evidence\nthat wasn’t presented at trial – add to Silver’s already tarnished\nreputation as ex-Assembly speaker. ", "She alluded that the secret documents\nare related to “misuses of [Silver’s] public office.” “", "This is not one\nof his better moments,” Caproni said in court. ", "The judge also noted that\nLowell’s\nclient was a public figure — and for that reason, there was a public\ninterest in the matter.", "In filings, prosecutors insisted the information\ngoes to Silver’s “ethics or integrity, separation of his personal\nbusiness from his official position, and/or character for truthfulness\nand honesty.” “", "The Government did not seek to admit evidence of those\nrelationships at trial on its direct case, but asserted that such\nevidence would be relevant and admissible if the defendant introduced\ncharacter evidence suggesting that he was careful to separate his\npersonal business from official business or that he was a man of\nintegrity or a good family man,” one of the filings states. ", "Documents\nallege there is “credible and corroborated evidence that while serving\nas Speaker of the Assembly, the defendant engaged in extramarital\nrelationships with two women.” ", "In one instance, the information was\ngained “inadvertent” by investigators who were listening to Silver’s\nphone calls. ", "Silver’s relationship with the lobbyist “regularly lobbied\nthe defendant on behalf of clients who had business before the state”\nthe document states while she was able to “obtained certain clients in\npart because of her access to the defendant.” ", "In one of the recordings\nwith the lobbyist, Silver and the woman discuss an inquiry from a\nreporter about “affairs” with state legislators. “", "I don’t think he\ncaught us,” Silver is alleged to have said in the conversation. ", "Silver\nacknowledges to the woman that it is “not safe” they be seen together in\npublic. ", "In the record conversation, the lobbyist complained to Silver\nthat she was not being treated well by a top member of Silver’s staff.", "\nThe second woman, meanwhile, was the beneficiary of a state job that\nSilver “used his official position” to secure for her. ", "The unnamed post\nwas one Silver “exercised a particularly high level of control.” ", "Silver\nkept two different cell phones, one that appeared to be for official use\nand a second that he used for personal discussions and was billed to a\ndifferent name.", "Flashback‘Silver’-spoon gal climbing the ladder\n(NYP) A former state assemblywoman and close ally of Speaker Sheldon\nSilver has quietly left her cushy job at the state Education Department\nfor an even higher-paying one in state Family Court. ", "Janele\nHyer-Spencer, a motorcycle-riding former beauty queen, left her post as a\nlegislative liaison for the Education Department on Jan. 29.", "\nHyer-Spencer, a Democrat, was hired in September 2011 — after voters had\nbooted her from her Assembly seat. ", "As The Post reported last year,\nSilver — who has sway with the Board of Regents, which oversees the\neducation agency — recommended Hyer-Spencer for he $84,000-a-year\nposition. ", "In March, Hyer-Spencer quietly took a new job as a “support”\nmagistrate with the New York City Family Court. ", "She’s now making $99,600\nto work on child- support, paternity and other family issues, state\npayroll records show. ", "Silver’s childhood friend Jonathan Lippman is\nchief judge of the New York Court of Appeals and oversees administration\nof the state courts.", "Skelos Judge denies new trial for disgraced former Majority LeaderDean Skelos. * ", "New YorkEthics Rules Quiet on Lawmaker-Lobbyist Relationships (WSJ) * U.S. Cites Extramarital Affairs as Misuse of Power in Sheldon Silver Case\n(NYT) Two women were connected to Mr. Silver’s position as State\nAssembly speaker, according to newly unsealed papers from his federal\ncorruption trial.", "\n\nNYT Tries to Make It OK Not To Send A Message to Corrupt Albany by Sending Skelos to Jail Prosecutors\nwant former state Senate Majority Leader Dean Skelos to be sentenced to\n12 to 15 years in prison for his conviction on federal corruption\ncharges, and his son to see about 10 to 12 years in prison\n\nAlbany corruption mapped: * This,\nas former legislative leaders Sheldon Silver and Dean Skelos await\nsentencing after their landmark convictions for abuse of their offices.", "\nAnd after countless other lawmakers have headed off to prison in recent\nyears. ", "And after the Legislature failed to deliver on its No. ", "1 reform\npromise last year — to get the ball rolling on amending the state\nConstitution to strip pensions from legislator-felons like Silver and\nSkelos. ", "Now comes a new Quinnipiac Poll showing that 86 percent of New\nYorkers say corruption in Albany is a serious problem. ", "So serious, in fact, that 48 percent said all current\nelected officials should be voted out of office so new officials can\nstart with a clean slate. ", "And 48 percent also see Cuomo as “part of the\nproblem.”