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tomekkorbak
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pii-pile-chunk3-1750000-1800000

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train · 50k rows

texts sequence	meta dict	scores sequence	avg_score float64 0 0.33	num_sents int64 5 5
[ "Q:\n\nhow to clean string data\n\nI extract values from pandas and for number values I embarrass in bracket float(num) which return only integer.", "\nHowever when I request a string object like: \na.subject - it returns \n20 Math\nName: Class10, dtype: object\n\nhowe to get only Math without the rest in more efficient way?", "\n\nA:\n\nProblem is one element Series, so instead a.subject select by index and columns labels by DataFrame.loc: \na.loc['Class10','subject']\n\nOr DataFrame.at:\na.at['Class10','subject']\n\nOr if you want first value of subject:\na.loc[a.index[0], 'subject']\n\nOr:\na.iloc[0, a.columns.get_loc('subject')]\n\nAlso is possible select by column name and then by position:\na.subject.iat[0]\na.subject.iloc[0]\na.subject.to_numpy()[0]\n\nIf possible a.subject is sometimes empty, selecting failed. ", "Then use:\nnext(iter(a.subject), 'no match')\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0, 0.005780346820809248, 0, 0 ]	0.001445	5
[ "Brentford are close to agreeing a deal to sign forward Joel Valencia from Polish side Piast Gliwice.", "\n\nThe 24-year-old Ecuadorean scored six goals in 33 appearances in the Polish top flight last season and previously played for Spain at youth level.", "\n\nThe Bees have been keen to sign another forward this summer regardless of whether Neal Maupay, Said Benrahma or Ollie Watkins, who have all attracted Premier League interest, leave the club.", "\n\nAnd they want to bring Valencia in before the opening game of the season, against Birmingham this weekend.", "\n\nClick here to subscribe to West London Sport’s YouTube channel\n\n\n\n\n\n\n\n" ]	{ "pile_set_name": "OpenWebText2" }	[ 0.02, 0, 0.020833333333333332, 0.009259259259259259, 0.027777777777777776 ]	0.015574	5
[ "::================================================================::\n:: Copyright (c) 2010-2011 Zipline Games, Inc.\n:: All Rights Reserved.", "\n:: http://getmoai.com\n::================================================================::\n\n\t@echo off\n\tsetlocal\n\tset CYGWIN=nodosfilewarning\n\tbash run-host.sh %\n\n\tif %ERRORLEVEL% == 2 (\n\t\tset install_cmd=ant release install\n\t\tset ERRORLEVEL=0\n\t) else (\n\t\tset install_cmd=ant debug install\t\n\t)\n\n\tif %ERRORLEVEL% == 0 (\n\t\tpushd build\\project\n\t\t\tcall ant uninstall \n\t\t\tcall ant clean\n\t\t\tcall %install_cmd%\n\t\t\tcall adb shell am start -a android.intent.action.", "MAIN -n com.distinctdev.tmt2/com.distinctdev.tmt2.MoaiActivity\n\t\t\tcall adb logcat -c\n\t\t\tcall adb logcat MoaiLog:V AndroidRuntime:E :S\n\t\tpopd\n\t)\n\n\tendlocal\n\t@pause\n" ]	{ "pile_set_name": "Github" }	[ 0, 0.004366812227074236, 0.018292682926829267 ]	0.007553	5
[ "Q:\n\nFetch data nested relations eloquent with() in Laravel\n\nI have a model file \"Student\" that contains the relation :\n public function implementations()\n {\n return $this->hasMany(Implementation::class);\n }\n\nIn my Implementation model, I have theses relations :\npublic function score()\n {\n return $this->belongsTo(Score::class, 'id', 'implementation_id');\n }\n\npublic function project()\n {\n return $this->belongsTo(Project::class);\n }\n\nI would like to retrieve a table with all its data.", "\nI tried this\npublic function getStudents($id)\n{\n $event = Event::where('id', $id)->first();\n $data = $event->students()->with('implementations')->get();\n\n return response()->json($data);\n}\n\nIt works. ", "But I do not have the result I would like. ", "I would also like to recover the implementations data with theproject and score relationships\nI tried that but it does not work\npublic function getStudents($id)\n{\n $event = Event::where('id', $id)->first();\n $data = $event->students()->with('implementations')->with('project', 'score')->get();\n\n return response()->json($data);\n}\n\nThank you very much for your help!", "\n\nA:\n\nHave you tried Event::with('students', 'students.implementations') yet? ", "You can eager load relations of relations using the dot notation.", "\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0.0019267822736030828, 0.004761904761904762, 0, 0.00267379679144385, 0, 0.015384615384615385, 0 ]	0.003535	5
[ "-1). ", "Suppose -9s + cs = -33. ", "What is the tens digit of 4/(-6) + 418/s?", "\n1\nLet h be (-4)/(-12) + (4328/6)/(-1). ", "Let o = -506 - h. What is the tens digit of o?", "\n1\nSuppose -3x - 2187 = -5m, -m + 2m + 5x - 443 = 0. ", "What is the hundreds digit of m?", "\n4\nLet y = 671 + -49. ", "What is the units digit of y?", "\n2\nSuppose 0 = -23a + 5a + 18810. ", "What is the hundreds digit of a?", "\n0\nSuppose -1 = g - 3. ", "Suppose -gb + 1 = -3. ", "Suppose 3o - 11 = -bj, -j - 5o + 25 = 4j. ", "What is the units digit of j?", "\n4\nSuppose -4p - 71 = w - 9p, 326 = -4w - p. Let k = w - -118. ", "What is the tens digit of k?", "\n3\nSuppose 3n - v - 514 = 0, 3v = -3n + 616 - 94. ", "What is the units digit of n?", "\n2\nLet n = -31 + 16. ", "Let b = -13 - n. Suppose -3w + 30 = 3j, -bj + 20 = -6j. ", "What is the units digit of w?", "\n5\nLet g(h) = 2h*2 + 1. ", "Suppose 2t = -2t. ", "Let p be 6 - 3 - (-1 - t). ", "What is the tens digit of g(p)?", "\n3\nSuppose 0 = 2l - 14i + 9i - 3337, l - 5i = 1681. ", "What is the tens digit of l?", "\n5\nLet u = 79 + 45. ", "What is the hundreds digit of u?", "\n1\nLet t = 9 + -4. ", "Suppose 2l - tl - 9 = -3w, 2w = -2l + 6. ", "Suppose 0j = -wj + 93. ", "What is the units digit of j?", "\n1\nSuppose 0 = -2k + k + 1. ", "Suppose d - k = 2. ", "Suppose 0 = -dp + 65 + 31. ", "What is the tens digit of p?", "\n3\nSuppose 0 = -23g + 28g - 21375. ", "What is the thousands digit of g?", "\n4\nWhat is the tens digit of (14/(-6))/(-3(-10)/(-4590))?", "\n5\nLet r(k) = -k3 + 7k*2 - 2k + 10. ", "Let b be r(7). ", "Let v be (2/b)/((-11)/1606). ", "Let i = v - 36. ", "What is the tens digit of i?", "\n3\nSuppose -4s = 3i - 1094, 5i + 3s - 1030 = 808. ", "Suppose -79 = 5c + 4q, -2c - 26 = 5q + 9. ", "What is the tens digit of i/12 - c/90?", "\n3\nLet b(l) = -5 - 6l2 - l2 + 11l*2 + 4. ", "What is the units digit of b(5)?", "\n9\nWhat is the tens digit of ((-45)/(-2))/(54/324)?", "\n3\nSuppose 3y = 671 + 838. ", "What is the tens digit of y?", "\n0\nLet p(j) = j3 - j2 - 4. ", "What is the hundreds digit of p(7)?", "\n2\nLet p(s) = s*2 + 4s - 8. ", "Let t be p(-7). ", "Suppose -m - t = -2m - 5x, 2m - 65 = 3x. ", "What is the units digit of 8/m - 38/(-14)?", "\n3\nWhat is the tens digit of 0 + 11 + -1 + 21?", "\n3\nLet i(b) = -b*2 - 8b - 3. ", "Let r be i(-7). ", "Suppose -14 = -rg + 6. ", "Suppose -go + 128 = -2. ", "What is the tens digit of o?", "\n2\nLet r(j) = -6j2 - 2j - 1. ", "Let a be r(-1). ", "Let n(q) = -q + 3q + 8688 - 8695 + 2q*2. ", "What is the tens digit of n(a)?", "\n3\nLet k(y) = 23y. ", "Suppose -4z + 3 = -3z. ", "Let l(t) = 8t. ", "Let f(w) = zk(w) - 8l(w). ", "What is the tens digit of f(3)?", "\n1\nSuppose -5c + 0g - 10 = -2g, -2c + 2g = -2. ", "Let m be 1/c-4-23. ", "Let v = -7 - m. What is the units digit of v?", "\n6\nSuppose 6 = c + 3. ", "Suppose 34 = 5r - 4f, -cr + f + 0 = -19. ", "Let m(u) = -u3 + 6u*2 + 1. ", "What is the units digit of m(r)?", "\n1\nSuppose 3x = -k + 1864, -6 = -2x - x. What is the thousands digit of k?", "\n1\nSuppose 7s + 102 = 4s. ", "Let p = 75 + s. What is the units digit of p?", "\n1\nLet t(s) = 93s + 690. ", "What is the units digit of t(13)?", "\n9\nWhat is the units digit of 21(53 + -4) - 0?", "\n9\nLet p(h) = h3 - 2h*2 + 3h - 2. ", "Let y be p(2). ", "Suppose -2 = -ys + 2v, 3s - 2 - 5 = -4v. ", "What is the units digit of s?", "\n1\nSuppose 20p - 48956 = 5064. ", "What is the tens digit of p?", "\n0\nSuppose 2z + 0z - 6 = 0, 2s - 7 = z. Let c = 77 - s. What is the units digit of c?", "\n2\nLet l = 950 - 195. ", "What is the hundreds digit of l?", "\n7\nLet x(r) = -17r - 6. ", "Let h(n) = -33n - 11. ", "Let j(l) = -6h(l) + 11x(l). ", "Suppose 0t = a + 2t - 2, a - t = 8. ", "What is the tens digit of j(a)?", "\n6\nLet n(i) = 19i2 + 9i - 16. ", "What is the hundreds digit of n(-6)?", "\n6\nLet h = -121 - -179. ", "Suppose 4s = -5r + 146, -3r + s + h + 16 = 0. ", "What is the tens digit of r?", "\n2\nLet s(o) = -9 + o2 + 4o - 4o - 7. ", "What is the tens digit of s(10)?", "\n8\nSuppose 6v = 1299 + 645. ", "What is the tens digit of v?", "\n2\nSuppose -2g + 6 = -2. ", "Let o(r) = -3 + 15r - r*2 - gr + r. What is the tens digit of o(8)?", "\n2\nWhat is the hundreds digit of -5 + -1 + 242/1?", "\n2\nWhat is the tens digit of 7115/30 - ((-28)/24)/(-7)?", "\n3\nSuppose -4524 = -7f + 4436. ", "What is the units digit of f?", "\n0\nSuppose 5i + 2m - 4m = 307, -2i + 2m + 124 = 0. ", "Let t = i + -30. ", "What is the tens digit of t?", "\n3\nSuppose 6q = 4q - p + 3900, -p = 4q - 7802. ", "What is the tens digit of q?", "\n5\nSuppose -2v + 2m + 2m - 314 = 0, 4m = -16. ", "What is the units digit of (v - 0)/(5 + -2 + -4)?", "\n5\nSuppose -11s + 8000 + 5728 = 0. ", "What is the thousands digit of s?", "\n1\nSuppose -3r - 17 = -2r - 5o, 2r - 10 = -o. ", "Suppose -4p = -r + 19. ", "Let c(n) = n2 + 9. ", "What is the tens digit of c(p)?", "\n2\nLet m(g) = -17g - 1. ", "Let z be m(-7). ", "Let t = z + -64. ", "Let v = t - 29. ", "What is the tens digit of v?", "\n2\nLet n(z) = z*2 + 15z + 3. ", "What is the tens digit of n(11)?", "\n8\nLet y(a) = 9a2 + 5a - 4. ", "What is the tens digit of y(13)?", "\n8\nLet n = 221 + 958. ", "What is the tens digit of n?", "\n7\nLet s be 2(-3 - 28/(-2)). ", "Suppose b = 2f + 13, -b + 3 = f - s. What is the tens digit of b?", "\n2\nSuppose 423 = 3y - 285. ", "Suppose 0p = 3d + 2p - 226, y = 3d + 4p. ", "What is the tens digit of d?", "\n7\nSuppose -138 - 108 = 3m. ", "Let r = m - -115. ", "What is the tens digit of r?", "\n3\nLet u(d) = 2d - 4. ", "Let g be u(4). ", "Suppose -h - 4h = -2f + 5, -gf + 5 = -5h. ", "Let y = f - -2. ", "What is the units digit of y?", "\n2\nSuppose 25 = 2k + 3k. ", "Suppose 2i - 437 = b, 3i - 443 = i - kb. ", "What is the tens digit of (2 - i/9)-3?", "\n6\nSuppose 5k - 2y - 235 - 38 = 0, 179 = 3k - 5y. ", "Let x = 33 + -2. ", "Let h = k - x. What is the units digit of h?", "\n2\nLet t(m) be the first derivative of -6m - 1/4m*4 + 1 - 14/3m*3 - 17/2m*2. ", "What is the tens digit of t(-13)?", "\n4\nLet a(r) = -11r - 2. ", "Let v be a(-5). ", "Let z(p) = 12 - v + 24 + 3p + 5p. ", "What is the units digit of z(6)?", "\n1\nLet z = 588 - -403. ", "What is the hundreds digit of z?", "\n9\nSuppose 5b - 13 - 107 = 0. ", "Suppose 4g - 88 + b = 0. ", "What is the units digit of g?", "\n6\nLet r be (-4)/(-8)2 - 11/1. ", "What is the units digit of (-1)/((2/(-4))/((-435)/r))?", "\n7\nSuppose -3c - c = 0. ", "Suppose 0 = -ct + 3t - 3y - 450, -306 = -2t - y. Let z = t - 108. ", "What is the tens digit of z?", "\n4\nWhat is the units digit of (-28100)/(-21) - 356/3738?", "\n8\nSuppose 8i - 3i = 325. ", "Let p = i + 4. ", "What is the tens digit of p?", "\n6\nLet p(v) = 9v - 9. ", "Suppose 0r - 3r = -12. ", "Let w = r + 3. ", "What is the tens digit of p(w)?", "\n5\nLet n(v) = 5v*2 + 3v - 4. ", "Let m be n(5). ", "Suppose -5i + 7i - m = 0. ", "Suppose 5o + 2k - i = 175, -3o = -3k - 150. ", "What is the tens digit of o?", "\n4\nLet q be (10/(-2))/(30/(-36)). ", "Suppose -x - q + 34 = 0. ", "Suppose 0 = 3p - x + 10. ", "What is the units digit of p?", "\n6\nSuppose 8w + 25461 = 31w. ", "What is the units digit of w?", "\n7\nSuppose -5l + 2l = 75. ", "Let y = 25 + l. What is the tens digit of 22 - (y + 8/4)?", "\n2\nWhat is the hundreds digit of (-66)/(243/42 - 6)?", "\n3\nWhat is the units digit of (3315/170)/((-1)/(-26))?", "\n7\nLet w(y) = 122y2 - y + 6. ", "Let f(b) = -b2 - 1. ", "Let j(m) = 5f(m) + w(m). ", "What is the units digit of j(1)?", "\n7\nLet w(p) be the first derivative of -7p*2/2 + 5p + 1. ", "Let y be w(-3). ", "Let h = y + 3. ", "What is the units digit of h?", "\n9\nWhat is the units digit of 958/3 - (3 - 16/6)?", "\n9\nWhat is the hundreds digit of (-3594)/48-42?", "\n5\nLet n(j) = -62j3 - 5j*2 + 3j + 19. ", "What is the hundreds digit of n(-3)?", "\n6\nSuppose -4t - 3a + 995 = 0, 4a - 7a - 1264 = -5t. ", "What is the tens digit of t?", "\n5\nLet m = -200 - -117. ", "Suppose 4t = 3s + 590, -s - 4s + 606 = 4t. ", "Let x = m + t. What is the tens digit of x?", "\n6\nWhat is the tens digit of (5 + -6)/(3/(-1326))?", "\n4\nLet f = 437 - -1698. ", "What is the units digit of f?", "\n5\nLet m = 57 - 33. ", "Suppose 4r = -20, -d - 3r = r + m. What is the units digit of (-165)/(-105) + d/7?", "\n1\nSuppose 5m + 116 = 16. ", "Let n(w) = 8w2 - 5w + 8. ", "Let a be n(2). ", "Let o = a + m. What is the tens digit of o?", "\n1\nSuppose 17 = 5n - 3. ", "Let r(z) = z + 5. ", "Let b(v) = -v - 5. ", "Let h(x) = nr(x) + 3b(x). ", "What is the tens digit of h(11)?", "\n1\nWhat is the tens digit of 6035/15 + 4/(-12)?", "\n0\nLet n = 9008 + -4905. ", "What is the hundreds digit of n?", "\n1\nSuppose -69 = -0b - 3b. ", "Suppose 0 = 3n - 218 + b. What is the units digit of n?", "\n5\nLet i(x) be the second derivative of -7x6/720 + x4/12 - x. Let v(l) be the third derivative of i(l). ", "What is the tens digit of v(-2)?", "\n1\nSuppose -2r + 715 = -f, 2r + 115f - 118f = 725. ", "What is the units digit of r?", "\n5\nLet o(k) = k2 + k - 6. ", "Let u be o(-3). ", "Suppose 5c + 5*b -" ]	{ "pile_set_name": "DM Mathematics" }	[ 0.2, 0.038461538461538464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.015151515151515152, 0, 0, 0, 0, 0, 0, 0, 0, 0.037037037037037035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.05263157894736842, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.021739130434782608, 0.02631578947368421, 0, 0.03125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.041666666666666664, 0, 0, 0, 0, 0, 0, 0, 0, 0.0625, 0, 0.03225806451612903, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02631578947368421, 0.03225806451612903, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.034482758620689655, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.011904761904761904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.04, 0, 0, 0, 0, 0, 0, 0, 0, 0.04, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.009174311926605505, 0, 0, 0, 0, 0, 0 ]	0.00337	5
[ "/***************************************************************\n\|\n\| AP4 - Sample Table Interface\n\|\n\| Copyright 2002-2008 Axiomatic Systems, LLC\n\|\n\|\n\| This file is part of Bento4/AP4 (MP4 Atom Processing Library).", "\n\|\n\| Unless you have obtained Bento4 under a difference license,\n\| this version of Bento4 is Bento4\|GPL.", "\n\| Bento4\|GPL is free software; you can redistribute it and/or modify\n\| it under the terms of the GNU General Public License as published by\n\| the Free Software Foundation; either version 2, or (at your option)\n\| any later version.", "\n\|\n\| Bento4\|GPL is distributed in the hope that it will be useful,\n\| but WITHOUT ANY WARRANTY; without even the implied warranty of\n\| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. ", " See the\n\| GNU General Public License for more details.", "\n\|\n\| You should have received a copy of the GNU General Public License\n\| along with Bento4\|GPL; see the file COPYING. ", " If not, write to the\n\| Free Software Foundation, 59 Temple Place - Suite 330, Boston, MA\n\| 02111-1307, USA.", "\n\|\n *************************************************************/\n\n#ifndef _AP4_SAMPLE_TABLE_H_\n#define _AP4_SAMPLE_TABLE_H_\n\n/----------------------------------------------------------------------\n\| includes\n+---------------------------------------------------------------------/\n#include \"Ap4Types.h\"\n#include \"Ap4DynamicCast.h\"\n\n/----------------------------------------------------------------------\n\| class references\n+---------------------------------------------------------------------/\nclass AP4_Sample;\nclass AP4_ContainerAtom;\nclass AP4_SampleDescription;\n\n/----------------------------------------------------------------------\n\| AP4_SampleTable\n+---------------------------------------------------------------------/\nclass AP4_SampleTable {\npublic:\n AP4_IMPLEMENT_DYNAMIC_CAST(AP4_SampleTable)\n\n // constructors and destructor\n virtual ~AP4_SampleTable() {};\n\n // methods\n virtual AP4_Result GenerateStblAtom(AP4_ContainerAtom& stbl);\n virtual AP4_Cardinal GetSampleCount() = 0;\n virtual AP4_Result GetSample(AP4_Ordinal sample_index, AP4_Sample& sample) = 0;\n virtual AP4_Result GetSampleChunkPosition(AP4_Ordinal sample_index, \n AP4_Ordinal& chunk_index,\n AP4_Ordinal& position_in_chunk) = 0;\n virtual AP4_Cardinal GetSampleDescriptionCount() = 0;\n virtual AP4_SampleDescription* GetSampleDescription(AP4_Ordinal index) = 0;\n virtual AP4_Result GetSampleIndexForTimeStamp(AP4_UI64 ts,\n AP4_Ordinal& index) = 0;\n virtual AP4_Ordinal GetNearestSyncSampleIndex(AP4_Ordinal index, bool before=true) = 0;\n};\n\n#endif // _AP4_SAMPLE_TABLE_H_\n" ]	{ "pile_set_name": "Github" }	[ 0.008928571428571428, 0.00909090909090909, 0.00823045267489712, 0.00510204081632653, 0.017241379310344827, 0.016129032258064516, 0.017543859649122806, 0.0022701475595913734 ]	0.010567	5
[ "Q:\n\nAndroid : App Crash When scrolling List View with 2 Different Cells\n\nI want to implement the two cells type in my app Image and text so i'm just testing this, my app works fine and load perfectly but tis crashes when i start scrolling with the following error \njava.lang.", "ArrayIndexOutOfBoundsException: length=2; index=2130968624\n\nthis is my adapter \n public class myadapter extends ArrayAdapter<myobject> {\n\n Context context;\n List<myobject> objectlist;\n\n public myadapter(Context context, int resource, List<myobject> objects) {\n super(context, resource, objects);\n this.context = context;\n this.objectlist = objects;\n }\n\n @Override\n public View getView(int position, View convertView, ViewGroup parent) {\n\n ViewHolder2 tvholder;\n ViewHolder ivholder;\n\n LayoutInflater inflater =(LayoutInflater) context.getSystemService(Context.", "LAYOUT_INFLATER_SERVICE);\n\n if (getItemViewType(position) == R.layout.textcell){\n\n if(convertView==null){\n convertView= inflater.inflate(getItemViewType(position),parent,false);\n tvholder= new ViewHolder2(convertView);\n convertView.setTag(tvholder);\n }else{\n tvholder = (ViewHolder2)convertView.getTag();\n }\n tvholder.", "TV.setText(objectlist.get(position).getText());\n }else{\n if(convertView==null){\n convertView= inflater.inflate(getItemViewType(position),parent,false);\n ivholder = new ViewHolder(convertView);\n convertView.setTag(ivholder);\n }else{\n ivholder=(ViewHolder) convertView.getTag();\n }\n ivholder.", "IV.setImageResource(objectlist.get(position).getImage());\n }\n return convertView;\n }\n\n @Override\n public int getViewTypeCount() {\n return 2;\n }\n\n @Override\n public int getItemViewType(int position) {\n if(objectlist.get(position).getType()==1){\n return R.layout.textcell;\n\n }else{\n return R.layout.imagecell;\n }\n }\n\n}\nclass ViewHolder{\n ImageView IV;\n\n public ViewHolder(View view){\n IV = (ImageView)view.findViewById(R.id.", "IV);\n\n }\n\n}\nclass ViewHolder2{\n\n TextView TV;\n public ViewHolder2(View view){\n\n TV = (TextView)view.findViewById(R.id.", "TV);\n\n }\n\n}\n\nmy object :\npublic class myobject {\n\n int type;\n String Text;\n int Image;\n public myobject(){\n this.type = 0;\n this.", "Text = null;\n this.", "Image = 0;\n }\n public myobject(int type,String Text,int Image){\n this.type=type;\n this.", "Image = Image;\n this.", "Text = Text;\n }\n public int getType(){ return type;}\n public String getText (){return Text;}\n public int getImage (){return Image;}\n}\n\nUse in Main Activity :\npublic class MainActivity extends AppCompatActivity {\n\nListView LV;\nList<myobject> myobjectList = new ArrayList<>();\nmyadapter myadapter;\n@Override\nprotected void onCreate(Bundle savedInstanceState) {\n super.onCreate(savedInstanceState);\n setContentView(R.layout.activity_main);\n LV = (ListView) findViewById(R.id.", "LV);\n myobject myobject1 = new myobject(1,\"teeeeeexxxxt\",0);\n myobject myobject2 = new myobject(2,null,R.mipmap.ic_launcher);\n myobject myobject3 = new myobject(1,\"teeeeeexxxxt\",0);\n myobject myobject4 = new myobject(1,\"teeeeeexxxxt\",0);\n myobject myobject5 = new myobject(2,null,R.mipmap.ic_launcher);\n myobject myobject6 = new myobject(2,null,R.mipmap.ic_launcher);\n myobject myobject7 = new myobject(2,null,R.mipmap.ic_launcher);\n myobject myobject8 = new myobject(1,\"teeeeeexxxxt\",0);\n myobject myobject9 = new myobject(1,\"teeeeeexxxxt\",0);\n myobjectList.add(myobject1);\n myobjectList.add(myobject2);\n myobjectList.add(myobject3);\n myobjectList.add(myobject4);\n myobjectList.add(myobject5);\n myobjectList.add(myobject6);\n myobjectList.add(myobject7);\n myobjectList.add(myobject8);\n myobjectList.add(myobject9);\n myadapter = new myadapter(this,0,myobjectList);\n LV.setAdapter(myadapter);\n}\n\nI really don't know what is causing this fatal error + is my implementation consider to be the most optimize approach for the 2 different cells type ?", "\nany ideas would be much appreciated \n\nA:\n\nBefore solving your issue I want to clarify something first. ", "While using the ArrayAdapter you don't have to store yourself the list of objects or the context, since it is done for you when the adapter is created. ", "that being said, every call like objectlist.get(position) would be something like this getItem(position), and to obtain the context you simply call getContext.", "\nNow let's explore the issue. ", "According to Adapter class documentation, the getItemViewType(int position) method has to return a value between 0 and getViewTypeCount() - 1. ", "\n\nAn integer representing the type of View. ", "Two views should share the same type if one can be converted to the other in getView(int, View, ViewGroup). ", "Note: Integers must be in the range 0 to getViewTypeCount() - 1. ", "IGNORE_ITEM_VIEW_TYPE can also be returned. ", "\n\nThe problem in you code is that you are returning the id of a layout file, which usually is a very big number, and thus IndexOutOfBounds is thrown. ", "\nA possible solution for this would be to return the getItem(position).getType() - 1 instead of what you are currently returning. ", "After this, the getView method can be changed to match the different layouts and view holders.", "\n@Override\npublic View getView(int position, View convertView, ViewGroup parent) {\n\n ViewHolder2 tvholder;\n ViewHolder ivholder;\n\n LayoutInflater inflater =(LayoutInflater) getContext().getSystemService(Context.", "LAYOUT_INFLATER_SERVICE);\n if (convertView == null) {\n switch (getItemViewType(position)) {\n case 0:\n convertView = inflater.inflate(R.layout.textcell, null);\n tvholder = new ViewHolder2(convertView);\n tvholder.", "TV.setText(getItem(position).getText());\n convertView.setTag(tvholder);\n break;\n case 1:\n convertView = inflater.inflate(R.layout.imagecell, null);\n ivholder = new ViewHolder(convertView);\n ivholder.", "IV.setImageResource(getItem(position).getImage());\n convertView.setTag(ivholder);\n break;\n }\n } else {\n switch (getItemViewType(position)) {\n case 0:\n tvholder = (ViewHolder2) convertView.getTag();\n tvholder.", "TV.setText(getItem(position).getText());\n break;\n case 1:\n ivholder = (ViewHolder) convertView.getTag();\n ivholder.", "IV.setImageResource(getItem(position).getImage());\n break;\n }\n }\n return convertView;\n}\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0.007272727272727273, 0.008051529790660225, 0.004662004662004662, 0, 0.007692307692307693, 0.007462686567164179, 0.006329113924050633, 0, 0.009345794392523364, 0, 0.012170385395537525, 0.005434782608695652, 0, 0.006578947368421052, 0, 0, 0.013986013986013986, 0, 0.018518518518518517, 0.015384615384615385, 0, 0, 0, 0, 0.00909090909090909, 0.0035971223021582736, 0, 0.0033783783783783786, 0.005847953216374269, 0.008547008547008548 ]	0.005112	5
[ "\nAt first glance, this is very much a town on the up - a place where newly wealthy citizens pour their riches into gaudy, Beverly Hills-style homes, proud to show off just what they have achieved.", "\n\nBut the brightly-coloured streets hide a much darker secret: this is a town allegedly built on British benefits, where law-abiding locals fear their neighbours return.", "\n\nWelcome to Tandarei, a town where many houses were built on the back of Britain's generous benefits system - and the ability of the criminal underclass to manipulate it.", "\n\nLuxurious: Sprawling mansions paid for by illegally obtained funds line the streets of the tiny Romanian town of Tandarei (pictured, a home where a member of the Radu gypsy gang lived)\n\nLavish: Many of the homes in Tandarei, worth as much as as £500,000, lie empty most of the year\n\nTandarei, some 100 miles east of the Romanian capital Bucharest, has changed beyond recognition in recent years: the number of mansions in this 12,000-strong town has tripled since it first attracted international attention.", "\n\nHOW DO THE LAVISH MANSION OWNERS EXPLOIT THE SYSTEM? ", "It is thought that those living in the extravagant mansions in Tandarei have exploited the British benefits system to send money back to their home country. ", "Neighbours say the homeowners spend most of their time living in the UK, only returning to Romania for holidays and special occasions. ", "In Britain, despite tightening rules on benefits that can be claimed by migrants, employed workers still have access to the benefits system. ", "Claiming child benefits, for example, means a family with three children would be able to claim more than £2,500 a year. ", "In a country where the average annual salary is just over £4,000, that money can go a long way. ", "Advertisement\n\nOf those, more than 300 - most with gleaming BMWs and brand new Volkswagens parked on the expertly-paved driveways outside - are feared to have been paid for by the British taxpayer through money earned illegally or through benefits scams in the UK.", "\n\nSome, with balconies protruding from every bedroom, are thought to belong to Gypsy gangsters who flout Europe's free movement rules to fleece Britons out of tens of thousands of pounds.", "\n\nMany of the cars parked outside the houses have British number plates. ", "Critics have held this up as evidence that Romanian gypsies travelled to the UK to claim benefits and sent the money to their relatives back home, where the average annual salary is around £4,100.", "\n\nMore than 3,000 Romanians were found to be claiming benefits in the UK as of February, government statistics revealed.", "\n\nThe rules may have been tightened in recent years - rules that stipulate an EU migrant who is unemployed have to be in the country for three months before they can claim JSA for a total of three months, and they cannot claim housing benefits - but many still find a way around them.", "\n\nFor example, those who arrive as an employed worker have a different classification under EU rules. ", "That means they have the same access to the benefits system that any UK national has - which means £20.70 a week for your oldest child, and an additional £13.70 a week for all other children.", "\n\nOver a year, it means a family with three children would be able to claim more than £2,500 - more than half the country's average salary.", "\n\nAdded to other possible benefits - and the odd undeclared, untaxed job on the side - it is not hard to see how Romania's criminal underbelly manage to fund such lifestyles in their home country.", "\n\nFor the hardworking citizens of this eastern European country, it is more than a little galling.", "\n\nTandarei local Alecu Vasile, 60, told MailOnline: 'I don't think one can make such houses with honest money... I am barely making ends meet.'", "\n\nScared: One Tandarei local told MailOnline he refuses to go out at night when the gypsies who own mansions like these come back to town, saying: 'It's just too dangerous and I would end up returning without my wallet'these mansions come back to town, saying: 'It's just too dangerous and I would end up returning without my wallet'\n\nSuspicious: Many of the cars parked outside the lavish homes have British number plates (left), which some have held up as evidence that gypsies are travelling to the UK to claim benefits\n\nIssues: The gypsies are thought to live in primitive annexes at the back of the house, which locals have claimed are poorly built\n\nThreatened: Tandarei residents say they are under siege from gypsies (pictured, one of the mansions thought to have been built by gypsies) and claim that peace only returns to the area when the gypsies are out of the country\n\nHowever, that is not to say the locals of this small town want their gypsy neighbours to return any time soon. ", "In fact, they live in constant fear of them returning from the UK, where some 5,000 local gypsies are thought to have settled in recent years.", "\n\nI am glad they are abroad. ", "When they come back I don't go out after dark, and I don't visit the annual fair here anymore. ", "It's just too dangerous. ", "Tandarei local\n\nTandarei locals talk of being under siege, saying peace only returns to the area when the gypsies are out of the country. ", "When they come back for public holidays and special occasions including Orthodox Cross Day, chaos reigns.", "\n\nOne local said: 'I am glad they are abroad. ", "When they come back I don't go out after dark, and I don't visit the annual fair here anymore. ", "It's just too dangerous and I would end up returning without my wallet.", "\n\n'When they come back, they want all their families around them. ", "And the family is always bigger. ", "There is a joke here - three gypsies went to the UK, and 10 came back.", "\n\n'They want big families, gypsies have always had large families but now they are really cashing in with the kids. ", "All of them know about getting benefits abroad, they give each other advice on how to do it. ", "This is where they get their cash.'", "\n\nAnother neighbour further down the same street said: 'I lost my son after he got into a fight with the gypsy. ", "He was killed. ", "I never really got much detail from the police, other than the fact that it was a gypsy.", "\n\n'We have more gypsies here than anywhere else, about three quarters the people living in this town are gypsies now. ", "Soon there will not be any Romanians left here.'", "\n\nGalling: Tandarei local Alecu Vasile (pictured), 60 told MailOnline: 'I don't think one can make such houses with honest money... I am barely making ends meet'\n\nIllicit: More than 300 of the mansions in Tandarei are thought to have been funded by the British taxpayer through money earned illegally or through benefits scams in the UK\n\nCaught red handed: Adrian Radu, left, illegally claimed £29,000 in income support and tax credits from the UK between 2008 to 2010, when he was in Romania. ", "Meanwhile, Ilie Schian, right, falsely claimed £35,000 in benefits in a year. ", "Both had homes in Tandarei\n\nEven when the gypsies are in town, it isn't like the homes are full of life: locals say the houses are built to be shown off rather than be lived in.", "\n\nThe gypsies only use the main building for family parties and functions but stay in the primitive annexes built at the back of the lavish properties, they told MailOnline.", "\n\nThe gypsies here all know about benefits. ", "They are lazy, they even hire Romanians to do the work on their houses because they can't be bothered even when they are home Tandarei local\n\n'They are too badly built, I think they are scared to live in them,' said one neighbour, who chose to stay anonymous for fear of reprisal.", "\n\nAnother said: 'They leave some family members behind and tell them not to use the house - and only open up when the rest come back.'", "\n\nBut, the neighbours claim, they aren't keeping house for their better-off relatives in that time.", "\n\n'They are lazy, they even hire Romanians to do the work on their houses because they can't be bothered even when they are home,' one person told MailOnline.", "\n\nAs a result, many Romanians in town end up working for their gypsy neighbours as caretakers - keeping the houses clean and gardens well maintained while they are abroad.", "\n\nTwo of the lavish houses belong to a Roma gypsy gang known as the Radu clan.", "\n\nThe garish, orange home has been deserted since they were arrested in the UK five years ago.", "\n\nAdrian Radu, 33, the son of one of the gang leaders, Constantin Radu, illegally claimed £29,000 in income support and tax credits from the UK between 2008 to 2010, when he was in Romania.", "\n\nWhen police arrested him in Tandarei he was living in a new marble-floored, six-bedroom mansion and driving an expensive Audi Q7 car.", "\n\nThe driveway now lies empty and from the gates outside hangs a sign announcing the owners are living abroad.", "\n\nGangsters: Two of the lavish houses (pictured, one of them), many of which lie empty most of the year, belong to a Romanian gypsy gang known as the Radu clan, locals claimed\n\nReturn: Most of the wealthy gypsies (pictured, the homes they are thought to live in) come back for public holidays and special occasions including Orthodox Cross Day\n\nEmployed: Many Romanians in town end up working for their gypsy neighbours as caretakers - keeping the houses clean and gardens well maintained while they are abroad\n\nThere have been other instances of his compatriots being punished for illegally claiming benefits in the UK. ", "Romanian gypsy Ilie Schian was sentenced to three years behind bars for defrauding the British taxpayer of 114,000 in benefits.", "\n\nI heard they got some benefits in the UK for having a lot of children. ", "Roger [one of the Radu clan] has eight children Tandarei local\n\nSchian, who was jailed in 2010, created a false identity to claim the money which he spent on sports cars and a nine bedroom home in his home country.", "\n\n'I heard they got some benefits in the UK for having a lot of children,' said a neighbour who refused to disclose her name.", "\n\nShe added: 'Roger [one of the Radu clan] has eight children. ", "I don't know when they have time to make some many children.'", "\n\nShe said Dudu and Roger, both from the same gang, have luxurious objects inside the houses which they only open on holidays, adding: 'Last year, Dudu changed all of his furniture. ", "But the three houses across the road that belong to his cousins are empty.'", "\n\nIn many ways, Tandarei has not changed for decades. ", "There are still the communist housing blocks built by Nicolae Ceausescu, the country’s last Communist leader who bulldozed villages to force people into urban areas.", "\n\nBut the rapid influx of wealth gypsy families has put pressure on local communities who said they are often approached about selling their homes.", "\n\nPrimitive: More than 3,000 Romanians were found to be claiming benefits in the UK as of February (pictured, poor residents of Tandarei)\n\nHumble: Barbu Paraschiva Florica, 80, who lives on a pension of just £85 a month, still works the land like most Romanian villagers\n\nOne woman said: 'I have heard that in other areas people were really put under pressure, and things got quite nasty.", "\n\n'I get asked a couple of times a year, they are always friendly and polite, and I can't say they are intimidating. ", "But they are really keen to have their families nearby and want to buy up the land.'" ]	{ "pile_set_name": "OpenWebText2" }	[ 0, 0, 0.005847953216374269, 0.0019646365422396855, 0, 0, 0, 0, 0, 0, 0.003787878787878788, 0.0053475935828877, 0, 0, 0, 0.007042253521126761, 0.00980392156862745, 0, 0, 0, 0, 0.013986013986013986, 0, 0, 0, 0, 0, 0, 0.009523809523809525, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.006072874493927126, 0.01282051282051282, 0, 0.005780346820809248, 0, 0, 0, 0, 0.006329113924050633, 0, 0.01282051282051282, 0.010638297872340425, 0.005291005291005291, 0.014814814814814815, 0, 0.00322061191626409, 0.007874015748031496, 0, 0.014018691588785047, 0, 0.031746031746031744, 0, 0.016483516483516484, 0, 0.018518518518518517, 0.006060606060606061, 0, 0.005154639175257732, 0, 0 ]	0.003218	5
[ "1. ", "Field of the Invention\nThe present invention relates to a distance measuring apparatus, and more particularly, to a passive distance measuring apparatus which does not emit light, such as infrared light, but instead utilities ambient light to measure a subject distance and which can be used in, for example, a camera.", "\n2. ", "Description of Related Art\nSome lens-shutter type cameras are provided with an autofocusing system provided with a passive distance measuring apparatus. ", "This passive distance measuring apparatus includes a pair of image forming lenses (i.e., distance measurement optical system) and a pair of line sensors or light receiving sensors on which subject images are respectively formed through the pair of image forming lenses so as to calculate a subject distance based on triangulation. ", "In cameras of this type, a photographing optical system, a finder optical system and the distance measurement optical system are provided which are independent of each other. ", "In some cameras of this type, the distance measuring apparatus is constructed as a single unit, i.e., a distance measuring unit consisting of the pair of image forming lenses, the pair of line sensors each comprised of an array of a large number of light receiving elements (i.e., photodiodes) on which a plurality of subject images of a common subject are projected, and an arithmetic operating portion for calculating a subject distance based on triangulation in accordance with the data outputted from the pair of line sensors. ", "In the distance measuring unit, the optical axis of the distance measurement optical system does not coincide with either the optical axis of the photographing optical system nor the optical axis of the finder optical system.", "\nIn conventional cameras of this type, in the case where the photographing optical system is a zoom lens an(the finder optical system is a zoom finder whose magnification varies in accordance with the varied focal length of the zoom lens, the relationship among the finder view formed through the finder optical system, the AF frame which is observed in the finder view and the distance measuring unit will now be described.", "\nWhen zooming is effected towards the telephoto extremity, a subject image observed in the finder view is magnified due to a variation in the magnification of the zoom finder. ", "However, the distance measuring unit always receives on its pair of line sensors subject images of constant magnification due to the magnification of the pair of image forming lenses of the distance measuring unit being fixed, and not varied in accordance with the varied focal length of either the zoom lens or the zoom finder, and furthermore, the size of the AF frame does not change in the finder view. ", "Due to this, on the telephoto extremity side, the focus measuring area indicated by the AF frame, superimposed on a magnified or close-up subject image in the finder view, becomes smaller than the actual focus measuring area determined by the light receiving area lb of each line sensor in the distance measuring unit.", "\nAccordingly, there is a difference in size between the AF frame in the finder view and the light receiving area of each line sensor in the distance measuring unit. ", "Due to this difference, in conventional cameras of this type, i is often the case that a subject, or subjects, observe out of the AF frame, but close to the AF frame are sometimes erroneously brought into focus through th distance measuring unit as a main subject or subjects especially when the zoom lens is on the telephoto side. ", "As a result, the main subject is blurry in the resulting picture.", "\nFurthermore, in conventional cameras of the type in which the optical axis of the distance measurement optical system of the distance measuring unit is not aligned with the optical axis of the photographing optical system nor the finder optical system, the optical axis of the distance measurement optical system in the distance measuring unit and the optical axis of the photographing lens are not always arranged to be precisely parallel to each other in an assembling process. ", "If so, that a common subject may not always be captured at the same time by both the distance measuring optical system in the distance measuring unit, and the photographing lens. ", "It is not necessary to adjust the position of the distance measuring unit in the case where a deviation from an optimum arrangement between the optical axis of the distance measurement optical system in the distance measuring unit and the optical axis of the photographing lens is small, i.e., within an acceptable limit. ", "However, if the deviation falls outside the acceptable limit, it is necessary to adjust the distance measuring unit by moving or swinging it so that both the optical axes may be placed parallel to each other to eliminate the deviation. ", "In an adjustment of this kind, the distance measuring unit is moved or swung mechanically relative to the camera body.", "\nAfter the distance measuring unit has been moved or swung for adjustment, data outputted from the distance measuring unit is checked to find out if it corresponds to predetermined reference data. ", "If the data does not correspond, to the reference data the distance measuring unit is readjusted. ", "Therefore, the adjusting operation, in which the distance measuring unit is firstly moved and data is subsequently checked, has to be repeated until such a time that the checked data corresponds to the predetermined reference data, thus resulting in a troublesome, time consuming operation.", "\nFurthermore, in conventional cameras where the camera has a macro photographing mode for close-up photography in which the optical axis of the distance measurement optical system of the distance measuring unit is not aligned with the optical axis of the photographing optical system nor the finder optical system, and such that the optical axis of the distance measurement optical system of the distance measuring unit deviates from that of the photographing lens by a large distance in left and right directions of the camera, a deviation occurs between the two positions. ", "In other words, the position of a light receiving area on the line sensor on which subject images ar projected in regular photography where a distance of subject located on the optical axis of the photographing lens beyond a predetermined distance from the camera is measured, and another position of a light receiving area on the line sensor on which subject images are projected in macro photography for a close-up where a distance of a subject close to the camera is measured within a certain distance range. ", "As a result, the AF frame in the finder view and the light receiving area of each line sensor of the distance measuring unit do not correspond to each other in macro photography, thereby the subject distance cannot be precisely measured.", "\nIn a known lens-shutter type camera which has an autofocusing system provided with a distance measuring apparatus including a pair of image forming lenses, a pair of left and right line sensors each comprised of an array of a large number of light receiving elements, used to define a single light receiving area and an arithmetic operating portion for calculating a subject distance based on triangulation in accordance with the data outputted from the pair of line sensors, so that the subject distance can be calculated. ", "However, in the measurement of the subject distance using one light receiving area at each ine sensor, as mentioned above, there is only one measurement of the subject distance to be effected, and hence, if no optimum value is obtained by the single measurement or calculation, no focusing can be carried out, thus leading to a missed photographic opportunity.", "\nTo solve this problem, it is also known to divide the light receiving elements of each line sensor into a plurality of blocks or groups (i.e., a plurality of light receiving areas), so that the subject distance can be calculated based on sensor data obtained from the pairs of corresponding light receiving areas of the line sensors. ", "However, in this solution, since a plurality of measurements obtained, based on the sensor data supplied from each pair of light receiving areas, are compared to detect the largest value corresponding to the closest distance, so that the focusing can be effected ii accordance with the detected largest value, the comparison operation must be carried out for each measurement contrary to a fast photographing operation.", "\nIn a conventional distance measuring apparatus i known cameras, the subject light is split into two halve by a beam splitting optical system. ", "The two halves are converged onto, and received by, respective left and right line sensors. ", "Each line sensor respectively converts to received subject light into electrical image signals which are used for calculation. ", "Namely, for example, correlativity (degree of coincidence) of the subject image data corresponding to the light receiving areas of the left and right line sensors is evaluated based on the image data at different light receiving areas. ", "When a high degree of coincidence is obtained, position data of the light receiving areas corresponding thereto is detected to calculate a distance between the left and right subject images, based on the position data, and subsequently, the subject distance is calculated, using the calculated distance between the left and right subject images.", "\nHowever, under conditions having a harmful influence, such as a backlit condition, the amount of light to be received by the left line sensor can be remarkably different from the amount of light to be received by the right line sensor. ", "If this difference occurs, the reference level of image data of the left line sensor (left image data) is different from that of the image data of the right line sensor (right image data), and hence the degree ol coincidence decreases. ", "Consequently, it is judged that the subject distance cannot be measured or the subject distance is incorrectly measured. ", "In addition, it is difficult to distinguish the incorrect measurement from that caused by the existence of images of subjects at far and close distances in a light receiving area. ", "Moreover, in some cases, even when a correct measurement has been obtained, the apparatus judges that no distance can be measured.", "\nFurthermore, in a conventional distance measuring apparatus, if the contrast of a subject is low, or if ages of subjects at a close distance and at a far stance coexist in a light receiving area, or in the case of a succession of subjects having a repetitive pattern across the light receiving area, no subject distance can be measured. ", "To minimize the occurrence of a subject distance not being able to be measured, a multiple measurement type distance measuring unit is known in which subjects contained in a plurality of light receiving areas an be measured.", "\nHowever, in a conventional multiple measurement type distance measuring apparatus, the angle of view, i.e., the number of light receiving elements of each line sensor that are used to measure the subject distance for each light receiving area is fixed. ", "If the angle of view is large, i.e., the number of light receiving elements in each light receiving area is large, the subject can be measured in a wide range. ", "Accordingly, the probability that no subject distance can be measured for a subject having a low contrast can be reduced, but the probability that images of subjects at a close distance and at a far distance coexist in a common light receiving area is increased. ", "Conversely if the angle of view is small, i.e., the number of light receiving elements in each light receiving area is small the probability that images of subjects at a close distance and at a far distance coexist in a common light receiving area is reduced, but the subject is measured in a narrow range, and accordingly, the probability that no subject distance can be measured for a subject having a low contrast is increased.", "\nAlso, in the known multiple measurement type distance measuring apparatus mentioned above, one measurement which meets predetermined requirements is selected from a number of measurements. ", "In an apparatus of this type, the reliability and validity of the measurements are judged relying only upon a single predetermined reference level (judgement level). ", "Namely, if the reference level (judgement level) is high, reliability is increased, but the probability that the measurements do not meet the high reference level increases. ", "Hence, there is likely to be a condition such that no subject distance can be measured. ", "Conversely, if the reference level is low, reliability is reduced, thus resulting in an increase in the occurrence of incorrect measurements.", "\nMoreover, in conventional cameras, it is necessary to measure rays of light at a plurality of light receiving areas in order to judge whether there is a backlit state, through the functions of the camera. ", "To this end, it is necessary to provide a plurality of photosensors which detect rays in the light receiving areas or to use a split-type photosensor." ]	{ "pile_set_name": "USPTO Backgrounds" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0.0023584905660377358, 0, 0.002457002457002457, 0.0031446540880503146, 0.006060606060606061, 0.006024096385542169, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.004219409282700422, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	0.000458	5
[ "The analgesic effect of crossing the arms.", "\nThe ability to determine precisely the location of sensory stimuli is fundamental to how we interact with the world; indeed, to our survival. ", "Crossing the hands over the body midline impairs this ability to localize tactile stimuli. ", "We hypothesized that crossing the arms would modulate the intensity of pain evoked by noxious stimulation of the hand. ", "In two separate experiments, we show (1) that the intensity of both laser-evoked painful sensations and electrically-evoked nonpainful sensations were decreased when the arms were crossed over the midline, and (2) that these effects were associated with changes in the multimodal cortical processing of somatosensory information. ", "Critically, there was no change in the somatosensory-specific cortical processing of somatosensory information. ", "Besides studies showing relief of phantom limb pain using mirrors, this is the first evidence that impeding the processes by which the brain localises a noxious stimulus can reduce pain, and that this effect reflects modulation of multimodal neural activities. ", "By showing that the neural mechanisms by which pain emerges from nociception represent a possible target for analgesia, we raise the possibility of novel approaches to the treatment of painful clinical conditions. ", "Crossing the arms over the midline impairs multimodal processing of somatosensory stimuli and induces significant analgesia to noxious hand stimulation." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	0	5
[ "/! ", "Responsive 2.0.2\n 2014-2016 SpryMedia Ltd - datatables.net/license\n /\n\n/\n @summary Responsive\n * @description Responsive tables plug-in for DataTables\n * @version 2.0.2\n * @file dataTables.responsive.js\n * @author SpryMedia Ltd (www.sprymedia.co.uk)\n * @contact www.sprymedia.co.uk/contact\n * @copyright Copyright 2014-2016 SpryMedia Ltd.\n \n This source file is free software, available under the following license:\n * MIT license - http://datatables.net/license/mit\n \n This source file is distributed in the hope that it will be useful, but\n * WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY\n * or FITNESS FOR A PARTICULAR PURPOSE. ", "See the license files for details.", "\n \n For details please refer to: http://www.datatables.net\n /\n(function( factory ){\n\tif ( typeof define === 'function' && define.amd ) {\n\t\t// AMD\n\t\tdefine( ['jquery', 'datatables.net'], function ( $ ) {\n\t\t\treturn factory( $, window, document );\n\t\t} );\n\t}\n\telse if ( typeof exports === 'object' ) {\n\t\t// CommonJS\n\t\tmodule.exports = function (root, $) {\n\t\t\tif ( ! ", "root ) {\n\t\t\t\troot = window;\n\t\t\t}\n\n\t\t\tif ( ! ", "$ \|\| ! ", "$.fn.dataTable ) {\n\t\t\t\t$ = require('datatables.net')(root, $).$;\n\t\t\t}\n\n\t\t\treturn factory( $, root, root.document );\n\t\t};\n\t}\n\telse {\n\t\t// Browser\n\t\tfactory( jQuery, window, document );\n\t}\n}(function( $, window, document, undefined ) {\n'use strict';\nvar DataTable = $.fn.dataTable;\n\n\n/\n Responsive is a plug-in for the DataTables library that makes use of\n * DataTables' ability to change the visibility of columns, changing the\n * visibility of columns so the displayed columns fit into the table container.", "\n * The end result is that complex tables will be dynamically adjusted to fit\n * into the viewport, be it on a desktop, tablet or mobile browser.", "\n \n Responsive for DataTables has two modes of operation, which can used\n * individually or combined:\n \n * Class name based control - columns assigned class names that match the\n * breakpoint logic can be shown / hidden as required for each breakpoint.", "\n * * Automatic control - columns are automatically hidden when there is no\n * room left to display them. ", "Columns removed from the right.", "\n \n In additional to column visibility control, Responsive also has built into\n * options to use DataTables' child row display to show / hide the information\n * from the table that has been hidden. ", "There are also two modes of operation\n * for this child row display:\n \n * Inline - when the control element that the user can use to show / hide\n * child rows is displayed inside the first column of the table.", "\n * * Column - where a whole column is dedicated to be the show / hide control.", "\n \n Initialisation of Responsive is performed by:\n \n * Adding the class `responsive` or `dt-responsive` to the table. ", "In this case\n * Responsive will automatically be initialised with the default configuration\n * options when the DataTable is created.", "\n * * Using the `responsive` option in the DataTables configuration options. ", "This\n * can also be used to specify the configuration options, or simply set to\n * `true` to use the defaults.", "\n \n @class\n * @param {object} settings DataTables settings object for the host table\n * @param {object} [opts] Configuration options\n * @requires jQuery 1.7+\n * @requires DataTables 1.10.3+\n \n @example\n * $('#example').DataTable( {\n * responsive: true\n * } );\n * } );\n /\nvar Responsive = function ( settings, opts ) {\n\t// Sanity check that we are using DataTables 1.10 or newer\n\tif ( ! ", "DataTable.versionCheck \|\| ! ", "DataTable.versionCheck( '1.10.3' ) ) {\n\t\tthrow 'DataTables Responsive requires DataTables 1.10.3 or newer';\n\t}\n\n\tthis.s = {\n\t\tdt: new DataTable.", "Api( settings ),\n\t\tcolumns: [],\n\t\tcurrent: []\n\t};\n\n\t// Check if responsive has already been initialised on this table\n\tif ( this.s.dt.settings()[0].responsive ) {\n\t\treturn;\n\t}\n\n\t// details is an object, but for simplicity the user can give it as a string\n\t// or a boolean\n\tif ( opts && typeof opts.details === 'string' ) {\n\t\topts.details = { type: opts.details };\n\t}\n\telse if ( opts && opts.details === false ) {\n\t\topts.details = { type: false };\n\t}\n\telse if ( opts && opts.details === true ) {\n\t\topts.details = { type: 'inline' };\n\t}\n\n\tthis.c = $.extend( true, {}, Responsive.defaults, DataTable.defaults.responsive, opts );\n\tsettings.responsive = this;\n\tthis._constructor();\n};\n\n$.extend( Responsive.prototype, {\n\t/ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * \n\t Constructor\n\t /\n\n\t/\n\t Initialise the Responsive instance\n\t \n\t @private\n\t /\n\t_constructor: function ()\n\t{\n\t\tvar that = this;\n\t\tvar dt = this.s.dt;\n\t\tvar dtPrivateSettings = dt.settings()[0];\n\t\tvar oldWindowWidth = $(window).width();\n\n\t\tdt.settings()[0]._responsive = this;\n\n\t\t// Use DataTables' throttle function to avoid processor thrashing on\n\t\t// resize\n\t\t$(window).on( 'resize.dtr orientationchange.dtr', DataTable.util.throttle( function () {\n\t\t\t// iOS has a bug whereby resize can fire when only scrolling\n\t\t\t// See: http://stackoverflow.com/questions/8898412\n\t\t\tvar width = $(window).width();\n\n\t\t\tif ( width !", "== oldWindowWidth ) {\n\t\t\t\tthat._resize();\n\t\t\t\toldWindowWidth = width;\n\t\t\t}\n\t\t} ) );\n\n\t\t// DataTables doesn't currently trigger an event when a row is added, so\n\t\t// we need to hook into its private API to enforce the hidden rows when\n\t\t// new data is added\n\t\tdtPrivateSettings.oApi._fnCallbackReg( dtPrivateSettings, 'aoRowCreatedCallback', function (tr, data, idx) {\n\t\t\tif ( $.inArray( false, that.s.current ) !", "== -1 ) {\n\t\t\t\t$('td, th', tr).each( function ( i ) {\n\t\t\t\t\tvar idx = dt.column.index( 'toData', i );\n\n\t\t\t\t\tif ( that.s.current[idx] === false ) {\n\t\t\t\t\t\t$(this).css('display', 'none');\n\t\t\t\t\t}\n\t\t\t\t} );\n\t\t\t}\n\t\t} );\n\n\t\t// Destroy event handler\n\t\tdt.on( 'destroy.dtr', function () {\n\t\t\tdt.off( '.dtr' );\n\t\t\t$( dt.table().body() ).off( '.dtr' );\n\t\t\t$(window).off( 'resize.dtr orientationchange.dtr' );\n\n\t\t\t// Restore the columns that we've hidden\n\t\t\t$.each( that.s.current, function ( i, val ) {\n\t\t\t\tif ( val === false ) {\n\t\t\t\t\tthat._setColumnVis( i, true );\n\t\t\t\t}\n\t\t\t} );\n\t\t} );\n\n\t\t// Reorder the breakpoints array here in case they have been added out\n\t\t// of order\n\t\tthis.c.breakpoints.sort( function (a, b) {\n\t\t\treturn a.width < b.width ? ", "1 :\n\t\t\t\ta.width > b.width ? ", "-1 : 0;\n\t\t} );\n\n\t\tthis._classLogic();\n\t\tthis._resizeAuto();\n\n\t\t// Details handler\n\t\tvar details = this.c.details;\n\n\t\tif ( details.type !", "== false ) {\n\t\t\tthat._detailsInit();\n\n\t\t\t// DataTables will trigger this event on every column it shows and\n\t\t\t// hides individually\n\t\t\tdt.on( 'column-visibility.dtr', function (e, ctx, col, vis) {\n\t\t\t\tthat._classLogic();\n\t\t\t\tthat._resizeAuto();\n\t\t\t\tthat._resize();\n\t\t\t} );\n\n\t\t\t// Redraw the details box on each draw which will happen if the data\n\t\t\t// has changed. ", "This is used until DataTables implements a native\n\t\t\t// `updated` event for rows\n\t\t\tdt.on( 'draw.dtr', function () {\n\t\t\t\tthat._redrawChildren();\n\t\t\t} );\n\n\t\t\t$(dt.table().node()).addClass( 'dtr-'+details.type );\n\t\t}\n\n\t\tdt.on( 'column-reorder.dtr', function (e, settings, details) {\n\t\t\tthat._classLogic();\n\t\t\tthat._resizeAuto();\n\t\t\tthat._resize();\n\t\t} );\n\n\t\t// Change in column sizes means we need to calc\n\t\tdt.on( 'column-sizing.dtr', function () {\n\t\t\tthat._resize();\n\t\t});\n\n\t\tdt.on( 'init.dtr', function (e, settings, details) {\n\t\t\tthat._resizeAuto();\n\t\t\tthat._resize();\n\n\t\t\t// If columns were hidden, then DataTables needs to adjust the\n\t\t\t// column sizing\n\t\t\tif ( $.inArray( false, that.s.current ) ) {\n\t\t\t\tdt.columns.adjust();\n\t\t\t}\n\t\t} );\n\n\t\t// First pass - draw the table for the current viewport size\n\t\tthis._resize();\n\t},\n\n\n\t/ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * \n\t Private methods\n\t /\n\n\t/\n\t Calculate the visibility for the columns in a table for a given\n\t * breakpoint. ", "The result is pre-determined based on the class logic if\n\t * class names are used to control all columns, but the width of the table\n\t * is also used if there are columns which are to be automatically shown\n\t * and hidden.", "\n\t \n\t @param {string} breakpoint Breakpoint name to use for the calculation\n\t * @return {array} Array of boolean values initiating the visibility of each\n\t * column.", "\n\t * @private\n\t /\n\t_columnsVisiblity: function ( breakpoint )\n\t{\n\t\tvar dt = this.s.dt;\n\t\tvar columns = this.s.columns;\n\t\tvar i, ien;\n\n\t\t// Create an array that defines the column ordering based first on the\n\t\t// column's priority, and secondly the column index. ", "This allows the\n\t\t// columns to be removed from the right if the priority matches\n\t\tvar order = columns\n\t\t\t.map( function ( col, idx ) {\n\t\t\t\treturn {\n\t\t\t\t\tcolumnIdx: idx,\n\t\t\t\t\tpriority: col.priority\n\t\t\t\t};\n\t\t\t} )\n\t\t\t.sort( function ( a, b ) {\n\t\t\t\tif ( a.priority !", "== b.priority ) {\n\t\t\t\t\treturn a.priority - b.priority;\n\t\t\t\t}\n\t\t\t\treturn a.columnIdx - b.columnIdx;\n\t\t\t} );\n\n\t\t// Class logic - determine which columns are in this breakpoint based\n\t\t// on the classes. ", "If no class control (i.e. `auto`) then `-` is used\n\t\t// to indicate this to the rest of the function\n\t\tvar display = $.map( columns, function ( col ) {\n\t\t\treturn col.auto && col.minWidth === null ?", "\n\t\t\t\tfalse :\n\t\t\t\tcol.auto === true ?", "\n\t\t\t\t\t'-' :\n\t\t\t\t\t$.inArray( breakpoint, col.includeIn ) !", "== -1;\n\t\t} );\n\n\t\t// Auto column control - first pass: how much width is taken by the\n\t\t// ones that must be included from the non-auto columns\n\t\tvar requiredWidth = 0;\n\t\tfor ( i=0, ien=display.length ; i<ien ; i++ ) {\n\t\t\tif ( display[i] === true ) {\n\t\t\t\trequiredWidth += columns[i].minWidth;\n\t\t\t}\n\t\t}\n\n\t\t// Second pass, use up any remaining width for other columns. ", "For\n\t\t// scrolling tables we need to subtract the width of the scrollbar. ", "It\n\t\t// may not be requires which makes this sub-optimal, but it would\n\t\t// require another full redraw to make complete use of those extra few\n\t\t// pixels\n\t\tvar scrolling = dt.settings()[0].oScroll;\n\t\tvar bar = scrolling.sY \|\| scrolling.sX ? ", "scrolling.iBarWidth : 0;\n\t\tvar widthAvailable = dt.table().container().offsetWidth - bar;\n\t\tvar usedWidth = widthAvailable - requiredWidth;\n\n\t\t// Control column needs to always be included. ", "This makes it sub-\n\t\t// optimal in terms of using the available with, but to stop layout\n\t\t// thrashing or overflow. ", "Also we need to account for the control column\n\t\t// width first so we know how much width is available for the other\n\t\t// columns, since the control column might not be the first one shown\n\t\tfor ( i=0, ien=display.length ; i<ien ; i++ ) {\n\t\t\tif ( columns[i].control ) {\n\t\t\t\tusedWidth -= columns[i].minWidth;\n\t\t\t}\n\t\t}\n\n\t\t// Allow columns to be shown (counting by priority and then right to\n\t\t// left) until we run out of room\n\t\tvar empty = false;\n\t\tfor ( i=0, ien=order.length ; i<ien ; i++ ) {\n\t\t\tvar colIdx = order[i].columnIdx;\n\n\t\t\tif ( display[colIdx] === '-' && ! ", "columns[colIdx].control && columns[colIdx].minWidth ) {\n\t\t\t\t// Once we've found a column that won't fit we don't let any\n\t\t\t\t// others display either, or columns might disappear in the\n\t\t\t\t// middle of the table\n\t\t\t\tif ( empty \|\| usedWidth - columns[colIdx].minWidth < 0 ) {\n\t\t\t\t\tempty = true;\n\t\t\t\t\tdisplay[colIdx] = false;\n\t\t\t\t}\n\t\t\t\telse {\n\t\t\t\t\tdisplay[colIdx] = true;\n\t\t\t\t}\n\n\t\t\t\tusedWidth -= columns[colIdx].minWidth;\n\t\t\t}\n\t\t}\n\n\t\t// Determine if the 'control' column should be shown (if there is one).", "\n\t\t// This is the case when there is a hidden column (that is not the\n\t\t// control column). ", "The two loops look inefficient here, but they are\n\t\t// trivial and will fly through. ", "We need to know the outcome from the\n\t\t// first , before the action in the second can be taken\n\t\tvar showControl = false;\n\n\t\tfor ( i=0, ien=columns.length ; i<ien ; i++ ) {\n\t\t\tif ( ! ", "columns[i].control && ! ", "columns[i].never && ! ", "display[i] ) {\n\t\t\t\tshowControl = true;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\t\tfor ( i=0, ien=columns.length ; i<ien ; i++ ) {\n\t\t\tif ( columns[i].control ) {\n\t\t\t\tdisplay[i] = showControl;\n\t\t\t}\n\t\t}\n\n\t\t// Finally we need to make sure that there is at least one column that\n\t\t// is visible\n\t\tif ( $.inArray( true, display ) === -1 ) {\n\t\t\tdisplay[0] = true;\n\t\t}\n\n\t\treturn display;\n\t},\n\n\n\t/\n\t Create the internal `columns` array with information about the columns\n\t * for the table. ", "This includes determining which breakpoints the column\n\t * will appear in, based upon class names in the column, which makes up the\n\t * vast majority of this method.", "\n\t \n\t @private\n\t /\n\t_classLogic: function ()\n\t{\n\t\tvar that = this;\n\t\tvar calc = {};\n\t\tvar breakpoints = this.c.breakpoints;\n\t\tvar dt = this.s.dt;\n\t\tvar columns = dt.columns().eq(0).map( function (i) {\n\t\t\tvar column = this.column(i);\n\t\t\tvar className = column.header().className;\n\t\t\tvar priority = dt.settings()[0].aoColumns[i].responsivePriority;\n\n\t\t\tif ( priority === undefined ) {\n\t\t\t\tvar dataPriority = $(column.header()).data('priority');\n\n\t\t\t\tpriority = dataPriority !", "== undefined ?", "\n\t\t\t\t\tdataPriority 1 :\n\t\t\t\t\t10000;\n\t\t\t}\n\n\t\t\treturn {\n\t\t\t\tclassName: className,\n\t\t\t\tincludeIn: [],\n\t\t\t\tauto: false,\n\t\t\t\tcontrol: false,\n\t\t\t\tnever: className.match(/\\bnever\\b/) ? ", "true : false,\n\t\t\t\tpriority: priority\n\t\t\t};\n\t\t} );\n\n\t\t// Simply add a breakpoint to `includeIn` array, ensuring that there are\n\t\t// no duplicates\n\t\tvar add = function ( colIdx, name ) {\n\t\t\tvar includeIn = columns[ colIdx ].includeIn;\n\n\t\t\tif ( $.inArray( name, includeIn ) === -1 ) {\n\t\t\t\tincludeIn.push( name );\n\t\t\t}\n\t\t};\n\n\t\tvar column = function ( colIdx, name, operator, matched ) {\n\t\t\tvar size, i, ien;\n\n\t\t\tif ( ! ", "operator ) {\n\t\t\t\tcolumns[ colIdx ].includeIn.push( name );\n\t\t\t}\n\t\t\telse if ( operator === 'max-' ) {\n\t\t\t\t// Add this breakpoint and all smaller\n\t\t\t\tsize = that._find( name ).width;\n\n\t\t\t\tfor ( i=0, ien=breakpoints.length ; i<ien ; i++ ) {\n\t\t\t\t\tif ( breakpoints[i].width <= size ) {\n\t\t\t\t\t\tadd( colIdx, breakpoints[i].name );\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t\telse if ( operator === 'min-' ) {\n\t\t\t\t// Add this breakpoint and all larger\n\t\t\t\tsize = that._find( name ).width;\n\n\t\t\t\tfor ( i=0, ien=breakpoints.length ; i<ien ; i++ ) {\n\t\t\t\t\tif ( breakpoints[i].width >= size ) {\n\t\t\t\t\t\tadd( colIdx, breakpoints[i].name );\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t\telse if ( operator === 'not-' ) {\n\t\t\t\t// Add all but this breakpoint\n\t\t\t\tfor ( i=0, ien=breakpoints.length ; i<ien ; i++ ) {\n\t\t\t\t\tif ( breakpoints[i].name.indexOf( matched ) === -1 ) {\n\t\t\t\t\t\tadd( colIdx, breakpoints[i].name );\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t};\n\n\t\t// Loop over each column and determine if it has a responsive control\n\t\t// class\n\t\tcolumns.each( function ( col, i ) {\n\t\t\tvar classNames = col.className.split(' ');\n\t\t\tvar hasClass = false;\n\n\t\t\t// Split the class name up so multiple rules can be applied if needed\n\t\t\tfor ( var k=0, ken=classNames.length ; k<ken ; k++ ) {\n\t\t\t\tvar className = $.trim( classNames[k] );\n\n\t\t\t\tif ( className === 'all' ) {\n\t\t\t\t\t// Include in all\n\t\t\t\t\thasClass = true;\n\t\t\t\t\tcol.includeIn = $.map( breakpoints, function (a) {\n\t\t\t\t\t\treturn a.name;\n\t\t\t\t\t} );\n\t\t\t\t\treturn;\n\t\t\t\t}\n\t\t\t\telse if ( className === 'none' \|\| col.never ) {\n\t\t\t\t\t// Include in none (default) and no auto\n\t\t\t\t\thasClass = true;\n\t\t\t\t\treturn;\n\t\t\t\t}\n\t\t\t\telse if ( className === 'control' ) {\n\t\t\t\t\t// Special column that is only visible, when one of the other\n\t\t\t\t\t// columns is hidden. ", "This is used for the details control\n\t\t\t\t\thasClass = true;\n\t\t\t\t\tcol.control = true;\n\t\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\t\t$.each( breakpoints, function ( j, breakpoint ) {\n\t\t\t\t\t// Does this column have a class that matches this breakpoint?", "\n\t\t\t\t\tvar brokenPoint = breakpoint.name.split('-');\n\t\t\t\t\tvar re = new RegExp( '(min\\\\-\|max\\\\-\|not\\\\-)?('+brokenPoint[0]+')(\\\\-[_a-zA-Z0-9])?' );", "\n\t\t\t\t\tvar match = className.match( re );\n\n\t\t\t\t\tif ( match ) {\n\t\t\t\t\t\thasClass = true;\n\n\t\t\t\t\t\tif ( match[2] === brokenPoint[0] && match[3] === '-'+brokenPoint[1] ) {\n\t\t\t\t\t\t\t// Class name matches breakpoint name fully\n\t\t\t\t\t\t\tcolumn( i, breakpoint.name, match[1], match[2]+match[3] );\n\t\t\t\t\t\t}\n\t\t\t\t\t\telse if ( match[2] === brokenPoint[0] && ! ", "match[3] ) {\n\t\t\t\t\t\t\t// Class name matched primary breakpoint name with no qualifier\n\t\t\t\t\t\t\tcolumn( i, breakpoint.name, match[1], match[2] );\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t} );\n\t\t\t}\n\n\t\t\t// If there was no control class, then automatic sizing is used\n\t\t\tif ( ! ", "hasClass ) {\n\t\t\t\tcol.auto = true;\n\t\t\t}\n\t\t} );\n\n\t\tthis.s.columns = columns;\n\t},\n\n\n\t/*\n\t Show the details for the child row\n\t \n\t @param {DataTables.", "Api} row API instance for the row\n\t * @param {boolean} update Update flag\n\t * @private\n\t /\n\t_detailsDisplay: function ( row, update )\n\t{\n\t\tvar that = this;\n\t\tvar dt = this.s.dt;\n\t\tvar details = this.c.details;\n\n\t\tif ( details && details.type ) {\n\t\t\tvar res = details.display( row, update, function () {\n\t\t\t\treturn details.renderer(\n\t\t\t\t\tdt, row[0], that._detailsObj(row[0])\n\t\t\t\t);\n\t\t\t} );\n\n\t\t\tif ( res === true \|\| res === false ) {\n\t\t\t\t$(dt.table().node()).triggerHandler( 'responsive-display.dt', [dt, row, res, update] );\n\t\t\t}\n\t\t}\n\t},\n\n\n\t/\n\t Initialisation for the details handler\n\t \n\t @private\n\t /\n\t_detailsInit: function ()\n\t{\n\t\tvar that = this;\n\t\tvar dt = this.s.dt;\n\t\tvar details = this.c.details;\n\n\t\t// The inline type always uses the first child as the target\n\t\tif ( details.type === 'inline' ) {\n\t\t\tdetails.target = 'td:first-child, th:first-child';\n\t\t}\n\n\t\t// Keyboard accessibility\n\t\tdt.on( 'draw.dtr', function () {\n\t\t\tthat._tabIndexes();\n\t\t} );\n\t\tthat._tabIndexes(); // Initial draw has already happened\n\n\t\t$( dt.table().body() ).on( 'keyup.dtr', 'td, th', function (e) {\n\t\t\tif ( e.keyCode === 13 && $(this).data('dtr-keyboard') ) {\n\t\t\t\t$(this).click();\n\t\t\t}\n\t\t} );\n\n\t\t// type.target can be a string jQuery selector or a column index\n\t\tvar target = details.target;\n\t\tvar selector = typeof target === 'string' ? ", "target : 'td, th';\n\n\t\t// Click handler to show / hide the details rows when they are available\n\t\t$( dt.table().body() )\n\t\t\t.on( 'click.dtr mousedown.dtr mouseup.dtr', selector, function (e) {\n\t\t\t\t// If the table is not collapsed (i.e. there is no hidden columns)\n\t\t\t\t// then take no action\n\t\t\t\tif ( ! ", "$(dt.table().node()).hasClass('collapsed' ) ) {\n\t\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\t\t// Check that the row is actually a DataTable's controlled node\n\t\t\t\tif ( ! ", "dt.row( $(this).closest('tr') ).length ) {\n\t\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\t\t// For column index, we determine if we should act or not in the\n\t\t\t\t// handler - otherwise it is already okay\n\t\t\t\tif ( typeof target === 'number' ) {\n\t\t\t\t\tvar targetIdx = target < 0 ?", "\n\t\t\t\t\t\tdt.columns().eq(0).length + target :\n\t\t\t\t\t\ttarget;\n\n\t\t\t\t\tif ( dt.cell( this ).index().column !", "== targetIdx ) {\n\t\t\t\t\t\treturn;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t\t// $().closest() includes itself in its check\n\t\t\t\tvar row = dt.row( $(this).closest('tr') );\n\n\t\t\t\t// Check event type to do an action\n\t\t\t\tif ( e.type === 'click' ) {\n\t\t\t\t\t// The renderer is given as a function so the caller can execute it\n\t\t\t\t\t// only when they need (i.e. if hiding there is no point is running\n\t\t\t\t\t// the renderer)\n\t\t\t\t\tthat._detailsDisplay( row, false );\n\t\t\t\t}\n\t\t\t\telse if ( e.type === 'mousedown' ) {\n\t\t\t\t\t// For mouse users, prevent the focus ring from showing\n\t\t\t\t\t$(this).css('outline', 'none');\n\t\t\t\t}\n\t\t\t\telse if ( e.type === 'mouseup' ) {\n\t\t\t\t\t// And then re-allow at the end of the click\n\t\t\t\t\t$(this).blur().css('outline', '');\n\t\t\t\t}\n\t\t\t} );\n\t},\n\n\n\t/\n\t Get the details to pass to a renderer for a row\n\t * @param {int} rowIdx Row index\n\t * @private\n\t /\n\t_detailsObj: function ( rowIdx )\n\t{\n\t\tvar that = this;\n\t\tvar dt = this.s.dt;\n\n\t\treturn $.map( this.s.columns, function( col, i ) {\n\t\t\tif ( col.never ) {\n\t\t\t\treturn;\n\t\t\t}\n\n\t\t\treturn {\n\t\t\t\ttitle: dt.settings()[0].aoColumns[ i ].sTitle,\n\t\t\t\tdata: dt.cell( rowIdx, i ).render( that.c.orthogonal ),\n\t\t\t\thidden: dt.column( i ).visible() && !", "that.s.current[ i ],\n\t\t\t\tcolumnIndex: i,\n\t\t\t\trowIndex: rowIdx\n\t\t\t};\n\t\t} );\n\t},\n\n\n\t/\n\t Find a breakpoint object from a name\n\t \n\t @param {string} name Breakpoint name to find\n\t * @return {object} Breakpoint description object\n\t * @private\n\t /\n\t_find: function ( name )\n\t{\n\t\tvar breakpoints = this.c.breakpoints;\n\n\t\tfor ( var i=0, ien=breakpoints.length ; i<ien ; i++ ) {\n\t\t\tif ( breakpoints[i].name === name ) {\n\t\t\t\treturn breakpoints[i];\n\t\t\t}\n\t\t}\n\t},\n\n\n\t/\n\t Re-create the contents of the child rows as the display has changed in\n\t * some way.", "\n\t \n\t @private\n\t /\n\t_redrawChildren: function ()\n\t{\n\t\tvar that = this;\n\t\tvar dt = this.s.dt;\n\n\t\tdt.rows( {page: 'current'} ).iterator( 'row', function ( settings, idx ) {\n\t\t\tvar row = dt.row( idx );\n\n\t\t\tthat._detailsDisplay( dt.row( idx ), true );\n\t\t} );\n\t},\n\n\n\t/\n\t Alter the table display for a resized viewport. ", "This involves first\n\t * determining what breakpoint the window currently is in, getting the\n\t * column visibilities to apply and then setting them.", "\n\t \n\t @private\n\t /\n\t_resize: function ()\n\t{\n\t\tvar that = this;\n\t\tvar dt = this.s.dt;\n\t\tvar width = $(window).width();\n\t\tvar breakpoints = this.c.breakpoints;\n\t\tvar breakpoint = breakpoints[0].name;\n\t\tvar columns = this.s.columns;\n\t\tvar i, ien;\n\t\tvar oldVis = this.s.current.slice();\n\n\t\t// Determine what breakpoint we are currently at\n\t\tfor ( i=breakpoints.length-1 ; i>=0 ; i-- ) {\n\t\t\tif ( width <= breakpoints[i].width ) {\n\t\t\t\tbreakpoint = breakpoints[i].name;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t\t\n\t\t// Show the columns for that break point\n\t\tvar columnsVis = this._columnsVisiblity( breakpoint );\n\t\tthis.s.current = columnsVis;\n\n\t\t// Set the class before the column visibility is changed so event\n\t\t// listeners know what the state is. ", "Need to determine if there are\n\t\t// any columns that are not visible but can be shown\n\t\tvar collapsedClass = false;\n\t\tfor ( i=0, ien=columns.length ; i<ien ; i++ ) {\n\t\t\tif ( columnsVis[i] === false && ! ", "columns[i].never && ! ", "columns[i].control ) {\n\t\t\t\tcollapsedClass = true;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\t\t$( dt.table().node() ).toggleClass( 'collapsed', collapsedClass );\n\n\t\tvar changed = false;\n\n\t\tdt.columns().eq(0).each( function ( colIdx, i ) {\n\t\t\tif ( columnsVis[i] !", "== oldVis[i] ) {\n\t\t\t\tchanged = true;\n\t\t\t\tthat._setColumnVis( colIdx, columnsVis[i] );\n\t\t\t}\n\t\t} );\n\n\t\tif ( changed ) {\n\t\t\tthis._redrawChildren();\n\n\t\t\t// Inform listeners of the change\n\t\t\t$(dt.table().node()).trigger( 'responsive-resize.dt', [dt, this.s.current] );\n\t\t}\n\t},\n\n\n\t/\n\t Determine the width of each column in the table so the auto column hiding\n\t * has that information to work with. ", "This method is never going to be 100%\n\t * perfect since column widths can change slightly per page, but without\n\t * seriously compromising performance this is quite effective.", "\n\t \n\t @private\n\t /\n\t_resizeAuto: function ()\n\t{\n\t\tvar dt = this.s.dt;\n\t\tvar columns = this.s.columns;\n\n\t\t// Are we allowed to do auto sizing?", "\n\t\tif ( ! ", "this.c.auto ) {\n\t\t\treturn;\n\t\t}\n\n\t\t// Are there any columns that actually need auto-sizing, or do they all\n\t\t// have classes defined\n\t\tif ( $.inArray( true, $.map( columns, function (c) { return c.auto; } ) ) === -1 ) {\n\t\t\treturn;\n\t\t}\n\n\t\t// Clone the table with the current data in it\n\t\tvar tableWidth = dt.table().node().offsetWidth;\n\t\tvar columnWidths = dt.columns;\n\t\tvar clonedTable = dt.table().node().cloneNode( false );\n\t\tvar clonedHeader = $( dt.table().header().cloneNode( false ) ).appendTo( clonedTable );\n\t\tvar clonedBody = $( dt.table().body() ).clone( false, false ).empty().appendTo( clonedTable ); // use jQuery because of IE8\n\n\t\t// Header\n\t\tvar headerCells = dt.columns()\n\t\t\t.header()\n\t\t\t.filter( function (idx) {\n\t\t\t\treturn dt.column(idx).visible();\n\t\t\t} )\n\t\t\t.to$()\n\t\t\t.clone( false )\n\t\t\t.css( 'display', 'table-cell' );\n\n\t\t// Body rows - we don't need to take account of DataTables' column\n\t\t// visibility since we implement our own here (hence the `display` set)\n\t\t$(clonedBody)\n\t\t\t.append( $(dt.rows( { page: 'current' } ).nodes()).clone( false ) )\n\t\t\t.find( 'th, td' ).css( 'display', '' );\n\n\t\t// Footer\n\t\tvar footer = dt.table().footer();\n\t\tif ( footer ) {\n\t\t\tvar clonedFooter = $( footer.cloneNode( false ) ).appendTo( clonedTable );\n\t\t\tvar footerCells = dt.columns()\n\t\t\t\t.header()\n\t\t\t\t.filter( function (idx) {\n\t\t\t\t\treturn dt.column(idx).visible();\n\t\t\t\t} )\n\t\t\t\t.to$()\n\t\t\t\t.clone( false )\n\t\t\t\t.css( 'display', 'table-cell' );\n\n\t\t\t$('<tr/>')\n\t\t\t\t.append( footerCells )\n\t\t\t\t.appendTo( clonedFooter );\n\t\t}\n\n\t\t$('<tr/>')\n\t\t\t.append( headerCells )\n\t\t\t.appendTo( clonedHeader );\n\n\t\t// In the inline case extra padding is applied to the first column to\n\t\t// give space for the show / hide icon. ", "We need to use this in the\n\t\t// calculation\n\t\tif ( this.c.details.type === 'inline' ) {\n\t\t\t$(clonedTable).addClass( 'dtr-inline collapsed' );\n\t\t}\n\n\t\tvar inserted = $('<div/>')\n\t\t\t.css( {\n\t\t\t\twidth: 1,\n\t\t\t\theight: 1,\n\t\t\t\toverflow: 'hidden'\n\t\t\t} )\n\t\t\t.append( clonedTable );\n\n\t\tinserted.insertBefore( dt.table().node() );\n\n\t\t// The cloned header now contains the smallest that each column can be\n\t\theaderCells.each( function (i) {\n\t\t\tvar idx = dt.column.index( 'fromVisible', i );\n\t\t\tcolumns[ idx ].minWidth = this.offsetWidth \|\| 0;\n\t\t} );\n\n\t\tinserted.remove();\n\t},\n\n\t/\n\t Set a column's visibility.", "\n\t \n\t We don't use DataTables' column visibility controls in order to ensure\n\t * that column visibility can Responsive can no-exist. ", "Since only IE8+ is\n\t * supported (and all evergreen browsers of course) the control of the\n\t * display attribute works well.", "\n\t \n\t @param {integer} col Column index\n\t * @param {boolean} showHide Show or hide (true or false)\n\t * @private\n\t /\n\t_setColumnVis: function ( col, showHide )\n\t{\n\t\tvar dt = this.s.dt;\n\t\tvar display = showHide ? '' : '", "none'; // empty string will remove the attr\n\n\t\t$( dt.column( col ).header() ).css( 'display', display );\n\t\t$( dt.column( col ).footer() ).css( 'display', display );\n\t\tdt.column( col ).nodes().to$().css( 'display', display );\n\t},\n\n\n\t/\n\t Update the cell tab indexes for keyboard accessibility. ", "This is called on\n\t * every table draw - that is potentially inefficient, but also the least\n\t * complex option given that column visibility can change on the fly. ", "Its a\n\t * shame user-focus was removed from CSS 3 UI, as it would have solved this\n\t * issue with a single CSS statement.", "\n\t \n\t @private\n\t /\n\t_tabIndexes: function ()\n\t{\n\t\tvar dt = this.s.dt;\n\t\tvar cells = dt.cells( { page: 'current' } ).nodes().to$();\n\t\tvar ctx = dt.settings()[0];\n\t\tvar target = this.c.details.target;\n\n\t\tcells.filter( '[data-dtr-keyboard]' ).removeData( '[data-dtr-keyboard]' );\n\n\t\tvar selector = typeof target === 'number' ?", "\n\t\t\t':eq('+target+')' :\n\t\t\ttarget;\n\n\t\t$( selector, dt.rows( { page: 'current' } ).nodes() )\n\t\t\t.attr( 'tabIndex', ctx.iTabIndex )\n\t\t\t.data( 'dtr-keyboard', 1 );\n\t}\n} );\n\n\n/\n List of default breakpoints. ", "Each item in the array is an object with two\n * properties:\n \n * `name` - the breakpoint name.", "\n * * `width` - the breakpoint width\n \n @name Responsive.breakpoints\n * @static\n /\nResponsive.breakpoints = [\n\t{ name: 'desktop', width: Infinity },\n\t{ name: 'tablet-l', width: 1024 },\n\t{ name: 'tablet-p', width: 768 },\n\t{ name: 'mobile-l', width: 480 },\n\t{ name: 'mobile-p', width: 320 }\n];\n\n\n/\n Display methods - functions which define how the hidden data should be shown\n * in the table.", "\n \n @namespace\n * @name Responsive.defaults\n * @static\n /\nResponsive.display = {\n\tchildRow: function ( row, update, render ) {\n\t\tif ( update ) {\n\t\t\tif ( $(row.node()).hasClass('parent') ) {\n\t\t\t\trow.child( render(), 'child' ).show();\n\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t\telse {\n\t\t\tif ( ! ", "row.child.isShown() ) {\n\t\t\t\trow.child( render(), 'child' ).show();\n\t\t\t\t$( row.node() ).addClass( 'parent' );\n\n\t\t\t\treturn true;\n\t\t\t}\n\t\t\telse {\n\t\t\t\trow.child( false );\n\t\t\t\t$( row.node() ).removeClass( 'parent' );\n\n\t\t\t\treturn false;\n\t\t\t}\n\t\t}\n\t},\n\n\tchildRowImmediate: function ( row, update, render ) {\n\t\tif ( (! ", "update && row.child.isShown()) \|\| ! ", "row.responsive.hasHidden() ) {\n\t\t\t// User interaction and the row is show, or nothing to show\n\t\t\trow.child( false );\n\t\t\t$( row.node() ).removeClass( 'parent' );\n\n\t\t\treturn false;\n\t\t}\n\t\telse {\n\t\t\t// Display\n\t\t\trow.child( render(), 'child' ).show();\n\t\t\t$( row.node() ).addClass( 'parent' );\n\n\t\t\treturn true;\n\t\t}\n\t},\n\n\t// This is a wrapper so the modal options for Bootstrap and jQuery UI can\n\t// have options passed into them. ", "This specific one doesn't need to be a\n\t// function but it is for consistency in the `modal` name\n\tmodal: function ( options ) {\n\t\treturn function ( row, update, render ) {\n\t\t\tif ( ! ", "update ) {\n\t\t\t\t// Show a modal\n\t\t\t\tvar close = function () {\n\t\t\t\t\tmodal.remove(); // will tidy events for us\n\t\t\t\t\t$(document).off( 'keypress.dtr' );\n\t\t\t\t};\n\n\t\t\t\tvar modal = $('<div class=\"dtr-modal\"/>')\n\t\t\t\t\t.append( $('<div class=\"dtr-modal-display\"/>')\n\t\t\t\t\t\t.append( $('<div class=\"dtr-modal-content\"/>')\n\t\t\t\t\t\t\t.append( render() )\n\t\t\t\t\t\t)\n\t\t\t\t\t\t.append( $('<div class=\"dtr-modal-close\">×</div>' )\n\t\t\t\t\t\t\t.click( function () {\n\t\t\t\t\t\t\t\tclose();\n\t\t\t\t\t\t\t} )\n\t\t\t\t\t\t)\n\t\t\t\t\t)\n\t\t\t\t\t.append( $('<div class=\"dtr-modal-background\"/>')\n\t\t\t\t\t\t.click( function () {\n\t\t\t\t\t\t\tclose();\n\t\t\t\t\t\t} )\n\t\t\t\t\t)\n\t\t\t\t\t.appendTo( 'body' );\n\n\t\t\t\t$(document).on( 'keyup.dtr', function (e) {\n\t\t\t\t\tif ( e.keyCode === 27 ) {\n\t\t\t\t\t\te.stopPropagation();\n\n\t\t\t\t\t\tclose();\n\t\t\t\t\t}\n\t\t\t\t} );\n\t\t\t}\n\t\t\telse {\n\t\t\t\t$('div.dtr-modal-content')\n\t\t\t\t\t.empty()\n\t\t\t\t\t.append( render() );\n\t\t\t}\n\n\t\t\tif ( options && options.header ) {\n\t\t\t\t$('div.dtr-modal-content').prepend(\n\t\t\t\t\t'<h2>'+options.header( row )+'</h2>'\n\t\t\t\t);\n\t\t\t}\n\t\t};\n\t}\n};\n\n\n/\n Responsive default settings for initialisation\n \n @namespace\n * @name Responsive.defaults\n * @static\n /\nResponsive.defaults = {\n\t/\n\t List of breakpoints for the instance. ", "Note that this means that each\n\t * instance can have its own breakpoints. ", "Additionally, the breakpoints\n\t * cannot be changed once an instance has been creased.", "\n\t \n\t @type {Array}\n\t * @default Takes the value of `Responsive.breakpoints`\n\t /\n\tbreakpoints: Responsive.breakpoints,\n\n\t/\n\t Enable / disable auto hiding calculations. ", "It can help to increase\n\t * performance slightly if you disable this option, but all columns would\n\t * need to have breakpoint classes assigned to them\n\t \n\t @type {Boolean}\n\t * @default `true`\n\t /\n\tauto: true,\n\n\t/\n\t Details control. ", "If given as a string value, the `type` property of the\n\t * default object is set to that value, and the defaults used for the rest\n\t * of the object - this is for ease of implementation.", "\n\t \n\t The object consists of the following properties:\n\t \n\t * `display` - A function that is used to show and hide the hidden details\n\t * * `renderer` - function that is called for display of the child row data.", "\n\t * The default function will show the data from the hidden columns\n\t * * `target` - Used as the selector for what objects to attach the child\n\t * open / close to\n\t * * `type` - `false` to disable the details display, `inline` or `column`\n\t * for the two control types\n\t \n\t @type {Object\|string}\n\t /\n\tdetails: {\n\t\tdisplay: Responsive.display.childRow,\n\n\t\trenderer: function ( api, rowIdx, columns ) {\n\t\t\tvar data = $.map( columns, function ( col, i ) {\n\t\t\t\treturn col.hidden ?", "\n\t\t\t\t\t'<li data-dtr-index=\"'+col.columnIndex+'\" data-dt-row=\"'+col.rowIndex+'\" data-dt-column=\"'+col.columnIndex+'\">'+\n\t\t\t\t\t\t'<span class=\"dtr-title\">'+\n\t\t\t\t\t\t\tcol.title+\n\t\t\t\t\t\t'</span> '+\n\t\t\t\t\t\t'<span class=\"dtr-data\">'+\n\t\t\t\t\t\t\tcol.data+\n\t\t\t\t\t\t'</span>'+\n\t\t\t\t\t'</li>' :\n\t\t\t\t\t'';\n\t\t\t} ).join('');\n\n\t\t\treturn data ?", "\n\t\t\t\t$('<ul data-dtr-index=\"'+rowIdx+'\"/>').append( data ) :\n\t\t\t\tfalse;\n\t\t},\n\n\t\ttarget: 0,\n\n\t\ttype: 'inline'\n\t},\n\n\t/\n\t Orthogonal data request option. ", "This is used to define the data type\n\t * requested when Responsive gets the data to show in the child row.", "\n\t \n\t @type {String}\n\t /\n\torthogonal: 'display'\n};\n\n\n/\n * API\n /\nvar Api = $.fn.dataTable.", "Api;\n\n// Doesn't do anything - work around for a bug in DT... Not documented\nApi.register( 'responsive()', function () {\n\treturn this;\n} );\n\nApi.register( 'responsive.index()', function ( li ) {\n\tli = $(li);\n\n\treturn {\n\t\tcolumn: li.data('dtr-index'),\n\t\trow: li.parent().data('dtr-index')\n\t};\n} );\n\nApi.register( 'responsive.rebuild()', function () {\n\treturn this.iterator( 'table', function ( ctx ) {\n\t\tif ( ctx._responsive ) {\n\t\t\tctx._responsive._classLogic();\n\t\t}\n\t} );\n} );\n\nApi.register( 'responsive.recalc()', function () {\n\treturn this.iterator( 'table', function ( ctx ) {\n\t\tif ( ctx._responsive ) {\n\t\t\tctx._responsive._resizeAuto();\n\t\t\tctx._responsive._resize();\n\t\t}\n\t} );\n} );\n\nApi.register( 'responsive.hasHidden()', function () {\n\tvar ctx = this.context[0];\n\n\treturn ctx._responsive ?", "\n\t\t$.inArray( false, ctx._responsive.s.current ) !", "== -1 :\n\t\tfalse;\n} );\n\n\n/\n Version information\n \n @name Responsive.version\n * @static\n */\nResponsive.version = '2.0.2';\n\n\n$.fn.dataTable.", "Responsive = Responsive;\n$.fn.", "DataTable.", "Responsive = Responsive;\n\n// Attach a listener to the document which listens for DataTables initialisation\n// events so we can automatically initialise\n$(document).on( 'preInit.dt.dtr', function (e, settings, json) {\n\tif ( e.namespace !", "== 'dt' ) {\n\t\treturn;\n\t}\n\n\tif ( $(settings.nTable).hasClass( 'responsive' ) \|\|\n\t\t $(settings.nTable).hasClass( 'dt-responsive' ) \|\|\n\t\t settings.oInit.responsive \|\|\n\t\t DataTable.defaults.responsive\n\t) {\n\t\tvar init = settings.oInit.responsive;\n\n\t\tif ( init !", "== false ) {\n\t\t\tnew Responsive( settings, $.isPlainObject( init ) ? 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[ "GET THE LATEST NEWS FROM ACROSS THE COUNTY IN YOUR INBOX SIGN UP Thank you for subscribing See our privacy notice Invalid Email\n\nArchaelogists are digging to unearth the secret behind one of the Forests oldest historical sites.", "\n\nMysterious Soudley Camp has baffled historians for years with several theories being put forward for exactly what it is.", "\n\nNow archaelogists have moved in to trawl the ground for clues to real history of the mystery hillock.", "\n\nAnd on Sunday they will be showing members of the public what they have found in the first sheme to examine 1,700 sites discovered by a specialist aerial survey of the Forest of the Dean, many of them previously unknown to archaeologists.", "\n\nThe enigmatic archaeological site is on a promontory above the Soudley Brook, with a large bank and ditch defending its more accessible western side.", "\n\nNobody knows why it was built or even when it was built.", "\n\nTheories include that it is a Neolithic hilltop enclosure, defensive Iron Age settlement, or an early medieval castle.", "\n\n“The site is officially recorded as an Iron Age 'promontory fort' or defended farmstead, but it doesn't quite fit the typical form for these sites,” explains a spokesman for the project.", "\n\n“The team are hoping to find answers to some of these questions. ", "In addition to three trenches and six small test pits, environmental samples will be taken across the ditch in the hope of establishing its depth.”", "\n\nThe archaeology open day is being held on Sunday October 29 2017 between 11am-3pm.", "\n\nAs well as revealing any finds from the initial dig by Worcestershire Archive & Archaeology, there will be site tours, children's activities and news of a five year project designed to get the Forest to yield its age-old secrets.", "\n\nAnother major aspect of the Programme is to survey and investigate the 1,700 archaeological sites identified by the LiDAR survey.", "\n\nArchaeologist Andy Walsh, who is leading the excavation, said that: “The excavations will hopefully answer some of our long held questions about Soudley Camp, as well as being a great opportunity for local people to get involved in uncovering the heritage of the Forest of Dean.”", "\n\nThe Soudley Camp excavation is part of the £2.5 million Foresters' Forest Programme, a Heritage Lottery Funded Landscape Partnership being led by the Forestry Commission.", "\n\nThere will be information available about this work presented at the Open Day and an opportunity to sign up to help surveying them over the next five years.", "\n\nAccess to Soudley Camp is off the road to Soudley School, on the right before the school buildings. ", "Please feel free to drop in between 11am and 3pm on Sunday 29 October." ]	{ "pile_set_name": "OpenWebText2" }	[ 0.004405286343612335, 0, 0, 0.004166666666666667, 0, 0, 0.008333333333333333, 0, 0, 0, 0, 0.008658008658008658, 0, 0.010676156583629894, 0.023255813953488372, 0, 0.0196078431372549, 0 ]	0.004395	5
[ "Modeling Impaired Coaptation Effects on Mitral Leaflet Homeostasis Using a Flow-Culture Bioreactor.", "\nMitral valve (MV) regurgitation constitutes an increasing burden of adult and pediatric cardiac disease tending to worsen over time. ", "Whether altered mechanical forces on leaflets cause valve disease is unknown. ", "Here we show that MV leaflet coaptive strain disruption alters expression of genes critical to leaflet homeostasis. ", "We used a flow-culture bioreactor of rat MVs with flow-induced cyclic coaptation (cycling valve group; n = 4) or in a sustained open state (open valve group; n = 4). ", "After 3 days of culture, leaflet RNA expression was profiled. ", "More than 48 genes exhibited markedly changed expression when coaptive leaflet strain was disrupted for 3 days (change >fourfold; p < 0.05; cycling vs open valves). ", "Genes exhibiting highly altered expression included Angpt2, Vegf, Cd74, RT1-Da (HLA-DRA), and Igfbp3. ", "Pathway analysis indicated the most significant signaling pathways regulating the expression changes were Hif1α and Tnfα when MV closure was disrupted. ", "Disruption of normal MV coaptive strain markedly alters the expression of leaflet genes, demonstrating that cyclic strain is critically important to leaflet homeostasis. ", "We demonstrate a pattern of MV gene expression changes in which hypoxia signaling is prominently increased in response to disrupted strain cycles. ", "Coaptive strain regulation of MV leaflet homeostasis implicates altered strain as a mechanism potentially initiating valve disease. ", "Early repair may prevent progression of disease driven by altered coaptation." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0.010101010101010102, 0, 0, 0, 0, 0.016129032258064516, 0, 0.029411764705882353, 0, 0, 0, 0, 0 ]	0.00428	5
[ "Satellite signal based positioning technologies, which are mainly used outdoors, are usually not suited to deliver a satisfactory performance when used for indoor positioning, since satellite signals of global navigation satellite systems (GNSS), like the global positioning system (GPS), do not penetrate through walls and roofs strongly enough for an adequate signal reception indoors. ", "Thus, these positioning technologies are not able to deliver a performance indoors that would enable seamless, equal and accurate navigation experience outdoors and indoors.", "\nTherefore, several dedicated solutions for indoor positioning have been developed and commercially deployed during the past years. ", "Examples comprise solutions that are based on pseudolites, which are ground based GPS-like short-range beacons, ultra-sound positioning solutions, Bluetooth low energy (BLE) based positioning solutions, cellular network based positioning solutions and wireless local area network (WLAN) based positioning solutions.", "\nA WLAN based positioning solution, for instance, may be divided in two stages, a training stage and a positioning stage.", "\nIn the training stage, learning data is collected. ", "The data may be collected in the form of fingerprints that are based on measurements by mobile devices. ", "A fingerprint may contain a location estimate and measurements taken from a radio interface. ", "The location estimate may be for example GNSS based, sensor-based, or manually inputted. ", "Measurements taken from the radio interface may comprise, by way of example, measured radio signal strengths and an identification of WLAN access points transmitting the radio signals. ", "The training may be a continuous background process, in which mobile devices of a large number of consumers are continuously reporting measured data to a server. ", "Consumers may consent to a participation in such a data collection, if their device is equipped with the needed functionality. ", "This approach is also referred to as crowd-sourcing. ", "A crowd-sourcing based training stage may enable an exhaustive survey of a site, for instance all floors, spaces and rooms of a building, in a short time at limited costs. ", "Alternatively or in addition, mobile devices may be used for collecting fingerprints in a systematic manner. ", "Collected fingerprint data may be uploaded to a database in a server or in the cloud, where algorithms may be run to generate radio models of WLAN access points and/or radio maps for positioning purposes.", "\nIn the positioning stage, a mobile device may estimate its current location based on own measurements taken from the radio interface and on the data or a subset of data that is available from the training stage. ", "Model data or radio map data that has been generated in the training stage may be transferred to mobile devices by a server via the Internet as assistance data for use in position determinations. ", "Alternatively, model data and/or radio map data may be stored in a positioning server to which the mobile devices may connect to via the Internet for obtaining a position estimate.", "\nA similar approach could be used for a positioning that is based on other types of terrestrial transmitters or on a combination of different types of terrestrial transmitters." ]	{ "pile_set_name": "USPTO Backgrounds" }	[ 0.005154639175257732, 0, 0, 0.0031746031746031746, 0.008264462809917356, 0, 0, 0, 0.011235955056179775, 0.005405405405405406, 0, 0, 0, 0, 0, 0.004901960784313725, 0, 0, 0.005555555555555556, 0 ]	0.002185	5
[ "Get the biggest stories sent straight to your inbox Sign up for regular updates and breaking news from WalesOnline Thank you for subscribing We have more newsletters Show me See our privacy notice Invalid Email\n\nDivers have filmed a stunning video of some of their trips to a disused quarry where the water reaches depths of up to 100m.\n\nGraham Owen and Artur Jablonski filmed their dive in Dorothea Quarry, in the Nantlle Valley in Gwynedd over several trips during the autumn.", "\n\nThe video shows them swimming in murky green and dark waters, swimming among abandoned cars and slate caverns.", "\n\nGraham, who is blind and can only make out the difference between light and dark, has been diving for around 12 years.", "\n\nAfter being diagnosed with a deteriorating eye condition in 2001, his sight eventually got worse and now he can only make out light and dark.", "\n\nHe decided to take up diving in 2004 to try and fill up the gaps as he could no longer enjoy his old hobbies, reading, cycling and fishing.", "\n\nGraham, who makes the four and a half hour-journey each way from north Yorkshire to Dorothea Quarry when weather doesn’t allow him to go sea diving, tries to go diving every week – sometimes with club 50mPlusDivers and also on his own.", "\n\nThey make it a tradition to stop either at Junction 39 on the A55 or at Colwyn Bay for breakfast on the way.", "\n\nHis first 100m dive was at Dorothea in 2007, so when Artur said he wanted to dive down further than the 90m he had already been to, Graham decided to take on the role of being his guide.", "\n\nAnd Artur decided to film what they saw.", "\n\nGraham said: “I use it for preparation for diving in the sea and deep sea diving. ", "I’ve been to Dorothea probably too many times – I’ve been there hundreds of times.", "\n\n“I’ve dived most parts of the quarry. ", "There’s still a couple of bits I haven’t explored as much as I could do.", "\n\n“To explore it all you’ve got to cover an awful lot of ground.", "\n\nOn the long trips to the quarry, Graham, who lives with wife Tracy and guide dog Gypsy, said: “I can only comment on the beautiful scenery my friends tell me about.", "\n\n“Although I’m blind I know that area of the quarry reasonably well. ", "I’ve done quite a few dives with him since. ", "I’ve been acting as a bit of a guide.", "\n\n“I can tell the difference between light and dark. ", "I carry quite a few lights with me – it’s pretty simple.", "\n\n“I can usually find my way around. ", "I love diving. ", "That’s why I dive every week.”", "\n\nGraham, who works for the Royal British Legion, says he mostly dives in the UK because diving in clear blue seas mean there is no contrast in light for him.", "\n\nHe said: “Diving in clear blue water is not all that good for me. ", "There’s no difference between light and dark.", "\n\n“Diving off the North Sea or Anglesey, it’s dark to green water. ", "That means I can use torches and make out light.", "\n\n“It’s easier for me.”" ]	{ "pile_set_name": "OpenWebText2" }	[ 0.012552301255230125, 0, 0, 0, 0, 0.004219409282700422, 0.00909090909090909, 0.015957446808510637, 0.023809523809523808, 0.011904761904761904, 0.012195121951219513, 0, 0, 0, 0.018072289156626505, 0, 0, 0, 0, 0, 0, 0, 0, 0.006329113924050633, 0, 0, 0.014925373134328358, 0, 0 ]	0.00445	5
[ "Distribution and immunochemical character of neurotensin-like material in representative vertebrates and invertebrates: apparent conservation of the COOH-terminal region during evolution.", "\nUsing a radioimmunoassay for bovine neurotensin (NT) and various region specific antisera which react selectively with different portions of the molecule, the presence of immunoreactive NT (iNT) in a wide range of vertebrate and invertebrate species has been demonstrated. ", "While antisera directed towards the N-terminal region of NT recognized only mammalian forms of NT, antisera directed towards the C-terminal region of NT recognized materials from all species examined, including representatives of all vertebrates and invertebrate classes. ", "When extracts of the brain and gut of the vertebrates examined were chromatographed on Sephadex G-25 multiple NT-like substances were observed, and the patterns of iNT obtained seemed to fall into three groups: (a) mammals, (b) birds and reptiles and (c) amphibians and fish. ", "Extracts of invertebrates also exhibited multiple peaks of iNT on Sephadex G-25 and the profiles observed resembled those for lower vertebrates. ", "Partially purified iNT obtained from chicken, turtle, dogfish and lobster was shown to increase hematocrit and induce cyanosis in anesthetized rats. ", "These findings indicate (a) that NT-like substances appear to be present throughout the animal kingdom, (b) that the C-terminal region of NT is highly conserved while the N-terminal region varies, and (c) that in any one animal multiple substances sharing C-terminal homologies with NT exist. ", "These findings are consistent with the notion that NT and related peptides participate in important processes basic to animal life and that their functioning depends highly upon elements located in their C-terminal regions. ", "They further suggest the existence of an entire family of NT-related peptides in each animal form, possibly distributed differently and functioning differently in the various organs of the animal." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0, 0.003676470588235294, 0, 0.006896551724137931, 0, 0.0034129692832764505, 0, 0 ]	0.001554	5
[ "Honestly, i think that after ep 15, they ruined it.", "\nHe finally beat the game and if the story continues, it will drag more hate into the series.", "\nAfter ALO you think they learn a lesson about VRMMORPGs and how evil the owners can be.", "\n\nLong story short, to those that are wondering if the series will come back for season 3, the answer is yes.", "\n\nThe series have made quite a profit for the production companies(not to mention the profits from licensing feeds, games, novels, etc..). ", "In addition, SOA has been one of the top-tier anime for the year 2012.", "\n\nWhile there is way too much content to be crammed into season 3, you can expect the main storyline to be more or less the same, with some parts omitted from the anime series(much like in season 1).", "\n\nAnime should be out anywhere from early March to as late as mid June. ", "In the end, it is up for the animation companies to decide when's the best time to release the anime for maximum profit and exposure.", "\n\n Many people are debating whether the SOA and ALO arcs are to be considered one or two seasons, but regardless of the outcome, let's just pretend that that number 3 following the \"Season\" in the title stands for the whatever-next-gen season that will cover GGO will be.", "\n\nYou can pretend all you want, but SAO had one season broadcast over two cours. ", "There has only been one SAO series. ", "If there is another, it will be season 2, not season 3.", "\n\nI expect it will get more, however, as it has plenty of source material left and was insanely popular in terms of sales.", "\n\nGood and bad have no bearing on what gets a 2nd season and what doesn't, other than the fact that if something is sufficiently bad it won't sell.", "\n\nThe only thing that matters is sales figures and the desire of the creators to make another season. ", "In some cases, desire can override sales figures, or sales figures are secondary to other considerations, like with Chihayafuru. ", "For that show, it was the impact the anime had on manga sales that ensured a second season, even though the DVD/BluRay sales were quite modest.", "\n\nIn some cases, the show could sell tons but there will be no more seasons because there is no more story to tell. ", "In others, like Haruhi, the sales figures were there, but the desire to make more anime seems to be lacking.", "\n\nSpoiler Alert! ", "Click to show or hide\n\nThe DVD/Blu-Ray sales have been amazing, to say the least; modest would be an understatement. ", "However, regardless of whatever the next SAO series will be called and whether they'll focus solely on spoiler.", "\n\nSpoiler Alert! ", "Click to show or hide\n\nSpoiler - Gun Gale Online(GGO) and may even expand into 7th and 8th novel, although they're more like side stories, thus it is way too early to predict whether they'll be included. ", "Either way, GGO has a solid storyline so expect an amazing anime season.", "\n\nThe \"modest\" was referring to the sales figures for Chihayafuru, which I was using as an example of the type of show that can get a second season without having high BluRay/DVD sales.", "\n\nNot sure if its just me, but the show makes me a little mad at it.", "\nNot because its a bad show, but because the storyline for the show had so much potential to. ", "Yet, most of that potential for a great series was ruined.", "\nThat what pisses me off, that the potential for the series was not even close to fully used.", "\nI think season was should of just focused soley on SAO aincard for atleast 25 episodes to give it better development. ", "Then 2nd season would be alfheim online which wasnt as good as aincard arc, but I think they could of done a better job on that arc to if it had been given more episodes.", "\n\nHopefully they will see this is and fix the problem when they do a season 2 and give it enough episodes. ", "For i know its not possible for season 1 to be redone just for aincard.", "\n\nAlso not sure if my posts relates here at all, but this was a SAO topic and I just wanted to get this said and starting a new topic would of been a waste.", "\n\nNot sure if its just me, but the show makes me a little mad at it.", "\nNot because its a bad show, but because the storyline for the show had so much potential to. ", "Yet, most of that potential for a great series was ruined.", "\nThat what pisses me off, that the potential for the series was not even close to fully used.", "\nI think season was should of just focused soley on SAO aincard for atleast 25 episodes to give it better development. ", "Then 2nd season would be alfheim online which wasnt as good as aincard arc, but I think they could of done a better job on that arc to if it had been given more episodes.", "\n\nHopefully they will see this is and fix the problem when they do a season 2 and give it enough episodes. ", "For i know its not possible for season 1 to be redone just for aincard.", "\n\nAlso not sure if my posts relates here at all, but this was a SAO topic and I just wanted to get this said and starting a new topic would of been a waste.", "\n\nTo be honest, I think that the ending of the original SAO should've been the ending for season 1. ", "I would've loved to see more detailed scenary of everyday life in aincrad, maybe even continued side stories of the \"Laughing Coffin\"; however, the move to merge SAO and ALO has been very bold, especially given that just when things got real in SAO, the storyline got immediately cut off.. in essence, I did not fancy the lacking of a smooth transition between SAO and ALO.", "\n\nI can only hope that in Season 2 they will focus more on the storyline to give a sense of depth to the story.", "\n\nNot sure if its just me, but the show makes me a little mad at it.", "\nNot because its a bad show, but because the storyline for the show had so much potential to. ", "Yet, most of that potential for a great series was ruined.", "\nThat what pisses me off, that the potential for the series was not even close to fully used.", "\nI think season was should of just focused soley on SAO aincard for atleast 25 episodes to give it better development. ", "Then 2nd season would be alfheim online which wasnt as good as aincard arc, but I think they could of done a better job on that arc to if it had been given more episodes.", "\n\nHopefully they will see this is and fix the problem when they do a season 2 and give it enough episodes. ", "For i know its not possible for season 1 to be redone just for aincard.", "\n\nAlso not sure if my posts relates here at all, but this was a SAO topic and I just wanted to get this said and starting a new topic would of been a waste.", "\n\nNot sure if its just me, but the show makes me a little mad at it.", "\nNot because its a bad show, but because the storyline for the show had so much potential to. ", "Yet, most of that potential for a great series was ruined.", "\nThat what pisses me off, that the potential for the series was not even close to fully used.", "\nI think season was should of just focused soley on SAO aincard for atleast 25 episodes to give it better development. ", "Then 2nd season would be alfheim online which wasnt as good as aincard arc, but I think they could of done a better job on that arc to if it had been given more episodes.", "\n\nHopefully they will see this is and fix the problem when they do a season 2 and give it enough episodes. ", "For i know its not possible for season 1 to be redone just for aincard.", "\n\nAlso not sure if my posts relates here at all, but this was a SAO topic and I just wanted to get this said and starting a new topic would of been a waste.", "\n\nIve yet to be able to get into reading light novels. ", "Maybe that will be my next step haha.", "\nAt first I was only able to watch dub series, then subs, then started reading manga. ", "Guess the next thing is to get into reading the novels.", "\n\nI think ill give it a shot. ", "Meaning as I liked the anime for the most part so the novel must be a lot better.", "\n\nNot sure if its just me, but the show makes me a little mad at it.", "\nNot because its a bad show, but because the storyline for the show had so much potential to. ", "Yet, most of that potential for a great series was ruined.", "\nThat what pisses me off, that the potential for the series was not even close to fully used.", "\nI think season was should of just focused soley on SAO aincard for atleast 25 episodes to give it better development. ", "Then 2nd season would be alfheim online which wasnt as good as aincard arc, but I think they could of done a better job on that arc to if it had been given more episodes.", "\n\nHopefully they will see this is and fix the problem when they do a season 2 and give it enough episodes. ", "For i know its not possible for season 1 to be redone just for aincard.", "\n\nAlso not sure if my posts relates here at all, but this was a SAO topic and I just wanted to get this said and starting a new topic would of been a waste.", "\n\nIve yet to be able to get into reading light novels. ", "Maybe that will be my next step haha.", "\nAt first I was only able to watch dub series, then subs, then started reading manga. ", "Guess the next thing is to get into reading the novels.", "\n\nI think ill give it a shot. ", "Meaning as I liked the anime for the most part so the novel must be a lot better.", "\n\nThanks for the link.", "\n\nyea, the novel is a LOT better. ", "there's a ton of stuff that was cut out of the anime, especially the Aincrad arc.", "\n\nAs a light novel fan of SAO, personally I hated the anime....\nIt just didnt feel right..... it was emotionless..... It was dead feeling....\nGuh.... Sinon! ", "Yuuki!!!!! ", "I wanna see you!! ", "But I dont care for KiriAsu" ]	{ "pile_set_name": "Pile-CC" }	[ 0, 0, 0.011363636363636364, 0, 0, 0, 0, 0, 0, 0.003676470588235294, 0.012345679012345678, 0.027777777777777776, 0, 0, 0, 0, 0, 0, 0, 0.009259259259259259, 0, 0, 0.008849557522123894, 0, 0, 0.013888888888888888, 0.005405405405405406, 0.014705882352941176, 0, 0, 0, 0.008403361344537815, 0.0058823529411764705, 0, 0, 0.00641025641025641, 0.014705882352941176, 0, 0, 0, 0.008403361344537815, 0.0058823529411764705, 0, 0, 0.00641025641025641, 0.01, 0.0160857908847185, 0, 0.014705882352941176, 0, 0, 0, 0.008403361344537815, 0.0058823529411764705, 0, 0, 0.00641025641025641, 0.014705882352941176, 0, 0, 0, 0.008403361344537815, 0.0058823529411764705, 0, 0, 0.00641025641025641, 0, 0, 0, 0, 0, 0, 0.014705882352941176, 0, 0, 0, 0.008403361344537815, 0.0058823529411764705, 0, 0, 0.00641025641025641, 0, 0, 0, 0, 0, 0, 0, 0.029411764705882353, 0.012345679012345678, 0.012738853503184714, 0, 0, 0.037037037037037035 ]	0.004119	5
[ "Q:\n\nGuardar cadena de caracteres en C\n\n¿Cómo podría leer por teclado una cadena de caracteres y almacenarla en una variable? ", "La variable no debe tener un tamaño fijo. ", "Me está costando un poco. ", "Gracias!", "\nLo siento apenas tengo nada de código, todo lo que pruebo está mal. ", "Estoy intentando hacerlo con un malloc pero no hay manera :(\n\nA:\n\n¿Cómo podría leer por teclado una cadena de caracteres y almacenarla en una variable?", "\n\nPara leer un valor desde el teclado puede usarse scanf. ", "A esta función le debes indicar el formato de los datos que quieres leer y la dirección de la variable en que quieres leerlos, veámoslo en un ejemplo:\nint numero = 0;\nscanf(\"%d\", &numero);\n\nEl \"%d\" indica que pretendes leer un número, si quisieras leer una cadena de caracteres deberías usar \"%s\":\nchar cadena_de_caracteres[100];\nscanf(\"%s\", cadena_de_caracteres);\n\nAquí no usamos el operador dirección-de (el et &) porque el nombre del arreglo equivale a la dirección del primer elemento del mismo. ", "Hay que tener en cuenta que leer \"%s\" añade el carácter de control de final de cadena: el carácter nulo.", "\n\nLa variable no debe tener un tamaño fijo.", "\n\nSi no es tamaño fijo: es tamaño variable. ", "Para ello deberás averiguar primero el tamaño de la cadena que quieres leer y seguidamente leer la cadena:\nint longitud_de_la_cadena = 0;\nprintf(\"Longitud de la cadena: \");\nscanf(\"%d\", &longitud_de_la_cadena);\n\nchar cadena = (char )malloc(longitud_de_la_cadena + 1);\nprintf(\"Cadena: \");\nscanf(\"%s\", cadena);\n\nprintf(\"\\\"%s\\\" es la cadena de %d caracteres introducida.\\n\", cadena, longitud_de_la_cadena);\n\nEl código anterior introduciendo los valores 6 y patata muestra:\n\nLongitud de la cadena: 6\nCadena: patata\n\"patata\" es la cadena de 6 caracteres introducida.", "\n\nAquí usamos malloc para alojar el tamaño que necesitamos para nuestra cadena de longitud variable, no debemos olvidar liberar la memoria solicitada antes de acabar el programa usando la función free:\nfree(cadena);\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0, 0, 0, 0, 0.028985507246376812, 0, 0.034482758620689655, 0.022, 0.019230769230769232, 0, 0, 0.010676156583629894, 0.013824884792626729 ]	0.009938	5
[ "Body found in loch in hunt for Sanjay Dhital\n\nSanjay Dhital has not been seen since Boxing Day\n\nDAVID McCANN\n\nRESCUERS drafted in to trace a missing Nepalese student have recovered a body from a shallow loch after a major search operation.", "\n\nSpecialist teams were scrambled to comb the city’s Holyrood Park in a bid to find Sanjay Dhital, 24, who vanished on Boxing Day.", "\n\nSanjay Dhital has not been seen since Boxing Day\n\nToday, police confirmed a body had been retrieved from St Margaret’s Loch, a short walk from the Palace of Holyroodhouse.", "\n\nInvestigations are continuing to identify the remains. ", "Volunteers from the Borders Search and Rescue Unit and Tweed Valley Mountain Rescue had joined police in a sweep of “hard to reach areas” around Arthur’s Seat on Sunday.", "\n\nThey carried out rope-access searches of higher ground before concentrating on the three lochs situated within the Royal Park.", "\n\nIn a statement, a police spokesman thanked rescue teams for their efforts.", "\n\n“Lothian and Borders Police searching for missing man Sanjay Dhital have recovered the body of a male from St Margaret’s Loch in Holyrood Park, while assisted by the Borders Underwater Search Team. ", "Inquiries are ongoing to identity the male and the family of Sanjay Dhital will be fully updated with the progress of this investigation.", "\n\n“We would also like to thank Tweed Valley Mountain Rescue Team and Borders Search and Rescue Team for their continued support.”", "\n\nThe family of Mr Dhital went public with concerns over his safety after the Edinburgh College student failed to contact them for several days.", "\n\nThe search for Mr Dhital widened to Arthur’s Seat after door-to-door enquiries around Leith Walk drew a blank.", "\n\nSpearheading the investigation, Inspector Kevin McLean, previously warned that the probe would be extended to Arthur’s Seat “as there is a possibility Sanjay may have come to some harm”. ", "The final year student, who worked part-time at Saigon Saigon restaurant in South St Andrew Street, was said to regularly contact his family in Katmandu, Nepal.", "\n\nHis brother Sailesh previously told how the family were “so proud” of the hard work Mr Dhital put into his studies and how unusual it was for him to miss classes.", "\n\nHe spoke of the family’s worry and described his brother’s disappearance as “extremely out of character.", "\n\nSailesh took to the Evening News’ Facebook page earlier this month to urge readers to come forward with information to assist the police investigation." ]	{ "pile_set_name": "Pile-CC" }	[ 0.0041841004184100415, 0.007692307692307693, 0.005780346820809248, 0, 0.011834319526627219, 0, 0, 0.025, 0.0072992700729927005, 0.007751937984496124, 0.006944444444444444, 0.026785714285714284, 0.010582010582010581, 0.0125, 0.006097560975609756, 0, 0.006535947712418301 ]	0.008176	5
[ "Q:\n\nHow to configure git in WebStorm\n\nI just installed WebStorm from JetBrains, and cloned my repo using SourceTree to disk. ", "Then I opened the project in WebStorm and everything is working except the git in WebStorm.", "\nIn SourceTree everything is working fine, but in WebStorm I can't do anything, I can't pull, commit or whatever. ", "\nI'm receiving this popup: Can't start Git: git.exe. ", "I know that probably I must set the good path to this file, but I don't know where it is.", "\n\nPlease could you give me an advice where should I find this file, or how to resolve this problem?", "\nRemember that in SourceTree this repository is working.", "\n\nA:\n\nYou may have to install git from the link below, then use the 'Fix it' link if it's not found automatically.", "\nhttps://git-scm.com/download/win\n\nA:\n\nYou'll need to click on the \"Fix it\" option, and change the path to the git.exe file. ", " As Windows is strange (personal opinion, not answer fact) this can be in a number of locations. ", " From this github page it could be in one of the following locations:\n\nGit - C:\\Program Files (x86)\\Git\\bin\nSmartGit - C:\\Program Files\n (x86)\\SmartGit\\git\\bin\\git.exe\nGitHub For Windows -\n C:\\Users\\'username'\\AppData\\Local\\GitHub\\PortableGit_'numbersandletters'\\cmd\\git.exe\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0.024, 0.02197802197802198, 0.008771929824561403, 0.018867924528301886, 0, 0, 0, 0, 0.008, 0, 0.010676156583629894 ]	0.00839	5
[ "INTRODUCTION\n============\n\nDysphagia refers to a difficulty in the whole or part of swallowing. ", "This disorder occurs in the oral, pharyngeal and esophageal phases, thereby leading to a disorder of function where food in the oral cavity is transferred to the gastrointestinal tract. ", "In severe cases, it may cause complications, including aspiration pneumonia, bronchospasm, dehydration, malnutrition, and suffocation.[@B1] Causes of dysphagia are diverse. ", "According to Utsinger et al.", ",[@B2] it is known that among symptoms arising from cervical osteophytosis, dysphagia is developed at a ratio of 17%. ", "The anterior cervical osteophytosis is observed even in 20-30% among healthy people[@B3] and may be a direct cause of dysphagia.[@B4] Excessive osteophytosis of the cervical vertebrae may cause dysphasia via mechanisms, such as (1) a mechanical pressure on esophagus, (2) inflammation and edema on periphery, (3) cricopharyngeal spasm, and (4) abnormal recurvation of epiglottis.[@B3],[@B5] The therapeutic approaches considered for dysphagia include medication to reduce inflammation and edema around the cervical vertebrae, and a surgical treatment to restore the movement of epiglottis by correcting the anatomical compression and deformity of cervical vertebrae.[@B3] Because of the side effects and mortality of surgical treatments, however, there is skepticism in using surgical treatments. ", "Hence, we conducted a study on the effects of surgical treatments for patients with dysphagia caused by the anterior cervical osteophytes through 3 patient cases. ", "One patient underwent surgical removal of the osteophytes because of severe weight loss from malnutrition and repetitive aspiration pneumonia, even though the patient had received conservative treatment for dysphagia by anterior cervical osteophyte. ", "A second patient underwent surgical removal of the osteophyte in the early stage for mild dysphagia symptoms. ", "The third patient needed a re-operation because of dysphagia caused by reossification found in the long term follow-up period even though the patient had undergone surgical removal of the anterior cervical osteophyte.", "\n\nCASE REPORTS\n============\n\nCase 1\n------\n\nA 75-year-old male patient visited the hospital complaining of dysphagia and weight loss (as much as 5 kg) that had occurred 3 months prior to this visit. ", "Twenty years earlier, he had a received craniotomy on the left frontal parietal region because of traumatic subdural hemorrhage from falling and had recovered without sequelae. ", "He had taken drug treatment for hypertension, but has no difficulty in daily living activity. ", "For his dysphagia, he complained of more difficulties in swallowing solid foods rather than liquid foods and this was gradually progressing. ", "Seven months after the onset of dysphagia, he was hospitalized, at which time he could only take small amounts of liquid foods instead of regular meals and his weight loss during 10 months since the onset of dysphagia was approximately 10 kg. ", "The patient did not complain of speech disturbance or dyspnea and both movements of the tongue and gag reflex were normal. ", "On his brain MRI scan, partial encephalomalacia was observed on the lesion where the left frontal parietal craniotomy had performed and left inferior temporal gyrus; this was not different compared with a prior brain MRI scan, and any additional lesions which might induce dysphagia was not observed. ", "An endoscopic examination was performed with suspicion of a pharyngolaryngeal tumor, but no abnormal findings were detected. ", "There were also no abnormal results in routine blood and tumor marker tests. ", "As excessive osteophytosis on the anterior part of the cervical vertebrae from C3^rd^ to C6^th^ levels were observed in the cervical plain radiograph, a 3D cervical CT was performed and the identified posterior part of the pharyngolaryngeal cavity was compressed and narrowed by osteophytes from C2^nd^ to C7^th^ vertebrae levels ([Fig. ", "1](#F1){ref-type=\"fig\"}). ", "As the dysphagia by anterior cervical osteophytes was suspected, a VFSS (Video Fluroscopic Swallowing Study) was performed ([Fig. ", "2](#F2){ref-type=\"fig\"}). ", "Findings revealed that a movement of the epiglottis displayed an abnormal recurvation by osteophytes, with at least 50% of food remaining in the epiglottic valleculae. ", "Pyriform sinuses were observed in all tested materials, and asymptomatic aspiration was shown as 8 points of the PAS (Penetration-Aspiration Scale) in 2 cc of diluted barium swallowing test. ", "After the above examinations, an electronic stimulator, VitalStim® (Chaltanooga group, Austin, USA), was conducted one hour a day for 10 days. ", "The treatment sessions were completed in two weeks. ", "The electronic stimulation used a 2-channel form with an alternating current, wherein one of the electrical pads of the first channel was attached between the musculus biventer mandibulae muscle and hyoid bone and another electrical pad was attached between the hyoid bone and thyroid cartilage. ", "The electrical pad of the second channel was attached between the thyroid and cricoid cartilages and vertically to the inferior part of the cricoid cartilage. ", "A week after completing the electronic stimulation treatment, a VFSS was performed, where it was found that aspiration and nasal regurgitation had disappeared and the remaining amount of food shown in the epiglottic valleculae and pyriform sinuses were reduced to below 10%. ", "Thus, it was possible to change his diet from liquid form to regular meals. ", "After one month, however, dysphagia began to progress again and aspiration pneumonia had developed, which required hospitalization. ", "Compared with previous findings, VFSS results revealed an increase in the amount of retention of contrast in the epiglottic valleculae and pyriform sinuses by 10-50% and the movement of epiglottis had decreased in all tested materials. ", "It was suggested that his symptoms has worsened compared to previous findings. ", "Due to persistent dysphagia, his diet was changed back to liquid food. ", "He also received consultation in our department of neurosurgery for operation due to severe general weakness caused by insufficient nutrition. ", "Next, he decided to have an operation after 2 year 7 months since the onset of dysphagia. ", "Osteophytes cervical vertebrae from C2^nd^ to C7^th^ levels were removed via an anterior approach ([Fig. ", "1](#F1){ref-type=\"fig\"}). ", "After the operation, he recovered without any side effects and 1 month later, VFSS was performed. ", "Based on the nasal reflux that had been observed in the swallowing water test disappeared and food remaining in the epiglottic valleculae and pyriform sinuses were below 10%. ", "In spite of the formation of the inner wall membrane, the remaining food was removed by chin tuck and repetitive swallowing. ", "It was determined that the epiglottic motion had improved and the remainder in the epiglottic valleculae and pyriform sinus had reduced remarkably ([Fig. ", "2](#F2){ref-type=\"fig\"}). ", "The patient was able to return to a general diet, had gained approximately 6kg of weight, and was satisfied with his postoperative improvement of symptoms in spite of having subjective dysphagia for waterless biscuits.", "\n\nCase 2\n------\n\nA 62 year-old male patient visited our department of neurosurgery, complaining of dysphagia and limited movement range of the cervical vertebrae that has occurred for 7 months. ", "He was diagnosed as having hypertension 3 years before and receiving medication. ", "He felt no discomfort when taking a meal, but complained of difficulties in swallowing a tablet. ", "There was no language disorder or dyspnea. ", "During a physical examination, both motion and gag reflux of his tongue were normal. ", "As an imaging test, a 3D cervical CT was performed and the posterior part of the pharyngolaryngeal cavity was compressed by an anterior bony spur of the 3^rd^-6^th^ cervical vertebrae ([Fig. ", "3](#F3){ref-type=\"fig\"}). ", "VFSS findings had determined that there was a remainder of 10-50% in the epiglottic valleculae and pyriform sinuses due to motor abnormality of the cricopharyngeal muscle caused by an anterior bony spur on the cervical vertebrae with the height of upper esophageal sphincter in swallowing cookies. ", "In a swallowing test involving 10 cc of water, vocal cord penetration was shown, but it was removed spontaneously ([Fig. ", "3](#F3){ref-type=\"fig\"}). ", "The bony spur on the 4^th^-6^th^ cervical vertebrae with anterior approach was removed. ", "VFSS findings performed 2 weeks after the operation suggested that there was no remarkable change in the remainder of the epiglottic valleculae that was shown in swallowing cookies, but the remainder of the pyriform sinuses decreased dramatically, and the phenomenon of vocal cord penetration that had appeared during the water swallowing test also disappeared ([Fig. ", "3](#F3){ref-type=\"fig\"}). ", "The patient reported a reduction in the number of feeling difficulties in taking tablet after surgery, but a complete improvement of the symptoms was not shown.", "\n\nCase 3\n------\n\nAfter complaining of dysphagia, a 61-year-old male patient was operated under the diagnosis of diffuse idiopathic hyperostosis on the 2^nd^-5^th^ cervical vertebra, and had since experienced symptoms improvement. ", "However, his dysphagia began to progress again to being able to swallow only liquid food since approximately May, 2010. ", "He was hospitalized in our department of orthopedics with 170 cm height, 46.8 kg of weight, and 16.18 of BMI. ", "His medical history was unremarkable. ", "In imaging tests performed after hospitalization, diffuse idiopathic hyperostosis on the 1^st^-3^rd^ cervical vertebrae and anterior bony spur ranging from the 2^nd^ cervical vertebrae to the 1^st^ thoracic vertebrae were found ([Fig. ", "4](#F4){ref-type=\"fig\"}). ", "VFSS findings showed that there was normal swallowing reflex in the pharyngeal phase, but because of an anterior bony spur on the 2^nd^-4^th^ cervical vertebrae, there was an epiglottic recurvation disorder. ", "There was also a remainder of 10-50% in the pyriform sinuses and with an increase of sample viscosity, not only did the amount of remainder in the pyriform sinuses increase but his complaint for the feeling of sticking in his throat got similarly worse. ", "In addition, asymptomatic aspiration was observed in 5 cc of a diluted barium test ([Fig. ", "4](#F4){ref-type=\"fig\"}). ", "Next, there was removal of the osteophyte on the 2^nd^, 3^rd^, 4^th^, and 5^th^ cervical vertebrae discectomy, and fixation of the 3^rd^ and 4^th^ cervical vertebrae with an anterior approach for the improvement of dysphagia ([Fig. ", "4](#F4){ref-type=\"fig\"}). ", "One month after the operation, VFSS findings determined that no aspiration was observed, the amount of remainder in the pyriform sinuses had decreased, but the amount of remainder increased with an increase of sample viscosity. ", "Sinse abnormal movement of the epiglottis still remained, a 10-time application of VitalStim® was performed. ", "After electric stimulation treatment, VFSS findings determined that the amount of remainder in the pyriform sinuses after swallowing was reduced and aspiration that had previously been observed had disappeared. ", "He was able to have regular meals and improvement on symptoms of dysphagia increased by 80% compared with preoperative conditions.", "\n\nDISCUSSION\n==========\n\nCauses resulting in an anterior cervical bony spur include: 1) ankylosing spondylitis; 2) diffuse idiopathic skeletal hyperosteosis (DISH) causing ossification of the anterior longitudinal ligament and tendon; and 3) degenerative intervertebral disc inflammation or intervertebral osteochondrosis.[@B6] The most common symptom caused by an anterior cervical bony spur is the worsening of dysphagia in consuming solid food. ", "Approximately 28% of patients with the anterior cervical bony spur complain of dysphagia, 4% of which will visit a hospital with such a complaint.[@B6],[@B7] Dysphagia due to cervical osteophytosis is mainly developed from a mechanical obstruction of cricoid cartilage, secondary inflammation and edema. ", "This results in pains and muscular spasm, as well as diseases, such as tumor in the hypopharynx, larynx, esophagus, vertebrae, lung, and mediastrinum, esophagitis, esophageal motor disease, esophageal stricture, pharyngoesophageal diverticulum, neuromuscular disease, cricopharyngeal rigidity, gastroesophageal reflux, stroke, and globus hystericus.[@B6] Therefore, it is important to perform a full medical history, neurological, and physical examination, as well as a blood test, endoscopic test, radiological test, and VFSS when patients complain of dysphagia. ", "Treatment by cervical hyperostosis should be decided depending on pathogenesis of dysphagia, its severity, and conditions. ", "A preferred treatment is to take anti-inflammatory agent or steroids to reduce edema or inflammation of the pharynx, bronchus, larynx, and esophagus regions.[@B3] Where there is no improvement even after drug medication and rehabilitation treatment and general weakness continues to progress from severe weight loss or continued aspiration pneumonia as shown in the patient of case 1, surgical treatment should be considered. ", "This surgical treatment removes the mechanical compression of esophagus, and in most cases, there is an improvement of symptoms.[@B3] However, there are certain cases, such as the patient of case 3, where dysphagia reoccurs from reossification in long term follow-up even though the bony spur on the anterior cervical vertebra causing dysphagia had been removed. ", "Miyamoto et al.[@B10] has identified that for all the patients who had their bony spur on the anterior cervical vertebra removed, reossification developed and growth rate of the bony spur was 1mm a year on average. ", "The side effects of bony spur removal of the anterior cervical vertebrae include recurrent neuropalsy, hematoma, infection, and fistula formation.[@B5] There is therefore skepticism in the successful surgical treatment of old patients who often develops anterior cervical bony spur due to mortality and morbidity resulting from the surgery. ", "The authors have observed a case where even though dysphagia symptoms were not severe, surgery to completely control the symptoms was difficult. ", "In other cases, it was difficult to utilize conservative treatments to treat older patients with dysphagia due to anterior cervical osteophyte. ", "In a third case, after removal of the anterior cervical bony spur and improvement of the dysphagia symptoms, the symptoms reoccurred from reossification and additional surgery was needed. ", "Although surgical treatment is not the preferred approach for patients with dysphagia due to anterior cervical bony spur, it should be considered as one of the methods to improve the symptoms and resolve problems, such as aspiration pneumonia and weight loss resulting from the dysphagia. ", "There is also a need to guide appropriate timing of surgical treatment for patients and a possibility of symptom reoccurrence from reossification after surgery with recommend long term follow-up.", "\n\n![", "Three-dimensional reconstruction computed tomography of cervical spine: anterior cervical osteophytes are revealed from C2 to C7 levels with the C4 level being the most prominent (A). ", "Post-anterior approach of the cervical spine osteophytes resection at C2 to C7 levels (B).](arm-36-729-g001){#F1}\n\n![", "The first video fluroscopic swallowing study (VFSS) showed a nasal regurgitation of contrast (A). ", "After completing ten sessions of neuromuscular electrical stimulation (VitalStim®), the nasal regurgitation vanished. ", "However, VFSS still showed minimal amount of retention of contrast in the valleculae and pyriform sinuses (B). ", "7 months later, the patient was suffering from an exacerbated symptom of difficulty in swallowing. ", "A 10 cc water swallowing test showed moderate amount of retention of contrast in the valleculae and pyriform sinuses (C). ", "After removing the anterior cervical osteophytes, retention of contrast in the valleculae and pyriform sinuses was not evident at follow-up VFSS (D).](arm-36-729-g002){#F2}\n\n![", "Three-dimensional reconstruction computed tomography of the cervical spine revealed anterior cervical osteophytes from C4 to C6 levels (A). ", "Post-anterior approach of the cervical spine osteophytes resection at C4-5-6 levels (B). ", "Pre-operative video fluroscopic swallowing study (VFSS) showed the presence of laryngeal penetration in 10 cc water swallowing test (C). ", "After removing the anterior cervical osteophytes, laryngeal penetration was not detected at follow-up VFSS (D).](arm-36-729-g003){#F3}\n\n![", "The lateral view of cervical X-ray revealed anterior cervical osteophytes at C2 and C3 levels (A). ", "Post-anterior approach of the cervical spine osteophytes resection at C2-3-4-5 levels (B). ", "Pre-operative video fluroscopic swallowing study (VFSS) showed the presence of laryngeal penetration in a 5 cc water swallowing test (C). ", "After removing the anterior cervical osteophytes, laryngeal penetration and retention of contrast in pyriform sinuses were not detected at follow-up VFSS (D).](arm-36-729-g004){#F4}\n" ]	{ "pile_set_name": "PubMed Central" }	[ 0, 0, 0.005780346820809248, 0, 0.00847457627118644, 0.006273525721455458, 0.006134969325153374, 0.004, 0, 0, 0, 0, 0, 0, 0, 0, 0.0033222591362126247, 0, 0, 0.005934718100890208, 0, 0.007692307692307693, 0, 0, 0.005235602094240838, 0.006993006993006993, 0, 0.0033783783783783786, 0.006289308176100629, 0, 0, 0.007575757575757576, 0, 0, 0.014084507042253521, 0, 0, 0.009523809523809525, 0, 0, 0, 0, 0.006493506493506494, 0, 0, 0, 0, 0, 0, 0, 0.010471204188481676, 0, 0, 0.008264462809917356, 0, 0, 0.002717391304347826, 0, 0, 0, 0, 0.00909090909090909, 0, 0.00425531914893617, 0, 0, 0, 0.011111111111111112, 0, 0.008620689655172414, 0, 0, 0.009174311926605505, 0, 0, 0.006696428571428571, 0.013157894736842105, 0.0035460992907801418, 0, 0.004694835680751174, 0.005509641873278237, 0.004651162790697674, 0.008797653958944282, 0, 0, 0.010638297872340425, 0.0034602076124567475, 0, 0, 0.005434782608695652, 0.008547008547008548, 0, 0.00847457627118644, 0, 0, 0, 0, 0, 0, 0, 0, 0.010101010101010102, 0, 0, 0 ]	0.00252	5
[ "Q:\n\nassigning Object references and performance\n\nWhen I assign variable as such:\n$app.prototype = {\n\n init: function() {\n\n self = this;\n }\n}\n\nis it actually creating a reference to \"this\" or copying the whole instance into the new variable?", "\njust wondering for performance reasons\n\nA:\n\nIt is just a reference, as long as this is an Object. ", "In strict mode, this may also be a primitive (number, string, boolean), then it would create a copy.", "\nA single assignment will never be a performance issue.", "\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0, 0.010101010101010102, 0, 0, 0 ]	0.00202	5
[ "The invention relates generally to computing systems and more particularly to a method and system for providing secure data transmissions between Internet users.", "\nThe Internet is a global network of computers that uses a common communication protocol, the Transfer Control Protocol/Internet Protocol (TCP/IP), to transmit data from one location to another. ", "Many application specific tasks, such as E-mail transmission and file transfer, are not directly supported by TCP/IP. ", "Instead, support for these services is implemented by application specific protocols that in turn rely on TCP/IP for basic data transport services. ", "One problem that is relatively unknown to individuals that make use of the Internet is the ease by which information can be obtained during transmission by unauthorized eavesdroppers. ", "For example, most E-mail transmissions over the Internet are sent in cleartext. ", "Cleartext is unencrypted data that can be intercepted anywhere along the path between a sender and the recipient.", "\nAccordingly, sensitive business or personal information should not be transmitted in cleartext over the Internet. ", "To do so is to risk its publication. ", "To avoid this risk, sensitive data is often sent by courier services or other means at great cost.", "\nEncryption mechanisms can be used to ensure the integrity of information sent over the Internet. ", "Two common encryption techniques, symmetric key encryption and public key encryption, are described below. ", "In a symmetric key encryption, a unique key is identified and used by the sender to encrypt and by the receiver to decrypt a message. ", "In public key encryption, separate keys are used to encrypt and to decrypt.", "\nBoth symmetric key and public key encryption require a key exchange. ", "That is, where symmetric key encryption is used, the sender must provide the recipient with the key so that the recipient can decrypt an associated message. ", "In public key encryption, the key exchange includes the publication of a recipient\"\"s public key that in turn is used by the sender to encrypt a message. ", "A corresponding private key is used by the recipient to subsequently decrypt the encrypted message. ", "Publication can be by posting the public key, for example, to a central site, or by providing the public key directly to the sender. ", "In each of these scenarios, the recipient\"\"s computer must include a decryption engine (software) that uses an appropriate key to decrypt the message. ", "Because there are a variety of encryption algorithms being used on the Internet, a recipient needs to have many different types of decryption engines installed to be able to receive secure messages universally. ", "If the intended recipient does not have a particular decryption engine, the sender cannot utilize that particular encryption technique to send the secure message.", "\nOften a sender will desire to send the same information, for example, over the Internet, to plural recipients who have different decryption engines installed. ", "This adds an additional level of difficulty to the transmission process, because the sender must select the appropriate encryption engine for each recipient. ", "For those recipients who do not have any decryption engine installed, the message simply cannot be sent securely.", "\nWith the promulgation of the Internet, a globally available decryption engine has been installed in almost all new personal computers in the form of a web browser that supports the secure socket layer (SSL) protocol. ", "What is desirable is a system that allows the recipient to use this universally available decryption engine to receive secure messages from any sender regardless of what encryption engine the sender uses. ", "In addition, the system should allow a sender to use one encryption engine to deliver the message to any recipient regardless of what decryption engine the recipient uses. ", "In case the sender and the recipient have compatible encryption and decryption engines, the message may be sent directly. ", "In case the sender\"\"s encryption engine and the recipient\"\"s decryption engine are not compatible, the system will translate the message format to ensure universal interoperability between encryption and decryption engines\nA system and method for providing secure E-mail services. ", "The system includes a forwarding service operable to receive an E-mail message for delivery to a recipient, store the message at least temporarily in a storage means and check for recipient preferences for delivery of the E-mail message content. ", "If no preference is specified and if Web-based delivery is specified, the system provides an E-mail notification to the recipient including a secure link to the message and responds to a page request from the recipient indicating the message including extracting the message from the storage means, formatting the message as a page and delivering the page to the recipient\"\"s web browser. ", "If a preference for delivery other than Web-based is specified, the system delivers the message in accordance with the recipient\"\"s preference.", "\nImplementations of the invention can include one or more of the following advantages. ", "Messages can be encrypted using any available encryption means at the sender and sent to a forwarding service. ", "The forwarding service can forward the message to each recipient according to the recipient\"\"s decryption capability and preference.", "\nA system is provided for secure E-mail services. ", "Secure E-mail messages can be composed or generated using the secure messaging system (using a particular encryption service), the result of which can be attached as a MIME or SMIME message to a conventional E-mail message for transfer to a recipient. ", "In the event the recipient does not have the required decryption capabilities, the E-mail message can be forwarded to a forwarding service. ", "The forwarding service provides an E-mail notification to the recipient of the message. ", "A recipient is not required to have a special viewer or reader and can merely retrieve the message through a web browser by linking to the forwarding service via a secure link such as SSL. ", "Alternatively, if the recipient has designated a preference for delivery, the message can be re-encrypted according to the recipient\"\"s preference and delivered to the recipient directly in accordance with the predefined delivery instructions.", "\nThese and other advantages of the present invention will become apparent from the following description and from the claims." ]	{ "pile_set_name": "USPTO Backgrounds" }	[ 0, 0.005128205128205128, 0.00847457627118644, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0045871559633027525, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.007936507936507936, 0, 0, 0.005291005291005291, 0, 0 ]	0.000731	5
[ "2016-17 Student Discipline Days Missed Report All Offenses\n\nOffense:\n\nThe Student Discipline Days Missed Report reports on days missed by public school students in Massachusetts due to disciplines that the students received for offenses committed, as reported by school districts in the School Safety Discipline Report (SSDR). ", "Days missed is reported by percentage of students in specific ranges of days missed. ", "For more detailed information on the SSDR collection, see the\ndocuments at the School Safety Discipline Report (SSDR) page on the ESE website." ]	{ "pile_set_name": "Pile-CC" }	[ 0.0030581039755351682, 0, 0.02112676056338028 ]	0.008062	5
[ "(a) Civil Penalties.— ", "Whoever knowingly authorizes, consents to, or permits a violation of subsection (a) or (b) ofsection\n14103 or who knowingly violates subsection (a) of such section is liable to the United States for a civil penalty of not more than $10,000 for each violation.", "\n\n(b) Criminal Penalties.— ", "Whoever knowingly violates section\n14103(b) of this title shall be fined under title 18 or imprisoned not more than 2 years, or both." ]	{ "pile_set_name": "Pile-CC" }	[ 0, 0, 0.037037037037037035, 0 ]	0.009259	5
[ "\n788 S.W.2d 399 (1990)\nDavid MIDKIFF and Lexi Midkiff, Relators,\nv.\nHonorable William R. SHAVER, Judge, Respondent.", "\nNo. ", "07-89-0406-CV.", "\nCourt of Appeals of Texas, Amarillo.", "\nMarch 22, 1990.", "\n400 John Steven Dwyre, Lubbock, for relators.", "\nBefore REYNOLDS, C.J., and BOYD and POFF, JJ.", "\nREYNOLDS, Chief Justice.", "\nWe granted leave to file this original mandamus proceeding to determine whether respondent, the Honorable William R. Shaver, Judge of the 140th District Court of Lubbock County, correctly held that the entire medical records of relators, David and Lexi Midkiff, were discoverable when they claimed damages for mental anguish with physical manifestations caused by the real parties in interest. ", "Determining that only those records reasonably related to medical attention sought for the symptoms of the mental anguish alleged are discoverable, we conditionally grant the writ of mandamus.", "\nRelators sought to recover from the real parties in interest, American General Fire and Casualty Company, Walker and Solomon Agency, and Jim Solomon, damages allegedly arising from the mishandling of their insurance claim for water damage to their building and contents on 27 May 1987. ", "After alleging violations of the Texas statutory law and the common law duty of good faith and fair dealing, relators included in their notice letter, sent in compliance with the Texas Deceptive Trade Practices Act, damages of $45,000 for mental anguish, albeit no specific dollar amount was contained in their petition.", "\nAfterwards, in confirming their claims were for mental anguish and not for physical injuries, relators, in answering interrogatories, described their symptoms of the mental anguish. ", "David listed stomachaches, headaches, high stress, ongoing depression, anger, and frustration. ", "Lexi listed rapid heartbeat, shortness of breath, dizziness, exhaustion, stomachaches, headaches, ongoing frustration, depression, anger, and high stress. ", "Both answered that no health care provider had been seen in relation to mental anguish.", "\nLater, relators were requested in writing to execute sworn authorizations to provide \"a complete copy of all medical and/or hospital records pertaining to [relators].\" ", "Objecting to the request, relators did not execute the medical authorization.", "\nStill later, when deposed, David testified that he had not seen any doctor about his physical symptoms. ", "When asked if she had sought medical attention for any of the symptoms of mental anguish, Lexi affirmed that she had, but, on the instruction of her counsel, declined to identify the doctor. ", "Both relators refused, on instructions of counsel, to answer certain questions pertaining to medical attention in connection with their claims for mental anguish.", "\nThereafter, the real parties in interest moved the trial court to compel discovery. ", "401 Relators responded, invoking the physician-patient privilege provided by Texas Rules of Civil Evidence 509(b) and the confidentiality-of-mental-health-information privilege provided by Texas Rules of Civil Evidence 510(b).", "\nBy an order signed 12 December 1989, Respondent found that relators' assertion of mental anguish exceeds the common emotional reaction and places their emotional and mental condition in issue. ", "He thereupon ordered relators to execute the medical authorizations requested, provide to the real parties in interest the names and addresses of all health care providers they have seen or from whom they have sought medical attention since 28 May 1987, and resubmit themselves for deposition and answer the certified questions they previously refused to answer, as well as additional questions that may bear upon answers given to the certified questions.", "\nRelators contend that respondent so clearly abused his discretion by making the order that he should be compelled to rescind it. ", "This obtains, they submit, because they have limited their action to exclude any issue of physical or mental injury, and have consistently represented to all parties and courts that they will not offer medical or psychiatric evidence on the issue of mental anguish. ", "Therefore, they conclude, since there is no basis for respondent's finding that their assertion of mental anguish exceeds the common emotional reaction and raises their claims to mental injury, his order is in derogation of their invoked privileges.", "\nAntithetically, the real parties in interest, embracing respondent's findings, justify his order as being grounded on a procedural rule of discovery with this provision:\nh. Medical Records; Medical Authorization. ", "Any party alleging physical or mental injury and damages arising from the occurrence which is the subject of the case shall be required, upon written request, to produce, or furnish an authorization permitting the full disclosure of, medical records not theretofore furnished to the requesting party which are reasonably related to the injury or damages asserted.", "\nTex.", "R.Civ.", "P. 166b(2)(h) (emphasis added). ", "They defend respondent's findings on the grounds that (1) relators' allegations of $45,000 damages for mental anguish makes it clear they were alleging more than mere mental anguish; (2) relators testified to physical manifestations; and (3) Lexi sought medical attention for some of her symptoms.", "\nGiven respondent's findings, the real parties in interest point out that an exception exists to each of the confidential privileges upon which relators rely\nas to communication or record relevant to an issue of the physical, mental or emotional condition of a patient in any proceeding in which any party relies upon the condition as a part of the party's claim or defense.", "\nTex.", "R.Civ.", "Evid. ", "509(d)(4), 510(d)(5) (emphasis added).", "\nAs a further reason, the real parties in interest submit that, as a practical matter, the medical records sought may or may not establish a pre-existing or unrelated condition bearing directly on whether relators' claimed physical conditions have any causal connection to their claims in this action. ", "However, on submission, they conceded that under the state of the record, respondent's order, and logically their production request, is overbroad in encompassing all of relators' medical and hospital records without limitation as to time or subject matter.", "\nAcceptance of the concession entitles relators to relief from the ordered disclosure of all their medical and hospital records. ", "Then, the remaining and crucial question is whether, as relators contend, respondent abused his discretion by allowing any discovery at all.", "\nAlthough the scope of discovery rests within the discretion of the trial court, Ginsberg v. Fifth Court of Appeals, 686 S.W.2d 105, 108 (Tex.1985), mandamus will lie to vacate orders which are void and for which there is no adequate remedy by appeal, or where there has been a gross abuse of discretion. ", "State v. Sewell, 487 402 S.W.2d 716, 718 (Tex.1972). ", "An abuse of discretion occurs when the trial court's action is arbitrary, unreasonable or based upon a gross and prejudicial error of law, Johnson v. Fourth Court of Appeals, 700 S.W.2d 916, 918 (Tex.1985), or is without reference to any guiding rules and principles. ", "Downer v. Aquamarine Operators, Inc., 701 S.W.2d 238, 241-42 (Tex.1985), cert. ", "denied, 476 U.S. 1159, 106 S.Ct. ", "2279, 90 L.Ed.2d 721 (1986). ", "Then, by attacking respondent's order on the clear-abuse-of-discretion ground, relators have assumed the heavy burden of establishing that respondent lacked the discretion to make the decision entered, because the facts and law required a different decision. ", "Johnson v. Fourth Court of Appeals, 700 S.W.2d at 917-18.", "\nIn the past, the distinction between mental anguish and mental injury was not firmly drawn in Texas law. ", "The blurring occurred in recognized exceptions to the general rule that recovery for mental anguish requires proof of a physical injury, or a physical manifestation of mental anguish. ", "The exceptions permitted recovery for mental anguish without proof of physical manifestations in cases of intentional torts, gross negligence, or a willful and wanton disregard for another's rights, because the \"nature of the torts assumes that the claimants will suffer mental injury\" and, therefore, \"[t]here is no need to require proof of physical manifestation of the mental injury.\" ", "Moore v. Lillebo, 722 S.W.2d 683, 684-85 (Tex.1986) (emphasis added).", "\nLater, it was settled that a routine allegation of mental anguish does not raise an issue of the party's mental condition in the absence of an assertion of mental injury that exceeds the common emotional reaction to an injury or loss. ", "Coates v. Whittington, 758 S.W.2d 749, 753 (Tex.1988). ", "In this regard, mental anguish is the emotional distress that typically accompanies the tortious act, id. at 752; Moore v. Lillebo, 722 S.W.2d at 688, and it may, though it need not, result in physical injury or physical manifestations. ", "St. Elizabeth Hosp. ", "v. Garrard, 730 S.W.2d 649, 652-53 (Tex. ", "1987).", "\nIn this case, relators' allegation of mental anguish was the ordinary one. ", "Although afterwards they identified both emotional and physical manifestations of their mental anguish, the physical manifestations named were only those commonly associated with mental anguish. ", "See e.g., id. at 652; Moore v. Lillebo, 722 S.W.2d at 686.", "\nThen, contrary to respondent's finding, relators did not place their mental condition in issue so as to justify discovery of their medical or mental health records on that condition pursuant to the authorization of rule 166b(2)(h), supra, or under the mental condition exception of rules 509(d)(4), or 510(d)(5), supra. ", "This determination is not altered by the fact that they valued their mental anguish at $45,000, a sum viewed by the real parties in interest as extending their allegation to more than mere mental anguish. ", "The amount sought does not convert a mental anguish allegation into some other claim; rather, the amount is, like any other damage demand, only a claim subject to proof, which is best submitted to jurors for evaluation based upon their own experiences. ", "St. Elizabeth Hosp. ", "v. Garrard, 730 S.W.2d at 654. ", "Neither is the determination altered by the fact that Lexi sought medical attention for some of the symptoms of her mental anguish. ", "Absent a showing that she sought psychiatric treatment or proposes to offer psychiatric or psychological testimony to prove her mental anguish, her mental condition is not in issue. ", "Coates v. Whittington, 758 S.W.2d at 752.", "\nNevertheless, since the record does show that Lexi has sought medical attention for some of the symptoms of her mental anguish, a connection is established between her mental anguish complaint and the medical attention she sought. ", "In this regard, we are mindful of the representation that medical evidence will not be offered on the issue of mental anguish; but, so long as she seeks damages by relying upon the symptoms of mental anguish for which she sought medical attention, she cannot use her invoked privileges as a shield to prevent discovery of medical and 403 mental health records related to her asserted emotional condition. ", "Tex.", "R.Civ.", "Evid. ", "509(d)(4), 510(d)(5); Ginsberg v. Fifth Court of Appeals, 686 S.W.2d at 107.", "\nSimilarly, so long as she and David pursue their claims for mental anguish with the described physical manifestations, neither of them may refuse to answer questions pertaining to medical attention sought in connection with those claims. ", "Ginsberg v. Fifth Court of Appeals, 686 S.W.2d at 107. ", "Without regard to whether the information elicited by the questions will be admissible at trial, the discovery is at least authorized, with limitations, from the appearance that the questions are so connected with the allegation that they are reasonably calculated to lead to the discovery of admissible evidence. ", "Tex.", "R.Civ.", "P. 166b(2)(a); Jampole v. Touchy, 673 S.W.2d 569, 573 (Tex.1984).", "\nIt follows that under this record, the scope of discovery should have been limited to the medical and hospital records and questions related to the medical attention sought for the symptoms of the respective mental anguish claims. ", "Consequently, respondent clearly abused his discretion by subjecting all of relators' medical records to discovery by ordering the execution of the medical authorizations requested, and mandamus is proper to require the vacation of the order. ", "West v. Solito, 563 S.W.2d 240, 246 (Tex.1978).", "\nWe have not overlooked relators' oblique reference to requiring an in camera inspection by the trial court of any discovery we find less intrusive than that ordered by respondent. ", "Although we have determined, aside from the concession by the real parties in interest, that as a matter of law respondent's discovery order is overbroad, it is respondent's discretion, not ours, that is to be exercised in independently deciding the discoverability and admissibility of medical evidence upon the record as constituted when presented for his decision. ", "Ginsberg v. Fifth Court of Appeals, 686 S.W.2d at 108. ", "Consequently, an in camera inspection of any materials claimed to be privileged is a matter for respondent to decide first. ", "Loftin v. Martin, 776 S.W.2d 145, 147 (Tex.1989); Peeples v. Hon. ", "Fourth Supreme Judicial Dist., ", "701 S.W.2d 635, 637 (Tex.1985).", "\nWe are confident that respondent will promptly set aside his 12 December 1989 discovery order. ", "The writ of mandamus will issue only if he fails to do so.", "\n" ]	{ "pile_set_name": "FreeLaw" }	[ 0.034782608695652174, 0, 0, 0.02702702702702703, 0, 0.02127659574468085, 0.08695652173913043, 0.04, 0.012658227848101266, 0, 0.010452961672473868, 0.003125, 0, 0.010526315789473684, 0.0064516129032258064, 0, 0.005917159763313609, 0, 0.009523809523809525, 0.005235602094240838, 0, 0, 0.008849557522123894, 0, 0, 0, 0, 0, 0.009345794392523364, 0, 0, 0, 0, 0.003367003367003367, 0, 0, 0, 0, 0, 0, 0, 0, 0.007142857142857143, 0.006557377049180328, 0.018518518518518517, 0.007462686567164179, 0.012658227848101266, 0, 0, 0, 0.03508771929824561, 0, 0, 0, 0.028985507246376812, 0, 0.01818181818181818, 0.004219409282700422, 0.05, 0, 0, 0, 0, 0.034482758620689655, 0, 0, 0, 0.05, 0.03225806451612903, 0.007575757575757576, 0, 0.024390243902439025, 0.004310344827586207, 0, 0, 0, 0, 0.039473684210526314, 0, 0.05454545454545454, 0, 0, 0, 0.015384615384615385, 0, 0, 0.02127659574468085, 0, 0, 0.05454545454545454, 0, 0.030303030303030304, 0.03225806451612903, 0, 0, 0, 0 ]	0.009125	5
[ "Acute pulmonary edema as a complication of anti-snake venom therapy.", "\nPolyvalent Anti-snake Venom (ASV) is a life-saving antivenin for severe envenomation due to snake bite in India. ", "ASV infusion is occasionally associated with severe allergic reactions, i.e. anaphylaxis and death. ", "We report a rare instance of non-cardiogenic pulmonary edema due to ASV infusion in an eleven years old boy." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0.017543859649122806, 0.01, 0.009259259259259259 ]	0.009201	5
[ "The dust released in the CARE experiment scattered sunlight, creating a bright cloud that could be seen at visible wavelengths for several minutes. ", "The cloud’s effects on the ionosphere lingered longer, however, and were detected by radar for about four hours after the dust’s release. ", "This image was taken about seven minutes after the rocket launched (Image: Adhikarimayum Gopal/NRL) A NASA Black Brant XII rocket launches on Saturday evening carrying the CARE experiment (Image: NASA)\n\nUpdate on 23 September: The dust released in the CARE experiment scattered sunlight, creating a bright cloud that could be seen at visible wavelengths for several minutes before it dispersed. ", "The cloud’s effects on the ionosphere lingered longer, however, and were detected by radar for about four hours after the dust’s release. ", "Researchers are still analysing the data and expect to know more about the results in the coming weeks. ", "Watch a video of the cloud\n\n\nSee a gallery of noctilucent clouds\n\nThe study of Earth’s mysterious noctilucent clouds got a boost on Saturday, when a rocket was launched to create an artificial cloud at the edge of space.", "\n\n“Noctilucent”, or night-shining, clouds float dozens of kilometres higher than other clouds, at an altitude of about 80 kilometres. ", "Because of their height, they can be seen glowing before sunrise or after sunset as the sun illuminates them from below the horizon.", "\n\nThe clouds were first observed above polar regions in 1885 – suggesting they may have been caused by the eruption of Krakatoa two years before. ", "But in recent years they have spread to latitudes as low as 40°, while also growing in number and getting brighter – a change that some attribute to global warming.", "\n\nThe ice-covered particles in these clouds are commonly thought to get their start as tiny dust particles that had been sloughed off comets and meteoroids. ", "See a gallery of noctilucent clouds\n\nThese particles build up a charge as they are bombarded by fast-moving electrons and ions. ", "Since charged particles reflect radio waves, they are good candidates for radar studies, which could help measure the dust at an early stage in the clouds’ formation. ", "But the radar data is hard to interpret.", "\n\nTo get a better sense of how high-flying dust reflects radio waves, researchers launched the Charged Aerosol Release Experiment (CARE) at 2346 GMT on Saturday from NASA’s Wallops Flight Facility in Virginia. ", "The experiment, which blasted off on a Black Brant XII suborbital sounding rocket, spewed more than 100 kilograms of aluminium oxide into the atmosphere at an altitude of about 280 km.", "\n\nRadar scatter\n\nA combination of ground- and space-based instruments will watch this cloud for days and perhaps months as its particles become charged, sink, and disperse. ", "Laser pulses will be used to measure the density of the particles in the cloud. ", "These will be compared with radar measurements of the plume.", "\n\n“Our primary science goal is to understand [how] radar [scatters] from a dusty plasma,” says CARE’s principal investigator, Paul Bernhardt of the Naval Research Laboratory in Washington, DC. “", "We want to understand what kind of information you get back when you send out radar pulses.”", "\n\nRadar has been used to examine icy dust that hovers some 90 km above the Earth and can grow to become the ice particles inside noctilucent clouds, says Scott Bailey of Virginia Tech in Blacksburg. ", "He is a lead scientist for NASA’s Aeronomy of Ice in the Mesosphere spacecraft, which launched in 2007 to study noctilucent clouds.", "\n\nControlled experiment\n\nBut at the moment, interpreting radar measurements of these proto-cloud particles is difficult. ", "Although they reflect radar brightly, it is difficult to say how large the particles are or how many there might be, Bailey says.", "\n\nStudying an artificial cloud created in a controlled manner could help resolve these uncertainties. “", "If the radar could be used to say exactly what the population of particles is up there that the ice is forming around, that would be a major step forward,” Bailey told New Scientist.", "\n\nThe CARE experiment could also pave the way for future launches that would use the uppermost part of Earth’s atmosphere as a large physics laboratory for studying charged dust, Bernhardt says. ", "Dusty plasmas, like those that will be created in the CARE experiment, are seen in a range of environments, from Saturn’s rings and comet tails to the dust hovering above the lunar surface.", "\n\nSee a gallery of noctilucent clouds" ]	{ "pile_set_name": "OpenWebText2" }	[ 0.006756756756756757, 0, 0.012658227848101266, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.009523809523809525, 0.005434782608695652, 0, 0, 0, 0.015463917525773196, 0, 0.005025125628140704, 0.015267175572519083, 0, 0.007751937984496124, 0, 0.01098901098901099, 0.005128205128205128, 0.010582010582010581, 0 ]	0.003486	5
[ "Familok\n\nFamilok is a type of house for many families, designed for workers of the heavy industry, mainly coal miners, built at the end of the 19th century and beginning of the 20th century in the cities and towns of Poland.", "\n\n\"Familok\" is a Silesian way of pronouncing the original German name, Familien-Block (lit. ", "family apartment house).", "\n\nIn several towns they are protected by conservationists and renovated due to the historical significance. ", "The protected familoks include the ones in Nikiszowiec of Katowice, Kolonia Zgorzelec in Bytom, Ruda Śląska, cities situated in Poland, and Bohumín situated in Karviná District, Moravian-Silesian Region, Czech Republic, on the border with Poland.", "\n\nExternal links \n Old familoks in Katowice-Nikiszowiec in black and white\n\nCategory:House types\nCategory:History of Silesia\nCategory:Architecture of Poland\nCategory:Architecture of Germany" ]	{ "pile_set_name": "Wikipedia (en)" }	[ 0.004464285714285714, 0.010869565217391304, 0, 0, 0.012195121951219513, 0.010582010582010581 ]	0.006352	5
[ "Plenary session\n\nA plenary session or plenum is a session of a conference which all members of all parties are to attend. ", "Such a session may include a broad range of content, from keynotes to panel discussions, and is not necessarily related to a specific style of presentation or deliberative process.", "\n\nThe term has been used in the teaching profession to describe when information is summarized. ", "This often encourages class participation.", "\n\nThe Congress of Vienna is an example of a congress that did not meet in plenary sessions.", "\n\nWhen a session is not fully attended, it must have a quorum to conduct business or make decisions—the minimum number of members required (by the group's charter or bylaws) to conduct its business.", "\n\nSome organizations have standing committees that conduct the organization's business between congresses, conferences, or other meetings. ", "Such committees may themselves have quorum requirements and plenary sessions.", "\n\nSee also\n\n Floor (legislative)\n\nCategory:Meetings\n\nes:Asamblea\nja:本会議" ]	{ "pile_set_name": "Wikipedia (en)" }	[ 0, 0, 0, 0, 0.01098901098901099, 0, 0, 0, 0 ]	0.001221	5
[ "Does the thought of a Norris Trophy candidate who will turn 37-years-young in December raise an eyebrow? ", "What if I added that this defenseman is part of the “lacking unit” on Philadelphia’s blue line? ", "Absurd as it may sound, Mark Streit could very well vie for the award that’s given to the league’s top defensive player. ", "But don’t take my word for it – see for yourself.", "\n\nAn Offensive Defenseman\n\nWhen former Flyers GM Paul Holmgren acquired Mark Streit from the New York Islanders, he essentially killed two birds with one stone. ", "The 9th-round pick of the Montreal Canadiens in 2004 enjoyed a benchmark year in 2007-08, showcasing his positional dexterity by launching 62-points for the Habs. ", "It was Streit’s offensive prowess that led Montreal to use him at times as an actual forward.", "\n\nWhen Streit hightailed to Long Island the following season, the Swiss defender continued his scoring ways, setting a career-high in goals with 16. ", "And after solidifying a power play presence in his final season with Montreal (34 power play points), he did the same on the Islanders’ man advantage, scoring 62 percent (10 goals) of his total goals (16) on the power play.", "\n\n“An overage draft pick for the Montreal Canadiens (ninth round in 2004 at age 26), Streit played three years with the Habs, then joined the Islanders as a free agent in 2008. ", "He led them in scoring his first season there with 16 goals and 56 points. ", "But after two superb seasons Streit was cross-checked by teammate Matt Moulson during an Islanders intra-squad scrimmage in September 2010. ", "He fell awkwardly into the boards and wound up missing the entire season with a shoulder injury. ", "Many observers feel he hasn’t quite regained his pre-injury form.” — ", "Rob Parent, Daily Times News\n\nhttps://twitter.com/FlyersNation/status/517853390345605120\n\nDespite the uncertainty thrusted onto Streit since his shoulder injury in 2010, he was tapped to become the Islanders’ 13th captain in team history in 2011. ", "While wearing the “C” in Long Island, Streit would appear in every single regular season game (82-games in 2001-12, 48-games in 2012-13), while notching 34 power play points throughout that span.", "\n\n“What’s not up for debate are the man’s skills with the puck. ", "We did find out pretty quickly why the Candiens tried to play him as a forward.” — ", "Dan Saraceni, Lighthouse Hockey\n\nMany groaned when Holmgren pulled a trade and sign with Streit, not so much because of his age at the time he was acquired, but at the cost. ", "Streit’s age, of course, played into the uneasiness of his four-year, $21 million deal. ", "But based on past and present signings throughout the free agent market, especially at the ever so valuable blue line position, the figures were not only on par for what the market was demanding, it’s been money well spent for the Flyers to this point.", "\n\n“The limited free agent options are the number one reason why the Flyers overpaid Mark Streit last summer fter acquiring his rights from the Islanders was that they still had to pay him according to open market prices to get him to forgo unrestricted free agency. ", "It is also the same reason why the team committed a lengthy big-dollar extension to Andrew MacDonald to pre-empt his UFA status. ", "That’s the price to pay for having traded away so many draft picks over the years and for not having NHL-ready defensemen in the farm system who are currently capable of filling top-six roles on an every game basis.” — ", "Bill Meltzer, Hockey Buzz\n\nI'm expecting Mark Streit to have a very good season and for him still to get lumped in with the Flyers \"bad contracts\" anyway. — ", "Charlie O'Connor (@charlieo_conn) October 1, 2014\n\nStreit avoided much criticism in his first season with the Flyers, due in large part to the frustration surrounding Vinny Lecavalier, but also by quietly putting together another steady season on Philadelphia’s fragile blue line. ", "Streit reached the 10-goal mark for the fifth time in his NHL career, while registering an 8.3 shooting percentage, his highest since his career-year 62-point campaign with Montreal. ", "He did this while adding 15 power play points and a pair of game-winning goals, while logging an average time on ice of 20:39.", "\n\n“He became a good player for us last year,” said Flyers coach Craig Berube. “", "Not that he wasn’t a good player, but coming to a new team and in a new environment it took a little bit … to find his niche.”", "\n\nStill, even with his body of work in the past, Streit has only cracked the top 10 twice among other Norris Trophy candidates, finishing eighth in 2009, and 10th the following year. ", "Even more stunning, Streit finished 13th in voting in the aftermath of his 62-point season with the Habs in 2008.", "\n\nNeedless to say, the likelihood of Streit pushing his way into Norris Trophy conversation this season is an uphill climb. ", "Especially with teammate Kimmo Timonen finishing 12th in the voting last July, despite Streit outscoring Brayden Schenn, Matt Read, and Timonen himself. ", "In fact, Streit scored nine more points than the closest Flyer to last season’s Norris Trophy.", "\n\nAn Increased Role\n\nAlthough Timonen was held in higher regard by everyone from fans and analysts, to Norris Trophy voters, Streit will be the focus of Philadelphia’s blue line now that Timonen has been subtracted from the equation. ", "Even with Braydon Coburn and Andrew MacDonald evening out the team’s top defensive pairings, Streit will undoubtedly be leaned on more in various phases.", "\n\n“I’ve been experienced at doing that,” said Streit. “", "When I was with the Islanders I was their captain for a long time and I was an assistant captain for the Swiss national team. ", "So I think I can help the team and I want to take a little bit more responsibility in the locker room and on the ice than I did last year.”", "\n\nLeadership aside, Streit will be counted on to quarterback the team’s top power play unit. ", "And although the Flyers’ power play went 0-5 in their preseason finale against Washington, Streit’s five power play points in four preseason games factored immensely into his NHL preseason-leading eight points.", "\n\n“One player who looked terrific all through training camp was veteran defenseman Mark Streit, whose eight points led the NHL in preseason scoring entering Friday. “", "Streit will be the Flyers’ new, first-unit power play quarterback. ", "He scored a goal in this game, giving him two in the preseason along with six assists. ", "Streit is also a likely candidate to wear an “A” this season along with Wayne Simmonds as alternate captains.” — ", "Tim Panaccio, CSN Philly\n\nhttps://www.youtube.com/watch?v=GoXC-22K3E0\n\nStreit will begin the season on Philadelphia’s second pairing, along with Nicklas Grossmann. ", "And despite the array of disdain aimed at Grossmann, Streit has increasingly developed a chemistry with his beefier counterpart. ", "This can be seen throughout their time together last season, which began at a rather pedestrian rate, but later blossomed after the Olympic break.", "\n\n“Early in the season, the Streit-Grossmann pairing could be fairly called a mess. ", "Streit alternated between passive defense without the puck and overly-aggressive offense with the puck. ", "Grossmann was struggling when initiating the breakout, and even his usual solid positional play in the defensive zone did not prevent a deluge of goals against with him on the ice. “", "But as the season has progressed, things have dramatically improved. ", "Streit’s style is still aggressive, but now it is complemented by the forwards, whose commitment to backchecking and temporarily moving into coverage has allowed Streit to freelance far more effectively.” — ", "Charlie O’Connor, Broad Street Hockey\n\nEven if this odd couple pairing were to be broken up at some point during the season, an increase in minutes doesn’t necessarily spell doom for the nine-year veteran. ", "Streit’s average time on ice of 20:39 last season was his lowest since the 2007-08 season where he logged an average time of 17:31. ", "But what about his age, you ask? ", "Considering Streit’s total playing time of 83:26 in four preseason games, it looks like that can be easily dismissed.", "\n\nYes, preseason is preseason. ", "But if Streit can produce at the rate he’s done in four preseason games, he’ll demand Norris Trophy votes – even if he doesn’t represent the status quo of elite puck-possessing defensemen.", "\n\nThe Norris Trophy Trend\n\nWhy does it matter that Streit possesses the offensive skill set that can drive a power play rush? ", "To answer that, look a little closer at past Norris Trophy winners.", "\n\nIs it age? ", "Not quite, although Streit’s advanced years, by NHL standards anyway, certainly don’t handicap his chances at joining the mix. ", "In fact, in the past 15 years, a defenseman age 30 or above took home the hardware 11 times. ", "That’s not to say being an experienced veteran holds a distinct advantage. ", "After all, of these 11 years, Nicklas Lidstrom accounted for seven of them, which included two separate runs of winning the award in three consecutive years.", "\n\nThe true trend can be found in the category that doesn’t normally define a defenseman in the first place. ", "It’s scoring.", "\n\nAlthough P.K. Subban won the award in 2013 with only 38-points, he was the lowest scoring defenseman to win the Norris since Washington’s Rod Langway won it with 33-points in 1984. ", "Additionally, the only Norris Trophy candidate to win the award without exceeding 30 points was Doug Harvey, producing only 27-points for Montreal in 1960.", "\n\n“The Norris Trophy is one of the hardest awards to predict, because its definition seems to change almost every year. ", "It is defined as the “defense player who demonstrates throughout the season the greatest all-round ability in the position”, but the area of focus always changes, whether it be for an offensive defenseman like Erik Karlsson, or a bruising body like 7-time winner Nicklas Lidstrom.” — ", "Jake Reiser, TRL Hockey\n\nPerhaps Bobby Orr is to blame for transforming the historical award from one that proclaims the best defensive player to the best offensive defenseman. ", "After all, he was the first defenseman to win the Norris Trophy with triple digit point totals, and did so six times. ", "Is it any surprise that since Orr’s monstrous scoring run ended, three other 100-point scoring defensemen (Denis Potvin, Paul Coffey, and Brian Leetch) had their names added to the list?", "\n\n#Zdeno Chara deserved the #Norris Trophy. #", "Erik Karlsson only knows offense. ", "Someday he may learn defense. ", "The kid was a playoff disaster. — ", "Stan Fischler (@StanFischler) June 21, 2012\n\nErik Karlsson’s award-winning year of 2012, however, brought the discussion back to the quesiton: how is the “best defenseman” determined?", "\n\n“That’s not quite how most who have seen Karlsson would describe his game. ", "Even the Senators appeared to understand his limitations. ", "Karlsson led the team in overall ice time at 25:19 a game, but rarely was used when Ottawa was protecting a precarious lead late. ", "And he certainly wasn’t trusted often when Ottawa was down a man, averaging just 33 seconds a game on the penalty kill. ", "Sixteen other Senators averaged more shorthanded time than that. “", "Contrast that with Wednesday’s other finalists, Shea Weber of Nashville and Zdeno Chara of Boston. ", "Weber was a workhorse as well, averaging 26:09 in ice time, which included a healthy 2:16 of penalty kill time and 3:31 on the power play. ", "Chara checked in at 25:00 overall, 2:43 shorthanded and 2:39 on the power play. ", "Weber and Chara also provided a physical presence that Karlsson does not bring to the game. ", "Weber dished out 177 hits with his 6-foot-4, 232-pound frame, while Chara pounded foes with his mammoth 6-foot-9, 255-pound body 166 times. ", "Karlsson, at just 6-foot, 180 pounds, wisely shied away from so many collisions, managing just 60 hits.” — ", "Douglas Flynn, NESN\n\nAlong with point-scoring, another tendency in those who won is a positive plus-minus. ", "And even though Nicklas Lidstrom came out on top in 2011 with a minus-two rating, only he and Randy Carlyle in 1981 were the only defensemen to capture the trophy with a negative plus-minus since the statistic was first tracked in 1968. ", "With Lidstrom’s manageable minus-two rating in 2011, is there any wonder left as to why Karlsson yielded the award to Duncan Keith this past year?", "\n\nKarlsson, who led all defensemen in points with 74, turned in a minus-15 rating for an Ottawa Senators team that carried an astounding minus-29 goal differential. ", "Duncan Keith, on the other hand, not only scored 13-points less than Karlsson, he also skated at an average of nearly three minutes less than Ottawa’s new captain. ", "Keith’s plus-22 rating, though, was a glaring contrast, which falls into the evolving stat category of winning the Norris Trophy.", "\n\nThese circumstances, as murky as they are, actually help Streit’s cause. ", "After all, who’s going to mistake his presence on the blue line with that of Drew Doughty, or Niklas Kronwall? ", "But with the anticipation of Streit’s offensive numbers to jump, along with his plus-three rating for a Flyers team that finished the season with a plus-one goal differential, it’s not preposterous to suggest his name could, or should, creep into the discussion.", "\n\nIf McDonagh continues on this path, he should absolutely win the Norris Trophy at some point in his career. ", "Offense matters for that trophy. — ", "Dan Rosen (@drosennhl) March 27, 2014\n\nWould it have been laughable to suggest that Streit would outscore Ryan McDonagh, Ryan Suter, and Zdeno Chara? ", "That’s exactly what Streit did last season. ", "If Streit can surpass last year’s totals, why should it be considered shear lunacy to include his name this season with the list of this season’s Norris Trophy candidates?" ]	{ "pile_set_name": "OpenWebText2" }	[ 0.009523809523809525, 0, 0.008264462809917356, 0, 0.024844720496894408, 0.006134969325153374, 0.010752688172043012, 0.006711409395973154, 0.004484304932735426, 0.01694915254237288, 0, 0.007142857142857143, 0, 0, 0.016194331983805668, 0, 0, 0.012048192771084338, 0.017241379310344827, 0.011363636363636364, 0.003968253968253968, 0.007518796992481203, 0.015503875968992248, 0.0045662100456621, 0.025477707006369428, 0.014234875444839857, 0.00546448087431694, 0, 0.02531645569620253, 0, 0.01092896174863388, 0.017699115044247787, 0.008064516129032258, 0.026143790849673203, 0.031914893617021274, 0.01282051282051282, 0.0196078431372549, 0.01818181818181818, 0, 0, 0.010752688172043012, 0.014285714285714285, 0.012048192771084338, 0.029850746268656716, 0, 0.017699115044247787, 0.024390243902439025, 0.015503875968992248, 0, 0.011904761904761904, 0.009615384615384616, 0.005494505494505495, 0, 0.00966183574879227, 0.009708737864077669, 0, 0, 0, 0, 0.010638297872340425, 0.015873015873015872, 0.014925373134328358, 0, 0.015748031496062992, 0, 0, 0.006369426751592357, 0, 0, 0.01092896174863388, 0.012903225806451613, 0, 0.007042253521126761, 0.01694915254237288, 0, 0.016129032258064516, 0.022222222222222223, 0.029411764705882353, 0, 0, 0.01639344262295082, 0.012987012987012988, 0, 0.007692307692307693, 0, 0, 0.020202020202020204, 0.007194244604316547, 0.0125, 0.03260869565217391, 0.007142857142857143, 0.009345794392523364, 0.009345794392523364, 0.008438818565400843, 0.02054794520547945, 0.006060606060606061, 0.012195121951219513, 0.007751937984496124, 0.013333333333333334, 0.018018018018018018, 0.007633587786259542, 0.00909090909090909, 0, 0.04, 0.022727272727272728, 0.011695906432748537 ]	0.010019	5