* ", "Bharara recommends up to 15 years for Skelos (PoliticoNY)The memo was a rebuke of the defense’s argument that the duo should avoid prison time *Federal prosecutors asked a judge to\nsentence former state Senate Majority Leader Dean Skelos to at least 12\nyears in prison, following his conviction on eight counts of public\ncorruption charges, and asked that Skelos’ son, Adam, be sentenced to\nmore than 10 years.* ", "Prosecutors:Dean Skelos' $95k pension should draw big fine (LoHud) Silver he sentencing for former Assembly Speaker Sheldon Silver has been postponed again. ", "According to court documents, it’s now scheduled to take place on May 12th, moved from April 13.", "\n\nLongtime aide insists Sheldon Silver ‘cared for all New Yorkers’ (NYP) Sheldon Silver’s longtime chief of staff has gone to bat for her old boss, vouching that the convicted former Assembly speaker “always cared for and worked to help all New Yorkers,” new court filings show. ", "Judith Rapfogel — whose crooked hubby William Rapfogel is\ncurrently in prison for bilking $9 million from the non-profit he ran —\nbegged Manhattan federal Judge Valerie Caproni for mercy at Silver’s\nsentencing in a two-page letter filed Tuesday.", "“I could write volumes\nabout the good work Shelly did for the people of the state of New York,”\nRapfogel wrote, even playing the 9/11 card. “", "We let people use our\nphones so they could call their loved ones,” she wrote. “", "Shelly also\nworked hard for minorities. ", "He did what he felt was right, even if it\nwent against his religious beliefs and even if it meant he would have to\n‘answer’ to friends and family.”", "\n\nSilver Disbarred and Skelos Delayed Until After the Special to Replace Him\n\nFormer Speaker Silver Disbarred(YNN) * Sentencing for former Senate Leader, Dean Skelos, and his son Adam, has been changedonce again. ", "First the judge moved the sentencing date to April 25. ", "Now, the pair will go before the judge on the 28.* ", "Sheldon Silver Stripped of Law License (DNAINFO) The disgraced former Assembly Speaker was officially disbarred Tuesday after an appeals court ruling.* ", "Sheldon Silver, Ex-New York Assembly Speaker, Is Disbarred (NYT) * The hits just keep coming for Shelly Silver (NYP) First Sheldon Silver’s name was removed from his Assembly office door in Albany, now it’s been stricken from an official state list of practicing attorneys. ", "Silver was automatically disbarred when he wasconvicted last November,\nso the disciplinary committee’s finding, released Tuesday, is mostly a\nceremonial slap in the face to the ex-speaker. ", "The five-member Manhattan\nDepartmental Disciplinary Committee unanimously rejected the disgraced\nlawmaker’s plea to keep his name on the attorney roll pending the appeal\nof his guilty verdict.* ", "Former Assembly Speaker Sheldon Silver was\nautomatically disbarred when he was convicted last November, and now a\ndisciplinary committee rejected his plea to remain an attorney pending\nhis appeal in court, the Postreports: * A Court of Appeals panel ruled that controversial secret evidence\nkept out of former Assembly speaker Sheldon Silver’s trial can become\npublic if the judge believes it is relevant to his sentencing, scheduled\nfor April 13, Newsday reports: * A state appeals court disbarred former\nAssembly Speaker Sheldon Silver after he was convicted in November of\nfelony extortion for taking nearly $4 million from two law firms during\nhis time as a legislator.* ", "Silver’s lawyers argued that\nthe disbarment should be delayed until a federal judge decides on their\nmotion for a new trial, but the appeals court denied the request.", "\n\nOn the Day He is To Be Put in Jail for the Rest of His Life the NYP Writes How is Woman Tried to Grab His Penis At A Ranger Game\n\nSheldon Silver ‘got lucky’ with his mistress during a Rangers game (NYP) Former Assembly Speaker Sheldon Silver will be sentenced Tuesday in a corruption case that unearthed his illicit affairs with two women, whom he bedded at cheap Albany hotels. ", "Silver allegedly romped with former Assemblywoman Janele Hyer-Spencer at a Red Carpet Inn near Interstate 90, reserving the same $50-a-night drive-to-the-door room at the two-star hotel when he was in town for legislative business, employees told The Post. “", "He requested the same room all the time,” a groundskeeper told The Post. ", "At one Rangers game, she sat next to Silver and allegedly got a little too frisky after downing several vodka tonics. “", "I was there when Hyer-Spencer grabbed his penis,” said a source who attended the game. “", "She got drunk and started grabbing and touching him, then put her legs on him and tried to kiss him. ", "He made another Assembly member