[ "india\n\nUpdated: Dec 31, 2018 15:47 IST\n\nThe entire state of Nagaland has been declared “disturbed area” for six more months, till June-end, under the controversial AFSPA, which empowers security forces to conduct operations anywhere and arrest anyone without any prior notice.", "\n\nIn a notification, the Home Ministry said the central government is of the opinion that the area comprising the whole of state of Nagaland is in such a disturbed and dangerous condition that the use of armed forces in aid of civilian power is necessary.", "\n\n“Now, therefore, in exercise of the powers conferred by Section 3 of the Armed Forces (Special Powers) Act, 1958 (No. ", "28 of 1958), the central government hereby declares that whole of the said state to be a ‘disturbed area’ for a period of six months with effect from 30th December, 2018, for the purpose of that Act,” the notification said.", "\n\nA home ministry official said the decision to continue the declaration of Nagaland as “disturbed area” has been taken as killings, loot and extortion have been going on in various parts of the state which necessitated the action for the convenience of the security forces operating there.", "\n\nThere have been demands from various organisations in the Northeast as well as in Jammu and Kashmir for repealing the controversial Armed Forces (Special Powers) Act (AFSPA), which, they say, gives “sweeping powers” to security forces.", "\n\nThe AFSPA has been in force in Nagaland for several decades. ", "It has not been withdrawn even after a framework agreement was signed on August 3, 2015 by Naga insurgent group NSCN-IM general secretary Thuingaleng Muivah and government interlocutor R N Ravi in presence of Prime Minister Narendra Modi.", "\n\nThe framework agreement came after over 80 rounds of negotiations spanning 18 years with the first breakthrough in 1997 when the ceasefire agreement was sealed after decades of insurgency in Nagaland." ]	{ "pile_set_name": "OpenWebText2" }	[ 0.007246376811594203, 0.00392156862745098, 0.008333333333333333, 0, 0, 0.004219409282700422, 0.015873015873015872, 0.012605042016806723, 0 ]	0.0058	5
[ "Q:\n\nCan't connect to internet on Kubuntu 14.04, BCM4311\n\nWhen I hover over the check box for WiFi it says \"Wireless disabled\". ", "I don't have access to any form of internet on the laptop. ", "It is a Dell Inspiron E1505. ", "\nOutput of lspci -knn \| grep Net -A3; rfkill list:\n0b:00.0 Network controller [0280]: Broadcom Corporation BCM4311 \n 802.11b/g WLAN [14e4:4311] (rev 01)\nSubsystem: Dell Wireless 1390 WLAN Mini-Card [1028:0007]\nKernel driver in use: wl\n\nA:\n\nYou have a wrong driver installed.", "\nConnect to the internet by wire and run:\nsudo apt update\nsudo apt purge bcmwl-kernel-source\nsudo apt install firmware-b43-installer\nsudo modprobe b43\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0.007874015748031496, 0, 0, 0.0036101083032490976, 0.019736842105263157 ]	0.006244	5
[ "Q:\n\njQuery draggable - how to access the coordinates\n\nHow can you get access to the dynamically-changing coordinates of a draggable object? ", "I don't just want the coordinates at stop, but a constant stream of position information.", "\nIn other words, if I drag object A around, I should be able to get object B to move around in parallel by (1) observing the changes in object A and then (2) applying them to the position of object B.\nIn this code, I want the red block (obj2) to move with the blue (obj1). ", "\n<html>\n<head>\n<style>\n#obj1 {\n position:fixed;\n top:50px;\n left:50px;\n width: 40px;\n height: 40px;\n background-color: blue;\n}\n#obj2 {\n position:fixed;\n top:150px;\n left:150px;\n width: 40px;\n height: 40px;\n background-color: red;\n}\n</style>\n<script src=\"//ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js\" type=\"text/javascript\"></script>\n<script src=\"//ajax.googleapis.com/ajax/libs/jqueryui/1.8.18/jquery-ui.min.js\" type=\"text/javascript\"></script>\n\n<script type=\"text/javascript\">\n $(function () {\n $('#obj1').draggable();\n })\n</script>\n</head>\n\n<body>\n <div id=\"obj1\"></div>\n <div id=\"obj2\"></div>\n</body>\n</html>\n\nA:\n\nYou can use drag event of draggable:\n$(\"#obj1\").draggable({\n drag: function(event, ui) {\n var pos = ui.position;\n $(\"#obj2\").css({\n left: pos.left + 100,\n top: pos.top + 100\n });\n }\n});\n\nDEMO: http://jsfiddle.net/kPEfL/\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0, 0, 0, 0.0010582010582010583 ]	0.000265	5
[ "The clinical significance and assessment of poor peer relations: peer neglect versus peer rejection.", "\nPositive peer relations play a fundamental role in fostering adaptive social-emotional development, and children who experience peer difficulties are at increased risk for poor social development and later maladjustment. ", "Rejected children who are actively disliked by peers are particularly likely to show cross-situational conduct problems and to experience continued rejection over time. ", "Neglected children, who have few friends but are not actively disliked, often evidence social withdrawal; the clinical and predictive significance of their peer problem is yet to be determined empirically. ", "The advantages of including cross-situational ratings of children's behavioral problems along with ratings of their peer relations for clinical assessments are discussed. ", "Specific assessment strategies are presented." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0, 0, 0, 0, 0 ]	0	5
[ "Mast cell proliferation and alterations in bFGF amount and localization are involved in the response of muscle to dystrophin deficiency in hypertrophic feline dystrophy.", "\nTo test the hypothesis that basic fibroblast growth factor and mast cells play a key role in the phenotypic differences between human dystrophinopathies and hypertrophic feline muscular dystrophy, serial sections of dystrophin-deficient, carrier and normal cat muscle biopsy specimens were examined. ", "They were stained immunohistochemically for dystrophin and different markers of differentiation such as desmin, vimentin and utrophin. ", "Basic fibroblast growth factor was increased in the myofibers of dystrophic cats compared to normal controls and carriers. ", "An association of basic fibroblast growth factor with fiber regeneration and necrosis was shown. ", "The amount of mast cells was markedly increased in muscle tissue of dystrophic cats with a clear predominance of tryptase-positive cells present in large amounts in the endomysium. ", "Mast cells, like basic fibroblast growth factor, were concentrated in areas of muscle fiber regeneration and necrosis. ", "Our data concerning basic fibroblast growth factor and mast cells are consistent with a highly abnormal cellular environment in feline dystrophic muscle with very high levels of basic fibroblast growth factor which is likely modulated by mast cells." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	0	5
[ "Q:\n\nTCL: searching a list for elements containing a particular character using lsearch\n\nIn the following list:\n{12 34 23 54 67 75 46}\n\nUsing lsearch, what is the search pattern to be used for finding all the elements from this list which has the number '4' in it? ", "\n(i.e the output should return {34 54 46})\n\nA:\n\nReference: lsearch\nYou can use:\n set newlist [lsearch -all -inline -glob $mylist 4]\n\n-glob is the default, I put it in for documentation purposes.", "\n-all indicates to return all results, not just the first match.", "\n-inline indicates to return the list as the result.", "\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0, 0, 0, 0, 0 ]	0	5
[ "// ALERT STYLES\n// ------------\n\n// Base alert styles\n.alert {\n padding: 8px 35px 8px 14px;\n margin-bottom: @baseLineHeight;\n text-shadow: 0 1px 0 rgba(255,255,255,.5);\n background-color: @warningBackground;\n border: 1px solid @warningBorder;\n .border-radius(4px);\n color: @warningText;\n}\n.alert-heading {\n color: inherit;\n}\n\n// Adjust close link position\n.alert .close {\n position: relative;\n top: -2px;\n right: -21px;\n line-height: 18px;\n}\n\n// Alternate styles\n// ----------------\n\n.alert-success {\n background-color: @successBackground;\n border-color: @successBorder; \n color: @successText;\n}\n.alert-danger,\n.alert-error {\n background-color: @errorBackground;\n border-color: @errorBorder;\n color: @errorText;\n}\n.alert-info {\n background-color: @infoBackground;\n border-color: @infoBorder;\n color: @infoText;\n}\n\n// Block alerts\n// ------------------------\n.alert-block {\n padding-top: 14px;\n padding-bottom: 14px;\n}\n.alert-block > p,\n.alert-block > ul {\n margin-bottom: 0;\n}\n.alert-block p + p {\n margin-top: 5px;\n}\n" ]	{ "pile_set_name": "Github" }	[ 0.012452107279693486 ]	0.012452	5
[ "Q:\n\nUnity3D: Cross Platform Video Streaming?", "\n\nWe are working on a prototyp application using unity3d. ", "Your goal is to create a fluid and fun to use cross platform app.", "\nThe problem we facing right now is streaming (h.264 - mp4) video content over the web. ", "This will be a major feature of our app.", "\nI have already tried MovieTextures and the www class but it seems the files must be in ogg format which we can not provide. ", "On the other hand handheld.playfullscreenmovie seems to be an android and ios only feature which uses the build in video player. ", "This would be great if it would be supported on other platforms (e.g. Win8-Phone) as well.", "\nIs there another cross platform option to stream (h.264 - mp4) video content over the web and display in full screen or as gui object? ", "Or are there any plans to support something like this in the near future? ", "Or is there a stable plugin for such a task?", "\nThanks\n\nA:\n\nmp4 is not a streamable container. ", "If you read the ISO specification, you will see that MP4 can not be streamed. ", "This is because the MOOV atom can not be written until all frames are know and accounted for. ", "This 100% incompatible for live video. ", "There are supersets of MP4 used in DASH that make this possible. ", "Essentially, they create a little mp4 (called a fragment) file every couple seconds. ", "Alternatively you can use a container designed for streaming such as FLV or TS.", "\nYou will probably need to step outside the unity sdk a bit to enable this.", "\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01282051282051282, 0, 0, 0, 0, 0.012658227848101266, 0, 0 ]	0.001274	5
[ "A cross-sectional study of the impact of physiotherapy and self directed exercise on the functional outcome of internally fixed isolated unimalleolar Weber B ankle fractures.", "\nThis study aimed to measure the functional outcome and quality of life in a group of patients with the same fracture type (unimalleolar Weber B ankle fractures) treated operatively at various time points and to explore the determinants of such outcomes. ", "A cross-sectional retrospective population study was conducted. ", "Validated Patient Related Outcome Measures (PROMs) and patient interviews were used. ", "Fifty-one patients were included with a mean age of 54.9 years. ", "Mean follow-up was 25 months (range 4-46 months). ", "Mean functional scores were high (mean AOFAS 79.2, O&M 75.7, VAS-FA 80.5). ", "However, 32% of patients did not classify themselves as fully recovered during interviews. ", "Patient reported self-directed exercise had a statistically significant positive effect on self-reported patient perceptions of outcome (p=0.022) and PROMs (AOFAS p=0.01, O&M p=0.016, VAS-FA p=0.011). ", "Formal physiotherapy rehabilitation was found to have no effect on self-reported patient perceptions (p=0.242) or PROMs (AOFAS p=0.8, O&M p=0.73, VAS-FA p=0.46). ", "Our finding that physical activity is associated with improved outcome would suggest structured exercise programmes should be considered in place of physiotherapy to optimise patient outcomes." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0, 0, 0, 0, 0, 0.02666666666666667, 0, 0.01990049751243781, 0.018518518518518517, 0 ]	0.005917	5
[ "Linda Merhi, 40, appears in Sydney court charged with five counts of making funds available to a terrorist organisation\n\nThis article is more than 2 years old\n\nThis article is more than 2 years old\n\nA former federal public servant has appeared in a Sydney court over allegations she transferred more than $30,000 to fund the terrorism of Islamic State.", "\n\nLinda Merhi, 40, was arrested by the New South Wales joint counter-terrorism team at Parramatta early on Tuesday.", "\n\nIt is alleged she made five transfers via Western Union, which were destined for Isis, between February and October 2015.", "\n\nAustralian federal police Det Supt Ben McQuillan said there was no evidence to suggest Merhi was involved in planning a domestic attack.", "\n\n“We are continuing to investigate both the source of the funds, the methodologies that were used to transfer those funds and the recipients of those funds offshore,” he said in Sydney.", "\n\nMerhi, from the western Sydney suburb of Guildford, faced Parramatta local court on Tuesday afternoon, charged with five counts of intentionally making funds available to or collecting funds on behalf of a terrorist organisation. ", "She showed little emotion during the brief appearance.", "\n\nHer lawyer, Mona El Baba, indicated she would make a bail application next Tuesday and the magistrate, Tim Keady, adjourned the matter.", "\n\nEl Baba refused to comment on the allegations outside court.", "\n\nAccording to court documents, Merhi is accused of transferring the money in sums of $1,982, $2,790.08, $9,810.24, $7,940.26 and $8,000 across the nine-month period.", "\n\nWhen questioned about the length of time between Merhi’s alleged transfers and her arrest, the NSW assistant police commissioner Michael Willing said such complex investigations took time.", "\n\n“There’s a lot of information and evidence to sift through and that’s certainly been the case on this occasion,” he said.", "\n\nMerhi is an Australian citizen, holds no other citizenship and was not known to police. ", "Willing said there was no evidence to suggest her alleged crimes were linked to her employment in a federal government department.", "\n\n“I want to reassure the community that there is no current or impending threat to the community as part of today’s arrest,” he said.", "\n\nIn 2016 in Guildford a 16-year old Sydney schoolgirl was arrested under the same police operation, along with a 20-year-old man accused of raising funds for Islamic State. ", "McQuillan confirmed Merhi’s arrest was linked to those matters but declined to elaborate.", "\n\nOperation Peqin has also investigated the October 2015 shooting of the 58-year-old police employee Curtis Cheng outside Parramatta police headquarters.", "\n\nMcQuillan declined to detail any links between Tuesday’s arrest and previous matters, citing the sensitive nature of the investigation, but said Operation Peqin had been set up to investigate a broad group of people.", "\n\n" ]	{ "pile_set_name": "OpenWebText2" }	[ 0.005681818181818182, 0.017391304347826087, 0.016260162601626018, 0.021739130434782608, 0, 0.008620689655172414, 0, 0.014598540145985401, 0, 0.006024096385542169, 0.015789473684210527, 0, 0.011111111111111112, 0, 0, 0.005747126436781609, 0.02247191011235955, 0.013071895424836602, 0.009174311926605505, 0 ]	0.008384	5
[ "Genotoxicity testing: phage T7 inactivation test of various furan and arenofuran derivatives.", "\nThe genotoxic activities of 28 furan and arenofuran derivatives were tested by the phage T7-inactivation test. ", "The genotoxic activity of the compounds was characterized quantitatively. ", "All the compounds studied have pronounced genotoxic activities in our system. ", "Empirical rules relating structure to genotoxic activity were found. ", "Data obtained with our system were compared with the results of other biological systems (Salmonella assay, SOS Chromotest, CHO/HGPRT, gene amplification) in the case of some compounds included as references." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0, 0, 0, 0, 0.009615384615384616 ]	0.001603	5
[ "World News\n\nShot down airliners\n\nby\nThe Canadian Press \| Story:\n119330 -\nJul 17, 2014 / 1:28 pm\n\nPhoto: The Canadian Press. ", "All rights reserved.", "\n\nFILE - In this July 4, 1988 file photo, people looking for family members walk amid bodies of victims from Iran Air Flight 655 in a morgue in Bandar Abbas, Iran, a day after the plane was shot down over the Persian Gulf by the guided missile cruiser USS Vincennes while the plane was still in Iranian airspace. (", "AP Photo/The Canadian Press, Mohammad Sayyad)\n\nAs unthinkable as shooting down an airliner with hundreds of passengers is, it has happened before. ", "Among the most notable cases in recent decades were an Iranian plane shot down by the U.S. Navy and a South Korean airliner destroyed by a Russian fighter jet.", "\n\nOn July 3, 1988, Iran Air Flight 655, with 290 people on board, was shot down over the Persian Gulf by the guided missile cruiser USS Vincennes while the plane was still in Iranian airspace. ", "The incident took place toward the end of the Persian Gulf War. ", "U.S. officials later determined the Vincennes mistook the Airbus A330 for a fighter jet. ", "The plane was en route from Tehran to Dubai. ", "There were no survivors. ", "The U.S. government eventually reached a financial settlement with the families of the Iranians victims.", "\n\nFive years earlier, Korean Air Lines Flight 007, with 269 passengers and crew, was shot down by a Russian fighter jet west of Sakhalin Island in the East Sea off as it strayed into prohibited Soviet airspace. ", "The plane was en route from New York to Seoul on Sept. 1, 1983, following a route that took it over Alaska before crossing the Pacific Ocean. ", "All on board were killed, including Larry McDonald, a conservative Republican congressman from Georgia. ", "The Soviet Union initially denied knowledge of the incident and later insisted the plane was spying. ", "Soviet leaders refused to release the plane's flight data recorder until several years later. ", "The incident marked an especially tense moment in the Cold War. ", "The incident helped lead to the commercial release of GPS for civilian use, including aviation. ", "The technology was developed by the U.S. military.", "\n\nLibyan Airlines Flight 114 entered Israeli-controlled airspace over the Sinai Peninsula. ", "It was intercepted by two Israeli F-4 Phantom jets fighters, refused to land and was shot down. ", "The Boeing 727 was en route from Tripoli to Cairo via Benghazi on Feb. 21, 1973 but was off course. ", "Five of the 113 people on board survived.", "\n\nComments on this story are pre-moderated and approval times may vary. ", "Before they appear, comments are reviewed by moderators to ensure they meet our submission guidelines. ", "Keep it clean, keep it civil, keep it truthful, stay on topic and be responsible. ", "Comments are open and welcome for three days after the story is published. ", "We reserve the right to close comments before then. ", "Comments that appear on the site are not the opinion of Castanet, but only of the comment writer." ]	{ "pile_set_name": "Pile-CC" }	[ 0.016129032258064516, 0, 0, 0.013605442176870748, 0.006289308176100629, 0, 0, 0.011235955056179775, 0, 0, 0, 0.004739336492890996, 0, 0.009615384615384616, 0, 0, 0, 0.010416666666666666, 0, 0, 0, 0.01, 0, 0, 0, 0, 0, 0, 0.010309278350515464 ]	0.003184	5
[ "In the early 1970s, together with Gregory Isaacs he formed the African Museum record label, although Isaacs soon took sole control of the label, while Dunkley formed a new label, Silver Ring. ", "In 1972 he teamed up with producer Jimmy Radway for two of his most popular singles, \"Keep The Pressure On\" and \"Black Cinderella\". ", "The same year saw the release of Dunkley's Sonia Pottinger produced debut album, Presenting Errol Dunkley , which included the track \"A Little Way Different\"." ]	{ "pile_set_name": "Pile-CC" }	[ 0.015625, 0.007575757575757576, 0.0189873417721519 ]	0.014063	5
[ "ClexaCon 2018 Will Promote LGBTQ+ Women’s Rights\n\nRepresentation has become increasingly important for women who love women, especially in media portrayals. ", "Often enough, storylines of lesbian female relationships are dangled at gay audiences as a form of queerbaiting only to deliver short-lived story arcs. ", "For many LGBTQ+ women, especially younger ones, the connection to these few characters portrayed on-screen are some of the only representation they experience. ", "Yet popular lesbian and bi characters in the media are often met with abrupt and tragic deaths by showrunners. ", "The trend of this trope for gay female characters has been dubbed “bury your gays” and “dead lesbian syndrome.”", "\n\n- Advertisement -\n\nOne of those characters was Commander Lexa of the CW show “The 100” who died suddenly from a stray bullet despite her complex and well-received portrayal throughout the show prior to her unnecessarily devastating demise, adding to the “bury your gays” trope. ", "The lack of consideration in how she was written off the show despite the impact her character as well as her relationship with the bisexual lead character, Clarke Griffin, had on the LGBTQ+ community. ", "Her death inspired an uproar from the community against the trope. ", "One of the most impactful and inspirational movements Lexa’s death has created is the annual ClexaCon which is the largest convention for LGBTQ+ women and allies promoting LGBTQ+ women’s representation in entertainment.", "\n\nThe convention returns for its second year at Las Vegas and includes special guests such as Anna Silk (“Lost Girl”), Natasha Negovanlis (“Carmilla”) and Sarah Shahi (“The L Word”). ", "ClexaCon connects over 3,000 fans, celebrities, creators and writers from over 40 countries and all 50 U.S. states to celebrate queer female characters and stories by and for queer women.", "\n\nLast year’s inaugural event included Sara Ramirez, known for her role as bisexual Dr. Callie Torres from “Grey’s Anatomy,” expressing her own struggles as a biracial and bisexual woman during a queer women of color pop-up panel. ", "Ramirez was just one of the major figures at the event who created conversations to counter the lack of representation of queer female characters as well as directors, producers and writers.", "\n\nThis year plans to do the same with many familiar faces of the few beloved queer characters on-screen as well as some of the women who work behind-the-scenes to keep that representation afloat.", "\n\nIn the current political climate, ClexaCon presents an opportunity to embrace diversity and inclusion and represent as well as open the conversation on where queer women stand behind and in front of the camera. ", "The 2018 convention takes place April 5-9 at the Tropicana Hotel in Las Vegas.", "\n\n11 COMMENTS\n\nHi! ", "Someone in my Myspace group shared this website with us so I came to check it out. ", "I’m definitely enjoying the information. ", "I’m bookmarking and will be tweeting this to my followers! ", "Superb blog and amazing design and style.", "\n\nAre you tired of your ac repair in Dubai? ", "Are you looking for Certified Professionals to carry out your ac repair with improved facilities and in an expert way?. ", "Hot and humid conditions are not easy to tolerate, especially when you are not used to them. ", "But, thanks to the air conditioners – living in such extreme settings can also become a pleasant experience, and more so if you are in Dubai.", "\n\nI personally came right here from a different page on the subject of projectors and considered I should look into this. ", "I enjoy the things I see thus now I”m following you. ", "Looking towards looking at the website yet again.", "\n\nMy friends and I certainly love your blog and find nearly all of the blogposts to be just what I am trying to find. ", "Would you offer guest writers to post content for you? ", "I wouldn’t mind producing a post on tiny house plans or perhaps on some of the subjects you’re writing about on this page. ", "Nice blog!", "\n\nAppreciating the dedication you invested in the site and in depth material you display. ", "It is awesome to discover a site occasionally which is just not the same expired re-written stuff. ", "Great read! ", "We’ve saved your webpage and I am adding the RSS feeds to my Ethereum exchange rate website.", "\n\nI was conversing with a friend of mine about this article and regarding speeding fines too. ", "I think you made a few very good points in this case, we’re also looking forward to find out more stuff from you.", "\n\nGET CONNECTED\n\nThe Pride L.A. distributes 20,000 copies of its print edition every other week. ", "We are the only LGBT newspaper serving Los Angeles and America's only LGBT newspaper distributed residentially door to door. ", "You will find The Pride LA at homes in West Hollywood, Hollywood and at key community gathering spots and retail locations in Los Angeles." ]	{ "pile_set_name": "Pile-CC" }	[ 0, 0, 0, 0, 0, 0.0035714285714285713, 0.009900990099009901, 0, 0.0091324200913242, 0.01639344262295082, 0.0053475935828877, 0.008658008658008658, 0.005263157894736842, 0, 0.004694835680751174, 0.01282051282051282, 0, 0, 0, 0, 0.024390243902439025, 0, 0.008333333333333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.010869565217391304, 0, 0, 0, 0, 0.007246376811594203 ]	0.003088	5
[ "Q:\n\nAndroid: Proper way to handle Activities\n\nFirstly, I'll explain the situation I'm in with my applicaton before I get onto the main question I have. ", "Firstly, I want to find out if the way that I am handling activities is a proper way of handling activities, as I feel it might well not be which in turn is causing my problems.", "\nCurrently I have 3 activities setup. ", "Main.class, Login.class and Display.class. ", "The Main activity doesn't have any UI associated with it at all, it launches other activities. ", "So, the first activity that get's launched when the app is launched is the Main activity, and it goes and reads from a SharedPreferences store whether or not the user is logged in. ", "If they aren't logged in, it will open up Login.class, if they are logged in, it will open up Display.class (both of which have UI's associated with them). ", "It uses startActivityForResult().", "\nBecause of the way I decided to go around working with activities, I needed to override the back button on both Login.class and Display.class: otherwise, it will go back to the Main.class, and re-run the launch activity sequence, which will inturn re-launch the activity that was just running (therefore the back button is useless). ", "So, I overrode the back button to send back an integer of -1 and then finish() the current activity. ", "I've overridden the onActivityResult(int, int, Intent) for Main.class, and if it receives a -1, it will finish() as well, instead of trying to re-launch the activity.", "\nNow, that all worked for how I wanted it, though I have a feeling that it's the completely wrong way to handle activities, and it's causing problems for me later down the track.", "\nIn my application, I decided I wanted to put an app widget and a notification in, both of which will open the app when clicked (via an intent that launches Main.class). ", "I got it all working so that it would do that, though it seems as though starting a new Activity causes problems.", "\nWhat happens is basically, if the application is already running, and someone pulls down the notification and clicks on it, it will open up a new activity of the same application. ", "This is problematic, especially with the way I handle back buttons: When you open a new one, and press the back button, it will close the new one (as expected,) but will then take you back to the OLD one. ", "You can then press the back button again and exit it, but obviously I don't want to release an app that needs the back button to be pressed twice. ", "What is the best way to sort this problem out? ", "I'm happy to completely change the way I handle activities if that's a major part of the problem.", "\nThanks,\nJosh.", "\n\nA:\n\nActually how you set a -1 (which is fine) and then call finish() is perfectly acceptable. ", " I forget the property values, but if you want only a single instance of an Activity there is a way to set that in the manifest ... Task affinity or one of those values - you'll have to look it up. ", " \nAs an alternate, you can override the Application class and use your own to manage application state. ", " Think of it as a singleton tracker for the main Activity .. \"if it already exists use that one, otherwise create a new instance\" kind of thing. ", " When creating your main Activity set a reference in your newly extended Application class (make sure you null this out when main is shutting down), then check to see if a reference is available when onCreate() fires again ... if there is a reference already there use that instance of Main .. if not, proceed as normal and set it.", "\nFood for thought ...\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0, 0, 0, 0, 0.010526315789473684, 0, 0.00641025641025641, 0, 0, 0.009900990099009901, 0.006024096385542169, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.010416666666666666, 0, 0, 0, 0, 0 ]	0.001665	5
[ "The lack of diversity among Oscar nods has, sadly, become tradition and things don't seem to be getting any better. ", "In fact, they're getting worse.", "\n\nFollowing in last year's footsteps, not a single actor of color is up for an award this year. ", "The only films featuring a cast with people of color that are nominated this year are \"Straight Outta Compton\" for Best Screenplay, \"What Happened, Miss Simone\" for Best Documentary and \"Creed\" for Best Supporting Actor -- but for these films, only their white contributors were recognized. \"", "The Revenant,\" whose director, Alejandro González Iñárritu, is Mexican is also nominated. ", "It bypassed actors like Will Smith, for \"Concussion,\" Idris Elba in \"Beasts Of No Nation,\" Samuel L. Jackson in \"The Hateful Eight,\" and Michael B. Jordan and Ryan Coogler for \"Creed,\" all of whom have been heavily praised for their performances this year.", "\n\nWidespread fury erupted last year by people everywhere who flooded social media with #OscarsSoWhite to voice their frustration with the Academy for recognizing so few actors of color. ", "That hashtag, which was created by twitter user @ReignOfApril, has now resurfaced, bubbling up similar expressions of disappointment by the dismal state of diversity among this year's nods.", "\n\n\"The whole discussion about diversity is a great discussion, because now it's at the top of everybody's mind, not just the academy's,\" Isaacs said last year during an Academy reception.", "\n\nAnd while widespread change is understandably slow to come, there has been no progress in the last year.", "\n\nHowever, Isaacs is far from the only person to be held accountable for the lack of representation and recognition of actors of color. ", "Hollywood executives are are mostly white and mostly male and they have failed to prioritize color-conscious casting in their films.", "\n\nUClA's 2015 Hollywood Diversity report highlights that the problem starts at the top, which is dominated by white, male gatekeepers who run the industry's top three talent agencies and major studios. ", "In 2013, 94 percent of CEOs and/or chairs and 92 percent of senior management in the film industry were white, according to the report.", "\n\nMeanwhile, Chris Rock will be the host of this year's Academy Awards when it airs on Sunday Feb. 28. ", "Rock, who has been vocal about diversity (and the lack of it) in Hollywood, wrote a viral op-ed in The Hollywood Reporter last year about this very same issue.", "\n\n\"It's a white industry,\" he wrote. \"", "Just as the NBA is a black industry. ", "I'm not even saying it's a bad thing. ", "It just is.\"", "\n\nAnd while Rock was spot-on about many of his observations, I disagree with one: it IS a bad thing." ]	{ "pile_set_name": "Pile-CC" }	[ 0.008620689655172414, 0, 0, 0.00684931506849315, 0.022222222222222223, 0.01953125, 0.010752688172043012, 0.005291005291005291, 0.0053475935828877, 0, 0, 0, 0.0049504950495049506, 0, 0.019417475728155338, 0, 0, 0.02702702702702703, 0, 0, 0 ]	0.006191	5
[ "As we move into the prophetic time frame relative to the Return of Jesus, the church needs to be awakened, alerted, challenged and taught regarding the common destiny of the Church and Israel. ", "Christian media (Radio and TV) is obviously the best opportunity that we have through which to accomplish this. ", "The return of the Lord is vitally linked with the attitude of the Jewish nation. (", "Matthew 23:39)\n\nTHE MESSIAH COMES TO ISRAEL\n\nMonday, April 18, 2011\n\nAN IMMINENT WAR IN THE MIDDLE EAST\n\nThe Bible is more up to date than tomorrow’s Newspaper. ", "It is a book of history which is also the most accurate and reliable book of prophecy, predicting all the events that will happen at the end of this turbulent age in which we live. ", "A dramatic event will soon happen in the Middle East that will transform the nation of Israel and subsequently impact every nation on earth. ", "This pamphlet contains details of this event that have seldom been recognized even by ardent students of the Bible. ", "It certainly deserves your thoughtful consideration. ", "It may change your life and destiny forever!", "\n\nA war against Israel is certainly inevitable in the very near future.", "All the indications of this are presently extremely evident. ", "The stage has been carefully set by Iran using several terrorist agencies in Gaza, Lebanon, Syria and Egypt. ", "This war has also been graphically predicted in the Bible. ", "The enemy armies are sitting on Israel’s borders awaiting the strategic moment to strike. ", "This war will be intended to annihilate the Jewish nation but will have several unforeseen results that will explode upon the world.", "\n\nIt will be followed by a visitation and revelation of Messiah to Israel. ", "These results will begin in Israel and Jerusalem but the impact will ultimately be felt all around the world.", "\n\nIn our present troubled world three thingsare currently imminent and inevitable. ", "The first is a vicious attack on Israel by all her surrounding neighbours with the aim of totally destroying the Jewish State. ", "The second thing is a miraculous, supernatural intervention by Almighty God to save, deliver and preserve Israel and her population. ", "The third thing will be the visitation and revelation of the Jewish Messiah who will have led Israel to this amazing victory(Zechariah 12:10).", "\n\nThe first of these critical events, the attack upon Israel, will be made by mortal men under the banner of a false god. ", "As such it will be flawed and unsuccessful. ", "The response to the attack will be made by the true God who has declared Himself to be the saviour, deliverer and King of Israel. ", "In the wake of this amazing victory Israel will recognize the identity of their deliverer and the whole nation will humbly acknowledge Him as their long awaited Messiah.", "\n\nFor some years now Israel has been living under the serious threat and threshold of a possible nuclear war. ", "The threats have been consistently made by the President of Iran and the religious Mullahs who support him. ", "President Ahmadinejad is obviously a mentally deranged psychopathic tyrant, capable of anything who is certainly a dangerous person whose threats need to be seriously considered. ", "He is an Haman/Hitler tyrant who must certainly never be underestimated.", "He is spending billions of dollars of his nation’s budget to produce weapons of mass destruction that include nuclear warheads.", "He has also been supplied with hitech missiles capable of reaching targets hundreds of miles away bearing highly destructive warheads.", "\n\nAhmadinejad has already launched the early stages of this war under the auspices of his minions in Syria, Lebanon, Gaza and Egypt.", "Thousands of highly trained terrorist - fanatically minded men and women have dedicated their lives to the cause of destroying Israel.", "They have already launched several efforts to attack, invade and destroy the structure of the Jewish State but each attack so far has been defeated. ", "Nevertheless they continue to persuade themselves that their task is not an impossible one.", "They are constantly planning further more effective attacks and have surreptitiously gained the support of numerous nations and organizations.", "\n\nThe world in general and the church in particular needs to wake up and realize that these threats are more than empty threats. ", "They are explicit, intentional and extremely serious. ", "Not only is Israel under intimidation, the entire world will suffer fearful repercussions from such a war.", "\n\nThe Bible Clearly Predicts These Events\n\nFew people have recognized it. ", "Even fewer are evidently truly convinced that it will happen any time soon. ", "Even though the Bible foretells it and the present world situation confirms it, most people thrust their heads into the proverbial sand and try to ignore the possibility. ", "Secularists of all shades have tried to prove that the Bible is outmoded, unreliable and inaccurate. ", "But they will soon see that Bible prophecy concerning the days in which we now live is meticulously accurate and in considerable detail. ", "Hundreds of prophecies that occur in the Bible have already been fulfilled with amazing accuracy. ", "These were mainly concerning the first coming of Christ to this earth. ", "However there are yet many predictions still to be fulfilled concerning the End Times of this age. ", "Some of those prophecies refer to a war that will be launched upon Israel by her closest neighbours backed by several other nations.", "We will look into some of these prophecies in Psalm 83, Joel 3, Zechariah 12 and elsewhere. ", "Not only does the Bible predict an amazing, startling, supernatural victory for Israel. ", "It also predicts the greatest event that has happened to Israel since the exodus from Egypt.", "It will be the spiritual re-birth and transformation of Israel as a precursor to a worldwide harvest from all nations into the Kingdom of God.", "\n\nA Modern Day Haman/Hitler Has Arisen\n\nThe Book of Esther is coming to life again. ", "And God is calling out to those who “have come to the Kingdom for such a time as this” to be watchmen on behalf of Jerusalem. ", "This great drama was played out on the stage of Persia (modern Iran) when a psychopathic maniac determined to completely annihilate all Jews throughout a vast kingdom. ", "The thrilling story of how God intervened and saved the Jews through the intervention of a young unknown Jewish girl is still celebrated to this day among Jews. ", "How ironic that another madman has taken the centre stage in Iran and declared to all the world his intention to annihilate the Jewish State and restore their land to Islamic rule.", "\n\nBible believers who recognize that Bible prophecy is accurate to the finest detail may understand that history often repeats itself and that this will be the case with Iran. ", "Firstly because a new potential destroyer has arisen breathing fearsome threats against Jews. ", "Secondly because Jehovah God will once again outwit the destroyer and obliterate him.", "Israel is about to be dramatically rescued once again and the ultimate result will be even more sensational than was their deliverance and exodus from Egypt.", "\n\nIran Is Frantically Stockpiling Nuclear Weapons And Missiles\n\nWorking in and with Syria, Lebanon, Russia, North Korea and China, Iran has been working for several years now on a plan to wipe out the Jewish presence in “Palestine.", "”Not only has Ahmadinejad made verbal threats of annihilation he has also made many concrete steps towards his objective by creating a nuclear arsenal at tremendous expense.", "Not even a madman would expend so much money, time and effort into the project he had no intention of fulfilling. ", "The scenario is so much like what happened in Germany in the 1930’s. ", "Initially at that time the world did not take Hitler seriously. ", "Although he had laboriously made his plans widely known to all and sundry, no one took him seriously until he had invaded and devastated several European nations. ", "By the time the world awoke to the dreadful reality that Hitler really mean to carry out his plans it was too late to save millions from tragedy and genocide.", "\n\nIslamic Resolve And Determination\n\nThe agents of Islam have a maniacaland fanatical dedication that defies the understanding of the non Muslim world. ", "The perpetrators of international terrorism are filled with a dark obsession with death.", "Christians may talk, preach and sing about the impending Kingdom of God but their dedication to its reality pales desperately compared to the dedication of Islamic disciples.", "When most Christian speak of dying with Christ they usually have a sentimental, idealistic euphoria with purely spiritual application. ", "In complete contrast when Muslims volunteer for martyrdom they have a very real purpose in mind such as strapping a bomb around their waist and blowing a group of innocent people into eternity.", "The Islamic vision of world domination is not a fairy story. ", "They fully intend to literally gain ascendancy over all humanity and many of them are prepared to enthusiastically lay down their lives to attain it.", "\n\nThe Predicted Result Of The War\n\nThe war that will soon be launched by Israel’s nearest neighbours will produce an amazing, supernatural victory for Israel. ", "The Israeli Defence Force that has already gained an awesome respect through the victories they have won against overwhelming odds, will gain a victory that will eclipse all previous victories.", "This time it will not be Israel’s military skills and strategies that will win the day. ", "It will become recognized by every nation on earth that this victory has been procured with direct divine aid.", "The world will be staggered and stand amazed in awe and wonder before the unusual event in Israel.", "\n\nThe Messianic Unveiling\n\nIsaiah prophesied that Jehovah’s servant (the Messiah) would bring Jacob back to Him and gather Israel to Him.", "He further declared that this task alone was too small for Messiah and that He would also be a light to the Gentiles to bring salvation to the ends of the earth.", "\n\nIsaiah 49:5-6\n\n5 \"And now the LORD says, Who formed Me from the womb to be His Servant, To bring Jacob back to Him, So that Israel is gathered to Him (For I shall be glorious in the eyes of the LORD, And My God shall be My strength),\n\n6 Indeed He says, 'It is too small a thing that You should be My Servant To raise up the tribes of Jacob, And to restore the preserved ones of Israel; I will also give You as a light to the Gentiles, That You should be My salvation to the ends of the earth.", "'\"NKJV\n\nImmediately after the victory has been won the world will then witness a tremendous spiritual phenomena when Israel’s deliver will reveal His true identity as the long promised Messiah.", "\n\nIsrael will become a Messianic Nation when Jehovah pours upon her the anointing of the Holy Spirit and reveals His Messiah. ", "A great army of reapers from the ranks of the house of David will combine with a multitude of Gentile believers to be the “One New Man” and gather in the greatest harvest of all from a world that is experiencing great tribulation.", "Not only will the awe and reverence of God be upon the nations. ", "The knowledge of the Lord Jehovah will also cover the earth as the waters cover the sea (Isaiah 11:9).", "\n\nTo condense and abbreviate what is going to happen soon in the Middle East let us look at what the Bible, the only truly reliable predictor of the future says:\n\n1.A vicious attack, will be soon be launched by all Israel’s Muslim neighbours\n\nPsalms 83:2-8\n\n2 Don't you hear the tumult of your enemies? ", "Don't you see what your arrogant enemies are doing?", "\n\n4 \"Come,\" they say, \"let us wipe out Israel as a nation. ", "We will destroy the very memory of its existence.\"", "\n\n5 This was their unanimous decision. ", "They signed a treaty as allies against you —\n\n6 these Edomites and Ishmaelites, Moabites and Hagrites,\n\n7 Gebalites, Ammonites, and Amalekites, and people from Philistia and Tyre.", "\n\n8 Assyria has joined them, too, and is allied with the descendants of Lot. ", "NLT\n\n2.Jehovah God will completely destroy the enemy armies that lead the attack blowing them way like chaff before the wind\n\nPsalms 83:13-18\n\n13 O my God, blow them away like whirling dust, like chaff before the wind!", "\n\n14 As a fire roars through a forest and as a flame sets mountains ablaze,\n\n15 chase them with your fierce storms; terrify them with your tempests.", "\n\n16 Utterly disgrace them until they submit to your name, O LORD.", "\n\n17 Let them be ashamed and terrified forever. ", "Make them failures in everything they do,\n\n18 until they learn that you alone are called the LORD, that you alone are the Most High, supreme over all the earth. ", "NLT\n\nZechariah 12:5-6\n\n5 And the governors (Hebrew -Alluphim i.e. generals) of Judah shall say in their heart, 'The inhabitants of Jerusalem are my strength in the LORD of hosts, their God.'", "\n\n6 In that day I will make the governors of Judah like a firepan in the woodpile, and like a fiery torch in the sheaves; they shall devour all the surrounding peoples on the right hand and on the left, but Jerusalem shall be inhabited again in her own place — Jerusalem. ", "NKJV\n\nZechariah 12:8-9\n\n8 On that day the LORD will defend the people of Jerusalem; the weakest among them will be as mighty as King David! ", "And the royal descendants will be like God, like the angel of the LORD who goes before them!", "\n\n9 For my plan is to destroy all the nations that come against Jerusalem.", "NLT\n\n3.God will pour out His Holy Spirit on Israel imparting grace and prayers of national repentance to the citizens.", "\n\nZechariah 12:10-14\n\n\"And I will pour on the house of David and on the inhabitants of Jerusalem the Spirit of grace and supplication; then they will look on Me whom they pierced. ", "Yes, they will mourn for Him as one mourns for his only son, and grieve for Him as one grieves for a firstborn.", "\n\n11 In that day there shall be a great mourning in Jerusalem, like the mourning at Hadad Rimmon in the plain of Megiddo.", "\n\n12 And the land shall mourn, every family by itself: the family of the house of David by itself, and their wives by themselves; the family of the house of Nathan by itself, and their wives by themselves;\n\n13 the family of the house of Levi by itself, and their wives by themselves; the family of Shimei by itself, and their wives by themselves;\n\n14 all the families that remain, every family by itself, and their wives by themselves. ", "NKJV\n\nEvery person in Israel must immediately prepare themselves for the following events in the very near future\n\n1.A vicious war will be launched against Israel by all near neighbours\n\n2.A miraculous, supernatural intervention and deliverance will be achieved by God.", "\n\n3.A revelation will occur concerning the “Angel of the Lord” Messiah.", "\n\n4.A national recognition of the true Messiah will happen.(Zechariah 12:10)\n\n5.A time of peace and prosperity for Israel will follow. ", "Isaiah 60:1-3\n\n1\"Arise, Jerusalem! ", "Let your light shine for all the nations to see! ", "For the glory of the LORD is shining upon you.", "\n\n2 Darkness as black as night will cover all the nations of the earth, but the glory of the LORD will shine over you.", "\n\n3 All nations will come to your light. ", "Mighty kings will come to see your radiance. ", "NLT\n\n15 For the LORD will remove his hand of judgment and will disperse the armies of your enemy. ", "And the LORD himself, the King of Israel, will live among you! ", "At last your troubles will be over, and you will fear disaster no more.", "\n\n16 On that day the announcement to Jerusalem will be, \"Cheer up, Zion! ", "Don't be afraid!", "\n\n17 For the LORD your God has arrived to live among you. ", "He is a mighty Savior. ", "He will rejoice over you with great gladness. ", "With his love, he will calm all your fears. ", "He will exult over you by singing a happy song.\" ", "NLT\n\n8.The appearance of the ONE NEW MAN who is both Jew and Gentile will eventuate.", "\n\nEvery person on earth should urgently prepare themselves for this imminent and inevitable event that will ultimately impact all the nations on earth. ", "We must earnestly anticipate the event by calling on God for His mercy and grace to grant us salvation.", "\n\nIsaiah 55:6 Seek the LORDwhile you can find him. ", "Call on him now while he is near. ", "NLT\n\nGod is about to intervene directly in human affairs. ", "He will judge all nations according to their attitude towards Israel. ", "He will also save all whose hearts are surrendered to Him.", "\n\nPsalms 79:6-7\n\n6 Pour out your wrath on the nations that refuse to recognize you — on kingdoms that do not call upon your name.", "\n\n7 For they have devoured your people Israel, making the land a desolate wilderness. ", "NLT\n\nLinks\n\nNEW BOOK RELEASE\n\nThe Messiah Comes to Israel is a contemporary commentary about the inevitable battle predicted in the Bible between Israel and her surroundingneighbor nations. ", "With headlines from today's news coupled with Scripture, author Gerald Rowlands presents an epic account of the past, present, and future of God's chosen people. ", "Within these pages, the author investigates and answers many vital questions:\n\nIs it possible, even probable, that a major Bible prophecy, which has been largely overlooked by most Jewish and Gentile Bible believers, isabout to be fulfilled in the immediate future?", "\n\nDoes the prophet Zechariah predict the exact moment in the prophetic future when the Messiah will dramatically reveal Himself again tothe entire population of Israel?", "\n\nWill the descendants of King David finally embrace their long-promised Messiah and declare Him to the world?", "\n\nThis intriguing book is an introduction to an amazing new possibility that is largely overlooked by authors writing about prophetic subjects.", "The Messiah Comes to Israel encourages a fresh approach to many Scriptures that predict glorious things for Israel- not in the distant future of the Millennium but in the very near future.", "\n\nAddThis\n\nTHE PROPHETIC FUTURE OF THE MIDDLE EAST\n\nHow the descendants of Abraham will affect the future of the world.", "\n\nThe world is currently faced with several possible disasters including global warming, economic collapse and new deadly diseases. ", "However the greatest and most imminent threat is in the Middle East in a war that is about to be unleashed upon Israel which will have the potential to seriously devastate the whole world. ", "This war will undermine the social, political, economic and religious aspects of world society. ", "It is a war that will be conducted by fanatical Islamic forces in their determined ultimate purpose to assume total world domination. ", "Although Islam presents itself publicly as a religion of peace it is actually a religious, political ideology with ambitions to transform the world into an international enclave of Islam. ", "The real power behind this plan is actually a spiritual one and the only power that can withstand and defeat it is also a spiritual power. ", "No political humanistic power can defeat the determined objective of Islam. ", "Only the authority of Jehovah the true God, can achieve victory over the principality of Allah.", "\n\nZechariah predicted this war some 2,500 years ago. ", "He also predicted that in its aftermath, the long awaited Jewish Messiah would appear again to Israel. ", "This miraculous appearance will totally transform Israel and subsequently introduce a new era of peace and prosperity for Israel. ", "God’s glorious light will arise over Jerusalem and all the nations will recognize that God’s presence is there. ", "This horrendous clash of ideologies is inevitable yet many people are too fearful to acknowledge this. ", "Political correctness dictates that we should not even speak of such things lest we offend someone. ", "However, it would be absolute foolishness to capitulate to such ideas and leave ourselves totally unprepared for events that will surely happen and will forever change the world in which we live.", "\n\nGerald Rowlands\n\nQueensland, Australia\n\nISRAEL'S SPECTACULAR PROPHETIC FUTURE\n\nISRAEL'S SPECTACULAR PROPHETIC FUTURE\n\nMost Christian commentators today predict only doom and gloom for Israel in the prophetic future. ", "However I firmly believe that God has a very different agenda for Israel and it is thrilling and exciting. ", "In fact God has made many glorious prophetic pledges to Israel promising peace, prosperity, exaltation and great spiritual blessings in the future. ", "Sadly the Church has taken most of them to herself leaving Israel with only predictions of gloom and judgment to be experienced during the Great Tribulation. ", "The Church has also assigned the many positive promises for Israel to a fulfilment in the Millennium but I personally believe that many of these prophecies will actually be fulfilled long before the Millennium. ", "A considerable number of these predictions were made through the writings of Isaiah. ", "I believe the fulfilment of these and others will transpire following the fulfilment of Zechariah 12: 9, 10." ]	{ "pile_set_name": "Pile-CC" }	[ 0.0051813471502590676, 0.008928571428571428, 0, 0.012422360248447204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.007692307692307693, 0, 0, 0.009259259259259259, 0.00558659217877095, 0.013888888888888888, 0, 0, 0.007575757575757576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.010101010101010102, 0, 0, 0, 0, 0, 0.023809523809523808, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.005780346820809248, 0, 0, 0.015625, 0, 0.006329113924050633, 0.006578947368421052, 0, 0, 0, 0, 0, 0, 0, 0.0051813471502590676, 0, 0, 0, 0.0072992700729927005, 0, 0.0020242914979757085, 0, 0.007936507936507936, 0, 0, 0.00980392156862745, 0, 0, 0, 0, 0, 0.027932960893854747, 0.012987012987012988, 0.0045871559633027525, 0, 0, 0, 0, 0.005263157894736842, 0, 0.007142857142857143, 0, 0, 0.00847457627118644, 0, 0, 0, 0.0022935779816513763, 0.0037174721189591076, 0, 0, 0, 0, 0, 0, 0, 0, 0.01020408163265306, 0.015873015873015872, 0, 0, 0, 0, 0, 0, 0, 0, 0.011904761904761904, 0, 0, 0, 0, 0.017241379310344827, 0, 0, 0, 0, 0.005263157894736842, 0.006172839506172839, 0.0037735849056603774, 0, 0, 0, 0.010638297872340425, 0, 0, 0, 0, 0, 0.010638297872340425, 0, 0.013157894736842105, 0, 0, 0.009708737864077669, 0, 0, 0, 0, 0, 0, 0, 0, 0.006329113924050633, 0.004739336492890996, 0, 0.009259259259259259 ]	0.002239	5
[ "A Bozeman Mainstay Will Breathe New Life into North 7th St.\n\nBozeman, MT – June 17, 2015 – (RealEstateRama) — Construction will soon begin on one of the two large vacant buildings on North 7th. ", "Last week, Universal Athletic Services purchased the IGA building and began a large rehabilitation of the site.", "\n\nUniversal is a Bozeman success story. ", "Started in the back of a car by Larry Aasheim and Dick Hart in 1971, the partners wanted to provide high quality, specialty sporting goods for Montana’s young athletes. ", "Today, Universal has 13 locations in five states. ", "The three Bozeman locations are at capacity, and the new, consolidated facility on 7th will allow the business to continue to grow.", "\n\nUniversal’s new facility will mean good jobs for Bozeman; they plan to start adding as soon as this year to their 60 person Bozeman team. ", "But their community involvement goes well beyond jobs. ", "They are strong contributors to youth athletics offering scholarships to young athletes and sponsoring athletic events, and their staff members volunteer as administrators and coaches on local sports teams. ", "Bozeman’s schools and sports leagues will continue to benefit as Universal grows.", "\n\nAs part of their commitment to Bozeman, Dick and Larry were intent on keeping their headquarters in the downtown core if at all possible. ", "However, the cost of staying downtown was significantly higher than moving to the outskirts of town. ", "Universal identified the vacant IGA building on North 7th as the ideal space and location, but the estimated cost for rehabilitating the building was much greater than for constructing a new one. ", "To make the location work, Universal partnered with First Interstate Bank and Montana Community Development Corporation (Montana CDC) to bring New Markets Tax Credits (NMTC) to Bozeman for the third time.", "\n\n“We work with banks to turn the federal tax credits into cash and then use the money to invest in businesses that will have a profound effect on areas that need revitalization” said Montana CDC’s president, Dave Glaser. “", "In the case of Universal, over $1 million of subsidy was provided to the project through the NMTC program.”", "\n\nThe project helped First Interstate jump back into the New Markets Tax Credit arena. “", "We are dealing with a homegrown Bozeman company that we know, trust and believe in,” said Bruce Parker, Bozeman Regional President of First Interstate. “", "The tax credit funding made the financing more doable for both Universal and First Interstate – which clearly contributed to the feasibility of doing the project. ", "The expertise of Montana CDC has been critical to both borrower and lender to get the job done.”", "\n\nIn May, there may be more tax credits available for Montana businesses. ", "Each year, the federal government authorizes $3.5 billion for the country. ", "Montana CDC has secured just under $300 million for Montana and Idaho and hopes to receive more this year. “", "We would love to see more projects in Bozeman,” said Glaser. “", "As of today in Bozeman, we have funded three projects, Universal, Block G and Town and Country Foods, totaling almost $30MM in capital to the Bozeman area. ", "Imagine the possibilities of what we could do in the coming years.”", "\n\nSenators Daines and Tester would like to see more new markets tax credits for Montana and have been supportive of the program for years. “", "This project will mean a lot for the Bozeman community and Montana’s economy. ", "It’s exciting to see this local business— a made-in-Montana success story—thriving and creating new, good Montana jobs,” said Senator Steve Daines.", "\n\nPopular\n\nRecent\n\nThere’s no better place to live, work, and play than Montana. ", "Building a successful life here starts with having an affordable and accessible place to call home. ", "Still, for many Montanans finding a stable home can come with barriers. ", "We know families are encountering rising housing costs, a low supply of affordable apartments, and housing choice barriers. ", "Every day our teams here at the Montana Department of Commerce are working to break down these barriers and make access to safe housing affordable and accessible\n\nRealEstateRama - Professional Services · Government & Public Policy.", "\nRealEstateRama is a press release distribution platform. ", "We provide press\nreleases from more than 2,000 Government & Public Policy sources." ]	{ "pile_set_name": "Pile-CC" }	[ 0.010309278350515464, 0.018018018018018018, 0.025, 0.011834319526627219, 0.02, 0.007633587786259542, 0.014285714285714285, 0, 0, 0, 0.02142857142857143, 0, 0.00510204081632653, 0.03431372549019608, 0.008968609865470852, 0.009345794392523364, 0.022727272727272728, 0.026143790849673203, 0.006134969325153374, 0.010416666666666666, 0, 0, 0.009259259259259259, 0.016129032258064516, 0.01282051282051282, 0, 0, 0.01282051282051282, 0.006802721088435374, 0, 0, 0, 0, 0.004329004329004329, 0, 0 ]	0.008717	5
[ "Burton's Custom X is classed as a Pro-Caliber snowboard, and Burton are fully aware that this is a strong statement, but the Custom X has repeatedly delivered for snowboarding's most demanding riders. ", "Burton say this is down to 'precise design and powerful drive'. ", "The Custom X is the hardest charging board Burton make, so mush so they say thats it's 'only choice in camber for riders who own podiums and stack serious footage'.", "\n\nRider Weight\n\nIn 1977, well before snowboards were allowed in ski resorts, carpenter Jake Burton started making snowboard prototypes in a barn in south Vermont. ", "He didn’t do it to be cool, he found a need, tested it and built it.", "\n\nAt the time, “snurfers” were a trendy backyard toy, but Jake and the early pioneers saw them as an opportunity to bring the joy of surfing to snow.", "\n\nWith countless snowboard innovations over the years, Burton continue to push the boundaries of snowboarding, both through the world’s best products and supporting the world’s best athletes and events." ]	{ "pile_set_name": "Pile-CC" }	[ 0.009950248756218905, 0.015625, 0.006097560975609756, 0.006134969325153374, 0, 0.006711409395973154, 0.0049504950495049506 ]	0.007067	5
[ "Source of the postNo, there should be no duplicates. ", "If you look at Asteroids-bin.sc for 2003qw111 there's a \"remove\" command right above the barycenter Manwe-Thorondor:\n\nThanks, I did found this to be true for 2007 TY430 (Mors) aswell, so there should be no problem. ", "Just one thing I wasnt to ask you. ", "I did realize the SpaceEngine \"SolarSys.sc\" 0.981 had discovery dates and method displayed for Uranus, Neptune, many moons and Pluto + Charon.", "\n\nI did realize that if this info is displayed on these objects sure should it be the others as well and I did add discovery info on the rest of Dwarf planets + Dysnomia and Vesta, Pallas and Hygiea. ", "I did also fix problems and typos in these files.", "\n\nAfter this I did go through all the named Solar asteroids included in SE and added the same information on them. ", "I did not touch \"Asteroids-bin.sc\" however would you mind if I would add this information on your file for named bin asteroids + their named moons or you could do this yourself after its next update is finished?", "\n\nYou can go and see my files in 0.981 beta test thread if you wish Mosfet. ", "Since if I remember right you have access to it.", "\n\nExample from SolarSys.sc:\n\nMoon \"Ganymede/Jupiter III\"{ ParentBody \"Jupiter\" Class \"IceWorld\"\n\nDiscMethod \"Imaging\" DiscDate \"1610.01.08\"\n\nMass 0.0248 Radius 2631.2\n\nPlanet \"Uranus\"{ ParentBody \"Sol\" Class \"IceGiant\"\n\nDiscMethod \"Imaging\" DiscDate \"1781.03.13\"\n\nMass 14.536 Radius 25559 Oblateness 0.02293\n\nExample of my additions in SolarSys.sc:\n\nAsteroid \"Pallas/(2) Pallas\"{ ParentBody \"Sol\"\n\nDiscMethod \"Imaging\" DiscDate \"1802.03.28\"\n\nMass 0.0000345 Radius 263\n\nExamples I added to Asteroids.sc, Asteroids-small.sc, KuiperBelt.sc, KuiperBelt-small.sc and Comets.sc:\n\nI have finished adding the discovery times of binary asteroids/TNO:s and their moons. ", "I did add the dates for named objects and those objects that were known as \"beta\", \"gamma\", \"A\", \"B\" or something similar. ", "I did also fix the typo on moon of Polonskaya, named Hektor's moon and added the \"\|\" symbols as they will be needed in next SE version.", "\n\nHowever I did have problem with (47171) 1999 TC36. ", "I think there might be an error there because the catalog says largest object in this triple system is \"1999 TC36 A2\". ", "Shouldnt the largest compont be A1 instead of A2? ", "I was not entirely sure which object was which, so could you add their discovery dates plese?", "\n\nAlso were you going to add the moons of 2007 OR10 and Sisyphus as the data was already presented on this thread. ", "Could you also add the second ever discovered TNO binary 1998 WW31 and S/2000 (1998 WW31) 1? ", "The primary is already present in SE but its moon is missing.", "\n\nHello! ", "Do you consider adding the moon of TNO 1998 WW31 soon or have you already added it? ", "As it is a true binary system with two nerly same sized bodies (148 km and 123 km, diameter ratio 0.833) orbiting around one another I do not know how can I calculate the orbit of the primary around the mass center / barycenter to write the information on this object to the files as I did with Sisyphus.", "\n\nIt's been added in the last update . ", "Whenever I update Asteroid-bin.sc I also update the list of asteroids contained in first post. ", "Since 1998 WW31 doesn't appear to have a designation number yet, it's listed in \"Others\" category in that post.", "\n\nIt's been added in the last update . ", "Whenever I update Asteroid-bin.sc I also update the list of asteroids contained in first post. ", "Since 1998 WW31 doesn't appear to have a designation number yet, it's listed in \"Others\" category in that post.", "\n\nHi Mosfet! ", "I don't know if you remember but I helped you with asteroids on the old forum.", "Here are some asteroids. ", "The first three are main belt, the fourth is a moon of comet Siding Spring.", "Should comet moons be classified as comets or asteroids?", "\n\nHi Mosfet! ", "I don't know if you remember but I helped you with asteroids on the old forum.", "Here are some asteroids. ", "The first three are main belt, the fourth is a moon of comet Siding Spring.", "Should comet moons be classified as comets or asteroids?", "\n\nHello! ", "I am not Mosfet, but I can tell you right away from the objects designation that this Siding Spring included in the list you posted is not any of the comets called \"Siding Spring\". ", "Designation similar to (2343) is a minor planet, and not a comet designation. ", "A comet designation would be either C/ or 2343P/. However there is not yet any periodic comet with such a high number as over 2000." ]	{ "pile_set_name": "Pile-CC" }	[ 0, 0.009302325581395349, 0, 0.007042253521126761, 0.015, 0, 0, 0.004739336492890996, 0.013157894736842105, 0, 0.004545454545454545, 0, 0.014814814814814815, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.003289473684210526, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0055248618784530384, 0, 0 ]	0.0018	5
[ "using System.", "Collections.", "Generic;\nusing Microsoft.", "AspNetCore.", "Mvc.", "Rendering;\n\nnamespace Nop.", "Web.", "Framework.", "Models\n{\n /// <summary>\n /// Represents the store mapping supported model\n /// </summary>\n public partial interface IStoreMappingSupportedModel\n {\n #region Properties\n\n /// <summary>\n /// Gets or sets identifiers of the selected stores\n /// </summary>\n IList<int> SelectedStoreIds { get; set; }\n\n /// <summary>\n /// Gets or sets items for the all available stores\n /// </summary>\n IList<SelectListItem> AvailableStores { get; set; }\n\n #endregion\n }\n}" ]	{ "pile_set_name": "Github" }	[ 0.07142857142857142, 0, 0.08, 0, 0, 0, 0, 0, 0.0018587360594795538 ]	0.017032	5
[ "et i = -12 - 3. ", "Let a = i - -11. ", "Let s = 0.01 - 0.31. ", "What is the second biggest value in -0.1, s, a?", "\ns\nLet g = 0.24 - -0.06. ", "Let z be (-4)/(-30) + 160/(-75). ", "Which is the smallest value? ", " (a) -5 (b) z (c) g\na\nLet h be 2/(-5) + 184/(-15). ", "Let s = h + 43/3. ", "Let l = -23/45 + 1/9. ", "What is the biggest value in -1/2, l, s?", "\ns\nLet y be (3/(-4))/((-27)/(-24)). ", "What is the third biggest value in y, -0.2, 4?", "\ny\nLet j = -4.118 - -0.088. ", "Let c = 0.03 + j. Let p = 0.057 + -5.057. ", "What is the third biggest value in c, p, -2?", "\np\nLet z = -1.9 - -10. ", "Let k = 8 - z. Which is the second biggest value? ", " (a) -0.5 (b) k (c) 4\nb\nSuppose -2w + 4w = 32. ", "Let b be w/30 + 1/(-3). ", "What is the smallest value in -5, b, -1/6?", "\n-5\nSuppose j - 3 = 2. ", "Suppose 3 = jr - r + 3m, 4m - 4 = r. Which is the second smallest value? ", " (a) -1 (b) r (c) 0.1\nb\nLet n be 3/3 - 284/4. ", "Let z = n - -349/5. ", "Let u = -4 + 3. ", "What is the third biggest value in z, 0, u?", "\nu\nLet r = 5.5 - -2. ", "Let y = 7 - r. Let i = -6.4 + 6. ", "Which is the smallest value? ", " (a) y (b) 0.4 (c) i\na\nLet o = 0.64 - 0.54. ", "Which is the third smallest value? ", " (a) 10 (b) -3 (c) o\na\nLet n = 50 - 49.8. ", "Which is the third smallest value? ", " (a) -0.1 (b) -3 (c) n (d) 1/6\nd\nLet z be (-4)/(-10) + (-2358)/45. ", "Let k = z - -262/5. ", "Which is the smallest value? ", " (a) k (b) 2/17 (c) 5\nb\nLet p = 0.17 - 1.77. ", "Let x = 1.2 + p. What is the third smallest value in -4, -3, x?", "\nx\nLet q(v) = -v3 + 2v*2 + v - 2. ", "Let t be q(2). ", "Let z = 0.04 + 0.04. ", "Let x = 3.08 - z. Which is the second biggest value? ", " (a) -2 (b) x (c) t\nc\nLet w be (-128)/(-22) + 162/(-27). ", "What is the third smallest value in -0.3, 11, w, -2/3?", "\nw\nLet d = 0.39 - -0.01. ", "Let i = -6 - -6.3. ", "Let m = d - i. Which is the second smallest value? ", " (a) m (b) 2/11 (c) 1\nb\nLet g = -16 - -13. ", "Which is the biggest value? ", " (a) -2/5 (b) g (c) 6\nc\nSuppose -4t - 14 = g, 6 - 14 = 4t + 4g. ", "Let l = 2 - 2.4. ", "Which is the smallest value? ", " (a) -1/7 (b) t (c) l\nb\nLet m = -1.1 - -0.7. ", "What is the smallest value in m, 0.1, -0.3?", "\nm\nLet p(q) = 4q + 7. ", "Let r be p(-7). ", "Let x be (-2)/535/r. Let i be ((8/7)/(-4))/2. ", "Which is the third biggest value? ", " (a) 0.3 (b) x (c) i\nc\nLet x be 38/8 - 92/23. ", "Which is the second biggest value? ", " (a) x (b) -4 (c) -12\nb\nLet w be (-1 + 18/15)3. ", "Suppose 4m - 14 = d + 2d, m + 3 = 4d. ", "Suppose 4x = m + 3. ", "Which is the biggest value? ", " (a) x (b) w (c) -0.2\na\nLet g = 0.35 + -4.35. ", "What is the second smallest value in g, 0.2, -1.1, -2?", "\n-2\nLet x = -1.08 - -0.08. ", "Which is the third biggest value? ", " (a) -2/5 (b) x (c) 4\nb\nLet t = -0.848 + -0.052. ", "What is the third biggest value in 2, t, 2/17, -5?", "\nt\nLet u be (-122)/106 + 4/4. ", "Let w = u - -300/583. ", "What is the third biggest value in w, 5, 3?", "\nw\nLet x = 4 - 4. ", "Let n = x - 1. ", "Let r = n + -3. ", "Which is the third smallest value? ", " (a) 1/8 (b) 0.5 (c) r\nb\nLet x = -104 + 100. ", "What is the biggest value in x, -12, -3?", "\n-3\nLet s = 2.7 + -2.9. ", "What is the second smallest value in s, -2/3, -5?", "\n-2/3\nLet t = -7 + 4. ", "Let v = -96.7 - -87. ", "Let z = -10 - v. What is the third smallest value in t, z, -1?", "\nz\nSuppose 0 = -c - 30 + 4. ", "Let j be -2(-1 + (-28)/c). ", "Let r = 0.3 - 2.3. ", "What is the smallest value in -2/3, j, r?", "\nr\nLet d = 53/38 - -2/19. ", "Let r be (-3)/((-6)/(-10))-1. ", "Which is the third biggest value? ", " (a) -0.6 (b) r (c) d\na\nSuppose -4n + h - 60 = 0, 3h + 2 = -3n + 2n. ", "Let z = -14 - n. Which is the biggest value? ", " (a) -4 (b) -3 (c) z\nc\nLet r = 7 - 7. ", "Let o = 9.3 - 9. ", "What is the biggest value in r, -4, o?", "\no\nSuppose -10 + 8 = d. Let a = 2 - 7. ", "What is the third biggest value in -0.1, a, d?", "\na\nLet v be (2/(-28))/(44/(-154)). ", "Which is the second biggest value? ", " (a) 2 (b) v (c) -0.3\nb\nLet l = 1.73 + -3.73. ", "What is the third biggest value in 0.4, 0.2, -1/5, l?", "\n-1/5\nLet q be 6-110/(-135). ", "Let g(f) = -f + 7. ", "Let r be g(5). ", "Which is the third smallest value? ", " (a) r (b) q (c) 3\nc\nLet h = 9 + -9.4. ", "Let d = h + 0.4. ", "What is the third smallest value in d, 1, 0.4?", "\n1\nLet w be 14/6 + 5/(-15). ", "Let z(k) = -4k + 3k + 2 + 4 + w. Let y be z(6). ", "What is the smallest value in 1, y, 1/5?", "\n1/5\nLet n = -91 - -90. ", "Let j = -4 + 1. ", "Which is the second smallest value? ", " (a) j (b) n (c) 0\nb\nLet m(d) = -d - 10. ", "Let h be m(-12). ", "What is the biggest value in 4, h, -5?", "\n4\nLet q = -10 - -7.9. ", "Let j = -0.9 + q. Let x = 0 + j. Which is the second biggest value? ", " (a) 3/4 (b) 0.4 (c) x\nb\nLet w = -38 + 188/5. ", "What is the second smallest value in 0.4, -2/3, w, -7?", "\n-2/3\nLet m = -3.4 + 0.4. ", "Let d = -0.9 - 0.1. ", "Let n = d - -2. ", "Which is the third smallest value? ", " (a) 0 (b) n (c) m\nb\nLet i be (-22)/442/276. ", "Let d = -2/23 - i. Which is the third smallest value? ", " (a) -2 (b) -0.3 (c) d\nc\nLet b = 0.027 + 0.073. ", "Let j be (8/36)/(2/(-6)). ", "What is the second smallest value in -0.3, b, j?", "\n-0.3\nLet o(p) = -p + 8. ", "Let y be o(5). ", "What is the fourth smallest value in y, 6/11, 5, -3/4?", "\n5\nLet x = -4 + 9. ", "Let v = 10 + 0. ", "Let g = v - 7. ", "Which is the second biggest value? ", " (a) x (b) g (c) 0.5\nb\nLet t = 20/19 + -218/171. ", "What is the fourth biggest value in 0, t, 1, -1?", "\n-1\nLet p = -0.3 - -1.3. ", "Let d(o) = o*3 - 12o*2 - 12o + 18. ", "Let f be d(12). ", "Let h be (-2 - -5) + f/35. ", "What is the smallest value in h, -1/7, p?", "\nh\nLet w = 15 - 19. ", "Let k be ((-10)/4)/((-1)/2). ", "Which is the second biggest value? ", " (a) k (b) w (c) 2/13\nc\nLet j = -37/210 + -1/42. ", "What is the smallest value in -0.4, j, -2/7?", "\n-0.4\nLet p = 133 - 125.9. ", "Let s = p + -7. ", "Let f = -0.6 + s. Which is the smallest value? ", " (a) 2 (b) -4 (c) f\nb\nSuppose -14 = 3x - 5o, -14 = 5x - 5o - 4. ", "Let p = -0.1 - -0.2. ", "Which is the smallest value? ", " (a) x (b) 2/5 (c) p\nc\nLet k(w) = -w*2 - 10w + 9. ", "Let z = 17 + -33. ", "Let o = 5 + z. Let h be k(o). ", "What is the biggest value in h, 5, -2/7?", "\n5\nSuppose c = -3h - h + 22, 5c - 2h = 0. ", "What is the fourth smallest value in -1, c, 0.02, -4/5?", "\nc\nLet z = -1.7 - -1.8. ", "Let t = -0.7 - z. What is the second biggest value in -1/4, t, -2/7?", "\n-2/7\nLet f = -0.045 - 0.055. ", "Which is the second biggest value? ", " (a) -0.4 (b) 0.1 (c) f\nc\nLet a = 38.5 - 39. ", "Let z = 6.3 - 6. ", "What is the third smallest value in -5, a, z?", "\nz\nLet y = -11 + 10. ", "Let w = -47/45 - -19/15. ", "Which is the second smallest value? ", " (a) w (b) y (c) 2/5\na\nSuppose -15v = -10v + 5. ", "Which is the smallest value? ", " (a) v (b) 0.4 (c) 3/7 (d) 0.5\na\nLet o = 27 - 28.05. ", "Let k = o + 1. ", "Let u = 0.15 - k. Which is the second smallest value? ", " (a) 4 (b) -1 (c) u\nc\nLet q = -31 - -30. ", "Which is the third smallest value? ", " (a) 4 (b) 0.8 (c) q\na\nLet q = 11 - 6. ", "Let m = 0.09 + 3.91. ", "Which is the biggest value? ", " (a) q (b) m (c) 0.5\na\nLet d = -8.87 - 0.13. ", "Let l = -8 - d. What is the biggest value in -2, 4, l?", "\n4\nLet o = 30 + -32. ", "What is the second smallest value in 0.4, 2, o?", "\n0.4\nLet b be (-8)/126/20. ", "What is the biggest value in 2/13, b, 4/3?", "\n4/3\nSuppose 0 = 4a + 3 + 1. ", "Let r = 0.03 + -0.83. ", "Let n = r - -5.8. ", "What is the smallest value in -2/9, n, a?", "\na\nSuppose -2 = 2m + 4. ", "Let j be m/((-3)/(-2)) - 4. ", "What is the third biggest value in -3/7, j, 1/8?", "\nj\nLet x be (-2 - -4)/(-2) + 1. ", "Suppose 2s + 3s - 20 = x. Let m be (2/s)/((-6)/(-60)). ", "Which is the biggest value? ", " (a) -2 (b) -3 (c) m\nc\nLet h = 0.02 + -3.02. ", "Let u = h - -3.5. ", "What is the biggest value in u, 1, 4?", "\n4\nLet r = 0.4 + 0. ", "Let z = -0.7 + 5.7. ", "Let d be (1/(-14))/(1/8). ", "Which is the second smallest value? ", " (a) z (b) d (c) r\nc\nLet m = -7 + 4. ", "Let h = 0.02 - 0.02. ", "What is the second smallest value in m, h, 4?", "\nh\nLet t = 10 - 6. ", "Let g = t + -4.5. ", "Which is the second smallest value? ", " (a) g (b) -2 (c) 2/3\na\nLet w = -20 - -17. ", "Which is the fourth smallest value? ", " (a) -2 (b) w (c) 2 (d) -6\nc\nLet h be (21/84)/((-7)/8). ", "Which is the third biggest value? ", " (a) 0 (b) h (c) 2\nb\nLet o be 6 + (-3)/(3 - 2). ", "Suppose 13 = oj + 1. ", "Which is the biggest value? ", " (a) j (b) -1 (c) 0.5\na\nLet w = 9 + -10. ", "Let r be (-3 - -1 - (-88)/24) + -3. ", "Which is the second biggest value? ", " (a) 0 (b) w (c) r\nb\nLet n = -0.24 + -0.06. ", "Let c = -4.7 + n. Let o = 164 + -163. ", "What is the second smallest value in c, 2, o?", "\no\nSuppose -3j - 3 = -3i - j, -5j = 5*i - 30. ", "What is the second smallest value in -0.03, 0, i?", "\n0\nLet u = -18 + 128/7. ", "Let x = 0.08 + 3.92. ", "Let s = 22 - 464/21. 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[ "---\nabstract: \|\n The Heisenberg groups are examples of sub-Riemannian manifolds homeomorphic, but not diffeomorphic to the Euclidean space. ", "Their metric is derived from curves which are only allowed to move in so-called horizontal directions.", "\n\n We report on some recent progress in the Analysis of the Hölder topology of the Heisenberg group, some related and some unrelated to density questions for Sobolev maps into the Heisenberg group.", "\n\n In particular we describe the main ideas behind a result by Hajłasz, Mirra, and the author regarding Gromov’s conjecture, which is based on the linking number. ", "We do not prove or disprove the Gromov Conjecture.", "\naddress: 'Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA'\nauthor:\n- Armin Schikorra\nbibliography:\n- 'bib.bib'\ntitle: 'Hölder-Topology of the Heisenberg group'\n---\n\nH=W-problem for maps into manifolds and the role of topology\n============================================================\n\nWhen are Sobolev maps into manifolds essentially smooth?", "\n\nTo study this question, let us be more precise. ", "Let $\\mathcal{N} \\subset {\\mathbb{R}}^N$ be a (for presentations sake) smooth, compact Riemannian manifold without boundary embedded in the Euclidean space ${\\mathbb{R}}^N$. There are two ways to define the Sobolev space of maps from a $d+1$-dimensional domain $\\Omega \\subset {\\mathbb{R}}^{d+1}$ into $\\mathcal{N}$.\n\n1. ", " (The restriction space) Let $W^{1,p}(\\Omega,\\mathcal{N})$ be all maps $u \\in W^{1,p}(\\Omega,{\\mathbb{R}}^N)$ so that $u(x) \\in \\mathcal{N}$ for almost every $x \\in \\Omega$.\n\n2. ", " (The functional analytic space) Let $C^{\\infty}(\\Omega,\\mathcal{N})$ be all smooth functions maps from $\\Omega$ into $\\mathcal{N}$. Set $$H^{1,p}(\\Omega,\\mathcal{N}) := \\operatorname{closure}_{\\\|\\cdot\\\|_{W^{1,p}}} (C^{\\infty}(\\Omega,\\mathcal{N})),$$ to be the closure of $C^{\\infty}(\\Omega,\\mathcal{N})$ under the $W^{1,p}$-norm $$\\\|f\\\|_{W^{1,p}} = {\\left (\\\|f\\\|_{L^p}^p + \\\|Df\\\|_{L^p}^p \\right )}^{\\frac{1}{p}}.$$\n\nThe above question can then be translated into: when is $H = W$, i.e. $H^{1,p}(\\Omega,\\mathcal{N}) = W^{1,p}(\\Omega,\\mathcal{N})$?", "\n\n(Actually, it is always true the $H^{1,p}(\\Omega,\\mathcal{N}) \\subset W^{1,p}(\\Omega,\\mathcal{N})$, the other direction is the interesting one).", "\n\nThe answer of this question depends on the topology of $\\mathcal{N}$, and also of $\\Omega$. More precisely, the homotopy classes of $\\mathcal{N}$ play a role.", "\n\nTwo continuous maps $f,g: \\S^k \\to \\mathcal{N}$ belong to the same homotopy class (which we denote as elements of $\\pi_k(\\mathcal{N})$) if they can be continuously transformed into one another, that is there exists a homotopy $H: [0,1] \\times \\S^k \\to \\mathcal{N}$ which is continuous and $H(0,\\cdot) = f(\\cdot)$ and $H(1,\\cdot) = g(\\cdot)$. It is easy to check that this induces an equivalence class.", "\n\nWe say that $\\pi_k(\\mathcal{N})$ is trivial, $\\pi_k(\\mathcal{N}) = \\{0\\}$ if and only if for any continuous (or smooth) map $f: \\S^k \\to \\mathcal{N}$ there exists an extended map $F: \\overline{\\B^{k+1}} \\to \\mathcal{N}$ such that\n\n1. ", " $F$ is continous/smooth on $\\overline{\\B^{k+1}}$\n\n2. ", " $F \\big \|_{\\partial \\B^{k+1}} = f$.\n\nThat is to say, any map is (continously/smoothly) deformable to a constant map.", "\n\nThe following is the celebrated result by Bethuel [@Bethuel-1991], see also [@Bethuel-Zheng-1988; @Hang-Lin-2003].", "\n\n\\[th:HWBethuel\\] Let $\\Omega = \\B^{d+1} \\subset {\\mathbb{R}}^{d+1}$ be a ball\n\n- Assume $p \\geq d+1$. Then $W^{1,p}(\\B^{d+1},\\mathcal{N}) = H^{1,p}(\\B^{d+1},\\mathcal{N})$.\n\n- Assume $1 \\leq p < d+1$. Then $W^{1,p}(\\B^{d+1},\\mathcal{N}) = H^{1,p}(\\B^{d+1},\\mathcal{N})$ if and only if $\\pi_{\\lfloor p\\rfloor} \\mathcal{N} = \\{0\\}$.\n\nThe first statement is actually due to Schoen-Uhlenbeck [@Schoen-Uhlenbeck-1983]. ", "Many extensions, e.g. to more general Sobolev spaces, exists; see [@Hajlasz-1994; @Riviere-2000; @Mironescu-2004; @Bousquet-Ponce-VanSchaftingen-2013; @Brezis-Mironescu-2015; @Bousquet-Ponce-VanSchaftingen-2015] and references within.", "\n\nWhy is the topology of the target manifold so important? ", "How does a nontrivial homotopy group obstruct smooth approximation?", "\n\nLet us look at a special case:\n\nAssume that $\\pi_{\\lfloor p\\rfloor} \\mathcal{N} \\neq \\{0\\}$. Then we can find a (w.lo.g. ", "smooth) map $\\varphi : \\S^{d} \\to \\mathcal{N}$ that is nontrivial as an element of $\\pi_{d}(\\mathcal{N})$. That is, any map $\\Phi: \\B^{d+1} \\to \\mathcal{N}$ which coincides with $\\varphi$ at the boundary $\\Phi \\big \|_{\\partial \\B^{d+1}} = \\varphi$ is necessarily discontinuous. ", "So we cannot extend $\\varphi$ to a continuous map on $\\B^{d+1}$. On the other hand, we can easily extend $\\varphi$ to a map on $\\B^{d+1}$ which is in $W^{1,p}(\\B^{d+1},\\mathcal{N})$. Simply take $$\\Phi(x) := \\varphi\\left (\\frac{x}{\|x\|} \\right ) \\in W^{1,q}(\\B^{d+1},\\mathcal{N})\\quad \\forall 1 \\leq q < d+1.$$ This map $\\Phi: \\B^{d+1} \\to \\mathcal{N}$ cannot be approximated in $W^{1,p}$ by smooth functions $\\Phi_k \\in W^{1,p}(\\B^{d+1},\\mathcal{N})$. This is because of the topological restriction that $\\Phi$ bridges, but continuous functions $\\Phi_k$ cannot bridge. ", "More precisely, assume that $\\Phi_k \\to \\Phi$ in $W^{1,p}(\\B^{d+1},{\\mathbb{R}}^N)$. Essentially by Fubini’s theorem we can find a radius $r \\in (0,1)$ so that as functions restricted to the $r$-sphere $r \\S^{d}$ we have convergence $$\\Phi_k\\big \|_{r \\S^{d}}\\xrightarrow{k \\to \\infty} \\Phi\\big \|_{r \\S^{d}} \\quad \\mbox{in $W^{1,p}(r\\S^{d},\\mathcal{N}$)}.$$ In that case we have three facts:\n\n1. ", " As an element of $\\pi_k(\\mathcal{N})$ the map $\\Phi_k\\big \|_{r \\S^{d}}: r \\S^{d} \\to \\mathcal{N}$ is trivial: it can be continuously extended to all of $\\B^{d+1}$ by $\\Phi_k$.\n\n2. ", " As an element of $\\pi_k(\\mathcal{N})$ the map $\\Phi\\big \|_{r \\S^{d}}: r \\S^{d} \\to \\mathcal{N}$ is nontrivial: $\\Phi(rx) = \\varphi(x)$ on $\\S^{d}$.\n\n3. ", " $\\Phi_k\\big \|_{r \\S^{d}} \\xrightarrow{k \\to \\infty} \\Phi\\big \|_{r \\S^{d}}$ uniformly: Since $p > d$ and the latter is the dimension of the $r\\S^{d}$, we have that $W^{1,p}(r\\S^{d}) \\subset C^0(r\\S^{d})$.\n\nThe third fact implies that for $k \\in \\N$ sufficiently large, $\\Phi_k\\big \|_{r \\S^{d}}$ and $\\Phi\\big \|_{r \\S^{d}}$ are the same as elements of $\\pi_{d-1}(\\mathcal{N})$, since they are uniformly close to each other. ", "This makes (1) and (2) impossible, and we have a contradiction.", "\n\nA crucial ingredient in the argument above, albeit somewhat hidden, is that we can jump as we wish between smooth and continuous elements of the homotopy group $\\pi_{d-1}(\\mathcal{N})$. Behind this lies the following density fact, which follows directly from convolution arguments and the existence of a nearest-point projection $\\Pi: B_\\delta(\\mathcal{N}) \\to \\mathcal{N}$ in a small tubular neighborhood of $B_\\delta(\\mathcal{N})$ for some $\\delta > 0$.\n\n\\[la:continuouslipschitz\\] Let $u: \\Omega \\to \\mathcal{N}$ be continuous ($C^\\alpha$-Hölder continuous, $C^{0,1}$-Lipschitz continuous). ", "Then we can approximate $u$ by smooth or Lipschitz-continuous $u_k$ so that $u_k$ converges to $u$ in $C^0$, ($C^\\beta$ for $\\beta < \\alpha$,or $1$, respectively).", "\n\nThis fails if $\\mathcal{N}$ becomes a metric space $X$. One example of a metric space with still a lot of “smooth structure” are the Heisenberg groups.", "\n\nA crude introduction to the Heisenberg group\n============================================\n\nThe metric of a manifold $X \\subset {\\mathbb{R}}^{N}$ could be described in the following way. ", "To measure the distance between any two points $p, q \\in X$, we take the minimum length of tangential curves between $p$ and $q$ in $X$: a smooth curve $\\gamma:[0,1] \\to {\\mathbb{R}}^N$ is a tangential curve between $p$ and $q$ if\n\n1. ", " $\\gamma(0) = p$, $\\gamma(1) = q$, and\n\n2. ", " at any $t \\in (0,1)$, the derivative of $\\gamma$ belongs to the tangential space $T_{\\gamma(t)} X$ of $X$.\n\nOf course, for $X$ a smooth embedded manifold this is just equivalent to saying that $\\gamma(t)$ maps into the manifold $X$ at any point $t \\in [0,1]$. So in some sense it is equivalent to see a manifold $X$ as a distribution of tangent planes $T_p X$. Why are the two points of view equivalent? ", "It is essentially Frobenius theorem, the tangent plane distribution is integrable (see, e.g., [@Lang-1999]).", "\n\nNow we drop the integrability condition of the (previously tangent) planes, and call them horizontal planes $H_p X$: For any $p \\in X$ define a linear space $H_p X \\subset {\\mathbb{R}}^N$. Let us also assume that the spaces $H_p X$ vary smoothly (in a suitable sense). ", "We define a metric $d_X(p,q)$ as the minimal length of horizontal curves connecting $p$ and $q$. Horizontal curve connecting $p$ and $q$ simply means\n\n1. ", " $\\gamma(0) = p$, $\\gamma(1) = q$, and\n\n2. ", " at any $t \\in (0,1)$, the derivative of $\\gamma$ belongs to the tangential space $T_{\\gamma(t)} X$ of $X$.\n\nThis metric is called the Carnot-Carathéodory metric, and $(X,HX,{\\mathbb{R}}^N)$ is a sub-Riemannian-manifold. ", "Observe that in principle the distance between two points could be infinite.", "\n\nOne of the simplest (non-trivial) examples of a sub-Riemannian manifold is the Heisenberg group $\\H_n$. We take $X = {\\mathbb{R}}^{2n+1}$, and define $$\\mathcal{L}(\\gamma) = \\int_0^1 \|\\gamma'(t)\| \\quad \\mbox{for any absolutely continuous curve $\\gamma: [0,1] \\to X$.}$$ At a point $p = (p_1,\\ldots,p_{2n+1}) \\in {\\mathbb{R}}^{2n+1}$, the horizontal plane distribution is given by the kernel of a $1$-form $\\alpha$, $H_p \\H_n := \\ker \\alpha$, where $$\\label{eq:alpha}\n \\alpha := dp_{2n+1} + 2 \\sum_{j=1}^n \n (p_{2j}\\, dp_{2j-1}- p_{2j-1}\\, dp_{2j}).$$ That is, $$H_p \\H_n = \\left \\{v = (v_1,\\ldots,v_{2n+1}) \\in {\\mathbb{R}}^{2n+1}:\\ v_{2n+1} + 2 \\sum_{j=1}^n \n (p_{2j}\\,v_{2j-1}- p_{2j-1}\\, v_{2j}) = 0 \\right \\}.$$\n\nOne can show that under the resulting Carnot-Carathéodory metric $d_{cc}$ the metric space $(\\H_n,d_{cc})$ is connected. ", "Also, $d_{cc}$ is equivalent to the so-called Korányi-metric $d_{\\H_n}$ which we shall use from now on. ", "It is defined as follows: for $p = (p_1,\\ldots,p_{2n+1})$, $q = (q_1,\\ldots,q_{2n+1})$ by $$\\label{eq:dcc}\n d_{\\H_n}(p,q) = \\left (\\sum_{i=1}^{2n} \\left \|p_{i}-q_i \\right \|^4+ \\Big \|p_{2n+1} -q_{2n+1} + 2 \\sum_{j=1}^n \\det \\left ( \\begin{array}{cc} \n p_{2j-1}-q_{2j-1}& q_{2j-1}\\\\\n p_{2j}-q_{2j}& q_{2j}\n \\end{array} \\right ) \\Big\|^2 \\right )^{\\frac{1}{4}}.$$\n\nA remark in passing: The Heisenberg group is called a group since it really has a Lie group structure. ", "For two elements $(z,t)$ and $(z',t') \\in \\mathbb{C}^n \\times {\\mathbb{R}}\\equiv {\\mathbb{R}}^{2n+1}$ the group law of the Heisenberg group is $$(z,t)(z',t')=\\left(z+z',t+t'+2\\, {\\rm Im}\\, \\left(\\sum_{j=1}^n z_j\n \\overline{z_j'}\\right)\\right).