switch seats with her.” ", "Silver allegedly even got his gal pal a job. ", "Cynthia Woodside, a laid-off state Education Department lobbyist whose job was taken by Hyer-Spencer, told The Post on Monday that she faced hardships after losing the position. “", "I was out of work for nearly two years before I found another job at a much lower salary,’’ she said by e-mail, though she stopped short of blaming Silver. ", "Silver will be sentenced for trading political favors to enrich himself, but he balked Monday at having to fork over all of his suspected ill-gotten gains. ", "The government is asking he be forced to forfeit “all of his crime proceeds,” which it put at $5.2 million, plus a $1 million fine. ", "But in a one-page memo to Manhattan federal Judge Valerie Caproni, his lawyers argued that “requiring Mr. Silver to forfeit the amount calculated ‘would defy the purpose and spirit of forfeiture law.’ ’* ", "Ex-Assembly Speaker Silver could be facing prison time (NYDN)*\n\nFormer Assembly Speaker Sheldon Silver will be sentenced today in a corruption case that brought to light his extramarital affairs with two women – a former staffer-turned-lobbyist and a former assemblywoman – details of which are still emerging.", "\n\nSilver 5 Months After Being Convicted Still Driving Around With Govt Parking Placard That Allows Him to Park Anywhere\n\nSheldon Silver still enjoying politician perks (NYP) Five months after he was expelled from the Assembly for his corruption conviction, Sheldon Silver is still driving a car with government parking placards. ", "A permit indicating that “this vehicle is on official business” was displayed in the windshield of a Toyota Camry seen parked near the ex-speaker’s Grand Street home in February. ", "Silver was spotted getting into the car Friday, but dashed back into his co-op building when a photographer tried to snap a picture. ", "Such state placards allow their holders to park just about anywhere for free. ", "Silver’s longtime chief of staff, Judith Rapfogel, has the same Assembly permit in her Toyota Avalon. ", "It was seen displayed in the windshield on April 9. ", "On Friday, it was there again, but turned over. ", "The car had a ticket on it. ", "Rapfogel left the Assembly in January. ", "A spokesman for Assembly Speaker Carl Heastie said that Heastie was “unaware” Silver and Rapfogel still had parking placards and that he would ask for them back.", "\n\nThe Lobbyist Who Silver Was Sleeping With Business Fell Apart After Silver's Arrest\n\nMeet the women who allegedly slept with Sheldon Silver (NYP) One, Janele Hyer-Spencer, is a motorcycle-riding former beauty queen who’d blast around Albany in a Yamaha V-Star motorcycle and who allegedly got two state jobs through Sheldon Silver’s influence. ", "The other, once-powerful lobbyist Patricia Lynch, was caught on tape by the feds huffing to the then-Assembly speaker that since one of his aides was rude to her, she’d only deal directly with him. ", "Lynch served for six years as Silver’s communications director before starting her own two-person PR firm in 2001 that quickly grew into one of the largest lobbyists in the state — thanks to her Silver connections. ", "Her extraordinary access to Silver — then one of the three most powerful politicians in the state — won her an enviable client list that included MadisonSquareGarden.", "Silver killed the West Side Stadium that MSG opposed during the Bloomberg administration. ", "When Silver got in trouble, Lynch’s business took a nose-dive and she sold it in August 2015 to MWW, a giant PR and lobbying firm. ", "In 2010, Silver helped Hyer-Spencer get an $84,000 job with the state Education Department, sources have told The Post. * ", "TARNISHED SILVER: Shocked neighbor describes former Assembly speaker's mistress as 'quiet,' while an Albany source calls her 'insufferable' and pushy (NYDN)\n\nJudge Caproni Silver's Sex and Corruption Matter in Sentencing\n\nSheldon Silver’s alleged affairs could lead to stiffer sentence (NYP) Revelations of Sheldon Silver’s alleged affairs with two women for whom he did favors while in office could earn him a stiffer prison sentence, a prominent defense attorney told The Post. ", "Jeremy Saland, a former Manhattan prosecutor, said Silver’s relationships with former Staten Island Assemblywoman Janele Hyer-Spencer and lobbyist Patricia Lynch are relevant to determining punishment on May 3. “", "It can be relevant in this context in federal sentencing when this theory of a conflict of interest and his own personal gain supersedes that of his constituency, taxpayers and the residents of New York state,” Saland said. ", "If true, the affair allegations “in no way trump what he’s convicted of, which, by itself, is significant behavior.”", "\n\nJudge Plans to Unseal Secret Papers in Sheldon Silver’sCase(NYT) From the tidbits of information