$$ If we write $z = x+iy$, a basis of left invariant vector fields is given by $$\\label{XY}\nX_j=\\frac{\\partial}{\\partial x_j} + 2y_j\\frac{\\partial}{\\partial t},\\\nY_j=\\frac{\\partial}{\\partial y_j}-2x_j\\frac{\\partial}{\\partial t},\\ j=1,\\ldots,n, \\\n\\mbox{and}\\\nT=\\frac{\\partial}{\\partial t}\\, .$$ The horizontal space $H_{(z,t)}\\H_n$ is then spanned by $X_1,\\ldots,X_n,Y_1,\\ldots,Y_n$.\n\nIn particular a geodesic (or in fact any Lipschitz curve) cannot move “straight up” in the $(2n+1)$th $T$-direction. ", "When you want to find a geodesic between the origin $(0,\\ldots,0,0)$ with $(0,\\ldots,0,t)$ one needs to circle around the $2n+1$th axis. ", "For the structure of geodesics we refer to [@Hajlasz-Zimmerman-2015].", "\n\nWe will not go more into details of the geometry of the Heisenberg group. ", "The interested reader is referred to [@Capogna-Danielli-Pauls-Tyson-2007].", "\n\nHorizontal maps and Sobolev maps into the Heisenberg group\n----------------------------------------------------------\n\nAn easy computation implies that any map into the Heisenberg group which is Lipschitz with respect to the metric $d_{\\H_n}$ satisfies almost everywhere $f^\\ast \\alpha = 0$.\n\n\\[la:lipschitzhorizontal\\] Let $f: \\Omega \\subset {\\mathbb{R}}^d \\to \\H_n$ be Lipschitz, that is $$d_{\\H_n}(f(x),f(y)) {\\lesssim}\\ \|x-y\|.$$ Then, at any point where $f$ is differentiable, for $\\alpha$ the 1-form from $$f^\\ast \\alpha = 0.$$\n\nThe Lipschitz-condition implies in particular $$\\left \|\\frac{f_{2n+1}(x) -f_{2n+1}(x+h)}{\|h\|} + 2 \\sum_{j=1}^n \\det \\left ( \\begin{array}{cc} \n \\frac{f_{2j-1}(x)-f_{2j-1}(x+h)}{\|h\|}& f_{2j-1}(x+h)\\\\\n \\frac{f_{2j}(x)-f_{2j}(x+h)}{\|h\|}& f_{2j}(x+h)\n \\end{array} \\right ) \\right \| {\\lesssim}\|h\|.$$ It is worth noting, and becomes important later, that this computation actualy shows in some sense: if $f \\in C^{\\frac{1}{2}+\\eps}(\\Omega,\\H_n)$ then $f^\\ast(\\alpha) = 0$. Cf. ", "Proposition \\[pr:approx\\].", "\n\nMaps $f: \\Omega \\to \\H_n$ which satisfy $f^\\ast\\alpha = 0$ are called horizontal maps. ", "The Sobolev space $W^{1,p}(\\Omega,\\H_n)$ is defined as $$W^{1,p}(\\Omega,\\H_n) = \\left \\{ f \\in W^{1,p}(\\Omega,{\\mathbb{R}}^{2n+1}) \\quad \\mbox{such that }\\ f^\\ast \\alpha = 0 \\mbox{ a.e. ", "in $\\Omega$}\\right \\}.$$ Another definition of $W^{1,p}(\\Omega,\\H_n)$ is as follows: embed the separable metric space $(\\H_n,d_{\\H_n})$ in $\\ell^\\infty$ with the Kuratowski-embedding. ", "Sobolev maps $W^{1,p}$ into the Banach space $\\ell^\\infty$ are well-defined, and $W^{1,p}(\\Omega,\\H_n)$ are all those maps $f \\in W^{1,p}(\\Omega,\\ell^\\infty)$ that pointwise a.e. ", "belong to $\\H_n\\subset \\ell^\\infty$. Both definitions coincide, [@Capogna-Lin-2001; @Dejarnette-Hajlasz-Lukyanenko-Tyson-2014].", "\n\nTopology of the Heisenberg group\n--------------------------------\n\nWhen we want to study density questions in Sobolev spaces $W^{1,p}$ (since $\\H_n$ is a metric space, we will ask for density of Lipschitz mappings), in view of Bethuel’s theorem, Theorem \\[th:HWBethuel\\], we would like to understand the topology of $\\H_n$. But we stumble over the following (simple) fact:\n\nAll homotopy classes of $\\H_n$ are trivial, i.e. $\\pi_k(\\H_n) = 0$ for any $k \\in \\N$.\n\nThis is actually quite easy to see: every map into ${\\mathbb{R}}^{2n+1}$ which is continuous with respect to the Euclidean metric is also continuous with respect to the $\\H_n$-metric. ", "We even have\n\n\\[la:comparison\\] We can estimate this distance in terms of the usual ${\\mathbb{R}}^{2n+1}$-norm $\|\\cdot\|$, $$\\frac{1}{(\|p\|+\|q\| + 1)}\\, \|p-q\| {\\lesssim}d_{\\H}(p,q) {\\lesssim}\\ (\|p\|^{\\frac{1}{2}}+\|q\|^{\\frac{1}{2}} + 1)\\, \|p-q\|^{\\frac{1}{2}}.$$ In particular, $(\\H_n,d_{\\H_n})$ is homeomorphic to $({\\mathbb{R}}^{2n+1},\|\\cdot\|)$.\n\nIn particular, any map $f: \\Omega \\subset {\\mathbb{R}}^d \\to {\\mathbb{R}}^{2n+1}$ that is Lipschitz with respect to the $\\H_n$-metric is also (locally) Lipschitz with respect to the Euclidean metric. ", "But the converse is false, maps which are Lipschitz with respect to the Euclidean metric might be merely $C^{\\frac{1}{2}}$ with respect to the $\\H_n$-metric. ", "For example, considered as a map into the Heisenberg group even the identity $\\id: {\\mathbb{R}}^{2n+1} \\to {\\mathbb{R}}^{2n+1}$ is only $C^{\\frac{1}{2}}_{loc}({\\mathbb{R}}^{2n+1},\\H_n)$.\n\nActually, one can show that the Hausdorff dimension of any open set in $\\H_n$ equals $2n+2$. Thus we have the disturbing situation that $(\\H_n,d_{\\H_n})$ is homeomorphic to ${\\mathbb{R}}^{2n+1}$ (actually even $C^{\\frac{1}{2}}$-homeomorphic), but not Lipschitz-homeomorphic, not even locally.", "\n\nHölder-Topology and density results on the Heisenberg group\n===========================================================\n\nSo in order to understand questions of density in Sobolev spaces, we need to find suitable nontrivial topological quantities on the Heisenberg group.", "\n\nFor $\\gamma \\in (0,1]$ the $k$-th $C^\\gamma$-homotopy group $\\pi_k^\\gamma(X)$ of a metric space $X$ is defined as the class of maps $f \\in C^\\gamma(\\S^k,\\H_n)$, where two maps $f, g \\in C^\\gamma(\\S^{k},\\H_n)$ are identified, if there exists a $C^\\gamma$ homotopy $H \\in C^\\gamma([0,1] \\times \\S^{k},\\H_n)$ so that $H(0,\\cdot) = f$ and $H(1,\\cdot) = g$.\n\nWe write $\\pi^{\\lip}_k(X)$ for $\\pi^{1}_k(X)$.\n\nHere is what is known on homotopy groups:\n\n${}$\n\n1. ", " $\\pi^{\\lip}_m(\\H_n)= \\{0\\}$ for all $1\\leq m<n$.\n\n2. ", " $\\pi_m^{\\lip}(\\H_1)=\\{ 0\\}$ for all $m\\geq 2$.\n\n3. ", " $\\pi^{\\rm \\gamma}_n(\\H_n)\\neq \\{0\\}$ when $\\frac{n+1}{n+2} < \\gamma \\leq 1$.\n\n4. ", " $\\pi_{4n-1}^\\gamma(\\H_{2n}) \\neq \\{0\\}$ when $\\frac{4n+1}{4n+2} < \\gamma \\leq 1$.\n\n\\(1) was proven in [@Dejarnette-Hajlasz-Lukyanenko-Tyson-2014; @WengerY1]. (", "2) is due to [@WengerY2]. ", "For (3) there are several proofs in the Lipschitz case [@Balogh-Faessler-2009; @Dejarnette-Hajlasz-Lukyanenko-Tyson-2014; @Hajlasz-Schikorra-Tyson-2014]. ", "For Lipschitz homotopy groups, (4) was the main result of [@Hajlasz-Schikorra-Tyson-2014]. ", "The Hölder-groups are from a forthcoming paper [@Hajlasz-Mirra-Schikorra-2016]. ", "In a more recent paper, [@H18] Hajłasz proved that for $n \\geq 2$, $\\pi^{n+1}_{\\lip}(\\H_{n}) \\neq \\{0\\}$.\n\nIt may seem natural to hope that the counterpart of Theorem \\[th:HWBethuel\\] holds for Lipschitz Homotopy $\\pi_k^{\\lip}(\\H_n)$. For example, $\\pi_d^\\lip(\\H_n) = 0$ if and only if Lipschitz maps are dense in $W^{1,p}(\\B^{d+1},\\H_n)$ for $d < p < d+1$. However, we do not know this: we cannot just run the algorithm for Bethuel’s Theorem \\[th:HWBethuel\\] described above. ", "$W^{1,p}(\\S^d)$ on a $d$-dimensional manifold embeds merely into $C^{1-\\frac{d}{p}}$, and $1-\\frac{d}{p} < \\frac{1}{d+1} \\leq \\frac{1}{2}$, so convergence in $W^{1,p}(\\S^d,\\H_n)$ means nothing in terms of convergence in Homotopy groups.", "\n\nThe counterpart of Lemma \\[la:continuouslipschitz\\] is unknown in the Heisenberg group (and it actually false for $C^{\\gamma}$, $\\gamma < \\frac{1}{2}$). ", "Related to this we do not know (although it seems quite likely at least for $\\gamma \\approx 1$ whether $\\pi_k^\\gamma (\\H_n) = \\pi_k^\\lip(\\H_n)$ for any $k$. The technical issue with this is that in contrast with Riemannian manifolds here we do not have a projection $\\Pi$ that could map non-horizontal lines which are uniformly close to a horizontal line into the “nearest horizontal line”, so we cannot (i.e. do not understand how to) approximate even Hölder maps with Lipschitz maps.", "\n\nEven though it is not an immediate consequence of the non-triviality of the corresponding Lipschitz-Homotopy groups, we the following non-density results are known:\n\nLet $\\mathcal{M}$ be a smooth compact Riemannian manifold possibly with boundary.", "\n\n1. ", " If $\\dim\\M \\leq n$ then the Lipschitz maps $\\lip(\\M,\\H_n)$ are dense in $W^{1,p}(\\M,\\H_n)$, for any $1 < p <\\infty$.\n\n2. ", " If $\\dim\\M\\geq n+1$ and $n\\leq p<n+1$, then Lipschitz maps $\\lip(\\M,\\H_n)$ are not dense in $W^{1,p}(\\M,\\H_n)$.\n\n3. ", " If $\\M$ is a compact Riemannian manifold with or without boundary of dimension $\\dim\\M\\geq 4n$, then Lipschitz mappings $\\lip(\\M,\\H_{2n})$ are not dense in $W^{1,p}(\\M,\\H_{2n})$ when $4n-1\\leq p<4n$.\n\n\\(1) is due to [@Dejarnette-Hajlasz-Lukyanenko-Tyson-2014], see also [@Hajlasz-Schikorra-2014]. (", "2) is due to [@Dejarnette-Hajlasz-Lukyanenko-Tyson-2014], (3) is from [@Hajlasz-Schikorra-Tyson-2014].", "\n\nLet us remark another interesting topological fact of the Heisenberg group, even though it is not (necessarily) related to density questions.", "\n\n\\[th:gromov\\] Let $k \\geq n+1$, $\\gamma \\in (\\frac{1}{2},1]$, $\\theta > 0$ and $$\\label{eq:gammatheta}\n 2\\gamma + \\theta (k-1) -k > 0.$$ Then there is no injective $f: \\Omega \\subset {\\mathbb{R}}^k \\to \\H_n$ which is $C^\\gamma$ with respect to the $\\H_n$-metric and $C^\\theta$ with respect to the Euclidean metric.", "\n\nTheorem \\[th:gromov\\] is from the forthcoming paper [@Hajlasz-Mirra-Schikorra-2016]. ", "For $\\gamma = \\theta > \\frac{k}{k+1}$ it was proven by Gromov, [@GromovCarnotCaratheodory], see also Pansu’s [@Pansu-2016], using microflexibility arguments. ", "We also refer to the work by LeDonne and Züst [@LeDonne-Zust-2012]. ", "For $\\theta = 1$ this can be found in [@BaloghHajlaszWildrick]. ", "Theorem \\[th:gromov\\] is so far among the closest results we have to proving a conjecture by Gromov, see also the recent [@WengerYoung18] and references within.", "\n\nThere is no embedding $f \\in C^{\\gamma}(\\Omega,\\H_n)$ whenever $\\Omega$ is an open subset of ${\\mathbb{R}}^k$, $k \\geq n+1$, and $\\gamma > \\frac{1}{2}$.\n\nLet us remark that there is a construction due to Hajłasz and Mirra [@H14] that might serve as a counterexample to the Gromov’s conjecture, or at least show that there are embedded curves into the Heisenberg group $\\H_1$ that can be extended to a $C^{2/3}$-map (not necessarily embedded). ", "Currently the Hölder regularity of this construction can only be measured from a numerical point of view, but this numerical evidence hints toward a $C^{2/3}$-regularity rather than a $C^{1/2}$-regularity as predicted by Gromov’s conjecture. ", "The details will be published in the forthcoming [@Hajlasz-Mirra-Schikorra-2016]. ", "Also the recent [@WengerYoung18] can be interpreted towards that direction.", "\n\nIngredient: rank-condition for Lipschitz-maps\n=============================================\n\nIn this section we state the main reason that – while working on the Heisenberg-group – we actually don’t need to work with the Heisenberg group: derivatives of Lipschitz maps into the Heisenberg group (below we will see what to do with Hölder maps) have a low rank.", "\n\nWe recall the so-called contact-form $\\alpha$ whose kernel is the horizontal space distribution of the Heisenberg group $\\H_n$, $$\\tag{\\ref{eq:alpha}}\n \\alpha := dp_{2n+1} + 2 \\sum_{j=1}^n \n (p_{2j}\\, dp_{2j-1}- p_{2j-1}\\, dp_{2j}).$$ Note that $$d\\alpha = 4 \\sum_{j=1}^n dp_{2j} \\wedge dp_{2j-1}.$$\n\nFrom Lemma \\[la:lipschitzhorizontal\\] we learned that any map $f \\in \\lip(\\Omega,\\H_n)$ satisfies $$f^\\ast (\\alpha) = 0.$$ Clearly, this implies also $$f^\\ast (d\\alpha) = 0.$$ It is a not difficult but a lengthy, combinatorial proof to show that any $(n+1)$-form can be decomposed into terms containing $\\alpha$ or $d\\alpha$.\n\nActually the following is well-known to experts as the a version of the Lefschetz-Lemma.", "\n\n\\[la:rank\\] For any $k \\geq n+1$, any $k$-form $\\kappa$ has the form $$\\kappa = \\alpha \\wedge \\beta + d\\alpha \\wedge \\sigma$$ for some $(k-1)$-form $\\beta$ and some $(k-2)$-form $\\sigma$.\n\nIn particular, if $f \\in \\lip(\\Omega,\\H_n)$, then $$f^\\ast (\\kappa) = 0\\quad \\mbox{for any $k$-form $\\kappa$}.$$\n\nWe only discuss the three-dimensional situation. ", "For the general $2n+1$ more combinatorical reasoning is needed.", "\n\nTake $(x,y,z) \\in {\\mathbb{R}}^3$ and a $2$-form $\\kappa$ $$\\kappa = \\kappa_1\\, dy \\wedge dz + \\kappa_2\\, dx \\wedge dz + \\kappa_3\\, dx \\wedge dy.$$ Observe $d\\alpha = 4 dx \\wedge dy$, and $\\alpha = dz + 2 (y\\, dx- x\\, dy)$. Thus $$\\kappa_1\\, dy \\wedge dz = \\kappa_1\\, dy \\wedge \\alpha -2 \\kappa_1 \\,y\\, dy \\wedge dx = \\kappa_1\\, dy \\wedge \\alpha -\\frac{1}{2} \\kappa_1 \\,y\\, d\\alpha,$$ $$\\kappa_2\\, dx \\wedge dz = \\kappa_2\\, dx \\wedge \\alpha + 2 \\kappa_2\\, y\\, dx \\wedge dy = \\kappa_2\\, dx \\wedge \\alpha - \\frac{1}{2} \\kappa_2\\, y\\, d\\alpha,$$ and $$\\kappa_3\\, dx \\wedge dy = -\\frac{1}{4}\\kappa_3\\, d\\alpha.$$\n\nAn equivalent formulation for Lipschitz functions (but as we shall see, the above statement is more useful for Hölder functions)\n\nLet $f \\in \\lip(\\Omega,\\H_n)$, then $$\\rank Df \\leq n \\quad \\mbox{a.e. ", "in $\\Omega$}.$$\n\nThis is a very rigid statement, recall that the $n$-th Heisenberg group $\\H_n$ is homeomorphic to ${\\mathbb{R}}^{2n+1}$!", "\n\nIngredient: linking number\n==========================\n\n\\[pr:linking\\] Let $k < N-1$ and $\\varphi: \\S^k \\to {\\mathbb{R}}^{N}$ a Lipschitz embedding. ", "Then there exists a smooth $k$-form $\\omega$ on ${\\mathbb{R}}^N$ so that $$\\int_{\\S^k} \\varphi^\\ast (\\omega) \\neq 0.$$\n\nThe reason for this to be true is the linking number. ", "Usually the linking number $\\mathcal{L}(A,B)$ of a $k$-dimensional (closed) object $A$ and disjoint a (closed) $N-k-1$-dimensional object measures how many times object $A$ winds around object $B$. ’closed’ means that $A$ and $B$ have no boundaries (and are in fact a boundary of a $k+1$ and a $N-k$-dimensional object, respectively). ", "For $N=3$, $k=1$ both objects are just curves.", "\n\nAny $(N-k-1)$-dimensional closed object $B$ can be measured by an closed (and thus exact) $k+1$ differential form $\\eta_B = d\\omega_B$. This is Poincaré-duality. ", "The disjointness of $A$ and $B$ is just that $\\eta_B$ has no support in $A$.", "\n\nIn algebraic terms, the linking number $\\mathcal{L}(A,B)$ is the homology class of $B$ in $H_{N-k-1}({\\mathbb{R}}^N \\backslash A,{\\mathbb{Z}})$ or equivalently the cohomology class of $\\eta_B$ in $H^{k+1}({\\mathbb{R}}^N \\backslash A,{\\mathbb{Z}})$.\n\nIn analytic terms, the linking number is $$\\mathcal{L}(A,B) \\equiv \\mathcal{L}(A,\\eta_B) = \\int_{A} \\omega_B,$$ which simply means, as is shown in [@Hajlasz-Mirra-Schikorra-2016], that the map $$\\eta = d\\omega \\mapsto \\int_{\\S^k} \\varphi^\\ast (\\omega)$$ is an isomorphism on $H_{k+1}({\\mathbb{R}}^N \\backslash A,{\\mathbb{Z}})$.\n\nSo the statement of Proposition \\[pr:linking\\] is simply saying that if $\\varphi(\\S^k)$ is an embedded $k$-sphere in ${\\mathbb{R}}^N$, then there exists some object $B$ linked to it. ", "The latter is a standard fact from algebraic topology, and we adapt the standard proof, see e.g. [@Vick-1994 Corollary 1.29]. ", "We will sketch the proof in Section \\[s:linkingproof\\].", "\n\nImplication for Gromov’s theorem (Lipschitz case) {#s:lipschitzgromov}\n-------------------------------------------------\n\nObserve that Proposition \\[pr:linking\\] implies in particular the Lipschitz version of Gromov’s result, Theorem \\[th:gromov\\].", "\n\nLet $\\Phi: \\B^{n+1} \\to \\H_n$ be a Lipschitz embedding. ", "In particular, $\\Phi$ is Lipschitz as a map into ${\\mathbb{R}}^{2n+1}$. Let $\\varphi := \\Phi \\big \|_{\\S^{n}}$ be the boundary map of $\\Phi$, which is of course still an embedding. ", "In view of Proposition \\[pr:linking\\] we find a $n$-form $\\omega$ in ${\\mathbb{R}}^{2n+1}$ so that $$0 \\neq \\int_{\\S^n} \\varphi^\\ast (\\omega).$$ With Stokes’ theorem $$=\\int_{\\B^{n+1}} \\Phi^\\ast (d\\omega).$$ Since $d\\omega$ is an $n+1$-form, and the rank-condition, Lemma \\[la:rank\\], tells us that $$= 0.$$ We have a contradiction, so $\\Phi$ could not have been an embedding.", "\n\nActually we even showed\n\n\\[la:noextension\\] No Lipschitz embedding $\\varphi: \\S^n \\to \\H_n$ can be Lipschitz extended to $\\Phi: \\B^{n+1} \\to \\H_n$.\n\nLipschitz case: \n================\n\nNon-triviality\n--------------\n\nTheorem \\[th:gromov\\] tells us that it is impossible to Lipschitz-embeds objects in to the $\\H_n$ if their dimension is larger than $n+1$. This bound on the dimension is sharp, the following was shown by [@Balogh-Faessler-2009 Section 4], [@Dejarnette-Hajlasz-Lukyanenko-Tyson-2014 Theorem 3.2], [@Ekholm-Etnyre-Sullivan-2005 Example 3.1].", "\n\n\\[th:Snembedding\\] For any $n\\geq 1$ there is a bi-Lipschitz embedding $\\varphi: \\S^n \\to \\H_n$.\n\nClearly, we can consider $\\varphi$ to be an element of $\\pi_n^{\\lip}(\\H_n)$. In view of Lemma \\[la:noextension\\] it is a non-trivial element of $\\pi_n^{\\lip}(\\H_n)$.\n\nSo what about density?", "\n----------------------\n\nNote that we have a quantitative way to measure the nontriviality of the homotopy group. ", "Take $\\varphi$ from above. ", "As a map into ${\\mathbb{R}}^{2n+1}$, $\\varphi$ is an embedding, so in view of Proposition \\[pr:linking\\] we can find a $n$-form $\\omega$ so that $$\\label{eq:nontrivialityn}\n \\int_{\\S^n} \\varphi^\\ast (\\omega) \\neq 0.$$ Now we let the standard algorithm run and obtain non-density of Lipschitz maps for the Sobolev maps $W^{1,p}(\\B^{n+1},\\H_n)$, $n < p < n+1$.\n\nTake $\\varphi$ and $\\omega$ from above so that holds. ", "Set $\\Phi(x) := \\Phi(x/\|x\|) \\in W^{1,p}(\\B^{n+1},\\H_n)$ for any $p < n+1$. This $\\Phi$ can not be $W^{1,p}$-approximated by Lipschitz maps in $\\lip(\\B^{n+1},\\H_n)$. If there was an approximation $\\Phi_k \\to \\Phi$ in $W^{1,p}(\\B^{n+1},\\H_n)$, then on some sphere $r\\S^{n}$, $r \\in (0,1)$ (we pretend for simplicity that $r=1$) $$\\Phi_k\\big \|_{\\S^{n}} \\xrightarrow{k\\to \\infty} \\varphi \\quad \\mbox{in $W^{1,p}(\\S^n,\\H_n)$}.$$ Since $\\Phi_k$ is a Lipschitz map into $\\H_n$ and $d\\omega$ is a $n+1$-form, by the rank condition, Lemma \\[la:rank\\], and Stokes’ theorem $$0 = \\int_{\\B^{n+1}} \\Phi_k^\\ast (d\\omega) = \\int_{\\S^{n}} \\Phi_k^\\ast (\\omega)$$ Now $\\omega$ is an $n$-form, and thus $\|\\Phi_k^\\ast (\\omega)\| \\leq \|D\\Phi_k\|^n\\ w(\\Phi_k)$ (for some smooth $w$). ", "Since $\\Phi_k \\to \\varphi \\in W^{1,p}(\\S^n,\\H_n)$, $p > n$, the integral above converges. ", "We thus have $$0 = \\lim_{k \\to \\infty} \\int_{\\S^{n}} \\Phi_k^\\ast (\\omega) = \\int_{\\S^{n}} \\varphi^\\ast (\\omega) \\overset{\\eqref{eq:nontrivialityn}}{\\neq} 0,$$ a contradiction. ", "We conclude that there is no Lipschitz approximation for $\\Phi$, and thus Lipschitz functions are not dense in $W^{1,p}(\\B^{n+1},\\H_n)$ if $p \\in (n,n+1)$.\n\nLipschitz case: \n================\n\nFor this we employ another version of linking number, the one that Hopf [@Hopf] used to define his Hopf invariant, and showed that $\\pi_{4n-1}(\\S^{2n}) \\neq 0$.\n\nAnother linking number: the Hopf invariant\n------------------------------------------\n\nLet $\\varphi: \\S^{4n-1} \\to \\S^{2n}$. Take the volume form $\\eta$ of $\\S^{2n}$. Then $\\varphi^\\ast(\\eta)$ is a closed form: $d\\varphi^\\ast(\\eta)=\\varphi^\\ast(d\\eta) = 0$, since $d\\eta$ is a $2n+1$-form; but $\\varphi$ is a map into $\\S^{2n}$ so surely its derivative $D\\varphi$ can only have rank at most $\\leq 2n$. But in $\\S^{4n-1}$ any closed $2n$-form is exact, so $\\varphi^\\ast(\\eta) = d\\omega_\\varphi$. The Hopf invariant is then defined as $$\\mathcal{H}(\\varphi) = \\int_{\\S^{4n-1}} \\omega_\\varphi \\wedge \\varphi^\\ast(\\eta).$$ As explained in [@BT82], $\\mathcal{H}(\\varphi)$ measures the linking number between the two $(2n-1)$-dimensional “curves” $\\varphi^{-1}(q)$, $\\varphi^{-1}(p)$.\n\nHopf then showed\n\n\\[th:hopf\\] \\[la:hopffibration\\] For any $n \\in \\mathbb{N}$ there exists a smooth map $\\varphi: \\S^{4n-1} \\to \\S^{2n}$, such that ${\\mathcal{H}}(\\varphi) \\neq 0$.\n\nAdaption to the Heisenberg group\n--------------------------------\n\nThe main observation is that what makes the Hopf invariant actually homotopy invariant is the rank-condition $\\rank D\\varphi \\leq 2n$.\n\nSo take Theorem \\[th:hopf\\] the nontrivial map $\\varphi_1 : \\S^{4n-1} \\to \\S^{2n}$ and from Theorem \\[th:Snembedding\\] the bi-Lipschitz embedding $\\varphi_2 : \\S^{2n} \\to \\H_{2n}$. We can Lipschitz extend its inverse $\\varphi_2^{-1}: {\\mathbb{R}}^{4n+1} \\to {\\mathbb{R}}^{2n+1}$. Set $\\varphi := \\varphi_2 \\circ \\varphi_1 $ $\\in \\lip(\\S^{4n-1} ,\\H_{2n})$. Again, this is an element of $\\pi^{\\lip}_{4n-1}(\\H_{2n})$ and we will show that it is non-trivial.", "\n\nAssume on the contrary that $\\varphi$ is a trivial element of $\\pi^{\\lip}_{4n-1}(\\H_{2n})$. Then we find a Lipschitz extension of $\\varphi$, $\\Phi \\in \\lip(\\B^{4n},\\H_n)$. Set $\\Phi_1 := \\varphi_2^{-1} \\circ \\Phi \\in \\lip(\\B^{4n},{\\mathbb{R}}^{2n+1})$.\n\nTake $\\eta$ the volume form of $\\S^{2n}$, so that $$0 \\neq {\\mathcal{H}}(\\varphi_1) = \\int_{\\S^{4n-1}} \\omega_{\\varphi_1} \\wedge \\varphi_1^\\ast(\\eta)$$ Now $\\Phi_1^\\ast(d\\eta) = \\Phi^\\ast((\\varphi_2^{-1})^\\ast(d\\eta)) = 0$, since $(\\varphi_2^{-1})^\\ast(d\\eta)$ is an $(2n+1)$-form, and we have again the rank-condition Lemma \\[la:rank\\]. ", "Thus we find $\\omega_{\\Phi_1}$ so that $\\Phi_1^\\ast(\\eta) = d\\omega_{\\Phi_1}$. We then use Stokes’ theorem, $$= \\int_{\\B^{4n}} d {\\left (\\omega_{\\Phi_1} \\wedge \\Phi_1^\\ast(\\eta) \\right )} = \\int_{\\B^{4n}} \\Phi_1 (\\eta \\wedge \\eta).$$ With the rank-condition, Lemma \\[la:rank\\], since $\\eta \\wedge \\eta$ is a $4n$-form, $$0 \\neq {\\mathcal{H}}(\\varphi_1) =0.$$ We have our contradiction.", "\n\nFor the density argument we argue as above. ", "Since we have a quantification of the nontriviality, $0 \\neq {\\mathcal{H}}(\\varphi_1)$, we simply need to check convergence for Sobolev spaces.", "\n\nApproximation and rank conditions for Hölder-maps\n=================================================\n\nEssentially all the above arguments crucially rely on the rank-condition, that any Lipschitz map $\\varphi \\in \\lip(\\Omega,\\H_n)$ has $\\rank D\\varphi \\leq n$. For Hölder maps $\\varphi$, there is no derivative $D\\varphi$ which could have a rank. ", "So we approximate Hölder maps $\\varphi \\in C^\\nu(\\Omega,\\H_n)$ with smooth maps $\\varphi_\\eps \\in C^\\infty(\\Omega,{\\mathbb{R}}^{2n+1})$ (e.g. by mollification). ", "Note, however, that there is absolutely no reason why the approximations $\\varphi_\\eps$ are Lipschitz maps as maps into the Heisenberg group.", "\n\nThe main observation to overcome this issue is the following:\n\n\\[pr:approx\\] For $\\varphi \\in C^\\gamma(\\Omega,\\H_n)$ there exist $\\varphi_\\eps \\in C^\\infty(\\Omega,{\\mathbb{R}}^{2n+1})$ so that $\\varphi_\\eps \\to f$ in $C^\\gamma(\\Omega,{\\mathbb{R}}^{2n+1})$ and moreover $$\\label{eq:firstorderest}\n \\\|\\varphi_\\eps^\\ast (\\alpha) \\\|_\\infty {\\lesssim}\\eps^{2\\gamma-1},$$ where $\\alpha$ is the contact form , and $$\\label{eq:approxgeneral}\n \\\|\\varphi_\\eps^\\ast (\\kappa) \\\|_\\infty {\\lesssim}\\eps^{k(\\gamma-1)},$$ for any $k$-form $\\kappa$.\n\nWhile is the standard estimate for approximations ($\\\|D \\varphi_\\eps\\\| {\\lesssim}\\eps^{\\gamma-1} [\\varphi]_{C^\\gamma}$), gives us “a special direction” in which the approximation is better - if $\\gamma > \\frac{1}{2}$ it is actually convergent.", "\n\nIn particular, we have the following replacement for $\\rank D\\phi \\leq n+1$:\n\n\\[pr:hoeldermapsintoHn\\] Let $\\Phi \\in C^{\\nu}(\\overline{\\B^{k+1}},\\H_n)$ with boundary data $\\varphi = \\Phi \\big\|_{\\S^k}$. If $\\nu > \\frac{k+1}{k+2}$ and $\\kappa$ is any smooth $k$-form on ${\\mathbb{R}}^{2n+1}$, $k \\geq n$, for $\\Phi_\\eps$ the approximation of $\\Phi$ as in Proposition \\[pr:approx\\], $$\\lim_{\\eps \\to 0} \\int_{\\S^{k}} \\varphi_\\eps^\\ast(\\kappa) = 0.$$\n\nWe have with Stokes’ theorem $$\\int_{\\S^{k}} \\varphi_\\eps^\\ast(\\kappa) = \\int_{\\B^{k+1}} \\Phi_\\eps^\\ast(d\\kappa).$$ In view of Lemma \\[la:rank\\], $d\\kappa = \\alpha \\wedge \\beta + d\\alpha \\wedge \\sigma$ $$= \\int_{\\B^{k+1}} \\Phi_\\eps^\\ast(\\alpha)\\wedge \\Phi_\\eps^\\ast(\\beta)+ \\int_{\\B^{k+1}} \\Phi_\\eps^\\ast(d\\alpha)\\wedge \\Phi_\\eps^\\ast(\\sigma)$$ and again Stokes’ theorem $$= \\int_{\\B^{k+1}} \\Phi_\\eps^\\ast(\\alpha)\\wedge \\Phi_\\eps^\\ast(\\beta) + \\int_{\\S^{k}} \\Phi_\\eps^\\ast(\\alpha)\\wedge \\Phi_\\eps^\\ast(\\sigma) - \\int_{\\B^{k+1}} \\Phi_\\eps^\\ast(\\alpha)\\wedge d\\Phi_\\eps^\\ast(\\sigma).$$ Now with and , $$\\left \|\\int_{\\S^{k}} \\varphi_\\eps^\\ast(\\kappa)\\right \| {\\lesssim}\\eps^{2\\gamma-1} \\eps^{k(\\gamma-1)} \\xrightarrow{\\eps \\to 0} 0,$$ whenever $\\nu > \\frac{k+1}{k+2}$.\n\nThe linking number: Proof of Proposition \\[pr:linking\\] {#s:linkingproof}\n=======================================================\n\nFor Hölder maps we need to adapt Proposition \\[pr:linking\\].", "\n\nLet $k < N-1$ and $\\varphi: \\S^k \\to {\\mathbb{R}}^N$ be a $C^{\\sigma}$-embedding for $\\sigma > \\frac{k}{k+1}$. For an exact form $\\eta = d\\omega \\in C^\\infty({\\bigwedge\\nolimits}^{k+1} {\\mathbb{R}}^N)$, we define the linking number between $\\eta$ and $\\varphi(\\S^k)$ by $$\\label{eq:linking}\n \\mathcal{L}(\\varphi(\\S^k),\\eta) := \\lim_{\\eps \\to 0} \\int_{\\S^k} \\varphi_\\eps^\\ast(\\omega).$$ Here, $\\varphi_\\eps$ is any smooth approximation of $\\varphi$ in $C^\\sigma$.\n\n\\[la:lconverges\\] If $\\sigma > \\frac{k}{k+1}$, converges and is independent of the choice of the approximation.", "\n\nThis can be proven in various ways: with the help of paraproducts [@Sickel-Youssfi-1999a], Fourier transform estimates a la [@Tartar84]. ", "Actually this convergence is in some sense related to “integration by compensation” for Jacobians, as observed by Coifman-Lions-Meyer-Semmes [@CLMS], see also [@LenzmanN-Schikorra-commutators]).", "\n\nThe simplest argument (for our purposes) is a beautiful trick, due to Brezis and Nguyen [@Brezis-NguyeN-2011]. ", "Take $\\Phi_\\eps$ the harmonic extension of $\\varphi_\\eps$ in $\\B^{k+1}$, ${\\Delta }\\Phi_\\eps = 0$, $\\Phi_\\eps \\big \|_{\\S^{k}} = \\varphi_\\eps$. Then, by Stokes theorem, $$\\int_{\\S^k} \\varphi_\\eps^\\ast(\\omega) = \\int_{\\B^{k+1}} \\Phi_\\eps^\\ast(d\\omega).$$ Now observe that $d\\omega$ is a (bounded) $k+1$-form, so $$\\left \|\\int_{\\B^{k+1}} \\Phi_\\eps^\\ast(d\\omega) \\right \|{\\lesssim}\\\|D \\Phi_\\eps\\\|_{L^{k+1}(\\B^{k+1})}^{k+1}.$$ But $\\Phi_\\eps$ is an extension of $\\varphi_\\eps$, in other words, $\\varphi_\\eps$ is the trace of the harmonic function $\\Phi_\\eps$. Trace theorems for Sobolev mappings $W^{1,k+1}(\\B^{k+1}) \\hookrightarrow W^{\\frac{k}{k+1},k+1}(\\partial \\B^{k+1})$ imply $$\\left \|\\int_{\\B^{k+1}} \\Phi_\\eps^\\ast(d\\omega) \\right \|{\\lesssim}\\\| \\varphi_\\eps\\\|^{k+1}_{W^{\\frac{k}{k+1},k+1}(\\S^k)} {\\lesssim}\\\|\\varphi_\\eps \\\|_{C^{\\sigma}}^{k+1}.$$ Using this argument one can show that $$\\int_{\\S^k} \\varphi_\\eps^\\ast(\\omega)$$ is a Cauchy sequence as $\\eps \\to 0$, in particular, is converging.", "\n\nObserve that for maps as in Proposition \\[pr:hoeldermapsintoHn\\] we thus have that the linking number is necessarily zero, which then – just as in Section \\[s:lipschitzgromov\\] contradicts the following proposition, which is simply the extension to Hölder maps from Proposition \\[pr:linking\\].", "\n\n\\[pr:linkinghoelder\\] Let $k < N-1$ and $\\varphi: \\S^k \\to {\\mathbb{R}}^N$ a $C^{\\sigma}$-embedding for $\\sigma > \\frac{k}{k+1}$. Then there exists a smooth $k$-form $\\omega$ on ${\\mathbb{R}}^N$ so that $$\\mathcal{L}(\\varphi(\\S^k),d\\omega) \\neq 0.$$\n\nSo we can measure* the linking number for $C^{\\frac{k}{k+1}+\\eps}$-embeddings $\\varphi: \\S^k \\to {\\mathbb{R}}^{2n+1}$. By standard algebraic arguments (essentially the arguments we do below), for all $C^\\sigma$-embedding, even if $\\sigma \\leq \\frac{k}{k+1}$ there is a linked object $B$ so that the algebraic linking number is nontrivial – which is just saying that the cohomology group $H_c^{k+1}({\\mathbb{R}}^{2n+1}\\backslash \\varphi(\\S^k)) \\neq 0$. But this algebraic linking number we cannot “measure” in analytic terms.", "\n\nMoreover, note that in Proposition \\[pr:hoeldermapsintoHn\\] we can only show for $C^{\\frac{k+1}{k+2}+\\eps}$-embeddings $\\varphi$ into the Heisenberg group that our analytic linking number is always zero.", "\n\nSo only when $\\varphi$ is a $C^{\\frac{k+1}{k+2}+\\eps}$-embedding into the Heisenberg group can we compare the algebraic linking number (nonzero, since it is an embedding) and the analytic linking number (zero, since it is a $C^{\\frac{k+1}{k+2}+\\eps}$-map into the Heisenberg group).", "\n\nProof of Proposition \\[pr:linkinghoelder\\]\n------------------------------------------\n\nWe split a sphere $\\S^\\ell$ into its equator, which we denote $\\S^{\\ell-1}$ and its closed upper hemisphere $S^\\ell_+$ and lower hemisphere $\\S^\\ell_-$, i.e. $\\S^{\\ell}_+ \\cap \\S^{\\ell}_- = \\S^{\\ell-1}$. We argue by induction on the dimension of the sphere $\\S^\\ell$, $\\ell = 0,\\ldots,k$.\n\nWe will pretend that t$\\varphi$ is a Lipschitz map purely for notational reasons. ", "The argument works exactly as is for the $C^\\sigma$-embeddings, everything is just a matter of supports.", "\n\nThe induction claim is $$\\tag{I} \\forall \\ell = 0,\\ldots, k: \\quad \\exists \\mbox{ $\\omega_\\ell$, a smooth $\\ell$-form, $d\\omega_\\ell = 0$ around $\\varphi(\\S^\\ell)$, and $\\int_{\\S^\\ell} \\varphi^\\ast(\\omega_\\ell) \\neq 0$}$$\n\n### Case $\\ell = 0$ {#case-ell-0 .unnumbered}\n\nBy the decomposition above, $\\S^0$ are simply to points, which we may denote with $\\{-1,+1\\}$. Since $\\varphi$ is an embedding, $\\varphi(-1) \\neq \\varphi(+1)$. So we just pick $\\omega_0$ a $0$-form (i.e. function on ${\\mathbb{R}}^N$) to be constantly $1$ around $\\varphi(-1)$ and constantly $-1$ around $\\varphi(+1)$. Then $d\\omega_0 = 0$ around $\\varphi(\\S^0)$, and $$\\int_{\\S^0} \\varphi^\\ast(\\omega_0) = \\omega_0(\\varphi(1))-\\omega_0(\\varphi(-1)) = 2\\neq 0$$\n\n### Case $(\\ell-1) \\to \\ell$ {#case-ell-1-to-ell .unnumbered}\n\nWe assume that we have found an $\\ell$-form $\\omega_{\\ell-1}$, $\\eta_{\\ell-1} := d\\omega_{\\ell-1}$ is zero around $\\varphi(\\S^{\\ell-1})$, and $$\\int_{\\S^{\\ell-1}} \\varphi^\\ast(\\omega_{\\ell-1}) \\neq 0.$$ Having $\\eta_{\\ell-1} = d\\omega_{\\ell-1}$ we first construct a closed $(\\ell+1)$-form $\\eta_{\\ell}$. Define open subsets of ${\\mathbb{R}}^N$ as follows: $U: = {\\mathbb{R}}^N \\backslash \\varphi(\\S^\\ell_+)$, $V: = {\\mathbb{R}}^N \\backslash \\varphi(\\S^\\ell_-)$.\n\nThe support of $\\eta_{\\ell-1}$ is bounded away from $\\varphi(\\S^{\\ell-1})$, thus $$\\supp \\eta_{\\ell-1} \\subset {\\mathbb{R}}^N \\backslash \\varphi(\\S^{\\ell-1}) = U \\cup V$$ By a cutoff-argument, since , we can find two $\\ell$-forms $\\gamma_{U}$ and $\\gamma_{V}$ supported in $U$ and $V$, respectively, and so that $$\\label{eq:etalm1split}\n \\eta_{\\ell-1} = \\gamma_U + \\gamma_V$$ We define $$\\omega_{\\ell} := \\gamma_U, \\quad \\eta_{\\ell} := d\\gamma_U.$$ Since $d\\eta_{\\ell-1}=d\\circ d\\omega_{\\ell-1} = 0$ we actually have $$\\eta_{\\ell} =d\\gamma_U = -d\\gamma_V.$$ In particular, $$\\supp \\eta_\\ell \\subset \\supp \\gamma_U \\cap \\supp \\gamma_V \\subset U \\cap V \\subset {\\mathbb{R}}^N \\backslash \\varphi(\\S^\\ell).$$ Thus, we have found $$\\omega_\\ell,\n \\mbox{ smooth $\\ell$-form, $d\\omega_\\ell \\equiv \\eta_\\ell = 0$ around $\\varphi(\\S^\\ell)$},$$ i.e., $\\omega_\\ell$ is almost as needed for the induction claim $(I)$, we just need to confirm that $$\\label{eq:stepintnzero}\n \\int_{\\S^{\\ell}} \\varphi^\\ast(\\omega_{\\ell}) \\neq 0.$$ So let us compute . ", "In view of the support of $\\gamma_U$ and $\\gamma_V$ and $$\\int_{\\S^{\\ell}} \\varphi^\\ast(\\omega_{\\ell}) = \\int_{\\S^{\\ell}_-} \\varphi^\\ast(\\gamma_U) = \\int_{\\S^{\\ell}_-} \\varphi^\\ast(\\eta_{\\ell-1}-\\gamma_V) = \\int_{\\S^{\\ell}_-} \\varphi^\\ast(\\eta_{\\ell-1}).$$ Now we use Stokes’ theorem on $\\S^\\ell_-$. Observe that by the orientation of $\\partial \\S^\\ell_- = -\\S^{\\ell-1}$ we get a sign. ", "$$\\int_{\\S^{\\ell}_-} \\varphi^\\ast(\\eta_{\\ell-1}) = \\int_{\\S^{\\ell}_-} \\varphi^\\ast(d\\omega_{\\ell-1}) = \\int_{\\S^{\\ell-1}} \\varphi^\\ast(\\omega_{\\ell}).$$ That is, we have by induction hypothesis $$\\int_{\\S^{\\ell}} \\varphi^\\ast(\\omega_{\\ell}) = -\\int_{\\S^{\\ell-1}} \\varphi^\\ast(\\omega_{\\ell-1}) \\neq 0,$$ and is proven.", "\n\nLet us put the above argument into perspective of algebraic topology. ", "By induction hypothesis, $\\eta_{\\ell-1}$ is an element of the cohomology group $H^{\\ell}({\\mathbb{R}}^N \\backslash \\varphi(\\S^{\\ell-1}))$. We just used the exact Mayer-Vietoris sequence, $$\\ldots \\to H^{\\ell}(U) \\oplus H^{\\ell}(U) \\to H^{\\ell}(U \\cup V) \\xrightarrow{c} H^{\\ell+1}(U \\cap V) \\to H^{\\ell+1}(U) \\oplus H^{\\ell+1}(U) \\to \\ldots$$ where we observe $U \\cap V = {\\mathbb{R}}^N \\backslash \\varphi(\\S^{\\ell})$, $U \\cup V = {\\mathbb{R}}^N \\backslash \\varphi(\\S^{\\ell-1})$. Also, since $U$ and $V$ are homeomorphic to ${\\mathbb{R}}^N$ (that is $\\S^{N}$) with a cube taken away, $$H^{\\ell+1}(U) = H^{\\ell+1}(V) = H^{\\ell}(U) =H^{\\ell}(V) = 0.$$ Thus, the Mayer-Vietoris sequence is simply $$0 \\to H^{\\ell}( {\\mathbb{R}}^N \\backslash \\varphi(\\S^{\\ell-1})) \\xrightarrow{c} H^{\\ell+1}({\\mathbb{R}}^N \\backslash \\varphi(\\S^{\\ell})) \\to 0.$$ This just means that the connecting homomorphism $c: H^{\\ell}({\\mathbb{R}}^N \\backslash \\varphi(\\S^{\\ell-1})) \\xrightarrow{c} H^{\\ell+1}({\\mathbb{R}}^N \\backslash \\varphi(\\S^{\\ell})))$ is an isomorphism. ", "On the other hand $c$ is known, and all we did above is set $\\eta_{\\ell} := c(\\eta_{\\ell-1})$.\n\nActually one can show that $\\eta = d\\omega \\mapsto \\int_{\\S^k} \\varphi^\\ast(\\omega)$ is an isomorphism on $H^{k+1}({\\mathbb{R}}^N \\backslash \\varphi(\\S^k))$.\n\nAcknowledgement {#acknowledgement .unnumbered}\n===============\n\nThis text was mainly written while the author was preparing a lecture for the 19th Rencontres d’Analyse at UCLouvain in October 2016. ", "He likes express his gratitude to UCLouvain and the organizers Pierre Bousquet, Jean Van Schaftingen, Augusto Ponce for the kind invitation and their hospitality.", "\n" ]	{ "pile_set_name": "ArXiv" }	[ 0, 0, 0.005, 0.018072289156626505, 0, 0.010050251256281407, 0, 0.006230529595015576, 0.011235955056179775, 0.0018281535648994515, 0.00684931506849315, 0, 0.0024813895781637717, 0.00423728813559322, 0, 0, 0.02586206896551724, 0.00477326968973747, 0.029914529914529916, 0, 0, 0, 0, 0.0017482517482517483, 0, 0, 0, 0.0070921985815602835, 0, 0, 0.012269938650306749, 0, 0, 0, 0, 0.007407407407407408, 0.018518518518518517, 0, 0, 0, 0.004484304932735426, 0, 0.0023752969121140144, 0, 0.008620689655172414, 0.009370816599732263, 0, 0.014492753623188406, 0, 0.013513513513513514, 0.00496031746031746, 0, 0, 0.005376344086021506, 0, 0.00558659217877095, 0.015748031496062992, 0.006172839506172839, 0.007366482504604052, 0.006329113924050633, 0.00625, 0.003676470588235294, 0.0043859649122807015, 0, 0, 0, 0.0125, 0.038461538461538464, 0.025974025974025976, 0.02197802197802198, 0.0125, 0.012578616352201259, 0.00423728813559322, 0.0064516129032258064, 0.002061855670103093, 0.004016064257028112, 0, 0.00819672131147541, 0, 0.010033444816053512, 0.0196078431372549, 0, 0.0031645569620253164, 0.011494252873563218, 0.0189873417721519, 0.029411764705882353, 0, 0.0125, 0.008988764044943821, 0.004132231404958678, 0.012195121951219513, 0.013333333333333334, 0.00554016620498615, 0.005547850208044383, 0.002824858757062147, 0, 0.018404907975460124, 0.0072992700729927005, 0.006666666666666667, 0.005747126436781609, 0, 0, 0, 0, 0.009162303664921465, 0.007936507936507936, 0, 0.02, 0.017241379310344827, 0.011111111111111112, 0.005319148936170213, 0.014388489208633094, 0.0034602076124567475, 0, 0, 0.007246376811594203, 0.007894736842105263, 0.011111111111111112, 0.02824858757062147, 0.007095793208312215, 0.010067114093959731, 0.010362694300518135, 0, 0.006944444444444444, 0.005763688760806916, 0, 0.0070921985815602835, 0.0012836970474967907, 0.004261363636363636, 0.0017331022530329288, 0.014388489208633094, 0.015463917525773196, 0.02654867256637168, 0.0030181086519114686, 0, 0.001282051282051282, 0, 0, 0.0021691973969631237, 0, 0.0056595559425337396, 0.0025906735751295338, 0.003134796238244514, 0, 0.013358778625954198, 0.004415011037527594, 0.018518518518518517, 0 ]	0.006388	5
[ "A’s win; can Dunn acquisition fill Cespedes hole?", "\n\nOakland Athletics’ Adam Dunn celebrates in the dugout after his two-run home run against the Seattle Mariners during the first inning of a baseball game on Monday, Sept. 1, 2014, in Oakland, Calif. (AP Photo/Marcio Jose Sanchez)\n\nIf there was ever a team that needed to exercise that age-old baseball cliché and turn the calendar page, it was the Oakland A’s on Monday morning.", "\n\nAfter fourteen consecutive months of posting a winning record, the Athletics would very much like to completely forget August 2014. ", "During those 31 days, the A’s went from a two-game division-leading world-beater to trailing the Angels by five games and looking like a team in full collapse mode.", "\n\n“It was a little ugly and it didn’t end very well, based on the series in Anaheim,” said Bob Melvin. “", "It’s good to turn the page.”", "\n\nThe A’s turned the page in a big way, against Seattle. ", "Adam Dunn, who Billy Beane once likened to Paul Bunyan, arrived in Oakland after the A’s acquired him on Sunday. ", "And he immediately started swinging a big axe, hitting a towering two-run home run in his first at-bat, jumpstarting the A’s offense and leading the team to a 6-1 victory.", "\n\n“It was a little bit storybook,” Melvin said.", "\n\nThe A’s had been having a storybook season until last month. ", "The deal for Dunn is a clear concession that something has gone terribly wrong with the team since the trade of Yoenis Cespedes for Jon Lester, on the day before Awful August began.", "\n\nThe A’s, however, don’t buy that theory.", "\n\n“Lester’s been good for us, ” Melvin said firmly. “", "It’s nice to have him. ", "Certainly the offense hasn’t been as good, but we weren’t swinging the bat real well right before (Cespedes) left either.”", "\n\nBut Melvin allowed that taking Cespedes out of the lineup changed the dynamic, and other players feel more pressure to produce.", "\n\n“It was probably a little bit of a shock to them to lose a guy like that,” Melvin said. “", "But now we have a guy like Adam Dunn, who can effect the lineup as well. ”", "\n\nDunn did that instantly on Monday, after a huge welcome from the sold-out Coliseum. ", "Dunn was effusive about the hometown reception, calling it “the best crowd I’ve ever played for.”", "\n\nAs the A’s have bumbled and slipped from their perch as the best team in baseball, social media has crackled with criticism of the trade, that Beane ruined the team, that he overplayed his hand.", "\n\nI was supportive of the Lester-Cespedes trade at the time and still think it’s a good deal for a few reasons: I admired the go-for-it attitude of a general manager realizing that his team had a real opportunity to get to the World Series, I believe that pitching wins in October and I liked keeping Lester away from the competition. ", "Combine those factors with The Chronicle’s Susan Slusser’s reporting that the A’s didn’t believe they could resign Cespedes and were planning to trade him in the offseason anyway, it seemed like a smart deal.", "\n\nBut it certainly has had ramifications. ", "The trade was made with October in mind and the A’s still have to get to October.", "\n\nThere are some things that Beane can’t quantify on his computer – the intangibles of team chemistry and mental pressures. ", "And those elements clearly were affected after Cespedes left for Boston.", "\n\n“I think we were more beat down,” Melvin said. “", "The effort was always there….When you talk about staying loose it’s sometimes misinterpreted as there’s no urgency to what they’re doing.", "\n\n“That wasn’t the case but there are times when you can press and that’s not playing loose. ", "One of the keys for this team was that it has been playing loose, like they don’t know what the score is.”", "\n\nJumping early on the Mariners brought the looseness back. ", "Dunn, who said he was as nervous as he’d been in a long time when he stepped to the plate, was able to participate in the loosey-goosey A’s when he got back to the dugout and had to run through the tunnel of player’ outstretched hands.", "\n\nThe A’s will need to adjust as well. ", "Dunn is such a huge man – at 6-6, 285 pounds – that he was whacked on the head.", "\n\n“We were all joking that we have to get a tall tunnel,” Jed Lowrie said.", "\n\nMelvin was also loose after the game, something he certainly hadn’t been in Anaheim, especially after the final game when he was ejected and had to watch the final seven innings on television and then lashed into the team in a closed-door meeting.", "\n\nMelvin said that watching his team unravel on the screen was disturbing – which means he has a clear idea what A’s fans have been going through in recent weeks.", "\n\n“It is a different perspective,” Melvin said. “", "I’m not used to it and I saw some things that needed addressing.”", "\n\nHe addressed them in Anaheim. ", "And Beane addressed the gaping hole in the lineup. ", "And the A’s were finally feeling good again on Monday afternoon.", "\n\nThere’s a firm belief in sports that you don’t mess with a good thing. ", "And Beane messed with a very good thing. ", "The A’s are still a very good team but they have to reconfigure their chemistry and their offense. ", "They started to do that Monday." ]	{ "pile_set_name": "Pile-CC" }	[ 0.02040816326530612, 0.0079155672823219, 0.007462686567164179, 0.006097560975609756, 0.009615384615384616, 0, 0, 0.035398230088495575, 0, 0.02127659574468085, 0, 0.011049723756906077, 0, 0.018867924528301886, 0, 0, 0.007751937984496124, 0.01098901098901099, 0.013513513513513514, 0.011627906976744186, 0.010309278350515464, 0.00510204081632653, 0, 0.004807692307692308, 0, 0, 0, 0, 0.02, 0, 0, 0, 0.016666666666666666, 0.00425531914893617, 0, 0.012658227848101266, 0.013513513513513514, 0.004016064257028112, 0.006172839506172839, 0.02040816326530612, 0, 0, 0.0196078431372549, 0, 0, 0.024390243902439025, 0, 0 ]	0.007164	5
[ "Archives\n\nCategories\n\nMeta\n\nOur last night in Hong Kong was spent with great food and tons of people. ", "Conversation varied from the legality of weather balloons to the relationship between the color of LEDs and the color of stars (got my answer: of course it has to do with the electron band gap, even though LEDs produce light in a completely different way than the black box radiation of stars.)", "\n\nPeople worked together to create a web server to control the color of the room’s lighting and brainstormed how to track the position of a flexible mesh of LEDs with OpenCV. ", "We ate mango mochi (made in Kowloon!) ", "and politely argued about the glycemic index of sugar vs flour and tried to recall why corn was ever subsidized in the first place. ", "We found things around the space that connected us back home (Super sweet corn invented at UIUC, aerosol manufactured in Somerset xD).", "\n\nThe Dim Sum Labs Fridge. ", "Taping the wifi-controlled MOSFETs to the ceiling.", "\n\nThe BBQ, if there was any doubt, was cooked on the shell of a PowerMac G5. ", "We consulted each other about whether anodized aluminum was okay to burn under our food (we’re pretty sure it is, unless Apple dyed it a slightly shinier gray or something).", "\n\nWe learned about each other’s projects: an activist group collating tweets of UK police kettling into a compass telling protesters how to avoid the police lines. ", "A helium balloon lost at sea. ", "A CNC machine that performs micro-pipetting. ", "Running a web server on the ESP2866 (a surprisingly powerful programmable wifi microchip for under $2).", "\n\nToday was a lot of walking. ", "We met up with a local event organizer for lunch in the hilly Mid Levels of Hong Kong — but the restaurant was a tight fit for 18 people (and more trickling in…) so a few of us decided to walk back to central station. ", "Half way there we intercepted a couple others from our group and joined up with them. ", "It was a long walk for lunch in a subway station but it was nice to see more of the center of the city, with all of its elevated pedestrian walkways.", "\n\nOn the way back we took the escalators through the city, which seems like a really neat way to commute. ", "Elevated moving sidewalks, pretty futuristic you know? ", "The video might be boring but you can see what it’s like, anyway.", "\n\nWe arrived at a very cool destination called PMQ: a mixed use historic building that’s a lot of fun to explore the balconies and shops to the mixture of pianists practicing or improvising on the public pianos.", "\n\nThere were some nice exhibits about its history: it was originally a government school (British Colonial government, that is) in the 19th century sitting right between a neighborhood full of western foreigners and a neighborhood full of Chinese. ", "The road that runs through both neighborhoods is called “Hollywood Road” (so named before Hollywood, California existed) and this school brought people from both neighborhoods together to study. ", "Chinese students enrolled in English and westerners enrolled in Chinese classics (OK now I’m just reading the wiki article 🙂\n\nA video playing in an exhibit also covered the building’s brief stint as a family dormitory for policemen. ", "A man being interviewed recalled that each of the balconies was a shared dining area for two families, and from one balcony and you could look around to see who was having dinner and what they were cooking, and that it was a festive atmosphere every night with families all eating together. ", "I could picture it standing there, and it seems like a really good design for a family residence. ", "However, it was abandoned in 2000 and since renovated into this big mix of start ups, art studios, and craft shops (I bet a few of these shops have Etsy stores, I’ll put it that way).", "\n\nClick to zoom and check out the smiley face balloon just chilling out.", "\n\nEventually we met up with some guys at Brinc, an “internet of things accelerator” with an office on the top floor of the building. ", "I learned what an accelerator does! ", "I had always lumped them into the same category as shared work spaces and incubators, just as something mysterious where people spend a lot of other people’s money. ", "But it made sense that there’s a lot of people with an idea that they want to bring to market, but without experience working with manufacturers they risk bankrupting themselves without ever getting a finished product out of a factory.", "\n\nSo these guys make their experience getting new technology made at existing factories available to newbies, as well as marketing and business consulting like “Does your product have any desirability to the consumer?”, “", "How does your product stack up against its competition”, you know, value proposition stuff. [", "Insert guy’s name when I find his business card again] told us a lot of engineers think they have a good product just because they made something and it works. ", "They hadn’t really gone through the rest of the process of whether it’s marketable, or even manufacturable. ", "So the accelerators work with these startups to make sure they have a good product before spending hundreds of thousands of dollars approaching factories.", "\n\nImagining a group of guys building something and thinking they could just kickstart it and then order 1,000 of their widgets made me wonder, do any of these teams even have a friend that went to business school? ", "Did anyone raise these questions before they moved to San Francisco looking for investors? ", "So I asked [guy from Brinc] if the teams that come to him are mixes of business people and tech people, and he confirmed that it’s not too often they find a team that already has a balance of expertise, so that’s why they often serve to connect these startups with whatever talent they’re missing.", "\n\nThis made me realize that CUCFabLab working with the business school at U of I is a really unique, very positive partnership if it can encourage tech folks to mingle with the business minded, just so that if either of them has a good idea, they have a wider perspective of what the process of bringing hardware to market entails.", "\n\nI thought it was very interesting to learn that this Brinc accelerator would bring start up teams out to live in Hong Kong, with the idea that if you’re going to be paying thousands of dollars for consultants and so on, you better be paying people that work directly with the factories that will make your product. ", "We heard stories of start ups that burn through millions of dollars of funds by hiring teams and lawyers and talent to start a business without even making it across the pacific to start building their thing.", "\n\nAfterwards, most of the group went on to the MakerBay hackerspace but I was feeling drained of energy, tired of being wet and a little sick, so I made my way back to Kowloon in search of a good Ramen shop. ", "Found “Butao” and got a very spicy pork belly ramen and had myself a good sinus-clearing cry.", "\n\nCNC Plasmascreen Coffeetable\n\nBeing a university affiliated FabLab has some perks: we get to pull useful items from University Surplus (one department upgrades their computer lab, other departments call dibs on the old hardware, sometimes really new stuff, sometimes really old stuff).", "\n\nNearly all of the computer equipment at CUCFabLab was pulled second-hand this way, then topped off with RAM and upgraded to SSDs. ", "A funny assortment of other supplies end up getting collected: decades old oscilliscopes, a 1980s bandsaw, and this big old 60″ plasma screen display.", "\n\nIt weighs about 100 pounds and is fairly low resolution (not quite 720p if I remember right) and it took up an awful lot of table space, so it quickly got basemented. ", "That was until my Fab Academy assignment was to ‘make something big’ and I remembered that I always wanted a coffee table that was a giant computer screen.", "\n\nThe neat thing about plasma screens is that a lot of the electronics are bonded to the glass (tho I can’t recall where I heard that…) and as a result, they often have a pretty thick slab of glass to start with, so it’s sturdy enough that I don’t feel nervous about setting my laptop and maybe a cup of coffee on the screen (tho a spill of the latter might be fairly disastrous if you don’t contain it before it drips into the edges…).", "\n\nPutting a big slab of acrylic or glass on top of a large display is often the most expensive part of this kind of object, so avoiding that part altogether meant I just needed a cheap MDF base for the TV to sit on. ", "Like most TVs, there’s the front body of the screen that tries to be thinner while the power supply and mainboard sits in a sort of hump on the backside. ", "So the design of a base that goes up to this edge but leaves room for the hump turns out looking like a pool table.", "\n\nIt was designed using the Rhino plugin Grasshopper, which proved to be a very intuitive interface for parametric design. ", "It is a matter of dictating the size and position of 3 rectangles (the top of the table, the base of the table, and one that can be scaled and moved as a midpoint) and then creating “lofted curves” through each set of corners. ", "This is an automatic function that creates the whole smooth shape pictured without any work on my part. ", "I get to just change the position of the midpoint of the curve until I like the look of the resulting curve. ", "Then I just subtracted a box with the inner dimensions I needed from the larger shape.", "\n\nAfter that, I have a program to do the work of planning my assembly as well. ", "The free 123D Make by Autodesk has a great workflow to open your 3D file, type in your material parameters (“I’m using 4′ by 8′ sheets of material 1/2 inch thick”)\n\nI got the pieces cut at the architecture lab with lots of help. ", "I learned that with this slotted construction technique it’s necessary to drill holes at every interior corner (so in the CAD file you select each of these corners and create ‘points’ on a separate layer to export as a drill file). ", "This was about $40 worth of MDF and took less than an hour to cut out on Architecture’s giant fancy CNC machine.", "\n\nAssembling it took a lot longer. ", "Lots of rubber malleting.", "\n\nI started playing with processing sketches (like the rainbow above), but it takes up a lot of space and there’s not a good spot for it at the lab, but the TV is unvierstity property so it can’t be taken off campus, so it is hidden in a corner — the interactive processing sketches will wait for now.", "\n\nI think it is not an uncommon experience for people who are bit by the 3D Printing bug to look at each object in their daily life and wonder “Could I print that?” ", "It’s also fun to look at objects and think of how you would manipulate a cube, a sphere, or a cylinder (common ‘primitive’ shapes in 3D design).", "\n\nSo I had been practicing Blender and noted that the lenses of my eyeglasses just pop in and out of my super-cheap plastic frames — no screws required. ", "And of course I thought “I could print that.” ", "It wasn’t until a newcomer to Makerspace Urbana wandered in with the same idea that I made progress.", "\n\nThe second design iteration\n\nBasically, I knew how to trace the 2D oval shape of the lens (take a picture, draw a bezier curve in Inkscape on top of the photograph, import that bezier curve into Blender, convert it to a mesh, and start building the frame outward from that. ", "But the lenses aren’t flat, and I didn’t have a clue how to measure and mimic that curvature in Blender. ", "I wish I could remember the guy’s name (this was a couple years ago) but an optician walks into Makerspace with he same idea, except he knows about these lookup tables where you can find the curvature of particular prescriptions. ", "It’s a pretty straight forward set of numbers: a sphere of a certain radius a certain distance from the lens. ", "That information made it trivial to take my bezier curve in Blender deform into the actual curvature of my lens using the “ShrinkWrap” modifier. ", "Position the curve at the right distance from the sphere, and ‘shrinkwrap’ the curve to the surface of the sphere.", "\n\nModelling the outline and curvature of my prescription lens.", "\n\nThe lens has a bezel top and bottom which I could measure the height of, but the angle of the bezel was just eyeballed. ", "I simply extruded this ring outward to create the first test fit (printed at MakerLab). ", "Plastic is now one of my favorite materials because of how forgiving it can be: it stretches and snaps and even tho I did very rough measurements, the lens snapped right into place.", "\n\nFrom there, I printed some pince-nez style frames that I wore around for a while before sitting back down to model the earpieces in Blender. ", "The first iteration was printed in one solid piece, face down, earpieces being build straight into the air with no supports. ", "This worked great for a few inches, but I learned that the plastic being extruded applies a significant amount of pressure on the plastic beneath it, so that as the towering earpieces grew, they began being pushed side to side as the nozzle worked on the next layer such that subsequent layers were not stacking up straight. ", "The night that I was determined to finish a pair (I had by now broken my manufactured frames from popping the lenses in and out so much), I wanted to be able to see on the bike ride home, so I had to finish these. ", "Our of desperation, I braced myself against the frame of the printer and held onto the earpieces to stabilise them by hand for the last 20 minutes of the print. ", "They still turned out looking like a dog had gnawed on the ends of the frame (the misaligned top of the print) but that sits behind my ears and I told myself it gave it a more homemade touch.", "\n\nTo get the lenses to fit into these frames took a few more tries (I used the same file, but the original print was done in PLA on a Makerbot, and these were now in ABS, and between the expansion and contraction of plastic and the slightly differing calibration of printers, well, point is these things aren’t always consistent.)", "\n\nI got a lot of mileage out of this design, printing a few alternative colors, including glow in the dark. ", "They looked a bit toyish, which is a style of its own. ", "The real trick though is that they were printed with the earpieces straight up and down at a width that’s just a bit skinnier than my head: so when stretched over my face, they actually pinch just enough that they never fell off (but were still suitably comfortable.)", "\n\nThe next iteration (pictured at the top) was designed with hinges, but without a lot of thought into how to prevent the hinge from swinging both ways. ", "After printing the pieces separately, I drilled a 1/32″ hole through the pivot point, stuck 20 gauge copper wire into the hole, snipped off the remainder, and filled the hole top and bottom with superglue, pivoting the hinge as it dried so that it only adhered to the top and bottom.", "\n\nI liked the look of these (that PETT plastic carries light like fiber optic, so they kind of sparkle), but they did fall off my face time to time owing to the backwards bending hinges, so when I accidentally stepped on them in my morning stupor, I just went out and got contacts.", "\n\nHong Kong\n\nThat’s Innovation Tower! ", "Looks like a cruise ship from the year 2070, right? ", "Possibly interplanetary space-worthy? ", "It houses the school of design at Hong Kong Polytechnic University and was the first stop of Noisebridge’s Hacker Trip To China 2015.", "\n\nWe met with William of Dim Sum Labs outside our hotel who took us on a tour of the PolyTechnic University, pointing our the tight grouping of the Business School, Design School, and Textiles School. ", "We interrupted a couple of classes, where students were happy to explain what they were working on. ", "I met one guy doing a papercraft mech (you know, those giant flying fighting robots) which he designed in CAD and broke out all kinds of engineering drawings of how to fold this complex origami. ", "A girl was working on a chair made of bamboo and cord, taking advantage of its tension. ", "Always something being cut in two (I think I saw some chiseling going on) and folded into shape.", "\n\nSo it’s a very well equipped university lab, open only to design students. ", "Reminded me that I wish I had access to ceramics wheels again. ", "The thing that attracted my attention the most was the excellent signage! ", "Maybe a boring thing but it’s a topic of constant discussion at CUCFabLab — how to make the signs better, how to make sigs that express rules and expectations and capabilities. ", "So when I saw the wall-sized page-turning displays of materials, I said to myself “Duh!” ", "and when I saw a big poster listing all the tools available at the lab with a key connecting it to its picture, I said to myself, “duh!” ", "There was even a big poster by the laser cutters describing what line weight and file format to use.", "\n\nSo I got organizationally inspired. ", "After concluding our tour, we had a big lunch (I’ve been impressed so far with Hong Kong restaurant’s capacity to cater to a group of 18 people without warning) and headed to Dim Sum Labs, but not before topping off our ‘Octupus Cards’ — which is the tap to pay card for all the public transit systems as well as convenience stores. ", "I forget who it was, but somebody had an app on their phone that could read any NFC chip and dump all of its information on the screen, so with one tap we found out the model # of the microchip and the software version running on these featureless plastic cards. ", "Neat stuff — we joked about editing the information (chiefly, the current balance), but there’s some pretty tight encryption running on those little plastic cards, too.", "\n\n“Do you think I can edit the balance of this without putting cash on it?”", "\n\nDim Sum Labs is a one room affair (I think I heard 400 sq ft), which they pay about $1,500 USD/month for. ", "They’ve got some great self-screen-printed tshirts (William is wearing one in the pics) and a great RGB LED lighting system — kind of looks like christmas lights in the picture. ", "One of the members was working on an upgrade: to make the color of the whole room programmable (switching a few amps on and off is a little tougher than blinking one LED).", "\n\nI was reminded of my dream-classroom for teaching intro to programming: individually addressable LEDs covering the ceiling such that each student in a classroom could start by controlling just the one LED, getting to know how to blink it and effect its color. ", "Then each student could work their way up to controlling larger arrangements: perhaps a row of 5 LEDs, then a grid of 5 x 5 LEDs, until the students’ combined work is creating undulating colors across the whole ceiling.", "\n\nThe benefit of this is twofold:\n\nbasic programming is a lot more interesting if you get to control something not on your computer screen (I learned by manipulating strings in a command line, but I see people blinking LEDs are a lot more enthusiastic about a few lines of code.)", "\n\nAs a teacher / mentor, you don’t have to squint and bend down to someone’s screen to see how they’re doing. ", "You can see the progress of the whole class at once. ", "Better yet, the students can see the results of each others work, too, leading to un-plannable “how did you do that?!” ", "learning moments.", "\n\nSo I was going on about how I wanted to build a room like that, and the guy I was talking to (I’ll learn everyone’s names soon enough…) said “Oh, we got a ceiling you could do that with at our hackerspace in Chico (California)”\n\n!!!!", "\n\nThen a guy across the table says “What? ", "You live in Chico? ", "I grew up in Chico!” ", "The bigger the city, the smaller the world.", "\n\nThe rooftop at Dim Sum Labs.", "\n\nAfter hanging out a Dim Sum Labs for an hour or two, and we connected to an acquaintance that was told “We’d like to visit Dim Subs Labs and other places of Geek Interest” by Mitch so we ended up at a very cool espresso bar / third wave coffee shop (that’s the kind where they roast the beans behind the counter and let you pick out which farm you want to try the flavor of) that had local art for sale, the majority of which was laser cut upstairs.", "\n\nAgain, I was inspired and surprised by dioramas that communicated the capabilities of the space. ", "Just a general feeling of “why didn’t I think of that?” ", "all day. ", "So they’ve got these products they sell, both as little assemble-it-yourself kits like the bud vase and as assembled products which you can inspect all of the parts. ", "I’d love to build some of these at my home FabLab as well, just to get people’s minds going on what you can do with these tools.", "\n\nAfterwards we wandered an electronics market, tho it was late enough that most booths were closed. ", "A few people were figuring out SIM cards and international power adapters. ", "Mitch was testing the charge rate of different USB cables which is a shocking discovery that merits further investigation: some USB cables charged his phone at a piddling 80mAH and others charged at 10 times that rate. ", "Like, what? ", "It’s four wires, there’s nothing in there, how can one cable charge so much faster than another? ", "Hmm…\n\nAt the Makers in Motion summer camp in Peoria, IL, the CUCFabLab team tried out a new activity to complement the camper’s visit to the museum’s planetarium. ", "At the end of the camp, we had a whole sky-full of glowing constellations. ", "The creative soldering abilities of 7th and 8th graders surprised us — this was just a day after assembling their first ‘blinky badge’!", "\n\nThe afternoon started by asking the class what they learned during the planetarium show. ", "There was some conversation about stars burning at different intensities with different colors, and some review of how red-shift and blue-shift are used to determine the movement and velocity of stars and galaxies.", "\n\nWe then asked if anyone had a favorite constellation, or if they knew any mythical stories about them, but that didn’t get very far. ", "So, we let everyone open their laptops and pull up the wikipedia’s list of constellations. (", "You know, I just realized how nice it is to have a laptop-based computer lab, since you get to dictate whether people are looking at computer screens or each other. ", "You’re much less likely to look across the table or up at the instructor if you have a computer screen in front of you already.)", "\n\nEveryone was encouraged to read through the descriptions and mythologies of different constellations for about 10 minutes before we would go around the room and share what we learned. ", "This was pretty fun — the wiki articles often have nice art and interesting origin stories for the students to share with each other (we didn’t discourage looking over each other’s shoulders). ", "When time was up, we asked each student what constellation they chose to look at and if they could tell us a little about it. ", "Some people had constellations with very intriguing mythologies (Anything involving the god Jupiter gets pretty crazy) and we had some laughs over the absurd story lines of Greek gods.", "\n\nWhat followed was our standard intro to Inkscape: here’s how you can draw circles, here’s how you can draw lines. ", "You can turn circles into lines and vice versa. ", "You can copy paste pictures, and turn those into lines, too! ", "Oh, and all those lines we have? ", "We can have our 30 watt laser beam follow them for us.", "\n\nThe most difficult part is finding suitable constellation art with a strong border to trace using Inkscape’s “trace bitmap” feature. ", "A few of the outlines had to be drawn by hand with the Bezier Curve / Line tool — the snake and the big dipper come to mind — but that’s a good learning experience, too. ", "After we had the outline, we went through the process of creating the cut outs the LEDs pop into.", "\n\nCreate a 0.9 mm circle\n\nDuplicate that circle and move it 3 mm away (using the X and Y coordinates at the top of the program)\n\nGroup the pair of circles\n\nCopy paste the pair of circles anywhere you want to place a star/LED\n\nEdit, 6 months later: Really great constellation art can be found on wiki, here:\n\nStudents who finished that early were asked to draw red lines between the stars forming their constellations that could be lasered at low power (or in one case, trace an outline of the ram with a red line since all of its stars surround it.) ", "When the files looked like they were coming together, we had everyone save their inkscape file to a shared folder on google drive. ", "Only do this if you have really good internet! ", "A locally networked shared folder would do the trick, too. ", "It’s always fun to see the kids’ names fill up the folder on the instructor’s screen so we can make sure everyone got their file in the same place.", "\n\nAfter snack we wrapped up the day by learning how to solder with the ever-popular Blinky Badge! ", "That night Virginia and I checked each file for proper line weight and color (our Epilog laser likes to have 0.001″, solid black lines) and compiled all the Inkscape files into two cut files we could knock out the next morning.", "\n\nThe next day the kids were greeted with wooden versions of their digital designs. ", "To start the electronics portion of the project, we asked the students to review what they knew about circuits and the blinky badge — just that you’ve got a battery with + and -, and you’ve got an LED with + and -. ", "We passed around batteries and LEDs of different colors and let everyone experiment. ", "Pretty soon they figured out you can put multiple LEDs on one battery. (", "Check out the super-informative Evil Mad Scientist blog for reasons why this works out OK without the ‘proper’ resistors in series.) ", "We also stumbled upon the question of why you can’t mix colors —remembering that elecricity will take whatever path requires it to do the least amount of work and some colors like red and yellow take less voltage to illuminate than others like blue and white. ", "Hey, that’s kind of like how cooler, less energetic stars are red and yellow while hotter, intensely burning stars are blue and white. ", "Probably just a coincidence and nothing to do with band gaps and photon wavelengths. (", "You get to decide if you want to bring up band gaps and photons with your age group!)", "\n\nSo everybody knows all the positives have to connect and all the negatives have to connect and they can’t touch. ", "Next step was to design the circuit that would connect the LEDs in their constellation. ", "We passed out red and blue markers and asked everyone to trace their constellation on paper and then mark where their stars are by eyeballing it. ", "This was presented as the puzzle it is: how do you rotate each LED in its place and run a piece of copper between all of them so that they connect without crossing wires? (", "Or, at least avoid it as much as possible. ", "Everyone learned that electric tape is a very useful insulator if you don’t want two pieces of metal to touch.)", "\n\nLike I said, I was really impressed with everyone’s problem solving and stick-to-it-edness on this task. ", "Kids even commented that it was fun! ", "I think the imminent danger of things burning along with the puffs of steam and being trusted with a soldering iron made this a really good experience for everyone. ", "If you’re planning on doing this activity yourself, make sure you enforce the rule to put your soldering iron away if you’re not actively melting something. ", "The only injuries I’ve ever seen in teaching people to solder (2 minor burns in hundreds of students) is when you get distracted and forget you’re holding a burn-stick. ", "To accommodate our kid-to-iron ratio, students had to share, and we also made sure everyone knew not to hand the iron to each other — put the iron back in its holder and let the other person pick it up. ", "Take a close look at the pictures of the solder joints, even when tape overlaps tape its important to join them with a dab of solder as the underside of the tape is non-conductive adhesive. ", "Sometimes you can avoid tape altogether if your LED’s leads reach each other.", "\n\nThere were just a few (maybe 3 or 4 out of 15) that had some persistent problems getting illuminated, but even those kids stuck with it. ", "We were lucky enough to have about 3:1 ratio of teacher-helpers and even if they couldn’t find the error right away just helping the student inspect the circuit for problems helped them persevere. ", "Most of the problems were just weak connections somewhere along the line, solved with another dab of solder. ", "I think the hardest to track down problem we had was one where copper tape was stacked above electric tape stacked above the opposite copper tape, and when soldering on top of this sandwich, the copper absorbed enough heat to melt through the insulator in between, but just enough so we didn’t see it until totally disassembling that part of the circuit.", "\n\nFor display, the finished products were taped to black foam core and its wires (jumper cables soldered on after the fact) stuck through to the back. ", "Arduinos were programmed to blink and fade the constellations. ", "When they’re taken home, they could still be illuminated by AAs or button cell batteries.", "\n\nHere’s a video of the FabLab portion of the camp that includes these constellations.", "\n\nWe ran the workshop at a skillshare at the Museum of Science and Industry, here’s some photos of that by Suzanne Linder!", "\n\nThose are LEDs on DIY circuitboards weaved into a patch of cotton. ", "The hand loom it was made on was laser cut, gifted to me by Walter Gonzales of Fab Lab Lima (Thanks, Walter!). ", "Stainless Steel is used as a warp thread and can provide power to light up the LEDs, controlling each row individually.", "\n\nThe cooler part is that with Arduino, you can write a program that switches these threads from output to input very quickly. ", "This means that each thread can act as a touch sensor (Like the Celestial Celeste) but if touch is detected, electricity can immediately be output down the same thread.", "\n\nI’ve got a video of plain steel thread acting as a touch sensor (this is the Makey Makey method of using a large pull-up resistor and detecting when the sensor pin becomes grounded via your skin).", "\n\nUnfortunately, I didn’t use LEDs with built in resistors (like the Adafruit sewable LEDs) so I can’t power them with 5V directly. ", "Long story short, the detection circuit becomes more complicated if I have to use resistors before the output. ", "Another option I’ve yet to try is detecting and powering the LEDs with an Arduino running at 3.3V (like the Adafruit Floras).", "\n\n10/11/15 Update: Got it blinking with a Flora. ", "Will probably have to mill my own board to integrate the resistors needed to sense touch and power LEDs. ", "Or I could probably solder megaohm resistors to these same LEDs boards and weave them in…\n\nWith a newfound ability to take digital design and make physical objects, it’s only natural to find a way to go the other direction. ", "3D Scanning is the technique that closes the gap in the promise of 3D printers being replicator machines. ", "In fact, the ‘Maker Replicator’ has a companion: the $1400 “Makerbot Digitizer.” ", "Essentially, it’s a motorized turntable, two lasers illuminating either side of the object-to-be-digitized, and a camera with a live feed to the fine tuned software that gives you a 3D model ready to print inside of ten minutes.", "\n\nMakerspace Urbana has a mission of technology proliferation to people of all classes and creeds, and at $1400, the Makerbot Digitizer is another piece of new technology that’s priced out of reach of the general population. ", "So I was very impressed to see James, a fellow member of Makerspace Urbana, playing with a different set of hardware to achieve the same result — a simple handheld laser and an old webcam (specifically a Playstation Eyetoy — talk about repurposing).", "\n\nThis blue laser isn’t something many people would have sitting around, but can be ordered online for about $10 before shipping. ", "It’s 5mw and 405nm wavelength. ", "A simple filter that can be ordered along with it turns the dot into a sharp straight line. ", "However, any old red laser would work as well (though it would require very dim lights, higher power lasers will work much better), and can be converted from a red dot to a red line using a small plastic cylinder, for instance: a lego lightsaber!", "\n\nSo the components for a 3D scanner can be hacked together (perhaps you have a busted cd or bluray player that could have its laser beam harvested) — but how about the software? ", "James had been using the free trial of DAVID3 laser scanning software. ", "It offered a very intuitive scanning workflow, but would only allow you to save one side of the object at a time unless you pony up hundreds of dollars for a license.", "\n\nThis strategy of digitizing an object works by using a calibration pattern that the software recognizes (that’s the piece of paper with dots printed on it) to determine how far away the background is from the camera. ", "When a laser-line is projected across the object, the line takes the shape of the object. ", "The software compares the form-fitting shape of the laser line with the straight line that hits the background, and creates a “point cloud” representing the one side of the object the camera can see.", "\n\nThe Makerbot Digitizer has the turntable wired up to the computer, so it can scan the object while it rotates. ", "But without this integrated turntable, we have to scan the object one side at a time — and manually piece the point clouds together after the fact. ", "The DAVID3 software automatically aligns these point clouds, but saving the result is a privilege of the paid version.", "\n\nFrom left to right: aligning two point clouds, the completed 8-sided point cloud and all its associated noise, and the surface reconstruction ready to print.", "\n\nBut no matter, the free and open source “MeshLab” allows you to align point clouds semi-automatically. ", "For each of the 8 angles captured, you have to give MeshLab some hints as to how they line up, and it uses its fancy algorithms to piece the two together. ", "Here is (someone else’s) video tutorial that shows the whole process.", "\n\nI used that technique to piece together 8 scans of my cactus, and was able to create a ‘watertight’ mesh, a continuous volume without any holes — using a MeshLab filter called “Surface Reconstruction: Poisson.”", "\n\nThe generated mesh is solid, seamless and ready to print. ", "While the general likeness was captured, I’m not so satisfied with the detail. ", "Perhaps using a higher resolution camera would help, but I think most of the detail was lost in the noise resulting from the laser’s light-scatter — a result of the material bending and blurring the laser-line. ", "So whatever laser scanner you use, the detail you capture will be reliant on how sharply the object reflects the laser.", "\n\nAfter trying this method out on a few different objects, I came across 123D Catch : a cloud service that generates meshes from photographs. ", "I’ve found it vastly more practical than setting up and calibrating lasers and cameras — even with a couple dozen pictures from my camera phone I can get very detailed meshes, with the photographic data applied to the surface. ", "You can download the results to use how you please (under a non-commercial agreement), but it is a free service by Autodesk that they can pull anytime. ", "Since then I’ve learned to use Agisoft — equally powerful photostitching software, for $60 with education discount. ", "At least it’s something you can own and run on your own computer!", "\n\nWith a team of new friends, I got to build a musical instrument that combines LEGOs and Arduino. ", "An ultrasonic distance sensor hangs under a gantry and plays different notes according to the LEGOs underneath it. ", "Our hurried first build was fragile, but pulled off a successful live demo in front of the audience.", "\n\n(We called it FORTissimo since you could build LEGO forts that make loud noises.)", "\n\nThanks to Nora’s suggestion to join the facebook group Hackathon Hackers, I found out about an event I couldn’t pass up: a music/technology hackathon put on by a the People’s Music School (@PeoplesMusicSch ). ", "Only trouble was I was living 300 miles away at a cabin in the woods of Southern IL. ", "Luckily I wasn’t too far from an Amtrak station, and I scheduled a roundtrip on the City of New Orleans inside of the 24 hours I had off work (it seemed that way at the time).", "\n\nAfter a few hours of spotty sleep on the train, and a drowsy cab ride to Merchandise Mart, I can’t tell you how refreshing it was to walk off the elevator into a sunlit atrium filled with the sounds of a string quartet. ", "Throughout the day a few students of the music school would set up in one room or another to give a soundtrack to the brainstorming and building. ", "It was awesome.", "\n\nThis was the first hackathon I’d participated in. ", "The way teams were divvied up was a bit awkward: after opening remarks, the audience was asked if anyone had an idea for a team yet — perhaps they were expecting more small groups to show up ready to go, but I think most of the people came as individuals. ", "So instead a few people introduced themselves and said what comes to their mind when they think about tech / music / education. ", "I introduced myself and said I liked to use Arduino to teach music and coding.", "\n\nIn the coffeecake fueled team-forming mingling that came afterward, I was approached by a couple different people who had ideas for software to help people learn music, and I ended up sitting down with a couple of women who had kids studying music — it was a lot of fun to think about what makes practicing difficult for anyone (I had dropped out of music school a few years before partly because I couldn’t quite stomach the 4 hours a day in the practice booth that my professors recommended).", "\n\nWe identified that the repetition of material coupled with the lack of feedback makes sitting in a practice room a pretty dull experience. ", "So we brainstormed ways of automating feedback — perhaps a program could take a recorded example of a teacher playing a passage, and compare a student trying to copy it. ", "I still think a computer could quickly point out wrong notes and wrong timing so that you don’t practice the same passage incorrectly over and over, but we agreed that replacing a music teacher with an app was pretty pie-in-the-sky.", "\n\nPeople’s movement from one team to another was pretty fluid, which was great — it meant ideas got around. ", "Having people work around each other openly, brainstorming on white boards makes it pretty easy to join a conversation, and not long after, join a team. ", "After bouncing ideas off a few different people during the morning, I came across a table scattered with LEGOs. ", "Alex and Ania had brought their hack-kit with them and already had some beeps going on while constructing lego towers. ", "Of course I sat down to ask them what they had going on. ", "Alex had seen an Instuctables for an Arduino Distance Sensor with Buzzer and LED before coming to the hackathon and brought his Arduino, distance sensor, and piezo buzzer. ", "After catching me up, he complained that his main concern is that the buzzer wasn’t a loud enough output. ", "I showed him that it was really easy to control the sound from a laptop via Arduino, but he insisted that he doesn’t want the product to be tethered to a computer to work. ", "Luckily (well, I was going to a music-tech hackathon) I had speakers and transistors in my laptop bag and built two simple one-transistor amplifiers to output some simple square wave tones. ", "We rubber-banded the mini breadboard to the top of their gantry. ", "Happy with the improvement, they let me join their team and commence a couple hours of programming and debugging to get each note of a major scale to be triggered by a particular height of LEGOs.", "\n\nNote the kid in the background who looks jealous that we got to play with LEGO.", "\n\nThe live demo went great, playing a melody up and down a major scale (cleverly avoiding the bug we never worked out when going from the highest tower back down to nothing). ", "Among the rest of the presentations, ours was the only one that was more than theoretical (though there were some web mockups that were pretty impressive for 6 hours of design time). ", "I’d still like to explore software that compares a student practicing to some standard and tells the student what they can do to improve. ", "I’d also like to actually build FORTissimo as a kit. ", "It really would be pretty cheap and versatile. ", "But for now it was just a fun weekend." ]	{ "pile_set_name": "Pile-CC" }	[ 0, 0, 0, 0, 0, 0.014925373134328358, 0, 0, 0.025974025974025976, 0.005780346820809248, 0, 0.03333333333333333, 0.022222222222222223, 0.009708737864077669, 0, 0.0045871559633027525, 0, 0, 0, 0, 0, 0, 0, 0, 0.004291845493562232, 0, 0, 0.00546448087431694, 0, 0.007518796992481203, 0, 0, 0, 0, 0, 0.00625, 0, 0, 0, 0, 0, 0, 0, 0, 0.004807692307692308, 0, 0.003484320557491289, 0, 0, 0, 0.0064516129032258064, 0, 0, 0, 0, 0.008130081300813009, 0, 0, 0, 0, 0, 0.004366812227074236, 0.004310344827586207, 0.017857142857142856, 0, 0, 0, 0, 0, 0.006535947712418301, 0, 0.01, 0.007246376811594203, 0.009523809523809525, 0, 0, 0.006896551724137931, 0, 0, 0, 0.011363636363636364, 0, 0.006993006993006993, 0, 0, 0, 0, 0, 0.0030303030303030303, 0, 0, 0, 0, 0, 0.0035587188612099642, 0, 0, 0, 0.015037593984962405, 0.024875621890547265, 0, 0.005128205128205128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.003003003003003003, 0.0038022813688212928, 0, 0, 0.009259259259259259, 0.0056179775280898875, 0, 0, 0, 0, 0, 0.018867924528301886, 0, 0, 0, 0, 0, 0, 0, 0.03333333333333333, 0.0066518847006651885, 0, 0, 0, 0, 0, 0, 0.013333333333333334, 0.0136986301369863, 0, 0, 0.012269938650306749, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0058823529411764705, 0, 0, 0, 0, 0, 0, 0.01020408163265306, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01639344262295082, 0.014492753623188406, 0.018018018018018018, 0.008403361344537815, 0.007874015748031496, 0, 0, 0.015151515151515152, 0, 0.016, 0.02040816326530612, 0, 0, 0.009433962264150943, 0.012345679012345678, 0, 0.0044444444444444444, 0.012048192771084338, 0, 0, 0.010869565217391304, 0.0040650406504065045, 0, 0.028169014084507043, 0, 0, 0, 0, 0, 0, 0.00847457627118644, 0, 0, 0, 0, 0.0047169811320754715, 0, 0, 0, 0, 0, 0, 0.006578947368421052, 0, 0, 0.010101010101010102, 0, 0, 0, 0.014218009478672985, 0, 0.005714285714285714, 0.0045045045045045045, 0, 0, 0, 0, 0, 0.01282051282051282, 0, 0, 0, 0, 0, 0, 0, 0.008403361344537815, 0, 0.01744186046511628, 0, 0.005813953488372093, 0, 0, 0, 0.012345679012345678, 0, 0, 0, 0, 0, 0 ]	0.002632	5
[ "---\nabstract: 'The task of approximating a function of $d$ variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. ", "When $d$ is large, this task is challenged by the so-called [curse of dimensionality]{}. ", "As a typical example, standard polynomial spaces, such as those of total degree type, are often uneffective to reach a prescribed accuracy unless a prohibitive number of evaluations is invested. ", "In recent years it has been shown that, for certain relevant applications, there are substantial advantages in using certain [sparse]{} polynomial spaces having anisotropic features with respect to the different variables. ", "These applications include in particular the numerical approximation of high-dimensional parametric and stochastic partial differential equations. ", "We start by surveying several results in this direction, with an emphasis on the numerical algorithms that are available for the construction of the approximation, in particular through interpolation or discrete least-squares fitting. ", "All such algorithms rely on the assumption that the set of multi-indices associated with the polynomial space is [downward closed]{}. ", "In the present paper we introduce some tools for the study of approximation in multivariate spaces under this assumption, and use them in the derivation of error bounds, sometimes independent of the dimension $d$, and in the development of adaptive strategies.'", "\nauthor:\n- 'Albert Cohen[^1] and Giovanni Migliorati[^2]'\ndate: 'December 15, 2016'\ntitle: ' Multivariate approximation in downward closed polynomial spaces [^3] '\n---\n\n[AMS classification numbers:]{} 41A65, 41A25, 41A10, 41A05, 65N12, 65N15.", "\n\n[Keywords:]{} Multivariate approximation, error estimates, convergence rates, interpolation, least squares, downward closed set, parametric PDEs, PDEs with stochastic data, adaptive approximation.", "\n\nIntroduction {#sec:1}\n============\n\nThe mathematical modeling of complex physical phenomena often demands for functions that depend on a large number of variables. ", "One typical instance occurs when a quantity of interest $u$ is given as the solution to an equation written in general form as $${\\cal P}(u,y)=0,\n\\label{eq:problem}$$ where $y=(y_j)_{j=1,\\dots,d}\\in \\mathbb{R}^d$ is a vector that concatenates various physical parameters which have an influence on $u$.\n\nSupposing that we are able to solve the above problem, either exactly or approximately by numerical methods, for any $y$ in some domain of interest $U\\subset\\mathbb{R}^d$ we thus have access to the [parameter-to-solution]{} map $$y \\mapsto u(y).", "\n\\label{eq:solmap}$$ The quantity $u(y)$ may be of various forms, namely:\n\n1. ", " a real number, that is, $u(y)\\in\\mathbb{R}$;\n\n2. ", " a function in some Banach space, for example when is a partial differential equation (PDE);\n\n3. ", " a vector of eventually large dimension, in particular when is a PDE whose solution is numerically approximated using some numerical method with fixed discretization parameters.", "\n\nAs a guiding example which will be further discussed in this paper, consider the elliptic diffusion equation $$-{\\rm div}(a\\nabla u)=f,\n\\label{eq:ellip}$$ set on a given bounded Lipschitz domain $D\\subset \\mathbb{R}^k$ (say with $k=1,2$ or $3$), for some fixed right-hand side $f\\in L^2(D)$, homogeneous Dirichlet boundary conditions $u_{\|\\partial D}=0$, and where $a$ has the general form $$a=a(y)=\\overline a+\\sum_{j\\geq 1} y_j\\psi_j.", "\n\\label{eq:para}$$ Here, $\\overline a$ and $\\psi_j$ are given functions in $L^\\infty(D)$, and the $y_j$ range in finite intervals that, up to renormalization, can all be assumed to be $[-1,1]$. In this example $y=(y_j)_{j\\geq 1}$ is countably infinite-dimensional, that is, $d=\\infty$. The standard weak formulation of in $H^1_0(D)$, $$\\int_D a\\nabla u\\nabla v=\\int_D fv, \\quad v\\in H^1_0(D),$$ is ensured to be well-posed for all such $a$ under the so-called [uniform ellipticity assumption]{} $$\\sum_{j\\geq 1}\|\\psi_j\| \\leq \\overline a-r, \\quad \\mbox{a.e. ", "on } D,\n\\label{eq:uea}$$ for some $r>0$. In this case, the map $y\\mapsto u(y)$ acts from $U=[-1,1]^\\mathbb{N}$ to $H^1_0(D)$. However, if we consider the discretization of in some finite element space $V_h \\subset H_0^1(D)$, where $h$ refers to the corresponding mesh size, using for instance the Galerkin method, then the resulting map $$y\\mapsto u_h(y),$$ acts from $U=[-1,1]^\\mathbb{N}$ to $ V_h$. Likewise, if we consider a quantity of interest such as the flux $q(u)=\\int_{\\Sigma} a \\nabla u \\cdot \\sigma$ over a given interface ${\\Sigma} \\subset D$ with $\\sigma$ being the outward pointing normal vector, then the resulting map $$y\\mapsto q(y)=q(u(y)),$$ acts from $U=[-1,1]^\\mathbb{N}$ to $\\mathbb{R}$. In all three cases, the above maps act from $U$ to some finite- or infinite-dimensional Banach space $V$, which is either $H^1_0$, $V_h$ or $\\mathbb{R}$.\n\nIn the previous instances, the functional dependence between the input parameters $y$ and the output $u(y)$ is described in clear mathematical terms by equation . ", "In other practical instances, the output $u(y)$ can be the outcome of a complex physical experiment or numerical simulation with input parameter $y$. However the dependence on $y$ might not be given in such clear mathematical terms.", "\n\nIn all the abovementioned cases, we assume that are we are able to query the map at any given parameter value $y\\in U$, eventually up to some uncertainty. ", "Such uncertainty may arise due to:\n\n- measurement errors, when $y\\mapsto u(y)$ is obtained by a physical experiment, or\n\n- computational errors, when $y\\mapsto u(y)$ is obtained by a numerical computation.", "\n\nThe second type of errors may result from the spatial discretization when solving a PDE with a given method, and from the round-off errors when solving the associated discrete systems.", "\n\nOne common way of modeling such errors is by assuming that we observe $u$ at the selected points $y$ up to a an additive noise $\\eta$ which may depend on $y$, that is, we evaluate $$y\\mapsto u(y)+\\eta(y),\n\\label{eq:noisy}$$ where $\\eta$ satisfies a uniform bound $$\\\|\\eta\\\|_{L^\\infty(U,V)}:=\\sup_{y\\in U} \\\|\\eta(y)\\\|_V\\leq \\varepsilon,\n\\label{eq:noisebound}$$ for some $\\varepsilon>0$ representing the noise level.", "\n\nQueries of the exact $u(y)$ or of the noisy $u(y)+\\eta(y)$ are often expensive since they require numerically solving a PDE, or setting up a physical experiment, or running a time-consuming simulation algorithm. ", "A natural objective is therefore to approximate the map from some fixed number $m$ of such queries at points $\\{y^1,\\dots,y^m\\}\\in U$. Such approximations $y\\mapsto \\widetilde u(y)$ are sometimes called [surrogate or reduced models]{}.", "\n\nLet us note that approximation of the map is sometimes a preliminary task for solving other eventually more complicated problems, such as:\n\n1. ", " [Optimization and Control]{}, i.e. find a $y$ which minimizes a certain criterion depending on $u(y)$. In many situations, the criterion takes the form of a convex functional of $u(y)$, and the minimization is subject to feasibility constraints. ", "See e.g. the monographs [@BV; @NW2006] and references therein for an overview of classical formulations and numerical methods for optimization problems.", "\n\n2. ", " [Inverse Problems]{}, i.e. find an estimate $y$ from some data depending on the output $u(y)$. Typically, we face an ill-posed problem, where the parameter-to-solution map does not admit a global and stable inverse. ", "Nonetheless, developing efficient numerical methods for approximating the parameter-to-solution map, i.e. solving the so-called direct problem, is a first step towards the construction of numerical methods for solving the more complex inverse problem, see e.g. [@Tara].", "\n\n3. ", " [Uncertainty Quantification]{}, i.e. describe the stochastic properties of the solution $u(y)$ in the case where the parameter $y$ is modeled by a random variable distributed according to a given probability density. ", "We may for instance be interested in computing the expectation or variance of the $V$-valued random variable $u(y)$. Note that this task amounts in computing multivariate integrals over the domain $U$ with respect to the given probability measure. ", "This area also embraces, among others, optimization and inverse problems whenever affected by uncertainty in the data. ", "We refer to e.g. [@LK] for the application of polynomial approximation to uncertainty quantification, and to [@Stu] for the Bayesian approach to inverse problems.", "\n\nThere exist many approaches for approximating an unknown function of one or several variables from its evaluations at given points. ", "One of the most classical approach consists in picking the approximant in a given suitable $n$-dimensional space of elementary functions, such that $$n\\leq m.\n\\label{eq:mn}$$ Here, by “suitable” we mean that the space should have the ability to approximate the target function to some prescribed accuracy, taking for instance advantage of its smoothness properties. ", "By “elementary” we mean that such functions should have simple explicit form which can be efficiently exploited in numerical computations. ", "The simplest type of such functions are obviously polynomials in the variables $y_j$. As a classical example, we may decide to use, for some given $k\\in\\mathbb{N}_0$, the total degree polynomial space of order $k$, namely $$\\mathbb{P}_k:={\\rm span}\\left\\{y\\mapsto y^\\nu\\; : \\; \|\\nu\|:=\\\|\\nu\\\|_1=\\sum_{j=1}^d \\nu_j\\leq k\\right\\},$$ with the standard notation $$\\quad y^\\nu:=\\prod_{j=1}^dy_j^{\\nu_j}, \\quad \\nu=(\\nu_j)_{j=1,\\dots,d}.$$ Note that since $u(y)$ is $V$-valued, this means that we actually use the $V$-valued polynomial space $$\\mathbb{V}_k:=V\\otimes \\mathbb{P}_k=\\left\\{y\\mapsto \\sum_{\|\\nu\|\\leq k} w_\\nu y^\\nu\\; : \\; w_\\nu\\in V\\right\\}.$$ Another classical example is the polynomial space of degree $k$ in each variable, namely $$\\mathbb{Q}_k:={\\rm span}\\left\\{y\\mapsto y^\\nu\\; : \\; \\\|\\nu\\\|_\\infty=\\max_{j=1,\\dots,d} \\nu_j\\leq k\\right\\}.$$ A critical issue encountered by choosing such spaces is the fact that, for a fixed value of $k$, the dimension of $\\mathbb{P}_k$ grows with $d$ like $d^k$, and that of $\\mathbb{Q}_k$ grows like $k^d$, that is, exponentially in $d$. Since capturing the fine structure of the map typically requires a large polynomial degree $k$ in some coordinates, we expect in view of that the number of needed evaluations $m$ becomes prohibitive as the number of variables becomes large. ", "This state of affairs is a manifestation of the so-called [curse of dimensionality]{}. ", "From an approximation theoretic or information-based complexity point of view, the curse of dimensionality is expressed by the fact that functions in standard smoothness classes such as $C^s(U)$ cannot be approximated in $L^\\infty(U)$ with better rate then $n^{-s/d}$ by any method using $n$ degrees of freedom or $n$ evaluations, see e.g. [@DHM; @NW].", "\n\nTherefore, in high dimension, one is enforced to give up on classical polynomial spaces of the above form, and instead consider more general spaces of the general form $$\\mathbb{P}_\\Lambda:={\\rm span}\\{y\\mapsto y^\\nu\\; : \\; \\in \\Lambda\\},\n\\label{eq:plambda}$$ where $\\Lambda$ is a subset of $\\mathbb{N}^d_0$ with a given cardinality $n:=\\#(\\Lambda)$. In the case of infinitely many variables $d=\\infty$, we replace $\\mathbb{N}_0^d$ by the set $${\\cal F}:=\\ell^0(\\mathbb{N},\\mathbb{N}_0):=\\{\\nu=(\\nu_j)_{j\\geq 1} \\; :\\: \\#({\\rm supp}(\\nu))<\\infty\\},$$ of finitely supported sequences of nonnegative integers. ", "For $V$-valued functions, we thus use the space $$\\mathbb{V}_\\Lambda=V\\otimes \\mathbb{P}_\\Lambda:=\\left\\{y\\mapsto \\sum_{\\nu\\in\\Lambda} w_\\nu y^\\nu\\; : \\; w_\\nu\\in V\\right\\}.$$ Note that $\\mathbb{V}_\\Lambda=\\mathbb{P}_\\Lambda$ in the particular case where $V=\\mathbb{R}$.\n\nThe main objective when approximating the map is to maintain a reasonable trade-off between accuracy measured in a given error norm and complexity measured by $n$, exploiting the different importance of each variable. ", "Intuitively, large polynomial degrees should only be allocated to the most important variables. ", "In this sense, if $d$ is the dimension and $k$ is the largest polynomial degree in any variable appearing in $\\Lambda$, we view $\\Lambda$ as a very [sparse]{} subset of $\\{0,\\dots,k\\}^d$.\n\nAs generally defined by , the space $\\mathbb{P}_\\Lambda$ does not satisfy some natural properties of usual polynomial spaces such as closure under differentiation in any variable, or invariance by a change of basis when replacing the monomials $y^\\nu$ by other tensorized basis functions of the form $$\\phi_\\nu(y)=\\prod_{j\\geq 1} \\phi_{\\nu_j}(y_j),$$ where the univariate functions $\\{\\phi_0,\\dots,\\phi_k\\}$ form a basis of $\\mathbb{P}_k$ for any $k\\geq 0$, for example with the Legendre or Chebyshev polynomials. ", "In order to fulfill these requirements, we ask that the set $\\Lambda$ has the following natural property.", "\n\n\\[thm:defdc\\] A set $\\Lambda\\subset \\mathbb{N}_0^d$ or $\\Lambda\\subset {\\cal F}$ is [downward closed]{} if and only if $$\\nu \\in \\Lambda \\textrm{ and } \\widetilde \\nu \\leq \\nu \\implies \\widetilde \\nu \\in \\Lambda,$$ where $ \\widetilde \\nu \\leq \\nu$ means that $\\widetilde \\nu_j\\leq \\nu_j$ for all $j$.\n\nDownward closed sets are also called lower sets. ", "We sometimes use the terminology of downward closed polynomial spaces for the corresponding $\\mathbb{P}_\\Lambda$. To our knowledge, such spaces have been first considered in [@K] in the bivariate case $d=2$ and referred to as [polynômes pleins]{}. ", "Their study in general dimension $d$ has been pursued in [@LL] and [@DR]. ", "The objective of the present paper is to give a survey of recent advances on the use of downward closed polynomial spaces for high-dimensional approximation.", "\n\nThe outline is the following. ", "We review in Section \\[sec:2\\] several polynomial approximation results obtained in [@BCM1; @BCDM] in which the use of well-chosen index sets allows one to [break the curse of dimensionality]{} for relevant classes of functions defined on $U=[-1,1]^d$, e.g. such as those occuring when solving the elliptic PDE with parametric diffusion coefficient . ", "Indeed, we obtain an algebraic convergence rate $n^{-s}$, where $s$ is independent of $d$ in the sense that such a rate may even hold when $d=\\infty$. Here, we consider the error between the map and its approximant in either norms $L^\\infty(U,V)=L^\\infty(U,V,d\\mu)$ or $L^2(U,V)=L^2(U,V,d\\mu)$, where $d\\mu$ is the uniform probability measure, $$d\\mu:=\\bigotimes_{j\\geq 1} \\frac {dy_j} 2.$$ We also consider the case of lognormal diffusion coefficients of the form $$a=\\exp(b), \\quad b=b(y)=\\sum_{j\\geq 1} y_j\\psi_j,\n\\label{eq:lognormal}$$ where the $y_j$ are i.i.d. ", "standard Gaussians random variables. ", "In this case, we have $U=\\mathbb{R}^d$ and the error is measured in $L^2(U,V,d\\gamma)$ where $$d\\gamma:=\\bigotimes_{j\\geq 1} g(y_j)dy_j, \\quad g(t):=\\frac 1 {\\sqrt{2\\pi}} e^{-t^2/2},\n\\label{eq:gaussmeasure}$$ is the tensorized Gaussian probability measure. ", "The above approximation results are established by using $n$-term truncations of polynomial expansions, such as Taylor, Legendre or Hermite, which do not necessarily result in downward closed index sets. ", "In the present paper we provide a general approach to establish similar convergence rates with downward closed polynomial spaces.", "\n\nThe coefficients in the polynomial expansions cannot be computed exactly from a finite number of point evaluations of . ", "One first numerical procedure that builds a polynomial approximation from point evaluations is interpolation. ", "In this case the number $m$ of samples is exactly equal to the dimension $n$ of the polynomial space. ", "We discuss in Section \\[sec:3\\] a general strategy to choose evaluation points and compute the interpolant in arbitrarily high dimension. ", "One of its useful features is that the evaluations and interpolants are updated in a sequential manner as the polynomial space is enriched. ", "We study the stability of this process and its ability to achieve the same convergence rates in $L^\\infty$ established in Section \\[sec:2\\].", "\n\nA second numerical procedure for building a polynomial approximation is the least-squares method, which applies to the overdetermined case $m>n$. To keep the presentation concise, we confine to results obtained in the analysis of this method only for the case of evaluations at random points. ", "In Section \\[sec:4\\] we discuss standard least squares, both in the noisy and noiseless cases, and in particular explain under which circumstances the method is stable and compares favorably with the best approximation error in $L^2$. Afterwards we discuss the more general method of weighted least squares, which allows one to optimize the relation between the dimension of the polynomial space $n$ and the number of evaluation points $m$ that warrants stability and optimal accuracy.", "\n\nThe success of interpolation and least squares is critically tied to the choice of proper downward closed sets $(\\Lambda_n)_{n\\geq 1}$ with $\\#(\\Lambda_n)=n$. The set $\\Lambda_n^$ that gives the best polynomial approximation among all possible downward closed sets of cardinality $n$ is often not accessible. ", "In practice we need to rely on some a-priori analysis to select “suboptimal yet good” sets. ", "An alternative strategy is to select the sequence $(\\Lambda_n)_{n\\geq 1}$ in an adaptive manner, that is, make use of the computation of the approximation for $\\Lambda_{n-1}$ in order to choose $\\Lambda_n$. We discuss in Section \\[sec:5\\] several adaptive and nonadaptive strategies which make use of the downward closed structure of such sets. ", "While our paper is presented in the framework of polynomial approximation, the concept of downward closed set may serve to define multivariate approximation procedures in other nonpolynomial frameworks. ", "At the end of the paper we give some remarks on this possible extension, including, as a particular example, approximation by sparse piecewise polynomial spaces using hierarchical bases, such as sparse grid spaces.", "\n\nLet us finally mention that another class of frequently used methods in high-dimensional approximation is based on Reproducing Kernel Hilbert Space (RKHS) or equivalently Gaussian process regression, also known as [kriging]{}. ", "In such methods, for a given Mercer kernel $K(\\cdot,\\cdot)$ the approximant is typically searched by minimizing the associated RKHS norm among all functions agreeing with the data at the evaluation points, or equivalently by computing the expectation of a Gaussian process with covariance function $K$ conditional to the observed data. ", "Albeit natural competitors, these methods do not fall in the category discussed in the present paper, in the sense that the space where the approximation is picked varies with the evaluation points. ", "It is not clear under which circumstances they may also break the curse of dimensionality.", "\n\nSparse Approximation in Downward Closed Polynomial Spaces {#sec:2}\n=========================================================\n\nTruncated Polynomial Expansions {#sec:2.1}\n-------------------------------\n\nAs outlined in the previous section, we are interested in deriving polynomial approximations of the map acting from $U=[-1,1]^d$ with $d\\in \\mathbb{N}$ or $d=\\infty$ to the Banach space $V$. Our first vehicle to derive such approximations, together with precise error bounds for relevant classes of maps, consists in truncating certain polynomial expansions of written in general form as $$\\sum_{\\nu\\in{\\cal F}} u_\\nu \\phi_\\nu,\n\\label{eq:expan}$$ where for each $\\nu=(\\nu_j)_{j\\geq 1}\\in{\\cal F}$ the function $\\phi_\\nu:U\\to \\mathbb{R}$ has the tensor product form $$\\phi_\\nu(y)=\\prod_{j\\geq 1} \\phi_{\\nu_j}(y_j),$$ and $u_\\nu\\in V$. Here we assume that $(\\phi_k)_{k\\geq 0}$ is a sequence of univariate polynomials such that $\\phi_0\\equiv 1$ and the degree of $\\phi_k$ is equal to $k$. This implies that $\\{\\phi_0,\\dots,\\phi_k\\}$ is a basis of $\\mathbb{P}_k$ and that the above product only involves a finite number of factors, even in the case where $d=\\infty$. Thus, we obtain polynomial approximations of by fixing some sets $\\Lambda_n\\subset {\\cal F}$ with $\\#(\\Lambda_n)=n$ and defining $$u_{\\Lambda_n}:=\\sum_{\\nu\\in\\Lambda_n} u_\\nu \\phi_\\nu.", "\n\\label{eq:nterm}$$ Before discussing specific examples, let us make some general remarks on the truncation of countable expansions with $V$-valued coefficients, not necessarily of tensor product or polynomial type.", "\n\nThe series is said to converge [conditionally]{} with limit $u$ in a given norm $\\\|\\cdot\\\|$ if and only if there exists an exhaustion $(\\Lambda_n)_{n\\geq 1}$ of ${\\cal F}$ (which means that for any $\\nu\\in{\\cal F}$ there exists $n_0$ such that $\\nu\\in\\Lambda_n$ for all $n\\geq n_0$), with the convergence property $$\\lim_{n\\to +\\infty} \\left\\\|u-u_{\\Lambda_n}\\right\\\| =0.", "\n\\label{eq:condconv}$$ The series is said to converge [unconditionally]{} towards $u$ in the same norm, if and only if holds for every exhaustion $(\\Lambda_n)_{n\\geq 1}$ of ${\\cal F}$.\n\nAs already mentioned in the introduction, we confine our attention to the error norms $L^\\infty(U,V)$ or $L^2(U,V)$ with respect to the uniform probability measure $d\\mu$. We are interested in establishing unconditional convergence, as well as estimates of the error between $u$ and its truncated expansion, for both types of norm.", "\n\nIn the case of the $L^2$ norm, unconditional convergence can be established when $(\\phi_\\nu)_{\\nu\\in{\\cal F}}$ is an orthonormal basis of $L^2(U)$. In this case we know from standard Hilbert space theory that if belongs to $L^2(U,V)$ then the inner products $$u_\\nu:=\\int_{U} u(y)\\phi_\\nu(y) \\, d\\mu,\\quad \\nu\\in{\\cal F},$$ are elements of $V$, and the series converges unconditionally towards $u$ in $L^2(U,V)$. In addition, the error is given by $$\\left\\\|u-u_{\\Lambda_n}\\right\\\|_{L^2(U,V)}= \\left( \\sum_{\\nu\\notin\\Lambda_n} \\\|u_\\nu\\\|_V^2\\right)^{1/2},\n\\label{eq:estimL2}$$ for any exhaustion $(\\Lambda_n)_{n\\geq 1}$. Let us observe that, since $d\\mu$ is a probability measure, the $L^\\infty(U,V)$ norm controls the $L^2(U,V)$ norm, and thus the above holds whenever the map $u$ is uniformly bounded over $U$.\n\nFor the $L^\\infty$ norms, consider an expansion where the functions $\\phi_\\nu:U\\mapsto \\mathbb{R}$ are normalized such that $\\\|\\phi_\\nu\\\|_{L^\\infty(U)}=1$, for all $\\nu\\in{\\cal F}$. Then $(\\\|u_\\nu\\\|_V)_{\\nu\\in {\\cal F}}\\in \\ell^1({\\cal F})$, and it is easily checked that, whenever the expansion converges conditionally to a function $u$ in $L^\\infty(U,V)$, it also converges unconditionally to $u$ in $L^\\infty(U,V)$. In addition, for any exhaustion $(\\Lambda_n)_{n\\geq 1}$, we have the error estimate $$\\left\\\|u-u_{\\Lambda_n}\\right\\\|_{L^\\infty(U,V)}\\leq \\sum_{\\nu\\notin\\Lambda_n} \\\|u_\\nu\\\|_V.\n\\label{eq:estimLinf}$$ The above estimate is simply obtained by triangle inequality, and therefore generally it is not as sharp as . ", "One particular situation is when $(\\phi_\\nu)_{\\nu\\in {\\cal F}}$ is an orthogonal basis of $L^2(U)$ normalized in $L^\\infty$. Then, if $u\\in L^2(U,V)$ and the $$u_\\nu:=\\frac {1}{\\\|\\phi_\\nu\\\|_{L^2(U,V)}^2}\\int_{U} u(y)\\phi_\\nu(y) \\, d\\mu,\\quad \\nu\\in{\\cal F},$$ satisfy $(\\\|u_\\nu\\\|_V)_{\\nu\\in {\\cal F}}\\in \\ell^1({\\cal F})$, we find on the one hand that converges unconditionally to a limit in $L^\\infty(U,V)$ and in turn in $L^2(U,V)$. On the other hand, we know that it converges toward $u\\in L^2(U,V)$. Therefore, its limit in $L^\\infty(U,V)$ is also $u$.\n\nA crucial issue is the choice of the sets $\\Lambda_n$ that we decide to use when defining the $n$-term truncation . ", "Ideally, we would like to use the set $\\Lambda_n$ which minimizes the truncation error in some given norm $\\\|\\cdot\\\|$ among all sets of cardinality $n$.\n\nIn the case of the $L^2$ error, if $(\\phi_\\nu)_{\\nu\\in{\\cal F}}$ is an orthonormal basis of $L^2(U)$, the estimate shows that the optimal $\\Lambda_n$ is the set of indices corresponding to the $n$ largest $\\\|u_\\nu\\\|_V$. This set is not necessarily unique, in which case any realization of $\\Lambda_n$ is optimal.", "\n\nIn the case of the $L^\\infty$ error, there is generally no simple description of the optimal $\\Lambda_n$. However, when the $\\phi_\\nu$ are normalized in $L^\\infty(U)$, the right-hand side in the estimate provides an upper bound for the truncation error. ", "This bound is minimized by again taking for $\\Lambda_n$ the set of indices corresponding to the $n$ largest $\\\|u_\\nu\\\|_V$, with the error now bounded by the $\\ell^1$ tail of the sequence $(\\\|u_\\nu\\\|_V)_{\\nu\\in {\\cal F}}$, in contrast to the $\\ell^2$ tail which appears in .", "\n\nThe properties of a given sequence $(c_\\nu)_{\\nu\\in{\\cal F}}$ which ensure a certain rate of decay $n^{-s}$ of its $\\ell^q$ tail after one retains its $n$ largest entries are well understood. ", "Here, we use the following result, see [@CD], originally invoked by Stechkin in the particular case $q=2$. This result says that the rate of decay is governed by the $\\ell^p$ summability of the sequence for values of $p$ smaller than $q$.\n\n\\[thm:stechkin\\] Let $0<p<q<\\infty$ and let $(c_\\nu)_{\\nu\\in{\\cal F}}\\in \\ell^p({\\cal F})$ be a sequence of nonnegative numbers. ", "Then, if $\\Lambda_n$ is a set of indices which corresponds to the $n$ largest $c_\\nu$, one has $$\\left(\\sum_{\\nu\\notin\\Lambda_n} c_\\nu^q\\right)^{1/q} \\leq C (n+1)^{-s}, \\quad C:=\\\|(c_\\nu)_{\\nu\\in{\\cal F}}\\\|_{\\ell^p}, \\quad s:=\\frac 1 q-\\frac 1 p.$$\n\nIn view of or , application of the above result shows that $\\ell^p$ summability of the sequence $(\\\|u_\\nu\\\|_V)_{\\nu\\in {\\cal F}}$ implies a convergence rate $n^{-s}$ when retaining the terms corresponding to the $n$ largest $\\\|u_\\nu\\\|_V$ in . ", "From , when $(\\phi_\\nu)_{\\nu \\in{\\cal F}}$ is an orthonormal basis, we obtain $s=\\frac 1 p-\\frac 1 2$ if $p<2$. From , when the $\\phi_\\nu$ are normalized in $L^\\infty(U)$, we obtain $s=\\frac 1 p-1$ if $p<1$.\n\nIn the present setting of polynomial approximation, we mainly consider four types of series corresponding to four different choices of the univariate functions $\\phi_k$:\n\n- Taylor (or power) series of the form $$\\sum_{\\nu\\in{\\cal F}} t_\\nu y^\\nu, \\quad t_{\\nu}:=\\frac 1 {\\nu !}", "\\partial^\\nu u(y=0), \\quad \\nu!:=\\prod_{j\\geq 1} \\nu_j!,", "\n \\label{eq:taylor}$$ with the convention that $0!=1$.\n\n- Legendre series of the form $$\\sum_{\\nu\\in{\\cal F}} w_\\nu L_\\nu(y), \\quad L_\\nu(y)=\\prod_{j\\geq 1}L_{\\nu_j}(y_j),\\quad w_\\nu:=\\int_U u(y)L_\\nu(y) \\, d\\mu,\n \\label{eq:legendre}$$ where $(L_k)_{k\\geq 0}$ is the sequence of Legendre polynomials on $[-1,1]$ normalized with respect to the uniform measure $\\int_{-1}^1 \|L_k(t)\|^2 \\frac {dt}2=1$, so that $(L_\\nu)_{\\nu\\in {\\cal F}}$ is an orthonormal basis of $L^2(U,d\\mu)$.\n\n- Renormalized Legendre series of the form $$\\sum_{\\nu\\in{\\cal F}} \\widetilde w_\\nu \\widetilde L_\\nu(y), \\quad \\widetilde L_\\nu(y)=\\prod_{j\\geq 1}\\widetilde L_{\\nu_j}(y_j), \\quad \\widetilde w_\\nu:=\\left(\\prod_{j\\geq 1} (1+2\\nu_j)\\right)^{1/2} w_\\nu,\n \\label{eq:renormlegendre}$$ where $(\\widetilde L_k)_{k\\geq 0}$ is the sequence of Legendre polynomials on $[-1,1]$ with the standard normalization $\\\|\\widetilde L_k\\\|_{L^\\infty([-1,1])}=\\widetilde L_k(1)=1$, so that $\\widetilde L_k=(1+2k)^{-1/2} L_k$.\n\n- Hermite series of the form $$\\sum_{\\nu\\in{\\cal F}} h_\\nu H_\\nu(y), \\quad H_\\nu(y)=\\prod_{j\\geq 1}H_{\\nu_j}(y_j),\\quad h_\\nu:=\\int_U u(y)H_\\nu(y) \\, d\\gamma,\n \\label{eq:hermite}$$ with $(H_k)_{k\\geq 0}$ being the sequence of Hermite polynomials normalized according to $\\int_{\\mathbb{R}} \| H_k(t)\|^2 g(t)dt=1$, and $d\\gamma$ given by . ", "In this case $U=\\mathbb{R}^d$ and $(H_\\nu)_{\\nu \\in {\\cal F}}$ is an orthonormal basis of $L^2(U,d\\gamma)$.\n\nWe may therefore estimate the $L^2$ error resulting from the truncation of the Legendre series by application of , or the $L^\\infty$ error resulting from the truncation of the Taylor series or renormalized Legendre series by application of . ", "According to Lemma \\[thm:stechkin\\], we derive convergence rates that depend on the value of $p$ such that of the coefficient sequences $(\\\|t_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$, $(\\\|w_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$, $(\\\|\\widetilde w_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$ or $(\\\|h_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$ belong to $\\ell^p({\\cal F})$.\n\nIn a series of recent papers such summability results have been obtained for various types of parametric PDEs. ", "We refer in particular to [@CDS; @BCM1] for the elliptic PDE with affine parameter dependence , to [@HS; @BCDM] for the lognormal dependence , and to [@CCS2] for more general PDEs and parameter dependence. ", "One specific feature is that these conditions can be fulfilled in the infinite-dimensional framework. ", "We thus obtain convergence rates that are immune to the curse of dimensionality, in the sense that they hold with $d=\\infty$. Here, we mainly discuss the results established in [@BCM1; @BCDM] which have the specificity of taking into account the support properties of the functions $\\psi_j$.\n\nOne problem with this approach is that the sets $\\Lambda_n$ associated to the $n$ largest values in these sequences are generally not downward closed. ", "In the next sections, we revisit these results in order to establish similar convergence rates for approximation in downward closed polynomial spaces.", "\n\nSummability Results {#sec:2.2}\n-------------------\n\nThe summability results in [@BCM1; @BCDM] are based on certain weighted $\\ell^2$ estimates which can be established for the previously defined coefficient sequences under various relevant conditions for the elliptic PDE . ", "We first report below these weighted estimates. ", "The first one from [@BCM1] concerns the affine parametrization . ", "Here, we have $V=H^1_0(D)$ and $V'$ denotes its dual $H^{-1}(D)$.\n\n\\[thm:theosumaff\\] Assume that $\\rho=(\\rho_j)_{j\\geq 1}$ is a sequence of positive numbers such that $$\\sum_{j\\geq 1} \\rho_j\|\\psi_j(x)\|\\leq \\overline a(x)-\\widetilde r, \\quad x\\in D,\n\\label{eq:uearho}$$ for some fixed number $\\widetilde r >0$. Then, one has $$\\sum_{\\nu\\in {\\cal F}}\\left( \\rho^\\nu \\\|t_\\nu\\\|_V\\right)^2<\\infty, \\quad \\rho^\\nu=\\prod_{j\\geq 1} \\rho_j^{\\nu_j},\n\\label{eq:wl2t}$$ as well as $$\\sum_{\\nu\\in {\\cal F}}\\left(\\beta(\\nu)^{-1} \\rho^\\nu \\\|w_\\nu\\\|_V\\right)^2=\\sum_{\\nu\\in {\\cal F}}\\left(\\beta(\\nu)^{-2} \\rho^\\nu \\\|\\widetilde w_\\nu\\\|_V\\right)^2<\\infty, \n\\label{eq:wl2l}$$ with $$\\beta(\\nu):=\\prod_{j\\geq 1} (1+2\\nu_j)^{1/2}.$$ The constants bounding these sums depend on $\\widetilde r$, $\\\|f\\\|_{V'}$, $\\overline a_{\\min}$ and $\\\|\\overline a\\\|_{L^\\infty}$.\n\nA few words are in order concerning the proof of these estimates. ", "The first estimate is established by first proving that the uniform ellipticity assumption implies the $\\ell^2$ summability of the Taylor sequence $(\\\|t_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$. Since the assumption means that holds with the $\\psi_j$ replaced by $\\rho_j\\psi_j$, this gives the $\\ell^2$ summability of the Taylor sequence for the renormalized map $$y\\mapsto u(\\rho y), \\quad \\rho y=(\\rho_jy_j)_{j\\geq 1},$$ which is equivalent to . ", "The second estimate is established by first showing that $\\sum_{j\\geq 1} \\rho_j\|\\psi_j\|\\leq \\overline a-\\widetilde r$ implies finiteness of the weighted Sobolev-type norm $$\\sum_{\\nu\\in{\\cal F}}\\frac{ \\rho^{2\\nu} }{\\nu!}\\int_U \\left\\\| \\partial^\\nu u(y) \\right\\\|_V^2 \\prod_{j\\geq 1} (1 - \|y_j\|)^{2\\nu_j} \\, d\\mu<\\infty.$$ Then, one uses the Rodrigues formula $L_k(t) = \\left(\\frac {d}{dt}\\right)^k\\left( \\frac{\\sqrt{2 k + 1}}{k! ", "\\,2^{k}} ( t^2 - 1)^{k} \\right)$ in each variable $y_j$ to bound the weighted $\\ell^2$ sum in by this norm.", "\n\nAs shown in [@BCM1], the above result remains valid for more general classes of orthogonal polynomials of Jacobi type, such as the Chebyshev polynomials which are associated with the univariate measure $\\frac {dt}{2\\pi\\sqrt{1-t^2}}$.\n\nThe second weighted $\\ell^2$ estimate from [@BCDM] concerns the lognormal parametrization .", "\n\nLet $r\\geq 0$ be an integer. ", "Assume that there exists a positive sequence $\\rho=(\\rho_j)_{j\\geq 1}$ such that $\\sum_{j\\geq 1} \\exp(-\\rho_j^2)<\\infty$ and such that $$\\sum_{j\\geq 1} \\rho_j\|\\psi_j(x)\|=K< C_r:=\\frac{\\ln 2}{\\sqrt r}, \\quad x\\in D.\n\\label{eq:psicr}$$ Then, one has $$\\label{eq:wl2h}\n\\sum_{\\nu\\in {\\cal F}} \\xi_\\nu \\\|h_\\nu\\\|_V^2<\\infty,$$ where $$\\xi_\\nu:=\\sum_{\\\|\\widetilde \\nu\\\|_{\\ell^\\infty}\\leq r}{\\nu\\choose \\widetilde \\nu} \\rho^{2\\widetilde \\nu}=\\prod_{j\\geq 1}\\left(\\sum_{l=0}^r {\\nu_j\\choose l}\\rho_j^{2l}\\right),\n\\quad {\\nu\\choose \\widetilde \\nu}:=\\prod_{j\\geq 1}{\\nu_j\\choose \\widetilde \\nu_j},$$ with the convention that ${k \\choose l}=0$ when $l>k$. The constant bounding this sum depends on $\\\|f\\\|_{V'}$, $\\sum_{j\\geq 1} \\exp(-\\rho_j^2)$ and on the difference $C_r-K$.\n\nSimilar to the weighted $\\ell^2$ estimate for the Legendre coefficients, the proof of follows by first establishing finiteness of a weighed Sobolev-type norm $$\\sum_{\\\|\\nu\\\|_{\\ell^\\infty} \\leq r}\\frac {\\rho^{2\\nu}}{\\nu !} ", "\\int_U \\\|\\partial^\\nu u(y)\\\|_V^2 \\, d\\gamma<\\infty,$$ under the assumption in the above theorem. ", "Then one uses the Rodrigues formula $H_k(t) = \\frac{(-1)^k}{\\sqrt{k!} } ", "\\frac{g^{(k)}(t)}{g(t)}$, with $g$ given by , in each variable $y_j$ to bound the weighted $\\ell^2$ sum in by this norm.", "\n\nIn summary, the various estimates expressed in the above theorems all take the form $$\\sum_{\\nu\\in{\\cal F}} (\\omega_\\nu c_\\nu)^2 <\\infty,$$ where $$c_\\nu\\in \\{ \\\|t_\\nu\\\|_V, \\\|w_\\nu\\\|_V,\\\|\\widetilde w_\\nu\\\|_V,\\\|h_\\nu\\\|_V\\},$$ or equivalently $$\\omega_\\nu\\in \\{\\rho^\\nu,\\rho^\\nu \\beta(\\nu)^{-1},\\rho^\\nu \\beta(\\nu)^{-2}, \\xi_\\nu^{1/2}\\}.$$\n\nThen, one natural strategy for establishing $\\ell^p$ summabilty of the sequence $(c_\\nu)_{\\nu\\in{\\cal F}}$ is to invoke Hölder’s inequality, which gives, for all $0<p<2$, $$\\left(\\sum_{\\nu\\in{\\cal F}} \|c_\\nu\|^p\\right)^{1/p}\\leq \\left(\\sum_{\\nu\\in{\\cal F}} (\\omega_\\nu c_\\nu)^2\\right)^{1/2} \\left(\\sum_{\\nu\\in{\\cal F}} \|\\kappa_\\nu\|^q\\right)^{1/q} <\\infty, \\quad \\frac 1 q:=\\frac 1 p-\\frac 1 2,$$ where the sequence $(\\kappa_\\nu)_{\\nu\\in {\\cal F}}$ is defined by $$\\kappa_\\nu:=\\omega_\\nu^{-1}.$$ Therefore $\\ell^p$ summability of $(c_\\nu)_{\\nu\\in{\\cal F}}$ follows from $\\ell^q$ summability of $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}$ with $0<q<\\infty$ such that $\\frac 1 q=\\frac 1 p-\\frac 1 2$. This $\\ell^q$ summability can be related to that of the univariate sequence $$b=(b_j)_{j\\geq 1},\\quad b_j:=\\rho_j^{-1}.$$ Indeed, from the factorization $$\\sum_{\\nu\\in{\\cal F}} b^{q\\nu}=\\prod_{j\\geq 1} \\sum_{n\\geq 0} b_j^{nq},$$ one readily obtains the following elementary result, see [@CD] for more details.", "\n\n\\[thm:lemmaq\\] For any $0<q<\\infty$, one has $$b\\in \\ell^q(\\mathbb{N})\\quad {\\rm and}\\quad \\\|b\\\|_{\\ell^\\infty}<1 \\iff (b^\\nu)_{\\nu\\in{\\cal F}} \\in \\ell^q({\\cal F}).$$\n\nIn the case $\\omega_\\nu=\\rho^\\nu$, i.e.* $\\kappa_\\nu=b^\\nu$, this shows that the $\\ell^p$ summability of the Taylor coefficients $(\\\|t_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$ follows if the assumption holds with $b=(\\rho_j^{-1})_{j\\geq 1}\\in \\ell^q(\\mathbb{N})$ and $\\rho_j>1$ for all $j$. By a similar factorization, it is also easily checked that for any algebraic factor of the form $\\alpha(\\nu):=\\prod_{j\\geq 1}(1+c_1\\nu_j)^{c_2}$ with $c_1,c_2\\geq 0$, one has $$b\\in \\ell^q(\\mathbb{N})\\quad {\\rm and}\\quad \\\|b\\\|_{\\ell^\\infty}<1 \\iff (\\alpha(\\nu)b^\\nu)_{\\nu\\in{\\cal F}} \\in \\ell^q({\\cal F}).$$ This allows us to reach a similar conclusion in the cases $\\omega_\\nu=\\beta(\\nu)^{-1}\\rho^\\nu$ or $\\omega_\\nu=\\beta(\\nu)^{-2}\\rho^\\nu$, which correspond to the Legendre coefficients $(\\\|w_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$ and $(\\\|\\widetilde w_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$, in view of .", "\n\nLikewise, in the case where $\\omega_\\nu=\\xi_\\nu^{1/2}$, using the factorization $$\\sum_{\\nu\\in {\\cal F}} \\kappa_\\nu^q \n = \\prod_{j\\geq 1} \\sum_{n \\geq 0} \\left( \\sum_{l=0}^r {n \\choose l}\\rho_j^{2l} \\right)^{-q/2},$$ it is shown in [@BCDM] that the sum on the left converges if $b\\in \\ell^q$, provided that $r$ was chosen large enough such that $q>\\frac 2 r$. This shows that the $\\ell^p$ summability of the Hermite coefficients $(\\\|h_\\nu\\\|_V)_{\\nu\\in{\\cal F}}$ follows if the assumption holds with $b=(\\rho_j^{-1})_{j\\geq 1}\\in \\ell^q(\\mathbb{N})$. Note that, since the sequence $b$ can be renormalized, we may replace by the condition $$\\sup_{x\\in D}\\sum_{j\\geq 1} \\rho_j\|\\psi_j(x)\|<\\infty,\n\\label{eq:psicr1}$$ without a specific bound.", "\n\nApproximation by Downward Closed Polynomials {#sec:2.3}\n--------------------------------------------\n\nThe above results, combined with Lemma \\[thm:stechkin\\], allow us to build polynomial approximations $u_{\\Lambda_n}$ with provable convergence rates $n^{-s}$ in $L^\\infty$ or $L^2$ by $n$-term trunctation of the various polynomial expansions. ", "However, we would like to obtain such convergence rates with sets $\\Lambda_n$ that are in addition downward closed.", "\n\nNotice that if a sequence $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}$ of nonnegative numbers is monotone nonincreasing, that is $$\\nu\\leq \\widetilde \\nu \\implies \\kappa_{\\widetilde \\nu} \\leq \\kappa_{\\nu},$$ then the set $\\Lambda_n$ corresponding to the $n$ largest values of $\\kappa_\\nu$ (up to a specific selection in case of equal values) is downward closed. ", "More generally, there exists a sequence $(\\Lambda_n)_{n\\geq 1}$ of downward closed realizations of such sets which is nested, i.e. $\\Lambda_1 \\subset \\Lambda_2 \\ldots $, with $\\Lambda_1=0_{{\\cal F}}:=(0,0,\\ldots)$.\n\nFor any sequence $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}$ tending to $0$, in the sense that $\\#\\{\\nu \\; : \\; \|\\kappa_\\nu\|>\\delta\\} <\\infty$ for all $\\delta >0$, we introduce its [monotone majorant]{} $(\\widehat \\kappa_{\\nu})_{\\nu\\in{\\cal F}}$ defined by $$\\widehat \\kappa_\\nu:=\\max_{\\widetilde \\nu\\geq \\nu} \|\\kappa_{\\widetilde \\nu}\|,$$ that is the smallest monotone nonincreasing sequence that dominates $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}$. In order to study best $n$-term approximations using downward closed sets, we adapt the $\\ell^q$ spaces as follows.", "\n\n\\[thm:deflpm\\] For $0<q<\\infty$, we say that $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}\\in \\ell^\\infty({\\cal F})$ belongs to $\\ell^q_m({\\cal F})$ if and only if its monotone majorant $(\\widehat \\kappa_\\nu)_{\\nu\\in{\\cal F}}$ belongs to $\\ell^q({\\cal F})$.\n\nWe are now in position to state a general theorem that gives a condition for approximation using downward closed sets in terms of weighted $\\ell^2$ summability.", "\n\n\\[thm:theowlower\\] Let $(c_\\nu)_{\\nu\\in{\\cal F}}$ and $(\\omega_\\nu)_{\\nu\\in{\\cal F}}$ be positive sequences such that $$\\sum_{\\nu\\in{\\cal F}}(\\omega_\\nu c_\\nu)^2<\\infty,$$ and such that $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}\\in \\ell^q_m({\\cal F})$ for some $0<q<\\infty$ with $\\kappa_\\nu=\\omega_\\nu^{-1}$. Then, for any $0<r\\leq 2$ such that $\\frac 1 q>\\frac 1 r-\\frac 1 2$, there exists a nested sequence $(\\Lambda_n)_{n\\geq 1}$ of downward closed sets such that $\\#(\\Lambda_n)=n$ and $$\\left(\\sum_{\\nu \\notin \\Lambda_n} c_\\nu^r\\right)^{1/r} \\leq Cn^{-s}, \\quad s:=\\frac 1 q+\\frac 1 2-\\frac 1 r>0.", "\n\\label{eq:rdownwardrate}$$\n\nWith $(\\widehat \\kappa_\\nu)_{\\nu\\in{\\cal F}}$ being the monotone majorant of $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}$, we observe that $$A^2:=\\sum_{\\nu\\in{\\cal F}}(\\widehat \\kappa_\\nu^{-1} c_\\nu)^2\\leq \\sum_{\\nu\\in{\\cal F}}(\\kappa_\\nu^{-1} c_\\nu)^2=\\sum_{\\nu\\in{\\cal F}}(\\omega_\\nu c_\\nu)^2 <\\infty.$$ We pick a nested sequence $(\\Lambda_n)_{n\\geq 1}$ of downward closed sets, such that $\\Lambda_n$ consists of the indices corresponding to the $n$ largest $\\widehat \\kappa_\\nu$. Denoting by $(\\widehat \\kappa_n)_{n\\geq 1}$ the decreasing rearrangement of $(\\widehat \\kappa_\\nu)_{\\nu\\in{\\cal F}}$, we observe that $$n \\widehat \\kappa_n^q \\leq \\sum_{j= 1}^n \\widehat \\kappa_j^q \\leq B^q, \\quad B:=\\\|(\\widehat \\kappa_\\nu)_{\\nu\\in{\\cal F}}\\\|_{\\ell^q}<\\infty.$$ With $p$ such that $\\frac 1 p=\\frac 1 r-\\frac 1 2$, we find that $$\\begin{aligned}\n\\left(\\sum_{\\nu \\notin \\Lambda_n} c_\\nu^r\\right)^{1/r}\n& \\leq \\left( \\sum_{\\nu \\notin \\Lambda_n} (\\widehat \\kappa_\\nu^{-1} c_\\nu)^2\\right)^{1/2}\\left(\\sum_{\\nu \\notin \\Lambda_n} \\widehat \\kappa_\\nu^p\\right)^{1/p}\\\\\n&\\leq A \\left(\\widehat \\kappa_{n+1}^{p-q}\\sum_{\\nu \\notin \\Lambda_n} \\widehat \\kappa_\\nu^q\\right)^{1/p}\\\\\n&\\leq A B (n+1)^{1/p-1/q},\\end{aligned}$$ where we have used Hölder’s inequality and the properties of $(\\widehat \\kappa_n)_{n\\geq 1}$. This gives with $C:=AB$.\n\nWe now would like to apply the above result with $c_\\nu\\in \\{ \\\|t_\\nu\\\|_V, \\\|w_\\nu\\\|_V,\\\|\\widetilde w_\\nu\\\|_V,\\\|h_\\nu\\\|_V\\}$, and the corresponding weight sequences $\\omega_\\nu\\in \\{\\rho^\\nu,\\rho^\\nu \\beta(\\nu)^{-1},\\rho^\\nu \\beta(\\nu)^{-2}, \\xi_\\nu^{1/2}\\}$, or equivalently $\\kappa_\\nu\\in \\{b^\\nu,b^\\nu \\beta(\\nu),b^\\nu \\beta(\\nu)^2, \\xi_\\nu^{-1/2}\\}$. In the case of the Taylor series, where $\\kappa_\\nu=b^\\nu$, we readily see that if $b_j<1$ for all $j\\geq 1$, then the sequence $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}$ is monotone nonincreasing, and therefore Lemma \\[thm:lemmaq\\] shows that $b\\in \\ell^q$ implies $(\\kappa_\\nu)_{\\nu\\in{\\cal F}}\\in\\ell^q_m({\\cal F})$. By application of Theorem \\[thm:theowlower\\] with the value $r=1$, this leads to the following result.", "\n\n\\[thm:theotaylor\\] If holds with $(\\rho_j^{-1})_{j\\geq 1}\\in \\ell^q(\\mathbb{N})$ for some $0<q<\\infty$ and $\\rho_j>1$ for all $j$, then $$\\\|u-u_{\\Lambda_n}\\\|_{L^\\infty(U,V)}\\leq Cn^{-s}, \\quad s:=\\frac 1 q-\\frac 1 2,$$ where $u_{\\Lambda_n}$ is the truncated Taylor series and $\\Lambda_n$ is any downward closed set corresponding to the $n$ largest $\\kappa_\\nu$.\n\nIn the case of the Legendre series, the weight $\\kappa_\\nu=b^\\nu \\beta(\\nu)$ is not monotone nonincreasing due to the presence of the algebraic factor $\\beta(\\nu)$. However, the following result holds.", "\n\n\\[thm:lemmaqm\\] For any $0<q<\\infty$ and for any algebraic factor of the form $\\alpha(\\nu):=\\prod_{j\\geq 1}(1+c_1\\nu_j)^{c_2}$ with $c_1,c_2\\geq 0$, one has $$b\\in \\ell^q(\\mathbb{N})\\quad {\\rm and}\\quad \\\|b\\\|_{\\ell^\\infty}<1 \\iff (\\alpha(\\nu) b^\\nu)_{\\nu\\in{\\cal F}} \\in \\ell^q_m({\\cal F}).$$\n\nThe implication from right to left is a consequence of Lemma \\[thm:lemmaq\\], and so we concentrate on the implication from left to right. ", "For this it suffices to find a majorant $\\widetilde \\kappa_\\nu$ of $\\kappa_\\nu:=\\alpha(\\nu) b^\\nu$ which is monotone nonincreasing and such that $(\\widetilde \\kappa_\\nu)_{\\nu\\in{\\cal F}} \\in \\ell^q({\\cal F})$. We notice that for any $\\tau>1$, there exists $C=C(\\tau,c_1,c_2)\\geq 1$ such that $$(1+c_1n)^{c_2}\\leq C\\tau^n,\\quad n\\geq 0.$$ For some $J\\geq 1$ and $\\tau$ to be fixed further, we may thus write $$\\kappa_\\nu\\leq \\widetilde \\kappa_\\nu:= C^J \\prod_{j=1}^J(\\tau b_j)^{\\nu_j} \\prod_{j>J} (1+c_1\\nu_j)^{c_2}b_j^{\\nu_j}.$$ Since $\\\|b\\\|_{\\ell^\\infty}<1$ we can take $\\tau>1$ such that $\\theta:=\\tau\\\|b\\\|_{\\ell^\\infty}<1$. By factorization, we find that $$\\sum_{\\nu\\in {\\cal F}} \\widetilde \\kappa_\\nu^q=C^{Jq} \\left(\\prod_{j=1}^J \\left(\\sum_{n\\geq 0} \\theta^{qn}\\right)\\right) \\left( \\prod_{j>J} \\left(\\sum_{n\\geq 0} (1+c_1n)^{qc_2} b_j^{nq}\\right)\\right).$$ The first product is bounded by $(1-\\theta^q)^{-J}$. Each factor in the second product is a converging series which is bounded by $1+cb_j^q$ for some $c>0$ that depends on $c_1$, $c_2$ and $\\\|b\\\|_{\\ell^\\infty}$. It follows that this second product converges. ", "Therefore $(\\widetilde \\kappa_\\nu)_{\\nu\\in{\\cal F}}$ belongs to $\\ell^q({\\cal F})$.\n\nFinally, we show that $\\widetilde \\kappa_\\nu$ is monotone nonincreasing provided that $J$ is chosen large enough. ", "It suffices to show that $\\widetilde \\kappa_{\\nu+e_j}\\leq \\widetilde \\kappa_\\nu$ for all $\\nu\\in {\\cal F}$ and for all $j\\geq 1$ where $$e_j:=(0,\\dots,0,1,0,\\dots),$$ is the Kronecker sequence of index $j$. When $j\\leq J$ this is obvious since $\\widetilde \\kappa_{\\nu+e_j}=\\tau b_j\\widetilde \\kappa_\\nu\\leq \\theta \\widetilde \\kappa_\\nu \\leq \\widetilde \\kappa_\\nu$. When $j>J$, we have $$\\widetilde \\kappa_{\\nu+e_j}\\widetilde \\kappa_{\\nu}^{-1}=b_j\\left(\\frac {1+c_1(\\nu_j+1)}{1+c_1\\nu_j} \\right)^{c_2}.$$ Noticing that the sequence $a_n:=\\left(\\frac {1+c_1(n+1)}{1+c_1n} \\right)^{c_2}$ converges toward $1$ and is therefore bounded, and that $b_j$ tends to $0$ as $j\\to +\\infty$, we find that for $J$ sufficiently large, the right-hand side in the above equation is bounded by $1$ for all $\\nu$ and $j>J$.\n\nFrom Lemma \\[thm:lemmaqm\\], by applying Theorem \\[thm:theowlower\\] with $r=1$ or $r=2$, we obtain the following result.", "\n\n\\[thm:theoleg\\] If holds with $(\\rho_j^{-1})_{j\\geq 1}\\in \\ell^q(\\mathbb{N})$ for some $0<q<\\infty$ and $\\rho_j>1$ for all $j$, then $$\\\|u-u_{\\Lambda_n}\\\|_{L^2(U,V)}\\leq Cn^{-s}, \\quad s:=\\frac 1 q,$$ where $u_{\\Lambda_n}$ is the truncated Legendre series and $\\Lambda_n$ is any downward closed set corresponding to the $n$ largest $\\widehat \\kappa_\\nu$ where $\\kappa_\\nu:=b^\\nu \\beta(\\nu)$. If $q<2$, we also have $$\\\|u-u_{\\Lambda_n}\\\|_{L^\\infty(U,V)}\\leq Cn^{-s}, \\quad s:=\\frac 1 q-\\frac 1 2,$$ with $\\Lambda_n$ any downward closed set corresponding to the $n$ largest $\\widehat \\kappa_\\nu$ where $\\kappa_\\nu:=b^\\nu \\beta(\\nu)^2$.\n\nFinally, in the case of the Hermite coefficients, which corresponds to the weight $$\\kappa_\\nu:= \\prod_{j\\geq 1}\\left( \\sum_{l=0}^r {\\nu_j \\choose l}b_j^{-2l} \\right)^{-1/2},\n\\label{eq:bnuherm}$$ we can establish a similar summability result.", "\n\n\\[thm:lemmaqmh\\] For any $0<q<\\infty$ and any integer $r\\geq 1$ such that $q> \\frac 2 r$, we have $$b\\in \\ell^q(\\mathbb{N})\\implies (\\kappa_\\nu)_{\\nu\\in{\\cal F}} \\in \\ell^q\n({\\cal F}),$$ where $\\kappa_\\nu$ is given by . ", "In addition, for any integer $r\\geq 0$, the sequence $(\\kappa_\\nu)_{\\nu \\in {\\cal F}}$ is monotone nonincreasing.", "\n\nFor any $\\nu \\in {\\cal F}$ and any $k\\geq 1$ we have $$\\begin{aligned}\n\\kappa_{\\nu + e_k} \n& = \n\\left(\n\\sum_{l=0}^r \\binom{\\nu_k + 1}{ l} b_k^{-2l}\n\\right)^{-1/2}\n\\prod_{j \\geq 1 \\atop j \\neq k} \\left(\n\\sum_{l=0}^r \\binom{\\nu_j}{ l} b_j^{-2l}\n\\right)^{-1/2}\n\\\\\n& \\leq \n\\left(\n\\sum_{l=0}^r \\binom{\\nu_k}{ l} b_k^{-2l}\n\\right)^{-1/2}\n\\prod_{j \\geq 1 \\atop j \\neq k} \n\\left(\n\\sum_{l=0}^r \\binom{\\nu_j}{ l} b_j^{-2l}\n\\right)^{-1/2}\n=\n\\kappa_{\\nu}, \\end{aligned}$$ and therefore the sequence $(\\kappa_\\nu)_{\\nu \\in {\\cal F}}$ is monotone nonincreasing.", "\n\nNow we check that $(\\kappa_\\nu)_{\\nu\\in{\\cal F}} \\in \\ell^q({\\cal F})$, using the factorization $$\\label{eq:factorization_proof}\n\\sum_{\\nu\\in{\\cal F}} \\kappa_\\nu^q=\\prod_{j\\geq 1} \\sum_{n \\geq 0}\\left( \\sum_{l=0}^r {n \\choose l}b_j^{-2l} \\right)^{-q/2} \n\\leq \n\\prod_{j\\geq 1}\\sum_{n\\geq 0}{n \\choose r\\wedge n}^{-q/2}b_j^{q(r\\wedge n)}.$$ where the inequality follows from the fact that the value $l=n\\wedge r:=\\min\\{n,r\\}$ is contained in the sum.", "\n\nThe $j$th factor $F_j$ in the rightmost product in may be written as $$F_j= 1+b_j^q+\\cdots+b_j^{(r-1)q}+C_{r,q}b_j^{rq},$$ where $$C_{r,q} := \\sum_{n \\geq r} {n\\choose r}^{-q/2} = (r!)^{q/2} \\sum_{n\\geq 0} \\bigl[(n+1)\\cdots (n+r)\\bigr]^{-q/2}<\\infty,$$ since we have assumed that $q> 2/r$. This shows that each $F_j$ is finite. ", "If $b\\in \\ell^q({{\\mathbb N}})$, there exists an integer $J\\geq 0$ such that $b_j <1$ for all $j> J$. For such $j$, we can bound $F_j$ by $1 + (C_{r,q} + r - 1) b_j^{q}$, which shows that the product converges.", "\n\nFrom this lemma, and by application of Theorem \\[thm:theowlower\\] with the value $r=2$, we obtain the following result for the Hermite series.", "\n\n\\[thm:theoherm\\] If holds with $(\\rho_j^{-1})_{j\\geq 1}\\in \\ell^q(\\mathbb{N})$ for some $0<q<\\infty$, then $$\\\|u-u_{\\Lambda_n}\\\|_{L^2(U,V)}\\leq Cn^{-s}, \\quad s:=\\frac 1 q,$$ where $u_{\\Lambda_n}$ is the truncated Hermite series and $\\Lambda_n$ is a downward closed set corresponding to the $n$ largest $\\kappa_\\nu$ given by .", "\n\nIn summary, we have established convergence rates for approximation by downward closed polynomial spaces of the solution map associated to the elliptic PDE with affine or lognormal parametrization. ", "The conditions are stated in terms of the control on the $L^\\infty$ norm of $\\sum_{j\\geq 1} \\rho_j\|\\psi_j\|$, where the $\\rho_j$ have a certain growth measured by the $\\ell^q$ summability of the sequence $b=(b_j)_{j\\geq 1}=(\\rho_j^{-1})_{j\\geq 1}$. This is a way to quantify the decay of the size of the $\\psi_j$, also taking their support properties into account, and in turn to quantify the anisotropic dependence of $u(y)$ on the various coordinates $y_j$. Other similar results have been obtained with different PDE models, see in particular [@CD]. ", "In the above results, the polynomial approximants are constructed by truncation of infinite series. ", "The remainder of the paper addresses the construction of downward closed polynomial approximants from evaluations of the solution map at $m$ points $\\{y^1,\\dots,y^m\\}\\in U$, and discusses the accuracy of these approximants.", "\n\nInterpolation {#sec:3}\n=============\n\nSparse Interpolation by Downward Closed Polynomials {#sec:3.1}\n---------------------------------------------------\n\nInterpolation is one of the most standard processes for constructing polynomial approximations based on pointwise evaluations. ", "Given a downward closed set $\\Lambda \\subset {\\cal F}$ of finite cardinality, and a set of points $$\\Gamma\\subset U, \\quad \\#(\\Gamma)=\\#(\\Lambda),$$ we would like to build an interpolation operator $I_\\Lambda$, that is, $I_\\Lambda u\\in \\mathbb{V}_\\Lambda$ is uniquely characterized by $$I_\\Lambda u(y)=u(y), \\quad y\\in\\Gamma,$$ for any $V$-valued function $u$ defined on $U$.\n\nIn the univariate case, it is well known that such an operator exists if and only if $\\Gamma$ is a set of pairwise distinct points, and that additional conditions are needed in the multivariate case. ", "Moreover, since the set $\\Lambda$ may come from a nested sequence $(\\Lambda_n)_{n\\geq 1}$ as discussed in Section \\[sec:2\\], we are interested in having similar nestedness properties for the corresponding sequence $(\\Gamma_n)_{n\\geq 1}$, where $$\\#(\\Gamma_n)=\\#(\\Lambda_n)=n.$$ Such a nestedness property allows us to recycle the $n$ evaluations of $u$ which have been used in the computation of $I_{\\Lambda_n} u$, and use only one additional evaluation for the next computation of $I_{\\Lambda_{n+1}} u$.\n\nIt turns out that such hierarchical interpolants can be constructed in a natural manner by making use of the downward closed structure of the index sets $\\Lambda_n$. This construction is detailed in [@CCS1] but its main principles can be traced from [@K]. ", "In order to describe it, we assume that the parameter domain is of either form $$U=[-1,1]^d \\quad {\\rm or} \\quad [-1,1]^\\mathbb{N},$$ with the convention that $d=\\infty$ in the second case. ", "However, it is easily check that the construction can be generalized in a straightforward manner to any domain with Cartesian product form $$U=\\underset{k\\geq 1}{\\times} J_k,$$ where the $J_k$ are finite or infinite intervals.", "\n\nWe start from a sequence of pairwise distinct points $$T=(t_k)_{k\\geq 0}\\subset [-1,1].$$ We denote by $I_k$ the univariate interpolation operator on the space $\n\\mathbb{V}_k:=V\\otimes \\mathbb{P}_k\n$ associated with the $k$-section $\\{t_0,\\dots,t_k\\}$ of this sequence, that is, $$I_ku(t_i)=u(t_i),\\quad i=0,\\dots,k,$$ for any $V$-valued function $u$ defined on $[-1,1]$. We express $I_k$ in the Newton form $$I_ku=I_0u+\\sum_{l=1}^k\\Delta_l u,\\quad \\Delta_l:=I_l-I_{l-1},\n\\label{eq:newton}$$ and set $I_{-1}=0$ so that we can also write $$I_ku=\\sum_{l=0}^k \\Delta_l u.$$ Obviously the difference operator $\\Delta_k$ annihilates the elements of $\\mathbb{V}_{k-1}$. In addition, since $\\Delta_k u(t_j)=0$ for $j=0,\\dots,k-1$, we have $$\\Delta_k u(t)=\\alpha_k B_k(t),$$ where $$B_{k}(t):=\\prod_{l=0}^{k-1}\\frac {t-t_l}{t_k-t_l}.$$ The coefficient $\\alpha_k\\in V$ can be computed inductively, since it is given by $$\\alpha_k=\\alpha_k(u):=u(t_k)-I_{k-1}u(t_k),$$ that is, the interpolation error at $t_k$ when using $I_{k-1}$. Setting $$B_0(t):=1,$$ we observe that the system $\\{B_0,\\dots,B_k\\}$ is a basis for $\\mathbb{P}_k$. It is sometimes called a [hierarchical basis]{}.", "\n\nIn the multivariate setting, we tensorize the grid $T$, by defining $$y_\\nu:=(t_{\\nu_j})_{j\\geq 1}\\in U, \\quad \\nu\\in{\\cal F}.$$ We first introduce the tensorized operator $$I_\\nu:=\\bigotimes_{j\\geq 1} I_{\\nu_j},$$ recalling that the application of a tensorized operator $\\otimes_{j\\geq 1} A_j$ to a multivariate function amounts in applying each univariate operator $A_j$ by freezing all variables except the $j$th one, and then applying $A_j$ to the unfrozen variable. ", "It is readily seen that $I_\\nu$ is the interpolation operator on the tensor product polynomial space $$\\mathbb{V}_\\nu=V\\otimes \\mathbb{P}_\\nu, \\quad \\mathbb{P}_\\nu:=\\bigotimes_{j\\geq 1} \\mathbb{P}_{\\nu_j},$$ associated to the grid of points $$\\Gamma_{\\nu}=\\underset{j\\geq 1}{\\times}\n\\{t_{0},\\dots,t_{\\nu_j}\\}.$$ This polynomial space corresponds to the particular downward closed index set of rectangular shape $$\\Lambda=R_\\nu:=\\{ \\widetilde \\nu \\; : \\; \\widetilde \\nu \\leq \\nu \\}.$$ Defining in a similar manner the tensorized difference operators $$\\Delta_\\nu:=\\bigotimes_{j\\geq 1}\\Delta_{\\nu_j},$$ we observe that $$I_\\nu=\\bigotimes_{j\\geq 1} I_{\\nu_j}=\\bigotimes_{j\\geq 1} (\\sum_{l=0}^{\\nu_j} \\Delta_l)=\\sum_{\\widetilde\\nu\\in R_\\nu} \\Delta_{\\widetilde\\nu}.$$ The following result from [@CCS1] shows that the above formula can be generalized to [any]{} downward closed set in order to define an interpolation operator. ", "We recall its proof for sake of completeness.", "\n\n\\[thm:Thmlowerint\\] Let $\\Lambda\\subset {\\cal F}$ be a finite downward closed set, and define the grid $$\\Gamma_\\Lambda:=\\{y_\\nu \\; : \\; \\nu\\in \\Lambda\\}.$$ Then, the interpolation operator onto $\\mathbb{V}_\\Lambda$ for this grid is defined by $$I_\\Lambda:=\\sum_{\\nu\\in \\Lambda} \\Delta_\\nu.", "\n\\label{eq:newtongen}$$\n\nFrom the downward closed set property, $\\mathbb{V}_\\nu\\subset \\mathbb{V}_\\Lambda$ for all $\\nu\\in\\Lambda$. Hence the image of $I_\\Lambda$ is contained in $\\mathbb{V}_\\Lambda$. With $I_\\Lambda$ defined by , we may write $$I_\\Lambda u=I_{\\nu}u+\\sum_{\\widetilde \\nu\\in\\Lambda, \\widetilde \\nu \\nleqslant \\nu} \\Delta_{\\widetilde \\nu} u,$$ for any $\\nu\\in \\Lambda$. Since $y_\\nu\\in \\Gamma_\\nu$, we know that $$I_\\nu u(y_\\nu)=u(y_\\nu).$$ On the other hand, if $\\widetilde \\nu \\nleqslant \\nu$, this means that there exists a $j\\geq 1$ such that $\\widetilde \\nu_j>\\nu_j$. For this $j$ we thus have $\\Delta_{\\widetilde \\nu} u(y)=0$ for all $y\\in U$ with the $j$th coordinate equal to $t_{\\nu_j}$ by application of $\\Delta_{\\nu_j}$ in the $j$th variable, so that $$\\Delta_{\\widetilde \\nu} u(y_\\nu)=0.$$ The interpolation property $I_\\Lambda u(y_\\nu)=u(y_\\nu)$ thus holds, for all $\\nu\\in \\Lambda$.\n\nThe decomposition should be viewed as a generalization of the Newton form . ", "In a similar way, its terms can be computed inductively: if $\\Lambda=\\widetilde \\Lambda\\cup \\{\\nu\\}$ where $\\widetilde \\Lambda$ is a downward closed set, we have $$\\Delta_\\nu u=\\alpha_\\nu B_\\nu,$$ where $$B_\\nu(y):=\\prod_{j\\geq 1} B_{\\nu_j}(y_j),$$ and $$\\alpha_\\nu=\\alpha_\\nu(u):=u(y_\\nu)-I_{\\widetilde \\Lambda} u(y_\\nu).$$ Therefore, if $(\\Lambda_n)_{n\\geq 1}$ is any nested sequence of downward closed index sets, we can compute $I_{\\Lambda_n}$ by $n$ iterations of $$I_{\\Lambda_{i}}u=I_{\\Lambda_{i-1}}u +\\alpha_{\\nu^i} B_{\\nu^i},$$ where $\\nu^i\\in \\Lambda_i$ is such that $\\Lambda_i=\\Lambda_{i-1} \\cup\\{\\nu^i\\}$.\n\nNote that $(B_\\nu)_{\\nu\\in \\Lambda}$ is a basis of $\\mathbb{P}_\\Lambda$ and that any $f \\in \\mathbb{V}_\\Lambda$ has the unique decomposition $$f=\\sum_{\\nu\\in \\Lambda} \\alpha_\\nu B_\\nu,$$ where the coefficients $\\alpha_\\nu=\\alpha_\\nu(f)\\in V$ are defined by the above procedure. ", "Also note that $\\alpha_\\nu(f)$ does not depend on the choice of $\\Lambda$ but only on $\\nu$ and $f$.\n\nStability and Error Estimates {#sec:3.2}\n-----------------------------\n\nThe pointwise evaluations of the function $u$ could be affected by errors, as modeled by and . ", "The stability of the interpolation operator with respect to such perturbations is quantified by the [Lebesgue constant]{}, which is defined by $$\\mathbb{L}_\\Lambda:=\\sup \\frac{\\\|I_\\Lambda f\\\|_{L^\\infty(U,V)}} {\\\|f\\\|_{L^\\infty(U,V)}},$$ where the supremum is taken over the set of all $V$-valued functions $f$ defined everywhere and uniformly bounded over $U$. It is easily seen that this supremum is in fact independent of the space $V$, so that we may also write $$\\mathbb{L}_\\Lambda:=\\sup \\frac{\\\|I_\\Lambda f\\\|_{L^\\infty(U)}} {\\\|f\\\|_{L^\\infty(U)}},$$ where the supremum is now taken over real-valued functions. ", "Obviously, we have $$\\\|u-I_\\Lambda(u+\\eta)\\\|_{L^\\infty(U,V)} \\leq \\\|u-I_\\Lambda u\\\|_{L^\\infty(U,V)}+ \\mathbb{L}_\\Lambda \\varepsilon,$$ where $\\varepsilon$ is the noise level from .", "\n\nThe Lebesgue constant also allows us to estimate the error of interpolation $\\\|u-I_\\Lambda u\\\|_{L^\\infty(U,V)}$ for the noiseless solution map in terms of the best approximation error in the $L^\\infty$ norm: for any $u\\in L^\\infty(U,V)$ and any $\\widetilde u\\in \\mathbb{V}_\\Lambda$ we have $$\\\|u-I_\\Lambda u\\\|_{L^\\infty(U,V)} \\leq \\\|u-\\widetilde u\\\|_{L^\\infty(U,V)}+\\\|I_\\Lambda \\widetilde u-I_\\Lambda u\\\|_{L^\\infty(U,V)},$$ which by infimizing over $\\widetilde u\\in \\mathbb{V}_\\Lambda$ yields $$\\\|u-I_\\Lambda u\\\|_{L^\\infty(U,V)} \\leq (1+\\mathbb{L}_\\Lambda)\\inf_{\\widetilde u\\in \\mathbb{V}_\\Lambda}\\\|u-\\widetilde u\\\|_{L^\\infty(U,V)}.$$ We have seen in Section \\[sec:2\\] that for relevant classes of solution maps $y\\mapsto u(y)$, there exist sequences of downward closed sets $(\\Lambda_n)_{n\\geq 1}$ with $\\#(\\Lambda_n)=n$, such that $$\\inf_{\\widetilde u\\in \\mathbb{V}_{\\Lambda_n}}\\\|u- \\widetilde u\\\|_{L^\\infty(U,V)} \\leq Cn^{-s}, \\quad n\\geq 1,$$ for some $s>0$. For such sets, we thus have $$\\\|u-I_{\\Lambda_n} u\\\|_{L^\\infty(U,V)} \\leq C(1+\\mathbb{L}_{\\Lambda_n})n^{-s}.", "\n\\label{eq:Intern}$$ This motivates the study of the growth of $\\mathbb{L}_{\\Lambda_n}$ as $n\\to +\\infty$.\n\nFor this purpose, we introduce the univariate Lebesgue constants $$\\mathbb{L}_k:=\\sup\\frac {\\\|I_k f\\\|_{L^\\infty([-1,1])}} {\\\|f\\\|_{L^\\infty([-1,1])}}.$$ Note that $\\mathbb{L}_0=1$. We also define an analog quantity for the difference operator $$\\mathbb{D}_k:=\\sup\\frac {\\\|\\Delta_k f\\\|_{L^\\infty([-1,1])}} {\\\|f\\\|_{L^\\infty([-1,1])}}.$$ In the particular case of the rectangular downward closed sets $\\Lambda=R_\\nu$, since $I_\\Lambda=I_\\nu=\\otimes_{j\\geq 1}I_{\\nu_j}$, we have $$\\mathbb{L}_{R_\\nu}=\\prod_{j\\geq 1} \\mathbb{L}_{\\nu_j}.$$ Therefore, if the sequence $T=(t_k)_{k\\geq 0}$ is such that $$\\mathbb{L}_k \\leq (1+k)^\\theta ,\\quad k\\geq 0,\n\\label{eq:lambdak}$$ for some $\\theta \\geq 1$, we find that $$\\mathbb{L}_{R_\\nu}\\leq \\prod_{j\\geq 1} (1+\\nu_j)^\\theta= (\\#(R_\\nu))^\\theta,$$ for all $\\nu\\in{\\cal F}$.\n\nFor arbitrary downward closed sets $\\Lambda$, the expression of $I_\\Lambda$ shows that $$\\mathbb{L}_\\Lambda\\leq \\sum_{\\nu\\in \\Lambda} \\prod_{j\\geq 1} \\mathbb{D}_{\\nu_j}.$$ Therefore, if the sequence $T=(t_k)_{k\\geq 0}$ is such that $$\\mathbb{D}_k \\leq (1+k)^\\theta ,\\quad k\\geq 0,\n\\label{eq:dak}$$ we find that $$\\mathbb{L}_\\Lambda \\leq \\sum_{\\nu\\in \\Lambda} \\prod_{j\\geq 1} (1+\\nu_j)^\\theta\n=\\sum_{\\nu\\in \\Lambda} (\\#(R_\\nu))^\\theta \\leq \\sum_{\\nu\\in \\Lambda} (\\#(\\Lambda))^\\theta = (\\#(\\Lambda))^{\\theta+1}.$$ The following result from [@CCS1] shows that this general estimate is also valid under the assumption on the growth of $\\mathbb{L}_k$.\n\n\\[thm:theoLeb\\] If the sequence $T=(t_k)_{k\\geq 0}$ is such that or holds for some $\\theta \\geq 1$, then $$\\mathbb{L}_{\\Lambda} \\leq (\\#(\\Lambda))^{\\theta+1},$$ for all downward closed sets $\\Lambda$.\n\nOne noticeable feature of the above result is that the bound on $\\mathbb{L}_\\Lambda$ only depends on $\\#(\\Lambda)$, independently of the number of variables, which can be infinite, as well as of the shape of $\\Lambda$.\n\nWe are therefore interested in univariate sequences $T=(t_k)_{k\\geq 0}$ such that $\\mathbb{L}_k$ and $\\mathbb{D}_k$ have moderate growth with $k$. For Chebyshev or Gauss-Lobatto points, given by $${\\cal C}_k:=\\left\\{\\cos\\left(\\frac {2 l+1}{2k+2} \\pi\\right)\\; : \\; l=0,\\dots, k\\right\\} \\quad {\\rm and}\\quad\n{\\cal G}_k:=\\left\\{\\cos\\left(\\frac {l}{k} \\pi\\right)\\; : \\; l=0,\\dots, k\\right\\},$$ it is well known that the Lebesgue constant has logarithmic growth $\\mathbb{L}_k\\sim \\ln(k)$, thus slower than algebraic. ", "However these points are not the $k$ section of a single sequence $T$, and therefore they are not convenient for our purposes. ", "Two examples of univariate sequences of interest are the following.", "\n\n- The [Leja points]{}: from an arbitrary $t_0\\in [-1,1]$ (usually taken to be $1$ or $0$), this sequence is recursively defined by $$t_k:=\\operatorname{argmax}\\left\\{ \\prod_{l=0}^{k-1}\|t-t_l\| \\; : \\; t\\in [-1,1]\\right\\}.$$ Note that this choice yields hierarchical basis functions $B_k$ that are uniformly bounded by $1$. Numerical computations of $\\mathbb{L}_k$ for the first $200$ values of $k$ indicates that the linear bound $$\\mathbb{L}_k \\leq 1+k,\n \\label{eq:lineark}$$ holds. ", "Proving that this bound, or any other algebraic growth bound, holds for all values of $k\\geq 0$ is currently an open problem.", "\n\n- The [$\\Re$-Leja]{} points: they are the real part of the Leja points defined on the complex unit disc $\\{\|z\|\\leq 1\\}$, taking for example $e_0=1$ and recursively setting $$e_k:=\\operatorname{argmax}\\left\\{ \\prod_{l=0}^{k-1}\|e-e_l\| \\; : \\; \|e\|\\leq 1\\right \\}.$$ These points have the property of accumulating in a regular manner on the unit circle according to the so-called Van der Corput enumeration [@CP1]. ", "It is proven in [@C] that the linear bound holds for the Lebesgue constant of the complex interpolation operator on the unit disc associated to these points. ", "The sequence of real parts $$t_k:=\\Re(e_k),$$ is defined after eliminating the possible repetitions corresponding to $e_k=\\overline e_l$ for two different values of $k=l$. These points coincide with the Gauss-Lobatto points for values of $k$ of the form $2^n+1$ for $n\\geq 0$. A quadratic bound $$\\mathbb{D}_k \\leq (1+k)^2,$$ is established in [@CC].", "\n\nIf we use such sequences, application of Theorem \\[thm:theoLeb\\] gives bounds of the form $$\\mathbb{L}_\\Lambda\\leq (\\#(\\Lambda))^{1+\\theta},$$ for example with $\\theta=2$ when using the $\\Re$-Leja points, or $\\theta=1$ when using the Leja points provided that the conjectured bound holds. ", "Combining with , we obtain the convergence estimate $$\\\|u-I_{\\Lambda_n} u\\\|_{L^\\infty(U,V)} \\leq C n^{-(s-1-\\theta)},$$ which reveals a serious deterioration of the convergence rate when using interpolation instead of truncated expansions.", "\n\nHowever, for the parametric PDE models discussed in Section \\[sec:2\\], it is possible to show that this deterioration actually does not occur, based on the following lemma which relates the interpolation error to the summability of coefficient sequences in general expansions of $u$.\n\n\\[thm:lemmaresid\\] Assume that $u$ admits an expansion of the type , where $\\\|\\phi_\\nu\\\|_{L^\\infty(U)}\\leq 1$ which is unconditionally convergent towards $u$ in $L^\\infty(U,V)$. Assume in addition that $y\\mapsto u(y)$ is continuous from $U$ equipped with the product topology toward $V$. If the univariate sequence $T=(t_k)_{k\\geq 0}$ is such that or holds for some $\\theta\\geq 1$, then, for any downward closed set $\\Lambda$, $$\\\| u-I_\\Lambda u \\\|_{L^\\infty(U,V)} \n\\leq \n2\\sum_{\\nu\\notin \\Lambda} \\pi (\\nu) \\\|u_\\nu\\\|_V, \\quad \\pi(\\nu) := \\prod_{j\\geq 1} (1+\\nu_j)^{\\theta+1}.", "\n\\label{eq:residual}$$\n\nThe unconditional convergence of and the continuity of $u$ with respect to the product topology allow us to say that the equality in holds everywhere in $U$. We may thus write $$I_\\Lambda u \n=\nI_\\Lambda\\left(\\sum_{\\nu\\in{\\cal F}} u_\\nu \\phi_\\nu\\right)\n=\n \\sum_{\\nu\\in{\\cal F}} u_\\nu I_\\Lambda \\phi_\\nu\n=\n\\sum_{\\nu\\in\\Lambda} u_\\nu \\phi_\\nu\n+\n\\sum_{\\nu\\notin\\Lambda} u_\\nu I_{\\Lambda}\\phi_\\nu,$$ where we have used that $I_\\Lambda \\phi_\\nu =\\phi_\\nu$ for every $\\nu\\in\\Lambda$ since $\\phi_\\nu\\in \\mathbb{P}_\\Lambda$. For the second sum on the right-hand side, we observe that for each $\\nu\\notin\\Lambda$, $$I_{\\Lambda}\\phi_\\nu=\\sum_{\\widetilde \\nu\\in \\Lambda}\\Delta_{\\widetilde \\nu} \\phi_\\nu\n=\\sum_{\\widetilde \\nu\\in \\Lambda\\cap R_\\nu}\\Delta_{\\widetilde \\nu} \\phi_\\nu=I_{\\Lambda\\cap R_\\nu} \\phi_\\nu,$$ since $\\Delta_{\\widetilde \\nu}$ annihilates $\\mathbb{P}_\\nu$ whenever $\\widetilde \\nu \\not\\leq \\nu$. Therefore $$u-I_\\Lambda u \n= \\sum_{\\nu\\not\\in\\Lambda} u_\\nu (I- I_{\\Lambda\\cap R_\\nu })\\phi_\\nu,$$ where $I$ stands for the identity operator. ", "This implies $$\\\|u-I_\\Lambda u \\\|_{L^\\infty(U,V)}\n\\leq\n\\sum_{\\nu\\not\\in\\Lambda} (1+\\mathbb{L}_{\\Lambda\\cap R_\\nu})\\\|u_\\nu\\\|_V \n\\leq \n2\\sum_{\\nu\\not\\in\\Lambda} \\mathbb{L}_{\\Lambda\\cap R_\\nu}\\\|u_\\nu\\\|_V \\; .$$ Since or holds, we obtain from Theorem \\[thm:theoLeb\\] that $$\\mathbb{L}_{\\Lambda\\cap R_\\nu} \n\\leq (\\#(\\Lambda\\cap R_\\nu))^{\\theta+1} \n\\leq (\\#(R_\\nu))^{\\theta+1} \n= \\pi(\\nu),$$ which yields .", "\n\nWe can apply the above lemma with the Taylor series or the renormalized Legendre series . ", "This leads us to analyze the $\\ell^1$ tail of the sequence $(c_\\nu)_{\\nu\\in{\\cal F}}$ where $c_\\nu$ is either $\\pi(\\nu)\\\|t_\\nu\\\|_V$ or $\\pi(\\nu)\\\|\\widetilde w_\\nu\\\|_V$. If holds, we know from Theorem \\[thm:theosumaff\\] that this sequence satisfies the bound $$\\sum_{\\nu\\in{\\cal F}}(\\omega_\\nu c_\\nu)^2 <\\infty,$$ where $\\omega_\\nu$ is either $\\pi(\\nu)^{-1}\\rho^\\nu$ or $\\pi(\\nu)^{-1}\\beta(\\nu)^{-2}\\rho^\\nu$. Since $\\pi(\\nu)$ has algebraic growth similar to $\\beta(\\nu)$, application of Lemma \\[thm:lemmaqm\\] and of Theorem \\[thm:theowlower\\] with the value $r=1$, leads to the following result.", "\n\n\\[thm:theointer\\] If holds with $(\\rho_j^{-1})_{j\\geq 1}\\in \\ell^q(\\mathbb{N})$ for some $0<q<\\infty$ and $\\rho_j>1$ for all $j$, then $$\\\|u-I_{\\Lambda_n}u\\\|_{L^\\infty(U,V)}\\leq Cn^{-s}, \\quad s:=\\frac 1 q-\\frac 1 2,$$ where $\\Lambda_n$ is any downward closed set corresponding to the $n$ largest $\\widehat \\kappa_\\nu$ where $\\kappa_\\nu$ is either $\\pi(\\nu)b^\\nu$ or $\\pi(\\nu) \\beta(\\nu)^2 b^\\nu$.\n\nDiscrete Least Squares Approximations {#sec:4}\n=====================================\n\nDiscrete Least Squares on $V$-valued Linear Spaces {#sec:4.1}\n--------------------------------------------------\n\nLeast-squares fitting is an alternative approach to interpolation for building a polynomial approximation of $u$ from $\\mathbb{V}_\\Lambda$. In this approach we are given $m$ observations $u^1,\\ldots,u^m$ of $u$ at points $y^1,\\ldots,y^m \\in U \\subseteq \\mathbb{R}^d$ where $m\\geq n=\\#(\\Lambda)$.\n\nWe first discuss the least-squares method in the more general setting of $V$-valued linear spaces, $$\\mathbb{V}_n:=V\\otimes \\mathbb{Y}_n,$$ where $\\mathbb{Y}_n$ is the space of real-valued functions defined everywhere on $U$ such that $\\dim(\\mathbb{Y}_n)=n$. In the next section, we discuss more specifically the case where $\\mathbb{Y}_n=\\mathbb{P}_\\Lambda$. Here we study the approximation error in the $L^2(U,V,d\\mu)$ norm for some given probability measure $d\\mu$, when the evaluation points $y^i$ are independent and drawn according to this probability measure. ", "For notational simplicity we use the shorthand $$\\\|\\cdot\\\|:=\\\|\\cdot \\\|_{L^2(U,V,d\\mu)}.$$\n\nThe [least-squares]{} method selects the approximant of $u$ in the space $\\mathbb{V}_n$ as $$u_L:=\\operatorname{argmin}_{\\widetilde u \\in \\mathbb{V}_n} \\frac 1 m \\sum_{i=1}^m \\\| \\widetilde u(y^i)-u^i \\\|_V^2.$$ In the noiseless case where $u^i:=u(y^i)$ for any $i=1,\\ldots,m$, this also writes $$u_L=\\operatorname{argmin}_{\\widetilde u \\in \\mathbb{V}_\\Lambda }\\\|u-\\widetilde u\\\|_m,\n\\label{eq:dls}$$ where the discrete seminorm is defined by $$\\\| f \\\|_m:= \\left( \\frac 1 m \\sum_{i=1}^m \\\|f(y^i) \\\|_V^2 \\right)^{1/2}.$$ Note that $\\\|f\\\|_m^2$ is an unbiased estimator of $\\\|f\\\|^2$ since we have $$\\mathbb{E}(\\\|f\\\|_m^2)=\\\|f\\\|^2.$$ Let $\\{\\phi_1,\\dots,\\phi_n\\}$ denote an arbitrary $L^2(U,d\\mu)$ orthonormal basis of the space $\\mathbb{Y}_n$. If we expand the solution to as $\\sum_{j=1}^n c_j \\phi_j$, with $c_j\\in V$, the $V$-valued vector ${\\bf c}=(c_1,\\dots,c_n)^t$ is the solution to the normal equations $${\\bf G} {\\bf c}={\\bf d},\n\\label{eq:sys}$$ where the matrix ${\\bf G}$ has entries $${\\bf G}_{j,k}=\\frac 1 m\\sum_{i=1}^m \\phi_j(y^i)\\phi_k(y^i),$$ and where the $V$-valued data vector ${\\bf d}=(d_1,\\dots,d_n)^t$ is given by $$d_j:=\\frac 1 m \\sum_{i=1}^m u^i \\phi_j(y^i).$$ This linear system always has at least one solution, which is unique when ${\\bf G}$ is nonsingular. ", "When ${\\bf G}$ is singular, we may define $u_L$ as the unique minimal $\\ell^2(\\mathbb{R}^n,V)$ norm solution to .", "\n\nIn the subsequent analysis, we sometimes work under the assumption of a known uniform bound $$\\\| u \\\|_{L^\\infty(U,V)}\\leq \\tau.", "\n\\label{eq:unibound}$$ We introduce the truncation operator $$z \\mapsto T_{\\tau} (z):=\n\\left\\{\n\\begin{array}{ll}\nz, \n& \n\\ \n\\textrm{ if } \\ \\\| z\\\|_V \\leq \\tau, \n\\\\\n\\frac{z}{\\\|z \\\|_V},\n&\n\\ \n\\textrm{ if } \\ \\\| z\\\|_V > \\tau,\n\\end{array}\n\\right.$$ and notice that it is a contraction: $\\\| T_{\\tau}(z)-T_{\\tau}(\\widetilde z)\\\|_V \\leq \\\|z -\\widetilde z\\\|_V $ for any $z,\\widetilde z \\in V$. The [truncated least-squares approximation]{} is defined by $$u_T:=T_{\\tau}\\circ u_L.$$ Note that, in view of , we have $\\\| u(y) - u_T(y) \\\|_V\\leq \\\| u(y) -u_L(y) \\\|_V$ for any $y\\in U$ and therefore $$\\\|u - u_T\\\|\\leq \\\|u -u_L\\\|.$$ Note that the random matrix ${\\bf G}$ concentrates toward its expectation which is the identity matrix ${\\bf I}$ as $m\\to \\infty$. In other words, the probability that ${\\bf G}$ is ill-conditioned becomes very small as $m$ increases. ", "The truncation operator aims at avoiding instabilities which may occur when ${\\bf G}$ is ill-conditioned. ", "As an alternative proposed in [@CM2016], we may define for some given $A>1$ the [conditioned least-squares approximation]{} by $$u_C:=u_L, \\ {\\rm if} \\ {\\rm cond}({\\bf G}) \\leq A, \\quad u_C:=0, \\ {\\rm otherwise},$$ where ${\\rm cond}({\\bf G}):={\\lambda_{\\max}({\\bf G})}/{\\lambda_{\\min}({\\bf G})}$ is the usual condition number.", "\n\nThe property that $\\\|{\\bf G}-{\\bf I}\\\|_2 \\leq \\delta$ for some $0<\\delta<1$ amounts to the norm equivalence $$(1-\\delta)\\\|f \\\|^2\\leq \\\|f\\\|_m^2\\leq (1+\\delta)\\\|f\\\|^2, \\quad f\\in \\mathbb{V}_n.$$ It is well known that if $m\\geq n$ is too much close to $n$, least-squares methods may become unstable and inaccurate for most sampling distributions. ", "For example, if $U=[-1,1]$ and $\\mathbb{Y}_n= \\mathbb{P}_{n-1}$ is the space of algebraic polynomials of degree $n-1$, then with $m=n$ the estimator coincides with the Lagrange polynomial interpolation which can be highly unstable and inaccurate, in particular for equispaced points. ", "Therefore, $m$ should be sufficiently large compared to $n$ for the probability that ${\\bf G}$ is ill-conditioned to be small. ", "This trade-off between $m$ and $n$ has been analyzed in [@CDL], using the function $$y \\mapsto k_n(y):=\\sum_{j=1}^n \|\\phi_j(y)\|^2,$$ which is the diagonal of the integral kernel of the $L^2(U,d\\mu)$ projector on $\\mathbb{Y}_n$. This function depends on $d\\mu$, but not on the chosen orthonormal basis. ", "It is strictly positive in $U$ under minimal assumptions on the orthonormal basis, for example if one element of the basis is the constant function over all $U$. Obviously, the function $k_n$ satisfies $$\\int_{U} k_n \\, d\\mu=n.$$ We define $$K_n:=\\\|k_n \\\|_{L^\\infty(U)} \\geq n.$$ The following results for the least-squares method with noiseless evaluations were obtained in [@CDL; @MNST; @CCMNT; @CM2016] for real-valued functions, however their proof extends in a straightforward manner to the present setting of $V$-valued functions. ", "They are based on a probabilistic bound for the event $\\\|{\\bf G}-{\\bf I}\\\|_2 > \\delta$ using the particular value $\\delta=\\frac 1 2$, or equivalently the value $A=\\frac{1+\\delta}{1-\\delta}=3$ as a bound on the condition number of ${\\bf G}$.\n\n\\[thm:theo1\\] For any $r>0$, if $m$ and $n$ satisfy $$K_n \\leq \\kappa\\frac m {\\ln m},\\;\\; {\\rm with}\\;\\; \\kappa:=\\kappa(r)=\\frac{1-\\ln 2} {2+2r},\n\\label{eq:condm}$$ then the following hold.", "\n\n1. ", " The matrix ${\\bf G}$ satisfies the tail bound $${\\rm Pr} \\, \\left\\{ \\\|{\\bf G}-{\\bf I}\\\|_2 > \\frac 1 2 \\right\\} \\leq\n 2m^{-r}.$$\n\n2. ", " If $u$ satisfies , then the truncated least-squares estimator satisfies, in the noiseless case, $$\\mathbb{E}(\\\|u-u_T\\\|^2)\\leq (1+\\zeta(m))\\inf_{\\widetilde u\\in \\mathbb{V}_n}\\\|u-\\widetilde u\\\|^2+8\\tau^2m^{-r},$$ where $\\zeta(m):= \\frac {4\\kappa} {\\ln (m)}\\to 0$ as $m\\to +\\infty$, and $\\kappa$ is as in .", "\n\n3. ", " The conditioned least-squares estimator satisfies, in the noiseless case, $$\\mathbb{E}(\\\|u-u_C\\\|^2)\\leq (1+\\zeta(m))\\inf_{\\widetilde u\\in \\mathbb{V}_n}\\\|u-\\widetilde u\\\|^2+2 \\\| u \\\|^2 m^{-r},$$ where $\\zeta(m)$ is as in (ii).", "\n\n4. ", " If $u$ satisfies , then the estimator $u_E\\in \\{u_L,u_T,u_C\\}$ satisfies, in the noiseless case, $$\\\|u- u_E\\\| \\leq (1+\\sqrt 2) \\inf_{\\widetilde u\\in \\mathbb{V}_n}\\\|u-\\widetilde u\\\|_{L^\\infty(U,V)},\n \\label{eq:nearoptimalprob}$$ with probability larger than $1-2m^{-r}$.\n\nIn the case of noisy evaluations modeled by –, the observations are given by $$u^i=u(y^i)+\\eta(y^i). ", "\n\\label{eq:noisy_observations}$$ The following result from [@CCMNT] shows that holds up to this additional perturbation.", "\n\n\\[thm:theo4\\] For any $r>0$, if $m$ and $n$ satisfy condition and $u$ satisfies , then the estimator $u_E\\in \\{u_L,u_T,u_C\\}$ in the noisy case satisfies $$\\\|u- u_E\\\|\\leq (1+\\sqrt 2)\n\\inf_{\\widetilde u \\in \\mathbb{V}_n}\\\|u-\\widetilde u\\\|_{L^\\infty(U,V)}\n+ \\sqrt 2 \\varepsilon,$$ with probability larger than $1-2n^{-r}$, where $\\varepsilon$ is the noise level in .", "\n\nSimilar results, with more general assumptions on the type of noise, are proven in [@CDL; @MNT2015; @CM2016].", "\n\nDownward Closed Polynomial Spaces and Weighted Least Squares {#sec:4.2}\n------------------------------------------------------------\n\nCondition shows that $K_n$ gives indications on the number $m$ of observations required to ensure stability and accuracy of the least-squares approximation. ", "In order to understand how demanding this condition is with respect to $m$, it is important to have sharp upper bounds for $K_n$. Such bounds have been proven when the measure $d\\mu$ on $U=[-1,1]^d$ has the form $$\\label{eq:jacobi_measure}\nd\\mu= C \\bigotimes_{j=1}^d (1-y_j)^{\\theta_1}(1+y_j)^{\\theta_2} dy_j,$$ where $\\theta_1,\\theta_2>-1$ are real shape parameters and $C$ is a normalization constant such that $\\int_U d\\mu=1$. Sometimes is called the Jacobi measure, because the Jacobi polynomials are orthonormal in $L^2(U,d\\mu)$. Remarkable instances of the measure are the uniform measure, when $\\theta_1=\\theta_2=0$, and the Chebyshev measure, when $\\theta_1=\\theta_2=-\\frac12$.\n\nWhen $\\mathbb{Y}_n=\\mathbb{P}_\\Lambda$ is a multivariate polynomial space and $\\Lambda$ is a downward closed multi-index set with $\\#(\\Lambda)=n$, it is proven in [@CCMNT; @M2015] that $K_n$ satisfies an upper bound which only depends on $n$ and on the choice of the measure through the values of $\\theta_1$ and $\\theta_2$.\n\n\\[thm:bounds\\_K\\_lemma\\] Let $d\\mu$ be the measure defined in . ", "Then it holds $$\\label{eq:up_bounds_cheby_jacobi}\nK_n \\leq \n\\left\\{\n\\begin{array}{ll}\nn^{\\frac{ \\ln 3 }{\\ln 2}},\n&\n\\quad \n\\textrm{ if } \\ \\theta_1=\\theta_2=-\\frac12, \n\\\\\nn^{2\\max\\{\\theta_1,\\theta_2\\}+2},\n&\n\\quad \\textrm{ if } \\ \\theta_1,\\theta_2\\in\\mathbb{N}_0.", "\n\\end{array}\n\\right.$$\n\nA remarkable property of both algebraic upper bounds in is that the exponent of $n$ is independent of the dimension $d$, and of the shape of the downward closed set $\\Lambda$. Both upper bounds are sharp in the sense that equality holds for multi-index sets of rectangular type $\\Lambda=R_\\nu$ corresponding to tensor product polynomial spaces.", "\n\nAs an immediate consequence of Theorem \\[thm:theo1\\] and Lemma \\[thm:bounds\\_K\\_lemma\\], we have the next corollary.", "\n\n\\[thm:corollary\\_std\\_ls\\] For any $r>0$, with multivariate polynomial spaces $\\mathbb{P}_\\Lambda$ and $\\Lambda$ downward closed, if $m$ and $n$ satisfy $$\\label{eq:bounds_corollary_std_ls}\n\\dfrac{m}{\\ln m} \\geq \\kappa\n\\left\\{\n\\begin{array}{ll}\nn^{\\frac{\\ln 3}{\\ln 2}},\n&\n\\quad \\textrm{ if } \\ \\theta_1=\\theta_2=-\\frac12,\n\\\\\nn^{2\\max\\{\\theta_1,\\theta_2 \\} +2},\n& \\quad \\textrm{ if } \\ \\theta_1,\\theta_2\\in\\mathbb{N}_0,\n\\end{array}\n\\right.$$ with $\\kappa=\\kappa(r)$ as in , then the same conclusions of Theorem \\[thm:theo1\\] hold true.", "\n\nOther types of results on the accuracy of least squares have been recently established in [@CMN], under conditions of the same type as .", "\n\nIn some situations, for example when $n$ is very large, the conditions might require a prohibitive number of observations $m$. It is therefore a legitimate question to ask whether there exist alternative approaches with less demanding conditions than between $m$ and $n$. At best, we would like that $m$ is of order only slightly larger than $n$, for example by a logarithmic factor. ", "In addition, the above analysis does not apply to situations where the basis functions $\\phi_k$ are unbounded, such as when using Hermite polynomials in the expansion . ", "It is thus desirable to ask for the development of approaches that also cover this case.", "\n\nThese questions have an affirmative answer by considering [weighted least-squares methods]{}, as proposed in [@DH; @JNZ; @CM2016]. ", "In the following, we survey some results from [@CM2016]. ", "For the space $\\mathbb{V}_n=V\\otimes \\mathbb{Y}_n$, the weighted least-squares approximation is defined as $$u_W:=\\operatorname{argmin}_{\\widetilde u \\in \\mathbb{V}_n} \\frac 1 m \\sum_{i=1}^m w^i \\\| \\widetilde u(y^i)-u^i \\\|_V^2,$$ for some given choice of weights $w^i \\geq 0$. This estimator is again computed by solving a linear system of normal equations now with the matrix ${\\bf G}$ with entries $${\\bf G}_{j,k}=\\frac 1 m\\sum_{i=1}^m w(y^i) \\phi_j(y^i)\\phi_k(y^i).$$ Of particular interest to us are weights of the form $$w^i=w(y^i),$$ where $w$ is some nonnegative function defined on $U$ such that $$\\int_{U} w^{-1} \\, d\\mu=1.", "\n\\label{eq:cond_weight_w_ls}$$ We then denote by $d\\sigma$ the probability measure $$d\\sigma:= w^{-1} d\\mu,\n\\label{eq:aux_measure_w_ls}$$ and we draw the independent points $y^1,\\ldots,y^m$ from $d\\sigma$. The case $w \\equiv 1$ and $d\\sigma=d\\mu$ corresponds to the previously discussed standard (unweighted) least-squares estimator $u_L$. As previously done for $u_L$, we associate to $u_W$ a truncated estimator $u_T$ and a conditioned estimator $u_C$, by replacing $u_L$ with $u_W$ in the corresponding definitions.", "\n\nLet us introduce the function $$y \\mapsto k_{n,w}(y):=\\sum_{j=1}^n w(y) \|\\phi_j(y)\|^2,$$ where once again $\\{\\phi_1,\\dots,\\phi_n\\}$ is an arbitrary $L^2(U,d\\mu)$ orthonormal basis of the space $\\mathbb{Y}_n$. Likewise, we define $$K_{n,w}:=\\\|k_{n,w} \\\|_{L^\\infty(U)}.$$ The following result, established in [@CM2016] for real-valued functions, extends Theorem \\[thm:theo1\\] to this setting. ", "Its proof in the $V$-valued setting is exactly similar.", "\n\n\\[thm:theo10\\] For any $r>0$, if $m$ and $n$ satisfy $$\\dfrac{m}{\\ln m} \\geq \\kappa \\, K_{n,w},\\;\\; {\\rm with}\\;\\; \\kappa:=\\kappa(r)=\\frac{1-\\ln 2}{2+2r},$$ then the same conclusions of Theorem \\[thm:theo1\\] hold true with $u_L$ replaced by $u_W$.\n\nIf we now choose $$w(y)=\\dfrac{ n }{ \\sum_{j=1}^n \|\\phi_j(y)\|^2 }, \n\\label{eq:opt_weights_w_ls}$$ that satisfies condition by construction, then the measure defined in takes the form $$d\\sigma= \\dfrac{ \\sum_{j=1}^n \|\\phi_j(y)\|^2 }{ n } d\\mu. ", "\n\\label{eq:opt_measure_w_ls}$$ The choice also gives $$K_{n,w}=\\\|k_{n,w} \\\|_{L^\\infty(U)}=n,$$ and leads to the next result, as a consequence of the previous theorem.", "\n\n\\[thm:theo11\\] For any $r>0$, if $m$ and $n$ satisfy $$\\dfrac{m}{\\ln m} \\geq \\kappa \\ n, \\;\\; {\\rm with}\\;\\; \\kappa:=\\kappa(r)=\\frac{1-\\ln 2}{2+2r},\n\\label{eq:condm_w_opt}$$ then the same conclusions of Theorem \\[thm:theo1\\] hold true with $u_L$ replaced by $u_W$, with $w$ given by and the weights taken as $w^i=w(y^i)$.\n\nThe above theorem ensures stability and accuracy of the weighted least-squares approximation, under the minimal condition that $m$ is linearly proportional to $n$, up to a logarithmic factor. ", "Clearly this is an advantage of weighted least squares compared to standard least squares, since condition is more demanding than in terms of the number of observations $m$.\n\nHowever, this advantage comes with some drawbacks that we now briefly recall, see [@CM2016] for an extensive description. ", "In general and are not product measures, even if $d\\mu$ is one. ", "Therefore, the first drawback of using weighted least squares concerns the efficient generation of independent samples from multivariate probability measures, whose computational cost could be prohibitively expensive, above all when the dimension $d$ is large. ", "In some specific settings, for example downward closed polynomial spaces $\\mathbb{Y}_n=\\mathbb{P}_\\Lambda$ with $\\#(\\Lambda)=n$, and when $d\\mu$ is a product measure, this drawback can be overcome. ", "We refer to [@CM2016], where efficient sampling algorithms have been proposed and analyzed. ", "For any $m$ and any downward closed set $\\Lambda$, these algorithms generate $m$ independent samples with proven bounds on the required computational cost. ", "The dependence on the dimension $d$ and $m$ of these bounds is linear. ", "For the general measure the efficient generation of the sample is a nontrivial task, and remains a drawback of such an approach.", "\n\nThe second drawback concerns the use of weighted least squares in a hierarchical context, where we are given a nested sequence $\\Lambda_1\\subset \\ldots \\subset \\Lambda_n$ of downward closed sets, instead of a single such set $\\Lambda$. Since the measure depends on $n$, the sets $(\\Lambda_n)_{n\\geq 1}$ are associated to different measures $(d\\sigma_n)_{n\\geq 1}$. Hence, recycling samples from the previous iterations of the adaptive algorithm is not as straighforward as in the case of standard least squares.", "\n\nAs a final remark, let us stress that the above results of Theorem \\[thm:theo10\\] and Theorem \\[thm:theo11\\] hold for general approximation spaces $\\mathbb{Y}_n$ other than polynomials.", "\n\nAdaptive Algorithms and Extensions {#sec:5}\n==================================\n\nSelection of Downward Closed Polynomial Spaces {#sec:5.1}\n----------------------------------------------\n\nThe interpolation and least-squares methods discussed in Section \\[sec:3\\] and Section \\[sec:4\\] allow us to construct polynomial approximations in $\\mathbb{V}_\\Lambda=V \\otimes \\mathbb{P}_\\Lambda$ of the map from its pointwise evaluations, for some given downward closed set $\\Lambda$. For these methods, we have given several convergence results in terms of error estimates either in $L^\\infty(U,V)$ or $L^2(U,V,d\\mu)$. In some cases, these estimates compare favorably with the error of best approximation $\\min_{\\widetilde u \\in \\mathbb{V}_\\Lambda} \\\|u-\\widetilde u\\\|$ measured in such norms.", "\n\nA central issue which still needs to be addressed is the choice of the downward closed set $\\Lambda$, so that this error of best approximation is well behaved, for a given map $u$. Ideally, for each given $n$, we would like to use the set $$\\Lambda_n=\\operatorname{argmin}_{\\Lambda\\in {\\cal D}_n}\\min_{\\widetilde u\\in \\mathbb{V}_{\\Lambda}} \\\|u-\\widetilde u\\\|,$$ where ${\\cal D}_n$ is the family of all downward closed sets $\\Lambda$ of cardinality $n$. However such sets $\\Lambda_n$ are not explicitely given to us, and in addition the resulting sequence $(\\Lambda_n)_{n\\geq 1}$ is generally not nested.", "\n\nConcrete selection strategies aim to produce “suboptimal yet good” nested sequences $(\\Lambda_n)_{n\\geq 1}$ different from the above. ", "Here, an important distinction should be made between [nonadaptive]{} and [adaptive]{} selection strategies.", "\n\nIn nonadaptive strategies, the selection of $\\Lambda_n$ is made in an a-priori manner, based on some available information on the given problem. ", "The results from Section \\[sec:2.3\\] show that, for relevant instances of solution maps associated to parametric PDEs, there exist nested sequences $(\\Lambda_n)_{n\\geq 1}$ of downward closed sets such that $\\#(\\Lambda_n)=n$ and $\\min_{\\widetilde u\\in \\mathbb{V}_{\\Lambda_n}} \\\|u-\\widetilde u\\\|$ decreases with a given convergence rate $n^{-s}$ as $n\\to \\infty$. In addition, these results provide constructive strategies for building the sets $\\Lambda_n$, since these sets are defined as the indices associated to the $n$ largest $\\widehat \\kappa_\\nu:=\\max_{\\widetilde \\nu\\geq \\nu} \\kappa_{\\widetilde \\nu}$ like in Theorem \\[thm:theoleg\\], or directly to the $n$ largest $\\kappa_\\nu$ like in Theorem \\[thm:theotaylor\\] and Theorem \\[thm:theoherm\\], and since the $\\kappa_{\\nu}$ are explicitely given numbers.", "\n\nIn the case where we build the polynomial approximation by interpolation, Theorem \\[thm:theointer\\] shows that a good choice of $\\Lambda_n$ is produced by taking $\\kappa_\\nu$ to be either $\\pi(\\nu)b^\\nu$ or $\\pi(\\nu) \\beta(\\nu)^2 b^\\nu$ where $b=(\\rho_j^{-1})_{j\\geq 1}$ is such that holds. ", "In the case where we build the polynomial approximation by least-squares methods, the various results from Section \\[sec:4\\] show that under suitable assumptions, the error is nearly as good as that of best approximation in $L^2(U,V, d\\mu)$ with respect to the relevant probability measure. ", "In the affine case, Theorem \\[thm:theoleg\\] shows that a good choice of $\\Lambda_n$ is produced by taking $\\kappa_\\nu$ to be $b^\\nu\\beta(\\nu)$ where $b=(\\rho_j^{-1})_{j\\geq 1}$ is such that holds. ", "In the lognormal case Theorem \\[thm:theoherm\\] shows that a good choice of $\\Lambda_n$ is produced by taking $\\kappa_\\nu$ to be given by where $b=(\\rho_j^{-1})_{j\\geq 1}$ is such that holds.", "\n\nLet us briefly discuss the complexity of identifying the downward closed set $\\Lambda_n$ associated to the $n$ largest $\\widehat \\kappa_\\nu$. For this purpose, we introduce for any downward closed set $\\Lambda$ its set of [neighbors]{} defined by $$N(\\Lambda):=\\{\\nu\\in {\\cal F}\\setminus \\Lambda \\mbox{ such that } \\Lambda\\cup\\{\\nu\\} \\mbox { is downward closed} \\}.$$ We may in principle define $\\Lambda_n=\\{\\nu^1,\\dots,\\nu^n\\}$ by the following induction.", "\n\n- Take $\\nu^1=0_{\\cal F}$ as the null multi-index.", "\n\n- Given $\\Lambda_k=\\{\\nu^1,\\dots,\\nu^k\\}$, choose a $\\nu^{k+1}$ maximizing $\\widehat \\kappa_\\nu$ over $\\nu\\in N(\\Lambda_k)$.\n\nIn the finite-dimensional case $d<\\infty$, we observe that $N(\\Lambda_k)$ is contained in the union of $N(\\Lambda_{k-1})$ with the set consisting of the indices $$\\nu^k+e_j, \\quad j=1,\\dots,d,$$ where $e_j$ is the Kroenecker sequence with $1$ at position $j$. As a consequence, since the values of the $\\widehat \\kappa_\\nu$ have already been computed for $\\nu\\in N(\\Lambda_{k-1})$, the step $k$ of the induction requires at most $d$ evaluations of $\\widehat \\kappa_\\nu$, and therefore the overall computation of $\\Lambda_n$ requires at most $nd$ evaluations.", "\n\nIn the infinite-dimensional case $d=\\infty$, the above procedure cannot be practically implemented, since the set of neighbors has infinite cardinality. ", "This difficulty can be circumvented by introducing a priority order among the variables, as done in the next definitions.", "\n\n\\[thm:defanchoredseq\\] A monotone nonincreasing positive sequence $(c_\\nu)_{\\nu\\in{\\cal F}}$ is said to be [anchored]{} if and only if $$l\\leq j \\implies c_{e_j} \\leq c_{e_l}.$$ A finite downward closed set $\\Lambda$ is said to be [anchored]{} if and only if $$e_j\\in \\Lambda \\quad {\\rm and}\\quad l\\leq j \\quad \\implies \\quad e_l\\in \\Lambda,$$ where $e_l$ and $e_j$ are the Kroenecker sequences with $1$ at position $l$ and $j$, respectively.", "\n\nObviously, if $(c_\\nu)_{\\nu\\in{\\cal F}}$ is anchored, one of the sets $\\Lambda_n$ corresponding to its $n$ largest values is anchored. ", "It is also readily seen that all sequences $(\\widehat \\kappa_\\nu)_{\\nu\\in{\\cal F}}$ that are used in Theorems \\[thm:theotaylor\\], \\[thm:theoleg\\], \\[thm:theoherm\\] or \\[thm:theointer\\] for the construction of $\\Lambda_n$ are anchored, provided that the sequence $b=(\\rho_j^{-1})_{j\\geq 1}$ is monotone nonincreasing. ", "This is always the case up to a rearrangement of the variables. ", "For any anchored set $\\Lambda$, we introduce the set of its [anchored neighbors]{} defined by $$\\widetilde N(\\Lambda):=\\{\\nu\\in N(\\Lambda)\\; : \\; \n\\nu_j=0\\;\\; {\\rm if}\\;\\; j >j(\\Lambda)+1\\},\n\\label{eq:redneighbors}$$ where $$j(\\Lambda):=\\max\\{j\\; : \\; \\nu_j>0\\; \\mbox{for some}\\; \\nu\\in \\Lambda\\}.$$ We may thus modify in the following way the above induction procedure.", "\n\n- Take $\\nu^1=0_{\\cal F}$ as the null multi-index.", "\n\n- Given $\\Lambda_k=\\{\\nu^1,\\dots,\\nu^k\\}$, choose a $\\nu^{k+1}$ maximizing $\\widehat \\kappa_\\nu$ over $\\nu\\in \\widetilde N(\\Lambda_k)$.\n\nThis procedure is now feasible in infinite dimension. ", "At each step $k$ the number of active variables is limited by $j(\\Lambda_{k}) \\leq k-1$, and the total number of evaluations of $\\widehat \\kappa_\\nu$ needed to construct $\\Lambda_n$ does not exceed $1+2+\\dots +(n-1)\\leq n^2/2$.\n\nIn adaptive strategies the sets $\\Lambda_n$ are not a-priori selected, but instead they are built in a recursive way, based on earlier computations. ", "For instance, one uses the previous set $\\Lambda_{n-1}$ and the computed polynomial approximation $u_{\\Lambda_{n-1}}$ to construct $\\Lambda_n$. If we impose that the sets $\\Lambda_n$ are nested, this means that we should select an index $\\nu^n\\notin \\Lambda_{n-1}$ such that $$\\Lambda_n:=\\Lambda_{n-1}\\cup\\{\\nu^n\\}.$$ The choice of the new index $\\nu^n$ is further limited to $N(\\Lambda_{n-1})$ if we impose that the constructed sets $\\Lambda_n$ are downward closed, or to $\\widetilde N(\\Lambda_{n-1})$ if we impose that these sets are anchored.", "\n\nAdaptive methods are known to sometimes perform significantly better than their nonadaptive counterpart. ", "In the present context, this is due to the fact that the a-priori choices of $\\Lambda_n$ based on the sequences $\\kappa_\\nu$ may fail to be optimal. ", "In particular, the guaranteed rate $n^{-s}$ based on such choices could be pessimistic, and better rates could be obtained by other choices. ", "However, convergence analysis of adaptive methods is usually more delicate. ", "We next give examples of possible adaptive strategies in the interpolation and least-squares frameworks.", "\n\nAdaptive Selection for Interpolation {#sec:5.2}\n------------------------------------\n\nWe first consider polynomial approximations obtained by interpolation as discussed in Section \\[sec:3\\]. ", "The hierarchical form $$I_\\Lambda u= \\sum_{\\nu\\in \\Lambda}\\alpha_\\nu B_\\nu,\n\\label{eq:hierexp}$$ may formally be viewed as a truncation of the expansion of $u$ in the hierarchical basis $$\\sum_{\\nu\\in {\\cal F}}\\alpha_\\nu B_\\nu,$$ which however may not always be converging, in contrast to the series discussed in Section \\[sec:2\\]. ", "Nevertheless, we could in principle take the same view, and use for $\\Lambda_n$ the set of indices corresponding to the $n$ largest terms of measured in some given metric $L^p(U,V,d\\mu)$. This amounts in choosing the indices of the $n$ largest $w_\\nu \\\|\\alpha_\\nu\\\|_V$, where the weight $w_\\nu$ is given by $$w_\\nu:=\\\|B_\\nu\\\|_{L^p(U,d\\mu)}.