gleaned at a hearing on Thursday in Federal District Court in Manhattan, it appeared that prosecutors had argued last fall — in a closed hearing and in sealed court papers — to be able to use certain evidence against Mr. Silver at trial. ", "His lawyers appear to have vigorously objected and the matter ultimately did not surface at trial. ", "Federal prosecutors showed at trial that he had obtained nearly $4 million in illicit fees in return for taking official actions that benefited a ColumbiaUniversity cancer researcher and two real estate developers in New York.", "The judge, Valerie E. Caproni, had indicated that she would revisit the issue of the secret information after the trial was over, and more recently asked the parties to file motions on the issue. ", "The sealed materials appear to include documents and a transcript of a pretrial hearing that was held on the issue. ", "In court on Thursday, Judge Caproni first held a public session limited to legal arguments, and indicated she favored the release of the materials, with redactions to protect the identities of people who are mentioned in the documents but are not parties to the case.", "\n\nThe NYT Says Silver Has Always Been A Supporter of NYC, Forgot How He Killed the Commuter Tax\n\nThe Times tried to cut Silver a break, writing that he had always been a major supporter of new York city.", "\n\nNot always... in 1999, silver and joe bruno (indicted but beat the rap on a technicality) Dean Skelos (under indictment) and Pataki conspired to eliminate the commuter tax because both parties were contesting a legislative seat in RocklandCounty. ", "That decision has cost New York city more than $5 billion. ", "Rudy slammed the bill and GOP senator Roy Goodman said it was the most foolish decision he had ever seen. ", "By the way, the tax for the mainly white commuters was about a buck a day.-Jim Callaghan * Commuter tax - Wikipedia, the free encyclopedia\n\n.", "\n.", "\n.NYP Editorial Editor Threaten By Silver After 1999 Story Against Repeal of the Commuter Tax\n\nThe theory behind the tax was and is sound: These commuters made extensive use of the city’s public conveyances and systems, not to mention the protection of the NYPD and the FDNY, as they spent 250 working days within its borders and should help pay for their upkeep. ", "That said, any politician philosophically opposed to such taxation would also have had a sound case opposing it on the grounds that it was, in effect, a user tax no other New York state resident had to pay (not to mention commuters from New Jersey and Connecticut, who had also been subject to it). ", "But this was not why Silver suddenly pushed through an end to the commuter tax in May 1999. ", "He did so because he was trying to secure victory for a Democrat in a special election in RocklandCounty, 60 miles north of the city. ", "The election wasn’t even for the state Assembly. ", "It was for a seat in the state Senate, then in the hands of the GOP, and which Silver was hoping to tilt to the Democratic Party. ", "I was then the editor of this paper’s editorial page, and we called him out on it. ", "We suggested his action made him ripe for a primary challenge in the next election since a rival could make the irrefutable case that Silver’s gameplaying had been directly and personally injurious to every single voter in his district. ", "The day the editorial ran, Silver called The Post in a quiet rage and spoke to one of my superiors. ", "Sixteen years later, here’s what I remember being told: Silver said we had done something very unfriendly, that this was not the sort of thing he liked to see or could take lying down. ", "Such unfriendliness was the sort of thing that could lead him to make life uncomfortable for us personally. ", "And me personally. ", "His effort at intimidation had no effect. ", "I stepped down from the editorial page at the end of the year, and my successor, Bob McManus, had no compunction whatsoever throughout his 15-year tenure about hitting Silver hard for his contemptible conduct as a public official. ", "Bob is still writing tough pieces about Silver; did so in this paper yesterday, in fact. ", "And here’s mine.", "\n\nThe Political Culture of Albany is Guilty . . . ", "Where Have All the Reform Gone . . .", "\n\nLost Reformers Who Empowered Silver Just As Guilty As Their Dear Leader\n\nSheldon Silver’saccomplices: What the former speaker's guilty verdict reveals about the cultureof New York's Capitol(NYDN) U.S. Attorney Preet Bharara, his assistants and the FBI did a high service in revealing which species of crimes Silver was committing — at a time when everyone in Albany knew to a moral certainty that the speaker was betraying the public trust and rigging the game to hide his predations. ", "Still, justice is incomplete. ", "There is sadness in that the letters of the law prohibit naming virtually the entire Assembly Democratic caucus as co-conspirators to Silver’s corruption. ", "They enabled him by vesting Silver with their proxies to do essentially whatever he wanted when the Legislature was in session. ", "Assembly members didn’t have to work. ", "They didn’t have to think. ", "They only had to do as they were told in the name of their caucus, including faithfully voting on bills they had never read. ", "Under Silver’s leadership, the Legislature was rated America’s worst. ", "His trial contained few new revelations, because Bharara had spelled out the case in detail in the criminal complaint in January. ", "Now, look back and remember how Silver’s Democratic colleagues struggled to keep him as leader after reading the document.", "SHED NO TEARS FORSHELDON SILVER, OR THOSE IN ALBANY WHO TURNED A BLIND EYE For the various elected officials and others who have expressed sadness for Silver, there is perhaps a misconception that corruption is a victimless crime, or at least one in which the victim is an abstraction. ", "Whereas Lopez may have violated the women who worked for him, Silver simply violated the “public trust.\" ", "Silver’s crimes were only possible because his colleagues in the Assembly, and the two other “men in the room,” accepted it as politics as usual. ", "These enablers had to be comfortable with Silver’s defense that corruption is “conduct which is normal, conduct which allows government to function.” ", "Or what U.S. Attorney Preet Bharara has deemed a “culture of corruption.", "”But on Tuesday, Cuomo contradicted himself by suggesting that the same ethics laws he had no problem taking credit for would not deter a public official with corrupt intentions. “", "I don’t care how strong the law is,” he said. “", "If a person is going to break the law, a person is going to break the law.” ", "If that’s so, then why wouldn’t Cuomo let the Moreland Commission, which he convened to “investigate and prosecute wrongdoing,” continue its work? ", "In a feat of Cuomoian logic he countered, “The Moreland Commission was not an investigative, prosecutorial, commission.”", "\n\nNot One of the Assemblywoman or Anyone Spoke Up Against the Silver Lopez Hush Fund\n\nTwo former Assembly staffers who claimed former Assembly Speaker Sheldon Silver didn’t take their sexual harassment claims seriously enough said they finally feel justice has been served,\n\nEven after Bharara persuasively declared in the complaint that the charges “go to the very core of what ails Albany,” including a “lack of transparency, lack of accountability and lack of principle, joined with an overabundance of greed, cronyism and self-dealing,” it took a public outcry to force Silver’s ouster after almost a week. ", "Manhattan underboss Assemblyman Richard Gottfried, who has spent four conscience-withering decades in the Assembly, went so far as to describe Silver as a hero. ", "Consigliere Assemblywoman Deborah Glick proclaimed that Silver has been “upholding Democratic principles in this state.", "”Better for them, Silver rewarded members who knelt to him with money for their districts. ", "That became the yardstick for success, not the drafting or passage of important legislation. ", "As long as they got their funds, they were happy to have Silver as dictator. ", "Even as he protected sex-harasser Vito Lopez and covered up ethics investigations.", "\n\nEven as he created a pot of secret funding for clandestine disbursement, money that was used in his bribery plot. ", "Even as he rigged creation of a state ethics commission to prevent the panel from examining his personal dealings. ", "Even as he refused to explain why a law firm was paying him hundreds of thousands of dollars a year — money that turned out to be part of his bribery plot. ", "Because Silver knew better than to directly extort money, he separated his actions and his payoffs and then offered the wildly unsuccessful defense that he had simply engaged in politics the New York way and so had committed no crimes.", "\n\nYes, indeed, Silver had done business the New York way. ", "Yes, indeed, he had exploited a system he created, a system blessed and defended by Gottfried and Glick, and by Silver’s successor as speaker, Carl Heastie, and by every other pliant member of the Assembly. ", "They enabled him. ", "They aided and abetted him. ", "And, they, too, are guilty.