$$ This weight is easily computable when $d\\mu$ is a tensor product measure, such as the uniform measure. ", "In the case where $p=\\infty$ and if we use the Leja sequence, we know that $\\\|B_\\nu\\\|_{L^\\infty(U)}=1$ and therefore this amounts to choosing the largest $\\\|\\alpha_\\nu\\\|_V$.\n\nThis selection strategy is not practially feasible since we cannot afford this exhaustive search over ${\\cal F}$. However, it naturally suggests the following adaptive greedy algorithm, which has been proposed in [@CCS1].", "\n\n- Initialize $\\Lambda_1:=\\{0_{{\\cal F}}\\}$ with the null multi-index.", "\n\n- Assuming that $\\Lambda_{n-1}$ has been selected and that the $(\\alpha_\\nu)_{\\nu\\in \\Lambda_{n-1}}$ have been computed, compute the $\\alpha_\\nu$ for $\\nu\\in N(\\Lambda_{n-1})$.\n\n- Set $$\\nu^n:=\\operatorname{argmax}\\{ w_\\nu\\\|\\alpha_\\nu\\\|_V\\; : \\; \\nu\\in N(\\Lambda_{n-1})\\}.", "\n \\label{eq:greedy}$$\n\n- Define $\\Lambda_{n}:=\\Lambda_{n-1} \\cup \\{\\nu^n\\}$.\n\nIn the case where $p=\\infty$ and if we use the Leja sequence, this strategy amounts in picking the index $\\nu^n$ that maximizes the interpolation error $\\\|u(y_{\\nu}) - I_{\\Lambda_{n-1}}u(y_{\\nu})\\\|_V$ among all $\\nu$ in $N(\\Lambda_{n-1})$. By the same considerations as previously discussed for the a-priori selection of $\\Lambda_n$, we find that in the finite-dimensional case, the above greedy algorithm requires at most $dn$ evaluation after $n$ steps. ", "When working with infinitely many variables $(y_j)_{j\\geq 1}$, we replace the infinite set $N(\\Lambda_n)$ in the algorithm by the finite set of anchored neighbors $\\widetilde N(\\Lambda_n)$ defined by . ", "Running $n$ steps of the resulting greedy algorithm requires at most $n^2/2$ evaluations.", "\n\nA very similar algorithm has been proposed in [@GG] in the different context of adaptive quadratures, that is, for approximating the integral of $u$ over the domain $U$ rather than $u$ itself. ", "In that case, the natural choice is to pick the new index $\\nu^n$ that maximizes $\|\\int_U \\Delta_\\nu u \\, d\\mu\|$ over $N(\\Lambda_n)$ or $\\widetilde N(\\Lambda_n)$.\n\nThe main defect of the above greedy algorithm is that it may fail to converge, even if there exist sequences $(\\Lambda_n)_{n\\geq 1}$ such that $I_{\\Lambda_n} u$ converges toward $u$. Indeed, if $\\Delta_\\nu u=0$ for a certain $\\nu$, then no index $\\widetilde \\nu\\geq \\nu$ will ever be selected by the algorithm. ", "As an example, if $u$ is of the form $$u(y)=u_1(y_1)u_2(y_2),$$ where $u_1$ and $u_2$ are nonpolynomial smooth functions such that $u_2(t_0)=u_2(t_1)$, then the algorithm could select sets $\\Lambda_n$ with indices $\\nu=(k,0)$ for $k=0,\\dots,n-1$, since the interpolation error at the point $(t_k,t_1)$ vanishes.", "\n\nOne way to avoid this problem is to adopt a more conservative selection rule which ensures that all of ${\\cal F}$ is explored, by alternatively using the rule , or picking the multi-index $\\nu\\in\\widetilde N(\\Lambda_n)$ which has appeared at the earliest stage in the neighbors of the previous sets $\\Lambda_k$. This is summarized by the following algorithm.", "\n\n- Initialize $\\Lambda_1:=\\{0_{\\cal F}\\}$ with the null multi-index.", "\n\n- Assuming that $\\Lambda_{n-1}$ has been selected and that the $(\\alpha_\\nu)_{\\nu\\in \\Lambda_{n-1}}$ have been computed, compute the $\\alpha_\\nu$ for $\\nu\\in \\widetilde N(\\Lambda_{n-1})$.\n\n- If $n$ is even, set $$\\nu^n:=\\operatorname{argmax}\\{ w_\\nu \\\|\\alpha_\\nu\\\|_V\\; : \\; \\nu\\in \\widetilde N(\\Lambda_{n-1})\\}.", "\n \\label{eq:greedy_even}$$\n\n- If $n$ is odd, set $$\\nu^{n}:={\\rm argmin} \\{k(\\nu)\\; : \\; \\nu\\in \\widetilde N(\\Lambda_{n-1})\\}, \\quad k(\\nu):=\\min\\{k\\; : \\; \\nu\\in \\widetilde N(\\Lambda_k)\\}.$$\n\n- Define $\\Lambda_{n}:=\\Lambda_{n-1} \\cup \\{\\nu^n\\}$.\n\nEven with such modifications, the convergence of the interpolation error produced by this algorithm is not generally guaranteed. ", "Understanding which additional assumptions on $u$ ensure convergence at some given rate, for a given univariate sequence $T$ such as Leja points, is an open problem.", "\n\nAnother variant to the above algorithms consists in choosing at the iteration $k$ more than one new index at a time within $N(\\Lambda_{k-1})$ or $ \\widetilde N(\\Lambda_{k-1})$. In this case, we have $n_k:=\\#(\\Lambda_k)\\geq k$. For example we may choose the smallest subset of indices that retains a fixed portion of the quantity $\\sum_{\\nu \\in \\Lambda_{k-1}} w_\\nu\\\|\\alpha_\\nu\\\|_V$. This type of modification turns out to be particularly relevant in the least-squares setting discussed in the next section.", "\n\nAdaptive Selection for Least Squares {#sec:5.3}\n------------------------------------\n\nIn this section we describe adaptive selections in polynomial spaces, for the least-squares methods that have been discussed in Section \\[sec:4\\]. ", "We focus on adaptive selection algorithms based on the standard (unweighted) least-squares method.", "\n\nAs a preliminary observation, it turns out that the most efficient available algorithms for adaptive selection of multi-indices might require the selection of more than one index at a time. ", "Therefore, we adopt the notation that $n_k:=\\#(\\Lambda_k)\\geq k$, where the index $k$ denotes the iteration in the adaptive algorithm.", "\n\nAs discussed in Section \\[sec:4\\], stability and accuracy of the least-squares approximation is ensured under suitable conditions between the number of samples and the dimension of the approximation space, see e.g. condition . ", "Hence, in the development of reliable iterative algorithms, such conditions need to be satisfied at each iteration. ", "When $d\\mu$ is the measure with shape parameters $\\theta_1,\\theta_2$, condition takes the form of $$\\label{eq:condm_adaptive_ls}\n\\dfrac{m_k}{\\ln m_k} \\geq \\kappa \\\n n_k^{s},$$ where $m_k$ denotes the number of samples at iteration $k$, and $$s=\n\\left\\{\n\\begin{array}{ll}\n\\ln 3 /\\ln 2, \n& \n\\quad\n\\textrm{ if } \\ \\theta_1=\\theta_2=-\\frac12, \n\\\\\n{2\\max\\{\\theta_1,\\theta_2 \\} +2}, \n&\n\\quad \n\\textrm{ if } \\ \\theta_1,\\theta_2\\in\\mathbb{N}_0. ", "\n\\end{array}\n\\right.$$ Since $n_k$ increases with $k$, the minimal number of samples $m_k$ that satisfies has to increase as well at each iteration. ", "At this point, many different strategies can be envisaged for progressively increasing $m_k$ such that remains satisfied at each iteration $k$. For example, one can double the number of samples by choosing $m_{k}=2 m_{k-1}$ whenever is broken, and keep $m_k=m_{k-1}$ otherwise. ", "The sole prescription for applying Corollary \\[thm:corollary\\_std\\_ls\\] is that the samples are independent and drawn from $d\\mu$. Since all the samples at all iterations are drawn from the same measure $d\\mu$, at the $k$th iteration, where $m_k$ samples are needed, it is possible to use $m_{k-1}$ samples from the previous iterations, thus generating only $m_{k}-m_{k-1}$ new samples.", "\n\nWe may now present a first adaptive algorithm based on standard least squares.", "\n\n- Initialize $\\Lambda_1:=\\{0_{\\cal F}\\}$ with the null multi-index.", "\n\n- Assuming that $\\Lambda_{k-1}$ has been selected, compute the least-squares approximation $$u_L=\\sum_{\\nu \\in \\Lambda_{k-1} \\cup N(\\Lambda_{k-1}) } c_\\nu \\phi_\\nu$$ of $u$ in $\\mathbb{V}_{\\Lambda_{k-1}\\cup N(\\Lambda_{k-1})}$, using a number of samples $m_k$ that satisfies condition with $n_k= \n \\#(\\Lambda_{k-1}\\cup N(\\Lambda_{k-1}))$.\n\n- Set $$\\nu^k:=\\operatorname{argmax}_{ \\nu\\in N(\\Lambda_{k-1})} \| c_\\nu \|^2.", "\n \\label{eq:greedy_ls}$$\n\n- Define $\\Lambda_{k}:=\\Lambda_{k-1} \\cup \\{\\nu^k\\}$.\n\nSimilarly to the previously discussed interpolation algorithms, in the case of infinitely many variables $(y_j)_{j\\geq 1}$ the set $N(\\Lambda_k)$ is infinite and should be replaced by the finite set of anchored neighbors $\\widetilde N(\\Lambda_k)$ defined by . ", "As for interpolation, we may define a more conservative version of this algorithm in order to ensure that all of ${\\cal F}$ is explored. ", "For example, when $k$ is even, we define $\\nu^{k}$ according to , and when $k$ is odd we pick for $\\nu^k$ the multi-index $\\nu\\in\\widetilde N(\\Lambda_k)$ which has appeared at the earliest stage in the neighbors of the previous sets $\\Lambda_k$. The resulting algorithm is very similar to the one presented for interpolation, with obvious modifications due to the use of least squares.", "\n\nAs announced at the beginning, it can be advantageous to select more than one index at a time from $\\widetilde{N}(\\Lambda_{k-1})$, at each iteration $k$ of the adaptive algorithm. ", "For describing the multiple selection of indices from $\\widetilde{N}(\\Lambda_{k-1})$, we introduce the so-called [bulk chasing]{} procedure. ", "Given a finite set $R \\subseteq \\widetilde{N}(\\Lambda_{k-1})$, a nonnegative function ${\\cal E}:R\\to\\mathbb{R}$ and a parameter $\\alpha \\in (0,1]$, we define the procedure $\\textrm{bulk}:= \\textrm{bulk}(R,{\\cal E},\\alpha)$ that computes a set $F\\subseteq R$ of minimal positive cardinality such that $$\\sum_{\\nu \\in F} {\\cal E}(\\nu) \\geq \\alpha \\sum_{\\nu \\in R} {\\cal E}(\\nu).$$ A possible choice for the function ${\\cal E}$ is $${\\cal E}(\\nu)={\\cal E}_L(\\nu):=\|c_\\nu\|^2, \\quad \\nu \\in R,$$ where $c_\\nu$ is given from an available least-squares estimator $$u_L=\\sum_{\\nu \\in \\Lambda} c_\\nu \\phi_\\nu,$$ that has been already computed on any downward closed set $R \\subset \\Lambda\\subseteq \\Lambda_{k-1}\\cup \\widetilde{N}(\\Lambda_{k-1})$. Another choice for ${\\cal E}$ is $${\\cal E}(\\nu)={\\cal E}_M( \\nu):= \n\\langle \\phi_{ \\nu}, \nu - \\widetilde{u}_L\n \\rangle_{m_{k-1}}, \n\\quad \\nu \\in R,$$ where $\\widetilde{u}_L$ is the truncation to $\\Lambda_{k-1}$ of a least-squares estimator $u_L= \\sum_{ \\nu \\in \\Lambda} c_{\\nu} \\phi_{\\nu}$ that has been already computed on any downward closed set $\\Lambda_{k-1} \\subset \\Lambda\\subseteq \\Lambda_{k-1} \\cup \\widetilde{N}(\\Lambda_{k-1})$, using a number of samples $m_{k-1}$ that satisfies condition with $n_k=\\#(\\Lambda)$. The discrete norm in ${\\cal E}_M(\\nu)$ uses the same $m_{k-1}$ evaluations of $u$ that have been used to compute the least-squares approximation $u_L$ on $\\Lambda$.\n\nBoth ${\\cal E}_L(\\nu)$ and ${\\cal E}_M(\\nu)$ should be viewed as estimators of the coefficient $\\langle u, \\phi_\\nu \\rangle$. The estimator ${\\cal E}_M(\\nu)$ is of Monte Carlo type and computationally cheap to calculate. ", "Combined use of the two estimators leads to the next algorithm for greedy selection with bulk chasing, that has been proposed in [@M2013].", "\n\n- Initialize $\\Lambda_1:=\\{0_{\\cal F}\\}$ with the null multi-index, and choose $\\alpha_1,\\alpha_2\\in(0,1]$.\n\n- Assuming that $\\Lambda_{k-1}$ has been selected, set $$F_1=\\textrm{bulk}(\\widetilde{N}(\\Lambda_{k-1}),\n {\\cal E}_M\n ,\\alpha_1 ),\n \\label{eq:greedy_ls_dorfler1}$$ where ${\\cal E}_M$ uses the least-squares approximation $u_L=\\sum_{\\nu \\in \\Lambda} c_\\nu \\phi_\\nu $ of $u$ in $\\mathbb{V}_{\\Lambda}$ that has been calculated at iteration $k-1$ on a downward closed set $ \\Lambda_{k-1} \\subset \\Lambda\\subseteq \\Lambda_{k-1} \\cup \\widetilde{N}(\\Lambda_{k-1})$ using a number of samples $m_{k-1}$ that satisfies with $n_k= \\#(\\Lambda)$.\n\n- Compute the least-squares approximation $$u_L=\\sum_{\\nu \\in \\Lambda_{k-1} \\cup F_1} c_\\nu \\phi_\\nu \n \\label{eq:computation_LS_greedy}$$ of $u$ on $\\mathbb{V}_{\\Lambda_{k-1} \\cup F_1}$ using a number of samples $m_{k}$ that satisfies with $n_k=\\#(\\Lambda_{k-1}\\cup F_1)$.\n\n- Set $$F_2=\\textrm{bulk}(F_1,\n {\\cal E}_L\n ,\\alpha_2 ), \n \\label{eq:greedy_ls_dorfler2}$$ where ${\\cal E}_L$ uses the least-squares approximation $u_L$ computed on $\\Lambda_{k-1}\\cup F_1$.\n\n- Define $\\Lambda_{k}=\\Lambda_{k-1} \\cup F_2$.\n\nThe set $\\widetilde{N}(\\Lambda_{k-1})$ can be large, and might contain many indices that are associated to small coefficients. ", "Discarding these indices is important in order to avoid unnecessary computational burden in the calculation of the least-squares approximation. ", "The purpose of the bulk procedure is to perform a preliminary selection of a set $F_1 \\subseteq \\widetilde{N}(\\Lambda_{k-1})$ of indices, using the cheap estimator ${\\cal E}_M$. At iteration $k$, ${\\cal E}_M$ in uses the estimator computed in at iteration $k-1$ and truncated to $\\Lambda_{k-1}$. Afterwards, at iteration $k$, the least-squares approximation in is calculated on $\\Lambda_{k-1}\\cup F_1$, using a number of samples $m_k$ which satisfies condition , with $n_k=\\#(\\Lambda_{k-1}\\cup F_1)$. The second bulk procedure selects a set $F_2$ of indices from $F_1$, using the more accurate estimator ${\\cal E}_L$. The convergence rate of the adaptive algorithm depends on the values given to the parameters $\\alpha_1$ and $\\alpha_2$.\n\nFinally we mention some open issues related to the development of adaptive algorithms using the weighted least-squares methods discussed in Section \\[sec:4\\], instead of standard least squares. ", "In principle the same algorithms described above can be used with the weighted least-squares estimator $u_W$ replacing the standard least-squares estimator $u_L$, provided that, at each iteration $k$, the number of samples $m_k$ satisfies $$\\dfrac{m_k}{\\ln m_k} \\geq \\kappa \\\n n_k,$$ and that the samples are drawn from the optimal measure, see Theorem \\[thm:theo11\\]. ", "This ensures that at each iteration $k$ of the adaptive algorithm, the weighted least-squares approximation remains stable and accurate. ", "However, no guarantees on stability and accuracy are ensured if the above conditions are not met, for example when the samples from previous iterations are recycled.", "\n\nApproximation in Downward Closed Spaces: beyond Polynomials {#sec:5.4}\n-----------------------------------------------------------\n\nThe concept of downward closed approximation spaces can be generalized beyond the polynomial setting. ", "We start from a countable index set $S$ equipped with a partial order $\\leq$, and assume that there exists a root index $0_S\\in S$ such that $0_S \\leq \\sigma$ for all $\\sigma\\in S$. We assume that $(B_\\sigma)_{\\sigma\\in S}$ is a basis of functions defined on $[-1,1]$ such that $B_{0_S} \\equiv 1$. We then define by tensorization a basis of functions on $U=[-1,1]^d$ when $d<\\infty$, or $U=[-1,1]^{{\\mathbb N}}$ in the case of infinitely many variables, according to $$B_\\nu(y)=\\prod_{j\\geq 1} B_{\\nu_j} (y_j), \\quad \\nu:=(\\nu_j)_{j\\geq 1}\\in {\\cal F},$$ where ${\\cal F}:=S^d$ in the case $d<\\infty$, or ${\\cal F}=\\ell^0({{\\mathbb N}},S)$, i.e.* the set of finitely supported sequences, in the case $d=\\mathbb{N}$.\n\nThe set ${\\cal F}$ is equipped with a partial order induced by its univariate counterpart: $\\nu\\leq \\widetilde \\nu$ if and only if $\\nu_j\\leq \\widetilde \\nu_j$ for all $j\\geq 1$. We may then define downward closed sets $\\Lambda\\subset {\\cal F}$ in the same way as in Definition \\[thm:defdc\\] which corresponds to the particular case $S=\\mathbb{N}$. We then define the associated downward closed approximation space by $$\\mathbb{V}_\\Lambda:=V\\otimes \\mathbb{B}_\\Lambda, \\quad \\mathbb{B}_\\Lambda:={\\rm span}\\{B_\\nu\\, : \\, \\nu\\in \\Lambda\\},$$ that is the space of functions of the form $\\sum_{\\nu\\in \\Lambda} u_\\nu B_\\nu$ with $u_\\nu\\in V$.\n\nGiven a sequence $T=(t_\\sigma)_{\\sigma\\in S}$ of pairwise distinct points we say that the basis $(B_\\sigma)_{\\sigma\\in S}$ is hierarchical when it satisfies $$B_\\sigma(t_\\sigma)=1 \\ {\\rm and} \\ B_\\sigma(t_{\\widetilde\\sigma})=0 \\ {\\rm if} \\ \\widetilde \\sigma \\leq \\sigma \\ {\\rm and} \\ \\widetilde \\sigma \\neq \\sigma.$$ We also define the tensorized grid $$y_\\nu:=(t_{\\nu_j})_{j\\geq 1}\\in U.$$ Then, if $\\Lambda\\subset {\\cal F}$ is a downward closed set, we may define an interpolation operator $I_\\Lambda$ onto $V_\\Lambda$ associated to the grid $$\\Gamma_\\Lambda:=\\{y_\\nu \\; : \\; \\nu\\in \\Lambda\\}.$$ In a similar manner as in the polynomial case, this operator is defined inductively by $$I_\\Lambda u:=I_{\\widetilde \\Lambda} u+\\alpha_{\\nu} B_\\nu,\\quad \\alpha_\\nu:=\\alpha_\\nu(u)=u(y_\\nu)-I_{\\widetilde \\Lambda} u(y_\\nu),$$ where $\\nu\\notin\\widetilde \\Lambda$ and $\\widetilde\\Lambda$ is any downward closed set such that $\\Lambda=\\widetilde\\Lambda\\cup\\{\\nu\\}$. We initialize this computation with $\\Lambda_1=\\{0_{\\cal F}\\}$, where $0_{\\cal F}$ is the null multi-index, by defining $I_{\\Lambda_1}u$ as the constant function with value $u(y_{0_{\\cal F}})$.\n\nExamples of relevant hierarchical systems include the classical piecewise linear hierarchical basis functions. ", "In this case the set $S$ is defined by $$S = \\{\\lambda_{-1},\\lambda_1,(0,0)\\} \\cup \\left\\{(j,k)\\; : \\; -2^{j-1}\\leq k\\leq 2^{j-1}-1,\\; j=1,2,\\dots \\right\\}$$ equipped with the partial order $\\lambda_{-1} \\leq \\lambda_{1} \\leq (0,0)$ and $$(j,k)\\leq (j+1,2k), \\quad\\quad\n(j,k)\\leq (j+1,2k+1), \n\\quad \\quad (j,k) \\in S.$$ The set $S$ is thus a binary tree where $\\lambda_{-1}$ is the root node, $(0,0)$ is a child of $\\lambda_1$ which is itself a child of $\\lambda_{-1}$, every node $(j,k)$ has two children $(j+1,2k)$ and $(j+1,2k+1)$, and the relation $\\widetilde \\lambda \\leq \\lambda$ means that $\\widetilde \\lambda$ is a parent of $\\lambda$. The index $j$ corresponds to the level of refinement, i.e. the depth of the node in the binary tree.", "\n\nWe associate with $S$ the sequence $$T := \\{t_{\\lambda_{-1}},t_{\\lambda_1},t_{(0,0)}\\} \\cup \\left\\{t_{(j,k)} := \\frac {2k+1}{2^j}: (j,k)\\in S, j\\geq1 \\right\\} ,$$ where $t_{\\lambda_{-1}}=-1$, $t_{\\lambda_1}=1$ and $t_{(0,0)}=0$. The hierarchical basis of piecewise linear functions defined over $[-1,1]$ is then given by $$B_{\\lambda_{-1}} \\equiv 1,\\quad \nB_{\\lambda_{1}} (t) = \\frac {1+t}{2},\\quad\nB_{(j,k)} (t) = H(2^j(t-t_{(j,k)})),\\quad \n(j,k) \\in S,$$ where $${H}(t):=\\max\\{0,1-\|t\|\\},$$ is the usual hat function. ", "In dimension $d=1$, the hierarchical interpolation amounts in the following steps: start by approximating $f$ with the constant function equal to $f(-1)$, then with the affine function that coincides with $f$ at $-1$ and $1$, then with the piecewise affine function that coincides with $f$ at $-1$, $0$ and $-1$; afterwards refine the approximation in further steps by interpolating $f$ at the midpoint of an interval between two adjacents interpolation points.", "\n\nOther relevant examples include piecewise polynomials, hierarchical basis functions, and more general interpolatory wavelets, see [@Co] for a survey.", "\n\n[99.]{}", "\n\nBachmayr, M., Cohen, A., Migliorati, G.: Sparse polynomial approximation of parametric elliptic PDEs. ", "Part I: affine coefficients. ", "to appear in ESAIM:M2AN\n\nBachmayr, M., Cohen, A., DeVore, R. Migliorati, G.: Sparse polynomial approximation of parametric elliptic PDEs. ", "Part II: lognormal coefficients. 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", "Theory 189, 137–159 (2015)\n\nMigliorati, G., Nobile, F., von Schwerin, E., Tempone, R.: Analysis of discrete $L^2$ projection on polynomial spaces with random evaluations. ", "Found. ", "Comput. ", "Math. ", "14, 419–456 (2014)\n\nMigliorati, G., Nobile, F., Tempone, R.: Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points. ", "J. Multivar. ", "Analysis 142, 167–182 (2015)\n\nMigliorati, G.: Adaptive Polynomial Approximation by means of random discrete least squares. ", "In: A. Abdulle, S. Deparis, D. Kressner, F. Nobile, M. Picasso (eds.) [", "N]{}umerical [M]{}athematics and [A]{}dvanced [A]{}pplications - [ENUMATH]{} 2013, pp. ", "547–554. ", "Springer, (2015)\n\nNocedal, J., Wright, S.J.: Numerical optimization. ", "Springer, (2006)\n\nNovak, E., Wozniakowski, H.: Tractability of Multivariate Problems - Volume II: Standard Information for Functionals. ", "EMS Tracts in Mathematics Vol. ", "12, (2010)\n\nStuart, A.M.: Inverse problems: a Bayesian perspective. ", "Acta Numer. ", "19, 451–559 (2010)\n\nTarantola, A.: Inverse problem theory and methods for model parameter estimation. ", "SIAM, (2005)\n\nTropp, J.: User friendly tail bounds for sums of random matrices. ", "Found. ", "Comput. ", "Math. ", "12, 389–434 (2012)\n\n[^1]: Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu 75005, Paris, France. ", "email: cohen@ljll.math.upmc.fr\n\n[^2]: Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu 75005, Paris, France. ", "email: migliorati@ljll.math.upmc.fr\n\n[^3]: This research is supported by Institut Universitaire de France and the ERC AdV project BREAD.", "\n" ]	{ "pile_set_name": "ArXiv" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0.008130081300813009, 0, 0, 0.0036231884057971015, 0, 0, 0.02040816326530612, 0, 0.0045662100456621, 0.0017857142857142857, 0.002912621359223301, 0, 0, 0, 0, 0.007211538461538462, 0.004672897196261682, 0, 0, 0, 0.012987012987012988, 0, 0, 0.003663003663003663, 0, 0, 0, 0, 0.012195121951219513, 0, 0, 0, 0.004528301886792453, 0, 0.005649717514124294, 0.006557377049180328, 0.004073319755600814, 0, 0.0028368794326241137, 0, 0.008426966292134831, 0, 0.02702702702702703, 0, 0, 0.008426966292134831, 0.00528169014084507, 0, 0, 0.00980392156862745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.002898550724637681, 0, 0, 0.008658008658008658, 0.002976190476190476, 0, 0, 0.0007385524372230429, 0, 0, 0.0019193857965451055, 0.004527813712807244, 0.007407407407407408, 0, 0.0038910505836575876, 0.003663003663003663, 0, 0.008130081300813009, 0.004048582995951417, 0.0020491803278688526, 0.017857142857142856, 0.006731488406881077, 0.011299435028248588, 0.004694835680751174, 0.024154589371980676, 0, 0.0045045045045045045, 0, 0.007246376811594203, 0, 0.015384615384615385, 0.0011001100110011, 0.0045662100456621, 0.013953488372093023, 0, 0.012195121951219513, 0, 0.0020222446916076846, 0.01020408163265306, 0, 0, 0.003745318352059925, 0.00484027105517909, 0.0013386880856760374, 0.002881844380403458, 0, 0, 0.002621231979030144, 0, 0.00676818950930626, 0.008053055423969682, 0.005291005291005291, 0.002304147465437788, 0.0017825311942959, 0, 0.004314994606256742, 0.003401360544217687, 0.009009009009009009, 0, 0.0036429872495446266, 0.004415011037527594, 0.0030211480362537764, 0.004761904761904762, 0.006944444444444444, 0.00303951367781155, 0, 0.0018115942028985507, 0, 0, 0.0035335689045936395, 0.0034602076124567475, 0.0013123359580052493, 0, 0, 0, 0.0021141649048625794, 0.006486486486486486, 0, 0.00684931506849315, 0.00101010101010101, 0.0011160714285714285, 0, 0, 0.005555555555555556, 0.005597014925373134, 0.005593288054334798, 0, 0, 0.004056795131845842, 0, 0.009569377990430622, 0, 0.005714285714285714, 0.003424657534246575, 0, 0.004624277456647399, 0.005597014925373134, 0.007462686567164179, 0.021505376344086023, 0.0016778523489932886, 0.004095563139931741, 0.0036310820624546117, 0, 0.015503875968992248, 0.0035046728971962616, 0, 0.006097560975609756, 0.002881844380403458, 0.0035211267605633804, 0, 0.0033112582781456954, 0.0111731843575419, 0.002320185614849188, 0, 0.014705882352941176, 0, 0, 0, 0, 0.0026595744680851063, 0.008264462809917356, 0.005434782608695652, 0.02702702702702703, 0, 0.005550416281221091, 0.0038022813688212928, 0.005420054200542005, 0, 0.0018656716417910447, 0.007246376811594203, 0, 0, 0, 0.022222222222222223, 0.017543859649122806, 0.004739336492890996, 0, 0.002544529262086514, 0, 0.002, 0, 0, 0.0033444816053511705, 0, 0, 0, 0.010869565217391304, 0, 0, 0, 0, 0, 0.0012755102040816326, 0.0033003300330033004, 0, 0, 0, 0.0012376237623762376, 0.006802721088435374, 0, 0.005050505050505051, 0, 0.002173913043478261, 0, 0.001451378809869376, 0, 0, 0.004464285714285714, 0, 0, 0, 0.008064516129032258, 0, 0, 0.005291005291005291, 0.001834862385321101, 0, 0, 0, 0, 0, 0, 0.0030120481927710845, 0, 0.005050505050505051, 0, 0.007168458781362007, 0, 0, 0, 0.005128205128205128, 0, 0.003215434083601286, 0.002777777777777778, 0, 0.0031446540880503146, 0.007792207792207792, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.006666666666666667, 0, 0, 0, 0, 0, 0, 0.0072992700729927005, 0, 0, 0, 0.006658595641646489, 0.007246376811594203, 0.006065200909780136, 0, 0.0010672358591248667, 0, 0, 0, 0, 0.003816793893129771, 0.008021390374331552, 0.0038314176245210726, 0, 0.006622516556291391, 0, 0.009615384615384616, 0, 0.028985507246376812, 0, 0.02702702702702703, 0.021621621621621623, 0.09090909090909091, 0.006993006993006993, 0.09090909090909091, 0.015503875968992248, 0.0196078431372549, 0.023809523809523808, 0, 0, 0, 0.020134228187919462, 0.1111111111111111, 0, 0.02631578947368421, 0.008130081300813009, 0, 0, 0, 0.020833333333333332, 0.07142857142857142, 0.014388489208633094, 0, 0, 0.011834319526627219, 0, 0, 0.014705882352941176, 0.008130081300813009, 0, 0, 0.01694915254237288, 0.07142857142857142, 0, 0.05, 0.019867549668874173, 0, 0, 0, 0, 0.02127659574468085, 0, 0.01639344262295082, 0, 0, 0, 0.006756756756756757, 0.011363636363636364, 0.018691588785046728, 0.02912621359223301, 0, 0.00625, 0.09090909090909091, 0.017142857142857144, 0, 0, 0, 0.0053475935828877, 0.07692307692307693, 0, 0.07042253521126761, 0.022988505747126436, 0, 0.043478260869565216, 0.014705882352941176, 0.03225806451612903, 0.014705882352941176, 0.07142857142857142, 0.009615384615384616, 0.0125, 0, 0, 0, 0.0379746835443038, 0.041666666666666664, 0.022058823529411766, 0 ]	0.006212	5
[ "[Involvement of veratridine-induced increase of reverse Na(+)/Ca(2+) exchange current in intracellular Ca(2+) overload and extension of action potential duration in rabbit ventricular myocytes].", "\nThe objectives of this study were to investigate the effects of veratridine (VER) on persistent sodium current (I(Na.", "P)), Na(+)/Ca(2+) exchange current (I(NCX)), calcium transients and the action potential (AP) in rabbit ventricular myocytes, and to explore the mechanism in intracellular calcium overload and myocardial contraction enhancement by using whole-cell patch clamp recording technique, visual motion edge detection system, intracellular calcium measurement system and multi-channel physiological signal acquisition and processing system. ", "The results showed that I(Na.", "P) and reverse I(NCX) in ventricular myocytes were obviously increased after giving 10, 20 μmol/L VER, with the current density of I(Na.", "P) increasing from (-0.22 ± 0.12) to (-0.61 ± 0.13) and (-2.15 ± 0.14) pA/pF (P < 0.01, n = 10) at -20 mV, and that of reverse I(NCX) increasing from (1.62 ± 0.12) to (2.19 ± 0.09) and (2.58 ± 0.11) pA/pF (P < 0.05, n = 10) at +50 mV. After adding 4 μmol/L tetrodotoxin (TTX), current density of I(Na.", "P) and reverse I(NCX) returned to (-0.07 ± 0.14) and (1.69 ± 0.15) pA/pF (P < 0.05, n = 10). ", "Another specific blocker of I(Na.", "P), ranolazine (RAN), could obviously inhibit VER-increased I(Na.", "P) and reverse I(NCX). ", "After giving 2.5 μmol/L VER, the maximal contraction rate of ventricular myocytes increased from (-0.91 ± 0.29) to (-1.53 ± 0.29) μm/s (P < 0.01, n = 7), the amplitude of contraction increased from (0.10 ± 0.04) to (0.16 ± 0.04) μm (P < 0.05, n = 7), and the baseline of calcium transients (diastolic calcium concentration) increased from (1.21 ± 0.08) to (1.37 ± 0.12) (P < 0.05, n = 7). ", "After adding 2 μmol/L TTX, the maximal contraction rate and amplitude of ventricular myocytes decreased to (-0.86 ± 0.24) μm/s and (0.09 ± 0.03) μm (P < 0.01, n = 7) respectively. ", "And the baseline of calcium transients reduced to (1.17 ± 0.09) (P < 0.05, n = 7). ", "VER (20 μmol/L) could extend action potential duration at 50% repolarization (APD(50)) and at 90% repolarization (APD(90)) in ventricular myocytes from (123.18 ± 23.70) to (271.90 ± 32.81) and from (146.94 ± 24.15) to (429.79 ± 32.04) ms (P < 0.01, n = 6) respectively. ", "Early afterdepolarizations (EADs) appeared in 3 out of the 6 cases. ", "After adding 4 μmol/L TTX, APD(50) and APD(90) were reduced to (99.07 ± 22.81) and (163.84 ± 26.06) ms (P < 0.01, n = 6) respectively, and EADs disappeared accordingly in 3 cases. ", "It could be suggested that: (1) As a specific agonist of the I(Na.", "P), VER could result in I(Na.", "P) increase and intracellular Na(+) overload, and subsequently intracellular Ca(2+) overload with the increase of reverse I(NCX). (", "2) The VER-increased I(Na.", "P) could further extend the action potential duration (APD) and induce EADs. (", "3) TTX could restrain the abnormal VER-induced changes of the above-mentioned indexes, indicating that these abnormal changes were caused by the increase of I(Na.", "P). ", "Based on this study, it is concluded that as the I(Na.", "P) agonist, VER can enhance reverse I(NCX) by increasing I(Na.", "P), leading to intracellular Ca(2+) overload and APD abnormal extension." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0.00847457627118644, 0.004618937644341801, 0, 0.007352941176470588, 0.0033222591362126247, 0, 0, 0.03076923076923077, 0, 0, 0, 0, 0.003703703703703704, 0, 0, 0, 0.034482758620689655, 0.007633587786259542, 0.038461538461538464, 0.01282051282051282, 0.006172839506172839, 0, 0, 0.016129032258064516, 0.013888888888888888 ]	0.007224	5
[ "You are here\n\nSOS Packaging\n\nThe company is operating in the printing sector since 1978 and it is rewarded in Europe and worldwide for its innovative and sustainable technology.", "Thanks to a dedicated in house Research&Development activity SOS Packaging has developed a specific overprinting technology and process allowing to overprint flexible packaging materials with external foil or laminated film, of any type or nature (polypropylene, aluminum, steel, paper, polyamide, polyethylene, polyester, sleeve, adhesive labels in rolls, Tetra Brik, Tetra Rex, Combibloc, Elopak, microwave boxes, cases, blister packs, clusters, sacks, bags…).The material composition (mono or multilayers) does not affect the results.", "The process is compatible with Food&Beverage regulations." ]	{ "pile_set_name": "Pile-CC" }	[ 0.005649717514124294, 0.0074487895716946, 0 ]	0.004366	5
[ "There are a large number of rechargeable batteries having a wide variety of voltages and charging schedules. (", "Charging schedule, as used herein, is the manner in which the charging is performed for a given battery. ", "For example, one charging schedule might call for a limited amount of current initially, and then a greater current when the battery voltage crosses a threshold, followed by a trickle charge after the battery voltage crosses a second threshold.) ", "It is typical that a charger be designed for a single battery type, and have a single output voltage and charging schedule. ", "Of course, dedicated battery chargers are not versatile, and can require a facility to have a number of chargers.", "\nOther chargers are not dedicated, but are “dumb” chargers that apply a constant voltage output with the charging current being controlled by the load, not the charger. ", "These chargers might work for any battery of a given voltage, but do not optimally charge batteries. ", "Thus, if such chargers are used to charge several batteries simultaneously, they cannot provide a unique charging current or voltage for each battery. ", "Rather, a single charging schedule is used for all batteries being charged. ", "This also diminishes the usefulness of chargers.", "\nSome battery chargers are inefficient because they have a poor power factor. ", "This causes increased costs when power is utility power, and can lessen the charging capacity, particularly when using generator power. ", "The use of generator power can cause another problem—generators often provide “dirty” power, i.e., power that is not perfectly sinusoidal, or not of a constant value. ", "Dirty power can result in improper charging.", "\nPrior art battery chargers are often design for a single input voltage and frequency. ", "While this might be sufficient for consumer battery chargers, some applications, such as industrial battery charging, or automotive charging, might be used at different locations where the input power is not the same.", "\nRechargeable batteries have a finite life, in that their ability to be charged diminishes over time. ", "Often, a user finds the battery is no longer chargeable by charging it, then using it, and having the battery become discharged in a short period of time.", "\nAccordingly, a battery charger that is versatile enough to charge different types of batteries, or to simultaneously charge batteries with different outputs, is desirable. ", "A modular design, where output circuits for particular batteries can be switched in and out by the user, is one manner to allow different charging schedules. ", "Also, a single output module could be used for any battery type, where the user selects the battery type, or the charger senses the battery type. ", "Preferably, such a charger will provide power factor correction, and be able to receive a wide range of inputs. ", "Also, it will preferably be able to receive dirty power, and still charge a battery. ", "A charger that provides the user a warning when a battery is defective is also desirable." ]	{ "pile_set_name": "USPTO Backgrounds" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	0	5
[ "A California man caught on camera allegedly punching two women after getting into an argument with a Los Angeles hot dog vendor surrendered himself to authorities Tuesday night.", "\n\nThe Los Angeles Police Department (LAPD) tweeted a video of the suspect Tuesday, reportedly showing the suspect throwing several punches at two women before running away from the scene.", "\n\nAttention Los Angeles — this guy brutally punched two women at a hotdog stand on Jan. 26 in the area of 6th & Spring. ", "Someone knows him, and we would like to be one of those people. ", "If you have any info contact Detective Gonzalez 213-996-1851 (after hours contact 213-486-6606). ", "pic.twitter.com/DN1Og1lToM — LAPD HQ (@LAPDHQ) January 29, 2019\n\nThe confrontation began after the victims allegedly overheard the suspect getting into an argument with a hot dog vendor over a $6 hot dog on January 26, Fox 11 LA reported.", "\n\nA second hot dog vendor reportedly offered to give the suspect a free hot dog for his troubles, but that did not seem to diffuse the situation.", "\n\nThe women reportedly intervened, getting into a verbal argument with the suspect. ", "The argument turned physical when the suspect allegedly punched both women in the face. ", "The women appear to try to unsuccessfully fight back. ", "Moments later, he fled the scene.", "\n\nThe LAPD’s video of the suspect went viral, gaining nearly two million views as of Tuesday evening. ", "But the police department’s viral video had such a wide reach, it convinced the suspect to turn himself in.", "\n\nPolice arrested Arka Sangbarani Oroojian on Tuesday evening after he surrendered to authorities, charging him with one count of assault with a deadly weapon.", "\n\nOroojian’s bail was set at $90,000." ]	{ "pile_set_name": "OpenWebText2" }	[ 0, 0.0053475935828877, 0, 0, 0.030927835051546393, 0.008403361344537815, 0, 0, 0, 0, 0, 0.00980392156862745, 0, 0.006289308176100629, 0 ]	0.004051	5
[ "Rybníček (Havlíčkův Brod District)\n\nRybníček is a village and municipality (obec) in Havlíčkův Brod District in the Vysočina Region of the Czech Republic.", "\n\nThe municipality covers an area of , and has a population of 68 (as at 3 July 2006).", "\n\nRybníček lies approximately north of Havlíčkův Brod, north of Jihlava, and south-east of Prague.", "\n\nReferences\nCzech Statistical Office: Municipalities of Havlíčkův Brod District\n\nCategory:Villages in Havlíčkův Brod District" ]	{ "pile_set_name": "Wikipedia (en)" }	[ 0.012987012987012988, 0, 0, 0.007936507936507936 ]	0.005231	5
[ "When the dark and cold weather starts to kick in we usually close the windows and reach for the thermostat to keep our homes cosy and insulated from the harsh wintry wind. ", "But the result can be stuffy, germ-ridden, dry and polluted indoor air, so what do we need to keep in mind when using the central heating through the winter months if we want our families to stay healthy?", "\n\nAdvertisement\n\nThe World Health Organisation recommends a minimum temperature of 18°C indoors, and advises that keeping rooms below 16°C increases the risk of respiratory disease, particularly for children. ", "Unfortunately, keeping the heating blasting out and doors and windows shut to keep out the cold can bring health hazards of its own.", "\n\nA fertile ground for germs\n\nIf you let yourself get chilled, your immune system can shut down as your body diverts energy to the immediate concern of keeping you warm. ", "But no matter how cold and wet you are, you can still only catch a cold or other winter virus from coming in contact with the virus itself.", "\n\nIn wintery conditions we spend far more of our time indoors where central heating, air-conditioning and closed windows all provide a nice cosy environment for germs to breed. ", "And spending more time cooped up together means that viruses spread more quickly from one person to another.", "\n\nOverly dry air\n\nIndoor heating dries out the air in the home, which can have several health implications. ", "First of all, it interferes with the functioning of the mucous membranes of your nose, making you more susceptible to colds and other viruses. ", "Secondly, very dry air can aggravate some respiratory conditions and illnesses, such as asthma, allergies and croup. ", "In fact, some cold or flu-like symptoms may actually be a reaction to dust, fungi and other pollutants that have collected in the stale and dry indoor air. ", "If the air in your home is too dry you will probably notice that you have dry skin and hands, and you may have itching and irritation.", "\n\nPoor air quality\n\nToo little ventilation in the home also leads to poor air quality as everyday pollutants build up and the oxygen levels decrease. ", "There are many potential pollutants and irritants in most homes: Fireplaces, cabinets, counter surfaces, carpet, curtains, cleaning products and all kinds of materials and surfaces release chemicals into the air over time. ", "You can smell some forms of pollution, even if you don’t know exactly what it is, which often is a prompt to throw open the windows for a while and let in fresh air. ", "But there are many pollutants that you can’t smell.", "\n\nThe most dangerous of these is the gas carbon monoxide – the most hazardous substance you’re likely to come into contact with on a daily basis. ", "Even low levels of exposure can have an effect on your general health. ", "The fact that you can’t see, smell or taste the gas makes it particularly dangerous. ", "Because one of the most common sources of the gas is the incomplete burning of fuels (such as oil, gas, wood and coal) often caused by faulty, unmaintained or badly fitted heating appliances, carbon monoxide poisoning is more common in winter when people have their heating on for longer periods of time and keep their windows shut so any gas produced can’t escape.", "\n\nWhat you can do\n\n• Keep up humidity levels – If heating your home has dried out the air there are several ways you can put back the moisture, and one of the easiest is to dry clothes indoors. ", "You can also stand small bowls of water on your radiators or leave a damp towel to dry on your radiator. ", "If you have a severe problem with air dryness, or your child is suffering from a related condition, like croup, then you might want to consider investing in an air humidifier.", "\n\nDry, heated indoor air is also dehydrating, so it’s important that you continue to drink plenty of fluids even if you don’t feel thirsty.", "\n\n•Air the house – Open up a few windows whenever the weather permits to get fresh air in the house and flush out all those nasty pollutants and germs.", "\n\n•Say no to smoke – If you’re a smoker then in winter time when the air is more static it’s even more important than ever not so smoke in the house. ", "If you have visitors who are smokers don’t feel embarrassed to tell them that you have a smoke-free house, even if you’re a smoker yourself.", "\n\n•Protect against carbon monoxide poisoning – Make sure that all your fuel appliances are properly installed and regularly maintained and get a carbon monoxide detector (not the same as a smoke alarm).", "\n\n•Check your cleaning products – Many home cleaning products are packed with irritants and air pollutants, despite, or often because of, all those clean smells. ", "Think about switching to milder cleaners or cleaners based on natural substances, but remember that even natural cleaners need to be kept well out of the reach of children.", "\n\n•Pass on the household perfumes – Chemical air fresheners, scents and even artificially scented candles can all worsen the air quality of your home. ", "If the air smells stale then try airing out your home instead, and if want to use scents then opt for those from natural essential oils.", "\n\n•Check the thermostat – Remember that you want to keep your house nice and warm, but not too warm. ", "A good temperature range is between 18 and 21 degrees.", "\n\n•Introduce a few plants – Household plants bring a double benefit to your indoor air by releasing both moisture and oxygen (during the day). ", "And of course a splash of colour can be a mental pick-me-up against the dreary winter darkness too.", "\n\n• Hygiene – When you know there are plenty of viruses around it makes sense to wash your hands more often than usual, particularly when you’re in contact with other people or using public transport etc. ", "Don’t just give them a quick rinse, make sure you get germs off them with warm water and soap.", "\n\nAdvertisement\n\n•Stop the spread -If you have a cold or flu then you can help prevent spread of the illness. ", "Step away from other people when you cough or sneeze and don’t forget to cover your mouth and nose." ]	{ "pile_set_name": "Pile-CC" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.006622516556291391, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	0.000162	5
[ "---\naddress: \|\n $^{1}$ Program in Cognitive Science, Indiana University, 1900 E 10th St, Bloomington, IN 47406, USA;\\\n $^{2}$ Department of Political Science, Indiana University, 1100 E 7th St, Bloomington, IN 47405, USA\\\n $^{3}$ Center for Complex Networks and Systems Research, Department of Informatics, Indiana University, , Bloomington, IN 47408, USA\\\n $^{4}$ Ostrom Workshop in Political Theory and Policy Analysis, 513 N Park Avenue, Bloomington, IN 47408, USA\\\n $^{5}$ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA\\\n---\n\nIntroduction\n============\n\nA society’s shared ideas about how one “ought” to behave govern essential features of economic and political life [@sherif1936psychology; @durkheim1938rules; @akerlof1976economics; @geertz1994thick; @ellickson2009order; @bowles2009microeconomics]. ", "Outside of idealized game-theoretic environments, for example, economic incentives are supplemented with norms about honesty and a higher wage is possible when workers believe they ought not to cheat their employer [@simon1951formal]. ", "And, while the rational structure of rules and laws is an important part of coordinating actions and desires [@brennan2008reason], people determine the legitimacy of these solutions based on beliefs about fairness and authority. ", "A police force without legitimacy cannot enforce the law [@tyler2006psychological; @tyler2008legitimacy].", "\n\nNorms are also under continuous development. ", "The modern norm against physical violence, for example, has unexpected roots and continues to evolve [@elias2000civilizing; @pinker2011better; @klingenstein2014civilizing]. ", "Yet, we understand far less about the history and development of norms than we do about economics or the law [@ehrlich2005evolution]. ", "We often lack the data that would allow us to track the coevolution of complex, interrelated and interpretive ideas, such as honesty, fairness, and authority, the way we can track prices and monetary flows or the creation and enforcement of statutes.", "\n\nOnline systems, such as Wikipedia, provide new opportunities to study the development of norms over time. ", "Along with information and code repositories at the center of the modern global economy, such as GNU/Linux, Wikipedia is a canonical example of a knowledge . ", "rely on norms, rather than markets or laws, for the majority of their governance [@ostrom90; @hess2011understanding]. ", "On Wikipedia, editors collaborate to write encyclopedic articles in a community-managed open source environment [@west2008getting; @o2007governance], and they rely on social norms to standardize and govern their editing decisions [@beschastnikh2008wikipedian]. ", "Wikipedia’s minute-by-minute server logs cover more than fifteen years of norm creation and evolution for a population of editors that has numbered in the tens of thousands. ", "Norms matter on Wikipedia in ways that make it impossible for participants to ignore: it is the system of norms, rather than just laws, that dictates what content is or is not included, who participates, and what they do.", "\n\nParalleling findings in the study of rule evolution in large academic institutions [@march2000dynamics], we expect Wikipedia’s norms to play a role in the preservation of institutional memory, to be a source of both institutional stability and change, and to bear a complex relationship to the circumstances that led to their creation. ", "Norm pages play key roles in coordinating behavior among the encyclopedia’s editors [@butler2008don]. ", "Editors commonly cite norms on article talk pages in an attempt to coordinate [@schneider2010qualitative], build consensus, and resolve disputes [@kriplean2007community; @beschastnikh2008wikipedian].", "\n\nThis study focuses on a subspace of the encyclopedia devoted to information and discussion about the norms of the encyclopedia itself. ", "The communities associated with each of Wikipedia’s 291 languages and editions have a great deal of independence to define and change the norms they use; thus, each can follow a different evolutionary trajectory. ", "Here, we focus solely on norms in the English-language Wikipedia. ", "We study the evolution of these norms using a subset of tightly-linked pages that establish, describe, and interpret them. ", "These pages, along with the relationships between them, allow us to quantify how editors describe expectations for behavior and, consequently, how they create and reinterpret the norms of .", "\n\nWe focus on the links between norm pages. ", "Online link formation occurs for a variety of reasons [@park2003hyperlink], including strategic association by the individual making the citation [@gonzalez2009opening]. ", "In the case of Wikipedia, links between pages in the encyclopedia “mainspace” encode information about semantic relationships [@strube2006wikirelate; @witten2008effective] and the relative importance of pages [@bellomi2005network; @lizorkin2009analysis]. ", "Extending these analyses to the norm pages of the encyclopedia allows us to see how norms are described, justified, and explained by reference to other norms. ", "Our use of this network parallels studies of citations in legal systems; researchers use legal citations to track influence via precedence [@fowler2008authority] and legitimation [@walsh1997meaning], as well as the prestige of the cited [@caldeira1985transmission; @walsh1997meaning]. ", "The parallel to legal citations is not exact: the pages within Wikipedia’s norm network are not (usually) created in response to a particular event, as in a court case, but rather in response to a perceived need; pages can be created by any user, rather than a particular judge or court; and pages can be retrospectively edited (leading, for example, to the potential for graph cycles when new links ).", "\n\nThis network perspective allows us to go beyond the tracking of a single behavior over time ( approach in studies of cultural evolution [@henrich2008five]) to look at the evolution of relationships between hundreds, and even thousands, of distinct ideas. ", "We use these data to ask three critical questions. ", "In a system where norms are constantly being discussed and created, how and when do some norms come to dominate over others? ", "What types of behavior do they govern? ", "Additionally, how do those core norms evolve over time?", "\n\nThe answers are surprising. ", "While some accounts of Wikipedia stress its flexibility and the ad hoc nature of its governance [@shirky2008here; @SOCF:SOCF1090; @konieczny2010adhocratic], we find that Wikipedia’s normative evolution is highly conservative. ", "Norms that dominate the system in Wikipedia’s later years were created early, when the population was much smaller. ", "These core norms tell editors how to write and format articles; they also describe how to collaborate with others when faced with disagreements and even heated arguments. ", "this, the core norms reference universal, rationalized principles, such as neutrality, verifiability, civility, and consensus. ", "Over time, the network neighborhoods of these norms decouple topologically. ", "do so, their internal semantic coherence rises, as measured using a topic model of the page text. ", "Wikipedia’s abstract core norms and decoupling process show that it adopts an “institutionalized organization” structure akin to bureaucratic systems that predate the information age [@meyer77].", "\n\nMethods\n=======\n\nTo gather data on the network of norms on Wikipedia, we spider links within the “namespace” reserved for (among other things) policies, guidelines, processes, and discussion. ", "These pages can be identified because they carry the special prefix “Wikipedia:” or “WP:”. ", "Network nodes are pages. ", "Directed edges between pages occur when one page links to another via at least one hyperlink that meets our filtering criteria; these links are found by parsing the raw HTML of each page and excluding standard navigational templates and lists. ", "Our network is thus both directed and unweighted. ", "We begin our spidering at the (arbitrarily selected) norm page “Assume good faith”. ", "Details of the spidering process, hyperlink filters and our post-processing of links between pages appear in Appendix \\[appendix\\_a\\]; both the raw data and our processed network are freely available online [@online_ref].", "\n\nEditors classify pages in the namespace by adding tags; these tags include, most notably, “policy”, “guideline”, and “essay”, among others. ", "When we download page text, we also record these categorizations. ", "These categorizations describe gradated levels of expectations for adherence [@morgan2010negotiating]. ", "In automatically-included “template” text, policies are described as “widely accepted standards” that “all editors should normally follow” [@policy_template], guidelines as “generally accepted standards” that “editors should attempt to follow” and for which “occasional exceptions may apply” [@guideline_template], while essays provide “advice or opinions”: “\\[s\\]ome essays represent widespread norms,” while “others only represent minority viewpoints” [@essay_template]. ", "A fourth category is the “proposal”, which describes potential policies and guidelines “still ... in development, under discussion, or in the process of gathering consensus for adoption” [@proposal_template].", "\n\nPrevious analysis of Wikipedia’s policy environment has emphasized the many, often overlapping, functions that norms play in the encyclopedia, such as policies that both attempt to control un-permitted use of copyrighted material and to establish legitimacy through the use of legal diction and grammar [@butler2008don]. ", "In the current study, we consider a complementary classification system that focuses on the types of interactions the norms govern, rather than their functions. ", "We propose three distinct based on, and extending, pre-existing classification of the norms that govern natural [@ostrom90] and knowledge commons [@hess2011understanding].", "\n\nNorms may attempt to regulate content creation (“user-content” norms) and interactions between users (“user-user” norms). ", "In addition, norms may attempt to define a more formal administrative structure with distinct roles, duties, and expectations for admins (“user-admin” norms). ", "of this paper independently categorized a random sample of forty pages using this scheme, and we calculated inter-coder reliability using Cohen’s kappa [@cohen1960coefficient].", "\n\nFor our semantic analysis, we include all text, except that found in special boxes whose text is replicated by template across multiple pages. ", "To build our distribution over one-grams, we normalize all text to lowercase, merge hyphenated words (“error-correction” to “errorcorrection”), and drop punctuation (“don’t” to “dont”). ", "We do neither stemming nor spelling correction.", "\n\nA critical external variable is the number of active users on the encyclopedia at any point in time. ", "Following [@halfaker2012rise], we define an active user as one who has made five or more edits within a month; these statistics are publicly maintained at [@wiki_stats].", "\n\nCentrality and Attention Measures\n---------------------------------\n\nThe pages in our corpus are created to explain the norms of Wikipedia to editors and influence their interactions with the encyclopedia’s editing community and content. ", "Users navigate the system of norms as a network structure and consequently encounter some pages more than others.", "\n\nWe measure this using eigenvector centrality (EC), which quantifies the importance of a page based on its overall accessibility within the network. ", "The EC of a page is the probability of happening across a page during a random walk; equivalent to the PageRank algorithm, it is used in the behavioral sciences to identify consensus on dominance and power [@ec_jess]. ", "We set $\\epsilon$, the probability of a random jump, to 0.15.", "\n\nWe expect some pages to become highly central to the network, while others remain largely peripheral. ", "We quantify the inequality of the system using the Gini coefficient (GC). ", "GC varies between zero (perfect equality; all pages have equal EC) and one (one page has a high EC; all other pages have the same low value). ", "GC is widely used in economics to measure income inequality. ", "provides a global measure of the extent to which a system is dominated by a few norms. ", "As a dimensionless quantity, it allows researchers to compare this system to others that might be the subject of later research.", "\n\nBecause we are interested in the ways in which the norm citation network evolves and the role that norms play in the context of this structure, EC is an ideal measure of a norm’s importance. ", "to quantifying structural importance, however, we expect EC to correlate with, and to predict, behavioral measures of the attention a page receives. ", "To measure the relationship between centrality and behavioral measures of attention, we track page view data (from Wikipedia’s server logs made available by StatsGrok [@stats_grok], see Appendix \\[page\\_views\\]), the total number of edits a page has received, the number of edits on its associated talk page, and the number of editors who have edited the page. ", "We perform a multivariate linear regression on these attention measures, along with page age and page size () as predictors of a page’s EC (see Appendix \\[regression\\_section\\]).", "\n\nInfluence and Overlap\n---------------------\n\nAn important feature of the norm network is the sphere of influence: the pages that rely on any particular page for context.", "\n\nConsider, for example, the norm page “Neutral Point of View” (NPOV), a page urging editors to describe article subjects without taking sides. ", "A page that links to NPOV relates its own subject to NPOV in some fashion. ", "For example, among many pages that link to NPOV is “Propaganda”, an essay urging editors to be wary of using propaganda outlets of authoritarian governments. ", "The Propaganda page links to the NPOV page in order to define the notion of “undue weight”; NPOV’s content can thus be said to influence the interpretation of what is found on Propaganda.", "\n\nInfluence is distinct from centrality; centrality measures the extent to which pages link to the page in question. ", "Conversely, influence measures the extent to which the content of that page influences other pages. ", "In our formalism, a node $p$ can be understood to influence a node $q$ when $q$ links to $p$. Influence need not be direct, however: $p$ can influence $q$ if $q$ links to $r$ and $r$ links to $p$. the non-local influence, we consider random walks on the direction-reversed network.", "\n\nMore formally, placing a random-walker at node $p$, we allow her to take $n$ steps from this starting point along the direction-reversed network; we write the resulting probability distribution over the final position as $p_i$, the probability of the walker ending up at node $i$. The distribution $p_i$ defines the influence that $p$ has on $i$.\n\nTo quantify the distance between two nodes, we then consider the influence overlap between nodes $p$ and $q$. Overlap quantifies the extent to which two random walkers, beginning at these nodes, will tend to visit the same pages. ", "If $p_i$ and $q_i$ are the probability distributions associated with the influence of node $p$ and $q$, then overlap is defined as: $$O(p, q) = \\frac{\\sum_{i=1}^N p_i q_i}{\\left(\\left[\\sum_{i=1}^N p^2_i\\right] \\left[\\sum_{i=1}^N q^2_i\\right]\\right)^{1/2}}$$\n\nFor multiple pages, we can compute the average pairwise overlap simply by averaging the overlap between all possible pairs within the set.", "\n\nHigh overlap between $p$ and $q$ indicates that two pages influence a large number of common nodes. ", "When $n$ goes to infinity, the random walkers converge to the stationary distribution, and the overlap is one; conversely, when $n$ is small, random walkers have less time to encounter each other. ", "We take $n$ equal to five, larger than the average shortest path (roughly three, in our network), so that nodes are potentially reachable, but much less than the convergence time to the stationary distribution.", "\n\nOverlap can be thought of as a measure of the separation of spheres of influence. ", "It invokes only local mechanisms: users traveling from one page to another by the links that connect them. ", "This is in contrast to a measure, such as shortest paths, which is computationally expensive and requires detailed, global knowledge of the network link-structure. ", "In general, for example, the number of nodes an algorithm needs to visit in order to determine the shortest path between two nodes will usually be much larger than the length of the final path.", "\n\nBoth influence and overlap require us to specify particular nodes of interest; we focus in this work on pairs of high-EC pages, or core norms.", "\n\nSemantic Coherence\n------------------\n\nWe consider the semantic relationships between pages. ", "This provides a notion of relatedness that is distinct from how norms connect via hyperlinks. ", "To do this, we do topic-modeling (latent Dirichlet allocation [@Blei2003]) on the one-grams of the visible, human-readable text on each page. ", "Topic models allow us to represent short texts even when they draw from a rich vocabulary: topics coarse-grain the underlying distributions over words. ", "With the resulting topic model, we can then compute the semantic distance between all pairs of pages using the Jensen–Shannon distance (JSD), a measure that quantifies the distinguishability of [@dedeo2013bootstrap]. ", "This gives us a weighted semantic network that we can compare to the network of hyperlinks between pages. ", "In particular, we can compute the semantic coherence: the Pearson correlation between $p_i$ (the influence of node $p$ on node $i$) and the negative JSD from node $p$ to node $i$, $J_i$. When nodes that are closely related topologically are also closely related semantically (JSD low), the coherence is high.", "\n\nCommunity Detection\n-------------------\n\nWe expect the links that editors make at the local level to give rise to distinct clusters, or norm bundles, at the global level. ", "We use the Louvain community detection algorithm [@blondel08] to detect clustering among the nodes in the network. ", "The Louvain algorithm maximizes the modularity at each local partition of the network. ", "The algorithm first assigns each node $i$ to a different cluster, then computes the potential modularity gain to $i$ for joining the cluster of its neighbor node $j$. Each $i$ will join the cluster of $j$ when the merge offers the highest positive modularity gain. ", "If there is no possible gain in modularity, $i$ remains in its initial cluster.", "\n\nResults\n=======\n\nAt first, Wikipedia’s population underwent exponential growth. ", "In mid-2007, however, population growth stalled and entered a period of secular decline [@halfaker2012rise]; see Figure \\[pop\\]. ", "Over the course of this rapid growth and longer timescale decay, users created a large number of pages establishing, describing, and interpreting community norms. ", "Our analysis finds a total of 1976 pages associated with norms. ", "17,235 edges between these nodes; the network density, $0.0044$, is of the same order of magnitude as those seen for academic citation networks [@yan2012scholarly]; 1872 (95%) of these pages are linked together in a giant component.", "\n\nThere are a total of 56 pages classified as policy and 113 marked as guideline; for concision, we refer to pages of both types as “policy”. ", "of non-policy pages (1807) are classified as “essays” (1255), followed by “proposals” (182) (suggestions either rejected by the community or under discussion), and “humor” pages similar to essays, but taking a more irreverent tone (125).", "\n\nWe were able to achieve good, but not perfect, agreement in categorizing pages as user-content, pages. ", "This is well above chance ($p\\ll10^{-3}$), with Cohen’s $\\kappa$ value, of $0.59$ indicating “moderate” agreement [@landis1977measurement]. ", "We disagreed, for example, on “Editors\\_should\\_be\\_logged-in\\_users\\_(failed\\_proposal)” (user-user vs. user-content) and “Paid\\_editor’s\\_bill\\_of\\_rights” (user-user vs. user-admin). ", "In the same sample of forty random pages, we encountered only one that we believed was not a norm, giving an approximate precision rate of 97.5%.", "\n\nNetwork Construction\n--------------------\n\n![", "Cumulative growth in policy (red/solid line) and non-policy (green/dashed line) pages, overlaid on active population (blue/dotted line). ", "Policy creation precedes the arrival of the majority of users, while the creation of non-policy pages, usually in the form of essay and commentary, lags the growth in population. ", "\\[pop\\]](users_policy_essay-eps-converted-to.pdf){width=\"4.5in\"}\n\nMost policy pages appear before the bulk of the population arrives: over half the policy pages were created by May 2005, before the population reached 20% of its maximum. ", "By the time the population did reach its maximum, in March of 2007, over 80% of the policy pages had already been created. ", "By contrast, the creation of non-policy pages in the form of essays and commentary lags population growth. ", "When the population reached its March 2007 maximum, less than one-third of the non-policy pages were in place. ", "It was not until a year later that half of the policy pages were in place. ", "shown in Figure \\[pop\\]. ", "Eigenvector centrality leads to a distinct hierarchy of pages, with some gaining a significant fraction of the overall centrality in the system. ", "This is shown in Appendix \\[scree\\_app\\], Figure \\[ec\\], broken out by four main page categories—policies, guidelines, essays, and proposals. ", "Policies and guidelines dominate the system by centrality. ", "Our centrality measure correlates with all of the of behavioral measures of attention we consider (see Appendix \\[page\\_views\\], Table \\[correlate\\]).", "\n\nThe hierarchy is established early and yet is remarkably stable over the lifetime of the system. ", "correlation between the eigenvector centrality of nodes in 2001 and their final values in 2015 is 0.87; year to year, it is always greater than 0.9. ", "The growth in nodes’ in-degree is roughly multiplicative; for nodes with degree less than one-hundred (93% of the total network), the growth rate is, on average, $12.7\\%\\pm0.3\\%$ from one year to the next. ", "There is some evidence for super-multiplicative returns to scale; the yearly growth rate for pages with in-degree less than ten is only $10.6\\%\\pm0.4\\%$.\n\nAll of this means that, as new pages enter the system, they fail to gain the prominence of the early core norms. ", "This leads to an increase in overall network inequality, shown in Figure \\[gini\\].", "\n\n![", "Evolution of the Gini coefficient over time. ", "As new pages enter the system, overall network inequality increases, stabilizing in 2008.\\[gini\\]](gini-eps-converted-to.pdf){width=\"4.5in\"}\n\nIn short, policy growth precedes population growth. ", "Policies have far greater centrality in the network than other page types. ", "Centrality in the network is unequally distributed and becomes less equal over time.", "\n\nCore Norms\n----------\n\nTable \\[ec\\_table\\] lists the top twenty pages in our network. ", "These core norms govern a range of behaviors, including user-content actions (write articles from a neutral point of view, \\#1; include only verifiable information, \\#2; and reliable sources, \\#3), user-user actions (find consensus, \\#6; assume good faith, \\#11; be civil, \\#16; do not “edit war”, \\#19), and user-admin relationships involving specially-defined roles (blocking policy, \\#13; the arbitration committee, \\#17). ", "In some cases, a norm spans multiple classes; “What Wikipedia is not”, for example, includes both “Wikipedia is not a dictionary” (a norm on the nature of the content to be included) and “Wikipedia is not a battleground” (a norm on how users should interact with each other).", "\n\n Rank Name Classification Creation Date\n ---------- ---------------------------------- ------------------------ -------------------\n 1 Neutral\\_point\\_of\\_view User-content 24 December 2001\n 2 Verifiability User-content 2 August 2003\n 3 Identifying\\_reliable\\_sources User-content 28 February 2005\n 4 What\\_Wikipedia\\_is\\_not User-user/user-content 24 September 2001\n 5 Biographies\\_of\\_living\\_persons User-content 17 December 2005\n 6 Consensus User-user 11 July 2004\n 7 Policies\\_and\\_guidelines User-user/user-content 1 November 2001\n 8 Administrators User-admin 16 May 2001\n 9 No\\_original\\_research User-content 21 December 2003\n 10 Citing\\_sources User-content 19 April 2002\n 11 Assume\\_good\\_faith User-user 3 March 2004\n 12 Notability User-content 7 September 2006\n 13 Blocking\\_policy User-admin 8 June 2003\n 14 Dispute\\_resolution User-user/user-admin 12 January 2004\n 15 Redirect User-content 25 February 2002\n 16 Civility User-user 5 February 2004\n 17 Arbitration\\_Committee User-admin 16 January 2004\n 18 Vandalism User-content 29 March 2002\n 19 Edit\\_warring User-user 26 April 2003\n 20 Talk\\_page\\_guidelines User-user 15 April 2005\n\n : Core norms. ", "Top twenty pages, by eigenvector centrality, in 2015. ", "All are either policy or guideline pages, and all were in place by the end of 2006. ", "The majority of these core norms were created before 2004, when the population was less than 3% of its peak.\\[ec\\_table\\]\n\nAll of these core norms were created early in the system’s history. ", "The majority were created before 2004, when the population was less than 3% of the March 2007 peak. ", "The earliest members of the community first defined and articulated its core norms.", "\n\nIt is important to note that while the most important norms are those that are created early, not all of the pages created early become, or remain, central to the network. ", "This is shown visually in Appendix \\[regression\\_section\\], Figure \\[regression\\_explain\\]; there are many old pages that never grew to importance and that have ECs comparable to the youngest pages. ", "Because of this, page age alone is not a significant predictor of eigenvector centrality. ", "We confirm this with a multivariate linear regression (see Table \\[regression\\_table\\]). ", "editors is a strong predictor; not only do high EC pages attract a large number of unique editors, but there are few low-EC pages that do.", "\n\nOverlap and Semantic Coherence\n------------------------------\n\nOver the course of network construction, core norms are drawn apart topologically. ", "At the same time, the semantic coherence of their neighborhoods rises.", "\n\nFigure \\[overlap\\] shows the average pairwise overlap between the top ten pages in our network (since some norms are created later, the number of norms in this final set is lower early on). ", "Early in the system history, when the network is small, overlap is very high. ", "The creation of new pages leads to decline in overlap; even in 2006, when all core norms are in place, the overlap continues to decline. ", "Figure \\[overlap\\] also shows the evolution of semantic coherence, which rises rapidly and .", "\n\nNetwork growth could have been imagined to drive a knitting together of distinct principles. ", "Instead, the opposite happens: core norms slowly draw apart as page creation leads to distinct spheres of influence. ", "Rather than nucleating around a set of densely-connected core principles, the norm network continues to condense around multiple points.", "\n\nWe note that the local clustering coefficient, a measure of the extent to which two nodes, linked to the same node, tend to also link together, remains essentially constant over the span of the data ( \\[app\\_clustering\\], Figure \\[clustering\\]). ", "The ways in which editors link together small groups of pages changes little while their cumulative effect produces large and lasting changes both in attention inequality and page overlap.", "\n\n![", "Evolution of influence overlap among the core norms (top twenty norms by eigenvector centrality) over time (solid line, labeled). ", "In terms of the pages they influence, core norms draw apart over time, stabilizing in 2008. ", "At the same time, semantic coherence (dashed line, labeled) increases. ", "Neighborhoods become topologically distinct, but internally coherent.\\[overlap\\]](overlap_clustering-eps-converted-to.pdf){width=\"4.5in\"}\n\nEmergent Clusters\n-----------------\n\nThe connected component of network, containing 95% of all nodes, partitions into 10 clusters. ", "In Table \\[community\\_table\\], we describe the top nine, which together nearly all of the giant component. ", "By inspecting the top ten nodes in each cluster, we classify them into user-content, user-user, and user-admin norms (see Table \\[topic\\_ec\\]). ", "A force-directed layout (ForceAtlas2, implemented in Gephi [@forceatlas]) allows us to visualize the norm network and the topological relationships between its emergent groups (see Figure \\[louvain\\]).", "\n\n Rank Fraction of System Classification Topic\n ---------- ------------------------ ------------------------ -------------------------\n 1 24.8% User-Content Article Quality\n 2 22.9% User-User Collaboration\n 3 17.1% User-Administration Administrators\n 4 14.7% User-Content Formatting Articles\n 5 10.5% User-Content Content Policies\n 6 5.4% User-User Wiki-larping\n 7 2.0% User-Content Page Templates\n 8 1.3% User-User/User-Content Experts and Credentials\n 9 1.0% User-User Humor\n\n : Top nine Louvain clusters, by number of nodes. ", "Communities fall into three classifications (user-user, user-content, user-administration), based on the interactions they govern; we determine these labels by inspecting the top ten nodes by centrality within each cluster.\\[community\\_table\\]\n\n --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n ![", "The topology of the norm network is organized around five central clusters, found using the Louvain algorithm. ", "Cluster themes are based on a sample of high-eigenvector centrality (EC) nodes in each cluster and confirmed by reference to a topic model of word usage. ", "Left panel: full network, with cluster membership indicated by color. ", "Right panel: cluster structure. ", "Each node is a Louvain cluster, and node size indicates cluster size by number of pages. ", "Edge weights are defined as the fraction of the origin cluster’s out-links that link to each other cluster (self-loops are not shown). ", "\\[louvain\\]](louvain_labelled_FINAL.pdf \"fig:\"){width=\"2.9in\"} ![", "The topology of the norm network is organized around five central clusters, found using the Louvain algorithm. ", "Cluster themes are based on a sample of high-eigenvector centrality (EC) nodes in each cluster and confirmed by reference to a topic model of word usage. ", "Left panel: full network, with cluster membership indicated by color. ", "Right panel: cluster structure. ", "Each node is a Louvain cluster, and node size indicates cluster size by number of pages. ", "Edge weights are defined as the fraction of the origin cluster’s out-links that link to each other cluster (self-loops are not shown). ", "\\[louvain\\]](comm_fracs_labelled_FINAL.pdf \"fig:\"){width=\"2.9in\"}\n --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n\nThe five largest clusters comprise roughly 90% of the network. ", "The Article Quality cluster includes nodes such as Neutral Point of View, Verifiability, and Reliable Sources, governing how articles should be written. ", "The Collaboration cluster includes pages on Consensus, Assume Good Faith, and Edit Warring, describing policies and norms associated with interpersonal interaction. ", "cluster contains pages relevant to administrative actions, such as the Blocking Policy and the Arbitration Committee. ", "The Formatting cluster contains articles such as Manual of Style, Article Titles, and Disambiguation. ", "Additionally, the Content Policies cluster contains articles on copyrights, copyright violations, and policies on image use and use of non-free content. ", "The remaining clusters include a small group of articles on page templates; one on the role of experts of Wikipedia; two groups of humor pages (Wiki-larping, a humorous take on Wikipedia as if it were a Dungeons and Dragons game, and a cluster of pages, including “Bad Jokes and Other Deleted Nonsense”).", "\n\nEach of the top nine clusters is associated with a distinct topic in our topic model (see Appendix \\[k20\\], Table \\[topic\\_list\\]); while the article quality cluster is the largest by node number, the topic associated with the collaboration cluster dominates the system by word. ", "Even task-based norms appear to draw on the semantics of interpersonal cooperation.", "\n\nDiscussion\n==========\n\nThe most influential pages in the norm network are also the earliest to be created. ", "A Matthew effect [@merton1968matthew] appears to operate for social norms, where later additions to the network do not grow in influence quickly enough to destabilize the hierarchy. ", "Why are there no normative revolutions ?", "\n\nPerhaps the earliest users know best: their policies work well and are simply adopted by those who come later; or, later users may join precisely because they subscribe to the norms that have already been articulated. ", "Users who disagree with these norms may find that reinterpretation, rather than replacement, is a more effective response given the disproportionate allocation of attention to early pages.", "\n\nThe fact that core norms are created so early means that a relatively small number of users set them in place. ", "This group may have created norms that meet their own needs, but not the needs of those who arrive later. ", "For example, if early users are predominantly university students with flexible working hours, for example, they may develop norms that implicitly rely on the possibility of responding to criticism in short, rapid bursts. ", "If later arrivals do not have the same flexibility, but the norms persist, they will find themselves at a relative disadvantage in conflicts that arise, even if the amount of effort they devote to the system each week is the same.", "\n\nRecent work [@shaw14] has suggested that early users later form an oligarchy that monopolizes power, subverts democratic control, and comes into increasing conflict with the larger collective. ", "If this is true, the enduring centrality of their own interests in the norm network may be of power.", "\n\nAlternatively, the influence of a small group of editors may persist via the core norms despite a gradual decentralization of power within the encyclopedia. ", "One ethnographic account of Wikipedia’s editing community [@forte2009decentralization] suggests that a group of “old-timers” brings important social norms with them into the encyclopedia’s increasingly local governance structures, such as WikiProject communities. ", "Our findings show that the structure of the norm network is, by measures of page count, clustering, core norm overlap, and semantic coherence, largely stable by 2008. ", "Thus, the core norms and global norm structure analyzed here may provide an early foundation of norms for small, decentralized communities that form later in the .", "\n\nMuch of Wikipedia’s network simply coordinates technical practices, such as article naming conventions. ", "The most important norms, however, attempt to rationalize the system around universal concepts, such as neutrality, verifiability, consensus, and civility. ", "An important insight comes from a theory of bureaucracy and institutionalized organization developed by Meyer and Rowan (1977 [@meyer77]). ", "They propose that norms such as these can function as institutional myths that make the system appear legitimate and less ad hoc, by connecting it to a rational framework.", "\n\nPage creation continues to grow long after the core norms are already in place. ", "What happens when editors continue to develop and refine this network?", "\n\nMeyer and Rowan’s theory predicts the phenomenon of decoupling, driven by the emergence of inconsistencies between different myths. ", "The essay Civil\\_POV\\_pushing, for example, describes how some users may be able to violate the neutrality norm by strict adherence to norms of civility. ", "In Meyer and Rowan’s theory, pages like these, that attempt to resolve inconsistencies between myths, will be rare. ", "Myths will instead tend to decouple from each other over time.", "\n\nOur quantitative findings are consistent with this prediction.", " As the system grows, the creation of norm-spanning pages, such as Civil\\_POV\\_pushing, are rare and insufficient to prevent the neighborhoods of the core norms drawing apart into separate spheres of influence with high internal semantic coherence. ", "In successful systems, decoupling is also expected to happen not only between myths, but between these myths and actual practice, a phenomenon pointed to by the existence of the page “Ignore\\_all\\_rules” (“if a rule prevents you from improving Wikipedia, ignore it”).", "\n\nOur findings are also consistent with Meyer and Rowan’s second major prediction: that systems become increasingly reliant on a logic of good faith rather than following procedure. ", "Not only is “Assume good faith” itself a core norm, but the associated topic dominates the system as a whole.", "\n\nThe norm network we study here is the culmination of over thirty thousand edits. ", "We analyze the development of this system over time via the editing community’s collective decisions and their allocation of attention within the network. ", "While this method tells us a great deal about the collective process of norm creation, we do not know how individual editors understand the relationships between norms or use them to guide how they edit and interact with others. ", "Rather than memorize the complex network in its entirety, an editor may coarse-grain its properties to form his or her own mental representation of the encyclopedia’s normative structure. ", "Editors’ mental representations might then inform their linking and editing behaviors, creating a feedback loop between the representation and the norm network as a whole.", "\n\nConclusions\n===========\n\nNorms are a crucial unit of cultural evolution, and they gain meaning and force from the relationships that connect them. ", "Our work here has studied the evolution, over fifteen years, of the interdependent network of norms at the center of Wikipedia.", "\n\nThe evolution of this network is a remarkably conservative process. ", "Early features are maintained, and in some cases even amplified, over the course of the network’s development. ", "Our findings are consistent with the “iron law” of oligarchy in peer-production systems; they also complement accounts of gradual decentralization in Wikipedia’s governance structure.", "\n\nThe encyclopedia’s core norms address universal principles, such as neutrality, verifiability, civility, and consensus. ", "The ambiguity and interpretability of these abstract concepts may drive them to decouple from each other over time. ", "Wikipedia is a paradigmatic example of a 21st Century knowledge commons. ", "Yet, its core norms play a structural role analogous to the institutional myths of rationalized 20th Century bureaucracies.", "\n\nCorpus Construction {#appendix_a}\n===================\n\nAs described in the main text, we build our corpus by spidering outward from the page “Assume good faith”, following all links in the Wikipedia namespace to build a directed, unweighted network. ", "Not all pages within the namespace are normative, however. ", "After completing the spidering process, we remove pages that are solely lists (e.g., the pages “List of guidelines” or “Lists of protected pages”) that describe “projects”, or other initiatives focused on outreach (e.g., “Wikipedia Loves Libraries”), or on adding a certain kind of content to the encyclopedia (e.g., “WikiProject Libertarianism”), or that serve as noticeboards (e.g., the “Village pump”, “Media copyright questions”), with filters on both page titles and editor-assigned categories.", "\n\nMany page names have synonyms (e.g., “AGF” redirects to “Assume good faith”); we merge synonyms. ", "Not all links between pages indicate a deliberate decision to connect one norm to another. ", "Many pages, for example, contain “boxes”, small code snippets that categorize pages or provide navigation indices to similar norms. ", "These boxes can be created by a single command and are replicated across multiple pages; we do not include out-bound links found in these boxes. ", "We do not count multiple links between pages; our edges are unweighted; a directed edge between A and B refers only to the presence of at least one link from A to B. Pages sometimes have internal links; we drop all self-edges. ", "Our spidering includes only pages that existed on 12:00:00 UTC, 20 August 2015.", "\n\nRelationship between Eigenvector Centrality and Attention Measures {#page_views}\n==================================================================\n\nTo compare the norm network structure and user attention, we measure the correlation between the centrality of a norm page and the percent of the network’s page views that the norm accumulates over a 31-day period (July 2015). ", "We find a moderate correlation [@cohen1992power], $r = 0.32$, between EC and page views. (", "The distribution of EC and page view values is slightly non-linear. ", "We conduct a power-law fit and find that $\\alpha = 1.42 \\pm 0.02$. Consequently, a page that doubles its EC more than doubles its share of the network’s page views. ", "For simplicity in this analysis, we present the linear correlations.)", "\n\nEC correlates significantly with all behavioral attention measures we consider; not just page views, but number of edits, number of talk page edits and number of editors; see Table \\[correlate\\].", "\n\n Attention Measure $\\textbf{\\emph{r}}$ $\\textbf{\\emph{p}}$ Value\n --------------------------- --------------------- -------------------------------\n Page views 0.32 $<$$10^{-3}$\n Number of edits 0.70 $<$$10^{-3}$\n Number of talk page edits 0.63 $<$$10^{-3}$\n Number of editors 0.72 $<$$10^{-3}$\n\n : Correlation of eigenvector centrality with behavioral measures of attention.\\[correlate\\]\n\n![", "The relationship between EC of a page and the percent of the network’s page views it accumulates.\\[ec\\_page\\_views\\]](ec_pageviews-eps-converted-to.pdf){width=\"3.5in\"}\n\nRegression on Age and Edits {#regression_section}\n===========================\n\nTo see how a page’s intrinsic properties affect its eigenvector centrality (EC) in the final network, we performed a multivariate regression with page age, number of page edits, number of talk page edits, number of editors and page size (in bytes) as predictors of EC. ", "Including pageviews as a predictor does not significantly improve $R^{2}$; we leave it out of our regression model.", "\n\nWe normalized all predictors by z-score to allow comparison between coefficients. ", "We considered two relationships between EC and predictor variables: a linear model and a logistic model. ", "We found the linear model has lower mean-squared error and report the coefficients in Table \\[regression\\_table\\].", "\n\n Predictor Coefficient $\\textbf{\\emph{p}}$ Value\n ---------------------- ----------------- -------------------------------\n Number of editors $95\\pm6$ $<$$10^{-3}$\n Number of talk edits $46\\pm3$ $<$$10^{-3}$\n Page size $2\\pm2$ n.d.", "\n Age $2\\pm2$ n.d.", "\n Number of edits $-30\\pm7$ $<$$10^{-3}$\n\n : Coefficients of a multivariate linear regression for page eigenvector centrality (EC). ", "The $R^2$ for the fit, including all predictors, is $0.57$. \\[regression\\_table\\]\n\nAs noted in the main text, our results show that age is a weak predictor of EC, once other variables are included. ", "The number of unique editors is a very strong predictor, as is the number of edits to the talk page. ", "Figure \\[regression\\_explain\\] shows the distinct effect of page age and number of editors. ", "While the most important pages are also the oldest, there are many old pages that are not important at all; the skewed distribution of eigenvector centrality means that this signal is largely washed out in a simple linear model that does not take into account the increasing variance. ", "To reach the top 1% in EC, you must be old; but to be old is not enough.", "\n\nBy contrast, pages with many editors tend to be high-EC, and there are very few pages with many editors that are not also high in EC. ", "High-EC pages not only attract more page views (see Section \\[page\\_views\\]), but also more editors. ", "Interestingly, the total number of edits has a negative coefficient in our regression; while there is a strong positive correlation between the number of editors and the number of edits, there are a number of low-EC pages with many edits by a small number of people (e.g., an essay, written in many stages, by a single author, that never gains traction).", "\n\n --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n ![", "Important pages are old, but not all old pages are important. [", "Left]{} panel: page age (from the end of our data, in August 2015) vs. eigenvector centrality; “core norms” ([top]{} twenty pages by EC) are marked by a lower bound in EC and a lower bound in age. ", "While the very top pages in the hierarchy are all old (in the [top-right]{} region), there are many old pages that have eigenvector centrality comparable to much younger pages. [", "Right]{} panel: number of (unique) editors on the page vs. eigenvector centrality. ", "A much tighter correlation shows that pages that attract many unique editors have higher EC. ", "When both effects are taken into account in a simple linear regression model, the number of editors dominates.\\[regression\\_explain\\]](ec_age-eps-converted-to.pdf \"fig:\"){width=\"2.8in\"} ![", "Important pages are old, but not all old pages are important. [", "Left]{} panel: page age (from the end of our data, in August 2015) vs. eigenvector centrality; “core norms” ([top]{} twenty pages by EC) are marked by a lower bound in EC and a lower bound in age. ", "While the very top pages in the hierarchy are all old (in the [top-right]{} region), there are many old pages that have eigenvector centrality comparable to much younger pages. [", "Right]{} panel: number of (unique) editors on the page vs. eigenvector centrality. ", "A much tighter correlation shows that pages that attract many unique editors have higher EC. ", "When both effects are taken into account in a simple linear regression model, the number of editors dominates.\\[regression\\_explain\\]](ec_editors-eps-converted-to.pdf \"fig:\"){width=\"2.8in\"}\n --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n\nCombined Scree Plot {#scree_app}\n===================\n\n![", "Ranked eigenvector centrality for pages, broken out by page category. ", "Policy ([blue]{} diamond) and guideline ([red]{} plus) pages dominate the system. ", "More interpretive essays ([green]{} squares; includes humor and related pages), the most common by number, appear at lower relative rank; the highest ranked essay, for example, has lower centrality than the 10th ranked policy. ", "or current ([grey]{} triangles), are the lowest ranked of all.\\[ec\\]](scree_plot_bradistyle-eps-converted-to.pdf){width=\"4.5in\"}\n\n![", "Eigenvector centrality for all the pages in our data, ordered by rank. ", "Major divisions (see text) are marked by vertical lines.\\[ec\\_app\\]](scree_plot_appendix-eps-converted-to.pdf){width=\"3.5in\"}\n\nFigure \\[ec\\] shows the rank distribution of EC, page by page, broken out by page class. ", "as the eigenvector centrality of the $i$-th ranked norm allows us to define the break size, $E_{i}-E_{i+1}$, between this norm and the next. ", "Ranking break-sizes allow us to note positions where the remainder of the norms in the system have significantly lower EC. ", "Constraining breaks to be greater than five pages apart leads to the top five divisions shown in Figure \\[ec\\_app\\]. ", "In the main paper, we list nodes up to the third break-point.", "\n\nLocal Clustering Coefficient {#app_clustering}\n============================\n\nOur work here focuses on the evolution of global network properties, such as eigenvector centrality, overlap and semantic coherence, that cannot be known by breaking the graph into subgraphs. ", "It is interesting to consider more local measures, however, since these are likely to be under far greater direct user control. ", "The example we consider here is average local clustering, defined as: $$\\kappa=\\sum_{i\\in G} \\frac{\\sum_{j,k\\in\\mathcal{N}(i)} \\delta_{jk}}{\|\\mathcal{N}(i)\|\|\\mathcal{N}(i)-1\|}$$ or, in other words, the number of edges connecting nodes in the neighborhood of $i$, as a fraction of the total number of possible connections between those neighbors. ", "If individuals have a tendency to connect up the network when they create a new node, by linking together nodes it links to, this will tend to increase the clustering. ", "Figure \\[clustering\\] shows this over time. ", "Despite large changes in both population and network size, clustering remains surprisingly constant, at around one-third.", "\n\n![", "The average local clustering coefficient, as a function of time. ", "Despite large-scale changes in overall network properties, this local property remains remarkably constant.[]{data-label=\"clustering\"}](overlap_clustering_cogsci-eps-converted-to.pdf){width=\"3.5in\"}\n\nClusters and Topic Modeling {#k20}\n===========================\n\nFor our base model with $k=20$ topics, Table \\[topic\\_list\\] shows the top twenty representative words for each topic; in this table we drop the word “wikipedia”, plurals (except the word “wikipedias”) and date/time terms (“january”, “utc”, etc.). ", "We use Jason Adams’ software package “lda-ruby” package ([<https://github.com/ealdent/lda-ruby>]{}), a ruby wrapper for the C code of David M. Blei; this code estimates model parameters using a variational Expectation Maximization algorithm (<http://www.cs.princeton.edu/~blei/lda-c/> [@Blei2003]). ", "In Table \\[topic\\_list\\], we show the topics, and their associated words, ordered by the topic’s (word-level) prevalence within the encyclopedia.", "\n\nFor each page, we can compute a distribution over topics; this is just the average of the word-level distributions. ", "By averaging these topic distributions over pages, we can compute the topic distribution for each Louvain community (Collaboration, Article Quality, etc.). ", "It turns out that each of the top eight communities has a different most-common topic. ", "This allows us to associate some of the topics we find with a particular cluster, and we list this correspondence in column three of Table \\[topic\\_list\\]. ", "the representative words for these eight topics provides complementary evidence in favor of the community labels, which were previously chosen by manual inspection of the top ten pages by eigenvector centrality (Table \\[topic\\_ec\\]).", "\n\n====\n\n\\[0.8\\]\n\n Rank Fraction Louvain Community Representative Words\n ---------- -------------- ----------------------- ----------------------------------------------------------------------------------------------------------\n editor, edit, dont, good, people, make, editing, policy, page, talk,\n time, article, faith, point, policies, encyclopedia, consensus, community, personal, user\n source, reliable, article, material, information, research, primary, view, original, editors,\n subject, published, secondary, policy, neutral, point, scientific, content, topic, claims\n article, deletion, page, deleted, discussion, content, delete, speedy, talk, tag,\n subject, information, policy, user, guidelines, criteria, notability, afd , time, essay\n article, information, content, encyclopedia, editors, people, wikipedias, subject, featured, quality,\n good, list, topic, readers, time, work, project, knowledge, number, lead\n consensus, policy, discussion, community, process, committee, arbitration, editors, administrator, user,\n request, policies, admin, block, dispute, page, wikimedia, proposal, information, made\n article, names, title, page, english, disambiguation, naming, redirect, conventions, common,\n term, style, citation, word, language, topic, book, usage, examples, cases\n user, edit, page, vandalism, account, ip, editing, talk, editors, bot,\n address, protection, administrators, userboxes, username, blocked, block, request, sock, template\n notable, article, notability, list, sources, coverage, criteria, information, subject, reliable,\n emojif , guideline, film, event, university, significant, general, topic, independent, inclusion\n page, link, text, image, file, wikimedia, search, commons, web, information,\n external, software, content, article, site, add, click, wiki, edit, make\n talk, edit, page, user, war, im, article, dont, people, time,\n contribs, good, contributions, back, long, list, things, make, day, ive\n copyright, image, public, nonfree, free, work, content, license, domain, law,\n fair, article, copyrighted, published, states, pma, united, subject, permission, media\n page, talk, template, namespace, user, link, article, text, category, section,\n special, edit, title, list, signature, ut , mediawiki, redirect, move, navbox\n list, chart, people, united, war, town, world, man, england, states,\n british, top, hot, songs, women, city, ireland, music, number, death\n category, day, categories, article, tip, stub, list, page, people, categorization,\n main, link, year, created, red, featured, create, template, sort, subcategories\n people, user, time, status, wikidragon, truth, wikifauna, wikipuma, credentials, names,\n editathon, work, turkish, years, page, make, real, history, group, greek\n support, oppose, policy, people, user, proposal, talk, userboxes, dont, image,\n offensive, pov , namespace, page, content, article, censorship, vote, npov , agree\n ban, topic, editing, indefinite, talk, sanctions, article, page, user, edit,\n discussion, banned, paid, related, editor, contribs , interest, coi , community, broadly\n quotation, style, citing, punctuation, american, mos, ads, dash, manual, inactive,\n en , english, issue, sentence, dashes, election, text, space, british, jumped\n text, template, page, line, article, gt, section, lt, enforcement, table,\n footnote, law, summary, infobox, style, agencies, synth , color, work, data\n article, station, number, year, state, route, highway, time, road, points,\n date, railway, britannica, ship, include, information, eb , county, class, official\n\n : Representative one-grams from each of the topics in our $k=20$ topic model, ranked by the weighted fraction of words assigned. ", "The top nine Louvain clusters are each dominated by a unique topic. ", "\\[topic\\_list\\]\n\n\\[0.8\\]\n\n Rank Cluster Name Top Pages\n ---------- ------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n 1 Article Quality Neutral\\_point\\_of\\_view; Verifiability; Identifying\\_reliable\\_sources; What\\_Wikipedia\\_is\\_not; Biographies\\_of\\_living\\_persons; No\\_original\\_research; Citing\\_sources\n 2 Collaboration Consensus; Policies\\_and\\_guidelines; Assume\\_good\\_faith; Dispute\\_resolution; Civility; Edit\\_warring; Talk\\_page\\_guidelines\n 3 Administrators Administrators; Blocking\\_policy; Arbitration\\_Committee; Vandalism; User\\_pages; Sock\\_puppetry; User\\_access\\_levels\n 4 Formatting Articles Redirect; Article\\_titles; Disambiguation; Manual\\_of\\_Style; Namespace; What\\_is\\_an\\_article?; ", "Categorization\n 5 Content Policies Copyrights; Copyright\\_violations; Non-free\\_content; Image\\_use\\_policy; General\\_disclaimer; Non-Wikipedia\\_disclaimers; Substitution\n 6 Wiki-larping Citation\\_needed; Wikibreak; WikiGnome; Wikipediholic; Talk\\_page\\_stalker; Wikipedia\\_is\\_a\\_volunteer\\_service; WikiDragon\n 7 Page Templates Overlink\\_crisis; Pruning\\_article\\_revisions; Disinfoboxes; Thinking\\_outside\\_the\\_infobox; Advanced\\_template\\_coding; Advanced\\_article\\_editing; Advanced\\_footnote\\_formatting\n 8 Experts and Credentials Expert\\_editors; Honesty; Expert\\_retention; Randy\\_in\\_Boise; Ten\\_Simple\\_Rules\\_for\\_Editing\\_Wikipedia; Conflicts\\_of\\_interest\\_(medicine); There\\_is\\_no\\_credential\\_policy\n 9 Humor Silly\\_Things; Rules\\_for\\_Fools; April\\_Fools; April\\_Fool’s\\_Main\\_Page; Unusual\\_articles; Yet\\_more\\_Best\\_of\\_BJAODN; Best\\_of\\_BJAODN\n\n : Top pages within each cluster, by eigenvector centrality. 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[ "Star Trek Discovery\n\nAlex and Johnny invite you to the grand opening of their brand new Star Trek: Discovery project, The DiscoTrek Podcast. ", "This week they discuss the third episode of Season 1, “Context is for Kings,” going over new characters, the ship itself and a basket full of premium Easter Eggs. ", "We’ll let you know when The DiscoTrek gets its own home on iTunes, Stitcher and all of our other current destinations.", "\n\nListen on Stitcher\n\nSocial Media Icons\n\nSubscribe to GoT Thrones\n\nSing us the Game of Thrones theme song!", "\n\nWant to be on the show? ", "Sing us your version of the \"Game of Thrones\" theme song! ", "You can email a recording to gotthronespodcast@gmail.com or give us a call at 213-290-4492 and record it on a voicemail." ]	{ "pile_set_name": "Pile-CC" }	[ 0.0070921985815602835, 0.012269938650306749, 0.025423728813559324, 0.009345794392523364, 0, 0, 0.016666666666666666 ]	0.010114	5