* ", "Silver leaves a complicated legacy marked by his liberal priorities and a talent for legislating but also suspicions in Albany that he suppressed potential scandals, such as sexual harassment allegations,*The whole political culture of Albanyis guilty in the Silver case, Newsday writes, as the Legislature refuses to take steps like banning outside income, trying public campaign financing and entertaining term limits:the Journal reports:\n\nSilver’s central argument for an appeal of his conviction seems likely to be that the government failed to prove a quid-pro-quo relationship existed between Silver and others who prosecutors said benefited from official actions he took on their behalf,The New York Times reports: * When they appeal his conviction on seven federal corruption charges, Silver’s attorneys are likely to arguethat the government failed to prove that a quid-pro-quo relationship existed between the former assemblyman and others who prosecutors said benefited from official actions he took on their behalf.", "\n\nWednesdayThe Questionable Ways of Albany,Exposed at Sheldon Silver’s Trial (NYT) The former speaker did not disclose Goldberg &amp; Iryami on his annual disclosure form. ", "Rather, for years he disclosed the income he received from another firm that he was associated with, Weitz &amp; Luxenberg, and often added “law practice — fees,” or some variation of that. ", "Mr. Silver’s lawyers argued that their client’s use of the words “law practice” made his disclosure forms accurate because Goldberg &amp; Iryami had made its payments to Mr. Silver through his law practice account. ", "Lisa Reid, the executive director and counsel for the Legislative Ethics Commission of New York, an agency that reviewed Mr. Silver’s annual disclosure forms, seemed to agree in her testimony. “", "Presuming that the income is coming from your clients and it is going into the law practice, yes, you would only need to list the income as coming from your law practice, correct,” Ms. Reid testified. ", "Mr. Silver’s lawyers argued that their client’s use of the words “law practice” made his disclosure forms accurate because Goldberg &amp; Iryami had made its payments to Mr. Silver through his law practice account. ", "Lisa Reid, the executive director and counsel for the Legislative Ethics Commission of New York, an agency that reviewed Mr. Silver’s annual disclosure forms, seemed to agree in her testimony. “", "Presuming that the income is coming from your clients and it is going into the law practice, yes, you would only need to list the income as coming from your law practice, correct,” Ms. Reid testified. * ", "During the one-month trial in Federal District Court in Manhattan, Silver’s political careerwas not the only thingto fall apart. ", "So, too, did the curtain around how many things in Albany really get done.** ", "Silver and his defense team will face an uphill battle inhis appeal,as legal experts who spoke with Politico New York say that the prosecution and the judge were on solid ground in their handling of the case: *Successful appeal unlikely for#SheldonSilver, experts say:\n\nNYT Dreams Of A Silver Return to Albany At 125 Years Old?", "\n\nBut Says Nothing About the Effects On Albany of the Corruption Exposed At Silver's Trial\n\nColleagues Ponder Sheldon Silver’s Role in Albanyif He Is Acquitted (NYT) If Mr. Silver were to be acquitted, however, he could return to Albany for the 2016 legislative session, which begins in January. ", "But few, if any, of his fellow Democrats believe that he could retake the positionhe cededtoCarl E. Heastie, a Bronx Democrat who was elected speaker in February. * ", "Another longtime member of the Assembly said a vindicated Mr. Silver — who remainedactive in the Assemblyafter his arrest and indictment — would be a force in the chamber because of his knowledge of the intricacies of state government. “", "No one knew more about the ins and outs than Shelly — no one’s even close,” the member said. “", "I have no doubt if he comes back, he will be very outspoken.”" ]

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[ "Housing sales dropped by 30 per cent nationwide last month, largely due to a new tax in British Columbia and Ontario experts say deterred home buyers in two of the country's hottest housing markets.", "\n\nThe Canadian Real Estate Association on Monday reported a 6.8 per cent drop in home sales through its MLS service, compared with June numbers. ", "The decline is part of a gradual dampening of Canada's once-booming real estate market.", "\n\nB.C. and Ontario account for roughly 85 per cent of the slump, as the implementation of the harmonized sales tax this summer pushed many home buyers to purchase earlier this year, the association said in a statement.", "\n\nThe two provinces typically represent more than half of the country's sales.", "\n\n\"Canadians were anticipating this change and it affected the sale of their home or the purchase of their home, and they decided to make that sale earlier than expected,\" said the CREA's Alyson Fair.", "\n\nThe decline also comes on the heels of an interest-rate hike as well as tighter mortgage rules, which may contribute to an even softer market in the months ahead, experts said.", "\n\nExperts are forecasting that average home prices will drop by about 10 per cent.", "\n\n\"We've come over a hump in prices and we're moving down into a valley,\" Grant Bishop of TD Economics told CTV News. \"", "And we'll be going downhill probably until mid-2011.