[ "In 2010, President Obama directed the CIA to assassinate an American citizen in Yemen, Anwar al-Awlaki, despite the fact that he had never been charged with (let alone convicted of) any crime, and the agency successfully carried out that order a year later with a September 2011 drone strike. ", "While that assassination created widespread debate — the once-again-beloved ACLU sued Obama to restrain him from the assassination on the ground of due process and then, when that suit was dismissed, sued Obama again after the killing was carried out — another drone killing carried out shortly thereafter was perhaps even more significant yet generated relatively little attention.", "\n\nTwo weeks after the killing of Awlaki, a separate CIA drone strike in Yemen killed his 16-year-old American-born son, Abdulrahman, along with the boy’s 17-year-old cousin and several other innocent Yemenis. ", "The U.S. eventually claimed that the boy was not their target but merely “collateral damage.” ", "Abdulrahman’s grief-stricken grandfather, Nasser al-Awlaki, urged the Washington Post “to visit a Facebook memorial page for Abdulrahman,” which explained: “Look at his pictures, his friends, and his hobbies. ", "His Facebook page shows a typical kid.”", "\n\nFew events pulled the mask off Obama officials like this one. ", "It highlighted how the Obama administration was ravaging Yemen, one of the world’s poorest countries: just weeks after he won the Nobel Prize, Obama used cluster bombs that killed 35 Yemeni women and children. ", "Even Obama-supporting liberal comedians mocked the arguments of the Obama DOJ for why it had the right to execute Americans with no charges: “Due Process Just Means There’s A Process That You Do,” snarked Stephen Colbert. ", "And a firestorm erupted when former Obama press secretary Robert Gibbs offered a sociopathic justification for killing the Colorado-born teenager, apparently blaming him for his own killing by saying he should have “had a more responsible father.”", "\n\nThe U.S. assault on Yemeni civilians not only continued but radically escalated over the next five years through the end of the Obama presidency, as the U.S. and the U.K. armed, supported, and provide crucial assistance to their close ally Saudi Arabia as it devastated Yemen through a criminally reckless bombing campaign. ", "Yemen now faces mass starvation, seemingly exacerbated, deliberately, by the U.S.-U.K.-supported air attacks. ", "Because of the West’s direct responsibility for these atrocities, they have received vanishingly little attention in the responsible countries.", "\n\nIn a hideous symbol of the bipartisan continuity of U.S. barbarism, Nasser al-Awlaki just lost another one of his young grandchildren to U.S. violence. ", "On Sunday, the Navy’s SEAL Team 6, using armed Reaper drones for cover, carried out a commando raid on what it said was a compound harboring officials of al Qaeda in the Arabian Peninsula. ", "A statement issued by President Trump lamented the death of an American service member and several others who were wounded, but made no mention of any civilian deaths. ", "U.S. military officials initially denied any civilian deaths, and (therefore) the CNN report on the raid said nothing about any civilians being killed.", "\n\nBut reports from Yemen quickly surfaced that 30 people were killed, including 10 women and children. ", "Among the dead: the 8-year-old granddaughter of Nasser al-Awlaki, Nawar, who was also the daughter of Anwar Awlaki.", "\n\nAs noted by my colleague Jeremy Scahill — who extensively interviewed the grandparents in Yemen for his book and film on Obama’s “Dirty Wars” — the girl “was shot in the neck and killed,” bleeding to death over the course of two hours. “", "Why kill children?” ", "the grandfather asked. “", "This is the new (U.S.) administration — it’s very sad, a big crime.”", "\n\nThe New York Times yesterday reported that military officials had been planning and debating the raid for months under the Obama administration, but Obama officials decided to leave the choice to Trump. ", "The new president personally authorized the attack last week. ", "They claim that the “main target” of the raid “was computer materials inside the house that could contain clues about future terrorist plots.” ", "The paper cited a Yemeni official saying that “at least eight women and seven children, ages 3 to 13, had been killed in the raid,” and that the attack also “severely damaged a school, a health facility and a mosque.”", "\n\nAs my colleague Matthew Cole reported in great detail just weeks ago, Navy SEAL Team 6, for all its public glory, has a long history of “‘revenge ops,’ unjustified killings, mutilations, and other atrocities.” ", "And Trump notoriously vowed during the campaign to target not only terrorists but also their families. ", "All of that demands aggressive, independent inquiries into this operation.", "\n\nPerhaps most tragic of all is that — just as was true in Iraq — al Qaeda had very little presence in Yemen before the Obama administration began bombing and droning it and killing civilians, thus driving people into the arms of the militant group. ", "As the late, young Yemeni writer Ibrahim Mothana told Congress in 2013:\n\nDrone strikes are causing more and more Yemenis to hate America and join radical militants. … ", "Unfortunately, liberal voices in the United States are largely ignoring, if not condoning, civilian deaths and extrajudicial killings in Yemen. ", "During George W. Bush’s presidency, the rage would have been tremendous. ", "But today there is little outcry, even though what is happening is in many ways an escalation of Mr. Bush’s policies. … ", "Defenders of human rights must speak out. ", "America’s counterterrorism policy here is not only making Yemen less safe by strengthening support for AQAP [al Qaeda in the Arabian Peninsula] but it could also ultimately endanger the United States and the entire world.", "\n\nThis is why it is crucial that — as urgent and valid protests erupt against Trump’s abuses — we not permit recent history to be whitewashed, or long-standing U.S. savagery to be deceitfully depicted as new Trumpian aberrations, or the war on terror framework engendering these new assaults to be forgotten. ", "Some current abuses are unique to Trump, but — as I detailed on Saturday — some are the decades-old byproduct of a mindset and system of war and executive powers that all need uprooting. ", "Obscuring these facts, or allowing those responsible to posture as opponents of all this, is not just misleading but counterproductive: Much of this resides on an odious continuum and did not just appear out of nowhere.", "\n\nIt’s genuinely inspiring to see pervasive rage over the banning of visa holders and refugees from countries like Yemen. ", "But it’s also infuriating that the U.S. continues to massacre Yemeni civilians, both directly and through its tyrannical Saudi partners. ", "That does not become less infuriating — Yemeni civilians are not less dead — because these policies and the war theories in which they are rooted began before the inauguration of Donald Trump. ", "It’s not just Trump but this mentality and framework that need vehement opposition." ]	{ "pile_set_name": "OpenWebText2" }	[ 0.010238907849829351, 0.005235602094240838, 0.014354066985645933, 0, 0.019138755980861243, 0, 0, 0, 0.009009009009009009, 0.004048582995951417, 0, 0, 0, 0.006493506493506494, 0.010582010582010581, 0.005952380952380952, 0.006622516556291391, 0, 0.017391304347826087, 0.008368200836820083, 0, 0, 0, 0.014634146341463415, 0, 0, 0, 0.009433962264150943, 0.009708737864077669, 0, 0.008, 0.011976047904191617, 0, 0.0136986301369863, 0.008333333333333333, 0, 0.00904977375565611, 0.003236245954692557, 0.0053475935828877, 0, 0, 0, 0.0051813471502590676, 0.012048192771084338 ]	0.005184	5
[ "Introduction {#Sec1}\n============\n\nElevated glucose concentrations (\\>3.5 mmol/l) normally suppress the release of glucagon from pancreatic alpha cells; dysregulation of this process is a feature of type 1 and type 2 diabetes \\[[@CR1], [@CR2]\\]. ", "Both direct \\[[@CR3]\\] and indirect \\[[@CR4]\\] effects of glucose on the release of glucagon have been described. ", "Whereas the latter appear to involve the release of secretory products, including insulin \\[[@CR3], [@CR5]\\], gamma-aminobutyric acid \\[[@CR6]--[@CR8]\\] or zinc ions \\[[@CR4], [@CR9]\\] from neighbouring beta cells, as well as somatostatin from delta cells \\[[@CR10], [@CR11]\\], the signalling events involved in the direct sensing of glucose are more controversial \\[[@CR12]\\]. ", "These may involve enhanced metabolism of glucose and the closure of ATP-sensitive K^+^ channels, followed by limited membrane depolarisation \\[[@CR13], [@CR14]\\]. ", "AMP-activated protein kinase (AMPK) appears also to be involved in the regulation of glucagon release \\[[@CR15]\\].", "\n\nPer-arnt-sim (PAS) domain-containing protein kinases (PASKs) are related to AMPK and are common in prokaryotes. ", "However, there is currently only one known mammalian counterpart \\[[@CR16], [@CR17]\\]. ", "We \\[[@CR18]\\] and others \\[[@CR19], [@CR20]\\] have shown that PASK is important for energy sensing and maintenance of normal cellular energy balance in mammalian systems.", "\n\nIn pancreatic beta cells, PASK activity is regulated by glucose and is involved in the regulation of glucose-induced preproinsulin and pancreatic duodenum homeobox-1 (Pdx1) gene expression \\[[@CR18], [@CR20]\\]. ", "Expression of the Pask gene in rodent islets and beta cell lines \\[[@CR18], [@CR20]\\] is also glucose-sensitive. ", "Recently, PASK has been implicated in regulation of lipogenic gene expression \\[[@CR19]\\] and might, therefore, influence glucose signalling through lipid intermediates as proposed for glucose-induced insulin secretion \\[[@CR21]\\].", "\n\nPask homozygote knockout mice (Pask^−/−^), which are globally inactivated for Pask, have previously been reported to display lower plasma insulin levels than control littermates \\[[@CR19]\\], but normal glucose tolerance \\[[@CR19], [@CR22]\\], reflecting enhanced insulin sensitivity \\[[@CR19]\\]. ", "Insulin secretion from Pask^−/−^ islets has variously been shown to be not different \\[[@CR22]\\] or lower \\[[@CR19]\\] than in control islets. ", "It has also been previously reported that total insulin content and/or beta cell mass were not altered in Pask^−/−^ mice \\[[@CR19], [@CR22]\\]. ", "However, data from these earlier studies are difficult to interpret for a number of reasons. ", "In the first instance, total islet insulin was not always measured, making it difficult to evaluate the insulin secretory capacity of Pask^−/−^ islets. ", "Moreover quantification of beta cell mass using pancreatic sections is prone to substantial variability \\[[@CR19]\\]. ", "Due to these limitations \\[[@CR19], [@CR22]\\], the role of PASK in the regulation of pancreatic hormone release and glucose homeostasis remains to be clarified.", "\n\nA recent report \\[[@CR20]\\] showed that inhibition of insulin gene expression by palmitate was reversed by Pask overexpression in MIN6 beta cells. ", "The loss of PASK, and hence the loss of regulation by Pdx1 and Mafa gene expression \\[[@CR18]\\], was proposed to be a mechanism by which insulin gene expression in the beta cell might be lost on exposure to palmitate \\[[@CR20]\\]. ", "Thus, PASK appears to exert a protective effect in mature beta cells. ", "Moreover, aberrant PASK expression and/or function may play a significant role in the development of diabetes and, interestingly, Pask^−/−^ mice develop glucose intolerance on a high-fat diet \\[[@CR18]\\].", "\n\nAlthough glucose homeostasis reflects the release of multiple islet hormones in addition to insulin, there are currently no published data on the role of PASK in other islet cell types. ", "The present study demonstrates that PASK is involved in the regulation of glucagon secretion from pancreatic alpha cells. ", "We show that PASK expression is decreased in the islets of human type 2 diabetic patients and that Pask is at least as strongly expressed in highly purified mouse alpha cells as in beta cells. ", "Silencing or ablation of Pask in clonal alpha cells or islets, respectively, drastically blunted the inhibition of glucagon secretion by glucose. ", "Whereas the insulin content of PASK-deficient islets was dramatically reduced, the acute regulation of insulin secretion by glucose was normal. ", "Thus, PASK regulates hormone release reciprocally from pancreatic alpha and beta cells. ", "Given that dysregulation of insulin and glucagon secretion are characteristics of type 2 diabetes, we propose that PASK may be a potential drug target to modulate glucagon release in vivo.", "\n\nMethods {#Sec2}\n=======\n\nMaterials Adenoviruses encoding for human PASK have been previously described \\[[@CR16]\\]. ", "All general chemicals and tissue culture reagents were purchased from Sigma (Poole, UK) or Invitrogen (Paisley, UK), unless otherwise stated in the text.", "\n\nIsolation and culture of islets Studies on human islets were conducted with local ethics committee approval at all sites (Charing Cross Research Ethics Committee Ref. ", "07/H0711/114). ", "Human islets were isolated as previously described in Oxford, UK \\[[@CR23]\\], or in Pisa, Italy \\[[@CR24]\\], and maintained in medium containing 11 mmol/l glucose for 10 days to allow the loss of exocrine tissue \\[[@CR25]\\]. ", "Human type 2 diabetic donors were selected according to established criteria \\[[@CR23], [@CR26]\\]. ", "Mouse pancreatic islets were isolated and cultured as described in \\[[@CR3]\\]. ", "Alpha-TC1-9 cells (passage 35--45; American Type Culture Collection, Manassas, VA, USA) were cultured as previously described \\[[@CR7]\\].", "\n\nLaser capture microdissection and microarray analysis These procedures were performed as described in Electronic supplementary material (ESM) Methods.", "\n\nRNA sequencing We prepared 300 ng of total RNA with a kit (mRNA-Seq 8; Illumina, Little Chesterford, UK). ", "For clustering and sequencing we used Illumina cluster generation and sequencing kits v4. ", "9pM were loaded to the flowcell (one sample per lane) and sequenced on a sequencer (GAIIx) with RTA software version 2.6 (Little Chesterford, UK). ", "On average we obtained 28 million reads per lane, passing Illumina's quality filtering. ", "Short reads (35 bp) were aligned to the mouse genome (Ensembl v54) using a mapping station (Genomatix) \\[[@CR27]\\] and to a database of known and potential splice junctions using Bowtie \\[[@CR28]\\]. ", "Up to three mismatches and no insertions or deletions were allowed, and, on average, more than 85% of the reads in a sample could be mapped to the genome. ", "Gene expression was measured as proposed by Mortazavi et al. ", "\\[[@CR29]\\] and reads per kilobase per million (RPKM) values were computed for every gene.", "\n\nMice Pask^−/−^ mice (kindly provided by R. Wenger, Institute of Physiology and ZIHP, Zurich, Switzerland) \\[[@CR30]\\] were back-crossed for ten generations with C57BL/6 mice prior to use. ", "Mice were housed with two to five animals per cage in a pathogen-free facility on a 12 h light--dark cycle with free access to standard mouse chow diet, unless otherwise stated. ", "All in vivo procedures were performed in the Imperial College Central Biomedical Service in accordance with the Principles of Laboratory Care and the UK Home Office (Animals Scientific Procedures Act, 1986), and approved by the local ethics committee. ", "Genotyping was performed as previously described \\[[@CR30]\\].", "\n\nIntraperitoneal glucose tolerance test An intraperitoneal glucose tolerance test was performed on 8-week-old mice as described in \\[[@CR31]\\], at 09:00 hours on each experimental day.", "\n\nMeasurement of total pancreatic insulin and glucagon Pancreases were excised from 8-week-old mice and suspended in ice-cold acid--ethanol (75.0% ethanol--23.4% molecular grade water--1.5% HCl--0.1% Triton X-100, vol./vol.) ", "prior to disruption by sonication (microsonicator; Misonix, Farmingdale, NY, USA) at 4°C. ", "Total protein was measured by Bradford's assay \\[[@CR32]\\], and insulin and glucagon content were measured by radioimmunoassay (Linco, Watford, UK).", "\n\nMeasurement of plasma glucagon At 8 weeks of age mice were starved overnight prior to being killed by cervical dislocation. ", "Blood (200 μl) was immediately removed by cardiac puncture. ", "Plasma was collected using high-speed centrifugation (2,000 g, 5 min) in heparin-coated tubes (Microvette; Sarstedt, Leicester, UK) and plasma glucagon assessed by radioimmunoassay (Linco, Watford, UK).", "\n\nManipulation of PASK content in alpha-TC1-9 cells and cultured islets of Langerhans Alpha-TC1-9 cells and islets were infected with adenoviruses encoding for PASK or enhanced green fluorescent protein at a multiplicity of infection of 100 and cultured for 48 h prior to use. ", "Alpha-TC1-9 cells were transfected with anti-Pask small interfering RNA (siRNA) or control siRNA (1 nmol/l) \\[[@CR18]\\]. ", "Protein content was assessed by western (immuno-)blot analysis.", "\n\nCulture of E13.5 rat pancreatic epithelia E13.5 rat pancreatic epithelia were isolated and cultured as previously described \\[[@CR33]\\]. ", "Epithelia were cultured in the presence of anti-Pask siRNA or control siRNA \\[[@CR18]\\] (1 nmol/l) for 10 days prior to RNA isolation for real-time quantitative PCR analysis.", "\n\nReal-time quantitative PCR analysis Highly purified primary mouse islet beta and alpha cells were obtained by fluorescence-activated cell sorting of transgenic mice expressing the fluorescent protein Venus selectively in the alpha cell under the preproglucagon promoter \\[[@CR34], [@CR35]\\]. ", "RNA was extracted from alpha-TC1-9 cells and cultured rat E13.5 explants using Trizol (Invitrogen) according to the manufacturer's guidelines. ", "Total RNA was subjected to DNAse treatment (Ambion, Warrington, UK), followed by cDNA conversion (high-capacity cDNA conversion kit; Applied Biosystems, Warrington, UK) and real-time quantitative PCR using SYBR green (Applied Biosystems) in a 7500 Real-Time PCR System (ABI, Warrington, UK).", "\n\nWestern (immuno-)blot analysis Western (immuno-)blot analysis was performed as previously described \\[[@CR18]\\].", "\n\nStatistical analysis Data are the means ± SE for the number of observations indicated. ", "Statistical significance and differences between means were assessed by Student's t test with Bonferroni correction for multiple analyses.", "\n\nResults {#Sec3}\n=======\n\nPASK gene expression is regulated by glucose in human pancreatic islets of Langerhans and is lowered in type 2 diabetes We have previously shown that Pask mRNA and protein levels are increased by high glucose in rat islets and clonal MIN6 beta cells \\[[@CR18]\\]. ", "Here, we first determined whether islet PASK expression may also be regulated by glucose or by diabetes in humans. ", "Measured in human islets of Langerhans by quantitative PCR, PASK mRNA was elevated after 24 h culture at 11 mmol/l glucose (2.7 ± 0.2-fold vs culture at 3 mmol/l glucose \\[means ± SE\\]; Fig.", " [1a](#Fig1){ref-type=\"fig\"}). ", "Measured after culture at 11 mmol/l glucose, PASK gene expression was significantly lower in islets from patients with type 2 diabetes than in control islets (Fig.", " [1b](#Fig1){ref-type=\"fig\"}). ", "Fig.", " 1PASK expression is regulated by glucose in human islets and is lowered in type 2 diabetic islets. ", "Real-time quantitative PCR on non-diabetic (a, b) or type 2 diabetic (T2D) (b) human islet RNA, following culture at the indicated glucose concentrations for 24 h (a) or at 11 mmol/l glucose (b); n = 3; \\*p \\< 0.05, \\\\p \\< 0.01. ", "cPask mRNA content in FACS-purified mouse alpha and beta cells; ^†^p = 0.07\n\nmRNA expression data obtained using whole islets may be confounded by variable degrees of contamination with other pancreatic cell types, as well as by other factors. ", "Therefore, we sought to further support the above results by using laser capture microdissection and array analysis to quantify mRNA levels selectively in beta cell-enriched samples \\[[@CR26]\\]. ", "A clear tendency for decreased PASK expression in islets in type 2 diabetic pancreases vs controls was also observed using this approach (ESM Fig.", " [1](#MOESM1){ref-type=\"\"}). ", "In contrast, consistent changes in levels of the AMPK-alpha1 and -alpha2 subunit (encoded by PRKAA1 and PRKAA2, respectively) were not observed with array data on samples obtained by laser capture microdissection. ", "However, with quantitative PCR done on the same samples with enough RNA (10 vs 10), a small but statistically significant decrease in PRKAA1 expression was apparent (18%; p \\< 0.019), using RPL32 as an internal control.", "\n\n**Pask is expressed in murine pancreatic beta and alpha cells** In the mouse, Pask mRNA has previously been shown to be most abundant in testes as well as in haemopoietic tissues including thymus and spleen \\[[@CR30]\\]. ", "Levels in other tissues, including islets, are much lower \\[[@CR30]\\] (G. A. Rutter and G. Sun, unpublished observations). ", "Indeed, the expression of Pask in adult mouse islets and its induction by glucose have recently been questioned, since expression in these cells of the lacZ gene, expressed in mice null for Pask alleles under the Pask promoter, was barely detectable by beta-Gal staining \\[[@CR22]\\]. ", "By contrast, we have previously detected Pask mRNA in mouse islets and MIN6 cells \\[[@CR18]\\], data recently confirmed by others \\[[@CR20]\\]. ", "Examined here in islets from mice on a mixed C57BL/6/sv129 background cultured at 11 mmol/l glucose, massive parallel sequencing (RNAseq) confirmed the presence of Pask mRNA at low but detectable levels, lying in the lower 30th percentile of all mRNAs at approximately 0.2 ± 0.3% (n = 3 female mice) of β-actin mRNA levels (ESM Fig.", " [2](#MOESM2){ref-type=\"\"}).To determine in which cell types Pask was expressed in mouse islets, we next compared the expression of Pask mRNA in highly purified primary mouse alpha and beta cells (Fig.", " [1c](#Fig1){ref-type=\"fig\"}). ", "These were obtained by fluorescence-activated cell sorting of transgenic mice selectively expressing the fluorescent protein, Venus, in the alpha cell \\[[@CR34], [@CR35]\\] and by real-time quantitative PCR analysis. ", "This approach confirmed the presence of Pask mRNA in both cell types and indicated that levels in purified alpha cells (1.45 ± 0.46% of beta-actin mRNA) tended to be higher than in beta cells (0.54 ± 0.044%; n = 3 preparations; p = 0.07 by two-tailed Student's t test).", "\n\nPask^−/−^ mice display normal glucose tolerance but impaired plasma glucagon concentration Given the greater expression of Pask in alpha than in beta cells and the dysregulation of glucagon secretion observed in type 2 diabetes, as reviewed by others \\[[@CR2]\\], we next analysed the potential contribution of this enzyme to the regulation of glucagon secretion using Pask^−/−^ mice. ", "At 8 weeks of age, Pask^−/−^ male (Fig.", " [2a, c, e](#Fig2){ref-type=\"fig\"}) and female (Fig.", " [2b, d](#Fig2){ref-type=\"fig\"}) mice displayed 25 ± 5% higher plasma glucose levels after 16 h of fasting than wild-type littermate control mice, but normal glucose tolerance after intraperitoneal injection of the sugar (Fig.", " [2a--d](#Fig2){ref-type=\"fig\"}). ", "Measured after fasting, plasma glucagon was significantly higher in Pask^−/−^ male mice than in littermate controls (91 ± 5.4 vs 58 ± 3 pg/ml; Fig.", " [2e](#Fig2){ref-type=\"fig\"}). ", "Fig.", " 2Pask^−/−^ mice display higher fasted glucose levels than littermate controls. ", "At 8 weeks of age, male (a, c) and female (b, d) Pask^−/−^ mice were starved for 16 h prior to an intraperitoneal glucose tolerance test (1 g glucose per kg body weight). ", "c, d Blood glucose at 0 min, as indicated by dotted squares (a, b), for male and female mice, respectively. ", "e Plasma glucagon concentrations from male mice following 16 h of fasting. ", "n = 8--10 mice per group; \\*p \\< 0.05, \\\\p \\< 0.01. ", "Black squares and solid lines, Pask^+/+^, wild-type; rhombuses and dotted lines, Pask^+/−^, heterozygote; black triangles and dashed lines, Pask^−/−^, homozygous knockout\n\nIslets of Langerhans from Pask^−/−^ mice display impaired glucose-regulated glucagon secretion We next examined whether the elevated plasma glucagon concentration was due to dysregulation of alpha cell function. ", "Supporting this view, the inhibition of glucagon secretion in response to elevated glucose was impaired in islets from Pask^−/−^ mice (Fig.", " [3a](#Fig3){ref-type=\"fig\"}). ", "Thus, Pask^−/−^ islets, in which Pask gene expression was undetectable (Fig.", " [3e](#Fig3){ref-type=\"fig\"}), secreted 2.04 ± 0.2-fold more glucagon at inhibitory (10 mmol/l) glucose concentrations than did islets from wild-type littermates (Fig.", " [3a](#Fig3){ref-type=\"fig\"}), whereas release at stimulatory (0.5 mmol/l) glucose was unaltered. ", "Interestingly, a slight inhibitory effect on glucagon secretion in Pask^−/−^ islets was still observed at 10 mmol/l glucose (Fig.", " [3a](#Fig3){ref-type=\"fig\"}). ", "Although glucose-stimulated insulin release when normalised to total islet insulin content was not affected by Pask deletion (Fig.", " [3b](#Fig3){ref-type=\"fig\"}), the total amount of insulin per islet was lower (0.38 ± 0.3-fold) in Pask^−/−^ than in wild-type islets (Fig.", " [3d](#Fig3){ref-type=\"fig\"}), i.e. the amount of insulin release was compromised in Pask^−/−^ islets, in agreement with published data \\[[@CR19]\\]. ", "Fig.", " 3Islets from Pask^−/−^ mice display abnormal inhibition of glucagon secretion in response to glucose. ", "a Glucagon and (b) insulin secretion in response to glucose was assessed in groups of ten mouse islets, as previously described \\[[@CR7]\\]. ", "Data presented ar e% secreted hormone/total hormone content in 10 islets. ", "White bars, islets exposed to 0.5 mmol/l glucose; black bars, islets exposed to 10 mmol/l glucose. ", "c Total glucagon and (d) insulin from mouse islets of each genotype. ", "n = 3 separate preparations of islets. ", "e Total RNA was extracted from groups of 100 islets using Tri-reagent (Invitrogen) and gene expression analysed by real-time quantitative PCR analysis using SYBR-green (Applied Biosystems). ", "Cyclophilin gene expression was used as the internal calibrator. ", "n = 3 Nd, not detected; black bars, Pask^+/+^ wild-type islets; grey bars, Pask^+/−^ heterozygote islets; white bars, Pask^−/−^ homozygous knockout mice islets. ", "\\*p \\< 0.05, \\\\p \\< 0.01The expression of mouse preproinsulin 2 (Ins2) and Pdx1 genes was strongly impaired in Pask^−/−^ mouse islets (Fig.", " [3e](#Fig3){ref-type=\"fig\"}), as previously reported \\[[@CR18], [@CR20]\\]. ", "Moreover, the insulin content of whole Pask^−/−^ mouse pancreases was 1.98 ± 0.3-fold lower than that of wild-type pancreases (67 ± 15 vs 133 ± 12 ng/mg protein for Pask^−/−^ and wild-type mice, respectively; n = 3 mice for each genotype). ", "While glucagon protein content in Pask^−/−^ islets (Fig.", " [3c](#Fig3){ref-type=\"fig\"}) was unaffected, preproglucagon (Gcg) gene expression was slightly but significantly increased, as was Prkaa2 mRNA expression (Fig.", " [3e](#Fig3){ref-type=\"fig\"}).", "\n\nGlucagon release is activated in the absence of Pask in alpha-TC1-9 cells Since the above experiments using intact islets did not allow ready discrimination between an action of PASK cell-autonomously in the alpha cell and an effect mediated by changes in the release of beta cell-derived factors, we next explored the role of the enzyme in the clonal alpha-TC1-9 cell line \\[[@CR3]\\]. ", "Culture of alpha-TC1-9 cells in the presence of an siRNA against Pask led to near complete ablation of Pask gene expression and protein content (Fig.", " [4a](#Fig4){ref-type=\"fig\"}). ", "Glucagon release from Pask-deficient alpha-TC1-9 cells at inhibitory (10 mmol/l) glucose concentrations was comparable to that observed in control cells at stimulatory (0.5 mmol/l) glucose concentrations (Fig.", " [4b](#Fig4){ref-type=\"fig\"}). ", "By contrast, addition of extracellular insulin (20 nmol/l) led to inhibition of glucagon secretion in control and Pask-silenced alpha-TC1-9 cells, indicating (1) the presence of distinct glucose and insulin signalling pathways in the alpha cell and (2) that the insulin signalling pathway in Pask-silenced alpha-TC1-9 cells was intact (Fig.", " [4b](#Fig4){ref-type=\"fig\"}). ", "Total glucagon protein content, as assessed by radioimmunoassay, was not different between alpha-TC1-9 cells treated with control or anti-Pask siRNA (data not shown). ", "Fig.", " 4PASK silencing activates glucagon secretion in alpha-TC1-9 cells. ", "a Transfection of alpha-TC1-9 cells with 1 nmol/l Pask siRNA led to decreased Pask expression and PASK protein content, as assessed by real-time quantitative PCR and western (immuno-)blot analysis. ", "The migration of molecular weight markers (BioRad, Hemel Hempstead, UK) is indicated on the western (immuno-)blot. ", "b Glucagon secretion in response to elevated glucose and insulin was assessed as described in Fig.", " [3](#Fig3){ref-type=\"fig\"}, n = 3. ", "Data presented are % secreted hormone/total hormone content per sample. ", "White bars, transfected with control; grey bars, transfected with anti-Pask siRNA. ", "\\*p \\< 0.05, \\\\p \\< 0.01\n\nGlucagon release is inhibited by PASK overexpression in alpha-TC1-9 cells and human islets of Langerhans The above findings indicated that PASK may be an inhibitor of glucagon release from alpha cells. ", "To test this hypothesis, we next explored the impact of forced activation of the enzyme in these cells. ", "Adenovirus-mediated overexpression of PASK in alpha-TC1-9 cells (Fig.", " [5a](#Fig5){ref-type=\"fig\"}) led to inhibition of glucagon secretion at normally stimulatory (1 mmol/l) glucose concentrations (0.36 ± 0.1-fold vs control). ", "Fig.", " 5Overexpression of PASK inhibits glucagon secretion in alpha-TC1-9 cells and human islets of Langerhans. ", "a Alpha-TC1-9 cells were infected with adenovirus encoding for PASK (grey bars) or enhanced green fluorescent protein (EGFP; control virus, white bars) at multiplicity of infection of 100 and cultured for 24 h prior to glucagon secretion as described in Fig.", " [3](#Fig3){ref-type=\"fig\"}, n = 3. ", "b Human islets of Langerhans were infected with adenovirus for human PASK or EGFP at multiplicity of infection of 100 and cultured for 48 h prior to glucagon secretion assay \\[[@CR3]\\], n = 3. ", "Data presented are % secreted hormone/total hormone content per sample. ", "c Western (immuno-)blot analysis of protein extracts from alpha-TC1-9 cells and human pancreatic islets after 48 h transduction with adenoviruses encoding for PASK or EGFP. ", "PASK protein content was normalised to tubulin protein content as assessed by densitometry using ImageJ (<http://rsbweb.nih.gov/ij/index.html>; n = 3). ", "Representative images from at least three separate preparations of each are shown. ", "\\*p \\< 0.05, \\\\p \\< 0.01Similarly, overexpression of PASK in human islets of Langerhans (Fig.", " [5b](#Fig5){ref-type=\"fig\"}) inhibited glucagon secretion at all glucose concentrations tested, while the stimulatory effects of KCl were largely maintained. ", "Interestingly, there was still an apparent effect of glucose on glucagon secretion in human islets overexpressing PASK (Fig.", " [5b](#Fig5){ref-type=\"fig\"}), consistent with a maintained effect on glucagon release mediated by beta cell-derived factors.", "\n\n*Silencing of Pask* gene expression in alpha-TC1-9 cells and E13.5 rat pancreatic epithelial explants causes increased AMPK-alpha2 and glucagon gene expression** In an effort to identify the mechanism(s) through which PASK may regulate glucagon secretion, we measured the expression of a number of potential target genes. ", "Pask gene expression was inhibited in alpha-TC1-9 cells treated with a siRNA against Pask (Fig.", " [6](#Fig6){ref-type=\"fig\"}). ", "In line with the above findings in Pask^−/−^ mouse islets (Fig.", " [3e](#Fig3){ref-type=\"fig\"}), preproglucagon (Gcg) gene expression was increased substantially by Pask ablation in alpha-TC1-9 cells (7.4 ± 1.3-fold vs control; Fig.", " [6a](#Fig6){ref-type=\"fig\"}), although total glucagon protein content was unaltered (Fig.", " [2c](#Fig2){ref-type=\"fig\"}), consistent with the relatively slow turnover of mature glucagon. ", "Prkaa2 (Fig.", " [6a](#Fig6){ref-type=\"fig\"}), but not Prkaa1 (data not shown) gene expression was also increased (4.3 ± 1.5-fold vs control) by Pask silencing. ", "Fig.", " 6Pask silencing in alpha-TC1-9 cells leads to increased expression of Gcg and Prkaa2. ", "Real-time quantitative PCR analysis, using SYBR green (Applied Biosystems), of RNA from alpha-TC1-9 cells treated with control or Pask siRNA, n = 3. ", "Cyclophilin gene expression was used as the internal calibrator for real-time quantitative PCR. ", "White bars, treated with control; grey bars, treated with anti-Pask siRNA. ", "\\\\p \\< 0.01To determine whether the dysregulation of glucagon gene expression and release in Pask^−/−^ mice was due to a role of the enzyme in the development of pancreatic alpha and beta cells, we next examined the impact of Pask silencing in developing pancreatic epithelia. ", "E13.5 rat pancreatic epithelial explants \\[[@CR33]\\], in which Pask gene expression was silenced with an anti-Pask siRNA, developed endocrine buds to an extent indistinguishable from that observed in explants treated with a control (scrambled) siRNA (ESM Fig.", " [3](#MOESM3){ref-type=\"\"}). ", "However, explants in which Pask was silenced displayed similar increases in Gcg and Prkaa2 gene expression (ESM Fig.", " [3](#MOESM3){ref-type=\"\"}) to those observed in alpha-TC1-9 cells (Fig.", " [6](#Fig6){ref-type=\"fig\"}). ", "Explants overexpressing Pask did not survive the 10 day culture period.", "\n\nDiscussion {#Sec4}\n==========\n\nThe present data indicate that PASK/Pask is expressed in human and mouse pancreatic islets, respectively, and regulated by glucose. ", "Moreover, in the mouse, Pask mRNA levels are at least as high in alpha cells as in beta cells. ", "Correspondingly, we provide evidence that changes in Pask gene expression within the islet regulate both insulin content \\[[@CR18], [@CR20]\\] and glucagon release, i.e. that PASK mediates a 'high glucose' signal in alpha and beta cells. ", "In the alpha cell, this might be achieved either via a cell-autonomous action on cellular activity and/or through changes in the release of beta cell-derived factors (Fig.", " [7](#Fig7){ref-type=\"fig\"}). ", "Either of these mechanisms are likely to modulate intracellular signalling within the alpha cell through changes in membrane excitability, levels of unbound Ca^2+^, cAMP, etc. ", "Fig.", " 7Proposed mechanism for PASK action in alpha cells. ", "Glucagon secretion is regulated by changes in extracellular glucose and other factors, including insulin and possibly other molecules released from pancreatic beta cells. ", "We propose (dashed lines) that PASK may be involved in cell-autonomous regulation of glucagon secretion, possibly through the regulation of Prkaa2 gene expression (AMPK-alpha2) (1) and/or an as yet unidentified pathway (2). ", "PASK may also regulate glucagon secretion through its action on beta cell function and/or beta cell mass (3)\n\nPASK is expressed in pancreatic islets An important finding of the present study is that Pask mRNA is clearly present in mouse islets maintained at permissive glucose concentrations (11 mmol/l), in contrast to a recent suggestion \\[[@CR22]\\]. ", "These results and those from another recent publication \\[[@CR20]\\] support our own previous findings \\[[@CR18]\\]. ", "We would stress, however, that the level of gene expression, at least at the mRNA level, was relatively low compared with tissues in which Pask is strongly expressed (notably in the testes) \\[[@CR22]\\], an observation that probably underlies the failure to detect significant expression using alternative approaches \\[[@CR22]\\].", "\n\nPASK regulates insulin and glucagon secretion It has previously been shown that islet architecture and beta cell mass in Pask^−/−^ mice are intact \\[[@CR19], [@CR22]\\]. ", "Thus, it was hypothesised in earlier studies that the observed decrease in insulin release may have been due to defective glucose-signalling in the beta cell \\[[@CR19]\\]. ", "In contrast, our data show that glucose-regulated insulin secretion was intact in Pask^−/−^ islets (Fig.", " [3b](#Fig3){ref-type=\"fig\"}), but that the insulin content of the islet (Fig.", " [3d](#Fig3){ref-type=\"fig\"}) and pancreas (see Results section) were lowered by Pask deletion. ", "This apparent discrepancy between the present and earlier \\[[@CR19], [@CR22]\\] studies may reflect differences in the genetic background, age and sex of the mice used. ", "We would, however, note that Pask^−/−^ beta cell mass was previously assessed by immunohistochemical analysis of fixed pancreatic sections, which may be prone to error.", "Nevertheless, it was previously reported that plasma insulin content was compromised in Pask^−/−^ mice \\[[@CR19]\\], a result consistent with the present findings. ", "In our hands, glucagon release from Pask^−/−^ mouse islets (Fig.", " [3a](#Fig3){ref-type=\"fig\"}) and human islets in which PASK was overexpressed (Fig.", " [5b](#Fig5){ref-type=\"fig\"}) still displayed some degree of glucose-responsiveness, even though this was markedly decreased compared with the control condition. ", "We hypothesise that this 'residual' regulation of release may be due, at least in part, to the release of insulin or other factors (Zn^2+^, gamma-aminobutyric acid, etc.) ", "from neighbouring pancreatic beta cells and is consistent with the maintained effect of exogenous insulin on glucagon release from alpha-TC1-9 cells (Fig.", " [4b](#Fig4){ref-type=\"fig\"}).Close inspection of the data of Fig.", " [3a](#Fig3){ref-type=\"fig\"} vs Fig.", " [4](#Fig4){ref-type=\"fig\"} reveals that whereas loss of Pask enhanced glucagon secretion from islets only at high (inhibitory) glucose levels (Fig.", " [3a](#Fig3){ref-type=\"fig\"}), stimulation of glucagon release was apparent at all glucose concentrations examined in alpha-TC1-9 cells (Fig.", " [4](#Fig4){ref-type=\"fig\"}). ", "The mechanisms responsible for this difference are unclear. ", "However, we note that while insulin mRNA was present at low but detectable levels in control alpha-TC-1-9 cells (C~t~ values ≥ 29; data not shown), silencing of Pask led to decreased insulin gene expression such that this was below the limit of detection. ", "Hence an action of Pask silencing on endogenous insulin secretion from alpha-TC-1-9 cells, and thus loss of tonic inhibition of glucagon secretion by this hormone, may contribute to the above mechanisms. ", "Further studies are needed to resolve this question.", "Interestingly, the increase in plasma glucagon levels measured after 16 h fasting in 8-week-old Pask^−/−^ mice was similar to that observed in alpha cell-specific insulin receptor knockout mice of the same age \\[[@CR5]\\]. ", "We have previously shown that PASK activity is not regulated by insulin, but that PASK may regulate insulin gene expression in pancreatic beta cells \\[[@CR18]\\]. ", "Thus, we propose that the regulation of insulin content by Pask is one of the mechanisms through which PASK may indirectly regulate glucagon release.", "\n\nA role for AMPK alpha2 downstream of PASK? ", "Our gene-expression studies revealed that expression of the catalytic subunit of another glucose-responsive fuel gauge, Prkaa2 (encoding AMPK-alpha2), is upregulated when Pask gene expression is compromised (Fig.", " [6](#Fig6){ref-type=\"fig\"}). ", "This is an interesting observation, since AMPK activity has been shown to be glucose-responsive in pancreatic beta cells \\[[@CR36]\\] and to regulate insulin release \\[[@CR37], [@CR38]\\]; in addition, we have recently shown that activation of AMPK in the alpha cell stimulates glucagon secretion \\[[@CR15]\\]. ", "However, as also observed here, Prkaa2 mRNA levels are normally much lower (more than tenfold) than Prkaa1 in purified mouse beta and alpha cells \\[[@CR31]\\], suggesting that the inappropriate activation of this isoform and an increase in AMPK activity in the nucleus (from which AMPK alpha1 is excluded in mature pancreatic endocrine cells) \\[[@CR36]\\] may impact on the transcription of key genes, including Gcg, to reprogram the alpha cell. ", "Interestingly, induction of Prkaa2 expression was also observed in E13.5 pancreatic epithelia \\[[@CR33]\\] in which Pask was silenced (Fig.", " [6c](#Fig6){ref-type=\"fig\"}), indicating that defects during pancreatic development may contribute to the dysregulation of glucagon release in Pask^−/−^ mice.", "\n\nPASK may have a role in the pathophysiology of type 2 diabetes The observation that pancreatic islets from patients with type 2 diabetes display lower PASK mRNA levels than islets from non-diabetic individuals (Fig.", " [1b](#Fig1){ref-type=\"fig\"}) suggests that lowered PASK activity may contribute to decreased insulin release and to enhanced glucagon secretion in this condition \\[[@CR1]\\]. ", "PASK may therefore represent a potential therapeutic target, the activation of which might favourably affect the secretion of both hormones in patients with type 2 diabetes.", "\n\nElectronic supplementary materials {#AppESM1}\n----------------------------------\n\nBelow is the link to the electronic supplementary material.", "\n\n###### \n\n(PDF 37.8 kb)\n\n###### \n\n(PDF 11.0 kb)\n\n###### \n\n(PDF 20.9 kb)\n\n###### \n\n(PDF 48.5 kb)\n\nThe authors thank S. Vakhshouri for technical assistance, and F. Semplici and M. K. Loder for scientific input during manuscript preparation. ", "This work was supported by a Juvenile Diabetes Research Foundation post-doctoral fellowship and an European Foundation for the Study of Diabetes Albert Renold travelling fellowship to G. da Silva Xavier, and by grants to G. A. Rutter from the Wellcome Trust (081958/2/07/2) and the Medical Research Council (G0401641). ", "H. Farhan, H. Kim and S. Caxaria were supported by Imperial College London BSc and MSc project funds. ", "The Diabetes Research and Wellness Foundation supported P. Johnson and S. Hughes.", "\n\nDuality of interest The authors declare that there is no duality of interest associated with this manuscript.", "\n\nOpen Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.", "\n\nH. Farhan and H. 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[ "The Raven Prince\n\nWidowed Anna Wren is having a wretched day. ", "After an arrogant man on horseback nearly crushes her, she arrives home to learn that she is in dire financial straits. ", "The Earl of Swartingham is in a quandary. ", "Having frightened off two secretaries, Edward de Raaf needs someone who can withstand his bad temper and boorish behavior. ", "When Anna becomes the earl's secretary, it would seem that both their problems are solved. ", "But when she discovers he plans to visit the most notorious brothel in London, she sees red-and decides to assuage her desires....\n\nWicked Intentions\n\nInfamous for his wild, sensual needs, Lazarus Huntington, Lord Caire, is searching for a savage killer in St. Giles, London's most notorious slum. ", "Widowed Temperance Dews knows St. Giles like the back of her hand-she's spent a lifetime caring for its inhabitants at the foundling home her family established. ", "Now that home is at risk.....\n\nDuke of Sin\n\nDevastatingly handsome. ", "Vain. ", "Unscrupulous. ", "Valentine Napier, the Duke of Montgomery, is the man London whispers about in boudoirs and back alleys. ", "A notorious rake and blackmailer, Montgomery has returned from exile intent on seeking revenge on those who have wronged him. ", "But what he finds in his own bedroom may lay waste to all his plans.", "\n\nDuke of Pleasure: Maiden Lane, Book 11\n\nBold. ", "Brave. ", "Brutally handsome. ", "Hugh Fitzroy, the Duke of Kyle, is the king's secret weapon. ", "Sent to defeat the notorious Lords of Chaos, he is ambushed in a London alley - and rescued by an unlikely ally: a masked stranger with the unmistakable curves of a woman.", "\n\nTo Taste Temptation: Legend of the Four Soldiers, Book 1\n\nBritain’s high society—le bon ton—loves nothing more than a good scandal, and they’re giddy with the appearance of wealthy Samuel Hartley. ", "Not only is he self-made, American, and in the habit of wearing moccasins, but he is also notorious for fleeing a battle in which several English gentlemen lost their lives. ", "Lady Emeline Gordon is captivated by Samuel. ", "Not only does he defy convention with his unusual dress, his sensual smile, and his forthright manner, but he survived the battle that killed her beloved brother.", "\n\nAn Offer from a Gentleman\n\nSophie Beckett never dreamed she'd be able to sneak into Lady Bridgerton's famed masquerade ball - or that Prince Charming would be waiting there for her! ", "Though the daughter of an earl, Sophie has been relegated to the role of servant by her disdainful stepmother. ", "But now, spinning in the strong arms of the debonair and devastatingly handsome Benedict Bridgerton, she feels like royalty. ", "Alas, she knows all enchantments must end when the clock strikes midnight.", "\n\nThe Duke and I\n\nSimon Basset, the irresistible Duke of Hastings, has hatched a plan to keep himself free from the town's marriage-minded society mothers. ", "He pretends to be engaged to the lovely Daphne Bridgerton. ", "After all, it isn't as if the brooding rogue has any real plans to marry - though there is something about the alluring Miss Bridgerton that sets Simon's heart beating a bit faster. ", "And as for Daphne, surely the clever debutante will attract some very worthy suitors now that it seems a duke has declared her desirable.", "\n\nMarrying Winterborne\n\nSavage ambition has brought common-born Rhys Winterborne vast wealth and success. ", "In business and beyond, Rhys gets exactly what he wants. ", "And from the moment he meets the shy, aristocratic Lady Helen Ravenel, he is determined to possess her. ", "If he must take her virtue to ensure she marries him, so much the better....\n\nA Scot in the Dark: Scandal & Scoundrel, Book II\n\nMiss Lillian Harwood has lived much of her life alone in a gilded cage, longing for love and companionship. ", "When an artist offers her pretty promises and begs her to pose for a scandalous portrait, Lily doesn't hesitate...until the lying libertine leaves her in disgrace. ", "With the painting now public, Lily has no choice but to turn to the one man who might save her from ruin.", "\n\nA Duke to Remember\n\nElise deVries is not what she seems. ", "By night the actress captivates London theatergoers with her chameleonlike ability to slip inside her characters. ", "By day she uses her mastery of disguise to work undercover for Chegarre & Associates, an elite agency known for its discreet handling of indelicate scandals. ", "But when Elise is tasked to find the missing Duke of Ashland, she finds herself center stage in a real-life romance as tumultuous as any drama.", "\n\nMine Till Midnight: The Hathaways, Book 1\n\nWhen an unexpected inheritance elevates her family to the ranks of the aristocracy, Amelia Hathaway discovers that tending to her younger sisters and wayward brother was easy compared to navigating the intricacies of the ton. ", "Even more challenging: the attraction she feels for the tall, dark, and dangerously handsome Cam Rohan.", "\n\nAmazon Customer says:\"It's different from the book - but not abridged\"\n\nSlightly Married: Bedwyn Saga Series, Book 1\n\nLike all the Bedwyn men, Aidan has a reputation for cool arrogance. ", "But this proud nobleman also possesses a loyal, passionate heart - and it is this fierce loyalty that has brought Colonel Lord Aidan to Ringwood Manor to honor a dying soldier's request. ", "Having promised to comfort and protect the man's sister, Aidan never expected to find a headstrong, fiercely independent woman who wants no part of his protection, nor did he expect the feelings this beguiling creature would ignite in his guarded heart.", "\n\nNot Quite a Lady: Carsington Brothers Series\n\nDarius Carsington is a spectacularly attractive rake, who's all brains and brawn...and no heart; a man who's equally expert at bedding loose-moraled women and writing scholarly papers. ", "He finds society's \"perfect darlings\" exceedingly boring. ", "Then why is he so intrigued by the supposedly faultless Lady Charlotte Hayward? ", "Darius senses a crack under her polished surface - and finding it is a challenge he can't resist.", "\n\nDo You Want to Start a Scandal\n\nOn the night of the Parkhurst ball, someone had a scandalous tryst in the library. ", "Was it Lord Canby, with the maid, on the divan? ", "Or Miss Fairchild, with a rake, against the wall? ", "Perhaps the butler did it. ", "All Charlotte Highwood knows is this: It wasn't her. ", "But rumors to the contrary are buzzing. ", "Unless she can discover the lovers' true identity, she'll be forced to marry Piers Brandon, Lord Granville - the coldest, most arrogantly handsome gentleman she's ever had the misfortune to embrace.", "\n\nA Night to Surrender: Spindle Cove, Book 1\n\nWelcome to Spindle Cove, where the ladies with delicate constitutions come for the sea air, and men in their prime are..nowhere to be found. ", "Or are they? ", "Spindle Cove is the destination of choice for certain types of well-bred young ladies: The painfully shy, young wives disenchanted with matrimony, and young girls too enchanted with the wrong men; it is a haven for those who live there. ", "Victor Bramwell, the new Earl of Rycliff, knows he doesn't belong here.", "\n\nThe Highlander: To Tempt a Highlander, Book 3\n\nThey call him the Demon Highlander. ", "The fearsome Lieutenant Colonel Liam MacKenzie is known for his superhuman strength, towering presence, and fiery passion in the heat of battle. ", "As laird to the MacKenzie clan, the undefeated marquess has vanquished his foes with all the rage and wrath of his barbaric Highland ancestors. ", "But when an English governess arrives to care for his children, the master of war finds himself up against his greatest opponent...in the game of love.", "\n\nHow to Capture a Duke: Matchmaking for Wallflowers, Book 1\n\nFiona Amberly is more intrigued by the Roman ruins near her manor house than she is by balls. ", "When her dying grandmother worries about Fiona's future, Fiona stammers that she's secretly engaged. ", "Soon she finds herself promising that she will introduce her husband-to-be by Christmas.", "\n\nCold-Hearted Rake\n\nDevon Ravenel, London's most wickedly charming rake, has just inherited an earldom. ", "But his powerful new rank in society comes with unwanted responsibilities...and more than a few surprises. ", "His estate is saddled with debt, and the late earl's three innocent sisters are still occupying the house - along with Kathleen, Lady Trenear, a beautiful young widow whose sharp wit and determination are a match for Devon's own.", "\n\nDuke of My Heart\n\nCaptain Maximus Harcourt, the unconventional tenth Duke of Alderidge, can deal with tropical storms, raging seas, and the fiercest of pirates. ", "But he's returned home from his latest voyage to find a naked earl - quite inconveniently deceased - tied to his missing sister's bed. ", "And he has only one place to turn. ", "Now he's at the mercy of the captivating Miss Ivory Moore of Chegarre & Associates, known throughout London for smoothing over the most dire of scandals.", "\n\nThe Rogue Not Taken: Scandal & Scoundrel, Book 1\n\nWhen Sophie, the least interesting of the Talbot sisters, lands her philandering brother-in-law backside first in a goldfish pond in front of all society, she becomes the target of very public aristocratic scorn. ", "Her only choice is to flee London, vowing to start a new life far from the aristocracy. ", "Unfortunately, the carriage in which she stows away isn't saving her from ruin. ", "It's filled with it.", "\n\nThe Other Duke: The Notorious Flynns, Volume 1\n\nFor years Serafina McPhee has been engaged to marry the heir to the duke of Hartholm; and for almost as long, she has been struggling to find a way out of that engagement. ", "When he suddenly dies, she does not mourn but thrills at the idea that she will be free. ", "Unfortunately, best-laid plans go awry when the next in line for the title, her intended's cousin, Raphael \"Rafe\" Flynn, is forced to take over the engagement. ", "But Serafina knows Rafe's reputation as a libertine and wants nothing to do with him, either, even if he is devastatingly handsome.", "\n\nMiss Wonderful: Carsington Brothers, Book 1\n\nWar hero Alistair Carsington really really loves women, and his romantic impulses have landed him in nearly as much danger as the Battle of Waterloo. ", "To avoid his usual temptations and perhaps even repay the friend who saved his life, he's exiled himself to a place far from civilization - Derbyshire - in winter! ", "Fate laughs at his good intentions and drives him straight into conflict with Miss Mirabel Oldridge, his match in tenacity, intelligence, and deviousness - who also happens to be wildly irresistible.", "\n\nA Rogue by Any Other Name\n\nA decade ago, the Marquess of Bourne was cast from society with nothing but his title. ", "Now a partner in London's most exclusive gaming hell, the cold, ruthless Bourne will do whatever it takes to regain his inheritance - including marrying perfect, proper Lady Penelope Marbury. ", "A broken engagement and years of disappointing courtships have left Penelope with little interest in a quiet, comfortable marriage, and a longing for something more. ", "How lucky that her new husband has access to an unexplored world of pleasures.", "\n\nSomeone to Love: A Westcott Novel, Book 1\n\nAnna Snow grew up in an orphanage in Bath knowing nothing of the family she came from. ", "Now she discovers that the late Earl of Riverdale was her father and that she has inherited his fortune. ", "She is also overjoyed to learn she has siblings. ", "However, they want nothing to do with her or her attempts to share her new wealth. ", "But the new earl's guardian is interested in Anna.", "\n\nPublisher's Summary\n\nTHE ONE THING A LADY MUST NEVER DO....\n\nWealthy Lady Georgina Maitland doesn't want a husband, though she could use a good steward to run her estates. ", "One look at Harry Pye, and Georgina knows she's not just dealing with a servant, but a man.", "\n\nIS FALL IN LOVE....\n\nHarry has known many aristocrats - including one particular nobleman who is his sworn enemy. ", "But Harry has never met a beautiful lady so independent, uninhibited, and eager to be in his arms.", "\n\nWITH HER SERVANT.", "\n\nStill, it's impossible to conduct a discreet liaison when poisoned sheep, murdered villagers, and an enraged magistrate have the county in an uproar. ", "The locals blame Harry for everything. ", "Soon it's all Georgina can do to keep her head above water and Harry's out of the noose...without missing another night of love.", "\n\nBook 2 of The Prince series and it's every bit as good as book 1 - well what else would you expect from the very talented mind of Ms Hoyt - and, although this is a trilogy, each book is a stand-alone book with the only connection being a nursery story about a Prince running through each one.", "\n\nIf you're like me and love a good historical romance then just press the Add to Cart key now because this has so many thing we love - a likeable strong heroine that's no beauty except in the eyes of her hero, her flawed and mentally tortured Land Steward Harry and, like a moth to a flame, the Lady just can't stay away from him.", "\n\nA very emotional roller-coaster of a plot that's funny, sad, tender, passionate, sexy and sweet - yet it's also got cruelty, suspicion, tragedy and bitterness at the same time. ", "Apart from their differences in the social divide dictated by Georgian England, Harry is also being framed for murder and Lady Georgina has a sister and three brothers who are all disapproving and giving her unwanted and unhelpful advice. ", "Despite all the negatives in their lives they desperately try hard to have a loving relationship but holding on to it proves even harder as the villain of the story (there's always one isn't there!) ", "tightens his net.", "\n\nWorth a credit? ", "Yes absolutely, EH books usually are, but there is strong verbalisations of the sex scenes - so be warned.", "\n\nIf you are interested in Historical fiction with romance then this is the book for you. ", "Very seductive, as well as moving. ", "This is definetly worth a credit. ", "Moira's voice is such that you just want to listen, and it calms your senses. ", "If you want to just sit by the pool and relax, or sit by the fire (depending on which hemisphere your in) then this book is must.", "\n\nCamden Smith owns DREAMFly Marketing, a full service marketing firm located in Southwest Florida. ", "She regularly reviews books and is an avid reader as well as audible client. ", "Favorite books are mysterious romances or those stories about personal growth.", "\n\nIf you like sex you'll like this novel. ", "A little too much slang for sexual organs for my taste - a bit crass but I loved the love story - it has real fight in it. ", "You always wonder who the murderer is and you think you know and then you don't - really great swings to the story.", "\n\nThe writer did not do a great job connecting the male character to the previous book's male lead character - she should have introduced and connected them earlier so we would understand why the heck this couple was important.", "\n\nI loved the author's first book, The Raven Prince. ", "But this second book had a downer element that caused me to give it 4 stars instead of 5. ", "In this story, the Lord of the area who also had police powers had the ability to arrest any innocent person he chose, lock them in a cell, and torture them without any local person being able to do anything about it. ", "He had absolute power and was so evil in his treatment of others, that it took away too much from the romance story for me. ", "I'm still glad that I read it, but it's not a favorite. ", "I enjoy this author's writing style and characters. ", "I plan to read her next book.", "\n\nAs others have said, this is the best of the three books in this series (Raven Prince, Leopard Prince, Serpent Prince). ", "You really don't need to read these in any order, as they don't connect much at all with each other. ", "Something about the personality of this heroine, and the commoner hero, really click. ", "Love everything about it. ", "I always love the stories where females from this time period defy convention and are as independent as possible. ", "This narrator is fabulous, cannot say enough about the great job she does.", "\n\nIt pains me to say this because I am a fan of Elizabeth Hoyt, but this book was a disappointment. ", "The book before this, Raven Prince, was a delight, but I just couldn't get into this one. ", "The basic story line about the affair between an earl's sister, Georgina, and her land management servant, Harry, had great potential,but it became tangled up with a number of subplots that were either confusing or almost irrelevant to the main story. ", "By about the middle of the book, the pace became cumbersome and only deteriorated after that. ", "I had to fast forward several times just to finish. ", "I cannot recommend this book.", "\n\nOh my, this book was so good I could not stop listening.", "Anna, the heroine is one of the funniest ever. ", "This has to be one of my favorite books of Elizabeth Hoyt. ", "The first book in this series, Raven Prince was good and totally worth the listen, however this one is just wonderful. ", "if you read/listen to Elizabeth Hoyt books you know about the Fairy Tales, I love the fact that in this book the heroine was the one that told it. ", "What a wonderful character Anna Wren is. ", "One of the best by far.", "\n\nThe narrator is so good it makes the book even better. ", "I would give this book 10 stars if I could. ", "Worth every credit or dollar. ", "I am on to the 3 book Serpent Prince, I see that it is 22 hours long and wont be able to finish it one day as I did this one, but I hope I want too.", "\n\nMen are such dolts sometimes, but we love them anyway 😘. ", "I loved this book, the heroine's personality is cute (think 18th Century Meg Ryan) and goes for what she wants just as soon as she figures out what that is. ", "The hero is obviously troubled but I like him quite a bit. ", "The banter between the two had me laughing out loud throughout the book. ", "It actually reminded me of some of Julia Quinn's dialogues. ", "The bad guy(s) are perfectly evil and there's a satisfying HEA. ", "What more can you ask for! ", "Also Moira Quirk is becoming one of my ultimate favorite narrators!", "\n\nWealthy Lady Georgina Maitland is unique when it comes to society, she was left with money to live her life no man, but when she meets Harry, she rethinks the no man part. ", "Love is not easy especially when your judged by money and name.", "\n\nHarry Pye helps run her estate but when they finally meet for the first time he can't stop thinking about her or keep his hands off her. ", "When sheep begin to die and he is the prime suspect he has to focus on finding the real killer and she is not making it easy.", "\n\nI hesitate to write a poor review ... but, nevertheless. ", "After enjoying the Raven Prince and Ms. Quirk's narration, it seemed only natural to follow with the Leopard Prince. ", "Unfortunately, they didn't seem to have much in common. ", "I found this book to be somewhat juvenile and was surprised by Ms. Quirk's narration. ", "It almost sounded like someone reading a fairytale, a bit cartoonish, with a little uninspiring sex thrown in here and there. ", "My impression of the main female character was that she was an uninspiring airhead that wasn't worth building a story around, pretty much the same for the male lead. ", "Still pondering how the two books could have been so different, even in narration. 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[ "Emma Watson To Replace Emma Stone in 'Little Women'\n\nConfirming what mis-informed grandparents have been errantly saying for the past decade, it turns out that Emma Watson and Emma Stone are actually interchangeable.", "\n\nVariety broke the news today that Watson would be taking over for Stone in the upcoming Columbia Pictures production of Little Women due to unforeseen scheduling conflicts. ", "The Greta Gerwig-directed adaptation is in negotiations with Meryl Streep, Laura Dern, Saoirse Ronan, Timothée Chalamet, and Florence Pugh to star in the upcoming production. ", "It won't be the first time the American literature classic has been adapted for the big screen with a recent BBC miniseries and the popular 1994 Winona Ryder-starring version being the most notable recent takes on the novel by Louisa May Alcott.", "\n\nMany roles are not currently set in stone, with Streep originally reported to be playing Marmee and now slated to be Aunt March. ", "Stone was initially reported to be cast in the role of Meg but it is unclear if Watson will remain as that particular character or another. ", "Production of Little Women is set to begin next month." ]	{ "pile_set_name": "Pile-CC" }	[ 0.013888888888888888, 0.022857142857142857, 0.022857142857142857, 0.012244897959183673, 0.007633587786259542, 0.02142857142857143, 0.018518518518518517 ]	0.017061	5
[ "/\n jQuery File Upload Processing Plugin 1.3.0\n * https://github.com/blueimp/jQuery-File-Upload\n \n Copyright 2012, Sebastian Tschan\n * https://blueimp.net\n \n Licensed under the MIT license:\n * http://www.opensource.org/licenses/MIT\n /\n\n/jslint nomen: true, unparam: true /\n/global define, window /\n\n(function (factory) {\n 'use strict';\n if (typeof define === 'function' && define.amd) {\n // Register as an anonymous AMD module:\n define([\n 'jquery',\n './jquery.fileupload'\n ], factory);\n } else {\n // Browser globals:\n factory(\n window.jQuery\n );\n }\n}(function ($) {\n 'use strict';\n\n var originalAdd = $.blueimp.fileupload.prototype.options.add;\n\n // The File Upload Processing plugin extends the fileupload widget\n // with file processing functionality:\n $.widget('blueimp.fileupload', $.blueimp.fileupload, {\n\n options: {\n // The list of processing actions:\n processQueue: [\n /\n {\n action: 'log',\n type: 'debug'\n }\n /\n ],\n add: function (e, data) {\n var $this = $(this);\n data.process(function () {\n return $this.fileupload('process', data);\n });\n originalAdd.call(this, e, data);\n }\n },\n\n processActions: {\n /\n log: function (data, options) {\n console[options.type](\n 'Processing \"' + data.files[data.index].name + '\"'\n );\n }\n */\n },\n\n _processFile: function (data, originalData) {\n var that = this,\n dfd = $.Deferred().resolveWith(that, [data]),\n chain = dfd.promise();\n this._trigger('process', null, data);\n $.each(data.processQueue, function (i, settings) {\n var func = function (data) {\n if (originalData.errorThrown) {\n return $.Deferred()\n .rejectWith(that, [originalData]).promise();\n }\n return that.processActions[settings.action].call(\n that,\n data,\n settings\n );\n };\n chain = chain.pipe(func, settings.always && func);\n });\n chain\n .done(function () {\n that._trigger('processdone', null, data);\n that._trigger('processalways', null, data);\n })\n .fail(function () {\n that._trigger('processfail', null, data);\n that._trigger('processalways', null, data);\n });\n return chain;\n },\n\n // Replaces the settings of each processQueue item that\n // are strings starting with an \"@\", using the remaining\n // substring as key for the option map,\n // e.g. \"@autoUpload\" is replaced with options.autoUpload:\n _transformProcessQueue: function (options) {\n var processQueue = [];\n $.each(options.processQueue, function () {\n var settings = {},\n action = this.action,\n prefix = this.prefix === true ? ", "action : this.prefix;\n $.each(this, function (key, value) {\n if ($.type(value) === 'string' &&\n value.charAt(0) === '@') {\n settings[key] = options[\n value.slice(1) \|\| (prefix ? ", "prefix +\n key.charAt(0).toUpperCase() + key.slice(1) : key)\n ];\n } else {\n settings[key] = value;\n }\n\n });\n processQueue.push(settings);\n });\n options.processQueue = processQueue;\n },\n\n // Returns the number of files currently in the processsing queue:\n processing: function () {\n return this._processing;\n },\n\n // Processes the files given as files property of the data parameter,\n // returns a Promise object that allows to bind callbacks:\n process: function (data) {\n var that = this,\n options = $.extend({}, this.options, data);\n if (options.processQueue && options.processQueue.length) {\n this._transformProcessQueue(options);\n if (this._processing === 0) {\n this._trigger('processstart');\n }\n $.each(data.files, function (index) {\n var opts = index ? ", "$.extend({}, options) : options,\n func = function () {\n if (data.errorThrown) {\n return $.Deferred()\n .rejectWith(that, [data]).promise();\n }\n return that._processFile(opts, data);\n };\n opts.index = index;\n that._processing += 1;\n that._processingQueue = that._processingQueue.pipe(func, func)\n .always(function () {\n that._processing -= 1;\n if (that._processing === 0) {\n that._trigger('processstop');\n }\n });\n });\n }\n return this._processingQueue;\n },\n\n _create: function () {\n this._super();\n this._processing = 0;\n this._processingQueue = $.Deferred().resolveWith(this)\n .promise();\n }\n\n });\n\n}));\n" ]	{ "pile_set_name": "Github" }	[ 0.002306805074971165, 0, 0.0008936550491510277, 0 ]	0.0008	5
[ "Elon Musk's Tesla battery in South Australia's Mid-North will no longer be the world's most powerful — with a new, bigger battery being built at Port Augusta.", "\n\nJay Weatherill at the launch of the Tesla lithium ion battery in December. ( ", "ABC News: Nick Harmsen )\n\nThe new battery will be built by Whyalla steelworks owner Sanjeev Gupta, who secured a $10 million loan from the State Government through its Renewable Technology Fund.", "\n\nThe British billionaire, who purchased the steelworks last year though his company Liberty House, also bought a controlling stake in South Australian renewable firm Zen Energy — creating SIMEC Zen Energy.", "\n\nThe 120 megawatts/140 megawatt hours storage facility is larger than the 100MW/129MWh battery built by Tesla in Jamestown last year.", "\n\nIt will support the new solar farm being built at the Whyalla steelworks and will create up to 100 jobs during construction, which will begin later this year.", "\n\nPremier Jay Weatherill said it would also benefit the broader South Australian community.", "\n\n\"We know that more renewable energy means cheaper power, and that's why we have increased our renewable energy target to 75 per cent and also introduced a new renewable storage target of 25 per cent,\" Mr Weatherill said.", "\n\n\"These targets will accelerate the transition from fossil fuels to renewables and lower bills for South Australians.\"", "\n\nMr Weatherill spruiked Labor's commitment over the past 12 months to fixing South Australia's energy problems.", "\n\n\"We cannot turn back, the momentum is growing. ", "Here we are ending the campaign, two billionaires duking out who is going to have the biggest battery here in South Australia,\" he said.", "\n\n\"There are plenty more of those deals to be done and plenty more companies to attract to South Australia.\"", "\n\nMr Weatherill saved the announcement for the last day of campaigning with South Australians taking to the polls on Saturday morning.", "\n\nMoney for the latest battery was committed by the State Government prior to caretaker period, meaning the funding will not be contingent on the election result.", "\n\nTesla launched its battery last year after Elon Musk promised to build it \"in 100 days or it's free\"." ]	{ "pile_set_name": "OpenWebText2" }	[ 0, 0.02531645569620253, 0.02577319587628866, 0.0048543689320388345, 0, 0, 0.01098901098901099, 0.0045045045045045045, 0, 0.008928571428571428, 0, 0, 0, 0, 0.006172839506172839, 0.009708737864077669 ]	0.006015	5
[ "The devil, they say, is in the details.", "\n\nThat well-worn cliché can be applied in equal measure to criminal investigations, corporate contracts and defence procurement deals.", "\n\nThe public has, over the past four months, been starved of the details in the case of Vice-Admiral Mark Norman, an extraordinary and significant bit of political theatre where all three of those interests intersect.", "\n\nThe release this week of a second tranche of unsealed information contained in the RCMP search warrant for Norman's home is undeniably a watershed in the story of the investigation into alleged leaks of cabinet secrets.", "\n\nBut it's also an important moment in the more than three-decade-long career of an officer who was — by all accounts — popular, competent and clearly opinionated.", "\n\nNorman, left, speaks with Vice-Admiral Ron Lloyd during a change of command ceremony back on June 23 in Ottawa. (", "Adrian Wyld/Canadian Press)\n\nThe court records lay out in black and white the RCMP's claim that Norman deliberately leaked cabinet information.", "\n\nWhile the Mounties consider his conversations suspect, they were unable to say — definitively — that he handed over a secret cabinet memo outlining government concerns about the planned $668-million project to lease a supply ship to the navy.", "\n\nInvestigators paid a lot of attention in the search warrant to the unsanctioned back channel email exchanges between Norman and Spencer Fraser, an executive at Federal Fleet Services Inc., which is partnered with Quebec's Chantier-Davie Shipyard.", "\n\nThe lease plan, championed by Chantier-Davie, was opposed both by rival Irving Shipbuilding in Nova Scotia and by bureaucrats within the Defence-Public Works establishment who believe the project undermines the national shipbuilding strategy.", "\n\nThose government officials are referred to in the email exchanges as \"The Knights of No.\"", "\n\nCase and career hinge on details\n\nThe devil is, indeed, in the details.", "\n\nThe back channel dialogue between Norman and Fraser is significant, and it's not an overstatement to say the entire case — and the admiral's career — could hinge on those details.", "\n\nIn the summer of 2015, Federal Fleet Services signed a letter of intent with the Conservative government, on the eve of the last election.", "\n\nThey agreed the company would get a sole-source contract and lease a supply ship to the navy, but the details were to be negotiated.", "\n\nIt was binding in the sense that should the government change its mind there would be an $89-million cancellation penalty.", "\n\nDave Perry, senior analyst for the Canadian Global Affairs Institute think-tank, says companies under contract are entitled to a slightly higher level of access to government officials and a more direct information pipeline.", "\n\nBut the letter of intent is not a final contract, and therefore, it allows Federal Fleet Services into the federal government tent, but only so far.", "\n\n\"They were in a legal grey zone, I guess,\" Perry said.", "\n\nHe said the recent court ruling that unsealed the search warrant, and the warrant itself, seem confused on the status of the arrangement.", "\n\nAnd there's the rub with Norman.", "\n\nThe courts might ultimately be called upon to decide whether the contents of the emails included \"leaked\" cabinet secrets.", "\n\nSince the RCMP applied for a warrant to search Norman's home, electronics and phone, it's a safe bet they didn't have enough evidence to charge him with a crime.", "\n\nFour months after the search, the Mounties have yet to make a move.", "\n\nThe peril of going outside the system\n\nRegardless of the criminal case, did Norman cross a line by having a back channel? ", "And, did he share too much in those exchanges?", "\n\nAnalysts and former federal officials say the answer to those questions is: Yes. ", "And yes.", "\n\n\"I've never seen that happen,\" said Alan Williams, who ran the purchasing branch of National Defence in the early 2000s. \"", "So, that's why I think it's inexcusable and, frankly, stupid.\"", "\n\nThere was a time, many years ago, when such kibitzing between the head of the navy and a shipyard executive was to be expected as projects got underway, said Ken Hansen, a former naval staff officer.", "\n\n\"Apparently, what [Norman] doesn't understand is that process has changed and it's not for him to circumvent process. ", "He can complain, officially. ", "He can raise objections, but he cannot go outside of this system,\" said Hansen, whose public complaints about the project irked Norman to the point where he asked Fraser to discredit the analyst.", "\n\nWith all of this water under the bridge, I can't imagine there hasn't been damage to his career. - ", "Dave Perry, senior analyst for the Canadian Global Affairs Institute\n\nHansen said he believes Norman was frustrated with the system and didn't believe Public Works bureaucrats, or politicians for that matter, could deliver the ship the navy needed.", "\n\nAnd then there are Norman's complaints about his political masters and his salty words about the alleged political interference of Halifax-based Irving Shipbuilding, which, Norman believed, wanted to kill the program for its own competitive, corporate reasons.", "\n\nNorman's lawyer didn't answer a request for comment. ", "The RCMP responded but said it wouldn't comment on an ongoing investigation.", "\n\nJordan Owens, a spokesperson for Defence Minister Harjit Sajjan, wouldn't address questions about Norman's remarks — or their potential impact on the relationship with Irving, which is under contract to build the next generation of navy frigates.", "\n\nBut Owens did say the government is \"working with partners at Irving Shipbuilding Inc. to ensure value for money for the duration of this long-term strategic sourcing relationship.\"", "\n\nIn light of the caustic — and often profane — email exchanges that are now public, Dave Perry wonders if there is any way back for the officer once touted as the next chief of the defence staff.", "\n\n\"With all of this water under the bridge, I can't imagine there hasn't been damage to his career.\"" ]	{ "pile_set_name": "OpenWebText2" }	[ 0, 0, 0.004608294930875576, 0.00904977375565611, 0, 0.008695652173913044, 0.013986013986013986, 0.004098360655737705, 0.012096774193548387, 0.012295081967213115, 0, 0, 0.0055248618784530384, 0.007142857142857143, 0, 0, 0.008849557522123894, 0.006666666666666667, 0, 0, 0.029411764705882353, 0, 0.012269938650306749, 0.014492753623188406, 0.008064516129032258, 0, 0, 0, 0.016129032258064516, 0, 0.004975124378109453, 0, 0, 0.015384615384615385, 0, 0.012096774193548387, 0.011450381679389313, 0.01818181818181818, 0.013157894736842105, 0.016129032258064516, 0.01092896174863388, 0.00510204081632653, 0 ]	0.00653	5
[ "Steps of Rome\n\n4.2Very good(46)\n\n1 Bird Avenue, Dublin, +35315672022Opens at 12:00\n\nThe original pasta and meat dishes, mouth-watering recipes are as authentic as our great-grandmother cooked them. ", "Full of flavours using the best Italian ingredients giving you the unique gourmet experience that Italians are well known for.", "Read more" ]	{ "pile_set_name": "Pile-CC" }	[ 0, 0, 0 ]	0	5
[ "2016 Women's European Water Polo Championship squads\n\nThis article shows all participating team squads at the 2016 Women's European Water Polo Championship, held in Serbia from 10–22 January 2016.", "\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nReferences\n\nCategory:European Water Polo Championship squads\nCategory:Women's European Water Polo Championship\nWomen squads\nEuro" ]	{ "pile_set_name": "Wikipedia (en)" }	[ 0, 0 ]	0	5
[ "Q:\n\nHow to convert properties when persisting or instantiating with JPA?", "\n\nI wonder if JPA is providing any mechanism to persist long for entity that has Date field?", "\nfor example\n@Entity\npublic class Trade {\n @Id\n @GeneratedValue\n private long id;\n\n // some jpa magic here maybe?", "\n private Date date;\n ...\n}\n\nwhen persisting this entity database keeps only longs as fields... But when instatiating this entity it converts long to Date.", "\nWhen all the DB stuff is handcoded you easily do this if you want. ", "I'm trying to reach flexibility you have when accessing database directly, but I want to do that using JPA. ", "So far this is the only thing i dont know how to do the right way.", "\n\nUPDATE\nDate type is just for an example, what i mean is some Custom type that i know the logic of converting from primitive to Custom instance... \n\nA:\n\nIf you want to store java.util.", "Date as long, you need to use a converter (since JPA 2.1). ", "e.g.:\nimport javax.persistence.", "AttributeConverter;\n\npublic class MyConverter implements AttributeConverter<Date, Long> {\n\n public Long convertToDatabaseColumn(Date attribute) {\n return attribute.getTime();\n }\n\n public Date convertToEntityAttribute(Long dbData) {\n return new Date(dbData);\n }\n\n}\n\nAnd the annotation for the field:\n@Convert(converter = MyConverter.class)\nprivate Date date;\n\nSee more in Example Converter - Java Persistence/Basic Attributes - Wikibooks (from the highly recommended book Java Persistence - Wikibooks)\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0.013888888888888888, 0.010869565217391304, 0.04, 0, 0, 0.009259259259259259, 0, 0, 0.01694915254237288, 0, 0.011363636363636364 ]	0.009303	5
[ "Malanichi\n\nMalanichi () is a rural locality (a village) in Chernushinsky District, Perm Krai, Russia. ", "The population was 39 as of 2010. ", "There is 1 street.", "\n\nReferences \n\nCategory:Rural localities in Perm Krai" ]	{ "pile_set_name": "Wikipedia (en)" }	[ 0.0196078431372549, 0, 0, 0.018867924528301886 ]	0.009619	5
[ "Q:\n\nOverride the behavior of base class private member in a derived class, C++\n\nSuppose I have a class coming from the software package, so I do not have a way to change the design, that has the following form:\nclass A\n{\npublic:\n A(int degree) \n {\n ...\n initialize_points();\n ...\n }\n ...\nprivate:\n ...\n void initialize_points() \n { \n int number = 1;\n // proceed to do computations using the number specified above\n ...\n }\n ...\n}\n\nWhat I need is to have a class B being similar to class A in everything but the number specified in the function initialize_points(). ", "Say, I want it to be 34 instead of 1.", "\nDue to lack of experience I don't quite understand how I can derive such a class B (and should I do so, maybe it is better to write this as a new class mimicking the implementation of A?) ", "from the class A since the function, whose behavior I want to override is the private member of the base class.", "\nThank you\n\nA:\n\nThe short answer is that this cannot be done in C++. ", "The primary mechanism by which a derived class could override what its base class does is virtual functions. ", "Unless the base class defines virtual functions, there's nothing that can be done in the derived class to override it.", "\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0, 0, 0, 0, 0, 0, 0, 0 ]	0	5