\"", "\n\nBut others say the real estate market is far from bottoming out.", "\n\n\"We're not seeing a huge slide,\" BNN's Andrew Bell told CTV News Channel on Monday.", "\n\n\"Things were pretty frenetic last year… We're actually still up year-on-year on sales, prices are holding -- so we're not seeing a dive in the housing market by any means.\"", "\n\nSo far, this year's sales are up 5.6 per cent from the first seven months of 2009. ", "But experts predict that lead to fade in the next few months, since sales grew dramatically in the second half of last year.", "\n\nActivity peaked last December as home buyers who had held off during the recession let loose on the market and took advantage of low interest rates.", "\n\nThat momentum lasted through the first half of this year, fuelled by fear of the HST, interest rate hikes and changes to mortgage rules.", "\n\nStill, sales fell in six of the last seven months, dropping 25 per cent in the past three months alone, said Douglas Porter, deputy chief economist at the Bank of Montreal. ", "That signals a shift towards a buyer's market, he added.", "\n\nBritish Columbia showed the largest decline at 14.1 per cent, with Ontario in second place with an eight-per-cent decrease. ", "Activity in the Prairies and Quebec was level with June numbers.", "\n\n\"We (and many others) were consistently warning of a significant second-half slowdown in housing activity but, if anything, the cooling looks even a bit chillier than expected,\" Porter wrote in a report Monday.", "\n\nWith files from The Canadian Press" ]

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[ "Contribution of the porcine aminopeptidase N (CD13) receptor density to porcine epidemic diarrhea virus infection.", "\nPorcine epidemic diarrhea virus (PEDV) and transmissible gastroenteritis virus (TGEV), which belong to group 1 coronaviruses, are important viral pathogens in pigs causing lethal diarrhea. ", "As with the other members in the group 1, theses viruses are also known to use the host aminopeptidase N (APN) as the major receptor for cell entry. ", "Remarkably, it was found that they utilize distinct cultured cell lines for in vitro virus propagation, since PEDV could not be replicated in swine testis (ST) cells expressing native porcine APN (pAPN), which are highly susceptible to TGEV. ", "To explain the mechanism causing this discrimination, we postulated that there may be a correlation between the pAPN expression level and PEDV infection. ", "As a first step toward understanding the role of cellular receptor density in PEDV replication, therefore, sub-lines of ST cells stably overexpressing recombinant pAPN were generated. ", "We initially confirmed that the control ST cells do express relatively low levels of endogenous pAPN. ", "In contrast, in the engineered stable cell lines, a high level of recombinant pAPN expression was demonstrated. ", "The introduction of a pAPN gene into nonpermissive ST cells was further found to be fully sufficient to support productive infection, revealing that constitutive overexpression of pAPN can directly rescue PEDV multiplication. ", "We further assessed whether the pAPN enzymatic function is relevant to PEDV infection. ", "The enzymatic active motif-null mutant pAPN still retained the ability to exert its receptor activity and consequently, to cause infectious virus production. ", "Moreover, the only APN inhibitor blocking the protease activity site had no obvious negative effect on viral infection, indicating that the enzymatic role of APN is dispensable for the process of virus replication. ", "Taken together, our results suggest that pAPN receptor density appears to be an important factor in contributing to efficient PEDV infection." ]

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[ "Expression cloning and characterization of a novel adipocyte long chain fatty acid transport protein.", "\nLong chain fatty acids (LCFAs) are an important energy substrate used by cardiac myocytes and other cells, but the mechanism whereby these molecules cross the plasma membrane is poorly understood. ", "We used an expression cloning strategy and a cDNA library from 3T3-L1 adipocytes to identify a cDNA that, when expressed in cultured cells, augments uptake of LCFAs. ", "This cDNA encodes a novel 646 amino acid fatty acid transport protein (FATP) with six predicted membrane-spanning regions and that is integrally associated with membranes. ", "Immunocytochemistry and subcellular fractionation of 3T3-L1 adipocytes show that FATP is localized to the plasma membrane. ", "We propose that FATP is a plasma membrane transporter for LCFAs." ]

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