[ "[Comparative study of the combined effect of HCFU and dipyridamole (DP) in colorectal carcinoma--TS inhibition rate. ", "Kinki Cooperative Study Group of Chemotherapy for Colorectal Carcinoma].", "\nIn the forty-seven medical centers in the Kinki district, a comparative trial was conducted to investigate the enhancement of the efficacy of HCEU due to dipyridamol (DP), which is a biochemical modulator in patients with colorectal cancer who have had a curative resection. ", "The trial consisted of two comparative groups: one group (Group A) received HCFU only for five days before operation and for two years from the second week, and the other group (Group B) was given HCFU + DP for the same trial period as Group A. The total number of patients collected was 653 (Group A: 327 patients; Group B: 326 patients) during the two-year trial period from October, 1991. ", "Thymidylate Synthetase (TS) activity in the primary lesions, which is an index of proximity effect, was measured, and the TS inhibition rate (TSIR) was calculated from the activities. ", "The results showed that the TSIR in the primary lesions for the HCFU + DP group (Group B: 0.33) was significantly higher than that of the HCFU group (Group A: 0.27) (p = 0.0006). ", "There was no increase in the side effects of HCFU due to combined administration with DP. ", "From the above results, the therapy with HCFU + DP is expected to be useful for patients with colorectal cancer who have undergone curative resection." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0.027777777777777776, 0, 0.007653061224489796, 0.010869565217391304, 0.01675977653631285, 0, 0 ]	0.007883	5
[ "Patent document JP-A-2004291838 describes a tank for windshield washing fluid formed from a tubular portion with accordion folds closed at its ends by a front wall and a rear wall, such that it can contract in the front-rear direction without breaking when it receives an impact. ", "The solution described in this patent imposes an arrangement for assembling the tank in the engine compartment, or a very specific application and it does not describe or suggest that the tubular portion with accordion folds can adopt a compact, stable retracted position that is suitable for saving space during storage or transport, for example.", "\nPatent document EP-A-1571047 describes a tank for windshield washing fluid constructed from a first rigid main tank portion, in which there is arranged a pump for driving the fluid, extended by a second expandable auxiliary tank portion provided with accordion folds. ", "The two rigid and expandable tank portions are supported on a rack with a suitable extensible part for adapting the expansion or retraction of the auxiliary tank portion in relation to the main tank portion, providing a tank with a variable volume. ", "The proposed solution again imposes a very specific and/or limited location area or arrangement in the engine compartment and does not describe or suggest that the accordion folds allow the auxiliary tank portion to adopt a compact, stable retracted position, and does not provide or suggest a flexible structure which can adapt to reduced non-linear spaces.", "\nPatent document JP-A-62286863 describes a rigid tank for detergent fluid in a vehicle. ", "The rigid tank is provided with a filling tube with a wall formed by a plurality of accordion folds providing it with flexibility. ", "The flexible filling tube does not act as a tank rather it only has the function of leading the fluid from the filling opening to the rigid tank during a filling operation.", "\nThe structure of a tube with folds in the form of an accordion is known, although in other fields of the art, patent documents U.S. Pat. ", "No. ", "4,846,510 and U.S. Pat. ", "No. ", "4,927,191 being among them. ", "The mentioned patents describe several applications, for example, such as a flexible connecting tube, a trap drain, a retractable neck for a container (in a manner similar to the aforementioned JP patent document), and even a body of a folding container with a small height; However, these patent documents do not describe or suggest such an adjustable structure in association to a pump for the construction of a suitable flexible elongated tank for containing windshield or headlight washing fluid in a vehicle.", "\nPatent document DE-A-19811019 relates to a conduit for windshield washing fluid comprising a manifold with several corrugated portions separated by several smooth sections and with leak-tight coupling means associated to both ends. ", "Like other background documents, it always describes the fluid guiding or circulating functionality through the mentioned conduit and by no means does it describe its possible use for fluid storage and its possible association to a pump.", "\nThe present invention provides a new structure concept for a windshield or headlight washing fluid tank or container that is especially favorable as regards manufacturing, logistics and assembly in a vehicle engine compartment." ]	{ "pile_set_name": "USPTO Backgrounds" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.004291845493562232, 0, 0 ]	0.000252	5
[ "[The indications and results in 313 liver transplants].", "\nThe authors report their experience on 313 liver transplantations performed in 255 patients. ", "In 51.7% the indication to liver transplant was the cirrhosis, post alcoholic in 39.5% and post-hepatitis in 24.1%. ", "The global mortality was 34.9% (89/255) with an actuarial survival of 53% at 74 months. ", "We registered 10 cases (3.2%) of arterial thrombosis and 5 cases (1.6%) complications of portal anastomosis." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0, 0, 0, 0 ]	0	5
[ "You are here\n\nFaith like a River: Themes from Unitarian Universalist History\n\nA Tapestry of Faith Program for\nAdults\n\nJackie Clement Alison Cornish\n\nFaith Like a River explores the dynamic course of Unitarian, Universalist, and Unitarian Universalist (UU) history—the people, ideas, and movements that have shaped our faith heritage. ", "It invites participants to place themselves into our history and consider its legacies. ", "What lessons do the stories of our history teach that can help us live more faithfully in the present? ", "What lessons do they offer to be lived into the future?", "\n\nAbout the Author\n\nJackie Clement\n\nThe Rev. Jackie Clement serves the Unitarian Universalist Church of Bloomington-Normal (Illimois) as Senior Minister. ", "She earned a Masters of Divinity degree from Andover-Newton Theological School and served congregations in Maine and Massachusetts before moving to Illinois in 2010. ", "Before entering the ministry, Jackie worked in the high tech industry as an engineer and a marketing manager for computer graphics systems. ", "She is author of \"Time/Money Balance\" in the UUA's Taking It Home series, a resource for families. ", "Her passions include history, cooking, and reading, but the visual arts remain a primary spiritual practice. ", "In achievement of a lifelong goal, Jackie now lives in Normal with her husband, John Ford.", "\n\nAlison Cornish\n\nThe Rev. Alison Cornish serves as minister of the Unitarian Universalist Congregation of the South Fork (Bridgehampton, New York). ", "A lifelong UU, she earned her M.Div. ", "from Andover-Newton Theological School. ", "She also holds a degree in art history and building conservation; she worked in the areas of architecture and building preservation for 20 years before being ordained in 2004. ", "In addition to parish ministry, Alison serves as an adjunct consultant to Partners for Sacred Places, a national organization helping congregations of all denominations care for their historic buildings. ", "Alison loves to be on, and around the water at her home in Sag Harbor, New York.", "\n\nAcknowledgments\n\nWe gratefully acknowledge the use of the following material:\n\nExcerpt from Unitarian Universalism: An Heretical History, a DVD produced by the Unitarian Universalist Church of Rockford, IL, 1995.", "\n\n\"Would You Harbor Me?\" ", "Words and music by Ysaye M. Barnwell copyright 1994 Barnwell's Notes Publishing, recorded by Sweet Honey In The Rock (R). ", "Used with permission. ", "Visit Ysaye M. Barnwell's website for further information.", "\n\n\"Humanist Manifesto I,\" copyright 1933 by The New Humanist and 1973 by the American Humanist Association. ", "Please note that this is no longer a current statement of humanist convictions; it has been superceded by Humanism and Its Aspirations: Humanist Manifesto III.", "\n\n\"Love and Power: The Universalist Dilemma,\" the John Murray Distinguished Lecture, delivered at the UUA General Assembly in Boston, June 2003, by Rev. Rosemary Bray McNatt.", "\n\n\"Of Madmen and Martyrs: A Unitarian Take on Knoxville,\" a blog post by Sara Robinson, July 28, 2008; used with permission.", "\n\n\"The Seven Tribes,\" a traditional story of the Khasi people as relayed by Darihun Khriam, the first woman minister in the Khasi Hills.", "\n\n\"Under Our Charge — the Utes and the Unitarians\" based on research by historian Ted Vetter and written for this program.", "\n\nPreface\n\nThucydides wrote that history is philosophy taught by examples. ", "If this is true, then we would do well to study the examples—the stories—from our own faith history to shape a philosophy for living our own faith. ", "This program provides such an opportunity.", "\n\nBy presenting the sweep of Unitarian Universalist history and heritage through the stories of its people and events, the program invites participants to place themselves into our history and consider its legacies. ", "What lessons do the stories of our history teach that can help us live more faithfully in the present? ", "What lessons do they offer to be lived into the future? ", "Engagement with our history and heritage does more than celebrate our Unitarian Universalist identity. ", "It grounds our faith, our Principles, and our spiritual growth in a wider tradition and offers a context for deepening faith, values, and spirit.", "\n\nAs one in the Tapestry of Faith series of curricula for adults, this program weaves Unitarian Universalist values, Principles and Sources with four strands: spiritual development, ethical development, Unitarian Universalist identity development and faith development:\n\nSpiritual Development. ", "In Everyday Spiritual Practice, Scott Alexander defines spirituality as our relationship with the Spirit of Life, however we understand it. ", "Our spirituality is our deep, reflective, and expressed response to the awe, wonder, joy, pain, and grief of being alive. ", "Tapestry of Faith programs seek to form children, youth, and adults who:\n\nKnow they are lovable beings of infinite worth, imbued with powers of the soul and obligated to use their gifts, talents and potentials in the service of life\n\nAppreciate the value of spiritual practice as a means of deepening faith and integrating beliefs and values with everyday life.", "\n\nEthical Development. ", "When we develop our ethics, we develop our moral values—our sense of what is right and wrong. ", "We also enhance our ability to act on those values, overcoming oppressions and despair. ", "Tapestry of Faith programs seek to form children, youth, and adults who:\n\nRealize they are moral agents, capable of making a difference in the lives of other people, challenging structures of social and political oppression and promoting the health and well being of the planet\n\nAccept that they are responsible for the stewardship and creative transformation of their religious heritage and community of faith in the service of diversity, justice and compassion.", "\n\nUnitarian Universalist Identity Development. ", "Participation in a Unitarian Universalist congregation does not automatically create a Unitarian Universalist identity. ", "Personal identification with Unitarian Universalism begins when individuals start to call themselves Unitarian Universalist and truly feel a part of a Unitarian Universalist congregation or community. ", "Identity is strengthened as individuals discover and resonate with the stories, symbols and practices of Unitarian Universalism. ", "Tapestry of Faith programs develop children, youth, and adults who:\n\nAffirm they are part of a Unitarian Universalist religious heritage and community of faith that has value and provides resources for living\n\nRecognize the need for community, affirming the importance of families, relationships and connections between and among generations\n\nAccept that they are responsible for the stewardship and creative transformation of their religious heritage and community of faith in the service of diversity, justice and compassion.", "\n\nFaith Development. ", "When we develop in faith, we develop as meaning-makers. ", "Faith is about embracing life's possibilities, growing in our sense of being \"at home in the universe.\" ", "Faith is practiced in relationships with others. ", "While faith has aspects that are internal and personal, it is best supported in a community with shared symbols, stories, traditions, and values. ", "Unitarian Universalist faith development emphasizes each person's religious journey—each person's lifelong process of bringing head, heart and hands to seeking and knowing ultimate meaning.", "\n\nWhile the primary focus of this program is Unitarian Universalist identity development, each strand is woven, to some degree, into each workshop.", "\n\nMay these workshops come to life in your hands and in the hearts, minds, and spirits of the people you teach.", "\n\nGail Forsyth-Vail, Developmental Editor\n\nThe Program\n\nTo acknowledge our ancestors means we are aware that we did not make ourselves, that the line stretches all the way back, perhaps to God; or to Gods. ", "We remember them because it is an easy thing to forget: that we are not the first to suffer, rebel, fight, love and die. ", "The grace with which we embrace life, in spite of the pain, the sorrow, is always a measure of what has gone before. — ", "Alice Walker\n\nHistory is often viewed as a linear progression, where events follow events and actions occur in reaction. ", "But history is not straightforward. ", "This program guides participants to explore the dynamic course of Unitarian, Universalist, and Unitarian Universalist history—the people, ideas, and movements that have shaped our faith heritage.", "\n\nThe program offers maximum flexibility, allowing congregations to customize a series of workshops to fit their interests and needs. ", "Workshops are organized thematically rather than chronologically so groups can choose areas of interest to them. ", "Just as congregations can customize the overall program, facilitators can tailor an individual workshop by selecting from a variety of different kinds of activities.", "\n\nWhile our history is largely influenced by and centered in Europe and North America, this program includes a broad a range of stories, people, and locations.", "\n\nThe authors hope this program inspires both facilitators and participants to continue to explore our shared and diverse heritage.", "\n\nGoals\n\nThis program will:\n\nIntroduce the rich history of Unitarian Universalism from the beginning of our theological heritage to contemporary times\n\nExplore our inheritance of theology, practice, and institutional organization as manifested in various times and places in our history\n\nPresent some of the events, historical settings, and people that influenced Unitarianism, Universalism, and Unitarian Universalism\n\nEncourage participants to explore the history of their own congregations\n\nGive participants the tools and inspiration to research more deeply topics of particular interest\n\nOffer participants a way to enter into the story of Unitarian Universalism so that it becomes personally relevant.", "\n\nLeaders\n\nA team of two or more adults, either lay leaders or religious professionals, should facilitate these workshops. ", "Although consistency of leadership offers many advantages, every workshop need not be led by the same facilitators. ", "Seek leaders who are:\n\nKnowledgeable about Unitarian Universalism\n\nCommitted to the Unitarian Universalist Principles, to the congregation, and to the faith development components of this program\n\nWilling and able to thoroughly prepare for each workshop\n\nEffective at speaking, teaching, and facilitating group process\n\nFlexible, and willing to modify workshop plans to support the full inclusion of all participants\n\nAble to listen deeply and to encourage participation of all individuals\n\nAble to demonstrate respect for individuals, regardless of age, race, social class, gender identity, and sexual orientation\n\nAble to honor the life experiences each participant will bring to the program.", "\n\nWhile knowledge of Unitarian Universalist history is helpful, it is not a requirement for effectively leading this program. ", "Willingness and ability to adequately prepare for each workshop, to research answers to questions raised by participants and to encourage participants' own research is far more valuable to creating a good learning and faith development experience for participants than is extensive knowledge of Unitarian Universalist history.", "\n\nParticipants\n\nThis program is intended for adults. ", "It can be adapted for youth or for a multigenerational program that includes youth and adults. ", "The workshops are equally suitable for first-time visitors and long-time congregational members. ", "Facilitators should be attentive to the differences in knowledge and life experience participants bring to the group, particularly if the group includes a wide age span.", "\n\nWorkshops can accommodate any number of participants. ", "Workshops of fewer than six participants can do small group activities in the full group, or skip some small group activities. ", "If the group has more than twenty-five participants, you will need at least three facilitators.", "\n\nIntegrating All Participants\n\nPeople with obvious and not-so-obvious disabilities may need accommodation in order to participate fully. ", "In addition to accommodating the accessibility needs of participants who request them, you are urged to follow these basic Accessibility Guidelines for Workshop Presenters:\n\nPrepare a few large print copies of all handouts.", "\n\nWrite clearly and use large letters on newsprint. ", "Use black or brown markers for maximum visibility (red and green are difficult for some to see).", "\n\nMake a printed copy of information you plan to post on newsprint, to give to any who request it.", "\n\nFace the group when you are speaking and urge others to do the same. ", "Be aware of facial hair or hand gestures that may prevent or interfere with lip reading.", "\n\nIn a large space or with a large group of people, use a microphone for presentations and for questions and answers. ", "If a particular activity will likely make it difficult for speakers to face those who are listening (e.g., a fishbowl, forced choice, or role play activity), obtain a microphone you can pass from speaker to speaker.", "\n\nIn a brainstorm activity, repeat clearly any word or phrase generated by the group in addition to writing it on newsprint.", "\n\nIf the group will listen to significant amounts of material read aloud, be ready to provide printed copies to any hearing impaired participants so they can read along.", "\n\nDuring small group work, position each group far enough from other groups to minimize noise interference.", "\n\nKeep aisles and doorways clear at all times during a workshop so people with mobility impairments or immediate needs can exit the room easily.", "\n\nOffer a variety of seating options—for example, straight chairs, soft chairs, chairs with arms, and chairs without arms—so participants can find seating that best suits their needs.", "\n\nWhen re-arranging furniture for small groups or other purposes, ensure clear pathways between groups.", "\n\nUse language that puts the person first, rather than the disability—for example, \"a person who uses a wheelchair,\" rather than \"a wheelchair-user\"; \"a child with dyslexia,\" rather than \"a dyslexic child; \"people with disabilities\" rather than \"the disabled.\"", "\n\nDo not ask individuals to read aloud. ", "Request volunteers or read the material yourself. ", "When possible, ask for volunteers before the workshop and give each volunteer a copy of the material they will read.", "\n\nAsk participants in advance about any food allergies. ", "Add to your group covenant an agreement to avoid bringing problem foods or to always offer an alternate snack.", "\n\nAsk participants in advance about any allergies to scents or perfumes. ", "If participants have allergies or sensitivities, invite members of the group to refrain from wearing perfumes and add this agreement to your covenant.", "\n\nParticipants bring a wide range of learning styles and preferences. ", "With this in mind, the workshops offer a variety of activities. ", "Review each workshop's Alternate Activities. ", "Plan each workshop to best suit the group." ]	{ "pile_set_name": "Pile-CC" }	[ 0.005988023952095809, 0, 0, 0, 0.012987012987012988, 0.006024096385542169, 0.007142857142857143, 0, 0, 0.022222222222222223, 0.026845637583892617, 0, 0.025, 0, 0.004901960784313725, 0.0125, 0.014018691588785047, 0, 0.03278688524590164, 0, 0.017241379310344827, 0.018518518518518517, 0.006289308176100629, 0.011494252873563218, 0.016129032258064516, 0.014705882352941176, 0.01639344262295082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.007142857142857143, 0, 0, 0, 0, 0, 0, 0, 0, 0.004975124378109453, 0.015503875968992248, 0, 0, 0, 0, 0, 0, 0.005291005291005291, 0, 0, 0.009708737864077669, 0, 0, 0.008264462809917356, 0, 0, 0, 0, 0, 0, 0, 0.004243281471004243, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.004484304932735426, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.022222222222222223, 0 ]	0.003299	5
[ "This paper explores the development of two significant crosscultural research projects in Pasifika psychology. ", "Both projects were designed to speak into the “silent space” of unexplored Pasifika practices and needs in the ..." ]	{ "pile_set_name": "Pile-CC" }	[ 0.009009009009009009, 0.008771929824561403 ]	0.00889	5
[ "Q:\n\nHow to conditionally ignore SIGTRAP in GDB?", "\n\nI'm trying to debug a program which triggers an unwanted SIGTRAP in a specific routine. ", "This signal is triggered in a library, but the same caller always shows up in the backtrace. ", "How can I tell GDB to ignore this signal if the caller is [some function], instead of breaking on it?", "\nI've tried to use skip function [some function] and even skip file [file that triggers SIGTRAP] (from 5.3 Skipping Over Functions and Files), but GDB still broke at that line. ", "And continue doesn't seem to support conditionals either. ", "I'd take any solution that doesn't require a modification of the debugged program, including Python scripts for GDB. ", "If relevant, you may also assume that an error is written to stderr before SIGTRAP is triggered.", "\nTwo years ago, someone asked How can I make GDB stop at SIGTRAP only at breakpoints?. ", "This hasn't received any answers, so I hope that the weaker version of the question (ignoring some specific SIGTRAPs) is answerable.", "\n\nA:\n\nYou can solve the problem at the source (the trigger of the SIGTRAP signal) or after the fact has happened (see this answer on ignoring certain SIGTRAPs). ", "Below I'll explain how to handle the first case (avoiding the trigger).", "\nIf you have code like:\nvoid debug_break() {\n asm(\"int3\");\n}\n\nthen you can set a breakpoint with commands to return immediately:\nbreak debug_break\ncommands\n return\n continue\nend\n\nIf you cannot return because the code is mixed:\n/* some code here */\nasm(\"int3\");\nprint_error();\n\nthen you can skip a line with the jump command. ", "Assuming that the int3 line is 1337, use:\nbreak file.c:1337\ncommands\n j +1\n c\nend\n\nIf the stuff is on a single line (asm(\"int3\"); print_error();, then change the line jump to incrementing the program counter (set $pc++). ", "This assumes that the instruction is one byte.", "\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0.0425531914893617, 0.011111111111111112, 0, 0.009900990099009901, 0.011299435028248588, 0, 0.017094017094017096, 0.010416666666666666, 0.022988505747126436, 0, 0.006211180124223602, 0, 0, 0, 0, 0 ]	0.008223	5
[ "This invention pertains to valves, in general, and to a calibrated position indicator for a rising stem valve, in particular.", "\nPrior art rising stem globe valves include indicators to show the position of the valve disc as a percent of full open. ", "One such valve includes a calibrated scale mounted to a valve bonnet by means of holding screws. ", "The valve stem extends beyond the bonnet and includes an indicator groove thereon. ", "The scale extends above the bonnet adjacent the valve stem and includes an elongated slot through which the indicator groove may be seen. ", "Graduated markings on the scale indicate the percent opening of the valve. ", "To calibrate the scale the holding screws are loosened and the scale is moved upward or downward.", "\nSuch a prior art arrangement requires the use of an extended shaft and scale. ", "Additionally, the bonnet barrel must have a flat land on which to mount the scale and must be cross-drilled and tapped for the mounting screws. ", "Further, a packing gland and nut are used between the shaft and the valve bonnet. ", "To remove the packing gland, it is necessary to remove or bend the scale out of the way. ", "Once the scale has been removed or bent, zero calibration of the scale is lost.", "\nStill further, the scale is in a fixed position relative to the bonnet and accordingly, when the valve is installed in a system, the position of the scale may be such that the scale cannot be easily read." ]	{ "pile_set_name": "USPTO Backgrounds" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	0	5
[ "Getty Images\n\nSan Francisco 49ers head coach Jim Harbaugh could be on his way out at the end of the 2014 season.", "\n\nCould Harbaugh get traded to another team?", "\n\nWill Harbaugh block any potential deal?", "\n\nWatch as Stephen Nelson and Bleacher Report NFL Insider Jason Cole discuss Harbaugh's future in the video above." ]	{ "pile_set_name": "OpenWebText2" }	[ 0.017857142857142856, 0, 0, 0.03508771929824561 ]	0.013236	5
[ "1. ", "Field of the Invention\nThis invention relates to railway drawbars and, more specifically, to shear mechanisms for railway drawbars.", "\n2. ", "Description of Related Art\nPrior art emergency release mechanisms, such as the shear bolts shown in U.S. Pat. ", "No. ", "6,499,613 to Grau et al., ", "are subject to premature failure. ", "These premature failures can be expensive to repair and can cause inconvenience.", "\nTherefore, it can be appreciated that an emergency release mechanism which lessens the number of premature failures of emergency release mechanisms is desirable." ]	{ "pile_set_name": "USPTO Backgrounds" }	[ 0, 0, 0, 0, 0, 0.038461538461538464, 0, 0, 0 ]	0.004274	5
[ "Survival of the fittest\n\n\"Survival of the fittest\" is a phrase that originated from Darwinian evolutionary theory as a way of describing the mechanism of natural selection. ", "The biological concept of fitness is defined as reproductive success. ", "In Darwinian terms the phrase is best understood as \"Survival of the form that will leave the most copies of itself in successive generations.\"", "\n\nHerbert Spencer first used the phrase, after reading Charles Darwin's On the Origin of Species, in his Principles of Biology (1864), in which he drew parallels between his own economic theories and Darwin's biological ones: \"This survival of the fittest, which I have here sought to express in mechanical terms, is that which Mr. Darwin has called 'natural selection', or the preservation of favoured races in the struggle for life.\"", "\n\nDarwin responded positively to Alfred Russel Wallace's suggestion of using Spencer's new phrase \"survival of the fittest\" as an alternative to \"natural selection\", and adopted the phrase in The Variation of Animals and Plants under Domestication published in 1868. ", "In On the Origin of Species, he introduced the phrase in the fifth edition published in 1869, intending it to mean \"better designed for an immediate, local environment\".", "\n\nHistory of the phrase\nHerbert Spencer first used the phrase – after reading Charles Darwin's On the Origin of Species – in his Principles of Biology of 1864 in which he drew parallels between his economic theories and Darwin's biological, evolutionary ones, writing, \"This survival of the fittest, which I have here sought to express in mechanical terms, is that which Mr. Darwin has called 'natural selection', or the preservation of favored races in the struggle for life.\"", "\n\nIn July 1866 Alfred Russel Wallace wrote to Darwin about readers thinking that the phrase \"natural selection\" personified nature as \"selecting\", and said this misconception could be avoided \"by adopting Spencer's term\" Survival of the fittest. ", "Darwin promptly replied that Wallace's letter was \"as clear as daylight. ", "I fully agree with all that you say on the advantages of H. Spencer's excellent expression of 'the survival of the fittest'. ", "This however had not occurred to me till reading your letter. ", "It is, however, a great objection to this term that it cannot be used as a substantive governing a verb\". ", "Had he received the letter two months earlier, he would have worked the phrase into the fourth edition of the Origin which was then being printed, and he would use it in his \"next book on Domestic Animals etc.\".", "\n\nDarwin wrote on page 6 of The Variation of Animals and Plants under Domestication published in 1868, \"This preservation, during the battle for life, of varieties which possess any advantage in structure, constitution, or instinct, I have called Natural Selection; and Mr. Herbert Spencer has well expressed the same idea by the Survival of the Fittest. ", "The term \"natural selection\" is in some respects a bad one, as it seems to imply conscious choice; but this will be disregarded after a little familiarity\". ", "He defended his analogy as similar to language used in chemistry, and to astronomers depicting the \"attraction of gravity as ruling the movements of the planets\", or the way in which \"agriculturists speak of man making domestic races by his power of selection\". ", "He had \"often personified the word Nature; for I have found it difficult to avoid this ambiguity; but I mean by nature only the aggregate action and product of many natural laws,—and by laws only the ascertained sequence of events.\"", "\n\nIn the first four editions of On the Origin of Species, Darwin had used the phrase \"natural selection\". ", "\nIn Chapter 4 of the 5th edition of The Origin published in 1869, Darwin implies again the synonym: \"Natural Selection, or the Survival of the Fittest\". ", "By \"fittest\" Darwin meant \"better adapted for the immediate, local environment\", not the common modern meaning of \"in the best physical shape\" (think of a puzzle piece, not an athlete). ", "In the introduction he gave full credit to Spencer, writing \"I have called this principle, by which each slight variation, if useful, is preserved, by the term Natural Selection, in order to mark its relation to man's power of selection. ", "But the expression often used by Mr. Herbert Spencer of the Survival of the Fittest is more accurate, and is sometimes equally convenient.\"", "\n\nIn The Man Versus The State, Spencer used the phrase in a postscript to justify a plausible explanation of how his theories would not be adopted by \"societies of militant type\". ", "He uses the term in the context of societies at war, and the form of his reference suggests that he is applying a general principle.", "\n\n \"Thus by survival of the fittest, the militant type of society becomes characterized by profound confidence in the governing power, joined with a loyalty causing submission to it in all matters whatever\".", "\n\nThough Spencer’s conception of organic evolution is commonly interpreted as a form of Lamarckism, Herbert Spencer is sometimes credited with inaugurating Social Darwinism. ", "The phrase \"survival of the fittest\" has become widely used in popular literature as a catchphrase for any topic related or analogous to evolution and natural selection. ", "It has thus been applied to principles of unrestrained competition, and it has been used extensively by both proponents and opponents of Social Darwinism.", "\n\nEvolutionary biologists criticise the manner in which the term is used by non-scientists and the connotations that have grown around the term in popular culture. ", "The phrase also does not help in conveying the complex nature of natural selection, so modern biologists prefer and almost exclusively use the term natural selection. ", "The biological concept of fitness refers to reproductive success, as opposed to survival, and is not explicit in the specific ways in which organisms can be more \"fit\" (increase reproductive success) as having phenotypic characteristics that enhance survival and reproduction (which was the meaning that Spencer had in mind).", "\n\nCritiquing the phrase \nWhile the phrase \"survival of the fittest\" is often used to mean \"natural selection\", it is avoided by modern biologists, because the phrase can be misleading. ", "For example, survival is only one aspect of selection, and not always the most important. ", "Another problem is that the word \"fit\" is frequently confused with a state of physical fitness. ", "In the evolutionary meaning \"fitness\" is the rate of reproductive output among a class of genetic variants.", "\n\nInterpreted as expressing a biological theory\nThe phrase can also be interpreted to express a theory or hypothesis: that \"fit\" as opposed to \"unfit\" individuals or species, in some sense of \"fit\", will survive some test. ", " Nevertheless, when extended to individuals it is a conceptual mistake, the phrase is a reference to the transgenerational survival of the heritable attributes; particular individuals are quite irrelevant. ", " This becomes more clear when referring to Viral quasispecies, in survival of the flattest, which makes it clear to survive makes no reference to the question of even being alive itself; rather the functional capacity of proteins to carry out work.", "\n\nInterpretations of the phrase as expressing a theory are in danger of being tautological, meaning roughly \"those with a propensity to survive have a propensity to survive\"; to have content the theory must use a concept of fitness that is independent of that of survival.", "\n\nInterpreted as a theory of species survival, the theory that the fittest species survive is undermined by evidence that while direct competition is observed between individuals, populations and species, there is little evidence that competition has been the driving force in the evolution of large groups such as, for example, amphibians, reptiles, and mammals. ", "Instead, these groups have evolved by expanding into empty ecological niches. ", "In the punctuated equilibrium model of environmental and biological change, the factor determining survival is often not superiority over another in competition but ability to survive dramatic changes in environmental conditions, such as after a meteor impact energetic enough to greatly change the environment globally. ", "The main land dwelling animals to survive the K-Pg impact 66 million years ago had the ability to live in tunnels, for example.", "\n\nIn 2010 Sahney et al. ", "argued that there is little evidence that intrinsic, biological factors such as competition have been the driving force in the evolution of large groups. ", "Instead, they cited extrinsic, abiotic factors such as expansion as the driving factor on a large evolutionary scale. ", "The rise of dominant groups such as amphibians, reptiles, mammals and birds occurred by opportunistic expansion into empty ecological niches and the extinction of groups happened due to large shifts in the abiotic environment.", "\n\nInterpreted as expressing a moral theory\n\nSocial Darwinists\nIt has been claimed that \"the survival of the fittest\" theory in biology was interpreted by late 19th century capitalists as \"an ethical precept that sanctioned cut-throat economic competition\" and led to the advent of the theory of \"social Darwinism\" which was used to justify laissez-faire economics, war and racism. ", "However, these ideas predate and commonly contradict Darwin's ideas, and indeed their proponents rarely invoked Darwin in support. ", "The term \"social Darwinism\" referring to capitalist ideologies was introduced as a term of abuse by Richard Hofstadter's Social Darwinism in American Thought published in 1944.", "\n\nAnarchists\nRussian anarchist Peter Kropotkin viewed the concept of \"survival of the fittest\" as supporting co-operation rather than competition. ", "In his book Mutual Aid: A Factor of Evolution he set out his analysis leading to the conclusion that the fittest was not necessarily the best at competing individually, but often the community made up of those best at working together. ", "He concluded that In the animal world we have seen that the vast majority of species live in societies, and that they find in association the best arms for the struggle for life: understood, of course, in its wide Darwinian sense – not as a struggle for the sheer means of existence, but as a struggle against all natural conditions unfavourable to the species. ", "The animal species, in which individual struggle has been reduced to its narrowest limits, and the practice of mutual aid has attained the greatest development, are invariably the most numerous, the most prosperous, and the most open to further progress.", "\n\nApplying this concept to human society, Kropotkin presented mutual aid as one of the dominant factors of evolution, the other being self-assertion, and concluded that In the practice of mutual aid, which we can retrace to the earliest beginnings of evolution, we thus find the positive and undoubted origin of our ethical conceptions; and we can affirm that in the ethical progress of man, mutual support not mutual struggle – has had the leading part. ", "In its wide extension, even at the present time, we also see the best guarantee of a still loftier evolution of our race.", "\n\nTautology\n\n\"Survival of the fittest\" is sometimes claimed to be a tautology. ", "The reasoning is that if one takes the term \"fit\" to mean \"endowed with phenotypic characteristics which improve chances of survival and reproduction\" (which is roughly how Spencer understood it), then \"survival of the fittest\" can simply be rewritten as \"survival of those who are better equipped for surviving\". ", "Furthermore, the expression does become a tautology if one uses the most widely accepted definition of \"fitness\" in modern biology, namely reproductive success itself (rather than any set of characters conducive to this reproductive success). ", "This reasoning is sometimes used to claim that Darwin's entire theory of evolution by natural selection is fundamentally tautological, and therefore devoid of any explanatory power.", "\n\nHowever, the expression \"survival of the fittest\" (taken on its own and out of context) gives a very incomplete account of the mechanism of natural selection. ", "The reason is that it does not mention a key requirement for natural selection, namely the requirement of heritability. ", "It is true that the phrase \"survival of the fittest\", in and by itself, is a tautology if fitness is defined by survival and reproduction. ", "Natural selection is the portion of variation in reproductive success that is caused by heritable characters (see the article on natural selection).", "\n\nIf certain heritable characters increase or decrease the chances of survival and reproduction of their bearers, then it follows mechanically (by definition of \"heritable\") that those characters that improve survival and reproduction will increase in frequency over generations. ", "This is precisely what is called \"evolution by natural selection\". ", "On the other hand, if the characters which lead to differential reproductive success are not heritable, then no meaningful evolution will occur, \"survival of the fittest\" or not: if improvement in reproductive success is caused by traits that are not heritable, then there is no reason why these traits should increase in frequency over generations. ", "In other words, natural selection does not simply state that \"survivors survive\" or \"reproducers reproduce\"; rather, it states that \"survivors survive, reproduce and therefore propagate any heritable characters which have affected their survival and reproductive success\". ", "This statement is not tautological: it hinges on the testable hypothesis that such fitness-impacting heritable variations actually exist (a hypothesis that has been amply confirmed.)", "\n\nMomme von Sydow suggested further definitions of 'survival of the fittest' that may yield a testable meaning in biology and also in other areas where Darwinian processes have been influential. ", "However, much care would be needed to disentangle tautological from testable aspects. ", "Moreover, an \"implicit shifting between a testable and an untestable interpretation can be an illicit tactic to immunize natural selection ... while conveying the impression that one is concerned with testable hypotheses\".", "\n\nSkeptic Society founder and Skeptic magazine publisher Michael Shermer addresses the tautology problem in his 1997 book, Why People Believe Weird Things, in which he points out that although tautologies are sometimes the beginning of science, they are never the end, and that scientific principles like natural selection are testable and falsifiable by virtue of their predictive power. ", "Shermer points out, as an example, that population genetics accurately demonstrate when natural selection will and will not effect change on a population. ", "Shermer hypothesizes that if hominid fossils were found in the same geological strata as trilobites, it would be evidence against natural selection.", "\n\nSee also\n\nNotes\n\nReferences\n\nExternal links\n\nOrigins of the phrase\n AboutDarwin.com — Darwin's Timeline\n Pioneers of Psychology\n Evolution Quotations compiled by GIGA\n\nTautology links\n Darwin's Untimely Burial by Stephen Jay Gould\n Evolution and Philosophy: A Good Tautology is Hard to Find by John Wilkins, part of the talk.origins archive.", "\n CA500: \"Survival of the fittest is a tautology\" from the talk.origins index to creationist claims by Mark Ridley.", "\n Is \"survival of the fittest\" a tautology by Don Lindsay.", "\n Darwin's Great Tautology by the Doubting Thomas\n\nMorality link\n CA002: Survival of the fittest implies that \"might makes right\"\n David Hume — Dialogues Concerning Natural Religion\n Evolution and philosophy — Does evolution make might right? ", "by John S. Wilkins.", "\n Darwinism and Laissez-Faire Capitalism from the Institute for Creation Research\n\nKropotkin: Mutual Aid\n \n Mutual Aid: A Factor of Evolution – HTML version at the Anarchy Archives\n\nCategory:Charles Darwin\nCategory:Herbert Spencer\nCategory:Biological evolution\nCategory:English phrases\nCategory:Metaphors\n\nta:தக்கன பிழைக்கும்" ]	{ "pile_set_name": "Wikipedia (en)" }	[ 0, 0, 0, 0.011494252873563218, 0.0149812734082397, 0.005917159763313609, 0.010482180293501049, 0.012195121951219513, 0.0273972602739726, 0.008, 0, 0, 0.004739336492890996, 0.011267605633802818, 0, 0, 0, 0.018867924528301886, 0.006535947712418301, 0.005376344086021506, 0.008403361344537815, 0.007194244604316547, 0.005555555555555556, 0, 0, 0.017241379310344827, 0, 0.006493506493506494, 0, 0, 0.003076923076923077, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0026246719160104987, 0.015267175572519083, 0.011363636363636364, 0.006802721088435374, 0, 0, 0, 0.002197802197802198, 0, 0, 0.0031847133757961785, 0, 0.0055248618784530384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.005128205128205128, 0, 0, 0.005141388174807198, 0, 0.006756756756756757, 0.011661807580174927, 0.008695652173913044, 0.017241379310344827, 0.00411522633744856, 0.05263157894736842, 0.012307692307692308 ]	0.004393	5
[ "The global stocks roller-coaster of recent days reminded me of three lessons I learned many years ago as an investor in emerging markets. ", "If well understood and applied, these precepts can turn unsettling volatility surges into longer-term opportunities.", "\n\nLong periods of market calm create the technical conditions for violent air pockets. ", "Until last week, the most distinctive feature of many market segments was historically low volatility, both implied and realized. ", "Although several economic and corporate reasons were liberally cited for this development (including the convergence of inflation rates worldwide and eternally supportive central banks, as well as healthy balance sheets and synchronized growth), an important determinant was the conditioning of the investor base to believe that every dip had become a buying opportunity, a simple investment strategy that had proven very remunerative for the last few years.", "The more investors believed, the greater the willingness to “buy the dip.” ", "Over time, the frequency, duration and severity of the dips diminished significantly. ", "That reinforced the behavior further.", "The economist Hyman Minsky had a lot to say about the phenomenon of prolonged stability breeding complacency as a precursor to instability. ", "This phenomenon is reinforced by the insights of behavioral finance and can lead markets to embrace paradigms that ultimately prove unsustainable and harmful (such as the idea well more than a decade ago that policy making had totally overcome the business cycle, and the notion that volatility had been flushed or hedged out of the financial system). ", "Continue Reading →" ]	{ "pile_set_name": "Pile-CC" }	[ 0, 0, 0, 0, 0, 0, 0, 0, 0.007142857142857143, 0, 0 ]	0.000649	5
[ "Marx Reloaded\n\nMarx Reloaded is a 2011 German documentary film written and directed by the British writer and theorist Jason Barker. ", "Featuring interviews with several well-known philosophers, the film aims to examine the relevance of Karl Marx's ideas in relation to the Great Recession. ", "The film's title is a wordplay on The Matrix Reloaded, the sequel to The Matrix, which is parodied in the documentary.", "\n\nBackground\nAccording to the film's website, \"Marx Reloaded … examines the relevance of German socialist philosopher Karl Marx's ideas for understanding the global economic and financial crisis of 2008–09.\" ", "The film also considers, in the context of an alleged revival of Marxist thinking, whether \"communism might provide the solution to the growing economic and environmental challenges facing the planet\".", "\n\nIn an interview with Verso Books, writer-director Jason Barker described his intention in making the film \"to reload or reimagine Marx as a thinker, without the usual totalitarian moralising.\" ", "Barker criticised the \"cliché\" according to which \"Marx's diagnoses of capitalism are validated whereas his 'prescription' of communism is rubbished on the grounds that it's 'utopian'.\" ", "Asked whether the renewed popularity of Marx is evidence of a return of communism as a political force, or \"just the spectre of Marx haunting the academies\", Barker replied that \"political thinking today is again converging on precisely the type of social conditions in which Marx lived.\"", "\n\nIn a separate interview, Barker also discussed the film's use of animation, in particular his decision to parody The Matrix, admitting that although it was an \"obvious parody\" and \"fun to make\", there was also a philosophical dimension to the animation scenes in which Marx meets Leon Trotsky and Slavoj Žižek.", "\n\nFilm\nMarx Reloaded features interviews with several well-known philosophers, among them those often associated with Marxism and Communist ideas, including John Gray, Michael Hardt, Antonio Negri, Nina Power, Jacques Rancière, Peter Sloterdijk, Alberto Toscano and Slavoj Žižek. ", " The film also includes animation scenes with Marx trapped in a surreal world resembling the 1999 science fiction–action film The Matrix, which starred Keanu Reeves and Laurence Fishburne. ", "In one such animated scene Marx (Jason Barker) encounters Leon Trotsky (Ivan Nikolic) in a pastiche of the red pill and blue pill scene in The Matrix in which Reeves' character Neo first meets Fishburne's character Morpheus.", "\n\nReception\nMarx Reloaded had its TV premiere on Arte on 11 April and was repeated on 20 April. ", "The film was subsequently broadcast on the Romanian television channel B1 TV on 12 August 2011, followed by a studio debate involving political analyst Dinu Flămând, journalist Cristian Tudor Popescu and writer Vasile Ernu. ", "\n\nOn 25 September 2011 the film was screened (out of competition) at the 2011 DMZ International Documentary Film Festival. ", "The screening was followed by a panel discussion involving writer-director Jason Barker, Professor Taek-Gwang Lee of Kyung Hee University and Yongjune Park, the editor of Indigo, an English-language Korean humanities magazine. ", "Both the film and director were the subject of national press coverage in the Hankook Ilbo.", "\n\nOn 3 October 2011 the film had its Serbian premiere at the Centre for Cultural Decontamination in Belgrade, with further screenings planned in the same venue on 20, 21 and 24 October.", "\n\nMarx Reloaded premiered in the UK on 10 February 2012 at the Institute of Contemporary Arts in London, where it screened to sell-out audiences until 20 April.", "\n\nReviews of the film have been positive. ", "Time Out London described it as containing \"enough interesting ideas to make this well worth a watch for those with an interest in philosophy, politics and the general state of the world as we know it.\" ", "Little White Lies called it an \"engaging hour-long talking-head-meets-animation doc\"; \"the film shines a light on the many causes of the financial crumble, creating a compelling dialogue of Marx's theories on capitalism as they apply to its contemporary form.\" ", "Subtitledonline.com awarded the film three out of a possible five stars, although criticized it for its \"failure to balance quirky presentation with challenging content\". ", "However, writing in CounterPunch, Louis J. Proyect gave an unqualified endorsement: \"I can't recommend this film highly enough... The film is a fast-paced and even exciting treatment of what might induce a yawn on the printed page\".", "\n\nAs well as reviews The Financial Times featured the film as part of its \"Capitalism in Crisis\" series, followed by an interview with Jason Barker and the editor of New Left Review, Robin Blackburn.", "\n\nThe London Evening Standard cited the film alongside the 2012 re-edition of The Communist Manifesto (introduced by Eric Hobsbawm) and Owen Jones' best-selling book Chavs: The Demonization of the Working Class as evidence of a resurgence of left-wing ideas.", "\n\nBlue or Red Pill?", "\n\nOn 16 December 2011, the first in a series of public debates entitled \"Blue or Red Pill?\" (", "Crvena ili plava pilula?) ", "was held at the Centre for Cultural Decontamination (CZKd), Belgrade, in which the social and political themes from the film were explored. ", "Serbian film director Želimir Žilnik – himself noted for his socially-engaged film-making, most recently in the 2009 film Stara škola kapitalizma – participated in the event along with Jason Barker.", "\n\nA second debate took place on 15 February 2012 at the Institute of Contemporary Arts (ICA), in which the BBC Newsnight economics editor Paul Mason, the blogger and The Independent journalist Laurie Penny, and Robin Blackburn joined Jason Barker. ", "The debate considered the implications of Marx's work in the context of a growing popular resistance to the global economic and financial crisis, and whether the revolutionary change advocated by Marx had finally arrived: \"Is humanity standing at a crossroads where a decision – and by whom or in whose name? – ", "for \"another world\" must be taken?\"", "\n\nSee also\nKarl Marx in film\n\nReferences\n\nExternal links\n\nMarx Reloaded Review at Der Tagesspiegel (German site) \nMarx Reloaded Review at The Original Sonic Truth blog \n\nMarx Reloaded blog (Korean site)\n\nCategory:2011 films\nCategory:German films\nCategory:German documentary films\nCategory:Works about Marxism\nCategory:Documentary films about philosophy\nCategory:Documentary films about ideologies\nCategory:Documentary films about the Great Recession\nCategory:2010s documentary films\nCategory:Films about communism\nCategory:Cultural depictions of Karl Marx\nCategory:Cultural depictions of Leon Trotsky" ]	{ "pile_set_name": "Wikipedia (en)" }	[ 0.015037593984962405, 0.0064516129032258064, 0.00847457627118644, 0.004807692307692308, 0, 0.015384615384615385, 0.010752688172043012, 0.010416666666666666, 0.016025641025641024, 0.03214285714285714, 0.015873015873015872, 0.03125, 0.010416666666666666, 0.017857142857142856, 0, 0.01762114537444934, 0, 0.005405405405405406, 0.0125, 0, 0, 0.0038314176245210726, 0.005847953216374269, 0.004310344827586207, 0.020100502512562814, 0.011627906976744186, 0, 0, 0.038461538461538464, 0.007142857142857143, 0.010101010101010102, 0.03225806451612903, 0.006430868167202572, 0, 0.008333333333333333 ]	0.010825	5
[ "Q:\n\nHow can I find who pushed a tag(s) to BitBucket\n\nWe deleted some unwanted tags from our bitbucket repository and (so we thought) all our local repositories, but obviously we have missed one repo somewhere as they keep getting re-pushed.", "\nHow can I find out who is pushing them?", "\n\nA:\n\nYou can't find that easily (maybe BitBucket support has some log), but, as a workaround, you could add a post-receive hook (like a POST one) in order for another git client to be notified of any push.", "\nThat git client could check if tags were pushed, and, if those tags are unwanted, push back their deletion.", "\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0.004166666666666667, 0, 0.009708737864077669, 0, 0 ]	0.002775	5
[ "The Secrets🔐 to Move up⬆️ the Corporate👥 Ladder for Interns Looking for Full Employment ...\n\nFor seniors starting their final year of college, ambitious freshwomen starting their first, and anyone in between who has experienced the grueling life of an intern, moving up the corporate ladder may seem like an unreachable dream. ", "But if you follow these simple steps you'll see it's easy as one, two, three... 4-5-6-7!", "\n\n1. ", "Choose the Right Internship\n\nThe first thing in turning your internship into an job is, of course, finding an internship! ", "But you have to make sure it's the right internship. ", "According to Forbes magazine, small and medium-sized companies are the best choice for interns seeking full employment, because they're more likely to be understaffed.", "\n\n2. ", "Keep It Professional\n\nThe company doesn't want to hire an intern full-time; interns are immature, awkward, and unprofessional. ", "They want to hire an employee who acts like they were born for this role.", "\n\n3. ", "Communication is Key\n\nIt's easy to assume that you know what you're doing after reading all of the paperwork, but you should talk to your supervisor about their exact expectations for you. ", "Make sure you have ongoing, open communication with your boss to ensure that your performance is consistently on point!", "\n\n4. ", "Volunteer\n\nBecome \"that girl\" who volunteers to fill in whenever possible. ", "This will show that you're invested in the company's best interest and willing to go above and beyond the demands of an internship. ", "Your employers won't know that you can handle the responsibilities of being a full-time employee until you prove it to them!", "\n\n5. ", "First One in, Last One out\n\nNothing says dedication like being the first one in the office and the last one out. ", "Arriving early demonstrates not only punctuality, but also an eagerness to start the work day well. ", "Leaving last shows that you want to make sure the day ended smoothly.", "\n\n6. ", "Show Interest\n\nIf you are trying to turn your internship into a full-time job, I would hope you have some interest in it! ", "Well, you have to let it show. ", "Act enthusiastic about all of the projects you're working on and focus on learning from this experience.", "\n\n7. ", "Find Balance\n\nBalance in general is a great philosophy to live by. ", "In the case of an internship, you want to focus on striking a balance between humility and confidence. ", "You shouldn't act entitled or like a know-it-all, but you also shouldn't be too timid. ", "It's important to know your strengths and know where you need to grow in order to make the most out of your internship and make a good impression.", "\n\nI wish you all the best of luck in turning internships into careers! ", "It can be tricky, but as long as you're focused on success, you can achieve your goal. ", "How did you turn your internship into a full-time position?" ]	{ "pile_set_name": "Pile-CC" }	[ 0.0030581039755351682, 0, 0, 0, 0, 0.005988023952095809, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.008849557522123894, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	0.000559	5
[ "My granddaughter Allyssa and I have a regular routine we go through when we say goodbye. ", "We wrap our arms around each other and begin to loudly wail with dramatic sobs for about twenty seconds. ", "Then we step back and casually say, “See ya,” and turn away. ", "Despite our silly practice, we always expect that we will see each other again—soon.", "\n\nBut sometimes the pain of separation from those we care about can be difficult. ", "When the apostle Paul said farewell to the elders from Ephesus, “They all wept as they embraced him . . . . ", "What grieved them most was [Paul’s] statement that they would never see his face again” (Acts 20:37–38).", "\n\nThe deepest sorrow, however, comes when we are parted by death and say goodbye for the last time in this life. ", "That separation seems unthinkable. ", "We mourn. ", "We weep. ", "How can we face the heartbreak of never again embracing the ones we have loved?", "\n\nStill . . . ", "we do not grieve like those who have no hope. ", "Paul writes of a future reunion for those who “believe that Jesus died and rose again” (1 Thessalonians 4:13–18). ", "He declares: “The Lord himself will come down from heaven, with a loud command, with the voice of the archangel,” and those who have died, along with those who are still alive, will be united with our Lord. ", "What a reunion!", "\n\nAnd—best of all—we will be forever with Jesus. ", "That’s an eternal hope. — ", "Cindy Hess Kasper\n\nThank You, Lord, for the assurance that this world is not all we have but that a blessed eternity awaits all who trust in You.", "\n\nAt death, God’s people don’t say “goodbye,” but “we’ll see you later.”" ]	{ "pile_set_name": "Pile-CC" }	[ 0.011235955056179775, 0, 0, 0, 0, 0.009259259259259259, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.006896551724137931, 0 ]	0.001304	5
[ "Kerr aiming for Bulls to make charge in the cup\n\nAdam Walsh heads for the line during Banbury Bulls victory against Leamington at Bodicote Park\n\nPublished:09:23Thursday 26 November 2015\n\nShare this article\n\nHead coach James Kerr is looking for Banbury Bulls to make progress in this weekend’s RFU Intermediate Cup tie with Camp Hill.", "\n\nBulls go into Saturday’s second round tie at Bodicote Park on the back of their seventh win of the Midlands Two West South campaign, a derby demolition of Leamington which sees them lead the way by three points from title rivals Berkswell & Balsall.", "\n\nWe knew we had the capability with ball in hand\n\nHead coach James Kerr\n\nThe Warwickshire outfit are fourth in Midlands Two West North ahead of Saturday’s tie and Kerr is expecting a tough test.", "\n\nHe said: “It would be nice to have a good cup run, we’ve got a strong squad so I’m all for doing well in the competition.", "\n\n“It doesn’t matter who we play it’s about our game. ", "There are one or two areas where we need to improve.”", "\n\nLooking back on Saturday’s victory, Kerr added: “All in all, it was a comfortable victory. ", "They put us under a bit of pressure at the start but we were phenomenal in defence to keep Leamington out.", "\n\n“The boys were ruthless in defence and once we broke their backs we could start scoring tries.", "\n\n“We knew we had the capability with ball in hand. ", "I would have preferred not to have conceded the late points but it’s difficult to keep that level up for 80 minutes.”" ]	{ "pile_set_name": "Pile-CC" }	[ 0.015015015015015015, 0.00398406374501992, 0.010256410256410256, 0, 0, 0, 0.010752688172043012, 0.009433962264150943, 0, 0, 0 ]	0.004495	5
[ "Q:\n\nBefore Insert Trigger SQL\n\nI have two identical tables, I_Subject and I_Temp_Subject and I want to copy the Temp_Subject table to the Subject table. ", "I_Temp_Subject is used by Simple Users and I_Subject is used by the Admin. ", "The Admin can insert new records directly to I_Subject and validates the content of I_Temp_Subject.", "\nBoth table IDs are set to auto increment. ", "The copy SQL command is as follows:\nINSERT INTO I_SUBJECT(ID,CATEGORY_ID,USER_NAME,SERIAL_NUMBER,ICON)\nSELECT ID,CATEGORY_ID,USER_NAME,SERIAL_NUMBER,ICON FROM I_TEMP_SUBJECT\n\nIf I do that then the following error occurs:\nSystem.", "Data.", "SqlClient.", "SqlException: Cannot insert explicit value for identity\ncolumn in table 'I_SUBJECT' when IDENTITY_INSERT is set to OFF.", "\n\nIf I don't include the ID in the above statement then everything is ok except the ID's are not identical.", "\nSo I want to include a before insert trigger to check if the insert has null ID then autoincrement (when the Admin inserts directly) else if the insert's ID !", "=null then copy the ID from the I_Temp_Subject (when the Admin validates).", "\n\nA:\n\nyou can turn off auto increament by using following statement as\nSET IDENTITY_INSERT dbo.<tablename> ON\n write your insert statement here \n\nand then turn off identity insert as\n SET IDENTITY_INSERT dbo. ", "OFF\ni.e.\n SET IDENTITY_INSERT dbo.", "I_SUBJECT ON\n INSERT INTO I_SUBJECT(ID,CATEGORY_ID,USER_NAME,SERIAL_NUMBER,ICON)\n SELECT ID,CATEGORY_ID,USER_NAME,SERIAL_NUMBER,ICON FROM I_TEMP_SUBJECT\n SET IDENTITY_INSERT dbo.", "I_SUBJECT OFF\n\n" ]	{ "pile_set_name": "StackExchange" }	[ 0.006535947712418301, 0.013333333333333334, 0, 0, 0.013157894736842105, 0, 0, 0.01680672268907563, 0.009345794392523364, 0.006289308176100629, 0.013513513513513514, 0, 0.02702702702702703, 0.010638297872340425, 0 ]	0.007777	5
[ "[Distribution and composition of organochlorine pesticides in surface water body of Chaohu Lake].", "\nBy the method of SPE-GC/ECD, this paper studied the distribution and composition of organochlorine pesticides (OCPs) in the surface water body of Chaohu Lake. ", "At the 13 sampling sites of study area, a total of 16 kinds of OCPs, including HCHs, DDTs, beta-Endosulfan, Aldrin, hexachlorobenzene, and Heptachlor, were detected. ", "The total OCPs concentration was 0.54-64.01 ng x L(-1), and the main components were HCHs and DDTs, whose average concentrations were 5.56 ng x L(-1) and 16.57 ng x L(-1), respectively, accounting for about 84.75% of the total. ", "The origins of OCPs in study area were historical residues and the recent discharge of pesticides. ", "The concentrations of all existences accorded with the target values of GB 3838-2002. ", "The concentrations of OCPs in the surface water body of Chaohu Lake were much lower, and the risk was low in general." ]	{ "pile_set_name": "PubMed Abstracts" }	[ 0, 0.0125, 0.024096385542168676, 0.0043859649122807015, 0, 0, 0 ]	0.005855	5
[ "/\n Copyright (C) 2007-2020 Crafter Software Corporation. ", "All Rights Reserved.", "\n \n This program is free software: you can redistribute it and/or modify\n * it under the terms of the GNU General Public License version 3 as published by\n * the Free Software Foundation.", "\n \n This program is distributed in the hope that it will be useful,\n * but WITHOUT ANY WARRANTY; without even the implied warranty of\n * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. ", " See the\n * GNU General Public License for more details.", "\n \n You should have received a copy of the GNU General Public License\n * along with this program. ", " If not, see <http://www.gnu.org/licenses/>.", "\n /\npackage upgrade\n\n@Grapes([\n @Grab(group = 'org.slf4j', module = 'slf4j-nop', version = '1.7.25'),\n @Grab(group = 'org.apache.commons', module = 'commons-lang3', version = '3.7'),\n @Grab(group = 'org.apache.commons', module = 'commons-collections4', version = '4.1'),\n @Grab(group = 'org.apache.commons', module = 'commons-configuration2', version = '2.5'),\n @Grab(group = 'commons-beanutils', module = 'commons-beanutils', version = '1.9.3'),\n @Grab(group = 'org.yaml', module = 'snakeyaml', version = '1.24'),\n @Grab(group = 'io.github.http-builder-ng', module = 'http-builder-ng-core', version = '1.0.3')\n])\n\nimport org.apache.commons.collections4.CollectionUtils\nimport upgrade.hooks.", "PostUpgradeHooks\n\nimport java.nio.file.", "Path\n\nimport static utils.", "EnvironmentUtils.", "\nimport static utils.", "ScriptUtils.", "\n\n/\n Builds the CLI and adds the possible options\n /\ndef buildCli(CliBuilder cli) {\n cli.h(longOpt: 'help', 'Show usage information')\n}\n\n/\n Prints the help info\n /\ndef printHelp(CliBuilder cli) {\n cli.usage()\n}\n\n/\n Exits the script with an error message, the usage and an error status.", "\n */\ndef exitWithError(CliBuilder cli, String msg) {\n println msg\n println ''\n\n printHelp(cli)\n\n System.exit(1)\n}\n\ndef postUpgrade(String oldVersion, String newVersion, String environment) {\n println \"========================================================================\"\n println \"Post-upgrade ${oldVersion} -> ${newVersion}\"\n println \"========================================================================\"\n\n Path binFolder = getCrafterBinFolder()\n Path dataFolder = getCrafterDataFolder()\n PostUpgradeHooks hooks = new PostUpgradeHooks(binFolder, dataFolder, oldVersion, newVersion, environment)\n\n hooks.execute()\n}\n\ncheckDownloadGrapesOnlyMode(getClass())\n\ndef cli = new CliBuilder(usage: 'post-upgrade [options] <old-version> <new-version> <environment>')\nbuildCli(cli)\n\ndef options = cli.parse(args)\nif (options) {\n // Show usage text when -h or --help option is used.", "\n if (options.help) {\n printHelp(cli)\n return\n }\n\n // Parse the options and arguments\n def extraArguments = options.arguments()\n if (CollectionUtils.isNotEmpty(extraArguments)) {\n def oldVersion = extraArguments[0]\n def newVersion = extraArguments[1]\n def environment = extraArguments[2]\n\n postUpgrade(oldVersion, newVersion, environment)\n } else {\n exitWithError(cli, 'No <target-installation-path> was specified')\n }\n}\n\n" ]	{ "pile_set_name": "Github" }	[ 0, 0, 0.010526315789473684, 0, 0.017857142857142856, 0, 0.022727272727272728, 0.010796221322537112, 0, 0, 0.05555555555555555, 0, 0.07692307692307693, 0.003278688524590164, 0.003278688524590164, 0.0040650406504065045 ]	0.012813	5
[ "1. ", "Field of the Invention\nThe present invention relates to an electronic storage device, more particularly to an electronic storage device having an electrical connector capable of rotating and allocating in multiple-direction.", "\n2. ", "Description of Related Art\nIn recent years, because of rapid development of Flash Memory technology, electronic data cannot only be stored in general hard disks, but also stored in solid memories conveniently. ", "Compared with general hard disks, solid memory is more compact with less weight and shake resistance. ", "Therefore, solid memories are widely used in different kinds of host systems, such as personal computers, notebooks, PDA (Personal Digital Assistance), and mobile phones et al. ", "Different types of electronic storage devices adopting solid memory as storage media are widely used in daily life, such as Express Card, Flash Memory Card, USB Flash Drive, and MP3 Player.", "\nHowever, no matter what type the electronic storage device belongs to, there must have an electrical connector, such as a USB connector, connects the host system and the electronic storage device, electronic data can then be transferred from the host system to the electronic storage device. ", "If the electrical connector of the electrical storage device is damaged, the electronic storage device cannot be used any longer. ", "Hence, after the electrical connector is separated from the host system, the electrical connector should be protected to lengthen the service life thereof. ", "CN1331379C, issued on Aug. 8, 2007, disclosed a Flash Drive apparatus which has a single body type rotary cover connecting with a main body which receives a USB connector inside by hinge means. ", "The rotary cover forms protection to the USB connector to some extent. ", "However, after long time use, the connection between the main body and the rotary cover is prone to become loose and cause relative rotation between the main body and the rotary cover, thus, it is not good for protection to the USB connector interface.", "\nFurther, as disclosed in CN200941307Y, issued on Aug. 29, 2008, a USB Flash drive apparatus utilized a U-shape metal ring which is capable of elastic deformation and can be served for rotating allocation. ", "However, the rotating structure of the USB Flash drive apparatus is relatively complex which is not good for improving production efficiency.", "\nHence, it is desirable to design an improved structure to address problems mentioned above." ]	{ "pile_set_name": "USPTO Backgrounds" }	[ 0, 0, 0, 0.004761904761904762, 0, 0, 0.015873015873015872, 0.0034129692832764505, 0, 0, 0.010309278350515464, 0.014084507042253521, 0.003968253968253968, 0.0048543689320388345, 0.0070921985815602835, 0 ]	0.004022	5
[ "namespace $safeprojectname$.Model\r\n{\r\n public class DataItem\r\n {\r\n public DataItem(string title)\r\n {\r\n Title = title;\r\n }\r\n\r\n public string Title\r\n {\r\n get;\r\n private set;\r\n }\r\n }\r\n}\r\n" ]	{ "pile_set_name": "Github" }	[ 0 ]	0	5
[ "The Pentagon confirmed Thursday that Chinese nationals fired lasers near a military base in east Africa against U.S. military aircraft in the region, injuring several pilots.", "\n\nPentagon Press Secretary Dana White said the U.S. government made diplomatic protests to the Chinese government over several recent incidents of laser firings near China's first overseas military base at Djibouti.", "\n\n\"These are very serious incidents. ", "There have been two minor injuries. ", "This activity poses a threat to our airmen,\" White told reporters.", "\n\n\"We have formally demarched the Chinese government, and we've requested that the Chinese investigate these incidents,\" she added.", "\n\nThe number of incidents is \"more than two but less than ten\" and the laser firings took place in recent weeks, White said.", "\n\nWhite said the Pentagon is confident that Chinese nationals were behind the laser firings but did not elaborate on the intelligence linking Beijing to the incidents.", "\n\nShe declined to speculate on the Chinese motive behind the laser attacks.", "\n\n\"I believe there have been cases where this has happened previously,\" White said. \"", "But what this started was these last few weeks we decided to become very serious about it, and we have demarched the Chinese, and we've asked for the investigation.\"", "\n\nChina's government has not commented on the incidents. ", "A Chinese military expert told the state-run Global Times newspaper that the U.S. accusations that China used a laser weapon in Djibouti was \"groundless.\"", "\n\nChina opened the military base in Djibouti last year and plans to deploy some 400 troops there.", "\n\nChina's government has asserted that the base is merely a logistics hub for anti-piracy operations as well as to support China's international infrastructure project called Belt and Road Initiative.", "\n\nThe U.S. government regards the Chinese base as part of Beijing's efforts to project military power around the world.", "\n\nThe Djibouti incidents appear similar to the 1997 incident involving a Russian merchant ship that was shadowing a Navy missile submarine and fired a laser on a Canadian surveillance helicopter.", "\n\nThe laser damaged the eyes of the Navy Lt. ", "Jack Daly and Canadian pilot Captain Patrick Barnes near Washington state and was covered up by the administration of President Bill Clinton.", "\n\nChina and the United States have battled over international trade and finance after the Trump administration announced it will impose tariffs on China for its unfair trade practices.", "\n\nThe U.S. and Chinese militaries also have squared off in the South China Sea where China is seeking to take control of the strategic waterway. ", "The U.S. military has been seeking to counter the illegal claim by sending ships and aircraft near disputed islands in the sea that have been militarized in recent years by China.", "\n\nA Federal Aviation Administration notice to airmen reported April 14 that \"there have been multiple lazing events involving a high power laser\" near the Chinese military base.", "\n\n\"Use extreme caution when transiting near this area,\" the notice states. \"", "If a laser is seen in or near Djibouti, notify immediately tower…\"\n\nThe notice also said U.S. military air crews were to contact military air controllers.", "\n\nIn one incident, air crew members flying aboard a C-130 transport suffered two minor eye injuries after exposure to what was described as \"military-grade laser beams\" that appear to have been fired from the Chinese base.", "\n\nThe laser incidents followed U.S. military exercises last month off the coast of Djibouti called Alligator Dagger. ", "The exercise was canceled April 5 after two separate air mishaps, including the crash of a Marine Corps Harrier jump jet and a CH-53 helicopters, in Djibouti.", "\n\nAbout 4,000 U.S. personnel are stationed at Camp Lemonnier in Djibouti. ", "The base has been used as a major launch point for U.S. military and special operations commando raids in the region.", "\n\nThe Chinese military base in the country is located about a mile from Camp Lemonnier and is Beijing's first overseas military base and has raised security concerns because it is located very close to the U.S. military base there.", "\n\nThe Washington Free Beacon disclosed in 2015 that China's military has deployed several types of hand-held blinding laser weapons.", "\n\nThe weapons, according to state-run Chinese media, are used to interfere and damage laser and night vision equipment.", "\n\nUse of the weapons violates China's announced commitment to a section of the 1998 U.N. Convention on Certain Conventional Weapons that bans the use of blinding lasers in combat.", "\n\nThe Chinese have marketed four types of laser guns, designated the BBQ-905 Laser Dazzler Weapon, the WJG-2002 Laser Gun, the PY132A Blinding Laser Weapon, and the PY131A Blinding Laser Weapon.", "\n\nMarine Corps Gen. Thomas Waldhauser, commander of the U.S. Africa Command, warned in congressional testimony in March that China is seeking to expand and possibly take over the strategic port in Djibouti, which owes Beijing an estimated $1.2 billion in construction debt.", "\n\nChina operates a naval port and \"multi-purpose\" port that offloads containers from freighters.", "\n\nWaldhauser said a Chinese takeover of ports in Djibouti would have \"significant consequences\" for U.S. military operations there.", "\n\n\"We are not naive to think that some of the activities the Chinese are doing in terms of counterintelligence there are taking place, but it just means that we have to be cautious,\" Waldhauser told the House Armed Services Committee March 6. \"", "We have to be on guard for that type of situation.\"" ]	{ "pile_set_name": "OpenWebText2" }	[ 0.005747126436781609, 0.013953488372093023, 0, 0, 0, 0, 0.008064516129032258, 0.005988023952095809, 0, 0, 0, 0, 0.006493506493506494, 0, 0, 0, 0.005128205128205128, 0.022222222222222223, 0.02127659574468085, 0.005434782608695652, 0, 0, 0.005649717514124294, 0, 0, 0, 0.008547008547008548, 0.006329113924050633, 0, 0, 0, 0.007575757575757576, 0, 0, 0.015463917525773196, 0.01098901098901099, 0, 0, 0.004098360655737705, 0 ]	0.003824	5
[ "\n\nShow HN: I built a faster way to burn your money on Etsy.com - JonathanBouman\nhttp://www.Scrollsy.com\n\n======\nJonathanBouman\nEverything 100% clientside jQuery & JSONP. ", "Hosted on Amazon Cloudfront so low\ncosts and no scalability issues.", "\n\nSome examples you should check:\n\nRegular search: <http://www.scrollsy.com/#s=nyan%20cat>\n\nTreasury listings: <http://www.scrollsy.com/#l=treasury>\n\nShop: <http://www.scrollsy.com/#un=machelspencePHOTO>\n\nColor search:\n[http://www.scrollsy.com/#c=art&color=0A9600](http://www.scrollsy.com/#c=art&color=0A9600)\n\nWould love to have some feedback!", "\n\n~~~\nignoreme\nYou really should have a fallback page for browsers with no Javascript.", "\nNoScript has become increasing popular and the \"Javscript Free\" page of a site\nis the first page those users will see (even if they go on to temporarily\nallow javascript for your app).", "\n\nIn your case, it is just a blank white page. ", "Since you are asking for\nsuggestions, I would suggest you just make it display a message. ", "One for\nsuggesting users with older browsers to download chrome or firefox and another\nmessage directed at those with Javascript intentionally disabled which gives a\nvery brief outline of what your app does and why they should enable JS to play\nwith it.", "\n\ne: I clicked through to the other mashups you have created which you linked in\nyour other comment. ", "They all do the same thing, just bring me to a blank page.", "\n\nee: To those down-voting, what do you disagree with? ", "Do you not think pure JS\nweb apps should have HTML fallback pages or do you disagree with the way I\nsaid it?", "\n\n~~~\njohnnyn\nI didn't downvote you but I personally never worry about users with JavaScript\ndisabled, and the companies I have worked for don't care either. ", "The number of\npeople without JavaScript is most likely way to low to spend time on an HTML\nfallback.", "\n\n[http://www.quora.com/What-percentage-of-Internet-users-\nuse-J...](http://www.quora.com/What-percentage-of-Internet-users-use-\nJavaScript-Is-it-safe-to-pretend-that-non-JavaScript-users-do-not-exist-when-\ndesigning-your-website?redirected_qid=12124)\n\n~~~\njerf\nAn adequate \"fallback\" is <noscript><p class='something_nice'>This site\nrequires Javascript to function</p></noscript>. ", "It's not exactly hard, and\nit's better than a blank white page.", "\n\nIt can also occur due to network problems on occasion or other technical\nissues; if you have JS beyond just progressive enhancement on your site you\nreally ought to have a <noscript> tag in there somewhere.", "\n\n------\ndjb_hackernews\nSo Pinterest.", "\n\nI say that as a compliment. ", "Great job.", "\n\nOnly thought is the constant Loading Items widget is annoying and isn't in\nline with how most sites do dynamic scrolling.", "\n\n~~~\nJonathanBouman\nThanks for the compliment! ", "The loader is something to re-code indeed. ", "Anyone\nhere with a good example of a nice scrolling loader?", "\n\n~~~\njmileham\nI agree, your app looks dangerous in a good way.", "\n\nI think the most important thing is that the loading animation be anchored to\nthe bottom of the loaded content so that it never obscures content that's\nalready loaded. ", "If the user manages to outrace your loader and gets to the\nbottom, some kind of indication that the app is churning away would no doubt\nbe welcome.", "\n\n~~~\nJonathanBouman\nThat's a good idea, got it on the list!", "\n\n------\nnatgordon\nThis is really great. ", "I like the \"exploding\" treasuries a lot.", "\n\nWhat was your motivation? ", "If you're looking for more exposure you can write a\nblog post for the Etsy blog. ", "I did that for my app and it drove a lot of\ntraffic (<http://www.etsy.com/blog/en/2011/handmade-code-babylist/>)\n\n~~~\nJonathanBouman\nThanks! ", "The Treasuries view is a nice one indeed, took me a night to find a\ngood way to keep it stupid simple and fast.", "\n\nMy motivation is coming from previous mashups I did in the same style.", "\n<http://Scrolldit.com> which was featured on TechCrunch\n([http://techcrunch.com/2011/10/25/scrolldit-i-heard-you-\nliked...](http://techcrunch.com/2011/10/25/scrolldit-i-heard-you-liked-\nscrolling-reddit-so-i-put-scrolling-in-your-reddit/)) and another mashup I did\n<http://www.ScrollFriends.com> (Facebook Scroller, no viral)\n\nHowever Scrolldit is (most of the time) a pure timewaster, check this: 377.913\n(unique visits) x 1.20 (avg minutes on the site) = 453495,6 minutes = an\nimpact of 314,93 wasted days on our world economy.", "\n\nHowever with all those minutes wasted I felt the need to do something\nproductive, I think Scrollsy.com is a good try. ", "Supporting all those small\nshopkeepers, trying to give them more exposure.", "\n\nGood idea to do the blog post, it's on the list!", "\n\n~~~\nherval\nWhat's your motivation for all these mashups?", "\n\n~~~\nJonathanBouman\nMultiple things: I love endless scrolling and visually rich designs, I want to\nlearn new techniques and ofcourse it's great to see other people using these\nmashups. ", "Btw this mashup was also some kind of compensation for the damage\nI've done with <http://Scrolldit.com>\n\n------\nrichcollins\nThe activity indicator is very intrusive. ", "Why not make it small and place it\nbelow the last item?", "\n\n~~~\nJonathanBouman\nIt's on the list to improve :)\n\n~~~\nmikehuffman\nAlong with everyone else's activity indicator complaint, I also think that\ncolor coding the bottom \"info bar\" area of each item according to category\nwould be useful for quickly scanning and separating all of that info with the\neye.", "\n\n~~~\nJonathanBouman\nGreat idea, I'll put it on the list. ", "Thanks.", "\n\n------\nauxbuss\nFYI: I get \"Connection Timeout. ", "Etsy.com is unreachable. ", "Try again.\" ", "in\nFirefox 9.0.1 on Ubuntu, but all is good in Chrome.", "\n\nI can image using this to gather ideas for gifts, and presumably buying a few\n(if I was US-based). ", "Nicely done.", "\n\n~~~\nJonathanBouman\nI think you hit the API Limit. ", "Just fixed a bug that used an old API key for\nAPI calls (got lower limits).", "\n\nBig chance you won't get that error if you retry it after 10 minutes (time\nneeded for Amazon Cloudfront to push the new version to all the edge\nlocations).", "\n\n------\njohnnyn\nThis is awesome man. ", "The wife and I just spent 30 minutes scrolling around and\nadded quite a few items to my Favorites. ", "You need to find a way to get an\naffiliate fee as soon as possible!", "\n\nThe Pinterest-influenced UI is such a great way to explore. ", "I'd much rather\nbrowse around on your site than the actual Etsy site anyday. ", "The new items\nflying in from the left does catch me off guard sometimes and I think the\nsearch input and browse dropdown need to be a bit larger but other that, very\nwell done.", "\n\n~~~\nJonathanBouman\nThanks for the kind words!", "\n\n------\njwpeddle\nI love browsing products like this. ", "I assume inspired by Pinterest? ", "A Toronto\nstartup is doing the same thing, but local shops/products.", "\n<http://shopcastr.com/>\n\n~~~\nJonathanBouman\nInspired by masonry jquery plugin and after the success of\n<http://Scrolldit.com> :)\n\n------\ndabent\nI did an Etsy search similar to this, with \"instant\" search instead of\nscrolling. ", "I have to say I like your approach better.", "\n\nA few questions about your Etsy API experience - can you now see who purchased\nthrough your site? ", "At the time they had no feedback loop and no sort of\naffiliate program. ", "Building my Etsy app was a lot of fun, but I had no way to\nmonetize my work. ", "I'm a bit out of the Etsy API loop now, but I do hope\nthey've come up with some way to help devs make money.", "\n\n~~~\nJonathanBouman\nI'm not sure if I could see who purchased through my site, as far as I know\nshopkeepers see it. ", "There is no sort of affiliate program. ", "So I don't see any\nmonetizing options for this moment.", "\n\n~~~\nfoolinator\nWhat motivated you to use the Etsy API? ", "I'm good friends with a number of\npeople there and worked a bit on their search too.", "\n\n~~~\nJonathanBouman\nIt's fast, it supports JSONP and their API team is great to work with (fast\nreplies on email). ", "I could recommend anyone to build a mashup on top of the\nEtsy API.", "\n\n~~~\nfoolinator\nThat's great to hear, Jonathan. ", "I personally know two of the people on that\nteam and they're brilliant programmers but never saw their view from the\noutside. ", "I'm glad to hear you're getting amazing support from them.", "\n\nIf you're enjoying it a lot and love to program, you should consider applying\nthere too.", "\n\n------\nshashashasha\nDid you post this on HN before? ", "It's still jarring how new items fly in from\nthe top left. ", "It's also constantly loading items, which is annoying.", "\n\nOtherwise, looks pretty cool. ", "You should also take a look at other fashion\nsites for the \"Quick Look\" interaction (using mouseover or some other light\ninteraction to provide more ui/information/larger image, vs opening a new\npage), which would be pretty great on a purely visual site like this.", "\n\n~~~\nJonathanBouman\nI posted it 5 hours ago on HN but had to delete it because of API limit I had\nto resolve before risking a viral.", "\n\nAfter they were resolved I posted it.", "\n\nTrick: Click the about link in the top left box and flag the disable animation\ncheckbox.", "\n\nDo you have any examples of those fashion sites?", "\n\n~~~\nlostsock\nYou should rename about to options (or make a second link).", "\n\nListing options in an about link is counter intuitive.", "\n\n~~~\nJonathanBouman\nI'll make a second link, good idea.", "\n\n------\nakg\nIt would be really awesome if something liked this was done for the\nrecommended reading lists on Amazon.com, although, not sure if Amazon has an\neasy API for that.", "\n\n~~~\nchaosmachine\nI made something sort of similar for Amazon a few years ago:\n\n<http://bigbooksearch.com/>\n\nIt's horizontal (like a bookshelf), instead of vertical, though.", "\n\n~~~\nakg\nNice! ", "I could definitely see a simply iOS app for something like that that\nmakes use of the cover-flow animation. ", "Could be a nice alternative to the\nAmazon.com store app if you can hook it up to user accounts and Amazon's\npersonalized recommendations.", "\n\n------\npkamb\nDoes Etsy have an affiliate/referral program?", "\n\n~~~\nJonathanBouman\nNo they doesn't, as far as I know.", "\n\n~~~\npatio11\nA life lesson which was news to me: there is some scale at which _every_\ncommercial site has an affiliate program. (", "Varies based on the site.)", "\n\n~~~\ndabent\nWhen I did an Etsy app, there was no affiliate program, which seemed to\nlargely stem from the fact that Etsy charged to little to sellers that they\nwere barely making a profit. ", "The idea of giving a cut to ousters seemed like a\nbad idea. ", "I'm not sure if it's changed. ", "But when one considers the number of\nEtsy apps that have been made just for the joy of it, it would seem to be in\nEtsy's favor to incentivize developers once they can get the numbers to work\nout.", "\n\n------\ndreur\nNoo why have you done that...\n\nSeriously I like is a lot, very well thought.", "\n\nSorry have to go back on Scrollsy...\n\n------\nhiptobecubic\nStart the scroll-loading earlier, and make the loading notification at least\n50% smaller. ", "It's annoying.", "\n\n------\nericingram\nThis is genius. ", "I'm going to do something like this.", "\n\n------\nriskish\ndoesn't pinterest already have a section where its exclusively etsy products?", "\n\n------\nkenrik\nNice Work!", "\n\nI have been working a lot with JSONP lately it's a great way to bring content\nCross domain/into Apps. ", "I just recently finished writing a Webservice/iPhone\nimplementation.", "\n\nSomething to consider, try preloading the content to give the user a smoother\nexperience. ", "My UITableViews (iPhone) were a bit clunky until I got around to\npre-caching my JSON results.", "\n\nAnyway, Keep up the good work!", "\n\n~~~\nJonathanBouman\nPre-caching JSON results is something I'm testing with, expect it within a\nshort time.", "\n\n" ]	{ "pile_set_name": "HackerNews" }	[ 0.011764705882352941, 0.014925373134328358, 0.01744186046511628, 0.011627906976744186, 0.005405405405405406, 0, 0, 0.003952569169960474, 0, 0, 0, 0, 0.012658227848101266, 0.01, 0.007853403141361256, 0, 0, 0, 0, 0, 0.008130081300813009, 0, 0, 0, 0.015873015873015872, 0, 0, 0, 0, 0, 0, 0.012345679012345678, 0.0070921985815602835, 0, 0, 0.011320754716981131, 0.008333333333333333, 0, 0, 0, 0, 0.006024096385542169, 0, 0, 0, 0, 0, 0.04, 0, 0.018518518518518517, 0, 0, 0, 0.013333333333333334, 0.006369426751592357, 0.02631578947368421, 0, 0, 0.016129032258064516, 0, 0, 0, 0, 0.03125, 0, 0.00881057268722467, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.017241379310344827, 0, 0.02040816326530612, 0, 0, 0, 0, 0, 0, 0, 0.003787878787878788, 0, 0, 0, 0, 0.013513513513513514, 0, 0, 0.017045454545454544, 0.011494252873563218, 0, 0, 0.0072992700729927005, 0.016666666666666666, 0, 0, 0, 0.005263157894736842, 0, 0, 0.005128205128205128, 0, 0.006666666666666667, 0, 0, 0, 0, 0, 0.009615384615384616, 0.014705882352941176, 0, 0, 0, 0, 0 ]	0.00392	5